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lfunc_lfunctions • Show schema
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{'Lhash': '2210317041623861758830945711282', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [0.9135454576426009, -0.4067366430758002], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.6691306063588582, -0.7431448254773942], 'a8': [0.0, 0.0], 'a9': [-0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3248913232240846, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]], [7, [[1.0, 0], [0.6691306063588582, 0.7431448254773942]]], [31, [[1.0, 0], [0.6691306063588582, -0.7431448254773942]]]], 'bad_primes': [3, 7, 31], 'central_character': '651.17', 'coefficient_field': 'CDF', 'conductor': 651, 'conductor_radical': 651, 'conjugate': '2371051114547755571843156884581', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.9135454576426009, 0.4067366430758002]], [[1.0, 0], [-0.30901699437494745, 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'5.75023306093386062072835403997898', '6.32570601936882436542067710095359', '7.03646161919591043870517873124650', '8.221716375336499466052333075636195', '8.585799480017565395844140426136228', '9.749365299863764681821334416193296', '11.08892267730122125113863702421947'], 'prelabel': '2-651-651.17-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5699923887422398, 'root_angle': -0.14670610378545829, 'root_number': '0.89565666512815581418438284857160 - 0.44474615030544171841037114034060*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07335305189272914', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74363270228082841656787205857', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84712714102701571400045086997', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.70168269131654433246116271288', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3248913232240846, 'bad_primes': [3, 7, 31], 'central_character': '651.17', 'conductor': 651, 'conductor_radical': 651, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/651/1/co/a/17/1'], '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': '2-651-651.17-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-651-651.17-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5699923887422398, 'root_angle': -0.07335305189272914, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74363270228082841656787205857', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2210317041623861758830945711282', 'Lhash_array': ['2210317041623861758830945711282'], 'label': '2-651-651.17-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/651/1/co/a/17/1'}