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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -2, 'Lhash': '1914017173175899179568179992517', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.633679947214205, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [7, [1, 0, 7]], [11, [1, 1]]], 'bad_primes': [2, 7, 11], 'central_character': '260876.1', 'coefficient_field': '1.1.1.1', 'conductor': 260876, 'conductor_radical': 154, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, 0, 2, 0, 9], [1, 0, -10, 0, 25], [1, 0, 7], [1, 1], [1, 0, 18, 0, 169], [1, 0, 26, 0, 289], [1, 0, 6, 0, 361], [1, 16, 110, 368, 529], [1, 0, 54, 0, 841], [1, 0, 10, 0, 961], [1, -4, 78, -148, 1369], [1, 0, 74, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, -86, 0, 2209], [1, 28, 302, 1484, 2809], [1, 0, -46, 0, 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'positive_zeros': ['1.50989331984010194201557058291256', '2.21072101718741916868872670441380', '2.97182172523047703774195232195440', '3.35485886243871762322388210983459', '4.25135230852627933522009234978817', '4.66180794577029847515972105997478', '5.32646135494688323743441817682956', '5.92221856819849171166113388152907', '6.33341735807205803870658227629236', '6.56345269675560905791803261211167', '7.40789779682054330247393673786313', '7.82021979681689371707293119013708', '8.166730852936611115960554871947122', '8.536757738003163472773938294826020'], 'prelabel': '4-260876-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.0195150091296186, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1686367337376013592, 'z1': {'__RealLiteral__': 0, 'data': '1.50989331984010194201557058291256', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.21072101718741916868872670441380', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.97182172523047703774195232195440', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.633679947214205, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 260876, 'conductor_radical': 154, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -16, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -7, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 2, 10], 'euler11': [1, 1, 0, 0, 0], 'euler13': [1, 0, 18, 0, 169], 'euler17': [1, 0, 26, 0, 289], 'euler19': [1, 0, 6, 0, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 16, 110, 368, 529], 'euler29': [1, 0, 54, 0, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, 0, 10, 0, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, 74, 0, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, -86, 0, 2209], 'euler5': [1, 0, -10, 0, 25], 'euler53': [1, 28, 302, 1484, 2809], 'euler59': [1, 0, -46, 0, 3481], 'euler61': [1, 0, 50, 0, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, 7, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, -54, 0, 5329], 'euler79': [1, 0, -98, 0, 6241], 'euler83': [1, 0, -122, 0, 6889], 'euler89': [1, 0, -50, 0, 7921], 'euler97': [1, 0, 94, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 0, 2, 0, 9], [1, 0, -10, 0, 25], [1, 0, 7, 0, 0], [1, 1, 0, 0, 0], [1, 0, 18, 0, 169], [1, 0, 26, 0, 289], [1, 0, 6, 0, 361], [1, 16, 110, 368, 529], [1, 0, 54, 0, 841], [1, 0, 10, 0, 961], [1, -4, 78, -148, 1369], [1, 0, 74, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, -86, 0, 2209], [1, 28, 302, 1484, 2809], [1, 0, -46, 0, 3481], [1, 0, 50, 0, 3721], [1, 8, 150, 536, 4489], [1, 0, 142, 0, 5041], [1, 0, -54, 0, 5329], [1, 0, -98, 0, 6241], [1, 0, -122, 0, 6889], [1, 0, -50, 0, 7921], [1, 0, 94, 0, 9409]], 'index': 8, 'instance_types': ['ECNF', 'BMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.0.7.1/5324.6/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/5324.6/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/5324.7/c', 'EllipticCurve/2.0.7.1/5324.7/c'], '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': '4-260876-1.1-c1e2-0-8', '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': '4-260876-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.0195150091296186, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1686367337376013592, 'z1': {'__RealLiteral__': 0, 'data': '1.50989331984010194201557058291256', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9642449
{'Lhash': '1914017173175899179568179992517', 'Lhash_array': ['1914017173175899179568179992517'], 'label': '4-260876-1.1-c1e2-0-8', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/5324.7/c'}
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id: 9642381
{'Lhash': '1914017173175899179568179992517', 'Lhash_array': ['1914017173175899179568179992517'], 'label': '4-260876-1.1-c1e2-0-8', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/5324.7/c'}
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id: 9642060
{'Lhash': '1914017173175899179568179992517', 'Lhash_array': ['1914017173175899179568179992517'], 'label': '4-260876-1.1-c1e2-0-8', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/5324.6/d'}
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id: 9641813
{'Lhash': '1914017173175899179568179992517', 'Lhash_array': ['1914017173175899179568179992517'], 'label': '4-260876-1.1-c1e2-0-8', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/5324.6/d'}