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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -2, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': -2, 'Lhash': '4023525583116229779305297765452', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-1.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.06937182332820595, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 2]], [17, [1, -5, 11, 17]]], 'bad_primes': [2, 17], 'central_character': '1088.1', 'coefficient_field': '1.1.1.1', 'conductor': 1088, 'conductor_radical': 34, 'degree': 4, 'euler_factors': [[1, 0, 2], [1, 0, 2, 0, 9], [1, 0, -2, 0, 25], [1, 2, 6, 14, 49], [1, 0, 10, 0, 121], [1, 0, 10, 0, 169], [1, -5, 11, 17], [1, 0, -2, 0, 361], [1, 6, 46, 138, 529], [1, 0, 22, 0, 841], [1, 2, 54, 62, 961], [1, 0, -2, 0, 1369], [1, 0, 46, 0, 1681], [1, 0, 58, 0, 1849], [1, -12, 130, -564, 2209], [1, 0, -26, 0, 2809], 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-2.462417729008384, -1.5543929938184669, -0.623030485524312], 'positive_zeros': ['3.17400203367696839713552335058299', '4.21524744281209647906717432747441', '5.48237499609119068897650555264154', '6.01912712781998810706342352491370', '7.25728763856226074637060722967711', '8.104427830147069626222932574670289', '8.766450619065699860669585506452049', '9.514581676057178887948389923580155', '10.05681574304479561828369141583929', '10.71210139881204999206150662239900', '11.76221275592136857524468249376687', '12.29726535287971277212019804410961', '12.86589430836834663288318270965305', '13.54189737490713903220419819081149', '14.19044829739582126239819958846222'], 'prelabel': '4-1088-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.5132107884928165, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 569863837532001628, 'z1': {'__RealLiteral__': 0, 'data': '3.17400203367696839713552335058299', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '4.21524744281209647906717432747441', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.48237499609119068897650555264154', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.06937182332820595, 'bad_primes': [2, 17], 'central_character': '1.1', 'conductor': 1088, 'conductor_radical': 34, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 4, 5, 0, 0, 0, 0, 0, -6, 0, 2, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, -10, 0, 0, 6, 0, -20, 0, 0, 0, 0, 0, -2, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, -8, 0, 0, -4], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, -5, 11, 17, 0], 'euler19': [1, 0, -2, 0, 361], 'euler2': [1, 0, 2, 0, 0], 'euler23': [1, 6, 46, 138, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, 2, 54, 62, 961], 'euler37': [1, 0, -2, 0, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, 58, 0, 1849], 'euler47': [1, -12, 130, -564, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 0, -26, 0, 2809], 'euler59': [1, 0, 10, 0, 3481], 'euler61': [1, 0, -50, 0, 3721], 'euler67': [1, 0, -26, 0, 4489], 'euler7': [1, 2, 6, 14, 49], 'euler71': [1, -6, 70, -426, 5041], 'euler73': [1, 20, 246, 1460, 5329], 'euler79': [1, 2, 78, 158, 6241], 'euler83': [1, 0, -86, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 8, 174, 776, 9409], 'euler_factors': [[1, 0, 2, 0, 0], [1, 0, 2, 0, 9], [1, 0, -2, 0, 25], [1, 2, 6, 14, 49], [1, 0, 10, 0, 121], [1, 0, 10, 0, 169], [1, -5, 11, 17, 0], [1, 0, -2, 0, 361], [1, 6, 46, 138, 529], [1, 0, 22, 0, 841], [1, 2, 54, 62, 961], [1, 0, -2, 0, 1369], [1, 0, 46, 0, 1681], [1, 0, 58, 0, 1849], [1, -12, 130, -564, 2209], [1, 0, -26, 0, 2809], [1, 0, 10, 0, 3481], [1, 0, -50, 0, 3721], [1, 0, -26, 0, 4489], [1, -6, 70, -426, 5041], [1, 20, 246, 1460, 5329], [1, 2, 78, 158, 6241], [1, 0, -86, 0, 6889], [1, 0, 142, 0, 7921], [1, 8, 174, 776, 9409]], 'index': 0, 'instance_types': ['G2Q', 'ECNF', 'HMF', 'HMF', 'ECNF'], 'instance_urls': ['Genus2Curve/Q/1088/a', 'EllipticCurve/2.2.8.1/17.2/a', 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-17.1-a', 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-17.2-a', 'EllipticCurve/2.2.8.1/17.1/a'], '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': True, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-1088-1.1-c1e2-0-0', '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': '4-1088-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.5132107884928165, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 569863837532001628, 'z1': {'__RealLiteral__': 0, 'data': '3.17400203367696839713552335058299', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9553730
{'Lhash': '4023525583116229779305297765452', 'Lhash_array': ['4023525583116229779305297765452'], 'label': '4-1088-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/17.1/a'}
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id: 9553288
{'Lhash': '4023525583116229779305297765452', 'Lhash_array': ['4023525583116229779305297765452'], 'label': '4-1088-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-17.2-a'}
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id: 9553102
{'Lhash': '4023525583116229779305297765452', 'Lhash_array': ['4023525583116229779305297765452'], 'label': '4-1088-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-17.1-a'}
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id: 9553501
{'Lhash': '4023525583116229779305297765452', 'Lhash_array': ['4023525583116229779305297765452'], 'label': '4-1088-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/17.2/a'}
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id: 1221804
{'Lhash': '569863837532001628', 'Lhash_array': ['569863837532001628'], 'label': '4-1088-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/1088/a'}