Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.43128 | 1.01207 | 0.506035 | − | 0.862513i | \(-0.331111\pi\) | ||||
0.506035 | + | 0.862513i | \(0.331111\pi\) | |||||||
\(3\) | −1.25448 | −0.724277 | −0.362139 | − | 0.932124i | \(-0.617953\pi\) | ||||
−0.362139 | + | 0.932124i | \(0.617953\pi\) | |||||||
\(4\) | 0.0485743 | 0.0242871 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.79552 | −0.733020 | ||||||||
\(7\) | 2.72576 | 1.03024 | 0.515120 | − | 0.857118i | \(-0.327747\pi\) | ||||
0.515120 | + | 0.857118i | \(0.327747\pi\) | |||||||
\(8\) | −2.79304 | −0.987490 | ||||||||
\(9\) | −1.42627 | −0.475423 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.42128 | 1.93609 | 0.968045 | − | 0.250777i | \(-0.0806860\pi\) | ||||
0.968045 | + | 0.250777i | \(0.0806860\pi\) | |||||||
\(12\) | −0.0609357 | −0.0175906 | ||||||||
\(13\) | 4.50692 | 1.24999 | 0.624997 | − | 0.780627i | \(-0.285100\pi\) | ||||
0.624997 | + | 0.780627i | \(0.285100\pi\) | |||||||
\(14\) | 3.90133 | 1.04268 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.09479 | −1.02370 | ||||||||
\(17\) | −7.34936 | −1.78248 | −0.891240 | − | 0.453531i | \(-0.850164\pi\) | ||||
−0.891240 | + | 0.453531i | \(0.850164\pi\) | |||||||
\(18\) | −2.04139 | −0.481161 | ||||||||
\(19\) | −2.46559 | −0.565646 | −0.282823 | − | 0.959172i | \(-0.591271\pi\) | ||||
−0.282823 | + | 0.959172i | \(0.591271\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.41942 | −0.746179 | ||||||||
\(22\) | 9.19068 | 1.95946 | ||||||||
\(23\) | 6.02048 | 1.25536 | 0.627679 | − | 0.778473i | \(-0.284005\pi\) | ||||
0.627679 | + | 0.778473i | \(0.284005\pi\) | |||||||
\(24\) | 3.50383 | 0.715217 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.45068 | 1.26508 | ||||||||
\(27\) | 5.55269 | 1.06861 | ||||||||
\(28\) | 0.132402 | 0.0250216 | ||||||||
\(29\) | 0.229668 | 0.0426482 | 0.0213241 | − | 0.999773i | \(-0.493212\pi\) | ||||
0.0213241 | + | 0.999773i | \(0.493212\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.08364 | 0.733443 | 0.366721 | − | 0.930331i | \(-0.380480\pi\) | ||||
0.366721 | + | 0.930331i | \(0.380480\pi\) | |||||||
\(32\) | −0.274717 | −0.0485636 | ||||||||
\(33\) | −8.05540 | −1.40227 | ||||||||
\(34\) | −10.5190 | −1.80400 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0692799 | −0.0115466 | ||||||||
\(37\) | 0.420726 | 0.0691669 | 0.0345835 | − | 0.999402i | \(-0.488990\pi\) | ||||
0.0345835 | + | 0.999402i | \(0.488990\pi\) | |||||||
\(38\) | −3.52896 | −0.572474 | ||||||||
\(39\) | −5.65386 | −0.905343 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.97215 | 0.932693 | 0.466346 | − | 0.884602i | \(-0.345570\pi\) | ||||
0.466346 | + | 0.884602i | \(0.345570\pi\) | |||||||
\(42\) | −4.89416 | −0.755186 | ||||||||
\(43\) | −6.55939 | −1.00030 | −0.500149 | − | 0.865939i | \(-0.666721\pi\) | ||||
−0.500149 | + | 0.865939i | \(0.666721\pi\) | |||||||
\(44\) | 0.311909 | 0.0470221 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.61702 | 1.27051 | ||||||||
\(47\) | −10.8362 | −1.58062 | −0.790308 | − | 0.612710i | \(-0.790079\pi\) | ||||
−0.790308 | + | 0.612710i | \(0.790079\pi\) | |||||||
\(48\) | 5.13685 | 0.741441 | ||||||||
\(49\) | 0.429757 | 0.0613938 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.21966 | 1.29101 | ||||||||
\(52\) | 0.218920 | 0.0303588 | ||||||||
\(53\) | 2.49871 | 0.343224 | 0.171612 | − | 0.985165i | \(-0.445102\pi\) | ||||
0.171612 | + | 0.985165i | \(0.445102\pi\) | |||||||
\(54\) | 7.94747 | 1.08151 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.61316 | −1.01735 | ||||||||
\(57\) | 3.09305 | 0.409684 | ||||||||
\(58\) | 0.328720 | 0.0431630 | ||||||||
\(59\) | 8.13951 | 1.05967 | 0.529837 | − | 0.848099i | \(-0.322253\pi\) | ||||
0.529837 | + | 0.848099i | \(0.322253\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1504 | 1.42766 | 0.713828 | − | 0.700321i | \(-0.246960\pi\) | ||||
0.713828 | + | 0.700321i | \(0.246960\pi\) | |||||||
\(62\) | 5.84484 | 0.742296 | ||||||||
\(63\) | −3.88766 | −0.489799 | ||||||||
\(64\) | 7.79638 | 0.974547 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11.5296 | −1.41919 | ||||||||
\(67\) | −8.55624 | −1.04531 | −0.522655 | − | 0.852544i | \(-0.675059\pi\) | ||||
−0.522655 | + | 0.852544i | \(0.675059\pi\) | |||||||
\(68\) | −0.356990 | −0.0432914 | ||||||||
\(69\) | −7.55260 | −0.909227 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.64665 | 0.432777 | 0.216389 | − | 0.976307i | \(-0.430572\pi\) | ||||
0.216389 | + | 0.976307i | \(0.430572\pi\) | |||||||
\(72\) | 3.98363 | 0.469475 | ||||||||
\(73\) | −8.50154 | −0.995030 | −0.497515 | − | 0.867455i | \(-0.665754\pi\) | ||||
−0.497515 | + | 0.867455i | \(0.665754\pi\) | |||||||
\(74\) | 0.602178 | 0.0700018 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.119764 | −0.0137379 | ||||||||
\(77\) | 17.5029 | 1.99464 | ||||||||
\(78\) | −8.09228 | −0.916271 | ||||||||
\(79\) | −3.50107 | −0.393901 | −0.196950 | − | 0.980413i | \(-0.563104\pi\) | ||||
−0.196950 | + | 0.980413i | \(0.563104\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.68696 | −0.298551 | ||||||||
\(82\) | 8.54784 | 0.943951 | ||||||||
\(83\) | −4.47496 | −0.491191 | −0.245595 | − | 0.969372i | \(-0.578983\pi\) | ||||
−0.245595 | + | 0.969372i | \(0.578983\pi\) | |||||||
\(84\) | −0.166096 | −0.0181226 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.38835 | −1.01237 | ||||||||
\(87\) | −0.288114 | −0.0308891 | ||||||||
\(88\) | −17.9349 | −1.91187 | ||||||||
\(89\) | −4.39063 | −0.465406 | −0.232703 | − | 0.972548i | \(-0.574757\pi\) | ||||
−0.232703 | + | 0.972548i | \(0.574757\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.2848 | 1.28779 | ||||||||
\(92\) | 0.292440 | 0.0304890 | ||||||||
\(93\) | −5.12286 | −0.531216 | ||||||||
\(94\) | −15.5096 | −1.59969 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.344629 | 0.0351735 | ||||||||
\(97\) | 12.9749 | 1.31740 | 0.658700 | − | 0.752406i | \(-0.271107\pi\) | ||||
0.658700 | + | 0.752406i | \(0.271107\pi\) | |||||||
\(98\) | 0.615104 | 0.0621349 | ||||||||
\(99\) | −9.15847 | −0.920461 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.70475 | 0.866155 | 0.433077 | − | 0.901357i | \(-0.357428\pi\) | ||||
0.433077 | + | 0.901357i | \(0.357428\pi\) | |||||||
\(102\) | 13.1960 | 1.30659 | ||||||||
\(103\) | 6.06555 | 0.597656 | 0.298828 | − | 0.954307i | \(-0.403404\pi\) | ||||
0.298828 | + | 0.954307i | \(0.403404\pi\) | |||||||
\(104\) | −12.5880 | −1.23436 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.57636 | 0.347367 | ||||||||
\(107\) | 8.17191 | 0.790009 | 0.395004 | − | 0.918679i | \(-0.370743\pi\) | ||||
0.395004 | + | 0.918679i | \(0.370743\pi\) | |||||||
\(108\) | 0.269718 | 0.0259536 | ||||||||
\(109\) | 15.0385 | 1.44043 | 0.720215 | − | 0.693751i | \(-0.244043\pi\) | ||||
0.720215 | + | 0.693751i | \(0.244043\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.527794 | −0.0500960 | ||||||||
