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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_320.13', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.9238795325112867, 0.3826834323650898], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.7071067811865476, 0.7071067811865476], 'algebraic': True, 'analytic_conductor': 34.388775934280005, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '320.13', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 320, 'conductor_radical': 10, 'conjugate': 'dirichlet_L_320.197', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^17', 0, 0, 0, 'a^18', 0, 'a^18', 0, 'a^11', 0, 'a^5', 0, 0, 0, 'a^0', 0, 'a^17', 0, 'a^3', 0, 'a^6', 0, 0, 0, 'a^19', 0, 'a^13', 0, 'a^8', 0, 'a^12', 0, 0, 0, 'a^19', 0, 'a^22', 0, 'a^2', 0, 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'198.44733140798091195978857996858', '198.87104313033511720897767117364', '199.7687988724046607359063184757'], 'prelabel': '1-320-320.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 34.388775934280005, 'root_angle': 0.4175418088252167, 'root_number': '0.256162411577431820996825909096+0.966633756339408221350196596557*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.208770904413', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(16)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.54207253113062582944492183523+0.489753686947932341824999844602*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.46992507326', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.62402855688', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.67507703977', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 34.388775934280005, 'bad_primes': [2, 5], 'central_character': '320.13', 'conductor': 320, 'conductor_radical': 10, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/320/13'], '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': '1-320-320.13-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': '1-320-320.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 34.388775934280005, 'root_angle': 0.20877090441260834, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46992507326', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_320.13', 'Lhash_array': ['dirichlet_L_320.13'], 'label': '1-320-320.13-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/320/13'}