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lfunc_lfunctions • Show schema
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{'Lhash': '1320435784575109323765851950731,1720271863372800332476712964986', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2482.695136051794, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [5, [1, 2, 1]], [13, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '6240.1', 'coefficient_field': '1.1.1.1', 'conductor': 38937600, 'conductor_radical': 390, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, 2, 1], [1, 0, 6, 0, 49], [1, 0, 14, 0, 121], [1, -2, 1], [1, -4, 6, -68, 289], [1, 8, 46, 152, 361], [1, -8, 62, -184, 529], [1, 4, 30, 116, 841], [1, 8, 70, 248, 961], [1, 4, 78, 148, 1369], [1, 4, 86, 164, 1681], [1, 8, 70, 344, 1849], [1, 8, 102, 376, 2209], [1, 4, 110, 212, 2809], [1, 0, 46, 0, 3481], [1, -12, 158, -732, 3721], [1, 0, 126, 0, 4489], [1, -16, 198, -1136, 5041], [1, -20, 214, -1460, 5329], [1, 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'1.35705521936650401298490173657220', '2.03406364065911879725986757058402', '2.43479526985920936623784068250317', '3.31207177792891291363343491147687', '3.46121125390384002069196025270617', '3.92170496559169759065824575124924', '4.05693533066938727376903134209698', '4.93845505461745544324141015095092', '4.97269078446986327272435223134462', '5.33793574754763320591074739203392', '5.51537177124581582668969735735240', '6.38749609240752239953024993449034', '6.47182732253031108130050905720420', '6.82024108839028276294187812984082', '6.84775307139191924109424521523358', '7.71878625959832598377336505726259', '7.72110541379366259502807123141845'], 'prelabel': '4-6240e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1256676814829683151, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04164016830613767829906517880', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.35705521936650401298490173657', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.03406364065911879725986757058', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2482.695136051794, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 38937600, 'conductor_radical': 390, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, -2, 0, 0, 0, 3, 0, 0, 0, 2, 0, 4, 0, 4, 0, -8, 0, 0, 0, 8, 0, 3, 0, -4, 0, -4, 0, -8, 0, 0, 0, 0, 0, -4, 0, -4, 0, -4, 0, -8, 0, -6, 0, -8, 0, -6, 0, -8, 0, -4, 0, 0, 0, 16, 0, 0, 0, 12, 0, 0, 0, -4, 0, 0, 0, -16, 0, 16, 0, 20, 0, -6, 0, 0, 0, 16, 0, 5, 0, -8, 0, -8, 0, 8, 0, 12, 0, 0, 0, 16, 0, 16, 0, 4, 0, 0, 0], 'euler11': [1, 0, 14, 0, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, -4, 6, -68, 289], 'euler19': [1, 8, 46, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -8, 62, -184, 529], 'euler29': [1, 4, 30, 116, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 8, 70, 248, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 4, 86, 164, 1681], 'euler43': [1, 8, 70, 344, 1849], 'euler47': [1, 8, 102, 376, 2209], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, 0, 46, 0, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, 0, 126, 0, 4489], 'euler7': [1, 0, 6, 0, 49], 'euler71': [1, -16, 198, -1136, 5041], 'euler73': [1, -20, 214, -1460, 5329], 'euler79': [1, -16, 190, -1264, 6241], 'euler83': [1, 8, 174, 664, 6889], 'euler89': [1, -12, 86, -1068, 7921], 'euler97': [1, -4, 166, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 2, 1, 0, 0], [1, 0, 6, 0, 49], [1, 0, 14, 0, 121], [1, -2, 1, 0, 0], [1, -4, 6, -68, 289], [1, 8, 46, 152, 361], [1, -8, 62, -184, 529], [1, 4, 30, 116, 841], [1, 8, 70, 248, 961], [1, 4, 78, 148, 1369], [1, 4, 86, 164, 1681], [1, 8, 70, 344, 1849], [1, 8, 102, 376, 2209], [1, 4, 110, 212, 2809], [1, 0, 46, 0, 3481], [1, -12, 158, -732, 3721], [1, 0, 126, 0, 4489], [1, -16, 198, -1136, 5041], [1, -20, 214, -1460, 5329], [1, -16, 190, -1264, 6241], [1, 8, 174, 664, 6889], [1, -12, 86, -1068, 7921], [1, -4, 166, -388, 9409]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6240/2/a/bh'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '4-6240e2-1.1-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': 2, 'prelabel': '4-6240e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.058799534005693, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1256676814829683151, 'z1': {'__RealLiteral__': 0, 'data': '1.04164016830613767829906517880', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1320435784575109323765851950731,1720271863372800332476712964986', 'Lhash_array': ['1320435784575109323765851950731', '1720271863372800332476712964986'], 'label': '4-6240e2-1.1-c1e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6240/2/a/bh'}