Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.31121 | −1.33438 | −0.667188 | − | 0.744890i | \(-0.732502\pi\) | ||||
−0.667188 | + | 0.744890i | \(0.732502\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.927476 | 0.414780 | 0.207390 | − | 0.978258i | \(-0.433503\pi\) | ||||
0.207390 | + | 0.978258i | \(0.433503\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.63809 | 0.619140 | 0.309570 | − | 0.950877i | \(-0.399815\pi\) | ||||
0.309570 | + | 0.950877i | \(0.399815\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.34167 | 0.780558 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.24191 | −0.675960 | −0.337980 | − | 0.941153i | \(-0.609744\pi\) | ||||
−0.337980 | + | 0.941153i | \(0.609744\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.71955 | −1.30897 | −0.654484 | − | 0.756076i | \(-0.727114\pi\) | ||||
−0.654484 | + | 0.756076i | \(0.727114\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.14359 | −0.553472 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.14119 | −0.519314 | −0.259657 | − | 0.965701i | \(-0.583610\pi\) | ||||
−0.259657 | + | 0.965701i | \(0.583610\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.96238 | 1.59728 | 0.798640 | − | 0.601809i | \(-0.205553\pi\) | ||||
0.798640 | + | 0.601809i | \(0.205553\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.78596 | −0.826165 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.04442 | 1.05184 | 0.525918 | − | 0.850536i | \(-0.323722\pi\) | ||||
0.525918 | + | 0.850536i | \(0.323722\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.13979 | −0.827958 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.52153 | 0.292818 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.17280 | −0.960565 | −0.480283 | − | 0.877114i | \(-0.659466\pi\) | ||||
−0.480283 | + | 0.877114i | \(0.659466\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00240 | −0.718852 | −0.359426 | − | 0.933174i | \(-0.617027\pi\) | ||||
−0.359426 | + | 0.933174i | \(0.617027\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.18151 | 0.901985 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.51929 | 0.256807 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.244212 | −0.0401481 | −0.0200741 | − | 0.999798i | \(-0.506390\pi\) | ||||
−0.0200741 | + | 0.999798i | \(0.506390\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.9079 | 1.74665 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.08326 | 1.10622 | 0.553110 | − | 0.833108i | \(-0.313441\pi\) | ||||
0.553110 | + | 0.833108i | \(0.313441\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.58664 | 1.46195 | 0.730974 | − | 0.682405i | \(-0.239066\pi\) | ||||
0.730974 | + | 0.682405i | \(0.239066\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.17185 | 0.323760 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.81916 | 0.848811 | 0.424406 | − | 0.905472i | \(-0.360483\pi\) | ||||
0.424406 | + | 0.905472i | \(0.360483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.31666 | −0.616666 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.94873 | 0.692960 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.15056 | 0.295403 | 0.147701 | − | 0.989032i | \(-0.452813\pi\) | ||||
0.147701 | + | 0.989032i | \(0.452813\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.07931 | −0.280375 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.0915 | −2.13137 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.38352 | −0.570686 | −0.285343 | − | 0.958425i | \(-0.592108\pi\) | ||||
−0.285343 | + | 0.958425i | \(0.592108\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.54367 | −0.709794 | −0.354897 | − | 0.934905i | \(-0.615484\pi\) | ||||
−0.354897 | + | 0.934905i | \(0.615484\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.83587 | 0.483274 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.37727 | −0.542934 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00112 | 0.733154 | 0.366577 | − | 0.930388i | \(-0.380530\pi\) | ||||
0.366577 | + | 0.930388i | \(0.380530\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.6587 | −1.40354 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.94600 | −0.586982 | −0.293491 | − | 0.955962i | \(-0.594817\pi\) | ||||
−0.293491 | + | 0.955962i | \(0.594817\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.67954 | 0.898823 | 0.449411 | − | 0.893325i | \(-0.351634\pi\) | ||||
0.449411 | + | 0.893325i | \(0.351634\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.56790 | 1.10481 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.67244 | −0.418514 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.29582 | −0.708336 | −0.354168 | − | 0.935182i | \(-0.615236\pi\) | ||||
−0.354168 | + | 0.935182i | \(0.615236\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.5416 | −1.17129 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.1766 | −1.66585 | −0.832926 | − | 0.553384i | \(-0.813336\pi\) | ||||
−0.832926 | + | 0.553384i | \(0.813336\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.98590 | −0.215401 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.9554 | 1.28175 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.2180 | 1.71911 | 0.859555 | − | 0.511044i | \(-0.170741\pi\) | ||||
0.859555 | + | 0.511044i | \(0.170741\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.73105 | −0.810434 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.25037 | 0.959218 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.45744 | 0.662520 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.2171 | 1.34199 | 0.670997 | − | 0.741460i | \(-0.265866\pi\) | ||||
0.670997 | + | 0.741460i | \(0.265866\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.24981 | −0.527626 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.62086 | −0.658800 | −0.329400 | − | 0.944191i | \(-0.606846\pi\) | ||||
−0.329400 | + | 0.944191i | \(0.606846\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.6851 | −1.24990 | −0.624948 | − | 0.780666i | \(-0.714880\pi\) | ||||
−0.624948 | + | 0.780666i | \(0.714880\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.51139 | −0.342677 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.31012 | −0.610023 | −0.305011 | − | 0.952349i | \(-0.598660\pi\) | ||||
−0.305011 | + | 0.952349i | \(0.598660\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4167 | −0.997738 | −0.498869 | − | 0.866677i | \(-0.666251\pi\) | ||||
