Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60224 | −1.84006 | −0.920032 | − | 0.391842i | \(-0.871838\pi\) | ||||
−0.920032 | + | 0.391842i | \(0.871838\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.77168 | 2.38584 | ||||||||
\(5\) | −2.58506 | −1.15607 | −0.578036 | − | 0.816011i | \(-0.696181\pi\) | ||||
−0.578036 | + | 0.816011i | \(0.696181\pi\) | |||||||
\(6\) | 2.60224 | 1.06236 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −7.21258 | −2.55003 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.72695 | 2.12725 | ||||||||
\(11\) | −0.115915 | −0.0349498 | −0.0174749 | − | 0.999847i | \(-0.505563\pi\) | ||||
−0.0174749 | + | 0.999847i | \(0.505563\pi\) | |||||||
\(12\) | −4.77168 | −1.37746 | ||||||||
\(13\) | 0.834967 | 0.231578 | 0.115789 | − | 0.993274i | \(-0.463060\pi\) | ||||
0.115789 | + | 0.993274i | \(0.463060\pi\) | |||||||
\(14\) | −2.60224 | −0.695479 | ||||||||
\(15\) | 2.58506 | 0.667459 | ||||||||
\(16\) | 9.22555 | 2.30639 | ||||||||
\(17\) | −5.62336 | −1.36386 | −0.681932 | − | 0.731415i | \(-0.738860\pi\) | ||||
−0.681932 | + | 0.731415i | \(0.738860\pi\) | |||||||
\(18\) | −2.60224 | −0.613355 | ||||||||
\(19\) | 3.68328 | 0.845003 | 0.422501 | − | 0.906362i | \(-0.361152\pi\) | ||||
0.422501 | + | 0.906362i | \(0.361152\pi\) | |||||||
\(20\) | −12.3351 | −2.75820 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0.301640 | 0.0643099 | ||||||||
\(23\) | 4.67180 | 0.974137 | 0.487069 | − | 0.873364i | \(-0.338066\pi\) | ||||
0.487069 | + | 0.873364i | \(0.338066\pi\) | |||||||
\(24\) | 7.21258 | 1.47226 | ||||||||
\(25\) | 1.68251 | 0.336503 | ||||||||
\(26\) | −2.17279 | −0.426119 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.77168 | 0.901762 | ||||||||
\(29\) | −3.88720 | −0.721836 | −0.360918 | − | 0.932598i | \(-0.617537\pi\) | ||||
−0.360918 | + | 0.932598i | \(0.617537\pi\) | |||||||
\(30\) | −6.72695 | −1.22817 | ||||||||
\(31\) | 3.08830 | 0.554676 | 0.277338 | − | 0.960772i | \(-0.410548\pi\) | ||||
0.277338 | + | 0.960772i | \(0.410548\pi\) | |||||||
\(32\) | −9.58198 | −1.69387 | ||||||||
\(33\) | 0.115915 | 0.0201783 | ||||||||
\(34\) | 14.6334 | 2.50960 | ||||||||
\(35\) | −2.58506 | −0.436954 | ||||||||
\(36\) | 4.77168 | 0.795280 | ||||||||
\(37\) | −10.6856 | −1.75670 | −0.878351 | − | 0.478017i | \(-0.841356\pi\) | ||||
−0.878351 | + | 0.478017i | \(0.841356\pi\) | |||||||
\(38\) | −9.58480 | −1.55486 | ||||||||
\(39\) | −0.834967 | −0.133702 | ||||||||
\(40\) | 18.6449 | 2.94802 | ||||||||
\(41\) | 11.6776 | 1.82374 | 0.911871 | − | 0.410478i | \(-0.134638\pi\) | ||||
0.911871 | + | 0.410478i | \(0.134638\pi\) | |||||||
\(42\) | 2.60224 | 0.401535 | ||||||||
\(43\) | −0.00633740 | −0.000966445 0 | −0.000483222 | − | 1.00000i | \(-0.500154\pi\) | ||||
−0.000483222 | 1.00000i | \(0.500154\pi\) | ||||||||
\(44\) | −0.553111 | −0.0833846 | ||||||||
\(45\) | −2.58506 | −0.385357 | ||||||||
\(46\) | −12.1572 | −1.79248 | ||||||||
\(47\) | −0.636054 | −0.0927780 | −0.0463890 | − | 0.998923i | \(-0.514771\pi\) | ||||
−0.0463890 | + | 0.998923i | \(0.514771\pi\) | |||||||
\(48\) | −9.22555 | −1.33159 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.37831 | −0.619187 | ||||||||
\(51\) | 5.62336 | 0.787428 | ||||||||
\(52\) | 3.98420 | 0.552508 | ||||||||
\(53\) | −2.34673 | −0.322349 | −0.161174 | − | 0.986926i | \(-0.551528\pi\) | ||||
−0.161174 | + | 0.986926i | \(0.551528\pi\) | |||||||
\(54\) | 2.60224 | 0.354121 | ||||||||
\(55\) | 0.299648 | 0.0404045 | ||||||||
\(56\) | −7.21258 | −0.963822 | ||||||||
\(57\) | −3.68328 | −0.487863 | ||||||||
\(58\) | 10.1155 | 1.32822 | ||||||||
\(59\) | −8.43296 | −1.09788 | −0.548939 | − | 0.835862i | \(-0.684968\pi\) | ||||
−0.548939 | + | 0.835862i | \(0.684968\pi\) | |||||||
\(60\) | 12.3351 | 1.59245 | ||||||||
\(61\) | 13.5378 | 1.73334 | 0.866669 | − | 0.498884i | \(-0.166256\pi\) | ||||
0.866669 | + | 0.498884i | \(0.166256\pi\) | |||||||
\(62\) | −8.03652 | −1.02064 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 6.48354 | 0.810443 | ||||||||
\(65\) | −2.15844 | −0.267721 | ||||||||
\(66\) | −0.301640 | −0.0371293 | ||||||||
\(67\) | 5.15720 | 0.630052 | 0.315026 | − | 0.949083i | \(-0.397987\pi\) | ||||
0.315026 | + | 0.949083i | \(0.397987\pi\) | |||||||
\(68\) | −26.8328 | −3.25396 | ||||||||
\(69\) | −4.67180 | −0.562418 | ||||||||
\(70\) | 6.72695 | 0.804024 | ||||||||
\(71\) | 0.734558 | 0.0871760 | 0.0435880 | − | 0.999050i | \(-0.486121\pi\) | ||||
0.0435880 | + | 0.999050i | \(0.486121\pi\) | |||||||
\(72\) | −7.21258 | −0.850011 | ||||||||
\(73\) | −9.88866 | −1.15738 | −0.578690 | − | 0.815548i | \(-0.696436\pi\) | ||||
−0.578690 | + | 0.815548i | \(0.696436\pi\) | |||||||
\(74\) | 27.8065 | 3.23244 | ||||||||
\(75\) | −1.68251 | −0.194280 | ||||||||
\(76\) | 17.5754 | 2.01604 | ||||||||
\(77\) | −0.115915 | −0.0132098 | ||||||||
\(78\) | 2.17279 | 0.246020 | ||||||||
\(79\) | −1.05167 | −0.118322 | −0.0591609 | − | 0.998248i | \(-0.518843\pi\) | ||||
−0.0591609 | + | 0.998248i | \(0.518843\pi\) | |||||||
\(80\) | −23.8486 | −2.66635 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −30.3881 | −3.35580 | ||||||||
\(83\) | 11.9797 | 1.31494 | 0.657470 | − | 0.753481i | \(-0.271627\pi\) | ||||
0.657470 | + | 0.753481i | \(0.271627\pi\) | |||||||
\(84\) | −4.77168 | −0.520633 | ||||||||
\(85\) | 14.5367 | 1.57673 | ||||||||
\(86\) | 0.0164915 | 0.00177832 | ||||||||
\(87\) | 3.88720 | 0.416752 | ||||||||
\(88\) | 0.836049 | 0.0891232 | ||||||||
\(89\) | −11.7675 | −1.24736 | −0.623678 | − | 0.781681i | \(-0.714362\pi\) | ||||
−0.623678 | + | 0.781681i | \(0.714362\pi\) | |||||||
\(90\) | 6.72695 | 0.709083 | ||||||||
\(91\) | 0.834967 | 0.0875284 | ||||||||
\(92\) | 22.2923 | 2.32413 | ||||||||
\(93\) | −3.08830 | −0.320242 | ||||||||
\(94\) | 1.65517 | 0.170717 | ||||||||
\(95\) | −9.52149 | −0.976884 | ||||||||
\(96\) | 9.58198 | 0.977956 | ||||||||
\(97\) | −13.3662 | −1.35714 | −0.678568 | − | 0.734538i | \(-0.737399\pi\) | ||||
−0.678568 | + | 0.734538i | \(0.737399\pi\) | |||||||
\(98\) | −2.60224 | −0.262866 | ||||||||
\(99\) | −0.115915 | −0.0116499 | ||||||||
\(100\) | 8.02841 | 0.802841 | ||||||||
\(101\) | 4.25024 | 0.422915 | 0.211458 | − | 0.977387i | \(-0.432179\pi\) | ||||
0.211458 | + | 0.977387i | \(0.432179\pi\) | |||||||
\(102\) | −14.6334 | −1.44892 | ||||||||
\(103\) | −10.8398 | −1.06807 | −0.534036 | − | 0.845461i | \(-0.679325\pi\) | ||||
−0.534036 | + | 0.845461i | \(0.679325\pi\) | |||||||
\(104\) | −6.02227 | −0.590532 | ||||||||
\(105\) | 2.58506 | 0.252276 | ||||||||
\(106\) | 6.10677 | 0.593142 | ||||||||
\(107\) | 8.44855 | 0.816752 | 0.408376 | − | 0.912814i | \(-0.366095\pi\) | ||||
0.408376 | + | 0.912814i | \(0.366095\pi\) | |||||||
\(108\) | −4.77168 | −0.459155 | ||||||||
\(109\) | −1.06337 | −0.101852 | −0.0509261 | − | 0.998702i | \(-0.516217\pi\) | ||||
−0.0509261 | + | 0.998702i | \(0.516217\pi\) | |||||||
\(110\) | −0.779757 | −0.0743469 | ||||||||
\(111\) | 10.6856 | 1.01423 | ||||||||
\(112\) | 9.22555 | 0.871733 | ||||||||
\(113\) | −3.70684 | −0.348711 | −0.174355 | − | 0.984683i | \(-0.555784\pi\) | ||||
