diff --git a/src/eko/basis_rotation.py b/src/eko/basis_rotation.py
index e31a7beb6..360da1b31 100644
--- a/src/eko/basis_rotation.py
+++ b/src/eko/basis_rotation.py
@@ -149,6 +149,9 @@
     (non_singlet_pids_map["ns+u"], 0),
     (non_singlet_pids_map["ns-u"], 0),
 )
+
+scet_labels = ((1, 1), (1, 21), (21, 1), (21, 21), (1,2), (1,-1), (1,-2))
+
 full_labels = (*singlet_labels, *non_singlet_labels)
 full_unified_labels = (
     *singlet_unified_labels,
diff --git a/src/eko/evolution_operator/beam_function.py b/src/eko/evolution_operator/beam_function.py
new file mode 100644
index 000000000..f66cf86cd
--- /dev/null
+++ b/src/eko/evolution_operator/beam_function.py
@@ -0,0 +1,160 @@
+"""SCET I kernels"""
+
+import copy
+import functools
+import logging
+
+import numba as nb
+import numpy as np
+
+import ekore.scet_I as scet_I
+
+from .. import basis_rotation as br
+from .. import scale_variations as sv
+from ..matchings import Segment
+from . import Operator, QuadKerBase
+
+logger = logging.getLogger(__name__)
+
+@nb.njit(cache=True)
+def quad_ker(
+    u,
+    order,
+    space,
+    nf,
+    mode0,
+    mode1,
+    is_log,
+    logx,
+    areas,
+):
+    r"""Raw kernel inside quad.
+
+    Parameters
+    ----------
+    u : float
+        quad argument
+    order : tuple(int,int)
+        perturbation matching order
+    mode0 : int
+        pid for first element in the singlet sector
+    mode1 : int
+        pid for second element in the singlet sector
+    is_log : boolean
+        logarithmic interpolation
+    logx : float
+        Mellin inversion point
+    areas : tuple
+        basis function configuration
+    
+    Returns
+    -------
+    ker : float
+        evaluated integration kernel
+
+    """
+    ker_base = QuadKerBase(u, is_log, logx, mode0)
+    integrand = ker_base.integrand(areas)
+    if integrand == 0.0:
+        return 0.0
+    indices = {21: 0, 1: 1, -1: 2, 2: 3, -2: 4}
+    A = scet_I.SCET_I_entry(order, space, nf, ker_base.n)
+    # select the needed matrix element
+    ker = A[indices[mode0], indices[mode1]]
+
+    # recombine everything
+    return np.real(ker * integrand)
+
+
+class SCET_I(Operator):
+    r"""
+    Internal representation of a single |SCET1| mathcing kernel.
+
+    The actual matrices are computed upon calling :meth:`compute`.
+
+    Parameters
+    ----------
+    config : dict
+        configuration
+    managers : dict
+        managers
+    order: tuple (int, int)
+        order in alpha_s and L
+    """
+
+    log_label = "Scet_I"
+    full_labels = br.scet_labels
+
+    def __init__(self, config, managers, order, space, nf):
+        super().__init__(config, managers, Segment(origin=1, target=1, nf=nf))
+        # order (alpha_s, L) of the SCET kernel
+        self.order_scet = order
+        self.space = space
+        self.nf = nf
+
+    @property
+    def labels(self):
+        """Necessary sector labels to compute.
+
+        Returns
+        -------
+        list(str)
+            sector labels
+        """
+        labels = []
+        
+        
+        labels.extend(
+            [
+                *br.scet_labels,
+            ]
+        )
+            
+        return labels
+
+    def quad_ker(self, label, logx, areas):
+        """Return partially initialized integrand function.
+
+        Parameters
+        ----------
+        label: tuple
+            operator element pids
+        logx: float
+            Mellin inversion point
+        areas : tuple
+            basis function configuration
+
+        Returns
+        -------
+        functools.partial
+            partially initialized integration kernel
+        """
+        return functools.partial(
+            quad_ker,
+            order=self.order_scet,
+            space=self.space,
+            nf=self.nf,
+            mode0=label[0],
+            mode1=label[1],
+            is_log=self.int_disp.log,
+            logx=logx,
+            areas=areas,
+        )
+
+    @property
+    def a_s(self):
+        """Return the computed values for :math:`a_s`.
+
+        Note that here you need to use :math:`a_s^{n_f+1}`
+        """
+        sc = self.managers["couplings"]
+        return sc.a_s(
+            self.q2_from
+            * (self.xif2 if self.sv_mode == sv.Modes.exponentiated else 1.0),
+            nf_to=self.nf + 1,
+        )
+
+    def compute(self):
+        """Compute the actual operators (i.e. run the integrations)."""
+        self.initialize_op_members()
+        self.integrate()
diff --git a/src/eko/evolution_operator/scet_kernel.py b/src/eko/evolution_operator/scet_kernel.py
new file mode 100644
index 000000000..97c468e10
--- /dev/null
+++ b/src/eko/evolution_operator/scet_kernel.py
@@ -0,0 +1,60 @@
+"""Defines the SCET kernel."""
+
+from .. import basis_rotation as br
+from .. import member
+
+
+class ScetKernel(member.OperatorBase):
+    """
+    Scet kernel for |PDF|.
+
+    """
+
+    @classmethod
+    def split_ad_to_evol_map(
+        cls,
+        op_members,
+        q2_thr,
+    ):
+        """
+        Create the instance from the |OME|.
+
+        Parameters
+        ----------
+            op_members : eko.beam_fuctions.SCET_I.op_members
+                Attribute of :class:`~eko.beam_fuctions.SCET_I` containing the scet kernels
+            nf : int
+                number of active flavors *below* the threshold
+            q2_thr: float
+                dummy value
+        """
+        
+        quark_names = br.flavor_basis_names
+        quarks = quark_names[8:]
+        
+        m = {}
+
+        for q1 in quarks:
+            for q2 in quarks:
+                if q1 == q2:
+                    m[f"{q1}.{q1}"] = op_members[(1, 1)]
+                    m[f"{q1}bar.{q1}bar"] = op_members[(1, 1)]
+                    m[f"{q1}.{q1}bar"] = op_members[(1, -1)]
+                    m[f"{q1}bar.{q1}"] = op_members[(1, -1)]         
+                else:
+                    m[f"{q1}.{q2}"] = op_members[(1, 2)]
+                    m[f"{q2}.{q1}"] = op_members[(1, 2)]
+                    m[f"{q1}bar.{q2}bar"] = op_members[(1, 2)]
+                    m[f"{q2}bar.{q1}bar"] = op_members[(1, 2)]
+                    m[f"{q1}.{q2}bar"] = op_members[(1, -2)]
+                    m[f"{q2}bar.{q1}"] = op_members[(1, -2)]
+    
+        for q in quarks:
+            m[f"{q}.g"] = op_members[(1, 21)]
+            m[f"{q}bar.g"] = op_members[(1, 21)]  
+            m[f"g.{q}"] = op_members[(21, 1)]
+            m[f"g.{q}bar"] = op_members[(21, 1)]
+
+        m[f"g.g"] = op_members[(21,21)]
+        
+        return cls.promote_names(m, q2_thr)
diff --git a/src/eko/io/items.py b/src/eko/io/items.py
index cbc7591e0..c3e823bcb 100644
--- a/src/eko/io/items.py
+++ b/src/eko/io/items.py
@@ -11,7 +11,7 @@
 from .. import matchings
 from . import exceptions
 from .types import EvolutionPoint as EPoint
-from .types import FlavorIndex, FlavorsNumber, SquaredScale
+from .types import FlavorIndex, FlavorsNumber, SquaredScale, Order, Space
 
 
 @dataclass(frozen=True)
@@ -98,6 +98,26 @@ def as_atlas(self) -> matchings.Matching:
         """The associated segment."""
         return matchings.Matching(self.scale, self.hq, self.inverse)
 
+@dataclass(frozen=True)
+class ScetKernel(Header):
+    """Information to compute a SCET matching operator.
+
+    """
+
+    order: Order
+    space: Space
+    nf: FlavorsNumber
+
+    @classmethod
+    def from_atlas(cls, scet_kernel: matchings.ScetKernel):
+        """Create instance from analogous :class:`eko.matchings.Atlas` object."""
+        return cls(**asdict(scet_kernel))
+    
+    @property
+    def as_atlas(self) -> matchings.ScetKernel:
+        """The associated segment."""
+        return matchings.ScetKernel(self.order, self.space, self.nf)
+
 
 Recipe = Union[Evolution, Matching]
 
diff --git a/src/eko/io/paths.py b/src/eko/io/paths.py
index 67100fdaa..a74457892 100644
--- a/src/eko/io/paths.py
+++ b/src/eko/io/paths.py
@@ -11,6 +11,7 @@
 PARTSDIR = "parts"
 MATCHINGDIR = "matching"
 OPERATORSDIR = "operators"
+SCETDIR = "scet"
 
 
 @dataclass
@@ -45,6 +46,11 @@ def recipes_matching(self):
         """Matching recipes folder."""
         return self.root / RECIPESDIR / MATCHINGDIR
 
+    @property
+    def recipes_scet(self):
+        """Scet recipes folder."""
+        return self.root / RECIPESDIR / SCETDIR
+
     @property
     def parts(self):
         """Parts folder."""
@@ -55,6 +61,11 @@ def parts_matching(self):
         """Matching parts folder."""
         return self.root / PARTSDIR / MATCHINGDIR
 
+    @property
+    def parts_scet(self):
+        """Scet kernel folder."""
+        return self.root / PARTSDIR / SCETDIR
+
     @property
     def operators(self):
         """Operators folder.
@@ -85,3 +96,5 @@ def bootstrap(self, theory: dict, operator: dict, metadata: dict):
         self.parts.mkdir()
         self.parts_matching.mkdir()
         self.operators.mkdir()
+        self.recipes_scet.mkdir()
+        self.parts_scet.mkdir()
diff --git a/src/eko/io/runcards.py b/src/eko/io/runcards.py
index e9260a6eb..fc5b6710c 100644
--- a/src/eko/io/runcards.py
+++ b/src/eko/io/runcards.py
@@ -31,6 +31,8 @@
     ScaleVariationsMethod,
     SquaredScale,
     T,
+    Space,
+    FlavorsNumber,
 )
 
 
@@ -51,6 +53,12 @@ class TheoryCard(DictLike):
     """|N3LO| anomalous dimension variation: ``(gg_var, gq_var, qg_var, qq_var)``."""
     matching_order: Optional[Order] = None
     """Matching conditions perturbative order tuple, ``(QCD, QED)``."""
+    space: Optional[Space] = None 
+    """Space to compute beam function kernels"""
+    orders: Optional[List[Order]] = None
+    """Beam function order"""
+    nf: Optional[FlavorsNumber] = None
+    """Number of active flavors to use to compute beam function"""
 
 
 @dataclass
diff --git a/src/eko/io/struct.py b/src/eko/io/struct.py
index fecba3c57..0d92809f2 100644
--- a/src/eko/io/struct.py
+++ b/src/eko/io/struct.py
@@ -18,7 +18,7 @@
 from .access import AccessConfigs
 from .bases import Bases
 from .inventory import Inventory
-from .items import Evolution, Matching, Operator, Recipe, Target
+from .items import Evolution, Matching, Operator, Recipe, Target, ScetKernel
 from .metadata import Metadata
 from .paths import InternalPaths
 from .runcards import OperatorCard, TheoryCard
@@ -49,6 +49,14 @@ def inventories(path: pathlib.Path, access: AccessConfigs) -> dict:
             paths.parts_matching, access, Matching, name="matching-parts"
         ),
         operators=Inventory(paths.operators, access, Target, name="operators"),
+        recipes_scet=Inventory(
+            paths.recipes_scet,
+            access,
+            ScetKernel,
+            contentless=True,
+            name="scet-recipes",
+        ),
+        scet_kernels=Inventory(paths.parts_scet, access, ScetKernel, name="scet_kernels"),
     )
 
 
@@ -90,6 +98,8 @@ class EKO:
     parts: Inventory[Evolution]
     parts_matching: Inventory[Matching]
     operators: Inventory[Target]
+    recipes_scet: Inventory[ScetKernel]
+    scet_kernels: Inventory[ScetKernel]
 
     # public containers
     # -----------------
@@ -179,8 +189,11 @@ def load_recipes(self, recipes: List[Recipe]):
             # leverage auto-save
             if isinstance(recipe, Evolution):
                 self.recipes[recipe] = None
-            else:
+            elif isinstance(recipe, Matching):
                 self.recipes_matching[recipe] = None
+            else:
+                self.recipes_scet[recipe] = None
+
 
     # operator management
     # -------------------
diff --git a/src/eko/io/types.py b/src/eko/io/types.py
index 5573bafbb..9f72fc747 100644
--- a/src/eko/io/types.py
+++ b/src/eko/io/types.py
@@ -24,6 +24,7 @@
 FlavorIndex = int
 IntrinsicFlavors = typing.List[FlavorIndex]
 N3LOAdVariation = typing.Tuple[int, int, int, int]
+Space = str
 
 # Evolution coordinates
 # ---------------------
diff --git a/src/eko/matchings.py b/src/eko/matchings.py
index 0dfcae24f..9b8ce0638 100644
--- a/src/eko/matchings.py
+++ b/src/eko/matchings.py
@@ -6,7 +6,7 @@
 import numpy as np
 
 from .io.types import EvolutionPoint as EPoint
-from .io.types import FlavorIndex, FlavorsNumber, SquaredScale
+from .io.types import FlavorIndex, FlavorsNumber, SquaredScale, Order, Space
 from .quantities.heavy_quarks import MatchingScales
 
 logger = logging.getLogger(__name__)
@@ -53,6 +53,19 @@ class Matching:
 MatchedPath = List[Union[Segment, Matching]]
 
 
+@dataclass(frozen=True)
+class ScetKernel:
+    """ScetKernel.
+
+    The order refers to the power of alpha_s and L.
+
+    """
+
+    order: Order
+    space: Space
+    nf: FlavorsNumber
+
+
 class Atlas:
     r"""Holds information about the matching scales.
 
diff --git a/src/eko/member.py b/src/eko/member.py
index edf8f89a3..4951d17a5 100644
--- a/src/eko/member.py
+++ b/src/eko/member.py
@@ -310,6 +310,44 @@ def to_flavor_basis_tensor(self, qed: bool):
                     ] += out_weight * (op.error * in_weight)
         return value_tensor, error_tensor
 
+    
+    def to_flavor_basis_tensor_scet(self):
+            """Convert the computations into an rank 4 tensor.
+
+            A sparse tensor defined with dot-notation (e.g. ``u.ubar``) is converted
+            to a plain rank-4 array over flavor operator space and momentum
+            fraction operator space.
+            """
+            
+            len_pids = len(br.flavor_basis_pids)
+            len_xgrid = list(self.op_members.values())[0].value.shape[0]
+            # dimension will be pids^2 * xgrid^2
+            value_tensor = np.zeros((len_pids, len_xgrid, len_pids, len_xgrid))
+            error_tensor = value_tensor.copy()
+
+            
+            for name, op in self.op_members.items():
+                # np.asarray might not be necessary
+                in_idx = np.where(np.asarray(br.flavor_basis_names)==name.input)[0][0]
+                out_idx = np.where(np.asarray(br.flavor_basis_names)==name.target)[0][0]
+                
+                value_tensor[
+                    out_idx,  # output pid (position)
+                    :,  # output momentum fraction
+                    in_idx,  # input pid (position)
+                    :,  # input momentum fraction
+                ] += op.value 
+                error_tensor[
+                    out_idx,  # output pid (position)
+                    :,  # output momentum fraction
+                    in_idx,  # input pid (position)
+                    :,  # input momentum fraction
+                ] += op.error 
+
+            # error can be removed (ongoing PR)
+            return value_tensor, error_tensor
+
+
 
 class ScalarOperator(OperatorBase):
     """Operator above space of real numbers."""
diff --git a/src/eko/runner/managed.py b/src/eko/runner/managed.py
index c353decde..5decd2061 100644
--- a/src/eko/runner/managed.py
+++ b/src/eko/runner/managed.py
@@ -50,3 +50,36 @@ def solve(theory: TheoryCard, operator: OperatorCard, path: Path):
             del eko.parts
             del eko.parts_matching
             del eko.operators[target]
+
+def solve_scet(theory: TheoryCard, operator: OperatorCard, path: Path):
+    """Compute SCET matching kernels in terms of evolution kernel operators (EKO)."""
+    with EKO.create(path) as builder:
+        eko = builder.load_cards(theory, operator).build()  # pylint: disable=E1101
+        
+        # Only required info is 
+        #  - the order in alpha_s and in log
+        #  - whether the computation is in k or tau space
+        #  - nf to be used in beam function computation (required only starting from NNLO)
+     
+        # These info should be passed in the runcard (see cards.examples)
+    
+        orders_alpha_L=theory.orders
+        space=theory.space
+        nf= theory.nf
+               
+        # create a recipe for the scet matching kernel and load it.
+        rec = recipes.create_scet_recipe(orders_alpha_L, space, nf)
+        eko.load_recipes(rec)
+        dummy_scale = 1000. # this dummy scale labels the specific order which is going to be computed
+        # compute scet kernel
+        for recipe in eko.recipes_scet:
+            target = Target(dummy_scale, nf)
+            eko.operators[target] = parts.scetI(eko, recipe)   # in order to load these object as ekos you need to save them in eko.operators using Target as indices
+            dummy_scale += 1 
+            #del eko.scet_kernels[recipe]
+            del eko.operators[target]
+
+        
+
+
+
diff --git a/src/eko/runner/parts.py b/src/eko/runner/parts.py
index 4752aa357..2ca2472fd 100644
--- a/src/eko/runner/parts.py
+++ b/src/eko/runner/parts.py
@@ -14,10 +14,12 @@
 
 from .. import evolution_operator as evop
 from ..evolution_operator import matching_condition
+from ..evolution_operator import scet_kernel
 from ..evolution_operator import operator_matrix_element as ome
+from ..evolution_operator import beam_function as bf
 from ..evolution_operator import physical
 from ..io import EKO
-from ..io.items import Evolution, Matching, Operator
+from ..io.items import Evolution, Matching, Operator, ScetKernel
 from ..quantities.heavy_quarks import QuarkMassScheme
 from . import commons
 