−0.498869 | + | 0.866677i | \(0.666251\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.564423 | 0.0535727 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.72556 | −0.350471 | −0.175236 | − | 0.984527i | \(-0.556069\pi\) | ||||
−0.175236 | + | 0.984527i | \(0.556069\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.67858 | 0.436280 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.0517 | −1.02173 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.50746 | −0.321528 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.97386 | −0.543078 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.3709 | −1.47611 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.47693 | −0.758200 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.78503 | 0.158396 | 0.0791981 | − | 0.996859i | \(-0.474764\pi\) | ||||
0.0791981 | + | 0.996859i | \(0.474764\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.1567 | −1.95079 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2964 | −0.899605 | −0.449802 | − | 0.893128i | \(-0.648506\pi\) | ||||
−0.449802 | + | 0.893128i | \(0.648506\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.4050 | 0.988940 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.41118 | 0.121455 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.0510 | 1.62764 | 0.813820 | − | 0.581117i | \(-0.197384\pi\) | ||||
0.813820 | + | 0.581117i | \(0.197384\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.9783 | 1.52490 | 0.762448 | − | 0.647049i | \(-0.223997\pi\) | ||||
0.762448 | + | 0.647049i | \(0.223997\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.4493 | −1.13263 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.5808 | 0.884810 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.79765 | −0.398423 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.97669 | 0.822864 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.2900 | 1.25261 | 0.626304 | − | 0.779579i | \(-0.284567\pi\) | ||||
0.626304 | + | 0.779579i | \(0.284567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.91268 | 0.562546 | 0.281273 | − | 0.959628i | \(-0.409243\pi\) | ||||
0.281273 | + | 0.959628i | \(0.409243\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.01396 | −0.405355 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.71213 | −0.298165 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.4402 | −1.71111 | −0.855557 | − | 0.517709i | \(-0.826785\pi\) | ||||
−0.855557 | + | 0.517709i | \(0.826785\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.97039 | −0.394178 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.26322 | 0.651233 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.3007 | −0.806816 | −0.403408 | − | 0.915020i | \(-0.632175\pi\) | ||||
−0.403408 | + | 0.915020i | \(0.632175\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.80572 | 0.374125 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3693 | 0.879785 | 0.439892 | − | 0.898051i | \(-0.355017\pi\) | ||||
0.439892 | + | 0.898051i | \(0.355017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.27417 | 0.713398 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.3036 | 1.24677 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.8059 | −1.58184 | −0.790921 | − | 0.611918i | \(-0.790398\pi\) | ||||
−0.790921 | + | 0.611918i | \(0.790398\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.78135 | −0.512622 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.1312 | 0.761509 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.0061 | −0.972121 | −0.486060 | − | 0.873925i | \(-0.661566\pi\) | ||||
−0.486060 | + | 0.873925i | \(0.661566\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9010 | −0.810267 | −0.405134 | − | 0.914258i | \(-0.632775\pi\) | ||||
−0.405134 | + | 0.914258i | \(0.632775\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.8126 | 0.947132 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.226500 | −0.0166526 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.80034 | 0.351036 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.49240 | 0.181295 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.7528 | 1.71869 | 0.859344 | − | 0.511397i | \(-0.170872\pi\) | ||||
0.859344 | + | 0.511397i | \(0.170872\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.8823 | 1.86305 | 0.931525 | − | 0.363677i | \(-0.118479\pi\) | ||||
0.931525 | + | 0.363677i | \(0.118479\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.1168 | 0.724477 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.0407 | 1.14285 | 0.571426 | − | 0.820654i | \(-0.306390\pi\) | ||||
0.571426 | + | 0.820654i | \(0.306390\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.7176 | 1.82307 | 0.911535 | − | 0.411222i | \(-0.134898\pi\) | ||||
0.911535 | + | 0.411222i | \(0.134898\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.8698 | −0.978303 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.47352 | −0.594724 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.56956 | 0.458838 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.8124 | 0.821018 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.6090 | −1.07970 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.55547 | −0.107083 | −0.0535415 | − | 0.998566i | \(-0.517051\pi\) | ||||
−0.0535415 | + | 0.998566i | \(0.517051\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.4312 | 0.783254 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.89138 | 0.606387 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.55629 | −0.445070 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.7490 | −1.19937 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.1054 | 0.679766 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0334 | −1.07368 | −0.536839 | − | 0.843685i | \(-0.680382\pi\) | ||||
−0.536839 | + | 0.843685i | \(0.680382\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.69403 | −0.646269 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.20576 | 0.611008 | 0.305504 | − | 0.952191i | \(-0.401175\pi\) | ||||
0.305504 | + | 0.952191i | \(0.401175\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.62169 | 0.107164 | 0.0535822 | − | 0.998563i | \(-0.482936\pi\) | ||||
0.0535822 | + | 0.998563i | \(0.482936\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.48777 | 0.558455 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.8223 | −1.56065 | −0.780326 | − | 0.625374i | \(-0.784947\pi\) | ||||
