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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2669.583', 'a10': [0.6854274223350397, 0.7281409538757884], 'a2': [0.9981755542233175, 0.06037849742228606], 'a3': [0.9632708010475163, 0.26853186747437674], 'a4': [0.992708874098054, 0.12053668025532305], 'a5': [0.7281409538757884, 0.6854274223350397], 'a6': [0.9452998150346402, 0.3262027892208693], 'a7': [-0.8710160199955156, 0.49125461108387736], 'a8': [0.9836199069471436, 0.18025503781390573], 'a9': [0.8557812723014475, 0.5173378141776568], 'algebraic': True, 'analytic_conductor': 12.39478389123765, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]], [157, [1]]], 'bad_primes': [17, 157], 'central_character': '2669.583', 'coeff_info': ['x^208 - 1', '0.999543784489533 + 0.0302030278008888*I', '\\\\zeta_{208}'], 'conductor': 2669, 'conductor_radical': 2669, 'conjugate': 'dirichlet_L_2669.1877', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^9', 'a^4', 'a^25', 'a^11', 'a^87', 'a^6', 'a^18', 'a^27', 'a^167', 'a^13', 'a^156', 'a^89', 'a^34', 'a^8', 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False, 'root_analytic_conductor': 12.39478389123765, 'root_angle': 0.1313375190683014, 'root_number': '0.678396840058448971071704866411+0.734695669919668987185904237457*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.131337519068', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(208)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.86638027653954939575764107258+0.736286013484245070616059716307*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.34516982129', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.46323153122', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.99488102032', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12.39478389123765, 'bad_primes': [17, 157], 'central_character': '2669.583', 'conductor': 2669, 'conductor_radical': 2669, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2669/583'], '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': '1-2669-2669.583-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': '1-2669-2669.583-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.39478389123765, 'root_angle': 0.1313375190683014, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34516982129', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2669.583', 'Lhash_array': ['dirichlet_L_2669.583'], 'factors': ['1-2669-2669.583-r0-0-0'], 'label': '1-2669-2669.583-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2669/583'}
Lfunction data - 1-2669-2669.583-r0-0-0