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lfunc_lfunctions • Show schema
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{'Lhash': '1587225219857420328740793083925', 'a10': [-4.383502307517328, 0.0], 'a2': [-1.0, 0.0], 'a3': [2.348894217500717, 0.0], 'a4': [1.0, 0.0], 'a5': [4.383502307517328, 0.0], 'a6': [-2.348894217500717, 0.0], 'a7': [0.4826959549916945, 0.0], 'a8': [-1.0, 0.0], 'a9': [2.5173040450083057, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.715214849384736, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '4598.1', 'coefficient_field': 'CDF', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.348894217500717, 0], [3.0, 0]], [[1.0, 0], [-4.383502307517328, 0], [5.0, 0]], [[1.0, 0], [-0.4826959549916945, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.732396525018045, 0], [13.0, 0]], [[1.0, 0], [4.180484389993128, 0], [17.0, 0]], [[1.0, 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[[1.0, 0], [18.633202877543678, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 101, 'label': '2-4598-1.1-c1-0-101', 'leading_term': '3.71762371402127087124342095401', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4598/2/a/bl/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.7176237140212707, 3.7111847781465634, 3.6917803586239972, 3.659156137572494, 3.6129160369995748, 3.5525618411220057, 3.47754479768799, 3.3873258397441273, 3.2814407258782126, 3.159566352565842, 3.021584690437045, 2.867641162526803, 2.6981947429123276, 2.514057548365721, 2.31642218347253, 2.1068755607003102, 1.887398346674353, 1.6603495902081533, 1.428436476913799, 1.1946695401932985, 0.9623040470376722, 0.7347686728901953, 0.5155829814539314, 0.3082656265457038, 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'5.65511702973582029872704008054798', '6.31723901047262290583855306603296', '6.77736437917999143664827973798128', '8.050631031439852347515816690849477', '8.370446971134105519519100614780777'], 'prelabel': '2-4598-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25209992372634408293157581465', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.96887321197883358656526089477', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.57215457398253165825447970588', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.715214849384736, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 4598, 'conductor_radical': 418, 'degree': 2, 'index': 101, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4598/2/a/bl/1/3'], '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': '2-4598-1.1-c1-0-101', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4598-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.059308116392889, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25209992372634408293157581465', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1587225219857420328740793083925', 'Lhash_array': ['1587225219857420328740793083925'], 'label': '2-4598-1.1-c1-0-101', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4598/2/a/bl/1/3'}