Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, 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("3330.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.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: | \(26.5901838731\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{113}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1110) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4.81507\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.81507 | 1.89016 | 0.945081 | − | 0.326837i | \(-0.105983\pi\) | ||||
0.945081 | + | 0.326837i | \(0.105983\pi\) | |||||||
\(14\) | 3.00000 | 0.801784 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.81507 | −0.645822 | −0.322911 | − | 0.946429i | \(-0.604661\pi\) | ||||
−0.322911 | + | 0.946429i | \(0.604661\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 4.81507 | 1.00401 | 0.502006 | − | 0.864864i | \(-0.332596\pi\) | ||||
0.502006 | + | 0.864864i | \(0.332596\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.81507 | 1.33655 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.00000 | 0.566947 | ||||||||
\(29\) | −3.81507 | −0.708441 | −0.354221 | − | 0.935162i | \(-0.615254\pi\) | ||||
−0.354221 | + | 0.935162i | \(0.615254\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.81507 | −0.685207 | −0.342604 | − | 0.939480i | \(-0.611309\pi\) | ||||
−0.342604 | + | 0.939480i | \(0.611309\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | −3.00000 | −0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −2.81507 | −0.456665 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −5.81507 | −0.908162 | −0.454081 | − | 0.890960i | \(-0.650032\pi\) | ||||
−0.454081 | + | 0.890960i | \(0.650032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.81507 | 0.886790 | 0.443395 | − | 0.896326i | \(-0.353774\pi\) | ||||
0.443395 | + | 0.896326i | \(0.353774\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.81507 | 0.709944 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.81507 | 0.945081 | ||||||||
\(53\) | 10.6301 | 1.46016 | 0.730081 | − | 0.683360i | \(-0.239482\pi\) | ||||
0.730081 | + | 0.683360i | \(0.239482\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.81507 | −0.500944 | ||||||||
\(59\) | −2.00000 | −0.260378 | −0.130189 | − | 0.991489i | \(-0.541558\pi\) | ||||
−0.130189 | + | 0.991489i | \(0.541558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.81507 | −0.488470 | −0.244235 | − | 0.969716i | \(-0.578537\pi\) | ||||
−0.244235 | + | 0.969716i | \(0.578537\pi\) | |||||||
\(62\) | −3.81507 | −0.484515 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.81507 | −0.845306 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6301 | −1.66519 | −0.832594 | − | 0.553884i | \(-0.813145\pi\) | ||||
−0.832594 | + | 0.553884i | \(0.813145\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.00000 | −0.358569 | ||||||||
\(71\) | −9.63015 | −1.14289 | −0.571444 | − | 0.820641i | \(-0.693617\pi\) | ||||
−0.571444 | + | 0.820641i | \(0.693617\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.81507 | 0.563562 | 0.281781 | − | 0.959479i | \(-0.409075\pi\) | ||||
0.281781 | + | 0.959479i | \(0.409075\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.81507 | −0.322911 | ||||||||
\(77\) | 3.00000 | 0.341882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.81507 | −0.642167 | ||||||||
\(83\) | −6.81507 | −0.748051 | −0.374026 | − | 0.927418i | \(-0.622023\pi\) | ||||
−0.374026 | + | 0.927418i | \(0.622023\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | 0.108465 | ||||||||
\(86\) | 5.81507 | 0.627055 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −1.18493 | −0.125602 | −0.0628010 | − | 0.998026i | \(-0.520003\pi\) | ||||
−0.0628010 | + | 0.998026i | \(0.520003\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.4452 | 2.14324 | ||||||||
\(92\) | 4.81507 | 0.502006 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.00000 | 0.825137 | ||||||||
\(95\) | 2.81507 | 0.288820 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.81507 | 0.590431 | 0.295216 | − | 0.955431i | \(-0.404609\pi\) | ||||
0.295216 | + | 0.955431i | \(0.404609\pi\) | |||||||
\(98\) | 2.00000 | 0.202031 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 9.63015 | 0.958235 | 0.479118 | − | 0.877751i | \(-0.340957\pi\) | ||||
0.479118 | + | 0.877751i | \(0.340957\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 6.81507 | 0.668273 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.6301 | 1.03249 | ||||||||
\(107\) | 18.8151 | 1.81892 | 0.909461 | − | 0.415790i | \(-0.136495\pi\) | ||||
0.909461 | + | 0.415790i | \(0.136495\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0000 | 1.24517 | 0.622587 | − | 0.782551i | \(-0.286082\pi\) | ||||
0.622587 | + | 0.782551i | \(0.286082\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.00000 | 0.283473 | ||||||||
\(113\) | −3.81507 | −0.358892 | −0.179446 | − | 0.983768i | \(-0.557430\pi\) | ||||
−0.179446 | + | 0.983768i | \(0.557430\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.81507 | −0.449008 | ||||||||
\(116\) | −3.81507 | −0.354221 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.00000 | −0.184115 | ||||||||
\(119\) | −3.00000 | −0.275010 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | −3.81507 | −0.345400 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.81507 | −0.342604 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.4452 | 0.926863 | 0.463432 | − | 0.886133i | \(-0.346618\pi\) | ||||
0.463432 | + | 0.886133i | \(0.346618\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.81507 | −0.597721 | ||||||||
\(131\) | −11.6301 | −1.01613 | −0.508065 | − | 0.861319i | \(-0.669639\pi\) | ||||
−0.508065 | + | 0.861319i | \(0.669639\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.44522 | −0.732293 | ||||||||
\(134\) | −13.6301 | −1.17747 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.1849 | 1.03351 | 0.516756 | − | 0.856133i | \(-0.327139\pi\) | ||||
0.516756 | + | 0.856133i | \(0.327139\pi\) | |||||||
\(140\) | −3.00000 | −0.253546 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.63015 | −0.808144 | ||||||||
