Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.447624 | 0.258436 | 0.129218 | − | 0.991616i | \(-0.458753\pi\) | ||||
0.129218 | + | 0.991616i | \(0.458753\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.901345 | 0.403094 | 0.201547 | − | 0.979479i | \(-0.435403\pi\) | ||||
0.201547 | + | 0.979479i | \(0.435403\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.57888 | 0.596760 | 0.298380 | − | 0.954447i | \(-0.403554\pi\) | ||||
0.298380 | + | 0.954447i | \(0.403554\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.79963 | −0.933211 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.73519 | −0.824690 | −0.412345 | − | 0.911028i | \(-0.635290\pi\) | ||||
−0.412345 | + | 0.911028i | \(0.635290\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.127802 | −0.0354459 | −0.0177229 | − | 0.999843i | \(-0.505642\pi\) | ||||
−0.0177229 | + | 0.999843i | \(0.505642\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.403464 | 0.104174 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.965178 | −0.234090 | −0.117045 | − | 0.993127i | \(-0.537342\pi\) | ||||
−0.117045 | + | 0.993127i | \(0.537342\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.08247 | −0.248336 | −0.124168 | − | 0.992261i | \(-0.539626\pi\) | ||||
−0.124168 | + | 0.992261i | \(0.539626\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.706743 | 0.154224 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.734871 | −0.153231 | −0.0766156 | − | 0.997061i | \(-0.524411\pi\) | ||||
−0.0766156 | + | 0.997061i | \(0.524411\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.18758 | −0.837516 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.59606 | −0.499611 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.81943 | 1.82342 | 0.911711 | − | 0.410833i | \(-0.134762\pi\) | ||||
0.911711 | + | 0.410833i | \(0.134762\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.56783 | 1.17962 | 0.589809 | − | 0.807543i | \(-0.299203\pi\) | ||||
0.589809 | + | 0.807543i | \(0.299203\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.22434 | −0.213130 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.42311 | 0.240550 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.91899 | −0.479879 | −0.239939 | − | 0.970788i | \(-0.577128\pi\) | ||||
−0.239939 | + | 0.970788i | \(0.577128\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0572072 | −0.00916049 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.43349 | 0.223873 | 0.111936 | − | 0.993715i | \(-0.464295\pi\) | ||||
0.111936 | + | 0.993715i | \(0.464295\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.61043 | 0.398087 | 0.199044 | − | 0.979991i | \(-0.436216\pi\) | ||||
0.199044 | + | 0.979991i | \(0.436216\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.52343 | −0.376171 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.70258 | −0.394212 | −0.197106 | − | 0.980382i | \(-0.563154\pi\) | ||||
−0.197106 | + | 0.980382i | \(0.563154\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.50715 | −0.643878 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.432037 | −0.0604973 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.901890 | 0.123884 | 0.0619421 | − | 0.998080i | \(-0.480271\pi\) | ||||
0.0619421 | + | 0.998080i | \(0.480271\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.46535 | −0.332427 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.484540 | −0.0641789 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.31776 | −0.822502 | −0.411251 | − | 0.911522i | \(-0.634908\pi\) | ||||
−0.411251 | + | 0.911522i | \(0.634908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.52676 | −0.707629 | −0.353815 | − | 0.935316i | \(-0.615116\pi\) | ||||
−0.353815 | + | 0.935316i | \(0.615116\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.42028 | −0.556902 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.115194 | −0.0142880 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.88478 | 0.474602 | 0.237301 | − | 0.971436i | \(-0.423737\pi\) | ||||
0.237301 | + | 0.971436i | \(0.423737\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.328946 | −0.0396004 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.68884 | 1.14985 | 0.574927 | − | 0.818205i | \(-0.305031\pi\) | ||||
0.574927 | + | 0.818205i | \(0.305031\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.43220 | −0.167627 | −0.0838134 | − | 0.996481i | \(-0.526710\pi\) | ||||
−0.0838134 | + | 0.996481i | \(0.526710\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.87446 | −0.216444 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.31853 | −0.492142 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.80388 | 1.10302 | 0.551511 | − | 0.834167i | \(-0.314051\pi\) | ||||
0.551511 | + | 0.834167i | \(0.314051\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.23684 | 0.804094 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.88746 | −0.536469 | −0.268234 | − | 0.963354i | \(-0.586440\pi\) | ||||
−0.268234 | + | 0.963354i | \(0.586440\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.869958 | −0.0943602 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.39541 | 0.471237 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.4486 | −1.74355 | −0.871776 | − | 0.489904i | \(-0.837032\pi\) | ||||
−0.871776 | + | 0.489904i | \(0.837032\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.201784 | −0.0211527 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.93992 | 0.304855 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.975680 | −0.100103 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.63007 | −0.876250 | −0.438125 | − | 0.898914i | \(-0.644357\pi\) | ||||
−0.438125 | + | 0.898914i | \(0.644357\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.65752 | 0.769610 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.46581 | 0.842380 | 0.421190 | − | 0.906972i | \(-0.361613\pi\) | ||||
0.421190 | + | 0.906972i | \(0.361613\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.82426 | −0.278282 | −0.139141 | − | 0.990273i | \(-0.544434\pi\) | ||||
−0.139141 | + | 0.990273i | \(0.544434\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.637019 | 0.0621667 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.1261 | −1.46230 | −0.731148 | − | 0.682219i | \(-0.761015\pi\) | ||||
−0.731148 | + | 0.682219i | \(0.761015\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.9868 | −1.43547 | −0.717737 | − | 0.696315i | \(-0.754822\pi\) | ||||
