Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(66\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64866 | −1.87288 | −0.936442 | − | 0.350822i | \(-0.885902\pi\) | ||||
−0.936442 | + | 0.350822i | \(0.885902\pi\) | |||||||
\(3\) | 1.22889 | 0.709499 | 0.354749 | − | 0.934961i | \(-0.384566\pi\) | ||||
0.354749 | + | 0.934961i | \(0.384566\pi\) | |||||||
\(4\) | 5.01539 | 2.50770 | ||||||||
\(5\) | −0.305577 | −0.136658 | −0.0683291 | − | 0.997663i | \(-0.521767\pi\) | ||||
−0.0683291 | + | 0.997663i | \(0.521767\pi\) | |||||||
\(6\) | −3.25491 | −1.32881 | ||||||||
\(7\) | −2.34072 | −0.884710 | −0.442355 | − | 0.896840i | \(-0.645857\pi\) | ||||
−0.442355 | + | 0.896840i | \(0.645857\pi\) | |||||||
\(8\) | −7.98675 | −2.82374 | ||||||||
\(9\) | −1.48983 | −0.496611 | ||||||||
\(10\) | 0.809369 | 0.255945 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 6.16336 | 1.77921 | ||||||||
\(13\) | −0.268014 | −0.0743337 | −0.0371669 | − | 0.999309i | \(-0.511833\pi\) | ||||
−0.0371669 | + | 0.999309i | \(0.511833\pi\) | |||||||
\(14\) | 6.19978 | 1.65696 | ||||||||
\(15\) | −0.375520 | −0.0969588 | ||||||||
\(16\) | 11.1234 | 2.78085 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 3.94606 | 0.930096 | ||||||||
\(19\) | 2.78504 | 0.638932 | 0.319466 | − | 0.947598i | \(-0.396497\pi\) | ||||
0.319466 | + | 0.947598i | \(0.396497\pi\) | |||||||
\(20\) | −1.53259 | −0.342697 | ||||||||
\(21\) | −2.87649 | −0.627701 | ||||||||
\(22\) | 2.64866 | 0.564696 | ||||||||
\(23\) | −2.45254 | −0.511389 | −0.255695 | − | 0.966758i | \(-0.582304\pi\) | ||||
−0.255695 | + | 0.966758i | \(0.582304\pi\) | |||||||
\(24\) | −9.81482 | −2.00344 | ||||||||
\(25\) | −4.90662 | −0.981325 | ||||||||
\(26\) | 0.709878 | 0.139218 | ||||||||
\(27\) | −5.51750 | −1.06184 | ||||||||
\(28\) | −11.7396 | −2.21858 | ||||||||
\(29\) | −5.07720 | −0.942812 | −0.471406 | − | 0.881916i | \(-0.656253\pi\) | ||||
−0.471406 | + | 0.881916i | \(0.656253\pi\) | |||||||
\(30\) | 0.994624 | 0.181593 | ||||||||
\(31\) | −7.06987 | −1.26979 | −0.634893 | − | 0.772600i | \(-0.718956\pi\) | ||||
−0.634893 | + | 0.772600i | \(0.718956\pi\) | |||||||
\(32\) | −13.4886 | −2.38446 | ||||||||
\(33\) | −1.22889 | −0.213922 | ||||||||
\(34\) | −2.64866 | −0.454241 | ||||||||
\(35\) | 0.715271 | 0.120903 | ||||||||
\(36\) | −7.47210 | −1.24535 | ||||||||
\(37\) | −7.59317 | −1.24831 | −0.624155 | − | 0.781301i | \(-0.714556\pi\) | ||||
−0.624155 | + | 0.781301i | \(0.714556\pi\) | |||||||
\(38\) | −7.37662 | −1.19665 | ||||||||
\(39\) | −0.329359 | −0.0527397 | ||||||||
\(40\) | 2.44057 | 0.385887 | ||||||||
\(41\) | 7.50921 | 1.17274 | 0.586371 | − | 0.810043i | \(-0.300556\pi\) | ||||
0.586371 | + | 0.810043i | \(0.300556\pi\) | |||||||
\(42\) | 7.61883 | 1.17561 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −5.01539 | −0.756099 | ||||||||
\(45\) | 0.455259 | 0.0678660 | ||||||||
\(46\) | 6.49593 | 0.957773 | ||||||||
\(47\) | −1.35156 | −0.197146 | −0.0985729 | − | 0.995130i | \(-0.531428\pi\) | ||||
−0.0985729 | + | 0.995130i | \(0.531428\pi\) | |||||||
\(48\) | 13.6694 | 1.97301 | ||||||||
\(49\) | −1.52102 | −0.217288 | ||||||||
\(50\) | 12.9960 | 1.83791 | ||||||||
\(51\) | 1.22889 | 0.172079 | ||||||||
\(52\) | −1.34420 | −0.186406 | ||||||||
\(53\) | −5.03813 | −0.692041 | −0.346020 | − | 0.938227i | \(-0.612467\pi\) | ||||
−0.346020 | + | 0.938227i | \(0.612467\pi\) | |||||||
\(54\) | 14.6140 | 1.98871 | ||||||||
\(55\) | 0.305577 | 0.0412040 | ||||||||
\(56\) | 18.6948 | 2.49819 | ||||||||
\(57\) | 3.42250 | 0.453321 | ||||||||
\(58\) | 13.4478 | 1.76578 | ||||||||
\(59\) | 10.9591 | 1.42675 | 0.713377 | − | 0.700781i | \(-0.247165\pi\) | ||||
0.713377 | + | 0.700781i | \(0.247165\pi\) | |||||||
\(60\) | −1.88338 | −0.243143 | ||||||||
\(61\) | 6.27375 | 0.803272 | 0.401636 | − | 0.915799i | \(-0.368442\pi\) | ||||
0.401636 | + | 0.915799i | \(0.368442\pi\) | |||||||
\(62\) | 18.7257 | 2.37816 | ||||||||
\(63\) | 3.48729 | 0.439357 | ||||||||
\(64\) | 13.4798 | 1.68498 | ||||||||
\(65\) | 0.0818989 | 0.0101583 | ||||||||
\(66\) | 3.25491 | 0.400651 | ||||||||
\(67\) | 6.17499 | 0.754395 | 0.377198 | − | 0.926133i | \(-0.376888\pi\) | ||||
0.377198 | + | 0.926133i | \(0.376888\pi\) | |||||||
\(68\) | 5.01539 | 0.608206 | ||||||||
\(69\) | −3.01389 | −0.362830 | ||||||||
\(70\) | −1.89451 | −0.226437 | ||||||||
\(71\) | −3.48195 | −0.413231 | −0.206616 | − | 0.978422i | \(-0.566245\pi\) | ||||
−0.206616 | + | 0.978422i | \(0.566245\pi\) | |||||||
\(72\) | 11.8989 | 1.40230 | ||||||||
\(73\) | −6.74516 | −0.789461 | −0.394731 | − | 0.918797i | \(-0.629162\pi\) | ||||
−0.394731 | + | 0.918797i | \(0.629162\pi\) | |||||||
\(74\) | 20.1117 | 2.33794 | ||||||||
\(75\) | −6.02969 | −0.696249 | ||||||||
\(76\) | 13.9681 | 1.60225 | ||||||||
\(77\) | 2.34072 | 0.266750 | ||||||||
\(78\) | 0.872360 | 0.0987753 | ||||||||
\(79\) | 2.73092 | 0.307252 | 0.153626 | − | 0.988129i | \(-0.450905\pi\) | ||||
0.153626 | + | 0.988129i | \(0.450905\pi\) | |||||||
\(80\) | −3.39905 | −0.380025 | ||||||||
\(81\) | −2.31089 | −0.256766 | ||||||||
\(82\) | −19.8893 | −2.19641 | ||||||||
\(83\) | −2.28648 | −0.250974 | −0.125487 | − | 0.992095i | \(-0.540049\pi\) | ||||
−0.125487 | + | 0.992095i | \(0.540049\pi\) | |||||||
\(84\) | −14.4267 | −1.57408 | ||||||||
\(85\) | −0.305577 | −0.0331445 | ||||||||
\(86\) | 2.64866 | 0.285612 | ||||||||
\(87\) | −6.23931 | −0.668924 | ||||||||
\(88\) | 7.98675 | 0.851390 | ||||||||
\(89\) | 4.36714 | 0.462916 | 0.231458 | − | 0.972845i | \(-0.425650\pi\) | ||||
0.231458 | + | 0.972845i | \(0.425650\pi\) | |||||||
\(90\) | −1.20583 | −0.127105 | ||||||||
\(91\) | 0.627347 | 0.0657638 | ||||||||
\(92\) | −12.3004 | −1.28241 | ||||||||
\(93\) | −8.68807 | −0.900911 | ||||||||
\(94\) | 3.57983 | 0.369231 | ||||||||
\(95\) | −0.851043 | −0.0873152 | ||||||||
\(96\) | −16.5759 | −1.69177 | ||||||||
\(97\) | −15.1278 | −1.53599 | −0.767997 | − | 0.640453i | \(-0.778747\pi\) | ||||
−0.767997 | + | 0.640453i | \(0.778747\pi\) | |||||||
\(98\) | 4.02865 | 0.406955 | ||||||||
\(99\) | 1.48983 | 0.149734 | ||||||||
\(100\) | −24.6086 | −2.46086 | ||||||||
\(101\) | 11.7091 | 1.16510 | 0.582552 | − | 0.812794i | \(-0.302054\pi\) | ||||
0.582552 | + | 0.812794i | \(0.302054\pi\) | |||||||
\(102\) | −3.25491 | −0.322284 | ||||||||
\(103\) | 6.68433 | 0.658627 | 0.329313 | − | 0.944221i | \(-0.393183\pi\) | ||||
0.329313 | + | 0.944221i | \(0.393183\pi\) | |||||||
\(104\) | 2.14056 | 0.209899 | ||||||||
\(105\) | 0.878988 | 0.0857804 | ||||||||
\(106\) | 13.3443 | 1.29611 | ||||||||
\(107\) | −4.08334 | −0.394752 | −0.197376 | − | 0.980328i | \(-0.563242\pi\) | ||||
−0.197376 | + | 0.980328i | \(0.563242\pi\) | |||||||
\(108\) | −27.6725 | −2.66278 | ||||||||
\(109\) | −4.10865 | −0.393538 | −0.196769 | − | 0.980450i | \(-0.563045\pi\) | ||||
−0.196769 | + | 0.980450i | \(0.563045\pi\) | |||||||
\(110\) | −0.809369 | −0.0771703 | ||||||||
\(111\) | −9.33115 | −0.885674 | ||||||||
\(112\) | −26.0368 | −2.46024 | ||||||||
\(113\) | 12.4171 | 1.16810 | 0.584051 | − | 0.811717i | \(-0.301467\pi\) | ||||
