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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_529.234', 'a10': [-0.6734257004449862, -0.7392549127196787], 'a2': [0.29955421201320154, -0.9540792808069725], 'a3': [-0.5562153568544751, 0.8310381921423642], 'a4': [-0.8205345481302998, -0.5715969343205093], 'a5': [0.5035802904143761, -0.8639484308141155], 'a6': [0.6262596677501294, 0.7796145384415926], 'a7': [-0.860805229884536, -0.50893453037049], 'a8': [-0.7911433720027622, 0.6116307423078887], 'a9': [-0.3812489535984979, -0.9244724092043258], 'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '529.234', 'coeff_info': ['x^253 - 1', '0.999691634078213 + 0.0248321717542501*I', '\\\\zeta_{253}'], 'conductor': 529, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_529.52', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^202', 'a^87', 'a^151', 'a^211', 'a^36', 'a^148', 'a^100', 'a^174', 'a^160', 'a^117', 'a^238', 'a^116', 'a^97', 'a^45', 'a^49', 'a^47', 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'197.30129038135970155192078693665', '198.01201554611734555816197809286', '199.0910484001571881049811144618', '199.25248808363360313257696429727'], 'prelabel': '1-23e2-529.234-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': 0.30726929025605776, 'root_number': '0.569157947928042521104268697598+0.822228210602348305280777284706*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.153634645128', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(253)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.673160761332775303391490537126-0.211897559432148372907479086175*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.22601030387', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.68978610823', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.77782949245', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'bad_primes': [23], 'central_character': '529.234', 'conductor': 529, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/529/234'], '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': '1-23e2-529.234-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': '1-23e2-529.234-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': 0.15363464512802888, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22601030387', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_529.234', 'Lhash_array': ['dirichlet_L_529.234'], 'label': '1-23e2-529.234-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/529/234'}