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lfunc_lfunctions • Show schema
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{'Lhash': '2310242387587160734495804981699', 'a10': [0.0, 0.0], 'a2': [1.6855439326707928, 0.0], 'a3': [1.0, 0.0], 'a4': [0.8410583489633225, 0.0], 'a5': [0.0, 0.0], 'a6': [1.6855439326707928, 0.0], 'a7': [-4.797932651931814, 0.0], 'a8': [-1.953447068224343, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.14726671250135, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [47, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 47], 'central_character': '3525.1', 'coefficient_field': 'CDF', 'conductor': 3525, 'conductor_radical': 705, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.6855439326707928, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.797932651931814, 0], [7.0, 0]], [[1.0, 0], [-4.987368775782867, 0], [11.0, 0]], [[1.0, 0], [-3.910321371192834, 0], [13.0, 0]], [[1.0, 0], [6.513971057416983, 0], [17.0, 0]], [[1.0, 0], 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'6.20723504525777995257010444853837', '6.55028640750459644382139487666439', '6.88609774868796798910628427356744', '8.537305809126125293963175107499451'], 'prelabel': '2-3525-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3053997693389086, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82245990115195922441416620902', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.97430301927446834008143164450', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68920749053424735481698602283', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.14726671250135, 'bad_primes': [3, 5, 47], 'central_character': '1.1', 'conductor': 3525, 'conductor_radical': 705, 'degree': 2, 'index': 131, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3525/2/a/t/1/4'], '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': '2-3525-1.1-c1-0-131', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3525-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3053997693389086, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82245990115195922441416620902', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2310242387587160734495804981699', 'Lhash_array': ['2310242387587160734495804981699'], 'label': '2-3525-1.1-c1-0-131', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3525/2/a/t/1/4'}