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lfunc_lfunctions • Show schema
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{'Lhash': '1608627337505236076133165229746', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -16, 'a6': 0, 'a7': 7, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.473925285786564, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -7]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.1', 'coefficient_field': '1.1.1.1', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1], [1], [1, 16, 125], [1, -7], [1, 8, 1331], [1, -28, 2197], [1, 54, 4913], [1, -110, 6859], [1, -48, 12167], [1, -110, 24389], [1, 12, 29791], [1, 246, 50653], [1, 182, 68921], [1, 128, 79507], [1, -324, 103823], [1, -162, 148877], [1, -810, 205379], [1, 488, 226981], [1, 244, 300763], [1, 768, 357911], [1, 702, 389017], [1, 440, 493039], [1, 1302, 571787], [1, 730, 704969], [1, -294, 912673], [1, -688, 1030301], [1, 1388, 1092727], [1, -244, 1225043], [1, -90, 1295029], [1, 1318, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, 16, 125], 1]], [[[1, -7], 1]], [[[1, 8, 1331], 1]], [[[1, -28, 2197], 1]], [[[1, 54, 4913], 1]], [[[1, -110, 6859], 1]], [[[1, -48, 12167], 1]], [[[1, -110, 24389], 1]], [[[1, 12, 29791], 1]], [[[1, 246, 50653], 1]], [[[1, 182, 68921], 1]], [[[1, 128, 79507], 1]], [[[1, -324, 103823], 1]], [[[1, -162, 148877], 1]], [[[1, -810, 205379], 1]], [[[1, 488, 226981], 1]], [[[1, 244, 300763], 1]], [[[1, 768, 357911], 1]], [[[1, 702, 389017], 1]], [[[1, 440, 493039], 1]], [[[1, 1302, 571787], 1]], [[[1, 730, 704969], 1]], [[[1, -294, 912673], 1]], [[[1, -688, 1030301], 1]], [[[1, 1388, 1092727], 1]], [[[1, -244, 1225043], 1]], [[[1, -90, 1295029], 1]], [[[1, 1318, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-1008-1.1-c3-0-28', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 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'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 267736808726278946, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26898321762764660535375187153', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88076824465994371591170499655', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80631318277586038798836781027', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 59.473925285786564, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -16, 0, 7, 0, 0, 0, -8, 0, 28, 0, 0, 0, -54, 0, 110, 0, 0, 0, 48, 0, 131, 0, 0, 0, 110, 0, -12, 0, 0, 0, -112, 0, -246, 0, 0, 0, -182, 0, -128, 0, 0, 0, 324, 0, 49, 0, 0, 0, 162, 0, 128, 0, 0, 0, 810, 0, -488, 0, 0, 0, -448, 0, -244, 0, 0, 0, -768, 0, -702, 0, 0, 0, -56, 0, -440, 0, 0, 0, -1302, 0, 864, 0, 0, 0, -730, 0, 196, 0, 0, 0, -1760, 0, 294, 0, 0, 0], 'euler11': [1, 8, 1331], 'euler13': [1, -28, 2197], 'euler17': [1, 54, 4913], 'euler19': [1, -110, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -48, 12167], 'euler29': [1, -110, 24389], 'euler3': [1, 0, 0], 'euler31': [1, 12, 29791], 'euler37': [1, 246, 50653], 'euler41': [1, 182, 68921], 'euler43': [1, 128, 79507], 'euler47': [1, -324, 103823], 'euler5': [1, 16, 125], 'euler53': [1, -162, 148877], 'euler59': [1, -810, 205379], 'euler61': [1, 488, 226981], 'euler67': [1, 244, 300763], 'euler7': [1, -7, 0], 'euler71': [1, 768, 357911], 'euler73': [1, 702, 389017], 'euler79': [1, 440, 493039], 'euler83': [1, 1302, 571787], 'euler89': [1, 730, 704969], 'euler97': [1, -294, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 16, 125], [1, -7, 0], [1, 8, 1331], [1, -28, 2197], [1, 54, 4913], [1, -110, 6859], [1, -48, 12167], [1, -110, 24389], [1, 12, 29791], [1, 246, 50653], [1, 182, 68921], [1, 128, 79507], [1, -324, 103823], [1, -162, 148877], [1, -810, 205379], [1, 488, 226981], [1, 244, 300763], [1, 768, 357911], [1, 702, 389017], [1, 440, 493039], [1, 1302, 571787], [1, 730, 704969], [1, -294, 912673]], 'index': 28, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/4/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/1008/4/a/c'], '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': '2-1008-1.1-c3-0-28', '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': '2-1008-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.711933952374499, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 267736808726278946, 'z1': {'__RealLiteral__': 0, 'data': '1.26898321762764660535375187153', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20137199
{'Lhash': '1608627337505236076133165229746', 'Lhash_array': ['1608627337505236076133165229746'], 'label': '2-1008-1.1-c3-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/4/a/c'}
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id: 24579685
{'Lhash': '1608627337505236076133165229746', 'Lhash_array': ['1608627337505236076133165229746'], 'label': '2-1008-1.1-c3-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/4/a/c/1/1'}