# q-expansion of newform 370.2.m.c, downloaded from the LMFDB on 29 April 2026. # 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 = 370 weight = 2 poly_data = [256, 0, 25392, 0, 58656, 0, 48248, 0, 19684, 0, 4431, 0, 559, 0, 37, 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], [[-128, 2272, 0, 8872, 0, 12700, 0, 7734, 0, 2361, 0, 381, 0, 31, 0, 1], 256], [[-384, -736, -1232, -8168, 3304, -12636, 5252, -7734, 2538, -2361, 546, -381, 54, -31, 2, -1], 256], [[384, -736, 1232, -8168, -3304, -12636, -5252, -7734, -2538, -2361, -546, -381, -54, -31, -2, -1], 256], [[0, 5632, 10640, 9576, 24280, 2188, 20652, -2018, 8286, -1237, 1670, -273, 162, -27, 6, -1], 256], [[0, 5632, -10640, 9576, -24280, 2188, -20652, -2018, -8286, -1237, -1670, -273, -162, -27, -6, -1], 256], [[768, 6528, 16240, 15864, 36184, 12708, 27876, 5682, 10102, 1637, 1870, 289, 170, 27, 6, 1], 256], [[768, -6528, 16240, -15864, 36184, -12708, 27876, -5682, 10102, -1637, 1870, -289, 170, -27, 6, -1], 256], [[-384, -1952, 15536, -9800, 36120, -13084, 27876, -7766, 10102, -2361, 1870, -381, 170, -31, 6, -1], 256], [[-384, 1952, 15536, 9800, 36120, 13084, 27876, 7766, 10102, 2361, 1870, 381, 170, 31, 6, 1], 256], [[128, 64, 11560, 0, 24892, 0, 17774, 0, 5975, 0, 1035, 0, 89, 0, 3, 0], 128], [[-128, 64, -11560, 0, -24892, 0, -17774, 0, -5975, 0, -1035, 0, -89, 0, -3, 0], 128], [[256, 1664, 16112, 7016, 36184, 12588, 27876, 10358, 10102, 4143, 1870, 835, 170, 81, 6, 3], 256], [[-128, 0, -8056, 0, -18092, 0, -13938, 0, -5051, 0, -935, 0, -85, 0, -3, 0], 64], [[320, 496, 10336, 440, 21684, 112, 15872, 8, 5513, 0, 985, 0, 87, 0, 3, 0], 64], [[-320, 496, -10336, 440, -21684, 112, -15872, 8, -5513, 0, -985, 0, -87, 0, -3, 0], 64]] hecke_ring_character_values = [[297, [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [261, [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] aps_data = [[-1, -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, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, -1, 0, 0, -1, -1, 0, 0, 0, 0, -1, 1], [0, -2, 0, 0, 0, -1, 1, 0, 0, -1, 0, 0, -1, -1, -1, 0], [-1, -1, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, -1], [-1, -1, 1, 0, 0, 1, -1, 0, 0, -1, -1, 0, 1, -1, -1, 0], [2, 0, 0, 0, 1, -1, 1, 1, 1, 1, 1, -1, 0, 1, -1, 1], [-2, -4, 