
# q-expansion of newform 117.4.g.f, downloaded from the LMFDB on 24 April 2024.

# We generate the q-expansion using the Hecke eigenvalues a_p at the primes.
# Each a_p is given as a linear combination
# of the following basis for the coefficient ring.

def make_data():

    from sage.all import prod, floor, prime_powers, gcd, QQ, primes_first_n, next_prime, RR

    def discrete_log(elts, gens, mod):
        # algorithm 2.2, page 16 of https://arxiv.org/abs/0903.2785
        def table_gens(gens, mod):
            T = [1]
            n = len(gens)
            r = [None]*n
            s = [None]*n
            for i in range(n):
                beta = gens[i]
                r[i] = 1
                N = len(T)
                while beta not in T:
                    for Tj in T[:N]:
                        T.append((beta*Tj) % mod)
                    beta = (beta*gens[i]) % mod
                    r[i] += 1
                s[i] = T.index(beta)
            return T, r, s
        T, r, s = table_gens(gens, mod)
        n = len(gens)
        N = [ prod(r[:j]) for j in range(n) ]
        Z = lambda s: [ (floor(s/N[j]) % r[j]) for j in range(n)]
        return [Z(T.index(elt % mod)) for elt in elts]
    def extend_multiplicatively(an):
        for pp in prime_powers(len(an)-1):
            for k in range(1, (len(an) - 1)//pp + 1):
                if gcd(k, pp) == 1:
                    an[pp*k] = an[pp]*an[k]
    from sage.all import PolynomialRing, NumberField, ZZ
    R = PolynomialRing(QQ, "x")
    f = R(poly_data)
    K = NumberField(f, "a")
    betas = [K([c/ZZ(den) for c in num]) for num, den in basis_data]
    convert_elt_to_field = lambda elt: sum(c*beta for c, beta in zip(elt, betas))
    # convert aps to K elements
    primes = primes_first_n(len(aps_data))
    good_primes = [p for p in primes if not p.divides(level)]
    aps = map(convert_elt_to_field, aps_data)
    if not hecke_ring_character_values:
        # trivial character
        char_values = dict(zip(good_primes, [1]*len(good_primes)))
    else:
        gens = [elt[0] for elt in hecke_ring_character_values]
        gens_values = [convert_elt_to_field(elt[1]) for elt in hecke_ring_character_values]
        char_values = dict([(
            p,prod(g**k for g, k in zip(gens_values, elt)))
            for p, elt in zip(good_primes, discrete_log(good_primes, gens, level))
            ])
    an_list_bound = next_prime(primes[-1])
    an = [0]*an_list_bound
    an[1] = 1
    
    from sage.all import PowerSeriesRing
    PS = PowerSeriesRing(K, "q")
    for p, ap in zip(primes, aps):
        if p.divides(level):
            euler_factor = [1, -ap]
        else:
            euler_factor = [1, -ap, p**(weight - 1) * char_values[p]]
        k = RR(an_list_bound).log(p).floor() + 1
        foo = (1/PS(euler_factor)).padded_list(k)
        for i in range(1, k):
            an[p**i] = foo[i]
    extend_multiplicatively(an)
    return PS(an)
level = 117
weight = 4
poly_data = [24920064, 0, 21016320, 0, 13705540, 0, 2869882, 0, 424113, 0, 33440, 0, 1899, 0, 52, 0, 1]

