Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(1\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32430 | −0.936424 | −0.468212 | − | 0.883616i | \(-0.655102\pi\) | ||||
−0.468212 | + | 0.883616i | \(0.655102\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.246218 | −0.123109 | ||||||||
\(5\) | −1.21552 | −0.543597 | −0.271799 | − | 0.962354i | \(-0.587618\pi\) | ||||
−0.271799 | + | 0.962354i | \(0.587618\pi\) | |||||||
\(6\) | 1.32430 | 0.540645 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.97468 | 1.05171 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.60972 | 0.509038 | ||||||||
\(11\) | −3.63830 | −1.09699 | −0.548494 | − | 0.836155i | \(-0.684799\pi\) | ||||
−0.548494 | + | 0.836155i | \(0.684799\pi\) | |||||||
\(12\) | 0.246218 | 0.0710771 | ||||||||
\(13\) | 0.340762 | 0.0945105 | 0.0472552 | − | 0.998883i | \(-0.484953\pi\) | ||||
0.0472552 | + | 0.998883i | \(0.484953\pi\) | |||||||
\(14\) | −1.32430 | −0.353935 | ||||||||
\(15\) | 1.21552 | 0.313846 | ||||||||
\(16\) | −3.44694 | −0.861735 | ||||||||
\(17\) | −5.62220 | −1.36358 | −0.681792 | − | 0.731546i | \(-0.738799\pi\) | ||||
−0.681792 | + | 0.731546i | \(0.738799\pi\) | |||||||
\(18\) | −1.32430 | −0.312141 | ||||||||
\(19\) | 3.82899 | 0.878430 | 0.439215 | − | 0.898382i | \(-0.355257\pi\) | ||||
0.439215 | + | 0.898382i | \(0.355257\pi\) | |||||||
\(20\) | 0.299284 | 0.0669218 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 4.81821 | 1.02725 | ||||||||
\(23\) | 3.44689 | 0.718727 | 0.359363 | − | 0.933198i | \(-0.382994\pi\) | ||||
0.359363 | + | 0.933198i | \(0.382994\pi\) | |||||||
\(24\) | −2.97468 | −0.607203 | ||||||||
\(25\) | −3.52251 | −0.704502 | ||||||||
\(26\) | −0.451273 | −0.0885019 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.246218 | −0.0465309 | ||||||||
\(29\) | 10.3910 | 1.92955 | 0.964777 | − | 0.263068i | \(-0.0847345\pi\) | ||||
0.964777 | + | 0.263068i | \(0.0847345\pi\) | |||||||
\(30\) | −1.60972 | −0.293893 | ||||||||
\(31\) | −2.06533 | −0.370945 | −0.185473 | − | 0.982649i | \(-0.559382\pi\) | ||||
−0.185473 | + | 0.982649i | \(0.559382\pi\) | |||||||
\(32\) | −1.38456 | −0.244757 | ||||||||
\(33\) | 3.63830 | 0.633346 | ||||||||
\(34\) | 7.44551 | 1.27689 | ||||||||
\(35\) | −1.21552 | −0.205460 | ||||||||
\(36\) | −0.246218 | −0.0410364 | ||||||||
\(37\) | −1.93053 | −0.317377 | −0.158688 | − | 0.987329i | \(-0.550726\pi\) | ||||
−0.158688 | + | 0.987329i | \(0.550726\pi\) | |||||||
\(38\) | −5.07074 | −0.822583 | ||||||||
\(39\) | −0.340762 | −0.0545656 | ||||||||
\(40\) | −3.61578 | −0.571705 | ||||||||
\(41\) | −3.22491 | −0.503647 | −0.251824 | − | 0.967773i | \(-0.581030\pi\) | ||||
−0.251824 | + | 0.967773i | \(0.581030\pi\) | |||||||
\(42\) | 1.32430 | 0.204345 | ||||||||
\(43\) | −4.17446 | −0.636600 | −0.318300 | − | 0.947990i | \(-0.603112\pi\) | ||||
−0.318300 | + | 0.947990i | \(0.603112\pi\) | |||||||
\(44\) | 0.895816 | 0.135049 | ||||||||
\(45\) | −1.21552 | −0.181199 | ||||||||
\(46\) | −4.56473 | −0.673033 | ||||||||
\(47\) | 11.1954 | 1.63301 | 0.816506 | − | 0.577337i | \(-0.195908\pi\) | ||||
0.816506 | + | 0.577337i | \(0.195908\pi\) | |||||||
\(48\) | 3.44694 | 0.497523 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.66488 | 0.659713 | ||||||||
\(51\) | 5.62220 | 0.787266 | ||||||||
\(52\) | −0.0839020 | −0.0116351 | ||||||||
\(53\) | −1.83376 | −0.251886 | −0.125943 | − | 0.992037i | \(-0.540196\pi\) | ||||
−0.125943 | + | 0.992037i | \(0.540196\pi\) | |||||||
\(54\) | 1.32430 | 0.180215 | ||||||||
\(55\) | 4.42242 | 0.596319 | ||||||||
\(56\) | 2.97468 | 0.397508 | ||||||||
\(57\) | −3.82899 | −0.507162 | ||||||||
\(58\) | −13.7608 | −1.80688 | ||||||||
\(59\) | 3.71579 | 0.483754 | 0.241877 | − | 0.970307i | \(-0.422237\pi\) | ||||
0.241877 | + | 0.970307i | \(0.422237\pi\) | |||||||
\(60\) | −0.299284 | −0.0386373 | ||||||||
\(61\) | −15.1855 | −1.94431 | −0.972155 | − | 0.234338i | \(-0.924708\pi\) | ||||
−0.972155 | + | 0.234338i | \(0.924708\pi\) | |||||||
\(62\) | 2.73513 | 0.347362 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 8.72745 | 1.09093 | ||||||||
\(65\) | −0.414203 | −0.0513756 | ||||||||
\(66\) | −4.81821 | −0.593081 | ||||||||
\(67\) | −3.40054 | −0.415443 | −0.207721 | − | 0.978188i | \(-0.566605\pi\) | ||||
−0.207721 | + | 0.978188i | \(0.566605\pi\) | |||||||
\(68\) | 1.38429 | 0.167870 | ||||||||
\(69\) | −3.44689 | −0.414957 | ||||||||
\(70\) | 1.60972 | 0.192398 | ||||||||
\(71\) | 8.89396 | 1.05552 | 0.527759 | − | 0.849394i | \(-0.323032\pi\) | ||||
0.527759 | + | 0.849394i | \(0.323032\pi\) | |||||||
\(72\) | 2.97468 | 0.350569 | ||||||||
\(73\) | 3.73549 | 0.437206 | 0.218603 | − | 0.975814i | \(-0.429850\pi\) | ||||
0.218603 | + | 0.975814i | \(0.429850\pi\) | |||||||
\(74\) | 2.55660 | 0.297199 | ||||||||
\(75\) | 3.52251 | 0.406744 | ||||||||
\(76\) | −0.942767 | −0.108143 | ||||||||
\(77\) | −3.63830 | −0.414622 | ||||||||
\(78\) | 0.451273 | 0.0510966 | ||||||||
\(79\) | −11.2227 | −1.26265 | −0.631327 | − | 0.775517i | \(-0.717489\pi\) | ||||
−0.631327 | + | 0.775517i | \(0.717489\pi\) | |||||||
\(80\) | 4.18982 | 0.468437 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.27077 | 0.471627 | ||||||||
\(83\) | −5.29508 | −0.581211 | −0.290605 | − | 0.956843i | \(-0.593857\pi\) | ||||
−0.290605 | + | 0.956843i | \(0.593857\pi\) | |||||||
\(84\) | 0.246218 | 0.0268646 | ||||||||
\(85\) | 6.83390 | 0.741241 | ||||||||
\(86\) | 5.52826 | 0.596127 | ||||||||
\(87\) | −10.3910 | −1.11403 | ||||||||
\(88\) | −10.8228 | −1.15371 | ||||||||
\(89\) | 5.11647 | 0.542345 | 0.271172 | − | 0.962531i | \(-0.412589\pi\) | ||||
0.271172 | + | 0.962531i | \(0.412589\pi\) | |||||||
\(90\) | 1.60972 | 0.169679 | ||||||||
\(91\) | 0.340762 | 0.0357216 | ||||||||
\(92\) | −0.848688 | −0.0884819 | ||||||||
\(93\) | 2.06533 | 0.214165 | ||||||||
\(94\) | −14.8261 | −1.52919 | ||||||||
\(95\) | −4.65421 | −0.477512 | ||||||||
\(96\) | 1.38456 | 0.141311 | ||||||||
\(97\) | 15.1531 | 1.53856 | 0.769280 | − | 0.638912i | \(-0.220615\pi\) | ||||
0.769280 | + | 0.638912i | \(0.220615\pi\) | |||||||
\(98\) | −1.32430 | −0.133775 | ||||||||
\(99\) | −3.63830 | −0.365663 | ||||||||
\(100\) | 0.867307 | 0.0867307 | ||||||||
\(101\) | 3.73324 | 0.371471 | 0.185736 | − | 0.982600i | \(-0.440533\pi\) | ||||
0.185736 | + | 0.982600i | \(0.440533\pi\) | |||||||
\(102\) | −7.44551 | −0.737215 | ||||||||
\(103\) | −8.36010 | −0.823745 | −0.411873 | − | 0.911241i | \(-0.635125\pi\) | ||||
−0.411873 | + | 0.911241i | \(0.635125\pi\) | |||||||
\(104\) | 1.01366 | 0.0993973 | ||||||||
\(105\) | 1.21552 | 0.118623 | ||||||||
\(106\) | 2.42846 | 0.235873 | ||||||||
\(107\) | −12.4964 | −1.20807 | −0.604035 | − | 0.796958i | \(-0.706441\pi\) | ||||
−0.604035 | + | 0.796958i | \(0.706441\pi\) | |||||||
\(108\) | 0.246218 | 0.0236924 | ||||||||
\(109\) | 6.07106 | 0.581502 | 0.290751 | − | 0.956799i | \(-0.406095\pi\) | ||||
0.290751 | + | 0.956799i | \(0.406095\pi\) | |||||||
\(110\) | −5.85663 | −0.558408 | ||||||||
\(111\) | 1.93053 | 0.183237 | ||||||||
\(112\) | −3.44694 | −0.325705 | ||||||||
