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lfunc_lfunctions • Show schema
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{'Lhash': '1072866725927085058297760405336,2167610137424008560396988396508', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.116451135324592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -2, 5]]], 'bad_primes': [2, 5], 'central_character': '640.1', 'coefficient_field': '1.1.1.1', 'conductor': 409600, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 0, 6, 0, 9], [1, -2, 5], [1, 0, -14, 0, 49], [1, 0, -22, 0, 121], [1, -12, 62, -156, 169], [1, 0, 30, 0, 289], [1, 0, -38, 0, 361], [1, 0, -46, 0, 529], [1, 0, -42, 0, 841], [1, 0, 62, 0, 961], [1, -4, 78, -148, 1369], [1, 20, 182, 820, 1681], [1, 0, 86, 0, 1849], [1, 0, -94, 0, 2209], [1, -28, 302, -1484, 2809], [1, 0, -118, 0, 3481], [1, 0, 22, 0, 3721], [1, 0, 134, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 110, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, 166, 0, 6889], 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'2.46820928880916121490131803546365', '3.10390762895250756848351725548926', '3.76762221979729374103780599959148', '3.93973282623656955346345631119288', '5.05080280077562764934099287219407', '5.68699361426989069092165727333918', '5.73681472321274272716718651272719', '6.08817597828249896892998079614518', '6.70345157950584420237967460650372', '7.07199505435686435711251716096430', '8.014066743832214300646375314542651', '8.395248025325154176219627201521624', '8.750650823645753158718143540585174', '8.760262332511950030321180966448125', '9.337043635161965010128317803858514', '10.12808288868102235352532880411576', '10.35795920313683108427023191836135', '10.75303934526943902420996081597008'], 'prelabel': '4-640e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.260625074921082, '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': 2177471019106870397, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.846342616596343495164064277755', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.70994289517454519158336061999', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.46820928880916121490131803546', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.116451135324592, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 409600, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, -6, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -20, 0, 0, 0, -12, 0, 0, 0, 14, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, -12, 62, -156, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 0, -38, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -46, 0, 529], 'euler29': [1, 0, -42, 0, 841], 'euler3': [1, 0, 6, 0, 9], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 20, 182, 820, 1681], 'euler43': [1, 0, 86, 0, 1849], 'euler47': [1, 0, -94, 0, 2209], 'euler5': [1, -2, 5, 0, 0], 'euler53': [1, -28, 302, -1484, 2809], 'euler59': [1, 0, -118, 0, 3481], 'euler61': [1, 0, 22, 0, 3721], 'euler67': [1, 0, 134, 0, 4489], 'euler7': [1, 0, -14, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 110, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 20, 278, 1780, 7921], 'euler97': [1, 0, -130, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 6, 0, 9], [1, -2, 5, 0, 0], [1, 0, -14, 0, 49], [1, 0, -22, 0, 121], [1, -12, 62, -156, 169], [1, 0, 30, 0, 289], [1, 0, -38, 0, 361], [1, 0, -46, 0, 529], [1, 0, -42, 0, 841], [1, 0, 62, 0, 961], [1, -4, 78, -148, 1369], [1, 20, 182, 820, 1681], [1, 0, 86, 0, 1849], [1, 0, -94, 0, 2209], [1, -28, 302, -1484, 2809], [1, 0, -118, 0, 3481], [1, 0, 22, 0, 3721], [1, 0, 134, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, 110, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, 166, 0, 6889], [1, 20, 278, 1780, 7921], [1, 0, -130, 0, 9409]], 'index': 12, 'instance_types': ['ECNF', 'HMF', 'ECNF', 'ECNF', 'CMF'], 'instance_urls': ['EllipticCurve/2.2.40.1/256.1/e', 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-256.1-e', 'EllipticCurve/2.0.4.1/25600.1/CMc', 'EllipticCurve/2.0.4.1/25600.3/CMc', 'ModularForm/GL2/Q/holomorphic/640/2/f/b'], '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': '4-640e2-1.1-c1e2-0-12', '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': '4-640e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.260625074921082, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2177471019106870397, 'z1': {'__RealLiteral__': 0, 'data': '0.846342616596343495164064277755', 'prec': 107}}
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lfunc_instances • Show schema
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id: 12517803
{'Lhash': '1072866725927085058297760405336,2167610137424008560396988396508', 'Lhash_array': ['1072866725927085058297760405336', '2167610137424008560396988396508'], 'factors': ['2-640-40.29-c1-0-5', '2-640-40.29-c1-0-15'], 'label': '4-640e2-1.1-c1e2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/640/2/f/b'}
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id: 9661679
{'Lhash': '_1072866725927085058297760405336', 'Lhash_array': ['_1072866725927085058297760405336'], 'factors': ['4-640e2-1.1-c1e2-0-12'], 'label': '4-640e2-1.1-c1e2-0-12', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/25600.3/CMc'}
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id: 9661570
{'Lhash': '_1072866725927085058297760405336', 'Lhash_array': ['_1072866725927085058297760405336'], 'factors': ['4-640e2-1.1-c1e2-0-12'], 'label': '4-640e2-1.1-c1e2-0-12', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/25600.1/CMc'}
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id: 9495818
{'Lhash': '_1072866725927085058297760405336', 'Lhash_array': ['_1072866725927085058297760405336'], 'factors': ['4-640e2-1.1-c1e2-0-12'], 'label': '4-640e2-1.1-c1e2-0-12', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-256.1-e'}
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id: 9495619
{'Lhash': '_1072866725927085058297760405336', 'Lhash_array': ['_1072866725927085058297760405336'], 'factors': ['4-640e2-1.1-c1e2-0-12'], 'label': '4-640e2-1.1-c1e2-0-12', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.40.1/256.1/e'}