−0.174355 | + | 0.984683i | \(0.555784\pi\) | |||||||
\(114\) | 9.58480 | 0.897699 | ||||||||
\(115\) | −12.0769 | −1.12617 | ||||||||
\(116\) | −18.5485 | −1.72218 | ||||||||
\(117\) | 0.834967 | 0.0771928 | ||||||||
\(118\) | 21.9446 | 2.02017 | ||||||||
\(119\) | −5.62336 | −0.515492 | ||||||||
\(120\) | −18.6449 | −1.70204 | ||||||||
\(121\) | −10.9866 | −0.998779 | ||||||||
\(122\) | −35.2287 | −3.18945 | ||||||||
\(123\) | −11.6776 | −1.05294 | ||||||||
\(124\) | 14.7364 | 1.32337 | ||||||||
\(125\) | 8.57589 | 0.767051 | ||||||||
\(126\) | −2.60224 | −0.231826 | ||||||||
\(127\) | 9.32079 | 0.827086 | 0.413543 | − | 0.910485i | \(-0.364291\pi\) | ||||
0.413543 | + | 0.910485i | \(0.364291\pi\) | |||||||
\(128\) | 2.29218 | 0.202602 | ||||||||
\(129\) | 0.00633740 | 0.000557977 0 | ||||||||
\(130\) | 5.61678 | 0.492624 | ||||||||
\(131\) | 3.48282 | 0.304296 | 0.152148 | − | 0.988358i | \(-0.451381\pi\) | ||||
0.152148 | + | 0.988358i | \(0.451381\pi\) | |||||||
\(132\) | 0.553111 | 0.0481421 | ||||||||
\(133\) | 3.68328 | 0.319381 | ||||||||
\(134\) | −13.4203 | −1.15934 | ||||||||
\(135\) | 2.58506 | 0.222486 | ||||||||
\(136\) | 40.5589 | 3.47790 | ||||||||
\(137\) | 1.52560 | 0.130341 | 0.0651703 | − | 0.997874i | \(-0.479241\pi\) | ||||
0.0651703 | + | 0.997874i | \(0.479241\pi\) | |||||||
\(138\) | 12.1572 | 1.03489 | ||||||||
\(139\) | 8.07704 | 0.685086 | 0.342543 | − | 0.939502i | \(-0.388712\pi\) | ||||
0.342543 | + | 0.939502i | \(0.388712\pi\) | |||||||
\(140\) | −12.3351 | −1.04250 | ||||||||
\(141\) | 0.636054 | 0.0535654 | ||||||||
\(142\) | −1.91150 | −0.160410 | ||||||||
\(143\) | −0.0967856 | −0.00809362 | ||||||||
\(144\) | 9.22555 | 0.768796 | ||||||||
\(145\) | 10.0486 | 0.834494 | ||||||||
\(146\) | 25.7327 | 2.12965 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −50.9882 | −4.19121 | ||||||||
\(149\) | −20.9577 | −1.71692 | −0.858461 | − | 0.512879i | \(-0.828579\pi\) | ||||
−0.858461 | + | 0.512879i | \(0.828579\pi\) | |||||||
\(150\) | 4.37831 | 0.357488 | ||||||||
\(151\) | −3.17563 | −0.258429 | −0.129215 | − | 0.991617i | \(-0.541246\pi\) | ||||
−0.129215 | + | 0.991617i | \(0.541246\pi\) | |||||||
\(152\) | −26.5660 | −2.15479 | ||||||||
\(153\) | −5.62336 | −0.454622 | ||||||||
\(154\) | 0.301640 | 0.0243069 | ||||||||
\(155\) | −7.98344 | −0.641245 | ||||||||
\(156\) | −3.98420 | −0.318991 | ||||||||
\(157\) | −5.31711 | −0.424351 | −0.212176 | − | 0.977232i | \(-0.568055\pi\) | ||||
−0.212176 | + | 0.977232i | \(0.568055\pi\) | |||||||
\(158\) | 2.73670 | 0.217720 | ||||||||
\(159\) | 2.34673 | 0.186108 | ||||||||
\(160\) | 24.7699 | 1.95824 | ||||||||
\(161\) | 4.67180 | 0.368189 | ||||||||
\(162\) | −2.60224 | −0.204452 | ||||||||
\(163\) | 13.9648 | 1.09381 | 0.546903 | − | 0.837196i | \(-0.315807\pi\) | ||||
0.546903 | + | 0.837196i | \(0.315807\pi\) | |||||||
\(164\) | 55.7219 | 4.35115 | ||||||||
\(165\) | −0.299648 | −0.0233275 | ||||||||
\(166\) | −31.1740 | −2.41957 | ||||||||
\(167\) | 23.7366 | 1.83679 | 0.918397 | − | 0.395661i | \(-0.129485\pi\) | ||||
0.918397 | + | 0.395661i | \(0.129485\pi\) | |||||||
\(168\) | 7.21258 | 0.556463 | ||||||||
\(169\) | −12.3028 | −0.946371 | ||||||||
\(170\) | −37.8280 | −2.90128 | ||||||||
\(171\) | 3.68328 | 0.281668 | ||||||||
\(172\) | −0.0302400 | −0.00230578 | ||||||||
\(173\) | −19.3101 | −1.46812 | −0.734059 | − | 0.679086i | \(-0.762376\pi\) | ||||
−0.734059 | + | 0.679086i | \(0.762376\pi\) | |||||||
\(174\) | −10.1155 | −0.766851 | ||||||||
\(175\) | 1.68251 | 0.127186 | ||||||||
\(176\) | −1.06938 | −0.0806078 | ||||||||
\(177\) | 8.43296 | 0.633860 | ||||||||
\(178\) | 30.6220 | 2.29522 | ||||||||
\(179\) | −6.85410 | −0.512299 | −0.256150 | − | 0.966637i | \(-0.582454\pi\) | ||||
−0.256150 | + | 0.966637i | \(0.582454\pi\) | |||||||
\(180\) | −12.3351 | −0.919401 | ||||||||
\(181\) | 2.43507 | 0.180997 | 0.0904985 | − | 0.995897i | \(-0.471154\pi\) | ||||
0.0904985 | + | 0.995897i | \(0.471154\pi\) | |||||||
\(182\) | −2.17279 | −0.161058 | ||||||||
\(183\) | −13.5378 | −1.00074 | ||||||||
\(184\) | −33.6957 | −2.48408 | ||||||||
\(185\) | 27.6229 | 2.03087 | ||||||||
\(186\) | 8.03652 | 0.589266 | ||||||||
\(187\) | 0.651834 | 0.0476668 | ||||||||
\(188\) | −3.03504 | −0.221353 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 24.7772 | 1.79753 | ||||||||
\(191\) | −1.00000 | −0.0723575 | ||||||||
\(192\) | −6.48354 | −0.467909 | ||||||||
\(193\) | −10.0769 | −0.725353 | −0.362676 | − | 0.931915i | \(-0.618137\pi\) | ||||
−0.362676 | + | 0.931915i | \(0.618137\pi\) | |||||||
\(194\) | 34.7822 | 2.49722 | ||||||||
\(195\) | 2.15844 | 0.154569 | ||||||||
\(196\) | 4.77168 | 0.340834 | ||||||||
\(197\) | 4.19816 | 0.299107 | 0.149553 | − | 0.988754i | \(-0.452216\pi\) | ||||
0.149553 | + | 0.988754i | \(0.452216\pi\) | |||||||
\(198\) | 0.301640 | 0.0214366 | ||||||||
\(199\) | −6.65383 | −0.471677 | −0.235839 | − | 0.971792i | \(-0.575784\pi\) | ||||
−0.235839 | + | 0.971792i | \(0.575784\pi\) | |||||||
\(200\) | −12.1353 | −0.858093 | ||||||||
\(201\) | −5.15720 | −0.363761 | ||||||||
\(202\) | −11.0602 | −0.778191 | ||||||||
\(203\) | −3.88720 | −0.272828 | ||||||||
\(204\) | 26.8328 | 1.87868 | ||||||||
\(205\) | −30.1874 | −2.10838 | ||||||||
\(206\) | 28.2077 | 1.96532 | ||||||||
\(207\) | 4.67180 | 0.324712 | ||||||||
\(208\) | 7.70304 | 0.534109 | ||||||||
\(209\) | −0.426949 | −0.0295327 | ||||||||
\(210\) | −6.72695 | −0.464204 | ||||||||
\(211\) | 16.5266 | 1.13774 | 0.568871 | − | 0.822427i | \(-0.307380\pi\) | ||||
0.568871 | + | 0.822427i | \(0.307380\pi\) | |||||||
\(212\) | −11.1979 | −0.769072 | ||||||||
\(213\) | −0.734558 | −0.0503311 | ||||||||
\(214\) | −21.9852 | −1.50288 | ||||||||
\(215\) | 0.0163825 | 0.00111728 | ||||||||
\(216\) | 7.21258 | 0.490754 | ||||||||
\(217\) | 3.08830 | 0.209648 | ||||||||
\(218\) | 2.76714 | 0.187415 | ||||||||
\(219\) | 9.88866 | 0.668214 | ||||||||
\(220\) | 1.42982 | 0.0963986 | ||||||||
\(221\) | −4.69532 | −0.315841 | ||||||||
\(222\) | −27.8065 | −1.86625 | ||||||||
\(223\) | −19.2287 | −1.28765 | −0.643825 | − | 0.765173i | \(-0.722653\pi\) | ||||
−0.643825 | + | 0.765173i | \(0.722653\pi\) | |||||||
\(224\) | −9.58198 | −0.640223 | ||||||||
\(225\) | 1.68251 | 0.112168 | ||||||||
\(226\) | 9.64611 | 0.641650 | ||||||||
\(227\) | −3.63510 | −0.241270 | −0.120635 | − | 0.992697i | \(-0.538493\pi\) | ||||
−0.120635 | + | 0.992697i | \(0.538493\pi\) | |||||||
\(228\) | −17.5754 | −1.16396 | ||||||||
\(229\) | −0.0867138 | −0.00573021 | −0.00286510 | − | 0.999996i | \(-0.500912\pi\) | ||||
−0.00286510 | + | 0.999996i | \(0.500912\pi\) | |||||||
\(230\) | 31.4269 | 2.07223 | ||||||||
\(231\) | 0.115915 | 0.00762667 | ||||||||
\(232\) | 28.0368 | 1.84070 | ||||||||
\(233\) | −21.3122 | −1.39621 | −0.698103 | − | 0.715998i | \(-0.745972\pi\) | ||||
−0.698103 | + | 0.715998i | \(0.745972\pi\) | |||||||
\(234\) | −2.17279 | −0.142040 | ||||||||
\(235\) | 1.64423 | 0.107258 | ||||||||
\(236\) | −40.2394 | −2.61936 | ||||||||
\(237\) | 1.05167 | 0.0683132 | ||||||||
\(238\) | 14.6334 | 0.948539 | ||||||||
