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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4235.1957', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9450008187146685, 0.32706796331742166], 'a3': [-0.8660254037844386, 0.5], 'a4': [0.7860530947427875, -0.6181589862206052], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.6548607339452851, -0.7557495743542583], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.5406408174555976, 0.8412535328311812], 'a9': [0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 19.66725731711931, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.1957', 'coeff_info': ['x^132 - 1', '0.998867339183008 + 0.0475819158237423*I', '\\\\zeta_{132}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.1913', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^59', 'a^55', 'a^118', 0, 'a^114', 0, 'a^45', 'a^110', 0, 0, 'a^41', 'a^129', 0, 0, 'a^104', 'a^31', 'a^37', 'a^68', 0, 0, 0, 'a^71', 'a^100', 0, 'a^56', 'a^33', 0, 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'194.51639184937098790504675259578', '195.23519648914523883354858153745', '195.43516146599929507237223747612', '196.41379653995968843195773810972', '196.78954918584194578861257608827', '197.18556719719501552447374307944', '197.996132195219215029771471626827', '198.4563243628440009841711480800', '199.00088769942952987632284874117', '199.0943152476891762119948588987', '199.987836162582114974534715129459'], 'prelabel': '1-4235-4235.1957-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': 0.6147129240712506, 'root_number': '-0.352631045965518002993820584482+0.935762440698099791682375873224*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(132)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.521690639027449848297463563571+0.182450817480484599839192453419*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.823059248709', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.59833215778', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.6416441451', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.66725731711931, 'bad_primes': [5, 7, 11], 'central_character': '4235.1957', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/1957'], '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': '1-4235-4235.1957-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': '1-4235-4235.1957-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': 0.3073564620356253, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.823059248709', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4235.1957', 'Lhash_array': ['dirichlet_L_4235.1957'], 'label': '1-4235-4235.1957-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/1957'}