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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1792.51', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.2270762630343732, 0.9738769792773336], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.5824776968678022, -0.8128466845916152], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.8968727415326883, -0.4422886902190013], 'algebraic': True, 'analytic_conductor': 192.57714523196805, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '1792.51', 'coeff_info': ['x^192 - 1', '0.999464587476366 + 0.0327190828217761*I', '\\\\zeta_{192}'], 'conductor': 1792, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_1792.1019', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^247', 0, 'a^317', 0, 0, 0, 'a^302', 0, 'a^97', 0, 'a^51', 0, 'a^180', 0, 'a^172', 0, 'a^155', 0, 0, 0, 'a^182', 0, 'a^250', 0, 'a^165', 0, 'a^15', 0, 'a^136', 0, 'a^152', 0, 0, 0, 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'198.58528018679614757516946357067', '199.14023293231191266657305827737', '199.49309083506377888789575268168'], 'prelabel': '1-1792-1792.51-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 192.57714523196805, 'root_angle': -0.5501395469460539, 'root_number': '-0.156867452226707520829143214510-0.987619664866947469422599780503*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.275069773473', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(192)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.766197592496315702099967433692+0.0929900408937479707968242598435*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.157250254553', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.11245133189', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.654693366', 'prec': 37}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 192.57714523196805, 'bad_primes': [2, 7], 'central_character': '1792.51', 'conductor': 1792, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1792/51'], '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': '1-1792-1792.51-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': '1-1792-1792.51-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 192.57714523196805, 'root_angle': -0.27506977347302697, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.157250254553', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1792.51', 'Lhash_array': ['dirichlet_L_1792.51'], 'label': '1-1792-1792.51-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1792/51'}