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lfunc_lfunctions • Show schema
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{'Lhash': '819077642782610050518103476417,1603430778715738962628080256373', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 29, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2227.9842459683314, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '800.1', 'coefficient_field': '1.1.1.1', 'conductor': 640000, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 0, -29, 0, 729], [1], [1, 0, -586, 0, 117649], [1, -30, 2887, -39930, 1771561], [1, 0, -4330, 0, 4826809], [1, 0, -9385, 0, 24137569], [1, -210, 24743, -1440390, 47045881], [1, 0, -24234, 0, 148035889], [1, -40, 49178, -975560, 594823321], [1, -460, 112482, -13703860, 887503681], [1, 0, -98390, 0, 2565726409], [1, 390, 175867, 26879190, 4750104241], [1, 0, -69014, 0, 6321363049], [1, 0, 22754, 0, 10779215329], [1, 0, -194070, 0, 22164361129], [1, -1120, 724358, -230024480, 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'positive_zeros': ['0.64613833073178231131757435988420', '1.26488385555692970705924787354519', '1.54790423162024687556825623202883', '2.78126844935986425972026293445335', '2.88791181688403196196396084694362', '3.82731252784844201825549473418091', '4.07163811184688328759868427161397', '4.71570131924286179387925384088359', '5.18653088557902217491367584193390', '5.58153553336405977469609779422101', '6.33301783298817688197392994370329', '6.60857381789066001051997728775750', '7.06974186968484141758342007935591', '7.63561133962991080667685581650985', '7.70072005272500346146200503195743', '8.588597613853944861855092057132987', '8.695014365901603831648621809635743', '9.390462472179069596155106907534952', '9.716079964802622421143196220287611', '10.05933523694180690769316812377069'], 'prelabel': '4-800e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.870336818860667, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 782358867241353576, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64613833073178231131757435988', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.26488385555692970705924787355', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.54790423162024687556825623203', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2227.9842459683314, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 640000, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 29, 0, 30, 0, 0, 0, 0, 0, 0, 0, 210, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 460, 0, 0, 0, 0, 0, 0, 0, 0, 0, -390, 0, 0, 0, 0, 0, 0, 0, 586, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1120, 0, -1460, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, -1660, 0, 112, 0, 0, 0, 0, 0, 0, 0, 1410, 0, 0, 0, 0, 0, 0, 0, 0, 0, 870, 0], 'euler11': [1, -30, 2887, -39930, 1771561], 'euler13': [1, 0, -4330, 0, 4826809], 'euler17': [1, 0, -9385, 0, 24137569], 'euler19': [1, -210, 24743, -1440390, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -24234, 0, 148035889], 'euler29': [1, -40, 49178, -975560, 594823321], 'euler3': [1, 0, -29, 0, 729], 'euler31': [1, -460, 112482, -13703860, 887503681], 'euler37': [1, 0, -98390, 0, 2565726409], 'euler41': [1, 390, 175867, 26879190, 4750104241], 'euler43': [1, 0, -69014, 0, 6321363049], 'euler47': [1, 0, 22754, 0, 10779215329], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -194070, 0, 22164361129], 'euler59': [1, -1120, 724358, -230024480, 42180533641], 'euler61': [1, 1460, 986862, 331392260, 51520374361], 'euler67': [1, 0, -536501, 0, 90458382169], 'euler7': [1, 0, -586, 0, 117649], 'euler71': [1, -80, 717422, -28632880, 128100283921], 'euler73': [1, 0, -677545, 0, 151334226289], 'euler79': [1, 1660, 1674978, 818444740, 243087455521], 'euler83': [1, 0, -1137949, 0, 326940373369], 'euler89': [1, -1410, 1906963, -994006290, 496981290961], 'euler97': [1, 0, 231010, 0, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -29, 0, 729], [1, 0, 0, 0, 0], [1, 0, -586, 0, 117649], [1, -30, 2887, -39930, 1771561], [1, 0, -4330, 0, 4826809], [1, 0, -9385, 0, 24137569], [1, -210, 24743, -1440390, 47045881], [1, 0, -24234, 0, 148035889], [1, -40, 49178, -975560, 594823321], [1, -460, 112482, -13703860, 887503681], [1, 0, -98390, 0, 2565726409], [1, 390, 175867, 26879190, 4750104241], [1, 0, -69014, 0, 6321363049], [1, 0, 22754, 0, 10779215329], [1, 0, -194070, 0, 22164361129], [1, -1120, 724358, -230024480, 42180533641], [1, 1460, 986862, 331392260, 51520374361], [1, 0, -536501, 0, 90458382169], [1, -80, 717422, -28632880, 128100283921], [1, 0, -677545, 0, 151334226289], [1, 1660, 1674978, 818444740, 243087455521], [1, 0, -1137949, 0, 326940373369], [1, -1410, 1906963, -994006290, 496981290961], [1, 0, 231010, 0, 832972004929]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/800/4/c/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': '4-800e2-1.1-c3e2-0-7', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-800e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.870336818860667, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 782358867241353576, 'z1': {'__RealLiteral__': 0, 'data': '0.64613833073178231131757435988', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '819077642782610050518103476417,1603430778715738962628080256373', 'Lhash_array': ['819077642782610050518103476417', '1603430778715738962628080256373'], 'label': '4-800e2-1.1-c3e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/800/4/c/d'}