−0.717737 | + | 0.696315i | \(0.754822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.30661 | −0.124018 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.0027 | −1.88170 | −0.940848 | − | 0.338830i | \(-0.889969\pi\) | ||||
−0.940848 | + | 0.338830i | \(0.889969\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.662372 | −0.0617665 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.357799 | 0.0330785 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.52390 | −0.139696 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.51875 | −0.319886 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.641663 | 0.0578568 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.28117 | −0.740691 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.02653 | −0.0910896 | −0.0455448 | − | 0.998962i | \(-0.514502\pi\) | ||||
−0.0455448 | + | 0.998962i | \(0.514502\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.16849 | 0.102880 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.10716 | 0.795696 | 0.397848 | − | 0.917451i | \(-0.369757\pi\) | ||||
0.397848 | + | 0.917451i | \(0.369757\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.70909 | −0.148197 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.33994 | −0.201390 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.7857 | −1.86128 | −0.930640 | − | 0.365935i | \(-0.880749\pi\) | ||||
−0.930640 | + | 0.365935i | \(0.880749\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.628032 | 0.0532689 | 0.0266345 | − | 0.999645i | \(-0.491521\pi\) | ||||
0.0266345 | + | 0.999645i | \(0.491521\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.20974 | −0.101879 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.349562 | 0.0292319 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.85069 | 0.735009 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.01751 | −0.166401 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.6024 | 0.868581 | 0.434291 | − | 0.900773i | \(-0.356999\pi\) | ||||
0.434291 | + | 0.900773i | \(0.356999\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.4339 | −1.41875 | −0.709377 | − | 0.704829i | \(-0.751024\pi\) | ||||
−0.709377 | + | 0.704829i | \(0.751024\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.70214 | 0.218455 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.91988 | 0.475496 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.640002 | 0.0510778 | 0.0255389 | − | 0.999674i | \(-0.491870\pi\) | ||||
0.0255389 | + | 0.999674i | \(0.491870\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.403708 | 0.0320161 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.16027 | −0.0914421 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.4870 | −1.52634 | −0.763170 | − | 0.646198i | \(-0.776358\pi\) | ||||
−0.763170 | + | 0.646198i | \(0.776358\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.10355 | −0.0859111 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.58619 | −0.432272 | −0.216136 | − | 0.976363i | \(-0.569346\pi\) | ||||
−0.216136 | + | 0.976363i | \(0.569346\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9837 | −0.998744 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.03052 | 0.231750 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.2916 | −1.61877 | −0.809383 | − | 0.587281i | \(-0.800198\pi\) | ||||
−0.809383 | + | 0.587281i | \(0.800198\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.61167 | −0.499795 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.82798 | −0.212564 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.1793 | −1.20930 | −0.604650 | − | 0.796491i | \(-0.706687\pi\) | ||||
−0.604650 | + | 0.796491i | \(0.706687\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.8341 | −1.62291 | −0.811456 | − | 0.584413i | \(-0.801325\pi\) | ||||
−0.811456 | + | 0.584413i | \(0.801325\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.47391 | −0.182877 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.63101 | −0.193436 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.63994 | 0.193052 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.09885 | −0.298148 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.0262 | 1.23197 | 0.615987 | − | 0.787757i | \(-0.288758\pi\) | ||||
0.615987 | + | 0.787757i | \(0.288758\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.80147 | −0.201654 | −0.100827 | − | 0.994904i | \(-0.532149\pi\) | ||||
−0.100827 | + | 0.994904i | \(0.532149\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0515634 | −0.00369253 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.21467 | 0.585271 | 0.292635 | − | 0.956224i | \(-0.405468\pi\) | ||||
0.292635 | + | 0.956224i | \(0.405468\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.1008 | 1.77935 | 0.889674 | − | 0.456597i | \(-0.150932\pi\) | ||||
0.889674 | + | 0.456597i | \(0.150932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.73892 | 0.122654 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.5037 | 1.08814 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.29206 | 0.0902417 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.05737 | 0.142997 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.96076 | 0.204800 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.99433 | −0.137295 | −0.0686476 | − | 0.997641i | \(-0.521868\pi\) | ||||
−0.0686476 | + | 0.997641i | \(0.521868\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.33696 | 0.297163 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.35290 | 0.160466 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.3698 | 0.703948 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.641089 | −0.0433208 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.123352 | 0.00829753 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.9920 | 1.53966 | 0.769830 | − | 0.638249i | \(-0.220341\pi\) | ||||
0.769830 | + | 0.638249i | \(0.220341\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.7237 | 0.781579 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.2522 | −1.60967 | −0.804836 | − | 0.593497i | \(-0.797747\pi\) | ||||
−0.804836 | + | 0.593497i | \(0.797747\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.04283 | 0.333240 | 0.166620 | − | 0.986021i | \(-0.446715\pi\) | ||||