\(143\) | 6.81507 | 0.569905 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.81507 | 0.316825 | ||||||||
\(146\) | 4.81507 | 0.398498 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.00000 | 0.0821995 | ||||||||
\(149\) | −2.00000 | −0.163846 | −0.0819232 | − | 0.996639i | \(-0.526106\pi\) | ||||
−0.0819232 | + | 0.996639i | \(0.526106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.81507 | −0.554603 | −0.277301 | − | 0.960783i | \(-0.589440\pi\) | ||||
−0.277301 | + | 0.960783i | \(0.589440\pi\) | |||||||
\(152\) | −2.81507 | −0.228333 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.00000 | 0.241747 | ||||||||
\(155\) | 3.81507 | 0.306434 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.18493 | −0.174376 | −0.0871881 | − | 0.996192i | \(-0.527788\pi\) | ||||
−0.0871881 | + | 0.996192i | \(0.527788\pi\) | |||||||
\(158\) | 12.0000 | 0.954669 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 14.4452 | 1.13844 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.63015 | −0.362661 | −0.181331 | − | 0.983422i | \(-0.558040\pi\) | ||||
−0.181331 | + | 0.983422i | \(0.558040\pi\) | |||||||
\(164\) | −5.81507 | −0.454081 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.81507 | −0.528952 | ||||||||
\(167\) | 11.1849 | 0.865516 | 0.432758 | − | 0.901510i | \(-0.357541\pi\) | ||||
0.432758 | + | 0.901510i | \(0.357541\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.4452 | 2.57271 | ||||||||
\(170\) | 1.00000 | 0.0766965 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.81507 | 0.443395 | ||||||||
\(173\) | 1.00000 | 0.0760286 | 0.0380143 | − | 0.999277i | \(-0.487897\pi\) | ||||
0.0380143 | + | 0.999277i | \(0.487897\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.00000 | 0.226779 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.18493 | −0.0888140 | ||||||||
\(179\) | −16.0000 | −1.19590 | −0.597948 | − | 0.801535i | \(-0.704017\pi\) | ||||
−0.597948 | + | 0.801535i | \(0.704017\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 20.4452 | 1.51550 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.81507 | 0.354972 | ||||||||
\(185\) | −1.00000 | −0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.81507 | 0.204227 | ||||||||
\(191\) | 16.6301 | 1.20332 | 0.601658 | − | 0.798754i | \(-0.294507\pi\) | ||||
0.601658 | + | 0.798754i | \(0.294507\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 5.81507 | 0.417498 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 14.8151 | 1.05553 | 0.527765 | − | 0.849390i | \(-0.323030\pi\) | ||||
0.527765 | + | 0.849390i | \(0.323030\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.63015 | 0.677575 | ||||||||
\(203\) | −11.4452 | −0.803297 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.81507 | 0.406142 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.81507 | 0.472540 | ||||||||
\(209\) | −2.81507 | −0.194723 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.4452 | −1.61404 | −0.807018 | − | 0.590527i | \(-0.798920\pi\) | ||||
−0.807018 | + | 0.590527i | \(0.798920\pi\) | |||||||
\(212\) | 10.6301 | 0.730081 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.8151 | 1.28617 | ||||||||
\(215\) | −5.81507 | −0.396585 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.4452 | −0.776952 | ||||||||
\(218\) | 13.0000 | 0.880471 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −6.81507 | −0.458431 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.18493 | −0.414173 | −0.207087 | − | 0.978323i | \(-0.566398\pi\) | ||||
−0.207087 | + | 0.978323i | \(0.566398\pi\) | |||||||
\(224\) | 3.00000 | 0.200446 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.81507 | −0.253775 | ||||||||
\(227\) | 14.1849 | 0.941487 | 0.470743 | − | 0.882270i | \(-0.343986\pi\) | ||||
0.470743 | + | 0.882270i | \(0.343986\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.6301 | 1.42936 | 0.714680 | − | 0.699451i | \(-0.246572\pi\) | ||||
0.714680 | + | 0.699451i | \(0.246572\pi\) | |||||||
\(230\) | −4.81507 | −0.317497 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.81507 | −0.250472 | ||||||||
\(233\) | −13.6301 | −0.892941 | −0.446470 | − | 0.894798i | \(-0.647319\pi\) | ||||
−0.446470 | + | 0.894798i | \(0.647319\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | −2.00000 | −0.130189 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.00000 | −0.194461 | ||||||||
\(239\) | 25.4452 | 1.64591 | 0.822957 | − | 0.568103i | \(-0.192323\pi\) | ||||
0.822957 | + | 0.568103i | \(0.192323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.0000 | −1.67481 | −0.837404 | − | 0.546585i | \(-0.815928\pi\) | ||||
−0.837404 | + | 0.546585i | \(0.815928\pi\) | |||||||
\(242\) | −10.0000 | −0.642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.81507 | −0.244235 | ||||||||
\(245\) | −2.00000 | −0.127775 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.1849 | −1.22071 | ||||||||
\(248\) | −3.81507 | −0.242257 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −9.63015 | −0.607849 | −0.303925 | − | 0.952696i | \(-0.598297\pi\) | ||||
−0.303925 | + | 0.952696i | \(0.598297\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.81507 | 0.302721 | ||||||||
\(254\) | 10.4452 | 0.655391 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.81507 | −0.425113 | −0.212556 | − | 0.977149i | \(-0.568179\pi\) | ||||
−0.212556 | + | 0.977149i | \(0.568179\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.00000 | 0.186411 | ||||||||
\(260\) | −6.81507 | −0.422653 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.6301 | −0.718513 | ||||||||
\(263\) | −1.44522 | −0.0891160 | −0.0445580 | − | 0.999007i | \(-0.514188\pi\) | ||||
−0.0445580 | + | 0.999007i | \(0.514188\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.6301 | −0.653005 | ||||||||
\(266\) | −8.44522 | −0.517810 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.6301 | −0.832594 | ||||||||
\(269\) | 0.815073 | 0.0496959 | 0.0248479 | − | 0.999691i | \(-0.492090\pi\) | ||||
0.0248479 | + | 0.999691i | \(0.492090\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.0000 | −1.21491 | −0.607457 | − | 0.794353i | \(-0.707810\pi\) | ||||