\(112\) | −11.1614 | −1.05465 | ||||||||
\(113\) | −1.44086 | −0.135545 | −0.0677725 | − | 0.997701i | \(-0.521589\pi\) | ||||
−0.0677725 | + | 0.997701i | \(0.521589\pi\) | |||||||
\(114\) | 4.42703 | 0.414630 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.0111559 | 0.00103580 | ||||||||
\(117\) | −6.42807 | −0.594275 | ||||||||
\(118\) | 11.6500 | 1.07247 | ||||||||
\(119\) | −20.0326 | −1.83638 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.2329 | 2.74844 | ||||||||
\(122\) | 15.9593 | 1.44489 | ||||||||
\(123\) | −7.49197 | −0.675528 | ||||||||
\(124\) | 0.198360 | 0.0178132 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.56435 | −0.495711 | ||||||||
\(127\) | −9.57494 | −0.849639 | −0.424819 | − | 0.905278i | \(-0.639662\pi\) | ||||
−0.424819 | + | 0.905278i | \(0.639662\pi\) | |||||||
\(128\) | 11.7083 | 1.03487 | ||||||||
\(129\) | 8.22866 | 0.724493 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.0280 | −0.876154 | −0.438077 | − | 0.898937i | \(-0.644340\pi\) | ||||
−0.438077 | + | 0.898937i | \(0.644340\pi\) | |||||||
\(132\) | −0.391285 | −0.0340570 | ||||||||
\(133\) | −6.72061 | −0.582751 | ||||||||
\(134\) | −12.2464 | −1.05793 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.5271 | 1.76018 | ||||||||
\(137\) | −23.1668 | −1.97927 | −0.989635 | − | 0.143605i | \(-0.954130\pi\) | ||||
−0.989635 | + | 0.143605i | \(0.954130\pi\) | |||||||
\(138\) | −10.8099 | −0.920202 | ||||||||
\(139\) | 8.41735 | 0.713951 | 0.356975 | − | 0.934114i | \(-0.383808\pi\) | ||||
0.356975 | + | 0.934114i | \(0.383808\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.5938 | 1.14480 | ||||||||
\(142\) | 5.21939 | 0.438001 | ||||||||
\(143\) | 28.9402 | 2.42010 | ||||||||
\(144\) | 5.84026 | 0.486689 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.1681 | −1.00704 | ||||||||
\(147\) | −0.539123 | −0.0444661 | ||||||||
\(148\) | 0.0204365 | 0.00167987 | ||||||||
\(149\) | 13.3137 | 1.09070 | 0.545351 | − | 0.838208i | \(-0.316396\pi\) | ||||
0.545351 | + | 0.838208i | \(0.316396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1749 | −1.15354 | −0.576769 | − | 0.816907i | \(-0.695687\pi\) | ||||
−0.576769 | + | 0.816907i | \(0.695687\pi\) | |||||||
\(152\) | 6.88651 | 0.558570 | ||||||||
\(153\) | 10.4821 | 0.847432 | ||||||||
\(154\) | 25.0516 | 2.01871 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.274632 | −0.0219882 | ||||||||
\(157\) | 5.97542 | 0.476891 | 0.238445 | − | 0.971156i | \(-0.423362\pi\) | ||||
0.238445 | + | 0.971156i | \(0.423362\pi\) | |||||||
\(158\) | −5.01102 | −0.398655 | ||||||||
\(159\) | −3.13459 | −0.248589 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.4104 | 1.29332 | ||||||||
\(162\) | −3.84580 | −0.302155 | ||||||||
\(163\) | 25.1548 | 1.97027 | 0.985136 | − | 0.171776i | \(-0.0549504\pi\) | ||||
0.985136 | + | 0.171776i | \(0.0549504\pi\) | |||||||
\(164\) | 0.290093 | 0.0226524 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.40494 | −0.497120 | ||||||||
\(167\) | 16.6419 | 1.28779 | 0.643894 | − | 0.765114i | \(-0.277318\pi\) | ||||
0.643894 | + | 0.765114i | \(0.277318\pi\) | |||||||
\(168\) | 9.55060 | 0.736845 | ||||||||
\(169\) | 7.31232 | 0.562486 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.51660 | 0.268921 | ||||||||
\(172\) | −0.318618 | −0.0242944 | ||||||||
\(173\) | 2.39950 | 0.182430 | 0.0912152 | − | 0.995831i | \(-0.470925\pi\) | ||||
0.0912152 | + | 0.995831i | \(0.470925\pi\) | |||||||
\(174\) | −0.412374 | −0.0312620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −26.2938 | −1.98197 | ||||||||
\(177\) | −10.2109 | −0.767498 | ||||||||
\(178\) | −6.28425 | −0.471024 | ||||||||
\(179\) | 25.4679 | 1.90356 | 0.951779 | − | 0.306785i | \(-0.0992534\pi\) | ||||
0.951779 | + | 0.306785i | \(0.0992534\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.99948 | 0.594597 | 0.297298 | − | 0.954785i | \(-0.403914\pi\) | ||||
0.297298 | + | 0.954785i | \(0.403914\pi\) | |||||||
\(182\) | 17.5830 | 1.30334 | ||||||||
\(183\) | −13.9879 | −1.03402 | ||||||||
\(184\) | −16.8155 | −1.23965 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.33227 | −0.537628 | ||||||||
\(187\) | −47.1923 | −3.45104 | ||||||||
\(188\) | −0.526358 | −0.0383886 | ||||||||
\(189\) | 15.1353 | 1.10093 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.5056 | 0.977234 | 0.488617 | − | 0.872498i | \(-0.337502\pi\) | ||||
0.488617 | + | 0.872498i | \(0.337502\pi\) | |||||||
\(192\) | −9.78044 | −0.705843 | ||||||||
\(193\) | 1.24421 | 0.0895602 | 0.0447801 | − | 0.998997i | \(-0.485741\pi\) | ||||
0.0447801 | + | 0.998997i | \(0.485741\pi\) | |||||||
\(194\) | 18.5707 | 1.33330 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.0208751 | 0.00149108 | ||||||||
\(197\) | 12.5227 | 0.892205 | 0.446103 | − | 0.894982i | \(-0.352812\pi\) | ||||
0.446103 | + | 0.894982i | \(0.352812\pi\) | |||||||
\(198\) | −13.1084 | −0.931571 | ||||||||
\(199\) | 5.20215 | 0.368771 | 0.184385 | − | 0.982854i | \(-0.440971\pi\) | ||||
0.184385 | + | 0.982854i | \(0.440971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.7337 | 0.757095 | ||||||||
\(202\) | 12.4590 | 0.876610 | ||||||||
\(203\) | 0.626018 | 0.0439379 | ||||||||
\(204\) | 0.447838 | 0.0313549 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.68152 | 0.604870 | ||||||||
\(207\) | −8.58682 | −0.596825 | ||||||||
\(208\) | −18.4549 | −1.27962 | ||||||||
\(209\) | −15.8323 | −1.09514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.75204 | 0.258301 | 0.129151 | − | 0.991625i | \(-0.458775\pi\) | ||||
0.129151 | + | 0.991625i | \(0.458775\pi\) | |||||||
\(212\) | 0.121373 | 0.00833592 | ||||||||
\(213\) | −4.57466 | −0.313451 | ||||||||
\(214\) | 11.6963 | 0.799545 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −15.5089 | −1.05525 | ||||||||
\(217\) | 11.1310 | 0.755622 | ||||||||
\(218\) | 21.5244 | 1.45782 | ||||||||
\(219\) | 10.6651 | 0.720678 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −33.1230 | −2.22809 | ||||||||
\(222\) | −0.755424 | −0.0507007 | ||||||||
\(223\) | −18.1649 | −1.21641 | −0.608207 | − | 0.793778i | \(-0.708111\pi\) | ||||
−0.608207 | + | 0.793778i | \(0.708111\pi\) | |||||||
\(224\) | −0.748813 | −0.0500322 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.06229 | −0.137181 | ||||||||
\(227\) | 1.55378 | 0.103128 | 0.0515639 | − | 0.998670i | \(-0.483579\pi\) | ||||
0.0515639 | + | 0.998670i | \(0.483579\pi\) | |||||||
\(228\) | 0.150243 | 0.00995006 | ||||||||
\(229\) | −0.469326 | −0.0310140 | −0.0155070 | − | 0.999880i | \(-0.504936\pi\) | ||||
−0.0155070 | + | 0.999880i | \(0.504936\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.9571 | −1.44467 | ||||||||
\(232\) | −0.641472 | −0.0421147 | ||||||||
\(233\) | −9.22233 | −0.604175 | −0.302087 | − | 0.953280i | \(-0.597683\pi\) | ||||