0, 0, -1, -1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0], [1, 2, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0], [0, 0, -1, 0, 1, -1, 0, 2, 0, 0, 1, 1, 0, 2, 0, 0], [-1, -4, 1, 2, 2, 1, 3, 0, 2, -1, -1, -2, -1, -1, -3, 0], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -2, 0, 0], [-2, -4, 1, 1, 1, 1, 1, -1, 2, -2, -2, -2, 2, 1, 0, 0], [-1, -1, 0, 2, 1, -1, 0, -1, 0, -1, 0, -1, -1, -2, 0, 1], [2, 0, 0, -2, 1, -2, -1, -1, -1, -2, 0, 0, 0, 0, 1, 0], [4, 2, 0, 0, 1, -2, 2, 2, -1, 1, 0, 0, 0, 0, 0, 2], [1, 2, -3, 0, 1, -1, 3, 2, -1, 0, 0, 0, -1, 1, 1, 2], [-1, -2, 1, 2, 1, 1, 1, 1, 1, 0, -1, -2, -2, -2, -2, -1], [1, 2, 1, 1, 0, 0, -3, 3, -2, 2, 1, 1, 2, 1, 0, 0], [1, 0, 1, 0, 1, -1, 1, 2, -1, 0, 2, 0, -1, 1, -1, 2], [1, 0, 0, -1, -1, -1, 1, 1, -2, -1, 0, 3, 0, 0, -1, 0], [0, 1, 0, -1, -3, 3, -1, 1, 0, 3, 0, 2, 0, 0, 1, -2], [-4, 0, 1, -1, -1, 1, 2, 2, 1, 1, 1, -1, 0, 2, -1, 1], [1, 0, 0, 0, 1, -1, 2, 2, -3, -3, 1, -1, 0, 0, -1, 1], [-6, 0, 0, 0, -1, 1, -1, -1, -1, -1, -1, 1, 0, -1, 3, -3], [8, 4, 0, 0, 2, 0, 0, 0, -2, -2, -1, 0, -2, 2, 0, 0], [0, 2, 0, -2, -2, 1, -4, -4, -1, 1, 0, 4, -2, -4, 4, 0], [4, 4, 0, 0, -2, 0, 2, -2, 2, 0, 0, 0, 0, 0, 2, 0], [-1, 1, 0, 0, 0, 1, -1, -2, 1, 1, 0, 2, -3, -6, 1, 1], [-1, 0, 0, 1, 1, -1, 1, 1, 0, -1, 0, -1, 2, 4, -1, 0], [1, 2, -4, -4, -5, -5, -1, 1, -1, 1, 4, 4, 2, 1, -1, -1], [-3, -4, 2, 1, -2, -1, 0, 2, 1, 1, 2, 1, 0, 0, 0, 2], [-6, 0, -2, 2, -1, 1, 2, 2, 2, 2, 2, -2, 0, 0, -2, 2], [-1, 1, 1, 2, 2, 4, -2, 1, 2, 2, 0, 0, 3, 3, 1, -1], [1, -2, 0, 1, 0, 2, -2, -2, 2, 2, 0, -4, 0, 0, 2, 0], [0, 0, 0, 0, 2, 2, -2, 2, 0, -2, 2, 1, 2, 0, -2, 0], [2, 4, -2, -4, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, -2, 0], [-1, -1, 0, 2, 2, 0, 4, 2, 2, 0, 0, -1, 2, 4, -4, 2], [-3, -6, 5, 5, -1, -1, -1, 1, -1, 1, -3, -3, -2, -1, -3, -3], [0, 1, 0, 0, 2, -1, 3, 3, 2, -3, -1, -2, 4, 4, -6, -3], [-3, -6, -1, -1, -4, -4, -1, 1, -2, 2, -2, -2, 2, 1, -2, -2], [1, 0, 0, 0, -3, 3, -3, -3, 1, 1, 2, -2, 0, 1, 5, -5], [1, 1, 0, -2, -1, 0, -2, -5, -1, 0, 0, 1, -3, -6, 2, 3], [5, 10, -3, -3, -2, -2, 1, -1, -2, 2, -4, -4, -2, -1, 0, 0], [-3, 0, 2, -2, 1, -1, -1, -1, 0, 0, -2, 2, 0, 1, 0, 0], [-2, -4, 4, 4, 1, 1, 5, -5, 5, -5, 1, 1, -6, -3, 1, 1], [0, -4, 0, 0, -2, 0, -2, 3, -2, 2, 0, 0, 1, 