−0.780326 | + | 0.625374i | \(0.784947\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.39713 | 0.352070 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.5509 | 0.945186 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.7980 | −0.763150 | −0.381575 | − | 0.924338i | \(-0.624618\pi\) | ||||
−0.381575 | + | 0.924338i | \(0.624618\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.0257 | −1.28997 | −0.644985 | − | 0.764195i | \(-0.723136\pi\) | ||||
−0.644985 | + | 0.764195i | \(0.723136\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.7992 | 1.27012 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.00360 | −0.255781 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −32.8593 | −2.09079 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 35.0763 | 2.22287 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.2162 | −0.897318 | −0.448659 | − | 0.893703i | \(-0.648098\pi\) | ||||
−0.448659 | + | 0.893703i | \(0.648098\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.3091 | −0.710999 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.58983 | 0.287426 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.9671 | 1.05838 | 0.529190 | − | 0.848504i | \(-0.322496\pi\) | ||||
0.529190 | + | 0.848504i | \(0.322496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.400041 | −0.0248573 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.1130 | −0.749777 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.7948 | −1.52891 | −0.764456 | − | 0.644675i | \(-0.776993\pi\) | ||||
−0.764456 | + | 0.644675i | \(0.776993\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.99460 | 0.122527 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −37.4832 | −2.29394 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.79501 | −0.292357 | −0.146179 | − | 0.989258i | \(-0.546697\pi\) | ||||
−0.146179 | + | 0.989258i | \(0.546697\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.2813 | 0.746036 | 0.373018 | − | 0.927824i | \(-0.378323\pi\) | ||||
0.373018 | + | 0.927824i | \(0.378323\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.8681 | 1.08142 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.28102 | 0.559666 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.95981 | −0.177838 | −0.0889188 | − | 0.996039i | \(-0.528341\pi\) | ||||
−0.0889188 | + | 0.996039i | \(0.528341\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.37231 | −0.561106 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.985114 | 0.0587670 | 0.0293835 | − | 0.999568i | \(-0.490646\pi\) | ||||
0.0293835 | + | 0.999568i | \(0.490646\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.6525 | −0.811557 | −0.405779 | − | 0.913971i | \(-0.633000\pi\) | ||||
−0.405779 | + | 0.913971i | \(0.633000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.9245 | −0.884050 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.6030 | 0.684905 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.4153 | −0.730313 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −30.5475 | −1.79073 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.3306 | −1.30457 | −0.652284 | − | 0.757975i | \(-0.726189\pi\) | ||||
−0.652284 | + | 0.757975i | \(0.726189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.06561 | −0.236709 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.41112 | −0.197933 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.8074 | −1.37682 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.7038 | 0.905151 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.3022 | 0.879086 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.14162 | −0.294408 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.4096 | −1.05069 | −0.525345 | − | 0.850889i | \(-0.676064\pi\) | ||||
−0.525345 | + | 0.850889i | \(0.676064\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 29.3178 | 1.66783 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.35161 | −0.416871 | −0.208436 | − | 0.978036i | \(-0.566837\pi\) | ||||
−0.208436 | + | 0.978036i | \(0.566837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.5636 | −1.21885 | −0.609424 | − | 0.792844i | \(-0.708599\pi\) | ||||
−0.609424 | + | 0.792844i | \(0.708599\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.55768 | 0.200453 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.62445 | −0.203570 | −0.101785 | − | 0.994806i | \(-0.532455\pi\) | ||||
−0.101785 | + | 0.994806i | \(0.532455\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.5969 | 0.649304 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.5840 | 0.813999 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.9078 | −0.829490 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.5379 | 1.08377 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.0751 | 1.33136 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.53230 | 0.525533 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.6796 | 1.24658 | 0.623291 | − | 0.781990i | \(-0.285795\pi\) | ||||
0.623291 | + | 0.781990i | \(0.285795\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.571864 | −0.0313379 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.56590 | 0.304098 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.8503 | −1.62605 | −0.813026 | − | 0.582228i | \(-0.802181\pi\) | ||||
−0.813026 | + | 0.582228i | \(0.802181\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.61054 | 0.467660 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.97300 | 0.485915 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5377 | −1.00094 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.8132 | −0.582162 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.12156 | 0.382305 | 0.191153 | − | 0.981560i | \(-0.438777\pi\) | ||||
0.191153 | + | 0.981560i | \(0.438777\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.9932 | −0.695512 | −0.347756 | − | 0.937585i | \(-0.613056\pi\) | ||||
−0.347756 | + | 0.937585i | \(0.613056\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.18093 | −0.383290 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.09603 | 0.0583357 | 0.0291679 | − | 0.999575i | \(-0.490714\pi\) | ||||
0.0291679 | + | 0.999575i | \(0.490714\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.58730 | −0.243468 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.10646 | 0.429039 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.3215 | 1.75864 | 0.879322 | − | 0.476228i | \(-0.157996\pi\) | ||||
