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  • lfunc_lfunctions • Show schema
    {'Lhash': '1219138637795591759513492009300', 'a10': [-3.1622776601683795, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-3.1622776601683795, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.067265720149466, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '1386.1', 'coefficient_field': 'CDF', 'conductor': 1386, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.1622776601683795, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.0, 0], [13.0, 0]], [[1.0, 0], [-7.162277660168379, 0], [17.0, 0]], [[1.0, 0], [-5.162277660168379, 0], [19.0, 0]], [[1.0, 0], [6.324555320336759, 0], [23.0, 0]], 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'8.417730207233797965216599747172595', '9.848443317916173747335658826716009'], 'prelabel': '2-1386-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.326750023694216, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.961730809401341751806754824200', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.84079256267322368630215735514', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.57050061363473802858282797451', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 11.067265720149466, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 1386, 'conductor_radical': 462, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1386/2/a/o/1/1'], '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': '2-1386-1.1-c1-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1386-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.326750023694216, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.961730809401341751806754824200', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1219138637795591759513492009300', 'Lhash_array': ['1219138637795591759513492009300'], 'factors': ['2-1386-1.1-c1-0-5'], 'label': '2-1386-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1386/2/a/o/1/1'}