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 | 1.12 | ||
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 | ||||||||
\(3\) | −0.799349 | −0.461505 | −0.230752 | − | 0.973013i | \(-0.574119\pi\) | ||||
−0.230752 | + | 0.973013i | \(0.574119\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.626001 | 0.279956 | 0.139978 | − | 0.990155i | \(-0.455297\pi\) | ||||
0.139978 | + | 0.990155i | \(0.455297\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.555593 | 0.209994 | 0.104997 | − | 0.994473i | \(-0.466517\pi\) | ||||
0.104997 | + | 0.994473i | \(0.466517\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.36104 | −0.787013 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.34364 | 0.405123 | 0.202562 | − | 0.979270i | \(-0.435073\pi\) | ||||
0.202562 | + | 0.979270i | \(0.435073\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.90044 | 0.804438 | 0.402219 | − | 0.915544i | \(-0.368239\pi\) | ||||
0.402219 | + | 0.915544i | \(0.368239\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.500394 | −0.129201 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.10341 | 0.510152 | 0.255076 | − | 0.966921i | \(-0.417899\pi\) | ||||
0.255076 | + | 0.966921i | \(0.417899\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.54470 | 1.96029 | 0.980144 | − | 0.198288i | \(-0.0635380\pi\) | ||||
0.980144 | + | 0.198288i | \(0.0635380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.444113 | −0.0969133 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.01796 | −1.67186 | −0.835930 | − | 0.548836i | \(-0.815071\pi\) | ||||
−0.835930 | + | 0.548836i | \(0.815071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.60812 | −0.921624 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.28534 | 0.824715 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.10061 | −0.390073 | −0.195036 | − | 0.980796i | \(-0.562483\pi\) | ||||
−0.195036 | + | 0.980796i | \(0.562483\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.16291 | −0.568076 | −0.284038 | − | 0.958813i | \(-0.591674\pi\) | ||||
−0.284038 | + | 0.958813i | \(0.591674\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.07404 | −0.186966 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.347802 | 0.0587892 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.9692 | −1.80333 | −0.901665 | − | 0.432436i | \(-0.857654\pi\) | ||||
−0.901665 | + | 0.432436i | \(0.857654\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.31847 | −0.371252 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.458903 | −0.0716686 | −0.0358343 | − | 0.999358i | \(-0.511409\pi\) | ||||
−0.0358343 | + | 0.999358i | \(0.511409\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.58754 | −0.394595 | −0.197298 | − | 0.980344i | \(-0.563217\pi\) | ||||
−0.197298 | + | 0.980344i | \(0.563217\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.47801 | −0.220329 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.5539 | −1.53944 | −0.769722 | − | 0.638379i | \(-0.779605\pi\) | ||||
−0.769722 | + | 0.638379i | \(0.779605\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.69132 | −0.955902 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.68136 | −0.235438 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.54386 | −0.761508 | −0.380754 | − | 0.924676i | \(-0.624336\pi\) | ||||
−0.380754 | + | 0.924676i | \(0.624336\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.841122 | 0.113417 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.83020 | −0.904682 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.89005 | 1.28757 | 0.643787 | − | 0.765204i | \(-0.277362\pi\) | ||||
0.643787 | + | 0.765204i | \(0.277362\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.357146 | 0.0457278 | 0.0228639 | − | 0.999739i | \(-0.492722\pi\) | ||||
0.0228639 | + | 0.999739i | \(0.492722\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.31178 | −0.165268 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.81568 | 0.225207 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.78050 | 0.339693 | 0.169846 | − | 0.985471i | \(-0.445673\pi\) | ||||
0.169846 | + | 0.985471i | \(0.445673\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.40915 | 0.771571 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.26348 | −0.505982 | −0.252991 | − | 0.967469i | \(-0.581414\pi\) | ||||
−0.252991 | + | 0.967469i | \(0.581414\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.79073 | −0.560713 | −0.280357 | − | 0.959896i | \(-0.590453\pi\) | ||||
−0.280357 | + | 0.959896i | \(0.590453\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.68350 | 0.425334 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.746518 | 0.0850736 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.7953 | 1.43958 | 0.719791 | − | 0.694191i | \(-0.244238\pi\) | ||||
0.719791 | + | 0.694191i | \(0.244238\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.65763 | 0.406404 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.7232 | 1.28679 | 0.643395 | − | 0.765535i | \(-0.277525\pi\) | ||||
0.643395 | + | 0.765535i | \(0.277525\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.31674 | 0.142820 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.67912 | 0.180020 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.1805 | 1.71513 | 0.857563 | − | 0.514379i | \(-0.171978\pi\) | ||||
0.857563 | + | 0.514379i | \(0.171978\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.61146 | 0.168927 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.52827 | 0.262169 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.34899 | 0.548795 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.3066 | −1.35108 | −0.675540 | − | 0.737323i | \(-0.736089\pi\) | ||||
−0.675540 | + | 0.737323i | \(0.736089\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.17239 | −0.318838 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6747 | −1.06217 | −0.531087 | − | 0.847317i | \(-0.678216\pi\) | ||||
−0.531087 | + | 0.847317i | \(0.678216\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.17714 | −0.707184 | −0.353592 | − | 0.935400i | \(-0.615040\pi\) | ||||
−0.353592 | + | 0.935400i | \(0.615040\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.278015 | −0.0271315 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.23427 | 0.796037 | 0.398018 | − | 0.917377i | \(-0.369698\pi\) | ||||
