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lfunc_lfunctions • Show schema
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{'Lhash': '1232458165749588293450087052957', 'a10': 0, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': 0, 'a6': 1, 'a7': -4, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.31697312181063, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1]], [37, [1, 1]]], 'bad_primes': [2, 3, 5, 37], 'central_character': '5550.1', 'coefficient_field': '1.1.1.1', 'conductor': 5550, 'conductor_radical': 1110, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1], [1, 4, 7], [1, 2, 11], [1, 2, 13], [1, -2, 17], [1, -2, 19], [1, 0, 23], [1, -2, 29], [1, -4, 31], [1, 1], [1, 6, 41], [1, -4, 43], [1, -10, 47], [1, 6, 53], [1, -4, 59], [1, -4, 61], [1, -12, 67], [1, -8, 71], [1, -2, 73], [1, 4, 79], [1, 4, 83], [1, 6, 89], [1, 12, 97], [1, 0, 101], [1, 6, 103], [1, -8, 107], [1, 16, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [1], [[[1, 4, 7], 1]], [[[1, 2, 11], 1]], [[[1, 2, 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2.0271030617576984, 1.6024705993055144, 1.1268506291030502, 0.6229552018423258, 0.1148926866526468, -0.37310496052811026, -0.8179826768713837, -1.1991201812083219, -1.499477731924655, -1.706564830171377], 'positive_zeros': ['0.972238064280248028855185164021848', '2.38791136708214022248822531236054', '3.08795703472397618089672444703999', '3.97758013969812929029850281589157', '5.12743183833987971514073272880556', '5.73308229592129608621771128856515', '6.54529828892243655106166867614930', '7.00566116256809770507293385520427', '7.74593670654687023683873447921937'], 'prelabel': '2-5550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.6570994526002565, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 951877291781518922, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.972238064280248028855185164022', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.38791136708214022248822531236', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08795703472397618089672444704', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.31697312181063, 'bad_primes': [2, 3, 5, 37], 'central_character': '1.1', 'conductor': 5550, 'conductor_radical': 1110, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, -4, -1, 1, 0, -2, -1, -2, 4, 0, 1, 2, -1, 2, 0, 4, 2, 0, 1, 0, 2, -1, -4, 2, 0, 4, -1, 2, -2, 0, 1, -1, -2, 2, 0, -6, -4, 4, -2, 0, 0, 10, -1, 9, 0, -2, -2, -6, 1, 0, 4, -2, -2, 4, 0, 4, -4, -4, 1, 0, -2, 12, 2, 0, 0, 8, -1, 2, 1, 0, 2, 8, -2, -4, 0, 1, 6, -4, 4, 0, -4, -2, 2, -6, 0, 8, 0, -4, -10, 0, 1, -12, -9, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, -2, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -2, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 1, 0], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -10, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, -4, 61], 'euler67': [1, -12, 67], 'euler7': [1, 4, 7], 'euler71': [1, -8, 71], 'euler73': [1, -2, 73], 'euler79': [1, 4, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, 12, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 0], [1, 4, 7], [1, 2, 11], [1, 2, 13], [1, -2, 17], [1, -2, 19], [1, 0, 23], [1, -2, 29], [1, -4, 31], [1, 1, 0], [1, 6, 41], [1, -4, 43], [1, -10, 47], [1, 6, 53], [1, -4, 59], [1, -4, 61], [1, -12, 67], [1, -8, 71], [1, -2, 73], [1, 4, 79], [1, 4, 83], [1, 6, 89], [1, 12, 97]], 'index': 49, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5550/b', 'ModularForm/GL2/Q/holomorphic/5550/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/5550/2/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-5550-1.1-c1-0-49', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.6570994526002565, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 951877291781518922, 'z1': {'__RealLiteral__': 0, 'data': '0.972238064280248028855185164022', 'prec': 107}}
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lfunc_instances • Show schema
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id: 21482985
{'Lhash': '1232458165749588293450087052957', 'Lhash_array': ['1232458165749588293450087052957'], 'label': '2-5550-1.1-c1-0-49', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5550/2/a/b'}
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id: 24570810
{'Lhash': '1232458165749588293450087052957', 'Lhash_array': ['1232458165749588293450087052957'], 'label': '2-5550-1.1-c1-0-49', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5550/2/a/b/1/1'}
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id: 34409
{'Lhash': '951877291781518922', 'Lhash_array': ['951877291781518922'], 'label': '2-5550-1.1-c1-0-49', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5550/b'}