@@ -157,3 +159,40 @@ def match(eko: EKO, recipe: Matching) -> Operator:
     ).to_flavor_basis_tensor(qed=binfo["qed"])
 
     return Operator(res, err)
+
+def scet_configs(eko: EKO) -> dict:
+    """Create configs for :class:`SCET_I`.
+    """
+    tcard = eko.theory_card
+    ocard = eko.operator_card
+    return dict(
+        order=tcard.order,
+        n_integration_cores=ocard.configs.n_integration_cores,
+        ModSV=ocard.configs.scvar_method,
+        matching_order=tcard.matching_order
+        if tcard.matching_order is not None
+        else tcard.order,
+    )
+
+def scetI(eko: EKO, recipe: ScetKernel) -> Operator:
+    """Compute scetI matching kernels"""
+    order = recipe.order
+    space = recipe.space
+    nf = recipe.nf # needed starting from NNLO 
+
+    kernel = bf.SCET_I(
+        scet_configs(eko),
+        managers(eko),
+        order,
+        space,
+        nf
+    )
+    kernel.compute()
+    
+    # dummy scale
+    scale=10
+    res, err = scet_kernel.ScetKernel.split_ad_to_evol_map(
+        kernel.op_members, scale
+    ).to_flavor_basis_tensor_scet()
+
+    return Operator(res, err)
diff --git a/src/eko/runner/recipes.py b/src/eko/runner/recipes.py
index 7a09554cb..ae77f1d41 100644
--- a/src/eko/runner/recipes.py
+++ b/src/eko/runner/recipes.py
@@ -1,9 +1,11 @@
 """Recipes containing instructions for atomic computations."""
 from typing import List
 
-from ..io.items import Evolution, Matching, Recipe
+from ..io.items import Evolution, Matching, Recipe, ScetKernel
+from ..io.types import Order, Space, FlavorsNumber
 from ..io.types import EvolutionPoint as EPoint
 from ..matchings import Atlas, Segment
+from ..matchings import ScetKernel as sk
 
 
 def elements(ep: EPoint, atlas: Atlas) -> List[Recipe]:
@@ -33,3 +35,13 @@ def create(evolgrid: List[EPoint], atlas: Atlas) -> List[Recipe]:
         recipes.extend(elements(ep, atlas))
 
     return list(set(recipes))
+
+def elements_scet(order: Order, space: Space, nf: FlavorsNumber) -> ScetKernel:
+    block = sk(order, space, nf)
+    return ScetKernel.from_atlas(block)
+
+def create_scet_recipe(orders: List[Order], space: Space, nf: FlavorsNumber) -> List[ScetKernel]:
+    recipes = []
+    for order in orders:
+        recipes.append(elements_scet(order, space, nf))
+    return list(set(recipes))
diff --git a/src/ekobox/apply.py b/src/ekobox/apply.py
index 336900798..fd083c80b 100644
--- a/src/ekobox/apply.py
+++ b/src/ekobox/apply.py
@@ -133,3 +133,91 @@ def apply_pdf_flavor(
                     )
 
     return out_grid
+
+
+def beam_function_from_pdf(
+    eko: EKO, lhapdf_like, mu2, targetgrid=None, flavor_rotation=None, labels=None
+):
+    """
+    Apply all available operators to the input PDFs.
+
+    Parameters
+    ----------
+        output : eko.output.EKO
+            eko output object containing all informations
+        lhapdf_like : object
+            object that provides an xfxQ2 callable (as `lhapdf <https://lhapdf.hepforge.org/>`_
+            and :class:`ekomark.toyLH.toyPDF` do) (and thus is in flavor basis)
+        targetgrid : list
+            if given, interpolates to the pdfs given at targetgrid (instead of xgrid)
+        flavor_rotation : np.ndarray
+            Rotation matrix in flavor space
+        labels : list
+            list of labels
+
+    Returns
+    -------
+        out_grid : dict
+            output PDFs and their associated errors for the computed mu2grid
+    """
+    # create pdfs
+    pdfs = np.zeros((len(eko.bases.inputpids), len(eko.bases.inputgrid)))
+    for j, pid in enumerate(eko.bases.inputpids):
+        if not lhapdf_like.hasFlavor(pid):
+            continue
+        pdfs[j] = np.array(
+            [lhapdf_like.xfxQ2(pid, x, mu2) / x for x in eko.bases.inputgrid.raw]
+        )
+    
+    # build output
+    out_grid = {}
+    for ep, elem in eko.items():
+        pdf_final = np.einsum(CONTRACTION, elem.operator, pdfs, optimize="optimal")
+        
+        if elem.error is not None:
+            error_final = np.einsum(CONTRACTION, elem.error, pdfs, optimize="optimal")
+        else:
+            error_final = None
+        out_grid[ep] = {
+            "pdfs": dict(zip(eko.bases.targetpids, pdf_final)),
+            "errors": None,
+        }
+        if error_final is not None:
+            out_grid[ep]["errors"] = dict(zip(eko.bases.targetpids, error_final))
+    qed = eko.theory_card.order[1] > 0
+    # rotate to evolution basis
+    if flavor_rotation is not None:
+        for q2, op in out_grid.items():
+            pdf = flavor_rotation @ np.array(
+                [op["pdfs"][pid] for pid in br.flavor_basis_pids]
+            )
+            if labels is None:
+                labels = list(range(flavor_rotation.shape[0]))
+            op["pdfs"] = dict(zip(labels, pdf))
+            if op["errors"] is not None:
+                errors = flavor_rotation @ np.array(
+                    [op["errors"][pid] for pid in br.flavor_basis_pids]
+                )
+                op["errors"] = dict(zip(labels, errors))
+
+    # rotate/interpolate to target grid
+    if targetgrid is not None:
+        b = interpolation.InterpolatorDispatcher(
+            xgrid=eko.bases.targetgrid,
+            polynomial_degree=eko.operator_card.configs.interpolation_polynomial_degree,
+            mode_N=False,
+        )
+
+        rot = b.get_interpolation(targetgrid)
+        for evpdf in out_grid.values():
+            for pdf_label in evpdf["pdfs"]:
+                evpdf["pdfs"][pdf_label] = np.matmul(rot, evpdf["pdfs"][pdf_label])
+                if evpdf["errors"] is not None:
+                    evpdf["errors"][pdf_label] = np.matmul(
+                        rot, evpdf["errors"][pdf_label]
+                    )
+
+    return out_grid
+
+
+    
diff --git a/src/ekobox/cards.py b/src/ekobox/cards.py
index 559790d30..01d764e03 100644
--- a/src/ekobox/cards.py
+++ b/src/ekobox/cards.py
@@ -52,6 +52,11 @@
     ),
 )
 
+_theory_scet = _theory 
+_theory_scet['space'] = 'k'
+_theory_scet['orders'] = [(0,1),(1,1),(2,1)]
+_theory_scet['nf'] = 5
+
 
 class example:
     """Provide runcards examples."""
@@ -66,6 +71,11 @@ def operator(cls) -> runcards.OperatorCard:
         """Provide example operator card object."""
         return runcards.OperatorCard.from_dict(_operator)
 
