
# q-expansion of newform 1050.2.bc.f, downloaded from the LMFDB on 17 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 = 1050
weight = 2
poly_data = [1679616, 0, -1306368, 0, 672624, 0, -194544, 0, 40705, 0, -5404, 0, 519, 0, -28, 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], [[0, 1559363223744, 0, -1048992541632, 0, 320563651380, 0, -54184962811, 0, 5822728240, 0, -340572477, 0, 12398488, 0, -2107], 1091452828032], [[1559363223744, 0, -1048992541632, 0, 320563651380, 0, -54184962811, 0, 5822728240, 0, -340572477, 0, 12398488, 0, -2107, 0], 181908804672], [[-87800666688, 0, 39264450624, 0, -15792050700, 0, 2897647075, 0, -398280184, 0, 26810709, 0, -1267888, 0, 11299, 0], 12993486048], [[100335652560, 0, -122817017232, 0, 32313724443, 0, -7670501839, 0, 1048998769, 0, -109750641, 0, 6070207, 0, -236299, 0], 136431603504], [[0, -348009515532, 0, 123446110131, 0, -45329453883, 0, 6704863382, 0, -823985897, 0, 32000682, 0, -908495, 0, -90523], 204647405256], [[0, 94833934272, 0, -35554785300, 0, 5273830425, 0, -479450177, 0, -14543173, 0, 5317761, 0, -458203, 0, 17575], 38980458144], [[-667398916800, 0, 163015417944, 0, -31002566364, 0, -7211681519, 0, 1771996688, 0, -307019433, 0, 19357688, 0, -961463, 0], 272863207008], [[-14125104000, 0, 9299398752, 0, -3406609584, 0, 718144501, 0, -98147980, 0, 9009267, 0, -483532, 0, 15973, 0], 3389605056], [[-242518237920, 0, 322801951680, 0, -134626595796, 0, 29388081667, 0, -4086660592, 0, 339648981, 0, -17467576, 0, 443203, 0], 90954402336], [[0, -63434342592, 0, 1083154212, 0, 9236878637, 0, -3994950813, 0, 733266583, 0, -85575203, 0, 5115945, 0, -198541], 90954402336], [[0, 7949027664, 0, -2301711228, 0, 642448512, 0, -12141473, 0, -4730788, 0, 1857273, 0, -127492, 0, 7603], 1917071712], [[0, 1746136865088, 0, -2905816074768, 0, 1107271381356, 0, -328567062775, 0, 51247418824, 0, -6005325921, 0, 351463840, 0, -14621479], 3274358484096], [[0, -14125104000, 0, 9299398752, 0, -3406609584, 0, 718144501, 0, -98147980, 0, 9009267, 0, -483532, 0, 15973], 3389605056], [[1746136865088, 0, -2905816074768, 0, 1107271381356, 0, -328567062775, 0, 51247418824, 0, -6005325921, 0, 351463840, 0, -14621479, 0], 545726414016]]

hecke_ring_character_values = [[701, [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], [127, [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]], [451, [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]
