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lfunc_lfunctions • Show schema
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{'Lhash': '1693288894951452621901370597084', 'a10': [-2.916311358078327, 0.0], 'a2': [-1.0, 0.0], 'a3': [-0.7177674802704308, 0.0], 'a4': [1.0, 0.0], 'a5': [2.916311358078327, 0.0], 'a6': [0.7177674802704308, 0.0], 'a7': [-1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.4848098442662367, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.35639318155513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7, 19], 'central_character': '5054.1', 'coefficient_field': 'CDF', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0.7177674802704308, 0], [3.0, 0]], [[1.0, 0], [-2.916311358078327, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.5638187563997885, 0], [11.0, 0]], [[1.0, 0], [1.7589564223729555, 0], [13.0, 0]], [[1.0, 0], [-1.3947745057138068, 0], [17.0, 0]], [[1.0, 0], [0, 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'5.45599702649994615944450144268167', '5.63287439539269870584735148868232', '6.49729012742200083185006016560558', '6.98971777392620322833019365994477', '7.953472183870087397123582365788103'], 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33576941047208968213458936862', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21365308701668306501813740112', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.03100948467862119741942205117', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.35639318155513, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'index': 121, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5054/2/a/bf/1/4'], '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': '2-5054-1.1-c1-0-121', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33576941047208968213458936862', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1693288894951452621901370597084', 'Lhash_array': ['1693288894951452621901370597084'], 'label': '2-5054-1.1-c1-0-121', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5054/2/a/bf/1/4'}