0.879322 | + | 0.476228i | \(0.157996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.4748 | 1.55130 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.8068 | 0.724670 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.12259 | 0.372814 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.17252 | 0.217804 | 0.108902 | − | 0.994053i | \(-0.465267\pi\) | ||||
0.108902 | + | 0.994053i | \(0.465267\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.5867 | 0.863468 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.52282 | 0.182895 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.42352 | 0.436153 | 0.218077 | − | 0.975932i | \(-0.430022\pi\) | ||||
0.218077 | + | 0.975932i | \(0.430022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.5919 | 1.01172 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.4133 | 1.25735 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.55042 | −0.387839 | −0.193920 | − | 0.981017i | \(-0.562120\pi\) | ||||
−0.193920 | + | 0.981017i | \(0.562120\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.12558 | −0.211360 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.3217 | −1.19168 | −0.595841 | − | 0.803103i | \(-0.703181\pi\) | ||||
−0.595841 | + | 0.803103i | \(0.703181\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.40610 | −0.173591 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.4488 | 1.14114 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.4690 | 1.08852 | 0.544260 | − | 0.838916i | \(-0.316810\pi\) | ||||
0.544260 | + | 0.838916i | \(0.316810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.8011 | −0.546233 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.7972 | 1.20041 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.83923 | −0.293803 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.2754 | −1.51948 | −0.759739 | − | 0.650228i | \(-0.774673\pi\) | ||||
−0.759739 | + | 0.650228i | \(0.774673\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −26.3593 | −1.31962 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.3609 | −1.36634 | −0.683170 | − | 0.730259i | \(-0.739399\pi\) | ||||
−0.683170 | + | 0.730259i | \(0.739399\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.8895 | 0.940954 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.77707 | −0.485826 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.547499 | 0.0271385 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.1522 | −0.897568 | −0.448784 | − | 0.893640i | \(-0.648143\pi\) | ||||
−0.448784 | + | 0.893640i | \(0.648143\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −44.0309 | −2.17188 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.18060 | −0.353334 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.0760 | −0.690962 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −41.5515 | −2.03478 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.5801 | 0.956552 | 0.478276 | − | 0.878209i | \(-0.341262\pi\) | ||||
0.478276 | + | 0.878209i | \(0.341262\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.9428 | −0.630791 | −0.315396 | − | 0.948960i | \(-0.602137\pi\) | ||||
−0.315396 | + | 0.948960i | \(0.602137\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.6266 | 0.662547 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.86406 | 0.429970 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.08103 | −0.439462 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.4544 | −1.18067 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.8333 | 0.955338 | 0.477669 | − | 0.878540i | \(-0.341482\pi\) | ||||
0.477669 | + | 0.878540i | \(0.341482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.5645 | 0.555756 | 0.277878 | − | 0.960616i | \(-0.410369\pi\) | ||||
0.277878 | + | 0.960616i | \(0.410369\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.0884 | 0.531646 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 35.1212 | 1.68008 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.0833 | 1.76989 | 0.884946 | − | 0.465694i | \(-0.154195\pi\) | ||||
0.884946 | + | 0.465694i | \(0.154195\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.1082 | −0.481343 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.8418 | −1.75041 | −0.875203 | − | 0.483756i | \(-0.839272\pi\) | ||||
−0.875203 | + | 0.483756i | \(0.839272\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.0419 | 0.713052 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −35.3384 | −1.67145 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.4391 | −0.492653 | −0.246326 | − | 0.969187i | \(-0.579223\pi\) | ||||
−0.246326 | + | 0.969187i | \(0.579223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.8800 | −0.747760 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.9766 | −0.750648 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.17036 | −0.336152 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.94526 | −0.184552 | −0.0922758 | − | 0.995733i | \(-0.529414\pi\) | ||||
−0.0922758 | + | 0.995733i | \(0.529414\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.25788 | −0.152065 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.40337 | 0.205085 | 0.102543 | − | 0.994729i | \(-0.467302\pi\) | ||||
0.102543 | + | 0.994729i | \(0.467302\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.7423 | −1.42872 | −0.714358 | − | 0.699780i | \(-0.753281\pi\) | ||||
−0.714358 | + | 0.699780i | \(0.753281\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.57950 | 0.397865 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.26516 | 0.382466 | 0.191233 | − | 0.981545i | \(-0.438751\pi\) | ||||
0.191233 | + | 0.981545i | \(0.438751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.83038 | 0.453925 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 49.5527 | 2.28327 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.4923 | −0.988219 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.8228 | −1.32248 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.03592 | 0.230579 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.8871 | 0.954358 | 0.477179 | − | 0.878806i | \(-0.341659\pi\) | ||||
