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lfunc_lfunctions • Show schema
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{'Lhash': '163270109363165208747062283486,1104238404539610429734397343684', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -28, 'a6': 0, 'a7': 98, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26136.183442385598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -98, 2401]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.1', 'coefficient_field': '1.1.1.1', 'conductor': 1016064, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1], [1, 28, 2342, 87500, 9765625], [1, -98, 2401], [1, 596, 209810, 95986396, 25937424601], [1, -532, 747678, -197527876, 137858491849], [1, 2100, 3445630, 2981699700, 2015993900449], [1, -2744, 6243606, -6794415656, 6131066257801], [1, 3660, 14411722, 23557015380, 41426511213649], [1, -720, 28281754, -14768027280, 420707233300201], [1, 3976, 26474190, 113829504376, 819628286980801], [1, -6788, 69768750, -470706780116, 4808584372417849], [1, -4004, 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'1.71116122489511082502060352037', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 26136.183442385598, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1016064, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -28, 0, 98, 0, 0, 0, -596, 0, 532, 0, 0, 0, -2100, 0, 2744, 0, 0, 0, -3660, 0, -1558, 0, 0, 0, 720, 0, -3976, 0, 0, 0, -2744, 0, 6788, 0, 0, 0, 4004, 0, -19480, 0, 0, 0, 21560, 0, 7203, 0, 0, 0, -57576, 0, 16688, 0, 0, 0, 22344, 0, -38724, 0, 0, 0, -14896, 0, -7288, 0, 0, 0, 3932, 0, 19292, 0, 0, 0, -58408, 0, -15632, 0, 0, 0, 22624, 0, 58800, 0, 0, 0, -112812, 0, 52136, 0, 0, 0, -76832, 0, -36036, 0, 0, 0], 'euler11': [1, 596, 209810, 95986396, 25937424601], 'euler13': [1, -532, 747678, -197527876, 137858491849], 'euler17': [1, 2100, 3445630, 2981699700, 2015993900449], 'euler19': [1, -2744, 6243606, -6794415656, 6131066257801], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 3660, 14411722, 23557015380, 41426511213649], 'euler29': [1, -720, 28281754, -14768027280, 420707233300201], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 3976, 26474190, 113829504376, 819628286980801], 'euler37': [1, -6788, 69768750, -470706780116, 4808584372417849], 'euler41': [1, -4004, 203212622, -463888228804, 13422659310152401], 'euler43': [1, 19480, 337403910, 2863724469640, 21611482313284249], 'euler47': [1, -21560, 472446158, -4944678350920, 52599132235830049], 'euler5': [1, 28, 2342, 87500, 9765625], 'euler53': [1, 57576, 1664335546, 24078023704968, 174887470365513049], 'euler59': [1, -22344, 1540856326, -15974268536856, 511116753300641401], 'euler61': [1, 38724, 1471462046, 32706147159924, 713342911662882601], 'euler67': [1, 7288, 1671047286, 9839711779816, 1822837804551761449], 'euler7': [1, -98, 2401, 0, 0], 'euler71': [1, -3932, 3486638858, -7094229808132, 3255243551009881201], 'euler73': [1, -19292, 2681901078, -39993697172156, 4297625829703557649], 'euler79': [1, 15632, 5584565598, 48100545629168, 9468276082626847201], 'euler83': [1, -22624, 7152673286, -89116855507232, 15516041187205853449], 'euler89': [1, 112812, 14123112334, 629948914560588, 31181719929966183601], 'euler97': [1, 36036, 8894455622, 309453393501252, 73742412689492826049], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 28, 2342, 87500, 9765625], [1, -98, 2401, 0, 0], [1, 596, 209810, 95986396, 25937424601], [1, -532, 747678, -197527876, 137858491849], [1, 2100, 3445630, 2981699700, 2015993900449], [1, -2744, 6243606, -6794415656, 6131066257801], [1, 3660, 14411722, 23557015380, 41426511213649], [1, -720, 28281754, -14768027280, 420707233300201], [1, 3976, 26474190, 113829504376, 819628286980801], [1, -6788, 69768750, -470706780116, 4808584372417849], [1, -4004, 203212622, -463888228804, 13422659310152401], [1, 19480, 337403910, 2863724469640, 21611482313284249], [1, -21560, 472446158, -4944678350920, 52599132235830049], [1, 57576, 1664335546, 24078023704968, 174887470365513049], [1, -22344, 1540856326, -15974268536856, 511116753300641401], [1, 38724, 1471462046, 32706147159924, 713342911662882601], [1, 7288, 1671047286, 9839711779816, 1822837804551761449], [1, -3932, 3486638858, -7094229808132, 3255243551009881201], [1, -19292, 2681901078, -39993697172156, 4297625829703557649], [1, 15632, 5584565598, 48100545629168, 9468276082626847201], [1, -22624, 7152673286, -89116855507232, 15516041187205853449], [1, 112812, 14123112334, 629948914560588, 31181719929966183601], [1, 36036, 8894455622, 309453393501252, 73742412689492826049]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/6/a/bj'], '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': '4-1008e2-1.1-c5e2-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 0, 'prelabel': '4-1008e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 12.714829545514345, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 1809606153005448218, 'z1': {'__RealLiteral__': 0, 'data': '0.12879740626776010187684498022', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '163270109363165208747062283486,1104238404539610429734397343684', 'Lhash_array': ['163270109363165208747062283486', '1104238404539610429734397343684'], 'factors': ['2-1008-1.1-c5-0-0', '2-1008-1.1-c5-0-33'], 'label': '4-1008e2-1.1-c5e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/6/a/bj'}