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lfunc_lfunctions • Show schema
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{'Lhash': '3077376630820375472210005541706', 'a10': [4.08959051764817, -3.247931450161876], 'a2': [2.255961458554044, -0.6044830509752939], 'a3': [0.0, 0.0], 'a4': [2.991911535996014, -1.7273809306988452], 'a5': [2.0512862679889294, -0.8900700235150318], 'a6': [0.0, 0.0], 'a7': [-1.4810021737648624, 2.1924033755912147], 'a8': [2.402507802267357, -2.402507802267357], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.515287663670333, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.0512862679889294, 0.8900700235150318]]], [7, [[1.0, 0], [1.4810021737648624, -2.1924033755912147]]]], 'bad_primes': [3, 5, 7], 'central_character': '315.233', 'coefficient_field': 'CDF', 'conductor': 315, 'conductor_radical': 105, 'conjugate': '2801093904956300895619324624545', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.255961458554044, 0.6044830509752939], [1.7320508075688772, -1.0]], [[1.0, 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'6.54802539500000999645666901102301', '7.37791744234415693776306484885228', '8.857074513532634633622191282116553', '10.39187492423421205852234193298679', '10.65682394693612978846812207025167', '12.29136442977428527932742802932176'], 'prelabel': '2-315-105.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5859658456821613, 'root_angle': 0.09279212395299939, 'root_number': '0.8347982397155291 + 0.5505559907655659*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.092792123953', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.42762211469494885255686100062', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.59439891543466186701565042351', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.71916069154435401385066027822', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.515287663670333, 'bad_primes': [3, 5, 7], 'central_character': '105.23', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/315/2/ce/a/233/15'], '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': '2-315-105.23-c1-0-13', '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': '2-315-105.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5859658456821613, 'root_angle': 0.09279212395299939, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.42762211469494885255686100062', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3077376630820375472210005541706', 'Lhash_array': ['3077376630820375472210005541706'], 'factors': ['2-315-105.23-c1-0-13'], 'label': '2-315-105.23-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/2/ce/a/233/15'}