Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.661798 | 0.467962 | 0.233981 | − | 0.972241i | \(-0.424825\pi\) | ||||
0.233981 | + | 0.972241i | \(0.424825\pi\) | |||||||
\(3\) | −2.32231 | −1.34078 | −0.670392 | − | 0.742007i | \(-0.733874\pi\) | ||||
−0.670392 | + | 0.742007i | \(0.733874\pi\) | |||||||
\(4\) | −1.56202 | −0.781012 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.53690 | −0.627436 | ||||||||
\(7\) | −0.917277 | −0.346698 | −0.173349 | − | 0.984860i | \(-0.555459\pi\) | ||||
−0.173349 | + | 0.984860i | \(0.555459\pi\) | |||||||
\(8\) | −2.35734 | −0.833446 | ||||||||
\(9\) | 2.39311 | 0.797703 | ||||||||
\(10\) | 0.661798 | 0.209279 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 3.62750 | 1.04717 | ||||||||
\(13\) | −1.28300 | −0.355839 | −0.177920 | − | 0.984045i | \(-0.556937\pi\) | ||||
−0.177920 | + | 0.984045i | \(0.556937\pi\) | |||||||
\(14\) | −0.607052 | −0.162241 | ||||||||
\(15\) | −2.32231 | −0.599617 | ||||||||
\(16\) | 1.56396 | 0.390991 | ||||||||
\(17\) | 1.41536 | 0.343275 | 0.171638 | − | 0.985160i | \(-0.445094\pi\) | ||||
0.171638 | + | 0.985160i | \(0.445094\pi\) | |||||||
\(18\) | 1.58376 | 0.373295 | ||||||||
\(19\) | −0.964916 | −0.221367 | −0.110684 | − | 0.993856i | \(-0.535304\pi\) | ||||
−0.110684 | + | 0.993856i | \(0.535304\pi\) | |||||||
\(20\) | −1.56202 | −0.349279 | ||||||||
\(21\) | 2.13020 | 0.464847 | ||||||||
\(22\) | −0.661798 | −0.141096 | ||||||||
\(23\) | 6.85951 | 1.43031 | 0.715153 | − | 0.698968i | \(-0.246357\pi\) | ||||
0.715153 | + | 0.698968i | \(0.246357\pi\) | |||||||
\(24\) | 5.47447 | 1.11747 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.849085 | −0.166519 | ||||||||
\(27\) | 1.40939 | 0.271236 | ||||||||
\(28\) | 1.43281 | 0.270775 | ||||||||
\(29\) | −2.38222 | −0.442367 | −0.221184 | − | 0.975232i | \(-0.570992\pi\) | ||||
−0.221184 | + | 0.975232i | \(0.570992\pi\) | |||||||
\(30\) | −1.53690 | −0.280598 | ||||||||
\(31\) | −0.451972 | −0.0811766 | −0.0405883 | − | 0.999176i | \(-0.512923\pi\) | ||||
−0.0405883 | + | 0.999176i | \(0.512923\pi\) | |||||||
\(32\) | 5.74971 | 1.01641 | ||||||||
\(33\) | 2.32231 | 0.404262 | ||||||||
\(34\) | 0.936683 | 0.160640 | ||||||||
\(35\) | −0.917277 | −0.155048 | ||||||||
\(36\) | −3.73809 | −0.623016 | ||||||||
\(37\) | −3.55440 | −0.584339 | −0.292170 | − | 0.956367i | \(-0.594377\pi\) | ||||
−0.292170 | + | 0.956367i | \(0.594377\pi\) | |||||||
\(38\) | −0.638580 | −0.103591 | ||||||||
\(39\) | 2.97951 | 0.477104 | ||||||||
\(40\) | −2.35734 | −0.372728 | ||||||||
\(41\) | 9.63575 | 1.50485 | 0.752426 | − | 0.658677i | \(-0.228884\pi\) | ||||
0.752426 | + | 0.658677i | \(0.228884\pi\) | |||||||
\(42\) | 1.40976 | 0.217531 | ||||||||
\(43\) | −10.4099 | −1.58749 | −0.793744 | − | 0.608252i | \(-0.791871\pi\) | ||||
−0.793744 | + | 0.608252i | \(0.791871\pi\) | |||||||
\(44\) | 1.56202 | 0.235484 | ||||||||
\(45\) | 2.39311 | 0.356744 | ||||||||
\(46\) | 4.53961 | 0.669329 | ||||||||
\(47\) | 3.79809 | 0.554008 | 0.277004 | − | 0.960869i | \(-0.410659\pi\) | ||||
0.277004 | + | 0.960869i | \(0.410659\pi\) | |||||||
\(48\) | −3.63200 | −0.524235 | ||||||||
\(49\) | −6.15860 | −0.879800 | ||||||||
\(50\) | 0.661798 | 0.0935924 | ||||||||
\(51\) | −3.28690 | −0.460258 | ||||||||
\(52\) | 2.00407 | 0.277915 | ||||||||
\(53\) | 1.82732 | 0.251002 | 0.125501 | − | 0.992093i | \(-0.459946\pi\) | ||||
0.125501 | + | 0.992093i | \(0.459946\pi\) | |||||||
\(54\) | 0.932729 | 0.126928 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 2.16233 | 0.288954 | ||||||||
\(57\) | 2.24083 | 0.296805 | ||||||||
\(58\) | −1.57655 | −0.207011 | ||||||||
\(59\) | 7.11938 | 0.926864 | 0.463432 | − | 0.886133i | \(-0.346618\pi\) | ||||
0.463432 | + | 0.886133i | \(0.346618\pi\) | |||||||
\(60\) | 3.62750 | 0.468308 | ||||||||
\(61\) | 4.53167 | 0.580220 | 0.290110 | − | 0.956993i | \(-0.406308\pi\) | ||||
0.290110 | + | 0.956993i | \(0.406308\pi\) | |||||||
\(62\) | −0.299114 | −0.0379875 | ||||||||
\(63\) | −2.19514 | −0.276562 | ||||||||
\(64\) | 0.677218 | 0.0846522 | ||||||||
\(65\) | −1.28300 | −0.159136 | ||||||||
\(66\) | 1.53690 | 0.189179 | ||||||||
\(67\) | 4.60895 | 0.563072 | 0.281536 | − | 0.959551i | \(-0.409156\pi\) | ||||
0.281536 | + | 0.959551i | \(0.409156\pi\) | |||||||
\(68\) | −2.21083 | −0.268102 | ||||||||
\(69\) | −15.9299 | −1.91773 | ||||||||
\(70\) | −0.607052 | −0.0725566 | ||||||||
\(71\) | 13.2959 | 1.57793 | 0.788966 | − | 0.614437i | \(-0.210617\pi\) | ||||
0.788966 | + | 0.614437i | \(0.210617\pi\) | |||||||
\(72\) | −5.64137 | −0.664842 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −2.35229 | −0.273448 | ||||||||
\(75\) | −2.32231 | −0.268157 | ||||||||
\(76\) | 1.50722 | 0.172890 | ||||||||
\(77\) | 0.917277 | 0.104533 | ||||||||
\(78\) | 1.97184 | 0.223266 | ||||||||
\(79\) | −15.3671 | −1.72894 | −0.864468 | − | 0.502688i | \(-0.832344\pi\) | ||||
−0.864468 | + | 0.502688i | \(0.832344\pi\) | |||||||
\(80\) | 1.56396 | 0.174856 | ||||||||
\(81\) | −10.4524 | −1.16137 | ||||||||
\(82\) | 6.37692 | 0.704213 | ||||||||
\(83\) | 10.4012 | 1.14168 | 0.570842 | − | 0.821060i | \(-0.306617\pi\) | ||||
0.570842 | + | 0.821060i | \(0.306617\pi\) | |||||||
\(84\) | −3.32742 | −0.363051 | ||||||||
\(85\) | 1.41536 | 0.153517 | ||||||||
\(86\) | −6.88922 | −0.742884 | ||||||||
\(87\) | 5.53225 | 0.593119 | ||||||||
\(88\) | 2.35734 | 0.251293 | ||||||||
\(89\) | −6.54366 | −0.693626 | −0.346813 | − | 0.937934i | \(-0.612736\pi\) | ||||
−0.346813 | + | 0.937934i | \(0.612736\pi\) | |||||||
\(90\) | 1.58376 | 0.166942 | ||||||||
\(91\) | 1.17686 | 0.123369 | ||||||||
\(92\) | −10.7147 | −1.11709 | ||||||||
\(93\) | 1.04962 | 0.108840 | ||||||||
\(94\) | 2.51357 | 0.259255 | ||||||||
\(95\) | −0.964916 | −0.0989983 | ||||||||
\(96\) | −13.3526 | −1.36279 | ||||||||
\(97\) | −14.5876 | −1.48114 | −0.740571 | − | 0.671978i | \(-0.765445\pi\) | ||||
−0.740571 | + | 0.671978i | \(0.765445\pi\) | |||||||
\(98\) | −4.07575 | −0.411713 | ||||||||
\(99\) | −2.39311 | −0.240517 | ||||||||
\(100\) | −1.56202 | −0.156202 | ||||||||
\(101\) | −12.2234 | −1.21628 | −0.608139 | − | 0.793830i | \(-0.708084\pi\) | ||||
−0.608139 | + | 0.793830i | \(0.708084\pi\) | |||||||
\(102\) | −2.17527 | −0.215383 | ||||||||
\(103\) | 1.49878 | 0.147679 | 0.0738397 | − | 0.997270i | \(-0.476475\pi\) | ||||
0.0738397 | + | 0.997270i | \(0.476475\pi\) | |||||||
\(104\) | 3.02446 | 0.296573 | ||||||||
\(105\) | 2.13020 | 0.207886 | ||||||||
\(106\) | 1.20932 | 0.117459 | ||||||||
\(107\) | 8.47369 | 0.819183 | 0.409591 | − | 0.912269i | \(-0.365671\pi\) | ||||
0.409591 | + | 0.912269i | \(0.365671\pi\) | |||||||
\(108\) | −2.20149 | −0.211839 | ||||||||
\(109\) | 1.07096 | 0.102580 | 0.0512899 | − | 0.998684i | \(-0.483667\pi\) | ||||
0.0512899 | + | 0.998684i | \(0.483667\pi\) | |||||||
\(110\) | −0.661798 | −0.0631000 | ||||||||
\(111\) | 8.25440 | 0.783473 | ||||||||
\(112\) | −1.43459 | −0.135556 | ||||||||
\(113\) | −17.9881 | −1.69218 | −0.846089 | − | 0.533042i | \(-0.821049\pi\) | ||||