\(113\) | 12.7669 | 1.20101 | 0.600506 | − | 0.799620i | \(-0.294966\pi\) | ||||
0.600506 | + | 0.799620i | \(0.294966\pi\) | |||||||
\(114\) | 5.07074 | 0.474919 | ||||||||
\(115\) | −4.18977 | −0.390698 | ||||||||
\(116\) | −2.55845 | −0.237546 | ||||||||
\(117\) | 0.340762 | 0.0315035 | ||||||||
\(118\) | −4.92083 | −0.452999 | ||||||||
\(119\) | −5.62220 | −0.515386 | ||||||||
\(120\) | 3.61578 | 0.330074 | ||||||||
\(121\) | 2.23720 | 0.203382 | ||||||||
\(122\) | 20.1103 | 1.82070 | ||||||||
\(123\) | 3.22491 | 0.290781 | ||||||||
\(124\) | 0.508523 | 0.0456668 | ||||||||
\(125\) | 10.3593 | 0.926563 | ||||||||
\(126\) | −1.32430 | −0.117978 | ||||||||
\(127\) | 1.83416 | 0.162756 | 0.0813778 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813778 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(128\) | −8.78869 | −0.776818 | ||||||||
\(129\) | 4.17446 | 0.367541 | ||||||||
\(130\) | 0.548531 | 0.0481094 | ||||||||
\(131\) | 4.33816 | 0.379026 | 0.189513 | − | 0.981878i | \(-0.439309\pi\) | ||||
0.189513 | + | 0.981878i | \(0.439309\pi\) | |||||||
\(132\) | −0.895816 | −0.0779708 | ||||||||
\(133\) | 3.82899 | 0.332015 | ||||||||
\(134\) | 4.50336 | 0.389031 | ||||||||
\(135\) | 1.21552 | 0.104615 | ||||||||
\(136\) | −16.7242 | −1.43409 | ||||||||
\(137\) | −5.05319 | −0.431723 | −0.215862 | − | 0.976424i | \(-0.569256\pi\) | ||||
−0.215862 | + | 0.976424i | \(0.569256\pi\) | |||||||
\(138\) | 4.56473 | 0.388576 | ||||||||
\(139\) | 13.8980 | 1.17881 | 0.589405 | − | 0.807838i | \(-0.299362\pi\) | ||||
0.589405 | + | 0.807838i | \(0.299362\pi\) | |||||||
\(140\) | 0.299284 | 0.0252941 | ||||||||
\(141\) | −11.1954 | −0.942820 | ||||||||
\(142\) | −11.7783 | −0.988413 | ||||||||
\(143\) | −1.23979 | −0.103677 | ||||||||
\(144\) | −3.44694 | −0.287245 | ||||||||
\(145\) | −12.6304 | −1.04890 | ||||||||
\(146\) | −4.94692 | −0.409410 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0.475331 | 0.0390720 | ||||||||
\(149\) | 22.0493 | 1.80635 | 0.903176 | − | 0.429271i | \(-0.141230\pi\) | ||||
0.903176 | + | 0.429271i | \(0.141230\pi\) | |||||||
\(150\) | −4.66488 | −0.380885 | ||||||||
\(151\) | −9.98536 | −0.812597 | −0.406298 | − | 0.913740i | \(-0.633181\pi\) | ||||
−0.406298 | + | 0.913740i | \(0.633181\pi\) | |||||||
\(152\) | 11.3900 | 0.923851 | ||||||||
\(153\) | −5.62220 | −0.454528 | ||||||||
\(154\) | 4.81821 | 0.388263 | ||||||||
\(155\) | 2.51046 | 0.201645 | ||||||||
\(156\) | 0.0839020 | 0.00671753 | ||||||||
\(157\) | 5.55643 | 0.443451 | 0.221726 | − | 0.975109i | \(-0.428831\pi\) | ||||
0.221726 | + | 0.975109i | \(0.428831\pi\) | |||||||
\(158\) | 14.8623 | 1.18238 | ||||||||
\(159\) | 1.83376 | 0.145427 | ||||||||
\(160\) | 1.68296 | 0.133049 | ||||||||
\(161\) | 3.44689 | 0.271653 | ||||||||
\(162\) | −1.32430 | −0.104047 | ||||||||
\(163\) | −13.9127 | −1.08972 | −0.544862 | − | 0.838525i | \(-0.683418\pi\) | ||||
−0.544862 | + | 0.838525i | \(0.683418\pi\) | |||||||
\(164\) | 0.794034 | 0.0620036 | ||||||||
\(165\) | −4.42242 | −0.344285 | ||||||||
\(166\) | 7.01230 | 0.544260 | ||||||||
\(167\) | −12.2355 | −0.946809 | −0.473404 | − | 0.880845i | \(-0.656975\pi\) | ||||
−0.473404 | + | 0.880845i | \(0.656975\pi\) | |||||||
\(168\) | −2.97468 | −0.229501 | ||||||||
\(169\) | −12.8839 | −0.991068 | ||||||||
\(170\) | −9.05016 | −0.694116 | ||||||||
\(171\) | 3.82899 | 0.292810 | ||||||||
\(172\) | 1.02783 | 0.0783713 | ||||||||
\(173\) | 7.46943 | 0.567891 | 0.283945 | − | 0.958840i | \(-0.408357\pi\) | ||||
0.283945 | + | 0.958840i | \(0.408357\pi\) | |||||||
\(174\) | 13.7608 | 1.04320 | ||||||||
\(175\) | −3.52251 | −0.266277 | ||||||||
\(176\) | 12.5410 | 0.945313 | ||||||||
\(177\) | −3.71579 | −0.279296 | ||||||||
\(178\) | −6.77576 | −0.507865 | ||||||||
\(179\) | 12.9833 | 0.970417 | 0.485208 | − | 0.874399i | \(-0.338744\pi\) | ||||
0.485208 | + | 0.874399i | \(0.338744\pi\) | |||||||
\(180\) | 0.299284 | 0.0223073 | ||||||||
\(181\) | −7.85925 | −0.584174 | −0.292087 | − | 0.956392i | \(-0.594350\pi\) | ||||
−0.292087 | + | 0.956392i | \(0.594350\pi\) | |||||||
\(182\) | −0.451273 | −0.0334506 | ||||||||
\(183\) | 15.1855 | 1.12255 | ||||||||
\(184\) | 10.2534 | 0.755890 | ||||||||
\(185\) | 2.34659 | 0.172525 | ||||||||
\(186\) | −2.73513 | −0.200550 | ||||||||
\(187\) | 20.4552 | 1.49584 | ||||||||
\(188\) | −2.75651 | −0.201039 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 6.16359 | 0.447154 | ||||||||
\(191\) | −11.4337 | −0.827316 | −0.413658 | − | 0.910432i | \(-0.635749\pi\) | ||||
−0.413658 | + | 0.910432i | \(0.635749\pi\) | |||||||
\(192\) | −8.72745 | −0.629850 | ||||||||
\(193\) | −20.5183 | −1.47694 | −0.738469 | − | 0.674287i | \(-0.764451\pi\) | ||||
−0.738469 | + | 0.674287i | \(0.764451\pi\) | |||||||
\(194\) | −20.0673 | −1.44075 | ||||||||
\(195\) | 0.414203 | 0.0296617 | ||||||||
\(196\) | −0.246218 | −0.0175870 | ||||||||
\(197\) | 1.38685 | 0.0988092 | 0.0494046 | − | 0.998779i | \(-0.484268\pi\) | ||||
0.0494046 | + | 0.998779i | \(0.484268\pi\) | |||||||
\(198\) | 4.81821 | 0.342415 | ||||||||
\(199\) | 6.38280 | 0.452464 | 0.226232 | − | 0.974073i | \(-0.427359\pi\) | ||||
0.226232 | + | 0.974073i | \(0.427359\pi\) | |||||||
\(200\) | −10.4783 | −0.740930 | ||||||||
\(201\) | 3.40054 | 0.239856 | ||||||||
\(202\) | −4.94394 | −0.347855 | ||||||||
\(203\) | 10.3910 | 0.729303 | ||||||||
\(204\) | −1.38429 | −0.0969197 | ||||||||
\(205\) | 3.91995 | 0.273781 | ||||||||
\(206\) | 11.0713 | 0.771375 | ||||||||
\(207\) | 3.44689 | 0.239576 | ||||||||
\(208\) | −1.17459 | −0.0814430 | ||||||||
\(209\) | −13.9310 | −0.963627 | ||||||||
\(210\) | −1.60972 | −0.111081 | ||||||||
\(211\) | 6.95383 | 0.478722 | 0.239361 | − | 0.970931i | \(-0.423062\pi\) | ||||
0.239361 | + | 0.970931i | \(0.423062\pi\) | |||||||
\(212\) | 0.451506 | 0.0310095 | ||||||||
\(213\) | −8.89396 | −0.609404 | ||||||||
\(214\) | 16.5490 | 1.13127 | ||||||||
\(215\) | 5.07414 | 0.346054 | ||||||||
\(216\) | −2.97468 | −0.202401 | ||||||||
\(217\) | −2.06533 | −0.140204 | ||||||||
\(218\) | −8.03994 | −0.544533 | ||||||||
\(219\) | −3.73549 | −0.252421 | ||||||||
\(220\) | −1.08888 | −0.0734124 | ||||||||
\(221\) | −1.91583 | −0.128873 | ||||||||
\(222\) | −2.55660 | −0.171588 | ||||||||
\(223\) | 27.2264 | 1.82322 | 0.911608 | − | 0.411060i | \(-0.134841\pi\) | ||||
0.911608 | + | 0.411060i | \(0.134841\pi\) | |||||||
\(224\) | −1.38456 | −0.0925096 | ||||||||
\(225\) | −3.52251 | −0.234834 | ||||||||
\(226\) | −16.9073 | −1.12466 | ||||||||
\(227\) | −22.8224 | −1.51478 | −0.757388 | − | 0.652965i | \(-0.773525\pi\) | ||||
−0.757388 | + | 0.652965i | \(0.773525\pi\) | |||||||
\(228\) | 0.942767 | 0.0624363 | ||||||||
\(229\) | 20.0672 | 1.32608 | 0.663039 | − | 0.748585i | \(-0.269267\pi\) | ||||
0.663039 | + | 0.748585i | \(0.269267\pi\) | |||||||
\(230\) | 5.54853 | 0.365859 | ||||||||
\(231\) | 3.63830 | 0.239382 | ||||||||
\(232\) | 30.9098 | 2.02933 | ||||||||
\(233\) | 24.9561 | 1.63493 | 0.817463 | − | 0.575981i | \(-0.195380\pi\) | ||||
0.817463 | + | 0.575981i | \(0.195380\pi\) | |||||||
\(234\) | −0.451273 | −0.0295006 | ||||||||
\(235\) | −13.6082 | −0.887701 | ||||||||
