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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3895.3552', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.30901699437494745, -0.9510565162951535], 'a3': [-0.7071067811865476, -0.7071067811865476], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.8910065241883679, 0.4539904997395468], 'a7': [0.4539904997395468, -0.8910065241883679], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [-7.040766286173228e-31, 1.0], 'algebraic': True, 'analytic_conductor': 418.57588207506444, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]], [41, [1]]], 'bad_primes': [5, 19, 41], 'central_character': '3895.3552', 'coeff_info': ['x^40 - 1', '0.987688340595138 + 0.156434465040231*I', '\\\\zeta_{40}'], 'conductor': 3895, 'conductor_radical': 3895, 'conjugate': 'dirichlet_L_3895.2203', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^32', 'a^25', 'a^24', 0, 'a^17', 'a^33', 'a^16', 'a^10', 0, 'a^11', 'a^9', 'a^17', 'a^25', 0, 'a^8', 'a^11', 'a^2', 0, 0, 'a^18', 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{'__RealLiteral__': 0, 'data': '1.73327443934', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.09732504274', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 418.57588207506444, 'bad_primes': [5, 19, 41], 'central_character': '3895.3552', 'conductor': 3895, 'conductor_radical': 3895, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3895/3552'], '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': '1-3895-3895.3552-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': '1-3895-3895.3552-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 418.57588207506444, 'root_angle': 0.12823717784176103, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.82876739062', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3895.3552', 'Lhash_array': ['dirichlet_L_3895.3552'], 'label': '1-3895-3895.3552-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3895/3552'}
Lfunction data - 1-3895-3895.3552-r1-0-0