0.166620 | + | 0.986021i | \(0.446715\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.93308 | −0.127187 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.35483 | −0.285294 | −0.142647 | − | 0.989774i | \(-0.545561\pi\) | ||||
−0.142647 | + | 0.989774i | \(0.545561\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.43596 | −0.158904 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.38845 | 0.285061 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.4760 | 0.807004 | 0.403502 | − | 0.914979i | \(-0.367793\pi\) | ||||
0.403502 | + | 0.914979i | \(0.367793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.29161 | 0.534110 | 0.267055 | − | 0.963681i | \(-0.413950\pi\) | ||||
0.267055 | + | 0.963681i | \(0.413950\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0275 | 0.707418 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.06249 | −0.259543 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.138342 | 0.00880249 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.18775 | −0.138643 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.5576 | 1.10822 | 0.554112 | − | 0.832442i | \(-0.313058\pi\) | ||||
0.554112 | + | 0.832442i | \(0.313058\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.01001 | 0.126368 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.389414 | −0.0243861 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.60355 | 0.287162 | 0.143581 | − | 0.989639i | \(-0.454138\pi\) | ||||
0.143581 | + | 0.989639i | \(0.454138\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.60873 | −0.286372 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.4908 | −1.70164 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.8831 | −0.856068 | −0.428034 | − | 0.903763i | \(-0.640794\pi\) | ||||
−0.428034 | + | 0.903763i | \(0.640794\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.812914 | 0.0499369 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.36281 | −0.450597 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.71959 | −0.165816 | −0.0829082 | − | 0.996557i | \(-0.526421\pi\) | ||||
−0.0829082 | + | 0.996557i | \(0.526421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.83383 | −0.415126 | −0.207563 | − | 0.978222i | \(-0.566553\pi\) | ||||
−0.207563 | + | 0.978222i | \(0.566553\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0903232 | −0.00546661 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.4538 | 0.690691 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.4311 | −0.987249 | −0.493625 | − | 0.869675i | \(-0.664328\pi\) | ||||
−0.493625 | + | 0.869675i | \(0.664328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.3875 | −1.10083 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.7034 | 0.936787 | 0.468394 | − | 0.883520i | \(-0.344833\pi\) | ||||
0.468394 | + | 0.883520i | \(0.344833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.5926 | −1.58076 | −0.790382 | − | 0.612615i | \(-0.790118\pi\) | ||||
−0.790382 | + | 0.612615i | \(0.790118\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.436738 | −0.0258701 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.26330 | 0.133598 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0684 | −0.945202 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.86302 | −0.226455 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.3129 | −1.24511 | −0.622557 | − | 0.782574i | \(-0.713906\pi\) | ||||
−0.622557 | + | 0.782574i | \(0.713906\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.69448 | −0.331545 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.10070 | 0.412024 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.0939179 | 0.00543141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.12155 | 0.237562 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.78950 | 0.217701 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.98152 | −0.285241 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.3391 | 1.61740 | 0.808699 | − | 0.588223i | \(-0.200172\pi\) | ||||
0.808699 | + | 0.588223i | \(0.200172\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.26420 | −0.0719181 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.2327 | −0.693655 | −0.346827 | − | 0.937929i | \(-0.612741\pi\) | ||||
−0.346827 | + | 0.937929i | \(0.612741\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.4674 | 1.38298 | 0.691489 | − | 0.722387i | \(-0.256955\pi\) | ||||
0.691489 | + | 0.722387i | \(0.256955\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.98419 | −0.224484 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.7231 | 0.770768 | 0.385384 | − | 0.922756i | \(-0.374069\pi\) | ||||
0.385384 | + | 0.922756i | \(0.374069\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.8580 | −1.50376 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.77081 | −0.377910 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.04478 | 0.0581330 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.535181 | 0.0296865 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.70844 | −0.370978 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.26704 | −0.235250 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.3649 | 1.77894 | 0.889469 | − | 0.456996i | \(-0.151074\pi\) | ||||
0.889469 | + | 0.456996i | \(0.151074\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.17210 | 0.447828 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.50153 | 0.191309 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.611067 | −0.0332869 | −0.0166435 | − | 0.999861i | \(-0.505298\pi\) | ||||
−0.0166435 | + | 0.999861i | \(0.505298\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.95369 | −0.486297 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.9643 | −0.972819 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.1684 | −0.981000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.296493 | −0.0159627 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.0394 | 1.23682 | 0.618409 | − | 0.785857i | \(-0.287778\pi\) | ||||
0.618409 | + | 0.785857i | \(0.287778\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.5411 | −1.31365 | −0.656827 | − | 0.754041i | \(-0.728102\pi\) | ||||
−0.656827 | + | 0.754041i | \(0.728102\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.331781 | 0.0177092 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.1596 | 1.81813 | 0.909067 | − | 0.416651i | \(-0.136796\pi\) | ||||
