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lfunc_lfunctions • Show schema
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{'Lhash': '1387634292251710718278678061291', 'a10': [5.700169592637544, 0], 'a2': [0, 2.805883701475779], 'a3': [0, 0], 'a4': [-3.872983346207417, 0], 'a5': [0, -2.031506006339283], 'a6': [0, 0], 'a7': [-0.5040171699309124, 0], 'a8': [0, 0.3563939586926006], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.673100788836337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '1089.485', 'coefficient_field': 'CDF', 'conductor': 1089, 'conductor_radical': 33, 'conjugate': '903674753794247769389834684023', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.805883701475779], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.031506006339283], [-25.0, 0]], [[1.0, 0], [0.5040171699309124, 0], [49.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-22.076661902843124, 0], [169.0, 0]], [[1.0, 0], [0, 11.981590691353341], [-289.0, 0]], [[1.0, 0], 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'1.98477896599178884780928844724013', '3.46544409900859677498883544901241', '3.57871185876543514126968879246835', '5.01359089791674693840793189009447', '6.18521053390602217384830818240007', '6.94990787589120012217214412359562', '8.170236012466068510398913138978808', '8.993729722474859411090233341289783', '9.731135062729649868763304717492992'], 'prelabel': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': -0.3040867239846964, 'root_number': '0.5773502691896257645091487805019574556476017512701268760 - 0.8164965809277260327324280249019637973219824935522233761*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1520433619923482', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09465044390140256520129479410', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98477896599178884780928844724', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46544409900859677498883544901', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.673100788836337, 'bad_primes': [3, 11], 'central_character': '3.2', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/3/b/h/485/7'], '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': '2-33e2-3.2-c2-0-41', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': -0.1520433619923482, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09465044390140256520129479410', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1387634292251710718278678061291', 'Lhash_array': ['1387634292251710718278678061291'], 'label': '2-33e2-3.2-c2-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/3/b/h/485/7'}