0.477179 | + | 0.878806i | \(0.341659\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.15257 | 0.0525526 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19.0980 | −0.868989 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.2586 | 0.556633 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.5595 | −0.705069 | −0.352534 | − | 0.935799i | \(-0.614680\pi\) | ||||
−0.352534 | + | 0.935799i | \(0.614680\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.8071 | 1.07660 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.253102 | −0.0114223 | −0.00571116 | − | 0.999984i | \(-0.501818\pi\) | ||||
−0.00571116 | + | 0.999984i | \(0.501818\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.0759 | 0.498835 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.86908 | −0.218849 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.10199 | −0.363424 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.2400 | −1.53279 | −0.766395 | − | 0.642369i | \(-0.777952\pi\) | ||||
−0.766395 | + | 0.642369i | \(0.777952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.2769 | −1.17396 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.14068 | −0.273257 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.4345 | −0.951940 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −42.7175 | −1.89342 | −0.946711 | − | 0.322084i | \(-0.895617\pi\) | ||||
−0.946711 | + | 0.322084i | \(0.895617\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.5798 | 0.556497 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.5935 | 0.467712 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.7651 | −0.518432 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.0460 | −0.573763 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 48.0867 | 2.11077 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.4226 | 0.500433 | 0.250217 | − | 0.968190i | \(-0.419498\pi\) | ||||
0.250217 | + | 0.968190i | \(0.419498\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.4767 | −0.895383 | −0.447691 | − | 0.894188i | \(-0.647754\pi\) | ||||
−0.447691 | + | 0.894188i | \(0.647754\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.6731 | 0.684030 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.56989 | 0.373310 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.44622 | 0.106357 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.2648 | −0.445453 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.4298 | −1.44801 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.85249 | −0.253025 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.0598 | 1.29717 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.67755 | 0.416842 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.60049 | −0.0688105 | −0.0344052 | − | 0.999408i | \(-0.510954\pi\) | ||||
−0.0344052 | + | 0.999408i | \(0.510954\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.1945 | 1.08120 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.66123 | −0.413842 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.8635 | −1.23411 | −0.617056 | − | 0.786919i | \(-0.711675\pi\) | ||||
−0.617056 | + | 0.786919i | \(0.711675\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.9815 | −0.554035 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −36.0150 | −1.53429 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.3131 | −0.438559 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.523489 | 0.0222209 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −45.1616 | −1.91356 | −0.956778 | − | 0.290818i | \(-0.906073\pi\) | ||||
−0.956778 | + | 0.290818i | \(0.906073\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −45.2446 | −1.91364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.0946 | −0.468414 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.4296 | 1.07173 | 0.535864 | − | 0.844304i | \(-0.319986\pi\) | ||||
0.535864 | + | 0.844304i | \(0.319986\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.45537 | −0.145368 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.2681 | −0.725191 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.0527 | −1.72102 | −0.860510 | − | 0.509433i | \(-0.829855\pi\) | ||||
−0.860510 | + | 0.509433i | \(0.829855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.65974 | 0.236853 | 0.118426 | − | 0.992963i | \(-0.462215\pi\) | ||||
0.118426 | + | 0.992963i | \(0.462215\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −54.8975 | −2.29338 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.8828 | −0.870875 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.70745 | 0.0710821 | 0.0355411 | − | 0.999368i | \(-0.488685\pi\) | ||||
0.0355411 | + | 0.999368i | \(0.488685\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −59.8194 | −2.48601 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.8607 | −1.03140 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.82136 | −0.199680 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.2501 | −0.423791 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.3906 | −0.428864 | −0.214432 | − | 0.976739i | \(-0.568790\pi\) | ||||
−0.214432 | + | 0.976739i | \(0.568790\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.8662 | −1.14821 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −37.0734 | −1.52499 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.8106 | −0.443938 | −0.221969 | − | 0.975054i | \(-0.571248\pi\) | ||||
−0.221969 | + | 0.975054i | \(0.571248\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.25308 | −0.133363 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −59.4386 | −2.43266 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.4973 | 0.837499 | 0.418749 | − | 0.908102i | \(-0.362469\pi\) | ||||
0.418749 | + | 0.908102i | \(0.362469\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.68916 | 0.0689023 | 0.0344512 | − | 0.999406i | \(-0.489032\pi\) | ||||
0.0344512 | + | 0.999406i | \(0.489032\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.0527 | 0.572269 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.54061 | −0.225258 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.9763 | −1.05435 | −0.527173 | − | 0.849758i | \(-0.676748\pi\) | ||||
−0.527173 | + | 0.849758i | \(0.676748\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.5840 | 0.793586 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.4638 | −1.11107 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.6415 | −0.591365 | −0.295682 | − | 0.955286i | \(-0.595547\pi\) | ||||