0.398018 | + | 0.917377i | \(0.369698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.3637 | 1.37580 | 0.687898 | − | 0.725807i | \(-0.258534\pi\) | ||||
0.687898 | + | 0.725807i | \(0.258534\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.76825 | 0.832245 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.429783 | −0.0404306 | −0.0202153 | − | 0.999796i | \(-0.506435\pi\) | ||||
−0.0202153 | + | 0.999796i | \(0.506435\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.01926 | −0.468048 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.84806 | −0.633103 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.16864 | 0.107129 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.19463 | −0.835875 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.366824 | 0.0330754 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.01470 | −0.537971 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.8935 | 1.58779 | 0.793895 | − | 0.608055i | \(-0.208050\pi\) | ||||
0.793895 | + | 0.608055i | \(0.208050\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.06835 | 0.182108 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.614900 | 0.0537241 | 0.0268620 | − | 0.999639i | \(-0.491449\pi\) | ||||
0.0268620 | + | 0.999639i | \(0.491449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.74737 | 0.411649 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.68263 | 0.230884 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.09359 | −0.435175 | −0.217587 | − | 0.976041i | \(-0.569819\pi\) | ||||
−0.217587 | + | 0.976041i | \(0.569819\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.43213 | 0.545566 | 0.272783 | − | 0.962076i | \(-0.412056\pi\) | ||||
0.272783 | + | 0.962076i | \(0.412056\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.43625 | 0.710461 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.89715 | 0.325896 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.31498 | −0.109203 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.34870 | 0.441153 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.91770 | 0.484796 | 0.242398 | − | 0.970177i | \(-0.422066\pi\) | ||||
0.242398 | + | 0.970177i | \(0.422066\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.65713 | −0.297613 | −0.148807 | − | 0.988866i | \(-0.547543\pi\) | ||||
−0.148807 | + | 0.988866i | \(0.547543\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.96624 | −0.401497 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.97999 | −0.159036 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.4656 | −1.47371 | −0.736857 | − | 0.676048i | \(-0.763691\pi\) | ||||
−0.736857 | + | 0.676048i | \(0.763691\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.43148 | 0.351439 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.45472 | −0.351081 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.8373 | −1.86708 | −0.933540 | − | 0.358472i | \(-0.883298\pi\) | ||||
−0.933540 | + | 0.358472i | \(0.883298\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.672350 | −0.0523424 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.11519 | −0.241061 | −0.120530 | − | 0.992710i | \(-0.538460\pi\) | ||||
−0.120530 | + | 0.992710i | \(0.538460\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.58744 | −0.352880 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.1744 | −1.54277 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.3868 | −1.77806 | −0.889032 | − | 0.457845i | \(-0.848621\pi\) | ||||
−0.889032 | + | 0.457845i | \(0.848621\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.56024 | −0.193536 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.90560 | −0.594222 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.70833 | −0.127687 | −0.0638434 | − | 0.997960i | \(-0.520336\pi\) | ||||
−0.0638434 | + | 0.997960i | \(0.520336\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.03069 | 0.596916 | 0.298458 | − | 0.954423i | \(-0.403528\pi\) | ||||
0.298458 | + | 0.954423i | \(0.403528\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.285484 | −0.0211036 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.86675 | −0.504854 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.82623 | 0.206675 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.38091 | 0.173185 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.33287 | 0.385873 | 0.192937 | − | 0.981211i | \(-0.438199\pi\) | ||||
0.192937 | + | 0.981211i | \(0.438199\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.0996 | −1.30284 | −0.651419 | − | 0.758718i | \(-0.725826\pi\) | ||||
−0.651419 | + | 0.758718i | \(0.725826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.45136 | −0.103934 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.36431 | 0.453438 | 0.226719 | − | 0.973960i | \(-0.427200\pi\) | ||||
0.226719 | + | 0.973960i | \(0.427200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.3253 | −1.65348 | −0.826742 | − | 0.562581i | \(-0.809808\pi\) | ||||
−0.826742 | + | 0.562581i | \(0.809808\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.22260 | −0.156770 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.16708 | −0.0819131 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.287274 | −0.0200641 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.9307 | 1.31578 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.4810 | 0.794158 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.96717 | −0.135426 | −0.0677129 | − | 0.997705i | \(-0.521570\pi\) | ||||
−0.0677129 | + | 0.997705i | \(0.521570\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.40801 | 0.233513 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.61980 | −0.110469 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.75729 | −0.119293 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.82947 | 0.258772 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.10082 | 0.410386 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.9131 | −0.931693 | −0.465847 | − | 0.884865i | \(-0.654250\pi\) | ||||
−0.465847 | + | 0.884865i | \(0.654250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.8800 | 0.725331 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.2586 | 1.34461 | 0.672304 | − | 0.740275i | \(-0.265305\pi\) | ||||
0.672304 | + | 0.740275i | \(0.265305\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.859061 | 0.0567683 | 0.0283842 | − | 0.999597i | \(-0.490964\pi\) | ||||
