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lfunc_lfunctions • Show schema
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{'Lhash': '1941143351737362449206546366314', 'a10': 0, 'a2': 2, 'a3': 0, 'a4': 4, 'a5': 0, 'a6': 0, 'a7': -14, 'a8': 8, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 79.65257850774987, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1350.1', 'coefficient_field': '1.1.1.1', 'conductor': 1350, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1, -2], [1], [1], [1, 14, 343], [1, -3, 1331], [1, 47, 2197], [1, -39, 4913], [1, -32, 6859], [1, -99, 12167], [1, -51, 24389], [1, -83, 29791], [1, 314, 50653], [1, 108, 68921], [1, 299, 79507], [1, 531, 103823], [1, 564, 148877], [1, -12, 205379], [1, -230, 226981], [1, -268, 300763], [1, -120, 357911], [1, 1106, 389017], [1, 739, 493039], [1, 1086, 571787], [1, 120, 704969], [1, -1642, 912673], [1, -33, 1030301], [1, -1198, 1092727], [1, -1542, 1225043], [1, 556, 1295029], [1, 1605, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [1], [1], [[[1, 14, 343], 1]], [[[1, -3, 1331], 1]], [[[1, 47, 2197], 1]], [[[1, -39, 4913], 1]], [[[1, -32, 6859], 1]], [[[1, -99, 12167], 1]], [[[1, -51, 24389], 1]], [[[1, -83, 29791], 1]], [[[1, 314, 50653], 1]], [[[1, 108, 68921], 1]], [[[1, 299, 79507], 1]], [[[1, 531, 103823], 1]], [[[1, 564, 148877], 1]], [[[1, -12, 205379], 1]], [[[1, -230, 226981], 1]], [[[1, -268, 300763], 1]], [[[1, -120, 357911], 1]], [[[1, 1106, 389017], 1]], [[[1, 739, 493039], 1]], [[[1, 1086, 571787], 1]], [[[1, 120, 704969], 1]], [[[1, -1642, 912673], 1]], [[[1, -33, 1030301], 1]], [[[1, -1198, 1092727], 1]], [[[1, -1542, 1225043], 1]], [[[1, 556, 1295029], 1]], [[[1, 1605, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 61, 'label': '2-1350-1.1-c3-0-61', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1350/4/a/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.8571811219866845e-60, 0.31062429767832006, 0.6181956036220686, 0.919680076641817, 1.2120825148236425, 1.4924664993296102, 1.7579754683508784, 2.0058549355525064, 2.2334759899203007, 2.4383601226610367, 2.6182053250567368, 2.770913292625728, 2.8946174595157133, 2.9877114767589035, 3.0488776428414193, 3.0771146988281406, 3.071764316659573, 3.032535541508411, 2.959526400182531, 2.8532418599869627, 2.7146073182282224, 2.5449768231570378, 2.346135273538959, 2.120293916565666, 1.8700785622032565, 1.598510055404881, 1.3089766943205046, 1.005198450472472, 0.6911830329186903, 0.37117403912747343, 0.04959164644685295, -0.26903348510191416, -0.5801322107174848, -0.8791736994308754, -1.161745732774434, -1.4236370196105008, -1.660919883656657, -1.8700315504145792, -2.0478521658684015, -2.1917776257154964, -2.2997852855837166, 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'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 2173285057133188910, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53129210161528466072454122651', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87369228441141289965083776799', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44202701952137217735425207239', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 79.65257850774987, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1350, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 4, 0, 0, -14, 8, 0, 0, 3, 0, -47, -28, 0, 16, 39, 0, 32, 0, 0, 6, 99, 0, 0, -94, 0, -56, 51, 0, 83, 32, 0, 78, 0, 0, -314, 64, 0, 0, -108, 0, -299, 12, 0, 198, -531, 0, -147, 0, 0, -188, -564, 0, 0, -112, 0, 102, 12, 0, 230, 166, 0, 64, 0, 0, 268, 156, 0, 0, 120, 0, -1106, -628, 0, 128, -42, 0, -739, 0, 0, -216, -1086, 0, 0, -598, 0, 24, -120, 0, 658, 396, 0, -1062, 0, 0, 1642, -294, 0, 0], 'euler11': [1, -3, 1331], 'euler13': [1, 47, 2197], 'euler17': [1, -39, 4913], 'euler19': [1, -32, 6859], 'euler2': [1, -2, 0], 'euler23': [1, -99, 12167], 'euler29': [1, -51, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -83, 29791], 'euler37': [1, 314, 50653], 'euler41': [1, 108, 68921], 'euler43': [1, 299, 79507], 'euler47': [1, 531, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 564, 148877], 'euler59': [1, -12, 205379], 'euler61': [1, -230, 226981], 'euler67': [1, -268, 300763], 'euler7': [1, 14, 343], 'euler71': [1, -120, 357911], 'euler73': [1, 1106, 389017], 'euler79': [1, 739, 493039], 'euler83': [1, 1086, 571787], 'euler89': [1, 120, 704969], 'euler97': [1, -1642, 912673], 'euler_factors': [[1, -2, 0], [1, 0, 0], [1, 0, 0], [1, 14, 343], [1, -3, 1331], [1, 47, 2197], [1, -39, 4913], [1, -32, 6859], [1, -99, 12167], [1, -51, 24389], [1, -83, 29791], [1, 314, 50653], [1, 108, 68921], [1, 299, 79507], [1, 531, 103823], [1, 564, 148877], [1, -12, 205379], [1, -230, 226981], [1, -268, 300763], [1, -120, 357911], [1, 1106, 389017], [1, 739, 493039], [1, 1086, 571787], [1, 120, 704969], [1, -1642, 912673]], 'index': 61, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1350/4/a/r/1/1', 'ModularForm/GL2/Q/holomorphic/1350/4/a/r'], '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': '2-1350-1.1-c3-0-61', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1350-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.924829326533358, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 2173285057133188910, 'z1': {'__RealLiteral__': 0, 'data': '1.53129210161528466072454122651', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21010658
{'Lhash': '1941143351737362449206546366314', 'Lhash_array': ['1941143351737362449206546366314'], 'label': '2-1350-1.1-c3-0-61', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1350/4/a/r'}
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id: 24591043
{'Lhash': '1941143351737362449206546366314', 'Lhash_array': ['1941143351737362449206546366314'], 'label': '2-1350-1.1-c3-0-61', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1350/4/a/r/1/1'}