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lfunc_lfunctions • Show schema
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{'Lhash': '1912959380072540622434042352286', 'a10': [2.2619546073986236, -3.917820304428929], 'a2': [-0.4697295765022776, -2.663968807354093], 'a3': [0.0, 0.0], 'a4': [-4.996698689942763, 1.8186495927360937], 'a5': [1.2811210619667155, 1.0749882105897164], 'a6': [0.0, 0.0], 'a7': [-0.4704018201862885, -0.17121226069245143], 'a8': [4.486858125871602, 7.771466240362887], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.82', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '793037968964655691101259995447', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.4697295765022776, 2.663968807354093], [-1.8793852415718169, 0.6840402866513374]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.2811210619667155, -1.0749882105897164], [0.8682408883346517, 4.924038765061041]], 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{'__RealLiteral__': 0, 'data': '4.75878126727127969688135375537', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.13', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/s/82/1'], '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': '2-3e6-27.13-c1-0-16', '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': '2-3e6-27.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.48148148148148145, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50905886821504996733171520773', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1912959380072540622434042352286', 'Lhash_array': ['1912959380072540622434042352286'], 'label': '2-3e6-27.13-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/s/82/1'}