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lfunc_lfunctions • Show schema
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{'Lhash': '1909516275997993414536426719861', 'a10': [0.0, 0.0], 'a2': [-3.5615528128088303, 0.0], 'a3': [3.0, 0.0], 'a4': [4.68465843842649, 0.0], 'a5': [0.0, 0.0], 'a6': [-10.68465843842649, 0.0], 'a7': [7.0, 0.0], 'a8': [11.807764064044152, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.976002753013837, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-7.0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.1', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[[1.0, 0], [3.5615528128088303, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.0, 0]], [[1.0, 0], [5.192235935955849, 0], [1331.0, 0]], [[1.0, 0], [54.54639781775011, 0], [2197.0, 0]], [[1.0, 0], [16.161925945838416, 0], [4913.0, 0]], [[1.0, 0], [-87.44695751729449, 0], [6859.0, 0]], [[1.0, 0], 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'6.80038337320182259248395398508952', '7.69531193756662675881230856221119', '8.189074437725777677509591503269715', '9.182752734382268522602132133825724', '9.849708628900840625392888038926832'], 'prelabel': '2-525-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.56560892922004, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50634273801803250279664283532', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61924209101489875657644639319', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17748629582954838913062794466', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.976002753013837, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/4/a/j/1/1'], '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': '2-525-1.1-c3-0-39', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-525-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.56560892922004, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50634273801803250279664283532', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1909516275997993414536426719861', 'Lhash_array': ['1909516275997993414536426719861'], 'label': '2-525-1.1-c3-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/4/a/j/1/1'}