0.909067 | + | 0.416651i | \(0.136796\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.73298 | 0.463498 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.682133 | −0.0361023 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.9085 | 0.628507 | 0.314254 | − | 0.949339i | \(-0.398246\pi\) | ||||
0.314254 | + | 0.949339i | \(0.398246\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8283 | −0.938329 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.57508 | −0.0826700 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.29091 | −0.0675693 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.95411 | −0.310802 | −0.155401 | − | 0.987851i | \(-0.549667\pi\) | ||||
−0.155401 | + | 0.987851i | \(0.549667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.01323 | −0.208921 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.42397 | 0.0739290 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5045 | 0.699234 | 0.349617 | − | 0.936893i | \(-0.386312\pi\) | ||||
0.349617 | + | 0.936893i | \(0.386312\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.70685 | −0.191421 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.25494 | −0.0646328 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3264 | −1.14683 | −0.573415 | − | 0.819265i | \(-0.694382\pi\) | ||||
−0.573415 | + | 0.819265i | \(0.694382\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.459499 | −0.0235408 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.1315 | 0.977573 | 0.488786 | − | 0.872403i | \(-0.337440\pi\) | ||||
0.488786 | + | 0.872403i | \(0.337440\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.89248 | −0.198379 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.30825 | −0.371499 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.32461 | 0.269969 | 0.134984 | − | 0.990848i | \(-0.456902\pi\) | ||||
0.134984 | + | 0.990848i | \(0.456902\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.709281 | 0.0358699 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.07658 | 0.205636 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.83667 | 0.444621 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.7991 | −0.692558 | −0.346279 | − | 0.938132i | \(-0.612555\pi\) | ||||
−0.346279 | + | 0.938132i | \(0.612555\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.765029 | −0.0382994 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.8332 | −1.43986 | −0.719931 | − | 0.694045i | \(-0.755827\pi\) | ||||
−0.719931 | + | 0.694045i | \(0.755827\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.839382 | −0.0418126 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.52289 | 0.324125 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.98398 | 0.395751 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.76400 | −0.334458 | −0.167229 | − | 0.985918i | \(-0.553482\pi\) | ||||
−0.167229 | + | 0.985918i | \(0.553482\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.75182 | −0.481022 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.97496 | −0.490836 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.40529 | −0.216247 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.281122 | 0.0137666 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.4135 | 1.73006 | 0.865032 | − | 0.501717i | \(-0.167298\pi\) | ||||
0.865032 | + | 0.501717i | \(0.167298\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.422696 | 0.0206010 | 0.0103005 | − | 0.999947i | \(-0.496721\pi\) | ||||
0.0103005 | + | 0.999947i | \(0.496721\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.56623 | 0.367883 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.04176 | 0.196054 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.72608 | −0.422284 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.156473 | 0.00755456 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.6898 | −0.659415 | −0.329707 | − | 0.944083i | \(-0.606950\pi\) | ||||
−0.329707 | + | 0.944083i | \(0.606950\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.9972 | 0.912946 | 0.456473 | − | 0.889737i | \(-0.349112\pi\) | ||||
0.456473 | + | 0.889737i | \(0.349112\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.96178 | 0.189953 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.795476 | 0.0380528 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.6855 | −0.987265 | −0.493633 | − | 0.869671i | \(-0.664331\pi\) | ||||
−0.493633 | + | 0.869671i | \(0.664331\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.6184 | 0.600874 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.7062 | −1.36387 | −0.681937 | − | 0.731411i | \(-0.738862\pi\) | ||||
−0.681937 | + | 0.731411i | \(0.738862\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.8259 | −0.702815 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.74588 | 0.224473 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.92732 | 0.0909558 | 0.0454779 | − | 0.998965i | \(-0.485519\pi\) | ||||
0.0454779 | + | 0.998965i | \(0.485519\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.92085 | −0.184626 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.80385 | −0.366657 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.181877 | −0.00852650 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.7613 | −1.57929 | −0.789645 | − | 0.613564i | \(-0.789735\pi\) | ||||
−0.789645 | + | 0.613564i | \(0.789735\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.50566 | 0.116954 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.9746 | 1.16318 | 0.581592 | − | 0.813480i | \(-0.302430\pi\) | ||||
0.581592 | + | 0.813480i | \(0.302430\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.36011 | 0.295579 | 0.147790 | − | 0.989019i | \(-0.452784\pi\) | ||||
0.147790 | + | 0.989019i | \(0.452784\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.64988 | 0.122885 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.4726 | 1.13245 | 0.566227 | − | 0.824249i | \(-0.308402\pi\) | ||||
0.566227 | + | 0.824249i | \(0.308402\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.13360 | 0.283223 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.286480 | 0.0132003 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.14002 | −0.328299 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.53293 | 0.207985 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.52496 | −0.115610 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.9355 | 0.865186 | 0.432593 | − | 0.901589i | \(-0.357599\pi\) | ||||
