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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '2220160689008643925956247152704', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.3504806021792133, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 3]]], 'bad_primes': [2, 3], 'central_character': '36864.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 2, 3], [1, 0, 2, 0, 25], [1, 0, 10, 0, 49], [1, 0, -14, 0, 121], [1, 0, 22, 0, 169], [1, 0, -34, 0, 289], [1, 12, 74, 228, 361], [1, 0, 14, 0, 529], [1, 0, 50, 0, 841], [1, 0, 58, 0, 961], [1, 0, 38, 0, 1369], [1, 0, -50, 0, 1681], [1, 4, 90, 172, 1849], [1, 0, -34, 0, 2209], [1, 0, 34, 0, 2809], [1, 0, -110, 0, 3481], [1, 0, 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-5.613129462879838], 'positive_zeros': ['1.75139797086746412243454574914640', '2.76608702409746176095302424854934', '3.84252961453441711169051333538222', '4.52827833300760369208621410126040', '4.97153580512610098325521001802584', '5.91562815270661005160626581722238', '6.09553790955098515565552989320949', '6.74848060717112410656014338963074', '7.19250214882024512254378722525109', '8.215028652014338750632346686889028', '8.364955351789872564250717727992689', '9.019660204875550419148497591381572', '9.730985256268271424878295911919706', '10.23233687889639886881720044924988'], 'prelabel': '4-192e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2731932061693510, 'z1': {'__RealLiteral__': 0, 'data': '1.75139797086746412243454574914640', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.76608702409746176095302424854934', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.84252961453441711169051333538222', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.3504806021792133, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -12, 0, 4, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0], 'euler11': [1, 0, -14, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, -34, 0, 289], 'euler19': [1, 12, 74, 228, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 14, 0, 529], 'euler29': [1, 0, 50, 0, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 0, 58, 0, 961], 'euler37': [1, 0, 38, 0, 1369], 'euler41': [1, 0, -50, 0, 1681], 'euler43': [1, 4, 90, 172, 1849], 'euler47': [1, 0, -34, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 0, 34, 0, 2809], 'euler59': [1, 0, -110, 0, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, 4, 138, 268, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, 110, 0, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, 0, -38, 0, 6241], 'euler83': [1, 0, -158, 0, 6889], 'euler89': [1, 0, 110, 0, 7921], 'euler97': [1, 20, 294, 1940, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 3, 0, 0], [1, 0, 2, 0, 25], [1, 0, 10, 0, 49], [1, 0, -14, 0, 121], [1, 0, 22, 0, 169], [1, 0, -34, 0, 289], [1, 12, 74, 228, 361], [1, 0, 14, 0, 529], [1, 0, 50, 0, 841], [1, 0, 58, 0, 961], [1, 0, 38, 0, 1369], [1, 0, -50, 0, 1681], [1, 4, 90, 172, 1849], [1, 0, -34, 0, 2209], [1, 0, 34, 0, 2809], [1, 0, -110, 0, 3481], [1, 0, 118, 0, 3721], [1, 4, 138, 268, 4489], [1, 0, 110, 0, 5041], [1, 12, 182, 876, 5329], [1, 0, -38, 0, 6241], [1, 0, -158, 0, 6889], [1, 0, 110, 0, 7921], [1, 20, 294, 1940, 9409]], 'index': 9, 'instance_types': ['ECNF', 'BMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.0.3.1/4096.1/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/4096.1/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/4096.1/a', 'EllipticCurve/2.0.3.1/4096.1/a'], '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': '4-192e2-1.1-c1e2-0-9', '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': '4-192e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2731932061693510, 'z1': {'__RealLiteral__': 0, 'data': '1.75139797086746412243454574914640', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9765075
{'Lhash': '2220160689008643925956247152704', 'Lhash_array': ['2220160689008643925956247152704'], 'label': '4-192e2-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/4096.1/a'}
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id: 9763903
{'Lhash': '2220160689008643925956247152704', 'Lhash_array': ['2220160689008643925956247152704'], 'label': '4-192e2-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/4096.1/a'}
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id: 9763768
{'Lhash': '2220160689008643925956247152704', 'Lhash_array': ['2220160689008643925956247152704'], 'label': '4-192e2-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/4096.1/b'}
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id: 9763767
{'Lhash': '2220160689008643925956247152704', 'Lhash_array': ['2220160689008643925956247152704'], 'label': '4-192e2-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/4096.1/b'}