−0.302087 | + | 0.953280i | \(0.597683\pi\) | |||||||
\(234\) | −9.20040 | −0.601449 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.395371 | 0.0257365 | ||||||||
\(237\) | 4.39204 | 0.285293 | ||||||||
\(238\) | −28.6723 | −1.85855 | ||||||||
\(239\) | −0.225938 | −0.0146147 | −0.00730736 | − | 0.999973i | \(-0.502326\pi\) | ||||
−0.00730736 | + | 0.999973i | \(0.502326\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 43.2718 | 2.78162 | ||||||||
\(243\) | −13.2873 | −0.852381 | ||||||||
\(244\) | 0.541620 | 0.0346737 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.7231 | −0.683682 | ||||||||
\(247\) | −11.1122 | −0.707054 | ||||||||
\(248\) | −11.4058 | −0.724268 | ||||||||
\(249\) | 5.61377 | 0.355758 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.1989 | −0.706870 | −0.353435 | − | 0.935459i | \(-0.614987\pi\) | ||||
−0.353435 | + | 0.935459i | \(0.614987\pi\) | |||||||
\(252\) | −0.188840 | −0.0118958 | ||||||||
\(253\) | 38.6592 | 2.43048 | ||||||||
\(254\) | −13.7045 | −0.859895 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.16510 | 0.0728188 | ||||||||
\(257\) | 28.9074 | 1.80319 | 0.901597 | − | 0.432578i | \(-0.142396\pi\) | ||||
0.901597 | + | 0.432578i | \(0.142396\pi\) | |||||||
\(258\) | 11.7775 | 0.733238 | ||||||||
\(259\) | 1.14680 | 0.0712585 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.327567 | −0.0202759 | ||||||||
\(262\) | −14.3530 | −0.886730 | ||||||||
\(263\) | 24.4338 | 1.50665 | 0.753327 | − | 0.657646i | \(-0.228448\pi\) | ||||
0.753327 | + | 0.657646i | \(0.228448\pi\) | |||||||
\(264\) | 22.4991 | 1.38472 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.61910 | −0.589785 | ||||||||
\(267\) | 5.50799 | 0.337083 | ||||||||
\(268\) | −0.415613 | −0.0253876 | ||||||||
\(269\) | −18.7127 | −1.14093 | −0.570467 | − | 0.821320i | \(-0.693238\pi\) | ||||
−0.570467 | + | 0.821320i | \(0.693238\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.4865 | −0.940735 | −0.470368 | − | 0.882471i | \(-0.655879\pi\) | ||||
−0.470368 | + | 0.882471i | \(0.655879\pi\) | |||||||
\(272\) | 30.0941 | 1.82472 | ||||||||
\(273\) | −15.4111 | −0.932720 | ||||||||
\(274\) | −33.1582 | −2.00316 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.366862 | −0.0220825 | ||||||||
\(277\) | 4.59879 | 0.276315 | 0.138157 | − | 0.990410i | \(-0.455882\pi\) | ||||
0.138157 | + | 0.990410i | \(0.455882\pi\) | |||||||
\(278\) | 12.0476 | 0.722568 | ||||||||
\(279\) | −5.82436 | −0.348695 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.6065 | 1.46790 | 0.733951 | − | 0.679203i | \(-0.237674\pi\) | ||||
0.733951 | + | 0.679203i | \(0.237674\pi\) | |||||||
\(282\) | 19.4566 | 1.15862 | ||||||||
\(283\) | 16.9758 | 1.00910 | 0.504552 | − | 0.863381i | \(-0.331658\pi\) | ||||
0.504552 | + | 0.863381i | \(0.331658\pi\) | |||||||
\(284\) | 0.177133 | 0.0105109 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 41.4217 | 2.44931 | ||||||||
\(287\) | 16.2786 | 0.960897 | ||||||||
\(288\) | 0.391820 | 0.0230882 | ||||||||
\(289\) | 37.0131 | 2.17724 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.2768 | −0.954163 | ||||||||
\(292\) | −0.412956 | −0.0241664 | ||||||||
\(293\) | −10.5453 | −0.616064 | −0.308032 | − | 0.951376i | \(-0.599670\pi\) | ||||
−0.308032 | + | 0.951376i | \(0.599670\pi\) | |||||||
\(294\) | −0.771638 | −0.0450029 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.17511 | −0.0683017 | ||||||||
\(297\) | 35.6554 | 2.06893 | ||||||||
\(298\) | 19.0557 | 1.10387 | ||||||||
\(299\) | 27.1338 | 1.56919 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.8793 | −1.03055 | ||||||||
\(302\) | −20.2883 | −1.16746 | ||||||||
\(303\) | −10.9200 | −0.627336 | ||||||||
\(304\) | 10.0961 | 0.579050 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 15.0029 | 0.857661 | ||||||||
\(307\) | 21.0573 | 1.20180 | 0.600902 | − | 0.799322i | \(-0.294808\pi\) | ||||
0.600902 | + | 0.799322i | \(0.294808\pi\) | |||||||
\(308\) | 0.850189 | 0.0484440 | ||||||||
\(309\) | −7.60914 | −0.432869 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.1373 | −0.744948 | −0.372474 | − | 0.928043i | \(-0.621490\pi\) | ||||
−0.372474 | + | 0.928043i | \(0.621490\pi\) | |||||||
\(312\) | 15.7915 | 0.894017 | ||||||||
\(313\) | 13.0387 | 0.736992 | 0.368496 | − | 0.929629i | \(-0.379873\pi\) | ||||
0.368496 | + | 0.929629i | \(0.379873\pi\) | |||||||
\(314\) | 8.55253 | 0.482647 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.170062 | −0.00956672 | ||||||||
\(317\) | 17.8804 | 1.00426 | 0.502131 | − | 0.864792i | \(-0.332550\pi\) | ||||
0.502131 | + | 0.864792i | \(0.332550\pi\) | |||||||
\(318\) | −4.48649 | −0.251590 | ||||||||
\(319\) | 1.47476 | 0.0825707 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.2515 | −0.572185 | ||||||||
\(322\) | 23.4879 | 1.30893 | ||||||||
\(323\) | 18.1205 | 1.00825 | ||||||||
\(324\) | −0.130517 | −0.00725095 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 36.0036 | 1.99405 | ||||||||
\(327\) | −18.8656 | −1.04327 | ||||||||
\(328\) | −16.6805 | −0.921025 | ||||||||
\(329\) | −29.5367 | −1.62841 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.0656 | −1.59759 | −0.798796 | − | 0.601602i | \(-0.794529\pi\) | ||||
−0.798796 | + | 0.601602i | \(0.794529\pi\) | |||||||
\(332\) | −0.217368 | −0.0119296 | ||||||||
\(333\) | −0.600068 | −0.0328835 | ||||||||
\(334\) | 23.8193 | 1.30333 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 14.0018 | 0.763862 | ||||||||
\(337\) | 25.4527 | 1.38650 | 0.693248 | − | 0.720699i | \(-0.256179\pi\) | ||||
0.693248 | + | 0.720699i | \(0.256179\pi\) | |||||||
\(338\) | 10.4660 | 0.569276 | ||||||||
\(339\) | 1.80754 | 0.0981722 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.2222 | 1.42001 | ||||||||
\(342\) | 5.03325 | 0.272167 | ||||||||
\(343\) | −17.9089 | −0.966989 | ||||||||
\(344\) | 18.3207 | 0.987785 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.43436 | 0.184632 | ||||||||
\(347\) | −19.1091 | −1.02583 | −0.512914 | − | 0.858440i | \(-0.671434\pi\) | ||||
−0.512914 | + | 0.858440i | \(0.671434\pi\) | |||||||
\(348\) | −0.0139949 | −0.000750208 0 | ||||||||
\(349\) | 11.4331 | 0.611998 | 0.305999 | − | 0.952032i | \(-0.401010\pi\) | ||||
0.305999 | + | 0.952032i | \(0.401010\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.0255 | 1.33576 | ||||||||
\(352\) | −1.76404 | −0.0940235 | ||||||||
\(353\) | −19.0551 | −1.01420 | −0.507101 | − | 0.861887i | \(-0.669283\pi\) | ||||
−0.507101 | + | 0.861887i | \(0.669283\pi\) | |||||||
\(354\) | −14.6147 | −0.776762 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.213272 | −0.0113034 | ||||||||
\(357\) | 25.1306 | 1.33005 | ||||||||
\(358\) | 36.4517 | 1.92653 | ||||||||
\(359\) | 32.6313 | 1.72221 | 0.861106 | − | 0.508425i | \(-0.169772\pi\) | ||||
0.861106 | + | 0.508425i | \(0.169772\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.9209 | −0.680045 | ||||||||