aps_data = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 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, 0, 0, -1, 0, 0, 0], [-1, 0, 0, 0, 1, 1, 0, 0, 1, -1, 1, 0, 0, 0, 0, -1], [0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, -1, 0], [0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0], [-1, 0, 0, 0, 0, -1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 1, 0, 1, 0], [-1, 0, 0, -1, 2, 2, 0, 0, 1, -2, 1, 0, 0, 0, 0, -1], [0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1], [0, -1, 0, 0, 0, 0, -3, -1, 0, 0, 0, 5, -1, 1, 1, 0], [-1, 0, 0, 0, 1, 0, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 7, 1, 0, 0, 0, 1, 1, -6, 0, 0], [0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, -5, 1, 0, 0, 0, 1, 1, 0, 1, 0], [-2, 0, 0, 0, 2, -4, 0, 0, 2, -2, 2, 0, 0, 0, 0, -2], [0, 0, 0, -1, -1, 1, 0, 0, 5, -6, -1, 0, 0, 0, 0, 1], [0, 3, -6, 0, 0, 0, -1, -1, 0, 0, 0, -1, -2, -2, 1, 0], [6, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1], [0, -1, 5, 0, 0, 0, -5, 0, 0, 0, 0, 0, 1, 12, 0, 0], [0, 0, 0, -1, -1, 1, 0, 0, 7, -8, 0, 0, 0, 0, 0, 0], [0, 1, -6, 0, 0, 0, 1, 1, 0, 0, 0, -5, 1, 0, 2, 0], [7, 0, 0, -2, 2, 9, 0, 0, 7, 3, -1, 0, 0, 0, 0, -1], [0, 2, 0, 0, 0, 0, 3, -4, 0, 0, 0, -4, -2, -5, 2, 0], [1, 0, 0, 2, 1, 1, 0, 0, 3, -1, -1, 0, 0, 0, 0, -3], [0, -3, 0, 0, 0, 0, 2, 2, 0, 0, 0, 3, 2, 0, 3, 0], [0, 2, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 6, -2, 0], [-11, 0, 0, -1, 1, -5, 0, 0, -5, -1, -1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 11, -2, 0, 0, 0, -2, -1, -12, 1, 0], [0, 1, 0, 0, 0, 0, -4, 2, 0, 0, 0, 2, 1, -5, 3, 0], [-6, 0, 0, 1, 1, 5, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, -3, -6, 0, 0, 0, 9, 0, 0, 0, 0, 0, 3, -12, 0, 0], [-3, 0, 0, 0, 3, 0, 0, 0, -2, 1, -3, 0, 0, 0, 0, 0], [-8, 0, 0, 4, 4, 4, 0, 0, 8, -4, 2, 0, 0, 0, 0, -2], [3, 0, 0, -1, -3, -8, 0, 0, -2, 1, -3, 0, 0, 0, 0, 2], [0, -1, -6, 0, 0, 0, 0, 0, 0, 0, 0, -12, -1, 0, 0, 0], [0, -1, 2, 0, 0, 0, 1, -1, 0, 0, 0, 0, 1, -6, -1, 0], [0, -2, 0, 0, 0, 0, -4, 4, 0, 0, 0, 4, 2, 6, -2, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -2, 0], [-10, 0, 0, 2, 2, -4, 0, 0, 10, -2, -2, 0, 0, 0, 0, -4], [5, 0, 0, 3, -2, 6, 0, 0, -3, 0, 1, 0, 0, 0, 0, 3], [-5, 0, 0, 0, 0, -5, 0, 0, 1, -1, -1, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, -2, 6, 0, 0, 0, 4, -2, 0, 0, 0, 4, -2, 6, -4, 0], [1, 0, 0, 2, -1, -5, 0, 0, -2, 3, -1, 0, 0, 0, 0, 