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lfunc_lfunctions • Show schema
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{'Lhash': '1359601749645166076050067363891,2332724992806372475684464655055', 'a10': -2, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 1, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.110407724657517, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1]], [7, [1, -1, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '378.1', 'coefficient_field': '1.1.1.1', 'conductor': 142884, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, -1, 1], [1], [1, 2, -1, 10, 25], [1, -1, 7], [1, -5, 14, -55, 121], [1, -12, 62, -156, 169], [1, 4, -1, 68, 289], [1, -4, -3, -76, 361], [1, 4, -7, 92, 529], [1, 14, 107, 406, 841], [1, 3, -22, 93, 961], [1, 8, 27, 296, 1369], [1, -12, 118, -492, 1681], [1, -16, 150, -688, 1849], [1, -6, -11, -282, 2209], [1, 6, -17, 318, 2809], [1, -7, -10, -413, 3481], [1, 0, -61, 0, 3721], [1, 10, 33, 670, 4489], [1, -8, 158, -568, 5041], [1, 13, 96, 949, 5329], 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['1.07253666696515717695817810771998', '1.84019554945691324312473519306801', '3.16585513149263045912795950808797', '3.77751641580697688276586904034181', '4.06368059801025279216366444096343', '4.22831925259862427095549030403407', '5.48322240473819835554297886333133', '5.67013401985455615137700811859285', '6.39218317429906017235492956272541', '6.58420840546510374209119620213373', '7.55720783839625913117175217511737', '7.67629939923188281731416952850009', '8.475734715203401914282448175798517', '8.980879058013000285634068643822406', '9.071480386247876814458494402307319', '9.488164441171811616303707442350077', '10.70261601664224664085062975676632', '10.83918973737132585995253991887452', '11.23231644065076563021275437414172', '11.45688228847364560918921616366141'], 'prelabel': '4-378e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.737338538225754, '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': 1296711901038946803, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07253666696515717695817810772', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84019554945691324312473519307', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16585513149263045912795950809', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.110407724657517, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 142884, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 0, -2, 0, 1, -1, 0, -2, 5, 0, 12, 1, 0, -1, -4, 0, 4, 0, 0, 5, -4, 0, 5, 12, 0, 0, -14, 0, -3, 0, 0, -4, -2, 0, -8, 4, 0, 2, 12, 0, 16, 0, 0, -4, 6, 0, -6, 5, 0, 0, -6, 0, -10, -1, 0, -14, 7, 0, 0, -3, 0, 1, -24, 0, -10, 0, 0, -2, 8, 0, -13, -8, 0, 0, 5, 0, 3, 2, 0, 12, 14, 0, 8, 16, 0, -5, 6, 0, 12, 0, 0, 6, -8, 0, -10, -6, 0, 0], 'euler11': [1, -5, 14, -55, 121], 'euler13': [1, -12, 62, -156, 169], 'euler17': [1, 4, -1, 68, 289], 'euler19': [1, -4, -3, -76, 361], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 4, -7, 92, 529], 'euler29': [1, 14, 107, 406, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 3, -22, 93, 961], 'euler37': [1, 8, 27, 296, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, -6, -11, -282, 2209], 'euler5': [1, 2, -1, 10, 25], 'euler53': [1, 6, -17, 318, 2809], 'euler59': [1, -7, -10, -413, 3481], 'euler61': [1, 0, -61, 0, 3721], 'euler67': [1, 10, 33, 670, 4489], 'euler7': [1, -1, 7, 0, 0], 'euler71': [1, -8, 158, -568, 5041], 'euler73': [1, 13, 96, 949, 5329], 'euler79': [1, -3, -70, -237, 6241], 'euler83': [1, -14, 215, -1162, 6889], 'euler89': [1, -6, -53, -534, 7921], 'euler97': [1, 10, 219, 970, 9409], 'euler_factors': [[1, -1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 2, -1, 10, 25], [1, -1, 7, 0, 0], [1, -5, 14, -55, 121], [1, -12, 62, -156, 169], [1, 4, -1, 68, 289], [1, -4, -3, -76, 361], [1, 4, -7, 92, 529], [1, 14, 107, 406, 841], [1, 3, -22, 93, 961], [1, 8, 27, 296, 1369], [1, -12, 118, -492, 1681], [1, -16, 150, -688, 1849], [1, -6, -11, -282, 2209], [1, 6, -17, 318, 2809], [1, -7, -10, -413, 3481], [1, 0, -61, 0, 3721], [1, 10, 33, 670, 4489], [1, -8, 158, -568, 5041], [1, 13, 96, 949, 5329], [1, -3, -70, -237, 6241], [1, -14, 215, -1162, 6889], [1, -6, -53, -534, 7921], [1, 10, 219, 970, 9409]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/g/d'], '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': '4-378e2-1.1-c1e2-0-9', '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': '4-378e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1296711901038946803, 'z1': {'__RealLiteral__': 0, 'data': '1.07253666696515717695817810772', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1359601749645166076050067363891,2332724992806372475684464655055', 'Lhash_array': ['1359601749645166076050067363891', '2332724992806372475684464655055'], 'label': '4-378e2-1.1-c1e2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/g/d'}