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lfunc_lfunctions • Show schema
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{'Lhash': '2556157395061776996959139437150', 'a10': [0.0, 2.0], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [-1.0, 1.4142135623730951], 'a4': [0.0, 1.0], 'a5': [1.4142135623730951, -1.4142135623730951], 'a6': [-0.2928932188134525, -1.7071067811865475], 'a7': [1.0, -1.0], 'a8': [-2.1213203435596424, -2.1213203435596424], 'a9': [-1.0, -2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.31141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, -1.4142135623730951]]], [13, [[1.0, 0], [2.0, 3.0]]]], 'bad_primes': [3, 13], 'central_character': '39.8', 'coefficient_field': 'CDF', 'conductor': 39, 'conductor_radical': 39, 'conjugate': '5335849369976998301751529074083', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -0.7071067811865476], [0, -2.0]], [[1.0, 0], [1.0, -1.4142135623730951]], [[1.0, 0], [-1.4142135623730951, 1.4142135623730951], [0, -5.0]], [[1.0, 0], 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'5.60369323473452934674015467315057', '6.70588095140817211226667910465563', '8.664988877066061889315090811529288', '10.08889150269282229426962884314352', '11.27655515850053202120672354428041', '12.04534595841437143990557330795692', '13.93288389298878883984517220529180', '14.46714382280142753892680151742110', '16.38478840930367891237437276030303'], 'prelabel': '2-39-39.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5580471018498292, 'root_angle': -0.3976702448901958, 'root_number': '0.3159695725215441 - 0.948769323513652*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.198835122445', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01645263655581689352851342192', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.60369323473452934674015467315', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.70588095140817211226667910466', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.31141656788299366, 'bad_primes': [3, 13], 'central_character': '39.8', 'conductor': 39, 'conductor_radical': 39, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/39/2/f/a/8/1'], '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': '2-39-39.8-c1-0-0', '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': '2-39-39.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5580471018498292, 'root_angle': -0.1988351224450979, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.01645263655581689352851342192', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2556157395061776996959139437150', 'Lhash_array': ['2556157395061776996959139437150'], 'label': '2-39-39.8-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/39/2/f/a/8/1'}