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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1021.144', 'a10': [0.510631193180907, -0.8597998514483725], 'a2': [0.5727351400805052, 0.8197404829072211], 'a3': [-0.9829730996839018, -0.18374951781657034], 'a4': [-0.3439489186339281, 0.9389883606150565], 'a5': [-0.4123563174739035, -0.9110226492460883], 'a6': [-0.4123563174739035, -0.9110226492460883], 'a7': [0.989091608371146, -0.1473016980546375], 'a8': [-0.9667184042691874, 0.2558427775944356], 'a9': [0.9324722294043558, 0.3612416661871529], 'algebraic': True, 'analytic_conductor': 4.741504066299603, 'analytic_normalization': 0, 'bad_lfactors': [[1021, [1]]], 'bad_primes': [1021], 'central_character': '1021.144', 'coeff_info': ['x^85 - 1', '0.997269173385788 + 0.0738525274748740*I', '\\\\zeta_{85}'], 'conductor': 1021, 'conductor_radical': 1021, 'conjugate': 'dirichlet_L_1021.78', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^45', 'a^26', 'a^58', 'a^58', 'a^83', 'a^39', 'a^5', 'a^71', 'a^31', 'a^71', 'a^55', 'a^11', 'a^18', 'a^52', 'a^41', 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'186.61994555114301072737446885007', '187.56491761032727845202930545304', '188.11592838168591829509418538918', '188.55793317531861188080218098802', '188.784999011196303731664006945603', '189.34545653143458588248811632037', '190.2376355437775469942617291725', '190.78468896790039922614448468439', '191.52609734102927442456058830582', '192.26556845292572276446302011791', '193.07549942197899749442869000025', '193.45788598699015034246239118196', '194.109887637086025945419255870247', '194.90155561036726644618917152130', '195.29818688332136488892662697096', '195.6663336195612335523811101333', '196.24017925240454187787530153570', '196.79235862759352149810689838862', '197.475368533176302651137635745623', '198.565200552828818033357538119826', '198.88047219162395691191384084261', '199.11207326635803812876792430503', '199.913124394052852202818246674243'], 'prelabel': '1-1021-1021.144-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.741504066299603, 'root_angle': 0.6199799998852766, 'root_number': '-0.368066132043403759764983106798+0.929799614133393619605446046979*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.309989999943', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(85)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.829996199748560109310336015258+0.371376256438135991809533938243*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.02706453673', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.4335681064', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.03977487434', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.741504066299603, 'bad_primes': [1021], 'central_character': '1021.144', 'conductor': 1021, 'conductor_radical': 1021, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1021/144'], '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': '1-1021-1021.144-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': '1-1021-1021.144-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.741504066299603, 'root_angle': 0.3099899999426383, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02706453673', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1021.144', 'Lhash_array': ['dirichlet_L_1021.144'], 'label': '1-1021-1021.144-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1021/144'}
Lfunction data - 1-1021-1021.144-r0-0-0