−0.846089 | + | 0.533042i | \(0.821049\pi\) | |||||||
\(114\) | 1.48298 | 0.138894 | ||||||||
\(115\) | 6.85951 | 0.639653 | ||||||||
\(116\) | 3.72108 | 0.345494 | ||||||||
\(117\) | −3.07035 | −0.283854 | ||||||||
\(118\) | 4.71159 | 0.433737 | ||||||||
\(119\) | −1.29828 | −0.119013 | ||||||||
\(120\) | 5.47447 | 0.499748 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.99905 | 0.271521 | ||||||||
\(123\) | −22.3772 | −2.01768 | ||||||||
\(124\) | 0.705991 | 0.0633998 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.45274 | −0.129421 | ||||||||
\(127\) | −1.08985 | −0.0967084 | −0.0483542 | − | 0.998830i | \(-0.515398\pi\) | ||||
−0.0483542 | + | 0.998830i | \(0.515398\pi\) | |||||||
\(128\) | −11.0512 | −0.976800 | ||||||||
\(129\) | 24.1749 | 2.12848 | ||||||||
\(130\) | −0.849085 | −0.0744697 | ||||||||
\(131\) | 0.670209 | 0.0585564 | 0.0292782 | − | 0.999571i | \(-0.490679\pi\) | ||||
0.0292782 | + | 0.999571i | \(0.490679\pi\) | |||||||
\(132\) | −3.62750 | −0.315733 | ||||||||
\(133\) | 0.885096 | 0.0767475 | ||||||||
\(134\) | 3.05019 | 0.263496 | ||||||||
\(135\) | 1.40939 | 0.121301 | ||||||||
\(136\) | −3.33649 | −0.286101 | ||||||||
\(137\) | −15.9919 | −1.36628 | −0.683138 | − | 0.730289i | \(-0.739385\pi\) | ||||
−0.683138 | + | 0.730289i | \(0.739385\pi\) | |||||||
\(138\) | −10.5424 | −0.897426 | ||||||||
\(139\) | −11.4484 | −0.971043 | −0.485521 | − | 0.874225i | \(-0.661370\pi\) | ||||
−0.485521 | + | 0.874225i | \(0.661370\pi\) | |||||||
\(140\) | 1.43281 | 0.121094 | ||||||||
\(141\) | −8.82032 | −0.742805 | ||||||||
\(142\) | 8.79919 | 0.738412 | ||||||||
\(143\) | 1.28300 | 0.107290 | ||||||||
\(144\) | 3.74274 | 0.311895 | ||||||||
\(145\) | −2.38222 | −0.197833 | ||||||||
\(146\) | 0.661798 | 0.0547708 | ||||||||
\(147\) | 14.3022 | 1.17962 | ||||||||
\(148\) | 5.55205 | 0.456376 | ||||||||
\(149\) | −11.8230 | −0.968580 | −0.484290 | − | 0.874907i | \(-0.660922\pi\) | ||||
−0.484290 | + | 0.874907i | \(0.660922\pi\) | |||||||
\(150\) | −1.53690 | −0.125487 | ||||||||
\(151\) | 3.20301 | 0.260657 | 0.130329 | − | 0.991471i | \(-0.458397\pi\) | ||||
0.130329 | + | 0.991471i | \(0.458397\pi\) | |||||||
\(152\) | 2.27464 | 0.184497 | ||||||||
\(153\) | 3.38711 | 0.273832 | ||||||||
\(154\) | 0.607052 | 0.0489177 | ||||||||
\(155\) | −0.451972 | −0.0363033 | ||||||||
\(156\) | −4.65407 | −0.372624 | ||||||||
\(157\) | 18.8438 | 1.50390 | 0.751950 | − | 0.659220i | \(-0.229113\pi\) | ||||
0.751950 | + | 0.659220i | \(0.229113\pi\) | |||||||
\(158\) | −10.1699 | −0.809076 | ||||||||
\(159\) | −4.24360 | −0.336540 | ||||||||
\(160\) | 5.74971 | 0.454554 | ||||||||
\(161\) | −6.29207 | −0.495885 | ||||||||
\(162\) | −6.91735 | −0.543478 | ||||||||
\(163\) | −1.80746 | −0.141571 | −0.0707854 | − | 0.997492i | \(-0.522551\pi\) | ||||
−0.0707854 | + | 0.997492i | \(0.522551\pi\) | |||||||
\(164\) | −15.0513 | −1.17531 | ||||||||
\(165\) | 2.32231 | 0.180791 | ||||||||
\(166\) | 6.88352 | 0.534265 | ||||||||
\(167\) | 12.8299 | 0.992806 | 0.496403 | − | 0.868092i | \(-0.334654\pi\) | ||||
0.496403 | + | 0.868092i | \(0.334654\pi\) | |||||||
\(168\) | −5.02160 | −0.387425 | ||||||||
\(169\) | −11.3539 | −0.873378 | ||||||||
\(170\) | 0.936683 | 0.0718403 | ||||||||
\(171\) | −2.30915 | −0.176585 | ||||||||
\(172\) | 16.2604 | 1.23985 | ||||||||
\(173\) | −1.30633 | −0.0993181 | −0.0496591 | − | 0.998766i | \(-0.515813\pi\) | ||||
−0.0496591 | + | 0.998766i | \(0.515813\pi\) | |||||||
\(174\) | 3.66123 | 0.277557 | ||||||||
\(175\) | −0.917277 | −0.0693396 | ||||||||
\(176\) | −1.56396 | −0.117888 | ||||||||
\(177\) | −16.5334 | −1.24272 | ||||||||
\(178\) | −4.33058 | −0.324591 | ||||||||
\(179\) | 15.7126 | 1.17441 | 0.587207 | − | 0.809437i | \(-0.300228\pi\) | ||||
0.587207 | + | 0.809437i | \(0.300228\pi\) | |||||||
\(180\) | −3.73809 | −0.278621 | ||||||||
\(181\) | −25.0696 | −1.86341 | −0.931704 | − | 0.363218i | \(-0.881678\pi\) | ||||
−0.931704 | + | 0.363218i | \(0.881678\pi\) | |||||||
\(182\) | 0.778846 | 0.0577319 | ||||||||
\(183\) | −10.5239 | −0.777951 | ||||||||
\(184\) | −16.1702 | −1.19208 | ||||||||
\(185\) | −3.55440 | −0.261324 | ||||||||
\(186\) | 0.694635 | 0.0509331 | ||||||||
\(187\) | −1.41536 | −0.103501 | ||||||||
\(188\) | −5.93270 | −0.432687 | ||||||||
\(189\) | −1.29280 | −0.0940372 | ||||||||
\(190\) | −0.638580 | −0.0463274 | ||||||||
\(191\) | −19.1417 | −1.38505 | −0.692524 | − | 0.721395i | \(-0.743501\pi\) | ||||
−0.692524 | + | 0.721395i | \(0.743501\pi\) | |||||||
\(192\) | −1.57271 | −0.113500 | ||||||||
\(193\) | 12.7752 | 0.919579 | 0.459789 | − | 0.888028i | \(-0.347925\pi\) | ||||
0.459789 | + | 0.888028i | \(0.347925\pi\) | |||||||
\(194\) | −9.65402 | −0.693118 | ||||||||
\(195\) | 2.97951 | 0.213367 | ||||||||
\(196\) | 9.61988 | 0.687134 | ||||||||
\(197\) | 5.09996 | 0.363357 | 0.181678 | − | 0.983358i | \(-0.441847\pi\) | ||||
0.181678 | + | 0.983358i | \(0.441847\pi\) | |||||||
\(198\) | −1.58376 | −0.112553 | ||||||||
\(199\) | −9.29350 | −0.658799 | −0.329399 | − | 0.944191i | \(-0.606846\pi\) | ||||
−0.329399 | + | 0.944191i | \(0.606846\pi\) | |||||||
\(200\) | −2.35734 | −0.166689 | ||||||||
\(201\) | −10.7034 | −0.754959 | ||||||||
\(202\) | −8.08945 | −0.569172 | ||||||||
\(203\) | 2.18516 | 0.153368 | ||||||||
\(204\) | 5.13422 | 0.359467 | ||||||||
\(205\) | 9.63575 | 0.672990 | ||||||||
\(206\) | 0.991891 | 0.0691083 | ||||||||
\(207\) | 16.4156 | 1.14096 | ||||||||
\(208\) | −2.00656 | −0.139130 | ||||||||
\(209\) | 0.964916 | 0.0667447 | ||||||||
\(210\) | 1.40976 | 0.0972828 | ||||||||
\(211\) | 16.2152 | 1.11630 | 0.558152 | − | 0.829739i | \(-0.311511\pi\) | ||||
0.558152 | + | 0.829739i | \(0.311511\pi\) | |||||||
\(212\) | −2.85432 | −0.196036 | ||||||||
\(213\) | −30.8771 | −2.11567 | ||||||||
\(214\) | 5.60787 | 0.383346 | ||||||||
\(215\) | −10.4099 | −0.709946 | ||||||||
\(216\) | −3.32240 | −0.226061 | ||||||||
\(217\) | 0.414583 | 0.0281438 | ||||||||
\(218\) | 0.708762 | 0.0480034 | ||||||||
\(219\) | −2.32231 | −0.156927 | ||||||||
\(220\) | 1.56202 | 0.105312 | ||||||||
\(221\) | −1.81590 | −0.122151 | ||||||||
\(222\) | 5.46274 | 0.366635 | ||||||||
\(223\) | −28.1438 | −1.88465 | −0.942323 | − | 0.334704i | \(-0.891364\pi\) | ||||
−0.942323 | + | 0.334704i | \(0.891364\pi\) | |||||||
\(224\) | −5.27407 | −0.352389 | ||||||||
\(225\) | 2.39311 | 0.159541 | ||||||||
\(226\) | −11.9045 | −0.791875 | ||||||||
\(227\) | 19.0019 | 1.26120 | 0.630600 | − | 0.776108i | \(-0.282809\pi\) | ||||
0.630600 | + | 0.776108i | \(0.282809\pi\) | |||||||
\(228\) | −3.50023 | −0.231809 | ||||||||
\(229\) | −6.80519 | −0.449699 | −0.224850 | − | 0.974393i | \(-0.572189\pi\) | ||||
−0.224850 | + | 0.974393i | \(0.572189\pi\) | |||||||
\(230\) | 4.53961 | 0.299333 | ||||||||
\(231\) | −2.13020 | −0.140157 | ||||||||
\(232\) | 5.61570 | 0.368689 | ||||||||
\(233\) | −3.68600 | −0.241478 | −0.120739 | − | 0.992684i | \(-0.538526\pi\) | ||||
−0.120739 | + | 0.992684i | \(0.538526\pi\) | |||||||
\(234\) | −2.03195 | −0.132833 | ||||||||