−0.607457 | + | 0.794353i | \(0.707810\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.4452 | −0.627592 | −0.313796 | − | 0.949490i | \(-0.601601\pi\) | ||||
−0.313796 | + | 0.949490i | \(0.601601\pi\) | |||||||
\(278\) | 12.1849 | 0.730803 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.00000 | −0.179284 | ||||||||
\(281\) | −12.4452 | −0.742420 | −0.371210 | − | 0.928549i | \(-0.621057\pi\) | ||||
−0.371210 | + | 0.928549i | \(0.621057\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.1849 | −0.664875 | −0.332437 | − | 0.943125i | \(-0.607871\pi\) | ||||
−0.332437 | + | 0.943125i | \(0.607871\pi\) | |||||||
\(284\) | −9.63015 | −0.571444 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.81507 | 0.402984 | ||||||||
\(287\) | −17.4452 | −1.02976 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 3.81507 | 0.224029 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.81507 | 0.281781 | ||||||||
\(293\) | 14.2603 | 0.833095 | 0.416548 | − | 0.909114i | \(-0.363240\pi\) | ||||
0.416548 | + | 0.909114i | \(0.363240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00000 | 0.116445 | ||||||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.00000 | −0.115857 | ||||||||
\(299\) | 32.8151 | 1.89774 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.4452 | 1.00553 | ||||||||
\(302\) | −6.81507 | −0.392163 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.81507 | −0.161456 | ||||||||
\(305\) | 3.81507 | 0.218450 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.0000 | −1.02731 | −0.513657 | − | 0.857996i | \(-0.671710\pi\) | ||||
−0.513657 | + | 0.857996i | \(0.671710\pi\) | |||||||
\(308\) | 3.00000 | 0.170941 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.81507 | 0.216682 | ||||||||
\(311\) | 21.4452 | 1.21605 | 0.608023 | − | 0.793919i | \(-0.291963\pi\) | ||||
0.608023 | + | 0.793919i | \(0.291963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.8904 | −1.74603 | −0.873015 | − | 0.487693i | \(-0.837839\pi\) | ||||
−0.873015 | + | 0.487693i | \(0.837839\pi\) | |||||||
\(314\) | −2.18493 | −0.123303 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.0000 | 0.675053 | ||||||||
\(317\) | −7.81507 | −0.438938 | −0.219469 | − | 0.975619i | \(-0.570433\pi\) | ||||
−0.219469 | + | 0.975619i | \(0.570433\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.81507 | −0.213603 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.4452 | 0.805001 | ||||||||
\(323\) | 2.81507 | 0.156635 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.81507 | 0.378032 | ||||||||
\(326\) | −4.63015 | −0.256440 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.81507 | −0.321084 | ||||||||
\(329\) | 24.0000 | 1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2603 | 1.05864 | 0.529321 | − | 0.848422i | \(-0.322447\pi\) | ||||
0.529321 | + | 0.848422i | \(0.322447\pi\) | |||||||
\(332\) | −6.81507 | −0.374026 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.1849 | 0.612012 | ||||||||
\(335\) | 13.6301 | 0.744694 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.8151 | −0.807028 | −0.403514 | − | 0.914973i | \(-0.632211\pi\) | ||||
−0.403514 | + | 0.914973i | \(0.632211\pi\) | |||||||
\(338\) | 33.4452 | 1.81918 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.00000 | 0.0542326 | ||||||||
\(341\) | −3.81507 | −0.206598 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 5.81507 | 0.313528 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.00000 | 0.0537603 | ||||||||
\(347\) | 31.2603 | 1.67814 | 0.839070 | − | 0.544023i | \(-0.183100\pi\) | ||||
0.839070 | + | 0.544023i | \(0.183100\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.2603 | −1.88744 | −0.943720 | − | 0.330745i | \(-0.892700\pi\) | ||||
−0.943720 | + | 0.330745i | \(0.892700\pi\) | |||||||
\(350\) | 3.00000 | 0.160357 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 23.8151 | 1.26755 | 0.633774 | − | 0.773518i | \(-0.281505\pi\) | ||||
0.633774 | + | 0.773518i | \(0.281505\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.63015 | 0.511115 | ||||||||
\(356\) | −1.18493 | −0.0628010 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.0000 | −0.845626 | ||||||||
\(359\) | −27.6301 | −1.45826 | −0.729132 | − | 0.684373i | \(-0.760076\pi\) | ||||
−0.729132 | + | 0.684373i | \(0.760076\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0754 | −0.582914 | ||||||||
\(362\) | −10.0000 | −0.525588 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 20.4452 | 1.07162 | ||||||||
\(365\) | −4.81507 | −0.252032 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.0000 | −1.09619 | −0.548096 | − | 0.836416i | \(-0.684647\pi\) | ||||
−0.548096 | + | 0.836416i | \(0.684647\pi\) | |||||||
\(368\) | 4.81507 | 0.251003 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.00000 | −0.0519875 | ||||||||
\(371\) | 31.8904 | 1.65567 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.2603 | 1.30793 | 0.653964 | − | 0.756526i | \(-0.273105\pi\) | ||||
0.653964 | + | 0.756526i | \(0.273105\pi\) | |||||||
\(374\) | −1.00000 | −0.0517088 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.00000 | 0.412568 | ||||||||
\(377\) | −26.0000 | −1.33907 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.63015 | 0.0837350 | 0.0418675 | − | 0.999123i | \(-0.486669\pi\) | ||||
0.0418675 | + | 0.999123i | \(0.486669\pi\) | |||||||
\(380\) | 2.81507 | 0.144410 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.6301 | 0.850872 | ||||||||
\(383\) | −1.55478 | −0.0794456 | −0.0397228 | − | 0.999211i | \(-0.512647\pi\) | ||||
−0.0397228 | + | 0.999211i | \(0.512647\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.00000 | −0.152894 | ||||||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.81507 | 0.295216 | ||||||||
\(389\) | −38.7055 | −1.96245 | −0.981224 | − | 0.192873i | \(-0.938219\pi\) | ||||
−0.981224 | + | 0.192873i | \(0.938219\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.81507 | −0.243509 | ||||||||
\(392\) | 2.00000 | 0.101015 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.8151 | 0.746373 | ||||||||
