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lfunc_lfunctions • Show schema
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{'Lhash': '727853402207044382386763472873', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [15.24588454160013, 0], 'a6': [0, 0], 'a7': [55.669794404940966, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 119.0821974725887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.449', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '1308365069413639016973094043204', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-15.24588454160013, 0], [625.0, 0]], [[1.0, 0], [-55.669794404940966, 0], [2401.0, 0]], [[1.0, 0], [98.39075113604954, 0], [14641.0, 0]], [[1.0, 0], [0, -135.8970198348735], [-28561.0, 0]], [[1.0, 0], [0, 285.36213714922], [-83521.0, 0]], [[1.0, 0], [0, -161.7729516666468], [-130321.0, 0]], [[1.0, 0], [0, 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['0.57417509373324222336163619292485', '1.78996318476002021244077287157077', '2.61757460752692082287367006607157', '3.92567175074579172636086326957874', '5.01779413929069298528667606779307', '5.57609403632020481091573601874534', '6.53887746069801963090192578432293', '7.72112772466675835071261545170777', '8.182449885777606611229546825389597', '9.031445557912791969947904868325751'], 'prelabel': '2-1152-24.5-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.912478979250714, 'root_angle': -0.1520433619923482, 'root_number': '0.5773502691896257645091487805019574556476017512701268760 - 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1520433619923482', 'prec': 64}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57417509373324222336163619292', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.78996318476002021244077287157', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.61757460752692082287367006607', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 119.0821974725887, 'bad_primes': [2, 3], 'central_character': '24.5', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/5/h/e/449/6'], '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': '2-1152-24.5-c4-0-30', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-1152-24.5-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.912478979250714, 'root_angle': -0.1520433619923482, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57417509373324222336163619292', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '727853402207044382386763472873', 'Lhash_array': ['727853402207044382386763472873'], 'factors': ['2-1152-24.5-c4-0-30'], 'label': '2-1152-24.5-c4-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/5/h/e/449/6'}