0.432593 | + | 0.901589i | \(0.357599\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.373052 | 0.0170097 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.519365 | −0.0236319 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.77866 | −0.353211 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.8295 | 1.53296 | 0.766481 | − | 0.642267i | \(-0.222006\pi\) | ||||
0.766481 | + | 0.642267i | \(0.222006\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.72285 | −0.394461 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.1072 | −0.546390 | −0.273195 | − | 0.961959i | \(-0.588080\pi\) | ||||
−0.273195 | + | 0.961959i | \(0.588080\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.47750 | −0.426845 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.90207 | 0.310225 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.2975 | 0.686186 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.3596 | 1.62768 | 0.813839 | − | 0.581090i | \(-0.197374\pi\) | ||||
0.813839 | + | 0.581090i | \(0.197374\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.50051 | −0.111715 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.63062 | 0.339558 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.81180 | −0.258111 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.0203 | 1.81819 | 0.909096 | − | 0.416587i | \(-0.136774\pi\) | ||||
0.909096 | + | 0.416587i | \(0.136774\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.26127 | −0.100033 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.81016 | 0.124071 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.54563 | −0.112174 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.39207 | 0.325103 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.53061 | −0.418347 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.83402 | 0.343215 | 0.171607 | − | 0.985165i | \(-0.445104\pi\) | ||||
0.171607 | + | 0.985165i | \(0.445104\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.8245 | −1.78513 | −0.892565 | − | 0.450919i | \(-0.851096\pi\) | ||||
−0.892565 | + | 0.450919i | \(0.851096\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.95954 | −0.129165 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.33913 | −0.276137 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4600 | −0.976520 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.6874 | 0.767568 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.183202 | −0.00793537 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.6338 | −0.589442 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.24226 | −0.312526 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.3279 | 0.531000 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.3073 | −1.00206 | −0.501030 | − | 0.865430i | \(-0.667045\pi\) | ||||
−0.501030 | + | 0.865430i | \(0.667045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.77345 | −0.419419 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.5083 | −0.578630 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.00198 | 0.0428416 | 0.0214208 | − | 0.999771i | \(-0.493181\pi\) | ||||
0.0214208 | + | 0.999771i | \(0.493181\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.4729 | 0.660367 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.6292 | −0.452821 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.4791 | 0.658239 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.17771 | −0.0499908 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.2243 | −1.83147 | −0.915737 | − | 0.401778i | \(-0.868392\pi\) | ||||
−0.915737 | + | 0.401778i | \(0.868392\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.333618 | −0.0141105 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.18170 | 0.0498915 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −43.0714 | −1.81524 | −0.907621 | − | 0.419790i | \(-0.862104\pi\) | ||||
−0.907621 | + | 0.419790i | \(0.862104\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0293 | −0.758499 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.4261 | 0.479850 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 45.1586 | 1.89315 | 0.946573 | − | 0.322491i | \(-0.104520\pi\) | ||||
0.946573 | + | 0.322491i | \(0.104520\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.24438 | −0.135773 | −0.0678866 | − | 0.997693i | \(-0.521626\pi\) | ||||
−0.0678866 | + | 0.997693i | \(0.521626\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.62134 | 0.318386 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.07733 | 0.128333 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.72220 | −0.0716960 | −0.0358480 | − | 0.999357i | \(-0.511413\pi\) | ||||
−0.0358480 | + | 0.999357i | \(0.511413\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.25400 | −0.0521146 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.71670 | −0.320143 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.46684 | −0.102166 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.322500 | 0.0133337 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.8085 | 0.735036 | 0.367518 | − | 0.930017i | \(-0.380208\pi\) | ||||
0.367518 | + | 0.930017i | \(0.380208\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.10949 | −0.292941 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.67708 | 0.151255 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.2632 | 0.626783 | 0.313391 | − | 0.949624i | \(-0.398535\pi\) | ||||
0.313391 | + | 0.949624i | \(0.398535\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.37356 | −0.0563104 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.2357 | 0.459847 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.2179 | −0.826082 | −0.413041 | − | 0.910712i | \(-0.635533\pi\) | ||||
−0.413041 | + | 0.910712i | \(0.635533\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.4812 | −0.957818 | −0.478909 | − | 0.877865i | \(-0.658968\pi\) | ||||
−0.478909 | + | 0.877865i | \(0.658968\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.8760 | −0.442904 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.17160 | −0.128944 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.16706 | −0.372079 | −0.186040 | − | 0.982542i | \(-0.559565\pi\) | ||||
−0.186040 | + | 0.982542i | \(0.559565\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.93981 | 0.281215 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.345395 | 0.0139732 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.4458 | 1.59320 | 0.796601 | − | 0.604505i | \(-0.206629\pi\) | ||||