\(395\) | −12.0000 | −0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.6301 | 0.784455 | 0.392227 | − | 0.919868i | \(-0.371705\pi\) | ||||
0.392227 | + | 0.919868i | \(0.371705\pi\) | |||||||
\(398\) | −4.00000 | −0.200502 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −32.4452 | −1.62024 | −0.810118 | − | 0.586266i | \(-0.800597\pi\) | ||||
−0.810118 | + | 0.586266i | \(0.800597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.0000 | −1.29515 | ||||||||
\(404\) | 9.63015 | 0.479118 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.4452 | −0.568017 | ||||||||
\(407\) | 1.00000 | 0.0495682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.6301 | 1.36622 | 0.683111 | − | 0.730314i | \(-0.260626\pi\) | ||||
0.683111 | + | 0.730314i | \(0.260626\pi\) | |||||||
\(410\) | 5.81507 | 0.287186 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.00000 | −0.295241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.81507 | 0.334539 | ||||||||
\(416\) | 6.81507 | 0.334136 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.81507 | −0.137690 | ||||||||
\(419\) | −6.44522 | −0.314870 | −0.157435 | − | 0.987529i | \(-0.550322\pi\) | ||||
−0.157435 | + | 0.987529i | \(0.550322\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.2603 | 0.646267 | 0.323134 | − | 0.946353i | \(-0.395264\pi\) | ||||
0.323134 | + | 0.946353i | \(0.395264\pi\) | |||||||
\(422\) | −23.4452 | −1.14130 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.6301 | 0.516246 | ||||||||
\(425\) | −1.00000 | −0.0485071 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.4452 | −0.553873 | ||||||||
\(428\) | 18.8151 | 0.909461 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.81507 | −0.280428 | ||||||||
\(431\) | −21.0000 | −1.01153 | −0.505767 | − | 0.862670i | \(-0.668791\pi\) | ||||
−0.505767 | + | 0.862670i | \(0.668791\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.81507 | −0.423625 | −0.211813 | − | 0.977310i | \(-0.567937\pi\) | ||||
−0.211813 | + | 0.977310i | \(0.567937\pi\) | |||||||
\(434\) | −11.4452 | −0.549388 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.0000 | 0.622587 | ||||||||
\(437\) | −13.5548 | −0.648413 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.4452 | 0.641705 | 0.320853 | − | 0.947129i | \(-0.396031\pi\) | ||||
0.320853 | + | 0.947129i | \(0.396031\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.81507 | −0.324160 | ||||||||
\(443\) | 7.63015 | 0.362519 | 0.181260 | − | 0.983435i | \(-0.441983\pi\) | ||||
0.181260 | + | 0.983435i | \(0.441983\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.18493 | 0.0561709 | ||||||||
\(446\) | −6.18493 | −0.292865 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.00000 | 0.141737 | ||||||||
\(449\) | 32.8904 | 1.55220 | 0.776098 | − | 0.630612i | \(-0.217196\pi\) | ||||
0.776098 | + | 0.630612i | \(0.217196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.81507 | −0.273821 | ||||||||
\(452\) | −3.81507 | −0.179446 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.1849 | 0.665732 | ||||||||
\(455\) | −20.4452 | −0.958487 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.0754 | 1.17298 | 0.586488 | − | 0.809958i | \(-0.300510\pi\) | ||||
0.586488 | + | 0.809958i | \(0.300510\pi\) | |||||||
\(458\) | 21.6301 | 1.01071 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.81507 | −0.224504 | ||||||||
\(461\) | −24.1849 | −1.12640 | −0.563202 | − | 0.826319i | \(-0.690431\pi\) | ||||
−0.563202 | + | 0.826319i | \(0.690431\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.63015 | 0.168707 | 0.0843536 | − | 0.996436i | \(-0.473117\pi\) | ||||
0.0843536 | + | 0.996436i | \(0.473117\pi\) | |||||||
\(464\) | −3.81507 | −0.177110 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.6301 | −0.631404 | ||||||||
\(467\) | −18.1849 | −0.841498 | −0.420749 | − | 0.907177i | \(-0.638233\pi\) | ||||
−0.420749 | + | 0.907177i | \(0.638233\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.8904 | −1.88814 | ||||||||
\(470\) | −8.00000 | −0.369012 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.00000 | −0.0920575 | ||||||||
\(473\) | 5.81507 | 0.267377 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.81507 | −0.129164 | ||||||||
\(476\) | −3.00000 | −0.137505 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.4452 | 1.16384 | ||||||||
\(479\) | 0.815073 | 0.0372416 | 0.0186208 | − | 0.999827i | \(-0.494072\pi\) | ||||
0.0186208 | + | 0.999827i | \(0.494072\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.81507 | 0.310741 | ||||||||
\(482\) | −26.0000 | −1.18427 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.0000 | −0.454545 | ||||||||
\(485\) | −5.81507 | −0.264049 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00000 | 0.0906287 | 0.0453143 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453143 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(488\) | −3.81507 | −0.172700 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.00000 | −0.0903508 | ||||||||
\(491\) | −12.8151 | −0.578336 | −0.289168 | − | 0.957278i | \(-0.593379\pi\) | ||||
−0.289168 | + | 0.957278i | \(0.593379\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.81507 | 0.171822 | ||||||||
\(494\) | −19.1849 | −0.863171 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.81507 | −0.171302 | ||||||||
\(497\) | −28.8904 | −1.29591 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.4452 | 0.646657 | 0.323328 | − | 0.946287i | \(-0.395198\pi\) | ||||
0.323328 | + | 0.946287i | \(0.395198\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.63015 | −0.429814 | ||||||||
\(503\) | −43.2603 | −1.92888 | −0.964441 | − | 0.264300i | \(-0.914859\pi\) | ||||
−0.964441 | + | 0.264300i | \(0.914859\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.63015 | −0.428536 | ||||||||
\(506\) | 4.81507 | 0.214056 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.4452 | 0.463432 | ||||||||
\(509\) | 14.4452 | 0.640273 | 0.320137 | − | 0.947371i | \(-0.396271\pi\) | ||||
0.320137 | + | 0.947371i | \(0.396271\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.4452 | 0.639019 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.81507 | −0.300600 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | 0.351840 | ||||||||
