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lfunc_lfunctions • Show schema
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{'Lhash': '1118066382150540400278539213644,2435713301469078633355500644728', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.008134635396548, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [3, [1, -2, 1]], [7, [1, 0, 1]], [13, [1, 6, 13]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.1', 'coefficient_field': '1.1.1.1', 'conductor': 298116, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, -2, 1], [1, 0, -1, 0, 25], [1, 0, 1], [1, 0, 3, 0, 121], [1, 6, 13], [1, -6, 43, -102, 289], [1, 0, -37, 0, 361], [1, 2, 47, 46, 529], [1, -10, 83, -290, 841], [1, 0, -62, 0, 961], [1, 0, -25, 0, 1369], [1, 0, -82, 0, 1681], [1, 2, 87, 86, 1849], [1, 0, -30, 0, 2209], [1, -28, 302, -1484, 2809], [1, 0, 78, 0, 3481], [1, 6, 131, 366, 3721], [1, 0, -70, 0, 4489], [1, 0, -42, 0, 5041], [1, 0, -25, 0, 5329], [1, 0, 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'2.86349550330828889337040673671210', '2.86521533116791941437839235681392', '3.92534040678059442665584062182319', '4.18675780044876769409520304301408', '4.96054312587536855532952426758109', '5.28186697409185948060013263027478', '5.89706123978545200226975534533232', '6.65867049724933434258730447768511', '7.26015157601889847259167581046574', '7.33807092747286015892275102406774', '8.179094225529055222791246943536191', '8.253158637349628081886891555853005', '8.717431507189508441762219730357404', '9.474835345348604022768159047682351', '9.566490198455084588934479518598757', '10.03045588248703020413097068827279', '10.48578500125122597595345153563564', '10.64424565668071911071373429550751'], 'prelabel': '4-546e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0880210608042034, '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': 191105832154368716, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.881998858320457016092041279158', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.92143899985575659444802638883', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.86349550330828889337040673671', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.008134635396548, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 298116, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, -1, 0, 0, 0, 0, 3, 0, 0, -2, -6, 0, 0, 1, 6, 0, 0, 0, 0, 0, -2, 0, 1, 0, 4, 0, 10, 0, 0, 0, 0, 0, 0, -3, 0, 0, -12, 0, 0, 0, -2, 0, 0, 0, 0, 2, -1, 0, 12, 6, 28, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, -1, 0, 0, 0, -6, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1], 'euler11': [1, 0, 3, 0, 121], 'euler13': [1, 6, 13, 0, 0], 'euler17': [1, -6, 43, -102, 289], 'euler19': [1, 0, -37, 0, 361], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 2, 47, 46, 529], 'euler29': [1, -10, 83, -290, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 0, -62, 0, 961], 'euler37': [1, 0, -25, 0, 1369], 'euler41': [1, 0, -82, 0, 1681], 'euler43': [1, 2, 87, 86, 1849], 'euler47': [1, 0, -30, 0, 2209], 'euler5': [1, 0, -1, 0, 25], 'euler53': [1, -28, 302, -1484, 2809], 'euler59': [1, 0, 78, 0, 3481], 'euler61': [1, 6, 131, 366, 3721], 'euler67': [1, 0, -70, 0, 4489], 'euler7': [1, 0, 1, 0, 0], 'euler71': [1, 0, -42, 0, 5041], 'euler73': [1, 0, -25, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, -130, 0, 6889], 'euler89': [1, 0, 78, 0, 7921], 'euler97': [1, 0, -190, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, -2, 1, 0, 0], [1, 0, -1, 0, 25], [1, 0, 1, 0, 0], [1, 0, 3, 0, 121], [1, 6, 13, 0, 0], [1, -6, 43, -102, 289], [1, 0, -37, 0, 361], [1, 2, 47, 46, 529], [1, -10, 83, -290, 841], [1, 0, -62, 0, 961], [1, 0, -25, 0, 1369], [1, 0, -82, 0, 1681], [1, 2, 87, 86, 1849], [1, 0, -30, 0, 2209], [1, -28, 302, -1484, 2809], [1, 0, 78, 0, 3481], [1, 6, 131, 366, 3721], [1, 0, -70, 0, 4489], [1, 0, -42, 0, 5041], [1, 0, -25, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, -130, 0, 6889], [1, 0, 78, 0, 7921], [1, 0, -190, 0, 9409]], 'index': 23, 'instance_types': ['ECNF', 'HMF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.13.1/1764.1/n', 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-1764.1-n', 'ModularForm/GL2/Q/holomorphic/546/2/c/d'], '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': '4-546e2-1.1-c1e2-0-23', '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': '4-546e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 191105832154368716, 'z1': {'__RealLiteral__': 0, 'data': '0.881998858320457016092041279158', 'prec': 107}}
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lfunc_instances • Show schema
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id: 11538101
{'Lhash': '1118066382150540400278539213644,2435713301469078633355500644728', 'Lhash_array': ['1118066382150540400278539213644', '2435713301469078633355500644728'], 'label': '4-546e2-1.1-c1e2-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/c/d'}
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id: 9524227
{'Lhash': '_1118066382150540400278539213644', 'Lhash_array': ['_1118066382150540400278539213644'], 'label': '4-546e2-1.1-c1e2-0-23', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-1764.1-n'}
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id: 9523914
{'Lhash': '_1118066382150540400278539213644', 'Lhash_array': ['_1118066382150540400278539213644'], 'label': '4-546e2-1.1-c1e2-0-23', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/1764.1/n'}