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lfunc_lfunctions • Show schema
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{'Lhash': '436647411171994125292602175608', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-23.13308284674815, 0], 'a6': [0, 0], 'a7': [4.131523191184554, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 119.0821974725887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.449', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '505713583116398282490101162204', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [23.13308284674815, 0], [625.0, 0]], [[1.0, 0], [-4.131523191184554, 0], [2401.0, 0]], [[1.0, 0], [212.4319908695769, 0], [14641.0, 0]], [[1.0, 0], [0, -36.71511950137164], [-28561.0, 0]], [[1.0, 0], [0, 99.60339919885807], [-83521.0, 0]], [[1.0, 0], [0, -316.9502953344114], [-130321.0, 0]], [[1.0, 0], [0, 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['0.34445407203955062900448534127170', '1.90175388475705392013386499959773', '3.07032326371996461842155660392165', '3.88659370341534681134587938344737', '5.05457173989307468910100617164334', '5.61275002697312993718980274390689', '6.95973949439037231727628720003873', '7.75704501395516457649766094398494', '8.100105198955391557823456000220053', '9.237836663875259479317598175522496'], 'prelabel': '2-1152-24.5-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.912478979250714, 'root_angle': -0.02704336199234818, 'root_number': '0.98559855965348878087536279295293935430859299804623856409 - 0.1691019787257627481429347680509755569866105044940151880*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.027043361992348185', 'prec': 70}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34445407203955062900448534127', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90175388475705392013386499960', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07032326371996461842155660392', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 119.0821974725887, 'bad_primes': [2, 3], 'central_character': '24.5', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/5/h/f/449/8'], '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': '2-1152-24.5-c4-0-16', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-1152-24.5-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.912478979250714, 'root_angle': -0.02704336199234818, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34445407203955062900448534127', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '436647411171994125292602175608', 'Lhash_array': ['436647411171994125292602175608'], 'factors': ['2-1152-24.5-c4-0-16'], 'label': '2-1152-24.5-c4-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/5/h/f/449/8'}