\(518\) | 3.00000 | 0.131812 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.81507 | −0.298861 | ||||||||
\(521\) | 9.81507 | 0.430006 | 0.215003 | − | 0.976613i | \(-0.431024\pi\) | ||||
0.215003 | + | 0.976613i | \(0.431024\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.2603 | −1.89164 | −0.945820 | − | 0.324691i | \(-0.894740\pi\) | ||||
−0.945820 | + | 0.324691i | \(0.894740\pi\) | |||||||
\(524\) | −11.6301 | −0.508065 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.44522 | −0.0630145 | ||||||||
\(527\) | 3.81507 | 0.166187 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.184927 | 0.00804031 | ||||||||
\(530\) | −10.6301 | −0.461744 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.44522 | −0.366147 | ||||||||
\(533\) | −39.6301 | −1.71657 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.8151 | −0.813447 | ||||||||
\(536\) | −13.6301 | −0.588733 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.815073 | 0.0351403 | ||||||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.1849 | 0.738838 | 0.369419 | − | 0.929263i | \(-0.379557\pi\) | ||||
0.369419 | + | 0.929263i | \(0.379557\pi\) | |||||||
\(542\) | −20.0000 | −0.859074 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −13.0000 | −0.556859 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.8904 | −1.70559 | −0.852796 | − | 0.522244i | \(-0.825095\pi\) | ||||
−0.852796 | + | 0.522244i | \(0.825095\pi\) | |||||||
\(548\) | −2.00000 | −0.0854358 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 10.7397 | 0.457527 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.0000 | 1.53088 | ||||||||
\(554\) | −10.4452 | −0.443775 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.1849 | 0.516756 | ||||||||
\(557\) | 0.369854 | 0.0156712 | 0.00783561 | − | 0.999969i | \(-0.497506\pi\) | ||||
0.00783561 | + | 0.999969i | \(0.497506\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.6301 | 1.67618 | ||||||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.4452 | −0.524970 | ||||||||
\(563\) | −23.4452 | −0.988098 | −0.494049 | − | 0.869434i | \(-0.664484\pi\) | ||||
−0.494049 | + | 0.869434i | \(0.664484\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.81507 | 0.160501 | ||||||||
\(566\) | −11.1849 | −0.470138 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.63015 | −0.404072 | ||||||||
\(569\) | 25.1849 | 1.05581 | 0.527904 | − | 0.849304i | \(-0.322978\pi\) | ||||
0.527904 | + | 0.849304i | \(0.322978\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.18493 | −0.175134 | −0.0875669 | − | 0.996159i | \(-0.527909\pi\) | ||||
−0.0875669 | + | 0.996159i | \(0.527909\pi\) | |||||||
\(572\) | 6.81507 | 0.284953 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −17.4452 | −0.728149 | ||||||||
\(575\) | 4.81507 | 0.200802 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.0000 | −0.915872 | −0.457936 | − | 0.888985i | \(-0.651411\pi\) | ||||
−0.457936 | + | 0.888985i | \(0.651411\pi\) | |||||||
\(578\) | −16.0000 | −0.665512 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.81507 | 0.158412 | ||||||||
\(581\) | −20.4452 | −0.848211 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.6301 | 0.440256 | ||||||||
\(584\) | 4.81507 | 0.199249 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.2603 | 0.589087 | ||||||||
\(587\) | −10.1849 | −0.420377 | −0.210188 | − | 0.977661i | \(-0.567408\pi\) | ||||
−0.210188 | + | 0.977661i | \(0.567408\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.7397 | 0.442522 | ||||||||
\(590\) | 2.00000 | 0.0823387 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | 0.0410997 | ||||||||
\(593\) | −7.63015 | −0.313333 | −0.156666 | − | 0.987652i | \(-0.550075\pi\) | ||||
−0.156666 | + | 0.987652i | \(0.550075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.00000 | 0.122988 | ||||||||
\(596\) | −2.00000 | −0.0819232 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 32.8151 | 1.34191 | ||||||||
\(599\) | −16.0000 | −0.653742 | −0.326871 | − | 0.945069i | \(-0.605994\pi\) | ||||
−0.326871 | + | 0.945069i | \(0.605994\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.6301 | −1.65734 | −0.828669 | − | 0.559739i | \(-0.810901\pi\) | ||||
−0.828669 | + | 0.559739i | \(0.810901\pi\) | |||||||
\(602\) | 17.4452 | 0.711014 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.81507 | −0.277301 | ||||||||
\(605\) | 10.0000 | 0.406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.26029 | 0.213509 | 0.106754 | − | 0.994285i | \(-0.465954\pi\) | ||||
0.106754 | + | 0.994285i | \(0.465954\pi\) | |||||||
\(608\) | −2.81507 | −0.114166 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.81507 | 0.154468 | ||||||||
\(611\) | 54.5206 | 2.20567 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.0754 | 1.90136 | 0.950678 | − | 0.310179i | \(-0.100389\pi\) | ||||
0.950678 | + | 0.310179i | \(0.100389\pi\) | |||||||
\(614\) | −18.0000 | −0.726421 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | 0.120873 | ||||||||
\(617\) | −30.0000 | −1.20775 | −0.603877 | − | 0.797077i | \(-0.706378\pi\) | ||||
−0.603877 | + | 0.797077i | \(0.706378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45.4452 | −1.82660 | −0.913299 | − | 0.407290i | \(-0.866474\pi\) | ||||
−0.913299 | + | 0.407290i | \(0.866474\pi\) | |||||||
\(620\) | 3.81507 | 0.153217 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.4452 | 0.859875 | ||||||||
\(623\) | −3.55478 | −0.142419 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −30.8904 | −1.23463 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.18493 | −0.0871881 | ||||||||
\(629\) | −1.00000 | −0.0398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.7055 | −1.62046 | −0.810230 | − | 0.586112i | \(-0.800658\pi\) | ||||
−0.810230 | + | 0.586112i | \(0.800658\pi\) | |||||||
\(632\) | 12.0000 | 0.477334 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.81507 | −0.310376 | ||||||||
\(635\) | −10.4452 | −0.414506 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.6301 | 0.540046 | ||||||||
