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lfunc_lfunctions • Show schema
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{'Lhash': '1770658586030482960123640738098', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.82842712474619, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.2935231424704, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '6048.1', 'coefficient_field': 'CDF', 'conductor': 6048, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.82842712474619, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.82842712474619, 0], [11.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [13.0, 0]], [[1.0, 0], [-0.1715728752538099, 0], [17.0, 0]], [[1.0, 0], [6.82842712474619, 0], [19.0, 0]], [[1.0, 0], [-4.0, 0], [23.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], 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'2-6048-1.1-c1-0-75', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/6048/2/a/y/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-6.903657573877204e-61, 0.19775787736508213, 0.3944996168741599, 0.5891696619739047, 0.7806364661176437, 0.9676614126801588, 1.1488754887913009, 1.3227654636074735, 1.4876707353444805, 1.641791408173599, 1.7832075877054396, 1.9099093756051033, 2.019836617403121, 2.1109271164839734, 2.181171765451997, 2.2286748522724498, 2.251717660227798, 2.2488233869287844, 2.2188213507212486, 2.160908428885475, 2.0747056804782384, 1.9603081495686538, 1.818325925643661, 1.6499146614196463, 1.456793918251884, 1.241251928851141, 1.0061356376042538, 0.7548251999902126, 0.49119249168963786, 0.21954358994251302, -0.05545436292585553, 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'7.940251506125181964542625213197898'], 'prelabel': '2-6048-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.949354152903016, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39680333501336359637658968782', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44097987761418239959035528206', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99228183304057857889543772363', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.2935231424704, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 6048, 'conductor_radical': 42, 'degree': 2, 'index': 75, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6048/2/a/y/1/2'], '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': '2-6048-1.1-c1-0-75', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6048-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.949354152903016, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39680333501336359637658968782', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1770658586030482960123640738098', 'Lhash_array': ['1770658586030482960123640738098'], 'label': '2-6048-1.1-c1-0-75', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6048/2/a/y/1/2'}