\(239\) | 3.59778 | 0.232721 | 0.116361 | − | 0.993207i | \(-0.462877\pi\) | ||||
0.116361 | + | 0.993207i | \(0.462877\pi\) | |||||||
\(240\) | 23.8486 | 1.53942 | ||||||||
\(241\) | 8.40658 | 0.541515 | 0.270758 | − | 0.962648i | \(-0.412726\pi\) | ||||
0.270758 | + | 0.962648i | \(0.412726\pi\) | |||||||
\(242\) | 28.5897 | 1.83782 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 64.5980 | 4.13546 | ||||||||
\(245\) | −2.58506 | −0.165153 | ||||||||
\(246\) | 30.3881 | 1.93747 | ||||||||
\(247\) | 3.07542 | 0.195684 | ||||||||
\(248\) | −22.2747 | −1.41444 | ||||||||
\(249\) | −11.9797 | −0.759181 | ||||||||
\(250\) | −22.3166 | −1.41142 | ||||||||
\(251\) | 16.3609 | 1.03269 | 0.516344 | − | 0.856381i | \(-0.327293\pi\) | ||||
0.516344 | + | 0.856381i | \(0.327293\pi\) | |||||||
\(252\) | 4.77168 | 0.300587 | ||||||||
\(253\) | −0.541533 | −0.0340459 | ||||||||
\(254\) | −24.2550 | −1.52189 | ||||||||
\(255\) | −14.5367 | −0.910323 | ||||||||
\(256\) | −18.9319 | −1.18324 | ||||||||
\(257\) | −15.4413 | −0.963199 | −0.481599 | − | 0.876391i | \(-0.659944\pi\) | ||||
−0.481599 | + | 0.876391i | \(0.659944\pi\) | |||||||
\(258\) | −0.0164915 | −0.00102671 | ||||||||
\(259\) | −10.6856 | −0.663971 | ||||||||
\(260\) | −10.2994 | −0.638740 | ||||||||
\(261\) | −3.88720 | −0.240612 | ||||||||
\(262\) | −9.06315 | −0.559924 | ||||||||
\(263\) | −32.0181 | −1.97432 | −0.987159 | − | 0.159740i | \(-0.948935\pi\) | ||||
−0.987159 | + | 0.159740i | \(0.948935\pi\) | |||||||
\(264\) | −0.836049 | −0.0514553 | ||||||||
\(265\) | 6.06644 | 0.372658 | ||||||||
\(266\) | −9.58480 | −0.587682 | ||||||||
\(267\) | 11.7675 | 0.720162 | ||||||||
\(268\) | 24.6085 | 1.50320 | ||||||||
\(269\) | 14.4482 | 0.880924 | 0.440462 | − | 0.897771i | \(-0.354815\pi\) | ||||
0.440462 | + | 0.897771i | \(0.354815\pi\) | |||||||
\(270\) | −6.72695 | −0.409389 | ||||||||
\(271\) | −18.8960 | −1.14785 | −0.573925 | − | 0.818908i | \(-0.694580\pi\) | ||||
−0.573925 | + | 0.818908i | \(0.694580\pi\) | |||||||
\(272\) | −51.8786 | −3.14560 | ||||||||
\(273\) | −0.834967 | −0.0505345 | ||||||||
\(274\) | −3.96998 | −0.239835 | ||||||||
\(275\) | −0.195029 | −0.0117607 | ||||||||
\(276\) | −22.2923 | −1.34184 | ||||||||
\(277\) | 13.7382 | 0.825449 | 0.412724 | − | 0.910856i | \(-0.364577\pi\) | ||||
0.412724 | + | 0.910856i | \(0.364577\pi\) | |||||||
\(278\) | −21.0184 | −1.26060 | ||||||||
\(279\) | 3.08830 | 0.184892 | ||||||||
\(280\) | 18.6449 | 1.11425 | ||||||||
\(281\) | 30.0517 | 1.79273 | 0.896366 | − | 0.443314i | \(-0.146197\pi\) | ||||
0.896366 | + | 0.443314i | \(0.146197\pi\) | |||||||
\(282\) | −1.65517 | −0.0985638 | ||||||||
\(283\) | 15.1964 | 0.903335 | 0.451668 | − | 0.892186i | \(-0.350829\pi\) | ||||
0.451668 | + | 0.892186i | \(0.350829\pi\) | |||||||
\(284\) | 3.50507 | 0.207988 | ||||||||
\(285\) | 9.52149 | 0.564004 | ||||||||
\(286\) | 0.251860 | 0.0148928 | ||||||||
\(287\) | 11.6776 | 0.689309 | ||||||||
\(288\) | −9.58198 | −0.564623 | ||||||||
\(289\) | 14.6222 | 0.860127 | ||||||||
\(290\) | −26.1490 | −1.53552 | ||||||||
\(291\) | 13.3662 | 0.783543 | ||||||||
\(292\) | −47.1855 | −2.76132 | ||||||||
\(293\) | 11.6374 | 0.679865 | 0.339933 | − | 0.940450i | \(-0.389596\pi\) | ||||
0.339933 | + | 0.940450i | \(0.389596\pi\) | |||||||
\(294\) | 2.60224 | 0.151766 | ||||||||
\(295\) | 21.7997 | 1.26923 | ||||||||
\(296\) | 77.0708 | 4.47965 | ||||||||
\(297\) | 0.115915 | 0.00672609 | ||||||||
\(298\) | 54.5371 | 3.15925 | ||||||||
\(299\) | 3.90080 | 0.225589 | ||||||||
\(300\) | −8.02841 | −0.463521 | ||||||||
\(301\) | −0.00633740 | −0.000365282 0 | ||||||||
\(302\) | 8.26378 | 0.475527 | ||||||||
\(303\) | −4.25024 | −0.244170 | ||||||||
\(304\) | 33.9803 | 1.94890 | ||||||||
\(305\) | −34.9960 | −2.00386 | ||||||||
\(306\) | 14.6334 | 0.836533 | ||||||||
\(307\) | 13.1049 | 0.747935 | 0.373968 | − | 0.927442i | \(-0.377997\pi\) | ||||
0.373968 | + | 0.927442i | \(0.377997\pi\) | |||||||
\(308\) | −0.553111 | −0.0315164 | ||||||||
\(309\) | 10.8398 | 0.616652 | ||||||||
\(310\) | 20.7749 | 1.17993 | ||||||||
\(311\) | 27.8159 | 1.57729 | 0.788647 | − | 0.614846i | \(-0.210782\pi\) | ||||
0.788647 | + | 0.614846i | \(0.210782\pi\) | |||||||
\(312\) | 6.02227 | 0.340944 | ||||||||
\(313\) | 22.2381 | 1.25697 | 0.628485 | − | 0.777822i | \(-0.283675\pi\) | ||||
0.628485 | + | 0.777822i | \(0.283675\pi\) | |||||||
\(314\) | 13.8364 | 0.780834 | ||||||||
\(315\) | −2.58506 | −0.145651 | ||||||||
\(316\) | −5.01822 | −0.282297 | ||||||||
\(317\) | −6.15878 | −0.345912 | −0.172956 | − | 0.984930i | \(-0.555332\pi\) | ||||
−0.172956 | + | 0.984930i | \(0.555332\pi\) | |||||||
\(318\) | −6.10677 | −0.342451 | ||||||||
\(319\) | 0.450587 | 0.0252280 | ||||||||
\(320\) | −16.7603 | −0.936931 | ||||||||
\(321\) | −8.44855 | −0.471552 | ||||||||
\(322\) | −12.1572 | −0.677492 | ||||||||
\(323\) | −20.7124 | −1.15247 | ||||||||
\(324\) | 4.77168 | 0.265093 | ||||||||
\(325\) | 1.40484 | 0.0779267 | ||||||||
\(326\) | −36.3397 | −2.01267 | ||||||||
\(327\) | 1.06337 | 0.0588044 | ||||||||
\(328\) | −84.2260 | −4.65060 | ||||||||
\(329\) | −0.636054 | −0.0350668 | ||||||||
\(330\) | 0.779757 | 0.0429242 | ||||||||
\(331\) | −2.93153 | −0.161131 | −0.0805656 | − | 0.996749i | \(-0.525673\pi\) | ||||
−0.0805656 | + | 0.996749i | \(0.525673\pi\) | |||||||
\(332\) | 57.1631 | 3.13723 | ||||||||
\(333\) | −10.6856 | −0.585567 | ||||||||
\(334\) | −61.7684 | −3.37982 | ||||||||
\(335\) | −13.3317 | −0.728386 | ||||||||
\(336\) | −9.22555 | −0.503295 | ||||||||
\(337\) | −16.4073 | −0.893764 | −0.446882 | − | 0.894593i | \(-0.647466\pi\) | ||||
−0.446882 | + | 0.894593i | \(0.647466\pi\) | |||||||
\(338\) | 32.0150 | 1.74138 | ||||||||
\(339\) | 3.70684 | 0.201328 | ||||||||
\(340\) | 69.3644 | 3.76181 | ||||||||
\(341\) | −0.357982 | −0.0193858 | ||||||||
\(342\) | −9.58480 | −0.518287 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.0457090 | 0.00246447 | ||||||||
\(345\) | 12.0769 | 0.650196 | ||||||||
\(346\) | 50.2495 | 2.70143 | ||||||||
\(347\) | −18.4212 | −0.988902 | −0.494451 | − | 0.869205i | \(-0.664631\pi\) | ||||
−0.494451 | + | 0.869205i | \(0.664631\pi\) | |||||||
\(348\) | 18.5485 | 0.994303 | ||||||||
\(349\) | −7.60569 | −0.407123 | −0.203562 | − | 0.979062i | \(-0.565252\pi\) | ||||
−0.203562 | + | 0.979062i | \(0.565252\pi\) | |||||||
\(350\) | −4.37831 | −0.234031 | ||||||||
\(351\) | −0.834967 | −0.0445673 | ||||||||
\(352\) | 1.11070 | 0.0592004 | ||||||||
\(353\) | 14.4737 | 0.770355 | 0.385178 | − | 0.922842i | \(-0.374140\pi\) | ||||
0.385178 | + | 0.922842i | \(0.374140\pi\) | |||||||
\(354\) | −21.9446 | −1.16634 | ||||||||
\(355\) | −1.89887 | −0.100782 | ||||||||
\(356\) | −56.1509 | −2.97599 | ||||||||
\(357\) | 5.62336 | 0.297620 | ||||||||
\(358\) | 17.8360 | 0.942664 | ||||||||
\(359\) | 3.77612 | 0.199296 | 0.0996479 | − | 0.995023i | \(-0.468228\pi\) | ||||
0.0996479 | + | 0.995023i | \(0.468228\pi\) | |||||||
\(360\) | 18.6449 | 0.982674 | ||||||||
\(361\) | −5.43343 | −0.285970 | ||||||||
\(362\) | −6.33664 | −0.333046 | ||||||||