1, -1, -3], [2, 1, -2, -4, 0, -1, 3, -3, 0, -1, -1, -2, -2, -2, 0, 3], [-3, -6, 0, 0, -1, -1, 1, -1, 3, -3, -4, -4, 2, 1, -3, -3], [-4, 2, 0, 2, 4, -4, 1, 0, 0, -4, 0, 1, -1, -2, -1, 1], [3, 1, 1, 0, -6, 5, -1, -2, 6, 1, 3, 0, 1, -1, 1, -2], [3, 6, 0, 0, 1, 1, 1, -1, -4, 4, -2, -2, -6, -3, 4, 4], [1, 3, -4, -2, -1, 2, 2, 1, 3, -2, 0, 0, 3, 0, 2, 3], [-3, -4, 5, 0, 5, -2, -2, -1, -5, -3, 0, 0, -1, 1, -1, -1], [-1, 0, 0, 0, 2, -2, -2, -2, -1, -1, -1, 1, 0, 8, 3, -3], [2, 3, -2, -1, -2, 2, 0, 2, 4, -2, 2, 1, 6, 0, 0, 2], [-1, 7, 1, 2, -1, 0, 0, 4, -1, 1, -1, -2, -2, -2, -4, -4], [8, -5, 0, -3, -1, -3, -2, -1, -4, -3, 0, 8, 1, 2, 2, -1], [2, -2, -2, -4, -2, 0, -4, 2, -2, 2, 3, 6, 0, 0, 2, -2], [10, 4, 2, 0, -3, 1, 1, 0, 3, 2, 2, 0, -1, 1, 1, 0], [2, 4, 0, 0, -6, -6, 0, 0, -2, 2, 1, 1, 4, 2, 2, 2], [-2, 5, 0, -3, -4, 4, -5, -2, 0, 4, 0, -4, 3, 6, 5, -3], [3, 2, 2, 1, -3, -6, -3, 3, -3, 6, 6, 3, 0, 0, -3, 0], [1, 0, 0, -1, -4, 2, -4, 0, -2, 2, 0, 4, 2, 4, 4, -4], [2, -2, 0, 0, 1, -2, -1, 3, -1, -2, 0, 0, 0, 0, 1, -4], [-1, 0, -1, 0, 2, 1, -1, 1, -2, -3, 1, 0, 0, 0, -2, 1], [0, 0, -2, 2, 6, -6, 5, 5, -4, -4, -1, 1, 0, 7, -2, 2], [8, 12, -8, -4, 0, -3, 2, 2, -3, 3, 4, 2, -4, 0, 2, 4], [13, 13, 0, 0, 5, 2, 0, -3, -3, -2, -8, -4, -1, 0, 0, -3], [13, 0, -2, 2, 4, -4, 1, 1, -1, -1, 1, -1, 0, 5, 1, -1], [-3, -3, 3, 0, 2, 1, -5, -4, -2, -3, -9, 0, -1, 1, -1, -4], [-1, 0, -1, 0, -4, 2, 0, 2, 4, 2, 8, 0, 2, -2, -2, 2], [13, 13, 0, 0, 1, -1, 4, 1, -2, 1, -4, -2, -5, 0, 4, 5], [-2, -4, 2, 4, -2, -1, -3, 0, -2, 1, -3, -6, 1, 1, 3, 0], [-2, -2, 2, 0, -5, 0, 2, 2, 5, 5, 2, 0, -2, 2, 0, 2], [0, 0, -2, -2, -2, -2, -3, 3, -1, 1, 2, 2, 2, 1, -3, -3], [7, 14, -2, -2, -3, -3, -2, 2, -4, 4, -5, -5, 4, 2, -2, -2], [1, 0, 0, -1, 1, 4, 2, 1, 5, 4, 0, -3, 1, 2, -2, 1], [1, 2, -2, -1, 0, -3, 0, 0, -3, 3, 2, 1, 0, 0, 0, 0], [-7, -14, 8, 8, 1, 1, 0, 0, 3, -3, 5, 5, 0, 0, -3, -3], [-14, -9, 4, 0, -3, 7, -1, -6, 3, -4, -7, 0, 1, -1, 5, -6], [0, 0, -1, -1, -3, -3, 4, -4, -1, 1, 3, 3, -4, -2, 5, 5], [1, 3, -5, 0, 0, 2, -4, -4, 0, -2, 3, 0, 0, 0, 0, -4], [-2, -4, -2, -2, -2, -2, 3, -3, 2, -2, 0, 0, -2, -1, -2, -2], [-9, -4, -1, 0, 1, 1, 1, -3, -1, -2, 2, 0, 0, 0, 4, -3], [-1, -4, 1, 2, -2, -7, 3, -1, -2, -5, 5, 10, -4, -4, -2, 1], [2, -4, 0, 2, 6, 0, 2, 0, 6, 0, 0, 2, 0, 0, -2, 