\(236\) | −0.914895 | −0.0595546 | ||||||||
\(237\) | 11.2227 | 0.728993 | ||||||||
\(238\) | 7.44551 | 0.482621 | ||||||||
\(239\) | 13.1443 | 0.850237 | 0.425118 | − | 0.905138i | \(-0.360232\pi\) | ||||
0.425118 | + | 0.905138i | \(0.360232\pi\) | |||||||
\(240\) | −4.18982 | −0.270452 | ||||||||
\(241\) | 22.6920 | 1.46172 | 0.730860 | − | 0.682528i | \(-0.239119\pi\) | ||||
0.730860 | + | 0.682528i | \(0.239119\pi\) | |||||||
\(242\) | −2.96274 | −0.190452 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.73896 | 0.239363 | ||||||||
\(245\) | −1.21552 | −0.0776567 | ||||||||
\(246\) | −4.27077 | −0.272294 | ||||||||
\(247\) | 1.30477 | 0.0830208 | ||||||||
\(248\) | −6.14370 | −0.390125 | ||||||||
\(249\) | 5.29508 | 0.335562 | ||||||||
\(250\) | −13.7188 | −0.867656 | ||||||||
\(251\) | −13.4776 | −0.850700 | −0.425350 | − | 0.905029i | \(-0.639849\pi\) | ||||
−0.425350 | + | 0.905029i | \(0.639849\pi\) | |||||||
\(252\) | −0.246218 | −0.0155103 | ||||||||
\(253\) | −12.5408 | −0.788434 | ||||||||
\(254\) | −2.42899 | −0.152408 | ||||||||
\(255\) | −6.83390 | −0.427955 | ||||||||
\(256\) | −5.81601 | −0.363500 | ||||||||
\(257\) | −1.01377 | −0.0632373 | −0.0316186 | − | 0.999500i | \(-0.510066\pi\) | ||||
−0.0316186 | + | 0.999500i | \(0.510066\pi\) | |||||||
\(258\) | −5.52826 | −0.344174 | ||||||||
\(259\) | −1.93053 | −0.119957 | ||||||||
\(260\) | 0.101985 | 0.00632481 | ||||||||
\(261\) | 10.3910 | 0.643185 | ||||||||
\(262\) | −5.74504 | −0.354930 | ||||||||
\(263\) | 18.1756 | 1.12076 | 0.560378 | − | 0.828237i | \(-0.310656\pi\) | ||||
0.560378 | + | 0.828237i | \(0.310656\pi\) | |||||||
\(264\) | 10.8228 | 0.666095 | ||||||||
\(265\) | 2.22897 | 0.136925 | ||||||||
\(266\) | −5.07074 | −0.310907 | ||||||||
\(267\) | −5.11647 | −0.313123 | ||||||||
\(268\) | 0.837277 | 0.0511448 | ||||||||
\(269\) | −8.78753 | −0.535785 | −0.267893 | − | 0.963449i | \(-0.586327\pi\) | ||||
−0.267893 | + | 0.963449i | \(0.586327\pi\) | |||||||
\(270\) | −1.60972 | −0.0979643 | ||||||||
\(271\) | 10.0417 | 0.609992 | 0.304996 | − | 0.952354i | \(-0.401345\pi\) | ||||
0.304996 | + | 0.952354i | \(0.401345\pi\) | |||||||
\(272\) | 19.3794 | 1.17505 | ||||||||
\(273\) | −0.340762 | −0.0206239 | ||||||||
\(274\) | 6.69196 | 0.404276 | ||||||||
\(275\) | 12.8159 | 0.772830 | ||||||||
\(276\) | 0.848688 | 0.0510850 | ||||||||
\(277\) | 17.0788 | 1.02617 | 0.513084 | − | 0.858338i | \(-0.328503\pi\) | ||||
0.513084 | + | 0.858338i | \(0.328503\pi\) | |||||||
\(278\) | −18.4051 | −1.10387 | ||||||||
\(279\) | −2.06533 | −0.123648 | ||||||||
\(280\) | −3.61578 | −0.216084 | ||||||||
\(281\) | −17.5354 | −1.04607 | −0.523037 | − | 0.852310i | \(-0.675201\pi\) | ||||
−0.523037 | + | 0.852310i | \(0.675201\pi\) | |||||||
\(282\) | 14.8261 | 0.882880 | ||||||||
\(283\) | 1.96482 | 0.116797 | 0.0583983 | − | 0.998293i | \(-0.481401\pi\) | ||||
0.0583983 | + | 0.998293i | \(0.481401\pi\) | |||||||
\(284\) | −2.18986 | −0.129944 | ||||||||
\(285\) | 4.65421 | 0.275692 | ||||||||
\(286\) | 1.64186 | 0.0970855 | ||||||||
\(287\) | −3.22491 | −0.190361 | ||||||||
\(288\) | −1.38456 | −0.0815858 | ||||||||
\(289\) | 14.6092 | 0.859363 | ||||||||
\(290\) | 16.7265 | 0.982216 | ||||||||
\(291\) | −15.1531 | −0.888288 | ||||||||
\(292\) | −0.919746 | −0.0538241 | ||||||||
\(293\) | 24.6510 | 1.44012 | 0.720062 | − | 0.693910i | \(-0.244113\pi\) | ||||
0.720062 | + | 0.693910i | \(0.244113\pi\) | |||||||
\(294\) | 1.32430 | 0.0772350 | ||||||||
\(295\) | −4.51661 | −0.262967 | ||||||||
\(296\) | −5.74269 | −0.333787 | ||||||||
\(297\) | 3.63830 | 0.211115 | ||||||||
\(298\) | −29.2000 | −1.69151 | ||||||||
\(299\) | 1.17457 | 0.0679272 | ||||||||
\(300\) | −0.867307 | −0.0500740 | ||||||||
\(301\) | −4.17446 | −0.240612 | ||||||||
\(302\) | 13.2236 | 0.760935 | ||||||||
\(303\) | −3.73324 | −0.214469 | ||||||||
\(304\) | −13.1983 | −0.756974 | ||||||||
\(305\) | 18.4583 | 1.05692 | ||||||||
\(306\) | 7.44551 | 0.425631 | ||||||||
\(307\) | −10.7166 | −0.611631 | −0.305816 | − | 0.952091i | \(-0.598929\pi\) | ||||
−0.305816 | + | 0.952091i | \(0.598929\pi\) | |||||||
\(308\) | 0.895816 | 0.0510438 | ||||||||
\(309\) | 8.36010 | 0.475590 | ||||||||
\(310\) | −3.32461 | −0.188825 | ||||||||
\(311\) | 9.36871 | 0.531251 | 0.265625 | − | 0.964076i | \(-0.414422\pi\) | ||||
0.265625 | + | 0.964076i | \(0.414422\pi\) | |||||||
\(312\) | −1.01366 | −0.0573871 | ||||||||
\(313\) | 19.8408 | 1.12147 | 0.560734 | − | 0.827996i | \(-0.310519\pi\) | ||||
0.560734 | + | 0.827996i | \(0.310519\pi\) | |||||||
\(314\) | −7.35840 | −0.415259 | ||||||||
\(315\) | −1.21552 | −0.0684868 | ||||||||
\(316\) | 2.76324 | 0.155444 | ||||||||
\(317\) | −11.2125 | −0.629755 | −0.314877 | − | 0.949132i | \(-0.601963\pi\) | ||||
−0.314877 | + | 0.949132i | \(0.601963\pi\) | |||||||
\(318\) | −2.42846 | −0.136181 | ||||||||
\(319\) | −37.8054 | −2.11670 | ||||||||
\(320\) | −10.6084 | −0.593027 | ||||||||
\(321\) | 12.4964 | 0.697480 | ||||||||
\(322\) | −4.56473 | −0.254383 | ||||||||
\(323\) | −21.5273 | −1.19781 | ||||||||
\(324\) | −0.246218 | −0.0136788 | ||||||||
\(325\) | −1.20034 | −0.0665828 | ||||||||
\(326\) | 18.4246 | 1.02044 | ||||||||
\(327\) | −6.07106 | −0.335731 | ||||||||
\(328\) | −9.59308 | −0.529689 | ||||||||
\(329\) | 11.1954 | 0.617221 | ||||||||
\(330\) | 5.85663 | 0.322397 | ||||||||
\(331\) | −26.9205 | −1.47969 | −0.739843 | − | 0.672780i | \(-0.765100\pi\) | ||||
−0.739843 | + | 0.672780i | \(0.765100\pi\) | |||||||
\(332\) | 1.30375 | 0.0715524 | ||||||||
\(333\) | −1.93053 | −0.105792 | ||||||||
\(334\) | 16.2035 | 0.886615 | ||||||||
\(335\) | 4.13343 | 0.225833 | ||||||||
\(336\) | 3.44694 | 0.188046 | ||||||||
\(337\) | −7.28486 | −0.396832 | −0.198416 | − | 0.980118i | \(-0.563580\pi\) | ||||
−0.198416 | + | 0.980118i | \(0.563580\pi\) | |||||||
\(338\) | 17.0622 | 0.928060 | ||||||||
\(339\) | −12.7669 | −0.693405 | ||||||||
\(340\) | −1.68263 | −0.0912536 | ||||||||
\(341\) | 7.51430 | 0.406922 | ||||||||
\(342\) | −5.07074 | −0.274194 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −12.4177 | −0.669516 | ||||||||
\(345\) | 4.18977 | 0.225569 | ||||||||
\(346\) | −9.89180 | −0.531787 | ||||||||
\(347\) | 28.6543 | 1.53824 | 0.769121 | − | 0.639103i | \(-0.220694\pi\) | ||||
0.769121 | + | 0.639103i | \(0.220694\pi\) | |||||||
\(348\) | 2.55845 | 0.137147 | ||||||||
\(349\) | 2.15367 | 0.115283 | 0.0576416 | − | 0.998337i | \(-0.481642\pi\) | ||||
0.0576416 | + | 0.998337i | \(0.481642\pi\) | |||||||
\(350\) | 4.66488 | 0.249348 | ||||||||
\(351\) | −0.340762 | −0.0181885 | ||||||||
\(352\) | 5.03743 | 0.268496 | ||||||||
\(353\) | −26.1391 | −1.39124 | −0.695621 | − | 0.718409i | \(-0.744871\pi\) | ||||
−0.695621 | + | 0.718409i | \(0.744871\pi\) | |||||||
\(354\) | 4.92083 | 0.261539 | ||||||||
\(355\) | −10.8108 | −0.573777 | ||||||||
\(356\) | −1.25977 | −0.0667677 | ||||||||
\(357\) | 5.62220 | 0.297559 | ||||||||
\(358\) | −17.1938 | −0.908722 | ||||||||
\(359\) | −1.05157 | −0.0554998 | −0.0277499 | − | 0.999615i | \(-0.508834\pi\) | ||||
−0.0277499 | + | 0.999615i | \(0.508834\pi\) | |||||||