0.0283842 | + | 0.999597i | \(0.490964\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.596729 | −0.0392619 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.8692 | 0.974113 | 0.487057 | − | 0.873370i | \(-0.338071\pi\) | ||||
0.487057 | + | 0.873370i | \(0.338071\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.60676 | −0.430977 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.2279 | −0.664374 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.39190 | 0.0900346 | 0.0450173 | − | 0.998986i | \(-0.485666\pi\) | ||||
0.0450173 | + | 0.998986i | \(0.485666\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.8940 | 1.41032 | 0.705160 | − | 0.709048i | \(-0.250875\pi\) | ||||
0.705160 | + | 0.709048i | \(0.250875\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.7798 | −1.01227 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.18877 | −0.267611 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.7834 | 1.57693 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.37094 | −0.593859 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.829354 | 0.0523484 | 0.0261742 | − | 0.999657i | \(-0.491668\pi\) | ||||
0.0261742 | + | 0.999657i | \(0.491668\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.7733 | −0.677310 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.05253 | −0.0659122 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.8402 | −1.48711 | −0.743556 | − | 0.668674i | \(-0.766862\pi\) | ||||
−0.743556 | + | 0.668674i | \(0.766862\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.09442 | −0.378689 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.95962 | 0.306993 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.32891 | −0.266932 | −0.133466 | − | 0.991053i | \(-0.542611\pi\) | ||||
−0.133466 | + | 0.991053i | \(0.542611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.47046 | −0.213189 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.9338 | −0.791538 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.3997 | −1.60962 | −0.804808 | − | 0.593535i | \(-0.797732\pi\) | ||||
−0.804808 | + | 0.593535i | \(0.797732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.7676 | −0.897070 | −0.448535 | − | 0.893765i | \(-0.648054\pi\) | ||||
−0.448535 | + | 0.893765i | \(0.648054\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.28812 | −0.0779607 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.19167 | −0.373372 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.7332 | 0.644893 | 0.322446 | − | 0.946588i | \(-0.395495\pi\) | ||||
0.322446 | + | 0.946588i | \(0.395495\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.46776 | 0.447083 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.9698 | −0.952676 | −0.476338 | − | 0.879262i | \(-0.658036\pi\) | ||||
−0.476338 | + | 0.879262i | \(0.658036\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.4609 | −1.87015 | −0.935077 | − | 0.354445i | \(-0.884670\pi\) | ||||
−0.935077 | + | 0.354445i | \(0.884670\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.27571 | −0.253271 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.254963 | −0.0150500 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.5757 | −0.739745 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.6366 | 0.623530 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.125371 | −0.00732426 | −0.00366213 | − | 0.999993i | \(-0.501166\pi\) | ||||
−0.00366213 | + | 0.999993i | \(0.501166\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.19118 | 0.360465 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.75797 | 0.334111 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.2556 | −1.34491 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.43762 | −0.0828628 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.53283 | 0.490198 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.223574 | 0.0128018 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.33839 | −0.190532 | −0.0952660 | − | 0.995452i | \(-0.530370\pi\) | ||||
−0.0952660 | + | 0.995452i | \(0.530370\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.73704 | 0.326369 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.02727 | 0.228366 | 0.114183 | − | 0.993460i | \(-0.463575\pi\) | ||||
0.114183 | + | 0.993460i | \(0.463575\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.5613 | −0.710009 | −0.355005 | − | 0.934865i | \(-0.615521\pi\) | ||||
−0.355005 | + | 0.934865i | \(0.615521\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.821174 | −0.0462679 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.1813 | 0.852669 | 0.426335 | − | 0.904566i | \(-0.359805\pi\) | ||||
0.426335 | + | 0.904566i | \(0.359805\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.82246 | −0.158028 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.58206 | −0.367375 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.9730 | 1.00004 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.3656 | −0.741389 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.4816 | −0.634936 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.86367 | −0.323275 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.9585 | −1.20695 | −0.603473 | − | 0.797383i | \(-0.706217\pi\) | ||||
−0.603473 | + | 0.797383i | \(0.706217\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.8988 | 1.41924 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.74060 | 0.0950991 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5450 | −0.846788 | −0.423394 | − | 0.905946i | \(-0.639161\pi\) | ||||
−0.423394 | + | 0.905946i | \(0.639161\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.343547 | 0.0186589 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.24982 | −0.230141 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.60679 | −0.410728 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.01214 | 0.216006 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.1596 | −1.45800 | −0.729001 | − | 0.684512i | \(-0.760015\pi\) | ||||
−0.729001 | + | 0.684512i | \(0.760015\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.5102 | −0.562598 | −0.281299 | − | 0.959620i | \(-0.590765\pi\) | ||||
−0.281299 | + | 0.959620i | \(0.590765\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.4294 | 0.663432 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.5220 | 0.932602 | 0.466301 | − | 0.884626i | \(-0.345586\pi\) | ||||