2], [-3, -8, 3, 6, 7, 7, 1, -1, 7, 0, -1, -2, -2, -2, 0, 1], [-12, 0, -1, 1, -8, 8, -4, -4, 5, 5, 0, 0, 0, 6, 7, -7], [-3, 7, 0, -4, -3, 1, 0, -3, -2, 1, 0, 1, -1, -2, 0, 3], [0, 0, 1, -1, -4, 4, -6, -6, 1, 1, -3, 3, 0, 4, 7, -7], [-4, 0, 0, 0, 5, -5, 8, 8, -1, -1, 2, -2, 0, 0, -9, 9], [-8, -6, 4, 0, 4, -4, -4, 0, -4, 0, -2, 0, -2, 2, -4, 0], [-11, -11, 0, 0, -3, -9, 1, -1, -6, 9, -2, -1, -2, 0, 1, 0], [-7, -13, 12, 6, 3, 8, 3, -5, 5, -8, -10, -5, -2, 0, 3, -2], [0, 7, 0, 0, 3, -2, 0, -5, 3, -5, 1, 2, -7, -7, 5, 5], [-3, 4, 3, 6, 5, 7, 5, -2, 5, 2, -3, -6, -5, -5, -3, 2], [-2, -4, 6, 6, -1, -1, -6, 6, -4, 4, 4, 4, 0, 0, -2, -2], [18, 0, -4, 4, 8, -8, 9, 9, -4, -4, 4, -4, 0, 1, -6, 6], [5, 4, 2, 1, 6, 2, 2, 2, -4, -2, 4, 2, -2, 0, 2, 4], [-2, 0, -4, 4, -4, 4, 5, 5, 6, 6, 7, -7, 0, -5, -4, 4], [5, 10, 4, 4, -6, -6, -2, 2, -6, 6, 0, 0, 0, 0, 0, 0], [5, 3, 4, 2, 0, -1, -5, 0, -1, 1, -12, -6, 5, 0, -5, -5], [16, 15, 2, 1, 4, 2, -3, 4, -2, -2, 2, 1, 5, 0, -3, 1], [-3, -12, 3, 6, 5, -1, 5, 0, 5, -6, -5, -10, 1, 1, -5, 0], [9, 18, -4, -4, 5, 5, -3, 3, -1, 1, -4, -4, 14, 7, 3, 3], [3, -5, -3, -6, 4, 2, -2, 0, 4, -2, -3, -6, 2, 2, 2, 0], [2, 3, -2, -1, -1, -5, -4, 1, -4, 5, 4, 2, -3, 0, -4, -3], [5, 5, 0, 0, -3, -5, 3, -5, -2, 5, -2, -1, -4, 0, 3, -2], [-4, 5, 0, -1, -7, -5, 0, -3, -12, -5, 0, 5, -3, -6, 0, 3], [0, 4, 0, -4, -2, 4, -6, 0, 2, 4, 0, -2, 0, 0, 6, -6], [-10, 0, -1, 1, -6, 6, -2, -2, 5, 5, -3, 3, 0, -4, 1, -1], [-5, -1, 0, 6, 3, -1, -1, 1, 2, -1, 0, -4, 0, 0, 1, -2], [-8, -7, -2, -1, 3, 3, 2, -3, 0, -3, 0, 0, -1, 0, 2, -1], [-16, 0, 2, -2, -2, 2, -1, -1, 2, 2, 4, -4, 0, 3, 0, 0], [0, 17, 0, 0, -1, -2, -2, -1, -1, -1, -2, -4, 7, 7, 3, 1], [-1, 8, 1, 2, 2, 4, 0, -2, 2, 2, 0, 0, 0, 0, 2, 2], [1, -3, -1, -2, 2, 3, 1, 2, 2, 1, -1, -2, 3, 3, -3, -2], [6, 1, 4, 0, 2, 1, -5, -5, -2, -3, -9, 0, 4, -4, 0, -5], [31, 19, -7, 0, 0, -2, 8, 9, 0, 2, -1, 0, -1, 1, -1, 9], [1, 2, 1, 1, 2, 2, -7, 7, -1, 1, -3, -3, -2, -1, -3, -3], [-2, -2, 0, 0, -4, 0, 2, 4, 4, 0, 2, 1, -4, 0, 2, 6], [-2, -1, -2, -1, 6, 8, 3, 2, 2, -8, 2, 1, 3, 0, 3, 5], [-10, 4, 0, 6, -6, 6, 0, -2, 0, 6, 0, -6, -2, -4, 0, 2], [-14, -28, 2, 2, 0, 0, 2, -2, 8, -8, 0, 0, -4, -2, -8, -8], [-2, -3, 2, 1, -4, 2, 3, -2, 6, -2, 4, 2, 3, 0, 3, 1], [5, 23, -5, -10, -4, -3, -5, -6, -4, 1, 1, 2, -3, -3, 