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lfunc_lfunctions • Show schema
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{'Lhash': '2348064917530057423849686881431', 'a10': [0.0, 3.289945082937479], 'a2': [0.7071067811865476, 0.7071067811865476], 'a3': [-1.6449725414687395, 0.5422779156612186], 'a4': [0.0, 1.0], 'a5': [2.32634247787643, 2.32634247787643], 'a6': [-1.5466196303899695, -0.7797228474864606], 'a7': [-1.766896782903509, -1.766896782903509], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [2.4118693243722484, -1.7840645622152114], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [1.6449725414687395, -0.5422779156612186]]], [13, [[1.0, 0], [-0.7668967829035088, 3.5230483000339703]]]], 'bad_primes': [2, 3, 13], 'central_character': '78.5', 'coefficient_field': 'CDF', 'conductor': 78, 'conductor_radical': 78, 'conjugate': '4250637435777241818161434871542', 'degree': 2, 'euler_factors': [[[1.0, 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'root_number': '0.37768442904118066 - 0.9259343778367004*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.188360209936', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85229661636046153072729210994', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.56914739323237194620808803590', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.71961690734794513396796625714', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6228331357659873, 'bad_primes': [2, 3, 13], 'central_character': '39.5', 'conductor': 78, 'conductor_radical': 78, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/78/2/g/a/5/4'], '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': '2-78-39.5-c1-0-1', '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': '2-78-39.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': -0.18836020993598732, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85229661636046153072729210994', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2348064917530057423849686881431', 'Lhash_array': ['2348064917530057423849686881431'], 'label': '2-78-39.5-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/g/a/5/4'}