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lfunc_lfunctions • Show schema
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{'Lhash': '4798712693068949832798479767427', 'a10': [-4.689150103963485, -2.794459040842106], 'a2': [0.9727429631696759, -0.4956372955515717], 'a3': [0.8722413777292786, -0.13814946243955425], 'a4': [-1.6505684655154471, 2.271812594435309], 'a5': [-2.6649375647185263, -4.230615531592547], 'a6': [0.779994636426135, -0.5666992749796664], 'a7': [1.6278298708410042, 1.6278298708410042], 'a8': [-1.162723701254628, 7.34114852994498], 'a9': [-7.81778889960565, 2.5401535944728546], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6812006609007424, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [2.6649375647185263, 4.230615531592547]]]], 'bad_primes': [5], 'central_character': '25.22', 'coefficient_field': 'CDF', 'conductor': 25, 'conductor_radical': 5, 'conjugate': '4499593756644277402316640713317', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9727429631696759, 0.4956372955515717], [2.3511410091698925, 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[-6551.828340757313, -2128.8180742490126]], [[1.0, 0], [30.314262307028546, 9.849700900324358], [6408.223612443959, 4655.84698340868]], [[1.0, 0], [-10.759723340422273, -67.93421953807554], [-8948.4907618211, 2907.5409000738805]], [[1.0, 0], [-69.51841393466171, 0], [10201.0, 0]], [[1.0, 0], [-65.2237540977557, 10.330427788638218], [10089.758581375285, -3278.3612933238173]], [[1.0, 0], [64.93529189735669, 64.93529189735669], [0, 11449.0]], [[1.0, 0], [84.47701457347718, -27.448245913877006], [9611.93091016875, -6983.476582486874]], [[1.0, 0], [105.1448424328075, 53.57397310259713], [7505.429886522589, 10330.338001173704]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-5e2-25.22-c2-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/25/3/f/a/22/3', 'plot_delta': 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'0.0310692657458', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.78551683894993114844835411628', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.85932041774539738289013968267', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.59625204027150619256792919361', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6812006609007424, 'bad_primes': [5], 'central_character': '25.22', 'conductor': 25, 'conductor_radical': 5, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/25/3/f/a/22/3'], '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': '2-5e2-25.22-c2-0-2', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-5e2-25.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8253488116552555, 'root_angle': 0.031069265745795285, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.78551683894993114844835411628', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4798712693068949832798479767427', 'Lhash_array': ['4798712693068949832798479767427'], 'label': '2-5e2-25.22-c2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/25/3/f/a/22/3'}