0.584051 | + | 0.811717i | \(0.301467\pi\) | |||||||
\(114\) | −9.06504 | −0.849018 | ||||||||
\(115\) | 0.749438 | 0.0698855 | ||||||||
\(116\) | −25.4641 | −2.36429 | ||||||||
\(117\) | 0.399296 | 0.0369150 | ||||||||
\(118\) | −29.0269 | −2.67214 | ||||||||
\(119\) | −2.34072 | −0.214574 | ||||||||
\(120\) | 2.99918 | 0.273787 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −16.6170 | −1.50444 | ||||||||
\(123\) | 9.22798 | 0.832059 | ||||||||
\(124\) | −35.4582 | −3.18424 | ||||||||
\(125\) | 3.02723 | 0.270764 | ||||||||
\(126\) | −9.23664 | −0.822865 | ||||||||
\(127\) | 7.54825 | 0.669799 | 0.334899 | − | 0.942254i | \(-0.391298\pi\) | ||||
0.334899 | + | 0.942254i | \(0.391298\pi\) | |||||||
\(128\) | −8.72632 | −0.771305 | ||||||||
\(129\) | −1.22889 | −0.108198 | ||||||||
\(130\) | −0.216922 | −0.0190253 | ||||||||
\(131\) | −16.5869 | −1.44920 | −0.724601 | − | 0.689169i | \(-0.757976\pi\) | ||||
−0.724601 | + | 0.689169i | \(0.757976\pi\) | |||||||
\(132\) | −6.16336 | −0.536451 | ||||||||
\(133\) | −6.51900 | −0.565269 | ||||||||
\(134\) | −16.3554 | −1.41290 | ||||||||
\(135\) | 1.68602 | 0.145110 | ||||||||
\(136\) | −7.98675 | −0.684858 | ||||||||
\(137\) | 6.56763 | 0.561110 | 0.280555 | − | 0.959838i | \(-0.409481\pi\) | ||||
0.280555 | + | 0.959838i | \(0.409481\pi\) | |||||||
\(138\) | 7.98277 | 0.679539 | ||||||||
\(139\) | −9.51047 | −0.806668 | −0.403334 | − | 0.915053i | \(-0.632149\pi\) | ||||
−0.403334 | + | 0.915053i | \(0.632149\pi\) | |||||||
\(140\) | 3.58736 | 0.303188 | ||||||||
\(141\) | −1.66092 | −0.139875 | ||||||||
\(142\) | 9.22250 | 0.773935 | ||||||||
\(143\) | 0.268014 | 0.0224125 | ||||||||
\(144\) | −16.5720 | −1.38100 | ||||||||
\(145\) | 1.55147 | 0.128843 | ||||||||
\(146\) | 17.8656 | 1.47857 | ||||||||
\(147\) | −1.86916 | −0.154166 | ||||||||
\(148\) | −38.0827 | −3.13038 | ||||||||
\(149\) | 17.3253 | 1.41934 | 0.709672 | − | 0.704533i | \(-0.248843\pi\) | ||||
0.709672 | + | 0.704533i | \(0.248843\pi\) | |||||||
\(150\) | 15.9706 | 1.30399 | ||||||||
\(151\) | 4.46772 | 0.363578 | 0.181789 | − | 0.983338i | \(-0.441811\pi\) | ||||
0.181789 | + | 0.983338i | \(0.441811\pi\) | |||||||
\(152\) | −22.2434 | −1.80418 | ||||||||
\(153\) | −1.48983 | −0.120446 | ||||||||
\(154\) | −6.19978 | −0.499592 | ||||||||
\(155\) | 2.16039 | 0.173526 | ||||||||
\(156\) | −1.65187 | −0.132255 | ||||||||
\(157\) | 20.9019 | 1.66815 | 0.834077 | − | 0.551648i | \(-0.186001\pi\) | ||||
0.834077 | + | 0.551648i | \(0.186001\pi\) | |||||||
\(158\) | −7.23327 | −0.575448 | ||||||||
\(159\) | −6.19130 | −0.491002 | ||||||||
\(160\) | 4.12179 | 0.325856 | ||||||||
\(161\) | 5.74071 | 0.452431 | ||||||||
\(162\) | 6.12077 | 0.480893 | ||||||||
\(163\) | −17.1059 | −1.33984 | −0.669921 | − | 0.742433i | \(-0.733672\pi\) | ||||
−0.669921 | + | 0.742433i | \(0.733672\pi\) | |||||||
\(164\) | 37.6616 | 2.94088 | ||||||||
\(165\) | 0.375520 | 0.0292342 | ||||||||
\(166\) | 6.05610 | 0.470045 | ||||||||
\(167\) | −12.0139 | −0.929661 | −0.464830 | − | 0.885400i | \(-0.653885\pi\) | ||||
−0.464830 | + | 0.885400i | \(0.653885\pi\) | |||||||
\(168\) | 22.9738 | 1.77247 | ||||||||
\(169\) | −12.9282 | −0.994475 | ||||||||
\(170\) | 0.809369 | 0.0620758 | ||||||||
\(171\) | −4.14924 | −0.317301 | ||||||||
\(172\) | −5.01539 | −0.382420 | ||||||||
\(173\) | 15.9146 | 1.20997 | 0.604983 | − | 0.796239i | \(-0.293180\pi\) | ||||
0.604983 | + | 0.796239i | \(0.293180\pi\) | |||||||
\(174\) | 16.5258 | 1.25282 | ||||||||
\(175\) | 11.4850 | 0.868188 | ||||||||
\(176\) | −11.1234 | −0.838457 | ||||||||
\(177\) | 13.4675 | 1.01228 | ||||||||
\(178\) | −11.5671 | −0.866989 | ||||||||
\(179\) | −4.98079 | −0.372282 | −0.186141 | − | 0.982523i | \(-0.559598\pi\) | ||||
−0.186141 | + | 0.982523i | \(0.559598\pi\) | |||||||
\(180\) | 2.28330 | 0.170187 | ||||||||
\(181\) | −7.45555 | −0.554166 | −0.277083 | − | 0.960846i | \(-0.589368\pi\) | ||||
−0.277083 | + | 0.960846i | \(0.589368\pi\) | |||||||
\(182\) | −1.66163 | −0.123168 | ||||||||
\(183\) | 7.70974 | 0.569921 | ||||||||
\(184\) | 19.5878 | 1.44403 | ||||||||
\(185\) | 2.32030 | 0.170592 | ||||||||
\(186\) | 23.0117 | 1.68730 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | −6.77863 | −0.494382 | ||||||||
\(189\) | 12.9149 | 0.939424 | ||||||||
\(190\) | 2.25412 | 0.163531 | ||||||||
\(191\) | −0.00220239 | −0.000159359 0 | −7.96795e−5 | − | 1.00000i | \(-0.500025\pi\) | ||||
−7.96795e−5 | 1.00000i | \(0.500025\pi\) | ||||||||
\(192\) | 16.5652 | 1.19549 | ||||||||
\(193\) | −19.2693 | −1.38703 | −0.693516 | − | 0.720441i | \(-0.743939\pi\) | ||||
−0.693516 | + | 0.720441i | \(0.743939\pi\) | |||||||
\(194\) | 40.0684 | 2.87674 | ||||||||
\(195\) | 0.100645 | 0.00720731 | ||||||||
\(196\) | −7.62849 | −0.544892 | ||||||||
\(197\) | 3.37152 | 0.240211 | 0.120105 | − | 0.992761i | \(-0.461677\pi\) | ||||
0.120105 | + | 0.992761i | \(0.461677\pi\) | |||||||
\(198\) | −3.94606 | −0.280434 | ||||||||
\(199\) | 16.8674 | 1.19570 | 0.597850 | − | 0.801608i | \(-0.296022\pi\) | ||||
0.597850 | + | 0.801608i | \(0.296022\pi\) | |||||||
\(200\) | 39.1880 | 2.77101 | ||||||||
\(201\) | 7.58837 | 0.535243 | ||||||||
\(202\) | −31.0135 | −2.18210 | ||||||||
\(203\) | 11.8843 | 0.834115 | ||||||||
\(204\) | 6.16336 | 0.431521 | ||||||||
\(205\) | −2.29464 | −0.160265 | ||||||||
\(206\) | −17.7045 | −1.23353 | ||||||||
\(207\) | 3.65387 | 0.253962 | ||||||||
\(208\) | −2.98122 | −0.206711 | ||||||||
\(209\) | −2.78504 | −0.192645 | ||||||||
\(210\) | −2.32814 | −0.160657 | ||||||||
\(211\) | 13.9706 | 0.961777 | 0.480889 | − | 0.876782i | \(-0.340314\pi\) | ||||
0.480889 | + | 0.876782i | \(0.340314\pi\) | |||||||
\(212\) | −25.2682 | −1.73543 | ||||||||
\(213\) | −4.27893 | −0.293187 | ||||||||
\(214\) | 10.8154 | 0.739324 | ||||||||
\(215\) | 0.305577 | 0.0208402 | ||||||||
\(216\) | 44.0669 | 2.99837 | ||||||||
\(217\) | 16.5486 | 1.12339 | ||||||||
\(218\) | 10.8824 | 0.737050 | ||||||||
\(219\) | −8.28905 | −0.560122 | ||||||||
\(220\) | 1.53259 | 0.103327 | ||||||||
\(221\) | −0.268014 | −0.0180286 | ||||||||
\(222\) | 24.7150 | 1.65877 | ||||||||
\(223\) | −4.83975 | −0.324094 | −0.162047 | − | 0.986783i | \(-0.551810\pi\) | ||||
−0.162047 | + | 0.986783i | \(0.551810\pi\) | |||||||
\(224\) | 31.5730 | 2.10956 | ||||||||
\(225\) | 7.31005 | 0.487337 | ||||||||
\(226\) | −32.8886 | −2.18772 | ||||||||
\(227\) | 10.1641 | 0.674614 | 0.337307 | − | 0.941395i | \(-0.390484\pi\) | ||||
0.337307 | + | 0.941395i | \(0.390484\pi\) | |||||||
\(228\) | 17.1652 | 1.13679 | ||||||||
\(229\) | −6.29198 | −0.415785 | −0.207893 | − | 0.978152i | \(-0.566660\pi\) | ||||
−0.207893 | + | 0.978152i | \(0.566660\pi\) | |||||||
\(230\) | −1.98501 | −0.130887 | ||||||||
\(231\) | 2.87649 | 0.189259 | ||||||||
\(232\) | 40.5503 | 2.66226 | ||||||||
\(233\) | 21.5526 | 1.41196 | 0.705981 | − | 0.708231i | \(-0.250507\pi\) | ||||
0.705981 | + | 0.708231i | \(0.250507\pi\) | |||||||
\(234\) | −1.05760 | −0.0691375 | ||||||||
\(235\) | 0.413007 | 0.0269416 | ||||||||
\(236\) | 54.9642 | 3.57786 | ||||||||
\(237\) | 3.35599 | 0.217995 | ||||||||
