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lfunc_lfunctions • Show schema
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{'Lhash': '2613076876589364364440878530056,3424857521160936274962443297717', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 3, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7029635590013517, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, 1]], [5, [1, -2, 5]], [7, [1, 0, 1]]], 'bad_primes': [3, 5, 7], 'central_character': '105.1', 'coefficient_field': '1.1.1.1', 'conductor': 11025, 'conductor_radical': 105, 'degree': 4, 'euler_factors': [[1, 0, -3, 0, 4], [1, 0, 1], [1, -2, 5], [1, 0, 1], [1, 12, 58, 132, 121], [1, 0, -22, 0, 169], [1, 0, -18, 0, 289], [1, -12, 74, -228, 361], [1, 0, -46, 0, 529], [1, -4, 62, -116, 841], [1, 20, 162, 620, 961], [1, 0, -58, 0, 1369], [1, -4, 86, -164, 1681], [1, 0, -70, 0, 1849], [1, 0, -94, 0, 2209], [1, 0, -70, 0, 2809], [1, -16, 182, -944, 3481], [1, 4, 126, 244, 3721], [1, 0, 122, 0, 4489], [1, -20, 242, -1420, 5041], [1, 0, -110, 0, 5329], [1, 8, 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'2.70173620439600678454391775595319', '3.31926418578659151487141795523092', '5.20934549967759721253207672093685', '5.53092384774540902824306223888143', '5.66673716415926716727854405041960', '6.96295836787847011215570227141724', '7.40285334522283855310331904914879', '7.77449242194542902577294645996863', '8.370119229283450604227174471650752', '9.590614160303390257499736002488739', '9.704083858777687059690286950372646', '10.65843719583477371813672800040579', '10.69192697832386041230196696031786', '11.27433118061208772548131650751188', '11.86948020238545760806007327417249', '12.59576519015341727507158702442038', '13.03878561228530477495552939210211', '13.34777610896378407247861108327276', '14.07765741036902913605419866631650'], 'prelabel': '4-105e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9156578079301484, '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': 1192844162976794530, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.06135419027838012408223731157', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70173620439600678454391775595', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31926418578659151487141795523', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7029635590013517, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 11025, 'conductor_radical': 105, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 3, 2, 0, 0, 0, -1, 0, -12, 0, 0, 0, 0, 5, 0, 0, 12, 6, 0, 0, 0, 0, -1, 0, 0, 0, 4, 0, -20, 0, 0, 0, 0, -3, 0, 0, 0, 0, 4, 0, 0, -36, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, -24, 0, 0, 0, 16, 0, -4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 36, 0, 0, -8, 10, 1, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 24, 0, 0, 0, 12, -3], 'euler11': [1, 12, 58, 132, 121], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, 0, -18, 0, 289], 'euler19': [1, -12, 74, -228, 361], 'euler2': [1, 0, -3, 0, 4], 'euler23': [1, 0, -46, 0, 529], 'euler29': [1, -4, 62, -116, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, 20, 162, 620, 961], 'euler37': [1, 0, -58, 0, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 0, -70, 0, 1849], 'euler47': [1, 0, -94, 0, 2209], 'euler5': [1, -2, 5, 0, 0], 'euler53': [1, 0, -70, 0, 2809], 'euler59': [1, -16, 182, -944, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, 122, 0, 4489], 'euler7': [1, 0, 1, 0, 0], 'euler71': [1, -20, 242, -1420, 5041], 'euler73': [1, 0, -110, 0, 5329], 'euler79': [1, 8, 174, 632, 6241], 'euler83': [1, 0, -102, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 0, -190, 0, 9409], 'euler_factors': [[1, 0, -3, 0, 4], [1, 0, 1, 0, 0], [1, -2, 5, 0, 0], [1, 0, 1, 0, 0], [1, 12, 58, 132, 121], [1, 0, -22, 0, 169], [1, 0, -18, 0, 289], [1, -12, 74, -228, 361], [1, 0, -46, 0, 529], [1, -4, 62, -116, 841], [1, 20, 162, 620, 961], [1, 0, -58, 0, 1369], [1, -4, 86, -164, 1681], [1, 0, -70, 0, 1849], [1, 0, -94, 0, 2209], [1, 0, -70, 0, 2809], [1, -16, 182, -944, 3481], [1, 4, 126, 244, 3721], [1, 0, 122, 0, 4489], [1, -20, 242, -1420, 5041], [1, 0, -110, 0, 5329], [1, 8, 174, 632, 6241], [1, 0, -102, 0, 6889], [1, 12, 214, 1068, 7921], [1, 0, -190, 0, 9409]], 'index': 8, 'instance_types': ['ECNF', 'HMF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.5.1/441.1/a', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-441.1-a', 'ModularForm/GL2/Q/holomorphic/105/2/d/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-105e2-1.1-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': 0, 'prelabel': '4-105e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9156578079301484, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1192844162976794530, 'z1': {'__RealLiteral__': 0, 'data': '2.06135419027838012408223731157', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9965931
{'Lhash': '2613076876589364364440878530056,3424857521160936274962443297717', 'Lhash_array': ['2613076876589364364440878530056', '3424857521160936274962443297717'], 'label': '4-105e2-1.1-c1e2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/2/d/a'}
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id: 9529293
{'Lhash': '_2613076876589364364440878530056', 'Lhash_array': ['_2613076876589364364440878530056'], 'label': '4-105e2-1.1-c1e2-0-8', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-441.1-a'}
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id: 9528898
{'Lhash': '_2613076876589364364440878530056', 'Lhash_array': ['_2613076876589364364440878530056'], 'label': '4-105e2-1.1-c1e2-0-8', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/441.1/a'}