\(360\) | −3.61578 | −0.190568 | ||||||||
\(361\) | −4.33886 | −0.228361 | ||||||||
\(362\) | 10.4080 | 0.547035 | ||||||||
\(363\) | −2.23720 | −0.117423 | ||||||||
\(364\) | −0.0839020 | −0.00439766 | ||||||||
\(365\) | −4.54056 | −0.237664 | ||||||||
\(366\) | −20.1103 | −1.05118 | ||||||||
\(367\) | −10.5881 | −0.552695 | −0.276347 | − | 0.961058i | \(-0.589124\pi\) | ||||
−0.276347 | + | 0.961058i | \(0.589124\pi\) | |||||||
\(368\) | −11.8812 | −0.619352 | ||||||||
\(369\) | −3.22491 | −0.167882 | ||||||||
\(370\) | −3.10760 | −0.161557 | ||||||||
\(371\) | −1.83376 | −0.0952041 | ||||||||
\(372\) | −0.508523 | −0.0263657 | ||||||||
\(373\) | 7.15747 | 0.370600 | 0.185300 | − | 0.982682i | \(-0.440674\pi\) | ||||
0.185300 | + | 0.982682i | \(0.440674\pi\) | |||||||
\(374\) | −27.0890 | −1.40074 | ||||||||
\(375\) | −10.3593 | −0.534951 | ||||||||
\(376\) | 33.3026 | 1.71745 | ||||||||
\(377\) | 3.54085 | 0.182363 | ||||||||
\(378\) | 1.32430 | 0.0681149 | ||||||||
\(379\) | 9.38840 | 0.482250 | 0.241125 | − | 0.970494i | \(-0.422484\pi\) | ||||
0.241125 | + | 0.970494i | \(0.422484\pi\) | |||||||
\(380\) | 1.14595 | 0.0587861 | ||||||||
\(381\) | −1.83416 | −0.0939670 | ||||||||
\(382\) | 15.1417 | 0.774719 | ||||||||
\(383\) | 1.00000 | 0.0510976 | ||||||||
\(384\) | 8.78869 | 0.448496 | ||||||||
\(385\) | 4.42242 | 0.225388 | ||||||||
\(386\) | 27.1724 | 1.38304 | ||||||||
\(387\) | −4.17446 | −0.212200 | ||||||||
\(388\) | −3.73096 | −0.189411 | ||||||||
\(389\) | −19.1768 | −0.972301 | −0.486150 | − | 0.873875i | \(-0.661599\pi\) | ||||
−0.486150 | + | 0.873875i | \(0.661599\pi\) | |||||||
\(390\) | −0.548531 | −0.0277760 | ||||||||
\(391\) | −19.3791 | −0.980045 | ||||||||
\(392\) | 2.97468 | 0.150244 | ||||||||
\(393\) | −4.33816 | −0.218831 | ||||||||
\(394\) | −1.83661 | −0.0925273 | ||||||||
\(395\) | 13.6414 | 0.686375 | ||||||||
\(396\) | 0.895816 | 0.0450164 | ||||||||
\(397\) | −27.8058 | −1.39553 | −0.697766 | − | 0.716326i | \(-0.745822\pi\) | ||||
−0.697766 | + | 0.716326i | \(0.745822\pi\) | |||||||
\(398\) | −8.45276 | −0.423699 | ||||||||
\(399\) | −3.82899 | −0.191689 | ||||||||
\(400\) | 12.1419 | 0.607094 | ||||||||
\(401\) | −13.9664 | −0.697450 | −0.348725 | − | 0.937225i | \(-0.613385\pi\) | ||||
−0.348725 | + | 0.937225i | \(0.613385\pi\) | |||||||
\(402\) | −4.50336 | −0.224607 | ||||||||
\(403\) | −0.703788 | −0.0350582 | ||||||||
\(404\) | −0.919192 | −0.0457315 | ||||||||
\(405\) | −1.21552 | −0.0603997 | ||||||||
\(406\) | −13.7608 | −0.682937 | ||||||||
\(407\) | 7.02383 | 0.348158 | ||||||||
\(408\) | 16.7242 | 0.827973 | ||||||||
\(409\) | 0.818225 | 0.0404586 | 0.0202293 | − | 0.999795i | \(-0.493560\pi\) | ||||
0.0202293 | + | 0.999795i | \(0.493560\pi\) | |||||||
\(410\) | −5.19121 | −0.256375 | ||||||||
\(411\) | 5.05319 | 0.249256 | ||||||||
\(412\) | 2.05841 | 0.101411 | ||||||||
\(413\) | 3.71579 | 0.182842 | ||||||||
\(414\) | −4.56473 | −0.224344 | ||||||||
\(415\) | 6.43628 | 0.315945 | ||||||||
\(416\) | −0.471805 | −0.0231321 | ||||||||
\(417\) | −13.8980 | −0.680586 | ||||||||
\(418\) | 18.4489 | 0.902364 | ||||||||
\(419\) | −19.1508 | −0.935576 | −0.467788 | − | 0.883841i | \(-0.654949\pi\) | ||||
−0.467788 | + | 0.883841i | \(0.654949\pi\) | |||||||
\(420\) | −0.299284 | −0.0146035 | ||||||||
\(421\) | −28.0335 | −1.36627 | −0.683135 | − | 0.730292i | \(-0.739384\pi\) | ||||
−0.683135 | + | 0.730292i | \(0.739384\pi\) | |||||||
\(422\) | −9.20899 | −0.448287 | ||||||||
\(423\) | 11.1954 | 0.544337 | ||||||||
\(424\) | −5.45485 | −0.264911 | ||||||||
\(425\) | 19.8043 | 0.960648 | ||||||||
\(426\) | 11.7783 | 0.570661 | ||||||||
\(427\) | −15.1855 | −0.734880 | ||||||||
\(428\) | 3.07684 | 0.148725 | ||||||||
\(429\) | 1.23979 | 0.0598578 | ||||||||
\(430\) | −6.71971 | −0.324053 | ||||||||
\(431\) | −22.4666 | −1.08218 | −0.541090 | − | 0.840965i | \(-0.681988\pi\) | ||||
−0.541090 | + | 0.840965i | \(0.681988\pi\) | |||||||
\(432\) | 3.44694 | 0.165841 | ||||||||
\(433\) | −37.5483 | −1.80446 | −0.902229 | − | 0.431257i | \(-0.858070\pi\) | ||||
−0.902229 | + | 0.431257i | \(0.858070\pi\) | |||||||
\(434\) | 2.73513 | 0.131290 | ||||||||
\(435\) | 12.6304 | 0.605583 | ||||||||
\(436\) | −1.49481 | −0.0715883 | ||||||||
\(437\) | 13.1981 | 0.631351 | ||||||||
\(438\) | 4.94692 | 0.236373 | ||||||||
\(439\) | 4.23051 | 0.201911 | 0.100956 | − | 0.994891i | \(-0.467810\pi\) | ||||
0.100956 | + | 0.994891i | \(0.467810\pi\) | |||||||
\(440\) | 13.1553 | 0.627153 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 2.53715 | 0.120680 | ||||||||
\(443\) | 24.1931 | 1.14945 | 0.574724 | − | 0.818347i | \(-0.305109\pi\) | ||||
0.574724 | + | 0.818347i | \(0.305109\pi\) | |||||||
\(444\) | −0.475331 | −0.0225582 | ||||||||
\(445\) | −6.21917 | −0.294817 | ||||||||
\(446\) | −36.0561 | −1.70730 | ||||||||
\(447\) | −22.0493 | −1.04290 | ||||||||
\(448\) | 8.72745 | 0.412333 | ||||||||
\(449\) | −1.90456 | −0.0898819 | −0.0449410 | − | 0.998990i | \(-0.514310\pi\) | ||||
−0.0449410 | + | 0.998990i | \(0.514310\pi\) | |||||||
\(450\) | 4.66488 | 0.219904 | ||||||||
\(451\) | 11.7332 | 0.552495 | ||||||||
\(452\) | −3.14346 | −0.147856 | ||||||||
\(453\) | 9.98536 | 0.469153 | ||||||||
\(454\) | 30.2238 | 1.41847 | ||||||||
\(455\) | −0.414203 | −0.0194182 | ||||||||
\(456\) | −11.3900 | −0.533385 | ||||||||
\(457\) | −16.9744 | −0.794029 | −0.397015 | − | 0.917812i | \(-0.629954\pi\) | ||||
−0.397015 | + | 0.917812i | \(0.629954\pi\) | |||||||
\(458\) | −26.5751 | −1.24177 | ||||||||
\(459\) | 5.62220 | 0.262422 | ||||||||
\(460\) | 1.03160 | 0.0480985 | ||||||||
\(461\) | −36.6093 | −1.70507 | −0.852533 | − | 0.522674i | \(-0.824935\pi\) | ||||
−0.852533 | + | 0.522674i | \(0.824935\pi\) | |||||||
\(462\) | −4.81821 | −0.224163 | ||||||||
\(463\) | −37.7860 | −1.75607 | −0.878033 | − | 0.478601i | \(-0.841144\pi\) | ||||
−0.878033 | + | 0.478601i | \(0.841144\pi\) | |||||||
\(464\) | −35.8170 | −1.66276 | ||||||||
\(465\) | −2.51046 | −0.116420 | ||||||||
\(466\) | −33.0494 | −1.53098 | ||||||||
\(467\) | 5.16106 | 0.238825 | 0.119413 | − | 0.992845i | \(-0.461899\pi\) | ||||
0.119413 | + | 0.992845i | \(0.461899\pi\) | |||||||
\(468\) | −0.0839020 | −0.00387837 | ||||||||
\(469\) | −3.40054 | −0.157023 | ||||||||
\(470\) | 18.0214 | 0.831265 | ||||||||
\(471\) | −5.55643 | −0.256027 | ||||||||
\(472\) | 11.0533 | 0.508768 | ||||||||
\(473\) | 15.1879 | 0.698342 | ||||||||
\(474\) | −14.8623 | −0.682647 | ||||||||
\(475\) | −13.4876 | −0.618856 | ||||||||
\(476\) | 1.38429 | 0.0634488 | ||||||||
\(477\) | −1.83376 | −0.0839622 | ||||||||
\(478\) | −17.4071 | −0.796182 | ||||||||
\(479\) | 16.7221 | 0.764054 | 0.382027 | − | 0.924151i | \(-0.375226\pi\) | ||||
0.382027 | + | 0.924151i | \(0.375226\pi\) | |||||||
\(480\) | −1.68296 | −0.0768161 | ||||||||
\(481\) | −0.657851 | −0.0299954 | ||||||||
\(482\) | −30.0511 | −1.36879 | ||||||||
\(483\) | −3.44689 | −0.156839 | ||||||||
\(484\) | −0.550841 | −0.0250382 | ||||||||
\(485\) | −18.4189 | −0.836357 | ||||||||
\(486\) | 1.32430 | 0.0600717 | ||||||||
\(487\) | −2.75869 | −0.125008 | −0.0625040 | − | 0.998045i | \(-0.519909\pi\) | ||||
