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lfunc_lfunctions • Show schema
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{'Lhash': '973719014359856403559755862343', 'a10': [0.28990296264583976, -2.6351971292893735e-61], 'a2': [0.30901699437494745, 0.9510565162951535], 'a3': [-0.8090169943749475, -0.5877852522924731], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [0.08958494217721005, -0.27571410171759636], 'a6': [0.30901699437494745, -0.9510565162951535], 'a7': [-0.8090169943749475, 0.5877852522924731], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [0.30901699437494745, 0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]], [3, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [7, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]], [11, [[1.0, 0], [-3.0666771100309003, -1.2631276668700304]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.379', 'coefficient_field': 'CDF', 'conductor': 462, 'conductor_radical': 462, 'conjugate': '2151308838032146186051347022930', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.08958494217721005, 0.27571410171759636], [-4.045084971874737, -2.9389262614623655]], [[1.0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-3.0666771100309003, -1.2631276668700304]], [[1.0, 0], [-1.1640655130520277, -3.5826252657136903], [-10.517220926874316, 7.641208279802151]], [[1.0, 0], [2.03092715299974, -6.250551063989508], [-13.753288904374106, -9.992349288972044]], [[1.0, 0], [0.8794879048230498, 0.6389853657202769], [5.871322893124001, 18.07007380960792]], [[1.0, 0], [-1.94616501485395, 0], [23.0, 0]], [[1.0, 0], [5.549094632301452, -4.031653242293276], [8.961492836873475, -27.580638972559452]], [[1.0, 0], [-1.4119466118224497, -4.3455248425763315], [-25.079526825623372, 18.221342821066667]], [[1.0, 0], 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[-67.14841053312064, -48.78617594027527]], [[1.0, 0], [11.855538787039595, 0], [89.0, 0]], [[1.0, 0], [1.1013980634478424, 3.38975468775013], [-78.4746484543699, 57.01516947236989]], [[1.0, 0], [-4.059376199572425, -12.493475300625098], [-81.71071643186968, 59.366310481539784]], [[1.0, 0], [-14.561936757186302, 10.579866344220322], [31.828750420619585, -97.95882117840081]], [[1.0, 0], [8.733589871072734, 6.345324463491198], [33.06481839811937, 101.76304724358143]], [[1.0, 0], [-0.6482427313546799, 0], [109.0, 0]], [[1.0, 0], [-10.409468505395393, -7.562921563102155], [34.91892036436906, 107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-462-11.5-c1-0-1', '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/462/2/j/e/379/1', 'plot_delta': {'__RealLiteral__': 0, 'data': 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'-0.280533303516', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76812886309882771550959494721', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75445705703679469998216964324', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84599303749077107244115526535', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'bad_primes': [2, 3, 7, 11], 'central_character': '11.5', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/462/2/j/e/379/1'], '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': '2-462-11.5-c1-0-1', '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': '2-462-11.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': -0.2805333035162825, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76812886309882771550959494721', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '973719014359856403559755862343', 'Lhash_array': ['973719014359856403559755862343'], 'label': '2-462-11.5-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/j/e/379/1'}