3], [6, 0, 0, -4, -5, 0, 0, 0, -4, 0, 1, 0, 0, 0, 0, 4], [0, 1, -5, 0, 0, 0, 1, 1, 0, 0, 0, -4, 1, 0, 2, 0], [0, 2, -6, 0, 0, 0, 10, 2, 0, 0, 0, -10, 4, 0, 2, 0], [-5, 0, 0, 2, -2, -7, 0, 0, 6, 6, -1, 0, 0, 0, 0, -1], [0, -2, 12, 0, 0, 0, -4, 4, 0, 0, 0, 10, -4, -6, -2, 0], [5, 0, 0, 2, -1, 8, 0, 0, -2, 4, 1, 0, 0, 0, 0, 2], [5, 0, 0, 1, -5, 0, 0, 0, -10, 5, 5, 0, 0, 0, 0, 4], [4, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0], [0, -4, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 2, 0, -4, 0], [0, 1, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 0, 2, -1, -23, 0, 0, 3, -7, -1, 0, 0, 0, 0, 3], [1, 0, 0, -3, -3, 2, 0, 0, 11, -14, -1, 0, 0, 0, 0, 1], [0, -3, -6, 0, 0, 0, 10, -2, 0, 0, 0, -2, 5, -10, 2, 0], [13, 0, 0, -2, -1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 2], [0, -1, 1, 0, 0, 0, -12, 1, 0, 0, 0, 1, 0, 24, -1, 0], [0, -3, 0, 0, 0, 0, -3, -3, 0, 0, 0, -3, -3, 0, -6, 0], [0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 0, -4, -4, 0], [-9, 0, 0, -3, 3, -3, 0, 0, -6, -3, -3, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 9, -3, 0, 0, 0, -1, -3, -6, -1, 0], [0, -7, 0, 0, 0, 0, 4, 4, 0, 0, 0, -2, 4, 0, 7, 0], [-6, 0, 0, -4, 4, -2, 0, 0, 7, 1, -1, 0, 0, 0, 0, -1], [0, 1, 6, 0, 0, 0, 1, -2, 0, 0, 0, 4, 1, 0, -1, 0], [0, 0, -6, 0, 0, 0, -5, 5, 0, 0, 0, 5, -5, 0, -5, 0], [-11, 0, 0, 1, -4, 0, 0, 0, -11, 6, 5, 0, 0, 0, 0, -1], [0, 1, 0, 0, 0, 0, -14, 7, 0, 0, 0, 7, -8, 12, -7, 0], [-4, 0, 0, -4, -4, 8, 0, 0, -2, -2, -2, 0, 0, 0, 0, 2], [0, 0, -12, 0, 0, 0, 2, -2, 0, 0, 0, -26, -2, 0, -2, 0], [0, -1, 10, 0, 0, 0, -1, 1, 0, 0, 0, 6, -1, -12, -1, 0], [10, 0, 0, -1, 3, 26, 0, 0, 1, 5, 2, 0, 0, 0, 0, -1], [0, -3, 0, 0, 0, 0, 11, -1, 0, 0, 0, 17, -1, -6, 3, 0], [-9, 0, 0, -8, 3, -3, 0, 0, 1, -3, -3, 0, 0, 0, 0, 5], [0, -2, 24, 0, 0, 0, -4, 4, 0, 0, 0, 16, -4, -2, -2, 0], [-10, 0, 0, 0, 0, -10, 0, 0, 2, -2, -2, 0, 0, 0, 0, -2], [0, 0, 0, -4, 0, 8, 0, 0, 9, -18, 0, 0, 0, 0, 0, -4], [1, 0, 0, 5, 0, 0, 0, 0, -7, 6, 5, 0, 0, 0, 0, -5], [1, 0, 0, 5, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, -5], [5, 0, 0, -1, -5, 3, 0, 0, -10, 15, -5, 0, 0, 0, 0, 4], [0, -2, -2, 0, 0, 0, -8, 1, 0, 0, 0, -1, -2, -6, -1, 0], [-12, 0, 0, 1, -1, -13, 0, 0, -7, -6, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 2, -6, 3, 0], [4, 0, 0, -1, 3, 14, 0, 0, 1, 4, 2, 0, 0, 0, 0, -1], [0, 6, 0, 0, 0, 0, 9, -5, 0, 0, 0, 13, -5, -7, -6, 0], [0, 0, 0, -2, 2, 4, 0, 0, 