# The entries in the following list give a basis for the
# coefficient ring in terms of a root of the defining polynomial above.
# Each line consists of the coefficients of the numerator, and a denominator.
basis_data  = [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 1], [[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 1], [[-25929136118756652288, 0, -16925010973113963820, 0, -3269311083458423326, 0, -531022140611344875, 0, -42518671468817696, 0, -2537753710344969, 0, -70185147718972, 0, -1400516976091, 0], 19347670437452567808], [[86786355372439580, 0, -1404077250081792, 0, -909387204879920, 0, -300483724727391, 0, -25222482239398, 0, -1728612264289, 0, -48809305790, 0, -1058387435, 0], 7751470527825548], [[209921486006331191040, 0, 135634859424724819780, 0, 40174000892884504378, 0, 3608907912699869841, 0, 232118184426369680, 0, 3580765159783899, 0, 32435361605764, 0, -3479246660543, 0], 19347670437452567808], [[0, -25929136118756652288, 0, -16925010973113963820, 0, -3269311083458423326, 0, -531022140611344875, 0, -42518671468817696, 0, -2537753710344969, 0, -70185147718972, 0, -1400516976091], 19347670437452567808], [[-23244445912812483840, 0, -15167145799755754540, 0, -3094708740121478686, 0, -473329265463685803, 0, -37675954878853280, 0, -2205860155601481, 0, -60813761007292, 0, -1197306588571, 0], 1488282341342505216], [[-127620970309043600, 0, 60732266200759296, 0, 39334834178898960, 0, 11062740994006466, 0, 1090978794448674, 0, 74769775086507, 0, 2174587212793, 0, 45779722905, 0], 31005882111302192], [[-774173355811127376, 0, 38073901724052480, 0, 24659554213054800, 0, 7787903072151153, 0, 683949768407370, 0, 46874211134535, 0, 1329441616294, 0, 28699944525, 0], 15502941055651096], [[0, -1164787241335121880, 0, 40882056224216064, 0, 26478328622814640, 0, 8388870521605935, 0, 734394732886166, 0, 50331435663113, 0, 1427060227874, 0, 30816719395], 124023528445208768], [[-18546238052410189056, 0, -12090881746378888300, 0, -2665131110836616798, 0, -372366733955282427, 0, -29201200846415552, 0, -1625046434800377, 0, -44413834261852, 0, -841688410411, 0], 248047056890417536], [[0, -3545557154855825304, 0, 63347292225524736, 0, 41028523900893360, 0, 13196610117244191, 0, 1137954448716534, 0, 77989231891737, 0, 2208009120514, 0, 47750918355], 124023528445208768], [[0, 703930756872383389440, 0, 459070608412657863300, 0, 97960598478417753242, 0, 14210731889366257665, 0, 1120914160002984480, 0, 63652785294026075, 0, 1745816677861620, 0, 33607973109585], 51593787833206847488], [[0, -158684086080771134208, 0, -103533222838252967860, 0, -21153010608954516306, 0, -3226765545524312013, 0, -256467609267026336, 0, -14943180757095135, 0, -411639246983524, 0, -8076330538717], 3968752910246680576], [[0, -5889521404981408392, 0, 388040469476994048, 0, 251324517862118480, 0, 74225315136481925, 0, 6970659092283562, 0, 477731203563991, 0, 13760478427434, 0, 292503248765], 124023528445208768], [[0, 3753967810211603741952, 0, 2445232621808654880780, 0, 543168352364046381326, 0, 74328934137893879075, 0, 5741356569946908384, 0, 304046254612699633, 0, 8180796288455388, 0, 147991404382739], 51593787833206847488]]