+    @classmethod
+    def theory_scet(cls) -> runcards.TheoryCard:
+        """Provide example theory card object."""
+        return runcards.TheoryCard.from_dict(_theory_scet)
+
     @classmethod
     def raw_theory(cls):
         """Provide example theory card unstructured."""
diff --git a/src/ekore/scet_I/__init__.py b/src/ekore/scet_I/__init__.py
new file mode 100644
index 000000000..af88be8c9
--- /dev/null
+++ b/src/ekore/scet_I/__init__.py
@@ -0,0 +1,83 @@
+"""SCET 1 kernels"""
+
+import numba as nb
+import numpy as np
+
+from ..harmonics import cache as c
+from . import k_space as k
+from . import tau_space as tau
+
+@nb.njit(cache=True)
+def A_entries(n, nf, order, space, cache):
+    r"""Compute the beam function matching kernel at the given order.
+
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    numpy.ndarray
+        `
+
+    """
+    if space=='k':
+        Agg = k.A_gg(n, nf, order, cache)
+        Agq = k.A_gq(n, nf, order, cache)
+        Aqg = k.A_qg(n, nf, order, cache)
+        Aqq = k.A_qq(n, nf, order, cache)
+        AqQ2 = k.A_qQ2(n, nf, order, cache)
+        Aqqbar = k.A_qqbar(n, nf, order, cache)
+        AqQ2bar = k.A_qQ2bar(n, nf, order, cache)
+
+    if space=='tau':
+        Agg = tau.A_gg(n, nf, order, cache)
+        Agq = tau.A_gq(n, nf, order, cache)
+        Aqg = tau.A_qg(n, nf, order, cache)
+        Aqq = tau.A_qq(n, nf, order, cache)
+        AqQ2 = tau.A_qQ2(n, nf, order, cache)
+        Aqqbar = tau.A_qqbar(n, nf, order, cache)
+        AqQ2bar = tau.A_qQ2bar(n, nf, order, cache)
+
+    A_S = np.array(
+        [
+            [Agg, Agq, Agq, Agq, Agq],
+            [Aqg, Aqq, Aqqbar, AqQ2, AqQ2bar],
+            [Aqg, Aqqbar, Aqq, AqQ2bar, AqQ2],
+            [Aqg, AqQ2, AqQ2bar, Aqq, Aqqbar],
+            [Aqg, AqQ2bar, AqQ2bar, Aqqbar, Aqq],
+        ],
+        np.complex_,
+    )
+    return A_S
+
+
+@nb.njit(cache=True)
+def SCET_I_entry(order, space, nf, n):
+    r"""Compute the tower of the singlet |OME|.
+
+    Parameters
+    ----------
+    matching_order : tuple(int,int)
+        perturbative matching order
+    n : complex
+        Mellin variable
+    nf: int
+        number of active flavor below threshold
+    L : float
+        :math:``\ln(\mu_F^2 / m_h^2)``
+
+    Returns
+    -------
+    numpy.ndarray
+        singlet |OME|
+
+    """
+    cache = c.reset()
+    A = np.zeros((5, 5), np.complex_)
+    A = k.A_entries(n, nf, order, space, cache)
+
+    return A
\ No newline at end of file
diff --git a/src/ekore/scet_I/k_space/__init__.py b/src/ekore/scet_I/k_space/__init__.py
new file mode 100644
index 000000000..6a44406f2
--- /dev/null
+++ b/src/ekore/scet_I/k_space/__init__.py
@@ -0,0 +1,267 @@
+import numba as nb
+import numpy as np
+
+from eko.constants import CF, zeta2
+from . import as1, as2
+from ...harmonics import cache as c
+
+
+@nb.njit(cache=True)
+def A_gg(n, nf, order, cache):
+    r"""
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    complex
+        :math:`A_{gg}`
+
+    """
+
+    if order == (1, 0):
+        res = as1.Agg10(n, cache)
+
+    if order == (1, 1):
+        res = as1.Agg11(n, cache)
+
+    if order == (1, 2):
+        res = as1.Agg12(n, cache)
+
+    if order == (2, 0):
+        res = as2.Agg20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.Agg21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.Agg22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.Agg23(n, nf, cache)
+
+    if order == (2, 4):
+        res = as2.Agg24(n, nf, cache)
+
+    return res
+
+@nb.njit(cache=True)
+def A_gq(n, nf, order, cache):
+    r"""
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    complex
+        :math:`A_{gq}`
+
+    """
+
+    if order == (1, 0):
+        res = as1.Agq10(n, cache)
+
+    if order == (1, 1):
+        res = as1.Agq11(n, cache)
+
+    if order == (1, 2):
+        res = as1.Agq12(n, cache)
+    
+    if order == (2, 0):
+        res = as2.Agq20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.Agq21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.Agq22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.Agq23(n, nf, cache)
+
+    if order == (2, 4):
+        res = as2.Agq24(n, nf, cache)
+
+    return res
+
+@nb.njit(cache=True)
+def A_qg(n, nf, order, cache):
+    r"""
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    complex
+        |NLO| :math:`A_{qg}`
+
+    """
+
+    if order == (1, 0):
+        res = as1.Aqg10(n, cache)
+
+    if order == (1, 1):
+        res = as1.Aqg11(n, cache)
+
+    if order == (1, 2):
+        res = as1.Aqg12(n, cache)
+
+    if order == (2, 0):
+        res = as2.Aqg20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.Aqg21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.Aqg22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.Aqg23(n, nf, cache)
+
+    if order == (2, 4):
+        res = as2.Aqg24(n, nf, cache)
+
+    return res
+
+@nb.njit(cache=True)
+def A_qq(n, nf, order, cache):
+    r"""
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    complex
+        |NLO| :math:`A_{qq}`
+
+    """
+
+    if order == (1, 0):
+        res = as1.Aqq10(n, cache)
+
+    if order == (1, 1):
+        res = as1.Aqq11(n, cache)
+
+    if order == (1, 2):
+        res = as1.Aqq12(n, cache)
+
+    if order == (2, 0):
+        res = as2.Aqq20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.Aqq21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.Aqq22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.Aqq23(n, nf, cache)
+
+    if order == (2, 4):
+        res = as2.Aqq24(n, nf, cache)
+
+    return res
+
+@nb.njit(cache=True)
+def A_qQ2(n, nf, order, cache):
+    if order == (1, 0):
+        res = 0.0
+
+    if order == (1, 1):
+        res = 0.0
+
+    if order == (1, 2):
+        res = 0.0
+
+    if order == (2, 0):
+        res = as2.AqQ20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.AqQ21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.AqQ22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.AqQ23(n, nf, cache)
+
+    if order == (2, 4):
+        res = as2.AqQ24(n, nf, cache)
+
+    return res
+
+
+@nb.njit(cache=True)
+def A_qQ2bar(n, nf, order, cache):
+    if order == (1, 0):
+        res = 0.0
+
+    if order == (1, 1):
+        res = 0.0
+
+    if order == (1, 2):
+        res = 0.0
+
+    if order == (2, 0):
+        res = as2.AqQbar20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.AqQbar21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.AqQbar22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.AqQbar23(n, nf, cache)
+
+    if order == (2, 4):
+        res = as2.AqQbar24(n, nf, cache)
+
+    return res
+
+@nb.njit(cache=True)
+def A_qqbar(n, nf, order, cache):
+    if order == (1, 0):
+        res = 0.0
+
+    if order == (1, 1):
+        res = 0.0
+
+    if order == (1, 2):
+        res = 0.0
+
+    if order == (2, 0):
+        res = as2.Aqqbar20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.Aqqbar21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.Aqqbar22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.Aqqbar23(n, nf, cache)
+
+    if order == (2, 4):
+        res = as2.Aqqbar24(n, nf, cache)
+
+    return res
+
+
+
diff --git a/src/ekore/scet_I/k_space/as1.py b/src/ekore/scet_I/k_space/as1.py
new file mode 100644
index 000000000..b9157a882
--- /dev/null
+++ b/src/ekore/scet_I/k_space/as1.py
@@ -0,0 +1,119 @@
+r"""SCET 1 kernel entries.
+
+"""
+import numba as nb
+import numpy as np
+
+from eko.constants import CF, zeta2
+from ...harmonics import cache as c
+
+
+@nb.njit(cache=True)
+def Agg10(n, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    res = (
+        (
+            3
+            * (
+                -2
+                - n
+                + 5 * np.power(n, 2)
+                + 2 * np.power(n, 3)
+                + 2 * np.power(n, 4)
+                + 2 * np.power(n, 2) * zeta2
+                - np.power(n, 3) * zeta2
+                - 3 * np.power(n, 4) * zeta2
+                + np.power(n, 5) * zeta2
+                + np.power(n, 6) * zeta2
+            )
+        )
+        / (np.power(-1 + n, 2) * np.power(n, 2) * (1 + n) * (2 + n))
+        - (6 * (1 + n + np.power(n, 2)) * S1) / ((-1 + n) * n * (1 + n) * (2 + n))
+        + (3 * np.power(S1, 2)) / 2.0
+        - (3 * S2) / 2.0
+    )
+    return res
+
+
+@nb.njit(cache=True)
+def Agg11(n, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = (-6 * (1 + n + np.power(n, 2))) / ((-1 + n) * n * (1 + n) * (2 + n)) + 3 * S1
+    return res
+
+
+@nb.njit(cache=True)
+def Agg12(n, cache):
+    res = 1.5
+    return res
+
+
+@nb.njit(cache=True)
+def Agq10(n, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = (2 * (-2 + 5 * np.power(n, 2) + np.power(n, 4))) / (
+        3.0 * np.power(-1 + n, 2) * np.power(n, 2) * (1 + n)
+    ) - (2 * (2 + n + np.power(n, 2)) * S1) / (3.0 * (-1 + n) * n * (1 + n))
+    return res
+
+
+@nb.njit(cache=True)
+def Agq11(n, cache):
+    res = (-2 * (2 + n + np.power(n, 2))) / (3.0 * (-1 + n) * n * (1 + n))
+    return res
+
+
+@nb.njit(cache=True)
+def Agq12(n, cache):
+    res = 0
+    return res
+
+
+@nb.njit(cache=True)
+def Aqg10(n, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = 1 / (4.0 * np.power(n, 2)) + ((-2 - n - np.power(n, 2)) * S1) / (
+        4.0 * n * (1 + n) * (2 + n)
+    )
+    return res
+
+
+@nb.njit(cache=True)
+def Aqg11(n, cache):
+    res = (-2 - n - np.power(n, 2)) / (4.0 * n * (1 + n) * (2 + n))
+    return res
+
+
+@nb.njit(cache=True)
+def Aqg12(n, cache):
+    res = 0
+    return res
+
+
+@nb.njit(cache=True)
+def Aqq10(n, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    res = (
+        (2 * (1 + 2 * n + 2 * np.power(n, 2) * zeta2 + 2 * np.power(n, 3) * zeta2))
+        / (3.0 * np.power(n, 2) * (1 + n))
+        - (2 * S1) / (3.0 * n * (1 + n))
+        + (2 * np.power(S1, 2)) / 3.0
+        - (2 * S2) / 3.0
+    )
+    return res
+
+
+@nb.njit(cache=True)
+def Aqq11(n, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = -2 / (3.0 * n * (1 + n)) + (4 * S1) / 3.0
+    return res
+
+
+@nb.njit(cache=True)
+def Aqq12(n, cache):
+    res = 0.6666666666666666
+    return res
+
diff --git a/src/ekore/scet_I/k_space/as2.py b/src/ekore/scet_I/k_space/as2.py
new file mode 100644
index 000000000..3e0a1ec7c
--- /dev/null
+++ b/src/ekore/scet_I/k_space/as2.py
@@ -0,0 +1,596 @@
+r"""SCET 1 nnlo kernel entries.
+
+"""
+import numba as nb
+import numpy as np
+
+from eko.constants import CF, zeta2, zeta3
+from ...harmonics import cache as c
+
+
+
+
+
+@nb.njit(cache=True)
+def Agg20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = 16.86111111111111 - 99/(4.*np.power(-1 + n,3)) + 201/(4.*np.power(-1 + n,2)) + 63/(2.*np.power(n,4)) + 327/(8.*np.power(n,3)) + 937/(16.*np.power(n,2)) - 29.349156166471147/n + 45/np.power(1 + n,4) - 249/(8.*np.power(1 + n,3)) + 1351/(16.*np.power(1 + n,2)) + 33/(4.*np.power(2 + n,3)) + 215/(4.*np.power(2 + n,2)) - 165/(8.*np.power(3 + n,3)) + 825/(32.*np.power(3 + n,2)) + 75.11973727168703/np.power(4 + n,4) - 327.93971046698647/np.power(4 + n,3) + 489.8658778292528/np.power(4 + n,2) - 790.4536913761124/np.power(5 + n,4) + 906.1743071114438/np.power(5 + n,3) - 731.1896273676689/np.power(5 + n,2) + 320.7706707471764/np.power(6 + n,4) + 775.585407692871/np.power(6 + n,3) + 866.7481273153206/np.power(6 + n,2) + (238.9194899614054 - 0.7187584125804691*nf)/(5 + n) + (91.0344525497889 + 0.06959835991327973*nf)/(6 + n) - (41*nf)/54. + (17*nf)/(18.*np.power(-1 + n,3)) - (235*nf)/(108.*np.power(-1 + n,2)) - (5*nf)/(3.*np.power(n,4)) + (17*nf)/(12.*np.power(n,3)) - (61*nf)/(24.*np.power(n,2)) + (4.981889500151358*nf)/n - (5*nf)/(3.*np.power(1 + n,4)) + (31*nf)/(12.*np.power(1 + n,3)) - (13*nf)/(4.*np.power(1 + n,2)) - (4*nf)/(9.*np.power(2 + n,3)) + (5*nf)/(18.*np.power(2 + n,2)) + nf/(2.*np.power(3 + n,3)) - (247*nf)/(216.*np.power(3 + n,2)) + (0.05188597791606392*nf)/np.power(4 + n,4) + (0.18500946222330533*nf)/np.power(4 + n,3) - (0.48075977710297113*nf)/np.power(4 + n,2) + (1.1304591631668428*nf)/np.power(5 + n,4) + (0.3443730808411247*nf)/np.power(5 + n,3) + (1.7408117318945497*nf)/np.power(5 + n,2) - (0.17871955042920698*nf)/np.power(6 + n,4) - (0.44591765410290274*nf)/np.power(6 + n,3) - (0.5854839347981557*nf)/np.power(6 + n,2) + (-892.7765462248292 + 4.967170666760481*nf)/(4 + n) - (67*np.power(np.pi,2))/96. - (15*np.power(np.pi,2))/(4.*np.power(-1 + n,2)) + (9*np.power(np.pi,2))/(4.*np.power(n,2)) - (12*np.power(np.pi,2))/np.power(1 + n,2) - (15*np.power(np.pi,2))/(4.*np.power(3 + n,2)) + (5*nf*np.power(np.pi,2))/144. + (nf*np.power(np.pi,2))/(6.*np.power(n,2)) - (5*nf*np.power(np.pi,2))/(18.*n) + (nf*np.power(np.pi,2))/(6.*np.power(1 + n,2)) - (11*np.power(np.pi,4))/80. + (-2656.1846361137755 + 13.004950411872356*nf - (7*nf*np.power(np.pi,2))/54.)/(2 + n) + (2285.159409762382 - 14.193864160201342*nf + (5*nf*np.power(np.pi,2))/72.)/(3 + n) - (957.4913212153385*S1)/n + (5.0360604026719304*nf*S1)/n + (2798.17031768792*(1/(1 + n) + S1))/(1 + n) - (15.938321904510403*nf*(1/(1 + n) + S1))/(1 + n) - (2183.014017811476*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (22.221146077608847*nf*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (1794.9072797413023*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (7.947769036822255*nf*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (853.6048603446067*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (19.06077749915008*nf*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (596.5490079602517*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (1.4142094467758806*nf*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (696.429863570809*(np.power(S1,2)/2. + S2/2.))/n + (3.248573734966296*nf*(np.power(S1,2)/2. + S2/2.))/n + (16.75 - (5*nf)/6. - (9*np.power(np.pi,2))/4.)*(-(S1/n) + np.power(S1,2)/2. + S2/2.) - (3035.637132022108*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (10.911345647839301*nf*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (5411.123832618697*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (14.997551679700479*nf*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (2160.722395241362*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (4.59716254754814*nf*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (4801.597341431533*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (11.67698516839526*nf*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (391.291617977227*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.7549571459803536*nf*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (176.89773541521075*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (0.5230267409975893*nf*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - 2*(-4.125 + nf/4.)*(-0.5*np.power(S1,2)/n + np.power(S1,3)/6. - S2/(2.*n) + (S1*S2)/2. + S3/3.) + (210.00253110794813*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (2.6555253520083517*nf*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (836.4108709560046*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (5.391211881797062*nf*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (1508.7868305034372*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (2.774833944288212*nf*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (1946.2704453635947*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (5.470750943316969*nf*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (405.03205178858434*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) - (0.5627962717575428*nf*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) + 27*(-0.16666666666666666*np.power(S1,3)/n + np.power(S1,4)/24. - (S1*S2)/(2.*n) + (np.power(S1,2)*S2)/4. + np.power(S2,2)/8. - S3/(3.*n) + (S1*S3)/3. + S(4,n)/4.) - (33*zeta3)/8. + (nf*zeta3)/4. - (2*nf*zeta3)/(3.*n) - (-(1/n) + S1)*(-16.833333333333332 + (7*nf)/9. + (11*np.power(np.pi,2))/16. - (nf*np.power(np.pi,2))/24. + (99*zeta3)/4.) + (-100.25 + (455*nf)/162. + (11*np.power(np.pi,2))/16. - (17*nf*np.power(np.pi,2))/216. + 36*zeta3)/(-1 + n) + (976.3258434434753 - 6.952739586572729*nf + (nf*np.power(np.pi,2))/18. - (2*nf*zeta3)/3.)/(1 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agg21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = 16.833333333333332 - 9/np.power(-1 + n,3) + 99/(4.*np.power(-1 + n,2)) - 18/np.power(n,3) - 45/(2.*np.power(n,2)) - 34.08160990247799/n - 54/np.power(1 + n,3) + 99/(4.*np.power(1 + n,2)) - 9/np.power(3 + n,3) + 99/(4.*np.power(3 + n,2)) - 6.959090024543352/np.power(4 + n,4) + 31.316953909265823/np.power(4 + n,3) - 129.72126276003138/np.power(4 + n,2) - 316.61176078013756/np.power(5 + n,4) + 96.1184068916528/np.power(5 + n,3) - 654.8831560964019/np.power(5 + n,2) + 163.9946761397813/np.power(6 + n,4) + 313.3624782120564/np.power(6 + n,3) + 359.0418188870436/np.power(6 + n,2) + (-1337.6273882811697 - 4.494055935519254*nf)/(3 + n) + (-145.9640592388291 - 0.241465589995501*nf)/(5 + n) + (-54.23457261672672 - 0.05502440947592218*nf)/(6 + n) - (7*nf)/9. - (17*nf)/(18.*np.power(-1 + n,2)) + (4*nf)/(3.*np.power(n,3)) - nf/np.power(n,2) + (0.7500000000000284*nf)/n + (4*nf)/(3.*np.power(1 + n,3)) - (13*nf)/(6.*np.power(1 + n,2)) + (4*nf)/(9.*np.power(2 + n,2)) - nf/(2.*np.power(3 + n,2)) + (0.011275640927692523*nf)/np.power(4 + n,4) - (0.06468931095091934*nf)/np.power(4 + n,3) - (0.2799909715053025*nf)/np.power(4 + n,2) + (0.1898720429119991*nf)/np.power(5 + n,4) - (0.020034311566906212*nf)/np.power(5 + n,3) + (0.17777890986621123*nf)/np.power(5 + n,2) - (0.043565667449617394*nf)/np.power(6 + n,4) - (0.11212805286729775*nf)/np.power(6 + n,3) - (0.15807930699413783*nf)/np.power(6 + n,2) + (539.8396237029783 + 1.3459753921080742*nf)/(4 + n) + (1555.7729975239774 + 3.0194412078803183*nf)/(2 + n) - (11*np.power(np.pi,2))/16. + (nf*np.power(np.pi,2))/24. - (nf*np.power(np.pi,2))/(9.*n) + (-16.75 + (235*nf)/108. + (3*np.power(np.pi,2))/2.)/(-1 + n) + (-518.9660076919846 - 1.6408845017926574*nf - (nf*np.power(np.pi,2))/9.)/(1 + n) + (550.4770242673264*S1)/n + (2.1408845017040483*nf*S1)/n - (-16.75 + (5*nf)/6. + (9*np.power(np.pi,2))/4.)*(-(1/n) + S1) - (1609.5965772517004*(1/(1 + n) + S1))/(1 + n) - (6.161410970014396*nf*(1/(1 + n) + S1))/(1 + n) + (1196.2222768020379*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (6.989681660926549*nf*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) - (1196.7004235975921*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (1.9576914148918718*nf*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (702.1423904308235*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (5.0760908464004215*nf*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) + (392.7053093491044*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (0.35075576110765155*nf*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (492.74315777416973*(np.power(S1,2)/2. + S2/2.))/n + (0.4208329523824698*nf*(np.power(S1,2)/2. + S2/2.))/n + (8.25 - nf/2.)