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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2349.1984', 'a10': [-0.3420201433256687, 0.9396926207859084], 'a2': [-0.11609291412523023, -0.993238357741943], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9730448705798238, 0.23061587074244017], 'a5': [-0.8936326403234123, -0.44879918020046217], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.28680323271109026, -0.9579895123154889], 'a8': [0.3420201433256687, 0.9396926207859084], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 252.43510834257418, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [29, [1]]], 'bad_primes': [3, 29], 'central_character': '2349.1984', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 2349, 'conductor_radical': 87, 'conjugate': 'dirichlet_L_2349.1699', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^79', 0, 'a^50', 'a^62', 0, 'a^76', 'a^21', 0, 'a^33', 'a^55', 0, 'a^38', 'a^47', 0, 'a^100', 'a^15', 0, 'a^39', 'a^4', 0, 'a^26', 'a^32', 0, 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{'__RealLiteral__': 0, 'data': '0.357440229225', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(108)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.547446305379849723271857451211-0.291653061109600983704105354902*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0158673731437', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '0.928095758146', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '1.85605297154', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 252.43510834257418, 'bad_primes': [3, 29], 'central_character': '2349.1984', 'conductor': 2349, 'conductor_radical': 87, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2349/1984'], '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': '1-2349-2349.1984-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': '1-2349-2349.1984-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 252.43510834257418, 'root_angle': 0.3574402292248714, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0158673731437', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2349.1984', 'Lhash_array': ['dirichlet_L_2349.1984'], 'factors': ['1-2349-2349.1984-r1-0-0'], 'label': '1-2349-2349.1984-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2349/1984'}
Lfunction data - 1-2349-2349.1984-r1-0-0