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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': 1, 'A3': 0, 'A4': -1, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': -3, 'A9': 4, 'Lhash': '966919409447550226219278723142', 'a10': [-0.316227766016838, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [-0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-1.0606601717798214, 0], 'a9': [1.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.85378114310941, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 2]], [5, [1, 1]], [17, [1, 0, 17]]], 'bad_primes': [2, 5, 17], 'central_character': '578000.1', 'coefficient_field': '1.1.1.1', 'conductor': 578000, 'conductor_radical': 170, 'degree': 4, 'euler_factors': [[1, -1, 2], [1, 0, -4, 0, 9], [1, 1], [1, 0, 8, 0, 49], [1, 0, 2, 0, 121], [1, -4, 14, -52, 169], [1, 0, 17], [1, 0, -22, 0, 361], [1, 0, -12, 0, 529], [1, 2, 34, 58, 841], [1, 0, -26, 0, 961], [1, -8, 86, -296, 1369], [1, -6, 90, -246, 1681], [1, 0, 46, 0, 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-2.451441064290363, -1.559081283614557, -0.7872585464795405, -0.20021202474100588, 0.1701916673986935, 0.32654326067697276], 'positive_zeros': ['0.76276492061256062585794041150584', '1.57140055456994220509686407528432', '2.51401669856695691459383293470728', '3.27678918189018206342394694620233', '3.70156366369627751113161337172908', '4.24314176505705422983824620319580', '4.47579008721709265204829625692179', '5.05903994966954782375761579897635', '5.62609126748486005743729472885479', '6.19302152531675459797361142348695', '6.42085190811480104298234040968918', '7.07994345148301250183978142141467', '7.54841064146580130342095731405313', '7.946049674596831865571597876104593', '8.424043056861788788961494821196878'], 'prelabel': '4-578000-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.463885451133873, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.85378114310941, 'bad_primes': [2, 5, 17], 'central_character': '1.1', 'conductor': 578000, 'conductor_radical': 170, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, -1, -1, 0, 0, -3, 4, -1, 0, 0, 4, 0, 0, -1, 0, 4, 0, 1, 0, 0, 0, 0, 1, 4, 0, 0, -2, 0, 0, 5, 0, 0, 0, -4, 8, 0, 0, 3, 6, 0, 0, 0, -4, 0, 0, 0, -8, 1, 0, -4, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 7, -4, 0, 0, 0, 0, 0, 0, -12, 0, 8, 0, 0, 0, 0, 0, 1, 7, 6, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -2, -8, 0, -1], 'euler11': [1, 0, 2, 0, 121], 'euler13': [1, -4, 14, -52, 169], 'euler17': [1, 0, 17, 0, 0], 'euler19': [1, 0, -22, 0, 361], 'euler2': [1, -1, 2, 0, 0], 'euler23': [1, 0, -12, 0, 529], 'euler29': [1, 2, 34, 58, 841], 'euler3': [1, 0, -4, 0, 9], 'euler31': [1, 0, -26, 0, 961], 'euler37': [1, -8, 86, -296, 1369], 'euler41': [1, -6, 90, -246, 1681], 'euler43': [1, 0, 46, 0, 1849], 'euler47': [1, 0, -70, 0, 2209], 'euler5': [1, 1, 0, 0, 0], 'euler53': [1, -2, 98, -106, 2809], 'euler59': [1, 0, 30, 0, 3481], 'euler61': [1, 0, -74, 0, 3721], 'euler67': [1, 0, -38, 0, 4489], 'euler7': [1, 0, 8, 0, 49], 'euler71': [1, 0, 14, 0, 5041], 'euler73': [1, 0, 142, 0, 5329], 'euler79': [1, 0, 66, 0, 6241], 'euler83': [1, 0, -106, 0, 6889], 'euler89': [1, 0, 174, 0, 7921], 'euler97': [1, 2, 26, 194, 9409], 'euler_factors': [[1, -1, 2, 0, 0], [1, 0, -4, 0, 9], [1, 1, 0, 0, 0], [1, 0, 8, 0, 49], [1, 0, 2, 0, 121], [1, -4, 14, -52, 169], [1, 0, 17, 0, 0], [1, 0, -22, 0, 361], [1, 0, -12, 0, 529], [1, 2, 34, 58, 841], [1, 0, -26, 0, 961], [1, -8, 86, -296, 1369], [1, -6, 90, -246, 1681], [1, 0, 46, 0, 1849], [1, 0, -70, 0, 2209], [1, -2, 98, -106, 2809], [1, 0, 30, 0, 3481], [1, 0, -74, 0, 3721], [1, 0, -38, 0, 4489], [1, 0, 14, 0, 5041], [1, 0, 142, 0, 5329], [1, 0, 66, 0, 6241], [1, 0, -106, 0, 6889], [1, 0, 174, 0, 7921], [1, 2, 26, 194, 9409]], 'index': 1, 'instance_types': ['BMF', 'ECNF', 'BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/36125.9/g', 'EllipticCurve/2.0.4.1/36125.4/g', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/36125.4/g', 'EllipticCurve/2.0.4.1/36125.9/g'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-578000-1.1-c1e2-0-1', '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': '4-578000-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.463885451133873, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 893133810425083039, 'z1': {'__RealLiteral__': 0, 'data': '0.76276492061256062585794041150584', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9673029
{'Lhash': '966919409447550226219278723142', 'Lhash_array': ['966919409447550226219278723142'], 'label': '4-578000-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/36125.9/g'}
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id: 9672968
{'Lhash': '966919409447550226219278723142', 'Lhash_array': ['966919409447550226219278723142'], 'label': '4-578000-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/36125.4/g'}
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id: 9672778
{'Lhash': '966919409447550226219278723142', 'Lhash_array': ['966919409447550226219278723142'], 'label': '4-578000-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/36125.4/g'}
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id: 9671546
{'Lhash': '966919409447550226219278723142', 'Lhash_array': ['966919409447550226219278723142'], 'label': '4-578000-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/36125.9/g'}