Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1681,2,Mod(1,1681)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1681, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1681.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1681 = 41^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1681.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: | \(13.4228525798\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 41) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 1681.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.706693 | 0.499707 | 0.249854 | − | 0.968284i | \(-0.419618\pi\) | ||||
0.249854 | + | 0.968284i | \(0.419618\pi\) | |||||||
\(3\) | −0.343106 | −0.198093 | −0.0990463 | − | 0.995083i | \(-0.531579\pi\) | ||||
−0.0990463 | + | 0.995083i | \(0.531579\pi\) | |||||||
\(4\) | −1.50059 | −0.750293 | ||||||||
\(5\) | −2.37819 | −1.06356 | −0.531779 | − | 0.846883i | \(-0.678476\pi\) | ||||
−0.531779 | + | 0.846883i | \(0.678476\pi\) | |||||||
\(6\) | −0.242471 | −0.0989883 | ||||||||
\(7\) | 4.91274 | 1.85684 | 0.928420 | − | 0.371531i | \(-0.121167\pi\) | ||||
0.928420 | + | 0.371531i | \(0.121167\pi\) | |||||||
\(8\) | −2.47384 | −0.874634 | ||||||||
\(9\) | −2.88228 | −0.960759 | ||||||||
\(10\) | −1.68065 | −0.531467 | ||||||||
\(11\) | −1.70460 | −0.513955 | −0.256977 | − | 0.966417i | \(-0.582727\pi\) | ||||
−0.256977 | + | 0.966417i | \(0.582727\pi\) | |||||||
\(12\) | 0.514861 | 0.148627 | ||||||||
\(13\) | −3.97013 | −1.10112 | −0.550558 | − | 0.834797i | \(-0.685585\pi\) | ||||
−0.550558 | + | 0.834797i | \(0.685585\pi\) | |||||||
\(14\) | 3.47180 | 0.927877 | ||||||||
\(15\) | 0.815971 | 0.210683 | ||||||||
\(16\) | 1.25293 | 0.313232 | ||||||||
\(17\) | 2.74718 | 0.666288 | 0.333144 | − | 0.942876i | \(-0.391890\pi\) | ||||
0.333144 | + | 0.942876i | \(0.391890\pi\) | |||||||
\(18\) | −2.03688 | −0.480098 | ||||||||
\(19\) | 0.965030 | 0.221393 | 0.110697 | − | 0.993854i | \(-0.464692\pi\) | ||||
0.110697 | + | 0.993854i | \(0.464692\pi\) | |||||||
\(20\) | 3.56867 | 0.797979 | ||||||||
\(21\) | −1.68559 | −0.367826 | ||||||||
\(22\) | −1.20463 | −0.256827 | ||||||||
\(23\) | 6.75640 | 1.40881 | 0.704403 | − | 0.709800i | \(-0.251215\pi\) | ||||
0.704403 | + | 0.709800i | \(0.251215\pi\) | |||||||
\(24\) | 0.848790 | 0.173258 | ||||||||
\(25\) | 0.655768 | 0.131154 | ||||||||
\(26\) | −2.80566 | −0.550236 | ||||||||
\(27\) | 2.01825 | 0.388412 | ||||||||
\(28\) | −7.37199 | −1.39317 | ||||||||
\(29\) | −0.507132 | −0.0941721 | −0.0470860 | − | 0.998891i | \(-0.514993\pi\) | ||||
−0.0470860 | + | 0.998891i | \(0.514993\pi\) | |||||||
\(30\) | 0.576641 | 0.105280 | ||||||||
\(31\) | −0.590143 | −0.105993 | −0.0529964 | − | 0.998595i | \(-0.516877\pi\) | ||||
−0.0529964 | + | 0.998595i | \(0.516877\pi\) | |||||||
\(32\) | 5.83311 | 1.03116 | ||||||||
\(33\) | 0.584858 | 0.101811 | ||||||||
\(34\) | 1.94141 | 0.332949 | ||||||||
\(35\) | −11.6834 | −1.97486 | ||||||||
\(36\) | 4.32510 | 0.720851 | ||||||||
\(37\) | 4.25416 | 0.699380 | 0.349690 | − | 0.936866i | \(-0.386287\pi\) | ||||
0.349690 | + | 0.936866i | \(0.386287\pi\) | |||||||
\(38\) | 0.681980 | 0.110632 | ||||||||
\(39\) | 1.36218 | 0.218123 | ||||||||
\(40\) | 5.88325 | 0.930223 | ||||||||
\(41\) | 0 | 0 | ||||||||
\(42\) | −1.19120 | −0.183805 | ||||||||
\(43\) | −5.38687 | −0.821490 | −0.410745 | − | 0.911750i | \(-0.634731\pi\) | ||||
−0.410745 | + | 0.911750i | \(0.634731\pi\) | |||||||
\(44\) | 2.55789 | 0.385617 | ||||||||
\(45\) | 6.85459 | 1.02182 | ||||||||
\(46\) | 4.77470 | 0.703990 | ||||||||
\(47\) | 5.02690 | 0.733249 | 0.366624 | − | 0.930369i | \(-0.380513\pi\) | ||||
0.366624 | + | 0.930369i | \(0.380513\pi\) | |||||||
\(48\) | −0.429888 | −0.0620490 | ||||||||
\(49\) | 17.1350 | 2.44786 | ||||||||
\(50\) | 0.463426 | 0.0655384 | ||||||||
\(51\) | −0.942574 | −0.131987 | ||||||||
\(52\) | 5.95752 | 0.826160 | ||||||||
\(53\) | 7.62835 | 1.04783 | 0.523917 | − | 0.851769i | \(-0.324470\pi\) | ||||
0.523917 | + | 0.851769i | \(0.324470\pi\) | |||||||
\(54\) | 1.42628 | 0.194092 | ||||||||
\(55\) | 4.05385 | 0.546620 | ||||||||
\(56\) | −12.1533 | −1.62406 | ||||||||
\(57\) | −0.331108 | −0.0438563 | ||||||||
\(58\) | −0.358387 | −0.0470585 | ||||||||
\(59\) | 8.42739 | 1.09715 | 0.548577 | − | 0.836100i | \(-0.315170\pi\) | ||||
0.548577 | + | 0.836100i | \(0.315170\pi\) | |||||||
\(60\) | −1.22443 | −0.158074 | ||||||||
\(61\) | 0.695295 | 0.0890234 | 0.0445117 | − | 0.999009i | \(-0.485827\pi\) | ||||
0.0445117 | + | 0.999009i | \(0.485827\pi\) | |||||||
\(62\) | −0.417049 | −0.0529653 | ||||||||
\(63\) | −14.1599 | −1.78398 | ||||||||
\(64\) | 1.61636 | 0.202045 | ||||||||
\(65\) | 9.44171 | 1.17110 | ||||||||
\(66\) | 0.413315 | 0.0508755 | ||||||||
\(67\) | −4.08016 | −0.498471 | −0.249235 | − | 0.968443i | \(-0.580179\pi\) | ||||
−0.249235 | + | 0.968443i | \(0.580179\pi\) | |||||||
\(68\) | −4.12237 | −0.499911 | ||||||||
\(69\) | −2.31816 | −0.279074 | ||||||||
\(70\) | −8.25658 | −0.986850 | ||||||||
\(71\) | 7.27140 | 0.862956 | 0.431478 | − | 0.902123i | \(-0.357992\pi\) | ||||
0.431478 | + | 0.902123i | \(0.357992\pi\) | |||||||
\(72\) | 7.13029 | 0.840313 | ||||||||
\(73\) | 9.72685 | 1.13844 | 0.569221 | − | 0.822185i | \(-0.307245\pi\) | ||||
0.569221 | + | 0.822185i | \(0.307245\pi\) | |||||||
\(74\) | 3.00638 | 0.349485 | ||||||||
\(75\) | −0.224998 | −0.0259806 | ||||||||
\(76\) | −1.44811 | −0.166110 | ||||||||
\(77\) | −8.37423 | −0.954332 | ||||||||
\(78\) | 0.962641 | 0.108998 | ||||||||
\(79\) | −8.70415 | −0.979294 | −0.489647 | − | 0.871921i | \(-0.662874\pi\) | ||||
−0.489647 | + | 0.871921i | \(0.662874\pi\) | |||||||
\(80\) | −2.97970 | −0.333140 | ||||||||
\(81\) | 7.95436 | 0.883818 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.81920 | 0.528976 | 0.264488 | − | 0.964389i | \(-0.414797\pi\) | ||||
0.264488 | + | 0.964389i | \(0.414797\pi\) | |||||||
\(84\) | 2.52938 | 0.275978 | ||||||||
\(85\) | −6.53329 | −0.708635 | ||||||||
\(86\) | −3.80686 | −0.410504 | ||||||||
\(87\) | 0.174000 | 0.0186548 | ||||||||
\(88\) | 4.21689 | 0.449522 | ||||||||
\(89\) | 3.68307 | 0.390405 | 0.195202 | − | 0.980763i | \(-0.437464\pi\) | ||||
0.195202 | + | 0.980763i | \(0.437464\pi\) | |||||||
\(90\) | 4.84409 | 0.510612 | ||||||||
\(91\) | −19.5042 | −2.04460 | ||||||||
\(92\) | −10.1386 | −1.05702 | ||||||||
\(93\) | 0.202482 | 0.0209964 | ||||||||
\(94\) | 3.55247 | 0.366410 | ||||||||
\(95\) | −2.29502 | −0.235464 | ||||||||
\(96\) | −2.00138 | −0.204265 | ||||||||
\(97\) | 4.08190 | 0.414454 | 0.207227 | − | 0.978293i | \(-0.433556\pi\) | ||||
0.207227 | + | 0.978293i | \(0.433556\pi\) | |||||||
\(98\) | 12.1092 | 1.22321 | ||||||||
\(99\) | 4.91312 | 0.493787 | ||||||||
\(100\) | −0.984036 | −0.0984036 | ||||||||
\(101\) | −10.4203 | −1.03686 | −0.518428 | − | 0.855121i | \(-0.673482\pi\) | ||||
−0.518428 | + | 0.855121i | \(0.673482\pi\) | |||||||
\(102\) | −0.666110 | −0.0659547 | ||||||||
\(103\) | 0.409816 | 0.0403804 | 0.0201902 | − | 0.999796i | \(-0.493573\pi\) | ||||
0.0201902 | + | 0.999796i | \(0.493573\pi\) | |||||||
\(104\) | 9.82146 | 0.963073 | ||||||||
\(105\) | 4.00865 | 0.391204 | ||||||||
\(106\) | 5.39090 | 0.523611 | ||||||||
