Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,4,Mod(1,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.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: | \(21.4176933321\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.35008\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.96812 | 1.40294 | 0.701471 | − | 0.712698i | \(-0.252527\pi\) | ||||
0.701471 | + | 0.712698i | \(0.252527\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 7.74597 | 0.968246 | ||||||||
\(5\) | −11.4919 | −1.02787 | −0.513935 | − | 0.857829i | \(-0.671813\pi\) | ||||
−0.513935 | + | 0.857829i | \(0.671813\pi\) | |||||||
\(6\) | −11.9044 | −0.809989 | ||||||||
\(7\) | 13.5724 | 0.732840 | 0.366420 | − | 0.930450i | \(-0.380583\pi\) | ||||
0.366420 | + | 0.930450i | \(0.380583\pi\) | |||||||
\(8\) | −1.00803 | −0.0445492 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −45.6014 | −1.44204 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −23.2379 | −0.559017 | ||||||||
\(13\) | 67.5220 | 1.44056 | 0.720279 | − | 0.693685i | \(-0.244014\pi\) | ||||
0.720279 | + | 0.693685i | \(0.244014\pi\) | |||||||
\(14\) | 53.8569 | 1.02813 | ||||||||
\(15\) | 34.4758 | 0.593441 | ||||||||
\(16\) | −65.9677 | −1.03075 | ||||||||
\(17\) | 87.1706 | 1.24365 | 0.621823 | − | 0.783158i | \(-0.286392\pi\) | ||||
0.621823 | + | 0.783158i | \(0.286392\pi\) | |||||||
\(18\) | 35.7131 | 0.467647 | ||||||||
\(19\) | 112.271 | 1.35562 | 0.677811 | − | 0.735236i | \(-0.262929\pi\) | ||||
0.677811 | + | 0.735236i | \(0.262929\pi\) | |||||||
\(20\) | −89.0161 | −0.995231 | ||||||||
\(21\) | −40.7172 | −0.423105 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 126.952 | 1.15092 | 0.575462 | − | 0.817829i | \(-0.304822\pi\) | ||||
0.575462 | + | 0.817829i | \(0.304822\pi\) | |||||||
\(24\) | 3.02410 | 0.0257205 | ||||||||
\(25\) | 7.06453 | 0.0565163 | ||||||||
\(26\) | 267.935 | 2.02102 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 105.131 | 0.709569 | ||||||||
\(29\) | 194.446 | 1.24509 | 0.622547 | − | 0.782583i | \(-0.286098\pi\) | ||||
0.622547 | + | 0.782583i | \(0.286098\pi\) | |||||||
\(30\) | 136.804 | 0.832563 | ||||||||
\(31\) | −159.444 | −0.923771 | −0.461886 | − | 0.886940i | \(-0.652827\pi\) | ||||
−0.461886 | + | 0.886940i | \(0.652827\pi\) | |||||||
\(32\) | −253.704 | −1.40153 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 345.903 | 1.74476 | ||||||||
\(35\) | −155.973 | −0.753264 | ||||||||
\(36\) | 69.7137 | 0.322749 | ||||||||
\(37\) | −321.855 | −1.43007 | −0.715035 | − | 0.699088i | \(-0.753589\pi\) | ||||
−0.715035 | + | 0.699088i | \(0.753589\pi\) | |||||||
\(38\) | 445.506 | 1.90186 | ||||||||
\(39\) | −202.566 | −0.831706 | ||||||||
\(40\) | 11.5843 | 0.0457908 | ||||||||
\(41\) | 438.437 | 1.67006 | 0.835029 | − | 0.550206i | \(-0.185451\pi\) | ||||
0.835029 | + | 0.550206i | \(0.185451\pi\) | |||||||
\(42\) | −161.571 | −0.593592 | ||||||||
\(43\) | −4.08802 | −0.0144981 | −0.00724905 | − | 0.999974i | \(-0.502307\pi\) | ||||
−0.00724905 | + | 0.999974i | \(0.502307\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −103.427 | −0.342623 | ||||||||
\(46\) | 503.759 | 1.61468 | ||||||||
\(47\) | 57.5565 | 0.178627 | 0.0893135 | − | 0.996004i | \(-0.471533\pi\) | ||||
0.0893135 | + | 0.996004i | \(0.471533\pi\) | |||||||
\(48\) | 197.903 | 0.595101 | ||||||||
\(49\) | −158.790 | −0.462945 | ||||||||
\(50\) | 28.0329 | 0.0792890 | ||||||||
\(51\) | −261.512 | −0.718019 | ||||||||
\(52\) | 523.023 | 1.39481 | ||||||||
\(53\) | 722.952 | 1.87368 | 0.936840 | − | 0.349758i | \(-0.113736\pi\) | ||||
0.936840 | + | 0.349758i | \(0.113736\pi\) | |||||||
\(54\) | −107.139 | −0.269996 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −13.6814 | −0.0326475 | ||||||||
\(57\) | −336.814 | −0.782669 | ||||||||
\(58\) | 771.585 | 1.74679 | ||||||||
\(59\) | −2.95160 | −0.00651298 | −0.00325649 | − | 0.999995i | \(-0.501037\pi\) | ||||
−0.00325649 | + | 0.999995i | \(0.501037\pi\) | |||||||
\(60\) | 267.048 | 0.574597 | ||||||||
\(61\) | −612.326 | −1.28525 | −0.642626 | − | 0.766180i | \(-0.722155\pi\) | ||||
−0.642626 | + | 0.766180i | \(0.722155\pi\) | |||||||
\(62\) | −632.691 | −1.29600 | ||||||||
\(63\) | 122.151 | 0.244280 | ||||||||
\(64\) | −478.984 | −0.935515 | ||||||||
\(65\) | −775.959 | −1.48071 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 424.621 | 0.774264 | 0.387132 | − | 0.922024i | \(-0.373466\pi\) | ||||
0.387132 | + | 0.922024i | \(0.373466\pi\) | |||||||
\(68\) | 675.220 | 1.20415 | ||||||||
\(69\) | −380.855 | −0.664486 | ||||||||
\(70\) | −618.919 | −1.05679 | ||||||||
\(71\) | 205.460 | 0.343431 | 0.171715 | − | 0.985147i | \(-0.445069\pi\) | ||||
0.171715 | + | 0.985147i | \(0.445069\pi\) | |||||||
\(72\) | −9.07231 | −0.0148497 | ||||||||
\(73\) | −596.421 | −0.956245 | −0.478122 | − | 0.878293i | \(-0.658682\pi\) | ||||
−0.478122 | + | 0.878293i | \(0.658682\pi\) | |||||||
\(74\) | −1277.16 | −2.00631 | ||||||||
\(75\) | −21.1936 | −0.0326297 | ||||||||
\(76\) | 869.650 | 1.31258 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −803.806 | −1.16684 | ||||||||
\(79\) | 812.877 | 1.15767 | 0.578834 | − | 0.815445i | \(-0.303508\pi\) | ||||
0.578834 | + | 0.815445i | \(0.303508\pi\) | |||||||
\(80\) | 758.097 | 1.05947 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1739.77 | 2.34299 | ||||||||
\(83\) | −66.1858 | −0.0875281 | −0.0437641 | − | 0.999042i | \(-0.513935\pi\) | ||||
−0.0437641 | + | 0.999042i | \(0.513935\pi\) | |||||||
\(84\) | −315.394 | −0.409670 | ||||||||
\(85\) | −1001.76 | −1.27831 | ||||||||
\(86\) | −16.2218 | −0.0203400 | ||||||||
\(87\) | −583.338 | −0.718855 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −430.347 | −0.512547 | −0.256273 | − | 0.966604i | \(-0.582495\pi\) | ||||
−0.256273 | + | 0.966604i | \(0.582495\pi\) | |||||||
\(90\) | −410.412 | −0.480681 | ||||||||
\(91\) | 916.435 | 1.05570 | ||||||||
\(92\) | 983.363 | 1.11438 | ||||||||
\(93\) | 478.331 | 0.533339 | ||||||||
\(94\) | 228.391 | 0.250603 | ||||||||
\(95\) | −1290.21 | −1.39340 | ||||||||
\(96\) | 761.111 | 0.809172 | ||||||||
\(97\) | 810.581 | 0.848474 | 0.424237 | − | 0.905551i | \(-0.360542\pi\) | ||||
0.424237 | + | 0.905551i | \(0.360542\pi\) | |||||||
\(98\) | −630.099 | −0.649485 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 54.7216 | 0.0547216 | ||||||||
\(101\) | −252.688 | −0.248945 | −0.124472 | − | 0.992223i | \(-0.539724\pi\) | ||||
−0.124472 | + | 0.992223i | \(0.539724\pi\) | |||||||
\(102\) | −1037.71 | −1.00734 | ||||||||
\(103\) | −1959.38 | −1.87440 | −0.937201 | − | 0.348790i | \(-0.886592\pi\) | ||||
−0.937201 | + | 0.348790i | \(0.886592\pi\) | |||||||
\(104\) | −68.0645 | −0.0641757 | ||||||||
\(105\) | 467.919 | 0.434897 | ||||||||
\(106\) | 2868.76 | 2.62866 | ||||||||
\(107\) | −259.775 | −0.234705 | −0.117352 | − | 0.993090i | \(-0.537441\pi\) | ||||
−0.117352 | + | 0.993090i | \(0.537441\pi\) | |||||||
\(108\) | −209.141 | −0.186339 | ||||||||
\(109\) | 1218.89 | 1.07109 | 0.535543 | − | 0.844508i | \(-0.320107\pi\) | ||||
