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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_676.271', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.8451900855437947, -0.5344658261278011], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.6631226582407952, -0.7485107481711011], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.7212024473438146, 0.6927243535095994], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.4286925614030542, -0.9034504346103823], 'algebraic': True, 'analytic_conductor': 3.1393308019770143, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [13, [1]]], 'bad_primes': [2, 13], 'central_character': '676.271', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 676, 'conductor_radical': 26, 'conjugate': 'dirichlet_L_676.227', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^142', 0, 'a^99', 0, 'a^215', 0, 'a^128', 0, 'a^223', 0, 0, 0, 'a^85', 0, 'a^98', 0, 'a^221', 0, 'a^45', 0, 'a^208', 0, 'a^42', 0, 'a^114', 0, 'a^76', 0, 'a^153', 0, 'a^53', 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'199.680907345311404200570381464322'], 'prelabel': '1-26e2-676.271-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1393308019770143, 'root_angle': 0.388560157790927, 'root_number': '-0.764715146087138546494848604275+0.644368485685734285959146097471*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.388560157791', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.787832502399583445524761253633-0.168282189773075767898894227428*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.68568155404', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.66676927566', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.63941918103', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.1393308019770143, 'bad_primes': [2, 13], 'central_character': '676.271', 'conductor': 676, 'conductor_radical': 26, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/676/271'], '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': '1-26e2-676.271-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': '1-26e2-676.271-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1393308019770143, 'root_angle': 0.388560157790927, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68568155404', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_676.271', 'Lhash_array': ['dirichlet_L_676.271'], 'factors': ['1-26e2-676.271-r0-0-0'], 'label': '1-26e2-676.271-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/676/271'}
Lfunction data - 1-26e2-676.271-r0-0-0