*(-(S1/n) + np.power(S1,2)/2. + S2/2.) + (2044.6883276518818*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (1.8685772552991469*nf*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (3375.4249360137287*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (3.2857436451256987*nf*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (1186.915553438676*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (1.221107178720968*nf*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (2839.576419871591*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (2.8540969274069123*nf*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (197.81889970310104*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.2050095935230768*nf*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (13.606906922105907*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.06739772448375828*nf*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + 27*(-0.5*np.power(S1,2)/n + np.power(S1,3)/6. - S2/(2.*n) + (S1*S2)/2. + S3/3.) + (376.9276566603408*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.15155940569821733*nf*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (1365.5990389768906*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (0.0650472766211539*nf*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (1285.4794674795335*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (0.39665120819282607*nf*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (1971.3002461896854*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (0.4305210192151828*nf*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (316.45751052850346*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) - (0.11533914681325617*nf*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) - (99*zeta3)/4.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agg22(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    res = 8.375 - (387*(1/(-1 + n) - 1/n))/8. + 33/(8.*(-1 + n)) + 9*(-np.power(-1 + n,-2) + 2/np.power(n,2) - np.power(1 + n,-2)) + (177*(1/(-1 + n) - 2/n + 1/(1 + n)))/4. - 9*(-np.power(-1 + n,-2) + 3/np.power(n,2) - 3/np.power(1 + n,2) + np.power(2 + n,-2)) - (165*(1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n)))/8. - (5*nf)/12. + (19*(1/(-1 + n) - 1/n)*nf)/12. - nf/(4.*(-1 + n)) - (2*nf)/(3.*np.power(n,2)) - ((-np.power(n,-2) + np.power(1 + n,-2))*nf)/3. - (4*(1/(-1 + n) - 2/n + 1/(1 + n))*nf)/3. + (17*(1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n))*nf)/36. - (9*np.power(np.pi,2))/8. + (33*(-(1/n) + S1))/8. + (27*(-(1/n) + S1))/(2.*(-1 + n)) - (nf*(-(1/n) + S1))/4. + (81*(S1/n - (-(1/n) + S1)/(-1 + n)))/2. - 27*((2*S1)/n - (-(1/n) + S1)/(-1 + n) - (1/(1 + n) + S1)/(1 + n)) + (27*((3*S1)/n - (-(1/n) + S1)/(-1 + n) - (3*(1/(1 + n) + S1))/(1 + n) + ((3 + 2*n)/((1 + n)*(2 + n)) + S1)/(2 + n)))/2. + (27*(-(S1/n) + np.power(S1,2)/2. + S2/2.))/2. - 9*((-1 + 2*n - 2*np.power(n,2))/(np.power(-1 + n,2)*np.power(n,2)) - np.power(np.pi,2)/6. + S2)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agg23(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = 1.375 - (27*(1/(-1 + n) - 1/n))/2. + 9/(2.*(-1 + n)) + 9*(1/(-1 + n) - 2/n + 1/(1 + n)) - (9*(1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n)))/2. - nf/12. + (9*(-(1/n) + S1))/2.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agg24(n, nf, cache):
+    res = 1.125
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agq20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -31/(3.*np.power(-1 + n,3)) + 41/(2.*np.power(-1 + n,2)) + 106/(9.*np.power(n,4)) + 218/(9.*np.power(n,3)) + 275/(18.*np.power(n,2)) + 3.9571005767767033/n + 55/(9.*np.power(1 + n,4)) + 109/(18.*np.power(1 + n,3)) + 235/(18.*np.power(1 + n,2)) + 2/(27.*np.power(2 + n,3)) + 11/(2.*np.power(2 + n,2)) - 17/(27.*np.power(3 + n,3)) - 133/(648.*np.power(3 + n,2)) + 0.8223698702784716/np.power(4 + n,4) - 5.553806921999574/np.power(4 + n,3) + 8.366771900574946/np.power(4 + n,2) - 10.949382219584912/np.power(5 + n,4) + 13.849432222845577/np.power(5 + n,3) - 11.204433049821336/np.power(5 + n,2) + 4.893356281716537/np.power(6 + n,4) + 11.549634451584822/np.power(6 + n,3) + 12.475711611014834/np.power(6 + n,2) + (6.388313909027405 - 0.134021867309814*nf)/(5 + n) + (1.359582492100278 - 0.06271239231491248*nf)/(6 + n) + (-30.731748568486335 + 0.4736664950001651*nf)/(4 + n) + (4*nf)/(9.*np.power(-1 + n,3)) - (20*nf)/(27.*np.power(-1 + n,2)) - (4*nf)/(9.*np.power(n,3)) + (20*nf)/(27.*np.power(n,2)) - (1.4176103655531436*nf)/n + (2*nf)/(9.*np.power(1 + n,3)) - (10*nf)/(27.*np.power(1 + n,2)) - (0.004644855507486117*nf)/np.power(4 + n,4) + (0.02752704333289802*nf)/np.power(4 + n,3) - (0.09517404464347873*nf)/np.power(4 + n,2) - (0.07255605248969821*nf)/np.power(5 + n,4) - (0.03179629006284005*nf)/np.power(5 + n,3) - (0.20919521412223563*nf)/np.power(5 + n,2) + (0.013862164596313922*nf)/np.power(6 + n,4) + (0.02517890833768235*nf)/np.power(6 + n,3) + (0.0212374019159726*nf)/np.power(6 + n,2) - (35*np.power(np.pi,2))/(27.*np.power(-1 + n,2)) + (23*np.power(np.pi,2))/(27.*np.power(n,2)) - (34*np.power(np.pi,2))/(27.*np.power(1 + n,2)) + (2*nf*np.power(np.pi,2))/(27.*n) + (45.1926665533455 + 0.762659604639619*nf - (5*nf*np.power(np.pi,2))/27.)/(1 + n) + (69.23881799080559 - 0.8795772240770414*nf - (nf*np.power(np.pi,2))/27.)/(3 + n) + (-70.31617353640735 + 0.5439611002122565*nf + (4*nf*np.power(np.pi,2))/27.)/(2 + n) - (33.12620941527203*S1)/n + (1.112012896833687*nf*S1)/n + (65.56287458498312*(1/(1 + n) + S1))/(1 + n) - (1.9018156986716952*nf*(1/(1 + n) + S1))/(1 + n) - (8.644527254534509*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (1.3405078700407942*nf*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (79.57601966082686*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (0.21651223044957663*nf*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (81.67970586795522*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (0.1011287567994526*nf*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (22.8341684335303*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (0.06323221534253937*nf*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (53.33789727658772*(np.power(S1,2)/2. + S2/2.))/n - (0.8514951640659054*nf*(np.power(S1,2)/2. + S2/2.))/n - (209.38938481508063*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (2.0144131547924555*nf*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (343.35224129840924*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (2.2005831896264394*nf*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (112.89899341228728*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (0.3699829026393649*nf*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (278.9327211039544*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (1.2524445030058606*nf*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (18.211470512693634*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) + (0.044092487422282514*nf*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (42.35673152829946*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.1536011983541577*nf*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (84.9840789038495*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.6928663157980264*nf*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (47.238518782072774*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (1.2366573944297772*nf*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (44.361657515641326*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (0.4710596322174849*nf*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (31.732712904995193*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (1.0887862720427495*nf*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (13.46221764856785*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) + (0.07966563716064384*nf*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) + (-37.9537037037037 + (56*nf)/81. - (19*np.power(np.pi,2))/36. + (nf*np.power(np.pi,2))/27. + 16*zeta3)/(-1 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agq21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -4/np.power(-1 + n,3) + 31/(3.*np.power(-1 + n,2)) - 56/(9.*np.power(n,3)) - 136/(9.*np.power(n,2)) - 2.5845323553137938/n - 62/(9.*np.power(1 + n,3)) - 53/(9.*np.power(1 + n,2)) + 16/(27.*np.power(2 + n,2)) + 26/(27.*np.power(3 + n,2)) - 0.14933365678240723/np.power(4 + n,4) + 0.9647209308996265/np.power(4 + n,3) - 1.982113627904677/np.power(4 + n,2) - 4.384606883281288/np.power(5 + n,4) + 0.36359029018821026/np.power(5 + n,3) - 9.467016995505801/np.power(5 + n,2) + 2.211128073305879/np.power(6 + n,4) + 4.231801095479696/np.power(6 + n,3) + 5.088080180162337/np.power(6 + n,2) + (10.277957980256247 - 0.12859726389884807*nf)/(2 + n) + (3.170265036181056 - 0.09384997386592911*nf)/(4 + n) + (-0.6181579611503486 - 0.014540356149953873*nf)/(6 + n) + (-1.3016152241058507 + 0.007082899233404929*nf)/(5 + n) + (-11.512424159396804 + 0.19850336286089515*nf)/(3 + n) + (1.9179438020673558 + 0.40177170219080016*nf)/(1 + n) - (4*nf)/(9.*np.power(-1 + n,2)) + (4*nf)/(9.*np.power(n,2)) - (0.7407407407407416*nf)/n - (2*nf)/(9.*np.power(1 + n,2)) - (0.0008863218377414114*nf)/np.power(4 + n,4) + (0.005097260396606985*nf)/np.power(4 + n,3) - (0.017265120383839497*nf)/np.power(4 + n,2) - (0.012118814258166404*nf)/np.power(5 + n,4) - (0.005454377177093399*nf)/np.power(5 + n,3) - (0.03901864982081938*nf)/np.power(5 + n,2) + (0.0012055454368091521*nf)/np.power(6 + n,4) + (0.0017644538166461156*nf)/np.power(6 + n,3) - (0.0012268733773057319*nf)/np.power(6 + n,2) + (-5.611111111111111 + (20*nf)/27. + (8*np.power(np.pi,2))/27.)/(-1 + n) - (0.5459413560733313*S1)/n - (0.03140133181504437*nf*S1)/n + (7.587265449211114*(1/(1 + n) + S1))/(1 + n) + (0.1460549984559635*nf*(1/(1 + n) + S1))/(1 + n) - (30.001169125420553*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) - (0.2695284562563078*nf*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) - (34.827837457006034*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (0.11116535834688081*nf*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (50.60599490839494*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) + (0.246268696183586*nf*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) + (8.515020914227193*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (0.019771451778683467*nf*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (44.740062385880165*(np.power(S1,2)/2. + S2/2.))/n - (0.003514147373606059*nf*(np.power(S1,2)/2. + S2/2.))/n + (120.24209639626389*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (0.022049693029882415*nf*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (151.08967480822122*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (0.05324005464746588*nf*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (35.322077931643875*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (0.03603483030742922*nf*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (100.99484768365971*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (0.06256347949916376*nf*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (5.025982156932755*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) + (0.008175859799454994*nf*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (5.609244884938891*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.004785442284985393*nf*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (29.321403901051205*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.023673044154066444*nf*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (61.16631983010827*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (0.04681036563897463*nf*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (33.06640155599856*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (0.02282837795917319*nf*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (63.66298493340651*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (0.04624725484237912*nf*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (6.857577436588011*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) + (0.00450388688668764*nf*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agq22(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = 6*(-np.power(-1 + n,-2) + np.power(n,-2)) - (83*(1/(-1 + n) - 1/n))/9. + 61/(9.*np.power(-1 + n,2)) - 1/(2.*(-1 + n)) - (29*(-np.power(-1 + n,-2) + 2/np.power(n,2) - np.power(1 + n,-2)))/9. + (14*(1/(-1 + n) - 2/n + 1/(1 + n)))/9. - (2*(1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n)))/3. + nf/(9.*(-1 + n)) + ((1/(-1 + n) - 2/n + 1/(1 + n))*nf)/9. - (22*(-(1/n) + S1))/(9.*(-1 + n)) + (22*((2*S1)/n - (-(1/n) + S1)/(-1 + n) - (1/(1 + n) + S1)/(1 + n)))/9.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agq23(n, nf, cache):
+    res = -2/(-1 + n) + 2/n - 1/(1 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agq24(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqg20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -43/(24.*np.power(n,4)) - 131/(48.*np.power(n,3)) - 131/(48.*np.power(n,2)) + 1.1911888331830194/n - 65/(12.*np.power(1 + n,4)) + 11/(4.*np.power(1 + n,3)) - 35/(6.*np.power(1 + n,2)) + 10.4053926591844/(1 + n) + np.power(2 + n,-4) - 93/(8.*np.power(2 + n,3)) - 133/(16.*np.power(2 + n,2)) - 25.265257982477284/(2 + n) - 2/(3.*np.power(3 + n,3)) + 259/(216.*np.power(3 + n,2)) + 22.97169476938314/(3 + n) + 0.4356820271802718/np.power(4 + n,4) - 3.648167146799966/np.power(4 + n,3) + 4.666958361067362/np.power(4 + n,2) - 15.820612873505851/(4 + n) - 7.1928985308380415/np.power(5 + n,4) + 7.53926563139814/np.power(5 + n,3) - 8.133967097702559/np.power(5 + n,2) + 3.444952575663905/(5 + n) + 2.7973273410525477/np.power(6 + n,4) + 6.933209170846717/np.power(6 + n,3) + 7.7669270528116305/np.power(6 + n,2) + 0.8562998184468253/(6 + n) - (13*np.power(np.pi,2))/(144.*np.power(n,2)) + (29*np.power(np.pi,2))/(36.*np.power(1 + n,2)) - (23*np.power(np.pi,2))/(36.*np.power(2 + n,2)) + (1.4444444444444444 + np.power(np.pi,2)/24.)/(-1 + n) - (10.89551676742556*S1)/n + (33.91512411485418*(1/(1 + n) + S1))/(1 + n) - (32.378345212125026*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (6.620037270621037*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (6.441410088535398*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (3.567742461035917*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (7.6259459441578015*(np.power(S1,2)/2. + S2/2.))/n - (30.5656098627976*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (53.554742347589425*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (17.361870636087808*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (45.48836064089401*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (2.738588424143426*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (1.9793278380704296*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (1.798659292989602*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (7.6689995392226145*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (13.748022057194886*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (18.839009328234496*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (3.6056770564355105*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqg21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -13/(12.*(-1 + n)) + 7/(6.*np.power(n,3)) + 5/(4.*np.power(n,2)) + 1.2533223444746522/n + 31/(6.*np.power(1 + n,3)) - 4/(3.*np.power(1 + n,2)) - 9.031235230715703/(1 + n) - 4/(3.*np.power(2 + n,3)) + 187/(24.*np.power(2 + n,2)) + 15.59250486448689/(2 + n) + 8/(9.*np.power(3 + n,2)) - 6.751578556990447/(3 + n) - 0.027929527280142082/np.power(4 + n,4) + 0.23338391067360553/np.power(4 + n,3) + 0.258640725494089/np.power(4 + n,2) - 0.13219179925426255/(4 + n) - 1.9121251865638547/np.power(5 + n,4) + 0.7183060788586074/np.power(5 + n,3) - 3.625926729243089/np.power(5 + n,2) + 0.27384591274603937/(5 + n) + 1.1071257185432037/np.power(6 + n,4) + 2.188753500072866/np.power(6 + n,3) + 2.6088729631688365/np.power(6 + n,2) + 0.25216076260294745/(6 + n) + (2.589788341299843*S1)/n - (4.805726932211193*(1/(1 + n) + S1))/(1 + n) + (1.7872567498248921*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) - (8.820553422050553*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (6.449707930794049*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) + (2.5495273323429615*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (3.201963174657092*(np.power(S1,2)/2. + S2/2.))/n + (10.902815064311243*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (17.462853189309797*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (6.112153339962495*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (13.324634261966189*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (1.1328537109852865*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.3849560009944391*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (3.291205854414084*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (9.2864975060617*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (7.304185697789013*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (11.961817401644986*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (1.722615948786082*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqg22(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = (41*(1/(-1 + n) - 1/n))/12. - 1/(8.*(-1 + n)) - 35/(24.*np.power(n,2)) - (2*(-np.power(n,-2) + np.power(1 + n,-2)))/3. - (93*(1/(-1 + n) - 2/n + 1/(1 + n)))/16. - (2*(-np.power(n,-2) + 2/np.power(1 + n,2) - np.power(2 + n,-2)))/3. + (133*(1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n)))/48. - (17*S1)/(24.*n) - (17*(-(S1/n) + (1/(1 + n) + S1)/(1 + n)))/12. + (17*(-(S1/n) + (2*(1/(1 + n) + S1))/(1 + n) - ((3 + 2*n)/((1 + n)*(2 + n)) + S1)/(2 + n)))/12.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqg23(n, nf, cache):