\(107\) | 13.9793 | 1.35143 | 0.675715 | − | 0.737163i | \(-0.263835\pi\) | ||||
0.675715 | + | 0.737163i | \(0.263835\pi\) | |||||||
\(108\) | −3.02855 | −0.291423 | ||||||||
\(109\) | 15.3340 | 1.46873 | 0.734366 | − | 0.678753i | \(-0.237479\pi\) | ||||
0.734366 | + | 0.678753i | \(0.237479\pi\) | |||||||
\(110\) | 2.86482 | 0.273150 | ||||||||
\(111\) | −1.45963 | −0.138542 | ||||||||
\(112\) | 6.15531 | 0.581622 | ||||||||
\(113\) | 8.06399 | 0.758596 | 0.379298 | − | 0.925274i | \(-0.376165\pi\) | ||||
0.379298 | + | 0.925274i | \(0.376165\pi\) | |||||||
\(114\) | −0.233992 | −0.0219153 | ||||||||
\(115\) | −16.0680 | −1.49835 | ||||||||
\(116\) | 0.760995 | 0.0706566 | ||||||||
\(117\) | 11.4430 | 1.05791 | ||||||||
\(118\) | 5.95558 | 0.548255 | ||||||||
\(119\) | 13.4962 | 1.23719 | ||||||||
\(120\) | −2.01858 | −0.184270 | ||||||||
\(121\) | −8.09435 | −0.735850 | ||||||||
\(122\) | 0.491360 | 0.0444856 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.885560 | 0.0795256 | ||||||||
\(125\) | 10.3314 | 0.924068 | ||||||||
\(126\) | −10.0067 | −0.891466 | ||||||||
\(127\) | −10.7614 | −0.954923 | −0.477462 | − | 0.878653i | \(-0.658443\pi\) | ||||
−0.477462 | + | 0.878653i | \(0.658443\pi\) | |||||||
\(128\) | −10.5240 | −0.930195 | ||||||||
\(129\) | 1.84827 | 0.162731 | ||||||||
\(130\) | 6.67239 | 0.585207 | ||||||||
\(131\) | −16.2642 | −1.42101 | −0.710505 | − | 0.703692i | \(-0.751534\pi\) | ||||
−0.710505 | + | 0.703692i | \(0.751534\pi\) | |||||||
\(132\) | −0.877629 | −0.0763878 | ||||||||
\(133\) | 4.74094 | 0.411092 | ||||||||
\(134\) | −2.88342 | −0.249089 | ||||||||
\(135\) | −4.79977 | −0.413098 | ||||||||
\(136\) | −6.79607 | −0.582758 | ||||||||
\(137\) | 17.7338 | 1.51510 | 0.757549 | − | 0.652779i | \(-0.226397\pi\) | ||||
0.757549 | + | 0.652779i | \(0.226397\pi\) | |||||||
\(138\) | −1.63823 | −0.139455 | ||||||||
\(139\) | −2.13028 | −0.180688 | −0.0903438 | − | 0.995911i | \(-0.528797\pi\) | ||||
−0.0903438 | + | 0.995911i | \(0.528797\pi\) | |||||||
\(140\) | 17.5320 | 1.48172 | ||||||||
\(141\) | −1.72476 | −0.145251 | ||||||||
\(142\) | 5.13864 | 0.431225 | ||||||||
\(143\) | 6.76747 | 0.565924 | ||||||||
\(144\) | −3.61129 | −0.300941 | ||||||||
\(145\) | 1.20605 | 0.100157 | ||||||||
\(146\) | 6.87389 | 0.568888 | ||||||||
\(147\) | −5.87913 | −0.484902 | ||||||||
\(148\) | −6.38373 | −0.524740 | ||||||||
\(149\) | −1.51731 | −0.124303 | −0.0621513 | − | 0.998067i | \(-0.519796\pi\) | ||||
−0.0621513 | + | 0.998067i | \(0.519796\pi\) | |||||||
\(150\) | −0.159005 | −0.0129827 | ||||||||
\(151\) | 2.09591 | 0.170563 | 0.0852815 | − | 0.996357i | \(-0.472821\pi\) | ||||
0.0852815 | + | 0.996357i | \(0.472821\pi\) | |||||||
\(152\) | −2.38733 | −0.193638 | ||||||||
\(153\) | −7.91812 | −0.640142 | ||||||||
\(154\) | −5.91801 | −0.476887 | ||||||||
\(155\) | 1.40347 | 0.112729 | ||||||||
\(156\) | −2.04406 | −0.163656 | ||||||||
\(157\) | −6.91424 | −0.551816 | −0.275908 | − | 0.961184i | \(-0.588979\pi\) | ||||
−0.275908 | + | 0.961184i | \(0.588979\pi\) | |||||||
\(158\) | −6.15116 | −0.489360 | ||||||||
\(159\) | −2.61734 | −0.207568 | ||||||||
\(160\) | −13.8722 | −1.09670 | ||||||||
\(161\) | 33.1924 | 2.61593 | ||||||||
\(162\) | 5.62129 | 0.441650 | ||||||||
\(163\) | 7.72291 | 0.604905 | 0.302453 | − | 0.953164i | \(-0.402195\pi\) | ||||
0.302453 | + | 0.953164i | \(0.402195\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.39090 | −0.108281 | ||||||||
\(166\) | 3.40569 | 0.264333 | ||||||||
\(167\) | 18.9794 | 1.46867 | 0.734336 | − | 0.678786i | \(-0.237494\pi\) | ||||
0.734336 | + | 0.678786i | \(0.237494\pi\) | |||||||
\(168\) | 4.16988 | 0.321713 | ||||||||
\(169\) | 2.76194 | 0.212457 | ||||||||
\(170\) | −4.61703 | −0.354110 | ||||||||
\(171\) | −2.78149 | −0.212706 | ||||||||
\(172\) | 8.08346 | 0.616358 | ||||||||
\(173\) | 12.9720 | 0.986242 | 0.493121 | − | 0.869961i | \(-0.335856\pi\) | ||||
0.493121 | + | 0.869961i | \(0.335856\pi\) | |||||||
\(174\) | 0.122965 | 0.00932193 | ||||||||
\(175\) | 3.22162 | 0.243531 | ||||||||
\(176\) | −2.13574 | −0.160987 | ||||||||
\(177\) | −2.89149 | −0.217338 | ||||||||
\(178\) | 2.60280 | 0.195088 | ||||||||
\(179\) | −0.553509 | −0.0413712 | −0.0206856 | − | 0.999786i | \(-0.506585\pi\) | ||||
−0.0206856 | + | 0.999786i | \(0.506585\pi\) | |||||||
\(180\) | −10.2859 | −0.766666 | ||||||||
\(181\) | −24.0251 | −1.78577 | −0.892885 | − | 0.450285i | \(-0.851322\pi\) | ||||
−0.892885 | + | 0.450285i | \(0.851322\pi\) | |||||||
\(182\) | −13.7835 | −1.02170 | ||||||||
\(183\) | −0.238560 | −0.0176349 | ||||||||
\(184\) | −16.7142 | −1.23219 | ||||||||
\(185\) | −10.1172 | −0.743830 | ||||||||
\(186\) | 0.143092 | 0.0104920 | ||||||||
\(187\) | −4.68282 | −0.342442 | ||||||||
\(188\) | −7.54329 | −0.550151 | ||||||||
\(189\) | 9.91512 | 0.721219 | ||||||||
\(190\) | −1.62187 | −0.117663 | ||||||||
\(191\) | −12.4328 | −0.899606 | −0.449803 | − | 0.893128i | \(-0.648506\pi\) | ||||
−0.449803 | + | 0.893128i | \(0.648506\pi\) | |||||||
\(192\) | −0.554583 | −0.0400236 | ||||||||
\(193\) | 3.25333 | 0.234179 | 0.117090 | − | 0.993121i | \(-0.462643\pi\) | ||||
0.117090 | + | 0.993121i | \(0.462643\pi\) | |||||||
\(194\) | 2.88465 | 0.207106 | ||||||||
\(195\) | −3.23951 | −0.231986 | ||||||||
\(196\) | −25.7125 | −1.83661 | ||||||||
\(197\) | 13.5417 | 0.964807 | 0.482404 | − | 0.875949i | \(-0.339764\pi\) | ||||
0.482404 | + | 0.875949i | \(0.339764\pi\) | |||||||
\(198\) | 3.47206 | 0.246749 | ||||||||
\(199\) | −9.27629 | −0.657578 | −0.328789 | − | 0.944403i | \(-0.606641\pi\) | ||||
−0.328789 | + | 0.944403i | \(0.606641\pi\) | |||||||
\(200\) | −1.62226 | −0.114711 | ||||||||
\(201\) | 1.39993 | 0.0987434 | ||||||||
\(202\) | −7.36393 | −0.518124 | ||||||||
\(203\) | −2.49141 | −0.174863 | ||||||||
\(204\) | 1.41441 | 0.0990287 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.289614 | 0.0201784 | ||||||||
\(207\) | −19.4738 | −1.35352 | ||||||||
\(208\) | −4.97429 | −0.344905 | ||||||||
\(209\) | −1.64499 | −0.113786 | ||||||||
\(210\) | 2.83288 | 0.195488 | ||||||||
\(211\) | −27.2206 | −1.87394 | −0.936972 | − | 0.349405i | \(-0.886384\pi\) | ||||
−0.936972 | + | 0.349405i | \(0.886384\pi\) | |||||||
\(212\) | −11.4470 | −0.786183 | ||||||||
\(213\) | −2.49486 | −0.170945 | ||||||||
\(214\) | 9.87907 | 0.675320 | ||||||||
\(215\) | 12.8110 | 0.873702 | ||||||||
\(216\) | −4.99282 | −0.339718 | ||||||||
\(217\) | −2.89922 | −0.196812 | ||||||||
\(218\) | 10.8364 | 0.733936 | ||||||||
\(219\) | −3.33735 | −0.225517 | ||||||||
\(220\) | −6.08314 | −0.410125 | ||||||||
\(221\) | −10.9066 | −0.733660 | ||||||||
\(222\) | −1.03151 | −0.0692304 | ||||||||
\(223\) | 9.53126 | 0.638260 | 0.319130 | − | 0.947711i | \(-0.396609\pi\) | ||||
0.319130 | + | 0.947711i | \(0.396609\pi\) | |||||||
\(224\) | 28.6566 | 1.91470 | ||||||||
\(225\) | −1.89011 | −0.126007 | ||||||||
\(226\) | 5.69876 | 0.379076 | ||||||||
\(227\) | −1.52258 | −0.101057 | −0.0505286 | − | 0.998723i | \(-0.516091\pi\) | ||||
−0.0505286 | + | 0.998723i | \(0.516091\pi\) | |||||||
\(228\) | 0.496856 | 0.0329051 | ||||||||
\(229\) | −14.7408 | −0.974099 | −0.487049 | − | 0.873374i | \(-0.661927\pi\) | ||||
−0.487049 | + | 0.873374i | \(0.661927\pi\) | |||||||
\(230\) | −11.3551 | −0.748734 | ||||||||