0.796601 | + | 0.604505i | \(0.206629\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.578359 | 0.0233217 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.0522 | −0.686495 | −0.343247 | − | 0.939245i | \(-0.611527\pi\) | ||||
−0.343247 | + | 0.939245i | \(0.611527\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.9531 | −1.44508 | −0.722538 | − | 0.691332i | \(-0.757024\pi\) | ||||
−0.722538 | + | 0.691332i | \(0.757024\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.90776 | 0.0765560 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.9704 | −1.04048 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.4737 | 0.538948 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.32531 | 0.0529277 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.81734 | 0.112335 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.4393 | 1.60986 | 0.804932 | − | 0.593367i | \(-0.202202\pi\) | ||||
0.804932 | + | 0.593367i | \(0.202202\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.892710 | −0.0354820 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.925255 | −0.0367176 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.576022 | 0.0228228 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.1252 | −1.07306 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.0274 | 0.949025 | 0.474512 | − | 0.880249i | \(-0.342624\pi\) | ||||
0.474512 | + | 0.880249i | \(0.342624\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.72714 | −0.225856 | −0.112928 | − | 0.993603i | \(-0.536023\pi\) | ||||
−0.112928 | + | 0.993603i | \(0.536023\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.05321 | 0.0414703 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.3266 | −0.523922 | −0.261961 | − | 0.965079i | \(-0.584369\pi\) | ||||
−0.261961 | + | 0.965079i | \(0.584369\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.2803 | 0.678309 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.64177 | 0.181925 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.34007 | 0.130707 | 0.0653535 | − | 0.997862i | \(-0.479182\pi\) | ||||
0.0653535 | + | 0.997862i | \(0.479182\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.20869 | 0.320740 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00965 | 0.156431 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.8770 | 0.852207 | 0.426103 | − | 0.904674i | \(-0.359886\pi\) | ||||
0.426103 | + | 0.904674i | \(0.359886\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.79954 | 0.303367 | 0.151683 | − | 0.988429i | \(-0.451531\pi\) | ||||
0.151683 | + | 0.988429i | \(0.451531\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.0552152 | 0.00214438 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.54048 | −0.0597372 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.21601 | −0.279405 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.2918 | 0.397903 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.1167 | 0.583575 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.6284 | 0.679524 | 0.339762 | − | 0.940511i | \(-0.389653\pi\) | ||||
0.339762 | + | 0.940511i | \(0.389653\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.8712 | 0.418432 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.5792 | −1.05995 | −0.529977 | − | 0.848012i | \(-0.677800\pi\) | ||||
−0.529977 | + | 0.848012i | \(0.677800\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.6258 | −0.522911 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.8558 | −0.415997 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.636916 | 0.0243709 | 0.0121855 | − | 0.999926i | \(-0.496121\pi\) | ||||
0.0121855 | + | 0.999926i | \(0.496121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.6364 | −0.750270 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.25729 | 0.0861211 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.115263 | −0.00439118 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −51.5685 | −1.96176 | −0.980878 | − | 0.194623i | \(-0.937652\pi\) | ||||
−0.980878 | + | 0.194623i | \(0.937652\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.0903 | 0.459272 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.566073 | 0.0214724 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.38357 | −0.0524064 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.94933 | −0.0737303 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.0254 | −1.20958 | −0.604792 | − | 0.796384i | \(-0.706744\pi\) | ||||
−0.604792 | + | 0.796384i | \(0.706744\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.15972 | 0.119171 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.09039 | −0.0410666 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.3665 | 0.502698 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.6315 | 1.37573 | 0.687863 | − | 0.725841i | \(-0.258549\pi\) | ||||
0.687863 | + | 0.725841i | \(0.258549\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −27.4473 | −1.02935 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.82651 | −0.180754 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.315076 | 0.0117832 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.58455 | 0.208559 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.4462 | −0.650635 | −0.325317 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325317 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.45915 | −0.166068 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.71153 | 0.138033 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −41.1196 | −1.52714 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.0541 | −0.966294 | −0.483147 | − | 0.875539i | \(-0.660506\pi\) | ||||
−0.483147 | + | 0.875539i | \(0.660506\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.7743 | −0.621271 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.51953 | −0.0931883 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.0798 | −1.36957 | −0.684787 | − | 0.728743i | \(-0.740105\pi\) | ||||
−0.684787 | + | 0.728743i | \(0.740105\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.81847 | −0.0670752 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.6256 | −0.391400 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.5384 | −1.38087 | −0.690436 | − | 0.723393i | \(-0.742581\pi\) | ||||
−0.690436 | + | 0.723393i | \(0.742581\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0619252 | 0.00227488 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.654911 | −0.0240263 | −0.0120132 | − | 0.999928i | \(-0.503824\pi\) | ||||