0.466301 | + | 0.884626i | \(0.345586\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.66894 | −0.141653 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.934151 | −0.0494405 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.12608 | 0.217766 | 0.108883 | − | 0.994055i | \(-0.465273\pi\) | ||||
0.108883 | + | 0.994055i | \(0.465273\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 54.0118 | 2.84273 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.34972 | 0.385760 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.99901 | −0.156975 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.6987 | 0.610669 | 0.305335 | − | 0.952245i | \(-0.401232\pi\) | ||||
0.305335 | + | 0.952245i | \(0.401232\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.08349 | 0.0564041 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.08013 | −0.159912 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.6029 | −0.807888 | −0.403944 | − | 0.914784i | \(-0.632361\pi\) | ||||
−0.403944 | + | 0.914784i | \(0.632361\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.80785 | 0.248276 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.09269 | −0.313789 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.7859 | −0.964966 | −0.482483 | − | 0.875905i | \(-0.660265\pi\) | ||||
−0.482483 | + | 0.875905i | \(0.660265\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.3031 | −0.732772 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.5809 | 1.76700 | 0.883500 | − | 0.468431i | \(-0.155181\pi\) | ||||
0.883500 | + | 0.468431i | \(0.155181\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.467321 | 0.0238169 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.10928 | 0.310552 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.2021 | −0.821479 | −0.410739 | − | 0.911753i | \(-0.634729\pi\) | ||||
−0.410739 | + | 0.911753i | \(0.634729\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.8651 | −0.852903 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.491520 | −0.0247939 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00987 | 0.403020 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.9437 | −0.850380 | −0.425190 | − | 0.905104i | \(-0.639793\pi\) | ||||
−0.425190 | + | 0.905104i | \(0.639793\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.79481 | −0.189978 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.1156 | 0.555085 | 0.277542 | − | 0.960713i | \(-0.410480\pi\) | ||||
0.277542 | + | 0.960713i | \(0.410480\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.17384 | −0.456981 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.28968 | 0.113775 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.7387 | −0.730571 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.7477 | −1.02591 | −0.512953 | − | 0.858417i | \(-0.671448\pi\) | ||||
−0.512953 | + | 0.858417i | \(0.671448\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.07156 | 0.200835 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.49484 | 0.270383 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.33875 | 0.360245 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.14152 | −0.251781 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.57319 | 0.223415 | 0.111707 | − | 0.993741i | \(-0.464368\pi\) | ||||
0.111707 | + | 0.993741i | \(0.464368\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.78180 | 0.184314 | 0.0921569 | − | 0.995744i | \(-0.470624\pi\) | ||||
0.0921569 | + | 0.995744i | \(0.470624\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.9182 | 1.21156 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.69277 | −0.470169 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.198428 | 0.00960258 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.11519 | −0.150403 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.19119 | 0.105546 | 0.0527729 | − | 0.998607i | \(-0.483194\pi\) | ||||
0.0527729 | + | 0.998607i | \(0.483194\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.5781 | 1.42143 | 0.710717 | − | 0.703478i | \(-0.248371\pi\) | ||||
0.710717 | + | 0.703478i | \(0.248371\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.05113 | 0.0503979 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −68.5111 | −3.27733 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.470781 | 0.0224692 | 0.0112346 | − | 0.999937i | \(-0.496424\pi\) | ||||
0.0112346 | + | 0.999937i | \(0.496424\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.7985 | 0.752308 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.4202 | 1.63536 | 0.817678 | − | 0.575676i | \(-0.195261\pi\) | ||||
0.817678 | + | 0.575676i | \(0.195261\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.1290 | 0.480160 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.73031 | −0.223736 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.30590 | 0.250401 | 0.125200 | − | 0.992131i | \(-0.460043\pi\) | ||||
0.125200 | + | 0.992131i | \(0.460043\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.616601 | −0.0290346 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.92333 | 0.137350 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00878 | 0.0472923 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.1205 | −0.847643 | −0.423821 | − | 0.905746i | \(-0.639312\pi\) | ||||
−0.423821 | + | 0.905746i | \(0.639312\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.01384 | 0.420730 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.9439 | −0.789155 | −0.394577 | − | 0.918863i | \(-0.629109\pi\) | ||||
−0.394577 | + | 0.918863i | \(0.629109\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.1117 | 1.35294 | 0.676468 | − | 0.736472i | \(-0.263510\pi\) | ||||
0.676468 | + | 0.736472i | \(0.263510\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.58270 | 0.0733960 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.0748 | −0.651304 | −0.325652 | − | 0.945490i | \(-0.605584\pi\) | ||||
−0.325652 | + | 0.945490i | \(0.605584\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.54483 | 0.0713335 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.7605 | 0.680126 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.47672 | −0.159860 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −39.3750 | −1.80665 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.0893 | 0.599317 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.5663 | −0.665550 | −0.332775 | − | 0.943006i | \(-0.607985\pi\) | ||||