\(235\) | 3.79809 | 0.247760 | ||||||||
\(236\) | −11.1206 | −0.723891 | ||||||||
\(237\) | 35.6872 | 2.31813 | ||||||||
\(238\) | −0.859198 | −0.0556935 | ||||||||
\(239\) | −24.2962 | −1.57159 | −0.785796 | − | 0.618486i | \(-0.787747\pi\) | ||||
−0.785796 | + | 0.618486i | \(0.787747\pi\) | |||||||
\(240\) | −3.63200 | −0.234445 | ||||||||
\(241\) | −19.5774 | −1.26109 | −0.630544 | − | 0.776153i | \(-0.717168\pi\) | ||||
−0.630544 | + | 0.776153i | \(0.717168\pi\) | |||||||
\(242\) | 0.661798 | 0.0425420 | ||||||||
\(243\) | 20.0454 | 1.28591 | ||||||||
\(244\) | −7.07857 | −0.453159 | ||||||||
\(245\) | −6.15860 | −0.393459 | ||||||||
\(246\) | −14.8092 | −0.944198 | ||||||||
\(247\) | 1.23799 | 0.0787711 | ||||||||
\(248\) | 1.06545 | 0.0676562 | ||||||||
\(249\) | −24.1549 | −1.53075 | ||||||||
\(250\) | 0.661798 | 0.0418558 | ||||||||
\(251\) | 21.3969 | 1.35056 | 0.675280 | − | 0.737561i | \(-0.264023\pi\) | ||||
0.675280 | + | 0.737561i | \(0.264023\pi\) | |||||||
\(252\) | 3.42887 | 0.215998 | ||||||||
\(253\) | −6.85951 | −0.431254 | ||||||||
\(254\) | −0.721260 | −0.0452559 | ||||||||
\(255\) | −3.28690 | −0.205834 | ||||||||
\(256\) | −8.66812 | −0.541758 | ||||||||
\(257\) | −25.0175 | −1.56055 | −0.780276 | − | 0.625436i | \(-0.784921\pi\) | ||||
−0.780276 | + | 0.625436i | \(0.784921\pi\) | |||||||
\(258\) | 15.9989 | 0.996047 | ||||||||
\(259\) | 3.26037 | 0.202589 | ||||||||
\(260\) | 2.00407 | 0.124287 | ||||||||
\(261\) | −5.70092 | −0.352878 | ||||||||
\(262\) | 0.443543 | 0.0274022 | ||||||||
\(263\) | −4.93740 | −0.304453 | −0.152227 | − | 0.988346i | \(-0.548644\pi\) | ||||
−0.152227 | + | 0.988346i | \(0.548644\pi\) | |||||||
\(264\) | −5.47447 | −0.336930 | ||||||||
\(265\) | 1.82732 | 0.112252 | ||||||||
\(266\) | 0.585755 | 0.0359149 | ||||||||
\(267\) | 15.1964 | 0.930003 | ||||||||
\(268\) | −7.19928 | −0.439766 | ||||||||
\(269\) | −0.499581 | −0.0304600 | −0.0152300 | − | 0.999884i | \(-0.504848\pi\) | ||||
−0.0152300 | + | 0.999884i | \(0.504848\pi\) | |||||||
\(270\) | 0.932729 | 0.0567641 | ||||||||
\(271\) | −29.5644 | −1.79591 | −0.897953 | − | 0.440091i | \(-0.854946\pi\) | ||||
−0.897953 | + | 0.440091i | \(0.854946\pi\) | |||||||
\(272\) | 2.21357 | 0.134218 | ||||||||
\(273\) | −2.73304 | −0.165411 | ||||||||
\(274\) | −10.5834 | −0.639365 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 24.8829 | 1.49777 | ||||||||
\(277\) | −9.82010 | −0.590033 | −0.295016 | − | 0.955492i | \(-0.595325\pi\) | ||||
−0.295016 | + | 0.955492i | \(0.595325\pi\) | |||||||
\(278\) | −7.57655 | −0.454411 | ||||||||
\(279\) | −1.08162 | −0.0647548 | ||||||||
\(280\) | 2.16233 | 0.129224 | ||||||||
\(281\) | −3.91159 | −0.233346 | −0.116673 | − | 0.993170i | \(-0.537223\pi\) | ||||
−0.116673 | + | 0.993170i | \(0.537223\pi\) | |||||||
\(282\) | −5.83727 | −0.347604 | ||||||||
\(283\) | 0.551321 | 0.0327726 | 0.0163863 | − | 0.999866i | \(-0.494784\pi\) | ||||
0.0163863 | + | 0.999866i | \(0.494784\pi\) | |||||||
\(284\) | −20.7685 | −1.23238 | ||||||||
\(285\) | 2.24083 | 0.132735 | ||||||||
\(286\) | 0.849085 | 0.0502074 | ||||||||
\(287\) | −8.83865 | −0.521729 | ||||||||
\(288\) | 13.7597 | 0.810797 | ||||||||
\(289\) | −14.9968 | −0.882162 | ||||||||
\(290\) | −1.57655 | −0.0925781 | ||||||||
\(291\) | 33.8768 | 1.98589 | ||||||||
\(292\) | −1.56202 | −0.0914105 | ||||||||
\(293\) | 15.1630 | 0.885832 | 0.442916 | − | 0.896563i | \(-0.353944\pi\) | ||||
0.442916 | + | 0.896563i | \(0.353944\pi\) | |||||||
\(294\) | 9.46515 | 0.552018 | ||||||||
\(295\) | 7.11938 | 0.414506 | ||||||||
\(296\) | 8.37892 | 0.487015 | ||||||||
\(297\) | −1.40939 | −0.0817809 | ||||||||
\(298\) | −7.82446 | −0.453259 | ||||||||
\(299\) | −8.80073 | −0.508960 | ||||||||
\(300\) | 3.62750 | 0.209434 | ||||||||
\(301\) | 9.54872 | 0.550379 | ||||||||
\(302\) | 2.11975 | 0.121978 | ||||||||
\(303\) | 28.3866 | 1.63077 | ||||||||
\(304\) | −1.50909 | −0.0865525 | ||||||||
\(305\) | 4.53167 | 0.259482 | ||||||||
\(306\) | 2.24159 | 0.128143 | ||||||||
\(307\) | −3.00100 | −0.171276 | −0.0856382 | − | 0.996326i | \(-0.527293\pi\) | ||||
−0.0856382 | + | 0.996326i | \(0.527293\pi\) | |||||||
\(308\) | −1.43281 | −0.0816418 | ||||||||
\(309\) | −3.48063 | −0.198006 | ||||||||
\(310\) | −0.299114 | −0.0169885 | ||||||||
\(311\) | −27.5293 | −1.56104 | −0.780521 | − | 0.625129i | \(-0.785046\pi\) | ||||
−0.780521 | + | 0.625129i | \(0.785046\pi\) | |||||||
\(312\) | −7.02373 | −0.397640 | ||||||||
\(313\) | −2.10701 | −0.119095 | −0.0595476 | − | 0.998225i | \(-0.518966\pi\) | ||||
−0.0595476 | + | 0.998225i | \(0.518966\pi\) | |||||||
\(314\) | 12.4708 | 0.703768 | ||||||||
\(315\) | −2.19514 | −0.123682 | ||||||||
\(316\) | 24.0038 | 1.35032 | ||||||||
\(317\) | 22.1695 | 1.24516 | 0.622582 | − | 0.782555i | \(-0.286084\pi\) | ||||
0.622582 | + | 0.782555i | \(0.286084\pi\) | |||||||
\(318\) | −2.80841 | −0.157488 | ||||||||
\(319\) | 2.38222 | 0.133379 | ||||||||
\(320\) | 0.677218 | 0.0378576 | ||||||||
\(321\) | −19.6785 | −1.09835 | ||||||||
\(322\) | −4.16408 | −0.232055 | ||||||||
\(323\) | −1.36571 | −0.0759899 | ||||||||
\(324\) | 16.3268 | 0.907046 | ||||||||
\(325\) | −1.28300 | −0.0711679 | ||||||||
\(326\) | −1.19617 | −0.0662497 | ||||||||
\(327\) | −2.48711 | −0.137537 | ||||||||
\(328\) | −22.7147 | −1.25421 | ||||||||
\(329\) | −3.48390 | −0.192073 | ||||||||
\(330\) | 1.53690 | 0.0846035 | ||||||||
\(331\) | −31.6011 | −1.73695 | −0.868475 | − | 0.495732i | \(-0.834900\pi\) | ||||
−0.868475 | + | 0.495732i | \(0.834900\pi\) | |||||||
\(332\) | −16.2470 | −0.891669 | ||||||||
\(333\) | −8.50606 | −0.466129 | ||||||||
\(334\) | 8.49079 | 0.464595 | ||||||||
\(335\) | 4.60895 | 0.251814 | ||||||||
\(336\) | 3.33155 | 0.181751 | ||||||||
\(337\) | 15.6974 | 0.855090 | 0.427545 | − | 0.903994i | \(-0.359379\pi\) | ||||
0.427545 | + | 0.903994i | \(0.359379\pi\) | |||||||
\(338\) | −7.51400 | −0.408708 | ||||||||
\(339\) | 41.7739 | 2.26885 | ||||||||
\(340\) | −2.21083 | −0.119899 | ||||||||
\(341\) | 0.451972 | 0.0244757 | ||||||||
\(342\) | −1.52819 | −0.0826351 | ||||||||
\(343\) | 12.0701 | 0.651723 | ||||||||
\(344\) | 24.5396 | 1.32308 | ||||||||
\(345\) | −15.9299 | −0.857636 | ||||||||
\(346\) | −0.864524 | −0.0464771 | ||||||||
\(347\) | −18.1016 | −0.971744 | −0.485872 | − | 0.874030i | \(-0.661498\pi\) | ||||
−0.485872 | + | 0.874030i | \(0.661498\pi\) | |||||||
\(348\) | −8.64150 | −0.463233 | ||||||||
\(349\) | 13.0476 | 0.698424 | 0.349212 | − | 0.937044i | \(-0.386449\pi\) | ||||
0.349212 | + | 0.937044i | \(0.386449\pi\) | |||||||
\(350\) | −0.607052 | −0.0324483 | ||||||||
\(351\) | −1.80824 | −0.0965166 | ||||||||
\(352\) | −5.74971 | −0.306460 | ||||||||
\(353\) | −16.9950 | −0.904555 | −0.452278 | − | 0.891877i | \(-0.649388\pi\) | ||||
−0.452278 | + | 0.891877i | \(0.649388\pi\) | |||||||
\(354\) | −10.9418 | −0.581548 | ||||||||
\(355\) | 13.2959 | 0.705672 | ||||||||
\(356\) | 10.2213 | 0.541730 | ||||||||
\(357\) | 3.01500 | 0.159571 | ||||||||
\(358\) | 10.3986 | 0.549581 | ||||||||
