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  • lfunc_lfunctions • Show schema
    {'Lhash': '1870971825872922527131407857035', 'a10': [-1.1937873014981926, 0.0], 'a2': [-1.0, 0.0], 'a3': [-1.6388291694108212, 0.0], 'a4': [1.0, 0.0], 'a5': [1.1937873014981926, 0.0], 'a6': [1.6388291694108212, 0.0], 'a7': [2.0435865482325317, 0.0], 'a8': [-1.0, 0.0], 'a9': [-0.3142389534882377, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.430837619979368, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 29], 'central_character': '1682.1', 'coefficient_field': 'CDF', 'conductor': 1682, 'conductor_radical': 58, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [1.6388291694108212, 0], [3.0, 0]], [[1.0, 0], [-1.1937873014981926, 0], [5.0, 0]], [[1.0, 0], [-2.0435865482325317, 0], [7.0, 0]], [[1.0, 0], [3.682415717643353, 0], [11.0, 0]], [[1.0, 0], [-2.1564611783839944, 0], [13.0, 0]], [[1.0, 0], [-6.535173330354413, 0], [17.0, 0]], 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'7.64080535092400146134386375029470', '8.040610119978549353972865892501283', '8.944344313237129851681446292577817'], 'prelabel': '2-1682-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.664810720893968, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47593652820112294085842230992', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.50885852630779814634927688259', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.91720070203683245323678309126', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 13.430837619979368, 'bad_primes': [2, 29], 'central_character': '1.1', 'conductor': 1682, 'conductor_radical': 58, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1682/2/a/q/1/3'], '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': '2-1682-1.1-c1-0-38', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1682-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.664810720893968, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47593652820112294085842230992', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1870971825872922527131407857035', 'Lhash_array': ['1870971825872922527131407857035'], 'factors': ['2-1682-1.1-c1-0-38'], 'label': '2-1682-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1682/2/a/q/1/3'}