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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -2, 'A5': -3, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -1, 'Lhash': '3343964667419904175257154881450', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-1.0, 0], 'a5': [-1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5754418249421496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 3, 5]], [19, [1, 1, 19]]], 'bad_primes': [5, 19], 'central_character': '9025.1', 'coefficient_field': '1.1.1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'euler_factors': [[1, 0, 2, 0, 4], [1, 0, 1, 0, 9], [1, 3, 5], [1, 0, -2, 0, 49], [1, 6, 31, 66, 121], [1, 0, 23, 0, 169], [1, 0, 1, 0, 289], [1, 1, 19], [1, 0, -17, 0, 529], [1, -9, 76, -261, 841], [1, 12, 97, 372, 961], [1, 0, -10, 0, 1369], [1, 0, 73, 0, 1681], [1, 0, 7, 0, 1849], [1, 0, 79, 0, 2209], [1, 0, -73, 0, 2809], [1, -9, 82, 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-0.6851592384543582, -1.2326720699882945], 'positive_zeros': ['2.63792299456794529108614129707956', '3.60401610781285747484879091023071', '4.36902019806103263721464598563252', '5.03077182024000936944442191827294', '5.57733380179038841837323712732131', '6.66583993396032814586673339969307', '7.46730325217072203305692834102874', '7.907590442336435129393185114444869', '8.434380274846306746371413761129545', '8.902747827759237921715267272211448', '9.600825932349098521069904813407108', '10.32692888075682554881955096543836', '10.86663596298499142634886865183869', '11.20596463141761880232308913940580'], 'prelabel': '4-95e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.8709643042066444, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1825361187933151474, 'z1': {'__RealLiteral__': 0, 'data': '2.63792299456794529108614129707956', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.60401610781285747484879091023071', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.36902019806103263721464598563252', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5754418249421496, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -2, -3, 0, 0, 0, -1, 0, -6, 0, 0, 0, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, 4, 0, 0, 0, 9, 0, -12, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 12, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 18, 0, 0, 0, 9, 0, -19, 0, 0, 8, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 2, 0, 0, 9, 0, -8, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, -8], 'euler11': [1, 6, 31, 66, 121], 'euler13': [1, 0, 23, 0, 169], 'euler17': [1, 0, 1, 0, 289], 'euler19': [1, 1, 19, 0, 0], 'euler2': [1, 0, 2, 0, 4], 'euler23': [1, 0, -17, 0, 529], 'euler29': [1, -9, 76, -261, 841], 'euler3': [1, 0, 1, 0, 9], 'euler31': [1, 12, 97, 372, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, 0, 73, 0, 1681], 'euler43': [1, 0, 7, 0, 1849], 'euler47': [1, 0, 79, 0, 2209], 'euler5': [1, 3, 5, 0, 0], 'euler53': [1, 0, -73, 0, 2809], 'euler59': [1, -9, 82, -531, 3481], 'euler61': [1, 19, 192, 1159, 3721], 'euler67': [1, 0, -31, 0, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, -9, 142, -639, 5041], 'euler73': [1, 0, -35, 0, 5329], 'euler79': [1, -9, 178, -711, 6241], 'euler83': [1, 0, 142, 0, 6889], 'euler89': [1, 9, 16, 801, 7921], 'euler97': [1, 0, -13, 0, 9409], 'euler_factors': [[1, 0, 2, 0, 4], [1, 0, 1, 0, 9], [1, 3, 5, 0, 0], [1, 0, -2, 0, 49], [1, 6, 31, 66, 121], [1, 0, 23, 0, 169], [1, 0, 1, 0, 289], [1, 1, 19, 0, 0], [1, 0, -17, 0, 529], [1, -9, 76, -261, 841], [1, 12, 97, 372, 961], [1, 0, -10, 0, 1369], [1, 0, 73, 0, 1681], [1, 0, 7, 0, 1849], [1, 0, 79, 0, 2209], [1, 0, -73, 0, 2809], [1, -9, 82, -531, 3481], [1, 19, 192, 1159, 3721], [1, 0, -31, 0, 4489], [1, -9, 142, -639, 5041], [1, 0, -35, 0, 5329], [1, -9, 178, -711, 6241], [1, 0, 142, 0, 6889], [1, 9, 16, 801, 7921], [1, 0, -13, 0, 9409]], 'index': 4, 'instance_types': ['HMF', 'ECNF', 'ECNF', 'HMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-361.2-b', 'EllipticCurve/2.2.5.1/361.2/b', 'EllipticCurve/2.2.5.1/361.3/b', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-361.3-b'], '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': '4-95e2-1.1-c1e2-0-4', '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': '4-95e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.8709643042066444, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1825361187933151474, 'z1': {'__RealLiteral__': 0, 'data': '2.63792299456794529108614129707956', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9525810
{'Lhash': '3343964667419904175257154881450', 'Lhash_array': ['3343964667419904175257154881450'], 'label': '4-95e2-1.1-c1e2-0-4', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-361.3-b'}
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id: 9525622
{'Lhash': '3343964667419904175257154881450', 'Lhash_array': ['3343964667419904175257154881450'], 'label': '4-95e2-1.1-c1e2-0-4', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/361.3/b'}
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id: 9525504
{'Lhash': '3343964667419904175257154881450', 'Lhash_array': ['3343964667419904175257154881450'], 'label': '4-95e2-1.1-c1e2-0-4', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/361.2/b'}
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id: 9524927
{'Lhash': '3343964667419904175257154881450', 'Lhash_array': ['3343964667419904175257154881450'], 'label': '4-95e2-1.1-c1e2-0-4', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-361.2-b'}