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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_163.113', 'a10': [0.9257239692688904, 0.3781998581716425], 'a2': [-0.36017772480471044, -0.9328837047320006], 'a3': [0.4660435197025388, -0.8847617971766578], 'a4': [-0.7405440131090045, 0.6720078605555224], 'a5': [-0.6862416378687336, 0.7273736415730487], 'a6': [-0.993238357741943, -0.11609291412523023], 'a7': [-0.9812553106273847, 0.19271226054808968], 'a8': [0.8936326403234123, 0.44879918020046217], 'a9': [-0.5656068754865387, -0.8246750041091068], 'algebraic': True, 'analytic_conductor': 0.7569688176364694, 'analytic_normalization': 0, 'bad_lfactors': [[163, [1]]], 'bad_primes': [163], 'central_character': '163.113', 'coeff_info': ['x^81 - 1', '0.996992941167792 + 0.0774924206719309*I', '\\\\zeta_{81}'], 'conductor': 163, 'conductor_radical': 163, 'conjugate': 'dirichlet_L_163.88', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^56', 'a^67', 'a^31', 'a^30', 'a^42', 'a^38', 'a^6', 'a^53', 'a^5', 'a^40', 'a^17', 'a^21', 'a^13', 'a^16', 'a^62', 'a^33', 'a^28', 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'data': '0.221852614308', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(81)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.494227525340337853264665331056-0.203219547289940209133393996558*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.05551312538', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.99788815536', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.09271134411', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.7569688176364694, 'bad_primes': [163], 'central_character': '163.113', 'conductor': 163, 'conductor_radical': 163, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/163/113'], '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': '1-163-163.113-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': '1-163-163.113-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7569688176364694, 'root_angle': 0.22185261430759004, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.05551312538', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_163.113', 'Lhash_array': ['dirichlet_L_163.113'], 'label': '1-163-163.113-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/163/113'}
Lfunction data - 1-163-163.113-r0-0-0