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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_37.6', 'a10': [1.0, 0.0], 'a2': [2.9010907910729803e-30, -1.0], 'a3': [-1.0, -1.4081532572346456e-30], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [-7.040766286173228e-31, 1.0], 'a6': [-7.040766286173228e-31, 1.0], 'a7': [1.0, 0.0], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 3.976202217401126, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]]], 'bad_primes': [37], 'central_character': '37.6', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 37, 'conductor_radical': 37, 'conjugate': 'dirichlet_L_37.31', 'degree': 1, 'dirichlet_coefficients': [1, '-I', -1, -1, 'I', 'I', 1, 'I', 1, 1, -1, 1, 'I', '-I', '-I', 1, 'I', '-I', 'I', '-I', -1, 'I', 'I', '-I', -1, 1, -1, -1, '-I', -1, '-I', '-I', 1, 1, 'I', -1, 0, 1, '-I', -1, -1, 'I', 'I', 1, 'I', 1, 1, -1, 1, 'I', '-I', '-I', 1, 'I', '-I', 'I', '-I', -1, 'I', 'I', '-I', -1, 1, -1, -1, '-I', -1, '-I', '-I', 1, 1, 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lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.976202217401126, 'bad_primes': [37], 'central_character': '37.6', 'conductor': 37, 'conductor_radical': 37, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/37/6'], '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': '1-37-37.6-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': '1-37-37.6-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.976202217401126, 'root_angle': 0.11185788582218664, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89103207373', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_37.6', 'Lhash_array': ['dirichlet_L_37.6'], 'factors': ['1-37-37.6-r1-0-0'], 'label': '1-37-37.6-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/37/6'}
Lfunction data - 1-37-37.6-r1-0-0