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lfunc_lfunctions • Show schema
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{'Lhash': '2263510482337880552680458945632', 'a10': [-1.6248513046399427, -2.2801903561329437], 'a2': [0.8854044173366092, -0.8854044173366092], 'a3': [-1.7211794703754537, 0.1937555954239073], 'a4': [0.0, 0.4321180355216392], 'a5': [0.37007893718462054, -2.205230505015814], 'a6': [-1.3523878460274998, 1.6954919661715246], 'a7': [0.9578749984119398, 0.9578749984119398], 'a8': [2.1534080521348953, 2.1534080521348953], 'a9': [2.924917538483854, -0.6669763062280029], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.275736457606492, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7211794703754537, -0.1937555954239073]]], [5, [[1.0, 0], [-0.37007893718462054, 2.205230505015814]]], [19, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [3, 5, 19], 'central_character': '285.77', 'coefficient_field': 'CDF', 'conductor': 285, 'conductor_radical': 285, 'conjugate': '1583440854760471623598108094395', 'degree': 2, 'euler_factors': 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'root_number': '0.4789028196434985 + 0.8778679224903406*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.170517311309', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78559492807430950683927454388', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.20589653585576981723986504639', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.86003565820496750191662437347', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.275736457606492, 'bad_primes': [3, 5, 19], 'central_character': '15.2', 'conductor': 285, 'conductor_radical': 285, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/285/2/k/d/77/14'], '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': '2-285-15.2-c1-0-20', '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': '2-285-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5085544264647834, 'root_angle': 0.17051731130862485, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78559492807430950683927454388', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2263510482337880552680458945632', 'Lhash_array': ['2263510482337880552680458945632'], 'label': '2-285-15.2-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/285/2/k/d/77/14'}