0.535543 | + | 0.844508i | \(0.320107\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 965.564 | 0.825652 | ||||||||
\(112\) | −895.340 | −0.755372 | ||||||||
\(113\) | −323.016 | −0.268910 | −0.134455 | − | 0.990920i | \(-0.542928\pi\) | ||||
−0.134455 | + | 0.990920i | \(0.542928\pi\) | |||||||
\(114\) | −1336.52 | −1.09804 | ||||||||
\(115\) | −1458.92 | −1.18300 | ||||||||
\(116\) | 1506.17 | 1.20556 | ||||||||
\(117\) | 607.698 | 0.480186 | ||||||||
\(118\) | −11.7123 | −0.00913733 | ||||||||
\(119\) | 1183.11 | 0.911393 | ||||||||
\(120\) | −34.7528 | −0.0264373 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2429.78 | −1.80313 | ||||||||
\(123\) | −1315.31 | −0.964208 | ||||||||
\(124\) | −1235.04 | −0.894438 | ||||||||
\(125\) | 1355.31 | 0.969778 | ||||||||
\(126\) | 484.712 | 0.342711 | ||||||||
\(127\) | −1846.66 | −1.29027 | −0.645136 | − | 0.764068i | \(-0.723199\pi\) | ||||
−0.645136 | + | 0.764068i | \(0.723199\pi\) | |||||||
\(128\) | 128.963 | 0.0890536 | ||||||||
\(129\) | 12.2641 | 0.00837048 | ||||||||
\(130\) | −3079.10 | −2.07734 | ||||||||
\(131\) | −346.196 | −0.230895 | −0.115448 | − | 0.993314i | \(-0.536830\pi\) | ||||
−0.115448 | + | 0.993314i | \(0.536830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1523.79 | 0.993454 | ||||||||
\(134\) | 1684.95 | 1.08625 | ||||||||
\(135\) | 310.282 | 0.197814 | ||||||||
\(136\) | −87.8709 | −0.0554035 | ||||||||
\(137\) | −2432.05 | −1.51667 | −0.758335 | − | 0.651865i | \(-0.773987\pi\) | ||||
−0.758335 | + | 0.651865i | \(0.773987\pi\) | |||||||
\(138\) | −1511.28 | −0.932235 | ||||||||
\(139\) | −100.347 | −0.0612326 | −0.0306163 | − | 0.999531i | \(-0.509747\pi\) | ||||
−0.0306163 | + | 0.999531i | \(0.509747\pi\) | |||||||
\(140\) | −1208.16 | −0.729345 | ||||||||
\(141\) | −172.669 | −0.103130 | ||||||||
\(142\) | 815.288 | 0.481813 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −593.710 | −0.343582 | ||||||||
\(145\) | −2234.56 | −1.27979 | ||||||||
\(146\) | −2366.67 | −1.34156 | ||||||||
\(147\) | 476.371 | 0.267282 | ||||||||
\(148\) | −2493.08 | −1.38466 | ||||||||
\(149\) | −585.619 | −0.321985 | −0.160993 | − | 0.986956i | \(-0.551470\pi\) | ||||
−0.160993 | + | 0.986956i | \(0.551470\pi\) | |||||||
\(150\) | −84.0987 | −0.0457775 | ||||||||
\(151\) | 2586.79 | 1.39411 | 0.697053 | − | 0.717020i | \(-0.254494\pi\) | ||||
0.697053 | + | 0.717020i | \(0.254494\pi\) | |||||||
\(152\) | −113.173 | −0.0603919 | ||||||||
\(153\) | 784.535 | 0.414548 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1832.31 | 0.949516 | ||||||||
\(156\) | −1569.07 | −0.805296 | ||||||||
\(157\) | −706.935 | −0.359360 | −0.179680 | − | 0.983725i | \(-0.557506\pi\) | ||||
−0.179680 | + | 0.983725i | \(0.557506\pi\) | |||||||
\(158\) | 3225.59 | 1.62414 | ||||||||
\(159\) | −2168.85 | −1.08177 | ||||||||
\(160\) | 2915.54 | 1.44059 | ||||||||
\(161\) | 1723.04 | 0.843443 | ||||||||
\(162\) | 321.418 | 0.155882 | ||||||||
\(163\) | 2284.30 | 1.09767 | 0.548835 | − | 0.835931i | \(-0.315072\pi\) | ||||
0.548835 | + | 0.835931i | \(0.315072\pi\) | |||||||
\(164\) | 3396.12 | 1.61703 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −262.633 | −0.122797 | ||||||||
\(167\) | 3214.22 | 1.48936 | 0.744681 | − | 0.667420i | \(-0.232602\pi\) | ||||
0.744681 | + | 0.667420i | \(0.232602\pi\) | |||||||
\(168\) | 41.0443 | 0.0188490 | ||||||||
\(169\) | 2362.23 | 1.07521 | ||||||||
\(170\) | −3975.10 | −1.79339 | ||||||||
\(171\) | 1010.44 | 0.451874 | ||||||||
\(172\) | −31.6657 | −0.0140377 | ||||||||
\(173\) | −832.809 | −0.365996 | −0.182998 | − | 0.983113i | \(-0.558580\pi\) | ||||
−0.182998 | + | 0.983113i | \(0.558580\pi\) | |||||||
\(174\) | −2314.75 | −1.00851 | ||||||||
\(175\) | 95.8826 | 0.0414174 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.85480 | 0.00376027 | ||||||||
\(178\) | −1707.67 | −0.719073 | ||||||||
\(179\) | 1063.70 | 0.444161 | 0.222080 | − | 0.975028i | \(-0.428715\pi\) | ||||
0.222080 | + | 0.975028i | \(0.428715\pi\) | |||||||
\(180\) | −801.145 | −0.331744 | ||||||||
\(181\) | 83.6776 | 0.0343630 | 0.0171815 | − | 0.999852i | \(-0.494531\pi\) | ||||
0.0171815 | + | 0.999852i | \(0.494531\pi\) | |||||||
\(182\) | 3636.52 | 1.48108 | ||||||||
\(183\) | 1836.98 | 0.742041 | ||||||||
\(184\) | −127.972 | −0.0512728 | ||||||||
\(185\) | 3698.73 | 1.46993 | ||||||||
\(186\) | 1898.07 | 0.748244 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 445.830 | 0.172955 | ||||||||
\(189\) | −366.454 | −0.141035 | ||||||||
\(190\) | −5119.73 | −1.95486 | ||||||||
\(191\) | 2024.31 | 0.766881 | 0.383440 | − | 0.923566i | \(-0.374739\pi\) | ||||
0.383440 | + | 0.923566i | \(0.374739\pi\) | |||||||
\(192\) | 1436.95 | 0.540120 | ||||||||
\(193\) | 411.650 | 0.153530 | 0.0767649 | − | 0.997049i | \(-0.475541\pi\) | ||||
0.0767649 | + | 0.997049i | \(0.475541\pi\) | |||||||
\(194\) | 3216.48 | 1.19036 | ||||||||
\(195\) | 2327.88 | 0.854886 | ||||||||
\(196\) | −1229.98 | −0.448245 | ||||||||
\(197\) | 1476.28 | 0.533913 | 0.266957 | − | 0.963709i | \(-0.413982\pi\) | ||||
0.266957 | + | 0.963709i | \(0.413982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4841.72 | −1.72472 | −0.862362 | − | 0.506291i | \(-0.831016\pi\) | ||||
−0.862362 | + | 0.506291i | \(0.831016\pi\) | |||||||
\(200\) | −7.12129 | −0.00251776 | ||||||||
\(201\) | −1273.86 | −0.447022 | ||||||||
\(202\) | −1002.70 | −0.349255 | ||||||||
\(203\) | 2639.10 | 0.912454 | ||||||||
\(204\) | −2025.66 | −0.695219 | ||||||||
\(205\) | −5038.49 | −1.71660 | ||||||||
\(206\) | −7775.05 | −2.62968 | ||||||||
\(207\) | 1142.56 | 0.383641 | ||||||||
\(208\) | −4454.28 | −1.48485 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1856.76 | 0.610136 | ||||||||
\(211\) | −386.336 | −0.126050 | −0.0630248 | − | 0.998012i | \(-0.520075\pi\) | ||||
−0.0630248 | + | 0.998012i | \(0.520075\pi\) | |||||||
\(212\) | 5599.96 | 1.81418 | ||||||||
\(213\) | −616.379 | −0.198280 | ||||||||
\(214\) | −1030.82 | −0.329277 | ||||||||
\(215\) | 46.9793 | 0.0149021 | ||||||||
\(216\) | 27.2169 | 0.00857351 | ||||||||
\(217\) | −2164.03 | −0.676977 | ||||||||
\(218\) | 4836.70 | 1.50267 | ||||||||
\(219\) | 1789.26 | 0.552088 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5885.93 | 1.79154 | ||||||||
\(222\) | 3831.47 | 1.15834 | ||||||||
\(223\) | −4623.33 | −1.38835 | −0.694173 | − | 0.719808i | \(-0.744230\pi\) | ||||
−0.694173 | + | 0.719808i | \(0.744230\pi\) | |||||||
\(224\) | −3443.36 | −1.02710 | ||||||||
\(225\) | 63.5808 | 0.0188388 | ||||||||
\(226\) | −1281.77 | −0.377265 | ||||||||
\(227\) | −1826.28 | −0.533983 | −0.266992 | − | 0.963699i | \(-0.586030\pi\) | ||||
−0.266992 | + | 0.963699i | \(0.586030\pi\) | |||||||
\(228\) | −2608.95 | −0.757816 | ||||||||
\(229\) | 56.2259 | 0.0162249 | 0.00811247 | − | 0.999967i | \(-0.497418\pi\) | ||||
0.00811247 | + | 0.999967i | \(0.497418\pi\) | |||||||
\(230\) | −5789.17 | −1.65968 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −196.008 | −0.0554680 | ||||||||
\(233\) | −5718.16 | −1.60777 | −0.803883 | − | 0.594788i | \(-0.797236\pi\) | ||||