\(363\) | 10.9866 | 0.576645 | ||||||||
\(364\) | 3.98420 | 0.208829 | ||||||||
\(365\) | 25.5627 | 1.33801 | ||||||||
\(366\) | 35.2287 | 1.84143 | ||||||||
\(367\) | 31.1477 | 1.62590 | 0.812949 | − | 0.582335i | \(-0.197861\pi\) | ||||
0.812949 | + | 0.582335i | \(0.197861\pi\) | |||||||
\(368\) | 43.0999 | 2.24674 | ||||||||
\(369\) | 11.6776 | 0.607914 | ||||||||
\(370\) | −71.8815 | −3.73694 | ||||||||
\(371\) | −2.34673 | −0.121836 | ||||||||
\(372\) | −14.7364 | −0.764046 | ||||||||
\(373\) | 10.4761 | 0.542431 | 0.271216 | − | 0.962519i | \(-0.412574\pi\) | ||||
0.271216 | + | 0.962519i | \(0.412574\pi\) | |||||||
\(374\) | −1.69623 | −0.0877100 | ||||||||
\(375\) | −8.57589 | −0.442857 | ||||||||
\(376\) | 4.58759 | 0.236587 | ||||||||
\(377\) | −3.24569 | −0.167161 | ||||||||
\(378\) | 2.60224 | 0.133845 | ||||||||
\(379\) | 24.1122 | 1.23856 | 0.619281 | − | 0.785169i | \(-0.287424\pi\) | ||||
0.619281 | + | 0.785169i | \(0.287424\pi\) | |||||||
\(380\) | −45.4335 | −2.33069 | ||||||||
\(381\) | −9.32079 | −0.477518 | ||||||||
\(382\) | 2.60224 | 0.133142 | ||||||||
\(383\) | 11.0766 | 0.565988 | 0.282994 | − | 0.959122i | \(-0.408672\pi\) | ||||
0.282994 | + | 0.959122i | \(0.408672\pi\) | |||||||
\(384\) | −2.29218 | −0.116973 | ||||||||
\(385\) | 0.299648 | 0.0152715 | ||||||||
\(386\) | 26.2226 | 1.33470 | ||||||||
\(387\) | −0.00633740 | −0.000322148 0 | ||||||||
\(388\) | −63.7794 | −3.23791 | ||||||||
\(389\) | 24.8098 | 1.25791 | 0.628954 | − | 0.777442i | \(-0.283483\pi\) | ||||
0.628954 | + | 0.777442i | \(0.283483\pi\) | |||||||
\(390\) | −5.61678 | −0.284417 | ||||||||
\(391\) | −26.2712 | −1.32859 | ||||||||
\(392\) | −7.21258 | −0.364290 | ||||||||
\(393\) | −3.48282 | −0.175685 | ||||||||
\(394\) | −10.9246 | −0.550375 | ||||||||
\(395\) | 2.71862 | 0.136789 | ||||||||
\(396\) | −0.553111 | −0.0277949 | ||||||||
\(397\) | 28.6238 | 1.43659 | 0.718293 | − | 0.695741i | \(-0.244924\pi\) | ||||
0.718293 | + | 0.695741i | \(0.244924\pi\) | |||||||
\(398\) | 17.3149 | 0.867917 | ||||||||
\(399\) | −3.68328 | −0.184395 | ||||||||
\(400\) | 15.5221 | 0.776106 | ||||||||
\(401\) | 11.8383 | 0.591177 | 0.295589 | − | 0.955315i | \(-0.404484\pi\) | ||||
0.295589 | + | 0.955315i | \(0.404484\pi\) | |||||||
\(402\) | 13.4203 | 0.669344 | ||||||||
\(403\) | 2.57863 | 0.128451 | ||||||||
\(404\) | 20.2808 | 1.00901 | ||||||||
\(405\) | −2.58506 | −0.128452 | ||||||||
\(406\) | 10.1155 | 0.502022 | ||||||||
\(407\) | 1.23863 | 0.0613964 | ||||||||
\(408\) | −40.5589 | −2.00797 | ||||||||
\(409\) | −4.56857 | −0.225901 | −0.112951 | − | 0.993601i | \(-0.536030\pi\) | ||||
−0.112951 | + | 0.993601i | \(0.536030\pi\) | |||||||
\(410\) | 78.5549 | 3.87955 | ||||||||
\(411\) | −1.52560 | −0.0752522 | ||||||||
\(412\) | −51.7238 | −2.54825 | ||||||||
\(413\) | −8.43296 | −0.414959 | ||||||||
\(414\) | −12.1572 | −0.597492 | ||||||||
\(415\) | −30.9681 | −1.52016 | ||||||||
\(416\) | −8.00064 | −0.392264 | ||||||||
\(417\) | −8.07704 | −0.395534 | ||||||||
\(418\) | 1.11103 | 0.0543421 | ||||||||
\(419\) | 26.9077 | 1.31453 | 0.657265 | − | 0.753660i | \(-0.271713\pi\) | ||||
0.657265 | + | 0.753660i | \(0.271713\pi\) | |||||||
\(420\) | 12.3351 | 0.601889 | ||||||||
\(421\) | 14.4110 | 0.702348 | 0.351174 | − | 0.936310i | \(-0.385783\pi\) | ||||
0.351174 | + | 0.936310i | \(0.385783\pi\) | |||||||
\(422\) | −43.0064 | −2.09352 | ||||||||
\(423\) | −0.636054 | −0.0309260 | ||||||||
\(424\) | 16.9260 | 0.822000 | ||||||||
\(425\) | −9.46138 | −0.458944 | ||||||||
\(426\) | 1.91150 | 0.0926125 | ||||||||
\(427\) | 13.5378 | 0.655140 | ||||||||
\(428\) | 40.3137 | 1.94864 | ||||||||
\(429\) | 0.0967856 | 0.00467285 | ||||||||
\(430\) | −0.0426314 | −0.00205587 | ||||||||
\(431\) | 2.99499 | 0.144264 | 0.0721319 | − | 0.997395i | \(-0.477020\pi\) | ||||
0.0721319 | + | 0.997395i | \(0.477020\pi\) | |||||||
\(432\) | −9.22555 | −0.443865 | ||||||||
\(433\) | 19.3718 | 0.930950 | 0.465475 | − | 0.885061i | \(-0.345884\pi\) | ||||
0.465475 | + | 0.885061i | \(0.345884\pi\) | |||||||
\(434\) | −8.03652 | −0.385765 | ||||||||
\(435\) | −10.0486 | −0.481795 | ||||||||
\(436\) | −5.07405 | −0.243003 | ||||||||
\(437\) | 17.2076 | 0.823149 | ||||||||
\(438\) | −25.7327 | −1.22956 | ||||||||
\(439\) | 22.9468 | 1.09519 | 0.547595 | − | 0.836743i | \(-0.315543\pi\) | ||||
0.547595 | + | 0.836743i | \(0.315543\pi\) | |||||||
\(440\) | −2.16123 | −0.103033 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 12.2184 | 0.581169 | ||||||||
\(443\) | 16.4169 | 0.779990 | 0.389995 | − | 0.920817i | \(-0.372477\pi\) | ||||
0.389995 | + | 0.920817i | \(0.372477\pi\) | |||||||
\(444\) | 50.9882 | 2.41979 | ||||||||
\(445\) | 30.4197 | 1.44203 | ||||||||
\(446\) | 50.0378 | 2.36936 | ||||||||
\(447\) | 20.9577 | 0.991265 | ||||||||
\(448\) | 6.48354 | 0.306319 | ||||||||
\(449\) | 9.72314 | 0.458864 | 0.229432 | − | 0.973325i | \(-0.426313\pi\) | ||||
0.229432 | + | 0.973325i | \(0.426313\pi\) | |||||||
\(450\) | −4.37831 | −0.206396 | ||||||||
\(451\) | −1.35362 | −0.0637394 | ||||||||
\(452\) | −17.6879 | −0.831967 | ||||||||
\(453\) | 3.17563 | 0.149204 | ||||||||
\(454\) | 9.45942 | 0.443953 | ||||||||
\(455\) | −2.15844 | −0.101189 | ||||||||
\(456\) | 26.5660 | 1.24407 | ||||||||
\(457\) | 8.35758 | 0.390951 | 0.195475 | − | 0.980709i | \(-0.437375\pi\) | ||||
0.195475 | + | 0.980709i | \(0.437375\pi\) | |||||||
\(458\) | 0.225650 | 0.0105440 | ||||||||
\(459\) | 5.62336 | 0.262476 | ||||||||
\(460\) | −57.6269 | −2.68687 | ||||||||
\(461\) | 10.6655 | 0.496742 | 0.248371 | − | 0.968665i | \(-0.420105\pi\) | ||||
0.248371 | + | 0.968665i | \(0.420105\pi\) | |||||||
\(462\) | −0.301640 | −0.0140336 | ||||||||
\(463\) | 30.3694 | 1.41139 | 0.705693 | − | 0.708518i | \(-0.250636\pi\) | ||||
0.705693 | + | 0.708518i | \(0.250636\pi\) | |||||||
\(464\) | −35.8616 | −1.66483 | ||||||||
\(465\) | 7.98344 | 0.370223 | ||||||||
\(466\) | 55.4594 | 2.56911 | ||||||||
\(467\) | 0.0640863 | 0.00296556 | 0.00148278 | − | 0.999999i | \(-0.499528\pi\) | ||||
0.00148278 | + | 0.999999i | \(0.499528\pi\) | |||||||
\(468\) | 3.98420 | 0.184169 | ||||||||
\(469\) | 5.15720 | 0.238137 | ||||||||
\(470\) | −4.27870 | −0.197362 | ||||||||
\(471\) | 5.31711 | 0.244999 | ||||||||
\(472\) | 60.8234 | 2.79963 | ||||||||
\(473\) | 0.000734603 0 | 3.37771e−5 0 | ||||||||
\(474\) | −2.73670 | −0.125701 | ||||||||
\(475\) | 6.19717 | 0.284346 | ||||||||
\(476\) | −26.8328 | −1.22988 | ||||||||
\(477\) | −2.34673 | −0.107450 | ||||||||
\(478\) | −9.36231 | −0.428222 | ||||||||
\(479\) | 32.9683 | 1.50636 | 0.753179 | − | 0.657816i | \(-0.228519\pi\) | ||||
0.753179 | + | 0.657816i | \(0.228519\pi\) | |||||||
\(480\) | −24.7699 | −1.13059 | ||||||||
\(481\) | −8.92213 | −0.406814 | ||||||||
\(482\) | −21.8760 | −0.996423 | ||||||||
\(483\) | −4.67180 | −0.212574 | ||||||||
\(484\) | −52.4243 | −2.38292 | ||||||||
\(485\) | 34.5525 | 1.56895 | ||||||||
\(486\) | 2.60224 | 0.118040 | ||||||||
\(487\) | 18.3674 | 0.832306 | 0.416153 | − | 0.909295i | \(-0.363378\pi\) | ||||
0.416153 | + | 0.909295i | \(0.363378\pi\) | |||||||