−0.295682 | + | 0.955286i | \(0.595547\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.1836 | −0.612262 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.6291 | −0.951272 | −0.475636 | − | 0.879642i | \(-0.657782\pi\) | ||||
−0.475636 | + | 0.879642i | \(0.657782\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.1336 | 1.41214 | 0.706069 | − | 0.708143i | \(-0.250467\pi\) | ||||
0.706069 | + | 0.708143i | \(0.250467\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.67523 | 0.307996 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.5666 | 1.06437 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.8368 | 0.513471 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 36.0756 | 1.44072 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.522903 | 0.0208495 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.8590 | −1.50714 | −0.753571 | − | 0.657366i | \(-0.771670\pi\) | ||||
−0.753571 | + | 0.657366i | \(0.771670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.59501 | 0.142889 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.65558 | 0.0656995 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.3727 | 0.807196 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.5819 | −0.458174 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.79185 | 0.347257 | 0.173629 | − | 0.984811i | \(-0.444451\pi\) | ||||
0.173629 | + | 0.984811i | \(0.444451\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.47948 | −0.137217 | −0.0686087 | − | 0.997644i | \(-0.521856\pi\) | ||||
−0.0686087 | + | 0.997644i | \(0.521856\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.5498 | −0.809148 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.256222 | −0.0100731 | −0.00503657 | − | 0.999987i | \(-0.501603\pi\) | ||||
−0.00503657 | + | 0.999987i | \(0.501603\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.82745 | 0.385761 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.1529 | 0.593890 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.5106 | 1.23310 | 0.616552 | − | 0.787314i | \(-0.288529\pi\) | ||||
0.616552 | + | 0.787314i | \(0.288529\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.54971 | −0.373138 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.9830 | 0.701583 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.0526 | 0.508459 | 0.254229 | − | 0.967144i | \(-0.418178\pi\) | ||||
0.254229 | + | 0.967144i | \(0.418178\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.5272 | −1.30406 | −0.652028 | − | 0.758194i | \(-0.726082\pi\) | ||||
−0.652028 | + | 0.758194i | \(0.726082\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.3558 | −0.907063 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.5779 | 0.410192 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.0938 | −1.01036 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 37.0565 | 1.43269 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.4284 | 0.479793 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.3413 | −0.938287 | −0.469143 | − | 0.883122i | \(-0.655437\pi\) | ||||
−0.469143 | + | 0.883122i | \(0.655437\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.29880 | −0.242441 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −46.8524 | −1.80068 | −0.900342 | − | 0.435182i | \(-0.856684\pi\) | ||||
−0.900342 | + | 0.435182i | \(0.856684\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.6508 | 0.830882 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.2764 | −0.815314 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.3772 | 0.779711 | 0.389855 | − | 0.920876i | \(-0.372525\pi\) | ||||
0.389855 | + | 0.920876i | \(0.372525\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.6694 | 0.675113 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.74806 | −0.142998 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.1497 | −0.386673 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.0677 | −1.41012 | −0.705060 | − | 0.709147i | \(-0.749080\pi\) | ||||
−0.705060 | + | 0.709147i | \(0.749080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.59967 | −0.326674 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.6744 | 0.632497 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.1666 | −0.574476 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 55.0583 | 2.08249 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.7305 | 1.61391 | 0.806954 | − | 0.590614i | \(-0.201115\pi\) | ||||
0.806954 | + | 0.590614i | \(0.201115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.70029 | −0.0641278 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.4739 | −0.469793 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.8456 | −0.407889 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.96332 | −0.0737340 | −0.0368670 | − | 0.999320i | \(-0.511738\pi\) | ||||
−0.0368670 | + | 0.999320i | \(0.511738\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.7428 | −0.552897 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.1898 | −0.756114 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.81343 | 0.367002 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.2676 | 1.01833 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.6302 | 0.471025 | 0.235513 | − | 0.971871i | \(-0.424323\pi\) | ||||
0.235513 | + | 0.971871i | \(0.424323\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.7793 | −0.773861 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 46.2836 | 1.72130 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.4143 | 0.795307 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.7590 | −1.21496 | −0.607481 | − | 0.794334i | \(-0.707820\pi\) | ||||
−0.607481 | + | 0.794334i | \(0.707820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.1353 | −0.523528 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.5268 | −0.759211 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.6375 | 1.02081 | 0.510406 | − | 0.859933i | \(-0.329495\pi\) | ||||
0.510406 | + | 0.859933i | \(0.329495\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.25315 | 0.341307 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.4540 | −0.495583 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.6007 | 1.53031 | 0.765153 | − | 0.643848i | \(-0.222663\pi\) | ||||
0.765153 | + | 0.643848i | \(0.222663\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 75.9447 | 2.78990 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.4351 | −1.70354 | −0.851769 | − | 0.523918i | \(-0.824470\pi\) | ||||
