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  • lfunc_lfunctions • Show schema
    {'Lhash': '103184829344988929646366670101,545757730248285959595930690226,651051336554166795608387843298,906100307282503686913565133469,969766149372086836875994728491,1015420596663610127738782314078,1033151461586981824028770937246,1587436773538285731639456804367', 'a10': -160, 'a2': 4, 'a3': 2, 'a4': 0, 'a5': -40, 'a6': 8, 'a7': -32, 'a8': -44, 'a9': -25, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2791716692230790.5, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[5, [1, 40, 700, 7000, 43750, 175000, 437500, 625000, 390625]], [17, [1]]], 'bad_primes': [5, 17], 'central_character': '1445.1', 'coefficient_field': '1.1.1.1', 'conductor': 19008278076432370500390625, 'conductor_radical': 85, 'degree': 16, 'euler_factors': [[1, -4, 16, -20, 25, 136, -170, -272, 3904, -2176, -10880, 69632, 102400, -655360, 4194304, -8388608, 16777216], [1, -2, 29, -74, 1117, 724, 33510, -9120, 715922, -246240, 24428790, 14250492, 593619597, 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'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e8-0', 'trace_hash': 1274378859333542293, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.081398477882163589680451254129', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.43052693711502763806522014396', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '0.51358894669946963121213817615', 'prec': 97}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 2791716692230790.5, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 19008278076432370500390625, 'conductor_radical': 85, 'degree': 16, 'dirichlet_coefficients': [1, 4, 2, 0, -40, 8, -32, -44, -25, -160, 44, 0, 86, -128, -80, -121, 0, -100, 288, 0, -64, 176, -160, -88, 900, 344, -34, 0, 642, -320, 182, -16, 88, 0, 1280, 0, -490, 1152, 172, 1760, 72, -256, 1168, 0, 1000, -640, 216, -242, -259, 3600, 0, 0, 508, -136, -1760, 1408, 576, 2568, -918, 0, 1970, 728, 800, 618, -3440, 352, 2750, 0, -320, 5120, 1368, 1100, 582, -1960, 1800, 0, -1408, 688, 1256, 4840, -312, 288, 2534, 0, 0, 4672, 1284, -1936, 1200, 4000, -2752, 0, 364, 864, -11520, -32, -1698, -1036, -1100, 0], 'euler11': [1, -44, 3113, -81662, 7583982, -247447294, 15298441611, -372495383876, 20706399769338, -495791355938956, 27102122518824771, -583467775531498154, 23801784317341283022, -341122440010820891962, 17308022596901316600353, -325610997547359044453284, 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'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0, 0, 0, 0, 0], 'nu_real_doubled': [3, 3, 3, 3, 3, 3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '16-1445e8-1.1-c3e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.233512872049035, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e8-0', 'trace_hash': 1274378859333542293, 'z1': {'__RealLiteral__': 0, 'data': '0.081398477882163589680451254129', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '103184829344988929646366670101,545757730248285959595930690226,651051336554166795608387843298,906100307282503686913565133469,969766149372086836875994728491,1015420596663610127738782314078,1033151461586981824028770937246,1587436773538285731639456804367', 'Lhash_array': ['103184829344988929646366670101', '545757730248285959595930690226', '651051336554166795608387843298', '906100307282503686913565133469', '969766149372086836875994728491', '1015420596663610127738782314078', '1033151461586981824028770937246', '1587436773538285731639456804367'], 'factors': ['2-1445-1.1-c3-0-1', '2-1445-1.1-c3-0-33', '2-1445-1.1-c3-0-47', '2-1445-1.1-c3-0-85', '2-1445-1.1-c3-0-94', '2-1445-1.1-c3-0-103', '2-1445-1.1-c3-0-108', '2-1445-1.1-c3-0-188'], 'label': '16-1445e8-1.1-c3e8-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1445/4/a/r'}