Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6864,2,Mod(1,6864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("6864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6864.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: | \(54.8093159474\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3432) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.86620\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6864.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.34889 | −1.49767 | −0.748836 | − | 0.662756i | \(-0.769387\pi\) | ||||
−0.748836 | + | 0.662756i | \(0.769387\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.51730 | 0.951451 | 0.475726 | − | 0.879594i | \(-0.342185\pi\) | ||||
0.475726 | + | 0.879594i | \(0.342185\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.34889 | 0.864681 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.59859 | 1.84293 | 0.921465 | − | 0.388461i | \(-0.126993\pi\) | ||||
0.921465 | + | 0.388461i | \(0.126993\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.48270 | 0.340154 | 0.170077 | − | 0.985431i | \(-0.445598\pi\) | ||||
0.170077 | + | 0.985431i | \(0.445598\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.51730 | −0.549321 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.55191 | 0.323596 | 0.161798 | − | 0.986824i | \(-0.448271\pi\) | ||||
0.161798 | + | 0.986824i | \(0.448271\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.21509 | 1.24302 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.86620 | 0.346544 | 0.173272 | − | 0.984874i | \(-0.444566\pi\) | ||||
0.173272 | + | 0.984874i | \(0.444566\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.61650 | 0.290332 | 0.145166 | − | 0.989407i | \(-0.453628\pi\) | ||||
0.145166 | + | 0.989407i | \(0.453628\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.43018 | −1.42496 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.43018 | 1.05712 | 0.528558 | − | 0.848897i | \(-0.322733\pi\) | ||||
0.528558 | + | 0.848897i | \(0.322733\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.9475 | −1.70971 | −0.854855 | − | 0.518867i | \(-0.826354\pi\) | ||||
−0.854855 | + | 0.518867i | \(0.826354\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.59859 | 0.853778 | 0.426889 | − | 0.904304i | \(-0.359610\pi\) | ||||
0.426889 | + | 0.904304i | \(0.359610\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.34889 | −0.499224 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.697788 | −0.101783 | −0.0508915 | − | 0.998704i | \(-0.516206\pi\) | ||||
−0.0508915 | + | 0.998704i | \(0.516206\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.663180 | −0.0947400 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.59859 | −1.06402 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.73240 | −1.33685 | −0.668424 | − | 0.743781i | \(-0.733031\pi\) | ||||
−0.668424 | + | 0.743781i | \(0.733031\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.34889 | 0.451565 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.48270 | −0.196388 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.76700 | 0.620611 | 0.310306 | − | 0.950637i | \(-0.399569\pi\) | ||||
0.310306 | + | 0.950637i | \(0.399569\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.66318 | −0.212948 | −0.106474 | − | 0.994315i | \(-0.533956\pi\) | ||||
−0.106474 | + | 0.994315i | \(0.533956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.51730 | 0.317150 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.34889 | −0.415379 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.81369 | −0.588085 | −0.294043 | − | 0.955792i | \(-0.595001\pi\) | ||||
−0.294043 | + | 0.955792i | \(0.595001\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.55191 | −0.186828 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.965392 | 0.114571 | 0.0572855 | − | 0.998358i | \(-0.481755\pi\) | ||||
0.0572855 | + | 0.998358i | \(0.481755\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.21509 | −0.376298 | −0.188149 | − | 0.982140i | \(-0.560249\pi\) | ||||
−0.188149 | + | 0.982140i | \(0.560249\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.21509 | −0.717657 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.51730 | −0.286873 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.83159 | 0.993632 | 0.496816 | − | 0.867856i | \(-0.334502\pi\) | ||||
0.496816 | + | 0.867856i | \(0.334502\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.767005 | 0.0841897 | 0.0420948 | − | 0.999114i | \(-0.486597\pi\) | ||||
0.0420948 | + | 0.999114i | \(0.486597\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25.4469 | −2.76010 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.86620 | −0.200077 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.41811 | 0.362319 | 0.181159 | − | 0.983454i | \(-0.442015\pi\) | ||||
0.181159 | + | 0.983454i | \(0.442015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.51730 | 0.263885 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.61650 | −0.167623 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.96539 | −0.509438 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.96539 | −0.707228 | −0.353614 | − | 0.935391i | \(-0.615047\pi\) | ||||
−0.353614 | + | 0.935391i | \(0.615047\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.29638 | 0.626514 | 0.313257 | − | 0.949668i | \(-0.398580\pi\) | ||||
0.313257 | + | 0.949668i | \(0.398580\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.4648 | 1.52379 | 0.761896 | − | 0.647700i | \(-0.224269\pi\) | ||||
0.761896 | + | 0.647700i | \(0.224269\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.43018 | 0.822702 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0934 | −1.16911 | −0.584555 | − | 0.811354i | \(-0.698731\pi\) | ||||
−0.584555 | + | 0.811354i | \(0.698731\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.6453 | −1.69011 | −0.845056 | − | 0.534679i | \(-0.820433\pi\) | ||||
−0.845056 | + | 0.534679i | \(0.820433\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.43018 | −0.610326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.76700 | −0.260298 | −0.130149 | − | 0.991494i | \(-0.541546\pi\) | ||||