\(638\) | −3.81507 | −0.151040 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 45.4452 | 1.79498 | 0.897489 | − | 0.441037i | \(-0.145389\pi\) | ||||
0.897489 | + | 0.441037i | \(0.145389\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.0000 | 0.670415 | 0.335207 | − | 0.942144i | \(-0.391194\pi\) | ||||
0.335207 | + | 0.942144i | \(0.391194\pi\) | |||||||
\(644\) | 14.4452 | 0.569221 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.81507 | 0.110758 | ||||||||
\(647\) | 28.0754 | 1.10376 | 0.551878 | − | 0.833925i | \(-0.313911\pi\) | ||||
0.551878 | + | 0.833925i | \(0.313911\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.00000 | −0.0785069 | ||||||||
\(650\) | 6.81507 | 0.267309 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.63015 | −0.181331 | ||||||||
\(653\) | −4.00000 | −0.156532 | −0.0782660 | − | 0.996933i | \(-0.524938\pi\) | ||||
−0.0782660 | + | 0.996933i | \(0.524938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.6301 | 0.454427 | ||||||||
\(656\) | −5.81507 | −0.227040 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.0000 | 0.935617 | ||||||||
\(659\) | −11.2603 | −0.438639 | −0.219319 | − | 0.975653i | \(-0.570384\pi\) | ||||
−0.219319 | + | 0.975653i | \(0.570384\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.2603 | 1.79932 | 0.899658 | − | 0.436595i | \(-0.143816\pi\) | ||||
0.899658 | + | 0.436595i | \(0.143816\pi\) | |||||||
\(662\) | 19.2603 | 0.748572 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.81507 | −0.264476 | ||||||||
\(665\) | 8.44522 | 0.327492 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.3699 | −0.711284 | ||||||||
\(668\) | 11.1849 | 0.432758 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.6301 | 0.526578 | ||||||||
\(671\) | −3.81507 | −0.147279 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.8151 | 0.648173 | 0.324087 | − | 0.946027i | \(-0.394943\pi\) | ||||
0.324087 | + | 0.946027i | \(0.394943\pi\) | |||||||
\(674\) | −14.8151 | −0.570655 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 33.4452 | 1.28635 | ||||||||
\(677\) | 6.07536 | 0.233495 | 0.116748 | − | 0.993162i | \(-0.462753\pi\) | ||||
0.116748 | + | 0.993162i | \(0.462753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.4452 | 0.669486 | ||||||||
\(680\) | 1.00000 | 0.0383482 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.81507 | −0.146087 | ||||||||
\(683\) | −48.3357 | −1.84951 | −0.924756 | − | 0.380560i | \(-0.875731\pi\) | ||||
−0.924756 | + | 0.380560i | \(0.875731\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | −15.0000 | −0.572703 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.81507 | 0.221698 | ||||||||
\(689\) | 72.4452 | 2.75994 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.0754 | 0.725661 | 0.362831 | − | 0.931855i | \(-0.381810\pi\) | ||||
0.362831 | + | 0.931855i | \(0.381810\pi\) | |||||||
\(692\) | 1.00000 | 0.0380143 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.2603 | 1.18662 | ||||||||
\(695\) | −12.1849 | −0.462201 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.81507 | 0.220262 | ||||||||
\(698\) | −35.2603 | −1.33462 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.00000 | 0.113389 | ||||||||
\(701\) | −12.3699 | −0.467203 | −0.233601 | − | 0.972332i | \(-0.575051\pi\) | ||||
−0.233601 | + | 0.972332i | \(0.575051\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.81507 | −0.106172 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.8151 | 0.896292 | ||||||||
\(707\) | 28.8904 | 1.08654 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.630146 | −0.0236656 | −0.0118328 | − | 0.999930i | \(-0.503767\pi\) | ||||
−0.0118328 | + | 0.999930i | \(0.503767\pi\) | |||||||
\(710\) | 9.63015 | 0.361413 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.18493 | −0.0444070 | ||||||||
\(713\) | −18.3699 | −0.687956 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.81507 | −0.254869 | ||||||||
\(716\) | −16.0000 | −0.597948 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −27.6301 | −1.03115 | ||||||||
\(719\) | −34.0000 | −1.26799 | −0.633993 | − | 0.773339i | \(-0.718585\pi\) | ||||
−0.633993 | + | 0.773339i | \(0.718585\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11.0754 | −0.412182 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.0000 | −0.371647 | ||||||||
\(725\) | −3.81507 | −0.141688 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.0000 | −0.667583 | −0.333792 | − | 0.942647i | \(-0.608328\pi\) | ||||
−0.333792 | + | 0.942647i | \(0.608328\pi\) | |||||||
\(728\) | 20.4452 | 0.757750 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.81507 | −0.178214 | ||||||||
\(731\) | −5.81507 | −0.215078 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.55478 | 0.315978 | 0.157989 | − | 0.987441i | \(-0.449499\pi\) | ||||
0.157989 | + | 0.987441i | \(0.449499\pi\) | |||||||
\(734\) | −21.0000 | −0.775124 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.81507 | 0.177486 | ||||||||
\(737\) | −13.6301 | −0.502073 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.0754 | −0.701699 | −0.350849 | − | 0.936432i | \(-0.614107\pi\) | ||||
−0.350849 | + | 0.936432i | \(0.614107\pi\) | |||||||
\(740\) | −1.00000 | −0.0367607 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 31.8904 | 1.17073 | ||||||||
\(743\) | 27.4452 | 1.00687 | 0.503434 | − | 0.864034i | \(-0.332070\pi\) | ||||
0.503434 | + | 0.864034i | \(0.332070\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00000 | 0.0732743 | ||||||||
\(746\) | 25.2603 | 0.924845 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.00000 | −0.0365636 | ||||||||
\(749\) | 56.4452 | 2.06246 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000 | 0.145962 | 0.0729810 | − | 0.997333i | \(-0.476749\pi\) | ||||
0.0729810 | + | 0.997333i | \(0.476749\pi\) | |||||||
\(752\) | 8.00000 | 0.291730 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −26.0000 | −0.946864 | ||||||||
\(755\) | 6.81507 | 0.248026 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.1849 | 0.479214 | 0.239607 | − | 0.970870i | \(-0.422981\pi\) | ||||
0.239607 | + | 0.970870i | \(0.422981\pi\) | |||||||
