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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1375.312', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.368124552684678, -0.9297764858882515], 'a3': [0.9822872507286887, 0.18738131458572463], 'a4': [-0.7289686274214116, 0.6845471059286887], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.18738131458572463, -0.9822872507286887], 'a7': [0.9510565162951535, 0.30901699437494745], 'a8': [0.9048270524660196, 0.42577929156507266], 'a9': [0.9297764858882515, 0.368124552684678], 'algebraic': True, 'analytic_conductor': 147.76427159260942, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]]], 'bad_primes': [5, 11], 'central_character': '1375.312', 'coeff_info': ['x^100 - 1', '0.998026728428272 + 0.0627905195293134*I', '\\\\zeta_{100}'], 'conductor': 1375, 'conductor_radical': 55, 'conjugate': 'dirichlet_L_1375.498', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^69', 'a^3', 'a^38', 0, 'a^72', 'a^5', 'a^7', 'a^6', 0, 0, 'a^41', 'a^31', 'a^74', 0, 'a^76', 'a^57', 'a^75', 'a^42', 0, 'a^8', 0, 'a^19', 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'199.83110501847116741112325334310', '199.89647139562001512684711391202'], 'prelabel': '1-1375-1375.312-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 147.76427159260942, 'root_angle': 0.39956747420434346, 'root_number': '0.310309023178484850136149046691+0.950635739983519950573166916132*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.199783737102', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(100)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.18477001682485939566617655079-0.116289961918898093143640254704*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.23368351484', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.15691316514', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.55930789102', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 147.76427159260942, 'bad_primes': [5, 11], 'central_character': '1375.312', 'conductor': 1375, 'conductor_radical': 55, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1375/312'], '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': '1-1375-1375.312-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': '1-1375-1375.312-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 147.76427159260942, 'root_angle': 0.19978373710217173, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23368351484', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1375.312', 'Lhash_array': ['dirichlet_L_1375.312'], 'label': '1-1375-1375.312-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1375/312'}
Lfunction data - 1-1375-1375.312-r1-0-0