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lfunc_lfunctions • Show schema
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{'Lhash': '2257824265109745598604162884008', 'a10': [-4.799466389098405, -2.1657870834854997e-61], 'a2': [-1.1650000835566574, -0.6726131118473727], 'a3': [0.0, 0.0], 'a4': [-0.09518320354198738, -0.16486214456189205], 'a5': [3.0897850074263484, -1.783888205775672], 'a6': [0.0, 0.0], 'a7': [-2.096378493657038, -1.6140623319228562], 'a8': [0.0, 2.946538330309403], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.096378493657038, 1.6140623319228562]]], [13, [[1.0, 0], [-3.574195643083149, 0.47447392443150527]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.361', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '770284748283507947355267675040', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1650000835566574, 0.6726131118473727], [1.0, 1.7320508075688772]], [[1.0, 0], 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'6.28074476175231077605539394778825', '7.01193020450251062169558700517721', '8.249364899882803891390019359542395', '9.004325207379997649393550394104607', '9.580542103601198280550164130312694', '10.35480684610186397264303353712376'], 'prelabel': '2-819-91.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.8577655178922459, 'root_number': '-0.9018158837088923 + 0.4321204830719664*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.428882758946', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78110929360443965436896081262', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.98832824058091378173359812776', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17008471554116908280705842317', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '91.88', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/do/e/361/2'], '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': '2-819-91.88-c1-0-34', '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': '2-819-91.88-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.42888275894612293, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78110929360443965436896081262', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2257824265109745598604162884008', 'Lhash_array': ['2257824265109745598604162884008'], 'label': '2-819-91.88-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/do/e/361/2'}