\(359\) | 31.8130 | 1.67903 | 0.839514 | − | 0.543339i | \(-0.182840\pi\) | ||||
0.839514 | + | 0.543339i | \(0.182840\pi\) | |||||||
\(360\) | −5.64137 | −0.297326 | ||||||||
\(361\) | −18.0689 | −0.950997 | ||||||||
\(362\) | −16.5910 | −0.872004 | ||||||||
\(363\) | −2.32231 | −0.121890 | ||||||||
\(364\) | −1.83829 | −0.0963525 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −6.96471 | −0.364051 | ||||||||
\(367\) | −24.1869 | −1.26255 | −0.631274 | − | 0.775560i | \(-0.717468\pi\) | ||||
−0.631274 | + | 0.775560i | \(0.717468\pi\) | |||||||
\(368\) | 10.7280 | 0.559237 | ||||||||
\(369\) | 23.0594 | 1.20042 | ||||||||
\(370\) | −2.35229 | −0.122290 | ||||||||
\(371\) | −1.67616 | −0.0870219 | ||||||||
\(372\) | −1.63953 | −0.0850055 | ||||||||
\(373\) | 6.68523 | 0.346148 | 0.173074 | − | 0.984909i | \(-0.444630\pi\) | ||||
0.173074 | + | 0.984909i | \(0.444630\pi\) | |||||||
\(374\) | −0.936683 | −0.0484347 | ||||||||
\(375\) | −2.32231 | −0.119923 | ||||||||
\(376\) | −8.95338 | −0.461735 | ||||||||
\(377\) | 3.05638 | 0.157412 | ||||||||
\(378\) | −0.855571 | −0.0440058 | ||||||||
\(379\) | −28.3191 | −1.45466 | −0.727328 | − | 0.686290i | \(-0.759238\pi\) | ||||
−0.727328 | + | 0.686290i | \(0.759238\pi\) | |||||||
\(380\) | 1.50722 | 0.0773189 | ||||||||
\(381\) | 2.53096 | 0.129665 | ||||||||
\(382\) | −12.6680 | −0.648149 | ||||||||
\(383\) | −24.2648 | −1.23987 | −0.619937 | − | 0.784652i | \(-0.712842\pi\) | ||||
−0.619937 | + | 0.784652i | \(0.712842\pi\) | |||||||
\(384\) | 25.6644 | 1.30968 | ||||||||
\(385\) | 0.917277 | 0.0467488 | ||||||||
\(386\) | 8.45460 | 0.430328 | ||||||||
\(387\) | −24.9119 | −1.26634 | ||||||||
\(388\) | 22.7861 | 1.15679 | ||||||||
\(389\) | 23.7608 | 1.20472 | 0.602360 | − | 0.798224i | \(-0.294227\pi\) | ||||
0.602360 | + | 0.798224i | \(0.294227\pi\) | |||||||
\(390\) | 1.97184 | 0.0998478 | ||||||||
\(391\) | 9.70868 | 0.490989 | ||||||||
\(392\) | 14.5179 | 0.733266 | ||||||||
\(393\) | −1.55643 | −0.0785116 | ||||||||
\(394\) | 3.37514 | 0.170037 | ||||||||
\(395\) | −15.3671 | −0.773203 | ||||||||
\(396\) | 3.73809 | 0.187846 | ||||||||
\(397\) | 35.0518 | 1.75920 | 0.879599 | − | 0.475717i | \(-0.157811\pi\) | ||||
0.879599 | + | 0.475717i | \(0.157811\pi\) | |||||||
\(398\) | −6.15042 | −0.308293 | ||||||||
\(399\) | −2.05546 | −0.102902 | ||||||||
\(400\) | 1.56396 | 0.0781982 | ||||||||
\(401\) | 18.7538 | 0.936521 | 0.468261 | − | 0.883590i | \(-0.344881\pi\) | ||||
0.468261 | + | 0.883590i | \(0.344881\pi\) | |||||||
\(402\) | −7.08348 | −0.353292 | ||||||||
\(403\) | 0.579879 | 0.0288858 | ||||||||
\(404\) | 19.0933 | 0.949928 | ||||||||
\(405\) | −10.4524 | −0.519382 | ||||||||
\(406\) | 1.44613 | 0.0717703 | ||||||||
\(407\) | 3.55440 | 0.176185 | ||||||||
\(408\) | 7.74835 | 0.383600 | ||||||||
\(409\) | 29.3706 | 1.45228 | 0.726141 | − | 0.687545i | \(-0.241312\pi\) | ||||
0.726141 | + | 0.687545i | \(0.241312\pi\) | |||||||
\(410\) | 6.37692 | 0.314934 | ||||||||
\(411\) | 37.1380 | 1.83188 | ||||||||
\(412\) | −2.34113 | −0.115339 | ||||||||
\(413\) | −6.53044 | −0.321342 | ||||||||
\(414\) | 10.8638 | 0.533926 | ||||||||
\(415\) | 10.4012 | 0.510577 | ||||||||
\(416\) | −7.37686 | −0.361680 | ||||||||
\(417\) | 26.5868 | 1.30196 | ||||||||
\(418\) | 0.638580 | 0.0312340 | ||||||||
\(419\) | 2.24786 | 0.109815 | 0.0549075 | − | 0.998491i | \(-0.482514\pi\) | ||||
0.0549075 | + | 0.998491i | \(0.482514\pi\) | |||||||
\(420\) | −3.32742 | −0.162361 | ||||||||
\(421\) | −20.4664 | −0.997470 | −0.498735 | − | 0.866755i | \(-0.666202\pi\) | ||||
−0.498735 | + | 0.866755i | \(0.666202\pi\) | |||||||
\(422\) | 10.7312 | 0.522388 | ||||||||
\(423\) | 9.08924 | 0.441934 | ||||||||
\(424\) | −4.30762 | −0.209197 | ||||||||
\(425\) | 1.41536 | 0.0686551 | ||||||||
\(426\) | −20.4344 | −0.990051 | ||||||||
\(427\) | −4.15679 | −0.201161 | ||||||||
\(428\) | −13.2361 | −0.639791 | ||||||||
\(429\) | −2.97951 | −0.143852 | ||||||||
\(430\) | −6.88922 | −0.332228 | ||||||||
\(431\) | 32.6318 | 1.57182 | 0.785908 | − | 0.618343i | \(-0.212196\pi\) | ||||
0.785908 | + | 0.618343i | \(0.212196\pi\) | |||||||
\(432\) | 2.20423 | 0.106051 | ||||||||
\(433\) | −7.20781 | −0.346385 | −0.173193 | − | 0.984888i | \(-0.555408\pi\) | ||||
−0.173193 | + | 0.984888i | \(0.555408\pi\) | |||||||
\(434\) | 0.274371 | 0.0131702 | ||||||||
\(435\) | 5.53225 | 0.265251 | ||||||||
\(436\) | −1.67287 | −0.0801160 | ||||||||
\(437\) | −6.61885 | −0.316623 | ||||||||
\(438\) | −1.53690 | −0.0734358 | ||||||||
\(439\) | −35.1285 | −1.67659 | −0.838296 | − | 0.545216i | \(-0.816448\pi\) | ||||
−0.838296 | + | 0.545216i | \(0.816448\pi\) | |||||||
\(440\) | 2.35734 | 0.112382 | ||||||||
\(441\) | −14.7382 | −0.701820 | ||||||||
\(442\) | −1.20176 | −0.0571620 | ||||||||
\(443\) | 10.1155 | 0.480600 | 0.240300 | − | 0.970699i | \(-0.422754\pi\) | ||||
0.240300 | + | 0.970699i | \(0.422754\pi\) | |||||||
\(444\) | −12.8936 | −0.611901 | ||||||||
\(445\) | −6.54366 | −0.310199 | ||||||||
\(446\) | −18.6255 | −0.881943 | ||||||||
\(447\) | 27.4567 | 1.29866 | ||||||||
\(448\) | −0.621196 | −0.0293488 | ||||||||
\(449\) | −14.1635 | −0.668415 | −0.334208 | − | 0.942500i | \(-0.608469\pi\) | ||||
−0.334208 | + | 0.942500i | \(0.608469\pi\) | |||||||
\(450\) | 1.58376 | 0.0746589 | ||||||||
\(451\) | −9.63575 | −0.453730 | ||||||||
\(452\) | 28.0978 | 1.32161 | ||||||||
\(453\) | −7.43837 | −0.349485 | ||||||||
\(454\) | 12.5754 | 0.590193 | ||||||||
\(455\) | 1.17686 | 0.0551722 | ||||||||
\(456\) | −5.28240 | −0.247371 | ||||||||
\(457\) | 3.67434 | 0.171878 | 0.0859391 | − | 0.996300i | \(-0.472611\pi\) | ||||
0.0859391 | + | 0.996300i | \(0.472611\pi\) | |||||||
\(458\) | −4.50366 | −0.210442 | ||||||||
\(459\) | 1.99479 | 0.0931088 | ||||||||
\(460\) | −10.7147 | −0.499576 | ||||||||
\(461\) | 4.89385 | 0.227929 | 0.113965 | − | 0.993485i | \(-0.463645\pi\) | ||||
0.113965 | + | 0.993485i | \(0.463645\pi\) | |||||||
\(462\) | −1.40976 | −0.0655880 | ||||||||
\(463\) | 22.0672 | 1.02555 | 0.512774 | − | 0.858523i | \(-0.328618\pi\) | ||||
0.512774 | + | 0.858523i | \(0.328618\pi\) | |||||||
\(464\) | −3.72571 | −0.172962 | ||||||||
\(465\) | 1.04962 | 0.0486749 | ||||||||
\(466\) | −2.43939 | −0.113002 | ||||||||
\(467\) | −8.77814 | −0.406204 | −0.203102 | − | 0.979158i | \(-0.565102\pi\) | ||||
−0.203102 | + | 0.979158i | \(0.565102\pi\) | |||||||
\(468\) | 4.79596 | 0.221693 | ||||||||
\(469\) | −4.22768 | −0.195216 | ||||||||
\(470\) | 2.51357 | 0.115942 | ||||||||
\(471\) | −43.7611 | −2.01641 | ||||||||
\(472\) | −16.7828 | −0.772491 | ||||||||
\(473\) | 10.4099 | 0.478646 | ||||||||
\(474\) | 23.6177 | 1.08480 | ||||||||
\(475\) | −0.964916 | −0.0442734 | ||||||||
\(476\) | 2.02794 | 0.0929505 | ||||||||
\(477\) | 4.37298 | 0.200225 | ||||||||
\(478\) | −16.0792 | −0.735445 | ||||||||
\(479\) | 27.7489 | 1.26788 | 0.633939 | − | 0.773383i | \(-0.281437\pi\) | ||||
0.633939 | + | 0.773383i | \(0.281437\pi\) | |||||||
\(480\) | −13.3526 | −0.609459 | ||||||||
\(481\) | 4.56028 | 0.207931 | ||||||||
