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lfunc_lfunctions • Show schema
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{'Lhash': '540117168805264901274365594413,889299355685799795766035246498', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5846.857224180202, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 2, 1]], [19, [1, 2, 1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '9576.1', 'coefficient_field': '1.1.1.1', 'conductor': 91699776, 'conductor_radical': 798, 'degree': 4, 'euler_factors': [[1], [1], [1, 4, 14, 20, 25], [1, 2, 1], [1, -4, 26, -44, 121], [1, -2, 10, -26, 169], [1, -2, 18, -34, 289], [1, 2, 1], [1, 6, 38, 138, 529], [1, -10, 66, -290, 841], [1, -6, 54, -186, 961], [1, 10, 82, 370, 1369], [1, 0, 14, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 94, 0, 2209], [1, -2, 90, -106, 2809], [1, 4, 54, 236, 3481], [1, 4, 126, 244, 3721], [1, 12, 102, 804, 4489], [1, -6, -2, -426, 5041], [1, 20, 246, 1460, 5329], [1, -18, 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0.19684984220452845, 0.11441122675105311], 'positive_zeros': ['0.42607731870913130939555465244009', '0.70153349473876257868841530636861', '1.52196817292305346432031620227929', '1.76980991153540768376863713601669', '2.66144195653829354079566755846705', '2.82970041661384375884560329137239', '3.51297941035596890293402275488927', '3.58789587897799903431276403506495', '3.97319549997191632117540244165345', '4.26791466512881524167539492356335', '4.66293939515861899167726718694486', '4.84588209817386277044704354395489', '5.75058348493841252944320472382696', '5.79645148908963802216614021230289', '6.31480450206719184619501330049405', '6.39649675499337916231273539639558', '6.99337560207161330067812098485680', '7.07474396074337534150988546293142', '7.60358830764236590411092016299484', '7.84951657561159274106672978736497'], 'prelabel': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 956832446305626366, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42607731870913130939555465244', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.70153349473876257868841530637', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.52196817292305346432031620228', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5846.857224180202, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 91699776, 'conductor_radical': 798, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -4, 0, -2, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, -6, 0, 2, 0, 0, 0, 10, 0, 6, 0, 0, 0, 8, 0, -10, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, -16, 0, 0, 0, -4, 0, -4, 0, 0, 0, -8, 0, -12, 0, 0, 0, 6, 0, -20, 0, 0, 0, -8, 0, 18, 0, 0, 0, -10, 0, -8, 0, 0, 0, 16, 0, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0], 'euler11': [1, -4, 26, -44, 121], 'euler13': [1, -2, 10, -26, 169], 'euler17': [1, -2, 18, -34, 289], 'euler19': [1, 2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 6, 38, 138, 529], 'euler29': [1, -10, 66, -290, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -6, 54, -186, 961], 'euler37': [1, 10, 82, 370, 1369], 'euler41': [1, 0, 14, 0, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 4, 14, 20, 25], 'euler53': [1, -2, 90, -106, 2809], 'euler59': [1, 4, 54, 236, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 12, 102, 804, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, -6, -2, -426, 5041], 'euler73': [1, 20, 246, 1460, 5329], 'euler79': [1, -18, 222, -1422, 6241], 'euler83': [1, 10, 174, 830, 6889], 'euler89': [1, -16, 174, -1424, 7921], 'euler97': [1, 0, 126, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 4, 14, 20, 25], [1, 2, 1, 0, 0], [1, -4, 26, -44, 121], [1, -2, 10, -26, 169], [1, -2, 18, -34, 289], [1, 2, 1, 0, 0], [1, 6, 38, 138, 529], [1, -10, 66, -290, 841], [1, -6, 54, -186, 961], [1, 10, 82, 370, 1369], [1, 0, 14, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 94, 0, 2209], [1, -2, 90, -106, 2809], [1, 4, 54, 236, 3481], [1, 4, 126, 244, 3721], [1, 12, 102, 804, 4489], [1, -6, -2, -426, 5041], [1, 20, 246, 1460, 5329], [1, -18, 222, -1422, 6241], [1, 10, 174, 830, 6889], [1, -16, 174, -1424, 7921], [1, 0, 126, 0, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/bd'], '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': '4-9576e2-1.1-c1e2-0-1', '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': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 956832446305626366, 'z1': {'__RealLiteral__': 0, 'data': '0.42607731870913130939555465244', 'prec': 103}}
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{'Lhash': '540117168805264901274365594413,889299355685799795766035246498', 'Lhash_array': ['540117168805264901274365594413', '889299355685799795766035246498'], 'label': '4-9576e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bd'}