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  • lfunc_lfunctions • Show schema
    {'Lhash': '740026902332408595283053504814', 'a10': [222510.68215479856, -22113.261338079716], 'a2': [-25.88854381999832, 18.80912807335914], 'a3': [-246.101573959802, 757.4227626490007], 'a4': [316.4334022399462, -973.8818726862372], 'a5': [-6031.649130868967, -3528.077913267737], 'a6': [-7875.250366713664, -24237.52840476802], 'a7': [73958.01763280072, 0], 'a8': [10125.868871678278, 31164.21992595959], 'a9': [-369808.3231708138, -268681.4739939465], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38.41715902797945, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [25.88854381999832, -18.80912807335914]]], [5, [[1.0, 0], [6031.649130868967, 3528.077913267737]]]], 'bad_primes': [2, 5], 'central_character': '50.11', 'coefficient_field': 'CDF', 'conductor': 50, 'conductor_radical': 10, 'conjugate': '1412286710210799621493668130958', 'degree': 2, 'euler_factors': [[[1.0, 0], [25.88854381999832, -18.80912807335914]], 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-0.4515303194332766, 'root_number': '-0.9539837916450029 - 0.2998581752739513*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4515303194332766', 'prec': 64}, 'spectral_label': 'c11-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58377829206184513704250286738000', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.39756037806741047995893278943052', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.82421537934753193971941831261734', 'prec': 113}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 38.41715902797945, 'bad_primes': [2, 5], 'central_character': '25.11', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/12/d/b/11/1'], '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': '2-50-25.11-c11-0-8', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'prelabel': '2-50-25.11-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.198157712415799, 'root_angle': -0.4515303194332766, 'self_dual': False, 'spectral_label': 'c11-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58377829206184513704250286738000', 'prec': 113}}
  • lfunc_instances • Show schema
    {'Lhash': '740026902332408595283053504814', 'Lhash_array': ['740026902332408595283053504814'], 'factors': ['2-50-25.11-c11-0-8'], 'label': '2-50-25.11-c11-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/12/d/b/11/1'}