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lfunc_lfunctions • Show schema
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{'Lhash': '1262869890358401621865501110708,3042700143002569866890932109470', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.717283986318004, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [17, [1, -2, 17]]], 'bad_primes': [2, 17], 'central_character': '272.1', 'coefficient_field': '1.1.1.1', 'conductor': 73984, 'conductor_radical': 34, 'degree': 4, 'euler_factors': [[1], [1, 0, -2, 0, 9], [1, 0, -10, 0, 25], [1, 0, -10, 0, 49], [1, 0, -18, 0, 121], [1, 4, 30, 52, 169], [1, -2, 17], [1, 8, 54, 152, 361], [1, 0, -10, 0, 529], [1, 0, 6, 0, 841], [1, 0, -26, 0, 961], [1, 0, -10, 0, 1369], [1, 0, -82, 0, 1681], [1, -24, 230, -1032, 1849], [1, -16, 158, -752, 2209], [1, -12, 142, -636, 2809], [1, 8, 134, 472, 3481], [1, 0, -58, 0, 3721], [1, 8, 150, 536, 4489], [1, 0, -106, 0, 5041], [1, 0, -82, 0, 5329], [1, 0, -154, 0, 6241], [1, -8, 182, 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['0.996228684884488632246509041931134', '2.40026718912510933445283289055441', '2.67943085351653375449713383125273', '3.97507305024025642209311452287657', '4.30107750003002185772892906206498', '4.86096007328488008531224740394475', '5.75785155140974070054336847754363', '5.99033994894565169407786853752743', '6.94592676285430572717045162755679', '7.30723505835557254261518033070137', '7.48395248870592588027510989081572', '8.547041723071807033843932199956389', '8.700721178111605961356860273575868', '9.289046480681137100625397339414675', '9.776256155119552880110608634349086', '10.44403948167659640158134581646084', '10.79775067712982601333825348437679', '10.83862963460453809680211455226290', '11.81979498009659778183415607022860', '12.45173620367729600128500310069835'], 'prelabel': '4-272e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4737472425686935, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1021518543149906263, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.996228684884488632246509041931', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.40026718912510933445283289055', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.67943085351653375449713383125', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.717283986318004, 'bad_primes': [2, 17], 'central_character': '1.1', 'conductor': 73984, 'conductor_radical': 34, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 2, 0, -8, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 16, 0, 10, 0, 0, 0, 12, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 8, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -18, 0, 121], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, -2, 17, 0, 0], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -10, 0, 529], 'euler29': [1, 0, 6, 0, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, -26, 0, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, 0, -82, 0, 1681], 'euler43': [1, -24, 230, -1032, 1849], 'euler47': [1, -16, 158, -752, 2209], 'euler5': [1, 0, -10, 0, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, 0, -58, 0, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, 0, -106, 0, 5041], 'euler73': [1, 0, -82, 0, 5329], 'euler79': [1, 0, -154, 0, 6241], 'euler83': [1, -8, 182, -664, 6889], 'euler89': [1, 28, 374, 2492, 7921], 'euler97': [1, 0, -130, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -2, 0, 9], [1, 0, -10, 0, 25], [1, 0, -10, 0, 49], [1, 0, -18, 0, 121], [1, 4, 30, 52, 169], [1, -2, 17, 0, 0], [1, 8, 54, 152, 361], [1, 0, -10, 0, 529], [1, 0, 6, 0, 841], [1, 0, -26, 0, 961], [1, 0, -10, 0, 1369], [1, 0, -82, 0, 1681], [1, -24, 230, -1032, 1849], [1, -16, 158, -752, 2209], [1, -12, 142, -636, 2809], [1, 8, 134, 472, 3481], [1, 0, -58, 0, 3721], [1, 8, 150, 536, 4489], [1, 0, -106, 0, 5041], [1, 0, -82, 0, 5329], [1, 0, -154, 0, 6241], [1, -8, 182, -664, 6889], [1, 28, 374, 2492, 7921], [1, 0, -130, 0, 9409]], 'index': 7, 'instance_types': ['ECNF', 'HMF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.17.1/256.1/c', 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-256.1-c', 'ModularForm/GL2/Q/holomorphic/272/2/b/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-272e2-1.1-c1e2-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-272e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4737472425686935, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1021518543149906263, 'z1': {'__RealLiteral__': 0, 'data': '0.996228684884488632246509041931', 'prec': 107}}
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lfunc_instances • Show schema
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id: 10148244
{'Lhash': '1262869890358401621865501110708,3042700143002569866890932109470', 'Lhash_array': ['1262869890358401621865501110708', '3042700143002569866890932109470'], 'label': '4-272e2-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/272/2/b/b'}
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id: 9489860
{'Lhash': '_1262869890358401621865501110708', 'Lhash_array': ['_1262869890358401621865501110708'], 'label': '4-272e2-1.1-c1e2-0-7', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-256.1-c'}
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id: 9489523
{'Lhash': '_1262869890358401621865501110708', 'Lhash_array': ['_1262869890358401621865501110708'], 'label': '4-272e2-1.1-c1e2-0-7', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/256.1/c'}