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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2340.1267', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, 0.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 251.46792401942255, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '2340.1267', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 2340, 'conductor_radical': 390, 'conjugate': 'dirichlet_L_2340.1363', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^0', 0, 0, 0, 'a^13', 0, 0, 0, 0, 0, 'a^1', 0, 'a^13', 0, 0, 0, 'a^9', 0, 0, 0, 0, 0, 'a^10', 0, 'a^7', 0, 0, 0, 0, 0, 'a^2', 0, 0, 0, 'a^9', 0, 'a^9', 0, 0, 0, 'a^8', 0, 'a^0', 0, 0, 0, 'a^9', 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'194.92711727492898988967016841454', '195.46836581777642327697532136232', '196.15655101360663894527614639530', '196.39353773116772617284169487196', '197.35627494436469284294461399955', '197.85293521803446123619380115240', '198.25122113529601481660920554792', '198.90347553541813663411764396052', '199.30134254871069412402121929503'], 'prelabel': '1-2340-2340.1267-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 251.46792401942255, 'root_angle': -0.11248591833941916, 'root_number': '0.760463424282068517806657687256-0.649380766830363279902890151938*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.112485918339', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.39148310451564278040354502560-0.0902743083347866940049963677629*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.594661828849', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.53490947793', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.24120289633', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 251.46792401942255, 'bad_primes': [2, 3, 5, 13], 'central_character': '2340.1267', 'conductor': 2340, 'conductor_radical': 390, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2340/1267'], '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': '1-2340-2340.1267-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': '1-2340-2340.1267-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 251.46792401942255, 'root_angle': -0.11248591833941916, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.594661828849', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2340.1267', 'Lhash_array': ['dirichlet_L_2340.1267'], 'factors': ['1-2340-2340.1267-r1-0-0'], 'label': '1-2340-2340.1267-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2340/1267'}
Lfunction data - 1-2340-2340.1267-r1-0-0