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lfunc_lfunctions • Show schema
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{'Lhash': '1897667110963802007535750605684', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [0.7071067811865476, 0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.7071067811865476, -0.7071067811865476], 'a8': [0.0, 0.0], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.29694368251663644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [7, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [17, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [5, 7, 17], 'central_character': '595.489', 'coefficient_field': 'CDF', 'conductor': 595, 'conductor_radical': 595, 'conjugate': '1971302859146294074770624462007', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-0.7071067811865476, 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'group': 'GL2', 'index': 0, 'label': '2-595-595.489-c0-0-0', 'leading_term': '0.89388004868463455896702937634451', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/595/1/u/a/489/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.8938800486846346, 0.8967784636047108, 0.910431307271898, 0.9334625790974466, 0.9638933481875959, 0.9993858233441758, 1.037454661377277, 1.0756126258958965, 1.1114524881883494, 1.1426838227846106, 1.1671451385711689, 1.1828068015124389, 1.1877742090219823, 1.1802960018267123, 1.1587790795940809, 1.1218104406048799, 1.0681849296865964, 0.9969375044466435, 0.9073784005815239, 0.7991294717379862, 0.6721599368774686, 0.5268197611750631, 0.3638689161704217, 0.1845008112618786, -0.009641734182230924, -0.21645949543532525, -0.43340018636932853, 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'8.509710481976576844838145717479729', '8.832492386135214226746509030325462', '9.958210966115801455852850188849848', '10.80517933125481302527132041464467'], 'prelabel': '2-595-595.489-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5449253916974657, 'root_angle': -0.03898956518868466, 'root_number': '0.99250755668290301790481098985651 - 0.12218326369570446599622393355370*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.01949478259434233', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49699539496304710817003797098', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08343296203714461743507447948', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.59855347284396071552998000400', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.29694368251663644, 'bad_primes': [5, 7, 17], 'central_character': '595.489', 'conductor': 595, 'conductor_radical': 595, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/595/1/u/a/489/2'], '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': '2-595-595.489-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-595-595.489-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5449253916974657, 'root_angle': -0.01949478259434233, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49699539496304710817003797098', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1897667110963802007535750605684', 'Lhash_array': ['1897667110963802007535750605684'], 'label': '2-595-595.489-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/595/1/u/a/489/2'}