\(238\) | 6.19978 | 0.401872 | ||||||||
\(239\) | 26.5598 | 1.71801 | 0.859006 | − | 0.511966i | \(-0.171083\pi\) | ||||
0.859006 | + | 0.511966i | \(0.171083\pi\) | |||||||
\(240\) | −4.17705 | −0.269628 | ||||||||
\(241\) | 14.5493 | 0.937205 | 0.468603 | − | 0.883409i | \(-0.344758\pi\) | ||||
0.468603 | + | 0.883409i | \(0.344758\pi\) | |||||||
\(242\) | −2.64866 | −0.170262 | ||||||||
\(243\) | 13.7127 | 0.879669 | ||||||||
\(244\) | 31.4654 | 2.01436 | ||||||||
\(245\) | 0.464787 | 0.0296942 | ||||||||
\(246\) | −24.4418 | −1.55835 | ||||||||
\(247\) | −0.746429 | −0.0474942 | ||||||||
\(248\) | 56.4652 | 3.58555 | ||||||||
\(249\) | −2.80983 | −0.178066 | ||||||||
\(250\) | −8.01811 | −0.507110 | ||||||||
\(251\) | −11.0650 | −0.698418 | −0.349209 | − | 0.937045i | \(-0.613550\pi\) | ||||
−0.349209 | + | 0.937045i | \(0.613550\pi\) | |||||||
\(252\) | 17.4901 | 1.10177 | ||||||||
\(253\) | 2.45254 | 0.154190 | ||||||||
\(254\) | −19.9927 | −1.25446 | ||||||||
\(255\) | −0.375520 | −0.0235160 | ||||||||
\(256\) | −3.84659 | −0.240412 | ||||||||
\(257\) | −27.1089 | −1.69100 | −0.845502 | − | 0.533972i | \(-0.820699\pi\) | ||||
−0.845502 | + | 0.533972i | \(0.820699\pi\) | |||||||
\(258\) | 3.25491 | 0.202642 | ||||||||
\(259\) | 17.7735 | 1.10439 | ||||||||
\(260\) | 0.410755 | 0.0254739 | ||||||||
\(261\) | 7.56418 | 0.468211 | ||||||||
\(262\) | 43.9330 | 2.71419 | ||||||||
\(263\) | −8.33979 | −0.514254 | −0.257127 | − | 0.966378i | \(-0.582776\pi\) | ||||
−0.257127 | + | 0.966378i | \(0.582776\pi\) | |||||||
\(264\) | 9.81482 | 0.604060 | ||||||||
\(265\) | 1.53954 | 0.0945730 | ||||||||
\(266\) | 17.2666 | 1.05868 | ||||||||
\(267\) | 5.36673 | 0.328439 | ||||||||
\(268\) | 30.9700 | 1.89179 | ||||||||
\(269\) | −12.9135 | −0.787349 | −0.393675 | − | 0.919250i | \(-0.628796\pi\) | ||||
−0.393675 | + | 0.919250i | \(0.628796\pi\) | |||||||
\(270\) | −4.46570 | −0.271774 | ||||||||
\(271\) | 1.36880 | 0.0831487 | 0.0415744 | − | 0.999135i | \(-0.486763\pi\) | ||||
0.0415744 | + | 0.999135i | \(0.486763\pi\) | |||||||
\(272\) | 11.1234 | 0.674454 | ||||||||
\(273\) | 0.770939 | 0.0466593 | ||||||||
\(274\) | −17.3954 | −1.05089 | ||||||||
\(275\) | 4.90662 | 0.295880 | ||||||||
\(276\) | −15.1159 | −0.909868 | ||||||||
\(277\) | −15.5444 | −0.933973 | −0.466987 | − | 0.884264i | \(-0.654660\pi\) | ||||
−0.466987 | + | 0.884264i | \(0.654660\pi\) | |||||||
\(278\) | 25.1900 | 1.51080 | ||||||||
\(279\) | 10.5329 | 0.630590 | ||||||||
\(280\) | −5.71269 | −0.341398 | ||||||||
\(281\) | 1.08802 | 0.0649059 | 0.0324530 | − | 0.999473i | \(-0.489668\pi\) | ||||
0.0324530 | + | 0.999473i | \(0.489668\pi\) | |||||||
\(282\) | 4.39921 | 0.261969 | ||||||||
\(283\) | −7.45314 | −0.443043 | −0.221522 | − | 0.975155i | \(-0.571102\pi\) | ||||
−0.221522 | + | 0.975155i | \(0.571102\pi\) | |||||||
\(284\) | −17.4633 | −1.03626 | ||||||||
\(285\) | −1.04584 | −0.0619500 | ||||||||
\(286\) | −0.709878 | −0.0419759 | ||||||||
\(287\) | −17.5770 | −1.03754 | ||||||||
\(288\) | 20.0957 | 1.18415 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −4.10932 | −0.241308 | ||||||||
\(291\) | −18.5904 | −1.08979 | ||||||||
\(292\) | −33.8296 | −1.97973 | ||||||||
\(293\) | 7.13715 | 0.416957 | 0.208479 | − | 0.978027i | \(-0.433149\pi\) | ||||
0.208479 | + | 0.978027i | \(0.433149\pi\) | |||||||
\(294\) | 4.95076 | 0.288734 | ||||||||
\(295\) | −3.34885 | −0.194977 | ||||||||
\(296\) | 60.6447 | 3.52490 | ||||||||
\(297\) | 5.51750 | 0.320158 | ||||||||
\(298\) | −45.8888 | −2.65827 | ||||||||
\(299\) | 0.657314 | 0.0380134 | ||||||||
\(300\) | −30.2413 | −1.74598 | ||||||||
\(301\) | 2.34072 | 0.134917 | ||||||||
\(302\) | −11.8335 | −0.680940 | ||||||||
\(303\) | 14.3892 | 0.826640 | ||||||||
\(304\) | 30.9791 | 1.77677 | ||||||||
\(305\) | −1.91711 | −0.109774 | ||||||||
\(306\) | 3.94606 | 0.225581 | ||||||||
\(307\) | 5.22192 | 0.298031 | 0.149015 | − | 0.988835i | \(-0.452390\pi\) | ||||
0.149015 | + | 0.988835i | \(0.452390\pi\) | |||||||
\(308\) | 11.7396 | 0.668929 | ||||||||
\(309\) | 8.21429 | 0.467295 | ||||||||
\(310\) | −5.72213 | −0.324995 | ||||||||
\(311\) | −28.0808 | −1.59232 | −0.796158 | − | 0.605089i | \(-0.793138\pi\) | ||||
−0.796158 | + | 0.605089i | \(0.793138\pi\) | |||||||
\(312\) | 2.63051 | 0.148923 | ||||||||
\(313\) | −22.9588 | −1.29771 | −0.648854 | − | 0.760913i | \(-0.724751\pi\) | ||||
−0.648854 | + | 0.760913i | \(0.724751\pi\) | |||||||
\(314\) | −55.3620 | −3.12426 | ||||||||
\(315\) | −1.06563 | −0.0600417 | ||||||||
\(316\) | 13.6966 | 0.770495 | ||||||||
\(317\) | 25.7950 | 1.44879 | 0.724396 | − | 0.689384i | \(-0.242119\pi\) | ||||
0.724396 | + | 0.689384i | \(0.242119\pi\) | |||||||
\(318\) | 16.3986 | 0.919590 | ||||||||
\(319\) | 5.07720 | 0.284268 | ||||||||
\(320\) | −4.11912 | −0.230266 | ||||||||
\(321\) | −5.01797 | −0.280076 | ||||||||
\(322\) | −15.2052 | −0.847351 | ||||||||
\(323\) | 2.78504 | 0.154964 | ||||||||
\(324\) | −11.5900 | −0.643891 | ||||||||
\(325\) | 1.31504 | 0.0729455 | ||||||||
\(326\) | 45.3078 | 2.50937 | ||||||||
\(327\) | −5.04907 | −0.279214 | ||||||||
\(328\) | −59.9742 | −3.31152 | ||||||||
\(329\) | 3.16364 | 0.174417 | ||||||||
\(330\) | −0.994624 | −0.0547522 | ||||||||
\(331\) | 12.0946 | 0.664777 | 0.332389 | − | 0.943142i | \(-0.392145\pi\) | ||||
0.332389 | + | 0.943142i | \(0.392145\pi\) | |||||||
\(332\) | −11.4676 | −0.629366 | ||||||||
\(333\) | 11.3126 | 0.619924 | ||||||||
\(334\) | 31.8206 | 1.74115 | ||||||||
\(335\) | −1.88693 | −0.103094 | ||||||||
\(336\) | −31.9963 | −1.74554 | ||||||||
\(337\) | −8.40784 | −0.458004 | −0.229002 | − | 0.973426i | \(-0.573546\pi\) | ||||
−0.229002 | + | 0.973426i | \(0.573546\pi\) | |||||||
\(338\) | 34.2423 | 1.86254 | ||||||||
\(339\) | 15.2592 | 0.828767 | ||||||||
\(340\) | −1.53259 | −0.0831163 | ||||||||
\(341\) | 7.06987 | 0.382855 | ||||||||
\(342\) | 10.9899 | 0.594268 | ||||||||
\(343\) | 19.9453 | 1.07695 | ||||||||
\(344\) | 7.98675 | 0.430617 | ||||||||
\(345\) | 0.920976 | 0.0495837 | ||||||||
\(346\) | −42.1524 | −2.26613 | ||||||||
\(347\) | −7.83360 | −0.420530 | −0.210265 | − | 0.977644i | \(-0.567433\pi\) | ||||
−0.210265 | + | 0.977644i | \(0.567433\pi\) | |||||||
\(348\) | −31.2926 | −1.67746 | ||||||||
\(349\) | 27.2955 | 1.46109 | 0.730546 | − | 0.682863i | \(-0.239265\pi\) | ||||
0.730546 | + | 0.682863i | \(0.239265\pi\) | |||||||
\(350\) | −30.4200 | −1.62602 | ||||||||
\(351\) | 1.47877 | 0.0789308 | ||||||||
\(352\) | 13.4886 | 0.718943 | ||||||||
\(353\) | 13.0599 | 0.695108 | 0.347554 | − | 0.937660i | \(-0.387012\pi\) | ||||
0.347554 | + | 0.937660i | \(0.387012\pi\) | |||||||
\(354\) | −35.6708 | −1.89588 | ||||||||
\(355\) | 1.06400 | 0.0564714 | ||||||||
\(356\) | 21.9029 | 1.16085 | ||||||||
\(357\) | −2.87649 | −0.152240 | ||||||||
\(358\) | 13.1924 | 0.697241 | ||||||||
\(359\) | 33.2463 | 1.75467 | 0.877337 | − | 0.479875i | \(-0.159318\pi\) | ||||
0.877337 | + | 0.479875i | \(0.159318\pi\) | |||||||
\(360\) | −3.63604 | −0.191636 | ||||||||
\(361\) | −11.2436 | −0.591766 | ||||||||
\(362\) | 19.7472 | 1.03789 | ||||||||