\(482\) | −12.9563 | −0.590141 | ||||||||
\(483\) | 14.6121 | 0.664874 | ||||||||
\(484\) | −1.56202 | −0.0710011 | ||||||||
\(485\) | −14.5876 | −0.662387 | ||||||||
\(486\) | 13.2660 | 0.601759 | ||||||||
\(487\) | 30.3206 | 1.37396 | 0.686979 | − | 0.726677i | \(-0.258936\pi\) | ||||
0.686979 | + | 0.726677i | \(0.258936\pi\) | |||||||
\(488\) | −10.6827 | −0.483582 | ||||||||
\(489\) | 4.19747 | 0.189816 | ||||||||
\(490\) | −4.07575 | −0.184124 | ||||||||
\(491\) | 18.5130 | 0.835481 | 0.417740 | − | 0.908566i | \(-0.362822\pi\) | ||||
0.417740 | + | 0.908566i | \(0.362822\pi\) | |||||||
\(492\) | 34.9537 | 1.57583 | ||||||||
\(493\) | −3.37170 | −0.151854 | ||||||||
\(494\) | 0.819296 | 0.0368619 | ||||||||
\(495\) | −2.39311 | −0.107562 | ||||||||
\(496\) | −0.706868 | −0.0317393 | ||||||||
\(497\) | −12.1960 | −0.547066 | ||||||||
\(498\) | −15.9856 | −0.716334 | ||||||||
\(499\) | −33.3043 | −1.49090 | −0.745452 | − | 0.666560i | \(-0.767766\pi\) | ||||
−0.745452 | + | 0.666560i | \(0.767766\pi\) | |||||||
\(500\) | −1.56202 | −0.0698558 | ||||||||
\(501\) | −29.7949 | −1.33114 | ||||||||
\(502\) | 14.1604 | 0.632011 | ||||||||
\(503\) | 1.04345 | 0.0465251 | 0.0232626 | − | 0.999729i | \(-0.492595\pi\) | ||||
0.0232626 | + | 0.999729i | \(0.492595\pi\) | |||||||
\(504\) | 5.17470 | 0.230500 | ||||||||
\(505\) | −12.2234 | −0.543936 | ||||||||
\(506\) | −4.53961 | −0.201810 | ||||||||
\(507\) | 26.3673 | 1.17101 | ||||||||
\(508\) | 1.70237 | 0.0755304 | ||||||||
\(509\) | −29.7330 | −1.31789 | −0.658946 | − | 0.752190i | \(-0.728997\pi\) | ||||
−0.658946 | + | 0.752190i | \(0.728997\pi\) | |||||||
\(510\) | −2.17527 | −0.0963224 | ||||||||
\(511\) | −0.917277 | −0.0405779 | ||||||||
\(512\) | 16.3659 | 0.723279 | ||||||||
\(513\) | −1.35994 | −0.0600428 | ||||||||
\(514\) | −16.5566 | −0.730279 | ||||||||
\(515\) | 1.49878 | 0.0660443 | ||||||||
\(516\) | −37.7617 | −1.66237 | ||||||||
\(517\) | −3.79809 | −0.167040 | ||||||||
\(518\) | 2.15770 | 0.0948040 | ||||||||
\(519\) | 3.03369 | 0.133164 | ||||||||
\(520\) | 3.02446 | 0.132631 | ||||||||
\(521\) | −26.2559 | −1.15029 | −0.575145 | − | 0.818051i | \(-0.695054\pi\) | ||||
−0.575145 | + | 0.818051i | \(0.695054\pi\) | |||||||
\(522\) | −3.77285 | −0.165133 | ||||||||
\(523\) | −3.97375 | −0.173760 | −0.0868799 | − | 0.996219i | \(-0.527690\pi\) | ||||
−0.0868799 | + | 0.996219i | \(0.527690\pi\) | |||||||
\(524\) | −1.04688 | −0.0457333 | ||||||||
\(525\) | 2.13020 | 0.0929695 | ||||||||
\(526\) | −3.26756 | −0.142473 | ||||||||
\(527\) | −0.639703 | −0.0278659 | ||||||||
\(528\) | 3.63200 | 0.158063 | ||||||||
\(529\) | 24.0529 | 1.04578 | ||||||||
\(530\) | 1.20932 | 0.0525294 | ||||||||
\(531\) | 17.0374 | 0.739362 | ||||||||
\(532\) | −1.38254 | −0.0599407 | ||||||||
\(533\) | −12.3626 | −0.535485 | ||||||||
\(534\) | 10.0569 | 0.435206 | ||||||||
\(535\) | 8.47369 | 0.366350 | ||||||||
\(536\) | −10.8649 | −0.469290 | ||||||||
\(537\) | −36.4894 | −1.57463 | ||||||||
\(538\) | −0.330622 | −0.0142541 | ||||||||
\(539\) | 6.15860 | 0.265270 | ||||||||
\(540\) | −2.20149 | −0.0947372 | ||||||||
\(541\) | −15.6625 | −0.673382 | −0.336691 | − | 0.941615i | \(-0.609308\pi\) | ||||
−0.336691 | + | 0.941615i | \(0.609308\pi\) | |||||||
\(542\) | −19.5656 | −0.840416 | ||||||||
\(543\) | 58.2193 | 2.49843 | ||||||||
\(544\) | 8.13791 | 0.348910 | ||||||||
\(545\) | 1.07096 | 0.0458751 | ||||||||
\(546\) | −1.80872 | −0.0774061 | ||||||||
\(547\) | 14.7392 | 0.630202 | 0.315101 | − | 0.949058i | \(-0.397962\pi\) | ||||
0.315101 | + | 0.949058i | \(0.397962\pi\) | |||||||
\(548\) | 24.9796 | 1.06708 | ||||||||
\(549\) | 10.8448 | 0.462844 | ||||||||
\(550\) | −0.661798 | −0.0282192 | ||||||||
\(551\) | 2.29864 | 0.0979255 | ||||||||
\(552\) | 37.5522 | 1.59833 | ||||||||
\(553\) | 14.0959 | 0.599419 | ||||||||
\(554\) | −6.49892 | −0.276113 | ||||||||
\(555\) | 8.25440 | 0.350380 | ||||||||
\(556\) | 17.8827 | 0.758396 | ||||||||
\(557\) | −24.5129 | −1.03864 | −0.519322 | − | 0.854578i | \(-0.673816\pi\) | ||||
−0.519322 | + | 0.854578i | \(0.673816\pi\) | |||||||
\(558\) | −0.715813 | −0.0303028 | ||||||||
\(559\) | 13.3558 | 0.564891 | ||||||||
\(560\) | −1.43459 | −0.0606224 | ||||||||
\(561\) | 3.28690 | 0.138773 | ||||||||
\(562\) | −2.58868 | −0.109197 | ||||||||
\(563\) | 3.42956 | 0.144539 | 0.0722694 | − | 0.997385i | \(-0.476976\pi\) | ||||
0.0722694 | + | 0.997385i | \(0.476976\pi\) | |||||||
\(564\) | 13.7775 | 0.580139 | ||||||||
\(565\) | −17.9881 | −0.756765 | ||||||||
\(566\) | 0.364863 | 0.0153363 | ||||||||
\(567\) | 9.58770 | 0.402646 | ||||||||
\(568\) | −31.3429 | −1.31512 | ||||||||
\(569\) | 15.0678 | 0.631676 | 0.315838 | − | 0.948813i | \(-0.397714\pi\) | ||||
0.315838 | + | 0.948813i | \(0.397714\pi\) | |||||||
\(570\) | 1.48298 | 0.0621151 | ||||||||
\(571\) | −15.7541 | −0.659289 | −0.329644 | − | 0.944105i | \(-0.606929\pi\) | ||||
−0.329644 | + | 0.944105i | \(0.606929\pi\) | |||||||
\(572\) | −2.00407 | −0.0837944 | ||||||||
\(573\) | 44.4530 | 1.85705 | ||||||||
\(574\) | −5.84940 | −0.244149 | ||||||||
\(575\) | 6.85951 | 0.286061 | ||||||||
\(576\) | 1.62066 | 0.0675273 | ||||||||
\(577\) | 22.1891 | 0.923744 | 0.461872 | − | 0.886946i | \(-0.347178\pi\) | ||||
0.461872 | + | 0.886946i | \(0.347178\pi\) | |||||||
\(578\) | −9.92482 | −0.412818 | ||||||||
\(579\) | −29.6679 | −1.23296 | ||||||||
\(580\) | 3.72108 | 0.154510 | ||||||||
\(581\) | −9.54082 | −0.395820 | ||||||||
\(582\) | 22.4196 | 0.929322 | ||||||||
\(583\) | −1.82732 | −0.0756800 | ||||||||
\(584\) | −2.35734 | −0.0975474 | ||||||||
\(585\) | −3.07035 | −0.126943 | ||||||||
\(586\) | 10.0348 | 0.414536 | ||||||||
\(587\) | 24.3443 | 1.00480 | 0.502398 | − | 0.864636i | \(-0.332451\pi\) | ||||
0.502398 | + | 0.864636i | \(0.332451\pi\) | |||||||
\(588\) | −22.3403 | −0.921299 | ||||||||
\(589\) | 0.436115 | 0.0179698 | ||||||||
\(590\) | 4.71159 | 0.193973 | ||||||||
\(591\) | −11.8437 | −0.487183 | ||||||||
\(592\) | −5.55895 | −0.228471 | ||||||||
\(593\) | 17.7642 | 0.729490 | 0.364745 | − | 0.931107i | \(-0.381156\pi\) | ||||
0.364745 | + | 0.931107i | \(0.381156\pi\) | |||||||
\(594\) | −0.932729 | −0.0382703 | ||||||||
\(595\) | −1.29828 | −0.0532242 | ||||||||
\(596\) | 18.4679 | 0.756473 | ||||||||
\(597\) | 21.5824 | 0.883307 | ||||||||
\(598\) | −5.82431 | −0.238174 | ||||||||
\(599\) | 34.4258 | 1.40660 | 0.703301 | − | 0.710893i | \(-0.251709\pi\) | ||||
0.703301 | + | 0.710893i | \(0.251709\pi\) | |||||||
\(600\) | 5.47447 | 0.223494 | ||||||||
\(601\) | 47.5927 | 1.94135 | 0.970674 | − | 0.240399i | \(-0.0772783\pi\) | ||||
0.970674 | + | 0.240399i | \(0.0772783\pi\) | |||||||
\(602\) | 6.31932 | 0.257556 | ||||||||
\(603\) | 11.0297 | 0.449165 | ||||||||
\(604\) | −5.00318 | −0.203576 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 18.7862 | 0.763137 | ||||||||
\(607\) | −7.92900 | −0.321828 | −0.160914 | − | 0.986968i | \(-0.551444\pi\) | ||||
−0.160914 | + | 0.986968i | \(0.551444\pi\) | |||||||
\(608\) | −5.54799 | −0.225001 | ||||||||
