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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1441.1020', 'a10': [-0.9068743608505454, 0.4214011077725291], 'a2': [-0.943311813257743, -0.33190785312852844], 'a3': [-0.44319154559924134, -0.8964269372957038], 'a4': [0.7796743540632224, 0.6261851975383137], 'a5': [0.7155989607441211, -0.698511365248937], 'a6': [0.12053668025532305, 0.992708874098054], 'a7': [-0.9813701261394134, 0.19212671735370837], 'a8': [-0.5276402441061327, -0.8494679351215211], 'a9': [-0.6071625078187112, 0.7945776797137543], 'algebraic': True, 'analytic_conductor': 6.691975866344493, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [131, [1]]], 'bad_primes': [11, 131], 'central_character': '1441.1020', 'coeff_info': ['x^130 - 1', '0.998832226832327 + 0.0483133795255071*I', '\\\\zeta_{130}'], 'conductor': 1441, 'conductor_radical': 1441, 'conjugate': 'dirichlet_L_1441.931', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^72', 'a^88', 'a^14', 'a^114', 'a^30', 'a^61', 'a^86', 'a^46', 'a^56', 0, 'a^102', 'a^113', 'a^3', 'a^72', 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{'__RealLiteral__': 0, 'data': '2.53395135788', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.691975866344493, 'bad_primes': [11, 131], 'central_character': '1441.1020', 'conductor': 1441, 'conductor_radical': 1441, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1441/1020'], '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': '1-1441-1441.1020-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': '1-1441-1441.1020-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': -0.43088106451247254, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.565575720486', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1441.1020', 'Lhash_array': ['dirichlet_L_1441.1020'], 'label': '1-1441-1441.1020-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1441/1020'}