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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_799.563', 'a10': [0.7071067811865476, 0.7071067811865476], 'a2': [-7.040766286173228e-31, 1.0], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [0.7071067811865476, -0.7071067811865476], 'a6': [0.7071067811865476, 0.7071067811865476], 'a7': [-0.7071067811865476, -0.7071067811865476], 'a8': [2.9010907910729803e-30, -1.0], 'a9': [2.9010907910729803e-30, -1.0], 'algebraic': True, 'analytic_conductor': 85.86447491090539, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]], [47, [1]]], 'bad_primes': [17, 47], 'central_character': '799.563', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 799, 'conductor_radical': 799, 'conjugate': 'dirichlet_L_799.281', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^7', 'a^4', 'a^7', 'a^1', 'a^5', 'a^6', 'a^6', 'a^1', 'a^5', 'a^3', 'a^0', 'a^7', 'a^6', 'a^0', 0, 'a^0', 'a^6', 'a^3', 'a^4', 'a^7', 'a^5', 'a^5', 'a^6', 'a^2', 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'192.29600611978927908951679451135', '193.09408631324502646002825458054', '194.07050374637236049340938475973', '194.50566488064364948484031819465', '195.11234388875676725157960181821', '195.8292537352372157424725851359', '196.558048613330684341521748758476', '196.944100836233739974115153836105', '197.20970637239666221272414668338', '197.69893628942049878118612007662', '198.627456256482001567990893056959', '199.26169713190841770909285725194', '199.98094234673058122030176910838'], 'prelabel': '1-799-799.563-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 85.86447491090539, 'root_angle': -0.7648110510895731, 'root_number': '-0.739231464122773942105610997581-0.673451440306500482026900033760*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.382405525545', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(8)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.15375004497002177421258551922-0.276247063925004927672999743627*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.385954371363', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.11699753922', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.6700908543', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 85.86447491090539, 'bad_primes': [17, 47], 'central_character': '799.563', 'conductor': 799, 'conductor_radical': 799, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/799/563'], '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': '1-799-799.563-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': '1-799-799.563-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 85.86447491090539, 'root_angle': -0.3824055255447866, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.385954371363', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_799.563', 'Lhash_array': ['dirichlet_L_799.563'], 'label': '1-799-799.563-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/799/563'}