\(609\) | −5.07460 | −0.205633 | ||||||||
\(610\) | 2.99905 | 0.121428 | ||||||||
\(611\) | −4.87293 | −0.197138 | ||||||||
\(612\) | −5.29075 | −0.213866 | ||||||||
\(613\) | −42.2364 | −1.70591 | −0.852956 | − | 0.521983i | \(-0.825193\pi\) | ||||
−0.852956 | + | 0.521983i | \(0.825193\pi\) | |||||||
\(614\) | −1.98606 | −0.0801508 | ||||||||
\(615\) | −22.3772 | −0.902335 | ||||||||
\(616\) | −2.16233 | −0.0871229 | ||||||||
\(617\) | 11.8654 | 0.477683 | 0.238842 | − | 0.971059i | \(-0.423232\pi\) | ||||
0.238842 | + | 0.971059i | \(0.423232\pi\) | |||||||
\(618\) | −2.30348 | −0.0926594 | ||||||||
\(619\) | 1.88074 | 0.0755933 | 0.0377967 | − | 0.999285i | \(-0.487966\pi\) | ||||
0.0377967 | + | 0.999285i | \(0.487966\pi\) | |||||||
\(620\) | 0.705991 | 0.0283533 | ||||||||
\(621\) | 9.66770 | 0.387951 | ||||||||
\(622\) | −18.2188 | −0.730509 | ||||||||
\(623\) | 6.00235 | 0.240479 | ||||||||
\(624\) | 4.65985 | 0.186543 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −1.39441 | −0.0557320 | ||||||||
\(627\) | −2.24083 | −0.0894902 | ||||||||
\(628\) | −29.4345 | −1.17456 | ||||||||
\(629\) | −5.03075 | −0.200589 | ||||||||
\(630\) | −1.45274 | −0.0578786 | ||||||||
\(631\) | 36.9963 | 1.47280 | 0.736400 | − | 0.676547i | \(-0.236524\pi\) | ||||
0.736400 | + | 0.676547i | \(0.236524\pi\) | |||||||
\(632\) | 36.2255 | 1.44097 | ||||||||
\(633\) | −37.6568 | −1.49672 | ||||||||
\(634\) | 14.6717 | 0.582689 | ||||||||
\(635\) | −1.08985 | −0.0432493 | ||||||||
\(636\) | 6.62861 | 0.262841 | ||||||||
\(637\) | 7.90147 | 0.313068 | ||||||||
\(638\) | 1.57655 | 0.0624162 | ||||||||
\(639\) | 31.8185 | 1.25872 | ||||||||
\(640\) | −11.0512 | −0.436838 | ||||||||
\(641\) | −22.8528 | −0.902630 | −0.451315 | − | 0.892365i | \(-0.649045\pi\) | ||||
−0.451315 | + | 0.892365i | \(0.649045\pi\) | |||||||
\(642\) | −13.0232 | −0.513985 | ||||||||
\(643\) | 26.9278 | 1.06193 | 0.530964 | − | 0.847394i | \(-0.321830\pi\) | ||||
0.530964 | + | 0.847394i | \(0.321830\pi\) | |||||||
\(644\) | 9.82836 | 0.387292 | ||||||||
\(645\) | 24.1749 | 0.951885 | ||||||||
\(646\) | −0.903821 | −0.0355604 | ||||||||
\(647\) | −27.4271 | −1.07827 | −0.539136 | − | 0.842219i | \(-0.681249\pi\) | ||||
−0.539136 | + | 0.842219i | \(0.681249\pi\) | |||||||
\(648\) | 24.6398 | 0.967941 | ||||||||
\(649\) | −7.11938 | −0.279460 | ||||||||
\(650\) | −0.849085 | −0.0333039 | ||||||||
\(651\) | −0.962790 | −0.0377347 | ||||||||
\(652\) | 2.82329 | 0.110568 | ||||||||
\(653\) | −3.01776 | −0.118094 | −0.0590470 | − | 0.998255i | \(-0.518806\pi\) | ||||
−0.0590470 | + | 0.998255i | \(0.518806\pi\) | |||||||
\(654\) | −1.64596 | −0.0643622 | ||||||||
\(655\) | 0.670209 | 0.0261872 | ||||||||
\(656\) | 15.0700 | 0.588383 | ||||||||
\(657\) | 2.39311 | 0.0933641 | ||||||||
\(658\) | −2.30564 | −0.0898830 | ||||||||
\(659\) | −26.0426 | −1.01448 | −0.507239 | − | 0.861806i | \(-0.669334\pi\) | ||||
−0.507239 | + | 0.861806i | \(0.669334\pi\) | |||||||
\(660\) | −3.62750 | −0.141200 | ||||||||
\(661\) | 23.8916 | 0.929276 | 0.464638 | − | 0.885501i | \(-0.346185\pi\) | ||||
0.464638 | + | 0.885501i | \(0.346185\pi\) | |||||||
\(662\) | −20.9135 | −0.812827 | ||||||||
\(663\) | 4.21709 | 0.163778 | ||||||||
\(664\) | −24.5193 | −0.951532 | ||||||||
\(665\) | 0.885096 | 0.0343225 | ||||||||
\(666\) | −5.62929 | −0.218131 | ||||||||
\(667\) | −16.3409 | −0.632721 | ||||||||
\(668\) | −20.0406 | −0.775393 | ||||||||
\(669\) | 65.3585 | 2.52690 | ||||||||
\(670\) | 3.05019 | 0.117839 | ||||||||
\(671\) | −4.53167 | −0.174943 | ||||||||
\(672\) | 12.2480 | 0.472478 | ||||||||
\(673\) | −39.6098 | −1.52684 | −0.763422 | − | 0.645900i | \(-0.776482\pi\) | ||||
−0.763422 | + | 0.645900i | \(0.776482\pi\) | |||||||
\(674\) | 10.3885 | 0.400150 | ||||||||
\(675\) | 1.40939 | 0.0542473 | ||||||||
\(676\) | 17.7351 | 0.682119 | ||||||||
\(677\) | 41.5613 | 1.59733 | 0.798665 | − | 0.601775i | \(-0.205540\pi\) | ||||
0.798665 | + | 0.601775i | \(0.205540\pi\) | |||||||
\(678\) | 27.6459 | 1.06173 | ||||||||
\(679\) | 13.3808 | 0.513509 | ||||||||
\(680\) | −3.33649 | −0.127948 | ||||||||
\(681\) | −44.1282 | −1.69100 | ||||||||
\(682\) | 0.299114 | 0.0114537 | ||||||||
\(683\) | −7.14032 | −0.273217 | −0.136608 | − | 0.990625i | \(-0.543620\pi\) | ||||
−0.136608 | + | 0.990625i | \(0.543620\pi\) | |||||||
\(684\) | 3.60695 | 0.137915 | ||||||||
\(685\) | −15.9919 | −0.611017 | ||||||||
\(686\) | 7.98796 | 0.304982 | ||||||||
\(687\) | 15.8037 | 0.602950 | ||||||||
\(688\) | −16.2806 | −0.620693 | ||||||||
\(689\) | −2.34445 | −0.0893164 | ||||||||
\(690\) | −10.5424 | −0.401341 | ||||||||
\(691\) | 35.1901 | 1.33869 | 0.669347 | − | 0.742950i | \(-0.266574\pi\) | ||||
0.669347 | + | 0.742950i | \(0.266574\pi\) | |||||||
\(692\) | 2.04051 | 0.0775686 | ||||||||
\(693\) | 2.19514 | 0.0833866 | ||||||||
\(694\) | −11.9796 | −0.454739 | ||||||||
\(695\) | −11.4484 | −0.434264 | ||||||||
\(696\) | −13.0414 | −0.494333 | ||||||||
\(697\) | 13.6381 | 0.516579 | ||||||||
\(698\) | 8.63490 | 0.326836 | ||||||||
\(699\) | 8.56002 | 0.323770 | ||||||||
\(700\) | 1.43281 | 0.0541551 | ||||||||
\(701\) | −28.9200 | −1.09229 | −0.546147 | − | 0.837689i | \(-0.683906\pi\) | ||||
−0.546147 | + | 0.837689i | \(0.683906\pi\) | |||||||
\(702\) | −1.19669 | −0.0451661 | ||||||||
\(703\) | 3.42969 | 0.129353 | ||||||||
\(704\) | −0.677218 | −0.0255236 | ||||||||
\(705\) | −8.82032 | −0.332193 | ||||||||
\(706\) | −11.2473 | −0.423297 | ||||||||
\(707\) | 11.2123 | 0.421681 | ||||||||
\(708\) | 25.8255 | 0.970583 | ||||||||
\(709\) | −2.03807 | −0.0765415 | −0.0382707 | − | 0.999267i | \(-0.512185\pi\) | ||||
−0.0382707 | + | 0.999267i | \(0.512185\pi\) | |||||||
\(710\) | 8.79919 | 0.330228 | ||||||||
\(711\) | −36.7752 | −1.37918 | ||||||||
\(712\) | 15.4256 | 0.578100 | ||||||||
\(713\) | −3.10031 | −0.116107 | ||||||||
\(714\) | 1.99532 | 0.0746730 | ||||||||
\(715\) | 1.28300 | 0.0479814 | ||||||||
\(716\) | −24.5434 | −0.917230 | ||||||||
\(717\) | 56.4233 | 2.10717 | ||||||||
\(718\) | 21.0538 | 0.785721 | ||||||||
\(719\) | 15.4012 | 0.574367 | 0.287183 | − | 0.957876i | \(-0.407281\pi\) | ||||
0.287183 | + | 0.957876i | \(0.407281\pi\) | |||||||
\(720\) | 3.74274 | 0.139484 | ||||||||
\(721\) | −1.37480 | −0.0512002 | ||||||||
\(722\) | −11.9580 | −0.445030 | ||||||||
\(723\) | 45.4646 | 1.69085 | ||||||||
\(724\) | 39.1593 | 1.45534 | ||||||||
\(725\) | −2.38222 | −0.0884735 | ||||||||
\(726\) | −1.53690 | −0.0570396 | ||||||||
\(727\) | 32.7586 | 1.21495 | 0.607475 | − | 0.794339i | \(-0.292182\pi\) | ||||
0.607475 | + | 0.794339i | \(0.292182\pi\) | |||||||
\(728\) | −2.77427 | −0.102821 | ||||||||
\(729\) | −15.1946 | −0.562761 | ||||||||
\(730\) | 0.661798 | 0.0244942 | ||||||||
\(731\) | −14.7337 | −0.544946 | ||||||||
\(732\) | 16.4386 | 0.607589 | ||||||||
\(733\) | −26.5594 | −0.980993 | −0.490496 | − | 0.871443i | \(-0.663184\pi\) | ||||
−0.490496 | + | 0.871443i | \(0.663184\pi\) | |||||||
\(734\) | −16.0069 | −0.590824 | ||||||||
\(735\) | 14.3022 | 0.527543 | ||||||||