\(231\) | 2.87325 | 0.189046 | ||||||||
\(232\) | 1.25456 | 0.0823661 | ||||||||
\(233\) | −14.8872 | −0.975290 | −0.487645 | − | 0.873042i | \(-0.662144\pi\) | ||||
−0.487645 | + | 0.873042i | \(0.662144\pi\) | |||||||
\(234\) | 8.08670 | 0.528644 | ||||||||
\(235\) | −11.9549 | −0.779852 | ||||||||
\(236\) | −12.6460 | −0.823186 | ||||||||
\(237\) | 2.98645 | 0.193991 | ||||||||
\(238\) | 9.53763 | 0.618233 | ||||||||
\(239\) | −13.3732 | −0.865040 | −0.432520 | − | 0.901624i | \(-0.642375\pi\) | ||||
−0.432520 | + | 0.901624i | \(0.642375\pi\) | |||||||
\(240\) | 1.02235 | 0.0659926 | ||||||||
\(241\) | −3.99525 | −0.257357 | −0.128678 | − | 0.991686i | \(-0.541073\pi\) | ||||
−0.128678 | + | 0.991686i | \(0.541073\pi\) | |||||||
\(242\) | −5.72022 | −0.367710 | ||||||||
\(243\) | −8.78393 | −0.563490 | ||||||||
\(244\) | −1.04335 | −0.0667936 | ||||||||
\(245\) | −40.7502 | −2.60344 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.83130 | −0.243780 | ||||||||
\(248\) | 1.45992 | 0.0927048 | ||||||||
\(249\) | −1.65350 | −0.104786 | ||||||||
\(250\) | 7.30112 | 0.461763 | ||||||||
\(251\) | 27.3187 | 1.72434 | 0.862171 | − | 0.506618i | \(-0.169104\pi\) | ||||
0.862171 | + | 0.506618i | \(0.169104\pi\) | |||||||
\(252\) | 21.2481 | 1.33851 | ||||||||
\(253\) | −11.5169 | −0.724063 | ||||||||
\(254\) | −7.60503 | −0.477182 | ||||||||
\(255\) | 2.24162 | 0.140375 | ||||||||
\(256\) | −10.6699 | −0.666870 | ||||||||
\(257\) | 7.49785 | 0.467703 | 0.233851 | − | 0.972272i | \(-0.424867\pi\) | ||||
0.233851 | + | 0.972272i | \(0.424867\pi\) | |||||||
\(258\) | 1.30616 | 0.0813179 | ||||||||
\(259\) | 20.8996 | 1.29864 | ||||||||
\(260\) | −14.1681 | −0.878668 | ||||||||
\(261\) | 1.46170 | 0.0904767 | ||||||||
\(262\) | −11.4938 | −0.710089 | ||||||||
\(263\) | −11.9205 | −0.735048 | −0.367524 | − | 0.930014i | \(-0.619794\pi\) | ||||
−0.367524 | + | 0.930014i | \(0.619794\pi\) | |||||||
\(264\) | −1.44684 | −0.0890470 | ||||||||
\(265\) | −18.1416 | −1.11443 | ||||||||
\(266\) | 3.35039 | 0.205426 | ||||||||
\(267\) | −1.26369 | −0.0773363 | ||||||||
\(268\) | 6.12263 | 0.373999 | ||||||||
\(269\) | −21.1828 | −1.29154 | −0.645769 | − | 0.763533i | \(-0.723463\pi\) | ||||
−0.645769 | + | 0.763533i | \(0.723463\pi\) | |||||||
\(270\) | −3.39196 | −0.206428 | ||||||||
\(271\) | −3.83247 | −0.232806 | −0.116403 | − | 0.993202i | \(-0.537136\pi\) | ||||
−0.116403 | + | 0.993202i | \(0.537136\pi\) | |||||||
\(272\) | 3.44201 | 0.208703 | ||||||||
\(273\) | 6.69202 | 0.405020 | ||||||||
\(274\) | 12.5323 | 0.757105 | ||||||||
\(275\) | −1.11782 | −0.0674070 | ||||||||
\(276\) | 3.47860 | 0.209387 | ||||||||
\(277\) | −1.16792 | −0.0701734 | −0.0350867 | − | 0.999384i | \(-0.511171\pi\) | ||||
−0.0350867 | + | 0.999384i | \(0.511171\pi\) | |||||||
\(278\) | −1.50545 | −0.0902909 | ||||||||
\(279\) | 1.70096 | 0.101834 | ||||||||
\(280\) | 28.9029 | 1.72728 | ||||||||
\(281\) | 17.6959 | 1.05565 | 0.527826 | − | 0.849353i | \(-0.323007\pi\) | ||||
0.527826 | + | 0.849353i | \(0.323007\pi\) | |||||||
\(282\) | −1.21888 | −0.0725830 | ||||||||
\(283\) | 7.41025 | 0.440494 | 0.220247 | − | 0.975444i | \(-0.429314\pi\) | ||||
0.220247 | + | 0.975444i | \(0.429314\pi\) | |||||||
\(284\) | −10.9114 | −0.647470 | ||||||||
\(285\) | 0.787437 | 0.0466437 | ||||||||
\(286\) | 4.78252 | 0.282796 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −16.8126 | −0.990695 | ||||||||
\(289\) | −9.45303 | −0.556060 | ||||||||
\(290\) | 0.852310 | 0.0500494 | ||||||||
\(291\) | −1.40053 | −0.0821003 | ||||||||
\(292\) | −14.5960 | −0.854165 | ||||||||
\(293\) | −10.3526 | −0.604803 | −0.302401 | − | 0.953181i | \(-0.597788\pi\) | ||||
−0.302401 | + | 0.953181i | \(0.597788\pi\) | |||||||
\(294\) | −4.15474 | −0.242309 | ||||||||
\(295\) | −20.0419 | −1.16689 | ||||||||
\(296\) | −10.5241 | −0.611701 | ||||||||
\(297\) | −3.44030 | −0.199626 | ||||||||
\(298\) | −1.07227 | −0.0621149 | ||||||||
\(299\) | −26.8238 | −1.55126 | ||||||||
\(300\) | 0.337629 | 0.0194930 | ||||||||
\(301\) | −26.4643 | −1.52538 | ||||||||
\(302\) | 1.48117 | 0.0852315 | ||||||||
\(303\) | 3.57526 | 0.205393 | ||||||||
\(304\) | 1.20911 | 0.0693474 | ||||||||
\(305\) | −1.65354 | −0.0946814 | ||||||||
\(306\) | −5.59568 | −0.319884 | ||||||||
\(307\) | −1.37369 | −0.0784006 | −0.0392003 | − | 0.999231i | \(-0.512481\pi\) | ||||
−0.0392003 | + | 0.999231i | \(0.512481\pi\) | |||||||
\(308\) | 12.5663 | 0.716029 | ||||||||
\(309\) | −0.140611 | −0.00799906 | ||||||||
\(310\) | 0.991821 | 0.0563316 | ||||||||
\(311\) | 12.1498 | 0.688953 | 0.344477 | − | 0.938795i | \(-0.388056\pi\) | ||||
0.344477 | + | 0.938795i | \(0.388056\pi\) | |||||||
\(312\) | −3.36981 | −0.190778 | ||||||||
\(313\) | 30.1141 | 1.70215 | 0.851076 | − | 0.525042i | \(-0.175951\pi\) | ||||
0.851076 | + | 0.525042i | \(0.175951\pi\) | |||||||
\(314\) | −4.88624 | −0.275747 | ||||||||
\(315\) | 33.6748 | 1.89736 | ||||||||
\(316\) | 13.0613 | 0.734757 | ||||||||
\(317\) | −8.47148 | −0.475806 | −0.237903 | − | 0.971289i | \(-0.576460\pi\) | ||||
−0.237903 | + | 0.971289i | \(0.576460\pi\) | |||||||
\(318\) | −1.84965 | −0.103723 | ||||||||
\(319\) | 0.864455 | 0.0484002 | ||||||||
\(320\) | −3.84400 | −0.214886 | ||||||||
\(321\) | −4.79639 | −0.267708 | ||||||||
\(322\) | 23.4568 | 1.30720 | ||||||||
\(323\) | 2.65111 | 0.147512 | ||||||||
\(324\) | −11.9362 | −0.663122 | ||||||||
\(325\) | −2.60348 | −0.144415 | ||||||||
\(326\) | 5.45773 | 0.302275 | ||||||||
\(327\) | −5.26120 | −0.290945 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.6959 | 1.36153 | ||||||||
\(330\) | −0.982939 | −0.0541090 | ||||||||
\(331\) | −10.4458 | −0.574155 | −0.287077 | − | 0.957907i | \(-0.592684\pi\) | ||||
−0.287077 | + | 0.957907i | \(0.592684\pi\) | |||||||
\(332\) | −7.23162 | −0.396887 | ||||||||
\(333\) | −12.2617 | −0.671936 | ||||||||
\(334\) | 13.4126 | 0.733906 | ||||||||
\(335\) | 9.70338 | 0.530152 | ||||||||
\(336\) | −2.11193 | −0.115215 | ||||||||
\(337\) | 22.8689 | 1.24575 | 0.622875 | − | 0.782321i | \(-0.285964\pi\) | ||||
0.622875 | + | 0.782321i | \(0.285964\pi\) | |||||||
\(338\) | 1.95184 | 0.106166 | ||||||||
\(339\) | −2.76681 | −0.150272 | ||||||||
\(340\) | 9.80377 | 0.531684 | ||||||||
\(341\) | 1.00595 | 0.0544755 | ||||||||
\(342\) | −1.96566 | −0.106290 | ||||||||
\(343\) | 49.7906 | 2.68844 | ||||||||
\(344\) | 13.3262 | 0.718503 | ||||||||
\(345\) | 5.51302 | 0.296811 | ||||||||
\(346\) | 9.16721 | 0.492832 | ||||||||
\(347\) | −1.67186 | −0.0897500 | −0.0448750 | − | 0.998993i | \(-0.514289\pi\) | ||||
−0.0448750 | + | 0.998993i | \(0.514289\pi\) | |||||||
\(348\) | −0.261102 | −0.0139966 | ||||||||
\(349\) | 34.5435 | 1.84907 | 0.924536 | − | 0.381095i | \(-0.124453\pi\) | ||||
0.924536 | + | 0.381095i | \(0.124453\pi\) | |||||||
\(350\) | 2.27669 | 0.121694 | ||||||||
\(351\) | −8.01271 | −0.427687 | ||||||||
\(352\) | −9.94310 | −0.529969 | ||||||||
\(353\) | −25.6054 | −1.36284 | −0.681418 | − | 0.731894i | \(-0.738636\pi\) | ||||
−0.681418 | + | 0.731894i | \(0.738636\pi\) | |||||||
\(354\) | −2.04340 | −0.108605 | ||||||||
\(355\) | −17.2927 | −0.917803 | ||||||||
\(356\) | −5.52677 | −0.292918 | ||||||||
\(357\) | −4.63062 | −0.245078 | ||||||||
\(358\) | −0.391160 | −0.0206735 | ||||||||