−0.851769 | + | 0.523918i | \(0.824470\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.1811 | 0.519557 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −35.5387 | −1.30029 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.3366 | −0.377689 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.5190 | 0.858220 | 0.429110 | − | 0.903252i | \(-0.358827\pi\) | ||||
0.429110 | + | 0.903252i | \(0.358827\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.8566 | 1.19736 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.41135 | 0.233333 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.10379 | 0.112809 | 0.0564046 | − | 0.998408i | \(-0.482036\pi\) | ||||
0.0564046 | + | 0.998408i | \(0.482036\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26.1377 | 0.948739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.0334 | −0.943709 | −0.471854 | − | 0.881677i | \(-0.656415\pi\) | ||||
−0.471854 | + | 0.881677i | \(0.656415\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.0635 | −0.617739 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.65033 | −0.168133 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.6883 | 0.747010 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.8113 | −1.07502 | −0.537512 | − | 0.843256i | \(-0.680636\pi\) | ||||
−0.537512 | + | 0.843256i | \(0.680636\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39.2145 | −1.41228 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.4568 | 1.31126 | 0.655629 | − | 0.755083i | \(-0.272403\pi\) | ||||
0.655629 | + | 0.755083i | \(0.272403\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.5691 | 0.595179 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.924576 | 0.0331690 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 49.3164 | 1.76694 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.0885 | 0.396776 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.87056 | −0.281271 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.8853 | −0.709735 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.63676 | −0.0939903 | −0.0469952 | − | 0.998895i | \(-0.514965\pi\) | ||||
−0.0469952 | + | 0.998895i | \(0.514965\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 57.3059 | 2.04014 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.10280 | −0.216991 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.1636 | 0.929098 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.60992 | −0.163497 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.8288 | −1.12743 | −0.563717 | − | 0.825968i | \(-0.690629\pi\) | ||||
−0.563717 | + | 0.825968i | \(0.690629\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.4599 | −0.440800 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 37.9774 | 1.34186 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.2168 | −0.607568 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.66394 | 0.270118 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.0823 | 0.390114 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.0356 | −1.19663 | −0.598314 | − | 0.801262i | \(-0.704162\pi\) | ||||
−0.598314 | + | 0.801262i | \(0.704162\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.3277 | 0.678686 | 0.339343 | − | 0.940663i | \(-0.389795\pi\) | ||||
0.339343 | + | 0.940663i | \(0.389795\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.3846 | −0.995492 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.55369 | −0.334651 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 66.7458 | 2.33514 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.1036 | −0.632591 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.7195 | −0.513714 | −0.256857 | − | 0.966449i | \(-0.582687\pi\) | ||||
−0.256857 | + | 0.966449i | \(0.582687\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.93741 | 0.206965 | 0.103483 | − | 0.994631i | \(-0.467001\pi\) | ||||
0.103483 | + | 0.994631i | \(0.467001\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21.4503 | −0.746805 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.3160 | −0.880323 | −0.440162 | − | 0.897919i | \(-0.645079\pi\) | ||||
−0.440162 | + | 0.897919i | \(0.645079\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.36867 | 0.221193 | 0.110597 | − | 0.993865i | \(-0.464724\pi\) | ||||
0.110597 | + | 0.993865i | \(0.464724\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.84073 | 0.237302 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.24278 | 0.320243 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5448 | 0.364917 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.08976 | −0.210493 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.2227 | 0.663641 | 0.331821 | − | 0.943343i | \(-0.392337\pi\) | ||||
0.331821 | + | 0.943343i | \(0.392337\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.24211 | −0.0773140 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.27680 | −0.0784172 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.60157 | 0.295903 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.78571 | −0.336241 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.5537 | 1.08292 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.23191 | −0.0422292 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.94968 | −0.306431 | −0.153216 | − | 0.988193i | \(-0.548963\pi\) | ||||
−0.153216 | + | 0.988193i | \(0.548963\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.1212 | 0.517135 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.1176 | 0.516408 | 0.258204 | − | 0.966090i | \(-0.416869\pi\) | ||||
0.258204 | + | 0.966090i | \(0.416869\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.3192 | −0.625044 | −0.312522 | − | 0.949911i | \(-0.601174\pi\) | ||||
−0.312522 | + | 0.949911i | \(0.601174\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −26.8170 | −0.913920 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.1369 | −0.515267 | −0.257634 | − | 0.966243i | \(-0.582943\pi\) | ||||
−0.257634 | + | 0.966243i | \(0.582943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.2970 | −0.656116 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.6943 | 0.974511 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.1146 | 0.478807 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.3226 | −0.959675 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.9502 | 1.04750 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.8860 | −0.469432 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.3413 | −0.720644 | −0.360322 | − | 0.932828i | \(-0.617333\pi\) | ||||