+    res = -0.16666666666666666*1/n + (1/n - 1/(1 + n))/3. + (-(1/n) + 2/(1 + n) - 1/(2 + n))/3.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqg24(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqq20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -5/(6.*np.power(n,4)) - 13/(12.*np.power(n,3)) - 3/(2.*np.power(n,2)) - 0.7986297731997045/n - 5/(6.*np.power(1 + n,4)) - 13/(12.*np.power(1 + n,3)) - 1/(3.*np.power(1 + n,2)) + 1.0506711812659297/(1 + n) - 10/(9.*np.power(2 + n,3)) - 49/(27.*np.power(2 + n,2)) - 0.9163222241223545/(2 + n) + 2/(27.*np.power(3 + n,2)) - 0.2806436951458962/(3 + n) + 0.0014735182662902581/np.power(4 + n,4) - 0.009193655123305253/np.power(4 + n,3) + 0.055511612427147146/np.power(4 + n,2) + 0.09590718130594521/(4 + n) + 0.027588702894167733/np.power(5 + n,4) + 0.012667915026022089/np.power(5 + n,3) + 0.07943507877302992/np.power(5 + n,2) + 0.004407924616075398/(5 + n) - 0.007753800373369394/np.power(6 + n,4) - 0.014409903008843377/np.power(6 + n,3) - 0.01668441874933692/np.power(6 + n,2) + 0.019863644765988633/(6 + n) + np.power(np.pi,2)/(12.*np.power(n,2)) + np.power(np.pi,2)/(12.*np.power(1 + n,2)) + (0.6419753086419753 + np.power(np.pi,2)/54.)/(-1 + n) + (0.13983274560630196*S1)/n - (0.41275820879534736*(1/(1 + n) + S1))/(1 + n) + (0.8051014673999592*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (0.3773965825982953*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (0.8370826054908135*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (0.07248998131839572*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (0.49726721324576617*(np.power(S1,2)/2. + S2/2.))/n - (1.3737737224272497*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (1.6829683740128463*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (0.35105687464036983*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (1.1122682532660377*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (0.04525048620569524*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) + (0.10801897174901916*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.49084933211928516*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.8840516588729128*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (0.34564489589974434*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (0.787248701393219*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (0.059617493009172226*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqq21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -13/(27.*(-1 + n)) + 2/(3.*np.power(n,3)) + 1/(3.*np.power(n,2)) + 0.28502197771725984/n + 2/(3.*np.power(1 + n,3)) + np.power(1 + n,-2) - 1.3367058144318702/(1 + n) + 2/(3.*np.power(2 + n,2)) + 2.1906260706515757/(2 + n) - 1.0146549160375362/(3 + n) + 0.0008287014639471657/np.power(4 + n,4) - 0.004669402119497261/np.power(4 + n,3) + 0.015584039956958031/np.power(4 + n,2) + 0.3970774550559096/(4 + n) + 0.009974093945678364/np.power(5 + n,4) + 0.005829363347210827/np.power(5 + n,3) + 0.03288843984284437/np.power(5 + n,2) - 0.05168203279717121/(5 + n) - 0.0007839412569760368/np.power(6 + n,4) - 0.0012427255994616627/np.power(6 + n,3) + 0.0009493512253215492/np.power(6 + n,2) + 0.011798741323319263/(6 + n) + (0.45506112547578514*S1)/n - (1.2340398935538648*(1/(1 + n) + S1))/(1 + n) + (1.5405378426172631*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (0.4085445948909813*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (1.1013187546197853*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (0.06878491481037952*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (0.07621097625638995*(np.power(S1,2)/2. + S2/2.))/n - (0.3417710652584133*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (0.6078137269535574*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (0.23243730263921492*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (0.5349245518740918*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (0.03976638871665715*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.011098590750917119*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (0.026539607868124548*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.0044455027231418*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (0.05917450985066498*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (0.0615882478690015*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (0.017472781822012725*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqq22(n, nf, cache):
+    res = (5*(1/(-1 + n) - 1/n))/12. - 1/(3.*np.power(n,2)) + (np.power(n,-2) - np.power(1 + n,-2))/6. - (5*(1/(-1 + n) - 2/n + 1/(1 + n)))/12. + (1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n))/9.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqq23(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqq24(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQ20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -5/(6.*np.power(n,4)) - 13/(12.*np.power(n,3)) - 3/(2.*np.power(n,2)) - 0.7986297731997045/n - 5/(6.*np.power(1 + n,4)) - 13/(12.*np.power(1 + n,3)) - 1/(3.*np.power(1 + n,2)) + 1.0506711812659297/(1 + n) - 10/(9.*np.power(2 + n,3)) - 49/(27.*np.power(2 + n,2)) - 0.9163222241223545/(2 + n) + 2/(27.*np.power(3 + n,2)) - 0.2806436951458962/(3 + n) + 0.0014735182662902581/np.power(4 + n,4) - 0.009193655123305253/np.power(4 + n,3) + 0.055511612427147146/np.power(4 + n,2) + 0.09590718130594521/(4 + n) + 0.027588702894167733/np.power(5 + n,4) + 0.012667915026022089/np.power(5 + n,3) + 0.07943507877302992/np.power(5 + n,2) + 0.004407924616075398/(5 + n) - 0.007753800373369394/np.power(6 + n,4) - 0.014409903008843377/np.power(6 + n,3) - 0.01668441874933692/np.power(6 + n,2) + 0.019863644765988633/(6 + n) + np.power(np.pi,2)/(12.*np.power(n,2)) + np.power(np.pi,2)/(12.*np.power(1 + n,2)) + (0.6419753086419753 + np.power(np.pi,2)/54.)/(-1 + n) + (0.13983274560630196*S1)/n - (0.41275820879534736*(1/(1 + n) + S1))/(1 + n) + (0.8051014673999592*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (0.3773965825982953*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (0.8370826054908135*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (0.07248998131839572*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (0.49726721324576617*(np.power(S1,2)/2. + S2/2.))/n - (1.3737737224272497*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (1.6829683740128463*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (0.35105687464036983*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (1.1122682532660377*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (0.04525048620569524*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) + (0.10801897174901916*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.49084933211928516*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.8840516588729128*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (0.34564489589974434*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (0.787248701393219*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (0.059617493009172226*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQ21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -13/(27.*(-1 + n)) + 2/(3.*np.power(n,3)) + 1/(3.*np.power(n,2)) + 0.28502197771725984/n + 2/(3.*np.power(1 + n,3)) + np.power(1 + n,-2) - 1.3367058144318702/(1 + n) + 2/(3.*np.power(2 + n,2)) + 2.1906260706515757/(2 + n) - 1.0146549160375362/(3 + n) + 0.0008287014639471657/np.power(4 + n,4) - 0.004669402119497261/np.power(4 + n,3) + 0.015584039956958031/np.power(4 + n,2) + 0.3970774550559096/(4 + n) + 0.009974093945678364/np.power(5 + n,4) + 0.005829363347210827/np.power(5 + n,3) + 0.03288843984284437/np.power(5 + n,2) - 0.05168203279717121/(5 + n) - 0.0007839412569760368/np.power(6 + n,4) - 0.0012427255994616627/np.power(6 + n,3) + 0.0009493512253215492/np.power(6 + n,2) + 0.011798741323319263/(6 + n) + (0.45506112547578514*S1)/n - (1.2340398935538648*(1/(1 + n) + S1))/(1 + n) + (1.5405378426172631*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (0.4085445948909813*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (1.1013187546197853*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (0.06878491481037952*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (0.07621097625638995*(np.power(S1,2)/2. + S2/2.))/n - (0.3417710652584133*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (0.6078137269535574*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (0.23243730263921492*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (0.5349245518740918*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (0.03976638871665715*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.011098590750917119*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (0.026539607868124548*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.0044455027231418*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (0.05917450985066498*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (0.0615882478690015*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (0.017472781822012725*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQ22(n, nf, cache):
+    res = (5*(1/(-1 + n) - 1/n))/12. - 1/(3.*np.power(n,2)) + (np.power(n,-2) - np.power(1 + n,-2))/6. - (5*(1/(-1 + n) - 2/n + 1/(1 + n)))/12. + (1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n))/9.
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQ23(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQ24(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqqbar20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -np.power(n,-4) - 13/(12.*np.power(n,3)) - 17/(12.*np.power(n,2)) - 1.6405863611479914/n - 2/(3.*np.power(1 + n,4)) - 47/(36.*np.power(1 + n,3)) - 5/(36.*np.power(1 + n,2)) - 41.84428043405812/(1 + n) - 1/(3.*np.power(2 + n,4)) - 4/(9.*np.power(2 + n,3)) - 46/(27.*np.power(2 + n,2)) + 124.8879649874922/(2 + n) + 1/(3.*np.power(3 + n,4)) - 34/(27.*np.power(3 + n,3)) - 17/(81.*np.power(3 + n,2)) - 108.15988111676036/(3 + n) - 3.3671815998344403/np.power(4 + n,4) + 13.391781022848413/np.power(4 + n,3) - 24.88612174609606/np.power(4 + n,2) + 43.320673991234436/(4 + n) + 38.82696747282567/np.power(5 + n,4) - 47.521461097945725/np.power(5 + n,3) + 34.896326249104874/np.power(5 + n,2) - 12.31342113415528/(5 + n) - 16.295842720740655/np.power(6 + n,4) - 39.41640398123984/np.power(6 + n,3) - 44.209301659903545/np.power(6 + n,2) - 5.075215693136372/(6 + n) + (13*np.power(np.pi,2))/(108.*np.power(n,2)) + (5*np.power(np.pi,2))/(108.*np.power(1 + n,2)) + (2*np.power(np.pi,2))/(27.*np.power(2 + n,2)) - (2*np.power(np.pi,2))/(27.*np.power(3 + n,2)) + (0.6419753086419753 + np.power(np.pi,2)/54.)/(-1 + n) + (44.57561526466048*S1)/n - (135.11537460395684*(1/(1 + n) + S1))/(1 + n) + (110.70254327349599*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) - (81.01447137459289*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (33.32846515664826*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) + (27.523222283744982*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (29.983645015907463*(np.power(S1,2)/2. + S2/2.))/n + (134.45773874322774*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (240.78766391548692*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (97.6224237059175*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (216.11967611283566*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (17.8163177812485*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) + (4.964549940635965*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.13076210403699662*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (48.55663315700859*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (72.24774719378223*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (96.80897268888805*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (19.161619825303777*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqqbar21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -13/(27.*(-1 + n)) + 7/(9.*np.power(n,3)) + 2/(9.*np.power(n,2)) + 0.3244737480686852/n + 5/(9.*np.power(1 + n,3)) + 10/(9.*np.power(1 + n,2)) + 27.517693356274/(1 + n) + 2/(9.*np.power(2 + n,3)) + 1/(3.*np.power(2 + n,2)) - 81.92374015629414/(2 + n) - 2/(9.*np.power(3 + n,3)) + 17/(27.*np.power(3 + n,2)) + 72.114705314166/(3 + n) + 0.278832021511065/np.power(4 + n,4) - 1.8302170896235186/np.power(4 + n,3) + 7.56035067872129/np.power(4 + n,2) - 28.03618617637825/(4 + n) + 14.341632491127871/np.power(5 + n,4) - 5.1297691788810305/np.power(5 + n,3) + 30.955804756584733/np.power(5 + n,2) + 7.618474975959847/(5 + n) - 7.93710316431972/np.power(6 + n,4) - 15.00474989431131/np.power(6 + n,3) - 17.005981974415636/np.power(6 + n,2) + 2.8660604196926687/(6 + n) - (28.216567596518903*S1)/n + (86.62327420555926*(1/(1 + n) + S1))/(1 + n) - (71.71933800919118*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (53.412999002450206*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (21.74928857392622*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (18.35107902837314*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (19.975309522943995*(np.power(S1,2)/2. + S2/2.))/n - (86.90418147351276*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (150.01911201728237*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (54.453527107905*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (128.38534244021054*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (9.15842473440808*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.12928413519702175*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (14.833263126573382*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (60.32381411030171*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (60.36607529036273*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (90.67902221949461*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (15.04831991939943*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqqbar22(n, nf, cache):
+    res = (5*(1/(-1 + n) - 1/n))/12. - 1/(3.*np.power(n,2)) + (np.power(n,-2) - np.power(1 + n,-2))/6. - (5*(1/(-1 + n) - 2/n + 1/(1 + n)))/12. + (1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n))/9.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqqbar23(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqqbar24(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQbar20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -np.power(n,-4) - 13/(12.*np.power(n,3)) - 17/(12.*np.power(n,2)) - 1.6405863611479914/n - 2/(3.*np.power(1 + n,4)) - 47/(36.*np.power(1 + n,3)) - 5/(36.*np.power(1 + n,2)) - 41.84428043405812/(1 + n) - 1/(3.*np.power(2 + n,4)) - 4/(9.*np.power(2 + n,3)) - 46/(27.*np.power(2 + n,2)) + 124.8879649874922/(2 + n) + 1/(3.*np.power(3 + n,4)) - 34/(27.*np.power(3 + n,3)) - 17/(81.*np.power(3 + n,2)) - 108.15988111676036/(3 + n) - 3.3671815998344403/np.power(4 + n,4) + 13.391781022848413/np.power(4 + n,3) - 24.88612174609606/np.power(4 + n,2) + 43.320673991234436/(4 + n) + 38.82696747282567/np.power(5 + n,4) - 47.521461097945725/np.power(5 + n,3) + 34.896326249104874/np.power(5 + n,2) - 12.31342113415528/(5 + n) - 16.295842720740655/np.power(6 + n,4) - 39.41640398123984/np.power(6 + n,3) - 44.209301659903545/np.power(6 + n,2) - 5.075215693136372/(6 + n) + (13*np.power(np.pi,2))/(108.*np.power(n,2)) + (5*np.power(np.pi,2))/(108.*np.power(1 + n,2)) + (2*np.power(np.pi,2))/(27.*np.power(2 + n,2)) - (2*np.power(np.pi,2))/(27.*np.power(3 + n,2)) + (0.6419753086419753 + np.power(np.pi,2)/54.)/(-1 + n) + (44.57561526466048*S1)/n - (135.11537460395684*(1/(1 + n) + S1))/(1 + n) + (110.70254327349599*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) - (81.01447137459289*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (33.32846515664826*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) + (27.523222283744982*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (29.983645015907463*(np.power(S1,2)/2. + S2/2.))/n + (134.45773874322774*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (240.78766391548692*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (97.6224237059175*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (216.11967611283566*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (17.8163177812485*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) + (4.964549940635965*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.13076210403699662*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (48.55663315700859*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (72.24774719378223*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (96.80897268888805*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (19.161619825303777*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQbar21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -13/(27.*(-1 + n)) + 7/(9.*np.power(n,3)) + 2/(9.*np.power(n,2)) + 0.3244737480686852/n + 5/(9.*np.power(1 + n,3)) + 10/(9.*np.power(1 + n,2)) + 27.517693356274/(1 + n) + 2/(9.*np.power(2 + n,3)) + 1/(3.*np.power(2 + n,2)) - 81.92374015629414/(2 + n) - 2/(9.*np.power(3 + n,3)) + 17/(27.*np.power(3 + n,2)) + 72.114705314166/(3 + n) + 0.278832021511065/np.power(4 + n,4) - 1.8302170896235186/np.power(4 + n,3) + 7.56035067872129/np.power(4 + n,2) - 28.03618617637825/(4 + n) + 14.341632491127871/np.power(5 + n,4) - 5.1297691788810305/np.power(5 + n,3) + 30.955804756584733/np.power(5 + n,2) + 7.618474975959847/(5 + n) - 7.93710316431972/np.power(6 + n,4) - 15.00474989431131/np.power(6 + n,3) - 17.005981974415636/np.power(6 + n,2) + 2.8660604196926687/(6 + n) - (28.216567596518903*S1)/n + (86.62327420555926*(1/(1 + n) + S1))/(1 + n) - (71.71933800919118*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (53.412999002450206*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (21.74928857392622*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (18.35107902837314*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (19.975309522943995*(np.power(S1,2)/2. + S2/2.))/n - (86.90418147351276*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (150.01911201728237*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (54.453527107905*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (128.38534244021054*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (9.15842473440808*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.12928413519702175*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (14.833263126573382*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (60.32381411030171*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (60.36607529036273*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (90.67902221949461*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (15.04831991939943*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQbar22(n, nf, cache):
+    res = (5*(1/(-1 + n) - 1/n))/12. - 1/(3.*np.power(n,2)) + (np.power(n,-2) - np.power(1 + n,-2))/6. - (5*(1/(-1 + n) - 2/n + 1/(1 + n)))/12. + (1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n))/9.
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQbar23(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQbar24(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agg20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    S4 = c.get(c.S4, cache, n)
