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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_51.11', 'a10': [-0.3826834323650898, 0.9238795325112867], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-7.040766286173228e-31, 1.0], 'a5': [-0.3826834323650898, -0.9238795325112867], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.3826834323650898, -0.9238795325112867], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.23684300429116525, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '51.11', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 51, 'conductor_radical': 51, 'conjugate': 'dirichlet_L_51.14', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 0, 'a^4', 'a^11', 0, 'a^13', 'a^14', 0, 'a^5', 'a^9', 0, 'a^12', 'a^7', 0, 'a^8', 0, 0, 'a^2', 'a^15', 0, 'a^3', 'a^1', 0, 'a^6', 'a^6', 0, 'a^1', 'a^3', 0, 'a^15', 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'root_analytic_conductor': 0.23684300429116525, 'root_angle': -0.29026494322636043, 'root_number': '-0.250301930009192816313468588028-0.968167828340558494861049059023*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.290264943226', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(16)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.582109663146592283467635442073-0.372073596086206347696432136691*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.06674274448', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.338451739', 'prec': 37}, 'z3': {'__RealLiteral__': 0, 'data': '4.96109339477', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.23684300429116525, 'bad_primes': [3, 17], 'central_character': '51.11', 'conductor': 51, 'conductor_radical': 51, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/51/11'], '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': '1-51-51.11-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': '1-51-51.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.23684300429116525, 'root_angle': -0.29026494322636043, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06674274448', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_51.11', 'Lhash_array': ['dirichlet_L_51.11'], 'factors': ['1-51-51.11-r0-0-0'], 'label': '1-51-51.11-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/51/11'}
Lfunction data - 1-51-51.11-r0-0-0