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lfunc_lfunctions • Show schema
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{'Lhash': '1871299378823531144998858048629,2064460335733725047859915012638', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 237.9953425354976, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [7, [1, 2, 1]], [23, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '1932.1', 'coefficient_field': '1.1.1.1', 'conductor': 3732624, 'conductor_radical': 966, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, -1, 9, -5, 25], [1, 2, 1], [1, 4, 21, 44, 121], [1, -3, 27, -39, 169], [1, 0, 29, 0, 289], [1, 2, 19, 38, 361], [1, -2, 1], [1, -2, 39, -58, 841], [1, 8, 73, 248, 961], [1, 2, 55, 74, 1369], [1, -6, 71, -246, 1681], [1, 5, -9, 215, 1849], [1, 6, 98, 282, 2209], [1, 3, 77, 159, 2809], [1, 9, 137, 531, 3481], [1, 5, 67, 305, 3721], [1, 9, 153, 603, 4489], [1, 15, 187, 1065, 5041], [1, 14, 115, 1022, 5329], [1, 12, 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['1.47619492191824786851912018749550', '1.62857204923978028627735473440880', '2.69648303044189013539176822332609', '2.87585854646542638452068144524754', '3.84059241710182488095682273369893', '3.85544166182386658974120333312063', '4.76293495531927825566473534544758', '4.88057864523329737380107176581897', '5.61287756590038162270844640024001', '5.84197714289754961492890811541718', '6.07568979709678840556042024903547', '6.45173771275297721777090503582760', '7.12560688888952564741987005991595', '7.22458274767723424721983952467651', '7.940875296716682488891264803776282', '7.976278093522204236014832747717567', '8.835997115331228201459127588499201', '8.932526094701324319897592091111801'], 'prelabel': '4-1932e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9277344195491857, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1458442148755100134, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47619492191824786851912018750', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.62857204923978028627735473441', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.69648303044189013539176822333', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 237.9953425354976, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 3732624, 'conductor_radical': 966, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 1, 0, -2, 0, 3, 0, -4, 0, 3, 0, -2, 0, 0, 0, -2, 0, 4, 0, 2, 0, -8, 0, -4, 0, 2, 0, -8, 0, 8, 0, -2, 0, -2, 0, -6, 0, 6, 0, -5, 0, 3, 0, -6, 0, 3, 0, 0, 0, -3, 0, -4, 0, 4, 0, -9, 0, -5, 0, -6, 0, 3, 0, -9, 0, -4, 0, -15, 0, -14, 0, 16, 0, 8, 0, -12, 0, 5, 0, 2, 0, 0, 0, -4, 0, 1, 0, -6, 0, 16, 0, -2, 0, 4, 0, -12, 0], 'euler11': [1, 4, 21, 44, 121], 'euler13': [1, -3, 27, -39, 169], 'euler17': [1, 0, 29, 0, 289], 'euler19': [1, 2, 19, 38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -2, 1, 0, 0], 'euler29': [1, -2, 39, -58, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 8, 73, 248, 961], 'euler37': [1, 2, 55, 74, 1369], 'euler41': [1, -6, 71, -246, 1681], 'euler43': [1, 5, -9, 215, 1849], 'euler47': [1, 6, 98, 282, 2209], 'euler5': [1, -1, 9, -5, 25], 'euler53': [1, 3, 77, 159, 2809], 'euler59': [1, 9, 137, 531, 3481], 'euler61': [1, 5, 67, 305, 3721], 'euler67': [1, 9, 153, 603, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, 15, 187, 1065, 5041], 'euler73': [1, 14, 115, 1022, 5329], 'euler79': [1, 12, 189, 948, 6241], 'euler83': [1, -2, 87, -166, 6889], 'euler89': [1, -1, 167, -89, 7921], 'euler97': [1, -4, 193, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, -1, 9, -5, 25], [1, 2, 1, 0, 0], [1, 4, 21, 44, 121], [1, -3, 27, -39, 169], [1, 0, 29, 0, 289], [1, 2, 19, 38, 361], [1, -2, 1, 0, 0], [1, -2, 39, -58, 841], [1, 8, 73, 248, 961], [1, 2, 55, 74, 1369], [1, -6, 71, -246, 1681], [1, 5, -9, 215, 1849], [1, 6, 98, 282, 2209], [1, 3, 77, 159, 2809], [1, 9, 137, 531, 3481], [1, 5, 67, 305, 3721], [1, 9, 153, 603, 4489], [1, 15, 187, 1065, 5041], [1, 14, 115, 1022, 5329], [1, 12, 189, 948, 6241], [1, -2, 87, -166, 6889], [1, -1, 167, -89, 7921], [1, -4, 193, -388, 9409]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1932/2/a/d'], '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': '4-1932e2-1.1-c1e2-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-1932e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9277344195491857, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1458442148755100134, 'z1': {'__RealLiteral__': 0, 'data': '1.47619492191824786851912018750', 'prec': 103}}
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{'Lhash': '1871299378823531144998858048629,2064460335733725047859915012638', 'Lhash_array': ['1871299378823531144998858048629', '2064460335733725047859915012638'], 'label': '4-1932e2-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1932/2/a/d'}