+    res = 16.86111111111111 - 99/(4.*np.power(-1 + n,3)) + 201/(4.*np.power(-1 + n,2)) + 63/(2.*np.power(n,4)) + 327/(8.*np.power(n,3)) + 937/(16.*np.power(n,2)) - 29.349156166471147/n + 45/np.power(1 + n,4) - 249/(8.*np.power(1 + n,3)) + 1351/(16.*np.power(1 + n,2)) + 33/(4.*np.power(2 + n,3)) + 215/(4.*np.power(2 + n,2)) - 165/(8.*np.power(3 + n,3)) + 825/(32.*np.power(3 + n,2)) + 75.11973727168703/np.power(4 + n,4) - 327.93971046698647/np.power(4 + n,3) + 489.8658778292528/np.power(4 + n,2) - 790.4536913761124/np.power(5 + n,4) + 906.1743071114438/np.power(5 + n,3) - 731.1896273676689/np.power(5 + n,2) + 320.7706707471764/np.power(6 + n,4) + 775.585407692871/np.power(6 + n,3) + 866.7481273153206/np.power(6 + n,2) + (238.9194899614054 - 0.7187584125804691*nf)/(5 + n) + (91.0344525497889 + 0.06959835991327973*nf)/(6 + n) - (41*nf)/54. + (17*nf)/(18.*np.power(-1 + n,3)) - (235*nf)/(108.*np.power(-1 + n,2)) - (5*nf)/(3.*np.power(n,4)) + (17*nf)/(12.*np.power(n,3)) - (61*nf)/(24.*np.power(n,2)) + (4.981889500151358*nf)/n - (5*nf)/(3.*np.power(1 + n,4)) + (31*nf)/(12.*np.power(1 + n,3)) - (13*nf)/(4.*np.power(1 + n,2)) - (4*nf)/(9.*np.power(2 + n,3)) + (5*nf)/(18.*np.power(2 + n,2)) + nf/(2.*np.power(3 + n,3)) - (247*nf)/(216.*np.power(3 + n,2)) + (0.05188597791606392*nf)/np.power(4 + n,4) + (0.18500946222330533*nf)/np.power(4 + n,3) - (0.48075977710297113*nf)/np.power(4 + n,2) + (1.1304591631668428*nf)/np.power(5 + n,4) + (0.3443730808411247*nf)/np.power(5 + n,3) + (1.7408117318945497*nf)/np.power(5 + n,2) - (0.17871955042920698*nf)/np.power(6 + n,4) - (0.44591765410290274*nf)/np.power(6 + n,3) - (0.5854839347981557*nf)/np.power(6 + n,2) + (-892.7765462248292 + 4.967170666760481*nf)/(4 + n) - (67*np.power(np.pi,2))/96. - (15*np.power(np.pi,2))/(4.*np.power(-1 + n,2)) + (9*np.power(np.pi,2))/(4.*np.power(n,2)) - (12*np.power(np.pi,2))/np.power(1 + n,2) - (15*np.power(np.pi,2))/(4.*np.power(3 + n,2)) + (5*nf*np.power(np.pi,2))/144. + (nf*np.power(np.pi,2))/(6.*np.power(n,2)) - (5*nf*np.power(np.pi,2))/(18.*n) + (nf*np.power(np.pi,2))/(6.*np.power(1 + n,2)) - (11*np.power(np.pi,4))/80. + (-2656.1846361137755 + 13.004950411872356*nf - (7*nf*np.power(np.pi,2))/54.)/(2 + n) + (2285.159409762382 - 14.193864160201342*nf + (5*nf*np.power(np.pi,2))/72.)/(3 + n) - (957.4913212153385*S1)/n + (5.0360604026719304*nf*S1)/n + (2798.17031768792*(1/(1 + n) + S1))/(1 + n) - (15.938321904510403*nf*(1/(1 + n) + S1))/(1 + n) - (2183.014017811476*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (22.221146077608847*nf*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (1794.9072797413023*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (7.947769036822255*nf*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (853.6048603446067*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (19.06077749915008*nf*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (596.5490079602517*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (1.4142094467758806*nf*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (696.429863570809*(np.power(S1,2)/2. + S2/2.))/n + (3.248573734966296*nf*(np.power(S1,2)/2. + S2/2.))/n + (16.75 - (5*nf)/6. - (9*np.power(np.pi,2))/4.)*(-(S1/n) + np.power(S1,2)/2. + S2/2.) - (3035.637132022108*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (10.911345647839301*nf*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (5411.123832618697*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (14.997551679700479*nf*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (2160.722395241362*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (4.59716254754814*nf*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (4801.597341431533*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (11.67698516839526*nf*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (391.291617977227*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.7549571459803536*nf*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (176.89773541521075*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (0.5230267409975893*nf*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - 2*(-4.125 + nf/4.)*(-0.5*np.power(S1,2)/n + np.power(S1,3)/6. - S2/(2.*n) + (S1*S2)/2. + S3/3.) + (210.00253110794813*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (2.6555253520083517*nf*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (836.4108709560046*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (5.391211881797062*nf*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (1508.7868305034372*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (2.774833944288212*nf*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (1946.2704453635947*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (5.470750943316969*nf*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (405.03205178858434*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) - (0.5627962717575428*nf*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) + 27*(-0.16666666666666666*np.power(S1,3)/n + np.power(S1,4)/24. - (S1*S2)/(2.*n) + (np.power(S1,2)*S2)/4. + np.power(S2,2)/8. - S3/(3.*n) + (S1*S3)/3. + S4/4.) - (33*zeta3)/8. + (nf*zeta3)/4. - (2*nf*zeta3)/(3.*n) - (-(1/n) + S1)*(-16.833333333333332 + (7*nf)/9. + (11*np.power(np.pi,2))/16. - (nf*np.power(np.pi,2))/24. + (99*zeta3)/4.) + (-100.25 + (455*nf)/162. + (11*np.power(np.pi,2))/16. - (17*nf*np.power(np.pi,2))/216. + 36*zeta3)/(-1 + n) + (976.3258434434753 - 6.952739586572729*nf + (nf*np.power(np.pi,2))/18. - (2*nf*zeta3)/3.)/(1 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agg21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = 16.833333333333332 - 9/np.power(-1 + n,3) + 99/(4.*np.power(-1 + n,2)) - 18/np.power(n,3) - 45/(2.*np.power(n,2)) - 34.08160990247799/n - 54/np.power(1 + n,3) + 99/(4.*np.power(1 + n,2)) - 9/np.power(3 + n,3) + 99/(4.*np.power(3 + n,2)) - 6.959090024543352/np.power(4 + n,4) + 31.316953909265823/np.power(4 + n,3) - 129.72126276003138/np.power(4 + n,2) - 316.61176078013756/np.power(5 + n,4) + 96.1184068916528/np.power(5 + n,3) - 654.8831560964019/np.power(5 + n,2) + 163.9946761397813/np.power(6 + n,4) + 313.3624782120564/np.power(6 + n,3) + 359.0418188870436/np.power(6 + n,2) + (-1337.6273882811697 - 4.494055935519254*nf)/(3 + n) + (-145.9640592388291 - 0.241465589995501*nf)/(5 + n) + (-54.23457261672672 - 0.05502440947592218*nf)/(6 + n) - (7*nf)/9. - (17*nf)/(18.*np.power(-1 + n,2)) + (4*nf)/(3.*np.power(n,3)) - nf/np.power(n,2) + (0.7500000000000284*nf)/n + (4*nf)/(3.*np.power(1 + n,3)) - (13*nf)/(6.*np.power(1 + n,2)) + (4*nf)/(9.*np.power(2 + n,2)) - nf/(2.*np.power(3 + n,2)) + (0.011275640927692523*nf)/np.power(4 + n,4) - (0.06468931095091934*nf)/np.power(4 + n,3) - (0.2799909715053025*nf)/np.power(4 + n,2) + (0.1898720429119991*nf)/np.power(5 + n,4) - (0.020034311566906212*nf)/np.power(5 + n,3) + (0.17777890986621123*nf)/np.power(5 + n,2) - (0.043565667449617394*nf)/np.power(6 + n,4) - (0.11212805286729775*nf)/np.power(6 + n,3) - (0.15807930699413783*nf)/np.power(6 + n,2) + (539.8396237029783 + 1.3459753921080742*nf)/(4 + n) + (1555.7729975239774 + 3.0194412078803183*nf)/(2 + n) - (11*np.power(np.pi,2))/16. + (nf*np.power(np.pi,2))/24. - (nf*np.power(np.pi,2))/(9.*n) + (-16.75 + (235*nf)/108. + (3*np.power(np.pi,2))/2.)/(-1 + n) + (-518.9660076919846 - 1.6408845017926574*nf - (nf*np.power(np.pi,2))/9.)/(1 + n) + (550.4770242673264*S1)/n + (2.1408845017040483*nf*S1)/n - (-16.75 + (5*nf)/6. + (9*np.power(np.pi,2))/4.)*(-(1/n) + S1) - (1609.5965772517004*(1/(1 + n) + S1))/(1 + n) - (6.161410970014396*nf*(1/(1 + n) + S1))/(1 + n) + (1196.2222768020379*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (6.989681660926549*nf*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) - (1196.7004235975921*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (1.9576914148918718*nf*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (702.1423904308235*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (5.0760908464004215*nf*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) + (392.7053093491044*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (0.35075576110765155*nf*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (492.74315777416973*(np.power(S1,2)/2. + S2/2.))/n + (0.4208329523824698*nf*(np.power(S1,2)/2. + S2/2.))/n + (8.25 - nf/2.)*(-(S1/n) + np.power(S1,2)/2. + S2/2.) + (2044.6883276518818*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (1.8685772552991469*nf*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (3375.4249360137287*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (3.2857436451256987*nf*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (1186.915553438676*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (1.221107178720968*nf*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (2839.576419871591*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (2.8540969274069123*nf*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (197.81889970310104*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.2050095935230768*nf*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (13.606906922105907*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.06739772448375828*nf*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + 27*(-0.5*np.power(S1,2)/n + np.power(S1,3)/6. - S2/(2.*n) + (S1*S2)/2. + S3/3.) + (376.9276566603408*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.15155940569821733*nf*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (1365.5990389768906*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (0.0650472766211539*nf*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (1285.4794674795335*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (0.39665120819282607*nf*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (1971.3002461896854*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (0.4305210192151828*nf*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (316.45751052850346*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) - (0.11533914681325617*nf*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) - (99*zeta3)/4.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agg22(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    res = 8.375 - (387*(1/(-1 + n) - 1/n))/8. + 33/(8.*(-1 + n)) + 9*(-np.power(-1 + n,-2) + 2/np.power(n,2) - np.power(1 + n,-2)) + (177*(1/(-1 + n) - 2/n + 1/(1 + n)))/4. - 9*(-np.power(-1 + n,-2) + 3/np.power(n,2) - 3/np.power(1 + n,2) + np.power(2 + n,-2)) - (165*(1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n)))/8. - (5*nf)/12. + (19*(1/(-1 + n) - 1/n)*nf)/12. - nf/(4.*(-1 + n)) - (2*nf)/(3.*np.power(n,2)) - ((-np.power(n,-2) + np.power(1 + n,-2))*nf)/3. - (4*(1/(-1 + n) - 2/n + 1/(1 + n))*nf)/3. + (17*(1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n))*nf)/36. - (9*np.power(np.pi,2))/8. + (33*(-(1/n) + S1))/8. + (27*(-(1/n) + S1))/(2.*(-1 + n)) - (nf*(-(1/n) + S1))/4. + (81*(S1/n - (-(1/n) + S1)/(-1 + n)))/2. - 27*((2*S1)/n - (-(1/n) + S1)/(-1 + n) - (1/(1 + n) + S1)/(1 + n)) + (27*((3*S1)/n - (-(1/n) + S1)/(-1 + n) - (3*(1/(1 + n) + S1))/(1 + n) + ((3 + 2*n)/((1 + n)*(2 + n)) + S1)/(2 + n)))/2. + (27*(-(S1/n) + np.power(S1,2)/2. + S2/2.))/2. - 9*((-1 + 2*n - 2*np.power(n,2))/(np.power(-1 + n,2)*np.power(n,2)) - np.power(np.pi,2)/6. + S2)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agg23(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = 1.375 - (27*(1/(-1 + n) - 1/n))/2. + 9/(2.*(-1 + n)) + 9*(1/(-1 + n) - 2/n + 1/(1 + n)) - (9*(1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n)))/2. - nf/12. + (9*(-(1/n) + S1))/2.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agg24(n, nf, cache):
+    res = 1.125
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agq20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -31/(3.*np.power(-1 + n,3)) + 41/(2.*np.power(-1 + n,2)) + 106/(9.*np.power(n,4)) + 218/(9.*np.power(n,3)) + 275/(18.*np.power(n,2)) + 3.9571005767767033/n + 55/(9.*np.power(1 + n,4)) + 109/(18.*np.power(1 + n,3)) + 235/(18.*np.power(1 + n,2)) + 2/(27.*np.power(2 + n,3)) + 11/(2.*np.power(2 + n,2)) - 17/(27.*np.power(3 + n,3)) - 133/(648.*np.power(3 + n,2)) + 0.8223698702784716/np.power(4 + n,4) - 5.553806921999574/np.power(4 + n,3) + 8.366771900574946/np.power(4 + n,2) - 10.949382219584912/np.power(5 + n,4) + 13.849432222845577/np.power(5 + n,3) - 11.204433049821336/np.power(5 + n,2) + 4.893356281716537/np.power(6 + n,4) + 11.549634451584822/np.power(6 + n,3) + 12.475711611014834/np.power(6 + n,2) + (6.388313909027405 - 0.134021867309814*nf)/(5 + n) + (1.359582492100278 - 0.06271239231491248*nf)/(6 + n) + (-30.731748568486335 + 0.4736664950001651*nf)/(4 + n) + (4*nf)/(9.*np.power(-1 + n,3)) - (20*nf)/(27.*np.power(-1 + n,2)) - (4*nf)/(9.*np.power(n,3)) + (20*nf)/(27.*np.power(n,2)) - (1.4176103655531436*nf)/n + (2*nf)/(9.*np.power(1 + n,3)) - (10*nf)/(27.*np.power(1 + n,2)) - (0.004644855507486117*nf)/np.power(4 + n,4) + (0.02752704333289802*nf)/np.power(4 + n,3) - (0.09517404464347873*nf)/np.power(4 + n,2) - (0.07255605248969821*nf)/np.power(5 + n,4) - (0.03179629006284005*nf)/np.power(5 + n,3) - (0.20919521412223563*nf)/np.power(5 + n,2) + (0.013862164596313922*nf)/np.power(6 + n,4) + (0.02517890833768235*nf)/np.power(6 + n,3) + (0.0212374019159726*nf)/np.power(6 + n,2) - (35*np.power(np.pi,2))/(27.*np.power(-1 + n,2)) + (23*np.power(np.pi,2))/(27.*np.power(n,2)) - (34*np.power(np.pi,2))/(27.*np.power(1 + n,2)) + (2*nf*np.power(np.pi,2))/(27.*n) + (45.1926665533455 + 0.762659604639619*nf - (5*nf*np.power(np.pi,2))/27.)/(1 + n) + (69.23881799080559 - 0.8795772240770414*nf - (nf*np.power(np.pi,2))/27.)/(3 + n) + (-70.31617353640735 + 0.5439611002122565*nf + (4*nf*np.power(np.pi,2))/27.)/(2 + n) - (33.12620941527203*S1)/n + (1.112012896833687*nf*S1)/n + (65.56287458498312*(1/(1 + n) + S1))/(1 + n) - (1.9018156986716952*nf*(1/(1 + n) + S1))/(1 + n) - (8.644527254534509*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (1.3405078700407942*nf*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (79.57601966082686*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (0.21651223044957663*nf*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (81.67970586795522*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (0.1011287567994526*nf*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (22.8341684335303*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (0.06323221534253937*nf*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (53.33789727658772*(np.power(S1,2)/2. + S2/2.))/n - (0.8514951640659054*nf*(np.power(S1,2)/2. + S2/2.))/n - (209.38938481508063*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (2.0144131547924555*nf*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (343.35224129840924*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (2.2005831896264394*nf*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (112.89899341228728*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (0.3699829026393649*nf*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (278.9327211039544*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (1.2524445030058606*nf*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (18.211470512693634*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) + (0.044092487422282514*nf*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (42.35673152829946*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.1536011983541577*nf*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (84.9840789038495*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.6928663157980264*nf*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (47.238518782072774*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (1.2366573944297772*nf*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (44.361657515641326*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (0.4710596322174849*nf*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (31.732712904995193*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (1.0887862720427495*nf*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (13.46221764856785*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) + (0.07966563716064384*nf*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) + (-37.9537037037037 + (56*nf)/81. - (19*np.power(np.pi,2))/36. + (nf*np.power(np.pi,2))/27. + 16*zeta3)/(-1 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agq21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -4/np.power(-1 + n,3) + 31/(3.*np.power(-1 + n,2)) - 56/(9.*np.power(n,3)) - 136/(9.*np.power(n,2)) - 2.5845323553137938/n - 62/(9.*np.power(1 + n,3)) - 53/(9.*np.power(1 + n,2)) + 16/(27.*np.power(2 + n,2)) + 26/(27.*np.power(3 + n,2)) - 0.14933365678240723/np.power(4 + n,4) + 0.9647209308996265/np.power(4 + n,3) - 1.982113627904677/np.power(4 + n,2) - 4.384606883281288/np.power(5 + n,4) + 0.36359029018821026/np.power(5 + n,3) - 9.467016995505801/np.power(5 + n,2) + 2.211128073305879/np.power(6 + n,4) + 4.231801095479696/np.power(6 + n,3) + 5.088080180162337/np.power(6 + n,2) + (10.277957980256247 - 0.12859726389884807*nf)/(2 + n) + (3.170265036181056 - 0.09384997386592911*nf)/(4 + n) + (-0.6181579611503486 - 0.014540356149953873*nf)/(6 + n) + (-1.3016152241058507 + 0.007082899233404929*nf)/(5 + n) + (-11.512424159396804 + 0.19850336286089515*nf)/(3 + n) + (1.9179438020673558 + 0.40177170219080016*nf)/(1 + n) - (4*nf)/(9.*np.power(-1 + n,2)) + (4*nf)/(9.*np.power(n,2)) - (0.7407407407407416*nf)/n - (2*nf)/(9.*np.power(1 + n,2)) - (0.0008863218377414114*nf)/np.power(4 + n,4) + (0.005097260396606985*nf)/np.power(4 + n,3) - (0.017265120383839497*nf)/np.power(4 + n,2) - (0.012118814258166404*nf)/np.power(5 + n,4) - (0.005454377177093399*nf)/np.power(5 + n,3) - (0.03901864982081938*nf)/np.power(5 + n,2) + (0.0012055454368091521*nf)/np.power(6 + n,4) + (0.0017644538166461156*nf)/np.power(6 + n,3) - (0.0012268733773057319*nf)/np.power(6 + n,2) + (-5.611111111111111 + (20*nf)/27. + (8*np.power(np.pi,2))/27.)/(-1 + n) - (0.5459413560733313*S1)/n - (0.03140133181504437*nf*S1)/n + (7.587265449211114*(1/(1 + n) + S1))/(1 + n) + (0.1460549984559635*nf*(1/(1 + n) + S1))/(1 + n) - (30.001169125420553*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) - (0.2695284562563078*nf*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) - (34.827837457006034*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (0.11116535834688081*nf*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (50.60599490839494*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) + (0.246268696183586*nf*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) + (8.515020914227193*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (0.019771451778683467*nf*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (44.740062385880165*(np.power(S1,2)/2. + S2/2.))/n - (0.003514147373606059*nf*(np.power(S1,2)/2. + S2/2.))/n + (120.24209639626389*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (0.022049693029882415*nf*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (151.08967480822122*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (0.05324005464746588*nf*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (35.322077931643875*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (0.03603483030742922*nf*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (100.99484768365971*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (0.06256347949916376*nf*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (5.025982156932755*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) + (0.008175859799454994*nf*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (5.609244884938891*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.004785442284985393*nf*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (29.321403901051205*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.023673044154066444*nf*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (61.16631983010827*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (0.04681036563897463*nf*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (33.06640155599856*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (0.02282837795917319*nf*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (63.66298493340651*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (0.04624725484237912*nf*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (6.857577436588011*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n) + (0.00450388688668764*nf*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agq22(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = 6*(-np.power(-1 + n,-2) + np.power(n,-2)) - (83*(1/(-1 + n) - 1/n))/9. + 61/(9.*np.power(-1 + n,2)) - 1/(2.*(-1 + n)) - (29*(-np.power(-1 + n,-2) + 2/np.power(n,2) - np.power(1 + n,-2)))/9. + (14*(1/(-1 + n) - 2/n + 1/(1 + n)))/9. - (2*(1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n)))/3. + nf/(9.*(-1 + n)) + ((1/(-1 + n) - 2/n + 1/(1 + n))*nf)/9. - (22*(-(1/n) + S1))/(9.*(-1 + n)) + (22*((2*S1)/n - (-(1/n) + S1)/(-1 + n) - (1/(1 + n) + S1)/(1 + n)))/9.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agq23(n, nf, cache):