\(362\) | 11.4495 | 0.601774 | ||||||||
\(363\) | −37.9267 | −1.99064 | ||||||||
\(364\) | 0.596724 | 0.0312768 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −20.0207 | −1.04650 | ||||||||
\(367\) | −25.9119 | −1.35259 | −0.676294 | − | 0.736631i | \(-0.736415\pi\) | ||||
−0.676294 | + | 0.736631i | \(0.736415\pi\) | |||||||
\(368\) | −24.6526 | −1.28511 | ||||||||
\(369\) | −8.51788 | −0.443423 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.81087 | 0.353603 | ||||||||
\(372\) | −0.248839 | −0.0129017 | ||||||||
\(373\) | 17.0376 | 0.882176 | 0.441088 | − | 0.897464i | \(-0.354593\pi\) | ||||
0.441088 | + | 0.897464i | \(0.354593\pi\) | |||||||
\(374\) | −67.5456 | −3.49270 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 30.2659 | 1.56084 | ||||||||
\(377\) | 1.03509 | 0.0533100 | ||||||||
\(378\) | 21.6629 | 1.11422 | ||||||||
\(379\) | 32.3546 | 1.66194 | 0.830972 | − | 0.556314i | \(-0.187785\pi\) | ||||
0.830972 | + | 0.556314i | \(0.187785\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.0116 | 0.615374 | ||||||||
\(382\) | 19.3304 | 0.989030 | ||||||||
\(383\) | 12.2547 | 0.626183 | 0.313092 | − | 0.949723i | \(-0.398635\pi\) | ||||
0.313092 | + | 0.949723i | \(0.398635\pi\) | |||||||
\(384\) | −14.6878 | −0.749536 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.78082 | 0.0906413 | ||||||||
\(387\) | 9.35545 | 0.475564 | ||||||||
\(388\) | 0.630245 | 0.0319959 | ||||||||
\(389\) | 29.5698 | 1.49925 | 0.749624 | − | 0.661864i | \(-0.230234\pi\) | ||||
0.749624 | + | 0.661864i | \(0.230234\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −44.2467 | −2.23765 | ||||||||
\(392\) | −1.20033 | −0.0606258 | ||||||||
\(393\) | 12.5800 | 0.634578 | ||||||||
\(394\) | 17.9235 | 0.902975 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.444866 | −0.0223553 | ||||||||
\(397\) | 24.4885 | 1.22904 | 0.614520 | − | 0.788901i | \(-0.289350\pi\) | ||||
0.614520 | + | 0.788901i | \(0.289350\pi\) | |||||||
\(398\) | 7.44575 | 0.373222 | ||||||||
\(399\) | 8.43090 | 0.422073 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.96012 | −0.0978838 | −0.0489419 | − | 0.998802i | \(-0.515585\pi\) | ||||
−0.0489419 | + | 0.998802i | \(0.515585\pi\) | |||||||
\(402\) | 15.3629 | 0.766233 | ||||||||
\(403\) | 18.4046 | 0.916799 | ||||||||
\(404\) | 0.422827 | 0.0210364 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.896010 | 0.0444682 | ||||||||
\(407\) | 2.70160 | 0.133913 | ||||||||
\(408\) | −25.7509 | −1.27486 | ||||||||
\(409\) | −11.8558 | −0.586234 | −0.293117 | − | 0.956077i | \(-0.594692\pi\) | ||||
−0.293117 | + | 0.956077i | \(0.594692\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.0624 | 1.43354 | ||||||||
\(412\) | 0.294629 | 0.0145153 | ||||||||
\(413\) | 22.1863 | 1.09172 | ||||||||
\(414\) | −12.2902 | −0.604029 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.23813 | −0.0607042 | ||||||||
\(417\) | −10.5594 | −0.517098 | ||||||||
\(418\) | −22.6605 | −1.10836 | ||||||||
\(419\) | −11.3529 | −0.554625 | −0.277312 | − | 0.960780i | \(-0.589444\pi\) | ||||
−0.277312 | + | 0.960780i | \(0.589444\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.0831 | −1.12500 | −0.562500 | − | 0.826797i | \(-0.690160\pi\) | ||||
−0.562500 | + | 0.826797i | \(0.690160\pi\) | |||||||
\(422\) | 5.37024 | 0.261419 | ||||||||
\(423\) | 15.4553 | 0.751460 | ||||||||
\(424\) | −6.97900 | −0.338930 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.54764 | −0.317234 | ||||||||
\(427\) | 30.3932 | 1.47083 | ||||||||
\(428\) | 0.396945 | 0.0191870 | ||||||||
\(429\) | −36.3051 | −1.75282 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.8580 | −1.10103 | −0.550516 | − | 0.834825i | \(-0.685569\pi\) | ||||
−0.550516 | + | 0.834825i | \(0.685569\pi\) | |||||||
\(432\) | −22.7371 | −1.09394 | ||||||||
\(433\) | −40.5455 | −1.94849 | −0.974247 | − | 0.225483i | \(-0.927604\pi\) | ||||
−0.974247 | + | 0.225483i | \(0.927604\pi\) | |||||||
\(434\) | 15.9316 | 0.764743 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.730486 | 0.0349839 | ||||||||
\(437\) | −14.8441 | −0.710088 | ||||||||
\(438\) | 15.2647 | 0.729377 | ||||||||
\(439\) | 21.1447 | 1.00918 | 0.504591 | − | 0.863359i | \(-0.331643\pi\) | ||||
0.504591 | + | 0.863359i | \(0.331643\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.612948 | −0.0291880 | ||||||||
\(442\) | −47.4084 | −2.25499 | ||||||||
\(443\) | −21.1224 | −1.00355 | −0.501777 | − | 0.864997i | \(-0.667320\pi\) | ||||
−0.501777 | + | 0.864997i | \(0.667320\pi\) | |||||||
\(444\) | −0.0256372 | −0.00121669 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −25.9992 | −1.23110 | ||||||||
\(447\) | −16.7019 | −0.789971 | ||||||||
\(448\) | 21.2510 | 1.00402 | ||||||||
\(449\) | −10.5759 | −0.499108 | −0.249554 | − | 0.968361i | \(-0.580284\pi\) | ||||
−0.249554 | + | 0.968361i | \(0.580284\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.3489 | 1.80578 | ||||||||
\(452\) | −0.0699889 | −0.00329200 | ||||||||
\(453\) | 17.7822 | 0.835482 | ||||||||
\(454\) | 2.22390 | 0.104373 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.63903 | −0.404559 | ||||||||
\(457\) | 20.8957 | 0.977462 | 0.488731 | − | 0.872435i | \(-0.337460\pi\) | ||||
0.488731 | + | 0.872435i | \(0.337460\pi\) | |||||||
\(458\) | −0.671739 | −0.0313883 | ||||||||
\(459\) | −40.8087 | −1.90479 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.3670 | −0.575988 | −0.287994 | − | 0.957632i | \(-0.592988\pi\) | ||||
−0.287994 | + | 0.957632i | \(0.592988\pi\) | |||||||
\(462\) | −31.4268 | −1.46211 | ||||||||
\(463\) | −35.9887 | −1.67254 | −0.836268 | − | 0.548320i | \(-0.815267\pi\) | ||||
−0.836268 | + | 0.548320i | \(0.815267\pi\) | |||||||
\(464\) | −0.940440 | −0.0436588 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.1998 | −0.611468 | ||||||||
\(467\) | −19.4423 | −0.899684 | −0.449842 | − | 0.893108i | \(-0.648520\pi\) | ||||
−0.449842 | + | 0.893108i | \(0.648520\pi\) | |||||||
\(468\) | −0.312239 | −0.0144332 | ||||||||
\(469\) | −23.3222 | −1.07692 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.49608 | −0.345401 | ||||||||
\(472\) | −22.7340 | −1.04642 | ||||||||
\(473\) | −42.1197 | −1.93667 | ||||||||
\(474\) | 6.28625 | 0.288737 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.973067 | −0.0446005 | ||||||||
\(477\) | −3.56382 | −0.163176 | ||||||||
\(478\) | −0.323381 | −0.0147911 | ||||||||
\(479\) | 5.74347 | 0.262426 | 0.131213 | − | 0.991354i | \(-0.458113\pi\) | ||||
0.131213 | + | 0.991354i | \(0.458113\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.89618 | 0.0864583 | ||||||||
\(482\) | 1.43128 | 0.0651932 | ||||||||
\(483\) | −20.5866 | −0.936721 | ||||||||
\(484\) | 1.46854 | 0.0667518 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.0179 | −0.862670 | ||||||||
\(487\) | −7.70331 | −0.349070 | −0.174535 | − | 0.984651i | \(-0.555842\pi\) | ||||