\(363\) | 1.22889 | 0.0644999 | ||||||||
\(364\) | 3.14639 | 0.164916 | ||||||||
\(365\) | 2.06116 | 0.107886 | ||||||||
\(366\) | −20.4205 | −1.06740 | ||||||||
\(367\) | −6.15987 | −0.321542 | −0.160771 | − | 0.986992i | \(-0.551398\pi\) | ||||
−0.160771 | + | 0.986992i | \(0.551398\pi\) | |||||||
\(368\) | −27.2805 | −1.42209 | ||||||||
\(369\) | −11.1875 | −0.582397 | ||||||||
\(370\) | −6.14567 | −0.319498 | ||||||||
\(371\) | 11.7929 | 0.612255 | ||||||||
\(372\) | −43.5741 | −2.25921 | ||||||||
\(373\) | 12.2775 | 0.635704 | 0.317852 | − | 0.948140i | \(-0.397038\pi\) | ||||
0.317852 | + | 0.948140i | \(0.397038\pi\) | |||||||
\(374\) | 2.64866 | 0.136959 | ||||||||
\(375\) | 3.72013 | 0.192107 | ||||||||
\(376\) | 10.7946 | 0.556689 | ||||||||
\(377\) | 1.36076 | 0.0700827 | ||||||||
\(378\) | −34.2073 | −1.75943 | ||||||||
\(379\) | −25.0356 | −1.28599 | −0.642995 | − | 0.765870i | \(-0.722308\pi\) | ||||
−0.642995 | + | 0.765870i | \(0.722308\pi\) | |||||||
\(380\) | −4.26832 | −0.218960 | ||||||||
\(381\) | 9.27595 | 0.475221 | ||||||||
\(382\) | 0.00583337 | 0.000298461 0 | ||||||||
\(383\) | 1.90900 | 0.0975454 | 0.0487727 | − | 0.998810i | \(-0.484469\pi\) | ||||
0.0487727 | + | 0.998810i | \(0.484469\pi\) | |||||||
\(384\) | −10.7237 | −0.547240 | ||||||||
\(385\) | −0.715271 | −0.0364536 | ||||||||
\(386\) | 51.0377 | 2.59775 | ||||||||
\(387\) | 1.48983 | 0.0757325 | ||||||||
\(388\) | −75.8718 | −3.85181 | ||||||||
\(389\) | −2.30376 | −0.116805 | −0.0584026 | − | 0.998293i | \(-0.518601\pi\) | ||||
−0.0584026 | + | 0.998293i | \(0.518601\pi\) | |||||||
\(390\) | −0.266573 | −0.0134985 | ||||||||
\(391\) | −2.45254 | −0.124030 | ||||||||
\(392\) | 12.1480 | 0.613565 | ||||||||
\(393\) | −20.3834 | −1.02821 | ||||||||
\(394\) | −8.93001 | −0.449887 | ||||||||
\(395\) | −0.834505 | −0.0419885 | ||||||||
\(396\) | 7.47210 | 0.375487 | ||||||||
\(397\) | 0.285991 | 0.0143535 | 0.00717674 | − | 0.999974i | \(-0.497716\pi\) | ||||
0.00717674 | + | 0.999974i | \(0.497716\pi\) | |||||||
\(398\) | −44.6760 | −2.23941 | ||||||||
\(399\) | −8.01113 | −0.401058 | ||||||||
\(400\) | −54.5783 | −2.72891 | ||||||||
\(401\) | 19.2094 | 0.959272 | 0.479636 | − | 0.877467i | \(-0.340769\pi\) | ||||
0.479636 | + | 0.877467i | \(0.340769\pi\) | |||||||
\(402\) | −20.0990 | −1.00245 | ||||||||
\(403\) | 1.89482 | 0.0943879 | ||||||||
\(404\) | 58.7260 | 2.92173 | ||||||||
\(405\) | 0.706155 | 0.0350891 | ||||||||
\(406\) | −31.4775 | −1.56220 | ||||||||
\(407\) | 7.59317 | 0.376379 | ||||||||
\(408\) | −9.81482 | −0.485906 | ||||||||
\(409\) | 1.05361 | 0.0520977 | 0.0260489 | − | 0.999661i | \(-0.491707\pi\) | ||||
0.0260489 | + | 0.999661i | \(0.491707\pi\) | |||||||
\(410\) | 6.07772 | 0.300157 | ||||||||
\(411\) | 8.07088 | 0.398107 | ||||||||
\(412\) | 33.5245 | 1.65164 | ||||||||
\(413\) | −25.6522 | −1.26226 | ||||||||
\(414\) | −9.67786 | −0.475641 | ||||||||
\(415\) | 0.698695 | 0.0342976 | ||||||||
\(416\) | 3.61512 | 0.177246 | ||||||||
\(417\) | −11.6873 | −0.572330 | ||||||||
\(418\) | 7.37662 | 0.360802 | ||||||||
\(419\) | 9.92785 | 0.485007 | 0.242504 | − | 0.970151i | \(-0.422031\pi\) | ||||
0.242504 | + | 0.970151i | \(0.422031\pi\) | |||||||
\(420\) | 4.40847 | 0.215111 | ||||||||
\(421\) | 11.0239 | 0.537274 | 0.268637 | − | 0.963241i | \(-0.413427\pi\) | ||||
0.268637 | + | 0.963241i | \(0.413427\pi\) | |||||||
\(422\) | −37.0034 | −1.80130 | ||||||||
\(423\) | 2.01361 | 0.0979049 | ||||||||
\(424\) | 40.2383 | 1.95414 | ||||||||
\(425\) | −4.90662 | −0.238006 | ||||||||
\(426\) | 11.3334 | 0.549106 | ||||||||
\(427\) | −14.6851 | −0.710663 | ||||||||
\(428\) | −20.4796 | −0.989918 | ||||||||
\(429\) | 0.329359 | 0.0159016 | ||||||||
\(430\) | −0.809369 | −0.0390312 | ||||||||
\(431\) | −28.4669 | −1.37120 | −0.685600 | − | 0.727978i | \(-0.740460\pi\) | ||||
−0.685600 | + | 0.727978i | \(0.740460\pi\) | |||||||
\(432\) | −61.3733 | −2.95283 | ||||||||
\(433\) | 8.86759 | 0.426149 | 0.213075 | − | 0.977036i | \(-0.431652\pi\) | ||||
0.213075 | + | 0.977036i | \(0.431652\pi\) | |||||||
\(434\) | −43.8316 | −2.10398 | ||||||||
\(435\) | 1.90659 | 0.0914139 | ||||||||
\(436\) | −20.6065 | −0.986873 | ||||||||
\(437\) | −6.83041 | −0.326743 | ||||||||
\(438\) | 21.9549 | 1.04904 | ||||||||
\(439\) | 29.7520 | 1.41999 | 0.709993 | − | 0.704209i | \(-0.248698\pi\) | ||||
0.709993 | + | 0.704209i | \(0.248698\pi\) | |||||||
\(440\) | −2.44057 | −0.116349 | ||||||||
\(441\) | 2.26606 | 0.107908 | ||||||||
\(442\) | 0.709878 | 0.0337654 | ||||||||
\(443\) | 6.95523 | 0.330453 | 0.165227 | − | 0.986256i | \(-0.447164\pi\) | ||||
0.165227 | + | 0.986256i | \(0.447164\pi\) | |||||||
\(444\) | −46.7994 | −2.22100 | ||||||||
\(445\) | −1.33450 | −0.0632613 | ||||||||
\(446\) | 12.8189 | 0.606990 | ||||||||
\(447\) | 21.2908 | 1.00702 | ||||||||
\(448\) | −31.5525 | −1.49072 | ||||||||
\(449\) | 0.697151 | 0.0329006 | 0.0164503 | − | 0.999865i | \(-0.494763\pi\) | ||||
0.0164503 | + | 0.999865i | \(0.494763\pi\) | |||||||
\(450\) | −19.3618 | −0.912726 | ||||||||
\(451\) | −7.50921 | −0.353595 | ||||||||
\(452\) | 62.2766 | 2.92924 | ||||||||
\(453\) | 5.49033 | 0.257958 | ||||||||
\(454\) | −26.9212 | −1.26347 | ||||||||
\(455\) | −0.191703 | −0.00898716 | ||||||||
\(456\) | −27.3347 | −1.28006 | ||||||||
\(457\) | −1.47388 | −0.0689453 | −0.0344726 | − | 0.999406i | \(-0.510975\pi\) | ||||
−0.0344726 | + | 0.999406i | \(0.510975\pi\) | |||||||
\(458\) | 16.6653 | 0.778718 | ||||||||
\(459\) | −5.51750 | −0.257535 | ||||||||
\(460\) | 3.75873 | 0.175252 | ||||||||
\(461\) | 17.2361 | 0.802767 | 0.401383 | − | 0.915910i | \(-0.368529\pi\) | ||||
0.401383 | + | 0.915910i | \(0.368529\pi\) | |||||||
\(462\) | −7.61883 | −0.354460 | ||||||||
\(463\) | 12.5775 | 0.584526 | 0.292263 | − | 0.956338i | \(-0.405592\pi\) | ||||
0.292263 | + | 0.956338i | \(0.405592\pi\) | |||||||
\(464\) | −56.4756 | −2.62182 | ||||||||
\(465\) | 2.65487 | 0.123117 | ||||||||
\(466\) | −57.0856 | −2.64444 | ||||||||
\(467\) | 21.2580 | 0.983704 | 0.491852 | − | 0.870679i | \(-0.336320\pi\) | ||||
0.491852 | + | 0.870679i | \(0.336320\pi\) | |||||||
\(468\) | 2.00263 | 0.0925715 | ||||||||
\(469\) | −14.4539 | −0.667421 | ||||||||
\(470\) | −1.09391 | −0.0504585 | ||||||||
\(471\) | 25.6861 | 1.18355 | ||||||||
\(472\) | −87.5276 | −4.02878 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −8.88888 | −0.408280 | ||||||||
\(475\) | −13.6651 | −0.626999 | ||||||||
\(476\) | −11.7396 | −0.538086 | ||||||||
\(477\) | 7.50598 | 0.343675 | ||||||||
\(478\) | −70.3479 | −3.21764 | ||||||||
\(479\) | 6.12803 | 0.279997 | 0.139998 | − | 0.990152i | \(-0.455290\pi\) | ||||
0.139998 | + | 0.990152i | \(0.455290\pi\) | |||||||
\(480\) | 5.06522 | 0.231195 | ||||||||
\(481\) | 2.03508 | 0.0927914 | ||||||||
\(482\) | −38.5362 | −1.75528 | ||||||||
\(483\) | 7.05469 | 0.320999 | ||||||||
\(484\) | 5.01539 | 0.227972 | ||||||||
\(485\) | 4.62270 | 0.209906 | ||||||||
\(486\) | −36.3202 | −1.64752 | ||||||||
\(487\) | 18.4294 | 0.835117 | 0.417559 | − | 0.908650i | \(-0.362886\pi\) | ||||