+    res = -2/(-1 + n) + 2/n - 1/(1 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Agq24(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqg20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -43/(24.*np.power(n,4)) - 131/(48.*np.power(n,3)) - 131/(48.*np.power(n,2)) + 1.1911888331830194/n - 65/(12.*np.power(1 + n,4)) + 11/(4.*np.power(1 + n,3)) - 35/(6.*np.power(1 + n,2)) + 10.4053926591844/(1 + n) + np.power(2 + n,-4) - 93/(8.*np.power(2 + n,3)) - 133/(16.*np.power(2 + n,2)) - 25.265257982477284/(2 + n) - 2/(3.*np.power(3 + n,3)) + 259/(216.*np.power(3 + n,2)) + 22.97169476938314/(3 + n) + 0.4356820271802718/np.power(4 + n,4) - 3.648167146799966/np.power(4 + n,3) + 4.666958361067362/np.power(4 + n,2) - 15.820612873505851/(4 + n) - 7.1928985308380415/np.power(5 + n,4) + 7.53926563139814/np.power(5 + n,3) - 8.133967097702559/np.power(5 + n,2) + 3.444952575663905/(5 + n) + 2.7973273410525477/np.power(6 + n,4) + 6.933209170846717/np.power(6 + n,3) + 7.7669270528116305/np.power(6 + n,2) + 0.8562998184468253/(6 + n) - (13*np.power(np.pi,2))/(144.*np.power(n,2)) + (29*np.power(np.pi,2))/(36.*np.power(1 + n,2)) - (23*np.power(np.pi,2))/(36.*np.power(2 + n,2)) + (1.4444444444444444 + np.power(np.pi,2)/24.)/(-1 + n) - (10.89551676742556*S1)/n + (33.91512411485418*(1/(1 + n) + S1))/(1 + n) - (32.378345212125026*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (6.620037270621037*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (6.441410088535398*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (3.567742461035917*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (7.6259459441578015*(np.power(S1,2)/2. + S2/2.))/n - (30.5656098627976*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (53.554742347589425*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (17.361870636087808*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (45.48836064089401*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (2.738588424143426*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (1.9793278380704296*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (1.798659292989602*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (7.6689995392226145*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (13.748022057194886*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (18.839009328234496*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (3.6056770564355105*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqg21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -13/(12.*(-1 + n)) + 7/(6.*np.power(n,3)) + 5/(4.*np.power(n,2)) + 1.2533223444746522/n + 31/(6.*np.power(1 + n,3)) - 4/(3.*np.power(1 + n,2)) - 9.031235230715703/(1 + n) - 4/(3.*np.power(2 + n,3)) + 187/(24.*np.power(2 + n,2)) + 15.59250486448689/(2 + n) + 8/(9.*np.power(3 + n,2)) - 6.751578556990447/(3 + n) - 0.027929527280142082/np.power(4 + n,4) + 0.23338391067360553/np.power(4 + n,3) + 0.258640725494089/np.power(4 + n,2) - 0.13219179925426255/(4 + n) - 1.9121251865638547/np.power(5 + n,4) + 0.7183060788586074/np.power(5 + n,3) - 3.625926729243089/np.power(5 + n,2) + 0.27384591274603937/(5 + n) + 1.1071257185432037/np.power(6 + n,4) + 2.188753500072866/np.power(6 + n,3) + 2.6088729631688365/np.power(6 + n,2) + 0.25216076260294745/(6 + n) + (2.589788341299843*S1)/n - (4.805726932211193*(1/(1 + n) + S1))/(1 + n) + (1.7872567498248921*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) - (8.820553422050553*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (6.449707930794049*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) + (2.5495273323429615*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (3.201963174657092*(np.power(S1,2)/2. + S2/2.))/n + (10.902815064311243*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (17.462853189309797*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (6.112153339962495*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (13.324634261966189*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (1.1328537109852865*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.3849560009944391*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (3.291205854414084*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (9.2864975060617*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (7.304185697789013*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (11.961817401644986*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (1.722615948786082*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqg22(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = (41*(1/(-1 + n) - 1/n))/12. - 1/(8.*(-1 + n)) - 35/(24.*np.power(n,2)) - (2*(-np.power(n,-2) + np.power(1 + n,-2)))/3. - (93*(1/(-1 + n) - 2/n + 1/(1 + n)))/16. - (2*(-np.power(n,-2) + 2/np.power(1 + n,2) - np.power(2 + n,-2)))/3. + (133*(1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n)))/48. - (17*S1)/(24.*n) - (17*(-(S1/n) + (1/(1 + n) + S1)/(1 + n)))/12. + (17*(-(S1/n) + (2*(1/(1 + n) + S1))/(1 + n) - ((3 + 2*n)/((1 + n)*(2 + n)) + S1)/(2 + n)))/12.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqg23(n, nf, cache):
+    res = -0.16666666666666666*1/n + (1/n - 1/(1 + n))/3. + (-(1/n) + 2/(1 + n) - 1/(2 + n))/3.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqg24(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqq20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -5/(6.*np.power(n,4)) - 13/(12.*np.power(n,3)) - 3/(2.*np.power(n,2)) - 0.7986297731997045/n - 5/(6.*np.power(1 + n,4)) - 13/(12.*np.power(1 + n,3)) - 1/(3.*np.power(1 + n,2)) + 1.0506711812659297/(1 + n) - 10/(9.*np.power(2 + n,3)) - 49/(27.*np.power(2 + n,2)) - 0.9163222241223545/(2 + n) + 2/(27.*np.power(3 + n,2)) - 0.2806436951458962/(3 + n) + 0.0014735182662902581/np.power(4 + n,4) - 0.009193655123305253/np.power(4 + n,3) + 0.055511612427147146/np.power(4 + n,2) + 0.09590718130594521/(4 + n) + 0.027588702894167733/np.power(5 + n,4) + 0.012667915026022089/np.power(5 + n,3) + 0.07943507877302992/np.power(5 + n,2) + 0.004407924616075398/(5 + n) - 0.007753800373369394/np.power(6 + n,4) - 0.014409903008843377/np.power(6 + n,3) - 0.01668441874933692/np.power(6 + n,2) + 0.019863644765988633/(6 + n) + np.power(np.pi,2)/(12.*np.power(n,2)) + np.power(np.pi,2)/(12.*np.power(1 + n,2)) + (0.6419753086419753 + np.power(np.pi,2)/54.)/(-1 + n) + (0.13983274560630196*S1)/n - (0.41275820879534736*(1/(1 + n) + S1))/(1 + n) + (0.8051014673999592*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (0.3773965825982953*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (0.8370826054908135*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (0.07248998131839572*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (0.49726721324576617*(np.power(S1,2)/2. + S2/2.))/n - (1.3737737224272497*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (1.6829683740128463*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (0.35105687464036983*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (1.1122682532660377*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (0.04525048620569524*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) + (0.10801897174901916*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.49084933211928516*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.8840516588729128*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (0.34564489589974434*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (0.787248701393219*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (0.059617493009172226*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqq21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -13/(27.*(-1 + n)) + 2/(3.*np.power(n,3)) + 1/(3.*np.power(n,2)) + 0.28502197771725984/n + 2/(3.*np.power(1 + n,3)) + np.power(1 + n,-2) - 1.3367058144318702/(1 + n) + 2/(3.*np.power(2 + n,2)) + 2.1906260706515757/(2 + n) - 1.0146549160375362/(3 + n) + 0.0008287014639471657/np.power(4 + n,4) - 0.004669402119497261/np.power(4 + n,3) + 0.015584039956958031/np.power(4 + n,2) + 0.3970774550559096/(4 + n) + 0.009974093945678364/np.power(5 + n,4) + 0.005829363347210827/np.power(5 + n,3) + 0.03288843984284437/np.power(5 + n,2) - 0.05168203279717121/(5 + n) - 0.0007839412569760368/np.power(6 + n,4) - 0.0012427255994616627/np.power(6 + n,3) + 0.0009493512253215492/np.power(6 + n,2) + 0.011798741323319263/(6 + n) + (0.45506112547578514*S1)/n - (1.2340398935538648*(1/(1 + n) + S1))/(1 + n) + (1.5405378426172631*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (0.4085445948909813*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (1.1013187546197853*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (0.06878491481037952*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (0.07621097625638995*(np.power(S1,2)/2. + S2/2.))/n - (0.3417710652584133*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (0.6078137269535574*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (0.23243730263921492*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (0.5349245518740918*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (0.03976638871665715*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.011098590750917119*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (0.026539607868124548*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.0044455027231418*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (0.05917450985066498*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (0.0615882478690015*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (0.017472781822012725*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqq22(n, nf, cache):
+    res = (5*(1/(-1 + n) - 1/n))/12. - 1/(3.*np.power(n,2)) + (np.power(n,-2) - np.power(1 + n,-2))/6. - (5*(1/(-1 + n) - 2/n + 1/(1 + n)))/12. + (1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n))/9.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqq23(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqq24(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQ20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -5/(6.*np.power(n,4)) - 13/(12.*np.power(n,3)) - 3/(2.*np.power(n,2)) - 0.7986297731997045/n - 5/(6.*np.power(1 + n,4)) - 13/(12.*np.power(1 + n,3)) - 1/(3.*np.power(1 + n,2)) + 1.0506711812659297/(1 + n) - 10/(9.*np.power(2 + n,3)) - 49/(27.*np.power(2 + n,2)) - 0.9163222241223545/(2 + n) + 2/(27.*np.power(3 + n,2)) - 0.2806436951458962/(3 + n) + 0.0014735182662902581/np.power(4 + n,4) - 0.009193655123305253/np.power(4 + n,3) + 0.055511612427147146/np.power(4 + n,2) + 0.09590718130594521/(4 + n) + 0.027588702894167733/np.power(5 + n,4) + 0.012667915026022089/np.power(5 + n,3) + 0.07943507877302992/np.power(5 + n,2) + 0.004407924616075398/(5 + n) - 0.007753800373369394/np.power(6 + n,4) - 0.014409903008843377/np.power(6 + n,3) - 0.01668441874933692/np.power(6 + n,2) + 0.019863644765988633/(6 + n) + np.power(np.pi,2)/(12.*np.power(n,2)) + np.power(np.pi,2)/(12.*np.power(1 + n,2)) + (0.6419753086419753 + np.power(np.pi,2)/54.)/(-1 + n) + (0.13983274560630196*S1)/n - (0.41275820879534736*(1/(1 + n) + S1))/(1 + n) + (0.8051014673999592*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (0.3773965825982953*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (0.8370826054908135*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (0.07248998131839572*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (0.49726721324576617*(np.power(S1,2)/2. + S2/2.))/n - (1.3737737224272497*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (1.6829683740128463*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (0.35105687464036983*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (1.1122682532660377*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (0.04525048620569524*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) + (0.10801897174901916*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.49084933211928516*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.8840516588729128*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (0.34564489589974434*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (0.787248701393219*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (0.059617493009172226*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQ21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -13/(27.*(-1 + n)) + 2/(3.*np.power(n,3)) + 1/(3.*np.power(n,2)) + 0.28502197771725984/n + 2/(3.*np.power(1 + n,3)) + np.power(1 + n,-2) - 1.3367058144318702/(1 + n) + 2/(3.*np.power(2 + n,2)) + 2.1906260706515757/(2 + n) - 1.0146549160375362/(3 + n) + 0.0008287014639471657/np.power(4 + n,4) - 0.004669402119497261/np.power(4 + n,3) + 0.015584039956958031/np.power(4 + n,2) + 0.3970774550559096/(4 + n) + 0.009974093945678364/np.power(5 + n,4) + 0.005829363347210827/np.power(5 + n,3) + 0.03288843984284437/np.power(5 + n,2) - 0.05168203279717121/(5 + n) - 0.0007839412569760368/np.power(6 + n,4) - 0.0012427255994616627/np.power(6 + n,3) + 0.0009493512253215492/np.power(6 + n,2) + 0.011798741323319263/(6 + n) + (0.45506112547578514*S1)/n - (1.2340398935538648*(1/(1 + n) + S1))/(1 + n) + (1.5405378426172631*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (0.4085445948909813*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (1.1013187546197853*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (0.06878491481037952*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (0.07621097625638995*(np.power(S1,2)/2. + S2/2.))/n - (0.3417710652584133*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (0.6078137269535574*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (0.23243730263921492*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (0.5349245518740918*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (0.03976638871665715*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.011098590750917119*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n + (0.026539607868124548*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (0.0044455027231418*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (0.05917450985066498*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (0.0615882478690015*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (0.017472781822012725*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQ22(n, nf, cache):
+    res = (5*(1/(-1 + n) - 1/n))/12. - 1/(3.*np.power(n,2)) + (np.power(n,-2) - np.power(1 + n,-2))/6. - (5*(1/(-1 + n) - 2/n + 1/(1 + n)))/12. + (1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n))/9.
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQ23(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQ24(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqqbar20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -np.power(n,-4) - 13/(12.*np.power(n,3)) - 17/(12.*np.power(n,2)) - 1.6405863611479914/n - 2/(3.*np.power(1 + n,4)) - 47/(36.*np.power(1 + n,3)) - 5/(36.*np.power(1 + n,2)) - 41.84428043405812/(1 + n) - 1/(3.*np.power(2 + n,4)) - 4/(9.*np.power(2 + n,3)) - 46/(27.*np.power(2 + n,2)) + 124.8879649874922/(2 + n) + 1/(3.*np.power(3 + n,4)) - 34/(27.*np.power(3 + n,3)) - 17/(81.*np.power(3 + n,2)) - 108.15988111676036/(3 + n) - 3.3671815998344403/np.power(4 + n,4) + 13.391781022848413/np.power(4 + n,3) - 24.88612174609606/np.power(4 + n,2) + 43.320673991234436/(4 + n) + 38.82696747282567/np.power(5 + n,4) - 47.521461097945725/np.power(5 + n,3) + 34.896326249104874/np.power(5 + n,2) - 12.31342113415528/(5 + n) - 16.295842720740655/np.power(6 + n,4) - 39.41640398123984/np.power(6 + n,3) - 44.209301659903545/np.power(6 + n,2) - 5.075215693136372/(6 + n) + (13*np.power(np.pi,2))/(108.*np.power(n,2)) + (5*np.power(np.pi,2))/(108.*np.power(1 + n,2)) + (2*np.power(np.pi,2))/(27.*np.power(2 + n,2)) - (2*np.power(np.pi,2))/(27.*np.power(3 + n,2)) + (0.6419753086419753 + np.power(np.pi,2)/54.)/(-1 + n) + (44.57561526466048*S1)/n - (135.11537460395684*(1/(1 + n) + S1))/(1 + n) + (110.70254327349599*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) - (81.01447137459289*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (33.32846515664826*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) + (27.523222283744982*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (29.983645015907463*(np.power(S1,2)/2. + S2/2.))/n + (134.45773874322774*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (240.78766391548692*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (97.6224237059175*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (216.11967611283566*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (17.8163177812485*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) + (4.964549940635965*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.13076210403699662*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (48.55663315700859*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (72.24774719378223*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (96.80897268888805*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (19.161619825303777*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqqbar21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -13/(27.*(-1 + n)) + 7/(9.*np.power(n,3)) + 2/(9.*np.power(n,2)) + 0.3244737480686852/n + 5/(9.*np.power(1 + n,3)) + 10/(9.*np.power(1 + n,2)) + 27.517693356274/(1 + n) + 2/(9.*np.power(2 + n,3)) + 1/(3.*np.power(2 + n,2)) - 81.92374015629414/(2 + n) - 2/(9.*np.power(3 + n,3)) + 17/(27.*np.power(3 + n,2)) + 72.114705314166/(3 + n) + 0.278832021511065/np.power(4 + n,4) - 1.8302170896235186/np.power(4 + n,3) + 7.56035067872129/np.power(4 + n,2) - 28.03618617637825/(4 + n) + 14.341632491127871/np.power(5 + n,4) - 5.1297691788810305/np.power(5 + n,3) + 30.955804756584733/np.power(5 + n,2) + 7.618474975959847/(5 + n) - 7.93710316431972/np.power(6 + n,4) - 15.00474989431131/np.power(6 + n,3) - 17.005981974415636/np.power(6 + n,2) + 2.8660604196926687/(6 + n) - (28.216567596518903*S1)/n + (86.62327420555926*(1/(1 + n) + S1))/(1 + n) - (71.71933800919118*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (53.412999002450206*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (21.74928857392622*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (18.35107902837314*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (19.975309522943995*(np.power(S1,2)/2. + S2/2.))/n - (86.90418147351276*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (150.01911201728237*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (54.453527107905*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (128.38534244021054*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (9.15842473440808*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.12928413519702175*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (14.833263126573382*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (60.32381411030171*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (60.36607529036273*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (90.67902221949461*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (15.04831991939943*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqqbar22(n, nf, cache):
