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lfunc_lfunctions • Show schema
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{'Lhash': '3140468191520090388136021826750', 'a10': [-21.583123951777, 0.0], 'a2': [4.3166247903554, 0.0], 'a3': [-5.0, 0.0], 'a4': [10.6332495807108, 0.0], 'a5': [-5.0, 0.0], 'a6': [-21.583123951777, 0.0], 'a7': [0.0, 0.0], 'a8': [11.3667504192892, 0.0], 'a9': [-2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.455467951406456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [5.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 7], 'central_character': '245.1', 'coefficient_field': 'CDF', 'conductor': 245, 'conductor_radical': 35, 'conjugate': '3140468191520090388136021826750', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.3166247903554, 0], [8.0, 0]], [[1.0, 0], [5.0, 0], [27.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-19.7335008385784, 0], [1331.0, 0]], [[1.0, 0], [71.332495807108, 0], [2197.0, 0]], [[1.0, 0], [-31.332495807107996, 0], [4913.0, 0]], [[1.0, 0], [136.332495807108, 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'5.86149798837209534943728765147166', '6.60332938451781971481346140289967', '7.84200990705642548892143387115034', '9.400656195664871413315169362981850', '10.73759722190597981294620729364232', '11.55639106780278446091833485973523'], 'prelabel': '2-245-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.802034712020191, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.47739258038033237411274477461', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.00443109216199791205280469390', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.81715488063016183995797723016', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.455467951406456, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/4/a/i/1/2'], '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': '2-245-1.1-c3-0-38', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-245-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.802034712020191, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.47739258038033237411274477461', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3140468191520090388136021826750', 'Lhash_array': ['3140468191520090388136021826750'], 'label': '2-245-1.1-c3-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/4/a/i/1/2'}