−0.174535 | + | 0.984651i | \(0.555842\pi\) | |||||||
\(488\) | −31.1434 | −1.40980 | ||||||||
\(489\) | −31.5563 | −1.42702 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.3071 | 1.54826 | 0.774128 | − | 0.633029i | \(-0.218189\pi\) | ||||
0.774128 | + | 0.633029i | \(0.218189\pi\) | |||||||
\(492\) | −0.363917 | −0.0164066 | ||||||||
\(493\) | −1.68791 | −0.0760196 | ||||||||
\(494\) | −15.9048 | −0.715589 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.7216 | −0.750823 | ||||||||
\(497\) | 9.93987 | 0.445864 | ||||||||
\(498\) | 8.03490 | 0.360053 | ||||||||
\(499\) | 4.47335 | 0.200255 | 0.100127 | − | 0.994975i | \(-0.468075\pi\) | ||||
0.100127 | + | 0.994975i | \(0.468075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.8770 | −0.932716 | ||||||||
\(502\) | −16.0289 | −0.715403 | ||||||||
\(503\) | −19.9980 | −0.891666 | −0.445833 | − | 0.895116i | \(-0.647092\pi\) | ||||
−0.445833 | + | 0.895116i | \(0.647092\pi\) | |||||||
\(504\) | 10.8584 | 0.483672 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 55.3323 | 2.45982 | ||||||||
\(507\) | −9.17320 | −0.407396 | ||||||||
\(508\) | −0.465096 | −0.0206353 | ||||||||
\(509\) | 8.51666 | 0.377494 | 0.188747 | − | 0.982026i | \(-0.439557\pi\) | ||||
0.188747 | + | 0.982026i | \(0.439557\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.1731 | −1.02512 | ||||||||
\(512\) | −21.7489 | −0.961177 | ||||||||
\(513\) | −13.6907 | −0.604458 | ||||||||
\(514\) | 41.3747 | 1.82496 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.399701 | 0.0175959 | ||||||||
\(517\) | −69.5820 | −3.06021 | ||||||||
\(518\) | 1.64139 | 0.0721186 | ||||||||
\(519\) | −3.01013 | −0.132130 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.77481 | −0.0777559 | −0.0388779 | − | 0.999244i | \(-0.512378\pi\) | ||||
−0.0388779 | + | 0.999244i | \(0.512378\pi\) | |||||||
\(522\) | −0.468842 | −0.0205207 | ||||||||
\(523\) | 11.2858 | 0.493492 | 0.246746 | − | 0.969080i | \(-0.420639\pi\) | ||||
0.246746 | + | 0.969080i | \(0.420639\pi\) | |||||||
\(524\) | −0.487105 | −0.0212793 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 34.9718 | 1.52484 | ||||||||
\(527\) | −30.0121 | −1.30735 | ||||||||
\(528\) | 32.9852 | 1.43550 | ||||||||
\(529\) | 13.2462 | 0.575922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.6091 | −0.503793 | ||||||||
\(532\) | −0.326449 | −0.0141533 | ||||||||
\(533\) | 26.9160 | 1.16586 | ||||||||
\(534\) | 7.88349 | 0.341152 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 23.8979 | 1.03223 | ||||||||
\(537\) | −31.9491 | −1.37870 | ||||||||
\(538\) | −26.7832 | −1.15471 | ||||||||
\(539\) | 2.75959 | 0.118864 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.1557 | −1.55445 | −0.777227 | − | 0.629220i | \(-0.783374\pi\) | ||||
−0.777227 | + | 0.629220i | \(0.783374\pi\) | |||||||
\(542\) | −22.1655 | −0.952090 | ||||||||
\(543\) | −10.0352 | −0.430653 | ||||||||
\(544\) | 2.01900 | 0.0865637 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −22.0576 | −0.943978 | ||||||||
\(547\) | −16.6299 | −0.711045 | −0.355522 | − | 0.934668i | \(-0.615697\pi\) | ||||
−0.355522 | + | 0.934668i | \(0.615697\pi\) | |||||||
\(548\) | −1.12531 | −0.0480708 | ||||||||
\(549\) | −15.9034 | −0.678740 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.566267 | −0.0241238 | ||||||||
\(552\) | 21.0948 | 0.897853 | ||||||||
\(553\) | −9.54306 | −0.405812 | ||||||||
\(554\) | 6.58218 | 0.279650 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.408867 | 0.0173398 | ||||||||
\(557\) | 14.9409 | 0.633067 | 0.316534 | − | 0.948581i | \(-0.397481\pi\) | ||||
0.316534 | + | 0.948581i | \(0.397481\pi\) | |||||||
\(558\) | −8.33631 | −0.352904 | ||||||||
\(559\) | −29.5626 | −1.25037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 59.2020 | 2.49951 | ||||||||
\(562\) | 35.2189 | 1.48562 | ||||||||
\(563\) | 21.4419 | 0.903669 | 0.451835 | − | 0.892102i | \(-0.350770\pi\) | ||||
0.451835 | + | 0.892102i | \(0.350770\pi\) | |||||||
\(564\) | 0.660309 | 0.0278040 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.2971 | 1.02128 | ||||||||
\(567\) | −7.32400 | −0.307579 | ||||||||
\(568\) | −10.1852 | −0.427363 | ||||||||
\(569\) | −43.9351 | −1.84186 | −0.920928 | − | 0.389733i | \(-0.872567\pi\) | ||||
−0.920928 | + | 0.389733i | \(0.872567\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.17887 | −0.216729 | −0.108365 | − | 0.994111i | \(-0.534561\pi\) | ||||
−0.108365 | + | 0.994111i | \(0.534561\pi\) | |||||||
\(572\) | 1.40575 | 0.0587773 | ||||||||
\(573\) | −16.9426 | −0.707788 | ||||||||
\(574\) | 23.2993 | 0.972496 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.1197 | −0.463322 | ||||||||
\(577\) | −28.5960 | −1.19047 | −0.595233 | − | 0.803553i | \(-0.702940\pi\) | ||||
−0.595233 | + | 0.803553i | \(0.702940\pi\) | |||||||
\(578\) | 52.9762 | 2.20352 | ||||||||
\(579\) | −1.56084 | −0.0648664 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.1977 | −0.506044 | ||||||||
\(582\) | −23.2967 | −0.965680 | ||||||||
\(583\) | 16.0449 | 0.664512 | ||||||||
\(584\) | 23.7452 | 0.982583 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.0934 | −0.623501 | ||||||||
\(587\) | −37.0634 | −1.52977 | −0.764885 | − | 0.644166i | \(-0.777204\pi\) | ||||
−0.764885 | + | 0.644166i | \(0.777204\pi\) | |||||||
\(588\) | −0.0261875 | −0.00107995 | ||||||||
\(589\) | −10.0686 | −0.414869 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.7095 | −0.646204 | ||||||||
\(592\) | −1.72278 | −0.0708060 | ||||||||
\(593\) | −10.3353 | −0.424422 | −0.212211 | − | 0.977224i | \(-0.568066\pi\) | ||||
−0.212211 | + | 0.977224i | \(0.568066\pi\) | |||||||
\(594\) | 51.0330 | 2.09391 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.646704 | 0.0264900 | ||||||||
\(597\) | −6.52602 | −0.267092 | ||||||||
\(598\) | 38.8362 | 1.58813 | ||||||||
\(599\) | 4.02899 | 0.164620 | 0.0823100 | − | 0.996607i | \(-0.473770\pi\) | ||||
0.0823100 | + | 0.996607i | \(0.473770\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.22632 | −0.213186 | −0.106593 | − | 0.994303i | \(-0.533994\pi\) | ||||
−0.106593 | + | 0.994303i | \(0.533994\pi\) | |||||||
\(602\) | −25.5904 | −1.04299 | ||||||||
\(603\) | 12.2035 | 0.496964 | ||||||||
\(604\) | −0.688536 | −0.0280161 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.6296 | −0.634909 | ||||||||
\(607\) | −15.4091 | −0.625438 | −0.312719 | − | 0.949846i | \(-0.601240\pi\) | ||||
−0.312719 | + | 0.949846i | \(0.601240\pi\) | |||||||
\(608\) | 0.677341 | 0.0274698 | ||||||||
\(609\) | −0.785330 | −0.0318232 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.8377 | −1.97576 | ||||||||
\(612\) | 0.509163 | 0.0205817 | ||||||||
\(613\) | 1.06481 | 0.0430073 | 0.0215036 | − | 0.999769i | \(-0.493155\pi\) | ||||
0.0215036 | + | 0.999769i | \(0.493155\pi\) | |||||||
\(614\) | 30.1390 | 1.21631 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −48.8863 | −1.96968 | ||||||||
