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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1043', 'a10': [0.8158354250084526, 0.5782841510030146], 'a2': [-0.5228384531415806, 0.8524317872513432], 'a3': [-0.9994914186000327, 0.031888934521151754], 'a4': [-0.4532799038330384, -0.8913682341104104], 'a5': [0.06639766074910194, -0.9977932404296228], 'a6': [0.4953894057817187, -0.8686710174969784], 'a7': [-0.48612635358775175, -0.8738885331365072], 'a8': [0.9968227806620411, 0.07965139015231544], 'a9': [0.9979661917102114, -0.06374543280437904], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1043', 'coeff_info': ['x^2364 - 1', '0.999996467887392 + 0.00265785867577771*I', '\\\\zeta_{2364}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.3863', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^798', 'a^1170', 'a^1596', 'a^1798', 'a^1968', 'a^1582', 'a^30', 'a^2340', 'a^232', 'a^33', 'a^402', 'a^1360', 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21.961383672410207, 'root_angle': -0.01359378049612958, 'root_number': '0.996354591457811768142772745809-0.0853084291318097404377018814976*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2364)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.539084884655043593733232763310+0.0302827747152705413010881471867*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.519488928378', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.17161683758', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.05050773778', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1043', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1043'], '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': '1-4729-4729.1043-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': '1-4729-4729.1043-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.01359378049612958, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.519488928378', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1043', 'Lhash_array': ['dirichlet_L_4729.1043'], 'factors': ['1-4729-4729.1043-r0-0-0'], 'label': '1-4729-4729.1043-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1043'}
Lfunction data - 1-4729-4729.1043-r0-0-0