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lfunc_lfunctions • Show schema
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{'Lhash': '942104302894172262751095231229', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 3.5671756287491405], 'a4': [0, 0], 'a5': [-2.9127659944082858, 0], 'a6': [0, 0], 'a7': [-2.953589766858881, 0], 'a8': [0, 0], 'a9': [-3.7247419663418264, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.346150173626874, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 19], 'central_character': '1444.721', 'coefficient_field': 'CDF', 'conductor': 1444, 'conductor_radical': 38, 'conjugate': '539343695183101567829684966794', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.5671756287491405], [-9.0, 0]], [[1.0, 0], [2.9127659944082858, 0], [25.0, 0]], [[1.0, 0], [2.953589766858881, 0], [49.0, 0]], [[1.0, 0], [21.884527976612986, 0], [121.0, 0]], [[1.0, 0], [0, 10.077367930990787], [-169.0, 0]], [[1.0, 0], [-8.219589356330058, 0], [289.0, 0]], [[1.0, 0], [0, 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'2.12327664408002404959984441105277', '2.96722001018464922249151109295899', '4.20388495663339585186515592218248', '5.29005362635045314566009964273139', '6.16575465051691890017777372040696', '7.10702767037491932149594388991533', '7.65401032592005282417615076199658', '8.180327264962982976728411587020333', '9.229267133798620529762509798144581'], 'prelabel': '2-38e2-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.272650968579941, 'root_angle': -0.045853110455520645, 'root_number': '0.98964246947442240565937095500682987729870147505743890468 - 0.1435541103994132137494132905391795913631982307871052682*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.022926555227760322', 'prec': 70}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74318925319370702328852576260', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.12327664408002404959984441105', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96722001018464922249151109296', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.346150173626874, 'bad_primes': [2, 19], 'central_character': '19.18', 'conductor': 1444, 'conductor_radical': 38, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1444/3/c/d/721/19'], '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': '2-38e2-19.18-c2-0-24', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-38e2-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.272650968579941, 'root_angle': -0.022926555227760322, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74318925319370702328852576260', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '942104302894172262751095231229', 'Lhash_array': ['942104302894172262751095231229'], 'label': '2-38e2-19.18-c2-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1444/3/c/d/721/19'}