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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '1927567882616054017372694241325', 'a10': [0.0, 0], 'a2': [-0.7071067811865476, 0], 'a3': [-0.5773502691896257, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.40824829046386296, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.508938911357531, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1, 0, -1]]], 'bad_primes': [2, 3, 5], 'central_character': '86400.1', 'coefficient_field': '1.1.1.1', 'conductor': 86400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 1], [1, 1], [1, 0, -1], [1, 0, 2, 0, 49], [1, 0, -18, 0, 121], [1, 0, 2, 0, 169], [1, 0, -2, 0, 289], [1, 0, 38, 0, 361], [1, 12, 78, 276, 529], [1, 0, 54, 0, 841], [1, 0, -10, 0, 961], [1, 0, 34, 0, 1369], [1, 0, 54, 0, 1681], [1, 12, 86, 516, 1849], [1, 0, 30, 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-3.3298114445681595, -1.8619527235643283, -0.5213190418721577], 'positive_zeros': ['1.52058294475544939746414628065165', '2.26606102118794296161645987589202', '3.29944944595194631605420364640572', '3.94542085186066603008292301845763', '4.69422935284846289307808963793976', '5.28919876889298701185407020294774', '6.00608229850580921448158933135652', '6.34268542257277673475630397290176', '6.85144109644362439697166318928163', '7.52430148411020305138714516003117', '8.028691934241130197940422293501095', '8.320237225469500753093283173495168', '8.955026259947280058225096969686264', '9.617989795917646364552015710665471'], 'prelabel': '4-86400-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.532029010332009, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 680339261930451009, 'z1': {'__RealLiteral__': 0, 'data': '1.52058294475544939746414628065165', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.26606102118794296161645987589202', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.29944944595194631605420364640572', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.508938911357531, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 86400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, 0, -1, 1, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -12, 1, 1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -12, 0, 0, 12, 0, -1, -2, -1, 0, 0, -12, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 12, 0, 0, -1, 8, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -12, 0, 0, 0, 1, 0, 2, 0, 1], 'euler11': [1, 0, -18, 0, 121], 'euler13': [1, 0, 2, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 12, 78, 276, 529], 'euler29': [1, 0, 54, 0, 841], 'euler3': [1, 1, 0, 0, 0], 'euler31': [1, 0, -10, 0, 961], 'euler37': [1, 0, 34, 0, 1369], 'euler41': [1, 0, 54, 0, 1681], 'euler43': [1, 12, 86, 516, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, 0, 110, 0, 3721], 'euler67': [1, 0, -10, 0, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -8, 126, -584, 5329], 'euler79': [1, 0, 86, 0, 6241], 'euler83': [1, 0, 6, 0, 6889], 'euler89': [1, 0, -2, 0, 7921], 'euler97': [1, 0, 158, 0, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 1, 0, 0, 0], [1, 0, -1, 0, 0], [1, 0, 2, 0, 49], [1, 0, -18, 0, 121], [1, 0, 2, 0, 169], [1, 0, -2, 0, 289], [1, 0, 38, 0, 361], [1, 12, 78, 276, 529], [1, 0, 54, 0, 841], [1, 0, -10, 0, 961], [1, 0, 34, 0, 1369], [1, 0, 54, 0, 1681], [1, 12, 86, 516, 1849], [1, 0, 30, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, -26, 0, 3481], [1, 0, 110, 0, 3721], [1, 0, -10, 0, 4489], [1, 0, 142, 0, 5041], [1, -8, 126, -584, 5329], [1, 0, 86, 0, 6241], [1, 0, 6, 0, 6889], [1, 0, -2, 0, 7921], [1, 0, 158, 0, 9409]], 'index': 21, 'instance_types': ['HMF', 'ECNF', 'ECNF', 'HMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-150.1-d', 'EllipticCurve/2.2.24.1/150.1/d', 'EllipticCurve/2.2.24.1/150.1/f', 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-150.1-f'], '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': '4-86400-1.1-c1e2-0-21', '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': '4-86400-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.532029010332009, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 680339261930451009, 'z1': {'__RealLiteral__': 0, 'data': '1.52058294475544939746414628065165', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9511410
{'Lhash': '1927567882616054017372694241325', 'Lhash_array': ['1927567882616054017372694241325'], 'label': '4-86400-1.1-c1e2-0-21', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-150.1-f'}
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id: 9511405
{'Lhash': '1927567882616054017372694241325', 'Lhash_array': ['1927567882616054017372694241325'], 'label': '4-86400-1.1-c1e2-0-21', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/150.1/f'}
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id: 9511403
{'Lhash': '1927567882616054017372694241325', 'Lhash_array': ['1927567882616054017372694241325'], 'label': '4-86400-1.1-c1e2-0-21', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/150.1/d'}
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id: 9510794
{'Lhash': '1927567882616054017372694241325', 'Lhash_array': ['1927567882616054017372694241325'], 'label': '4-86400-1.1-c1e2-0-21', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-150.1-d'}