2, -10, 0, 0, 0, 0, 0, -2], [0, 5, -7, 0, 0, 0, -5, -9, 0, 0, 0, -2, -5, 0, 4, 0], [0, 1, -12, 0, 0, 0, -6, 6, 0, 0, 0, 0, -6, -12, 1, 0], [4, 0, 0, -5, -4, -18, 0, 0, 1, -6, -4, 0, 0, 0, 0, -1], [0, 1, 0, 0, 0, 0, -15, 2, 0, 0, 0, 2, -3, 24, -2, 0], [27, 0, 0, 1, 4, 0, 0, 0, 13, -6, -3, 0, 0, 0, 0, -1], [7, 0, 0, 2, 2, -9, 0, 0, 4, -2, 5, 0, 0, 0, 0, -5], [0, 0, -18, 0, 0, 0, -6, 6, 0, 0, 0, -12, 0, -6, 6, 0], [8, 0, 0, 5, -5, 3, 0, 0, -4, 9, 4, 0, 0, 0, 0, 4], [-14, 0, 0, -1, -2, -8, 0, 0, 3, 2, 2, 0, 0, 0, 0, 3], [0, 7, 0, 0, 0, 0, 10, -2, 0, 0, 0, -4, -2, -6, -7, 0], [-10, 0, 0, 2, -2, -12, 0, 0, 13, 13, -1, 0, 0, 0, 0, -1], [0, -3, 6, 0, 0, 0, -15, -1, 0, 0, 0, 5, -3, -12, -4, 0], [0, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -12, 0, 0], [0, -2, -6, 0, 0, 0, 15, -7, 0, 0, 0, -7, 9, -12, 7, 0], [-7, 0, 0, -2, -2, 9, 0, 0, 1, -3, 1, 0, 0, 0, 0, -1], [-3, 0, 0, 1, 3, 6, 0, 0, -4, 11, 3, 0, 0, 0, 0, -2], [0, 2, -12, 0, 0, 0, -4, 4, 0, 0, 0, -20, 6, 0, 4, 0], [0, 0, -6, 0, 0, 0, -24, -4, 0, 0, 0, 2, 0, 24, 4, 0], [0, 2, 0, 0, 0, 0, -5, -5, 0, 0, 0, 7, -5, 0, -2, 0], [6, 0, 0, 5, -6, 0, 0, 0, 17, 6, 6, 0, 0, 0, 0, 1], [11, 0, 0, -1, 3, 28, 0, 0, 1, -8, 2, 0, 0, 0, 0, -1], [0, -5, 24, 0, 0, 0, -2, 2, 0, 0, 0, 14, -2, -5, -5, 0], [0, 6, 6, 0, 0, 0, -5, -5, 0, 0, 0, 7, 1, 0, -5, 0], [0, -4, 6, 0, 0, 0, 8, 3, 0, 0, 0, 9, -4, 12, -1, 0], [-1, 0, 0, -2, 1, 11, 0, 0, -9, 19, 1, 0, 0, 0, 0, -3], [8, 0, 0, 5, 8, 0, 0, 0, 5, 0, -3, 0, 0, 0, 0, -5], [-2, 0, 0, -1, 2, -2, 0, 0, 3, -4, 2, 0, 0, 0, 0, -3], [0, 2, -23, 0, 0, 0, -4, -5, 0, 0, 0, -28, 2, -6, -3, 0], [0, -6, 12, 0, 0, 0, 10, 4, 0, 0, 0, 28, -2, 0, 4, 0], [0, -6, 12, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, -6, 0], [5, 0, 0, -7, -4, 2, 0, 0, 7, -8, -11, 0, 0, 0, 0, -7], [19, 0, 0, 1, 5, 12, 0, 0, -6, -5, -5, 0, 0, 0, 0, -6], [0, 0, -11, 0, 0, 0, 0, 2, 0, 0, 0, 13, 0, 0, -2, 0], [0, 5, -24, 0, 0, 0, 4, -4, 0, 0, 0, -16, 4, -6, 5, 0], [0, -2, 0, 0, 0, 0, 16, 6, 0, 0, 0, 6, 4, 0, 6, 0], [12, 0, 0, -5, -5, -7, 0, 0, 1, -6, 1, 0, 0, 0, 0, -1], [8, 0, 0, 2, -2, 0, 0, 0, 14, -6, 4, 0, 0, 0, 0, -2], [13, 0, 0, -9, -9, -4, 0, 0, -12, 3, -1, 0, 0, 0, 0, 1], [11, 0, 0, 1, -1, 10, 0, 0, -19, -16, 1, 0, 0, 0, 0, 1], [0, -7, 12, 0, 0, 0, 8, 3, 0, 0, 0, -9, 7, -1, 4, 0], [0, -1, 0, 0, 0, 0, 5, 5, 0, 0, 0, -20, 5, 0, 1, 0], [7, 0, 0, -5, 7, 7, 0, 0, 21, -7, -7, 0, 0, 0, 0, -2], [0, -6, 0, 0, 0, 0, 18, -7, 0, 0, 0, -7, 6, -12, 