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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_221.126', 'a10': [-0.1305261922200516, -0.9914448613738104], 'a2': [-0.25881904510252074, 0.9659258262890683], 'a3': [-0.6087614290087207, 0.7933533402912352], 'a4': [-0.8660254037844386, -0.5], 'a5': [-0.9238795325112867, 0.3826834323650898], 'a6': [-0.6087614290087207, -0.7933533402912352], 'a7': [0.7933533402912352, -0.6087614290087207], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [-0.25881904510252074, -0.9659258262890683], 'algebraic': True, 'analytic_conductor': 23.74974837961213, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]], [17, [1]]], 'bad_primes': [13, 17], 'central_character': '221.126', 'coeff_info': ['x^48 - 1', '0.991444861373810 + 0.130526192220052*I', '\\\\zeta_{48}'], 'conductor': 221, 'conductor_radical': 221, 'conjugate': 'dirichlet_L_221.107', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^17', 'a^28', 'a^21', 'a^31', 'a^43', 'a^42', 'a^34', 'a^35', 'a^23', 'a^45', 0, 'a^9', 'a^38', 'a^8', 0, 'a^0', 'a^46', 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'199.965143435152416537491200777627'], 'prelabel': '1-221-221.126-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 23.74974837961213, 'root_angle': 0.33766657754469437, 'root_number': '-0.523390683606822454215977969766+0.852092830807525966646142559393*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.337666577545', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(48)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.513945680090153964369828384123+0.392164782311582080869589440120*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.751445112189', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '3.44369582388', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.64079134452', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.74974837961213, 'bad_primes': [13, 17], 'central_character': '221.126', 'conductor': 221, 'conductor_radical': 221, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/221/126'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-221-221.126-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-221-221.126-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 23.74974837961213, 'root_angle': 0.33766657754469437, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.751445112189', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_221.126', 'Lhash_array': ['dirichlet_L_221.126'], 'factors': ['1-221-221.126-r1-0-0'], 'label': '1-221-221.126-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/221/126'}