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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_507.305', 'a10': [-0.9485364419471455, -0.3166679938014725], 'a2': [-0.9605181116313724, 0.27821746391645263], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8451900855437947, -0.5344658261278011], 'a5': [0.8229838658936564, 0.5680647467311558], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.3166679938014725, 0.9485364419471455], 'a8': [-0.6631226582407952, 0.7485107481711011], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.3544981014827604, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '507.305', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 507, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_507.128', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^71', 0, 'a^142', 'a^15', 0, 'a^31', 'a^57', 0, 'a^86', 'a^137', 0, 0, 'a^102', 0, 'a^128', 'a^148', 0, 'a^13', 'a^1', 0, 'a^52', 'a^104', 0, 'a^30', 0, 0, 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'186.98895964081815679523043998224', '187.750488964522118912196329739024', '188.87542564934481458469742835004', '189.14989883663940424140011040521', '189.6026362442055698421021938024', '190.231120419960703361627972795818', '190.8422784135681755282470556928', '191.62405190021948054093707495076', '192.33471427664472211201241142953', '192.952806347755992507544777721339', '193.23220990586902983388406491100', '194.23911189690674723707822080885', '194.93172126070002904980049775579', '195.842403301771796095409947168956', '196.370603912741423197051797855933', '197.00994590499505025316117114290', '197.59456702839482655182560845613', '198.218922038544223650133419650380', '198.717334777708819536770203861249', '199.44131970942016682499197829285'], 'prelabel': '1-507-507.305-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3544981014827604, 'root_angle': 0.2583826429980276, 'root_number': '0.688242199052449843983744434833+0.725480995921635432522032340226*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.129191321499', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.899338824502771963682556103890+0.233392871643162426620987120937*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.23895389822', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.30085322963', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.27077058565', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.3544981014827604, 'bad_primes': [3, 13], 'central_character': '507.305', 'conductor': 507, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/507/305'], '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': '1-507-507.305-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': '1-507-507.305-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3544981014827604, 'root_angle': 0.1291913214990138, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23895389822', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_507.305', 'Lhash_array': ['dirichlet_L_507.305'], 'label': '1-507-507.305-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/507/305'}