−0.332775 | + | 0.943006i | \(0.607985\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.8156 | −1.45067 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.56088 | 0.162026 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.32995 | −0.378243 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.4294 | −0.971061 | −0.485530 | − | 0.874220i | \(-0.661373\pi\) | ||||
−0.485530 | + | 0.874220i | \(0.661373\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.0543 | 0.861666 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.61968 | 0.253613 | 0.126806 | − | 0.991927i | \(-0.459527\pi\) | ||||
0.126806 | + | 0.991927i | \(0.459527\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.41844 | −0.198996 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.98592 | −0.0892606 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.36876 | −0.106253 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.1712 | 1.48495 | 0.742474 | − | 0.669875i | \(-0.233653\pi\) | ||||
0.742474 | + | 0.669875i | \(0.233653\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.49013 | 0.111251 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.68239 | −0.297362 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.66697 | 0.162856 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.2202 | 0.896245 | 0.448123 | − | 0.893972i | \(-0.352093\pi\) | ||||
0.448123 | + | 0.893972i | \(0.352093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.66170 | −0.117747 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 36.6170 | 1.61668 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.49290 | −0.197981 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.1807 | −0.623665 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.6942 | 0.820585 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.99252 | −0.0872940 | −0.0436470 | − | 0.999047i | \(-0.513898\pi\) | ||||
−0.0436470 | + | 0.999047i | \(0.513898\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.47470 | 0.414300 | 0.207150 | − | 0.978309i | \(-0.433581\pi\) | ||||
0.207150 | + | 0.978309i | \(0.433581\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.04653 | 0.0893177 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.65290 | −0.289805 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.2877 | 1.79512 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.3508 | −1.01334 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.33102 | −0.0576529 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.15466 | 0.222856 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.36556 | 0.0589281 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.99074 | −0.387258 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.41783 | 0.189937 | 0.0949686 | − | 0.995480i | \(-0.469725\pi\) | ||||
0.0949686 | + | 0.995480i | \(0.469725\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.41933 | −0.275480 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.99172 | 0.385163 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.631365 | −0.0269952 | −0.0134976 | − | 0.999909i | \(-0.504297\pi\) | ||||
−0.0134976 | + | 0.999909i | \(0.504297\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.843236 | −0.0359884 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.9490 | −0.764655 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.10897 | 0.302304 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.48893 | 0.232992 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.2181 | 0.856670 | 0.428335 | − | 0.903620i | \(-0.359100\pi\) | ||||
0.428335 | + | 0.903620i | \(0.359100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.50499 | −0.317427 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.25915 | −0.0953812 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.7104 | −0.830693 | −0.415346 | − | 0.909663i | \(-0.636340\pi\) | ||||
−0.415346 | + | 0.909663i | \(0.636340\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.269045 | −0.0113188 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.03215 | 0.0853424 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.0802769 | 0.00336538 | 0.00168269 | − | 0.999999i | \(-0.499464\pi\) | ||||
0.00168269 | + | 0.999999i | \(0.499464\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.8823 | −0.915746 | −0.457873 | − | 0.889018i | \(-0.651389\pi\) | ||||
−0.457873 | + | 0.889018i | \(0.651389\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.26283 | −0.178082 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.9478 | 1.54083 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.1912 | 0.674048 | 0.337024 | − | 0.941496i | \(-0.390580\pi\) | ||||
0.337024 | + | 0.941496i | \(0.390580\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.4679 | 0.601266 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.51333 | 0.270218 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.44897 | −0.308505 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.28689 | −0.177241 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.72740 | −0.277670 | −0.138835 | − | 0.990316i | \(-0.544336\pi\) | ||||
−0.138835 | + | 0.990316i | \(0.544336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.0261 | −1.11359 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.08731 | −0.209264 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.9777 | −1.35423 | −0.677116 | − | 0.735876i | \(-0.736771\pi\) | ||||
−0.677116 | + | 0.735876i | \(0.736771\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.731570 | 0.0299914 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.6450 | 0.763090 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.4962 | −1.61377 | −0.806885 | − | 0.590709i | \(-0.798848\pi\) | ||||
−0.806885 | + | 0.590709i | \(0.798848\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.9618 | 1.26296 | 0.631479 | − | 0.775393i | \(-0.282448\pi\) | ||||
0.631479 | + | 0.775393i | \(0.282448\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.56488 | −0.267343 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.75585 | −0.234009 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.0700 | −0.895795 | −0.447898 | − | 0.894085i | \(-0.647827\pi\) | ||||
−0.447898 | + | 0.894085i | \(0.647827\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.932906 | 0.0378033 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.6110 | −1.23839 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.1152 | −0.893225 | −0.446612 | − | 0.894728i | \(-0.647370\pi\) | ||||