−0.130149 | + | 0.991494i | \(0.541546\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.19719 | −0.484640 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.1280 | 1.75346 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.9475 | 0.987102 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.06922 | −0.363962 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.6332 | 1.12102 | 0.560508 | − | 0.828149i | \(-0.310606\pi\) | ||||
0.560508 | + | 0.828149i | \(0.310606\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.59859 | −0.492929 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.10382 | −0.271182 | −0.135591 | − | 0.990765i | \(-0.543293\pi\) | ||||
−0.135591 | + | 0.990765i | \(0.543293\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.73240 | 0.323640 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.34889 | 0.288227 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.813687 | 0.0695180 | 0.0347590 | − | 0.999396i | \(-0.488934\pi\) | ||||
0.0347590 | + | 0.999396i | \(0.488934\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.133802 | 0.0113489 | 0.00567446 | − | 0.999984i | \(-0.498194\pi\) | ||||
0.00567446 | + | 0.999984i | \(0.498194\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.697788 | 0.0587644 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.24970 | −0.519009 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.663180 | 0.0546982 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.0167 | −1.39406 | −0.697031 | − | 0.717041i | \(-0.745496\pi\) | ||||
−0.697031 | + | 0.717041i | \(0.745496\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.8783 | 1.86181 | 0.930904 | − | 0.365265i | \(-0.119022\pi\) | ||||
0.930904 | + | 0.365265i | \(0.119022\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.59859 | 0.614310 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.41348 | −0.434821 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.21509 | −0.416210 | −0.208105 | − | 0.978107i | \(-0.566730\pi\) | ||||
−0.208105 | + | 0.978107i | \(0.566730\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.73240 | 0.771829 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.90663 | 0.307886 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7203 | 0.839680 | 0.419840 | − | 0.907598i | \(-0.362086\pi\) | ||||
0.419840 | + | 0.907598i | \(0.362086\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.34889 | −0.260711 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.8258 | 1.84369 | 0.921846 | − | 0.387555i | \(-0.126680\pi\) | ||||
0.921846 | + | 0.387555i | \(0.126680\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.48270 | 0.113385 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.7958 | 1.73313 | 0.866566 | − | 0.499063i | \(-0.166322\pi\) | ||||
0.866566 | + | 0.499063i | \(0.166322\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.6453 | 1.18267 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.76700 | −0.358310 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.6799 | −0.798252 | −0.399126 | − | 0.916896i | \(-0.630686\pi\) | ||||
−0.399126 | + | 0.916896i | \(0.630686\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.18048 | −0.310733 | −0.155366 | − | 0.987857i | \(-0.549656\pi\) | ||||
−0.155366 | + | 0.987857i | \(0.549656\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.66318 | 0.122946 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.5340 | −1.58321 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.59859 | −0.555664 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.51730 | −0.183107 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.1626 | −0.735339 | −0.367669 | − | 0.929957i | \(-0.619844\pi\) | ||||
−0.367669 | + | 0.929957i | \(0.619844\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.7491 | 1.49355 | 0.746777 | − | 0.665075i | \(-0.231600\pi\) | ||||
0.746777 | + | 0.665075i | \(0.231600\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.34889 | 0.239819 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.2151 | −0.799042 | −0.399521 | − | 0.916724i | \(-0.630824\pi\) | ||||
−0.399521 | + | 0.916724i | \(0.630824\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.93078 | −0.136870 | −0.0684348 | − | 0.997656i | \(-0.521801\pi\) | ||||
−0.0684348 | + | 0.997656i | \(0.521801\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.81369 | 0.339531 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.69779 | 0.329720 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 36.6620 | 2.56058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.55191 | 0.107865 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.48270 | −0.102560 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.3310 | 1.19311 | 0.596557 | − | 0.802570i | \(-0.296535\pi\) | ||||
0.596557 | + | 0.802570i | \(0.296535\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.965392 | −0.0661476 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.7491 | −1.27868 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.06922 | 0.276236 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.21509 | 0.217256 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.59859 | 0.511137 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.7099 | 1.18594 | 0.592970 | − | 0.805224i | \(-0.297955\pi\) | ||||
0.592970 | + | 0.805224i | \(0.297955\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.21509 | 0.414339 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.5865 | −0.835397 | −0.417698 | − | 0.908586i | \(-0.637163\pi\) | ||||
−0.417698 | + | 0.908586i | \(0.637163\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.6978 | −1.23558 | −0.617792 | − | 0.786341i | \(-0.711973\pi\) | ||||
−0.617792 | + | 0.786341i | \(0.711973\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.51730 | 0.165626 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.6332 | 1.74480 | 0.872400 | − | 0.488793i | \(-0.162563\pi\) | ||||
0.872400 | + | 0.488793i | \(0.162563\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.33682 | 0.152437 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.83159 | −0.573673 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.4815 | −1.71295 | −0.856473 | − | 0.516192i | \(-0.827349\pi\) | ||||
−0.856473 | + | 0.516192i | \(0.827349\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.40604 | −0.154986 | −0.0774932 | − | 0.996993i | \(-0.524692\pi\) | ||||