13, 0], [-2, 0, 0, -2, 2, 0, 0, 0, 15, 7, -3, 0, 0, 0, 0, -3], [0, -1, -12, 0, 0, 0, 10, -2, 0, 0, 0, -14, -1, 11, -3, 0], [13, 0, 0, -5, -5, -8, 0, 0, -1, -4, -1, 0, 0, 0, 0, 1], [-8, 0, 0, -4, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 4], [0, 0, -6, 0, 0, 0, -9, 3, 0, 0, 0, 3, -3, 12, -3, 0], [0, 5, -12, 0, 0, 0, 20, -2, 0, 0, 0, -26, 3, 0, -2, 0], [0, 5, 0, 0, 0, 0, -23, 3, 0, 0, 0, 3, -5, 18, -8, 0], [-10, 0, 0, 2, 2, -4, 0, 0, 16, -2, -2, 0, 0, 0, 0, -4], [1, 0, 0, -5, 3, 8, 0, 0, 5, -4, -2, 0, 0, 0, 0, -5], [-4, 0, 0, 1, -1, -5, 0, 0, -16, -7, 4, 0, 0, 0, 0, 4], [0, -1, 11, 0, 0, 0, 3, 4, 0, 0, 0, 26, 3, 0, 4, 0], [0, 7, -18, 0, 0, 0, 1, -5, 0, 0, 0, -23, 7, -6, 2, 0], [2, 0, 0, 3, -2, 16, 0, 0, -4, 6, -2, 0, 0, 0, 0, 5], [-9, 0, 0, -6, -3, 0, 0, 0, -6, 0, -3, 0, 0, 0, 0, 6], [0, 3, -4, 0, 0, 0, 9, 5, 0, 0, 0, 1, 3, 6, 8, 0], [0, 0, 0, 0, 0, 0, -22, -4, 0, 0, 0, -4, -4, 0, -4, 0], [-28, 0, 0, -1, 1, -27, 0, 0, 2, -3, -2, 0, 0, 0, 0, -2], [0, 3, -12, 0, 0, 0, 7, -7, 0, 0, 0, -13, 7, 6, 3, 0], [0, -6, 0, 0, 0, 0, 19, 9, 0, 0, 0, 21, 9, -5, 6, 0], [-1, 0, 0, 0, 1, 0, 0, 0, 0, -6, 1, 0, 0, 0, 0, 0], [0, 0, 11, 0, 0, 0, -6, 7, 0, 0, 0, -4, 0, 6, -7, 0], [0, -4, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, -2, -18, -4, 0], [0, 1, 24, 0, 0, 0, -12, 0, 0, 0, 0, 0, -1, 22, 0, 0], [8, 0, 0, -1, -5, 0, 0, 0, -1, 0, 4, 0, 0, 0, 0, 1], [19, 0, 0, 2, 2, -21, 0, 0, 15, -13, -7, 0, 0, 0, 0, 7], [8, 0, 0, -6, 6, 14, 0, 0, 8, -14, -8, 0, 0, 0, 0, -8], [0, -4, 12, 0, 0, 0, -6, 6, 0, 0, 0, -6, 4, 10, -2, 0], [-1, 0, 0, -8, -1, -1, 0, 0, -15, 1, 1, 0, 0, 0, 0, 9], [0, 6, 0, 0, 0, 0, -14, -2, 0, 0, 0, -14, -2, 6, -6, 0], [0, -2, -12, 0, 0, 0, -10, 6, 0, 0, 0, 18, 2, 12, -4, 0], [0, 5, -24, 0, 0, 0, -2, -9, 0, 0, 0, -33, 5, -7, -4, 0], [4, 0, 0, 5, 5, -9, 0, 0, 20, -15, 2, 0, 0, 0, 0, -2], [0, 3, 12, 0, 0, 0, 21, -6, 0, 0, 0, -6, 3, -36, 6, 0], [0, 8, -30, 0, 0, 0, -6, -2, 0, 0, 0, -2, -6, 0, 2, 0], [10, 0, 0, -5, -10, -2, 0, 0, 7, -24, -10, 0, 0, 0, 0, 5], [0, 7, 0, 0, 0, 0, -19, -9, 0, 0, 0, -9, -2, 0, -9, 0], [-13, 0, 0, 4, 3, -20, 0, 0, -4, 18, 7, 0, 0, 0, 0, 4], [0, -2, 0, 0, 0, 0, 8, -4, 0, 0, 0, -22, -4, -6, 2, 0], [6, 0, 0, -2, 6, 6, 0, 0, 40, -6, -6, 0, 0, 0, 0, -4], [6, 0, 0, 2, -7, -2, 0, 0, -2, 22, -5, 0, 0, 0, 0, 2], [-4, 0, 0, 10, -10, -14, 0, 0, -10, 8, 4, 0, 0, 0, 0, 4], [0, 4, -7, 0, 0, 0, 16, 0, 0, 0, 0, -14, 4, 0, 0, 0], [1, 0, 0, 6, -1, 23, 0, 0, -12, 