\(359\) | 26.4143 | 1.39409 | 0.697047 | − | 0.717025i | \(-0.254497\pi\) | ||||
0.697047 | + | 0.717025i | \(0.254497\pi\) | |||||||
\(360\) | −16.9572 | −0.893720 | ||||||||
\(361\) | −18.0687 | −0.950985 | ||||||||
\(362\) | −16.9783 | −0.892362 | ||||||||
\(363\) | 2.77723 | 0.145767 | ||||||||
\(364\) | 29.2677 | 1.53405 | ||||||||
\(365\) | −23.1323 | −1.21080 | ||||||||
\(366\) | −0.168589 | −0.00881227 | ||||||||
\(367\) | 20.0908 | 1.04873 | 0.524366 | − | 0.851493i | \(-0.324302\pi\) | ||||
0.524366 | + | 0.851493i | \(0.324302\pi\) | |||||||
\(368\) | 8.46528 | 0.441283 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.14974 | −0.371697 | ||||||||
\(371\) | 37.4761 | 1.94566 | ||||||||
\(372\) | −0.303841 | −0.0157534 | ||||||||
\(373\) | 7.68309 | 0.397815 | 0.198908 | − | 0.980018i | \(-0.436261\pi\) | ||||
0.198908 | + | 0.980018i | \(0.436261\pi\) | |||||||
\(374\) | −3.30932 | −0.171121 | ||||||||
\(375\) | −3.54477 | −0.183051 | ||||||||
\(376\) | −12.4357 | −0.641324 | ||||||||
\(377\) | 2.01338 | 0.103694 | ||||||||
\(378\) | 7.00694 | 0.360398 | ||||||||
\(379\) | 23.3163 | 1.19768 | 0.598838 | − | 0.800870i | \(-0.295629\pi\) | ||||
0.598838 | + | 0.800870i | \(0.295629\pi\) | |||||||
\(380\) | 3.44388 | 0.176667 | ||||||||
\(381\) | 3.69232 | 0.189163 | ||||||||
\(382\) | −8.78617 | −0.449540 | ||||||||
\(383\) | −16.2989 | −0.832837 | −0.416418 | − | 0.909173i | \(-0.636715\pi\) | ||||
−0.416418 | + | 0.909173i | \(0.636715\pi\) | |||||||
\(384\) | 3.61084 | 0.184265 | ||||||||
\(385\) | 19.9155 | 1.01499 | ||||||||
\(386\) | 2.29910 | 0.117021 | ||||||||
\(387\) | 15.5265 | 0.789254 | ||||||||
\(388\) | −6.12524 | −0.310962 | ||||||||
\(389\) | −0.290902 | −0.0147493 | −0.00737466 | − | 0.999973i | \(-0.502347\pi\) | ||||
−0.00737466 | + | 0.999973i | \(0.502347\pi\) | |||||||
\(390\) | −2.28934 | −0.115925 | ||||||||
\(391\) | 18.5610 | 0.938671 | ||||||||
\(392\) | −42.3892 | −2.14098 | ||||||||
\(393\) | 5.58036 | 0.281492 | ||||||||
\(394\) | 9.56983 | 0.482121 | ||||||||
\(395\) | 20.7001 | 1.04153 | ||||||||
\(396\) | −7.37255 | −0.370485 | ||||||||
\(397\) | 28.2999 | 1.42033 | 0.710166 | − | 0.704035i | \(-0.248620\pi\) | ||||
0.710166 | + | 0.704035i | \(0.248620\pi\) | |||||||
\(398\) | −6.55548 | −0.328597 | ||||||||
\(399\) | −1.62665 | −0.0814343 | ||||||||
\(400\) | 0.821630 | 0.0410815 | ||||||||
\(401\) | 6.77610 | 0.338382 | 0.169191 | − | 0.985583i | \(-0.445885\pi\) | ||||
0.169191 | + | 0.985583i | \(0.445885\pi\) | |||||||
\(402\) | 0.989319 | 0.0493428 | ||||||||
\(403\) | 2.34294 | 0.116710 | ||||||||
\(404\) | 15.6365 | 0.777945 | ||||||||
\(405\) | −18.9169 | −0.939991 | ||||||||
\(406\) | −1.76066 | −0.0873801 | ||||||||
\(407\) | −7.25162 | −0.359450 | ||||||||
\(408\) | 2.33177 | 0.115440 | ||||||||
\(409\) | −16.9059 | −0.835945 | −0.417972 | − | 0.908460i | \(-0.637259\pi\) | ||||
−0.417972 | + | 0.908460i | \(0.637259\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.08457 | −0.300130 | ||||||||
\(412\) | −0.614965 | −0.0302971 | ||||||||
\(413\) | 41.4016 | 2.03724 | ||||||||
\(414\) | −13.7620 | −0.676365 | ||||||||
\(415\) | −11.4610 | −0.562596 | ||||||||
\(416\) | −23.1582 | −1.13542 | ||||||||
\(417\) | 0.730911 | 0.0357929 | ||||||||
\(418\) | −1.16250 | −0.0568597 | ||||||||
\(419\) | 12.2920 | 0.600504 | 0.300252 | − | 0.953860i | \(-0.402929\pi\) | ||||
0.300252 | + | 0.953860i | \(0.402929\pi\) | |||||||
\(420\) | −6.01533 | −0.293518 | ||||||||
\(421\) | −29.1328 | −1.41985 | −0.709924 | − | 0.704278i | \(-0.751271\pi\) | ||||
−0.709924 | + | 0.704278i | \(0.751271\pi\) | |||||||
\(422\) | −19.2366 | −0.936423 | ||||||||
\(423\) | −14.4889 | −0.704476 | ||||||||
\(424\) | −18.8713 | −0.916472 | ||||||||
\(425\) | 1.80151 | 0.0873861 | ||||||||
\(426\) | −1.76310 | −0.0854225 | ||||||||
\(427\) | 3.41580 | 0.165302 | ||||||||
\(428\) | −20.9772 | −1.01397 | ||||||||
\(429\) | −2.32196 | −0.112105 | ||||||||
\(430\) | 9.05342 | 0.436595 | ||||||||
\(431\) | −8.60832 | −0.414648 | −0.207324 | − | 0.978272i | \(-0.566475\pi\) | ||||
−0.207324 | + | 0.978272i | \(0.566475\pi\) | |||||||
\(432\) | 2.52872 | 0.121663 | ||||||||
\(433\) | 11.8393 | 0.568961 | 0.284481 | − | 0.958682i | \(-0.408179\pi\) | ||||
0.284481 | + | 0.958682i | \(0.408179\pi\) | |||||||
\(434\) | −2.04885 | −0.0983482 | ||||||||
\(435\) | −0.413805 | −0.0198404 | ||||||||
\(436\) | −23.0100 | −1.10198 | ||||||||
\(437\) | 6.52013 | 0.311900 | ||||||||
\(438\) | −2.35848 | −0.112692 | ||||||||
\(439\) | 30.4135 | 1.45156 | 0.725778 | − | 0.687929i | \(-0.241480\pi\) | ||||
0.725778 | + | 0.687929i | \(0.241480\pi\) | |||||||
\(440\) | −10.0286 | −0.478093 | ||||||||
\(441\) | −49.3878 | −2.35180 | ||||||||
\(442\) | −7.70765 | −0.366615 | ||||||||
\(443\) | 13.3534 | 0.634438 | 0.317219 | − | 0.948352i | \(-0.397251\pi\) | ||||
0.317219 | + | 0.948352i | \(0.397251\pi\) | |||||||
\(444\) | 2.19030 | 0.103947 | ||||||||
\(445\) | −8.75903 | −0.415218 | ||||||||
\(446\) | 6.73567 | 0.318943 | ||||||||
\(447\) | 0.520598 | 0.0246234 | ||||||||
\(448\) | 7.94075 | 0.375165 | ||||||||
\(449\) | 25.1502 | 1.18691 | 0.593456 | − | 0.804866i | \(-0.297763\pi\) | ||||
0.593456 | + | 0.804866i | \(0.297763\pi\) | |||||||
\(450\) | −1.33572 | −0.0629666 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −12.1007 | −0.569169 | ||||||||
\(453\) | −0.719121 | −0.0337873 | ||||||||
\(454\) | −1.07600 | −0.0504990 | ||||||||
\(455\) | 46.3847 | 2.17455 | ||||||||
\(456\) | 0.819108 | 0.0383582 | ||||||||
\(457\) | 32.1746 | 1.50506 | 0.752531 | − | 0.658556i | \(-0.228833\pi\) | ||||
0.752531 | + | 0.658556i | \(0.228833\pi\) | |||||||
\(458\) | −10.4172 | −0.486764 | ||||||||
\(459\) | 5.54448 | 0.258794 | ||||||||
\(460\) | 24.1114 | 1.12420 | ||||||||
\(461\) | 29.4423 | 1.37126 | 0.685632 | − | 0.727948i | \(-0.259526\pi\) | ||||
0.685632 | + | 0.727948i | \(0.259526\pi\) | |||||||
\(462\) | 2.03051 | 0.0944677 | ||||||||
\(463\) | 20.5209 | 0.953687 | 0.476843 | − | 0.878988i | \(-0.341781\pi\) | ||||
0.476843 | + | 0.878988i | \(0.341781\pi\) | |||||||
\(464\) | −0.635400 | −0.0294977 | ||||||||
\(465\) | −0.481539 | −0.0223308 | ||||||||
\(466\) | −10.5206 | −0.487359 | ||||||||
\(467\) | −24.6933 | −1.14267 | −0.571334 | − | 0.820718i | \(-0.693574\pi\) | ||||
−0.571334 | + | 0.820718i | \(0.693574\pi\) | |||||||
\(468\) | −17.1712 | −0.793741 | ||||||||
\(469\) | −20.0448 | −0.925581 | ||||||||
\(470\) | −8.44844 | −0.389698 | ||||||||
\(471\) | 2.37232 | 0.109311 | ||||||||
\(472\) | −20.8480 | −0.959607 | ||||||||
\(473\) | 9.18244 | 0.422209 | ||||||||
\(474\) | 2.11050 | 0.0969386 | ||||||||
\(475\) | 0.632836 | 0.0290365 | ||||||||
\(476\) | −20.2521 | −0.928255 | ||||||||
\(477\) | −21.9870 | −1.00672 | ||||||||
\(478\) | −9.45073 | −0.432266 | ||||||||
\(479\) | −29.0111 | −1.32555 | −0.662776 | − | 0.748817i | \(-0.730622\pi\) | ||||
−0.662776 | + | 0.748817i | \(0.730622\pi\) | |||||||
\(480\) | 4.75965 | 0.217247 | ||||||||
\(481\) | −16.8896 | −0.770098 | ||||||||
\(482\) | −2.82341 | −0.128603 | ||||||||
\(483\) | −11.3885 | −0.518196 | ||||||||
\(484\) | 12.1463 | 0.552103 | ||||||||
\(485\) | −9.70752 | −0.440796 | ||||||||
\(486\) | −6.20754 | −0.281580 | ||||||||
