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lfunc_lfunctions • Show schema
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{'Lhash': '681201050631948054030897500979', 'a10': [-8276694.440739941, -20772489.719208542], 'a2': [0.0, -128.0], 'a3': [0.0, 5604.611687946066], 'a4': [-16384.0, 0.0], 'a5': [162285.07593131674, -64661.67531828079], 'a6': [717390.2960570964, 0.0], 'a7': [0.0, 750783.9253885801], 'a8': [0.0, 2097152.0], 'a9': [-17062765.17266165, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.269350509992051, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '7.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 128.0]]], [5, [[1.0, 0], [-162285.07593131674, 64661.67531828079]]]], 'bad_primes': [2, 5], 'central_character': '10.9', 'coefficient_field': 'CDF', 'conductor': 10, 'conductor_radical': 10, 'conjugate': '2725217189741874153202203189602', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 128.0]], [[1.0, 0], [0, -5604.611687946066], [-14348907.0, 0]], [[1.0, 0], [-162285.07593131674, 64661.67531828079]], [[1.0, 0], [0, -750783.9253885801], [-4747561509943.0, 0]], [[1.0, 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'root_analytic_conductor': 3.7774793857798947, 'root_angle': -0.6206920100530137, 'root_number': '-0.3701450279697822 - 0.9289739814813164*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.310346005027', 'prec': 50}, 'spectral_label': 'c15-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53737287743902283786433586192', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41089025926777390271600539112', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.63175135186130461189813738602', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.269350509992051, 'bad_primes': [2, 5], 'central_character': '5.4', 'conductor': 10, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/16/b/a/9/4'], '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': '2-10-5.4-c15-0-0', 'motivic_weight': 15, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [15], 'order_of_vanishing': 0, 'prelabel': '2-10-5.4-c15-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7774793857798947, 'root_angle': -0.31034600502650683, 'self_dual': False, 'spectral_label': 'c15-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53737287743902283786433586192', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '681201050631948054030897500979', 'Lhash_array': ['681201050631948054030897500979'], 'label': '2-10-5.4-c15-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/16/b/a/9/4'}