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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1183.1069', 'a10': [0.99675730813421, 0.08046656871672588], 'a2': [-0.7485107481711011, 0.6631226582407952], 'a3': [0.6324453755953773, -0.7746049618276546], 'a4': [0.12053668025532305, -0.992708874098054], 'a5': [-0.6927243535095994, -0.7212024473438146], 'a6': [0.040265940109415144, 0.9991889981715696], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.5680647467311558, 0.8229838658936564], 'a9': [-0.20002569377604443, -0.9797906520422677], 'algebraic': True, 'analytic_conductor': 127.1310060320414, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [13, [1]]], 'bad_primes': [7, 13], 'central_character': '1183.1069', 'coeff_info': ['x^78 - 1', '0.996757308134210 + 0.0804665687167259*I', '\\\\zeta_{78}'], 'conductor': 1183, 'conductor_radical': 91, 'conjugate': 'dirichlet_L_1183.633', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^30', 'a^67', 'a^60', 'a^49', 'a^19', 0, 'a^12', 'a^56', 'a^1', 'a^22', 'a^49', 0, 0, 'a^38', 'a^42', 'a^51', 'a^8', 'a^65', 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'1-1183-1183.1069-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 127.1310060320414, 'root_angle': 0.41276590296183296, 'root_number': '-0.853511921501313920310271973397+0.521073315239933337782797465487*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.412765902962', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(78)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.684057372357786527881799393639-0.191017567160657533410807483253*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.113954363641', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.923699841282', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '1.95416956082', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 127.1310060320414, 'bad_primes': [7, 13], 'central_character': '1183.1069', 'conductor': 1183, 'conductor_radical': 91, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1183/1069'], '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': '1-1183-1183.1069-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': '1-1183-1183.1069-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 127.1310060320414, 'root_angle': 0.41276590296183296, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.113954363641', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1183.1069', 'Lhash_array': ['dirichlet_L_1183.1069'], 'factors': ['1-1183-1183.1069-r1-0-0'], 'label': '1-1183-1183.1069-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1183/1069'}
Lfunction data - 1-1183-1183.1069-r1-0-0