−0.0774932 | + | 0.996993i | \(0.524692\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.22092 | 0.141889 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.48270 | 0.0943417 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.767005 | −0.0486069 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.3714 | −0.717758 | −0.358879 | − | 0.933384i | \(-0.616841\pi\) | ||||
−0.358879 | + | 0.933384i | \(0.616841\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.55191 | −0.0975679 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 25.4469 | 1.59355 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.9642 | −0.871063 | −0.435531 | − | 0.900174i | \(-0.643439\pi\) | ||||
−0.435531 | + | 0.900174i | \(0.643439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.1867 | 1.00579 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.86620 | 0.115515 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.44064 | −0.0888339 | −0.0444170 | − | 0.999013i | \(-0.514143\pi\) | ||||
−0.0444170 | + | 0.999013i | \(0.514143\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.5928 | 2.00216 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.41811 | −0.209185 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.7324 | 0.837279 | 0.418639 | − | 0.908153i | \(-0.362507\pi\) | ||||
0.418639 | + | 0.908153i | \(0.362507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.2843 | 1.17144 | 0.585719 | − | 0.810514i | \(-0.300812\pi\) | ||||
0.585719 | + | 0.810514i | \(0.300812\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.51730 | −0.152354 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.21509 | −0.374784 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.10382 | −0.0663224 | −0.0331612 | − | 0.999450i | \(-0.510557\pi\) | ||||
−0.0331612 | + | 0.999450i | \(0.510557\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.61650 | 0.0967772 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.1101 | −1.02070 | −0.510351 | − | 0.859966i | \(-0.670484\pi\) | ||||
−0.510351 | + | 0.859966i | \(0.670484\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.03924 | 0.537327 | 0.268663 | − | 0.963234i | \(-0.413418\pi\) | ||||
0.268663 | + | 0.963234i | \(0.413418\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.96539 | 0.294124 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.5582 | −1.62671 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.7386 | 2.39639 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.96539 | 0.408319 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.1805 | 1.06212 | 0.531058 | − | 0.847336i | \(-0.321795\pi\) | ||||
0.531058 | + | 0.847336i | \(0.321795\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.9642 | −0.929471 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.55191 | 0.0897494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.0934 | 0.812328 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.29638 | −0.361718 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.56982 | 0.318927 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.947489 | −0.0540761 | −0.0270380 | − | 0.999634i | \(-0.508608\pi\) | ||||
−0.0270380 | + | 0.999634i | \(0.508608\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.4648 | −0.879761 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.2392 | 1.20437 | 0.602183 | − | 0.798358i | \(-0.294298\pi\) | ||||
0.602183 | + | 0.798358i | \(0.294298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.8079 | −1.00656 | −0.503280 | − | 0.864123i | \(-0.667874\pi\) | ||||
−0.503280 | + | 0.864123i | \(0.667874\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.43018 | −0.474987 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.58069 | −0.538105 | −0.269053 | − | 0.963125i | \(-0.586711\pi\) | ||||
−0.269053 | + | 0.963125i | \(0.586711\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.86620 | −0.104487 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0934 | 0.674986 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.2664 | 0.626880 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.21509 | 0.344751 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.6453 | 0.975786 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.75655 | −0.0968415 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.61530 | 0.473540 | 0.236770 | − | 0.971566i | \(-0.423911\pi\) | ||||
0.236770 | + | 0.971566i | \(0.423911\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.43018 | 0.352372 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.1205 | 0.880759 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.1626 | 1.75201 | 0.876004 | − | 0.482304i | \(-0.160200\pi\) | ||||
0.876004 | + | 0.482304i | \(0.160200\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.76700 | 0.150283 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.61650 | −0.0875383 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.2906 | −1.04159 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.19719 | 0.279807 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.9988 | 1.44937 | 0.724686 | − | 0.689079i | \(-0.241985\pi\) | ||||
0.724686 | + | 0.689079i | \(0.241985\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.6632 | 0.838431 | 0.419215 | − | 0.907887i | \(-0.362305\pi\) | ||||
0.419215 | + | 0.907887i | \(0.362305\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.74447 | 0.465421 | 0.232711 | − | 0.972546i | \(-0.425241\pi\) | ||||
0.232711 | + | 0.972546i | \(0.425241\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.23300 | −0.171590 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.1280 | −1.01236 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.7744 | −0.832544 | −0.416272 | − | 0.909240i | \(-0.636664\pi\) | ||||
−0.416272 | + | 0.909240i | \(0.636664\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8016 | −0.884295 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.7670 | 0.563571 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.66318 | 0.504414 | 0.252207 | − | 0.967673i | \(-0.418844\pi\) | ||||