\(488\) | −97.6425 | −4.42007 | ||||||||
\(489\) | −13.9648 | −0.631509 | ||||||||
\(490\) | 6.72695 | 0.303893 | ||||||||
\(491\) | −12.3677 | −0.558146 | −0.279073 | − | 0.960270i | \(-0.590027\pi\) | ||||
−0.279073 | + | 0.960270i | \(0.590027\pi\) | |||||||
\(492\) | −55.7219 | −2.51214 | ||||||||
\(493\) | 21.8591 | 0.984486 | ||||||||
\(494\) | −8.00300 | −0.360072 | ||||||||
\(495\) | 0.299648 | 0.0134682 | ||||||||
\(496\) | 28.4913 | 1.27930 | ||||||||
\(497\) | 0.734558 | 0.0329494 | ||||||||
\(498\) | 31.1740 | 1.39694 | ||||||||
\(499\) | 9.77414 | 0.437550 | 0.218775 | − | 0.975775i | \(-0.429794\pi\) | ||||
0.218775 | + | 0.975775i | \(0.429794\pi\) | |||||||
\(500\) | 40.9214 | 1.83006 | ||||||||
\(501\) | −23.7366 | −1.06047 | ||||||||
\(502\) | −42.5749 | −1.90021 | ||||||||
\(503\) | 1.28839 | 0.0574467 | 0.0287233 | − | 0.999587i | \(-0.490856\pi\) | ||||
0.0287233 | + | 0.999587i | \(0.490856\pi\) | |||||||
\(504\) | −7.21258 | −0.321274 | ||||||||
\(505\) | −10.9871 | −0.488920 | ||||||||
\(506\) | 1.40920 | 0.0626467 | ||||||||
\(507\) | 12.3028 | 0.546388 | ||||||||
\(508\) | 44.4758 | 1.97329 | ||||||||
\(509\) | 7.27679 | 0.322538 | 0.161269 | − | 0.986910i | \(-0.448441\pi\) | ||||
0.161269 | + | 0.986910i | \(0.448441\pi\) | |||||||
\(510\) | 37.8280 | 1.67505 | ||||||||
\(511\) | −9.88866 | −0.437448 | ||||||||
\(512\) | 44.6811 | 1.97464 | ||||||||
\(513\) | −3.68328 | −0.162621 | ||||||||
\(514\) | 40.1819 | 1.77235 | ||||||||
\(515\) | 28.0214 | 1.23477 | ||||||||
\(516\) | 0.0302400 | 0.00133124 | ||||||||
\(517\) | 0.0737284 | 0.00324257 | ||||||||
\(518\) | 27.8065 | 1.22175 | ||||||||
\(519\) | 19.3101 | 0.847618 | ||||||||
\(520\) | 15.5679 | 0.682698 | ||||||||
\(521\) | 37.8831 | 1.65969 | 0.829844 | − | 0.557995i | \(-0.188429\pi\) | ||||
0.829844 | + | 0.557995i | \(0.188429\pi\) | |||||||
\(522\) | 10.1155 | 0.442741 | ||||||||
\(523\) | 20.0741 | 0.877780 | 0.438890 | − | 0.898541i | \(-0.355372\pi\) | ||||
0.438890 | + | 0.898541i | \(0.355372\pi\) | |||||||
\(524\) | 16.6189 | 0.726000 | ||||||||
\(525\) | −1.68251 | −0.0734309 | ||||||||
\(526\) | 83.3188 | 3.63287 | ||||||||
\(527\) | −17.3666 | −0.756503 | ||||||||
\(528\) | 1.06938 | 0.0465389 | ||||||||
\(529\) | −1.17430 | −0.0510565 | ||||||||
\(530\) | −15.7863 | −0.685715 | ||||||||
\(531\) | −8.43296 | −0.365959 | ||||||||
\(532\) | 17.5754 | 0.761992 | ||||||||
\(533\) | 9.75045 | 0.422339 | ||||||||
\(534\) | −30.6220 | −1.32514 | ||||||||
\(535\) | −21.8400 | −0.944224 | ||||||||
\(536\) | −37.1967 | −1.60665 | ||||||||
\(537\) | 6.85410 | 0.295776 | ||||||||
\(538\) | −37.5978 | −1.62096 | ||||||||
\(539\) | −0.115915 | −0.00499283 | ||||||||
\(540\) | 12.3351 | 0.530816 | ||||||||
\(541\) | 27.4397 | 1.17973 | 0.589863 | − | 0.807503i | \(-0.299182\pi\) | ||||
0.589863 | + | 0.807503i | \(0.299182\pi\) | |||||||
\(542\) | 49.1720 | 2.11212 | ||||||||
\(543\) | −2.43507 | −0.104499 | ||||||||
\(544\) | 53.8829 | 2.31021 | ||||||||
\(545\) | 2.74887 | 0.117749 | ||||||||
\(546\) | 2.17279 | 0.0929868 | ||||||||
\(547\) | −9.06312 | −0.387511 | −0.193756 | − | 0.981050i | \(-0.562067\pi\) | ||||
−0.193756 | + | 0.981050i | \(0.562067\pi\) | |||||||
\(548\) | 7.27967 | 0.310972 | ||||||||
\(549\) | 13.5378 | 0.577779 | ||||||||
\(550\) | 0.507514 | 0.0216405 | ||||||||
\(551\) | −14.3177 | −0.609953 | ||||||||
\(552\) | 33.6957 | 1.43419 | ||||||||
\(553\) | −1.05167 | −0.0447215 | ||||||||
\(554\) | −35.7502 | −1.51888 | ||||||||
\(555\) | −27.6229 | −1.17253 | ||||||||
\(556\) | 38.5410 | 1.63450 | ||||||||
\(557\) | −3.14559 | −0.133283 | −0.0666415 | − | 0.997777i | \(-0.521228\pi\) | ||||
−0.0666415 | + | 0.997777i | \(0.521228\pi\) | |||||||
\(558\) | −8.03652 | −0.340213 | ||||||||
\(559\) | −0.00529152 | −0.000223808 0 | ||||||||
\(560\) | −23.8486 | −1.00779 | ||||||||
\(561\) | −0.651834 | −0.0275204 | ||||||||
\(562\) | −78.2018 | −3.29874 | ||||||||
\(563\) | −28.0855 | −1.18366 | −0.591831 | − | 0.806062i | \(-0.701595\pi\) | ||||
−0.591831 | + | 0.806062i | \(0.701595\pi\) | |||||||
\(564\) | 3.03504 | 0.127798 | ||||||||
\(565\) | 9.58240 | 0.403135 | ||||||||
\(566\) | −39.5449 | −1.66220 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −5.29806 | −0.222302 | ||||||||
\(569\) | 13.0055 | 0.545217 | 0.272609 | − | 0.962125i | \(-0.412114\pi\) | ||||
0.272609 | + | 0.962125i | \(0.412114\pi\) | |||||||
\(570\) | −24.7772 | −1.03780 | ||||||||
\(571\) | −22.7871 | −0.953609 | −0.476805 | − | 0.879009i | \(-0.658205\pi\) | ||||
−0.476805 | + | 0.879009i | \(0.658205\pi\) | |||||||
\(572\) | −0.461830 | −0.0193101 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | −30.3881 | −1.26837 | ||||||||
\(575\) | 7.86037 | 0.327800 | ||||||||
\(576\) | 6.48354 | 0.270148 | ||||||||
\(577\) | −4.11858 | −0.171459 | −0.0857294 | − | 0.996318i | \(-0.527322\pi\) | ||||
−0.0857294 | + | 0.996318i | \(0.527322\pi\) | |||||||
\(578\) | −38.0504 | −1.58269 | ||||||||
\(579\) | 10.0769 | 0.418783 | ||||||||
\(580\) | 47.9489 | 1.99097 | ||||||||
\(581\) | 11.9797 | 0.497000 | ||||||||
\(582\) | −34.7822 | −1.44177 | ||||||||
\(583\) | 0.272022 | 0.0112660 | ||||||||
\(584\) | 71.3228 | 2.95136 | ||||||||
\(585\) | −2.15844 | −0.0892404 | ||||||||
\(586\) | −30.2834 | −1.25100 | ||||||||
\(587\) | 38.0283 | 1.56960 | 0.784798 | − | 0.619752i | \(-0.212767\pi\) | ||||
0.784798 | + | 0.619752i | \(0.212767\pi\) | |||||||
\(588\) | −4.77168 | −0.196781 | ||||||||
\(589\) | 11.3751 | 0.468703 | ||||||||
\(590\) | −56.7281 | −2.33546 | ||||||||
\(591\) | −4.19816 | −0.172689 | ||||||||
\(592\) | −98.5805 | −4.05163 | ||||||||
\(593\) | 2.36301 | 0.0970370 | 0.0485185 | − | 0.998822i | \(-0.484550\pi\) | ||||
0.0485185 | + | 0.998822i | \(0.484550\pi\) | |||||||
\(594\) | −0.301640 | −0.0123764 | ||||||||
\(595\) | 14.5367 | 0.595946 | ||||||||
\(596\) | −100.003 | −4.09630 | ||||||||
\(597\) | 6.65383 | 0.272323 | ||||||||
\(598\) | −10.1508 | −0.415099 | ||||||||
\(599\) | 43.2745 | 1.76815 | 0.884074 | − | 0.467346i | \(-0.154790\pi\) | ||||
0.884074 | + | 0.467346i | \(0.154790\pi\) | |||||||
\(600\) | 12.1353 | 0.495420 | ||||||||
\(601\) | 14.0998 | 0.575143 | 0.287572 | − | 0.957759i | \(-0.407152\pi\) | ||||
0.287572 | + | 0.957759i | \(0.407152\pi\) | |||||||
\(602\) | 0.0164915 | 0.000672142 0 | ||||||||
\(603\) | 5.15720 | 0.210017 | ||||||||
\(604\) | −15.1531 | −0.616571 | ||||||||
\(605\) | 28.4009 | 1.15466 | ||||||||
\(606\) | 11.0602 | 0.449289 | ||||||||
\(607\) | −27.2079 | −1.10434 | −0.552168 | − | 0.833733i | \(-0.686199\pi\) | ||||
−0.552168 | + | 0.833733i | \(0.686199\pi\) | |||||||
\(608\) | −35.2931 | −1.43133 | ||||||||
\(609\) | 3.88720 | 0.157517 | ||||||||
\(610\) | 91.0681 | 3.68724 | ||||||||
\(611\) | −0.531084 | −0.0214854 | ||||||||
\(612\) | −26.8328 | −1.08465 | ||||||||
\(613\) | −25.8090 | −1.04242 | −0.521209 | − | 0.853429i | \(-0.674519\pi\) | ||||
−0.521209 | + | 0.853429i | \(0.674519\pi\) | |||||||
\(614\) | −34.1021 | −1.37625 | ||||||||
\(615\) | 30.1874 | 1.21727 | ||||||||
\(616\) | 0.836049 | 0.0336854 | ||||||||
