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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4021.28', 'a10': [0.9975275721840101, 0.07027618894529297], 'a2': [0.5852534275386132, 0.810850433529085], 'a3': [0.8620915448564065, 0.5067525710710252], 'a4': [-0.3149568511086103, 0.9491059908881351], 'a5': [0.640789908958026, -0.7677162839080364], 'a6': [0.09364148953435077, 0.9956059820218981], 'a7': [2.9010907910729803e-30, -1.0], 'a8': [-0.953912580814779, 0.3000846350003407], 'a9': [0.48640366342581104, 0.8737342137091522], 'algebraic': True, 'analytic_conductor': 432.11646259918723, 'analytic_normalization': 0, 'bad_lfactors': [[4021, [1]]], 'bad_primes': [4021], 'central_character': '4021.28', 'coeff_info': ['x^804 - 1', '0.999969463768933 + 0.00781482755238383*I', '\\\\zeta_{804}'], 'conductor': 4021, 'conductor_radical': 4021, 'conjugate': 'dirichlet_L_4021.3303', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^121', 'a^68', 'a^242', 'a^692', 'a^189', 'a^603', 'a^363', 'a^136', 'a^9', 'a^661', 'a^310', 'a^30', 'a^724', 'a^760', 'a^484', 'a^330', 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'0.992027192503516709651302484867+0.126024003005739349294896530788*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(804)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.07962746918692007799759640482+0.687095298943372505006133845988*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.56516011803', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.51528530443', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.66842112369', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 432.11646259918723, 'bad_primes': [4021], 'central_character': '4021.28', 'conductor': 4021, 'conductor_radical': 4021, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4021/28'], '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': '1-4021-4021.28-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': '1-4021-4021.28-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 432.11646259918723, 'root_angle': 0.0201108180488926, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56516011803', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4021.28', 'Lhash_array': ['dirichlet_L_4021.28'], 'label': '1-4021-4021.28-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4021/28'}
Lfunction data - 1-4021-4021.28-r1-0-0