−0.0625040 | + | 0.998045i | \(0.519909\pi\) | |||||||
\(488\) | −45.1721 | −2.04484 | ||||||||
\(489\) | 13.9127 | 0.629153 | ||||||||
\(490\) | 1.60972 | 0.0727197 | ||||||||
\(491\) | −32.4571 | −1.46477 | −0.732385 | − | 0.680890i | \(-0.761593\pi\) | ||||
−0.732385 | + | 0.680890i | \(0.761593\pi\) | |||||||
\(492\) | −0.794034 | −0.0357978 | ||||||||
\(493\) | −58.4201 | −2.63111 | ||||||||
\(494\) | −1.72792 | −0.0777427 | ||||||||
\(495\) | 4.42242 | 0.198773 | ||||||||
\(496\) | 7.11908 | 0.319656 | ||||||||
\(497\) | 8.89396 | 0.398949 | ||||||||
\(498\) | −7.01230 | −0.314229 | ||||||||
\(499\) | −25.0944 | −1.12338 | −0.561689 | − | 0.827348i | \(-0.689848\pi\) | ||||
−0.561689 | + | 0.827348i | \(0.689848\pi\) | |||||||
\(500\) | −2.55065 | −0.114068 | ||||||||
\(501\) | 12.2355 | 0.546640 | ||||||||
\(502\) | 17.8485 | 0.796616 | ||||||||
\(503\) | −26.4315 | −1.17852 | −0.589260 | − | 0.807943i | \(-0.700581\pi\) | ||||
−0.589260 | + | 0.807943i | \(0.700581\pi\) | |||||||
\(504\) | 2.97468 | 0.132503 | ||||||||
\(505\) | −4.53783 | −0.201931 | ||||||||
\(506\) | 16.6079 | 0.738309 | ||||||||
\(507\) | 12.8839 | 0.572193 | ||||||||
\(508\) | −0.451605 | −0.0200367 | ||||||||
\(509\) | −5.45591 | −0.241829 | −0.120915 | − | 0.992663i | \(-0.538583\pi\) | ||||
−0.120915 | + | 0.992663i | \(0.538583\pi\) | |||||||
\(510\) | 9.05016 | 0.400748 | ||||||||
\(511\) | 3.73549 | 0.165248 | ||||||||
\(512\) | 25.2795 | 1.11721 | ||||||||
\(513\) | −3.82899 | −0.169054 | ||||||||
\(514\) | 1.34254 | 0.0592169 | ||||||||
\(515\) | 10.1619 | 0.447786 | ||||||||
\(516\) | −1.02783 | −0.0452477 | ||||||||
\(517\) | −40.7321 | −1.79139 | ||||||||
\(518\) | 2.55660 | 0.112331 | ||||||||
\(519\) | −7.46943 | −0.327872 | ||||||||
\(520\) | −1.23212 | −0.0540321 | ||||||||
\(521\) | −37.7111 | −1.65215 | −0.826076 | − | 0.563559i | \(-0.809432\pi\) | ||||
−0.826076 | + | 0.563559i | \(0.809432\pi\) | |||||||
\(522\) | −13.7608 | −0.602294 | ||||||||
\(523\) | −28.6262 | −1.25174 | −0.625869 | − | 0.779928i | \(-0.715256\pi\) | ||||
−0.625869 | + | 0.779928i | \(0.715256\pi\) | |||||||
\(524\) | −1.06813 | −0.0466617 | ||||||||
\(525\) | 3.52251 | 0.153735 | ||||||||
\(526\) | −24.0700 | −1.04950 | ||||||||
\(527\) | 11.6117 | 0.505815 | ||||||||
\(528\) | −12.5410 | −0.545777 | ||||||||
\(529\) | −11.1189 | −0.483432 | ||||||||
\(530\) | −2.95184 | −0.128220 | ||||||||
\(531\) | 3.71579 | 0.161251 | ||||||||
\(532\) | −0.942767 | −0.0408741 | ||||||||
\(533\) | −1.09893 | −0.0475999 | ||||||||
\(534\) | 6.77576 | 0.293216 | ||||||||
\(535\) | 15.1896 | 0.656704 | ||||||||
\(536\) | −10.1155 | −0.436924 | ||||||||
\(537\) | −12.9833 | −0.560270 | ||||||||
\(538\) | 11.6374 | 0.501723 | ||||||||
\(539\) | −3.63830 | −0.156713 | ||||||||
\(540\) | −0.299284 | −0.0128791 | ||||||||
\(541\) | 32.1296 | 1.38136 | 0.690680 | − | 0.723161i | \(-0.257311\pi\) | ||||
0.690680 | + | 0.723161i | \(0.257311\pi\) | |||||||
\(542\) | −13.2983 | −0.571211 | ||||||||
\(543\) | 7.85925 | 0.337273 | ||||||||
\(544\) | 7.78426 | 0.333747 | ||||||||
\(545\) | −7.37950 | −0.316103 | ||||||||
\(546\) | 0.451273 | 0.0193127 | ||||||||
\(547\) | −3.57051 | −0.152664 | −0.0763319 | − | 0.997082i | \(-0.524321\pi\) | ||||
−0.0763319 | + | 0.997082i | \(0.524321\pi\) | |||||||
\(548\) | 1.24419 | 0.0531491 | ||||||||
\(549\) | −15.1855 | −0.648103 | ||||||||
\(550\) | −16.9722 | −0.723697 | ||||||||
\(551\) | 39.7869 | 1.69498 | ||||||||
\(552\) | −10.2534 | −0.436413 | ||||||||
\(553\) | −11.2227 | −0.477238 | ||||||||
\(554\) | −22.6176 | −0.960929 | ||||||||
\(555\) | −2.34659 | −0.0996074 | ||||||||
\(556\) | −3.42194 | −0.145122 | ||||||||
\(557\) | 11.0377 | 0.467682 | 0.233841 | − | 0.972275i | \(-0.424871\pi\) | ||||
0.233841 | + | 0.972275i | \(0.424871\pi\) | |||||||
\(558\) | 2.73513 | 0.115787 | ||||||||
\(559\) | −1.42250 | −0.0601653 | ||||||||
\(560\) | 4.18982 | 0.177052 | ||||||||
\(561\) | −20.4552 | −0.863621 | ||||||||
\(562\) | 23.2222 | 0.979570 | ||||||||
\(563\) | 16.1678 | 0.681390 | 0.340695 | − | 0.940174i | \(-0.389338\pi\) | ||||
0.340695 | + | 0.940174i | \(0.389338\pi\) | |||||||
\(564\) | 2.75651 | 0.116070 | ||||||||
\(565\) | −15.5185 | −0.652867 | ||||||||
\(566\) | −2.60202 | −0.109371 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 26.4566 | 1.11010 | ||||||||
\(569\) | 27.4893 | 1.15241 | 0.576206 | − | 0.817305i | \(-0.304533\pi\) | ||||
0.576206 | + | 0.817305i | \(0.304533\pi\) | |||||||
\(570\) | −6.16359 | −0.258164 | ||||||||
\(571\) | −11.9699 | −0.500925 | −0.250463 | − | 0.968126i | \(-0.580583\pi\) | ||||
−0.250463 | + | 0.968126i | \(0.580583\pi\) | |||||||
\(572\) | 0.305260 | 0.0127636 | ||||||||
\(573\) | 11.4337 | 0.477651 | ||||||||
\(574\) | 4.27077 | 0.178258 | ||||||||
\(575\) | −12.1417 | −0.506344 | ||||||||
\(576\) | 8.72745 | 0.363644 | ||||||||
\(577\) | 12.1567 | 0.506091 | 0.253045 | − | 0.967454i | \(-0.418568\pi\) | ||||
0.253045 | + | 0.967454i | \(0.418568\pi\) | |||||||
\(578\) | −19.3470 | −0.804728 | ||||||||
\(579\) | 20.5183 | 0.852711 | ||||||||
\(580\) | 3.10985 | 0.129129 | ||||||||
\(581\) | −5.29508 | −0.219677 | ||||||||
\(582\) | 20.0673 | 0.831815 | ||||||||
\(583\) | 6.67177 | 0.276316 | ||||||||
\(584\) | 11.1119 | 0.459812 | ||||||||
\(585\) | −0.414203 | −0.0171252 | ||||||||
\(586\) | −32.6454 | −1.34857 | ||||||||
\(587\) | 10.6062 | 0.437763 | 0.218882 | − | 0.975751i | \(-0.429759\pi\) | ||||
0.218882 | + | 0.975751i | \(0.429759\pi\) | |||||||
\(588\) | 0.246218 | 0.0101539 | ||||||||
\(589\) | −7.90814 | −0.325849 | ||||||||
\(590\) | 5.98137 | 0.246249 | ||||||||
\(591\) | −1.38685 | −0.0570475 | ||||||||
\(592\) | 6.65441 | 0.273495 | ||||||||
\(593\) | −28.5874 | −1.17394 | −0.586972 | − | 0.809607i | \(-0.699680\pi\) | ||||
−0.586972 | + | 0.809607i | \(0.699680\pi\) | |||||||
\(594\) | −4.81821 | −0.197694 | ||||||||
\(595\) | 6.83390 | 0.280163 | ||||||||
\(596\) | −5.42895 | −0.222379 | ||||||||
\(597\) | −6.38280 | −0.261230 | ||||||||
\(598\) | −1.55549 | −0.0636087 | ||||||||
\(599\) | 36.3073 | 1.48348 | 0.741738 | − | 0.670690i | \(-0.234002\pi\) | ||||
0.741738 | + | 0.670690i | \(0.234002\pi\) | |||||||
\(600\) | 10.4783 | 0.427776 | ||||||||
\(601\) | −11.4172 | −0.465718 | −0.232859 | − | 0.972510i | \(-0.574808\pi\) | ||||
−0.232859 | + | 0.972510i | \(0.574808\pi\) | |||||||
\(602\) | 5.52826 | 0.225315 | ||||||||
\(603\) | −3.40054 | −0.138481 | ||||||||
\(604\) | 2.45858 | 0.100038 | ||||||||
\(605\) | −2.71937 | −0.110558 | ||||||||
\(606\) | 4.94394 | 0.200834 | ||||||||
\(607\) | 24.5839 | 0.997830 | 0.498915 | − | 0.866651i | \(-0.333732\pi\) | ||||
0.498915 | + | 0.866651i | \(0.333732\pi\) | |||||||
\(608\) | −5.30145 | −0.215002 | ||||||||
\(609\) | −10.3910 | −0.421063 | ||||||||
\(610\) | −24.4445 | −0.989727 | ||||||||
\(611\) | 3.81496 | 0.154337 | ||||||||
\(612\) | 1.38429 | 0.0559566 | ||||||||
\(613\) | −25.1341 | −1.01516 | −0.507578 | − | 0.861606i | \(-0.669459\pi\) | ||||
−0.507578 | + | 0.861606i | \(0.669459\pi\) | |||||||
\(614\) | 14.1921 | 0.572747 | ||||||||