\(617\) | −7.13740 | −0.287341 | −0.143670 | − | 0.989626i | \(-0.545891\pi\) | ||||
−0.143670 | + | 0.989626i | \(0.545891\pi\) | |||||||
\(618\) | −28.2077 | −1.13468 | ||||||||
\(619\) | −21.7294 | −0.873377 | −0.436689 | − | 0.899613i | \(-0.643849\pi\) | ||||
−0.436689 | + | 0.899613i | \(0.643849\pi\) | |||||||
\(620\) | −38.0944 | −1.52991 | ||||||||
\(621\) | −4.67180 | −0.187473 | ||||||||
\(622\) | −72.3838 | −2.90232 | ||||||||
\(623\) | −11.7675 | −0.471457 | ||||||||
\(624\) | −7.70304 | −0.308368 | ||||||||
\(625\) | −30.5817 | −1.22327 | ||||||||
\(626\) | −57.8689 | −2.31291 | ||||||||
\(627\) | 0.426949 | 0.0170507 | ||||||||
\(628\) | −25.3715 | −1.01243 | ||||||||
\(629\) | 60.0889 | 2.39590 | ||||||||
\(630\) | 6.72695 | 0.268008 | ||||||||
\(631\) | −14.3936 | −0.573000 | −0.286500 | − | 0.958080i | \(-0.592492\pi\) | ||||
−0.286500 | + | 0.958080i | \(0.592492\pi\) | |||||||
\(632\) | 7.58524 | 0.301725 | ||||||||
\(633\) | −16.5266 | −0.656875 | ||||||||
\(634\) | 16.0267 | 0.636500 | ||||||||
\(635\) | −24.0948 | −0.956171 | ||||||||
\(636\) | 11.1979 | 0.444024 | ||||||||
\(637\) | 0.834967 | 0.0330826 | ||||||||
\(638\) | −1.17254 | −0.0464212 | ||||||||
\(639\) | 0.734558 | 0.0290587 | ||||||||
\(640\) | −5.92542 | −0.234223 | ||||||||
\(641\) | −9.79728 | −0.386969 | −0.193485 | − | 0.981103i | \(-0.561979\pi\) | ||||
−0.193485 | + | 0.981103i | \(0.561979\pi\) | |||||||
\(642\) | 21.9852 | 0.867686 | ||||||||
\(643\) | 3.56650 | 0.140649 | 0.0703245 | − | 0.997524i | \(-0.477597\pi\) | ||||
0.0703245 | + | 0.997524i | \(0.477597\pi\) | |||||||
\(644\) | 22.2923 | 0.878440 | ||||||||
\(645\) | −0.0163825 | −0.000645062 0 | ||||||||
\(646\) | 53.8988 | 2.12062 | ||||||||
\(647\) | 3.46572 | 0.136251 | 0.0681257 | − | 0.997677i | \(-0.478298\pi\) | ||||
0.0681257 | + | 0.997677i | \(0.478298\pi\) | |||||||
\(648\) | −7.21258 | −0.283337 | ||||||||
\(649\) | 0.977510 | 0.0383706 | ||||||||
\(650\) | −3.65575 | −0.143390 | ||||||||
\(651\) | −3.08830 | −0.121040 | ||||||||
\(652\) | 66.6354 | 2.60964 | ||||||||
\(653\) | −47.2089 | −1.84743 | −0.923714 | − | 0.383083i | \(-0.874862\pi\) | ||||
−0.923714 | + | 0.383083i | \(0.874862\pi\) | |||||||
\(654\) | −2.76714 | −0.108204 | ||||||||
\(655\) | −9.00329 | −0.351788 | ||||||||
\(656\) | 107.733 | 4.20626 | ||||||||
\(657\) | −9.88866 | −0.385793 | ||||||||
\(658\) | 1.65517 | 0.0645251 | ||||||||
\(659\) | −32.1506 | −1.25241 | −0.626204 | − | 0.779659i | \(-0.715392\pi\) | ||||
−0.626204 | + | 0.779659i | \(0.715392\pi\) | |||||||
\(660\) | −1.42982 | −0.0556558 | ||||||||
\(661\) | −6.28777 | −0.244566 | −0.122283 | − | 0.992495i | \(-0.539022\pi\) | ||||
−0.122283 | + | 0.992495i | \(0.539022\pi\) | |||||||
\(662\) | 7.62855 | 0.296492 | ||||||||
\(663\) | 4.69532 | 0.182351 | ||||||||
\(664\) | −86.4044 | −3.35314 | ||||||||
\(665\) | −9.52149 | −0.369228 | ||||||||
\(666\) | 27.8065 | 1.07748 | ||||||||
\(667\) | −18.1602 | −0.703167 | ||||||||
\(668\) | 113.263 | 4.38229 | ||||||||
\(669\) | 19.2287 | 0.743425 | ||||||||
\(670\) | 34.6922 | 1.34028 | ||||||||
\(671\) | −1.56924 | −0.0605798 | ||||||||
\(672\) | 9.58198 | 0.369633 | ||||||||
\(673\) | −7.11712 | −0.274345 | −0.137172 | − | 0.990547i | \(-0.543801\pi\) | ||||
−0.137172 | + | 0.990547i | \(0.543801\pi\) | |||||||
\(674\) | 42.6959 | 1.64458 | ||||||||
\(675\) | −1.68251 | −0.0647600 | ||||||||
\(676\) | −58.7051 | −2.25789 | ||||||||
\(677\) | 49.5207 | 1.90323 | 0.951617 | − | 0.307288i | \(-0.0994215\pi\) | ||||
0.951617 | + | 0.307288i | \(0.0994215\pi\) | |||||||
\(678\) | −9.64611 | −0.370457 | ||||||||
\(679\) | −13.3662 | −0.512949 | ||||||||
\(680\) | −104.847 | −4.02070 | ||||||||
\(681\) | 3.63510 | 0.139297 | ||||||||
\(682\) | 0.931557 | 0.0356712 | ||||||||
\(683\) | −7.26253 | −0.277893 | −0.138946 | − | 0.990300i | \(-0.544372\pi\) | ||||
−0.138946 | + | 0.990300i | \(0.544372\pi\) | |||||||
\(684\) | 17.5754 | 0.672014 | ||||||||
\(685\) | −3.94376 | −0.150683 | ||||||||
\(686\) | −2.60224 | −0.0993542 | ||||||||
\(687\) | 0.0867138 | 0.00330834 | ||||||||
\(688\) | −0.0584660 | −0.00222900 | ||||||||
\(689\) | −1.95945 | −0.0746489 | ||||||||
\(690\) | −31.4269 | −1.19640 | ||||||||
\(691\) | 43.8977 | 1.66995 | 0.834973 | − | 0.550291i | \(-0.185483\pi\) | ||||
0.834973 | + | 0.550291i | \(0.185483\pi\) | |||||||
\(692\) | −92.1415 | −3.50269 | ||||||||
\(693\) | −0.115915 | −0.00440326 | ||||||||
\(694\) | 47.9365 | 1.81964 | ||||||||
\(695\) | −20.8796 | −0.792009 | ||||||||
\(696\) | −28.0368 | −1.06273 | ||||||||
\(697\) | −65.6676 | −2.48734 | ||||||||
\(698\) | 19.7919 | 0.749133 | ||||||||
\(699\) | 21.3122 | 0.806100 | ||||||||
\(700\) | 8.02841 | 0.303445 | ||||||||
\(701\) | 24.9864 | 0.943724 | 0.471862 | − | 0.881673i | \(-0.343582\pi\) | ||||
0.471862 | + | 0.881673i | \(0.343582\pi\) | |||||||
\(702\) | 2.17279 | 0.0820067 | ||||||||
\(703\) | −39.3581 | −1.48442 | ||||||||
\(704\) | −0.751543 | −0.0283248 | ||||||||
\(705\) | −1.64423 | −0.0619254 | ||||||||
\(706\) | −37.6640 | −1.41750 | ||||||||
\(707\) | 4.25024 | 0.159847 | ||||||||
\(708\) | 40.2394 | 1.51229 | ||||||||
\(709\) | 45.5102 | 1.70917 | 0.854586 | − | 0.519309i | \(-0.173811\pi\) | ||||
0.854586 | + | 0.519309i | \(0.173811\pi\) | |||||||
\(710\) | 4.94133 | 0.185445 | ||||||||
\(711\) | −1.05167 | −0.0394406 | ||||||||
\(712\) | 84.8744 | 3.18080 | ||||||||
\(713\) | 14.4279 | 0.540330 | ||||||||
\(714\) | −14.6334 | −0.547639 | ||||||||
\(715\) | 0.250196 | 0.00935680 | ||||||||
\(716\) | −32.7055 | −1.22226 | ||||||||
\(717\) | −3.59778 | −0.134362 | ||||||||
\(718\) | −9.82638 | −0.366717 | ||||||||
\(719\) | −3.28730 | −0.122596 | −0.0612979 | − | 0.998120i | \(-0.519524\pi\) | ||||
−0.0612979 | + | 0.998120i | \(0.519524\pi\) | |||||||
\(720\) | −23.8486 | −0.888784 | ||||||||
\(721\) | −10.8398 | −0.403694 | ||||||||
\(722\) | 14.1391 | 0.526204 | ||||||||
\(723\) | −8.40658 | −0.312644 | ||||||||
\(724\) | 11.6194 | 0.431830 | ||||||||
\(725\) | −6.54027 | −0.242900 | ||||||||
\(726\) | −28.5897 | −1.06106 | ||||||||
\(727\) | 2.37891 | 0.0882289 | 0.0441144 | − | 0.999026i | \(-0.485953\pi\) | ||||
0.0441144 | + | 0.999026i | \(0.485953\pi\) | |||||||
\(728\) | −6.02227 | −0.223200 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −66.5205 | −2.46203 | ||||||||
\(731\) | 0.0356375 | 0.00131810 | ||||||||
\(732\) | −64.5980 | −2.38761 | ||||||||
\(733\) | −19.7643 | −0.730010 | −0.365005 | − | 0.931006i | \(-0.618933\pi\) | ||||
−0.365005 | + | 0.931006i | \(0.618933\pi\) | |||||||
\(734\) | −81.0540 | −2.99176 | ||||||||
\(735\) | 2.58506 | 0.0953512 | ||||||||
\(736\) | −44.7651 | −1.65006 | ||||||||
\(737\) | −0.597799 | −0.0220202 | ||||||||
\(738\) | −30.3881 | −1.11860 | ||||||||
\(739\) | −5.78584 | −0.212836 | −0.106418 | − | 0.994322i | \(-0.533938\pi\) | ||||
−0.106418 | + | 0.994322i | \(0.533938\pi\) | |||||||
\(740\) | 131.807 | 4.84534 | ||||||||
\(741\) | −3.07542 | −0.112978 | ||||||||
\(742\) | 6.10677 | 0.224187 | ||||||||
\(743\) | −14.3473 | −0.526350 | −0.263175 | − | 0.964748i | \(-0.584770\pi\) | ||||
