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lfunc_lfunctions • Show schema
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{'Lhash': '2170483632201913260481797713454', 'a10': [0.0, 0.0], 'a2': [1.4649659996959545, 0.0], 'a3': [1.260659420539418, 0.0], 'a4': [0.14612538026516747, 0.0], 'a5': [0.0, 0.0], 'a6': [1.846823188286651, 0.0], 'a7': [2.2558240502708777, 0.0], 'a8': [-2.7158632856107965, 0.0], 'a9': [-1.4107378254052192, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.71435515718304, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [229, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 229], 'central_character': '5725.1', 'coefficient_field': 'CDF', 'conductor': 5725, 'conductor_radical': 1145, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4649659996959545, 0], [2.0, 0]], [[1.0, 0], [-1.260659420539418, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.2558240502708777, 0], [7.0, 0]], [[1.0, 0], [1.3286027540553629, 0], [11.0, 0]], [[1.0, 0], [2.6780609737216654, 0], [13.0, 0]], [[1.0, 0], [-5.533385911820601, 0], 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0], [-28.602415682759382, 0], [227.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 331, 'label': '2-5725-1.1-c1-0-331', '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/5725/2/a/f/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.9848015524896962e-60, 0.3307976812786729, 0.6608307122772363, 0.9892718882937868, 1.3151725647434642, 1.637410847894101, 1.9546497806896261, 2.2653077899158944, 2.567542920326024, 2.8592516282497606, 3.1380822042153276, 3.4014622835057042, 3.646639405745683, 3.8707332010212805, 4.070797498828674, 4.243890458554362, 4.387150686025426, 4.4978772123122805, 4.57361115551948, 4.612216856264496, 4.61196027041776, 4.57158241993389, 4.490365748423754, 4.368191308113921, 4.205584824932871, 4.00374985395067, 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'6.01525330872228295557451794453122', '7.18195635351976431768106542207504', '7.70841271853595835516433473205942'], 'prelabel': '2-5725-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.761239173197694, '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': '1.71220968286619094356472276627', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66841986535042413266401081837', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.25448656858995856267184519294', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.71435515718304, 'bad_primes': [5, 229], 'central_character': '1.1', 'conductor': 5725, 'conductor_radical': 1145, 'degree': 2, 'index': 331, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5725/2/a/f/1/4'], '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': '2-5725-1.1-c1-0-331', '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': '2-5725-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.761239173197694, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71220968286619094356472276627', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2170483632201913260481797713454', 'Lhash_array': ['2170483632201913260481797713454'], 'label': '2-5725-1.1-c1-0-331', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5725/2/a/f/1/4'}