−0.446612 | + | 0.894728i | \(0.647370\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.229632 | 0.00925966 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.9062 | −0.801394 | −0.400697 | − | 0.916211i | \(-0.631232\pi\) | ||||
−0.400697 | + | 0.916211i | \(0.631232\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.52776 | −0.141793 | −0.0708964 | − | 0.997484i | \(-0.522586\pi\) | ||||
−0.0708964 | + | 0.997484i | \(0.522586\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −34.3597 | −1.37881 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.98975 | 0.360167 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.2754 | 0.771016 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.17734 | −0.366508 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.0728 | −0.919972 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.82512 | −0.311513 | −0.155757 | − | 0.987795i | \(-0.549782\pi\) | ||||
−0.155757 | + | 0.987795i | \(0.549782\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.57246 | 0.0624997 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.2013 | 0.444512 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.4078 | −0.768964 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.0662 | 0.398214 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.7259 | 0.976615 | 0.488307 | − | 0.872672i | \(-0.337615\pi\) | ||||
0.488307 | + | 0.872672i | \(0.337615\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.8969 | 0.942403 | 0.471201 | − | 0.882026i | \(-0.343820\pi\) | ||||
0.471201 | + | 0.882026i | \(0.343820\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.29479 | 0.0509822 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.92521 | −0.0756878 | −0.0378439 | − | 0.999284i | \(-0.512049\pi\) | ||||
−0.0378439 | + | 0.999284i | \(0.512049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.2887 | 0.521627 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.40469 | 0.0550541 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.8640 | −0.933869 | −0.466934 | − | 0.884292i | \(-0.654642\pi\) | ||||
−0.466934 | + | 0.884292i | \(0.654642\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.384928 | 0.0150404 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.3111 | 0.441289 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.51936 | −0.215004 | −0.107502 | − | 0.994205i | \(-0.534285\pi\) | ||||
−0.107502 | + | 0.994205i | \(0.534285\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.94338 | −0.153380 | −0.0766898 | − | 0.997055i | \(-0.524435\pi\) | ||||
−0.0766898 | + | 0.997055i | \(0.524435\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.87669 | −0.189395 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.97186 | 0.115244 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.8426 | 0.652147 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.1215 | 0.429981 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.479876 | 0.0185254 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.7473 | 0.491373 | 0.245687 | − | 0.969349i | \(-0.420987\pi\) | ||||
0.245687 | + | 0.969349i | \(0.420987\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.7474 | −0.760078 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.5077 | 1.21094 | 0.605469 | − | 0.795869i | \(-0.292986\pi\) | ||||
0.605469 | + | 0.795869i | \(0.292986\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.39305 | −0.283719 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.1937 | −0.620543 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.1126 | −0.846117 | −0.423058 | − | 0.906102i | \(-0.639043\pi\) | ||||
−0.423058 | + | 0.906102i | \(0.639043\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.18859 | −0.121830 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.686690 | −0.0261989 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.0796 | −0.612586 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.4525 | 1.38672 | 0.693360 | − | 0.720591i | \(-0.256130\pi\) | ||||
0.693360 | + | 0.720591i | \(0.256130\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.76256 | −0.0669541 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.02652 | 0.152735 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.965261 | −0.0365619 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.8857 | −0.449558 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.1084 | 0.948330 | 0.474165 | − | 0.880436i | \(-0.342750\pi\) | ||||
0.474165 | + | 0.880436i | \(0.342750\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −93.7287 | −3.53505 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.28111 | 0.198898 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.93079 | −0.223050 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.2932 | −1.17524 | −0.587619 | − | 0.809137i | \(-0.699935\pi\) | ||||
−0.587619 | + | 0.809137i | \(0.699935\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.2102 | −1.13297 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.3601 | 0.949743 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.43962 | 0.0912368 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.11262 | −0.0415514 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.9603 | −1.49027 | −0.745134 | − | 0.666915i | \(-0.767614\pi\) | ||||
−0.745134 | + | 0.666915i | \(0.767614\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.98756 | −0.148505 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.5010 | −0.650869 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.67985 | 0.359501 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.4728 | −1.83484 | −0.917422 | − | 0.397915i | \(-0.869734\pi\) | ||||
−0.917422 | + | 0.397915i | \(0.869734\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.64065 | 0.0607646 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.44265 | −0.201304 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.1027 | 0.705576 | 0.352788 | − | 0.935703i | \(-0.385234\pi\) | ||||
0.352788 | + | 0.935703i | \(0.385234\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.34829 | 0.123504 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.73600 | 0.137617 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.3657 | −0.565236 | −0.282618 | − | 0.959233i | \(-0.591203\pi\) | ||||
−0.282618 | + | 0.959233i | \(0.591203\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.8106 | −0.727760 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.7367 | −0.834127 | −0.417064 | − | 0.908877i | \(-0.636941\pi\) | ||||
