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lfunc_lfunctions • Show schema
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{'Lhash': '671742948967486510773222195235', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.1957405009506432, -1.2530780719437655], 'a4': [0.0, 0.0], 'a5': [0.311559479131835, -0.3713021285621452], 'a6': [0.0, 0.0], 'a7': [-0.9582753353036046, 2.6328398453669606], 'a8': [0.0, 0.0], 'a9': [-0.1404093087726096, 2.9967124029526087], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.1957405009506432, 1.2530780719437655]]]], 'bad_primes': [2, 3], 'central_character': '432.95', 'coefficient_field': 'CDF', 'conductor': 432, 'conductor_radical': 6, 'conjugate': '2192475576273470218806964518207', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.1957405009506432, 1.2530780719437655]], [[1.0, 0], [-0.311559479131835, 0.3713021285621452], [-0.8682408883346517, -4.924038765061041]], [[1.0, 0], [0.9582753353036046, 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-0.38427576780206996, 0.2997831738593487, 1.1288620724176688], 'positive_zeros': ['0.52991175079832334638775915137552', '3.04860133877712328254880639791325', '4.01618030468638084035696713264741', '5.33368131376240330235755945914564', '5.98442821899092836179184424099902', '7.24285900945925878081438086368822', '8.149454226107989542980193865515102', '9.508601051118116159400865990763187', '10.24647274197282169491953765268284', '10.73976481079350150142694135542966'], 'prelabel': '2-432-108.95-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': -0.4128301830145912, 'root_number': '0.27044194868045196 - 0.9627362839292595*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.206415091507', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52991175079832334638775915138', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.04860133877712328254880639791', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.01618030468638084035696713265', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'bad_primes': [2, 3], 'central_character': '108.95', 'conductor': 432, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/2/be/b/95/2'], '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': '2-432-108.95-c1-0-3', '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': '2-432-108.95-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': -0.2064150915072956, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.52991175079832334638775915138', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '671742948967486510773222195235', 'Lhash_array': ['671742948967486510773222195235'], 'label': '2-432-108.95-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/2/be/b/95/2'}