−0.0120132 | + | 0.999928i | \(0.503824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.55640 | 0.350119 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.6831 | 0.500639 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.8823 | −0.872639 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.0374 | −0.621704 | −0.310852 | − | 0.950458i | \(-0.600614\pi\) | ||||
−0.310852 | + | 0.950458i | \(0.600614\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.85920 | 0.286405 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.7140 | −0.571891 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.7650 | 1.66336 | 0.831678 | − | 0.555258i | \(-0.187381\pi\) | ||||
0.831678 | + | 0.555258i | \(0.187381\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.899728 | 0.0326581 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.97736 | 0.144179 | 0.0720896 | − | 0.997398i | \(-0.477033\pi\) | ||||
0.0720896 | + | 0.997398i | \(0.477033\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.6623 | −0.856632 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.43556 | 0.0880580 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.807422 | 0.0291543 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.5810 | 1.10278 | 0.551389 | − | 0.834248i | \(-0.314098\pi\) | ||||
0.551389 | + | 0.834248i | \(0.314098\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.06066 | 0.0742129 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.2675 | 1.37638 | 0.688192 | − | 0.725528i | \(-0.258405\pi\) | ||||
0.688192 | + | 0.725528i | \(0.258405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.5033 | −0.987948 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.06298 | −0.0740089 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.55171 | −0.0555957 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.5008 | −0.948273 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −25.4918 | −0.911001 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.576863 | 0.0205891 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.0437 | 0.821420 | 0.410710 | − | 0.911766i | \(-0.365281\pi\) | ||||
0.410710 | + | 0.911766i | \(0.365281\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.21440 | −0.221239 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.5818 | −1.12292 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.706331 | 0.0250825 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.363880 | 0.0129055 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 54.3456 | 1.92502 | 0.962510 | − | 0.271247i | \(-0.0874359\pi\) | ||||
0.962510 | + | 0.271247i | \(0.0874359\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.60847 | 0.0922811 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 46.0502 | 1.62710 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.91735 | 0.138240 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.04580 | −0.0368597 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.21735 | −0.0428529 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.0937 | 0.987720 | 0.493860 | − | 0.869541i | \(-0.335585\pi\) | ||||
0.493860 | + | 0.869541i | \(0.335585\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.6466 | −0.479198 | −0.239599 | − | 0.970872i | \(-0.577016\pi\) | ||||
−0.239599 | + | 0.970872i | \(0.577016\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.05899 | −0.107283 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.5645 | −0.615258 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.82572 | −0.0988593 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.564920 | 0.0197399 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.16976 | −0.285126 | −0.142563 | − | 0.989786i | \(-0.545534\pi\) | ||||
−0.142563 | + | 0.989786i | \(0.545534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.93119 | −0.137033 | −0.0685163 | − | 0.997650i | \(-0.521827\pi\) | ||||
−0.0685163 | + | 0.997650i | \(0.521827\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.12700 | 0.178499 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.6674 | −1.55324 | −0.776618 | − | 0.629972i | \(-0.783066\pi\) | ||||
−0.776618 | + | 0.629972i | \(0.783066\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.5802 | −1.33995 | −0.669974 | − | 0.742385i | \(-0.733695\pi\) | ||||
−0.669974 | + | 0.742385i | \(0.733695\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.35496 | −0.255141 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.35020 | 0.150726 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.03508 | −0.174246 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.0505 | −0.589350 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.85031 | −0.305547 | −0.152773 | − | 0.988261i | \(-0.548820\pi\) | ||||
−0.152773 | + | 0.988261i | \(0.548820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 67.4211 | 2.32487 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.02923 | 0.242099 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.7028 | −0.402587 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.55567 | −0.190895 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.9035 | −0.408526 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.14508 | 0.0735324 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.45889 | −0.0841907 | −0.0420953 | − | 0.999114i | \(-0.513403\pi\) | ||||
−0.0420953 | + | 0.999114i | \(0.513403\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.73154 | 0.0934169 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.1084 | −1.23344 | −0.616719 | − | 0.787183i | \(-0.711539\pi\) | ||||
−0.616719 | + | 0.787183i | \(0.711539\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.4366 | −1.07260 | −0.536301 | − | 0.844027i | \(-0.680179\pi\) | ||||
−0.536301 | + | 0.844027i | \(0.680179\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.01311 | 0.0345266 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.2863 | 0.384189 | 0.192094 | − | 0.981376i | \(-0.438472\pi\) | ||||
0.192094 | + | 0.981376i | \(0.438472\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.1910 | −0.652514 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.19262 | −0.244274 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.8155 | −0.909652 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.496483 | −0.0168227 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.1610 | 0.817726 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.0750 | −0.442014 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.09812 | 0.239687 | 0.119843 | − | 0.992793i | \(-0.461761\pi\) | ||||