\(736\) | 39.4402 | 1.45378 | ||||||||
\(737\) | −4.60895 | −0.169773 | ||||||||
\(738\) | 15.2607 | 0.561753 | ||||||||
\(739\) | 40.2441 | 1.48040 | 0.740202 | − | 0.672384i | \(-0.234730\pi\) | ||||
0.740202 | + | 0.672384i | \(0.234730\pi\) | |||||||
\(740\) | 5.55205 | 0.204097 | ||||||||
\(741\) | −2.87498 | −0.105615 | ||||||||
\(742\) | −1.10928 | −0.0407230 | ||||||||
\(743\) | 26.7560 | 0.981584 | 0.490792 | − | 0.871277i | \(-0.336707\pi\) | ||||
0.490792 | + | 0.871277i | \(0.336707\pi\) | |||||||
\(744\) | −2.47431 | −0.0907124 | ||||||||
\(745\) | −11.8230 | −0.433162 | ||||||||
\(746\) | 4.42427 | 0.161984 | ||||||||
\(747\) | 24.8913 | 0.910725 | ||||||||
\(748\) | 2.21083 | 0.0808358 | ||||||||
\(749\) | −7.77272 | −0.284009 | ||||||||
\(750\) | −1.53690 | −0.0561196 | ||||||||
\(751\) | −28.9489 | −1.05636 | −0.528179 | − | 0.849133i | \(-0.677125\pi\) | ||||
−0.528179 | + | 0.849133i | \(0.677125\pi\) | |||||||
\(752\) | 5.94007 | 0.216612 | ||||||||
\(753\) | −49.6902 | −1.81081 | ||||||||
\(754\) | 2.02271 | 0.0736627 | ||||||||
\(755\) | 3.20301 | 0.116569 | ||||||||
\(756\) | 2.01938 | 0.0734441 | ||||||||
\(757\) | 21.0738 | 0.765940 | 0.382970 | − | 0.923761i | \(-0.374901\pi\) | ||||
0.382970 | + | 0.923761i | \(0.374901\pi\) | |||||||
\(758\) | −18.7415 | −0.680724 | ||||||||
\(759\) | 15.9299 | 0.578218 | ||||||||
\(760\) | 2.27464 | 0.0825097 | ||||||||
\(761\) | −32.6056 | −1.18195 | −0.590975 | − | 0.806690i | \(-0.701257\pi\) | ||||
−0.590975 | + | 0.806690i | \(0.701257\pi\) | |||||||
\(762\) | 1.67499 | 0.0606784 | ||||||||
\(763\) | −0.982371 | −0.0355642 | ||||||||
\(764\) | 29.8998 | 1.08174 | ||||||||
\(765\) | 3.38711 | 0.122461 | ||||||||
\(766\) | −16.0584 | −0.580213 | ||||||||
\(767\) | −9.13414 | −0.329815 | ||||||||
\(768\) | 20.1300 | 0.726380 | ||||||||
\(769\) | −39.0585 | −1.40848 | −0.704242 | − | 0.709960i | \(-0.748713\pi\) | ||||
−0.704242 | + | 0.709960i | \(0.748713\pi\) | |||||||
\(770\) | 0.607052 | 0.0218766 | ||||||||
\(771\) | 58.0984 | 2.09236 | ||||||||
\(772\) | −19.9552 | −0.718202 | ||||||||
\(773\) | 9.80518 | 0.352668 | 0.176334 | − | 0.984330i | \(-0.443576\pi\) | ||||
0.176334 | + | 0.984330i | \(0.443576\pi\) | |||||||
\(774\) | −16.4867 | −0.592601 | ||||||||
\(775\) | −0.451972 | −0.0162353 | ||||||||
\(776\) | 34.3878 | 1.23445 | ||||||||
\(777\) | −7.57157 | −0.271629 | ||||||||
\(778\) | 15.7249 | 0.563763 | ||||||||
\(779\) | −9.29769 | −0.333124 | ||||||||
\(780\) | −4.65407 | −0.166642 | ||||||||
\(781\) | −13.2959 | −0.475764 | ||||||||
\(782\) | 6.42519 | 0.229764 | ||||||||
\(783\) | −3.35747 | −0.119986 | ||||||||
\(784\) | −9.63183 | −0.343994 | ||||||||
\(785\) | 18.8438 | 0.672565 | ||||||||
\(786\) | −1.03004 | −0.0367404 | ||||||||
\(787\) | −8.11030 | −0.289101 | −0.144551 | − | 0.989497i | \(-0.546174\pi\) | ||||
−0.144551 | + | 0.989497i | \(0.546174\pi\) | |||||||
\(788\) | −7.96625 | −0.283786 | ||||||||
\(789\) | 11.4662 | 0.408206 | ||||||||
\(790\) | −10.1699 | −0.361830 | ||||||||
\(791\) | 16.5001 | 0.586675 | ||||||||
\(792\) | 5.64137 | 0.200457 | ||||||||
\(793\) | −5.81412 | −0.206465 | ||||||||
\(794\) | 23.1972 | 0.823237 | ||||||||
\(795\) | −4.24360 | −0.150505 | ||||||||
\(796\) | 14.5167 | 0.514530 | ||||||||
\(797\) | −36.5238 | −1.29374 | −0.646869 | − | 0.762601i | \(-0.723922\pi\) | ||||
−0.646869 | + | 0.762601i | \(0.723922\pi\) | |||||||
\(798\) | −1.36030 | −0.0481542 | ||||||||
\(799\) | 5.37566 | 0.190177 | ||||||||
\(800\) | 5.74971 | 0.203283 | ||||||||
\(801\) | −15.6597 | −0.553308 | ||||||||
\(802\) | 12.4112 | 0.438256 | ||||||||
\(803\) | −1.00000 | −0.0352892 | ||||||||
\(804\) | 16.7189 | 0.589632 | ||||||||
\(805\) | −6.29207 | −0.221766 | ||||||||
\(806\) | 0.383763 | 0.0135175 | ||||||||
\(807\) | 1.16018 | 0.0408403 | ||||||||
\(808\) | 28.8148 | 1.01370 | ||||||||
\(809\) | 6.14707 | 0.216119 | 0.108060 | − | 0.994144i | \(-0.465536\pi\) | ||||
0.108060 | + | 0.994144i | \(0.465536\pi\) | |||||||
\(810\) | −6.91735 | −0.243051 | ||||||||
\(811\) | 37.3371 | 1.31108 | 0.655541 | − | 0.755160i | \(-0.272441\pi\) | ||||
0.655541 | + | 0.755160i | \(0.272441\pi\) | |||||||
\(812\) | −3.41327 | −0.119782 | ||||||||
\(813\) | 68.6575 | 2.40792 | ||||||||
\(814\) | 2.35229 | 0.0824478 | ||||||||
\(815\) | −1.80746 | −0.0633124 | ||||||||
\(816\) | −5.14060 | −0.179957 | ||||||||
\(817\) | 10.0446 | 0.351417 | ||||||||
\(818\) | 19.4374 | 0.679613 | ||||||||
\(819\) | 2.81636 | 0.0984117 | ||||||||
\(820\) | −15.0513 | −0.525613 | ||||||||
\(821\) | −45.1683 | −1.57638 | −0.788191 | − | 0.615430i | \(-0.788982\pi\) | ||||
−0.788191 | + | 0.615430i | \(0.788982\pi\) | |||||||
\(822\) | 24.5778 | 0.857251 | ||||||||
\(823\) | −33.2099 | −1.15762 | −0.578811 | − | 0.815461i | \(-0.696483\pi\) | ||||
−0.578811 | + | 0.815461i | \(0.696483\pi\) | |||||||
\(824\) | −3.53314 | −0.123083 | ||||||||
\(825\) | 2.32231 | 0.0808524 | ||||||||
\(826\) | −4.32183 | −0.150376 | ||||||||
\(827\) | 40.8527 | 1.42059 | 0.710293 | − | 0.703906i | \(-0.248562\pi\) | ||||
0.710293 | + | 0.703906i | \(0.248562\pi\) | |||||||
\(828\) | −25.6415 | −0.891103 | ||||||||
\(829\) | −43.8791 | −1.52398 | −0.761991 | − | 0.647587i | \(-0.775778\pi\) | ||||
−0.761991 | + | 0.647587i | \(0.775778\pi\) | |||||||
\(830\) | 6.88352 | 0.238930 | ||||||||
\(831\) | 22.8053 | 0.791107 | ||||||||
\(832\) | −0.868868 | −0.0301226 | ||||||||
\(833\) | −8.71665 | −0.302014 | ||||||||
\(834\) | 17.5951 | 0.609267 | ||||||||
\(835\) | 12.8299 | 0.443996 | ||||||||
\(836\) | −1.50722 | −0.0521284 | ||||||||
\(837\) | −0.637003 | −0.0220180 | ||||||||
\(838\) | 1.48763 | 0.0513893 | ||||||||
\(839\) | 21.0451 | 0.726556 | 0.363278 | − | 0.931681i | \(-0.381658\pi\) | ||||
0.363278 | + | 0.931681i | \(0.381658\pi\) | |||||||
\(840\) | −5.02160 | −0.173262 | ||||||||
\(841\) | −23.3250 | −0.804311 | ||||||||
\(842\) | −13.5446 | −0.466778 | ||||||||
\(843\) | 9.08391 | 0.312866 | ||||||||
\(844\) | −25.3286 | −0.871846 | ||||||||
\(845\) | −11.3539 | −0.390587 | ||||||||
\(846\) | 6.01524 | 0.206808 | ||||||||
\(847\) | −0.917277 | −0.0315180 | ||||||||
\(848\) | 2.85787 | 0.0981395 | ||||||||
\(849\) | −1.28034 | −0.0439410 | ||||||||
\(850\) | 0.936683 | 0.0321280 | ||||||||
\(851\) | −24.3814 | −0.835784 | ||||||||
\(852\) | 48.2308 | 1.65236 | ||||||||
\(853\) | 57.2895 | 1.96156 | 0.980778 | − | 0.195129i | \(-0.0625125\pi\) | ||||
0.980778 | + | 0.195129i | \(0.0625125\pi\) | |||||||
\(854\) | −2.75096 | −0.0941358 | ||||||||
\(855\) | −2.30915 | −0.0789713 | ||||||||
\(856\) | −19.9754 | −0.682744 | ||||||||
\(857\) | −20.5171 | −0.700850 | −0.350425 | − | 0.936591i | \(-0.613963\pi\) | ||||
−0.350425 | + | 0.936591i | \(0.613963\pi\) | |||||||
\(858\) | −1.97184 | −0.0673174 | ||||||||
\(859\) | −23.5681 | −0.804133 | −0.402067 | − | 0.915610i | \(-0.631708\pi\) | ||||
−0.402067 | + | 0.915610i | \(0.631708\pi\) | |||||||
\(860\) | 16.2604 | 0.554476 | ||||||||
\(861\) | 20.5261 | 0.699526 | ||||||||
\(862\) | 21.5956 | 0.735550 | ||||||||