23, -1, 0, 0, 0, 0, 7], [6, 0, 0, 7, 7, 0, 0, 0, -17, 12, 0, 0, 0, 0, 0, -7], [15, 0, 0, -7, -2, 0, 0, 0, -19, 6, -5, 0, 0, 0, 0, 7], [8, 0, 0, -6, -8, -32, 0, 0, -14, 20, -8, 0, 0, 0, 0, 2], [0, -4, -1, 0, 0, 0, 8, -1, 0, 0, 0, -2, -4, 12, -5, 0], [-12, 0, 0, -5, 5, -7, 0, 0, 0, -17, -6, 0, 0, 0, 0, -6], [0, -4, 0, 0, 0, 0, 38, 2, 0, 0, 0, 26, 2, -18, 4, 0], [12, 0, 0, 0, 0, 24, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, -2, -12, 0, 0, 0, 2, -8, 0, 0, 0, 4, 2, 0, 10, 0], [0, 4, 0, 0, 0, 0, 6, -6, 0, 0, 0, -6, 6, 18, 4, 0], [0, 1, -12, 0, 0, 0, 15, 2, 0, 0, 0, -22, 3, 0, 2, 0], [0, 0, 0, 0, 0, 18, 0, 0, 24, -48, 0, 0, 0, 0, 0, 0], [0, -1, 12, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, -2, -1, 0], [0, -6, 20, 0, 0, 0, 16, 2, 0, 0, 0, 2, 4, -24, -2, 0], [1, 0, 0, 7, 7, -8, 0, 0, -17, 24, 5, 0, 0, 0, 0, -5], [-8, 0, 0, 0, 4, -2, 0, 0, 46, -4, -4, 0, 0, 0, 0, -4], [0, -5, 0, 0, 0, 0, -7, 5, 0, 0, 0, 10, 5, 6, 5, 0], [0, -6, 6, 0, 0, 0, 0, 10, 0, 0, 0, 4, 6, 6, -4, 0], [10, 0, 0, -2, 2, 12, 0, 0, -3, -11, -3, 0, 0, 0, 0, -3], [4, 0, 0, -5, -5, 1, 0, 0, -10, 5, 2, 0, 0, 0, 0, -2], [0, 2, 18, 0, 0, 0, 11, -7, 0, 0, 0, -7, 5, -12, 7, 0], [0, -6, -18, 0, 0, 0, 30, -6, 0, 0, 0, -6, 12, -36, 6, 0], [1, 0, 0, 5, -1, -10, 0, 0, 12, -25, -1, 0, 0, 0, 0, 6], [0, 0, -48, 0, 0, 0, 2, -2, 0, 0, 0, -26, 2, 12, 0, 0], [0, -6, 12, 0, 0, 0, 0, 0, 0, 0, 0, -12, 6, 6, 6, 0], [0, -6, 0, 0, 0, 0, -36, 0, 0, 0, 0, 12, 0, 18, 6, 0], [36, 0, 0, 6, -12, 12, 0, 0, 0, 12, 12, 0, 0, 0, 0, 6], [0, 0, 0, 5, 0, 0, 0, 0, -5, 22, 5, 0, 0, 0, 0, 5], [0, 5, 12, 0, 0, 0, -2, 2, 0, 0, 0, 8, -2, -4, 5, 0], [0, 0, 0, -5, 0, 40, 0, 0, 5, -10, 0, 0, 0, 0, 0, -5], [26, 0, 0, -2, 0, 0, 0, 0, -14, 6, -2, 0, 0, 0, 0, 2], [0, 8, 12, 0, 0, 0, -16, 0, 0, 0, 0, 24, 8, 0, 0, 0], [-24, 0, 0, 1, -1, -25, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0], [0, -9, 12, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 12, -9, 0], [-30, 0, 0, -3, 3, -54, 0, 0, 3, -6, 0, 0, 0, 0, 0, -3], [-10, 0, 0, 9, -12, -11, 0, 0, -15, 12, 12, 0, 0, 0, 0, 3], [0, 4, 0, 0, 0, 0, -10, -8, 0, 0, 0, 4, -8, 1, -4, 0], [-9, 0, 0, -7, 4, -10, 0, 0, 7, 4, -3, 0, 0, 0, 0, -7], [0, -3, -5, 0, 0, 0, -9, 1, 0, 0, 0, 6, 3, 12, 2, 0], [0, 5, -36, 0, 0, 0, 2, -2, 0, 0, 0, -20, 2, -6, 5, 0], [2, 0, 0, 5, -2, -6, 0, 0, 5, -12, -2, 0, 0, 0, 0, 7], [-3, 0, 0, -4, -4, 7, 0, 0, 26, -30, 2, 0, 0, 0, 0, -2], [0, 0, 12, 0, 0, 0, -2, -5, 0, 0, 0, -5, 