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  • lfunc_lfunctions • Show schema
    {'Lhash': '560013972349752612595661733122,895081759386860479935760352475,1645539643944956040521622621687', 'a10': 0, 'a2': 3, 'a3': 0, 'a4': 4, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 172768.2590114603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [1]], [5, [1]], [31, [1, 3, 3, 1]]], 'bad_primes': [3, 5, 31], 'central_character': '6975.1', 'coefficient_field': '1.1.1.1', 'conductor': 339338109375, 'conductor_radical': 465, 'degree': 6, 'euler_factors': [[1, -3, 5, -7, 10, -12, 8], [1], [1], [1, 2, 9, 38, 63, 98, 343], [1, 2, 21, 36, 231, 242, 1331], [1, -6, 47, -154, 611, -1014, 2197], [1, -4, 47, -116, 799, -1156, 4913], [1, 8, 57, 272, 1083, 2888, 6859], [1, -14, 129, -720, 2967, -7406, 12167], [1, 16, 149, 938, 4321, 13456, 24389], [1, 3, 3, 1], [1, -8, 111, -518, 4107, -10952, 50653], [1, 4, 35, 344, 1435, 6724, 68921], [1, -2, 69, 28, 2967, -3698, 79507], [1, 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'5.28033980189679140955587911118214', '5.60020528458239895231990760703092', '5.75676985676852443743269371214119', '5.83196598435713284189776575828644', '6.31922024125828311458193441963398', '6.39435333405375968698295999486508', '6.89297254607190134576563131414219', '6.90109924633652150575161854755202', '6.93671119858379368346885290933097', '7.49555099231591270109475480608874', '7.60885915494742073605336536824631', '7.913614516282470242084080747766205', '7.914988891605803077667128947287241'], 'prelabel': '6-6975e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.4629521913143115, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 1686881729518592605, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44177312916424052158314077945', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.70609500695673463894405471007', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '1.29810189309947947989595162529', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 172768.2590114603, 'bad_primes': [3, 5, 31], 'central_character': '1.1', 'conductor': 339338109375, 'conductor_radical': 465, 'degree': 6, 'dirichlet_coefficients': [1, 3, 0, 4, 0, 0, -2, 4, 0, 0, -2, 0, 6, -6, 0, 3, 4, 0, -8, 0, 0, -6, 14, 0, 0, 18, 0, -8, -16, 0, -3, -1, 0, 12, 0, 0, 8, -24, 0, 0, -4, 0, 2, -8, 0, 42, 14, 0, -5, 0, 0, 24, 8, 0, 0, -8, 0, -48, 26, 0, -18, -9, 0, -2, 0, 0, 0, 16, 0, 0, -4, 0, 12, 24, 0, -32, 4, 0, 4, 0, 0, -12, -10, 0, 0, 6, 0, -8, 6, 0, -12, 56, 0, 42, 0, 0, -8, -15, 0, 0], 'euler11': [1, 2, 21, 36, 231, 242, 1331], 'euler13': [1, -6, 47, -154, 611, -1014, 2197], 'euler17': [1, -4, 47, -116, 799, -1156, 4913], 'euler19': [1, 8, 57, 272, 1083, 2888, 6859], 'euler2': [1, -3, 5, -7, 10, -12, 8], 'euler23': [1, -14, 129, -720, 2967, -7406, 12167], 'euler29': [1, 16, 149, 938, 4321, 13456, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, 3, 3, 1, 0, 0, 0], 'euler37': [1, -8, 111, -518, 4107, -10952, 50653], 'euler41': [1, 4, 35, 344, 1435, 6724, 68921], 'euler43': [1, -2, 69, 28, 2967, -3698, 79507], 'euler47': [1, -14, 49, 72, 2303, -30926, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -8, 87, -948, 4611, -22472, 148877], 'euler59': [1, -26, 379, -3534, 22361, -90506, 205379], 'euler61': [1, 18, 227, 1900, 13847, 66978, 226981], 'euler67': [1, 0, 65, 274, 4355, 0, 300763], 'euler7': [1, 2, 9, 38, 63, 98, 343], 'euler71': [1, 4, 215, 566, 15265, 20164, 357911], 'euler73': [1, -12, 155, -1618, 11315, -63948, 389017], 'euler79': [1, -4, 93, -1132, 7347, -24964, 493039], 'euler83': [1, 10, 205, 1272, 17015, 68890, 571787], 'euler89': [1, -6, 249, -1018, 22161, -47526, 704969], 'euler97': [1, 8, 51, -160, 4947, 75272, 912673], 'euler_factors': [[1, -3, 5, -7, 10, -12, 8], [1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 2, 9, 38, 63, 98, 343], [1, 2, 21, 36, 231, 242, 1331], [1, -6, 47, -154, 611, -1014, 2197], [1, -4, 47, -116, 799, -1156, 4913], [1, 8, 57, 272, 1083, 2888, 6859], [1, -14, 129, -720, 2967, -7406, 12167], [1, 16, 149, 938, 4321, 13456, 24389], [1, 3, 3, 1, 0, 0, 0], [1, -8, 111, -518, 4107, -10952, 50653], [1, 4, 35, 344, 1435, 6724, 68921], [1, -2, 69, 28, 2967, -3698, 79507], [1, -14, 49, 72, 2303, -30926, 103823], [1, -8, 87, -948, 4611, -22472, 148877], [1, -26, 379, -3534, 22361, -90506, 205379], [1, 18, 227, 1900, 13847, 66978, 226981], [1, 0, 65, 274, 4355, 0, 300763], [1, 4, 215, 566, 15265, 20164, 357911], [1, -12, 155, -1618, 11315, -63948, 389017], [1, -4, 93, -1132, 7347, -24964, 493039], [1, 10, 205, 1272, 17015, 68890, 571787], [1, -6, 249, -1018, 22161, -47526, 704969], [1, 8, 51, -160, 4947, 75272, 912673]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6975/2/a/bi'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '6-6975e3-1.1-c1e3-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-6975e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.4629521913143115, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1686881729518592605, 'z1': {'__RealLiteral__': 0, 'data': '0.44177312916424052158314077945', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '560013972349752612595661733122,895081759386860479935760352475,1645539643944956040521622621687', 'Lhash_array': ['560013972349752612595661733122', '895081759386860479935760352475', '1645539643944956040521622621687'], 'factors': ['2-6975-1.1-c1-0-24', '2-6975-1.1-c1-0-68', '2-6975-1.1-c1-0-192'], 'label': '6-6975e3-1.1-c1e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6975/2/a/bi'}