hecke_ring_character_values = [[92, [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [28, [-1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]
aps_data = [[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [3, 0, 3, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0], [0, 0, -4, -2, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1], [-31, 0, -31, 6, 1, 0, 6, 1, -1, 0, 1, 0, 0, 0, 0, 0], [0, -11, 0, 0, 0, 0, 0, 0, 0, -5, 0, -2, 0, 0, -1, 0], [0, 10, 0, 0, 0, 0, 0, 0, 0, 1, 0, 6, 0, 0, 0, 0], [28, 0, 0, -8, 0, 0, 0, 6, -3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 126, 0, 7, 0, -12, 0, 0, 0, -2, 0, 0, 0, 0, 0], [0, 49, 0, 0, 0, 0, 0, 0, 0, -6, 0, -4, 0, 0, 1, 0], [-11, 0, -11, -26, 7, 0, -26, 7, 0, 0, 0, 0, 0, 0, 0, 0], [0, 33, 0, 0, 0, 33, 0, 0, 0, 11, 0, -2, 11, 2, -1, -1], [0, 60, 0, 0, 0, 60, 0, 0, 0, 19, 0, -2, 19, 2, 6, 6], [0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -6, 4, 0, -6], [-148, 0, -148, -10, 15, 0, -10, 15, -3, 0, 3, 0, 0, 0, 0, 0], [0, 0, -273, 0, 1, 0, 30, 0, 0, 0, -8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, -11, 14, 0, 1], [-273, 0, 0, -6, 0, 0, 0, -8, -12, 0, 0, 0, 0, 0, 0, 0], [234, 0, 0, -16, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0], [0, -51, 0, 0, 0, -51, 0, 0, 0, -13, 0, 8, -13, -8, -7, -7], [0, -44, 0, 0, 0, 0, 0, 0, 0, -32, 0, -24, 0, 0, 8, 0], [558, 0, 558, 58, -48, 0, 58, -48, -1, 0, 1, 0, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 81, 0, 8, 0, 0, -8, 0], [435, 0, 0, 96, 0, 0, 0, -5, 10, 0, 0, 0, 0, 0, 0, 0], [0, -263, 0, 0, 0, 0, 0, 0, 0, -25, 0, 4, 0, 0, 1, 0], [596, 0, 0, 8, 0, 0, 0, 20, -23, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 77, 0, 0, 0, 0, 0, 0, -4, 20, 0, -15], [0, 0, 84, 0, 30, 0, 80, 0, 0, 0, -11, 0, 0, 0, 0, 0], [0, 72, 0, 0, 0, 72, 0, 0, 0, 28, 0, -24, 28, 24, -8, -8], [0, 0, 0, 0, 0, 143, 0, 0, 0, 0, 0, 0, -62, -24, 0, 15], [-644, 0, -644, -4, 2, 0, -4, 2, 31, 0, -31, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 344, 0, 0, 0, 0, 0, 0, 67, 10, 0, 14], [-547, 0, 0, -96, 0, 0, 0, 63, 29, 0, 0, 0, 0, 0, 0, 0], [-630, 0, 0, 124, 0, 0, 0, 77, -25, 0, 0, 0, 0, 0, 0, 0], [-454, 0, -454, 44, -24, 0, 44, -24, 23, 0, -23, 0, 0, 0, 0, 0], [0, 124, 0, 0, 0, 0, 0, 0, 0, -124, 0, 52, 0, 0, -40, 0], [0, 0, 0, 0, 0, 110, 0, 0, 0, 0, 0, 0, -2, 10, 0, -40], [0, -239, 0, 0, 0, 0, 0, 0, 0, 71, 0, -4, 0, 0, 33, 0], [1418, 0, 0, 150, 0, 0, 0, -81, -12, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -550, 0, 0, 0, 0, 0, 0, 114, 24, 0, 42], [0, 0, 1237, 0, 90, 0, 172, 0, 0, 0, 46, 0, 0, 0, 0, 0], [0, -194, 0, 0, 0, 0, 0, 0, 0, -46, 0, -28, 0, 0, -34, 0], [-2983, 0, -2983, -36, 61, 0, -36, 61, 24, 0, -24, 0, 0, 0, 0, 0], [0, 0, -22, 0, -168, 0, 36, 0, 0, 0, 7, 0, 0, 0, 0, 0], [0, 0, -2306, 0, -62, 0, 92, 0, 0, 0, 50, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, -7, -20, 0, -49], [-1106, 0, 0, -30, 0, 0, 0, -70, 18, 0, 0, 0, 0, 0, 0, 0], [0, 24, 0, 0, 0, 24, 0, 0, 0, 44, 0, -8, 44, 8, -20, -20], [0, 1191, 0, 0, 0, 1191, 0, 0, 0, 149, 0, 62, 149, -62, 21, 21], [-1511, 0, -1511, 286, -194, 0, 286, -194, -13, 0, 13, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 620, 0, 0, 0, 0, 0, 0, -120, 24, 0, 16], [0, -515, 0, 0, 0, 0, 0, 0, 0, -162, 0, -14, 0, 0, -37, 0], [0, 631, 0, 0, 0, 0, 0, 0, 0, 93, 0, -138, 0, 0, -55, 0], [0, 0, 0, 0, 0, -1138, 0, 0, 0, 0, 0, 0, -54, -94, 0, 12], [0, 0, 1436, 0, -218, 0, 436, 0, 0, 0, -53, 0, 0, 0, 0, 0], [-1432, 0, -1432, -494, -85, 0, -494, -85, -26, 0, 26, 0, 0, 0, 0, 0], [0, 819, 0, 0, 0, 819, 0, 0, 0, 76, 0, 96, 76, -96, -57, -57], [0, 0, 1735, 0, 25, 0, 74, 0, 0, 0, 48, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -166, 0, 0, 0, 0, 0, 0, -259, -16, 0, 78], [-2579, 0, 0, -114, 0, 0, 0, -133, 6, 0, 0, 0, 0, 0, 0, 0], [0, 537, 0, 0, 0, 537, 0, 0, 0, -49, 0, -26, -49, 26, 35, 35], [1078, 0, 0, -94, 0, 0, 0, 16, -57, 0, 0, 0, 0, 0, 0, 0], [0, 24, 0, 0, 0, 24, 0, 0, 0, -273, 0, -44, -273, 44, 56, 56], [552, 0, 552, 400, 150, 0, 400, 150, 7, 0, -7, 0, 0, 0, 0, 0], [1883, 0, 0, -358, 0, 0, 0, -16, -84, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1921, 0, 0, 0, 0, 0, 0, -27, -16, 0, -37], [0, 0, 1428, 0, 180, 0, -184, 0, 0, 0, -139, 0, 0, 0, 0, 0], [0, -485, 0, 0, 0, 0, 0, 0, 0, 614, 0, 126, 0, 0, -47, 0], [0, 783, 0, 0, 0, 783, 0, 0, 0, -207, 0, -18, -207, 18, 69, 69], [0, 0, 2573, 0, 309, 0, 24, 0, 0, 0, -74, 0, 0, 0, 0, 0], [-4476, 0, -4476, 134, -53, 0, 134, -53, -51, 0, 51, 0, 0, 0, 0, 0], [0, 0, 4040, 0, -18, 0, -336, 0, 0, 0, -43, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 386, 0, 0, 0, 0, 0, 0, 46, -264, 0, -34], [0, -804, 0, 0, 0, -804, 0, 0, 0, 125, 0, -182, 125, 182, -158, -158], [-44, 0, -44, -660, -120, 0, -660, -120, -111, 0, 111, 0, 0, 0, 0, 0], [0, -2021, 0, 0, 0, 0, 0, 0, 0, -130, 0, 92, 0, 0, 3, 0], [-191, 0, -191, -324, 234, 0, -324, 234, -50, 0, 50, 0, 0, 0, 0, 0], [0, 1438, 0, 0, 0, 0, 0, 0, 0, -254, 0, 208, 0, 0, -138, 0], [5156, 0, 0, -64, 0, 0, 0, -439, -37, 0, 0, 0, 0, 0, 0, 0], [0, -1043, 0, 0, 0, 0, 0, 0, 0, -601, 0, -42, 0, 0, 87, 0], [1385, 0, 1385, 174, -38, 0, 174, -38, -218, 0, 218, 0, 0, 0, 0, 0], [0, 0, 2313, 0, 29, 0, 292, 0, 0, 0, -220, 0, 0, 0, 0, 0], [0, 360, 0, 0, 0, 360, 0, 0, 0, -640, 0, -120, -640, 120, 116, 116], [0, 0, 0, 0, 0, -664, 0, 0, 0, 0, 0, 0, 272, 28, 0, 44], [0, 0, -2579, 0, 222, 0, 370, 0, 0, 0, 14, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1358, 0, 0, 0, 0, 0, 0, 819, -42, 0, 92], [2413, 0, 0, 68, 0, 0, 0, 49, 58, 0, 0, 0, 0, 0, 0, 0], [0, -1209, 0, 0, 0, -1209, 0, 0, 0, 637, 0, 16, 637, -16, 135, 135], [0, -224, 0, 0, 0, 0, 0, 0, 0, 404, 0, 84, 0, 0, 12, 0], [4625, 0, 4625, -432, -29, 0, -432, -29, 137, 0, -137, 0, 0, 0, 0, 0], [0, 1435, 0, 0, 0, 0, 0, 0, 0, -123, 0, 200, 0, 0, -53, 0], [1012, 0, 0, -780, 0, 0, 0, 356, -104, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2011, 0, 0, 0, 0, 0, 0, 211, 110, 0, -157], [0, -1112, 0, 0, 0, 0, 0, 0, 0, 177, 0, -40, 0, 0, 212, 0], [0, 1413, 0, 0, 0, 1413, 0, 0, 0, 244, 0, -138, 244, 138, -109, -109], [0, 0, 5735, 0, 79, 0, 82, 0, 0, 0, 239, 0, 0, 0, 0, 0], [476, 0, 0, -438, 0, 0, 0, -357, 229, 0, 0, 0, 0, 0, 0, 0], [-5275, 0, 0, 1130, 0, 0, 0, -445, -80, 0, 0, 0, 0, 0, 0, 0], [0, 574, 0, 0, 0, 0, 0, 0, 0, 863, 0, 40, 0, 0, -38, 0], [0, 0, 0, 