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lfunc_lfunctions • Show schema
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{'Lhash': '1327117794406637985447293599374,2305295402454887604090194120298', 'a10': -216, 'a2': 3, 'a3': 0, 'a4': -9, 'a5': -72, 'a6': 0, 'a7': 0, 'a8': 15, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5002.628862019118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': '1.1.1.1', 'conductor': 194481, 'conductor_radical': 21, 'degree': 4, 'euler_factors': [[1, -3, 18, -96, 1024], [1], [1, 72, 7546, 225000, 9765625], [1], [1, 480, 376614, 77304480, 25937424601], [1, -1296, 912362, -481195728, 137858491849], [1, 936, 807586, 1328986152, 2015993900449], [1, 216, 961814, 534837384, 6131066257801], [1, -504, 12784878, -3243916872, 41426511213649], [1, 6372, 31409694, 130697041428, 420707233300201], [1, -9936, 65931134, -284459244336, 819628286980801], [1, -11124, 115818446, -771382177668, 4808584372417849], [1, 20952, 339207826, 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'primitive': False, 'rational': True, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c5e2-0', 'trace_hash': 1711446753092949164, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04691134463053307894317112920', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.81855741798239935593978434442', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54203190746228453997094126595', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 5002.628862019118, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 194481, 'conductor_radical': 21, 'degree': 4, 'dirichlet_coefficients': [1, 3, 0, -9, -72, 0, 0, 15, 0, -216, -480, 0, 1296, 0, 0, -529, -936, 0, -216, 648, 0, -1440, 504, 0, -2362, 3888, 0, 0, -6372, 0, 9936, -5793, 0, -2808, 0, 0, 11124, -648, 0, -1080, -20952, 0, -6264, 4320, 0, 1512, -7920, 0, 0, -7086, 0, -11664, -2220, 0, 34560, 0, 0, -19116, -29736, 0, -17280, 29808, 0, 2799, -93312, 0, -20680, 8424, 0, 0, 92280, 0, 56592, 33372, 0, 1944, 0, 0, -56096, 38088, 0, -62856, 71352, 0, 67392, -18792, 0, -7200, -123192, 0, 0, -4536, 0, -23760, 15552, 0, 35856, 0, 0, 21258], 'euler11': [1, 480, 376614, 77304480, 25937424601], 'euler13': [1, -1296, 912362, -481195728, 137858491849], 'euler17': [1, 936, 807586, 1328986152, 2015993900449], 'euler19': [1, 216, 961814, 534837384, 6131066257801], 'euler2': [1, -3, 18, -96, 1024], 'euler23': [1, -504, 12784878, -3243916872, 41426511213649], 'euler29': [1, 6372, 31409694, 130697041428, 420707233300201], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -9936, 65931134, -284459244336, 819628286980801], 'euler37': [1, -11124, 115818446, -771382177668, 4808584372417849], 'euler41': [1, 20952, 339207826, 2427419123352, 13422659310152401], 'euler43': [1, 6264, 25906310, 920860886952, 21611482313284249], 'euler47': [1, 7920, -101923298, 1816412455440, 52599132235830049], 'euler5': [1, 72, 7546, 225000, 9765625], 'euler53': [1, 2220, 769983534, 928393994460, 174887470365513049], 'euler59': [1, 29736, 1614887590, 21258988955064, 511116753300641401], 'euler61': [1, 17280, 707051402, 14594624081280, 713342911662882601], 'euler67': [1, 20680, 781129014, 27920587212760, 1822837804551761449], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -92280, 5423120334, -166494284510280, 3255243551009881201], 'euler73': [1, -56592, 4777720274, -117319267591056, 4297625829703557649], 'euler79': [1, 56096, 4914766302, 172610555758304, 9468276082626847201], 'euler83': [1, -71352, 4792627990, -281058427959336, 15516041187205853449], 'euler89': [1, 123192, 14311603186, 687911451641208, 31181719929966183601], 'euler97': [1, -35856, -1009376254, -307907672254992, 73742412689492826049], 'euler_factors': [[1, -3, 18, -96, 1024], [1, 0, 0, 0, 0], [1, 72, 7546, 225000, 9765625], [1, 0, 0, 0, 0], [1, 480, 376614, 77304480, 25937424601], [1, -1296, 912362, -481195728, 137858491849], [1, 936, 807586, 1328986152, 2015993900449], [1, 216, 961814, 534837384, 6131066257801], [1, -504, 12784878, -3243916872, 41426511213649], [1, 6372, 31409694, 130697041428, 420707233300201], [1, -9936, 65931134, -284459244336, 819628286980801], [1, -11124, 115818446, -771382177668, 4808584372417849], [1, 20952, 339207826, 2427419123352, 13422659310152401], [1, 6264, 25906310, 920860886952, 21611482313284249], [1, 7920, -101923298, 1816412455440, 52599132235830049], [1, 2220, 769983534, 928393994460, 174887470365513049], [1, 29736, 1614887590, 21258988955064, 511116753300641401], [1, 17280, 707051402, 14594624081280, 713342911662882601], [1, 20680, 781129014, 27920587212760, 1822837804551761449], [1, -92280, 5423120334, -166494284510280, 3255243551009881201], [1, -56592, 4777720274, -117319267591056, 4297625829703557649], [1, 56096, 4914766302, 172610555758304, 9468276082626847201], [1, -71352, 4792627990, -281058427959336, 15516041187205853449], [1, 123192, 14311603186, 687911451641208, 31181719929966183601], [1, -35856, -1009376254, -307907672254992, 73742412689492826049]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/a/q'], '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': '4-21e4-1.1-c5e2-0-5', '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': 2, 'prelabel': '4-21e4-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 1711446753092949164, 'z1': {'__RealLiteral__': 0, 'data': '1.04691134463053307894317112920', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1327117794406637985447293599374,2305295402454887604090194120298', 'Lhash_array': ['1327117794406637985447293599374', '2305295402454887604090194120298'], 'label': '4-21e4-1.1-c5e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/q'}