−0.803883 | + | 0.594788i | \(0.797236\pi\) | |||||||
\(234\) | 2411.42 | 0.673673 | ||||||||
\(235\) | −661.435 | −0.183605 | ||||||||
\(236\) | −22.8630 | −0.00630616 | ||||||||
\(237\) | −2438.63 | −0.668380 | ||||||||
\(238\) | 4694.73 | 1.27863 | ||||||||
\(239\) | 2069.72 | 0.560164 | 0.280082 | − | 0.959976i | \(-0.409638\pi\) | ||||
0.280082 | + | 0.959976i | \(0.409638\pi\) | |||||||
\(240\) | −2274.29 | −0.611687 | ||||||||
\(241\) | 4050.63 | 1.08267 | 0.541337 | − | 0.840806i | \(-0.317918\pi\) | ||||
0.541337 | + | 0.840806i | \(0.317918\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −4743.06 | −1.24444 | ||||||||
\(245\) | 1824.81 | 0.475848 | ||||||||
\(246\) | −5219.31 | −1.35273 | ||||||||
\(247\) | 7580.79 | 1.95285 | ||||||||
\(248\) | 160.725 | 0.0411533 | ||||||||
\(249\) | 198.557 | 0.0505344 | ||||||||
\(250\) | 5378.02 | 1.36054 | ||||||||
\(251\) | −5572.20 | −1.40125 | −0.700626 | − | 0.713529i | \(-0.747096\pi\) | ||||
−0.700626 | + | 0.713529i | \(0.747096\pi\) | |||||||
\(252\) | 946.181 | 0.236523 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −7327.76 | −1.81018 | ||||||||
\(255\) | 3005.28 | 0.738030 | ||||||||
\(256\) | 4343.61 | 1.06045 | ||||||||
\(257\) | −2727.81 | −0.662085 | −0.331043 | − | 0.943616i | \(-0.607400\pi\) | ||||
−0.331043 | + | 0.943616i | \(0.607400\pi\) | |||||||
\(258\) | 48.6653 | 0.0117433 | ||||||||
\(259\) | −4368.34 | −1.04801 | ||||||||
\(260\) | −6010.55 | −1.43369 | ||||||||
\(261\) | 1750.01 | 0.415031 | ||||||||
\(262\) | −1373.75 | −0.323932 | ||||||||
\(263\) | 1746.18 | 0.409406 | 0.204703 | − | 0.978824i | \(-0.434377\pi\) | ||||
0.204703 | + | 0.978824i | \(0.434377\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8308.11 | −1.92590 | ||||||||
\(266\) | 6046.58 | 1.39376 | ||||||||
\(267\) | 1291.04 | 0.295919 | ||||||||
\(268\) | 3289.10 | 0.749678 | ||||||||
\(269\) | 2679.54 | 0.607340 | 0.303670 | − | 0.952777i | \(-0.401788\pi\) | ||||
0.303670 | + | 0.952777i | \(0.401788\pi\) | |||||||
\(270\) | 1231.24 | 0.277521 | ||||||||
\(271\) | −6953.32 | −1.55861 | −0.779306 | − | 0.626643i | \(-0.784428\pi\) | ||||
−0.779306 | + | 0.626643i | \(0.784428\pi\) | |||||||
\(272\) | −5750.45 | −1.28188 | ||||||||
\(273\) | −2749.31 | −0.609508 | ||||||||
\(274\) | −9650.66 | −2.12780 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2950.09 | −0.643386 | ||||||||
\(277\) | −1588.49 | −0.344559 | −0.172280 | − | 0.985048i | \(-0.555113\pi\) | ||||
−0.172280 | + | 0.985048i | \(0.555113\pi\) | |||||||
\(278\) | −398.190 | −0.0859058 | ||||||||
\(279\) | −1434.99 | −0.307924 | ||||||||
\(280\) | 157.226 | 0.0335574 | ||||||||
\(281\) | 801.544 | 0.170164 | 0.0850820 | − | 0.996374i | \(-0.472885\pi\) | ||||
0.0850820 | + | 0.996374i | \(0.472885\pi\) | |||||||
\(282\) | −685.173 | −0.144686 | ||||||||
\(283\) | −1993.13 | −0.418655 | −0.209327 | − | 0.977846i | \(-0.567127\pi\) | ||||
−0.209327 | + | 0.977846i | \(0.567127\pi\) | |||||||
\(284\) | 1591.48 | 0.332525 | ||||||||
\(285\) | 3870.64 | 0.804481 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5950.64 | 1.22389 | ||||||||
\(288\) | −2283.33 | −0.467176 | ||||||||
\(289\) | 2685.71 | 0.546654 | ||||||||
\(290\) | −8867.00 | −1.79548 | ||||||||
\(291\) | −2431.74 | −0.489867 | ||||||||
\(292\) | −4619.86 | −0.925880 | ||||||||
\(293\) | 1859.46 | 0.370754 | 0.185377 | − | 0.982667i | \(-0.440649\pi\) | ||||
0.185377 | + | 0.982667i | \(0.440649\pi\) | |||||||
\(294\) | 1890.30 | 0.374981 | ||||||||
\(295\) | 33.9196 | 0.00669449 | ||||||||
\(296\) | 324.441 | 0.0637086 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2323.81 | −0.451726 | ||||||||
\(299\) | 8572.03 | 1.65797 | ||||||||
\(300\) | −164.165 | −0.0315936 | ||||||||
\(301\) | −55.4843 | −0.0106248 | ||||||||
\(302\) | 10264.7 | 1.95585 | ||||||||
\(303\) | 758.065 | 0.143728 | ||||||||
\(304\) | −7406.29 | −1.39730 | ||||||||
\(305\) | 7036.81 | 1.32107 | ||||||||
\(306\) | 3113.13 | 0.581587 | ||||||||
\(307\) | 1127.92 | 0.209687 | 0.104844 | − | 0.994489i | \(-0.466566\pi\) | ||||
0.104844 | + | 0.994489i | \(0.466566\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5878.14 | 1.08219 | ||||||||
\(310\) | 7270.84 | 1.33212 | ||||||||
\(311\) | −1656.33 | −0.302000 | −0.151000 | − | 0.988534i | \(-0.548249\pi\) | ||||
−0.151000 | + | 0.988534i | \(0.548249\pi\) | |||||||
\(312\) | 204.194 | 0.0370519 | ||||||||
\(313\) | 9967.66 | 1.80002 | 0.900009 | − | 0.435872i | \(-0.143560\pi\) | ||||
0.900009 | + | 0.435872i | \(0.143560\pi\) | |||||||
\(314\) | −2805.20 | −0.504162 | ||||||||
\(315\) | −1403.76 | −0.251088 | ||||||||
\(316\) | 6296.51 | 1.12091 | ||||||||
\(317\) | −1867.37 | −0.330858 | −0.165429 | − | 0.986222i | \(-0.552901\pi\) | ||||
−0.165429 | + | 0.986222i | \(0.552901\pi\) | |||||||
\(318\) | −8606.27 | −1.51766 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 5504.45 | 0.961588 | ||||||||
\(321\) | 779.325 | 0.135507 | ||||||||
\(322\) | 6837.21 | 1.18330 | ||||||||
\(323\) | 9786.76 | 1.68591 | ||||||||
\(324\) | 627.423 | 0.107583 | ||||||||
\(325\) | 477.012 | 0.0814149 | ||||||||
\(326\) | 9064.37 | 1.53997 | ||||||||
\(327\) | −3656.67 | −0.618392 | ||||||||
\(328\) | −441.960 | −0.0743998 | ||||||||
\(329\) | 781.179 | 0.130905 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8078.97 | 1.34157 | 0.670786 | − | 0.741651i | \(-0.265957\pi\) | ||||
0.670786 | + | 0.741651i | \(0.265957\pi\) | |||||||
\(332\) | −512.673 | −0.0847487 | ||||||||
\(333\) | −2896.69 | −0.476690 | ||||||||
\(334\) | 12754.4 | 2.08949 | ||||||||
\(335\) | −4879.72 | −0.795843 | ||||||||
\(336\) | 2686.02 | 0.436114 | ||||||||
\(337\) | 7660.53 | 1.23827 | 0.619133 | − | 0.785286i | \(-0.287484\pi\) | ||||
0.619133 | + | 0.785286i | \(0.287484\pi\) | |||||||
\(338\) | 9373.59 | 1.50845 | ||||||||
\(339\) | 969.048 | 0.155255 | ||||||||
\(340\) | −7759.59 | −1.23771 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4009.55 | 0.633953 | ||||||||
\(343\) | −6810.49 | −1.07211 | ||||||||
\(344\) | 4.12087 | 0.000645879 0 | ||||||||
\(345\) | 4376.76 | 0.683005 | ||||||||
\(346\) | −3304.69 | −0.513471 | ||||||||
\(347\) | 6055.85 | 0.936874 | 0.468437 | − | 0.883497i | \(-0.344817\pi\) | ||||
0.468437 | + | 0.883497i | \(0.344817\pi\) | |||||||
\(348\) | −4518.52 | −0.696028 | ||||||||
\(349\) | −7051.57 | −1.08155 | −0.540776 | − | 0.841166i | \(-0.681869\pi\) | ||||
−0.540776 | + | 0.841166i | \(0.681869\pi\) | |||||||
\(350\) | 380.473 | 0.0581062 | ||||||||
\(351\) | −1823.10 | −0.277235 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3426.06 | −0.516574 | −0.258287 | − | 0.966068i | \(-0.583158\pi\) | ||||
−0.258287 | + | 0.966068i | \(0.583158\pi\) | |||||||
\(354\) | 35.1369 | 0.00527544 | ||||||||
\(355\) | −2361.13 | −0.353002 | ||||||||
\(356\) | −3333.45 | −0.496271 | ||||||||
\(357\) | −3549.34 | −0.526193 | ||||||||
\(358\) | 4220.89 | 0.623132 | ||||||||
\(359\) | −11247.1 | −1.65348 | −0.826740 | − | 0.562584i | \(-0.809807\pi\) | ||||
−0.826740 | + | 0.562584i | \(0.809807\pi\) | |||||||
