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lfunc_lfunctions • Show schema
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{'Lhash': '2510641712058925392605155181065', 'a10': [0.6180339887498949, 0.6180339887498949], 'a2': [-0.6420395219202062, -1.260073510670101], 'a3': [1.4510565162951536, 0.945745730372267], 'a4': [-1.1755705045849463, 1.618033988749895], 'a5': [-0.5877852522924731, 0.19098300562505258], 'a6': [0.260073510670101, -2.4356440152550474], 'a7': [2.48989828488278, -3.4270509831248424], 'a8': [2.793604493334841, 0.4424634841649486], 'a9': [1.2111300269652545, 2.744661009629995], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0540253066809016, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6420395219202062, 1.260073510670101]]], [3, [[1.0, 0], [-1.4510565162951536, -0.945745730372267]]], [11, [[1.0, 0], [-3.3090169943749475, -0.2245139882897927]]]], 'bad_primes': [2, 3, 11], 'central_character': '132.119', 'coefficient_field': 'CDF', 'conductor': 132, 'conductor_radical': 66, 'conjugate': 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[[1.0, 0], [0, -15.180339887498949], [-89.0, 0]], [[1.0, 0], [3.8090169943749475, -11.72294889640854], [-78.4746484543699, -57.01516947236989]], [[1.0, 0], [4.755282581475768, 1.545084971874737], [81.71071643186968, 59.366310481539784]], [[1.0, 0], [5.534825672617112, -7.618033988749895], [-31.828750420619585, -97.95882117840081]], [[1.0, 0], [3.4270509831248424, -2.48989828488278], [33.06481839811937, -101.76304724358143]], [[1.0, 0], [-17.23606797749979, 0], [109.0, 0]], [[1.0, 0], [0.5877852522924731, 0.8090169943749475], [-34.91892036436906, 107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-132-132.119-c1-0-8', '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/132/2/o/a/119/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': 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50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98054709366043475606211930123', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.33013277206191206055036986726', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.90116877152067596527976677874', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0540253066809016, 'bad_primes': [2, 3, 11], 'central_character': '132.119', 'conductor': 132, 'conductor_radical': 66, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/132/2/o/a/119/1'], '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': '2-132-132.119-c1-0-8', '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': '2-132-132.119-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0266573462849724, 'root_angle': 0.095429251028529, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98054709366043475606211930123', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2510641712058925392605155181065', 'Lhash_array': ['2510641712058925392605155181065'], 'label': '2-132-132.119-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/132/2/o/a/119/1'}