−0.263175 | + | 0.964748i | \(0.584770\pi\) | |||||||
\(744\) | 22.2747 | 0.816628 | ||||||||
\(745\) | 54.1768 | 1.98489 | ||||||||
\(746\) | −27.2613 | −0.998108 | ||||||||
\(747\) | 11.9797 | 0.438313 | ||||||||
\(748\) | 3.11034 | 0.113725 | ||||||||
\(749\) | 8.44855 | 0.308703 | ||||||||
\(750\) | 22.3166 | 0.814885 | ||||||||
\(751\) | −51.4173 | −1.87624 | −0.938122 | − | 0.346306i | \(-0.887436\pi\) | ||||
−0.938122 | + | 0.346306i | \(0.887436\pi\) | |||||||
\(752\) | −5.86795 | −0.213982 | ||||||||
\(753\) | −16.3609 | −0.596223 | ||||||||
\(754\) | 8.44608 | 0.307588 | ||||||||
\(755\) | 8.20919 | 0.298763 | ||||||||
\(756\) | −4.77168 | −0.173544 | ||||||||
\(757\) | 11.9672 | 0.434954 | 0.217477 | − | 0.976065i | \(-0.430217\pi\) | ||||
0.217477 | + | 0.976065i | \(0.430217\pi\) | |||||||
\(758\) | −62.7460 | −2.27904 | ||||||||
\(759\) | 0.541533 | 0.0196564 | ||||||||
\(760\) | 68.6745 | 2.49109 | ||||||||
\(761\) | 49.4610 | 1.79296 | 0.896480 | − | 0.443085i | \(-0.146116\pi\) | ||||
0.896480 | + | 0.443085i | \(0.146116\pi\) | |||||||
\(762\) | 24.2550 | 0.878665 | ||||||||
\(763\) | −1.06337 | −0.0384965 | ||||||||
\(764\) | −4.77168 | −0.172633 | ||||||||
\(765\) | 14.5367 | 0.525575 | ||||||||
\(766\) | −28.8240 | −1.04145 | ||||||||
\(767\) | −7.04125 | −0.254245 | ||||||||
\(768\) | 18.9319 | 0.683147 | ||||||||
\(769\) | −28.9451 | −1.04379 | −0.521894 | − | 0.853010i | \(-0.674774\pi\) | ||||
−0.521894 | + | 0.853010i | \(0.674774\pi\) | |||||||
\(770\) | −0.779757 | −0.0281005 | ||||||||
\(771\) | 15.4413 | 0.556103 | ||||||||
\(772\) | −48.0838 | −1.73057 | ||||||||
\(773\) | 27.1893 | 0.977932 | 0.488966 | − | 0.872303i | \(-0.337374\pi\) | ||||
0.488966 | + | 0.872303i | \(0.337374\pi\) | |||||||
\(774\) | 0.0164915 | 0.000592774 0 | ||||||||
\(775\) | 5.19611 | 0.186650 | ||||||||
\(776\) | 96.4051 | 3.46074 | ||||||||
\(777\) | 10.6856 | 0.383344 | ||||||||
\(778\) | −64.5612 | −2.31463 | ||||||||
\(779\) | 43.0121 | 1.54107 | ||||||||
\(780\) | 10.2994 | 0.368777 | ||||||||
\(781\) | −0.0851466 | −0.00304678 | ||||||||
\(782\) | 68.3641 | 2.44469 | ||||||||
\(783\) | 3.88720 | 0.138917 | ||||||||
\(784\) | 9.22555 | 0.329484 | ||||||||
\(785\) | 13.7450 | 0.490581 | ||||||||
\(786\) | 9.06315 | 0.323272 | ||||||||
\(787\) | 27.5386 | 0.981646 | 0.490823 | − | 0.871259i | \(-0.336696\pi\) | ||||
0.490823 | + | 0.871259i | \(0.336696\pi\) | |||||||
\(788\) | 20.0323 | 0.713620 | ||||||||
\(789\) | 32.0181 | 1.13987 | ||||||||
\(790\) | −7.07451 | −0.251700 | ||||||||
\(791\) | −3.70684 | −0.131800 | ||||||||
\(792\) | 0.836049 | 0.0297077 | ||||||||
\(793\) | 11.3036 | 0.401403 | ||||||||
\(794\) | −74.4860 | −2.64341 | ||||||||
\(795\) | −6.06644 | −0.215154 | ||||||||
\(796\) | −31.7499 | −1.12535 | ||||||||
\(797\) | −15.2187 | −0.539075 | −0.269537 | − | 0.962990i | \(-0.586871\pi\) | ||||
−0.269537 | + | 0.962990i | \(0.586871\pi\) | |||||||
\(798\) | 9.58480 | 0.339298 | ||||||||
\(799\) | 3.57676 | 0.126537 | ||||||||
\(800\) | −16.1218 | −0.569992 | ||||||||
\(801\) | −11.7675 | −0.415786 | ||||||||
\(802\) | −30.8062 | −1.08780 | ||||||||
\(803\) | 1.14625 | 0.0404502 | ||||||||
\(804\) | −24.6085 | −0.867875 | ||||||||
\(805\) | −12.0769 | −0.425653 | ||||||||
\(806\) | −6.71024 | −0.236358 | ||||||||
\(807\) | −14.4482 | −0.508602 | ||||||||
\(808\) | −30.6552 | −1.07845 | ||||||||
\(809\) | −18.6770 | −0.656648 | −0.328324 | − | 0.944565i | \(-0.606484\pi\) | ||||
−0.328324 | + | 0.944565i | \(0.606484\pi\) | |||||||
\(810\) | 6.72695 | 0.236361 | ||||||||
\(811\) | 40.3502 | 1.41689 | 0.708444 | − | 0.705767i | \(-0.249398\pi\) | ||||
0.708444 | + | 0.705767i | \(0.249398\pi\) | |||||||
\(812\) | −18.5485 | −0.650924 | ||||||||
\(813\) | 18.8960 | 0.662711 | ||||||||
\(814\) | −3.22321 | −0.112973 | ||||||||
\(815\) | −36.0997 | −1.26452 | ||||||||
\(816\) | 51.8786 | 1.81611 | ||||||||
\(817\) | −0.0233424 | −0.000816649 0 | ||||||||
\(818\) | 11.8885 | 0.415673 | ||||||||
\(819\) | 0.834967 | 0.0291761 | ||||||||
\(820\) | −144.044 | −5.03025 | ||||||||
\(821\) | 39.1286 | 1.36560 | 0.682799 | − | 0.730607i | \(-0.260763\pi\) | ||||
0.682799 | + | 0.730607i | \(0.260763\pi\) | |||||||
\(822\) | 3.96998 | 0.138469 | ||||||||
\(823\) | −26.6637 | −0.929440 | −0.464720 | − | 0.885458i | \(-0.653845\pi\) | ||||
−0.464720 | + | 0.885458i | \(0.653845\pi\) | |||||||
\(824\) | 78.1826 | 2.72362 | ||||||||
\(825\) | 0.195029 | 0.00679005 | ||||||||
\(826\) | 21.9446 | 0.763551 | ||||||||
\(827\) | 7.03774 | 0.244726 | 0.122363 | − | 0.992485i | \(-0.460953\pi\) | ||||
0.122363 | + | 0.992485i | \(0.460953\pi\) | |||||||
\(828\) | 22.2923 | 0.774712 | ||||||||
\(829\) | 3.27809 | 0.113853 | 0.0569264 | − | 0.998378i | \(-0.481870\pi\) | ||||
0.0569264 | + | 0.998378i | \(0.481870\pi\) | |||||||
\(830\) | 80.5866 | 2.79720 | ||||||||
\(831\) | −13.7382 | −0.476573 | ||||||||
\(832\) | 5.41355 | 0.187681 | ||||||||
\(833\) | −5.62336 | −0.194838 | ||||||||
\(834\) | 21.0184 | 0.727809 | ||||||||
\(835\) | −61.3604 | −2.12347 | ||||||||
\(836\) | −2.03726 | −0.0704602 | ||||||||
\(837\) | −3.08830 | −0.106747 | ||||||||
\(838\) | −70.0205 | −2.41882 | ||||||||
\(839\) | −34.5841 | −1.19398 | −0.596988 | − | 0.802250i | \(-0.703636\pi\) | ||||
−0.596988 | + | 0.802250i | \(0.703636\pi\) | |||||||
\(840\) | −18.6449 | −0.643311 | ||||||||
\(841\) | −13.8896 | −0.478953 | ||||||||
\(842\) | −37.5009 | −1.29237 | ||||||||
\(843\) | −30.0517 | −1.03503 | ||||||||
\(844\) | 78.8598 | 2.71447 | ||||||||
\(845\) | 31.8035 | 1.09407 | ||||||||
\(846\) | 1.65517 | 0.0569058 | ||||||||
\(847\) | −10.9866 | −0.377503 | ||||||||
\(848\) | −21.6499 | −0.743461 | ||||||||
\(849\) | −15.1964 | −0.521541 | ||||||||
\(850\) | 24.6208 | 0.844487 | ||||||||
\(851\) | −49.9210 | −1.71127 | ||||||||
\(852\) | −3.50507 | −0.120082 | ||||||||
\(853\) | −25.9995 | −0.890204 | −0.445102 | − | 0.895480i | \(-0.646833\pi\) | ||||
−0.445102 | + | 0.895480i | \(0.646833\pi\) | |||||||
\(854\) | −35.2287 | −1.20550 | ||||||||
\(855\) | −9.52149 | −0.325628 | ||||||||
\(856\) | −60.9359 | −2.08274 | ||||||||
\(857\) | −30.9279 | −1.05648 | −0.528238 | − | 0.849096i | \(-0.677147\pi\) | ||||
−0.528238 | + | 0.849096i | \(0.677147\pi\) | |||||||
\(858\) | −0.251860 | −0.00859835 | ||||||||
\(859\) | 2.78374 | 0.0949801 | 0.0474900 | − | 0.998872i | \(-0.484878\pi\) | ||||
0.0474900 | + | 0.998872i | \(0.484878\pi\) | |||||||
\(860\) | 0.0781722 | 0.00266565 | ||||||||
\(861\) | −11.6776 | −0.397973 | ||||||||
\(862\) | −7.79371 | −0.265455 | ||||||||
\(863\) | −38.6082 | −1.31424 | −0.657120 | − | 0.753786i | \(-0.728225\pi\) | ||||
−0.657120 | + | 0.753786i | \(0.728225\pi\) | |||||||
\(864\) | 9.58198 | 0.325985 | ||||||||
\(865\) | 49.9176 | 1.69725 | ||||||||
\(866\) | −50.4102 | −1.71301 | ||||||||
\(867\) | −14.6222 | −0.496594 | ||||||||
\(868\) | 14.7364 | 0.500186 | ||||||||
\(869\) | 0.121904 | 0.00413533 | ||||||||
\(870\) | 26.1490 | 0.886535 | ||||||||
\(871\) | 4.30610 | 0.145906 | ||||||||
\(872\) | 7.66963 | 0.259727 | ||||||||
\(873\) | −13.3662 | −0.452378 | ||||||||