0.252207 | + | 0.967673i | \(0.418844\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.9475 | −0.569904 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.4994 | −1.27195 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5582 | 0.702015 | 0.351007 | − | 0.936373i | \(-0.385839\pi\) | ||||
0.351007 | + | 0.936373i | \(0.385839\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.06922 | 0.210133 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.86620 | 0.0961141 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.419308 | 0.0215384 | 0.0107692 | − | 0.999942i | \(-0.496572\pi\) | ||||
0.0107692 | + | 0.999942i | \(0.496572\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.6332 | −0.647219 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.19719 | −0.163369 | −0.0816844 | − | 0.996658i | \(-0.526030\pi\) | ||||
−0.0816844 | + | 0.996658i | \(0.526030\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.43018 | 0.429642 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.59859 | 0.284593 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.6274 | 1.60357 | 0.801786 | − | 0.597612i | \(-0.203883\pi\) | ||||
0.801786 | + | 0.597612i | \(0.203883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.7924 | 0.596365 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.10382 | 0.156567 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.5761 | −1.48813 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.43018 | 0.322722 | 0.161361 | − | 0.986895i | \(-0.448412\pi\) | ||||
0.161361 | + | 0.986895i | \(0.448412\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.73240 | −0.186854 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.4769 | −0.623065 | −0.311533 | − | 0.950235i | \(-0.600842\pi\) | ||||
−0.311533 | + | 0.950235i | \(0.600842\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.61650 | 0.0805235 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.34889 | −0.166408 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.43018 | −0.318732 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.28431 | −0.261292 | −0.130646 | − | 0.991429i | \(-0.541705\pi\) | ||||
−0.130646 | + | 0.991429i | \(0.541705\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.813687 | −0.0401362 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.0000 | 0.590481 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.56862 | −0.126088 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.133802 | −0.00655230 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.81952 | −0.0888892 | −0.0444446 | − | 0.999012i | \(-0.514152\pi\) | ||||
−0.0444446 | + | 0.999012i | \(0.514152\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.0346 | 1.12264 | 0.561319 | − | 0.827599i | \(-0.310294\pi\) | ||||
0.561319 | + | 0.827599i | \(0.310294\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.697788 | −0.0339276 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 47.2260 | 2.29080 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.18673 | −0.202610 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.1038 | 1.11287 | 0.556436 | − | 0.830890i | \(-0.312168\pi\) | ||||
0.556436 | + | 0.830890i | \(0.312168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.7912 | −0.806931 | −0.403466 | − | 0.914995i | \(-0.632195\pi\) | ||||
−0.403466 | + | 0.914995i | \(0.632195\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.24970 | 0.299650 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.30101 | 0.110072 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.2606 | −1.92153 | −0.960766 | − | 0.277359i | \(-0.910541\pi\) | ||||
−0.960766 | + | 0.277359i | \(0.910541\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.663180 | −0.0315800 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.8604 | 0.801060 | 0.400530 | − | 0.916284i | \(-0.368826\pi\) | ||||
0.400530 | + | 0.916284i | \(0.368826\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.4469 | −0.542635 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.0167 | 0.804863 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.98793 | −0.329781 | −0.164890 | − | 0.986312i | \(-0.552727\pi\) | ||||
−0.164890 | + | 0.986312i | \(0.552727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.9475 | 0.515497 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.8783 | −1.07492 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.43018 | −0.395213 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.0346 | 1.26463 | 0.632313 | − | 0.774713i | \(-0.282106\pi\) | ||||
0.632313 | + | 0.774713i | \(0.282106\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.59859 | −0.354672 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.65574 | 0.216839 | 0.108420 | − | 0.994105i | \(-0.465421\pi\) | ||||
0.108420 | + | 0.994105i | \(0.465421\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.9417 | 1.48445 | 0.742227 | − | 0.670148i | \(-0.233769\pi\) | ||||
0.742227 | + | 0.670148i | \(0.233769\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.41348 | 0.251044 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.2738 | 1.40091 | 0.700453 | − | 0.713698i | \(-0.252981\pi\) | ||||
0.700453 | + | 0.713698i | \(0.252981\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.1175 | −0.559535 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.21509 | 0.240299 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.59859 | −0.257424 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.21509 | 0.422817 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.73240 | −0.445616 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.8783 | 1.41086 | 0.705432 | − | 0.708777i | \(-0.250753\pi\) | ||||
0.705432 | + | 0.708777i | \(0.250753\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.43018 | 0.293191 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.90663 | −0.177758 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.3264 | 1.05920 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.8378 | −0.944252 | −0.472126 | − | 0.881531i | \(-0.656513\pi\) | ||||
−0.472126 | + | 0.881531i | \(0.656513\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.7203 | −0.484790 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.4302 | −0.922001 | −0.461001 | − | 0.887400i | \(-0.652509\pi\) | ||||