5, 14, 5, 0], [-12, 0, 0, -6, 12, 0, 0, 0, 12, -12, -12, 0, 0, 0, 0, -6], [0, -8, 0, 0, 0, 0, -18, 6, 0, 0, 0, -18, 6, 12, 8, 0], [0, 5, -18, 0, 0, 0, -5, -1, 0, 0, 0, 17, -5, 0, -4, 0], [14, 0, 0, 1, -1, 13, 0, 0, 0, 13, 6, 0, 0, 0, 0, 6], [3, 0, 0, -15, -12, 0, 0, 0, -1, -7, -3, 0, 0, 0, 0, 15], [-7, 0, 0, 4, 4, 3, 0, 0, -5, 9, 7, 0, 0, 0, 0, -7], [0, -6, 24, 0, 0, 0, -1, 1, 0, 0, 0, 13, -1, 12, -6, 0], [0, 6, -6, 0, 0, 0, -6, -6, 0, 0, 0, 0, -6, 0, 0, 0], [0, 0, 0, -3, -3, -6, 0, 0, 3, 17, -6, 0, 0, 0, 0, -3], [0, 6, 0, 0, 0, 0, -33, 3, 0, 0, 0, -3, 3, 18, -6, 0], [2, 0, 0, -3, -10, -4, 0, 0, -7, 10, 10, 0, 0, 0, 0, 13], [0, -9, 0, 0, 0, 0, -15, 15, 0, 0, 0, 15, -15, 26, -9, 0], [-6, 0, 0, 4, -4, -10, 0, 0, 0, 16, 6, 0, 0, 0, 0, 6], [0, -9, 1, 0, 0, 0, 15, 12, 0, 0, 0, 14, 3, 0, 12, 0], [-9, 0, 0, -2, 9, 31, 0, 0, -1, 11, 9, 0, 0, 0, 0, -11], [11, 0, 0, 4, -7, 0, 0, 0, -20, 12, 11, 0, 0, 0, 0, -4], [2, 0, 0, -7, -2, -18, 0, 0, 17, -36, -2, 0, 0, 0, 0, -5], [0, 0, -1, 0, 0, 0, 6, 1, 0, 0, 0, 0, 0, 6, 1, 0], [0, -3, 6, 0, 0, 0, 38, -1, 0, 0, 0, 11, -4, 0, -1, 0], [-7, 0, 0, 3, -3, -10, 0, 0, 30, 35, 1, 0, 0, 0, 0, 1], [0, 1, 12, 0, 0, 0, 2, -2, 0, 0, 0, 4, 2, -12, 1, 0], [-14, 0, 0, 6, 2, -24, 0, 0, -6, -12, 8, 0, 0, 0, 0, 6], [12, 0, 0, 3, 3, 30, 0, 0, -3, 6, 6, 0, 0, 0, 0, 3], [0, 10, -6, 0, 0, 0, 9, -1, 0, 0, 0, -13, 9, 0, -1, 0], [-6, 0, 0, 8, 8, -2, 0, 0, 12, -4, 0, 0, 0, 0, 0, 0], [0, 7, -25, 0, 0, 0, 7, -2, 0, 0, 0, -2, -5, -24, 2, 0], [9, 0, 0, 0, 0, -9, 0, 0, 8, -8, 9, 0, 0, 0, 0, -9], [0, 1, 12, 0, 0, 0, 19, -6, 0, 0, 0, 6, 1, 18, -5, 0], [-3, 0, 0, 9, -9, -12, 0, 0, -15, 12, 9, 0, 0, 0, 0, 9], [0, -2, -12, 0, 0, 0, 4, -11, 0, 0, 0, 1, 2, -2, 13, 0], [25, 0, 0, 4, 1, 13, 0, 0, -1, -1, -1, 0, 0, 0, 0, -5], [31, 0, 0, 3, 7, 19, 0, 0, 9, -7, -7, 0, 0, 0, 0, -10], [0, 12, 12, 0, 0, 0, -42, -7, 0, 0, 0, -19, -12, 30, -5, 0], [0, -5, 0, 0, 0, 0, 18, 10, 0, 0, 0, 10, -5, 23, 5, 0], [24, 0, 0, -12, -12, -12, 0, 0, -12, 0, -12, 0, 0, 0, 0, 12], [0, -5, 36, 0, 0, 0, -12, 11, 0, 0, 0, 11, -6, 12, -11, 0], [5, 0, 0, -2, -3, 0, 0, 0, -16, 7, 1, 0, 0, 0, 0, 2], [0, 2, -6, 0, 0, 0, 20, 2, 0, 0, 0, 2, -4, -48, -2, 0], [8, 0, 0, -3, -3, -5, 0, 0, 22, -25, 4, 0, 0, 0, 0, -4], [6, 0, 0, -2, -6, -28, 0, 0, -4, 2, -6, 0, 0, 0, 0, 4], [0, -9, 6, 0, 0, 0, -1, 3, 0, 0, 0, 15, -6, 0, 3, 0], [0, 2, -12, 0, 0, 0, -2, -4, 0, 0, 0, 8, -2, 0, 2, 0], [0, 2, 12, 0, 0, 0, -11, 11, 0, 0, 0, 17, -11, -2, 