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lfunc_lfunctions • Show schema
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{'Lhash': '1721886077264539938020478238547', 'a10': [0.3230419109976908, 0.5595250028221438], 'a2': [0.8660254037844386, 0.5], 'a3': [-2.6808453463817865, 1.54778678238928], 'a4': [0.5, 0.8660254037844386], 'a5': [0.5595250028221438, 0.3230419109976908], 'a6': [-3.09557356477856, 0], 'a7': [0, 0], 'a8': [0, 1.0], 'a9': [3.29128784747792, -5.700677774165763], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-0.15565685766726362, 3.312970108929622]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.901', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '529824858246271265214390831065', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [2.6808453463817865, -1.54778678238928], [1.5, -2.598076211353316]], 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'7.943947402064829446959905607634494', '9.447236532734315824125176564301478', '10.32351411908031733923864586924194'], 'prelabel': '2-1078-77.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.1614382210331175, 'root_number': '0.8741210326741744135940518386211389123855657111271264506 + 0.4857081636503908992413060327392385507904975754132079591*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.08071911051655875', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35832860959836205056503349016', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21576874754179949364409360586', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99878307923946307825288002327', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.54', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/i/b/901/5'], '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': '2-1078-77.54-c1-0-29', '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': '2-1078-77.54-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.08071911051655875, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35832860959836205056503349016', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1721886077264539938020478238547', 'Lhash_array': ['1721886077264539938020478238547'], 'label': '2-1078-77.54-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/i/b/901/5'}