\(617\) | 37.7359 | 1.51919 | 0.759594 | − | 0.650397i | \(-0.225397\pi\) | ||||
0.759594 | + | 0.650397i | \(0.225397\pi\) | |||||||
\(618\) | −10.8908 | −0.438094 | ||||||||
\(619\) | 7.53328 | 0.302788 | 0.151394 | − | 0.988473i | \(-0.451624\pi\) | ||||
0.151394 | + | 0.988473i | \(0.451624\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 33.4298 | 1.34149 | ||||||||
\(622\) | −18.8032 | −0.753940 | ||||||||
\(623\) | −11.9678 | −0.479480 | ||||||||
\(624\) | 23.1514 | 0.926797 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 18.6621 | 0.745888 | ||||||||
\(627\) | 19.8613 | 0.793186 | ||||||||
\(628\) | 0.290252 | 0.0115823 | ||||||||
\(629\) | −3.09207 | −0.123289 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.18895 | −0.325997 | −0.162998 | − | 0.986626i | \(-0.552117\pi\) | ||||
−0.162998 | + | 0.986626i | \(0.552117\pi\) | |||||||
\(632\) | 9.77864 | 0.388973 | ||||||||
\(633\) | −4.70688 | −0.187082 | ||||||||
\(634\) | 25.5919 | 1.01638 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.152260 | −0.00603752 | ||||||||
\(637\) | 1.93688 | 0.0767419 | ||||||||
\(638\) | 2.11080 | 0.0835674 | ||||||||
\(639\) | −5.20109 | −0.205752 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.68523 | 0.224553 | 0.112277 | − | 0.993677i | \(-0.464186\pi\) | ||||
0.112277 | + | 0.993677i | \(0.464186\pi\) | |||||||
\(642\) | −14.6729 | −0.579092 | ||||||||
\(643\) | −37.7503 | −1.48872 | −0.744362 | − | 0.667776i | \(-0.767246\pi\) | ||||
−0.744362 | + | 0.667776i | \(0.767246\pi\) | |||||||
\(644\) | 0.797122 | 0.0314110 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25.9356 | 1.02042 | ||||||||
\(647\) | 4.20432 | 0.165289 | 0.0826445 | − | 0.996579i | \(-0.473663\pi\) | ||||
0.0826445 | + | 0.996579i | \(0.473663\pi\) | |||||||
\(648\) | 7.50480 | 0.294816 | ||||||||
\(649\) | 52.2661 | 2.05163 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.9637 | −0.547280 | ||||||||
\(652\) | 1.22187 | 0.0478523 | ||||||||
\(653\) | 26.8425 | 1.05043 | 0.525214 | − | 0.850970i | \(-0.323985\pi\) | ||||
0.525214 | + | 0.850970i | \(0.323985\pi\) | |||||||
\(654\) | −27.0020 | −1.05586 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −24.4547 | −0.954795 | ||||||||
\(657\) | 12.1255 | 0.473060 | ||||||||
\(658\) | −42.2755 | −1.64807 | ||||||||
\(659\) | 8.37755 | 0.326343 | 0.163171 | − | 0.986598i | \(-0.447828\pi\) | ||||
0.163171 | + | 0.986598i | \(0.447828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.20204 | 0.202336 | 0.101168 | − | 0.994869i | \(-0.467742\pi\) | ||||
0.101168 | + | 0.994869i | \(0.467742\pi\) | |||||||
\(662\) | −41.6012 | −1.61688 | ||||||||
\(663\) | 41.5523 | 1.61376 | ||||||||
\(664\) | 12.4988 | 0.485046 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.858867 | −0.0332804 | ||||||||
\(667\) | 1.38271 | 0.0535387 | ||||||||
\(668\) | 0.808368 | 0.0312767 | ||||||||
\(669\) | 22.7877 | 0.881022 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 71.5996 | 2.76407 | ||||||||
\(672\) | 0.939374 | 0.0362371 | ||||||||
\(673\) | −37.9105 | −1.46134 | −0.730672 | − | 0.682729i | \(-0.760793\pi\) | ||||
−0.730672 | + | 0.682729i | \(0.760793\pi\) | |||||||
\(674\) | 36.4300 | 1.40323 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.355191 | 0.0136612 | ||||||||
\(677\) | −2.59729 | −0.0998221 | −0.0499110 | − | 0.998754i | \(-0.515894\pi\) | ||||
−0.0499110 | + | 0.998754i | \(0.515894\pi\) | |||||||
\(678\) | 2.58711 | 0.0993572 | ||||||||
\(679\) | 35.3664 | 1.35724 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.94919 | −0.0746931 | ||||||||
\(682\) | 37.5314 | 1.43715 | ||||||||
\(683\) | 35.4303 | 1.35570 | 0.677852 | − | 0.735198i | \(-0.262911\pi\) | ||||
0.677852 | + | 0.735198i | \(0.262911\pi\) | |||||||
\(684\) | 0.170816 | 0.00653131 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −25.6327 | −0.978662 | ||||||||
\(687\) | 0.588763 | 0.0224627 | ||||||||
\(688\) | 26.8593 | 1.02400 | ||||||||
\(689\) | 11.2615 | 0.429028 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.68880 | 0.292496 | 0.146248 | − | 0.989248i | \(-0.453280\pi\) | ||||
0.146248 | + | 0.989248i | \(0.453280\pi\) | |||||||
\(692\) | 0.116554 | 0.00443071 | ||||||||
\(693\) | −24.9638 | −0.948295 | ||||||||
\(694\) | −27.3505 | −1.03821 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.804717 | 0.0305027 | ||||||||
\(697\) | −43.8915 | −1.66251 | ||||||||
\(698\) | 16.3640 | 0.619385 | ||||||||
\(699\) | 11.5693 | 0.437590 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.90080 | 0.0717923 | 0.0358962 | − | 0.999356i | \(-0.488571\pi\) | ||||
0.0358962 | + | 0.999356i | \(0.488571\pi\) | |||||||
\(702\) | 35.8186 | 1.35189 | ||||||||
\(703\) | −1.03734 | −0.0391240 | ||||||||
\(704\) | 50.0628 | 1.88681 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27.2733 | −1.02644 | ||||||||
\(707\) | 23.7270 | 0.892347 | ||||||||
\(708\) | −0.495987 | −0.0186403 | ||||||||
\(709\) | −37.7635 | −1.41824 | −0.709118 | − | 0.705090i | \(-0.750907\pi\) | ||||
−0.709118 | + | 0.705090i | \(0.750907\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.99346 | 0.187269 | ||||||||
\(712\) | 12.2632 | 0.459584 | ||||||||
\(713\) | 24.5855 | 0.920733 | ||||||||
\(714\) | 35.9690 | 1.34610 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.23708 | 0.0462320 | ||||||||
\(717\) | 0.283436 | 0.0105851 | ||||||||
\(718\) | 46.7046 | 1.74300 | ||||||||
\(719\) | −14.2675 | −0.532087 | −0.266043 | − | 0.963961i | \(-0.585716\pi\) | ||||
−0.266043 | + | 0.963961i | \(0.585716\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.5332 | 0.615729 | ||||||||
\(722\) | −18.4934 | −0.688253 | ||||||||
\(723\) | −1.25448 | −0.0466548 | ||||||||
\(724\) | 0.388569 | 0.0144410 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −54.2839 | −2.01466 | ||||||||
\(727\) | −48.4790 | −1.79799 | −0.898994 | − | 0.437961i | \(-0.855701\pi\) | ||||
−0.898994 | + | 0.437961i | \(0.855701\pi\) | |||||||
\(728\) | −34.3119 | −1.27168 | ||||||||
\(729\) | 24.7296 | 0.915911 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48.2073 | 1.78301 | ||||||||
\(732\) | −0.679454 | −0.0251134 | ||||||||
\(733\) | −8.26234 | −0.305176 | −0.152588 | − | 0.988290i | \(-0.548761\pi\) | ||||
−0.152588 | + | 0.988290i | \(0.548761\pi\) | |||||||
\(734\) | −37.0873 | −1.36892 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.65393 | −0.0609647 | ||||||||
\(737\) | −54.9420 | −2.02382 | ||||||||
\(738\) | −12.1915 | −0.448776 | ||||||||
\(739\) | −19.8239 | −0.729235 | −0.364618 | − | 0.931157i | \(-0.618800\pi\) | ||||
−0.364618 | + | 0.931157i | \(0.618800\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.9401 | 0.512103 | ||||||||
\(742\) | 9.74829 | 0.357871 | ||||||||
\(743\) | −6.46288 | −0.237100 | −0.118550 | − | 0.992948i | \(-0.537825\pi\) | ||||
