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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -1, 'Lhash': '2248154158573332091137757078865', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.362288917189448, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [5, [1, 1, 5]], [29, [1, -2, 1]]], 'bad_primes': [2, 5, 29], 'central_character': '84100.1', 'coefficient_field': '1.1.1.1', 'conductor': 84100, 'conductor_radical': 290, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, 0, 1, 0, 9], [1, 1, 5], [1, 0, 2, 0, 49], [1, 6, 27, 66, 121], [1, 0, -15, 0, 169], [1, 0, 10, 0, 289], [1, 0, 22, 0, 361], [1, 0, -34, 0, 529], [1, -2, 1], [1, 14, 107, 434, 961], [1, 0, 38, 0, 1369], [1, -8, 34, -328, 1681], [1, 0, -23, 0, 1849], [1, 0, -7, 0, 2209], [1, 0, 17, 0, 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-7.97865494241844, -7.294028537040265, -6.236400704406471, -4.932997085579482], 'positive_zeros': ['1.77348092460854087171065116547431', '2.62661510122108731021638197128301', '3.15829880853553865088623924261786', '3.96819737653166668580252003757875', '4.62547299646254388948411905763761', '5.44208114512005954876917038247421', '5.67797853663145081086873545770301', '6.26742052107305117261919960731961', '7.19939270998070999334336100693559', '7.46895723629394649810813192504485', '7.76643223735093624812883349252756', '8.462577963295780227342794972186811', '8.839735193779006045394842987948010', '9.484633320833228349581498017186215'], 'prelabel': '4-290e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.5217298244488515, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1725681785923968279, 'z1': {'__RealLiteral__': 0, 'data': '1.77348092460854087171065116547431', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.62661510122108731021638197128301', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.15829880853553865088623924261786', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.362288917189448, 'bad_primes': [2, 5, 29], 'central_character': '1.1', 'conductor': 84100, 'conductor_radical': 290, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, -1, 0, 0, 0, -1, 0, -6, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, -14, 0, 0, 0, 0, -1, 0, 0, 0, 0, 8, 0, 0, -6, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 6, 0, 0, 0, -4, 0, 4, 0, 0, 1, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, -22, -1, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -4], 'euler11': [1, 6, 27, 66, 121], 'euler13': [1, 0, -15, 0, 169], 'euler17': [1, 0, 10, 0, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 0, -34, 0, 529], 'euler29': [1, -2, 1, 0, 0], 'euler3': [1, 0, 1, 0, 9], 'euler31': [1, 14, 107, 434, 961], 'euler37': [1, 0, 38, 0, 1369], 'euler41': [1, -8, 34, -328, 1681], 'euler43': [1, 0, -23, 0, 1849], 'euler47': [1, 0, -7, 0, 2209], 'euler5': [1, 1, 5, 0, 0], 'euler53': [1, 0, 17, 0, 2809], 'euler59': [1, 4, -22, 236, 3481], 'euler61': [1, -4, 62, -244, 3721], 'euler67': [1, 0, 74, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 20, 226, 1420, 5041], 'euler73': [1, 0, 30, 0, 5329], 'euler79': [1, 22, 243, 1738, 6241], 'euler83': [1, 0, 134, 0, 6889], 'euler89': [1, 0, 114, 0, 7921], 'euler97': [1, 0, -194, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 0, 1, 0, 9], [1, 1, 5, 0, 0], [1, 0, 2, 0, 49], [1, 6, 27, 66, 121], [1, 0, -15, 0, 169], [1, 0, 10, 0, 289], [1, 0, 22, 0, 361], [1, 0, -34, 0, 529], [1, -2, 1, 0, 0], [1, 14, 107, 434, 961], [1, 0, 38, 0, 1369], [1, -8, 34, -328, 1681], [1, 0, -23, 0, 1849], [1, 0, -7, 0, 2209], [1, 0, 17, 0, 2809], [1, 4, -22, 236, 3481], [1, -4, 62, -244, 3721], [1, 0, 74, 0, 4489], [1, 20, 226, 1420, 5041], [1, 0, 30, 0, 5329], [1, 22, 243, 1738, 6241], [1, 0, 134, 0, 6889], [1, 0, 114, 0, 7921], [1, 0, -194, 0, 9409]], 'index': 23, 'instance_types': ['ECNF', 'HMF', 'HMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.2.5.1/3364.1/e', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-3364.1-d', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-3364.1-e', 'EllipticCurve/2.2.5.1/3364.1/d'], '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': '4-290e2-1.1-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': 1, 'prelabel': '4-290e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.5217298244488515, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1725681785923968279, 'z1': {'__RealLiteral__': 0, 'data': '1.77348092460854087171065116547431', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9523709
{'Lhash': '2248154158573332091137757078865', 'Lhash_array': ['2248154158573332091137757078865'], 'factors': ['4-290e2-1.1-c1e2-0-23'], 'label': '4-290e2-1.1-c1e2-0-23', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/3364.1/d'}
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id: 9523456
{'Lhash': '2248154158573332091137757078865', 'Lhash_array': ['2248154158573332091137757078865'], 'factors': ['4-290e2-1.1-c1e2-0-23'], 'label': '4-290e2-1.1-c1e2-0-23', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-3364.1-e'}
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id: 9523391
{'Lhash': '2248154158573332091137757078865', 'Lhash_array': ['2248154158573332091137757078865'], 'factors': ['4-290e2-1.1-c1e2-0-23'], 'label': '4-290e2-1.1-c1e2-0-23', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-3364.1-d'}
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id: 9522946
{'Lhash': '2248154158573332091137757078865', 'Lhash_array': ['2248154158573332091137757078865'], 'factors': ['4-290e2-1.1-c1e2-0-23'], 'label': '4-290e2-1.1-c1e2-0-23', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/3364.1/e'}