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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_35.4', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.5, -0.8660254037844386], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, 0.0], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 0.16253931667040752, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '35.4', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 35, 'conductor_radical': 35, 'conjugate': 'dirichlet_L_35.9', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^1', 'a^4', 0, 'a^0', 0, 'a^3', 'a^2', 0, 'a^4', 'a^5', 'a^3', 0, 0, 'a^2', 'a^1', 'a^1', 'a^2', 0, 0, 'a^3', 'a^5', 'a^4', 0, 'a^2', 'a^3', 0, 'a^0', 0, 'a^4', 'a^1', 'a^5', 'a^0', 0, 'a^0', 'a^5', 'a^1', 'a^4', 0, 'a^0', 0, 'a^3', 'a^2', 0, 'a^4', 'a^5', 'a^3', 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'190.57697518484028319525073747745', '191.41118241153524866911091767249', '192.011575739241300482778890320', '192.846866010794812652897043309573', '193.781727417343653083822953402323', '194.236241942039790442810466897219', '195.41526327531155825873829919264', '196.49361456099833629379153101560', '197.15653646225064784900581831041', '198.49770656142443187258317685154', '199.14714470399221195438585298383'], 'prelabel': '1-35-35.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.16253931667040752, 'root_angle': -0.1868396197206128, 'root_number': '0.832620433558760101183612459955-0.553844033659677836116874679804*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0934198098603', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.18255089938624057048104760643-0.288045336670613583048991045930*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.61073590463', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.09194190632', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.59516565957', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.16253931667040752, 'bad_primes': [5, 7], 'central_character': '35.4', 'conductor': 35, 'conductor_radical': 35, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/35/4'], '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': '1-35-35.4-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': '1-35-35.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.16253931667040752, 'root_angle': -0.0934198098603064, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.61073590463', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_35.4', 'Lhash_array': ['dirichlet_L_35.4'], 'label': '1-35-35.4-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/35/4'}