−0.118550 | + | 0.992948i | \(0.537825\pi\) | |||||||
\(744\) | 14.3084 | 0.524571 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 24.3857 | 0.892824 | ||||||||
\(747\) | 6.38249 | 0.233523 | ||||||||
\(748\) | −2.29233 | −0.0838159 | ||||||||
\(749\) | 22.2747 | 0.813898 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.3960 | −0.379354 | −0.189677 | − | 0.981846i | \(-0.560744\pi\) | ||||
−0.189677 | + | 0.981846i | \(0.560744\pi\) | |||||||
\(752\) | 44.3718 | 1.61807 | ||||||||
\(753\) | 14.0489 | 0.511970 | ||||||||
\(754\) | 1.48151 | 0.0539535 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.735185 | 0.0267384 | ||||||||
\(757\) | −52.5543 | −1.91012 | −0.955060 | − | 0.296413i | \(-0.904210\pi\) | ||||
−0.955060 | + | 0.296413i | \(0.904210\pi\) | |||||||
\(758\) | 46.3086 | 1.68201 | ||||||||
\(759\) | −48.4974 | −1.76034 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.0555 | 0.509512 | 0.254756 | − | 0.967005i | \(-0.418005\pi\) | ||||
0.254756 | + | 0.967005i | \(0.418005\pi\) | |||||||
\(762\) | 17.1920 | 0.622802 | ||||||||
\(763\) | 40.9914 | 1.48399 | ||||||||
\(764\) | 0.656027 | 0.0237342 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.5399 | 0.633742 | ||||||||
\(767\) | 36.6841 | 1.32459 | ||||||||
\(768\) | −1.46160 | −0.0527410 | ||||||||
\(769\) | 12.0208 | 0.433480 | 0.216740 | − | 0.976229i | \(-0.430458\pi\) | ||||
0.216740 | + | 0.976229i | \(0.430458\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36.2639 | −1.30601 | ||||||||
\(772\) | 0.0604366 | 0.00217516 | ||||||||
\(773\) | 2.43858 | 0.0877097 | 0.0438549 | − | 0.999038i | \(-0.486036\pi\) | ||||
0.0438549 | + | 0.999038i | \(0.486036\pi\) | |||||||
\(774\) | 13.3903 | 0.481305 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −36.2394 | −1.30092 | ||||||||
\(777\) | −1.43864 | −0.0516109 | ||||||||
\(778\) | 42.3228 | 1.51734 | ||||||||
\(779\) | −14.7249 | −0.527574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.4161 | 0.837896 | ||||||||
\(782\) | −63.3296 | −2.26466 | ||||||||
\(783\) | 1.27527 | 0.0455745 | ||||||||
\(784\) | −1.75976 | −0.0628487 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18.0056 | 0.642238 | ||||||||
\(787\) | 53.9723 | 1.92391 | 0.961953 | − | 0.273215i | \(-0.0880870\pi\) | ||||
0.961953 | + | 0.273215i | \(0.0880870\pi\) | |||||||
\(788\) | 0.608281 | 0.0216691 | ||||||||
\(789\) | −30.6519 | −1.09124 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.92745 | −0.139644 | ||||||||
\(792\) | 25.5800 | 0.908946 | ||||||||
\(793\) | 50.2537 | 1.78456 | ||||||||
\(794\) | 35.0499 | 1.24388 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.252691 | 0.00895638 | ||||||||
\(797\) | 20.8297 | 0.737827 | 0.368913 | − | 0.929464i | \(-0.379730\pi\) | ||||
0.368913 | + | 0.929464i | \(0.379730\pi\) | |||||||
\(798\) | 12.0670 | 0.427168 | ||||||||
\(799\) | 79.6388 | 2.81742 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.26222 | 0.221265 | ||||||||
\(802\) | −2.80549 | −0.0990653 | ||||||||
\(803\) | −54.5908 | −1.92647 | ||||||||
\(804\) | 0.521380 | 0.0183877 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.3422 | 0.927866 | ||||||||
\(807\) | 23.4748 | 0.826353 | ||||||||
\(808\) | −24.3127 | −0.855319 | ||||||||
\(809\) | −23.6812 | −0.832585 | −0.416293 | − | 0.909231i | \(-0.636671\pi\) | ||||
−0.416293 | + | 0.909231i | \(0.636671\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.0035 | 1.43983 | 0.719913 | − | 0.694064i | \(-0.244182\pi\) | ||||
0.719913 | + | 0.694064i | \(0.244182\pi\) | |||||||
\(812\) | 0.0304084 | 0.00106712 | ||||||||
\(813\) | 19.4275 | 0.681353 | ||||||||
\(814\) | 3.86676 | 0.135530 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −37.7526 | −1.32160 | ||||||||
\(817\) | 16.1728 | 0.565814 | ||||||||
\(818\) | −16.9691 | −0.593310 | ||||||||
\(819\) | −17.5214 | −0.612246 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.55405 | 0.124037 | 0.0620186 | − | 0.998075i | \(-0.480246\pi\) | ||||
0.0620186 | + | 0.998075i | \(0.480246\pi\) | |||||||
\(822\) | 41.5965 | 1.45084 | ||||||||
\(823\) | −49.8185 | −1.73657 | −0.868283 | − | 0.496070i | \(-0.834776\pi\) | ||||
−0.868283 | + | 0.496070i | \(0.834776\pi\) | |||||||
\(824\) | −16.9413 | −0.590180 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 31.7550 | 1.10490 | ||||||||
\(827\) | 28.2275 | 0.981566 | 0.490783 | − | 0.871282i | \(-0.336711\pi\) | ||||
0.490783 | + | 0.871282i | \(0.336711\pi\) | |||||||
\(828\) | −0.417098 | −0.0144952 | ||||||||
\(829\) | −27.2897 | −0.947810 | −0.473905 | − | 0.880576i | \(-0.657156\pi\) | ||||
−0.473905 | + | 0.880576i | \(0.657156\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.76912 | −0.200128 | ||||||||
\(832\) | 35.1377 | 1.21818 | ||||||||
\(833\) | −3.15843 | −0.109433 | ||||||||
\(834\) | −15.1136 | −0.523340 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.769041 | −0.0265978 | ||||||||
\(837\) | 22.6752 | 0.783768 | ||||||||
\(838\) | −16.2492 | −0.561319 | ||||||||
\(839\) | −32.4642 | −1.12079 | −0.560394 | − | 0.828226i | \(-0.689350\pi\) | ||||
−0.560394 | + | 0.828226i | \(0.689350\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9473 | −0.998181 | ||||||||
\(842\) | −33.0384 | −1.13858 | ||||||||
\(843\) | −30.8685 | −1.06317 | ||||||||
\(844\) | 0.182253 | 0.00627340 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 22.1209 | 0.760531 | ||||||||
\(847\) | 82.4075 | 2.83156 | ||||||||
\(848\) | −10.2317 | −0.351357 | ||||||||
\(849\) | −21.2958 | −0.730871 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.53297 | 0.0868292 | ||||||||
\(852\) | −0.222211 | −0.00761282 | ||||||||
\(853\) | −29.3273 | −1.00415 | −0.502073 | − | 0.864825i | \(-0.667429\pi\) | ||||
−0.502073 | + | 0.864825i | \(0.667429\pi\) | |||||||
\(854\) | 43.5012 | 1.48858 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22.8245 | −0.780126 | ||||||||
\(857\) | −36.6965 | −1.25353 | −0.626764 | − | 0.779209i | \(-0.715621\pi\) | ||||
−0.626764 | + | 0.779209i | \(0.715621\pi\) | |||||||
\(858\) | −51.9628 | −1.77398 | ||||||||
\(859\) | 32.9541 | 1.12438 | 0.562190 | − | 0.827008i | \(-0.309959\pi\) | ||||
0.562190 | + | 0.827008i | \(0.309959\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.4213 | −0.695956 | ||||||||
\(862\) | −32.7163 | −1.11432 | ||||||||
\(863\) | −0.594484 | −0.0202365 | −0.0101182 | − | 0.999949i | \(-0.503221\pi\) | ||||
−0.0101182 | + | 0.999949i | \(0.503221\pi\) | |||||||
\(864\) | −1.52542 | −0.0518958 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −58.0322 | −1.97201 | ||||||||
\(867\) | −46.4323 | −1.57692 | ||||||||
\(868\) | 0.540680 | 0.0183519 | ||||||||
\(869\) | −22.4813 | −0.762627 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.5623 | −1.30663 | ||||||||
\(872\) | −42.0033 | −1.42241 | ||||||||
\(873\) | −18.5057 | −0.626321 | ||||||||