\(360\) | 104.258 | 0.0152636 | ||||||||
\(361\) | 5745.85 | 0.837710 | ||||||||
\(362\) | 332.043 | 0.0482093 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7098.68 | 1.02218 | ||||||||
\(365\) | 6854.04 | 0.982895 | ||||||||
\(366\) | 7289.35 | 1.04104 | ||||||||
\(367\) | −5211.92 | −0.741308 | −0.370654 | − | 0.928771i | \(-0.620866\pi\) | ||||
−0.370654 | + | 0.928771i | \(0.620866\pi\) | |||||||
\(368\) | −8374.71 | −1.18631 | ||||||||
\(369\) | 3945.93 | 0.556686 | ||||||||
\(370\) | 14677.0 | 2.06222 | ||||||||
\(371\) | 9812.18 | 1.37311 | ||||||||
\(372\) | 3705.13 | 0.516404 | ||||||||
\(373\) | 82.0495 | 0.0113897 | 0.00569486 | − | 0.999984i | \(-0.498187\pi\) | ||||
0.00569486 | + | 0.999984i | \(0.498187\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4065.92 | −0.559902 | ||||||||
\(376\) | −58.0189 | −0.00795770 | ||||||||
\(377\) | 13129.4 | 1.79363 | ||||||||
\(378\) | −1454.13 | −0.197864 | ||||||||
\(379\) | −5821.60 | −0.789011 | −0.394506 | − | 0.918893i | \(-0.629084\pi\) | ||||
−0.394506 | + | 0.918893i | \(0.629084\pi\) | |||||||
\(380\) | −9993.96 | −1.34916 | ||||||||
\(381\) | 5539.98 | 0.744939 | ||||||||
\(382\) | 8032.72 | 1.07589 | ||||||||
\(383\) | −3538.65 | −0.472106 | −0.236053 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236053 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(384\) | −386.890 | −0.0514151 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1633.48 | 0.215393 | ||||||||
\(387\) | −36.7922 | −0.00483270 | ||||||||
\(388\) | 6278.73 | 0.821531 | ||||||||
\(389\) | 8142.86 | 1.06134 | 0.530668 | − | 0.847580i | \(-0.321941\pi\) | ||||
0.530668 | + | 0.847580i | \(0.321941\pi\) | |||||||
\(390\) | 9237.29 | 1.19935 | ||||||||
\(391\) | 11066.4 | 1.43134 | ||||||||
\(392\) | 160.066 | 0.0206239 | ||||||||
\(393\) | 1038.59 | 0.133307 | ||||||||
\(394\) | 5858.07 | 0.749049 | ||||||||
\(395\) | −9341.52 | −1.18993 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13241.7 | 1.67401 | 0.837005 | − | 0.547195i | \(-0.184304\pi\) | ||||
0.837005 | + | 0.547195i | \(0.184304\pi\) | |||||||
\(398\) | −19212.5 | −2.41969 | ||||||||
\(399\) | −4571.37 | −0.573571 | ||||||||
\(400\) | −466.031 | −0.0582539 | ||||||||
\(401\) | 5499.97 | 0.684926 | 0.342463 | − | 0.939531i | \(-0.388739\pi\) | ||||
0.342463 | + | 0.939531i | \(0.388739\pi\) | |||||||
\(402\) | −5054.84 | −0.627145 | ||||||||
\(403\) | −10766.0 | −1.33075 | ||||||||
\(404\) | −1957.32 | −0.241040 | ||||||||
\(405\) | −930.847 | −0.114208 | ||||||||
\(406\) | 10472.2 | 1.28012 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 263.613 | 0.0319872 | ||||||||
\(409\) | 11307.5 | 1.36704 | 0.683520 | − | 0.729931i | \(-0.260448\pi\) | ||||
0.683520 | + | 0.729931i | \(0.260448\pi\) | |||||||
\(410\) | −19993.3 | −2.40829 | ||||||||
\(411\) | 7296.14 | 0.875650 | ||||||||
\(412\) | −15177.3 | −1.81488 | ||||||||
\(413\) | −40.0603 | −0.00477297 | ||||||||
\(414\) | 4533.83 | 0.538226 | ||||||||
\(415\) | 760.603 | 0.0899675 | ||||||||
\(416\) | −17130.6 | −2.01898 | ||||||||
\(417\) | 301.042 | 0.0353527 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10437.1 | −1.21691 | −0.608455 | − | 0.793588i | \(-0.708210\pi\) | ||||
−0.608455 | + | 0.793588i | \(0.708210\pi\) | |||||||
\(420\) | 3624.48 | 0.421087 | ||||||||
\(421\) | −1981.89 | −0.229433 | −0.114716 | − | 0.993398i | \(-0.536596\pi\) | ||||
−0.114716 | + | 0.993398i | \(0.536596\pi\) | |||||||
\(422\) | −1533.03 | −0.176840 | ||||||||
\(423\) | 518.008 | 0.0595424 | ||||||||
\(424\) | −728.760 | −0.0834710 | ||||||||
\(425\) | 615.819 | 0.0702862 | ||||||||
\(426\) | −2445.87 | −0.278175 | ||||||||
\(427\) | −8310.73 | −0.941884 | ||||||||
\(428\) | −2012.21 | −0.227252 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 186.419 | 0.0209068 | ||||||||
\(431\) | −8834.65 | −0.987355 | −0.493678 | − | 0.869645i | \(-0.664348\pi\) | ||||
−0.493678 | + | 0.869645i | \(0.664348\pi\) | |||||||
\(432\) | 1781.13 | 0.198367 | ||||||||
\(433\) | 1610.08 | 0.178696 | 0.0893482 | − | 0.996000i | \(-0.471522\pi\) | ||||
0.0893482 | + | 0.996000i | \(0.471522\pi\) | |||||||
\(434\) | −8587.13 | −0.949759 | ||||||||
\(435\) | 6703.68 | 0.738889 | ||||||||
\(436\) | 9441.47 | 1.03707 | ||||||||
\(437\) | 14253.0 | 1.56022 | ||||||||
\(438\) | 7100.01 | 0.774547 | ||||||||
\(439\) | 8438.73 | 0.917446 | 0.458723 | − | 0.888579i | \(-0.348307\pi\) | ||||
0.458723 | + | 0.888579i | \(0.348307\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1429.11 | −0.154315 | ||||||||
\(442\) | 23356.1 | 2.51343 | ||||||||
\(443\) | −13158.2 | −1.41120 | −0.705601 | − | 0.708609i | \(-0.749323\pi\) | ||||
−0.705601 | + | 0.708609i | \(0.749323\pi\) | |||||||
\(444\) | 7479.23 | 0.799434 | ||||||||
\(445\) | 4945.52 | 0.526831 | ||||||||
\(446\) | −18345.9 | −1.94777 | ||||||||
\(447\) | 1756.86 | 0.185898 | ||||||||
\(448\) | −6500.96 | −0.685583 | ||||||||
\(449\) | −15508.4 | −1.63004 | −0.815018 | − | 0.579435i | \(-0.803273\pi\) | ||||
−0.815018 | + | 0.579435i | \(0.803273\pi\) | |||||||
\(450\) | 252.296 | 0.0264297 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −2502.07 | −0.260371 | ||||||||
\(453\) | −7760.37 | −0.804887 | ||||||||
\(454\) | −7246.88 | −0.749147 | ||||||||
\(455\) | −10531.6 | −1.08512 | ||||||||
\(456\) | 339.520 | 0.0348673 | ||||||||
\(457\) | 2014.57 | 0.206209 | 0.103105 | − | 0.994671i | \(-0.467122\pi\) | ||||
0.103105 | + | 0.994671i | \(0.467122\pi\) | |||||||
\(458\) | 223.111 | 0.0227626 | ||||||||
\(459\) | −2353.61 | −0.239340 | ||||||||
\(460\) | −11300.7 | −1.14543 | ||||||||
\(461\) | 4384.13 | 0.442927 | 0.221463 | − | 0.975169i | \(-0.428917\pi\) | ||||
0.221463 | + | 0.975169i | \(0.428917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14761.3 | −1.48167 | −0.740836 | − | 0.671685i | \(-0.765571\pi\) | ||||
−0.740836 | + | 0.671685i | \(0.765571\pi\) | |||||||
\(464\) | −12827.2 | −1.28337 | ||||||||
\(465\) | −5496.94 | −0.548204 | ||||||||
\(466\) | −22690.4 | −2.25560 | ||||||||
\(467\) | −8355.59 | −0.827945 | −0.413973 | − | 0.910289i | \(-0.635859\pi\) | ||||
−0.413973 | + | 0.910289i | \(0.635859\pi\) | |||||||
\(468\) | 4707.21 | 0.464938 | ||||||||
\(469\) | 5763.12 | 0.567412 | ||||||||
\(470\) | −2624.65 | −0.257588 | ||||||||
\(471\) | 2120.81 | 0.207477 | ||||||||
\(472\) | 2.97531 | 0.000290148 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −9676.77 | −0.937698 | ||||||||
\(475\) | 793.145 | 0.0766147 | ||||||||
\(476\) | 9164.35 | 0.882453 | ||||||||
\(477\) | 6506.56 | 0.624560 | ||||||||
\(478\) | 8212.90 | 0.785877 | ||||||||
\(479\) | −6649.18 | −0.634256 | −0.317128 | − | 0.948383i | \(-0.602719\pi\) | ||||
−0.317128 | + | 0.948383i | \(0.602719\pi\) | |||||||
\(480\) | −8746.63 | −0.831724 | ||||||||
\(481\) | −21732.3 | −2.06010 | ||||||||
\(482\) | 16073.4 | 1.51893 | ||||||||
\(483\) | −5169.11 | −0.486962 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9315.14 | −0.872121 | ||||||||
\(486\) | −964.253 | −0.0899988 | ||||||||
\(487\) | 4639.77 | 0.431721 | 0.215861 | − | 0.976424i | \(-0.430744\pi\) | ||||
