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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 58782.34041762576, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 14459006250000, 'conductor_radical': 390, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 24, 0, 0, 0, 0, 1, 0, 0, 0, 0, 20, 0, 0, 6, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 12, 0, 0, -1, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 6, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0], 'euler11': [1, -6, 5, -54, 444, -594, 605, -7986, 14641], 'euler13': [1, 0, -1, 0, 169, 0, 0, 0, 0], 'euler17': [1, 0, 34, 0, 867, 0, 9826, 0, 83521], 'euler19': [1, -6, -11, -54, 1164, -1026, -3971, -41154, 130321], 'euler2': [1, 0, -1, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, 30, 0, 371, 0, 15870, 0, 279841], 'euler29': [1, 8, -10, 128, 2779, 3712, -8410, 195112, 707281], 'euler3': [1, 0, -1, 0, 1, 0, 0, 0, 0], 'euler31': [1, -24, 340, -3096, 20454, -95976, 326740, -714984, 923521], 'euler37': [1, 0, -7, 0, -1320, 0, -9583, 0, 1874161], 'euler41': [1, -20, 218, -2000, 15043, -82000, 366458, -1378420, 2825761], 'euler43': [1, 0, -14, 0, -1653, 0, -25886, 0, 3418801], 'euler47': [1, 0, -170, 0, 11643, 0, -375530, 0, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -50, 0, 6243, 0, -140450, 0, 7890481], 'euler59': [1, -24, 314, -3456, 31179, -203904, 1093034, -4929096, 12117361], 'euler61': [1, -12, -14, -432, 12459, -26352, -52094, -2723772, 13845841], 'euler67': [1, 0, 70, 0, 411, 0, 314230, 0, 20151121], 'euler7': [1, 0, 5, 0, -24, 0, 245, 0, 2401], 'euler71': [1, -28, 446, -5488, 53539, -389648, 2248286, -10021508, 25411681], 'euler73': [1, 0, -164, 0, 17382, 0, -873956, 0, 28398241], 'euler79': [1, 24, 532, 6552, 72870, 517608, 3320212, 11832936, 38950081], 'euler83': [1, 0, 180, 0, 21878, 0, 1240020, 0, 47458321], 'euler89': [1, 6, -151, 54, 23844, 4806, -1196071, 4229814, 62742241], 'euler97': [1, 0, 130, 0, 7491, 0, 1223170, 0, 88529281], 'euler_factors': [[1, 0, -1, 0, 1, 0, 0, 0, 0], [1, 0, -1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 5, 0, -24, 0, 245, 0, 2401], [1, -6, 5, -54, 444, -594, 605, -7986, 14641], [1, 0, -1, 0, 169, 0, 0, 0, 0], [1, 0, 34, 0, 867, 0, 9826, 0, 83521], [1, -6, -11, -54, 1164, -1026, -3971, -41154, 130321], [1, 0, 30, 0, 371, 0, 15870, 0, 279841], [1, 8, -10, 128, 2779, 3712, -8410, 195112, 707281], [1, -24, 340, -3096, 20454, -95976, 326740, -714984, 923521], [1, 0, -7, 0, -1320, 0, -9583, 0, 1874161], [1, -20, 218, -2000, 15043, -82000, 366458, -1378420, 2825761], [1, 0, -14, 0, -1653, 0, -25886, 0, 3418801], [1, 0, -170, 0, 11643, 0, -375530, 0, 4879681], [1, 0, -50, 0, 6243, 0, -140450, 0, 7890481], [1, -24, 314, -3456, 31179, -203904, 1093034, -4929096, 12117361], [1, -12, -14, -432, 12459, -26352, -52094, -2723772, 13845841], [1, 0, 70, 0, 411, 0, 314230, 0, 20151121], [1, -28, 446, -5488, 53539, -389648, 2248286, -10021508, 25411681], [1, 0, -164, 0, 17382, 0, -873956, 0, 28398241], [1, 24, 532, 6552, 72870, 517608, 3320212, 11832936, 38950081], [1, 0, 180, 0, 21878, 0, 1240020, 0, 47458321], [1, 6, -151, 54, 23844, 4806, -1196071, 4229814, 62742241], [1, 0, 130, 0, 7491, 0, 1223170, 0, 88529281]], 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1950/2/z/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': '8-1950e4-1.1-c1e4-0-37', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-1950e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1394530168613975902, 'z1': {'__RealLiteral__': 0, 'data': '0.56145356035458715993867243585', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '711726942783768836096474634717,1313578376977531320079520662364,1406548139456089409359905374489,1451355592970644643061907808148', 'Lhash_array': ['711726942783768836096474634717', '1313578376977531320079520662364', '1406548139456089409359905374489', '1451355592970644643061907808148'], 'label': '8-1950e4-1.1-c1e4-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/z/d'}