\(874\) | −21.2461 | −0.718659 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.518047 | 0.0175032 | ||||||||
\(877\) | 6.05272 | 0.204386 | 0.102193 | − | 0.994765i | \(-0.467414\pi\) | ||||
0.102193 | + | 0.994765i | \(0.467414\pi\) | |||||||
\(878\) | 30.2641 | 1.02136 | ||||||||
\(879\) | 13.2290 | 0.446201 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.3380 | −0.415678 | −0.207839 | − | 0.978163i | \(-0.566643\pi\) | ||||
−0.207839 | + | 0.978163i | \(0.566643\pi\) | |||||||
\(882\) | −0.877302 | −0.0295403 | ||||||||
\(883\) | 9.65216 | 0.324821 | 0.162411 | − | 0.986723i | \(-0.448073\pi\) | ||||
0.162411 | + | 0.986723i | \(0.448073\pi\) | |||||||
\(884\) | −1.60892 | −0.0541139 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.2321 | −1.01567 | ||||||||
\(887\) | −2.95581 | −0.0992463 | −0.0496231 | − | 0.998768i | \(-0.515802\pi\) | ||||
−0.0496231 | + | 0.998768i | \(0.515802\pi\) | |||||||
\(888\) | 1.47415 | 0.0494693 | ||||||||
\(889\) | −26.0990 | −0.875332 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.2537 | −0.578021 | ||||||||
\(892\) | −0.882349 | −0.0295432 | ||||||||
\(893\) | 26.7176 | 0.894069 | ||||||||
\(894\) | −23.9051 | −0.799506 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 31.9139 | 1.06617 | ||||||||
\(897\) | −34.0390 | −1.13653 | ||||||||
\(898\) | −15.1371 | −0.505133 | ||||||||
\(899\) | 0.937879 | 0.0312800 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.3639 | −0.611790 | ||||||||
\(902\) | 54.8881 | 1.82757 | ||||||||
\(903\) | 22.4293 | 0.746401 | ||||||||
\(904\) | 4.02440 | 0.133849 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 25.4514 | 0.845566 | ||||||||
\(907\) | 4.99717 | 0.165928 | 0.0829641 | − | 0.996553i | \(-0.473561\pi\) | ||||
0.0829641 | + | 0.996553i | \(0.473561\pi\) | |||||||
\(908\) | 0.0754736 | 0.00250468 | ||||||||
\(909\) | −12.4153 | −0.411789 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.8938 | 0.758505 | 0.379252 | − | 0.925293i | \(-0.376181\pi\) | ||||
0.379252 | + | 0.925293i | \(0.376181\pi\) | |||||||
\(912\) | −12.6654 | −0.419393 | ||||||||
\(913\) | −28.7350 | −0.950990 | ||||||||
\(914\) | 29.9078 | 0.989261 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.0227972 | −0.000753240 0 | ||||||||
\(917\) | −27.3340 | −0.902649 | ||||||||
\(918\) | −58.4088 | −1.92778 | ||||||||
\(919\) | 41.2946 | 1.36218 | 0.681092 | − | 0.732198i | \(-0.261505\pi\) | ||||
0.681092 | + | 0.732198i | \(0.261505\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.4161 | −0.870440 | ||||||||
\(922\) | −17.7007 | −0.582940 | ||||||||
\(923\) | 16.4351 | 0.540969 | ||||||||
\(924\) | −1.06655 | −0.0350869 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −51.5101 | −1.69273 | ||||||||
\(927\) | −8.65109 | −0.284139 | ||||||||
\(928\) | −0.0630936 | −0.00207115 | ||||||||
\(929\) | −25.0144 | −0.820695 | −0.410347 | − | 0.911929i | \(-0.634593\pi\) | ||||
−0.410347 | + | 0.911929i | \(0.634593\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.05960 | −0.0347271 | ||||||||
\(932\) | −0.447968 | −0.0146737 | ||||||||
\(933\) | 16.4806 | 0.539549 | ||||||||
\(934\) | −27.8275 | −0.910544 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 17.9539 | 0.586841 | ||||||||
\(937\) | 23.0290 | 0.752326 | 0.376163 | − | 0.926554i | \(-0.377243\pi\) | ||||
0.376163 | + | 0.926554i | \(0.377243\pi\) | |||||||
\(938\) | −33.3807 | −1.08992 | ||||||||
\(939\) | −16.3569 | −0.533786 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.9931 | −1.23854 | −0.619271 | − | 0.785178i | \(-0.712572\pi\) | ||||
−0.619271 | + | 0.785178i | \(0.712572\pi\) | |||||||
\(942\) | −10.7290 | −0.349570 | ||||||||
\(943\) | 35.9552 | 1.17086 | ||||||||
\(944\) | −33.3296 | −1.08479 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −60.2853 | −1.96004 | ||||||||
\(947\) | −10.7536 | −0.349446 | −0.174723 | − | 0.984618i | \(-0.555903\pi\) | ||||
−0.174723 | + | 0.984618i | \(0.555903\pi\) | |||||||
\(948\) | 0.213340 | 0.00692896 | ||||||||
\(949\) | −38.3158 | −1.24378 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.4306 | −0.727364 | ||||||||
\(952\) | 55.9519 | 1.81341 | ||||||||
\(953\) | 26.7122 | 0.865294 | 0.432647 | − | 0.901563i | \(-0.357580\pi\) | ||||
0.432647 | + | 0.901563i | \(0.357580\pi\) | |||||||
\(954\) | −5.10085 | −0.165146 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.0109748 | −0.000354949 0 | ||||||||
\(957\) | −1.85006 | −0.0598041 | ||||||||
\(958\) | 8.22054 | 0.265594 | ||||||||
\(959\) | −63.1470 | −2.03912 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.3239 | −0.462062 | ||||||||
\(962\) | 2.71397 | 0.0875019 | ||||||||
\(963\) | −11.6553 | −0.375588 | ||||||||
\(964\) | 0.0485743 | 0.00156447 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −29.4652 | −0.948028 | ||||||||
\(967\) | −60.3341 | −1.94021 | −0.970107 | − | 0.242678i | \(-0.921974\pi\) | ||||
−0.970107 | + | 0.242678i | \(0.921974\pi\) | |||||||
\(968\) | −84.4418 | −2.71406 | ||||||||
\(969\) | −22.7319 | −0.730255 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.6051 | −1.72027 | −0.860135 | − | 0.510067i | \(-0.829621\pi\) | ||||
−0.860135 | + | 0.510067i | \(0.829621\pi\) | |||||||
\(972\) | −0.645421 | −0.0207019 | ||||||||
\(973\) | 22.9437 | 0.735540 | ||||||||
\(974\) | −11.0256 | −0.353284 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −45.6583 | −1.46149 | ||||||||
\(977\) | 8.77988 | 0.280893 | 0.140447 | − | 0.990088i | \(-0.455146\pi\) | ||||
0.140447 | + | 0.990088i | \(0.455146\pi\) | |||||||
\(978\) | −45.1660 | −1.44425 | ||||||||
\(979\) | −28.1935 | −0.901069 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.4490 | −0.684813 | ||||||||
\(982\) | 49.1032 | 1.56695 | ||||||||
\(983\) | 25.0304 | 0.798346 | 0.399173 | − | 0.916876i | \(-0.369297\pi\) | ||||
0.399173 | + | 0.916876i | \(0.369297\pi\) | |||||||
\(984\) | 20.9254 | 0.667078 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.41588 | −0.0769372 | ||||||||
\(987\) | 37.0534 | 1.17942 | ||||||||
\(988\) | −0.539768 | −0.0171723 | ||||||||
\(989\) | −39.4907 | −1.25573 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.6686 | 0.910690 | 0.455345 | − | 0.890315i | \(-0.349516\pi\) | ||||
0.455345 | + | 0.890315i | \(0.349516\pi\) | |||||||
\(992\) | −1.12185 | −0.0356186 | ||||||||
\(993\) | 36.4624 | 1.15710 | ||||||||
\(994\) | 14.2268 | 0.451246 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.272685 | 0.00864035 | ||||||||
\(997\) | 36.7733 | 1.16462 | 0.582312 | − | 0.812966i | \(-0.302148\pi\) | ||||
0.582312 | + | 0.812966i | \(0.302148\pi\) | |||||||
\(998\) | 6.40263 | 0.202672 | ||||||||
\(999\) | 2.33616 | 0.0739128 |
(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 | 6025.2.a.k.1.18 | 25 | ||
5.4 | even | 2 | 1205.2.a.d.1.8 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.a.d.1.8 | ✓ | 25 | 5.4 | even | 2 | ||
6025.2.a.k.1.18 | 25 | 1.1 | even | 1 | trivial |