0.215861 | + | 0.976424i | \(0.430744\pi\) | |||||||
\(488\) | 617.246 | 0.0572570 | ||||||||
\(489\) | −6852.90 | −0.633740 | ||||||||
\(490\) | 7241.05 | 0.667586 | ||||||||
\(491\) | 16552.1 | 1.52136 | 0.760680 | − | 0.649128i | \(-0.224866\pi\) | ||||
0.760680 | + | 0.649128i | \(0.224866\pi\) | |||||||
\(492\) | −10188.4 | −0.933590 | ||||||||
\(493\) | 16950.0 | 1.54845 | ||||||||
\(494\) | 30081.5 | 2.73974 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10518.1 | 0.952173 | ||||||||
\(497\) | 2788.58 | 0.251680 | ||||||||
\(498\) | 787.899 | 0.0708968 | ||||||||
\(499\) | −18627.9 | −1.67114 | −0.835572 | − | 0.549382i | \(-0.814863\pi\) | ||||
−0.835572 | + | 0.549382i | \(0.814863\pi\) | |||||||
\(500\) | 10498.2 | 0.938984 | ||||||||
\(501\) | −9642.65 | −0.859884 | ||||||||
\(502\) | −22111.2 | −1.96587 | ||||||||
\(503\) | −13449.7 | −1.19223 | −0.596115 | − | 0.802899i | \(-0.703290\pi\) | ||||
−0.596115 | + | 0.802899i | \(0.703290\pi\) | |||||||
\(504\) | −123.133 | −0.0108825 | ||||||||
\(505\) | 2903.88 | 0.255883 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7086.68 | −0.620770 | ||||||||
\(508\) | −14304.2 | −1.24930 | ||||||||
\(509\) | 2780.11 | 0.242095 | 0.121047 | − | 0.992647i | \(-0.461375\pi\) | ||||
0.121047 | + | 0.992647i | \(0.461375\pi\) | |||||||
\(510\) | 11925.3 | 1.03541 | ||||||||
\(511\) | −8094.86 | −0.700774 | ||||||||
\(512\) | 16204.3 | 1.39870 | ||||||||
\(513\) | −3031.33 | −0.260890 | ||||||||
\(514\) | −10824.3 | −0.928867 | ||||||||
\(515\) | 22517.1 | 1.92664 | ||||||||
\(516\) | 94.9971 | 0.00810468 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −17334.1 | −1.47030 | ||||||||
\(519\) | 2498.43 | 0.211308 | ||||||||
\(520\) | 782.193 | 0.0659643 | ||||||||
\(521\) | −18428.7 | −1.54966 | −0.774832 | − | 0.632168i | \(-0.782165\pi\) | ||||
−0.774832 | + | 0.632168i | \(0.782165\pi\) | |||||||
\(522\) | 6944.26 | 0.582265 | ||||||||
\(523\) | 3521.88 | 0.294457 | 0.147229 | − | 0.989103i | \(-0.452965\pi\) | ||||
0.147229 | + | 0.989103i | \(0.452965\pi\) | |||||||
\(524\) | −2681.62 | −0.223563 | ||||||||
\(525\) | −287.648 | −0.0239123 | ||||||||
\(526\) | 6929.04 | 0.574373 | ||||||||
\(527\) | −13898.8 | −1.14884 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3949.71 | 0.324625 | ||||||||
\(530\) | −32967.6 | −2.70192 | ||||||||
\(531\) | −26.5644 | −0.00217099 | ||||||||
\(532\) | 11803.2 | 0.961908 | ||||||||
\(533\) | 29604.2 | 2.40581 | ||||||||
\(534\) | 5123.00 | 0.415157 | ||||||||
\(535\) | 2985.32 | 0.241246 | ||||||||
\(536\) | −428.033 | −0.0344929 | ||||||||
\(537\) | −3191.10 | −0.256436 | ||||||||
\(538\) | 10632.7 | 0.852063 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2403.44 | 0.191532 | ||||||||
\(541\) | 3403.53 | 0.270479 | 0.135240 | − | 0.990813i | \(-0.456820\pi\) | ||||
0.135240 | + | 0.990813i | \(0.456820\pi\) | |||||||
\(542\) | −27591.6 | −2.18664 | ||||||||
\(543\) | −251.033 | −0.0198395 | ||||||||
\(544\) | −22115.5 | −1.74300 | ||||||||
\(545\) | −14007.4 | −1.10094 | ||||||||
\(546\) | −10909.6 | −0.855104 | ||||||||
\(547\) | −13015.0 | −1.01733 | −0.508665 | − | 0.860964i | \(-0.669861\pi\) | ||||
−0.508665 | + | 0.860964i | \(0.669861\pi\) | |||||||
\(548\) | −18838.6 | −1.46851 | ||||||||
\(549\) | −5510.94 | −0.428417 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21830.7 | 1.68788 | ||||||||
\(552\) | 383.915 | 0.0296023 | ||||||||
\(553\) | 11032.7 | 0.848385 | ||||||||
\(554\) | −6303.30 | −0.483396 | ||||||||
\(555\) | −11096.2 | −0.848662 | ||||||||
\(556\) | −777.286 | −0.0592882 | ||||||||
\(557\) | −5077.07 | −0.386216 | −0.193108 | − | 0.981177i | \(-0.561857\pi\) | ||||
−0.193108 | + | 0.981177i | \(0.561857\pi\) | |||||||
\(558\) | −5694.22 | −0.431999 | ||||||||
\(559\) | −276.032 | −0.0208853 | ||||||||
\(560\) | 10289.2 | 0.776424 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3180.62 | 0.238730 | ||||||||
\(563\) | 9844.19 | 0.736915 | 0.368458 | − | 0.929645i | \(-0.379886\pi\) | ||||
0.368458 | + | 0.929645i | \(0.379886\pi\) | |||||||
\(564\) | −1337.49 | −0.0998556 | ||||||||
\(565\) | 3712.08 | 0.276404 | ||||||||
\(566\) | −7908.97 | −0.587348 | ||||||||
\(567\) | 1099.36 | 0.0814267 | ||||||||
\(568\) | −207.110 | −0.0152996 | ||||||||
\(569\) | −5319.05 | −0.391891 | −0.195946 | − | 0.980615i | \(-0.562778\pi\) | ||||
−0.195946 | + | 0.980615i | \(0.562778\pi\) | |||||||
\(570\) | 15359.2 | 1.12864 | ||||||||
\(571\) | 10691.4 | 0.783573 | 0.391786 | − | 0.920056i | \(-0.371857\pi\) | ||||
0.391786 | + | 0.920056i | \(0.371857\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6072.94 | −0.442759 | ||||||||
\(574\) | 23612.8 | 1.71704 | ||||||||
\(575\) | 896.854 | 0.0650459 | ||||||||
\(576\) | −4310.85 | −0.311838 | ||||||||
\(577\) | −14719.5 | −1.06201 | −0.531005 | − | 0.847368i | \(-0.678186\pi\) | ||||
−0.531005 | + | 0.847368i | \(0.678186\pi\) | |||||||
\(578\) | 10657.2 | 0.766923 | ||||||||
\(579\) | −1234.95 | −0.0886405 | ||||||||
\(580\) | −17308.8 | −1.23916 | ||||||||
\(581\) | −898.299 | −0.0641441 | ||||||||
\(582\) | −9649.44 | −0.687255 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 601.213 | 0.0426000 | ||||||||
\(585\) | −6983.63 | −0.493568 | ||||||||
\(586\) | 7378.57 | 0.520147 | ||||||||
\(587\) | −9308.36 | −0.654510 | −0.327255 | − | 0.944936i | \(-0.606124\pi\) | ||||
−0.327255 | + | 0.944936i | \(0.606124\pi\) | |||||||
\(588\) | 3689.95 | 0.258794 | ||||||||
\(589\) | −17900.9 | −1.25228 | ||||||||
\(590\) | 134.597 | 0.00939198 | ||||||||
\(591\) | −4428.85 | −0.308255 | ||||||||
\(592\) | 21232.0 | 1.47404 | ||||||||
\(593\) | −23670.0 | −1.63914 | −0.819569 | − | 0.572981i | \(-0.805787\pi\) | ||||
−0.819569 | + | 0.572981i | \(0.805787\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13596.3 | −0.936793 | ||||||||
\(596\) | −4536.19 | −0.311761 | ||||||||
\(597\) | 14525.2 | 0.995770 | ||||||||
\(598\) | 34014.8 | 2.32604 | ||||||||
\(599\) | 7476.65 | 0.509996 | 0.254998 | − | 0.966942i | \(-0.417925\pi\) | ||||
0.254998 | + | 0.966942i | \(0.417925\pi\) | |||||||
\(600\) | 21.3639 | 0.00145363 | ||||||||
\(601\) | 12315.0 | 0.835841 | 0.417920 | − | 0.908484i | \(-0.362759\pi\) | ||||
0.417920 | + | 0.908484i | \(0.362759\pi\) | |||||||
\(602\) | −220.168 | −0.0149060 | ||||||||
\(603\) | 3821.59 | 0.258088 | ||||||||
\(604\) | 20037.2 | 1.34984 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3008.09 | 0.201643 | ||||||||
\(607\) | −7209.54 | −0.482086 | −0.241043 | − | 0.970514i | \(-0.577489\pi\) | ||||
−0.241043 | + | 0.970514i | \(0.577489\pi\) | |||||||
\(608\) | −28483.6 | −1.89994 | ||||||||
\(609\) | −7917.29 | −0.526806 | ||||||||
\(610\) | 27922.9 | 1.85339 | ||||||||
\(611\) | 3886.33 | 0.257323 | ||||||||
\(612\) | 6076.98 | 0.401385 | ||||||||
\(613\) | 8903.43 | 0.586633 | 0.293317 | − | 0.956015i | \(-0.405241\pi\) | ||||
0.293317 | + | 0.956015i | \(0.405241\pi\) | |||||||
\(614\) | 4475.73 | 0.294179 | ||||||||