−0.461001 | + | 0.887400i | \(0.652509\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.1805 | 0.638657 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.34889 | 0.150522 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.43018 | 0.109009 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.6406 | −1.23737 | −0.618683 | − | 0.785641i | \(-0.712333\pi\) | ||||
−0.618683 | + | 0.785641i | \(0.712333\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.8258 | −1.06446 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 41.9525 | 1.87057 | 0.935286 | − | 0.353894i | \(-0.115143\pi\) | ||||
0.935286 | + | 0.353894i | \(0.115143\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.0859 | −0.938311 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.41811 | −0.328802 | −0.164401 | − | 0.986394i | \(-0.552569\pi\) | ||||
−0.164401 | + | 0.986394i | \(0.552569\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.09337 | −0.358029 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.48270 | −0.0654626 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −51.7900 | −2.28214 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.697788 | 0.0306887 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.7958 | −1.00062 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.1867 | −1.32250 | −0.661252 | − | 0.750164i | \(-0.729975\pi\) | ||||
−0.661252 | + | 0.750164i | \(0.729975\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.2618 | 0.492443 | 0.246222 | − | 0.969214i | \(-0.420811\pi\) | ||||
0.246222 | + | 0.969214i | \(0.420811\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15.6453 | −0.682816 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.2831 | 0.535061 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5916 | −0.895286 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.76700 | 0.206870 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.9475 | −0.474188 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 40.4994 | 1.75094 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.6799 | 0.460871 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.663180 | 0.0285652 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.13963 | −0.220970 | −0.110485 | − | 0.993878i | \(-0.535240\pi\) | ||||
−0.110485 | + | 0.993878i | \(0.535240\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.18048 | 0.179402 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 59.0922 | 2.53123 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.1209 | 1.84372 | 0.921859 | − | 0.387525i | \(-0.126670\pi\) | ||||
0.921859 | + | 0.387525i | \(0.126670\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.66318 | −0.0709828 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.76700 | 0.117878 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.2318 | 0.945392 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.5340 | 0.914068 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.3085 | 1.15710 | 0.578548 | − | 0.815648i | \(-0.303619\pi\) | ||||
0.578548 | + | 0.815648i | \(0.303619\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.59859 | 0.236795 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.59859 | 0.320813 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.03461 | −0.212183 | −0.106092 | − | 0.994356i | \(-0.533834\pi\) | ||||
−0.106092 | + | 0.994356i | \(0.533834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.26641 | 0.389841 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.51730 | 0.105717 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.4014 | 0.519894 | 0.259947 | − | 0.965623i | \(-0.416295\pi\) | ||||
0.259947 | + | 0.965623i | \(0.416295\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.5744 | 0.651770 | 0.325885 | − | 0.945409i | \(-0.394338\pi\) | ||||
0.325885 | + | 0.945409i | \(0.394338\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.1626 | 0.424548 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.64528 | 0.402236 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.89618 | −0.120569 | −0.0602847 | − | 0.998181i | \(-0.519201\pi\) | ||||
−0.0602847 | + | 0.998181i | \(0.519201\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.7491 | −0.862303 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.93078 | 0.0801024 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.73240 | 0.403075 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.34889 | −0.138460 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.3714 | 0.634447 | 0.317223 | − | 0.948351i | \(-0.397250\pi\) | ||||
0.317223 | + | 0.948351i | \(0.397250\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.39677 | 0.0987574 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.2151 | 0.461327 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.38813 | 0.344459 | 0.172230 | − | 0.985057i | \(-0.444903\pi\) | ||||
0.172230 | + | 0.985057i | \(0.444903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −64.0576 | −2.62610 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.93078 | 0.0790217 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.2318 | 0.826649 | 0.413324 | − | 0.910584i | \(-0.364368\pi\) | ||||
0.413324 | + | 0.910584i | \(0.364368\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.7219 | 0.763684 | 0.381842 | − | 0.924228i | \(-0.375290\pi\) | ||||
0.381842 | + | 0.924228i | \(0.375290\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.81369 | −0.196028 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.34889 | −0.136152 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.56518 | 0.0635289 | 0.0317644 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317644 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.69779 | −0.190364 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.697788 | −0.0282295 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.4710 | −1.02877 | −0.514383 | − | 0.857561i | \(-0.671979\pi\) | ||||
−0.514383 | + | 0.857561i | \(0.671979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −36.6620 | −1.47835 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.1747 | −1.41608 | −0.708039 | − | 0.706173i | \(-0.750420\pi\) | ||||
−0.708039 | + | 0.706173i | \(0.750420\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.2197 | −1.09405 | −0.547027 | − | 0.837115i | \(-0.684240\pi\) | ||||