−0.417064 | + | 0.908877i | \(0.636941\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.70449 | 0.135722 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27.6790 | −1.01272 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.57490 | 0.167163 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.4892 | 0.528717 | 0.264359 | − | 0.964424i | \(-0.414840\pi\) | ||||
0.264359 | + | 0.964424i | \(0.414840\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.662944 | −0.0241590 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.28937 | −0.0833187 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.95561 | −0.252806 | −0.126403 | − | 0.991979i | \(-0.540343\pi\) | ||||
−0.126403 | + | 0.991979i | \(0.540343\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.61161 | 0.312582 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.1935 | −1.05826 | −0.529132 | − | 0.848540i | \(-0.677482\pi\) | ||||
−0.529132 | + | 0.848540i | \(0.677482\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.98038 | 0.288909 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.10887 | −0.112402 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.6855 | 1.03577 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.5303 | −0.632158 | −0.316079 | − | 0.948733i | \(-0.602367\pi\) | ||||
−0.316079 | + | 0.948733i | \(0.602367\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.0567 | 0.686309 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.8089 | 1.14409 | 0.572043 | − | 0.820223i | \(-0.306151\pi\) | ||||
0.572043 | + | 0.820223i | \(0.306151\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.5751 | 0.523552 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.87157 | 0.174767 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.92119 | −0.140491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.72859 | −0.204985 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.00182 | −0.321699 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.5595 | −0.412576 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.11212 | 0.324812 | 0.162406 | − | 0.986724i | \(-0.448075\pi\) | ||||
0.162406 | + | 0.986724i | \(0.448075\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.46031 | 0.123190 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.238784 | −0.00849019 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.03588 | 0.0367852 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.77411 | 0.0983877 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.0593 | 0.356320 | 0.178160 | − | 0.984002i | \(-0.442986\pi\) | ||||
0.178160 | + | 0.984002i | \(0.442986\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.1992 | −0.785351 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38.2027 | −1.34983 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.43703 | −0.227158 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.78866 | −0.0982874 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.1026 | 0.742845 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.3441 | 1.24263 | 0.621316 | − | 0.783560i | \(-0.286598\pi\) | ||||
0.621316 | + | 0.783560i | \(0.286598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.0787 | 1.61804 | 0.809021 | − | 0.587779i | \(-0.199998\pi\) | ||||
0.809021 | + | 0.587779i | \(0.199998\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.8045 | 0.414002 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.9222 | −0.522701 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.1097 | −0.773521 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.80473 | −0.132948 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.787685 | 0.0274904 | 0.0137452 | − | 0.999906i | \(-0.495625\pi\) | ||||
0.0137452 | + | 0.999906i | \(0.495625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.2719 | 0.880924 | 0.440462 | − | 0.897771i | \(-0.354815\pi\) | ||||
0.440462 | + | 0.897771i | \(0.354815\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.94931 | 0.172313 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.39440 | −0.291902 | −0.145951 | − | 0.989292i | \(-0.546624\pi\) | ||||
−0.145951 | + | 0.989292i | \(0.546624\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.5001 | −0.538341 | −0.269170 | − | 0.963093i | \(-0.586750\pi\) | ||||
−0.269170 | + | 0.963093i | \(0.586750\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.57954 | −0.297621 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.0746 | −0.487656 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.95012 | −0.0674865 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.5542 | −0.468500 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.7422 | −1.61372 | −0.806860 | − | 0.590743i | \(-0.798835\pi\) | ||||
−0.806860 | + | 0.590743i | \(0.798835\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.5875 | −0.847843 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.7654 | 0.439665 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.87174 | −0.0987910 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.10847 | −0.175529 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.1482 | 0.863085 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 87.9508 | 3.01492 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.8445 | 0.782181 | 0.391090 | − | 0.920352i | \(-0.372098\pi\) | ||||
0.391090 | + | 0.920352i | \(0.372098\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.6292 | −0.431909 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.5208 | 0.427702 | 0.213851 | − | 0.976866i | \(-0.431399\pi\) | ||||
0.213851 | + | 0.976866i | \(0.431399\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.3285 | −0.693598 | −0.346799 | − | 0.937940i | \(-0.612731\pi\) | ||||
−0.346799 | + | 0.937940i | \(0.612731\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.203805 | 0.00694564 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.5849 | 1.61981 | 0.809905 | − | 0.586562i | \(-0.199519\pi\) | ||||
0.809905 | + | 0.586562i | \(0.199519\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.6402 | −0.497780 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.0523 | 0.341396 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.1923 | 0.583208 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.06469 | 0.273262 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.4174 | 1.06332 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.34172 | −0.112971 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.2959 | 0.347667 | 0.173833 | − | 0.984775i | \(-0.444385\pi\) | ||||
