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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -3, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -6, 'Lhash': '161217989908240353,467045135390574132', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-1.5, 0], 'a5': [0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9643831138227159, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -1]], [11, [1, 2, 1]]], 'bad_primes': [5, 11], 'central_character': '15125.1', 'coefficient_field': '1.1.1.1', 'conductor': 15125, 'conductor_radical': 55, 'degree': 4, 'euler_factors': [[1, 0, 3, 0, 4], [1, 0, 6, 0, 9], [1, -1], [1, 0, 14, 0, 49], [1, 2, 1], [1, 0, 22, 0, 169], [1, 0, -2, 0, 289], [1, 8, 54, 152, 361], [1, 0, 30, 0, 529], [1, -12, 94, -348, 841], [1, 16, 126, 496, 961], [1, 0, 70, 0, 1369], [1, -4, 86, -164, 1681], [1, 0, 70, 0, 1849], [1, 0, -50, 0, 2209], [1, 0, 102, 0, 2809], [1, -8, 134, -472, 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-7.560404670698467, -5.049674676141459, -2.5765281281629493, -0.3851441668157382], 'positive_zeros': ['2.31804956482818418780108048276701', '3.25423179226253980082861279896285', '4.11816586584967359873614255585362', '5.09766059609940450216711100862429', '5.23353820210759730524176244525098', '6.16821463973303244938343944630412', '6.54918508631964327843106616025847', '7.82885193609770565758085877154728', '8.248642768475844318802620430882067', '8.631003161371790257232477095323773', '9.336297212975655357629362917616089', '9.365267708430525132762162914792497', '10.44930765910572775087302550356176', '10.82193865307292862841462120688179'], 'prelabel': '4-15125-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9909743176422299, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 628263125298814485, 'z1': {'__RealLiteral__': 0, 'data': '2.31804956482818418780108048276701', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.25423179226253980082861279896285', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.11816586584967359873614255585362', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9643831138227159, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 15125, 'conductor_radical': 55, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -3, 1, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, 5, 0, 0, -8, -3, 0, 0, 0, 0, 1, 0, 0, 0, 12, 0, -16, 0, 0, 0, 0, 18, 0, 0, 0, 0, 4, 0, 0, 6, -6, 0, 0, 0, -14, 0, 0, 0, 0, 0, -2, 0, 0, 0, 8, 0, -20, 0, 0, -3, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 24, 0, 0, 16, 5, 27, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -8, 0, 0, 0, 12, -3], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 3, 0, 4], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 0, 6, 0, 9], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, -1, 0, 0, 0], 'euler53': [1, 0, 102, 0, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, 20, 222, 1220, 3721], 'euler67': [1, 0, -122, 0, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, 0, -50, 0, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, 150, 0, 6889], 'euler89': [1, -20, 278, -1780, 7921], 'euler97': [1, 0, 94, 0, 9409], 'euler_factors': [[1, 0, 3, 0, 4], [1, 0, 6, 0, 9], [1, -1, 0, 0, 0], [1, 0, 14, 0, 49], [1, 2, 1, 0, 0], [1, 0, 22, 0, 169], [1, 0, -2, 0, 289], [1, 8, 54, 152, 361], [1, 0, 30, 0, 529], [1, -12, 94, -348, 841], [1, 16, 126, 496, 961], [1, 0, 70, 0, 1369], [1, -4, 86, -164, 1681], [1, 0, 70, 0, 1849], [1, 0, -50, 0, 2209], [1, 0, 102, 0, 2809], [1, -8, 134, -472, 3481], [1, 20, 222, 1220, 3721], [1, 0, -122, 0, 4489], [1, -16, 206, -1136, 5041], [1, 0, -50, 0, 5329], [1, -16, 222, -1264, 6241], [1, 0, 150, 0, 6889], [1, -20, 278, -1780, 7921], [1, 0, 94, 0, 9409]], 'index': 3, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-605.1-c', 'EllipticCurve/2.2.5.1/605.1/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, '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': '4-15125-1.1-c1e2-0-3', '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': 1, 'prelabel': '4-15125-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9909743176422299, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 628263125298814485, 'z1': {'__RealLiteral__': 0, 'data': '2.31804956482818418780108048276701', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9531515
{'Lhash': '161217989908240353,467045135390574132', 'Lhash_array': ['161217989908240353', '467045135390574132'], 'label': '4-15125-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/605.1/c'}
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id: 9531084
{'Lhash': '161217989908240353,467045135390574132', 'Lhash_array': ['161217989908240353', '467045135390574132'], 'label': '4-15125-1.1-c1e2-0-3', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-605.1-c'}