0.119843 | + | 0.992793i | \(0.461761\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.54018 | −0.321782 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.63729 | −0.0888526 | −0.0444263 | − | 0.999013i | \(-0.514146\pi\) | ||||
−0.0444263 | + | 0.999013i | \(0.514146\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.24123 | −0.210034 | −0.105017 | − | 0.994470i | \(-0.533490\pi\) | ||||
−0.105017 | + | 0.994470i | \(0.533490\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.54898 | −0.0856832 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.5186 | 0.823255 | 0.411627 | − | 0.911352i | \(-0.364961\pi\) | ||||
0.411627 | + | 0.911352i | \(0.364961\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.62076 | −0.0543586 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.7941 | −0.663128 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.92547 | 0.0978970 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.5831 | −0.487461 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0420399 | 0.00140367 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 64.4923 | 2.15094 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.870485 | −0.0290001 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.84491 | 0.0613946 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.6800 | −0.654185 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.2547 | −0.406911 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23.7012 | −0.786118 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.26239 | −0.306877 | −0.153438 | − | 0.988158i | \(-0.549035\pi\) | ||||
−0.153438 | + | 0.988158i | \(0.549035\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.3681 | 0.442421 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.22985 | −0.0737164 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.3791 | 0.474839 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.4107 | −1.69588 | −0.847942 | − | 0.530090i | \(-0.822158\pi\) | ||||
−0.847942 | + | 0.530090i | \(0.822158\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.6853 | 0.417994 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.23825 | −0.0407576 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.2235 | 0.401906 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.90688 | 0.259696 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.94174 | 0.0637065 | 0.0318532 | − | 0.999493i | \(-0.489859\pi\) | ||||
0.0318532 | + | 0.999493i | \(0.489859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.87886 | 0.159898 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.47567 | −0.179265 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.37950 | 0.0778180 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.7004 | 1.10094 | 0.550472 | − | 0.834854i | \(-0.314448\pi\) | ||||
0.550472 | + | 0.834854i | \(0.314448\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.9522 | 0.357411 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.5026 | 0.635766 | 0.317883 | − | 0.948130i | \(-0.397028\pi\) | ||||
0.317883 | + | 0.948130i | \(0.397028\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.05343 | −0.0343043 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.69448 | −0.120181 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.4170 | 1.08591 | 0.542954 | − | 0.839763i | \(-0.317306\pi\) | ||||
0.542954 | + | 0.839763i | \(0.317306\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.183038 | 0.00594168 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.14280 | 0.199194 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.7494 | 1.15804 | 0.579019 | − | 0.815314i | \(-0.303436\pi\) | ||||
0.579019 | + | 0.815314i | \(0.303436\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.3465 | 0.496600 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.0223 | −0.388625 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34.3970 | −1.11074 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.1364 | 0.391497 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.3475 | 1.36463 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.52509 | −0.0812855 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.9239 | −0.801499 | −0.400749 | − | 0.916188i | \(-0.631250\pi\) | ||||
−0.400749 | + | 0.916188i | \(0.631250\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.467668 | 0.0150237 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.1722 | −0.615266 | −0.307633 | − | 0.951505i | \(-0.599537\pi\) | ||||
−0.307633 | + | 0.951505i | \(0.599537\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.991585 | 0.0317887 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.239560 | 0.00767205 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.2149 | −0.486768 | −0.243384 | − | 0.969930i | \(-0.578257\pi\) | ||||
−0.243384 | + | 0.969930i | \(0.578257\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.9901 | 1.43789 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.9575 | 1.33960 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.8694 | 0.665632 | 0.332816 | − | 0.942992i | \(-0.392001\pi\) | ||||
0.332816 | + | 0.942992i | \(0.392001\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.40425 | 0.235919 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.91003 | −0.0607970 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.91833 | −0.0609993 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.6095 | 1.54413 | 0.772066 | − | 0.635543i | \(-0.219224\pi\) | ||||
0.772066 | + | 0.635543i | \(0.219224\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.4873 | 0.459741 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.6245 | 0.717244 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.6835 | −1.22512 | −0.612559 | − | 0.790425i | \(-0.709860\pi\) | ||||
−0.612559 | + | 0.790425i | \(0.709860\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.57786 | 0.239753 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8048.2.a.v.1.16 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.13 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.13 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.16 | 28 | 1.1 | even | 1 | trivial |