\(615\) | −3.91995 | −0.158068 | ||||||||
\(616\) | −10.8228 | −0.436061 | ||||||||
\(617\) | −28.9376 | −1.16499 | −0.582493 | − | 0.812836i | \(-0.697923\pi\) | ||||
−0.582493 | + | 0.812836i | \(0.697923\pi\) | |||||||
\(618\) | −11.0713 | −0.445354 | ||||||||
\(619\) | 0.0991748 | 0.00398617 | 0.00199309 | − | 0.999998i | \(-0.499366\pi\) | ||||
0.00199309 | + | 0.999998i | \(0.499366\pi\) | |||||||
\(620\) | −0.618121 | −0.0248243 | ||||||||
\(621\) | −3.44689 | −0.138319 | ||||||||
\(622\) | −12.4070 | −0.497476 | ||||||||
\(623\) | 5.11647 | 0.204987 | ||||||||
\(624\) | 1.17459 | 0.0470211 | ||||||||
\(625\) | 5.02063 | 0.200825 | ||||||||
\(626\) | −26.2752 | −1.05017 | ||||||||
\(627\) | 13.9310 | 0.556350 | ||||||||
\(628\) | −1.36810 | −0.0545930 | ||||||||
\(629\) | 10.8538 | 0.432770 | ||||||||
\(630\) | 1.60972 | 0.0641327 | ||||||||
\(631\) | −1.39530 | −0.0555459 | −0.0277730 | − | 0.999614i | \(-0.508842\pi\) | ||||
−0.0277730 | + | 0.999614i | \(0.508842\pi\) | |||||||
\(632\) | −33.3839 | −1.32794 | ||||||||
\(633\) | −6.95383 | −0.276390 | ||||||||
\(634\) | 14.8487 | 0.589718 | ||||||||
\(635\) | −2.22946 | −0.0884735 | ||||||||
\(636\) | −0.451506 | −0.0179034 | ||||||||
\(637\) | 0.340762 | 0.0135015 | ||||||||
\(638\) | 50.0659 | 1.98213 | ||||||||
\(639\) | 8.89396 | 0.351840 | ||||||||
\(640\) | 10.6828 | 0.422276 | ||||||||
\(641\) | −12.8855 | −0.508945 | −0.254473 | − | 0.967080i | \(-0.581902\pi\) | ||||
−0.254473 | + | 0.967080i | \(0.581902\pi\) | |||||||
\(642\) | −16.5490 | −0.653137 | ||||||||
\(643\) | −30.4827 | −1.20212 | −0.601061 | − | 0.799203i | \(-0.705255\pi\) | ||||
−0.601061 | + | 0.799203i | \(0.705255\pi\) | |||||||
\(644\) | −0.848688 | −0.0334430 | ||||||||
\(645\) | −5.07414 | −0.199794 | ||||||||
\(646\) | 28.5087 | 1.12166 | ||||||||
\(647\) | 28.6424 | 1.12605 | 0.563025 | − | 0.826440i | \(-0.309637\pi\) | ||||
0.563025 | + | 0.826440i | \(0.309637\pi\) | |||||||
\(648\) | 2.97468 | 0.116856 | ||||||||
\(649\) | −13.5191 | −0.530672 | ||||||||
\(650\) | 1.58961 | 0.0623498 | ||||||||
\(651\) | 2.06533 | 0.0809468 | ||||||||
\(652\) | 3.42556 | 0.134155 | ||||||||
\(653\) | −43.3526 | −1.69652 | −0.848260 | − | 0.529580i | \(-0.822349\pi\) | ||||
−0.848260 | + | 0.529580i | \(0.822349\pi\) | |||||||
\(654\) | 8.03994 | 0.314386 | ||||||||
\(655\) | −5.27312 | −0.206038 | ||||||||
\(656\) | 11.1161 | 0.434010 | ||||||||
\(657\) | 3.73549 | 0.145735 | ||||||||
\(658\) | −14.8261 | −0.577981 | ||||||||
\(659\) | −9.04320 | −0.352273 | −0.176136 | − | 0.984366i | \(-0.556360\pi\) | ||||
−0.176136 | + | 0.984366i | \(0.556360\pi\) | |||||||
\(660\) | 1.08888 | 0.0423847 | ||||||||
\(661\) | −38.6904 | −1.50488 | −0.752440 | − | 0.658660i | \(-0.771123\pi\) | ||||
−0.752440 | + | 0.658660i | \(0.771123\pi\) | |||||||
\(662\) | 35.6510 | 1.38561 | ||||||||
\(663\) | 1.91583 | 0.0744049 | ||||||||
\(664\) | −15.7512 | −0.611264 | ||||||||
\(665\) | −4.65421 | −0.180483 | ||||||||
\(666\) | 2.55660 | 0.0990664 | ||||||||
\(667\) | 35.8165 | 1.38682 | ||||||||
\(668\) | 3.01260 | 0.116561 | ||||||||
\(669\) | −27.2264 | −1.05263 | ||||||||
\(670\) | −5.47392 | −0.211476 | ||||||||
\(671\) | 55.2495 | 2.13288 | ||||||||
\(672\) | 1.38456 | 0.0534104 | ||||||||
\(673\) | −23.2958 | −0.897988 | −0.448994 | − | 0.893535i | \(-0.648218\pi\) | ||||
−0.448994 | + | 0.893535i | \(0.648218\pi\) | |||||||
\(674\) | 9.64737 | 0.371603 | ||||||||
\(675\) | 3.52251 | 0.135581 | ||||||||
\(676\) | 3.17225 | 0.122010 | ||||||||
\(677\) | 7.34575 | 0.282320 | 0.141160 | − | 0.989987i | \(-0.454917\pi\) | ||||
0.141160 | + | 0.989987i | \(0.454917\pi\) | |||||||
\(678\) | 16.9073 | 0.649321 | ||||||||
\(679\) | 15.1531 | 0.581521 | ||||||||
\(680\) | 20.3286 | 0.779568 | ||||||||
\(681\) | 22.8224 | 0.874556 | ||||||||
\(682\) | −9.95122 | −0.381052 | ||||||||
\(683\) | −11.0789 | −0.423921 | −0.211961 | − | 0.977278i | \(-0.567985\pi\) | ||||
−0.211961 | + | 0.977278i | \(0.567985\pi\) | |||||||
\(684\) | −0.942767 | −0.0360476 | ||||||||
\(685\) | 6.14226 | 0.234684 | ||||||||
\(686\) | −1.32430 | −0.0505622 | ||||||||
\(687\) | −20.0672 | −0.765611 | ||||||||
\(688\) | 14.3891 | 0.548580 | ||||||||
\(689\) | −0.624877 | −0.0238059 | ||||||||
\(690\) | −5.54853 | −0.211229 | ||||||||
\(691\) | 5.25568 | 0.199935 | 0.0999677 | − | 0.994991i | \(-0.468126\pi\) | ||||
0.0999677 | + | 0.994991i | \(0.468126\pi\) | |||||||
\(692\) | −1.83911 | −0.0699126 | ||||||||
\(693\) | −3.63830 | −0.138207 | ||||||||
\(694\) | −37.9470 | −1.44045 | ||||||||
\(695\) | −16.8933 | −0.640798 | ||||||||
\(696\) | −30.9098 | −1.17163 | ||||||||
\(697\) | 18.1311 | 0.686765 | ||||||||
\(698\) | −2.85211 | −0.107954 | ||||||||
\(699\) | −24.9561 | −0.943925 | ||||||||
\(700\) | 0.867307 | 0.0327811 | ||||||||
\(701\) | 34.7457 | 1.31233 | 0.656164 | − | 0.754619i | \(-0.272178\pi\) | ||||
0.656164 | + | 0.754619i | \(0.272178\pi\) | |||||||
\(702\) | 0.451273 | 0.0170322 | ||||||||
\(703\) | −7.39196 | −0.278793 | ||||||||
\(704\) | −31.7531 | −1.19674 | ||||||||
\(705\) | 13.6082 | 0.512514 | ||||||||
\(706\) | 34.6161 | 1.30279 | ||||||||
\(707\) | 3.73324 | 0.140403 | ||||||||
\(708\) | 0.914895 | 0.0343839 | ||||||||
\(709\) | 0.527890 | 0.0198253 | 0.00991267 | − | 0.999951i | \(-0.496845\pi\) | ||||
0.00991267 | + | 0.999951i | \(0.496845\pi\) | |||||||
\(710\) | 14.3168 | 0.537299 | ||||||||
\(711\) | −11.2227 | −0.420884 | ||||||||
\(712\) | 15.2198 | 0.570388 | ||||||||
\(713\) | −7.11898 | −0.266608 | ||||||||
\(714\) | −7.44551 | −0.278641 | ||||||||
\(715\) | 1.50700 | 0.0563584 | ||||||||
\(716\) | −3.19673 | −0.119467 | ||||||||
\(717\) | −13.1443 | −0.490884 | ||||||||
\(718\) | 1.39260 | 0.0519713 | ||||||||
\(719\) | 24.5972 | 0.917322 | 0.458661 | − | 0.888611i | \(-0.348329\pi\) | ||||
0.458661 | + | 0.888611i | \(0.348329\pi\) | |||||||
\(720\) | 4.18982 | 0.156146 | ||||||||
\(721\) | −8.36010 | −0.311346 | ||||||||
\(722\) | 5.74598 | 0.213843 | ||||||||
\(723\) | −22.6920 | −0.843924 | ||||||||
\(724\) | 1.93509 | 0.0719172 | ||||||||
\(725\) | −36.6023 | −1.35938 | ||||||||
\(726\) | 2.96274 | 0.109958 | ||||||||
\(727\) | −8.37422 | −0.310582 | −0.155291 | − | 0.987869i | \(-0.549632\pi\) | ||||
−0.155291 | + | 0.987869i | \(0.549632\pi\) | |||||||
\(728\) | 1.01366 | 0.0375687 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.01308 | 0.222554 | ||||||||
\(731\) | 23.4697 | 0.868057 | ||||||||
\(732\) | −3.73896 | −0.138196 | ||||||||
\(733\) | −12.9112 | −0.476886 | −0.238443 | − | 0.971156i | \(-0.576637\pi\) | ||||
−0.238443 | + | 0.971156i | \(0.576637\pi\) | |||||||
\(734\) | 14.0219 | 0.517557 | ||||||||
\(735\) | 1.21552 | 0.0448351 | ||||||||
\(736\) | −4.77242 | −0.175914 | ||||||||
\(737\) | 12.3722 | 0.455735 | ||||||||
\(738\) | 4.27077 | 0.157209 | ||||||||
\(739\) | −3.62813 | −0.133463 | −0.0667314 | − | 0.997771i | \(-0.521257\pi\) | ||||
−0.0667314 | + | 0.997771i | \(0.521257\pi\) | |||||||
\(740\) | −0.577775 | −0.0212394 | ||||||||
\(741\) | −1.30477 | −0.0479321 | ||||||||
\(742\) | 2.42846 | 0.0891515 | ||||||||
\(743\) | 6.94403 | 0.254752 | 0.127376 | − | 0.991855i | \(-0.459345\pi\) | ||||