\(758\) | 1.63015 | 0.0592096 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.81507 | 0.102113 | ||||||||
\(761\) | 19.8151 | 0.718296 | 0.359148 | − | 0.933281i | \(-0.383067\pi\) | ||||
0.359148 | + | 0.933281i | \(0.383067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.0000 | 1.41189 | ||||||||
\(764\) | 16.6301 | 0.601658 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.55478 | −0.0561765 | ||||||||
\(767\) | −13.6301 | −0.492156 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.73971 | 0.243040 | 0.121520 | − | 0.992589i | \(-0.461223\pi\) | ||||
0.121520 | + | 0.992589i | \(0.461223\pi\) | |||||||
\(770\) | −3.00000 | −0.108112 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.00000 | −0.0719816 | ||||||||
\(773\) | 28.6301 | 1.02975 | 0.514877 | − | 0.857264i | \(-0.327837\pi\) | ||||
0.514877 | + | 0.857264i | \(0.327837\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.81507 | −0.137041 | ||||||||
\(776\) | 5.81507 | 0.208749 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38.7055 | −1.38766 | ||||||||
\(779\) | 16.3699 | 0.586511 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.63015 | −0.344594 | ||||||||
\(782\) | −4.81507 | −0.172187 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.00000 | 0.0714286 | ||||||||
\(785\) | 2.18493 | 0.0779834 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.3699 | −0.654815 | −0.327407 | − | 0.944883i | \(-0.606175\pi\) | ||||
−0.327407 | + | 0.944883i | \(0.606175\pi\) | |||||||
\(788\) | 14.8151 | 0.527765 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.0000 | −0.426941 | ||||||||
\(791\) | −11.4452 | −0.406945 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.0000 | −0.923287 | ||||||||
\(794\) | 15.6301 | 0.554693 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.00000 | −0.141776 | ||||||||
\(797\) | −28.8904 | −1.02335 | −0.511676 | − | 0.859179i | \(-0.670975\pi\) | ||||
−0.511676 | + | 0.859179i | \(0.670975\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −32.4452 | −1.14568 | ||||||||
\(803\) | 4.81507 | 0.169920 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.4452 | −0.509127 | ||||||||
\(806\) | −26.0000 | −0.915811 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.63015 | 0.338787 | ||||||||
\(809\) | −40.0754 | −1.40897 | −0.704487 | − | 0.709717i | \(-0.748823\pi\) | ||||
−0.704487 | + | 0.709717i | \(0.748823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | −11.4452 | −0.401648 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.00000 | 0.0350500 | ||||||||
\(815\) | 4.63015 | 0.162187 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.3699 | −0.572709 | ||||||||
\(818\) | 27.6301 | 0.966065 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.81507 | 0.203071 | ||||||||
\(821\) | 42.0754 | 1.46844 | 0.734220 | − | 0.678911i | \(-0.237548\pi\) | ||||
0.734220 | + | 0.678911i | \(0.237548\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.0754 | −0.420921 | −0.210460 | − | 0.977602i | \(-0.567496\pi\) | ||||
−0.210460 | + | 0.977602i | \(0.567496\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | −0.208767 | ||||||||
\(827\) | −25.0754 | −0.871956 | −0.435978 | − | 0.899957i | \(-0.643597\pi\) | ||||
−0.435978 | + | 0.899957i | \(0.643597\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.5206 | 1.09476 | 0.547378 | − | 0.836886i | \(-0.315626\pi\) | ||||
0.547378 | + | 0.836886i | \(0.315626\pi\) | |||||||
\(830\) | 6.81507 | 0.236555 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.81507 | 0.236270 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.1849 | −0.387070 | ||||||||
\(836\) | −2.81507 | −0.0973613 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.44522 | −0.222646 | ||||||||
\(839\) | −18.0000 | −0.621429 | −0.310715 | − | 0.950503i | \(-0.600568\pi\) | ||||
−0.310715 | + | 0.950503i | \(0.600568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4452 | −0.498111 | ||||||||
\(842\) | 13.2603 | 0.456980 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.4452 | −0.807018 | ||||||||
\(845\) | −33.4452 | −1.15055 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.0000 | −1.03081 | ||||||||
\(848\) | 10.6301 | 0.365041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.00000 | −0.0342997 | ||||||||
\(851\) | 4.81507 | 0.165059 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.0754 | 1.44063 | 0.720317 | − | 0.693646i | \(-0.243997\pi\) | ||||
0.720317 | + | 0.693646i | \(0.243997\pi\) | |||||||
\(854\) | −11.4452 | −0.391647 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.8151 | 0.643086 | ||||||||
\(857\) | 12.2603 | 0.418804 | 0.209402 | − | 0.977830i | \(-0.432848\pi\) | ||||
0.209402 | + | 0.977830i | \(0.432848\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.445219 | −0.0151907 | −0.00759533 | − | 0.999971i | \(-0.502418\pi\) | ||||
−0.00759533 | + | 0.999971i | \(0.502418\pi\) | |||||||
\(860\) | −5.81507 | −0.198292 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.0000 | −0.715263 | ||||||||
\(863\) | 33.4452 | 1.13849 | 0.569244 | − | 0.822168i | \(-0.307236\pi\) | ||||
0.569244 | + | 0.822168i | \(0.307236\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.00000 | −0.0340010 | ||||||||
\(866\) | −8.81507 | −0.299548 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.4452 | −0.388476 | ||||||||
\(869\) | 12.0000 | 0.407072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −92.8904 | −3.14747 | ||||||||
\(872\) | 13.0000 | 0.440236 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.5548 | −0.458497 | ||||||||
\(875\) | −3.00000 | −0.101419 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.7055 | −0.834246 | −0.417123 | − | 0.908850i | \(-0.636962\pi\) | ||||
−0.417123 | + | 0.908850i | \(0.636962\pi\) | |||||||
\(878\) | 13.4452 | 0.453754 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | −53.8151 | −1.81308 | −0.906538 | − | 0.422124i | \(-0.861285\pi\) | ||||
−0.906538 | + | 0.422124i | \(0.861285\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.0000 | 0.908622 | 0.454311 | − | 0.890843i | \(-0.349885\pi\) | ||||
0.454311 | + | 0.890843i | \(0.349885\pi\) | |||||||