0.417559 | + | 0.908650i | \(0.362886\pi\) | |||||||
\(488\) | −50.1069 | −2.26823 | ||||||||
\(489\) | −21.0213 | −0.950616 | ||||||||
\(490\) | −1.23106 | −0.0556137 | ||||||||
\(491\) | 32.0801 | 1.44775 | 0.723877 | − | 0.689929i | \(-0.242358\pi\) | ||||
0.723877 | + | 0.689929i | \(0.242358\pi\) | |||||||
\(492\) | 46.2819 | 2.08655 | ||||||||
\(493\) | −5.07720 | −0.228665 | ||||||||
\(494\) | 1.97704 | 0.0889511 | ||||||||
\(495\) | −0.455259 | −0.0204624 | ||||||||
\(496\) | −78.6409 | −3.53108 | ||||||||
\(497\) | 8.15028 | 0.365590 | ||||||||
\(498\) | 7.44227 | 0.333496 | ||||||||
\(499\) | 2.01780 | 0.0903291 | 0.0451646 | − | 0.998980i | \(-0.485619\pi\) | ||||
0.0451646 | + | 0.998980i | \(0.485619\pi\) | |||||||
\(500\) | 15.1828 | 0.678994 | ||||||||
\(501\) | −14.7637 | −0.659593 | ||||||||
\(502\) | 29.3075 | 1.30806 | ||||||||
\(503\) | 24.3600 | 1.08616 | 0.543079 | − | 0.839682i | \(-0.317258\pi\) | ||||
0.543079 | + | 0.839682i | \(0.317258\pi\) | |||||||
\(504\) | −27.8521 | −1.24063 | ||||||||
\(505\) | −3.57804 | −0.159221 | ||||||||
\(506\) | −6.49593 | −0.288779 | ||||||||
\(507\) | −15.8873 | −0.705579 | ||||||||
\(508\) | 37.8574 | 1.67965 | ||||||||
\(509\) | −16.7090 | −0.740613 | −0.370307 | − | 0.928910i | \(-0.620747\pi\) | ||||
−0.370307 | + | 0.928910i | \(0.620747\pi\) | |||||||
\(510\) | 0.994624 | 0.0440427 | ||||||||
\(511\) | 15.7886 | 0.698444 | ||||||||
\(512\) | 27.6409 | 1.22157 | ||||||||
\(513\) | −15.3665 | −0.678446 | ||||||||
\(514\) | 71.8021 | 3.16706 | ||||||||
\(515\) | −2.04258 | −0.0900067 | ||||||||
\(516\) | −6.16336 | −0.271327 | ||||||||
\(517\) | 1.35156 | 0.0594417 | ||||||||
\(518\) | −47.0759 | −2.06840 | ||||||||
\(519\) | 19.5573 | 0.858469 | ||||||||
\(520\) | −0.654106 | −0.0286844 | ||||||||
\(521\) | 10.7142 | 0.469399 | 0.234700 | − | 0.972068i | \(-0.424589\pi\) | ||||
0.234700 | + | 0.972068i | \(0.424589\pi\) | |||||||
\(522\) | −20.0349 | −0.876905 | ||||||||
\(523\) | −19.4558 | −0.850743 | −0.425371 | − | 0.905019i | \(-0.639857\pi\) | ||||
−0.425371 | + | 0.905019i | \(0.639857\pi\) | |||||||
\(524\) | −83.1897 | −3.63416 | ||||||||
\(525\) | 14.1138 | 0.615978 | ||||||||
\(526\) | 22.0893 | 0.963138 | ||||||||
\(527\) | −7.06987 | −0.307968 | ||||||||
\(528\) | −13.6694 | −0.594884 | ||||||||
\(529\) | −16.9851 | −0.738481 | ||||||||
\(530\) | −4.07771 | −0.177124 | ||||||||
\(531\) | −16.3272 | −0.708542 | ||||||||
\(532\) | −32.6954 | −1.41752 | ||||||||
\(533\) | −2.01257 | −0.0871742 | ||||||||
\(534\) | −14.2146 | −0.615128 | ||||||||
\(535\) | 1.24778 | 0.0539460 | ||||||||
\(536\) | −49.3181 | −2.13022 | ||||||||
\(537\) | −6.12084 | −0.264134 | ||||||||
\(538\) | 34.2034 | 1.47461 | ||||||||
\(539\) | 1.52102 | 0.0655148 | ||||||||
\(540\) | 8.45606 | 0.363891 | ||||||||
\(541\) | −15.9516 | −0.685814 | −0.342907 | − | 0.939369i | \(-0.611412\pi\) | ||||
−0.342907 | + | 0.939369i | \(0.611412\pi\) | |||||||
\(542\) | −3.62549 | −0.155728 | ||||||||
\(543\) | −9.16203 | −0.393180 | ||||||||
\(544\) | −13.4886 | −0.578317 | ||||||||
\(545\) | 1.25551 | 0.0537801 | ||||||||
\(546\) | −2.04195 | −0.0873875 | ||||||||
\(547\) | 2.05413 | 0.0878280 | 0.0439140 | − | 0.999035i | \(-0.486017\pi\) | ||||
0.0439140 | + | 0.999035i | \(0.486017\pi\) | |||||||
\(548\) | 32.9392 | 1.40709 | ||||||||
\(549\) | −9.34685 | −0.398914 | ||||||||
\(550\) | −12.9960 | −0.554150 | ||||||||
\(551\) | −14.1402 | −0.602392 | ||||||||
\(552\) | 24.0712 | 1.02454 | ||||||||
\(553\) | −6.39232 | −0.271829 | ||||||||
\(554\) | 41.1719 | 1.74922 | ||||||||
\(555\) | 2.85138 | 0.121035 | ||||||||
\(556\) | −47.6988 | −2.02288 | ||||||||
\(557\) | 23.1470 | 0.980769 | 0.490384 | − | 0.871506i | \(-0.336856\pi\) | ||||
0.490384 | + | 0.871506i | \(0.336856\pi\) | |||||||
\(558\) | −27.8981 | −1.18102 | ||||||||
\(559\) | 0.268014 | 0.0113358 | ||||||||
\(560\) | 7.95623 | 0.336212 | ||||||||
\(561\) | −1.22889 | −0.0518837 | ||||||||
\(562\) | −2.88180 | −0.121561 | ||||||||
\(563\) | −2.41209 | −0.101658 | −0.0508288 | − | 0.998707i | \(-0.516186\pi\) | ||||
−0.0508288 | + | 0.998707i | \(0.516186\pi\) | |||||||
\(564\) | −8.33017 | −0.350764 | ||||||||
\(565\) | −3.79437 | −0.159631 | ||||||||
\(566\) | 19.7408 | 0.829769 | ||||||||
\(567\) | 5.40916 | 0.227163 | ||||||||
\(568\) | 27.8095 | 1.16686 | ||||||||
\(569\) | −9.59879 | −0.402402 | −0.201201 | − | 0.979550i | \(-0.564484\pi\) | ||||
−0.201201 | + | 0.979550i | \(0.564484\pi\) | |||||||
\(570\) | 2.77006 | 0.116025 | ||||||||
\(571\) | −23.3290 | −0.976290 | −0.488145 | − | 0.872763i | \(-0.662326\pi\) | ||||
−0.488145 | + | 0.872763i | \(0.662326\pi\) | |||||||
\(572\) | 1.34420 | 0.0562036 | ||||||||
\(573\) | −0.00270649 | −0.000113065 0 | ||||||||
\(574\) | 46.5554 | 1.94319 | ||||||||
\(575\) | 12.0337 | 0.501839 | ||||||||
\(576\) | −20.0827 | −0.836779 | ||||||||
\(577\) | 2.79422 | 0.116325 | 0.0581624 | − | 0.998307i | \(-0.481476\pi\) | ||||
0.0581624 | + | 0.998307i | \(0.481476\pi\) | |||||||
\(578\) | −2.64866 | −0.110170 | ||||||||
\(579\) | −23.6798 | −0.984098 | ||||||||
\(580\) | 7.78125 | 0.323099 | ||||||||
\(581\) | 5.35201 | 0.222039 | ||||||||
\(582\) | 49.2395 | 2.04104 | ||||||||
\(583\) | 5.03813 | 0.208658 | ||||||||
\(584\) | 53.8719 | 2.22924 | ||||||||
\(585\) | −0.122016 | −0.00504473 | ||||||||
\(586\) | −18.9039 | −0.780912 | ||||||||
\(587\) | −10.8416 | −0.447479 | −0.223740 | − | 0.974649i | \(-0.571827\pi\) | ||||
−0.223740 | + | 0.974649i | \(0.571827\pi\) | |||||||
\(588\) | −9.37456 | −0.386600 | ||||||||
\(589\) | −19.6898 | −0.811306 | ||||||||
\(590\) | 8.86995 | 0.365170 | ||||||||
\(591\) | 4.14322 | 0.170429 | ||||||||
\(592\) | −84.4617 | −3.47136 | ||||||||
\(593\) | −7.81014 | −0.320724 | −0.160362 | − | 0.987058i | \(-0.551266\pi\) | ||||
−0.160362 | + | 0.987058i | \(0.551266\pi\) | |||||||
\(594\) | −14.6140 | −0.599619 | ||||||||
\(595\) | 0.715271 | 0.0293232 | ||||||||
\(596\) | 86.8932 | 3.55928 | ||||||||
\(597\) | 20.7282 | 0.848347 | ||||||||
\(598\) | −1.74100 | −0.0711948 | ||||||||
\(599\) | −11.2999 | −0.461700 | −0.230850 | − | 0.972989i | \(-0.574151\pi\) | ||||
−0.230850 | + | 0.972989i | \(0.574151\pi\) | |||||||
\(600\) | 48.1576 | 1.96603 | ||||||||
\(601\) | −44.1176 | −1.79960 | −0.899798 | − | 0.436307i | \(-0.856286\pi\) | ||||
−0.899798 | + | 0.436307i | \(0.856286\pi\) | |||||||
\(602\) | −6.19978 | −0.252684 | ||||||||
\(603\) | −9.19971 | −0.374641 | ||||||||
\(604\) | 22.4074 | 0.911743 | ||||||||
\(605\) | −0.305577 | −0.0124235 | ||||||||
\(606\) | −38.1122 | −1.54820 | ||||||||
\(607\) | 31.2184 | 1.26712 | 0.633558 | − | 0.773695i | \(-0.281594\pi\) | ||||
0.633558 | + | 0.773695i | \(0.281594\pi\) | |||||||
\(608\) | −37.5661 | −1.52351 | ||||||||
\(609\) | 14.6045 | 0.591804 | ||||||||
\(610\) | 5.07778 | 0.205593 | ||||||||
\(611\) | 0.362238 | 0.0146546 | ||||||||
\(612\) | −7.47210 | −0.302042 | ||||||||
\(613\) | −38.9756 | −1.57421 | −0.787104 | − | 0.616820i | \(-0.788421\pi\) | ||||
−0.787104 | + | 0.616820i | \(0.788421\pi\) | |||||||
\(614\) | −13.8311 | −0.558177 | ||||||||