−0.360322 | + | 0.932828i | \(0.617333\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 51.6106 | 1.74078 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.9050 | 0.704307 | 0.352153 | − | 0.935942i | \(-0.385450\pi\) | ||||
0.352153 | + | 0.935942i | \(0.385450\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.4123 | −1.32633 | −0.663166 | − | 0.748473i | \(-0.730787\pi\) | ||||
−0.663166 | + | 0.748473i | \(0.730787\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.39647 | 0.315859 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.2238 | −1.21628 | −0.608139 | − | 0.793831i | \(-0.708084\pi\) | ||||
−0.608139 | + | 0.793831i | \(0.708084\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.92405 | 0.0980694 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.6332 | 0.791743 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 40.5152 | 1.35579 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0628 | −0.403216 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 55.0239 | 1.83719 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.7036 | 0.690504 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.60476 | −0.153407 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.2947 | −1.20781 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.1104 | −0.336083 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.82224 | 0.0605065 | 0.0302533 | − | 0.999542i | \(-0.490369\pi\) | ||||
0.0302533 | + | 0.999542i | \(0.490369\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.5039 | −0.514231 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.44791 | −0.180497 | −0.0902487 | − | 0.995919i | \(-0.528766\pi\) | ||||
−0.0902487 | + | 0.995919i | \(0.528766\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.0246 | 1.12605 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.8833 | 0.392851 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.8665 | −0.556981 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.6603 | −0.450612 | −0.225306 | − | 0.974288i | \(-0.572338\pi\) | ||||
−0.225306 | + | 0.974288i | \(0.572338\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.5484 | 1.40202 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.3429 | 0.768341 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.01098 | 0.0332410 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.7043 | −0.975617 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.3649 | −0.536916 | −0.268458 | − | 0.963291i | \(-0.586514\pi\) | ||||
−0.268458 | + | 0.963291i | \(0.586514\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.0542 | −0.984988 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.9911 | 0.556263 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.45220 | 0.145603 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.0582 | 1.63533 | 0.817664 | − | 0.575695i | \(-0.195269\pi\) | ||||
0.817664 | + | 0.575695i | \(0.195269\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49.8380 | 1.62640 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.1788 | −1.47279 | −0.736393 | − | 0.676554i | \(-0.763473\pi\) | ||||
−0.736393 | + | 0.676554i | \(0.763473\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.7310 | 1.16356 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.31164 | 0.0751977 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.3165 | −1.34261 | −0.671303 | − | 0.741183i | \(-0.734265\pi\) | ||||
−0.671303 | + | 0.741183i | \(0.734265\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36.2440 | −1.17653 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.37686 | 0.271638 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.12456 | 0.295573 | 0.147787 | − | 0.989019i | \(-0.452785\pi\) | ||||
0.147787 | + | 0.989019i | \(0.452785\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.0301 | 0.712878 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −26.8029 | −0.866415 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.2073 | 1.00774 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.9808 | −0.483252 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.7763 | −0.476158 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.0052 | 0.772756 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.94904 | 0.126993 | 0.0634963 | − | 0.997982i | \(-0.479775\pi\) | ||||
0.0634963 | + | 0.997982i | \(0.479775\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 34.4549 | 1.10685 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.61089 | 0.147971 | 0.0739853 | − | 0.997259i | \(-0.476428\pi\) | ||||
0.0739853 | + | 0.997259i | \(0.476428\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.4500 | 0.944124 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −45.1562 | −1.44616 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.6853 | −1.36562 | −0.682811 | − | 0.730595i | \(-0.739243\pi\) | ||||
−0.682811 | + | 0.730595i | \(0.739243\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.3593 | −1.16205 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.3925 | −0.778792 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.21195 | −0.293816 | −0.146908 | − | 0.989150i | \(-0.546932\pi\) | ||||
−0.146908 | + | 0.989150i | \(0.546932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.8774 | 0.474032 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.0311 | −0.701258 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.3591 | 1.53773 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.6293 | −1.79889 | −0.899444 | − | 0.437035i | \(-0.856028\pi\) | ||||
−0.899444 | + | 0.437035i | \(0.856028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −52.4172 | −1.66341 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.8524 | 0.756173 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.688610 | 0.0218085 | 0.0109042 | − | 0.999941i | \(-0.496529\pi\) | ||||
0.0109042 | + | 0.999941i | \(0.496529\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.371575 | −0.0117561 |
(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 | 8048.2.a.v.1.4 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.25 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.25 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.4 | 28 | 1.1 | even | 1 | trivial |