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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_529.357', 'a10': [0.7350596058898482, 0.678002489515386], 'a2': [0.15459452215555688, -0.987978002649601], 'a3': [-0.999922905547776, -0.012417043162265879], 'a4': [-0.95220106743899, -0.3054719744396332], 'a5': [-0.5562153568544751, 0.8310381921423642], 'a6': [-0.1668503692778238, 0.9859822281724219], 'a7': [-0.6358918939778535, 0.7717781411605659], 'a8': [-0.4490046601890406, 0.8935294148087819], 'a9': [0.9996916340782128, 0.024832171754250083], 'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '529.357', 'coeff_info': ['x^253 - 1', '0.999691634078213 + 0.0248321717542501*I', '\\\\zeta_{253}'], 'conductor': 529, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_529.163', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^196', 'a^127', 'a^139', 'a^87', 'a^70', 'a^91', 'a^82', 'a^1', 'a^30', 'a^101', 'a^13', 'a^85', 'a^34', 'a^214', 'a^25', 'a^246', 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'a^118'], [1, 'a^133'], [1, 'a^17'], [1, 'a^153'], [1, 'a^122']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-23e2-529.357-r0-0-0', 'leading_term': '0.0225066454000050766528862543477-0.124409570573967835700818047806*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/529/357', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.12642899326325643, -0.3680888402430586, -1.130019493090758, -1.896871273493867, -2.164921901257681, -1.6219617185716035, -0.45388220674059354, 0.6767725258160555, 1.028753231929148, 0.33070275952512906, -0.9313079028341106, -1.7853269501998987, -1.4943022950724032, -0.1994971432427059, 1.086737198210693, 1.2509405361500727, 0.05780409108914403, -1.5123696589623017, -1.9885595417340174, -0.7088818260664538, 1.416085307813269, 2.48088467222973, 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'198.46128400889434824525417443649', '199.10188657048680717999360535784', '199.56831764786345862503718303680'], 'prelabel': '1-23e2-529.357-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': -0.8860628974050525, 'root_number': '-0.936619133353545724988887256558-0.350349252940623422767200546413*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.443031448703', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(253)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.482802657949982911094001307185-0.113025782007415336513233485791*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0951174179558', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.98745585935', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.89908632913', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'bad_primes': [23], 'central_character': '529.357', 'conductor': 529, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/529/357'], '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': '1-23e2-529.357-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': '1-23e2-529.357-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': -0.44303144870252625, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0951174179558', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_529.357', 'Lhash_array': ['dirichlet_L_529.357'], 'label': '1-23e2-529.357-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/529/357'}