0.173833 | + | 0.984775i | \(0.444385\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.100215 | 0.00338018 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.4676 | 0.992788 | 0.496394 | − | 0.868097i | \(-0.334657\pi\) | ||||
0.496394 | + | 0.868097i | \(0.334657\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.61286 | 0.155235 | 0.0776176 | − | 0.996983i | \(-0.475269\pi\) | ||||
0.0776176 | + | 0.996983i | \(0.475269\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.94892 | −0.166356 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.6445 | −0.357407 | −0.178704 | − | 0.983903i | \(-0.557190\pi\) | ||||
−0.178704 | + | 0.983903i | \(0.557190\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.94149 | 0.333427 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.91455 | 0.164644 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −90.1799 | −3.01775 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.06942 | −0.0357468 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.5894 | 0.620681 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.64403 | 0.221591 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.6610 | −0.388485 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.14916 | 0.0382416 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.02722 | 0.167111 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.3731 | −0.643272 | −0.321636 | − | 0.946863i | \(-0.604233\pi\) | ||||
−0.321636 | + | 0.946863i | \(0.604233\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25.2034 | 0.835945 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.9169 | 1.05745 | 0.528727 | − | 0.848792i | \(-0.322670\pi\) | ||||
0.528727 | + | 0.848792i | \(0.322670\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.7518 | 0.521308 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.178714 | −0.00590809 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.341634 | 0.0112817 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.1320 | 1.02695 | 0.513474 | − | 0.858105i | \(-0.328358\pi\) | ||||
0.513474 | + | 0.858105i | \(0.328358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.66854 | 0.0879314 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.3660 | −0.407031 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.5475 | 1.66199 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.9455 | 0.556564 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.2020 | −1.08932 | −0.544661 | − | 0.838656i | \(-0.683342\pi\) | ||||
−0.544661 | + | 0.838656i | \(0.683342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −57.1753 | −1.87384 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.21920 | −0.105392 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.76922 | 0.0578598 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.71287 | 0.251969 | 0.125984 | − | 0.992032i | \(-0.459791\pi\) | ||||
0.125984 | + | 0.992032i | \(0.459791\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0409 | 0.327673 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.7214 | −1.29488 | −0.647440 | − | 0.762117i | \(-0.724160\pi\) | ||||
−0.647440 | + | 0.762117i | \(0.724160\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.67947 | 0.119820 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.49045 | 0.0484844 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.37654 | 0.109723 | 0.0548614 | − | 0.998494i | \(-0.482528\pi\) | ||||
0.0548614 | + | 0.998494i | \(0.482528\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.8952 | −0.451059 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.1352 | −0.393511 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.4780 | 1.73232 | 0.866161 | − | 0.499766i | \(-0.166581\pi\) | ||||
0.866161 | + | 0.499766i | \(0.166581\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.33839 | 0.108028 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.25613 | 0.0729305 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.82996 | −0.0913842 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.9960 | −0.677290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.4414 | −0.626492 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.3304 | −0.364738 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.790292 | 0.0254141 | 0.0127070 | − | 0.999919i | \(-0.495955\pi\) | ||||
0.0127070 | + | 0.999919i | \(0.495955\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.3667 | −0.461525 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.7817 | −1.24456 | −0.622282 | − | 0.782793i | \(-0.713794\pi\) | ||||
−0.622282 | + | 0.782793i | \(0.713794\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.57365 | 0.114566 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.6838 | 0.342155 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.126026 | 0.00403193 | 0.00201597 | − | 0.999998i | \(-0.499358\pi\) | ||||
0.00201597 | + | 0.999998i | \(0.499358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.7408 | 0.694837 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.9134 | −1.08277 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.93750 | 0.221272 | 0.110636 | − | 0.993861i | \(-0.464711\pi\) | ||||
0.110636 | + | 0.993861i | \(0.464711\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.98407 | 0.126943 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.68712 | 0.149193 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.7468 | 0.659709 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.83365 | −0.185312 | −0.0926560 | − | 0.995698i | \(-0.529536\pi\) | ||||
−0.0926560 | + | 0.995698i | \(0.529536\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.5525 | 0.557011 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.6016 | −0.462903 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.2725 | −1.27544 | −0.637721 | − | 0.770267i | \(-0.720123\pi\) | ||||
−0.637721 | + | 0.770267i | \(0.720123\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −47.0069 | −1.48723 |
(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.1.12 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.17 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.17 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.12 | 28 | 1.1 | even | 1 | trivial |