\(487\) | −26.3805 | −1.19541 | −0.597707 | − | 0.801715i | \(-0.703921\pi\) | ||||
−0.597707 | + | 0.801715i | \(0.703921\pi\) | |||||||
\(488\) | −1.72005 | −0.0778629 | ||||||||
\(489\) | −2.64978 | −0.119827 | ||||||||
\(490\) | −28.7979 | −1.30096 | ||||||||
\(491\) | −17.4748 | −0.788628 | −0.394314 | − | 0.918976i | \(-0.629018\pi\) | ||||
−0.394314 | + | 0.918976i | \(0.629018\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.39318 | −0.0627457 | ||||||||
\(494\) | −2.70755 | −0.121818 | ||||||||
\(495\) | −11.6843 | −0.525171 | ||||||||
\(496\) | −0.739406 | −0.0332003 | ||||||||
\(497\) | 35.7225 | 1.60237 | ||||||||
\(498\) | −1.16852 | −0.0523624 | ||||||||
\(499\) | −6.32000 | −0.282922 | −0.141461 | − | 0.989944i | \(-0.545180\pi\) | ||||
−0.141461 | + | 0.989944i | \(0.545180\pi\) | |||||||
\(500\) | −15.5031 | −0.693321 | ||||||||
\(501\) | −6.51196 | −0.290933 | ||||||||
\(502\) | 19.3059 | 0.861666 | ||||||||
\(503\) | −11.0972 | −0.494798 | −0.247399 | − | 0.968914i | \(-0.579576\pi\) | ||||
−0.247399 | + | 0.968914i | \(0.579576\pi\) | |||||||
\(504\) | 35.0292 | 1.56033 | ||||||||
\(505\) | 24.7813 | 1.10275 | ||||||||
\(506\) | −8.13892 | −0.361819 | ||||||||
\(507\) | −0.947639 | −0.0420861 | ||||||||
\(508\) | 16.1485 | 0.716472 | ||||||||
\(509\) | −21.0225 | −0.931808 | −0.465904 | − | 0.884835i | \(-0.654271\pi\) | ||||
−0.465904 | + | 0.884835i | \(0.654271\pi\) | |||||||
\(510\) | 1.58413 | 0.0701466 | ||||||||
\(511\) | 47.7855 | 2.11391 | ||||||||
\(512\) | 13.5076 | 0.596955 | ||||||||
\(513\) | 1.94767 | 0.0859917 | ||||||||
\(514\) | 5.29867 | 0.233714 | ||||||||
\(515\) | −0.974619 | −0.0429469 | ||||||||
\(516\) | −2.77349 | −0.122096 | ||||||||
\(517\) | −8.56883 | −0.376857 | ||||||||
\(518\) | 14.7696 | 0.648938 | ||||||||
\(519\) | −4.45077 | −0.195367 | ||||||||
\(520\) | −23.3573 | −1.02428 | ||||||||
\(521\) | 9.55125 | 0.418448 | 0.209224 | − | 0.977868i | \(-0.432906\pi\) | ||||
0.209224 | + | 0.977868i | \(0.432906\pi\) | |||||||
\(522\) | 1.03297 | 0.0452119 | ||||||||
\(523\) | −9.97758 | −0.436289 | −0.218145 | − | 0.975916i | \(-0.570000\pi\) | ||||
−0.218145 | + | 0.975916i | \(0.570000\pi\) | |||||||
\(524\) | 24.4058 | 1.06617 | ||||||||
\(525\) | −1.10536 | −0.0482418 | ||||||||
\(526\) | −8.42411 | −0.367309 | ||||||||
\(527\) | −1.62123 | −0.0706217 | ||||||||
\(528\) | 0.732785 | 0.0318904 | ||||||||
\(529\) | 22.6489 | 0.984735 | ||||||||
\(530\) | −12.8206 | −0.556890 | ||||||||
\(531\) | −24.2901 | −1.05410 | ||||||||
\(532\) | −7.11419 | −0.308439 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.893038 | −0.0386455 | ||||||||
\(535\) | −33.2454 | −1.43732 | ||||||||
\(536\) | 10.0937 | 0.435979 | ||||||||
\(537\) | 0.189912 | 0.00819532 | ||||||||
\(538\) | −14.9697 | −0.645390 | ||||||||
\(539\) | −29.2083 | −1.25809 | ||||||||
\(540\) | 7.20246 | 0.309945 | ||||||||
\(541\) | −4.87015 | −0.209384 | −0.104692 | − | 0.994505i | \(-0.533386\pi\) | ||||
−0.104692 | + | 0.994505i | \(0.533386\pi\) | |||||||
\(542\) | −2.70838 | −0.116335 | ||||||||
\(543\) | 8.24316 | 0.353748 | ||||||||
\(544\) | 16.0246 | 0.687048 | ||||||||
\(545\) | −36.4672 | −1.56208 | ||||||||
\(546\) | 4.72920 | 0.202391 | ||||||||
\(547\) | 20.1046 | 0.859611 | 0.429806 | − | 0.902921i | \(-0.358582\pi\) | ||||
0.429806 | + | 0.902921i | \(0.358582\pi\) | |||||||
\(548\) | −26.6110 | −1.13677 | ||||||||
\(549\) | −2.00403 | −0.0855300 | ||||||||
\(550\) | −0.789955 | −0.0336838 | ||||||||
\(551\) | −0.489398 | −0.0208491 | ||||||||
\(552\) | 5.73476 | 0.244088 | ||||||||
\(553\) | −42.7612 | −1.81839 | ||||||||
\(554\) | −0.825359 | −0.0350661 | ||||||||
\(555\) | 3.47127 | 0.147347 | ||||||||
\(556\) | 3.19666 | 0.135569 | ||||||||
\(557\) | 20.3234 | 0.861130 | 0.430565 | − | 0.902560i | \(-0.358314\pi\) | ||||
0.430565 | + | 0.902560i | \(0.358314\pi\) | |||||||
\(558\) | 1.20205 | 0.0508869 | ||||||||
\(559\) | 21.3866 | 0.904556 | ||||||||
\(560\) | −14.6385 | −0.618588 | ||||||||
\(561\) | 1.60671 | 0.0678352 | ||||||||
\(562\) | 12.5056 | 0.527517 | ||||||||
\(563\) | 16.0734 | 0.677415 | 0.338707 | − | 0.940892i | \(-0.390010\pi\) | ||||
0.338707 | + | 0.940892i | \(0.390010\pi\) | |||||||
\(564\) | 2.58815 | 0.108981 | ||||||||
\(565\) | −19.1777 | −0.806811 | ||||||||
\(566\) | 5.23677 | 0.220118 | ||||||||
\(567\) | 39.0777 | 1.64111 | ||||||||
\(568\) | −17.9883 | −0.754771 | ||||||||
\(569\) | 14.3261 | 0.600580 | 0.300290 | − | 0.953848i | \(-0.402916\pi\) | ||||
0.300290 | + | 0.953848i | \(0.402916\pi\) | |||||||
\(570\) | 0.556476 | 0.0233082 | ||||||||
\(571\) | 8.19798 | 0.343075 | 0.171537 | − | 0.985178i | \(-0.445127\pi\) | ||||
0.171537 | + | 0.985178i | \(0.445127\pi\) | |||||||
\(572\) | −10.1552 | −0.424609 | ||||||||
\(573\) | 4.26578 | 0.178205 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.43063 | 0.184770 | ||||||||
\(576\) | −4.65880 | −0.194117 | ||||||||
\(577\) | −4.94814 | −0.205994 | −0.102997 | − | 0.994682i | \(-0.532843\pi\) | ||||
−0.102997 | + | 0.994682i | \(0.532843\pi\) | |||||||
\(578\) | −6.68038 | −0.277867 | ||||||||
\(579\) | −1.11624 | −0.0463892 | ||||||||
\(580\) | −1.80979 | −0.0751474 | ||||||||
\(581\) | 23.6755 | 0.982224 | ||||||||
\(582\) | −0.989742 | −0.0410261 | ||||||||
\(583\) | −13.0033 | −0.538540 | ||||||||
\(584\) | −24.0627 | −0.995720 | ||||||||
\(585\) | −27.2136 | −1.12515 | ||||||||
\(586\) | −7.31608 | −0.302224 | ||||||||
\(587\) | −10.1283 | −0.418038 | −0.209019 | − | 0.977912i | \(-0.567027\pi\) | ||||
−0.209019 | + | 0.977912i | \(0.567027\pi\) | |||||||
\(588\) | 8.82214 | 0.363819 | ||||||||
\(589\) | −0.569506 | −0.0234661 | ||||||||
\(590\) | −14.1635 | −0.583101 | ||||||||
\(591\) | −4.64625 | −0.191121 | ||||||||
\(592\) | 5.33016 | 0.219068 | ||||||||
\(593\) | −15.1299 | −0.621310 | −0.310655 | − | 0.950523i | \(-0.600548\pi\) | ||||
−0.310655 | + | 0.950523i | \(0.600548\pi\) | |||||||
\(594\) | −2.43123 | −0.0997546 | ||||||||
\(595\) | −32.0964 | −1.31582 | ||||||||
\(596\) | 2.27685 | 0.0932633 | ||||||||
\(597\) | 3.18275 | 0.130261 | ||||||||
\(598\) | −18.9562 | −0.775175 | ||||||||
\(599\) | 3.27805 | 0.133937 | 0.0669687 | − | 0.997755i | \(-0.478667\pi\) | ||||
0.0669687 | + | 0.997755i | \(0.478667\pi\) | |||||||
\(600\) | 0.556609 | 0.0227235 | ||||||||
\(601\) | 7.14693 | 0.291529 | 0.145765 | − | 0.989319i | \(-0.453436\pi\) | ||||
0.145765 | + | 0.989319i | \(0.453436\pi\) | |||||||
\(602\) | −18.7021 | −0.762241 | ||||||||
\(603\) | 11.7602 | 0.478910 | ||||||||
\(604\) | −3.14510 | −0.127972 | ||||||||
\(605\) | 19.2499 | 0.782619 | ||||||||
\(606\) | 2.52661 | 0.102637 | ||||||||
\(607\) | 33.9444 | 1.37776 | 0.688880 | − | 0.724876i | \(-0.258103\pi\) | ||||
0.688880 | + | 0.724876i | \(0.258103\pi\) | |||||||
\(608\) | 5.62913 | 0.228291 | ||||||||
\(609\) | 0.854818 | 0.0346390 | ||||||||
\(610\) | −1.16854 | −0.0473130 | ||||||||
\(611\) | −19.9575 | −0.807392 | ||||||||
\(612\) | 11.8818 | 0.480294 | ||||||||
\(613\) | 15.4196 | 0.622792 | 0.311396 | − | 0.950280i | \(-0.399203\pi\) | ||||
0.311396 | + | 0.950280i | \(0.399203\pi\) | |||||||
\(614\) | −0.970776 | −0.0391773 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.7165 | 0.834691 | ||||||||