\(615\) | 15115.5 | 0.991080 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2749.78 | −0.179420 | −0.0897099 | − | 0.995968i | \(-0.528594\pi\) | ||||
−0.0897099 | + | 0.995968i | \(0.528594\pi\) | |||||||
\(618\) | 23325.1 | 1.51824 | ||||||||
\(619\) | −26559.8 | −1.72460 | −0.862299 | − | 0.506399i | \(-0.830976\pi\) | ||||
−0.862299 | + | 0.506399i | \(0.830976\pi\) | |||||||
\(620\) | 14193.0 | 0.919365 | ||||||||
\(621\) | −3427.69 | −0.221495 | ||||||||
\(622\) | −6572.52 | −0.423688 | ||||||||
\(623\) | −5840.83 | −0.375615 | ||||||||
\(624\) | 13362.8 | 0.857278 | ||||||||
\(625\) | −16458.2 | −1.05332 | ||||||||
\(626\) | 39552.9 | 2.52532 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5475.90 | −0.347949 | ||||||||
\(629\) | −28056.3 | −1.77850 | ||||||||
\(630\) | −5570.27 | −0.352262 | ||||||||
\(631\) | −26711.2 | −1.68519 | −0.842596 | − | 0.538546i | \(-0.818974\pi\) | ||||
−0.842596 | + | 0.538546i | \(0.818974\pi\) | |||||||
\(632\) | −819.407 | −0.0515732 | ||||||||
\(633\) | 1159.01 | 0.0727747 | ||||||||
\(634\) | −7409.95 | −0.464175 | ||||||||
\(635\) | 21221.7 | 1.32623 | ||||||||
\(636\) | −16799.9 | −1.04742 | ||||||||
\(637\) | −10721.8 | −0.666899 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1849.14 | 0.114477 | ||||||||
\(640\) | −1482.04 | −0.0915355 | ||||||||
\(641\) | 13617.5 | 0.839095 | 0.419548 | − | 0.907733i | \(-0.362189\pi\) | ||||
0.419548 | + | 0.907733i | \(0.362189\pi\) | |||||||
\(642\) | 3092.46 | 0.190108 | ||||||||
\(643\) | −7993.20 | −0.490235 | −0.245117 | − | 0.969493i | \(-0.578827\pi\) | ||||
−0.245117 | + | 0.969493i | \(0.578827\pi\) | |||||||
\(644\) | 13346.6 | 0.816660 | ||||||||
\(645\) | −140.938 | −0.00860376 | ||||||||
\(646\) | 38835.0 | 2.36524 | ||||||||
\(647\) | −27825.2 | −1.69076 | −0.845380 | − | 0.534166i | \(-0.820626\pi\) | ||||
−0.845380 | + | 0.534166i | \(0.820626\pi\) | |||||||
\(648\) | −81.6508 | −0.00494992 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1892.84 | 0.114220 | ||||||||
\(651\) | 6492.09 | 0.390853 | ||||||||
\(652\) | 17694.1 | 1.06281 | ||||||||
\(653\) | 25007.1 | 1.49863 | 0.749313 | − | 0.662216i | \(-0.230384\pi\) | ||||
0.749313 | + | 0.662216i | \(0.230384\pi\) | |||||||
\(654\) | −14510.1 | −0.867568 | ||||||||
\(655\) | 3978.46 | 0.237330 | ||||||||
\(656\) | −28922.7 | −1.72140 | ||||||||
\(657\) | −5367.79 | −0.318748 | ||||||||
\(658\) | 3099.81 | 0.183652 | ||||||||
\(659\) | −21087.2 | −1.24650 | −0.623248 | − | 0.782025i | \(-0.714187\pi\) | ||||
−0.623248 | + | 0.782025i | \(0.714187\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14271.0 | −0.839751 | −0.419876 | − | 0.907582i | \(-0.637926\pi\) | ||||
−0.419876 | + | 0.907582i | \(0.637926\pi\) | |||||||
\(662\) | 32058.3 | 1.88215 | ||||||||
\(663\) | −17657.8 | −1.03435 | ||||||||
\(664\) | 66.7175 | 0.00389931 | ||||||||
\(665\) | −17511.3 | −1.02114 | ||||||||
\(666\) | −11494.4 | −0.668769 | ||||||||
\(667\) | 24685.2 | 1.43301 | ||||||||
\(668\) | 24897.2 | 1.44207 | ||||||||
\(669\) | 13870.0 | 0.801562 | ||||||||
\(670\) | −19363.3 | −1.11652 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 10330.1 | 0.592994 | ||||||||
\(673\) | −9388.49 | −0.537741 | −0.268870 | − | 0.963176i | \(-0.586650\pi\) | ||||
−0.268870 | + | 0.963176i | \(0.586650\pi\) | |||||||
\(674\) | 30397.9 | 1.73722 | ||||||||
\(675\) | −190.742 | −0.0108766 | ||||||||
\(676\) | 18297.7 | 1.04106 | ||||||||
\(677\) | −3239.61 | −0.183912 | −0.0919561 | − | 0.995763i | \(-0.529312\pi\) | ||||
−0.0919561 | + | 0.995763i | \(0.529312\pi\) | |||||||
\(678\) | 3845.30 | 0.217814 | ||||||||
\(679\) | 11001.5 | 0.621796 | ||||||||
\(680\) | 1009.81 | 0.0569475 | ||||||||
\(681\) | 5478.83 | 0.308295 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20716.5 | 1.16061 | 0.580303 | − | 0.814401i | \(-0.302934\pi\) | ||||
0.580303 | + | 0.814401i | \(0.302934\pi\) | |||||||
\(684\) | 7826.85 | 0.437525 | ||||||||
\(685\) | 27948.9 | 1.55894 | ||||||||
\(686\) | −27024.8 | −1.50410 | ||||||||
\(687\) | −168.678 | −0.00936747 | ||||||||
\(688\) | 269.678 | 0.0149438 | ||||||||
\(689\) | 48815.2 | 2.69914 | ||||||||
\(690\) | 17367.5 | 0.958216 | ||||||||
\(691\) | −27118.1 | −1.49294 | −0.746469 | − | 0.665420i | \(-0.768253\pi\) | ||||
−0.746469 | + | 0.665420i | \(0.768253\pi\) | |||||||
\(692\) | −6450.91 | −0.354374 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24030.3 | 1.31438 | ||||||||
\(695\) | 1153.18 | 0.0629392 | ||||||||
\(696\) | 588.025 | 0.0320244 | ||||||||
\(697\) | 38218.8 | 2.07696 | ||||||||
\(698\) | −27981.5 | −1.51736 | ||||||||
\(699\) | 17154.5 | 0.928244 | ||||||||
\(700\) | 742.703 | 0.0401022 | ||||||||
\(701\) | 6409.27 | 0.345328 | 0.172664 | − | 0.984981i | \(-0.444763\pi\) | ||||
0.172664 | + | 0.984981i | \(0.444763\pi\) | |||||||
\(702\) | −7234.26 | −0.388945 | ||||||||
\(703\) | −36135.1 | −1.93863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1984.31 | 0.106005 | ||||||||
\(706\) | −13595.0 | −0.724723 | ||||||||
\(707\) | −3429.59 | −0.182437 | ||||||||
\(708\) | 68.5890 | 0.00364086 | ||||||||
\(709\) | −17210.3 | −0.911632 | −0.455816 | − | 0.890074i | \(-0.650653\pi\) | ||||
−0.455816 | + | 0.890074i | \(0.650653\pi\) | |||||||
\(710\) | −9369.24 | −0.495241 | ||||||||
\(711\) | 7315.89 | 0.385889 | ||||||||
\(712\) | 433.804 | 0.0228336 | ||||||||
\(713\) | −20241.6 | −1.06319 | ||||||||
\(714\) | −14084.2 | −0.738218 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8239.40 | 0.430057 | ||||||||
\(717\) | −6209.16 | −0.323411 | ||||||||
\(718\) | −44629.8 | −2.31974 | ||||||||
\(719\) | −10051.0 | −0.521335 | −0.260667 | − | 0.965429i | \(-0.583943\pi\) | ||||
−0.260667 | + | 0.965429i | \(0.583943\pi\) | |||||||
\(720\) | 6822.87 | 0.353157 | ||||||||
\(721\) | −26593.5 | −1.37364 | ||||||||
\(722\) | 22800.2 | 1.17526 | ||||||||
\(723\) | −12151.9 | −0.625082 | ||||||||
\(724\) | 648.164 | 0.0332719 | ||||||||
\(725\) | 1373.67 | 0.0703680 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1668.92 | 0.0851400 | 0.0425700 | − | 0.999093i | \(-0.486445\pi\) | ||||
0.0425700 | + | 0.999093i | \(0.486445\pi\) | |||||||
\(728\) | −923.798 | −0.0470306 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 27197.6 | 1.37894 | ||||||||
\(731\) | −356.355 | −0.0180305 | ||||||||
\(732\) | 14229.2 | 0.718478 | ||||||||
\(733\) | −18242.1 | −0.919221 | −0.459610 | − | 0.888121i | \(-0.652011\pi\) | ||||
−0.459610 | + | 0.888121i | \(0.652011\pi\) | |||||||
\(734\) | −20681.5 | −1.04001 | ||||||||
\(735\) | −5474.42 | −0.274731 | ||||||||
\(736\) | −32208.1 | −1.61305 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 15657.9 | 0.780998 | ||||||||
\(739\) | −9596.59 | −0.477694 | −0.238847 | − | 0.971057i | \(-0.576770\pi\) | ||||
−0.238847 | + | 0.971057i | \(0.576770\pi\) | |||||||
\(740\) | 28650.3 | 1.42325 | ||||||||
\(741\) | −22742.4 | −1.12748 | ||||||||
\(742\) | 38935.9 | 1.92639 | ||||||||
\(743\) | −5085.37 | −0.251096 | −0.125548 | − | 0.992088i | \(-0.540069\pi\) | ||||
−0.125548 | + | 0.992088i | \(0.540069\pi\) | |||||||
\(744\) | −482.174 | −0.0237599 | ||||||||