\(615\) | −2.81986 | −0.113708 | ||||||||
\(616\) | −18.6948 | −0.753234 | ||||||||
\(617\) | 37.8751 | 1.52480 | 0.762398 | − | 0.647108i | \(-0.224022\pi\) | ||||
0.762398 | + | 0.647108i | \(0.224022\pi\) | |||||||
\(618\) | −21.7569 | −0.875189 | ||||||||
\(619\) | 24.9471 | 1.00271 | 0.501355 | − | 0.865242i | \(-0.332835\pi\) | ||||
0.501355 | + | 0.865242i | \(0.332835\pi\) | |||||||
\(620\) | 10.8352 | 0.435152 | ||||||||
\(621\) | 13.5319 | 0.543015 | ||||||||
\(622\) | 74.3765 | 2.98222 | ||||||||
\(623\) | −10.2223 | −0.409547 | ||||||||
\(624\) | −3.66359 | −0.146661 | ||||||||
\(625\) | 23.6081 | 0.944322 | ||||||||
\(626\) | 60.8100 | 2.43046 | ||||||||
\(627\) | −3.42250 | −0.136681 | ||||||||
\(628\) | 104.831 | 4.18323 | ||||||||
\(629\) | −7.59317 | −0.302759 | ||||||||
\(630\) | 2.82250 | 0.112451 | ||||||||
\(631\) | −7.54870 | −0.300509 | −0.150255 | − | 0.988647i | \(-0.548009\pi\) | ||||
−0.150255 | + | 0.988647i | \(0.548009\pi\) | |||||||
\(632\) | −21.8112 | −0.867601 | ||||||||
\(633\) | 17.1683 | 0.682380 | ||||||||
\(634\) | −68.3222 | −2.71342 | ||||||||
\(635\) | −2.30657 | −0.0915334 | ||||||||
\(636\) | −31.0518 | −1.23128 | ||||||||
\(637\) | 0.407653 | 0.0161518 | ||||||||
\(638\) | −13.4478 | −0.532402 | ||||||||
\(639\) | 5.18753 | 0.205215 | ||||||||
\(640\) | 2.66656 | 0.105405 | ||||||||
\(641\) | 28.7321 | 1.13485 | 0.567425 | − | 0.823425i | \(-0.307940\pi\) | ||||
0.567425 | + | 0.823425i | \(0.307940\pi\) | |||||||
\(642\) | 13.2909 | 0.524550 | ||||||||
\(643\) | 33.0609 | 1.30380 | 0.651898 | − | 0.758307i | \(-0.273973\pi\) | ||||
0.651898 | + | 0.758307i | \(0.273973\pi\) | |||||||
\(644\) | 28.7919 | 1.13456 | ||||||||
\(645\) | 0.375520 | 0.0147861 | ||||||||
\(646\) | −7.37662 | −0.290229 | ||||||||
\(647\) | −35.9405 | −1.41297 | −0.706483 | − | 0.707730i | \(-0.749719\pi\) | ||||
−0.706483 | + | 0.707730i | \(0.749719\pi\) | |||||||
\(648\) | 18.4565 | 0.725041 | ||||||||
\(649\) | −10.9591 | −0.430182 | ||||||||
\(650\) | −3.48310 | −0.136618 | ||||||||
\(651\) | 20.3364 | 0.797045 | ||||||||
\(652\) | −85.7931 | −3.35992 | ||||||||
\(653\) | −42.8042 | −1.67506 | −0.837529 | − | 0.546394i | \(-0.816000\pi\) | ||||
−0.837529 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(654\) | 13.3733 | 0.522936 | ||||||||
\(655\) | 5.06856 | 0.198045 | ||||||||
\(656\) | 83.5278 | 3.26121 | ||||||||
\(657\) | 10.0492 | 0.392055 | ||||||||
\(658\) | −8.37939 | −0.326663 | ||||||||
\(659\) | −12.9986 | −0.506355 | −0.253178 | − | 0.967420i | \(-0.581476\pi\) | ||||
−0.253178 | + | 0.967420i | \(0.581476\pi\) | |||||||
\(660\) | 1.88338 | 0.0733104 | ||||||||
\(661\) | 51.3583 | 1.99761 | 0.998803 | − | 0.0489147i | \(-0.0155762\pi\) | ||||
0.998803 | + | 0.0489147i | \(0.0155762\pi\) | |||||||
\(662\) | −32.0344 | −1.24505 | ||||||||
\(663\) | −0.329359 | −0.0127913 | ||||||||
\(664\) | 18.2615 | 0.708685 | ||||||||
\(665\) | 1.99206 | 0.0772486 | ||||||||
\(666\) | −29.9631 | −1.16105 | ||||||||
\(667\) | 12.4520 | 0.482144 | ||||||||
\(668\) | −60.2543 | −2.33131 | ||||||||
\(669\) | −5.94751 | −0.229944 | ||||||||
\(670\) | 4.99784 | 0.193084 | ||||||||
\(671\) | −6.27375 | −0.242196 | ||||||||
\(672\) | 38.7997 | 1.49673 | ||||||||
\(673\) | −47.1410 | −1.81715 | −0.908576 | − | 0.417720i | \(-0.862829\pi\) | ||||
−0.908576 | + | 0.417720i | \(0.862829\pi\) | |||||||
\(674\) | 22.2695 | 0.857789 | ||||||||
\(675\) | 27.0723 | 1.04201 | ||||||||
\(676\) | −64.8399 | −2.49384 | ||||||||
\(677\) | −14.3021 | −0.549676 | −0.274838 | − | 0.961491i | \(-0.588624\pi\) | ||||
−0.274838 | + | 0.961491i | \(0.588624\pi\) | |||||||
\(678\) | −40.4164 | −1.55218 | ||||||||
\(679\) | 35.4100 | 1.35891 | ||||||||
\(680\) | 2.44057 | 0.0935914 | ||||||||
\(681\) | 12.4905 | 0.478638 | ||||||||
\(682\) | −18.7257 | −0.717043 | ||||||||
\(683\) | −3.73565 | −0.142941 | −0.0714703 | − | 0.997443i | \(-0.522769\pi\) | ||||
−0.0714703 | + | 0.997443i | \(0.522769\pi\) | |||||||
\(684\) | −20.8101 | −0.795694 | ||||||||
\(685\) | −2.00691 | −0.0766803 | ||||||||
\(686\) | −52.8284 | −2.01700 | ||||||||
\(687\) | −7.73213 | −0.294999 | ||||||||
\(688\) | −11.1234 | −0.424075 | ||||||||
\(689\) | 1.35029 | 0.0514419 | ||||||||
\(690\) | −2.43935 | −0.0928645 | ||||||||
\(691\) | −8.10503 | −0.308330 | −0.154165 | − | 0.988045i | \(-0.549269\pi\) | ||||
−0.154165 | + | 0.988045i | \(0.549269\pi\) | |||||||
\(692\) | 79.8180 | 3.03423 | ||||||||
\(693\) | −3.48729 | −0.132471 | ||||||||
\(694\) | 20.7485 | 0.787604 | ||||||||
\(695\) | 2.90618 | 0.110238 | ||||||||
\(696\) | 49.8318 | 1.88887 | ||||||||
\(697\) | 7.50921 | 0.284432 | ||||||||
\(698\) | −72.2964 | −2.73646 | ||||||||
\(699\) | 26.4858 | 1.00178 | ||||||||
\(700\) | 57.6020 | 2.17715 | ||||||||
\(701\) | 11.5512 | 0.436284 | 0.218142 | − | 0.975917i | \(-0.430000\pi\) | ||||
0.218142 | + | 0.975917i | \(0.430000\pi\) | |||||||
\(702\) | −3.91675 | −0.147828 | ||||||||
\(703\) | −21.1473 | −0.797584 | ||||||||
\(704\) | −13.4798 | −0.508040 | ||||||||
\(705\) | 0.507539 | 0.0191150 | ||||||||
\(706\) | −34.5912 | −1.30186 | ||||||||
\(707\) | −27.4079 | −1.03078 | ||||||||
\(708\) | 67.5448 | 2.53849 | ||||||||
\(709\) | 41.5861 | 1.56180 | 0.780900 | − | 0.624656i | \(-0.214761\pi\) | ||||
0.780900 | + | 0.624656i | \(0.214761\pi\) | |||||||
\(710\) | −2.81818 | −0.105764 | ||||||||
\(711\) | −4.06861 | −0.152585 | ||||||||
\(712\) | −34.8793 | −1.30716 | ||||||||
\(713\) | 17.3391 | 0.649354 | ||||||||
\(714\) | 7.61883 | 0.285128 | ||||||||
\(715\) | −0.0818989 | −0.00306284 | ||||||||
\(716\) | −24.9806 | −0.933571 | ||||||||
\(717\) | 32.6390 | 1.21893 | ||||||||
\(718\) | −88.0581 | −3.28630 | ||||||||
\(719\) | 27.6226 | 1.03015 | 0.515075 | − | 0.857145i | \(-0.327764\pi\) | ||||
0.515075 | + | 0.857145i | \(0.327764\pi\) | |||||||
\(720\) | 5.06402 | 0.188725 | ||||||||
\(721\) | −15.6462 | −0.582694 | ||||||||
\(722\) | 29.7804 | 1.10831 | ||||||||
\(723\) | 17.8795 | 0.664946 | ||||||||
\(724\) | −37.3925 | −1.38968 | ||||||||
\(725\) | 24.9119 | 0.925204 | ||||||||
\(726\) | −3.25491 | −0.120801 | ||||||||
\(727\) | 18.4052 | 0.682610 | 0.341305 | − | 0.939953i | \(-0.389131\pi\) | ||||
0.341305 | + | 0.939953i | \(0.389131\pi\) | |||||||
\(728\) | −5.01046 | −0.185700 | ||||||||
\(729\) | 23.7840 | 0.880890 | ||||||||
\(730\) | −5.45932 | −0.202059 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | 38.6674 | 1.42919 | ||||||||
\(733\) | 29.3185 | 1.08290 | 0.541452 | − | 0.840732i | \(-0.317875\pi\) | ||||
0.541452 | + | 0.840732i | \(0.317875\pi\) | |||||||
\(734\) | 16.3154 | 0.602212 | ||||||||
\(735\) | 0.571171 | 0.0210680 | ||||||||
\(736\) | 33.0812 | 1.21939 | ||||||||
\(737\) | −6.17499 | −0.227459 | ||||||||
\(738\) | 29.6318 | 1.09076 | ||||||||
\(739\) | −20.9128 | −0.769290 | −0.384645 | − | 0.923065i | \(-0.625676\pi\) | ||||
−0.384645 | + | 0.923065i | \(0.625676\pi\) | |||||||
\(740\) | 11.6372 | 0.427792 | ||||||||
\(741\) | −0.917278 | −0.0336970 | ||||||||
\(742\) | −31.2353 | −1.14668 | ||||||||
\(743\) | 0.238240 | 0.00874018 | 0.00437009 | − | 0.999990i | \(-0.498609\pi\) | ||||