11, 6], [13, 11, -9, 0, 2, -5, 7, 4, -2, 3, 1, 0, -3, 3, 3, 4], [4, 0, 5, -5, 1, -1, -4, -4, -10, -10, -7, 7, 0, 2, 6, -6], [-11, -8, 5, 0, -7, 4, -2, -5, 7, 3, -2, 0, -1, 1, 3, -5], [-19, 0, 1, -1, -2, 2, -3, -3, 2, 2, 2, -2, 0, 1, 6, -6], [8, 6, 4, 2, -1, -7, -4, 9, -6, 7, 8, 4, -1, 0, -4, 5], [10, 11, -2, -1, 7, -1, 3, 5, -8, 1, 8, 4, -6, 0, 3, 8], [-8, -16, 1, 1, -2, -2, -5, 5, -5, 5, 0, 0, 6, 3, -5, -5], [-4, -6, 8, 0, -1, 5, -7, -12, 1, -4, -2, 0, -1, 1, 5, -12], [4, 8, -3, -3, -6, -6, 0, 0, -7, 7, 6, 6, -8, -4, 5, 5], [3, 6, -6, -3, 2, 1, -4, 4, -1, -1, 4, 2, 12, 0, -4, 0], [5, 3, -1, 0, 0, -1, 3, 5, 0, 1, 3, 0, 4, -4, -2, 5], [-1, -9, 1, 2, 2, -5, 1, -2, 2, -7, -5, -10, -1, -1, 1, 2], [0, 10, 0, 0, 0, -4, 0, 2, 0, -4, 8, 16, 2, 2, -2, -2], [2, 3, 0, -5, 2, -6, -6, -4, -4, -6, 0, 6, 2, 4, 6, -2], [-5, -4, 5, 10, 3, -3, 7, -2, 3, -6, 4, 8, -11, -11, -5, 2], [-7, 5, 0, 2, -1, 3, -1, 1, 2, 3, 0, -5, 0, 0, 1, -2], [-5, -3, -4, -2, -1, 1, -7, 5, 2, -1, 4, 2, 10, 0, -7, -2], [29, 26, 6, 3, 4, 2, 2, 0, -2, -2, -8, -4, -8, 0, 2, 2], [3, 0, 0, 0, 13, -13, 3, 3, -7, -7, 2, -2, 0, 7, -3, 3], [15, 30, -4, -4, 1, 1, -1, 1, 0, 0, -2, -2, 6, 3, 8, 8], [4, -1, 0, -3, 9, -10, 10, 1, -1, -10, 0, 1, -3, -6, -10, 9], [-6, -12, -3, -3, 0, 0, -2, 2, 0, 0, 10, 10, -4, -2, 2, 2], [3, 7, -3, -6, -3, 1, -3, 3, -3, 4, -6, -12, 2, 2, 0, -3], [5, 6, -5, -10, -1, 3, -3, -2, -1, 4, 3, 6, 3, 3, 5, 2], [-2, -4, 1, 1, 4, 4, -10, 10, -5, 5, -3, -3, 12, 6, -9, -9], [-3, -6, 3, 6, 1, 5, -1, 0, 1, 4, 0, 0, -3, -3, 1, 0], [5, 10, -12, -12, 0, 0, 6, -6, 1, -1, -2, -2, -8, -4, 9, 9], [-4, -8, 3, 3, 2, 2, -4, 4, -5, 5, 7, 7, 4, 2, 1, 1], [4, 11, -4, -8, -8, 0, -6, -6, -8, 8, 0, 0, -10, -10, 12, 6], [-1, 0, 0, 1, -3, 0, -5, -1, -3, 0, 0, -1, 0, 0, 5, -4], [-5, -9, 8, 4, 5, 2, 5, -3, -3, -2, -18, -9, -6, 0, 5, 2], [17, 16, 2, 1, 3, -1, -1, 5, -4, 1, 0, 0, 6, 0, -1, 4], [10, -15, 0, 5, 4, -4, 9, 4, 0, -4, 0, -11, 3, 6, -9, 5], [-5, -7, 5, 10, 4, 5, 11, -4, 4, 1, -3, -6, -13, -13, -7, 4], [-31, -34, 6, 3, -6, 3, -4, -6, 9, -3, -6, -3, 8, 0, -4, -10], [16, 14, 4, 2, 8, 0, 2, 4, -8, 0, -4, -2, -2, 0, 2, 6], [-18, 13, 0, 5, 1, 4, 0, -1, 5, 4, 0, -7, 5, 10, 0, 1], [13, 26, -4, -4, -6, -6, 2, -2, -5, 5, -4, -4, -8, -4, -3, -3], [1, -2, 6, 3, 0, 1, 0, 0, 1, -1, 4, 2, -2, 0, 0, 0]]