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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_676.123', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.6927243535095994, -0.7212024473438146], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9350162426854148, 0.3546048870425356], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.6007422642379789, -0.7994427634035012], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.040265940109415144, 0.9991889981715696], 'algebraic': True, 'analytic_conductor': 3.1393308019770143, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [13, [1]]], 'bad_primes': [2, 13], 'central_character': '676.123', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 676, 'conductor_radical': 26, 'conjugate': 'dirichlet_L_676.11', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^98', 0, 'a^9', 0, 'a^133', 0, 'a^40', 0, 'a^233', 0, 0, 0, 'a^107', 0, 'a^94', 0, 'a^91', 0, 'a^75', 0, 'a^104', 0, 'a^18', 0, 'a^138', 0, 'a^92', 0, 'a^99', 0, 'a^19', 0, 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'199.883121653864791196043472388985'], 'prelabel': '1-26e2-676.123-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1393308019770143, 'root_angle': -0.36735700197238663, 'root_number': '-0.672347695903608482385869677877-0.740235486729127850149222062366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.367357001972', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.799728634968999083059132751646-0.340181714135309237608632572670*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.443632368551', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.92052301611', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.5038635457', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.1393308019770143, 'bad_primes': [2, 13], 'central_character': '676.123', 'conductor': 676, 'conductor_radical': 26, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/676/123'], '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': '1-26e2-676.123-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': '1-26e2-676.123-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1393308019770143, 'root_angle': -0.36735700197238663, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.443632368551', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_676.123', 'Lhash_array': ['dirichlet_L_676.123'], 'factors': ['1-26e2-676.123-r0-0-0'], 'label': '1-26e2-676.123-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/676/123'}
Lfunction data - 1-26e2-676.123-r0-0-0