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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_153.115', 'a10': [2.9010907910729803e-30, -1.0], 'a2': [0.5, 0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.8660254037844386, -0.5], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8660254037844386, 0.5], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.7105290128734958, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '153.115', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 153, 'conductor_radical': 51, 'conjugate': 'dirichlet_L_153.4', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 0, 'a^4', 'a^7', 0, 'a^5', 'a^6', 0, 'a^9', 'a^5', 0, 'a^4', 'a^7', 0, 'a^8', 0, 0, 'a^6', 'a^11', 0, 'a^7', 'a^1', 0, 'a^2', 'a^6', 0, 'a^9', 'a^11', 0, 'a^7', 'a^10', 0, 0, 'a^0', 0, 'a^3', 'a^8', 0, 'a^1', 'a^1', 0, 'a^2', 'a^9', 0, 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'197.46898137465941793467043481426', '198.33260391605366558376747500732', '198.926211880661949258153025308287', '199.69931579294937401920367787008'], 'prelabel': '1-153-153.115-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7105290128734958, 'root_angle': -0.46661632851676876, 'root_number': '-0.978081792684768487058956514140-0.208221052774568301277312900588*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.466616328517', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.587058567174605111600638354319+0.491814403191053674464554323760*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.75523777575', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.1445469913', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '5.11243766022', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.7105290128734958, 'bad_primes': [3, 17], 'central_character': '153.115', 'conductor': 153, 'conductor_radical': 51, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/153/115'], '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': '1-153-153.115-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': '1-153-153.115-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7105290128734958, 'root_angle': -0.46661632851676876, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.75523777575', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_153.115', 'Lhash_array': ['dirichlet_L_153.115'], 'factors': ['1-153-153.115-r0-0-0'], 'label': '1-153-153.115-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/153/115'}
Lfunction data - 1-153-153.115-r0-0-0