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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_2675.54', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.8424169109380739, 0.5388262690010142], 'a3': [0.9691700850693123, 0.24639266670650306], 'a4': [0.4193325036688935, 0.907832722128244], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.683682427927005, 0.7297796501299798], 'a7': [0.8294056854502018, 0.5586467658036525], 'a8': [-0.13591132614471826, 0.9907210058465421], 'a9': [0.8785813075865162, 0.4775928035047926], 'algebraic': True, 'analytic_conductor': 287.4686738256219, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [107, [1]]], 'bad_primes': [5, 107], 'central_character': '2675.54', 'coeff_info': ['x^530 - 1', '0.999929729520755 + 0.0118547889289482*I', '\\\\zeta_{530}'], 'conductor': 2675, 'conductor_radical': 535, 'conjugate': 'dirichlet_L_2675.644', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^48', 'a^21', 'a^96', 0, 'a^69', 'a^50', 'a^144', 'a^42', 0, 'a^208', 'a^117', 'a^407', 'a^98', 0, 'a^192', 'a^14', 'a^90', 'a^34', 0, 'a^71', 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'root_analytic_conductor': 287.4686738256219, 'root_angle': 0.4120399351240129, 'root_number': '-0.851126231708630917289998162698+0.524961082078915555577695965013*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.412039935124', 'prec': 40}, 'spectral_label': 'r1-0', 'st_group': 'mu(530)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.09269115540390195682438223090+1.64892501995593782430672059838*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.32515364749', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.38650867375', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.85011678072', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 287.4686738256219, 'bad_primes': [5, 107], 'central_character': '2675.54', 'conductor': 2675, 'conductor_radical': 535, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2675/54'], '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': '1-2675-2675.54-r1-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2675-2675.54-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 287.4686738256219, 'root_angle': 0.4120399351240129, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32515364749', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_2675.54', 'Lhash_array': ['dirichlet_L_2675.54'], 'factors': ['1-2675-2675.54-r1-0-0'], 'label': '1-2675-2675.54-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2675/54'}