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lfunc_lfunctions • Show schema
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{'Lhash': '404399525907032512966497294581', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-1.3341117163963756, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.4922894553219, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '7200.3601', 'coefficient_field': 'CDF', 'conductor': 7200, 'conductor_radical': 30, 'conjugate': '1240202869200549226413489421216', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.3341117163963756, 0], [7.0, 0]], [[1.0, 0], [0, 2.944184680483334], [-11.0, 0]], [[1.0, 0], [0, -2.041837065689994], [-13.0, 0]], [[1.0, 0], [3.6124081132760852, 0], [17.0, 0]], [[1.0, 0], [0, -5.359635379070571], [-19.0, 0]], [[1.0, 0], [-8.596094710260287, 0], [23.0, 0]], [[1.0, 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'4.70453548562190351068299931736985', '5.63889677872251459421447811207268', '6.55369749734176221620096691523966', '6.93763102770457330486503020471194', '7.65603467687674617803436462467551'], 'prelabel': '2-7200-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.582367008746141, 'root_angle': -0.5133093899197716, 'root_number': '-0.0418004991397708559972408841733954571385004493808625693 - 0.9991259771778862200958152934454848259584017104253548340*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2566546949598858', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31901497607796968337153564497', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.51839862921497071923731314970', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.71835642037563760169750496287', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.4922894553219, 'bad_primes': [2, 3, 5], 'central_character': '8.5', 'conductor': 7200, 'conductor_radical': 30, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7200/2/k/r/3601/3'], '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': '2-7200-8.5-c1-0-16', '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': '2-7200-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.582367008746141, 'root_angle': -0.2566546949598858, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31901497607796968337153564497', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '404399525907032512966497294581', 'Lhash_array': ['404399525907032512966497294581'], 'label': '2-7200-8.5-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7200/2/k/r/3601/3'}