\(617\) | 0.726595 | 0.0292516 | 0.0146258 | − | 0.999893i | \(-0.495344\pi\) | ||||
0.0146258 | + | 0.999893i | \(0.495344\pi\) | |||||||
\(618\) | −0.0993685 | −0.00399719 | ||||||||
\(619\) | −24.5798 | −0.987946 | −0.493973 | − | 0.869477i | \(-0.664456\pi\) | ||||
−0.493973 | + | 0.869477i | \(0.664456\pi\) | |||||||
\(620\) | −2.10603 | −0.0845800 | ||||||||
\(621\) | 13.6361 | 0.547197 | ||||||||
\(622\) | 8.58619 | 0.344275 | ||||||||
\(623\) | 18.0940 | 0.724920 | ||||||||
\(624\) | 1.70671 | 0.0683231 | ||||||||
\(625\) | −27.8488 | −1.11395 | ||||||||
\(626\) | 21.2814 | 0.850578 | ||||||||
\(627\) | 0.564406 | 0.0225402 | ||||||||
\(628\) | 10.3754 | 0.414024 | ||||||||
\(629\) | 11.6869 | 0.465988 | ||||||||
\(630\) | 23.7977 | 0.948125 | ||||||||
\(631\) | 13.6232 | 0.542333 | 0.271166 | − | 0.962533i | \(-0.412591\pi\) | ||||
0.271166 | + | 0.962533i | \(0.412591\pi\) | |||||||
\(632\) | 21.5327 | 0.856523 | ||||||||
\(633\) | 9.33956 | 0.371214 | ||||||||
\(634\) | −5.98674 | −0.237764 | ||||||||
\(635\) | 25.5927 | 1.01562 | ||||||||
\(636\) | 3.92754 | 0.155737 | ||||||||
\(637\) | −68.0282 | −2.69538 | ||||||||
\(638\) | 0.610904 | 0.0241859 | ||||||||
\(639\) | −20.9582 | −0.829093 | ||||||||
\(640\) | 25.0279 | 0.989315 | ||||||||
\(641\) | −9.49502 | −0.375031 | −0.187515 | − | 0.982262i | \(-0.560043\pi\) | ||||
−0.187515 | + | 0.982262i | \(0.560043\pi\) | |||||||
\(642\) | −3.38957 | −0.133776 | ||||||||
\(643\) | 39.6479 | 1.56356 | 0.781781 | − | 0.623554i | \(-0.214312\pi\) | ||||
0.781781 | + | 0.623554i | \(0.214312\pi\) | |||||||
\(644\) | −49.8081 | −1.96271 | ||||||||
\(645\) | −4.39553 | −0.173074 | ||||||||
\(646\) | 1.87352 | 0.0737126 | ||||||||
\(647\) | 40.5997 | 1.59614 | 0.798070 | − | 0.602564i | \(-0.205854\pi\) | ||||
0.798070 | + | 0.602564i | \(0.205854\pi\) | |||||||
\(648\) | −19.6778 | −0.773017 | ||||||||
\(649\) | −14.3653 | −0.563887 | ||||||||
\(650\) | −1.83986 | −0.0721654 | ||||||||
\(651\) | 0.994740 | 0.0389869 | ||||||||
\(652\) | −11.5889 | −0.453856 | ||||||||
\(653\) | 9.76983 | 0.382323 | 0.191161 | − | 0.981559i | \(-0.438775\pi\) | ||||
0.191161 | + | 0.981559i | \(0.438775\pi\) | |||||||
\(654\) | −3.71805 | −0.145387 | ||||||||
\(655\) | 38.6793 | 1.51133 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.0355 | −1.09377 | ||||||||
\(658\) | 17.4524 | 0.680364 | ||||||||
\(659\) | −39.0664 | −1.52181 | −0.760905 | − | 0.648863i | \(-0.775245\pi\) | ||||
−0.760905 | + | 0.648863i | \(0.775245\pi\) | |||||||
\(660\) | 2.08717 | 0.0812428 | ||||||||
\(661\) | −37.2590 | −1.44921 | −0.724603 | − | 0.689167i | \(-0.757977\pi\) | ||||
−0.724603 | + | 0.689167i | \(0.757977\pi\) | |||||||
\(662\) | −7.38199 | −0.286909 | ||||||||
\(663\) | 3.74214 | 0.145333 | ||||||||
\(664\) | −11.9219 | −0.462660 | ||||||||
\(665\) | −11.2748 | −0.437220 | ||||||||
\(666\) | −8.66523 | −0.335771 | ||||||||
\(667\) | −3.42639 | −0.132670 | ||||||||
\(668\) | −28.4802 | −1.10193 | ||||||||
\(669\) | −3.27024 | −0.126435 | ||||||||
\(670\) | 6.85730 | 0.264921 | ||||||||
\(671\) | −1.18520 | −0.0457540 | ||||||||
\(672\) | −9.83225 | −0.379287 | ||||||||
\(673\) | 32.0460 | 1.23528 | 0.617641 | − | 0.786460i | \(-0.288088\pi\) | ||||
0.617641 | + | 0.786460i | \(0.288088\pi\) | |||||||
\(674\) | 16.1613 | 0.622510 | ||||||||
\(675\) | 1.32350 | 0.0509416 | ||||||||
\(676\) | −4.14453 | −0.159405 | ||||||||
\(677\) | 36.6269 | 1.40769 | 0.703843 | − | 0.710356i | \(-0.251466\pi\) | ||||
0.703843 | + | 0.710356i | \(0.251466\pi\) | |||||||
\(678\) | −1.95528 | −0.0750922 | ||||||||
\(679\) | 20.0533 | 0.769576 | ||||||||
\(680\) | 16.1623 | 0.619796 | ||||||||
\(681\) | 0.522407 | 0.0200187 | ||||||||
\(682\) | 0.710901 | 0.0272218 | ||||||||
\(683\) | 45.5625 | 1.74340 | 0.871700 | − | 0.490040i | \(-0.163018\pi\) | ||||
0.871700 | + | 0.490040i | \(0.163018\pi\) | |||||||
\(684\) | 4.17386 | 0.159591 | ||||||||
\(685\) | −42.1742 | −1.61139 | ||||||||
\(686\) | 35.1867 | 1.34343 | ||||||||
\(687\) | 5.05766 | 0.192962 | ||||||||
\(688\) | −6.74936 | −0.257317 | ||||||||
\(689\) | −30.2856 | −1.15379 | ||||||||
\(690\) | 3.89601 | 0.148319 | ||||||||
\(691\) | 12.4918 | 0.475211 | 0.237606 | − | 0.971362i | \(-0.423637\pi\) | ||||
0.237606 | + | 0.971362i | \(0.423637\pi\) | |||||||
\(692\) | −19.4656 | −0.739970 | ||||||||
\(693\) | 24.1369 | 0.916884 | ||||||||
\(694\) | −1.18149 | −0.0448487 | ||||||||
\(695\) | 5.06619 | 0.192172 | ||||||||
\(696\) | −0.430449 | −0.0163161 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 24.4116 | 0.923994 | ||||||||
\(699\) | 5.10788 | 0.193198 | ||||||||
\(700\) | −4.83431 | −0.182720 | ||||||||
\(701\) | −33.2743 | −1.25675 | −0.628377 | − | 0.777909i | \(-0.716280\pi\) | ||||
−0.628377 | + | 0.777909i | \(0.716280\pi\) | |||||||
\(702\) | −5.66252 | −0.213718 | ||||||||
\(703\) | 4.10539 | 0.154838 | ||||||||
\(704\) | −2.75524 | −0.103842 | ||||||||
\(705\) | 4.10180 | 0.154483 | ||||||||
\(706\) | −18.0951 | −0.681019 | ||||||||
\(707\) | −51.1921 | −1.92528 | ||||||||
\(708\) | 4.33893 | 0.163067 | ||||||||
\(709\) | 27.8535 | 1.04606 | 0.523030 | − | 0.852314i | \(-0.324802\pi\) | ||||
0.523030 | + | 0.852314i | \(0.324802\pi\) | |||||||
\(710\) | −12.2206 | −0.458633 | ||||||||
\(711\) | 25.0878 | 0.940866 | ||||||||
\(712\) | −9.11133 | −0.341461 | ||||||||
\(713\) | −3.98724 | −0.149323 | ||||||||
\(714\) | −3.27242 | −0.122467 | ||||||||
\(715\) | −16.0943 | −0.601893 | ||||||||
\(716\) | 0.830587 | 0.0310405 | ||||||||
\(717\) | 4.58843 | 0.171358 | ||||||||
\(718\) | 18.6668 | 0.696639 | ||||||||
\(719\) | 29.5641 | 1.10255 | 0.551277 | − | 0.834322i | \(-0.314141\pi\) | ||||
0.551277 | + | 0.834322i | \(0.314141\pi\) | |||||||
\(720\) | 8.58831 | 0.320068 | ||||||||
\(721\) | 2.01332 | 0.0749800 | ||||||||
\(722\) | −12.7690 | −0.475214 | ||||||||
\(723\) | 1.37080 | 0.0509805 | ||||||||
\(724\) | 36.0517 | 1.33985 | ||||||||
\(725\) | −0.332561 | −0.0123510 | ||||||||
\(726\) | 1.96264 | 0.0728406 | ||||||||
\(727\) | 14.5061 | 0.538000 | 0.269000 | − | 0.963140i | \(-0.413307\pi\) | ||||
0.269000 | + | 0.963140i | \(0.413307\pi\) | |||||||
\(728\) | 48.2503 | 1.78827 | ||||||||
\(729\) | −20.8493 | −0.772195 | ||||||||
\(730\) | −16.3474 | −0.605044 | ||||||||
\(731\) | −14.7987 | −0.547349 | ||||||||
\(732\) | 0.357980 | 0.0132313 | ||||||||
\(733\) | 44.6474 | 1.64909 | 0.824544 | − | 0.565798i | \(-0.191432\pi\) | ||||
0.824544 | + | 0.565798i | \(0.191432\pi\) | |||||||
\(734\) | 14.1980 | 0.524059 | ||||||||
\(735\) | 13.9817 | 0.515721 | ||||||||
\(736\) | 39.4108 | 1.45270 | ||||||||
\(737\) | 6.95502 | 0.256191 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.65655 | −0.0977228 | −0.0488614 | − | 0.998806i | \(-0.515559\pi\) | ||||
−0.0488614 | + | 0.998806i | \(0.515559\pi\) | |||||||
\(740\) | 15.1817 | 0.558090 | ||||||||
\(741\) | 1.31454 | 0.0482909 | ||||||||
\(742\) | 26.4841 | 0.972261 | ||||||||
\(743\) | 30.6558 | 1.12465 | 0.562326 | − | 0.826916i | \(-0.309907\pi\) | ||||
0.562326 | + | 0.826916i | \(0.309907\pi\) | |||||||
\(744\) | −0.500907 | −0.0183641 | ||||||||
\(745\) | 3.60844 | 0.132203 | ||||||||
\(746\) | 5.42958 | 0.198791 | ||||||||
\(747\) | −13.8903 | −0.508219 | ||||||||
\(748\) | 7.02698 | 0.256932 | ||||||||