\(745\) | 6729.90 | 0.330959 | ||||||||
\(746\) | 325.582 | 0.0159791 | ||||||||
\(747\) | −595.672 | −0.0291760 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3525.77 | −0.172001 | ||||||||
\(750\) | −16134.1 | −0.785510 | ||||||||
\(751\) | −6152.28 | −0.298935 | −0.149467 | − | 0.988767i | \(-0.547756\pi\) | ||||
−0.149467 | + | 0.988767i | \(0.547756\pi\) | |||||||
\(752\) | −3796.87 | −0.184119 | ||||||||
\(753\) | 16716.6 | 0.809013 | ||||||||
\(754\) | 52099.0 | 2.51636 | ||||||||
\(755\) | −29727.2 | −1.43296 | ||||||||
\(756\) | −2838.54 | −0.136557 | ||||||||
\(757\) | 32336.0 | 1.55254 | 0.776269 | − | 0.630402i | \(-0.217110\pi\) | ||||
0.776269 | + | 0.630402i | \(0.217110\pi\) | |||||||
\(758\) | −23100.8 | −1.10694 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1300.58 | 0.0620750 | ||||||||
\(761\) | 39095.6 | 1.86231 | 0.931154 | − | 0.364627i | \(-0.118803\pi\) | ||||
0.931154 | + | 0.364627i | \(0.118803\pi\) | |||||||
\(762\) | 21983.3 | 1.04511 | ||||||||
\(763\) | 16543.2 | 0.784935 | ||||||||
\(764\) | 15680.3 | 0.742529 | ||||||||
\(765\) | −9015.83 | −0.426102 | ||||||||
\(766\) | −14041.8 | −0.662338 | ||||||||
\(767\) | −199.298 | −0.00938232 | ||||||||
\(768\) | −13030.8 | −0.612252 | ||||||||
\(769\) | −12565.9 | −0.589256 | −0.294628 | − | 0.955612i | \(-0.595196\pi\) | ||||
−0.294628 | + | 0.955612i | \(0.595196\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8183.42 | 0.382255 | ||||||||
\(772\) | 3188.63 | 0.148655 | ||||||||
\(773\) | 37205.4 | 1.73116 | 0.865578 | − | 0.500774i | \(-0.166951\pi\) | ||||
0.865578 | + | 0.500774i | \(0.166951\pi\) | |||||||
\(774\) | −145.996 | −0.00677999 | ||||||||
\(775\) | −1126.39 | −0.0522081 | ||||||||
\(776\) | −817.093 | −0.0377989 | ||||||||
\(777\) | 13105.0 | 0.605071 | ||||||||
\(778\) | 32311.8 | 1.48899 | ||||||||
\(779\) | 49223.9 | 2.26397 | ||||||||
\(780\) | 18031.7 | 0.827739 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 43913.0 | 2.00809 | ||||||||
\(783\) | −5250.04 | −0.239618 | ||||||||
\(784\) | 10475.0 | 0.477179 | ||||||||
\(785\) | 8124.06 | 0.369376 | ||||||||
\(786\) | 4121.24 | 0.187023 | ||||||||
\(787\) | 29516.6 | 1.33692 | 0.668459 | − | 0.743749i | \(-0.266954\pi\) | ||||
0.668459 | + | 0.743749i | \(0.266954\pi\) | |||||||
\(788\) | 11435.3 | 0.516959 | ||||||||
\(789\) | −5238.53 | −0.236371 | ||||||||
\(790\) | −37068.3 | −1.66940 | ||||||||
\(791\) | −4384.10 | −0.197068 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41345.5 | −1.85148 | ||||||||
\(794\) | 52544.7 | 2.34854 | ||||||||
\(795\) | 24924.3 | 1.11192 | ||||||||
\(796\) | −37503.8 | −1.66996 | ||||||||
\(797\) | 11288.6 | 0.501709 | 0.250855 | − | 0.968025i | \(-0.419288\pi\) | ||||
0.250855 | + | 0.968025i | \(0.419288\pi\) | |||||||
\(798\) | −18139.7 | −0.804687 | ||||||||
\(799\) | 5017.23 | 0.222149 | ||||||||
\(800\) | −1792.30 | −0.0792091 | ||||||||
\(801\) | −3873.12 | −0.170849 | ||||||||
\(802\) | 21824.5 | 0.960911 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −9867.30 | −0.432827 | ||||||||
\(805\) | −19801.0 | −0.866949 | ||||||||
\(806\) | −42720.6 | −1.86696 | ||||||||
\(807\) | −8038.62 | −0.350648 | ||||||||
\(808\) | 254.719 | 0.0110903 | ||||||||
\(809\) | −10197.4 | −0.443168 | −0.221584 | − | 0.975141i | \(-0.571123\pi\) | ||||
−0.221584 | + | 0.975141i | \(0.571123\pi\) | |||||||
\(810\) | −3693.71 | −0.160227 | ||||||||
\(811\) | −8747.22 | −0.378738 | −0.189369 | − | 0.981906i | \(-0.560644\pi\) | ||||
−0.189369 | + | 0.981906i | \(0.560644\pi\) | |||||||
\(812\) | 20442.3 | 0.883480 | ||||||||
\(813\) | 20860.0 | 0.899865 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26251.0 | −1.12826 | ||||||||
\(816\) | 17251.3 | 0.740095 | ||||||||
\(817\) | −458.968 | −0.0196539 | ||||||||
\(818\) | 44869.5 | 1.91788 | ||||||||
\(819\) | 8247.92 | 0.351899 | ||||||||
\(820\) | −39028.0 | −1.66209 | ||||||||
\(821\) | 2221.32 | 0.0944270 | 0.0472135 | − | 0.998885i | \(-0.484966\pi\) | ||||
0.0472135 | + | 0.998885i | \(0.484966\pi\) | |||||||
\(822\) | 28952.0 | 1.22849 | ||||||||
\(823\) | 19758.1 | 0.836844 | 0.418422 | − | 0.908253i | \(-0.362583\pi\) | ||||
0.418422 | + | 0.908253i | \(0.362583\pi\) | |||||||
\(824\) | 1975.12 | 0.0835032 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −158.964 | −0.00669620 | ||||||||
\(827\) | 41462.1 | 1.74338 | 0.871691 | − | 0.490056i | \(-0.163024\pi\) | ||||
0.871691 | + | 0.490056i | \(0.163024\pi\) | |||||||
\(828\) | 8850.27 | 0.371459 | ||||||||
\(829\) | 20493.2 | 0.858576 | 0.429288 | − | 0.903168i | \(-0.358764\pi\) | ||||
0.429288 | + | 0.903168i | \(0.358764\pi\) | |||||||
\(830\) | 3018.16 | 0.126219 | ||||||||
\(831\) | 4765.46 | 0.198931 | ||||||||
\(832\) | −32342.0 | −1.34766 | ||||||||
\(833\) | −13841.8 | −0.575740 | ||||||||
\(834\) | 1194.57 | 0.0495978 | ||||||||
\(835\) | −36937.6 | −1.53087 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4304.98 | 0.177780 | ||||||||
\(838\) | −41415.6 | −1.70725 | ||||||||
\(839\) | 36109.8 | 1.48588 | 0.742938 | − | 0.669360i | \(-0.233432\pi\) | ||||
0.742938 | + | 0.669360i | \(0.233432\pi\) | |||||||
\(840\) | −471.678 | −0.0193743 | ||||||||
\(841\) | 13420.2 | 0.550257 | ||||||||
\(842\) | −7864.36 | −0.321881 | ||||||||
\(843\) | −2404.63 | −0.0982442 | ||||||||
\(844\) | −2992.54 | −0.122047 | ||||||||
\(845\) | −27146.5 | −1.10517 | ||||||||
\(846\) | 2055.52 | 0.0835345 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −47691.5 | −1.93129 | ||||||||
\(849\) | 5979.39 | 0.241710 | ||||||||
\(850\) | 2443.64 | 0.0986074 | ||||||||
\(851\) | −40860.0 | −1.64590 | ||||||||
\(852\) | −4774.45 | −0.191984 | ||||||||
\(853\) | 25284.5 | 1.01492 | 0.507459 | − | 0.861676i | \(-0.330585\pi\) | ||||
0.507459 | + | 0.861676i | \(0.330585\pi\) | |||||||
\(854\) | −32978.0 | −1.32141 | ||||||||
\(855\) | −11611.9 | −0.464468 | ||||||||
\(856\) | 261.862 | 0.0104559 | ||||||||
\(857\) | −547.314 | −0.0218155 | −0.0109078 | − | 0.999941i | \(-0.503472\pi\) | ||||
−0.0109078 | + | 0.999941i | \(0.503472\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32971.6 | 1.30963 | 0.654817 | − | 0.755788i | \(-0.272746\pi\) | ||||
0.654817 | + | 0.755788i | \(0.272746\pi\) | |||||||
\(860\) | 363.900 | 0.0144289 | ||||||||
\(861\) | −17851.9 | −0.706610 | ||||||||
\(862\) | −35056.9 | −1.38520 | ||||||||
\(863\) | 1526.26 | 0.0602021 | 0.0301010 | − | 0.999547i | \(-0.490417\pi\) | ||||
0.0301010 | + | 0.999547i | \(0.490417\pi\) | |||||||
\(864\) | 6850.00 | 0.269724 | ||||||||
\(865\) | 9570.59 | 0.376196 | ||||||||
\(866\) | 6388.99 | 0.250701 | ||||||||
\(867\) | −8057.13 | −0.315611 | ||||||||
\(868\) | −16762.5 | −0.655480 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 26601.0 | 1.03662 | ||||||||
\(871\) | 28671.3 | 1.11537 | ||||||||
\(872\) | −1228.68 | −0.0477161 | ||||||||
\(873\) | 7295.22 | 0.282825 | ||||||||
\(874\) | 56557.7 | 2.18889 | ||||||||
\(875\) | 18394.7 | 0.710693 | ||||||||
\(876\) | 13859.6 | 0.534557 | ||||||||
\(877\) | −4727.50 | −0.182026 | −0.0910128 | − | 0.995850i | \(-0.529010\pi\) | ||||