\(884\) | −6.81507 | −0.229216 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.63015 | 0.256340 | ||||||||
\(887\) | −39.0754 | −1.31202 | −0.656011 | − | 0.754751i | \(-0.727758\pi\) | ||||
−0.656011 | + | 0.754751i | \(0.727758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.3357 | 1.05096 | ||||||||
\(890\) | 1.18493 | 0.0397188 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.18493 | −0.207087 | ||||||||
\(893\) | −22.5206 | −0.753623 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.0000 | 0.534821 | ||||||||
\(896\) | 3.00000 | 0.100223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32.8904 | 1.09757 | ||||||||
\(899\) | 14.5548 | 0.485429 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.6301 | −0.354142 | ||||||||
\(902\) | −5.81507 | −0.193621 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.81507 | −0.126887 | ||||||||
\(905\) | 10.0000 | 0.332411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.1849 | −1.16830 | −0.584148 | − | 0.811647i | \(-0.698571\pi\) | ||||
−0.584148 | + | 0.811647i | \(0.698571\pi\) | |||||||
\(908\) | 14.1849 | 0.470743 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −20.4452 | −0.677752 | ||||||||
\(911\) | −30.5206 | −1.01119 | −0.505596 | − | 0.862770i | \(-0.668727\pi\) | ||||
−0.505596 | + | 0.862770i | \(0.668727\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.81507 | −0.225546 | ||||||||
\(914\) | 25.0754 | 0.829419 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.6301 | 0.714680 | ||||||||
\(917\) | −34.8904 | −1.15218 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0000 | 0.791687 | 0.395843 | − | 0.918318i | \(-0.370452\pi\) | ||||
0.395843 | + | 0.918318i | \(0.370452\pi\) | |||||||
\(920\) | −4.81507 | −0.158748 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −24.1849 | −0.796488 | ||||||||
\(923\) | −65.6301 | −2.16024 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 3.63015 | 0.119294 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.81507 | −0.125236 | ||||||||
\(929\) | 7.44522 | 0.244270 | 0.122135 | − | 0.992514i | \(-0.461026\pi\) | ||||
0.122135 | + | 0.992514i | \(0.461026\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.63015 | −0.184521 | ||||||||
\(932\) | −13.6301 | −0.446470 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.1849 | −0.595029 | ||||||||
\(935\) | 1.00000 | 0.0327035 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.63015 | 0.314603 | 0.157302 | − | 0.987551i | \(-0.449721\pi\) | ||||
0.157302 | + | 0.987551i | \(0.449721\pi\) | |||||||
\(938\) | −40.8904 | −1.33512 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.00000 | −0.260931 | ||||||||
\(941\) | −41.2603 | −1.34505 | −0.672524 | − | 0.740076i | \(-0.734790\pi\) | ||||
−0.672524 | + | 0.740076i | \(0.734790\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.0000 | −0.911805 | ||||||||
\(944\) | −2.00000 | −0.0650945 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.81507 | 0.189064 | ||||||||
\(947\) | 57.4452 | 1.86672 | 0.933359 | − | 0.358943i | \(-0.116863\pi\) | ||||
0.933359 | + | 0.358943i | \(0.116863\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.8151 | 1.06522 | ||||||||
\(950\) | −2.81507 | −0.0913330 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.00000 | −0.0972306 | ||||||||
\(953\) | 48.8904 | 1.58372 | 0.791858 | − | 0.610705i | \(-0.209114\pi\) | ||||
0.791858 | + | 0.610705i | \(0.209114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.6301 | −0.538139 | ||||||||
\(956\) | 25.4452 | 0.822957 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.815073 | 0.0263338 | ||||||||
\(959\) | −6.00000 | −0.193750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.4452 | −0.530491 | ||||||||
\(962\) | 6.81507 | 0.219727 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −26.0000 | −0.837404 | ||||||||
\(965\) | 2.00000 | 0.0643823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.6301 | −0.438316 | −0.219158 | − | 0.975689i | \(-0.570331\pi\) | ||||
−0.219158 | + | 0.975689i | \(0.570331\pi\) | |||||||
\(968\) | −10.0000 | −0.321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.81507 | −0.186711 | ||||||||
\(971\) | −5.07536 | −0.162876 | −0.0814381 | − | 0.996678i | \(-0.525951\pi\) | ||||
−0.0814381 | + | 0.996678i | \(0.525951\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.5548 | 1.17189 | ||||||||
\(974\) | 2.00000 | 0.0640841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.81507 | −0.122118 | ||||||||
\(977\) | −21.0000 | −0.671850 | −0.335925 | − | 0.941889i | \(-0.609049\pi\) | ||||
−0.335925 | + | 0.941889i | \(0.609049\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.18493 | −0.0378704 | ||||||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.8151 | −0.408945 | ||||||||
\(983\) | 38.3357 | 1.22272 | 0.611359 | − | 0.791354i | \(-0.290623\pi\) | ||||
0.611359 | + | 0.791354i | \(0.290623\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.8151 | −0.472047 | ||||||||
\(986\) | 3.81507 | 0.121497 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −19.1849 | −0.610354 | ||||||||
\(989\) | 28.0000 | 0.890348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.55478 | −0.208219 | −0.104110 | − | 0.994566i | \(-0.533199\pi\) | ||||
−0.104110 | + | 0.994566i | \(0.533199\pi\) | |||||||
\(992\) | −3.81507 | −0.121129 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −28.8904 | −0.916349 | ||||||||
\(995\) | 4.00000 | 0.126809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.92464 | 0.0609538 | 0.0304769 | − | 0.999535i | \(-0.490297\pi\) | ||||
0.0304769 | + | 0.999535i | \(0.490297\pi\) | |||||||
\(998\) | 14.4452 | 0.457255 | ||||||||
\(999\) | 0 | 0 |
(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 | 3330.2.a.bf.1.2 | 2 | ||
3.2 | odd | 2 | 1110.2.a.q.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 8880.2.a.bh.1.2 | 2 | |||
15.14 | odd | 2 | 5550.2.a.bx.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.a.q.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
3330.2.a.bf.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5550.2.a.bx.1.1 | 2 | 15.14 | odd | 2 | |||
8880.2.a.bh.1.2 | 2 | 12.11 | even | 2 |