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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_473.59', 'a10': [-0.2225209339563144, -0.9749279121818236], 'a2': [-0.6910626489868646, -0.7227948638273916], 'a3': [0.4738686624729987, 0.880595531856738], 'a4': [-0.044864830350514924, 0.9989930665413147], 'a5': [0.8584487936018661, 0.5128992774059061], 'a6': [0.30901699437494745, -0.9510565162951535], 'a7': [-0.8090169943749475, 0.5877852522924731], 'a8': [0.753071466003611, -0.6579387259397126], 'a9': [-0.5508969814521025, 0.8345732537213026], 'algebraic': True, 'analytic_conductor': 2.1966027652886506, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [43, [1]]], 'bad_primes': [11, 43], 'central_character': '473.59', 'coeff_info': ['x^35 - 1', '0.983929588598630 + 0.178556894798637*I', '\\\\zeta_{35}'], 'conductor': 473, 'conductor_radical': 473, 'conjugate': 'dirichlet_L_473.465', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^22', 'a^6', 'a^9', 'a^3', 'a^28', 'a^14', 'a^31', 'a^12', 'a^25', 0, 'a^15', 'a^17', 'a^1', 'a^9', 'a^18', 'a^18', 'a^34', 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'-0.789366330044450216572152550904+0.613922468225553780596134813306*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.394795370633', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(35)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.698358104539248734480073745309+0.251701235925205279851955907176*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.12304988263', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.62655155881', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.6640414413', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.1966027652886506, 'bad_primes': [11, 43], 'central_character': '473.59', 'conductor': 473, 'conductor_radical': 473, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/473/59'], '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': '1-473-473.59-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': '1-473-473.59-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1966027652886506, 'root_angle': 0.3947953706329756, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.12304988263', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_473.59', 'Lhash_array': ['dirichlet_L_473.59'], 'label': '1-473-473.59-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/473/59'}
Lfunction data - 1-473-473.59-r0-0-0