\(874\) | −44.7783 | −1.51465 | ||||||||
\(875\) | 8.57589 | 0.289918 | ||||||||
\(876\) | 47.1855 | 1.59425 | ||||||||
\(877\) | 30.5332 | 1.03103 | 0.515517 | − | 0.856879i | \(-0.327600\pi\) | ||||
0.515517 | + | 0.856879i | \(0.327600\pi\) | |||||||
\(878\) | −59.7132 | −2.01522 | ||||||||
\(879\) | −11.6374 | −0.392520 | ||||||||
\(880\) | 2.76442 | 0.0931884 | ||||||||
\(881\) | −51.9298 | −1.74956 | −0.874780 | − | 0.484520i | \(-0.838994\pi\) | ||||
−0.874780 | + | 0.484520i | \(0.838994\pi\) | |||||||
\(882\) | −2.60224 | −0.0876221 | ||||||||
\(883\) | 5.34872 | 0.179999 | 0.0899994 | − | 0.995942i | \(-0.471313\pi\) | ||||
0.0899994 | + | 0.995942i | \(0.471313\pi\) | |||||||
\(884\) | −22.4046 | −0.753547 | ||||||||
\(885\) | −21.7997 | −0.732788 | ||||||||
\(886\) | −42.7207 | −1.43523 | ||||||||
\(887\) | 6.54742 | 0.219841 | 0.109920 | − | 0.993940i | \(-0.464940\pi\) | ||||
0.109920 | + | 0.993940i | \(0.464940\pi\) | |||||||
\(888\) | −77.0708 | −2.58633 | ||||||||
\(889\) | 9.32079 | 0.312609 | ||||||||
\(890\) | −79.1596 | −2.65344 | ||||||||
\(891\) | −0.115915 | −0.00388331 | ||||||||
\(892\) | −91.7532 | −3.07212 | ||||||||
\(893\) | −2.34276 | −0.0783976 | ||||||||
\(894\) | −54.5371 | −1.82399 | ||||||||
\(895\) | 17.7182 | 0.592255 | ||||||||
\(896\) | 2.29218 | 0.0765765 | ||||||||
\(897\) | −3.90080 | −0.130244 | ||||||||
\(898\) | −25.3020 | −0.844339 | ||||||||
\(899\) | −12.0049 | −0.400385 | ||||||||
\(900\) | 8.02841 | 0.267614 | ||||||||
\(901\) | 13.1965 | 0.439640 | ||||||||
\(902\) | 3.52245 | 0.117285 | ||||||||
\(903\) | 0.00633740 | 0.000210896 0 | ||||||||
\(904\) | 26.7359 | 0.889223 | ||||||||
\(905\) | −6.29478 | −0.209246 | ||||||||
\(906\) | −8.26378 | −0.274546 | ||||||||
\(907\) | −7.51348 | −0.249481 | −0.124741 | − | 0.992189i | \(-0.539810\pi\) | ||||
−0.124741 | + | 0.992189i | \(0.539810\pi\) | |||||||
\(908\) | −17.3455 | −0.575632 | ||||||||
\(909\) | 4.25024 | 0.140972 | ||||||||
\(910\) | 5.61678 | 0.186195 | ||||||||
\(911\) | 9.60176 | 0.318121 | 0.159060 | − | 0.987269i | \(-0.449154\pi\) | ||||
0.159060 | + | 0.987269i | \(0.449154\pi\) | |||||||
\(912\) | −33.9803 | −1.12520 | ||||||||
\(913\) | −1.38863 | −0.0459569 | ||||||||
\(914\) | −21.7485 | −0.719375 | ||||||||
\(915\) | 34.9960 | 1.15693 | ||||||||
\(916\) | −0.413770 | −0.0136714 | ||||||||
\(917\) | 3.48282 | 0.115013 | ||||||||
\(918\) | −14.6334 | −0.482973 | ||||||||
\(919\) | 31.9826 | 1.05501 | 0.527505 | − | 0.849552i | \(-0.323128\pi\) | ||||
0.527505 | + | 0.849552i | \(0.323128\pi\) | |||||||
\(920\) | 87.1054 | 2.87178 | ||||||||
\(921\) | −13.1049 | −0.431821 | ||||||||
\(922\) | −27.7542 | −0.914037 | ||||||||
\(923\) | 0.613332 | 0.0201881 | ||||||||
\(924\) | 0.553111 | 0.0181960 | ||||||||
\(925\) | −17.9787 | −0.591135 | ||||||||
\(926\) | −79.0286 | −2.59704 | ||||||||
\(927\) | −10.8398 | −0.356024 | ||||||||
\(928\) | 37.2471 | 1.22270 | ||||||||
\(929\) | 39.1814 | 1.28550 | 0.642750 | − | 0.766076i | \(-0.277793\pi\) | ||||
0.642750 | + | 0.766076i | \(0.277793\pi\) | |||||||
\(930\) | −20.7749 | −0.681235 | ||||||||
\(931\) | 3.68328 | 0.120715 | ||||||||
\(932\) | −101.695 | −3.33112 | ||||||||
\(933\) | −27.8159 | −0.910651 | ||||||||
\(934\) | −0.166768 | −0.00545682 | ||||||||
\(935\) | −1.68503 | −0.0551063 | ||||||||
\(936\) | −6.02227 | −0.196844 | ||||||||
\(937\) | 22.6694 | 0.740575 | 0.370288 | − | 0.928917i | \(-0.379259\pi\) | ||||
0.370288 | + | 0.928917i | \(0.379259\pi\) | |||||||
\(938\) | −13.4203 | −0.438188 | ||||||||
\(939\) | −22.2381 | −0.725712 | ||||||||
\(940\) | 7.84576 | 0.255900 | ||||||||
\(941\) | −32.3551 | −1.05475 | −0.527373 | − | 0.849634i | \(-0.676823\pi\) | ||||
−0.527373 | + | 0.849634i | \(0.676823\pi\) | |||||||
\(942\) | −13.8364 | −0.450815 | ||||||||
\(943\) | 54.5556 | 1.77657 | ||||||||
\(944\) | −77.7987 | −2.53213 | ||||||||
\(945\) | 2.58506 | 0.0840919 | ||||||||
\(946\) | −0.00191162 | −6.21520e−5 0 | ||||||||
\(947\) | −17.1025 | −0.555756 | −0.277878 | − | 0.960616i | \(-0.589631\pi\) | ||||
−0.277878 | + | 0.960616i | \(0.589631\pi\) | |||||||
\(948\) | 5.01822 | 0.162984 | ||||||||
\(949\) | −8.25671 | −0.268024 | ||||||||
\(950\) | −16.1266 | −0.523215 | ||||||||
\(951\) | 6.15878 | 0.199712 | ||||||||
\(952\) | 40.5589 | 1.31452 | ||||||||
\(953\) | 27.0201 | 0.875267 | 0.437634 | − | 0.899153i | \(-0.355817\pi\) | ||||
0.437634 | + | 0.899153i | \(0.355817\pi\) | |||||||
\(954\) | 6.10677 | 0.197714 | ||||||||
\(955\) | 2.58506 | 0.0836504 | ||||||||
\(956\) | 17.1675 | 0.555235 | ||||||||
\(957\) | −0.450587 | −0.0145654 | ||||||||
\(958\) | −85.7915 | −2.77180 | ||||||||
\(959\) | 1.52560 | 0.0492642 | ||||||||
\(960\) | 16.7603 | 0.540937 | ||||||||
\(961\) | −21.4624 | −0.692335 | ||||||||
\(962\) | 23.2176 | 0.748564 | ||||||||
\(963\) | 8.44855 | 0.272251 | ||||||||
\(964\) | 40.1135 | 1.29197 | ||||||||
\(965\) | 26.0494 | 0.838560 | ||||||||
\(966\) | 12.1572 | 0.391150 | ||||||||
\(967\) | 39.9680 | 1.28529 | 0.642643 | − | 0.766166i | \(-0.277838\pi\) | ||||
0.642643 | + | 0.766166i | \(0.277838\pi\) | |||||||
\(968\) | 79.2415 | 2.54692 | ||||||||
\(969\) | 20.7124 | 0.665379 | ||||||||
\(970\) | −89.9140 | −2.88696 | ||||||||
\(971\) | −1.35538 | −0.0434961 | −0.0217481 | − | 0.999763i | \(-0.506923\pi\) | ||||
−0.0217481 | + | 0.999763i | \(0.506923\pi\) | |||||||
\(972\) | −4.77168 | −0.153052 | ||||||||
\(973\) | 8.07704 | 0.258938 | ||||||||
\(974\) | −47.7965 | −1.53150 | ||||||||
\(975\) | −1.40484 | −0.0449910 | ||||||||
\(976\) | 124.894 | 3.99775 | ||||||||
\(977\) | 1.14587 | 0.0366596 | 0.0183298 | − | 0.999832i | \(-0.494165\pi\) | ||||
0.0183298 | + | 0.999832i | \(0.494165\pi\) | |||||||
\(978\) | 36.3397 | 1.16202 | ||||||||
\(979\) | 1.36404 | 0.0435949 | ||||||||
\(980\) | −12.3351 | −0.394029 | ||||||||
\(981\) | −1.06337 | −0.0339507 | ||||||||
\(982\) | 32.1838 | 1.02703 | ||||||||
\(983\) | −34.2850 | −1.09352 | −0.546761 | − | 0.837289i | \(-0.684139\pi\) | ||||
−0.546761 | + | 0.837289i | \(0.684139\pi\) | |||||||
\(984\) | 84.2260 | 2.68503 | ||||||||
\(985\) | −10.8525 | −0.345789 | ||||||||
\(986\) | −56.8828 | −1.81152 | ||||||||
\(987\) | 0.636054 | 0.0202458 | ||||||||
\(988\) | 14.6749 | 0.466871 | ||||||||
\(989\) | −0.0296071 | −0.000941450 0 | ||||||||
\(990\) | −0.779757 | −0.0247823 | ||||||||
\(991\) | −1.61563 | −0.0513221 | −0.0256610 | − | 0.999671i | \(-0.508169\pi\) | ||||
−0.0256610 | + | 0.999671i | \(0.508169\pi\) | |||||||
\(992\) | −29.5921 | −0.939549 | ||||||||
\(993\) | 2.93153 | 0.0930292 | ||||||||
\(994\) | −1.91150 | −0.0606291 | ||||||||
\(995\) | 17.2005 | 0.545293 | ||||||||
\(996\) | −57.1631 | −1.81128 | ||||||||
\(997\) | 41.3066 | 1.30819 | 0.654096 | − | 0.756411i | \(-0.273049\pi\) | ||||
0.654096 | + | 0.756411i | \(0.273049\pi\) | |||||||
\(998\) | −25.4347 | −0.805121 | ||||||||
\(999\) | 10.6856 | 0.338077 |
(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 | 4011.2.a.l.1.3 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.l.1.3 | ✓ | 28 | 1.1 | even | 1 | trivial |