0.00437009 | + | 0.999990i | \(0.498609\pi\) | |||||||
\(744\) | 69.3895 | 2.54394 | ||||||||
\(745\) | −5.29421 | −0.193965 | ||||||||
\(746\) | −32.5189 | −1.19060 | ||||||||
\(747\) | 3.40647 | 0.124636 | ||||||||
\(748\) | −5.01539 | −0.183381 | ||||||||
\(749\) | 9.55798 | 0.349241 | ||||||||
\(750\) | −9.85336 | −0.359794 | ||||||||
\(751\) | −10.1566 | −0.370619 | −0.185310 | − | 0.982680i | \(-0.559329\pi\) | ||||
−0.185310 | + | 0.982680i | \(0.559329\pi\) | |||||||
\(752\) | −15.0340 | −0.548232 | ||||||||
\(753\) | −13.5977 | −0.495527 | ||||||||
\(754\) | −3.60419 | −0.131257 | ||||||||
\(755\) | −1.36523 | −0.0496859 | ||||||||
\(756\) | 64.7736 | 2.35579 | ||||||||
\(757\) | 16.0606 | 0.583731 | 0.291865 | − | 0.956459i | \(-0.405724\pi\) | ||||
0.291865 | + | 0.956459i | \(0.405724\pi\) | |||||||
\(758\) | 66.3107 | 2.40851 | ||||||||
\(759\) | 3.01389 | 0.109397 | ||||||||
\(760\) | 6.79707 | 0.246556 | ||||||||
\(761\) | 7.26178 | 0.263239 | 0.131620 | − | 0.991300i | \(-0.457982\pi\) | ||||
0.131620 | + | 0.991300i | \(0.457982\pi\) | |||||||
\(762\) | −24.5688 | −0.890035 | ||||||||
\(763\) | 9.61722 | 0.348167 | ||||||||
\(764\) | −0.0110458 | −0.000399624 0 | ||||||||
\(765\) | 0.455259 | 0.0164599 | ||||||||
\(766\) | −5.05629 | −0.182691 | ||||||||
\(767\) | −2.93719 | −0.106056 | ||||||||
\(768\) | −4.72703 | −0.170572 | ||||||||
\(769\) | −28.2645 | −1.01924 | −0.509622 | − | 0.860399i | \(-0.670215\pi\) | ||||
−0.509622 | + | 0.860399i | \(0.670215\pi\) | |||||||
\(770\) | 1.89451 | 0.0682733 | ||||||||
\(771\) | −33.3138 | −1.19977 | ||||||||
\(772\) | −96.6430 | −3.47826 | ||||||||
\(773\) | −5.00944 | −0.180177 | −0.0900886 | − | 0.995934i | \(-0.528715\pi\) | ||||
−0.0900886 | + | 0.995934i | \(0.528715\pi\) | |||||||
\(774\) | −3.94606 | −0.141838 | ||||||||
\(775\) | 34.6892 | 1.24607 | ||||||||
\(776\) | 120.822 | 4.33725 | ||||||||
\(777\) | 21.8416 | 0.783565 | ||||||||
\(778\) | 6.10187 | 0.218763 | ||||||||
\(779\) | 20.9134 | 0.749302 | ||||||||
\(780\) | 0.504772 | 0.0180737 | ||||||||
\(781\) | 3.48195 | 0.124594 | ||||||||
\(782\) | 6.49593 | 0.232294 | ||||||||
\(783\) | 28.0135 | 1.00112 | ||||||||
\(784\) | −16.9188 | −0.604244 | ||||||||
\(785\) | −6.38714 | −0.227967 | ||||||||
\(786\) | 53.9887 | 1.92571 | ||||||||
\(787\) | −17.5022 | −0.623886 | −0.311943 | − | 0.950101i | \(-0.600980\pi\) | ||||
−0.311943 | + | 0.950101i | \(0.600980\pi\) | |||||||
\(788\) | 16.9095 | 0.602376 | ||||||||
\(789\) | −10.2487 | −0.364862 | ||||||||
\(790\) | 2.21032 | 0.0786396 | ||||||||
\(791\) | −29.0650 | −1.03343 | ||||||||
\(792\) | −11.8989 | −0.422810 | ||||||||
\(793\) | −1.68145 | −0.0597102 | ||||||||
\(794\) | −0.757492 | −0.0268824 | ||||||||
\(795\) | 1.89192 | 0.0670994 | ||||||||
\(796\) | 84.5967 | 2.99845 | ||||||||
\(797\) | 46.9875 | 1.66438 | 0.832191 | − | 0.554489i | \(-0.187086\pi\) | ||||
0.832191 | + | 0.554489i | \(0.187086\pi\) | |||||||
\(798\) | 21.2187 | 0.751135 | ||||||||
\(799\) | −1.35156 | −0.0478149 | ||||||||
\(800\) | 66.1833 | 2.33993 | ||||||||
\(801\) | −6.50632 | −0.229889 | ||||||||
\(802\) | −50.8792 | −1.79661 | ||||||||
\(803\) | 6.74516 | 0.238032 | ||||||||
\(804\) | 38.0587 | 1.34223 | ||||||||
\(805\) | −1.75423 | −0.0618284 | ||||||||
\(806\) | −5.01874 | −0.176778 | ||||||||
\(807\) | −15.8692 | −0.558623 | ||||||||
\(808\) | −93.5180 | −3.28995 | ||||||||
\(809\) | 39.8733 | 1.40187 | 0.700935 | − | 0.713225i | \(-0.252766\pi\) | ||||
0.700935 | + | 0.713225i | \(0.252766\pi\) | |||||||
\(810\) | −1.87036 | −0.0657179 | ||||||||
\(811\) | 14.4861 | 0.508677 | 0.254338 | − | 0.967115i | \(-0.418142\pi\) | ||||
0.254338 | + | 0.967115i | \(0.418142\pi\) | |||||||
\(812\) | 59.6045 | 2.09171 | ||||||||
\(813\) | 1.68210 | 0.0589939 | ||||||||
\(814\) | −20.1117 | −0.704915 | ||||||||
\(815\) | 5.22718 | 0.183100 | ||||||||
\(816\) | 13.6694 | 0.478525 | ||||||||
\(817\) | −2.78504 | −0.0974361 | ||||||||
\(818\) | −2.79066 | −0.0975730 | ||||||||
\(819\) | −0.934642 | −0.0326590 | ||||||||
\(820\) | −11.5085 | −0.401895 | ||||||||
\(821\) | −14.3373 | −0.500374 | −0.250187 | − | 0.968198i | \(-0.580492\pi\) | ||||
−0.250187 | + | 0.968198i | \(0.580492\pi\) | |||||||
\(822\) | −21.3770 | −0.745609 | ||||||||
\(823\) | −45.5240 | −1.58687 | −0.793433 | − | 0.608658i | \(-0.791708\pi\) | ||||
−0.793433 | + | 0.608658i | \(0.791708\pi\) | |||||||
\(824\) | −53.3861 | −1.85979 | ||||||||
\(825\) | 6.02969 | 0.209927 | ||||||||
\(826\) | 67.9440 | 2.36407 | ||||||||
\(827\) | −17.9070 | −0.622686 | −0.311343 | − | 0.950298i | \(-0.600779\pi\) | ||||
−0.311343 | + | 0.950298i | \(0.600779\pi\) | |||||||
\(828\) | 18.3256 | 0.636859 | ||||||||
\(829\) | 42.9478 | 1.49164 | 0.745820 | − | 0.666148i | \(-0.232058\pi\) | ||||
0.745820 | + | 0.666148i | \(0.232058\pi\) | |||||||
\(830\) | −1.85060 | −0.0642354 | ||||||||
\(831\) | −19.1023 | −0.662653 | ||||||||
\(832\) | −3.61278 | −0.125251 | ||||||||
\(833\) | −1.52102 | −0.0527001 | ||||||||
\(834\) | 30.9557 | 1.07191 | ||||||||
\(835\) | 3.67116 | 0.127046 | ||||||||
\(836\) | −13.9681 | −0.483096 | ||||||||
\(837\) | 39.0080 | 1.34831 | ||||||||
\(838\) | −26.2955 | −0.908362 | ||||||||
\(839\) | 46.3224 | 1.59923 | 0.799613 | − | 0.600515i | \(-0.205038\pi\) | ||||
0.799613 | + | 0.600515i | \(0.205038\pi\) | |||||||
\(840\) | −7.02025 | −0.242222 | ||||||||
\(841\) | −3.22207 | −0.111106 | ||||||||
\(842\) | −29.1987 | −1.00625 | ||||||||
\(843\) | 1.33706 | 0.0460507 | ||||||||
\(844\) | 70.0682 | 2.41185 | ||||||||
\(845\) | 3.95055 | 0.135903 | ||||||||
\(846\) | −5.33336 | −0.183365 | ||||||||
\(847\) | −2.34072 | −0.0804282 | ||||||||
\(848\) | −56.0411 | −1.92446 | ||||||||
\(849\) | −9.15908 | −0.314339 | ||||||||
\(850\) | 12.9960 | 0.445758 | ||||||||
\(851\) | 18.6225 | 0.638372 | ||||||||
\(852\) | −21.4605 | −0.735225 | ||||||||
\(853\) | 57.9110 | 1.98284 | 0.991418 | − | 0.130729i | \(-0.0417317\pi\) | ||||
0.991418 | + | 0.130729i | \(0.0417317\pi\) | |||||||
\(854\) | 38.8959 | 1.33099 | ||||||||
\(855\) | 1.26791 | 0.0433617 | ||||||||
\(856\) | 32.6126 | 1.11468 | ||||||||
\(857\) | −29.7489 | −1.01620 | −0.508101 | − | 0.861297i | \(-0.669652\pi\) | ||||
−0.508101 | + | 0.861297i | \(0.669652\pi\) | |||||||
\(858\) | −0.872360 | −0.0297819 | ||||||||
\(859\) | 38.6130 | 1.31746 | 0.658729 | − | 0.752381i | \(-0.271095\pi\) | ||||
0.658729 | + | 0.752381i | \(0.271095\pi\) | |||||||
\(860\) | 1.53259 | 0.0522608 | ||||||||
\(861\) | −21.6001 | −0.736131 | ||||||||
\(862\) | 75.3990 | 2.56810 | ||||||||
\(863\) | −53.2115 | −1.81134 | −0.905670 | − | 0.423983i | \(-0.860632\pi\) | ||||
−0.905670 | + | 0.423983i | \(0.860632\pi\) | |||||||
\(864\) | 74.4232 | 2.53193 | ||||||||
\(865\) | −4.86314 | −0.165352 | ||||||||
\(866\) | −23.4872 | −0.798128 | ||||||||
\(867\) | 1.22889 | 0.0417352 | ||||||||
\(868\) | 82.9977 | 2.81713 | ||||||||
\(869\) | −2.73092 | −0.0926400 | ||||||||
\(870\) | −5.04990 | −0.171208 | ||||||||
\(871\) | −1.65498 | −0.0560770 | ||||||||
\(872\) | 32.8148 | 1.11125 | ||||||||