−0.547027 | + | 0.837115i | \(0.684240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.55191 | −0.0622761 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.60442 | 0.344729 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.4481 | −0.697924 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.48270 | 0.0592132 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 48.8604 | 1.94819 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.61650 | 0.143970 | 0.0719852 | − | 0.997406i | \(-0.477067\pi\) | ||||
0.0719852 | + | 0.997406i | \(0.477067\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.3310 | −0.688845 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −42.3073 | −1.67891 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.663180 | −0.0262762 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.965392 | 0.0381903 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.49940 | −0.0987204 | −0.0493602 | − | 0.998781i | \(-0.515718\pi\) | ||||
−0.0493602 | + | 0.998781i | \(0.515718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.48852 | 0.334755 | 0.167377 | − | 0.985893i | \(-0.446470\pi\) | ||||
0.167377 | + | 0.985893i | \(0.446470\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.7491 | 0.738245 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.0218 | 1.88793 | 0.943965 | − | 0.330046i | \(-0.107064\pi\) | ||||
0.943965 | + | 0.330046i | \(0.107064\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.76700 | −0.187121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.06922 | −0.159485 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.49940 | 0.254341 | 0.127171 | − | 0.991881i | \(-0.459410\pi\) | ||||
0.127171 | + | 0.991881i | \(0.459410\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.3944 | 0.406142 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.21509 | −0.125433 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.12797 | 0.121849 | 0.0609243 | − | 0.998142i | \(-0.480595\pi\) | ||||
0.0609243 | + | 0.998142i | \(0.480595\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.5916 | −1.22877 | −0.614385 | − | 0.789007i | \(-0.710596\pi\) | ||||
−0.614385 | + | 0.789007i | \(0.710596\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.59859 | −0.295105 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.4994 | −0.484706 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.89618 | 0.112140 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.7099 | −0.684703 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.66318 | 0.0642064 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.60442 | 0.100393 | 0.0501966 | − | 0.998739i | \(-0.484015\pi\) | ||||
0.0501966 | + | 0.998739i | \(0.484015\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.21509 | −0.239219 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.5869 | −1.06025 | −0.530126 | − | 0.847919i | \(-0.677855\pi\) | ||||
−0.530126 | + | 0.847919i | \(0.677855\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.5340 | −0.672894 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.5865 | 0.482317 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.8950 | −1.37348 | −0.686742 | − | 0.726902i | \(-0.740960\pi\) | ||||
−0.686742 | + | 0.726902i | \(0.740960\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.72495 | −0.104115 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.6978 | 0.713365 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.73240 | −0.370775 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.3360 | 1.76271 | 0.881353 | − | 0.472458i | \(-0.156633\pi\) | ||||
0.881353 | + | 0.472458i | \(0.156633\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.51730 | −0.0956245 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.448088 | −0.0169969 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −83.1855 | −3.15088 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.6332 | −1.00736 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.0183 | 1.47370 | 0.736851 | − | 0.676055i | \(-0.236312\pi\) | ||||
0.736851 | + | 0.676055i | \(0.236312\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.53401 | 0.359582 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.33682 | −0.0880097 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.8499 | 0.596097 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.87083 | 0.295595 | 0.147798 | − | 0.989018i | \(-0.452782\pi\) | ||||
0.147798 | + | 0.989018i | \(0.452782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.83159 | 0.331211 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.50866 | 0.0939501 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.34889 | 0.125242 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.4815 | 0.988970 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.9988 | −1.52900 | −0.764499 | − | 0.644625i | \(-0.777013\pi\) | ||||
−0.764499 | + | 0.644625i | \(0.777013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.9296 | 1.44981 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.40604 | 0.0894814 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.5986 | 0.430761 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.3356 | −0.420415 | −0.210207 | − | 0.977657i | \(-0.567414\pi\) | ||||
−0.210207 | + | 0.977657i | \(0.567414\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.5415 | 1.57345 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.3881 | 1.19628 | 0.598141 | − | 0.801391i | \(-0.295906\pi\) | ||||
0.598141 | + | 0.801391i | \(0.295906\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.22092 | −0.0819199 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.81369 | 0.177314 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.0650 | 1.58417 | 0.792086 | − | 0.610410i | \(-0.208995\pi\) | ||||
0.792086 | + | 0.610410i | \(0.208995\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.48270 | −0.0544682 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.80161 | −0.212841 | −0.106420 | − | 0.994321i | \(-0.533939\pi\) | ||||
−0.106420 | + | 0.994321i | \(0.533939\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 56.9871 | 2.08785 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.767005 | 0.0280632 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.4427 | −1.11235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.73359 | −0.245712 | −0.122856 | − | 0.992424i | \(-0.539205\pi\) | ||||