0.127376 | + | 0.991855i | \(0.459345\pi\) | |||||||
\(744\) | 6.14370 | 0.225239 | ||||||||
\(745\) | −26.8014 | −0.981927 | ||||||||
\(746\) | −9.47866 | −0.347039 | ||||||||
\(747\) | −5.29508 | −0.193737 | ||||||||
\(748\) | −5.03646 | −0.184151 | ||||||||
\(749\) | −12.4964 | −0.456608 | ||||||||
\(750\) | 13.7188 | 0.500941 | ||||||||
\(751\) | −3.65813 | −0.133487 | −0.0667435 | − | 0.997770i | \(-0.521261\pi\) | ||||
−0.0667435 | + | 0.997770i | \(0.521261\pi\) | |||||||
\(752\) | −38.5898 | −1.40722 | ||||||||
\(753\) | 13.4776 | 0.491152 | ||||||||
\(754\) | −4.68916 | −0.170769 | ||||||||
\(755\) | 12.1374 | 0.441725 | ||||||||
\(756\) | 0.246218 | 0.00895488 | ||||||||
\(757\) | 3.64600 | 0.132516 | 0.0662580 | − | 0.997803i | \(-0.478894\pi\) | ||||
0.0662580 | + | 0.997803i | \(0.478894\pi\) | |||||||
\(758\) | −12.4331 | −0.451591 | ||||||||
\(759\) | 12.5408 | 0.455203 | ||||||||
\(760\) | −13.8448 | −0.502203 | ||||||||
\(761\) | −37.8893 | −1.37348 | −0.686742 | − | 0.726901i | \(-0.740960\pi\) | ||||
−0.686742 | + | 0.726901i | \(0.740960\pi\) | |||||||
\(762\) | 2.42899 | 0.0879930 | ||||||||
\(763\) | 6.07106 | 0.219787 | ||||||||
\(764\) | 2.81520 | 0.101850 | ||||||||
\(765\) | 6.83390 | 0.247080 | ||||||||
\(766\) | −1.32430 | −0.0478491 | ||||||||
\(767\) | 1.26620 | 0.0457198 | ||||||||
\(768\) | 5.81601 | 0.209867 | ||||||||
\(769\) | −41.2348 | −1.48696 | −0.743482 | − | 0.668756i | \(-0.766827\pi\) | ||||
−0.743482 | + | 0.668756i | \(0.766827\pi\) | |||||||
\(770\) | −5.85663 | −0.211058 | ||||||||
\(771\) | 1.01377 | 0.0365101 | ||||||||
\(772\) | 5.05198 | 0.181825 | ||||||||
\(773\) | −12.5336 | −0.450802 | −0.225401 | − | 0.974266i | \(-0.572369\pi\) | ||||
−0.225401 | + | 0.974266i | \(0.572369\pi\) | |||||||
\(774\) | 5.52826 | 0.198709 | ||||||||
\(775\) | 7.27516 | 0.261332 | ||||||||
\(776\) | 45.0755 | 1.61811 | ||||||||
\(777\) | 1.93053 | 0.0692573 | ||||||||
\(778\) | 25.3959 | 0.910486 | ||||||||
\(779\) | −12.3482 | −0.442419 | ||||||||
\(780\) | −0.101985 | −0.00365163 | ||||||||
\(781\) | −32.3589 | −1.15789 | ||||||||
\(782\) | 25.6639 | 0.917738 | ||||||||
\(783\) | −10.3910 | −0.371343 | ||||||||
\(784\) | −3.44694 | −0.123105 | ||||||||
\(785\) | −6.75395 | −0.241059 | ||||||||
\(786\) | 5.74504 | 0.204919 | ||||||||
\(787\) | −5.99542 | −0.213714 | −0.106857 | − | 0.994274i | \(-0.534079\pi\) | ||||
−0.106857 | + | 0.994274i | \(0.534079\pi\) | |||||||
\(788\) | −0.341469 | −0.0121643 | ||||||||
\(789\) | −18.1756 | −0.647068 | ||||||||
\(790\) | −18.0654 | −0.642738 | ||||||||
\(791\) | 12.7669 | 0.453940 | ||||||||
\(792\) | −10.8228 | −0.384570 | ||||||||
\(793\) | −5.17466 | −0.183758 | ||||||||
\(794\) | 36.8233 | 1.30681 | ||||||||
\(795\) | −2.22897 | −0.0790536 | ||||||||
\(796\) | −1.57156 | −0.0557025 | ||||||||
\(797\) | 25.4076 | 0.899983 | 0.449992 | − | 0.893033i | \(-0.351427\pi\) | ||||
0.449992 | + | 0.893033i | \(0.351427\pi\) | |||||||
\(798\) | 5.07074 | 0.179502 | ||||||||
\(799\) | −62.9426 | −2.22675 | ||||||||
\(800\) | 4.87711 | 0.172432 | ||||||||
\(801\) | 5.11647 | 0.180782 | ||||||||
\(802\) | 18.4958 | 0.653109 | ||||||||
\(803\) | −13.5908 | −0.479609 | ||||||||
\(804\) | −0.837277 | −0.0295285 | ||||||||
\(805\) | −4.18977 | −0.147670 | ||||||||
\(806\) | 0.932030 | 0.0328293 | ||||||||
\(807\) | 8.78753 | 0.309336 | ||||||||
\(808\) | 11.1052 | 0.390679 | ||||||||
\(809\) | −44.8406 | −1.57651 | −0.788255 | − | 0.615348i | \(-0.789015\pi\) | ||||
−0.788255 | + | 0.615348i | \(0.789015\pi\) | |||||||
\(810\) | 1.60972 | 0.0565597 | ||||||||
\(811\) | 15.6957 | 0.551151 | 0.275575 | − | 0.961279i | \(-0.411132\pi\) | ||||
0.275575 | + | 0.961279i | \(0.411132\pi\) | |||||||
\(812\) | −2.55845 | −0.0897839 | ||||||||
\(813\) | −10.0417 | −0.352179 | ||||||||
\(814\) | −9.30169 | −0.326024 | ||||||||
\(815\) | 16.9111 | 0.592371 | ||||||||
\(816\) | −19.3794 | −0.678414 | ||||||||
\(817\) | −15.9840 | −0.559208 | ||||||||
\(818\) | −1.08358 | −0.0378864 | ||||||||
\(819\) | 0.340762 | 0.0119072 | ||||||||
\(820\) | −0.965164 | −0.0337050 | ||||||||
\(821\) | −26.9222 | −0.939590 | −0.469795 | − | 0.882776i | \(-0.655672\pi\) | ||||
−0.469795 | + | 0.882776i | \(0.655672\pi\) | |||||||
\(822\) | −6.69196 | −0.233409 | ||||||||
\(823\) | −8.84287 | −0.308243 | −0.154122 | − | 0.988052i | \(-0.549255\pi\) | ||||
−0.154122 | + | 0.988052i | \(0.549255\pi\) | |||||||
\(824\) | −24.8686 | −0.866339 | ||||||||
\(825\) | −12.8159 | −0.446194 | ||||||||
\(826\) | −4.92083 | −0.171218 | ||||||||
\(827\) | −26.5690 | −0.923894 | −0.461947 | − | 0.886908i | \(-0.652849\pi\) | ||||
−0.461947 | + | 0.886908i | \(0.652849\pi\) | |||||||
\(828\) | −0.848688 | −0.0294940 | ||||||||
\(829\) | 42.3942 | 1.47241 | 0.736206 | − | 0.676757i | \(-0.236615\pi\) | ||||
0.736206 | + | 0.676757i | \(0.236615\pi\) | |||||||
\(830\) | −8.52359 | −0.295858 | ||||||||
\(831\) | −17.0788 | −0.592458 | ||||||||
\(832\) | 2.97399 | 0.103104 | ||||||||
\(833\) | −5.62220 | −0.194798 | ||||||||
\(834\) | 18.4051 | 0.637318 | ||||||||
\(835\) | 14.8725 | 0.514682 | ||||||||
\(836\) | 3.43007 | 0.118631 | ||||||||
\(837\) | 2.06533 | 0.0713884 | ||||||||
\(838\) | 25.3614 | 0.876096 | ||||||||
\(839\) | 0.577628 | 0.0199419 | 0.00997097 | − | 0.999950i | \(-0.496826\pi\) | ||||
0.00997097 | + | 0.999950i | \(0.496826\pi\) | |||||||
\(840\) | 3.61578 | 0.124756 | ||||||||
\(841\) | 78.9722 | 2.72318 | ||||||||
\(842\) | 37.1249 | 1.27941 | ||||||||
\(843\) | 17.5354 | 0.603951 | ||||||||
\(844\) | −1.71216 | −0.0589350 | ||||||||
\(845\) | 15.6606 | 0.538742 | ||||||||
\(846\) | −14.8261 | −0.509731 | ||||||||
\(847\) | 2.23720 | 0.0768712 | ||||||||
\(848\) | 6.32086 | 0.217059 | ||||||||
\(849\) | −1.96482 | −0.0674326 | ||||||||
\(850\) | −26.2269 | −0.899574 | ||||||||
\(851\) | −6.65432 | −0.228107 | ||||||||
\(852\) | 2.18986 | 0.0750232 | ||||||||
\(853\) | −2.86371 | −0.0980517 | −0.0490258 | − | 0.998798i | \(-0.515612\pi\) | ||||
−0.0490258 | + | 0.998798i | \(0.515612\pi\) | |||||||
\(854\) | 20.1103 | 0.688160 | ||||||||
\(855\) | −4.65421 | −0.159171 | ||||||||
\(856\) | −37.1727 | −1.27054 | ||||||||
\(857\) | −20.8218 | −0.711259 | −0.355630 | − | 0.934627i | \(-0.615734\pi\) | ||||
−0.355630 | + | 0.934627i | \(0.615734\pi\) | |||||||
\(858\) | −1.64186 | −0.0560523 | ||||||||
\(859\) | −47.2524 | −1.61223 | −0.806115 | − | 0.591758i | \(-0.798434\pi\) | ||||
−0.806115 | + | 0.591758i | \(0.798434\pi\) | |||||||
\(860\) | −1.24935 | −0.0426024 | ||||||||
\(861\) | 3.22491 | 0.109905 | ||||||||
\(862\) | 29.7526 | 1.01338 | ||||||||
\(863\) | 23.2301 | 0.790761 | 0.395380 | − | 0.918517i | \(-0.370613\pi\) | ||||
0.395380 | + | 0.918517i | \(0.370613\pi\) | |||||||
\(864\) | 1.38456 | 0.0471036 | ||||||||
\(865\) | −9.07925 | −0.308704 | ||||||||
\(866\) | 49.7254 | 1.68974 | ||||||||
\(867\) | −14.6092 | −0.496153 | ||||||||
\(868\) | 0.508523 | 0.0172604 | ||||||||
\(869\) | 40.8315 | 1.38512 | ||||||||
\(870\) | −16.7265 | −0.567083 | ||||||||
\(871\) | −1.15878 | −0.0392637 | ||||||||
