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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_187.24', 'a10': [-0.9238795325112867, -0.3826834323650898], 'a2': [-0.15643446504023087, -0.9876883405951378], 'a3': [-0.996917333733128, 0.07845909572784494], 'a4': [-0.9510565162951535, 0.30901699437494745], 'a5': [0.5224985647159489, -0.8526401643540922], 'a6': [0.23344536385590542, 0.9723699203976766], 'a7': [-0.07845909572784494, 0.996917333733128], 'a8': [0.4539904997395468, 0.8910065241883679], 'a9': [0.9876883405951378, -0.15643446504023087], 'algebraic': True, 'analytic_conductor': 0.868424349067606, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [17, [1]]], 'bad_primes': [11, 17], 'central_character': '187.24', 'coeff_info': ['x^80 - 1', '0.996917333733128 + 0.0784590957278449*I', '\\\\zeta_{80}'], 'conductor': 187, 'conductor_radical': 187, 'conjugate': 'dirichlet_L_187.39', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^58', 'a^39', 'a^36', 'a^67', 'a^17', 'a^21', 'a^14', 'a^78', 'a^45', 0, 'a^75', 'a^68', 'a^79', 'a^26', 'a^72', 0, 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'-0.170765823922390893034619322946-0.985311642771010287931427234674*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.277312079587', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(80)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.646205197528785940054314507139-0.400339504548914342348185908504*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.883285394181', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.25266900325', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.9494354397', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.868424349067606, 'bad_primes': [11, 17], 'central_character': '187.24', 'conductor': 187, 'conductor_radical': 187, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/187/24'], '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': '1-187-187.24-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-187-187.24-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.868424349067606, 'root_angle': -0.2773120795872438, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.883285394181', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_187.24', 'Lhash_array': ['dirichlet_L_187.24'], 'label': '1-187-187.24-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/187/24'}