−0.122856 | + | 0.992424i | \(0.539205\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.3714 | 0.414398 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −76.6169 | −2.78838 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.7491 | −0.681448 | −0.340724 | − | 0.940163i | \(-0.610672\pi\) | ||||
−0.340724 | + | 0.940163i | \(0.610672\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.55191 | 0.0563308 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.78371 | −0.354659 | −0.177330 | − | 0.984152i | \(-0.556746\pi\) | ||||
−0.177330 | + | 0.984152i | \(0.556746\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44.4185 | −1.60806 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −25.4469 | −0.920034 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.76700 | 0.172127 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.3240 | 1.70655 | 0.853273 | − | 0.521465i | \(-0.174614\pi\) | ||||
0.853273 | + | 0.521465i | \(0.174614\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.9642 | 0.502908 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.7895 | −0.531943 | −0.265971 | − | 0.963981i | \(-0.585693\pi\) | ||||
−0.265971 | + | 0.963981i | \(0.585693\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.0467 | 0.360887 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.1867 | −0.580696 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.2318 | −0.581565 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.965392 | −0.0345444 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.86620 | −0.0666925 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.4648 | 0.623345 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.7733 | −0.740486 | −0.370243 | − | 0.928935i | \(-0.620726\pi\) | ||||
−0.370243 | + | 0.928935i | \(0.620726\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.44064 | 0.0512883 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.96539 | −0.247661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.66318 | −0.0590613 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −32.5928 | −1.15595 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.6515 | 1.05031 | 0.525155 | − | 0.851006i | \(-0.324007\pi\) | ||||
0.525155 | + | 0.851006i | \(0.324007\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.30221 | −0.187579 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.41811 | 0.120773 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.21509 | 0.113458 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.0829 | −0.461112 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.7324 | −0.483403 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.34145 | −0.222954 | −0.111477 | − | 0.993767i | \(-0.535558\pi\) | ||||
−0.111477 | + | 0.993767i | \(0.535558\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.2046 | −0.920169 | −0.460085 | − | 0.887875i | \(-0.652181\pi\) | ||||
−0.460085 | + | 0.887875i | \(0.652181\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.2843 | −0.676330 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35.9012 | −1.25757 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.30101 | 0.290416 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.51730 | 0.0879617 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0062 | 0.349220 | 0.174610 | − | 0.984638i | \(-0.444133\pi\) | ||||
0.174610 | + | 0.984638i | \(0.444133\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.40604 | −0.293016 | −0.146508 | − | 0.989209i | \(-0.546803\pi\) | ||||
−0.146508 | + | 0.989209i | \(0.546803\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.21509 | 0.216382 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.7040 | −1.62406 | −0.812029 | − | 0.583617i | \(-0.801637\pi\) | ||||
−0.812029 | + | 0.583617i | \(0.801637\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.6032 | 1.16709 | 0.583544 | − | 0.812081i | \(-0.301666\pi\) | ||||
0.583544 | + | 0.812081i | \(0.301666\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.10382 | 0.0382912 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.03924 | −0.174599 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −79.7900 | −2.76125 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.61650 | −0.0558743 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.8258 | 0.408271 | 0.204135 | − | 0.978943i | \(-0.434562\pi\) | ||||
0.204135 | + | 0.978943i | \(0.434562\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.5173 | −0.879907 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.1101 | 0.589302 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.34889 | −0.115205 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.51730 | 0.0864956 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.03924 | −0.310226 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.97908 | 0.342079 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.6873 | 0.879517 | 0.439759 | − | 0.898116i | \(-0.355064\pi\) | ||||
0.439759 | + | 0.898116i | \(0.355064\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.96539 | −0.169813 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.4578 | −1.48449 | −0.742245 | − | 0.670129i | \(-0.766239\pi\) | ||||
−0.742245 | + | 0.670129i | \(0.766239\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.0093 | −0.955664 | −0.477832 | − | 0.878451i | \(-0.658577\pi\) | ||||
−0.477832 | + | 0.878451i | \(0.658577\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.5582 | 0.939180 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.5928 | −0.428663 | −0.214331 | − | 0.976761i | \(-0.568757\pi\) | ||||
−0.214331 | + | 0.976761i | \(0.568757\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −76.3407 | −2.59566 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −40.7386 | −1.38356 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.83159 | −0.299591 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.81369 | −0.163106 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.96539 | −0.235743 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.2435 | −0.346292 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.7312 | 1.03772 | 0.518859 | − | 0.854860i | \(-0.326357\pi\) | ||||
