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{'Lhash': '409507545236273821798364934796,776439526052975593423159762144,903887700795671142974302368700,1757105336645110734336927781196', 'a10': 0, 'a2': 0, 'a3': -4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55247.59061220756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 4, 10, 12, 9]], [5, [1, 0, -2, 0, 25]]], 'bad_primes': [2, 3, 5], 'central_character': '1920.1', 'coefficient_field': '1.1.1.1', 'conductor': 13589544960000, 'conductor_radical': 30, 'degree': 8, 'euler_factors': [[1], [1, 4, 10, 12, 9], [1, 0, -2, 0, 25], [1, 0, 4, 0, 102, 0, 196, 0, 2401], [1, 0, -44, 0, 726, 0, -5324, 0, 14641], [1, 16, 148, 880, 3766, 11440, 25012, 35152, 28561], [1, 0, -28, 0, 774, 0, -8092, 0, 83521], [1, 0, -20, 0, 822, 0, -7220, 0, 130321], [1, 0, -44, 0, 1542, 0, -23276, 0, 279841], [1, 0, 92, 0, 3798, 0, 77372, 0, 707281], [1, 0, 20, 0, 2022, 0, 19220, 0, 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'0.71304166986781221057140016004', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 55247.59061220756, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 13589544960000, 'conductor_radical': 30, 'degree': 8, 'dirichlet_coefficients': [1, 0, -4, 0, 0, 0, 0, 0, 6, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -37, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -44, 0, 726, 0, -5324, 0, 14641], 'euler13': [1, 16, 148, 880, 3766, 11440, 25012, 35152, 28561], 'euler17': [1, 0, -28, 0, 774, 0, -8092, 0, 83521], 'euler19': [1, 0, -20, 0, 822, 0, -7220, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -44, 0, 1542, 0, -23276, 0, 279841], 'euler29': [1, 0, 92, 0, 3798, 0, 77372, 0, 707281], 'euler3': [1, 4, 10, 12, 9, 0, 0, 0, 0], 'euler31': [1, 0, 20, 0, 2022, 0, 19220, 0, 923521], 'euler37': [1, -16, 244, -2032, 15574, -75184, 334036, -810448, 1874161], 'euler41': [1, 0, -100, 0, 5862, 0, -168100, 0, 2825761], 'euler43': [1, 0, -28, 0, 3894, 0, -51772, 0, 3418801], 'euler47': [1, 0, -140, 0, 9318, 0, -309260, 0, 4879681], 'euler5': [1, 0, -2, 0, 25, 0, 0, 0, 0], 'euler53': [1, 0, -196, 0, 15222, 0, -550564, 0, 7890481], 'euler59': [1, 0, -44, 0, 7446, 0, -153164, 0, 12117361], 'euler61': [1, 0, -52, 0, 8118, 0, -193492, 0, 13845841], 'euler67': [1, 0, -124, 0, 12822, 0, -556636, 0, 20151121], 'euler7': [1, 0, 4, 0, 102, 0, 196, 0, 2401], 'euler71': [1, 0, 284, 0, 30246, 0, 1431644, 0, 25411681], 'euler73': [1, 0, -100, 0, 13158, 0, -532900, 0, 28398241], 'euler79': [1, 0, -172, 0, 19878, 0, -1073452, 0, 38950081], 'euler83': [1, -24, 548, -6840, 78486, -567720, 3775172, -13722888, 47458321], 'euler89': [1, 0, -100, 0, 18342, 0, -792100, 0, 62742241], 'euler97': [1, 0, -388, 0, 56454, 0, -3650692, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 4, 10, 12, 9, 0, 0, 0, 0], [1, 0, -2, 0, 25, 0, 0, 0, 0], [1, 0, 4, 0, 102, 0, 196, 0, 2401], [1, 0, -44, 0, 726, 0, -5324, 0, 14641], [1, 16, 148, 880, 3766, 11440, 25012, 35152, 28561], [1, 0, -28, 0, 774, 0, -8092, 0, 83521], [1, 0, -20, 0, 822, 0, -7220, 0, 130321], [1, 0, -44, 0, 1542, 0, -23276, 0, 279841], [1, 0, 92, 0, 3798, 0, 77372, 0, 707281], [1, 0, 20, 0, 2022, 0, 19220, 0, 923521], [1, -16, 244, -2032, 15574, -75184, 334036, -810448, 1874161], [1, 0, -100, 0, 5862, 0, -168100, 0, 2825761], [1, 0, -28, 0, 3894, 0, -51772, 0, 3418801], [1, 0, -140, 0, 9318, 0, -309260, 0, 4879681], [1, 0, -196, 0, 15222, 0, -550564, 0, 7890481], [1, 0, -44, 0, 7446, 0, -153164, 0, 12117361], [1, 0, -52, 0, 8118, 0, -193492, 0, 13845841], [1, 0, -124, 0, 12822, 0, -556636, 0, 20151121], [1, 0, 284, 0, 30246, 0, 1431644, 0, 25411681], [1, 0, -100, 0, 13158, 0, -532900, 0, 28398241], [1, 0, -172, 0, 19878, 0, -1073452, 0, 38950081], [1, -24, 548, -6840, 78486, -567720, 3775172, -13722888, 47458321], [1, 0, -100, 0, 18342, 0, -792100, 0, 62742241], [1, 0, -388, 0, 56454, 0, -3650692, 0, 88529281]], 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1920/2/m/a'], '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': '8-1920e4-1.1-c1e4-0-25', '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': '8-1920e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9155174866275138, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1605848482566861933, 'z1': {'__RealLiteral__': 0, 'data': '0.32304449282992140779406087289', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '409507545236273821798364934796,776439526052975593423159762144,903887700795671142974302368700,1757105336645110734336927781196', 'Lhash_array': ['409507545236273821798364934796', '776439526052975593423159762144', '903887700795671142974302368700', '1757105336645110734336927781196'], 'label': '8-1920e4-1.1-c1e4-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1920/2/m/a'}