+    res = (5*(1/(-1 + n) - 1/n))/12. - 1/(3.*np.power(n,2)) + (np.power(n,-2) - np.power(1 + n,-2))/6. - (5*(1/(-1 + n) - 2/n + 1/(1 + n)))/12. + (1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n))/9.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqqbar23(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def Aqqbar24(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQbar20(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -np.power(n,-4) - 13/(12.*np.power(n,3)) - 17/(12.*np.power(n,2)) - 1.6405863611479914/n - 2/(3.*np.power(1 + n,4)) - 47/(36.*np.power(1 + n,3)) - 5/(36.*np.power(1 + n,2)) - 41.84428043405812/(1 + n) - 1/(3.*np.power(2 + n,4)) - 4/(9.*np.power(2 + n,3)) - 46/(27.*np.power(2 + n,2)) + 124.8879649874922/(2 + n) + 1/(3.*np.power(3 + n,4)) - 34/(27.*np.power(3 + n,3)) - 17/(81.*np.power(3 + n,2)) - 108.15988111676036/(3 + n) - 3.3671815998344403/np.power(4 + n,4) + 13.391781022848413/np.power(4 + n,3) - 24.88612174609606/np.power(4 + n,2) + 43.320673991234436/(4 + n) + 38.82696747282567/np.power(5 + n,4) - 47.521461097945725/np.power(5 + n,3) + 34.896326249104874/np.power(5 + n,2) - 12.31342113415528/(5 + n) - 16.295842720740655/np.power(6 + n,4) - 39.41640398123984/np.power(6 + n,3) - 44.209301659903545/np.power(6 + n,2) - 5.075215693136372/(6 + n) + (13*np.power(np.pi,2))/(108.*np.power(n,2)) + (5*np.power(np.pi,2))/(108.*np.power(1 + n,2)) + (2*np.power(np.pi,2))/(27.*np.power(2 + n,2)) - (2*np.power(np.pi,2))/(27.*np.power(3 + n,2)) + (0.6419753086419753 + np.power(np.pi,2)/54.)/(-1 + n) + (44.57561526466048*S1)/n - (135.11537460395684*(1/(1 + n) + S1))/(1 + n) + (110.70254327349599*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) - (81.01447137459289*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) + (33.32846515664826*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) + (27.523222283744982*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) - (29.983645015907463*(np.power(S1,2)/2. + S2/2.))/n + (134.45773874322774*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) - (240.78766391548692*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) - (97.6224237059175*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) + (216.11967611283566*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) + (17.8163177812485*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) + (4.964549940635965*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (0.13076210403699662*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) - (48.55663315700859*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) - (72.24774719378223*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) + (96.80897268888805*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) + (19.161619825303777*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQbar21(n, nf, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    S3 = c.get(c.S3, cache, n)
+    res = -13/(27.*(-1 + n)) + 7/(9.*np.power(n,3)) + 2/(9.*np.power(n,2)) + 0.3244737480686852/n + 5/(9.*np.power(1 + n,3)) + 10/(9.*np.power(1 + n,2)) + 27.517693356274/(1 + n) + 2/(9.*np.power(2 + n,3)) + 1/(3.*np.power(2 + n,2)) - 81.92374015629414/(2 + n) - 2/(9.*np.power(3 + n,3)) + 17/(27.*np.power(3 + n,2)) + 72.114705314166/(3 + n) + 0.278832021511065/np.power(4 + n,4) - 1.8302170896235186/np.power(4 + n,3) + 7.56035067872129/np.power(4 + n,2) - 28.03618617637825/(4 + n) + 14.341632491127871/np.power(5 + n,4) - 5.1297691788810305/np.power(5 + n,3) + 30.955804756584733/np.power(5 + n,2) + 7.618474975959847/(5 + n) - 7.93710316431972/np.power(6 + n,4) - 15.00474989431131/np.power(6 + n,3) - 17.005981974415636/np.power(6 + n,2) + 2.8660604196926687/(6 + n) - (28.216567596518903*S1)/n + (86.62327420555926*(1/(1 + n) + S1))/(1 + n) - (71.71933800919118*((3 + 2*n)/((1 + n)*(2 + n)) + S1))/(2 + n) + (53.412999002450206*((2*(5 + 2*n)*(5 + 5*n + np.power(n,2)))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + S1))/(4 + n) - (21.74928857392622*((11 + 12*n + 3*np.power(n,2))/((1 + n)*(2 + n)*(3 + n)) + S1))/(3 + n) - (18.35107902837314*((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + S1))/(5 + n) + (19.975309522943995*(np.power(S1,2)/2. + S2/2.))/n - (86.90418147351276*(np.power(1 + n,-2) + S1/(1 + n) + np.power(S1,2)/2. + S2/2.))/(1 + n) + (150.01911201728237*((7 + 9*n + 3*np.power(n,2))/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*S1)/((1 + n)*(2 + n)) + np.power(S1,2)/2. + S2/2.))/(2 + n) + (54.453527107905*((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + (2*(5 + 2*n)*(5 + 5*n + np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,2)/2. + S2/2.))/(4 + n) - (128.38534244021054*((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*S1)/((1 + n)*(2 + n)*(3 + n)) + np.power(S1,2)/2. + S2/2.))/(3 + n) - (9.15842473440808*((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S1)/((1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,2)/2. + S2/2.))/(5 + n) - (0.12928413519702175*(np.power(S1,3)/6. + (S1*S2)/2. + S3/3.))/n - (14.833263126573382*(np.power(1 + n,-3) + S1/np.power(1 + n,2) + np.power(S1,2)/(2.*(1 + n)) + np.power(S1,3)/6. + S2/(2.*(1 + n)) + (S1*S2)/2. + S3/3.))/(1 + n) + (60.32381411030171*(((3 + 2*n)*(5 + 6*n + 2*np.power(n,2)))/(np.power(1 + n,3)*np.power(2 + n,3)) + ((7 + 9*n + 3*np.power(n,2))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)) + ((3 + 2*n)*np.power(S1,2))/(2.*(1 + n)*(2 + n)) + np.power(S1,3)/6. + ((3 + 2*n)*S2)/(2.*(1 + n)*(2 + n)) + (S1*S2)/2. + S3/3.))/(2 + n) + (60.36607529036273*((2*(5 + 2*n)*(4676 + 16800*n + 26110*np.power(n,2) + 22850*np.power(n,3) + 12285*np.power(n,4) + 4150*np.power(n,5) + 860*np.power(n,6) + 100*np.power(n,7) + 5*np.power(n,8)))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)) + ((1660 + 4530*n + 5031*np.power(n,2) + 2900*np.power(n,3) + 915*np.power(n,4) + 150*np.power(n,5) + 10*np.power(n,6))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)) + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*np.power(S1,2))/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + np.power(S1,3)/6. + ((5 + 2*n)*(5 + 5*n + np.power(n,2))*S2)/((1 + n)*(2 + n)*(3 + n)*(4 + n)) + (S1*S2)/2. + S3/3.))/(4 + n) - (90.67902221949461*((575 + 1776*n + 2284*np.power(n,2) + 1560*np.power(n,3) + 595*np.power(n,4) + 120*np.power(n,5) + 10*np.power(n,6))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)) + ((85 + 180*n + 141*np.power(n,2) + 48*np.power(n,3) + 6*np.power(n,4))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)) + ((11 + 12*n + 3*np.power(n,2))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)) + np.power(S1,3)/6. + ((11 + 12*n + 3*np.power(n,2))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)) + (S1*S2)/2. + S3/3.))/(3 + n) - (15.04831991939943*((6998824 + 32953200*n + 70204540*np.power(n,2) + 89358060*np.power(n,3) + 75608005*np.power(n,4) + 44779500*np.power(n,5) + 19032390*np.power(n,6) + 5849760*np.power(n,7) + 1290800*np.power(n,8) + 199500*np.power(n,9) + 20510*np.power(n,10) + 1260*np.power(n,11) + 35*np.power(n,12))/(np.power(1 + n,3)*np.power(2 + n,3)*np.power(3 + n,3)*np.power(4 + n,3)*np.power(5 + n,3)) + ((48076 + 154350*n + 210945*np.power(n,2) + 160020*np.power(n,3) + 73725*np.power(n,4) + 21150*np.power(n,5) + 3695*np.power(n,6) + 360*np.power(n,7) + 15*np.power(n,8))*S1)/(np.power(1 + n,2)*np.power(2 + n,2)*np.power(3 + n,2)*np.power(4 + n,2)*np.power(5 + n,2)) + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*np.power(S1,2))/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + np.power(S1,3)/6. + ((274 + 450*n + 255*np.power(n,2) + 60*np.power(n,3) + 5*np.power(n,4))*S2)/(2.*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)) + (S1*S2)/2. + S3/3.))/(5 + n)
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQbar22(n, nf, cache):
+    res = (5*(1/(-1 + n) - 1/n))/12. - 1/(3.*np.power(n,2)) + (np.power(n,-2) - np.power(1 + n,-2))/6. - (5*(1/(-1 + n) - 2/n + 1/(1 + n)))/12. + (1/(-1 + n) - 3/n + 3/(1 + n) - 1/(2 + n))/9.
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQbar23(n, nf, cache):
+    res = 0.
+    return res
+
+
+
+@nb.njit(cache=True)
+def AqQbar24(n, nf, cache):
+    res = 0.
+    return res
+
diff --git a/src/ekore/scet_I/tau_space/__init__.py b/src/ekore/scet_I/tau_space/__init__.py
new file mode 100644
index 000000000..adde8ffcf
--- /dev/null
+++ b/src/ekore/scet_I/tau_space/__init__.py
@@ -0,0 +1,305 @@
+import numba as nb
+import numpy as np
+
+from eko.constants import CF, zeta2
+from . import as1, as2
+from ...harmonics import cache as c
+
+
+@nb.njit(cache=True)
+def A_gg(n, nf, order, cache):
+    r"""
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    complex
+        :math:`A_{gg}`
+
+    """
+
+    if order == (1, -1):
+        res = as1.Agg1m1(n, cache)
+
+    if order == (1, 0):
+        res = as1.Agg10(n, cache)
+
+    if order == (1, 1):
+        res = as1.Agg11(n, cache)
+
+    if order == (2, -1):
+        res = as2.Agg2m1(n, nf, cache)
+
+    if order == (2, 0):
+        res = as2.Agg20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.Agg21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.Agg22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.Agg23(n, nf, cache)
+
+    return res
+
+@nb.njit(cache=True)
+def A_gq(n, nf, order, cache):
+    r"""
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    complex
+        :math:`A_{gq}`
+
+    """
+
+    if order == (1, -1):
+        res = as1.Agq1m1(n, cache)
+
+    if order == (1, 0):
+        res = as1.Agq10(n, cache)
+
+    if order == (1, 1):
+        res = as1.Agq11(n, cache)
+    
+    if order == (2, -1):
+        res = as2.Agq2m1(n, nf, cache)
+
+    if order == (2, 0):
+        res = as2.Agq20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.Agq21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.Agq22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.Agq23(n, nf, cache)
+
+    return res
+
+@nb.njit(cache=True)
+def A_qg(n, nf, order, cache):
+    r"""
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    complex
+        |NLO| :math:`A_{qg}`
+
+    """
+
+    if order == (1, -1):
+        res = as1.Aqg1m1(n, cache)
+
+    if order == (1, 0):
+        res = as1.Aqg10(n, cache)
+
+    if order == (1, 1):
+        res = as1.Aqg11(n, cache)
+
+    if order == (2, -1):
+        res = as2.Aqg2m1(n, nf, cache)
+
+    if order == (2, 0):
+        res = as2.Aqg20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.Aqg21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.Aqg22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.Aqg23(n, nf, cache)
+
+    return res
+
+@nb.njit(cache=True)
+def A_qq(n, nf, order, cache):
+    r"""
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    complex
+        |NLO| :math:`A_{qq}`
+
+    """
+
+    if order == (1, -1):
+        res = as1.Aqq1m1(n, cache)
+
+    if order == (1, 0):
+        res = as1.Aqq10(n, cache)
+
+    if order == (1, 1):
+        res = as1.Aqq11(n, cache)
+
+    if order == (2, -1):
+        res = as2.Aqq2m1(n, nf, cache)
+
+    if order == (2, 0):
+        res = as2.Aqq20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.Aqq21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.Aqq22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.Aqq23(n, nf, cache)
+
+    return res
+
+@nb.njit(cache=True)
+def A_qQ2(n, nf, order, cache):
+    if order == (1, -1):
+        res = 0.0
+
+    if order == (1, 0):
+        res = 0.0
+
+    if order == (1, 1):
+        res = 0.0
+
+    if order == (2, -1):
+        res = as2.AqQ2m1(n, nf, cache)
+
+    if order == (2, 0):
+        res = as2.AqQ20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.AqQ21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.AqQ22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.AqQ23(n, nf, cache)
+
+    return res
+
+
+@nb.njit(cache=True)
+def A_qQ2bar(n, nf, order, cache):
+    if order == (1, -1):
+        res = 0.0
+
+    if order == (1, 0):
+        res = 0.0
+
+    if order == (1, 1):
+        res = 0.0
+
+    if order == (2, -1):
+        res = as2.AqQbar2m1(n, nf, cache)
+
+    if order == (2, 0):
+        res = as2.AqQbar20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.AqQbar21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.AqQbar22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.AqQbar23(n, nf, cache)
+
+    return res
+
+@nb.njit(cache=True)
+def A_qqbar(n, nf, order, cache):
+    if order == (1, -1):
+        res = 0.0
+
+    if order == (1, 0):
+        res = 0.0
+
+    if order == (1, 1):
+        res = 0.0
+
+    if order == (2, -1):
+        res = as2.Aqqbar2m1(n, nf, cache)
+
+    if order == (2, 0):
+        res = as2.Aqqbar20(n, nf, cache)
+
+    if order == (2, 1):
+        res = as2.Aqqbar21(n, nf, cache)
+
+    if order == (2, 2):
+        res = as2.Aqqbar22(n, nf, cache)
+
+    if order == (2, 3):
+        res = as2.Aqqbar23(n, nf, cache)
+
+    return res
+
+
+# @nb.njit(cache=True)
+# def A_entries(n, nf, order, cache):
+#     r"""Compute the beam function matching kernel at the given order.
+
+#     Parameters
+#     ----------
+#     n : complex
+#         Mellin moment
+#     cache: numpy.ndarray
+#         Harmonic sum cache
+
+#     Returns
+#     -------
+#     numpy.ndarray
+#         `
+
+#     """
+
+#     Agg = A_gg(n, nf, order, cache)
+#     Agq = A_gq(n, nf, order, cache)
+#     Aqg = A_qg(n, nf, order, cache)
+#     Aqq = A_qq(n, nf, order, cache)
+#     AqQ2 = A_qQ2(n, nf, order, cache)
+#     Aqqbar = A_qqbar(n, nf, order, cache)
+#     AqQ2bar = A_qQ2bar(n, nf, order, cache)
+
+#     A_S = np.array(
+#         [
+#             [Agg, Agq, Agq, Agq, Agq],
+#             [Aqg, Aqq, Aqqbar, AqQ2, AqQ2bar],
+#             [Aqg, Aqqbar, Aqq, AqQ2bar, AqQ2],
+#             [Aqg, AqQ2, AqQ2bar, Aqq, Aqqbar],
+#             [Aqg, AqQ2bar, AqQ2bar, Aqqbar, Aqq],
+#         ],
+#         np.complex_,
+#     )
+#     return A_S
+
+
diff --git a/src/ekore/scet_I/tau_space/as1.py b/src/ekore/scet_I/tau_space/as1.py
new file mode 100644
index 000000000..c739b2dee
--- /dev/null
+++ b/src/ekore/scet_I/tau_space/as1.py
@@ -0,0 +1,276 @@
+r"""SCET 1 kernel entries.
+
+"""
+import numba as nb
+import numpy as np
+
+from eko.constants import CF, zeta2
+from ...harmonics import cache as c
+
+
+@nb.njit(cache=True)
+def A_gg(n, order, cache):
+    r"""
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    complex
+        |NLO| :math:`A_{gg}`
+
+    """
+
+    if order == (1, -1):
+        res = Agg1m1(n, cache)
+
+    if order == (1, 0):
+        res = Agg10(n, cache)
+
+    if order == (1, 1):
+        res = Agg11(n, cache)
+
+    return res
+
+
+@nb.njit(cache=True)
+def A_gq(n, order, cache):
+    r"""
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    complex
+        |NLO| :math:`A_{gq}`
+
+    """
+
+    if order == (1, -1):
+        res = Agq1m1(n, cache)
+
+    if order == (1, 0):
+        res = Agq10(n, cache)
+
+    if order == (1, 1):
+        res = Agq11(n, cache)
+
+    return res
+
+
+@nb.njit(cache=True)
+def A_qg(n, order, cache):
+    r"""
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    complex
+        |NLO| :math:`A_{qg}`
+
+    """
+
+    if order == (1, -1):
+        res = Aqg1m1(n, cache)
+
+    if order == (1, 0):
+        res = Aqg10(n, cache)
+
+    if order == (1, 1):
+        res = Aqg11(n, cache)
+
+    return res
+
+
+@nb.njit(cache=True)
+def A_qq(n, order, cache):
+    r"""
+    Parameters
+    ----------
+    n : complex
+        Mellin moment
+    cache: numpy.ndarray
+        Harmonic sum cache
+
+    Returns
+    -------
+    complex
+        |NLO| :math:`A_{qq}`
+
+    """
+
+    if order == (1, -1):
+        res = Aqq1m1(n, cache)
+
+    if order == (1, 0):
+        res = Aqq10(n, cache)
+
+    if order == (1, 1):
+        res = Aqq11(n, cache)
+
+    return res
+
+
+@nb.njit(cache=True)
+def A_qQ2(n, order):
+    if order == (1, -1):
+        res = 0.0
+
+    if order == (1, 0):
+        res = 0.0
+
+    if order == (1, 1):
+        res = 0.0
+
+    return res
+
+
+@nb.njit(cache=True)
+def A_qQ2bar(n, order):
+    if order == (1, -1):
+        res = 0.0
+
+    if order == (1, 0):
+        res = 0.0
+
+    if order == (1, 1):
+        res = 0.0
+
+    return res
+
+
+@nb.njit(cache=True)
+def A_qqbar(n, order):
+    if order == (1, -1):
+        res = 0.0
+
+    if order == (1, 0):
+        res = 0.0
+
+    if order == (1, 1):
+        res = 0.0
+
+    return res
+
+
+@nb.njit(cache=True)
+def Agg1m1(n, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    res = (
+        (
+            3
+            * (
+                -4
+                - 2 * n
+                + 10 * np.power(n, 2)
+                + 4 * np.power(n, 3)
+                + 4 * np.power(n, 4)
+                + 2 * np.power(n, 2) * zeta2
+                - np.power(n, 3) * zeta2
+                - 3 * np.power(n, 4) * zeta2
+                + np.power(n, 5) * zeta2
+                + np.power(n, 6) * zeta2
+            )
+        )
+        / (2.0 * np.power(-1 + n, 2) * np.power(n, 2) * (1 + n) * (2 + n))
+        - (6 * (1 + n + np.power(n, 2)) * S1) / ((-1 + n) * n * (1 + n) * (2 + n))
+        + (3 * np.power(S1, 2)) / 2.0
+        - (3 * S2) / 2.0
+    )
+    return res
+
+
+@nb.njit(cache=True)
+def Agg10(n, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = (6 * (1 + n + np.power(n, 2))) / ((-1 + n) * n * (1 + n) * (2 + n)) - 3 * S1
+    return res
+
+
+@nb.njit(cache=True)
+def Agg11(n, cache):
+    res = 3.0
+    return res
+
+
+@nb.njit(cache=True)
+def Agq1m1(n, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = (2 * (-2 + 5 * np.power(n, 2) + np.power(n, 4))) / (
+        3.0 * np.power(-1 + n, 2) * np.power(n, 2) * (1 + n)
+    ) - (2 * (2 + n + np.power(n, 2)) * S1) / (3.0 * (-1 + n) * n * (1 + n))
+    return res
+
+
+@nb.njit(cache=True)
+def Agq10(n, cache):
+    res = (2 * (2 + n + np.power(n, 2))) / (3.0 * (-1 + n) * n * (1 + n))
+    return res
+
+
+@nb.njit(cache=True)
+def Agq11(n, cache):
+    res = 0
+    return res
+
+
+@nb.njit(cache=True)
+def Aqg1m1(n, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = 1 / (4.0 * np.power(n, 2)) + ((-2 - n - np.power(n, 2)) * S1) / (
+        4.0 * n * (1 + n) * (2 + n)
+    )
+    return res
+
+
+@nb.njit(cache=True)
+def Aqg10(n, cache):
+    res = (2 + n + np.power(n, 2)) / (4.0 * n * (1 + n) * (2 + n))
+    return res
+
+
+@nb.njit(cache=True)
+def Aqg11(n, cache):
+    res = 0
+    return res
+
+
+@nb.njit(cache=True)
+def Aqq1m1(n, cache):
+    S1 = c.get(c.S1, cache, n)
+    S2 = c.get(c.S2, cache, n)
+    res = (
+        (2 * (1 + 2 * n + np.power(n, 2) * zeta2 + np.power(n, 3) * zeta2))
+        / (3.0 * np.power(n, 2) * (1 + n))
+        - (2 * S1) / (3.0 * n * (1 + n))
+        + (2 * np.power(S1, 2)) / 3.0
+        - (2 * S2) / 3.0
+    )
+    return res
+
+
+@nb.njit(cache=True)
+def Aqq10(n, cache):
+    S1 = c.get(c.S1, cache, n)
+    res = 2 / (3.0 * n * (1 + n)) - (4 * S1) / 3.0
+    return res
+
+
+@nb.njit(cache=True)
+def Aqq11(n, cache):
+    res = 1.3333333333333333
+    return res