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lfunc_lfunctions • Show schema
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{'Lhash': '602052979520343555751656675402,3286591085754799176156552319448', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.308984173807213, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [5, [1, 2, 5]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '490.1', 'coefficient_field': '1.1.1.1', 'conductor': 240100, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, 0, 3, 0, 9], [1, 2, 5], [1], [1, 0, 22, 0, 121], [1, 0, -22, 0, 169], [1, 0, -30, 0, 289], [1, 4, 42, 76, 361], [1, 0, -45, 0, 529], [1, -2, 59, -58, 841], [1, 20, 162, 620, 961], [1, 0, -10, 0, 1369], [1, -6, 91, -246, 1681], [1, 0, -61, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, -70, 0, 2809], [1, -4, 122, -236, 3481], [1, -18, 203, -1098, 3721], [1, 0, -85, 0, 4489], [1, -12, 178, -852, 5041], [1, 0, -46, 0, 5329], [1, -20, 258, -1580, 6241], 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['0.47493605841542549925847141316584', '1.92285065984731881074930943091033', '2.59266321899983891570887367014349', '3.60656505690847192980830180824040', '3.74464901646632227273354820513725', '4.32131888863180932911347754335141', '5.27117429103822672790357983891076', '5.33256647568010760834851226251080', '6.01428805669115130069272882459760', '6.64714120899035296149152315967334', '7.12006120424806721003646622153480', '7.71749910702203284772542943787589', '8.039708844602938549015913210553627', '8.476055642707823217919944216769141', '9.065063327136548304541031009420801', '9.179472810046171780248909079024549', '9.767877890927488897866430958994338', '10.49506508414703429801356897994158', '10.74763762730017023390043941010573', '11.20625310417646513588492080101836'], 'prelabel': '4-490e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9780469405559467, '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': 255083596277899655, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47493605841542549925847141317', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92285065984731881074930943091', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.59266321899983891570887367014', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 15.308984173807213, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 240100, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, -2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 1, 0, 0, -4, 2, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, -20, 0, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 18, 0, 0, -1, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 20, -2, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 1], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, 4, 42, 76, 361], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 0, -45, 0, 529], 'euler29': [1, -2, 59, -58, 841], 'euler3': [1, 0, 3, 0, 9], 'euler31': [1, 20, 162, 620, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, -6, 91, -246, 1681], 'euler43': [1, 0, -61, 0, 1849], 'euler47': [1, 0, -30, 0, 2209], 'euler5': [1, 2, 5, 0, 0], 'euler53': [1, 0, -70, 0, 2809], 'euler59': [1, -4, 122, -236, 3481], 'euler61': [1, -18, 203, -1098, 3721], 'euler67': [1, 0, -85, 0, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -12, 178, -852, 5041], 'euler73': [1, 0, -46, 0, 5329], 'euler79': [1, -20, 258, -1580, 6241], 'euler83': [1, 0, -85, 0, 6889], 'euler89': [1, 14, 227, 1246, 7921], 'euler97': [1, 0, -194, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, 0, 3, 0, 9], [1, 2, 5, 0, 0], [1, 0, 0, 0, 0], [1, 0, 22, 0, 121], [1, 0, -22, 0, 169], [1, 0, -30, 0, 289], [1, 4, 42, 76, 361], [1, 0, -45, 0, 529], [1, -2, 59, -58, 841], [1, 20, 162, 620, 961], [1, 0, -10, 0, 1369], [1, -6, 91, -246, 1681], [1, 0, -61, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, -70, 0, 2809], [1, -4, 122, -236, 3481], [1, -18, 203, -1098, 3721], [1, 0, -85, 0, 4489], [1, -12, 178, -852, 5041], [1, 0, -46, 0, 5329], [1, -20, 258, -1580, 6241], [1, 0, -85, 0, 6889], [1, 14, 227, 1246, 7921], [1, 0, -194, 0, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/490/2/c/b'], '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': '4-490e2-1.1-c1e2-0-0', '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': 0, 'prelabel': '4-490e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9780469405559467, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 255083596277899655, 'z1': {'__RealLiteral__': 0, 'data': '0.47493605841542549925847141317', 'prec': 103}}
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{'Lhash': '602052979520343555751656675402,3286591085754799176156552319448', 'Lhash_array': ['602052979520343555751656675402', '3286591085754799176156552319448'], 'label': '4-490e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/490/2/c/b'}