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lfunc_lfunctions • Show schema
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{'Lhash': '1165773515857466062122060304561', 'a10': 2, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': -2, 'a6': 0, 'a7': -4, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.87147688462052, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '9126.1', 'coefficient_field': '1.1.1.1', 'conductor': 9126, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 2, 5], [1, 4, 7], [1, -2, 11], [1], [1, -6, 17], [1, 3, 19], [1, 4, 23], [1, 4, 29], [1, -5, 31], [1, -3, 37], [1, 6, 41], [1, -7, 43], [1, 10, 47], [1, -12, 53], [1, -10, 59], [1, -1, 61], [1, -11, 67], [1, 16, 71], [1, 5, 73], [1, 1, 79], [1, 0, 83], [1, 6, 89], [1, -7, 97], [1, 2, 101], [1, -16, 103], [1, -2, 107], [1, -17, 109], [1, 16, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, 2, 5], 1]], [[[1, 4, 7], 1]], [[[1, -2, 11], 1]], [1], [[[1, -6, 17], 1]], 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-1.1338679415500972, -0.9091380646742803, -0.625299733038976, -0.30725742551047275, 0.01819971192047728, 0.32405930832021795, 0.5847828408141124, 0.7779361026210299, 0.8856528022099506], 'positive_zeros': ['0.919633151002002238213231666565069', '2.15566173481552240708340121785768', '3.17434183398426959328104402213026', '3.66350345752162845202271348890479', '4.33607216669422279608954374660041', '5.62915593411303146463645006444804', '6.13256967104391770121389314834821', '6.85425688679637173788038592217441', '7.39817629290458357844831457914970'], 'prelabel': '2-9126-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.536479185508538, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 140551275781280965, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.919633151002002238213231666565', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.15566173481552240708340121786', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17434183398426959328104402213', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.87147688462052, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 9126, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -2, 0, -4, -1, 0, 2, 2, 0, 0, 4, 0, 1, 6, 0, -3, -2, 0, -2, -4, 0, -1, 0, 0, -4, -4, 0, 5, -1, 0, -6, 8, 0, 3, 3, 0, 2, -6, 0, 7, 2, 0, 4, -10, 0, 9, 1, 0, 0, 12, 0, -4, 4, 0, 4, 10, 0, 1, -5, 0, 1, 0, 0, 11, 6, 0, -8, -16, 0, -5, -3, 0, -3, -8, 0, -1, -2, 0, 6, 0, 0, -12, -7, 0, -2, -6, 0, 0, -4, 0, 10, 6, 0, 7, -9, 0, -1], 'euler11': [1, -2, 11], 'euler13': [1, 0, 0], 'euler17': [1, -6, 17], 'euler19': [1, 3, 19], 'euler2': [1, 1, 0], 'euler23': [1, 4, 23], 'euler29': [1, 4, 29], 'euler3': [1, 0, 0], 'euler31': [1, -5, 31], 'euler37': [1, -3, 37], 'euler41': [1, 6, 41], 'euler43': [1, -7, 43], 'euler47': [1, 10, 47], 'euler5': [1, 2, 5], 'euler53': [1, -12, 53], 'euler59': [1, -10, 59], 'euler61': [1, -1, 61], 'euler67': [1, -11, 67], 'euler7': [1, 4, 7], 'euler71': [1, 16, 71], 'euler73': [1, 5, 73], 'euler79': [1, 1, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 2, 5], [1, 4, 7], [1, -2, 11], [1, 0, 0], [1, -6, 17], [1, 3, 19], [1, 4, 23], [1, 4, 29], [1, -5, 31], [1, -3, 37], [1, 6, 41], [1, -7, 43], [1, 10, 47], [1, -12, 53], [1, -10, 59], [1, -1, 61], [1, -11, 67], [1, 16, 71], [1, 5, 73], [1, 1, 79], [1, 0, 83], [1, 6, 89], [1, -7, 97]], 'index': 89, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/9126/c', 'ModularForm/GL2/Q/holomorphic/9126/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/9126/2/a/c'], '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': '2-9126-1.1-c1-0-89', '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': '2-9126-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.536479185508538, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 140551275781280965, 'z1': {'__RealLiteral__': 0, 'data': '0.919633151002002238213231666565', 'prec': 107}}
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lfunc_instances • Show schema
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id: 22661444
{'Lhash': '1165773515857466062122060304561', 'Lhash_array': ['1165773515857466062122060304561'], 'factors': ['2-9126-1.1-c1-0-89'], 'label': '2-9126-1.1-c1-0-89', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9126/2/a/c'}
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id: 24587188
{'Lhash': '1165773515857466062122060304561', 'Lhash_array': ['1165773515857466062122060304561'], 'factors': ['2-9126-1.1-c1-0-89'], 'label': '2-9126-1.1-c1-0-89', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9126/2/a/c/1/1'}
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id: 39774
{'Lhash': '140551275781280965', 'Lhash_array': ['140551275781280965'], 'factors': ['2-9126-1.1-c1-0-89'], 'label': '2-9126-1.1-c1-0-89', 'type': 'ECQ', 'url': 'EllipticCurve/Q/9126/c'}