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lfunc_lfunctions • Show schema
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{'Lhash': '1647477695670032796208400788533', 'a10': [1.9432931554254107, -3.365882479197654], 'a2': [1.5052684055522954, -0.8690671191482565], 'a3': [-1.3348939299348108, 2.686644411868306], 'a4': [-0.4894446848307004, 0.8477430616213092], 'a5': [1.9364916731037085, -1.118033988749895], 'a6': [0.32550066170374053, 5.2042333721959295], 'a7': [2.934070242978031, 6.355409649209942], 'a8': [0.0, 8.653978082099025], 'a9': [-5.436116391646393, -7.172770634592563], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8610427757831176, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.3348939299348108, -2.686644411868306]]], [5, [[1.0, 0], [-1.9364916731037085, 1.118033988749895]]], [7, [[1.0, 0], [-2.934070242978031, -6.355409649209942]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.11', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': '3350484395915677275803504060952', 'degree': 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'6.44846412521882759303436777252987', '7.29920463470832880663546914105161', '8.886031487177644112716856014277322', '10.45640271089196112847887753194977', '11.32273367808857398680598906751411', '12.72452884369858109738864202607297', '13.46721378199116740649330076059559'], 'prelabel': '2-105-21.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6914617275549328, 'root_angle': -0.30404949629454336, 'root_number': '0.5774457579761909 - 0.8164290517830085*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.152024748147', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29963074633768867289222787532', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93829752235848479698122079859', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.45174740620404725243199332595', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8610427757831176, 'bad_primes': [3, 5, 7], 'central_character': '21.11', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/3/t/b/11/13'], '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': '2-105-21.11-c2-0-8', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-105-21.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6914617275549328, 'root_angle': -0.15202474814727168, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29963074633768867289222787532', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1647477695670032796208400788533', 'Lhash_array': ['1647477695670032796208400788533'], 'label': '2-105-21.11-c2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/3/t/b/11/13'}