\(872\) | 18.0595 | 0.611570 | ||||||||
\(873\) | 15.1531 | 0.512853 | ||||||||
\(874\) | −17.4783 | −0.591212 | ||||||||
\(875\) | 10.3593 | 0.350208 | ||||||||
\(876\) | 0.919746 | 0.0310753 | ||||||||
\(877\) | −40.0216 | −1.35143 | −0.675716 | − | 0.737162i | \(-0.736166\pi\) | ||||
−0.675716 | + | 0.737162i | \(0.736166\pi\) | |||||||
\(878\) | −5.60248 | −0.189074 | ||||||||
\(879\) | −24.6510 | −0.831456 | ||||||||
\(880\) | −15.2438 | −0.513869 | ||||||||
\(881\) | 50.0895 | 1.68756 | 0.843779 | − | 0.536690i | \(-0.180326\pi\) | ||||
0.843779 | + | 0.536690i | \(0.180326\pi\) | |||||||
\(882\) | −1.32430 | −0.0445916 | ||||||||
\(883\) | 13.5501 | 0.455999 | 0.227999 | − | 0.973661i | \(-0.426782\pi\) | ||||
0.227999 | + | 0.973661i | \(0.426782\pi\) | |||||||
\(884\) | 0.471714 | 0.0158655 | ||||||||
\(885\) | 4.51661 | 0.151824 | ||||||||
\(886\) | −32.0390 | −1.07637 | ||||||||
\(887\) | 38.2009 | 1.28266 | 0.641330 | − | 0.767265i | \(-0.278383\pi\) | ||||
0.641330 | + | 0.767265i | \(0.278383\pi\) | |||||||
\(888\) | 5.74269 | 0.192712 | ||||||||
\(889\) | 1.83416 | 0.0615159 | ||||||||
\(890\) | 8.23608 | 0.276074 | ||||||||
\(891\) | −3.63830 | −0.121888 | ||||||||
\(892\) | −6.70365 | −0.224455 | ||||||||
\(893\) | 42.8669 | 1.43449 | ||||||||
\(894\) | 29.2000 | 0.976595 | ||||||||
\(895\) | −15.7815 | −0.527516 | ||||||||
\(896\) | −8.78869 | −0.293610 | ||||||||
\(897\) | −1.17457 | −0.0392178 | ||||||||
\(898\) | 2.52222 | 0.0841676 | ||||||||
\(899\) | −21.4608 | −0.715759 | ||||||||
\(900\) | 0.867307 | 0.0289102 | ||||||||
\(901\) | 10.3098 | 0.343468 | ||||||||
\(902\) | −15.5383 | −0.517370 | ||||||||
\(903\) | 4.17446 | 0.138917 | ||||||||
\(904\) | 37.9775 | 1.26311 | ||||||||
\(905\) | 9.55308 | 0.317555 | ||||||||
\(906\) | −13.2236 | −0.439326 | ||||||||
\(907\) | −41.4321 | −1.37573 | −0.687865 | − | 0.725838i | \(-0.741452\pi\) | ||||
−0.687865 | + | 0.725838i | \(0.741452\pi\) | |||||||
\(908\) | 5.61930 | 0.186483 | ||||||||
\(909\) | 3.73324 | 0.123824 | ||||||||
\(910\) | 0.548531 | 0.0181836 | ||||||||
\(911\) | −7.02975 | −0.232906 | −0.116453 | − | 0.993196i | \(-0.537152\pi\) | ||||
−0.116453 | + | 0.993196i | \(0.537152\pi\) | |||||||
\(912\) | 13.1983 | 0.437039 | ||||||||
\(913\) | 19.2651 | 0.637581 | ||||||||
\(914\) | 22.4793 | 0.743548 | ||||||||
\(915\) | −18.4583 | −0.610214 | ||||||||
\(916\) | −4.94091 | −0.163252 | ||||||||
\(917\) | 4.33816 | 0.143259 | ||||||||
\(918\) | −7.44551 | −0.245738 | ||||||||
\(919\) | 13.5923 | 0.448368 | 0.224184 | − | 0.974547i | \(-0.428028\pi\) | ||||
0.224184 | + | 0.974547i | \(0.428028\pi\) | |||||||
\(920\) | −12.4632 | −0.410900 | ||||||||
\(921\) | 10.7166 | 0.353126 | ||||||||
\(922\) | 48.4819 | 1.59666 | ||||||||
\(923\) | 3.03073 | 0.0997575 | ||||||||
\(924\) | −0.895816 | −0.0294702 | ||||||||
\(925\) | 6.80030 | 0.223593 | ||||||||
\(926\) | 50.0402 | 1.64442 | ||||||||
\(927\) | −8.36010 | −0.274582 | ||||||||
\(928\) | −14.3869 | −0.472273 | ||||||||
\(929\) | −12.3717 | −0.405903 | −0.202951 | − | 0.979189i | \(-0.565053\pi\) | ||||
−0.202951 | + | 0.979189i | \(0.565053\pi\) | |||||||
\(930\) | 3.32461 | 0.109018 | ||||||||
\(931\) | 3.82899 | 0.125490 | ||||||||
\(932\) | −6.14464 | −0.201274 | ||||||||
\(933\) | −9.36871 | −0.306718 | ||||||||
\(934\) | −6.83481 | −0.223642 | ||||||||
\(935\) | −24.8638 | −0.813132 | ||||||||
\(936\) | 1.01366 | 0.0331324 | ||||||||
\(937\) | −41.3937 | −1.35227 | −0.676137 | − | 0.736776i | \(-0.736347\pi\) | ||||
−0.676137 | + | 0.736776i | \(0.736347\pi\) | |||||||
\(938\) | 4.50336 | 0.147040 | ||||||||
\(939\) | −19.8408 | −0.647479 | ||||||||
\(940\) | 3.35059 | 0.109284 | ||||||||
\(941\) | 14.4420 | 0.470795 | 0.235398 | − | 0.971899i | \(-0.424361\pi\) | ||||
0.235398 | + | 0.971899i | \(0.424361\pi\) | |||||||
\(942\) | 7.35840 | 0.239750 | ||||||||
\(943\) | −11.1159 | −0.361985 | ||||||||
\(944\) | −12.8081 | −0.416868 | ||||||||
\(945\) | 1.21552 | 0.0395409 | ||||||||
\(946\) | −20.1134 | −0.653944 | ||||||||
\(947\) | −50.7602 | −1.64949 | −0.824743 | − | 0.565508i | \(-0.808680\pi\) | ||||
−0.824743 | + | 0.565508i | \(0.808680\pi\) | |||||||
\(948\) | −2.76324 | −0.0897458 | ||||||||
\(949\) | 1.27291 | 0.0413205 | ||||||||
\(950\) | 17.8617 | 0.579512 | ||||||||
\(951\) | 11.2125 | 0.363589 | ||||||||
\(952\) | −16.7242 | −0.542036 | ||||||||
\(953\) | −2.46114 | −0.0797240 | −0.0398620 | − | 0.999205i | \(-0.512692\pi\) | ||||
−0.0398620 | + | 0.999205i | \(0.512692\pi\) | |||||||
\(954\) | 2.42846 | 0.0786242 | ||||||||
\(955\) | 13.8979 | 0.449727 | ||||||||
\(956\) | −3.23638 | −0.104672 | ||||||||
\(957\) | 37.8054 | 1.22208 | ||||||||
\(958\) | −22.1452 | −0.715479 | ||||||||
\(959\) | −5.05319 | −0.163176 | ||||||||
\(960\) | 10.6084 | 0.342385 | ||||||||
\(961\) | −26.7344 | −0.862400 | ||||||||
\(962\) | 0.871194 | 0.0280884 | ||||||||
\(963\) | −12.4964 | −0.402690 | ||||||||
\(964\) | −5.58719 | −0.179951 | ||||||||
\(965\) | 24.9404 | 0.802859 | ||||||||
\(966\) | 4.56473 | 0.146868 | ||||||||
\(967\) | −4.88071 | −0.156953 | −0.0784765 | − | 0.996916i | \(-0.525006\pi\) | ||||
−0.0784765 | + | 0.996916i | \(0.525006\pi\) | |||||||
\(968\) | 6.65496 | 0.213898 | ||||||||
\(969\) | 21.5273 | 0.691558 | ||||||||
\(970\) | 24.3922 | 0.783185 | ||||||||
\(971\) | −9.65980 | −0.309998 | −0.154999 | − | 0.987915i | \(-0.549537\pi\) | ||||
−0.154999 | + | 0.987915i | \(0.549537\pi\) | |||||||
\(972\) | 0.246218 | 0.00789746 | ||||||||
\(973\) | 13.8980 | 0.445548 | ||||||||
\(974\) | 3.65334 | 0.117061 | ||||||||
\(975\) | 1.20034 | 0.0384416 | ||||||||
\(976\) | 52.3437 | 1.67548 | ||||||||
\(977\) | 47.8634 | 1.53129 | 0.765643 | − | 0.643266i | \(-0.222421\pi\) | ||||
0.765643 | + | 0.643266i | \(0.222421\pi\) | |||||||
\(978\) | −18.4246 | −0.589154 | ||||||||
\(979\) | −18.6152 | −0.594946 | ||||||||
\(980\) | 0.299284 | 0.00956026 | ||||||||
\(981\) | 6.07106 | 0.193834 | ||||||||
\(982\) | 42.9831 | 1.37165 | ||||||||
\(983\) | 27.5373 | 0.878302 | 0.439151 | − | 0.898413i | \(-0.355279\pi\) | ||||
0.439151 | + | 0.898413i | \(0.355279\pi\) | |||||||
\(984\) | 9.59308 | 0.305816 | ||||||||
\(985\) | −1.68575 | −0.0537124 | ||||||||
\(986\) | 77.3660 | 2.46384 | ||||||||
\(987\) | −11.1954 | −0.356353 | ||||||||
\(988\) | −0.321259 | −0.0102206 | ||||||||
\(989\) | −14.3889 | −0.457541 | ||||||||
\(990\) | −5.85663 | −0.186136 | ||||||||
\(991\) | 58.4210 | 1.85580 | 0.927901 | − | 0.372825i | \(-0.121611\pi\) | ||||
0.927901 | + | 0.372825i | \(0.121611\pi\) | |||||||
\(992\) | 2.85957 | 0.0907915 | ||||||||
\(993\) | 26.9205 | 0.854297 | ||||||||
\(994\) | −11.7783 | −0.373585 | ||||||||
\(995\) | −7.75842 | −0.245958 | ||||||||
\(996\) | −1.30375 | −0.0413108 | ||||||||
\(997\) | −52.1960 | −1.65307 | −0.826533 | − | 0.562889i | \(-0.809690\pi\) | ||||
−0.826533 | + | 0.562889i | \(0.809690\pi\) | |||||||
\(998\) | 33.2326 | 1.05196 | ||||||||
\(999\) | 1.93053 | 0.0610792 |
(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 | 8043.2.a.o.1.14 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.o.1.14 | ✓ | 41 | 1.1 | even | 1 | trivial |