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lfunc_lfunctions • Show schema
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{'Lhash': '1964788370704576509401980292863', 'a10': [1207074045252611300000, 249913160610924500000], 'a2': [-2053599.295198327, -425178.1342742532], 'a3': [0, 8664572310.37139], 'a4': [4036493619374.1304, 1746291033758.6921], 'a5': [-587784602417307.4, 0], 'a6': [3683986689208063.0, -17793559589773624], 'a7': [0, -1084007383476745100], 'a8': [-7546855688185880000, -5302410862233428000], 'a9': [34344175809857760000, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.69108286884106, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '21.0', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [2053599.295198327, 425178.1342742532]]]], 'bad_primes': [2], 'central_character': '4.3', 'coefficient_field': 'CDF', 'conductor': 4, 'conductor_radical': 2, 'conjugate': '1651386707095481393063205161', 'degree': 2, 'euler_factors': [[[1.0, 0], [2053599.295198327, 425178.1342742532]], [[1.0, 0], [0, -8664572310.37139], [-109418989131512370000, 0]], [[1.0, 0], [587784602417307.4, 0], 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'root_angle': -0.8700302711435274, 'root_number': '-0.91779239014025055540802861760660647408764496569516256208 - 0.39706061073927506249018020624704220147795829785375523083*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4350151355717637', 'prec': 64}, 'spectral_label': 'c42-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54994473268172913790997425568', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86352451578898157777156145118', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.47930329791952300019854995912', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.69108286884106, 'bad_primes': [2], 'central_character': '4.3', 'conductor': 4, 'conductor_radical': 2, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4/43/b/a/3/3'], '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': '2-2e2-4.3-c42-0-15', 'motivic_weight': 42, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [42], 'order_of_vanishing': 0, 'prelabel': '2-2e2-4.3-c42-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.685138956584303, 'root_angle': -0.4350151355717637, 'self_dual': False, 'spectral_label': 'c42-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54994473268172913790997425568', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1964788370704576509401980292863', 'Lhash_array': ['1964788370704576509401980292863'], 'label': '2-2e2-4.3-c42-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4/43/b/a/3/3'}