−0.0910128 | + | 0.995850i | \(0.529010\pi\) | |||||||
\(878\) | 33485.9 | 1.28712 | ||||||||
\(879\) | −5578.39 | −0.214055 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10481.7 | −0.400838 | −0.200419 | − | 0.979710i | \(-0.564230\pi\) | ||||
−0.200419 | + | 0.979710i | \(0.564230\pi\) | |||||||
\(882\) | −5670.89 | −0.216495 | ||||||||
\(883\) | −37338.2 | −1.42302 | −0.711512 | − | 0.702674i | \(-0.751989\pi\) | ||||
−0.711512 | + | 0.702674i | \(0.751989\pi\) | |||||||
\(884\) | 45592.3 | 1.73465 | ||||||||
\(885\) | −101.759 | −0.00386507 | ||||||||
\(886\) | −52213.1 | −1.97984 | ||||||||
\(887\) | −46961.5 | −1.77769 | −0.888846 | − | 0.458207i | \(-0.848492\pi\) | ||||
−0.888846 | + | 0.458207i | \(0.848492\pi\) | |||||||
\(888\) | −973.322 | −0.0367822 | ||||||||
\(889\) | −25063.6 | −0.945563 | ||||||||
\(890\) | 19624.4 | 0.739114 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −35812.2 | −1.34426 | ||||||||
\(893\) | 6461.94 | 0.242151 | ||||||||
\(894\) | 6971.42 | 0.260804 | ||||||||
\(895\) | −12224.0 | −0.456539 | ||||||||
\(896\) | 1750.34 | 0.0652620 | ||||||||
\(897\) | −25716.1 | −0.957230 | ||||||||
\(898\) | −61539.1 | −2.28685 | ||||||||
\(899\) | −31003.1 | −1.15018 | ||||||||
\(900\) | 492.495 | 0.0182405 | ||||||||
\(901\) | 63020.1 | 2.33019 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 166.453 | 0.00613422 | ||||||||
\(904\) | 325.611 | 0.0119797 | ||||||||
\(905\) | −961.617 | −0.0353207 | ||||||||
\(906\) | −30794.1 | −1.12921 | ||||||||
\(907\) | −26343.8 | −0.964423 | −0.482211 | − | 0.876055i | \(-0.660166\pi\) | ||||
−0.482211 | + | 0.876055i | \(0.660166\pi\) | |||||||
\(908\) | −14146.3 | −0.517027 | ||||||||
\(909\) | −2274.20 | −0.0829816 | ||||||||
\(910\) | −41790.7 | −1.52236 | ||||||||
\(911\) | −1824.39 | −0.0663498 | −0.0331749 | − | 0.999450i | \(-0.510562\pi\) | ||||
−0.0331749 | + | 0.999450i | \(0.510562\pi\) | |||||||
\(912\) | 22218.9 | 0.806732 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 7994.06 | 0.289300 | ||||||||
\(915\) | −21110.4 | −0.762721 | ||||||||
\(916\) | 435.524 | 0.0157097 | ||||||||
\(917\) | −4698.70 | −0.169209 | ||||||||
\(918\) | −9339.39 | −0.335780 | ||||||||
\(919\) | −20121.9 | −0.722262 | −0.361131 | − | 0.932515i | \(-0.617609\pi\) | ||||
−0.361131 | + | 0.932515i | \(0.617609\pi\) | |||||||
\(920\) | 1470.64 | 0.0527017 | ||||||||
\(921\) | −3383.77 | −0.121063 | ||||||||
\(922\) | 17396.7 | 0.621400 | ||||||||
\(923\) | 13873.1 | 0.494732 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2273.75 | −0.0808222 | ||||||||
\(926\) | −58574.5 | −2.07870 | ||||||||
\(927\) | −17634.4 | −0.624800 | ||||||||
\(928\) | −49331.6 | −1.74503 | ||||||||
\(929\) | 34106.4 | 1.20452 | 0.602258 | − | 0.798301i | \(-0.294268\pi\) | ||||
0.602258 | + | 0.798301i | \(0.294268\pi\) | |||||||
\(930\) | −21812.5 | −0.769098 | ||||||||
\(931\) | −17827.6 | −0.627579 | ||||||||
\(932\) | −44292.7 | −1.55671 | ||||||||
\(933\) | 4968.99 | 0.174360 | ||||||||
\(934\) | −33156.0 | −1.16156 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −612.581 | −0.0213919 | ||||||||
\(937\) | 7703.60 | 0.268587 | 0.134293 | − | 0.990942i | \(-0.457124\pi\) | ||||
0.134293 | + | 0.990942i | \(0.457124\pi\) | |||||||
\(938\) | 22868.7 | 0.796046 | ||||||||
\(939\) | −29903.0 | −1.03924 | ||||||||
\(940\) | −5123.45 | −0.177775 | ||||||||
\(941\) | 9282.36 | 0.321569 | 0.160784 | − | 0.986990i | \(-0.448598\pi\) | ||||
0.160784 | + | 0.986990i | \(0.448598\pi\) | |||||||
\(942\) | 8415.61 | 0.291078 | ||||||||
\(943\) | 55660.3 | 1.92211 | ||||||||
\(944\) | 194.710 | 0.00671322 | ||||||||
\(945\) | 4211.27 | 0.144966 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33215.0 | 1.13975 | 0.569874 | − | 0.821732i | \(-0.306992\pi\) | ||||
0.569874 | + | 0.821732i | \(0.306992\pi\) | |||||||
\(948\) | −18889.5 | −0.647156 | ||||||||
\(949\) | −40271.6 | −1.37752 | ||||||||
\(950\) | 3147.29 | 0.107486 | ||||||||
\(951\) | 5602.11 | 0.191021 | ||||||||
\(952\) | −1192.62 | −0.0406019 | ||||||||
\(953\) | −798.262 | −0.0271335 | −0.0135668 | − | 0.999908i | \(-0.504319\pi\) | ||||
−0.0135668 | + | 0.999908i | \(0.504319\pi\) | |||||||
\(954\) | 25818.8 | 0.876221 | ||||||||
\(955\) | −23263.3 | −0.788254 | ||||||||
\(956\) | 16032.0 | 0.542376 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26384.7 | −0.889825 | ||||||||
\(959\) | −33008.7 | −1.11148 | ||||||||
\(960\) | −16513.4 | −0.555173 | ||||||||
\(961\) | −4368.76 | −0.146647 | ||||||||
\(962\) | −86236.3 | −2.89020 | ||||||||
\(963\) | −2337.98 | −0.0782349 | ||||||||
\(964\) | 31376.1 | 1.04829 | ||||||||
\(965\) | −4730.66 | −0.157809 | ||||||||
\(966\) | −20511.6 | −0.683179 | ||||||||
\(967\) | 33883.1 | 1.12679 | 0.563396 | − | 0.826187i | \(-0.309495\pi\) | ||||
0.563396 | + | 0.826187i | \(0.309495\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29360.3 | −0.973362 | ||||||||
\(970\) | −36963.6 | −1.22353 | ||||||||
\(971\) | 37313.7 | 1.23322 | 0.616609 | − | 0.787270i | \(-0.288506\pi\) | ||||
0.616609 | + | 0.787270i | \(0.288506\pi\) | |||||||
\(972\) | −1882.27 | −0.0621130 | ||||||||
\(973\) | −1361.95 | −0.0448737 | ||||||||
\(974\) | 18411.2 | 0.605680 | ||||||||
\(975\) | −1431.03 | −0.0470049 | ||||||||
\(976\) | 40393.8 | 1.32477 | ||||||||
\(977\) | 22242.2 | 0.728343 | 0.364172 | − | 0.931332i | \(-0.381352\pi\) | ||||
0.364172 | + | 0.931332i | \(0.381352\pi\) | |||||||
\(978\) | −27193.1 | −0.889100 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 14134.9 | 0.460737 | ||||||||
\(981\) | 10970.0 | 0.357029 | ||||||||
\(982\) | 65680.8 | 2.13438 | ||||||||
\(983\) | 6313.28 | 0.204845 | 0.102422 | − | 0.994741i | \(-0.467341\pi\) | ||||
0.102422 | + | 0.994741i | \(0.467341\pi\) | |||||||
\(984\) | 1325.88 | 0.0429547 | ||||||||
\(985\) | −16965.4 | −0.548793 | ||||||||
\(986\) | 67259.5 | 2.17239 | ||||||||
\(987\) | −2343.54 | −0.0755781 | ||||||||
\(988\) | 58720.5 | 1.89084 | ||||||||
\(989\) | −518.981 | −0.0166862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15619.7 | 0.500681 | 0.250340 | − | 0.968158i | \(-0.419457\pi\) | ||||
0.250340 | + | 0.968158i | \(0.419457\pi\) | |||||||
\(992\) | 40451.4 | 1.29469 | ||||||||
\(993\) | −24236.9 | −0.774557 | ||||||||
\(994\) | 11065.4 | 0.353092 | ||||||||
\(995\) | 55640.7 | 1.77279 | ||||||||
\(996\) | 1538.02 | 0.0489297 | ||||||||
\(997\) | 47936.3 | 1.52273 | 0.761364 | − | 0.648325i | \(-0.224530\pi\) | ||||
0.761364 | + | 0.648325i | \(0.224530\pi\) | |||||||
\(998\) | −73917.8 | −2.34452 | ||||||||
\(999\) | 8690.08 | 0.275217 |
(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 | 363.4.a.r.1.4 | yes | 4 | |
3.2 | odd | 2 | 1089.4.a.bb.1.1 | 4 | |||
11.10 | odd | 2 | inner | 363.4.a.r.1.1 | ✓ | 4 | |
33.32 | even | 2 | 1089.4.a.bb.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.4.a.r.1.1 | ✓ | 4 | 11.10 | odd | 2 | inner | |
363.4.a.r.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
1089.4.a.bb.1.1 | 4 | 3.2 | odd | 2 | |||
1089.4.a.bb.1.4 | 4 | 33.32 | even | 2 |