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lfunc_lfunctions • Show schema
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{'Lhash': '2088812666457019298721666584989', 'a10': [0, 0], 'a2': [0, 1.0], 'a3': [0, -1.4316271137897454], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [1.4316271137897454, 0], 'a7': [0, 3.0871895794825526], 'a8': [0, -1.0], 'a9': [0.9504438070620432, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.182796232447249, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1150.599', 'coefficient_field': 'CDF', 'conductor': 1150, 'conductor_radical': 230, 'conjugate': '276304643225171054997475973547', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 1.4316271137897454], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.0871895794825526], [-7.0, 0]], [[1.0, 0], [6.469260500334341, 0], [11.0, 0]], [[1.0, 0], [0, 3.9504438070620433], [-13.0, 0]], [[1.0, 0], [0, 3.4316271137897454], [-17.0, 0]], 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'4.49262621326057561544454997089665', '5.53436210961633479786582690391636', '6.84158478020766761801411552888054', '7.72725600707832388562184896869199', '8.553374421385525067653688698619820', '9.625876225215222728654414908039001', '10.15949267786694263820499857127477'], 'prelabel': '2-1150-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.03031289348926, 'root_angle': 0.6475836176504333, 'root_number': '-0.447213595499957939281834733746255247088123671922305145 + 0.894427190999915878563669467492510494176247343844610290*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.32379180882521663', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64778265089839964617259187778', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96239023006359401949048792511', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11973678190586253740737030984', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.182796232447249, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 1150, 'conductor_radical': 230, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1150/2/b/j/599/5'], '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': '2-1150-5.4-c1-0-26', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1150-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.03031289348926, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64778265089839964617259187778', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2088812666457019298721666584989', 'Lhash_array': ['2088812666457019298721666584989'], 'label': '2-1150-5.4-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1150/2/b/j/599/5'}