2, 0], [0, -13, 7, 0, 0, 0, 3, 4, 0, 0, 0, 18, -9, 0, 4, 0], [0, 4, 12, 0, 0, 0, -8, -2, 0, 0, 0, 10, 4, -12, 2, 0], [-6, 0, 0, 1, 6, 16, 0, 0, 16, -26, 6, 0, 0, 0, 0, -5], [0, 6, 2, 0, 0, 0, 6, -12, 0, 0, 0, -10, 6, 0, -6, 0], [0, -3, 18, 0, 0, 0, -33, -6, 0, 0, 0, 30, -9, 0, -6, 0], [-19, 0, 0, -6, 6, -13, 0, 0, -2, -18, -5, 0, 0, 0, 0, -5], [4, 0, 0, 4, -2, 4, 0, 0, -4, 14, 2, 0, 0, 0, 0, 4], [-6, 0, 0, -12, 6, 0, 0, 0, 12, -18, -6, 0, 0, 0, 0, -12], [0, 0, 6, 0, 0, 0, -12, 8, 0, 0, 0, 2, 0, 12, -8, 0], [0, -6, 0, 0, 0, 0, -3, -3, 0, 0, 0, -3, -9, 0, -3, 0], [-20, 0, 0, -7, -7, 27, 0, 0, -11, 4, -5, 0, 0, 0, 0, 5], [0, 4, -12, 0, 0, 0, -4, -6, 0, 0, 0, -6, 2, 12, 6, 0], [0, 6, 43, 0, 0, 0, -2, -4, 0, 0, 0, -4, -2, 0, 4, 0], [18, 0, 0, -7, -7, -11, 0, 0, -5, -2, -6, 0, 0, 0, 0, 6], [0, 3, -6, 0, 0, 0, -20, 2, 0, 0, 0, 8, -3, 17, -5, 0], [0, 3, 0, 0, 0, 0, -6, -6, 0, 0, 0, 13, -6, 0, -3, 0], [0, 8, 0, 0, 0, 0, -40, -4, 0, 0, 0, -16, -4, 18, -8, 0], [-15, 0, 0, 2, -3, -9, 0, 0, -41, 3, 3, 0, 0, 0, 0, 1], [-31, 0, 0, -6, 6, -25, 0, 0, 18, 0, -6, 0, 0, 0, 0, -6], [-10, 0, 0, 2, 2, 8, 0, 0, -20, 22, 4, 0, 0, 0, 0, -4], [0, -3, -24, 0, 0, 0, 33, 0, 0, 0, 0, 0, 3, -60, 0, 0], [-7, 0, 0, 6, 7, 14, 0, 0, 1, 5, 7, 0, 0, 0, 0, -1], [0, -5, 6, 0, 0, 0, 47, 2, 0, 0, 0, -4, 5, -42, 3, 0], [-10, 0, 0, 4, -7, -34, 0, 0, -4, -22, -3, 0, 0, 0, 0, 4], [0, 9, 24, 0, 0, 0, 7, -7, 0, 0, 0, 5, 7, -17, 9, 0], [25, 0, 0, 0, 0, 25, 0, 0, -5, -19, -7, 0, 0, 0, 0, -7], [0, -2, 5, 0, 0, 0, 16, 6, 0, 0, 0, 16, 4, 0, 6, 0], [0, 15, 6, 0, 0, 0, 3, -9, 0, 0, 0, -3, 15, -12, 6, 0], [0, 0, 0, 5, 0, 14, 0, 0, -36, 72, 0, 0, 0, 0, 0, 5], [18, 0, 0, 5, -7, 0, 0, 0, 5, 0, 12, 0, 0, 0, 0, -5], [0, 0, 0, -12, 0, -24, 0, 0, 24, -48, 0, 0, 0, 0, 0, -12], [0, 4, 0, 0, 0, 0, 39, -7, 0, 0, 0, -7, -3, 0, -7, 0], [0, -2, 12, 0, 0, 0, 3, -3, 0, 0, 0, 3, 3, 6, -2, 0], [13, 0, 0, 3, 2, 30, 0, 0, -3, 6, 5, 0, 0, 0, 0, 3], [0, -5, 11, 0, 0, 0, -25, 2, 0, 0, 0, -9, 5, 30, 3, 0], [7, 0, 0, 2, -7, -5, 0, 0, 3, -13, -7, 0, 0, 0, 0, 9], [2, 0, 0, 0, 0, -2, 0, 0, -32, 32, -8, 0, 0, 0, 0, 8], [0, -17, 6, 0, 0, 0, -17, 19, 0, 0, 0, 25, -17, 0, 2, 0], [-20, 0, 0, -5, 5, -15, 0, 0, 28, -9, -16, 0, 0, 0, 0, -16], [0, 0, 12, 0, 0, 0, -13, 3, 0, 0, 0, -9, 0, 13, -3, 0], [0, -11, 0, 0, 0, 0, 11, -1, 0, 0, 0, 1, -1, -6, 11, 0], [0, 6, 0, 0, 0, 0, -14, 10, 0, 0, 0, -2, 10, 12, -6, 0], [15, 0, 0, 4, -9, 3, 0, 0, -10, 9, 9, 0, 0, 0, 0, 5]]
