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lfunc_lfunctions • Show schema
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{'Lhash': '2075093728211516792449133031329', 'a10': [0.0, 0.0], 'a2': [-0.5954548095627132, 1.0313579837738696], 'a3': [1.5235855629996726, -2.6389276047938655], 'a4': [0.2908671395372659, 0.5037966639307707], 'a5': [0.0, 0.0], 'a6': [1.8144527025369384, 3.142724268724636], 'a7': [0.6091753400508947, 0.0], 'a8': [-3.074612186975708, 0.0], 'a9': [-3.1426259355620583, -5.443187789577162], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-3.6053198420742043, 2.4498303688921066]]]], 'bad_primes': [5, 19], 'central_character': '475.201', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '1678899458160745094034001190417', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5954548095627132, -1.0313579837738696], [-1.0, -1.7320508075688772]], [[1.0, 0], [-1.5235855629996726, 2.6389276047938655], [-1.5, 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[-29.5, -51.09549882328188]], [[1.0, 0], [-2.4909945783017475, -4.314529170997237], [-30.5, 52.827549630850754]], [[1.0, 0], [-4.238080745124772, -7.34057117713547], [-33.5, 58.023702053557386]], [[1.0, 0], [5.809949991687812, -10.063128575037666], [-35.5, -61.48780366869514]], [[1.0, 0], [-1.8616238285362836, 3.224427055605735], [-36.5, -63.21985447626402]], [[1.0, 0], [4.519082852150547, -7.827281103538019], [-39.5, -68.41600689897065]], [[1.0, 0], [-2.121783312975053, 0], [83.0, 0]], [[1.0, 0], [3.9660840597972493, 6.8694590986578765], [-44.5, 77.07626093681505]], [[1.0, 0], [4.836278495100152, -8.376680073066213], [-48.5, -84.00446416709055]], [[1.0, 0], [-0.4856322566393827, -0.841139742293739], [-50.5, 87.4685657822283]], [[1.0, 0], [-3.3414284188217143, 0], [103.0, 0]], [[1.0, 0], [9.516552309678682, 0], [107.0, 0]], [[1.0, 0], [2.7717842873867196, -4.800871213374893], [-54.5, -94.39676901250381]], [[1.0, 0], [1.541343459645393, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-475-19.11-c1-0-17', '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/475/2/e/e/201/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6834177687897947, 1.7223288460991644, 1.756706419390333, 1.7822447205612362, 1.7917654794724696, 1.7763191476442906, 1.7264427430210472, 1.6334095753519264, 1.4903944296272753, 1.2935189665391282, 1.0427384865370701, 0.7425075784871075, 0.4021403818069253, 0.03577357634230697, -0.3381481595029342, -0.6979128042895165, -1.020106502826777, -1.2816388357283948, -1.462091372170828, -1.546182674295812, -1.5260838098254867, -1.4032814547138168, -1.1896810399137316, -0.9076779951335338, -0.5890048021569547, -0.27228356698527983, 0.0006301392723933231, 0.18925141861635855, 0.25958452493991885, 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'8.722526392021306329443494033132524', '9.559397712025654047492132786780129', '9.956019079072939973617940596046798', '10.90816974921579773340553938152018'], 'prelabel': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.07560072944462214, 'root_number': '0.9719276199021302 + 0.23528004945464548*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0378003647223', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63696031685538137958470236119', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.24966801356794041294496311797', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73733934205580165168866284635', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '19.11', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/e/e/201/2'], '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': '2-475-19.11-c1-0-17', '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': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.03780036472231107, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63696031685538137958470236119', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2075093728211516792449133031329', 'Lhash_array': ['2075093728211516792449133031329'], 'label': '2-475-19.11-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/e/e/201/2'}