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{'Lhash': 'dirichlet_L_460.103', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.28173255684142967, 0.9594929736144974], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9898214418809327, 0.14231483827328514], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.8412535328311812, -0.5406408174555976], 'algebraic': True, 'analytic_conductor': 49.43386540552751, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [23, [1]]], 'bad_primes': [2, 5, 23], 'central_character': '460.103', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 460, 'conductor_radical': 230, 'conjugate': 'dirichlet_L_460.67', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^57', 0, 0, 0, 'a^45', 0, 'a^26', 0, 'a^52', 0, 'a^43', 0, 0, 0, 'a^27', 0, 'a^50', 0, 'a^14', 0, 0, 0, 0, 0, 'a^39', 0, 'a^38', 0, 'a^42', 0, 'a^21', 0, 0, 0, 'a^15', 0, 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'192.85728983254960256778289026018', '193.28411431542774184089351554049', '194.169658091390905281133347649328', '194.890854653295197993505149400859', '195.315082813992342581506454926333', '195.97784940314262506817692828680', '196.95154884528877215323279966111', '197.66608062967283598882211911659', '198.16760885691310914136247094327', '198.75461511694362694947378102823', '199.32395568758799284107913684743'], 'prelabel': '1-460-460.103-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 49.43386540552751, 'root_angle': 0.4355640752701814, 'root_number': '0.201051702279166519816958985886+0.979580631194109200890863167337*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.217782037635', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(44)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.12892426198856365492602403184+0.442093495051978261149720821485*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.02911025856', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.44413281944', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.8543002439', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 49.43386540552751, 'bad_primes': [2, 5, 23], 'central_character': '460.103', 'conductor': 460, 'conductor_radical': 230, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/460/103'], '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': '1-460-460.103-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': '1-460-460.103-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 49.43386540552751, 'root_angle': 0.2177820376350907, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02911025856', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_460.103', 'Lhash_array': ['dirichlet_L_460.103'], 'label': '1-460-460.103-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/460/103'}