0.518859 | + | 0.854860i | \(0.326357\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.1805 | −0.613213 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.7195 | 1.77617 | 0.888083 | − | 0.459683i | \(-0.152037\pi\) | ||||
0.888083 | + | 0.459683i | \(0.152037\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.8604 | −0.702007 | −0.351004 | − | 0.936374i | \(-0.614160\pi\) | ||||
−0.351004 | + | 0.936374i | \(0.614160\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.9642 | 0.536631 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.0093 | 0.873306 | 0.436653 | − | 0.899630i | \(-0.356164\pi\) | ||||
0.436653 | + | 0.899630i | \(0.356164\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.8016 | 1.06659 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.03461 | −0.0346218 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35.7658 | 1.19552 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.55191 | −0.0518168 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.01671 | 0.100613 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −73.9525 | −2.46372 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.0934 | −0.468998 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.0000 | 0.465376 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.38512 | 0.212014 | 0.106007 | − | 0.994365i | \(-0.466193\pi\) | ||||
0.106007 | + | 0.994365i | \(0.466193\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.29638 | 0.208838 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.8845 | −1.55335 | −0.776677 | − | 0.629899i | \(-0.783096\pi\) | ||||
−0.776677 | + | 0.629899i | \(0.783096\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.767005 | −0.0253841 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.56982 | −0.184132 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.81327 | −0.258017 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.3656 | −1.46349 | −0.731743 | − | 0.681581i | \(-0.761293\pi\) | ||||
−0.731743 | + | 0.681581i | \(0.761293\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.947489 | 0.0312208 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.965392 | 0.0317763 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.9642 | 1.31401 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.4648 | 0.507930 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.35935 | −0.143026 | −0.0715129 | − | 0.997440i | \(-0.522783\pi\) | ||||
−0.0715129 | + | 0.997440i | \(0.522783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.983295 | −0.0322262 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.2392 | −0.695342 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.4469 | 0.832202 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.5686 | −1.25998 | −0.629991 | − | 0.776603i | \(-0.716941\pi\) | ||||
−0.629991 | + | 0.776603i | \(0.716941\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.8079 | 0.581138 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.0501 | 1.66419 | 0.832093 | − | 0.554636i | \(-0.187142\pi\) | ||||
0.832093 | + | 0.554636i | \(0.187142\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.9895 | −0.553256 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.43018 | 0.274234 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.5928 | −1.25410 | −0.627048 | − | 0.778980i | \(-0.715737\pi\) | ||||
−0.627048 | + | 0.778980i | \(0.715737\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.21509 | −0.104366 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.58069 | 0.310675 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.4232 | −0.726357 | −0.363179 | − | 0.931720i | \(-0.618309\pi\) | ||||
−0.363179 | + | 0.931720i | \(0.618309\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.0334 | 1.10130 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.86620 | 0.0603256 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.04830 | 0.0661430 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3869 | −0.915708 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0934 | −0.389703 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −69.4865 | −2.23685 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.0618 | 0.355723 | 0.177861 | − | 0.984056i | \(-0.443082\pi\) | ||||
0.177861 | + | 0.984056i | \(0.443082\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.2664 | −0.361929 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.3073 | 1.67862 | 0.839310 | − | 0.543653i | \(-0.182959\pi\) | ||||
0.839310 | + | 0.543653i | \(0.182959\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.336820 | 0.0107979 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.21509 | −0.199042 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −60.1400 | −1.92405 | −0.962025 | − | 0.272960i | \(-0.911997\pi\) | ||||
−0.962025 | + | 0.272960i | \(0.911997\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.41811 | −0.109243 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.6453 | −0.563370 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.9642 | 0.509179 | 0.254589 | − | 0.967049i | \(-0.418060\pi\) | ||||
0.254589 | + | 0.967049i | \(0.418060\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37.5582 | 1.19670 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.75655 | 0.0559115 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.68853 | 0.276279 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.0230 | −0.731348 | −0.365674 | − | 0.930743i | \(-0.619162\pi\) | ||||
−0.365674 | + | 0.930743i | \(0.619162\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.61530 | −0.273398 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.46599 | 0.204986 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.9759 | −0.379279 | −0.189640 | − | 0.981854i | \(-0.560732\pi\) | ||||
−0.189640 | + | 0.981854i | \(0.560732\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.43018 | −0.203442 |
(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 | 6864.2.a.bn.1.1 | 3 | ||
4.3 | odd | 2 | 3432.2.a.n.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3432.2.a.n.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
6864.2.a.bn.1.1 | 3 | 1.1 | even | 1 | trivial |