\(873\) | 22.5379 | 0.762792 | ||||||||
\(874\) | 18.0914 | 0.611951 | ||||||||
\(875\) | −7.08592 | −0.239548 | ||||||||
\(876\) | −41.5728 | −1.40462 | ||||||||
\(877\) | 37.9204 | 1.28048 | 0.640241 | − | 0.768174i | \(-0.278835\pi\) | ||||
0.640241 | + | 0.768174i | \(0.278835\pi\) | |||||||
\(878\) | −78.8029 | −2.65947 | ||||||||
\(879\) | 8.77076 | 0.295831 | ||||||||
\(880\) | 3.39905 | 0.114582 | ||||||||
\(881\) | −28.5273 | −0.961108 | −0.480554 | − | 0.876965i | \(-0.659564\pi\) | ||||
−0.480554 | + | 0.876965i | \(0.659564\pi\) | |||||||
\(882\) | −6.00202 | −0.202099 | ||||||||
\(883\) | −22.2546 | −0.748928 | −0.374464 | − | 0.927242i | \(-0.622173\pi\) | ||||
−0.374464 | + | 0.927242i | \(0.622173\pi\) | |||||||
\(884\) | −1.34420 | −0.0452102 | ||||||||
\(885\) | −4.11536 | −0.138336 | ||||||||
\(886\) | −18.4220 | −0.618900 | ||||||||
\(887\) | 23.2626 | 0.781080 | 0.390540 | − | 0.920586i | \(-0.372288\pi\) | ||||
0.390540 | + | 0.920586i | \(0.372288\pi\) | |||||||
\(888\) | 74.5256 | 2.50091 | ||||||||
\(889\) | −17.6684 | −0.592578 | ||||||||
\(890\) | 3.53463 | 0.118481 | ||||||||
\(891\) | 2.31089 | 0.0774178 | ||||||||
\(892\) | −24.2733 | −0.812729 | ||||||||
\(893\) | −3.76416 | −0.125963 | ||||||||
\(894\) | −56.3922 | −1.88604 | ||||||||
\(895\) | 1.52202 | 0.0508754 | ||||||||
\(896\) | 20.4259 | 0.682381 | ||||||||
\(897\) | 0.807765 | 0.0269705 | ||||||||
\(898\) | −1.84652 | −0.0616190 | ||||||||
\(899\) | 35.8951 | 1.19717 | ||||||||
\(900\) | 36.6628 | 1.22209 | ||||||||
\(901\) | −5.03813 | −0.167845 | ||||||||
\(902\) | 19.8893 | 0.662242 | ||||||||
\(903\) | 2.87649 | 0.0957235 | ||||||||
\(904\) | −99.1722 | −3.29842 | ||||||||
\(905\) | 2.27824 | 0.0757313 | ||||||||
\(906\) | −14.5420 | −0.483126 | ||||||||
\(907\) | −1.81109 | −0.0601363 | −0.0300681 | − | 0.999548i | \(-0.509572\pi\) | ||||
−0.0300681 | + | 0.999548i | \(0.509572\pi\) | |||||||
\(908\) | 50.9769 | 1.69173 | ||||||||
\(909\) | −17.4447 | −0.578604 | ||||||||
\(910\) | 0.507755 | 0.0168319 | ||||||||
\(911\) | 30.3251 | 1.00472 | 0.502358 | − | 0.864660i | \(-0.332466\pi\) | ||||
0.502358 | + | 0.864660i | \(0.332466\pi\) | |||||||
\(912\) | 38.0698 | 1.26062 | ||||||||
\(913\) | 2.28648 | 0.0756714 | ||||||||
\(914\) | 3.90381 | 0.129127 | ||||||||
\(915\) | −2.35592 | −0.0778843 | ||||||||
\(916\) | −31.5567 | −1.04266 | ||||||||
\(917\) | 38.8253 | 1.28212 | ||||||||
\(918\) | 14.6140 | 0.482333 | ||||||||
\(919\) | 5.66088 | 0.186735 | 0.0933676 | − | 0.995632i | \(-0.470237\pi\) | ||||
0.0933676 | + | 0.995632i | \(0.470237\pi\) | |||||||
\(920\) | −5.98558 | −0.197339 | ||||||||
\(921\) | 6.41716 | 0.211452 | ||||||||
\(922\) | −45.6526 | −1.50349 | ||||||||
\(923\) | 0.933211 | 0.0307170 | ||||||||
\(924\) | 14.4267 | 0.474604 | ||||||||
\(925\) | 37.2568 | 1.22500 | ||||||||
\(926\) | −33.3135 | −1.09475 | ||||||||
\(927\) | −9.95854 | −0.327081 | ||||||||
\(928\) | 68.4841 | 2.24810 | ||||||||
\(929\) | 38.4670 | 1.26206 | 0.631030 | − | 0.775758i | \(-0.282632\pi\) | ||||
0.631030 | + | 0.775758i | \(0.282632\pi\) | |||||||
\(930\) | −7.03186 | −0.230584 | ||||||||
\(931\) | −4.23609 | −0.138832 | ||||||||
\(932\) | 108.095 | 3.54077 | ||||||||
\(933\) | −34.5082 | −1.12975 | ||||||||
\(934\) | −56.3052 | −1.84236 | ||||||||
\(935\) | 0.305577 | 0.00999343 | ||||||||
\(936\) | −3.18908 | −0.104238 | ||||||||
\(937\) | −29.2167 | −0.954466 | −0.477233 | − | 0.878777i | \(-0.658360\pi\) | ||||
−0.477233 | + | 0.878777i | \(0.658360\pi\) | |||||||
\(938\) | 38.2836 | 1.25000 | ||||||||
\(939\) | −28.2138 | −0.920722 | ||||||||
\(940\) | 2.07139 | 0.0675613 | ||||||||
\(941\) | 2.50868 | 0.0817805 | 0.0408902 | − | 0.999164i | \(-0.486981\pi\) | ||||
0.0408902 | + | 0.999164i | \(0.486981\pi\) | |||||||
\(942\) | −68.0338 | −2.21666 | ||||||||
\(943\) | −18.4166 | −0.599727 | ||||||||
\(944\) | 121.902 | 3.96758 | ||||||||
\(945\) | −3.94651 | −0.128380 | ||||||||
\(946\) | −2.64866 | −0.0861153 | ||||||||
\(947\) | −30.5531 | −0.992843 | −0.496422 | − | 0.868082i | \(-0.665353\pi\) | ||||
−0.496422 | + | 0.868082i | \(0.665353\pi\) | |||||||
\(948\) | 16.8316 | 0.546666 | ||||||||
\(949\) | 1.80780 | 0.0586836 | ||||||||
\(950\) | 36.1943 | 1.17430 | ||||||||
\(951\) | 31.6992 | 1.02792 | ||||||||
\(952\) | 18.6948 | 0.605901 | ||||||||
\(953\) | −1.83896 | −0.0595698 | −0.0297849 | − | 0.999556i | \(-0.509482\pi\) | ||||
−0.0297849 | + | 0.999556i | \(0.509482\pi\) | |||||||
\(954\) | −19.8808 | −0.643664 | ||||||||
\(955\) | 0.000672998 0 | 2.17777e−5 0 | ||||||||
\(956\) | 133.208 | 4.30825 | ||||||||
\(957\) | 6.23931 | 0.201688 | ||||||||
\(958\) | −16.2311 | −0.524401 | ||||||||
\(959\) | −15.3730 | −0.496420 | ||||||||
\(960\) | −5.06194 | −0.163373 | ||||||||
\(961\) | 18.9830 | 0.612355 | ||||||||
\(962\) | −5.39022 | −0.173788 | ||||||||
\(963\) | 6.08350 | 0.196038 | ||||||||
\(964\) | 72.9707 | 2.35023 | ||||||||
\(965\) | 5.88824 | 0.189549 | ||||||||
\(966\) | −18.6855 | −0.601195 | ||||||||
\(967\) | −27.5789 | −0.886878 | −0.443439 | − | 0.896305i | \(-0.646242\pi\) | ||||
−0.443439 | + | 0.896305i | \(0.646242\pi\) | |||||||
\(968\) | −7.98675 | −0.256704 | ||||||||
\(969\) | 3.42250 | 0.109947 | ||||||||
\(970\) | −12.2440 | −0.393130 | ||||||||
\(971\) | 57.4764 | 1.84451 | 0.922253 | − | 0.386587i | \(-0.126346\pi\) | ||||
0.922253 | + | 0.386587i | \(0.126346\pi\) | |||||||
\(972\) | 68.7745 | 2.20594 | ||||||||
\(973\) | 22.2614 | 0.713667 | ||||||||
\(974\) | −48.8133 | −1.56408 | ||||||||
\(975\) | 1.61604 | 0.0517547 | ||||||||
\(976\) | 69.7854 | 2.23378 | ||||||||
\(977\) | −8.73018 | −0.279303 | −0.139652 | − | 0.990201i | \(-0.544598\pi\) | ||||
−0.139652 | + | 0.990201i | \(0.544598\pi\) | |||||||
\(978\) | 55.6782 | 1.78039 | ||||||||
\(979\) | −4.36714 | −0.139575 | ||||||||
\(980\) | 2.33109 | 0.0744639 | ||||||||
\(981\) | 6.12121 | 0.195435 | ||||||||
\(982\) | −84.9692 | −2.71148 | ||||||||
\(983\) | −26.8766 | −0.857230 | −0.428615 | − | 0.903487i | \(-0.640998\pi\) | ||||
−0.428615 | + | 0.903487i | \(0.640998\pi\) | |||||||
\(984\) | −73.7015 | −2.34952 | ||||||||
\(985\) | −1.03026 | −0.0328268 | ||||||||
\(986\) | 13.4478 | 0.428264 | ||||||||
\(987\) | 3.88776 | 0.123749 | ||||||||
\(988\) | −3.74364 | −0.119101 | ||||||||
\(989\) | 2.45254 | 0.0779861 | ||||||||
\(990\) | 1.20583 | 0.0383236 | ||||||||
\(991\) | 27.4695 | 0.872598 | 0.436299 | − | 0.899802i | \(-0.356289\pi\) | ||||
0.436299 | + | 0.899802i | \(0.356289\pi\) | |||||||
\(992\) | 95.3623 | 3.02776 | ||||||||
\(993\) | 14.8629 | 0.471659 | ||||||||
\(994\) | −21.5873 | −0.684708 | ||||||||
\(995\) | −5.15429 | −0.163402 | ||||||||
\(996\) | −14.0924 | −0.446534 | ||||||||
\(997\) | −6.13159 | −0.194190 | −0.0970948 | − | 0.995275i | \(-0.530955\pi\) | ||||
−0.0970948 | + | 0.995275i | \(0.530955\pi\) | |||||||
\(998\) | −5.34446 | −0.169176 | ||||||||
\(999\) | 41.8953 | 1.32551 |
(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 | 8041.2.a.f.1.2 | ✓ | 66 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.f.1.2 | ✓ | 66 | 1.1 | even | 1 | trivial |