\(749\) | 68.6767 | 2.50939 | ||||||||
\(750\) | −2.50506 | −0.0914719 | ||||||||
\(751\) | −50.6405 | −1.84790 | −0.923949 | − | 0.382515i | \(-0.875058\pi\) | ||||
−0.923949 | + | 0.382515i | \(0.875058\pi\) | |||||||
\(752\) | 6.29835 | 0.229677 | ||||||||
\(753\) | −9.37322 | −0.341579 | ||||||||
\(754\) | 1.42284 | 0.0518168 | ||||||||
\(755\) | −4.98447 | −0.181403 | ||||||||
\(756\) | −14.8785 | −0.541125 | ||||||||
\(757\) | −28.9856 | −1.05350 | −0.526750 | − | 0.850020i | \(-0.676590\pi\) | ||||
−0.526750 | + | 0.850020i | \(0.676590\pi\) | |||||||
\(758\) | 16.4774 | 0.598487 | ||||||||
\(759\) | 3.95153 | 0.143431 | ||||||||
\(760\) | 5.67751 | 0.205945 | ||||||||
\(761\) | 38.9868 | 1.41327 | 0.706636 | − | 0.707577i | \(-0.250212\pi\) | ||||
0.706636 | + | 0.707577i | \(0.250212\pi\) | |||||||
\(762\) | 2.60933 | 0.0945262 | ||||||||
\(763\) | 75.3320 | 2.72720 | ||||||||
\(764\) | 18.6565 | 0.674968 | ||||||||
\(765\) | 18.8308 | 0.680828 | ||||||||
\(766\) | −11.5183 | −0.416174 | ||||||||
\(767\) | −33.4579 | −1.20809 | ||||||||
\(768\) | 3.66092 | 0.132102 | ||||||||
\(769\) | 2.64416 | 0.0953507 | 0.0476753 | − | 0.998863i | \(-0.484819\pi\) | ||||
0.0476753 | + | 0.998863i | \(0.484819\pi\) | |||||||
\(770\) | 14.0741 | 0.507196 | ||||||||
\(771\) | −2.57256 | −0.0926485 | ||||||||
\(772\) | −4.88189 | −0.175703 | ||||||||
\(773\) | −20.9380 | −0.753089 | −0.376544 | − | 0.926399i | \(-0.622888\pi\) | ||||
−0.376544 | + | 0.926399i | \(0.622888\pi\) | |||||||
\(774\) | 10.9724 | 0.394396 | ||||||||
\(775\) | −0.386997 | −0.0139013 | ||||||||
\(776\) | −10.0980 | −0.362496 | ||||||||
\(777\) | −7.17078 | −0.257250 | ||||||||
\(778\) | −0.205578 | −0.00737034 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 4.86116 | 0.174058 | ||||||||
\(781\) | −12.3948 | −0.443521 | ||||||||
\(782\) | 13.1169 | 0.469060 | ||||||||
\(783\) | −1.02352 | −0.0365776 | ||||||||
\(784\) | 21.4689 | 0.766748 | ||||||||
\(785\) | 16.4433 | 0.586888 | ||||||||
\(786\) | 3.94360 | 0.140663 | ||||||||
\(787\) | 22.3722 | 0.797482 | 0.398741 | − | 0.917064i | \(-0.369447\pi\) | ||||
0.398741 | + | 0.917064i | \(0.369447\pi\) | |||||||
\(788\) | −20.3205 | −0.723888 | ||||||||
\(789\) | 4.08999 | 0.145608 | ||||||||
\(790\) | 14.6286 | 0.520462 | ||||||||
\(791\) | 39.6163 | 1.40859 | ||||||||
\(792\) | −12.1543 | −0.431883 | ||||||||
\(793\) | −2.76041 | −0.0980251 | ||||||||
\(794\) | 19.9993 | 0.709750 | ||||||||
\(795\) | 6.22451 | 0.220761 | ||||||||
\(796\) | 13.9199 | 0.493376 | ||||||||
\(797\) | 20.1097 | 0.712321 | 0.356160 | − | 0.934425i | \(-0.384086\pi\) | ||||
0.356160 | + | 0.934425i | \(0.384086\pi\) | |||||||
\(798\) | −1.14954 | −0.0406933 | ||||||||
\(799\) | 13.8098 | 0.488555 | ||||||||
\(800\) | 3.82517 | 0.135240 | ||||||||
\(801\) | −10.6156 | −0.375085 | ||||||||
\(802\) | 4.78862 | 0.169092 | ||||||||
\(803\) | −16.5804 | −0.585108 | ||||||||
\(804\) | −2.10071 | −0.0740864 | ||||||||
\(805\) | −78.9377 | −2.78219 | ||||||||
\(806\) | 1.65574 | 0.0583210 | ||||||||
\(807\) | 7.26795 | 0.255844 | ||||||||
\(808\) | 25.7781 | 0.906869 | ||||||||
\(809\) | −9.18730 | −0.323008 | −0.161504 | − | 0.986872i | \(-0.551635\pi\) | ||||
−0.161504 | + | 0.986872i | \(0.551635\pi\) | |||||||
\(810\) | −13.3685 | −0.469720 | ||||||||
\(811\) | 18.4060 | 0.646324 | 0.323162 | − | 0.946344i | \(-0.395254\pi\) | ||||
0.323162 | + | 0.946344i | \(0.395254\pi\) | |||||||
\(812\) | 3.73857 | 0.131198 | ||||||||
\(813\) | 1.31495 | 0.0461172 | ||||||||
\(814\) | −5.12467 | −0.179620 | ||||||||
\(815\) | −18.3665 | −0.643351 | ||||||||
\(816\) | −1.18098 | −0.0413425 | ||||||||
\(817\) | −5.19849 | −0.181872 | ||||||||
\(818\) | −11.9473 | −0.417728 | ||||||||
\(819\) | 56.2166 | 1.96437 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.0353 | 0.629436 | 0.314718 | − | 0.949185i | \(-0.398090\pi\) | ||||
0.314718 | + | 0.949185i | \(0.398090\pi\) | |||||||
\(822\) | −4.29992 | −0.149977 | ||||||||
\(823\) | −44.4796 | −1.55046 | −0.775230 | − | 0.631679i | \(-0.782366\pi\) | ||||
−0.775230 | + | 0.631679i | \(0.782366\pi\) | |||||||
\(824\) | −1.01382 | −0.0353181 | ||||||||
\(825\) | 0.383531 | 0.0133528 | ||||||||
\(826\) | 29.2582 | 1.01802 | ||||||||
\(827\) | −44.9128 | −1.56177 | −0.780886 | − | 0.624674i | \(-0.785232\pi\) | ||||
−0.780886 | + | 0.624674i | \(0.785232\pi\) | |||||||
\(828\) | 29.2221 | 1.01554 | ||||||||
\(829\) | −45.0253 | −1.56379 | −0.781896 | − | 0.623409i | \(-0.785747\pi\) | ||||
−0.781896 | + | 0.623409i | \(0.785747\pi\) | |||||||
\(830\) | −8.09937 | −0.281133 | ||||||||
\(831\) | 0.400720 | 0.0139008 | ||||||||
\(832\) | −6.41716 | −0.222475 | ||||||||
\(833\) | 47.0729 | 1.63098 | ||||||||
\(834\) | 0.516530 | 0.0178860 | ||||||||
\(835\) | −45.1366 | −1.56202 | ||||||||
\(836\) | 2.46844 | 0.0853729 | ||||||||
\(837\) | −1.19105 | −0.0411688 | ||||||||
\(838\) | 8.68667 | 0.300076 | ||||||||
\(839\) | −10.9413 | −0.377737 | −0.188869 | − | 0.982002i | \(-0.560482\pi\) | ||||
−0.188869 | + | 0.982002i | \(0.560482\pi\) | |||||||
\(840\) | −9.91676 | −0.342161 | ||||||||
\(841\) | −28.7428 | −0.991132 | ||||||||
\(842\) | −20.5880 | −0.709508 | ||||||||
\(843\) | −6.07159 | −0.209117 | ||||||||
\(844\) | 40.8468 | 1.40601 | ||||||||
\(845\) | −6.56841 | −0.225960 | ||||||||
\(846\) | −10.2392 | −0.352031 | ||||||||
\(847\) | −39.7654 | −1.36636 | ||||||||
\(848\) | 9.55778 | 0.328216 | ||||||||
\(849\) | −2.54251 | −0.0872585 | ||||||||
\(850\) | 1.27311 | 0.0436674 | ||||||||
\(851\) | 28.7428 | 0.985290 | ||||||||
\(852\) | 3.74376 | 0.128259 | ||||||||
\(853\) | −16.7236 | −0.572607 | −0.286303 | − | 0.958139i | \(-0.592427\pi\) | ||||
−0.286303 | + | 0.958139i | \(0.592427\pi\) | |||||||
\(854\) | 2.41392 | 0.0826027 | ||||||||
\(855\) | 6.61489 | 0.226224 | ||||||||
\(856\) | −34.5825 | −1.18201 | ||||||||
\(857\) | 11.1225 | 0.379937 | 0.189968 | − | 0.981790i | \(-0.439161\pi\) | ||||
0.189968 | + | 0.981790i | \(0.439161\pi\) | |||||||
\(858\) | −1.64091 | −0.0560199 | ||||||||
\(859\) | −47.3689 | −1.61620 | −0.808102 | − | 0.589042i | \(-0.799505\pi\) | ||||
−0.808102 | + | 0.589042i | \(0.799505\pi\) | |||||||
\(860\) | −19.2240 | −0.655532 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.08343 | −0.207203 | ||||||||
\(863\) | 14.0929 | 0.479729 | 0.239864 | − | 0.970806i | \(-0.422897\pi\) | ||||
0.239864 | + | 0.970806i | \(0.422897\pi\) | |||||||
\(864\) | 11.7727 | 0.400514 | ||||||||
\(865\) | −30.8498 | −1.04892 | ||||||||
\(866\) | 8.36675 | 0.284314 | ||||||||
\(867\) | 3.24339 | 0.110151 | ||||||||
\(868\) | 4.35052 | 0.147666 | ||||||||
\(869\) | 14.8371 | 0.503313 | ||||||||
\(870\) | −0.292433 | −0.00991441 | ||||||||
\(871\) | 16.1988 | 0.548874 | ||||||||
\(872\) | −37.9339 | −1.28460 | ||||||||
\(873\) | −11.7652 | −0.398191 | ||||||||
\(874\) | 4.60773 | 0.155859 | ||||||||
\(875\) | 50.7554 | 1.71585 | ||||||||
\(876\) | 5.00797 | 0.169204 | ||||||||
\(877\) | −35.3772 | −1.19460 | −0.597301 | − | 0.802017i | \(-0.703760\pi\) | ||||
−0.597301 | + | 0.802017i | \(0.703760\pi\) | |||||||
\(878\) | 21.4930 | 0.725353 | ||||||||
\(879\) | 3.55203 | 0.119807 | ||||||||
\(880\) | 5.07918 | 0.171219 | ||||||||
\(881\) | −21.6923 | −0.730832 | −0.365416 | − | 0.930844i | \(-0.619073\pi\) | ||||