0, 0, -1096, 0, 0, 0, 0, 0, 0, -796, -416, 0, 4], [0, -4022, 0, 0, 0, 0, 0, 0, 0, -982, 0, -234, 0, 0, -164, 0], [-4439, 0, 0, -622, 0, 0, 0, 313, 203, 0, 0, 0, 0, 0, 0, 0], [4343, 0, 0, -162, 0, 0, 0, 516, -207, 0, 0, 0, 0, 0, 0, 0], [0, 4156, 0, 0, 0, 0, 0, 0, 0, 108, 0, -224, 0, 0, -104, 0], [0, 1569, 0, 0, 0, 1569, 0, 0, 0, -942, 0, -154, -942, 154, 91, 91], [0, -270, 0, 0, 0, -270, 0, 0, 0, -794, 0, 252, -794, -252, 66, 66], [0, 0, 10893, 0, 16, 0, 156, 0, 0, 0, 127, 0, 0, 0, 0, 0], [-4544, 0, -4544, 708, 456, 0, 708, 456, 168, 0, -168, 0, 0, 0, 0, 0], [0, 0, 6800, 0, 35, 0, 800, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2273, 0, 0, 0, 0, 0, 0, 214, 50, 0, -301], [-838, 0, 0, 968, 0, 0, 0, -484, 51, 0, 0, 0, 0, 0, 0, 0], [-12534, 0, -12534, 88, 144, 0, 88, 144, -149, 0, 149, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -565, 0, 0, 0, 0, 0, 0, 782, 352, 0, 39], [-6962, 0, -6962, -224, -344, 0, -224, -344, -305, 0, 305, 0, 0, 0, 0, 0], [0, -3392, 0, 0, 0, 0, 0, 0, 0, -464, 0, -348, 0, 0, 212, 0], [0, -3770, 0, 0, 0, 0, 0, 0, 0, 1222, 0, 306, 0, 0, -140, 0], [0, 0, 0, 0, 0, 470, 0, 0, 0, 0, 0, 0, 242, -284, 0, 194], [0, 0, -16658, 0, -29, 0, -946, 0, 0, 0, 267, 0, 0, 0, 0, 0], [0, 0, -5377, 0, -314, 0, 922, 0, 0, 0, 54, 0, 0, 0, 0, 0], [0, 3942, 0, 0, 0, 3942, 0, 0, 0, 870, 0, 18, 870, -18, 92, 92], [0, 0, 0, 0, 0, 2570, 0, 0, 0, 0, 0, 0, -122, -640, 0, -2], [0, 0, 7751, 0, -647, 0, -530, 0, 0, 0, 514, 0, 0, 0, 0, 0], [0, -3498, 0, 0, 0, -3498, 0, 0, 0, -134, 0, 302, -134, -302, -124, -124], [-4256, 0, -4256, 1252, 7, 0, 1252, 7, 125, 0, -125, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 326, 0, 0, 0, 0, 0, 0, -1270, -20, 0, -206], [41, 0, 0, -1460, 0, 0, 0, -743, 16, 0, 0, 0, 0, 0, 0, 0], [11696, 0, 0, -1192, 0, 0, 0, 89, 411, 0, 0, 0, 0, 0, 0, 0], [0, 0, -17254, 0, 14, 0, -2080, 0, 0, 0, 286, 0, 0, 0, 0, 0], [0, -3314, 0, 0, 0, 0, 0, 0, 0, -602, 0, -260, 0, 0, -46, 0], [0, 0, 12745, 0, 739, 0, -292, 0, 0, 0, -53, 0, 0, 0, 0, 0], [0, 0, 16070, 0, -396, 0, -696, 0, 0, 0, -140, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 596, 0, 0, 0, 0, 0, 0, 168, 40, 0, 32], [0, 0, -6188, 0, 532, 0, 854, 0, 0, 0, 60, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2942, 0, 0, 0, 0, 0, 0, -30, -354, 0, 296], [-9964, 0, -9964, 84, -614, 0, 84, -614, 25, 0, -25, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -4798, 0, 0, 0, 0, 0, 0, 958, -12, 0, 34], [0, -947, 0, 0, 0, 0, 0, 0, 0, 164, 0, 70, 0, 0, -245, 0], [-436, 0, 0, 2384, 0, 0, 0, -550, -55, 0, 0, 0, 0, 0, 0, 0], [0, 2050, 0, 0, 0, 0, 0, 0, 0, -42, 0, -98, 0, 0, 152, 0], [-5532, 0, -5532, 140, 736, 0, 140, 736, 436, 0, -436, 0, 0, 0, 0, 0], [0, -846, 0, 0, 0, -846, 0, 0, 0, 250, 0, 156, 250, -156, -290, -290], [0, 0, -8280, 0, 729, 0, -2080, 0, 0, 0, -47, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1372, 0, 0, 0, 0, 0, 0, 876, 416, 0, 392], [-1198, 0, 0, -458, 0, 0, 0, 391, -19, 0, 0, 0, 0, 0, 0, 0], [0, 4587, 0, 0, 0, 4587, 0, 0, 0, -86, 0, 172, -86, -172, 475, 475], [10631, 0, 0, -1618, 0, 0, 0, -355, -176, 0, 0, 0, 0, 0, 0, 0], [0, -3357, 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