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lfunc_lfunctions • Show schema
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{'Lhash': '4225767501989712439101119577404', 'a10': [-21.740852297878796, -3.258045866607423e-60], 'a2': [1.0, 1.7320508075688772], 'a3': [3.3117376914898995, -4.004047135432493], 'a4': [-2.0, 3.4641016151377544], 'a5': [-5.435213074469699, 9.414065194944163], 'a6': [10.246950765959598, 1.7320508075688772], 'a7': [-12.435213074469699, -21.538420847926304], 'a8': [-8.0, 0.0], 'a9': [-5.064786925530301, -26.520707633827897], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0620343801033316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, -1.7320508075688772]]], [3, [[1.0, 0], [-3.3117376914898995, 4.004047135432493]]]], 'bad_primes': [2, 3], 'central_character': '18.13', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '4598633802825532940903039220230', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, -1.7320508075688772]], [[1.0, 0], [-3.3117376914898995, 4.004047135432493]], 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[1295029.0, 0]], [[1.0, 0], [511.8635374788638, -886.5736534553283], [-721448.5, -1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-18-9.4-c3-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/18/4/c/b/13/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.2746754581453752, 1.2640969333709464, 1.2605228767287335, 1.2627405883134921, 1.269024608313166, 1.2771810048412051, 1.2845978922706416, 1.2883034031074971, 1.285035646787345, 1.27133166588155, 1.2436432743757597, 1.1984867946934852, 1.132631317577299, 1.0433264968784957, 0.9285663272724898, 0.7873800679309212, 0.620135721863016, 0.4288355947015605, 0.2173778962147474, -0.008246297214980413, -0.23985442869970908, -0.46710655036778487, -0.6777039793295037, 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'12.72052001372066200764273099935947', '14.16854064168078325209429092594420', '15.60504420665671828690061860086317', '16.41142751801919002512807144296293', '18.64231613099320194426544512281951'], 'prelabel': '2-18-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305505228291, 'root_angle': -0.11562146414599488, 'root_number': '0.9347521286397827 - 0.35530051787662104*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.057810732073', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.33354277687313836026402320475', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.32425418152774817954800103619', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.586624919062136920710889624436', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0620343801033316, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/4/c/b/13/2'], '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': '2-18-9.4-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-18-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305505228291, 'root_angle': -0.05781073207299744, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.33354277687313836026402320475', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4225767501989712439101119577404', 'Lhash_array': ['4225767501989712439101119577404'], 'label': '2-18-9.4-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/4/c/b/13/2'}