−0.365416 | + | 0.930844i | \(0.619073\pi\) | |||||||
\(882\) | −34.9020 | −1.17521 | ||||||||
\(883\) | −3.22329 | −0.108472 | −0.0542362 | − | 0.998528i | \(-0.517272\pi\) | ||||
−0.0542362 | + | 0.998528i | \(0.517272\pi\) | |||||||
\(884\) | 16.3664 | 0.550460 | ||||||||
\(885\) | 6.87651 | 0.231151 | ||||||||
\(886\) | 9.43673 | 0.317033 | ||||||||
\(887\) | −14.4724 | −0.485935 | −0.242967 | − | 0.970034i | \(-0.578121\pi\) | ||||
−0.242967 | + | 0.970034i | \(0.578121\pi\) | |||||||
\(888\) | 3.61089 | 0.121173 | ||||||||
\(889\) | −52.8681 | −1.77314 | ||||||||
\(890\) | −6.18994 | −0.207487 | ||||||||
\(891\) | −13.5590 | −0.454242 | ||||||||
\(892\) | −14.3025 | −0.478882 | ||||||||
\(893\) | 4.85111 | 0.162336 | ||||||||
\(894\) | 0.367902 | 0.0123045 | ||||||||
\(895\) | 1.31635 | 0.0440006 | ||||||||
\(896\) | −51.7014 | −1.72722 | ||||||||
\(897\) | 9.20341 | 0.307293 | ||||||||
\(898\) | 17.7735 | 0.593108 | ||||||||
\(899\) | 0.299280 | 0.00998156 | ||||||||
\(900\) | 2.83627 | 0.0945422 | ||||||||
\(901\) | 20.9564 | 0.698160 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.08007 | 0.302166 | ||||||||
\(904\) | −19.9490 | −0.663494 | ||||||||
\(905\) | 57.1361 | 1.89927 | ||||||||
\(906\) | −0.508198 | −0.0168837 | ||||||||
\(907\) | 42.1901 | 1.40090 | 0.700450 | − | 0.713702i | \(-0.252983\pi\) | ||||
0.700450 | + | 0.713702i | \(0.252983\pi\) | |||||||
\(908\) | 2.28476 | 0.0758225 | ||||||||
\(909\) | 30.0341 | 0.996168 | ||||||||
\(910\) | 32.7797 | 1.08664 | ||||||||
\(911\) | 46.8754 | 1.55305 | 0.776525 | − | 0.630087i | \(-0.216981\pi\) | ||||
0.776525 | + | 0.630087i | \(0.216981\pi\) | |||||||
\(912\) | −0.414855 | −0.0137372 | ||||||||
\(913\) | −8.21479 | −0.271870 | ||||||||
\(914\) | 22.7375 | 0.752090 | ||||||||
\(915\) | 0.567340 | 0.0187557 | ||||||||
\(916\) | 22.1198 | 0.730859 | ||||||||
\(917\) | −79.9018 | −2.63859 | ||||||||
\(918\) | 3.91824 | 0.129321 | ||||||||
\(919\) | −26.0204 | −0.858333 | −0.429167 | − | 0.903225i | \(-0.641193\pi\) | ||||
−0.429167 | + | 0.903225i | \(0.641193\pi\) | |||||||
\(920\) | 39.7495 | 1.31050 | ||||||||
\(921\) | 0.471322 | 0.0155306 | ||||||||
\(922\) | 20.8066 | 0.685230 | ||||||||
\(923\) | −28.8684 | −0.950215 | ||||||||
\(924\) | −4.31156 | −0.141840 | ||||||||
\(925\) | 2.78974 | 0.0917262 | ||||||||
\(926\) | 14.5020 | 0.476564 | ||||||||
\(927\) | −1.18120 | −0.0387959 | ||||||||
\(928\) | −2.95816 | −0.0971063 | ||||||||
\(929\) | −36.2974 | −1.19088 | −0.595440 | − | 0.803400i | \(-0.703022\pi\) | ||||
−0.595440 | + | 0.803400i | \(0.703022\pi\) | |||||||
\(930\) | −0.340300 | −0.0111589 | ||||||||
\(931\) | 16.5358 | 0.541939 | ||||||||
\(932\) | 22.3394 | 0.731753 | ||||||||
\(933\) | −4.16868 | −0.136477 | ||||||||
\(934\) | −17.4505 | −0.570999 | ||||||||
\(935\) | 11.1366 | 0.364207 | ||||||||
\(936\) | −28.3082 | −0.925282 | ||||||||
\(937\) | 11.1948 | 0.365719 | 0.182859 | − | 0.983139i | \(-0.441465\pi\) | ||||
0.182859 | + | 0.983139i | \(0.441465\pi\) | |||||||
\(938\) | −14.1655 | −0.462519 | ||||||||
\(939\) | −10.3324 | −0.337184 | ||||||||
\(940\) | 17.9394 | 0.585117 | ||||||||
\(941\) | −15.4599 | −0.503977 | −0.251989 | − | 0.967730i | \(-0.581085\pi\) | ||||
−0.251989 | + | 0.967730i | \(0.581085\pi\) | |||||||
\(942\) | 1.67650 | 0.0546234 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 10.5589 | 0.343664 | ||||||||
\(945\) | −23.5800 | −0.767058 | ||||||||
\(946\) | 6.48916 | 0.210981 | ||||||||
\(947\) | 37.9174 | 1.23215 | 0.616074 | − | 0.787688i | \(-0.288722\pi\) | ||||
0.616074 | + | 0.787688i | \(0.288722\pi\) | |||||||
\(948\) | −4.48143 | −0.145550 | ||||||||
\(949\) | −38.6169 | −1.25356 | ||||||||
\(950\) | 0.447221 | 0.0145098 | ||||||||
\(951\) | 2.90662 | 0.0942536 | ||||||||
\(952\) | −33.3873 | −1.08209 | ||||||||
\(953\) | −35.0022 | −1.13383 | −0.566916 | − | 0.823775i | \(-0.691864\pi\) | ||||
−0.566916 | + | 0.823775i | \(0.691864\pi\) | |||||||
\(954\) | −15.5381 | −0.503064 | ||||||||
\(955\) | 29.5675 | 0.956783 | ||||||||
\(956\) | 20.0676 | 0.649033 | ||||||||
\(957\) | −0.296600 | −0.00958772 | ||||||||
\(958\) | −20.5020 | −0.662388 | ||||||||
\(959\) | 87.1213 | 2.81329 | ||||||||
\(960\) | 1.31890 | 0.0425674 | ||||||||
\(961\) | −30.6517 | −0.988766 | ||||||||
\(962\) | −11.9357 | −0.384824 | ||||||||
\(963\) | −40.2923 | −1.29840 | ||||||||
\(964\) | 5.99522 | 0.193093 | ||||||||
\(965\) | −7.73701 | −0.249063 | ||||||||
\(966\) | −8.04819 | −0.258946 | ||||||||
\(967\) | 19.0146 | 0.611468 | 0.305734 | − | 0.952117i | \(-0.401098\pi\) | ||||
0.305734 | + | 0.952117i | \(0.401098\pi\) | |||||||
\(968\) | 20.0241 | 0.643600 | ||||||||
\(969\) | −0.909612 | −0.0292210 | ||||||||
\(970\) | −6.86023 | −0.220269 | ||||||||
\(971\) | −37.8905 | −1.21596 | −0.607982 | − | 0.793951i | \(-0.708021\pi\) | ||||
−0.607982 | + | 0.793951i | \(0.708021\pi\) | |||||||
\(972\) | 13.1810 | 0.422782 | ||||||||
\(973\) | −10.4655 | −0.335508 | ||||||||
\(974\) | −18.6429 | −0.597356 | ||||||||
\(975\) | 0.893272 | 0.0286076 | ||||||||
\(976\) | 0.871155 | 0.0278850 | ||||||||
\(977\) | 22.0118 | 0.704221 | 0.352110 | − | 0.935958i | \(-0.385464\pi\) | ||||
0.352110 | + | 0.935958i | \(0.385464\pi\) | |||||||
\(978\) | −1.87258 | −0.0598785 | ||||||||
\(979\) | −6.27815 | −0.200651 | ||||||||
\(980\) | 61.1492 | 1.95334 | ||||||||
\(981\) | −44.1969 | −1.41110 | ||||||||
\(982\) | −12.3493 | −0.394083 | ||||||||
\(983\) | 12.0990 | 0.385900 | 0.192950 | − | 0.981209i | \(-0.438195\pi\) | ||||
0.192950 | + | 0.981209i | \(0.438195\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32.2047 | −1.02613 | ||||||||
\(986\) | −0.984551 | −0.0313545 | ||||||||
\(987\) | −8.47331 | −0.269708 | ||||||||
\(988\) | 5.74919 | 0.182906 | ||||||||
\(989\) | −36.3958 | −1.15732 | ||||||||
\(990\) | −8.25721 | −0.262431 | ||||||||
\(991\) | 37.5585 | 1.19309 | 0.596543 | − | 0.802581i | \(-0.296541\pi\) | ||||
0.596543 | + | 0.802581i | \(0.296541\pi\) | |||||||
\(992\) | −3.44237 | −0.109295 | ||||||||
\(993\) | 3.58403 | 0.113736 | ||||||||
\(994\) | 25.2448 | 0.800717 | ||||||||
\(995\) | 22.0607 | 0.699372 | ||||||||
\(996\) | 2.48122 | 0.0786204 | ||||||||
\(997\) | 7.69301 | 0.243640 | 0.121820 | − | 0.992552i | \(-0.461127\pi\) | ||||
0.121820 | + | 0.992552i | \(0.461127\pi\) | |||||||
\(998\) | −4.46630 | −0.141378 | ||||||||
\(999\) | 8.58595 | 0.271647 |
(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 | 1681.2.a.m.1.13 | 24 | ||
41.34 | odd | 40 | 41.2.g.a.8.2 | ✓ | 24 | ||
41.35 | odd | 40 | 41.2.g.a.36.2 | yes | 24 | ||
41.40 | even | 2 | inner | 1681.2.a.m.1.14 | 24 | ||
123.35 | even | 40 | 369.2.u.a.118.2 | 24 | |||
123.116 | even | 40 | 369.2.u.a.172.2 | 24 | |||
164.35 | even | 40 | 656.2.bs.d.241.2 | 24 | |||
164.75 | even | 40 | 656.2.bs.d.49.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
41.2.g.a.8.2 | ✓ | 24 | 41.34 | odd | 40 | ||
41.2.g.a.36.2 | yes | 24 | 41.35 | odd | 40 | ||
369.2.u.a.118.2 | 24 | 123.35 | even | 40 | |||
369.2.u.a.172.2 | 24 | 123.116 | even | 40 | |||
656.2.bs.d.49.2 | 24 | 164.75 | even | 40 | |||
656.2.bs.d.241.2 | 24 | 164.35 | even | 40 | |||
1681.2.a.m.1.13 | 24 | 1.1 | even | 1 | trivial | ||
1681.2.a.m.1.14 | 24 | 41.40 | even | 2 | inner |