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lfunc_lfunctions • Show schema
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{'Lhash': '2714763127855233295028539854329', 'a10': [0.0, 0.0], 'a2': [2.414213562373095, 0.0], 'a3': [-1.0, 0.0], 'a4': [3.8284271247461903, 0.0], 'a5': [0.0, 0.0], 'a6': [-2.414213562373095, 0.0], 'a7': [1.0, 0.0], 'a8': [4.414213562373095, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.1', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2714763127855233295028539854329', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.414213562373095, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.8284271247461901, 0], [17.0, 0]], [[1.0, 0], [5.656854249492381, 0], [19.0, 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'9.083653609151694394209207435823134', '10.55765662806467945537028057206216', '11.29518608843858614815163999581715', '12.11879618305232732790366468939713'], 'prelabel': '2-273-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14157049850050474625482236726', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.81564192422094497201229732335', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.63869215328836944881622050919', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '1.1', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/a/c/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': '2-273-1.1-c1-0-6', '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': '2-273-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.14157049850050474625482236726', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2714763127855233295028539854329', 'Lhash_array': ['2714763127855233295028539854329'], 'label': '2-273-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/a/c/1/2'}