\(863\) | −18.1177 | −0.616734 | −0.308367 | − | 0.951267i | \(-0.599783\pi\) | ||||
−0.308367 | + | 0.951267i | \(0.599783\pi\) | |||||||
\(864\) | 8.10356 | 0.275689 | ||||||||
\(865\) | −1.30633 | −0.0444164 | ||||||||
\(866\) | −4.77012 | −0.162095 | ||||||||
\(867\) | 34.8271 | 1.18279 | ||||||||
\(868\) | −0.647589 | −0.0219806 | ||||||||
\(869\) | 15.3671 | 0.521294 | ||||||||
\(870\) | 3.66123 | 0.124127 | ||||||||
\(871\) | −5.91327 | −0.200363 | ||||||||
\(872\) | −2.52463 | −0.0854946 | ||||||||
\(873\) | −34.9096 | −1.18151 | ||||||||
\(874\) | −4.38034 | −0.148167 | ||||||||
\(875\) | −0.917277 | −0.0310096 | ||||||||
\(876\) | 3.62750 | 0.122562 | ||||||||
\(877\) | 23.4541 | 0.791989 | 0.395994 | − | 0.918253i | \(-0.370400\pi\) | ||||
0.395994 | + | 0.918253i | \(0.370400\pi\) | |||||||
\(878\) | −23.2480 | −0.784581 | ||||||||
\(879\) | −35.2132 | −1.18771 | ||||||||
\(880\) | −1.56396 | −0.0527212 | ||||||||
\(881\) | 30.6090 | 1.03124 | 0.515622 | − | 0.856816i | \(-0.327561\pi\) | ||||
0.515622 | + | 0.856816i | \(0.327561\pi\) | |||||||
\(882\) | −9.75372 | −0.328425 | ||||||||
\(883\) | −45.0103 | −1.51472 | −0.757359 | − | 0.652998i | \(-0.773511\pi\) | ||||
−0.757359 | + | 0.652998i | \(0.773511\pi\) | |||||||
\(884\) | 2.83648 | 0.0954013 | ||||||||
\(885\) | −16.5334 | −0.555763 | ||||||||
\(886\) | 6.69439 | 0.224902 | ||||||||
\(887\) | −15.9761 | −0.536426 | −0.268213 | − | 0.963360i | \(-0.586433\pi\) | ||||
−0.268213 | + | 0.963360i | \(0.586433\pi\) | |||||||
\(888\) | −19.4584 | −0.652982 | ||||||||
\(889\) | 0.999693 | 0.0335286 | ||||||||
\(890\) | −4.33058 | −0.145161 | ||||||||
\(891\) | 10.4524 | 0.350167 | ||||||||
\(892\) | 43.9612 | 1.47193 | ||||||||
\(893\) | −3.66484 | −0.122639 | ||||||||
\(894\) | 18.1708 | 0.607722 | ||||||||
\(895\) | 15.7126 | 0.525214 | ||||||||
\(896\) | 10.1370 | 0.338655 | ||||||||
\(897\) | 20.4380 | 0.682405 | ||||||||
\(898\) | −9.37335 | −0.312793 | ||||||||
\(899\) | 1.07670 | 0.0359099 | ||||||||
\(900\) | −3.73809 | −0.124603 | ||||||||
\(901\) | 2.58632 | 0.0861629 | ||||||||
\(902\) | −6.37692 | −0.212328 | ||||||||
\(903\) | −22.1751 | −0.737940 | ||||||||
\(904\) | 42.4041 | 1.41034 | ||||||||
\(905\) | −25.0696 | −0.833342 | ||||||||
\(906\) | −4.92270 | −0.163546 | ||||||||
\(907\) | 22.8758 | 0.759578 | 0.379789 | − | 0.925073i | \(-0.375997\pi\) | ||||
0.379789 | + | 0.925073i | \(0.375997\pi\) | |||||||
\(908\) | −29.6814 | −0.985012 | ||||||||
\(909\) | −29.2520 | −0.970229 | ||||||||
\(910\) | 0.778846 | 0.0258185 | ||||||||
\(911\) | 5.38740 | 0.178492 | 0.0892462 | − | 0.996010i | \(-0.471554\pi\) | ||||
0.0892462 | + | 0.996010i | \(0.471554\pi\) | |||||||
\(912\) | 3.50458 | 0.116048 | ||||||||
\(913\) | −10.4012 | −0.344231 | ||||||||
\(914\) | 2.43167 | 0.0804325 | ||||||||
\(915\) | −10.5239 | −0.347910 | ||||||||
\(916\) | 10.6299 | 0.351221 | ||||||||
\(917\) | −0.614767 | −0.0203014 | ||||||||
\(918\) | 1.32015 | 0.0435714 | ||||||||
\(919\) | −9.81772 | −0.323857 | −0.161928 | − | 0.986803i | \(-0.551771\pi\) | ||||
−0.161928 | + | 0.986803i | \(0.551771\pi\) | |||||||
\(920\) | −16.1702 | −0.533116 | ||||||||
\(921\) | 6.96925 | 0.229645 | ||||||||
\(922\) | 3.23874 | 0.106662 | ||||||||
\(923\) | −17.0586 | −0.561490 | ||||||||
\(924\) | 3.32742 | 0.109464 | ||||||||
\(925\) | −3.55440 | −0.116868 | ||||||||
\(926\) | 14.6040 | 0.479918 | ||||||||
\(927\) | 3.58675 | 0.117804 | ||||||||
\(928\) | −13.6971 | −0.449628 | ||||||||
\(929\) | 2.41234 | 0.0791463 | 0.0395732 | − | 0.999217i | \(-0.487400\pi\) | ||||
0.0395732 | + | 0.999217i | \(0.487400\pi\) | |||||||
\(930\) | 0.694635 | 0.0227780 | ||||||||
\(931\) | 5.94254 | 0.194759 | ||||||||
\(932\) | 5.75762 | 0.188597 | ||||||||
\(933\) | 63.9315 | 2.09302 | ||||||||
\(934\) | −5.80936 | −0.190088 | ||||||||
\(935\) | −1.41536 | −0.0462873 | ||||||||
\(936\) | 7.23787 | 0.236577 | ||||||||
\(937\) | −19.4876 | −0.636631 | −0.318315 | − | 0.947985i | \(-0.603117\pi\) | ||||
−0.318315 | + | 0.947985i | \(0.603117\pi\) | |||||||
\(938\) | −2.79787 | −0.0913537 | ||||||||
\(939\) | 4.89312 | 0.159681 | ||||||||
\(940\) | −5.93270 | −0.193503 | ||||||||
\(941\) | −41.5585 | −1.35477 | −0.677383 | − | 0.735630i | \(-0.736886\pi\) | ||||
−0.677383 | + | 0.735630i | \(0.736886\pi\) | |||||||
\(942\) | −28.9610 | −0.943602 | ||||||||
\(943\) | 66.0965 | 2.15240 | ||||||||
\(944\) | 11.1344 | 0.362395 | ||||||||
\(945\) | −1.29280 | −0.0420547 | ||||||||
\(946\) | 6.88922 | 0.223988 | ||||||||
\(947\) | 11.7014 | 0.380244 | 0.190122 | − | 0.981760i | \(-0.439112\pi\) | ||||
0.190122 | + | 0.981760i | \(0.439112\pi\) | |||||||
\(948\) | −55.7442 | −1.81049 | ||||||||
\(949\) | −1.28300 | −0.0416479 | ||||||||
\(950\) | −0.638580 | −0.0207183 | ||||||||
\(951\) | −51.4844 | −1.66950 | ||||||||
\(952\) | 3.06048 | 0.0991908 | ||||||||
\(953\) | 54.8326 | 1.77620 | 0.888102 | − | 0.459647i | \(-0.152024\pi\) | ||||
0.888102 | + | 0.459647i | \(0.152024\pi\) | |||||||
\(954\) | 2.89403 | 0.0936977 | ||||||||
\(955\) | −19.1417 | −0.619412 | ||||||||
\(956\) | 37.9513 | 1.22743 | ||||||||
\(957\) | −5.53225 | −0.178832 | ||||||||
\(958\) | 18.3642 | 0.593319 | ||||||||
\(959\) | 14.6690 | 0.473685 | ||||||||
\(960\) | −1.57271 | −0.0507589 | ||||||||
\(961\) | −30.7957 | −0.993410 | ||||||||
\(962\) | 3.01798 | 0.0973037 | ||||||||
\(963\) | 20.2785 | 0.653465 | ||||||||
\(964\) | 30.5803 | 0.984925 | ||||||||
\(965\) | 12.7752 | 0.411248 | ||||||||
\(966\) | 9.67027 | 0.311136 | ||||||||
\(967\) | −16.3740 | −0.526552 | −0.263276 | − | 0.964721i | \(-0.584803\pi\) | ||||
−0.263276 | + | 0.964721i | \(0.584803\pi\) | |||||||
\(968\) | −2.35734 | −0.0757678 | ||||||||
\(969\) | 3.17159 | 0.101886 | ||||||||
\(970\) | −9.65402 | −0.309972 | ||||||||
\(971\) | −6.92576 | −0.222258 | −0.111129 | − | 0.993806i | \(-0.535447\pi\) | ||||
−0.111129 | + | 0.993806i | \(0.535447\pi\) | |||||||
\(972\) | −31.3114 | −1.00431 | ||||||||
\(973\) | 10.5014 | 0.336659 | ||||||||
\(974\) | 20.0661 | 0.642960 | ||||||||
\(975\) | 2.97951 | 0.0954208 | ||||||||
\(976\) | 7.08736 | 0.226861 | ||||||||
\(977\) | 44.9939 | 1.43948 | 0.719741 | − | 0.694242i | \(-0.244260\pi\) | ||||
0.719741 | + | 0.694242i | \(0.244260\pi\) | |||||||
\(978\) | 2.77787 | 0.0888266 | ||||||||
\(979\) | 6.54366 | 0.209136 | ||||||||
\(980\) | 9.61988 | 0.307296 | ||||||||
\(981\) | 2.56293 | 0.0818282 | ||||||||
\(982\) | 12.2519 | 0.390973 | ||||||||
\(983\) | −41.6828 | −1.32947 | −0.664737 | − | 0.747078i | \(-0.731456\pi\) | ||||
−0.664737 | + | 0.747078i | \(0.731456\pi\) | |||||||
\(984\) | 52.7506 | 1.68163 | ||||||||
\(985\) | 5.09996 | 0.162498 | ||||||||
\(986\) | −2.23139 | −0.0710618 | ||||||||
\(987\) | 8.09068 | 0.257529 | ||||||||
\(988\) | −1.93376 | −0.0615212 | ||||||||
\(989\) | −71.4065 | −2.27059 | ||||||||
\(990\) | −1.58376 | −0.0503350 | ||||||||
\(991\) | 10.6280 | 0.337611 | 0.168806 | − | 0.985649i | \(-0.446009\pi\) | ||||
0.168806 | + | 0.985649i | \(0.446009\pi\) | |||||||
\(992\) | −2.59871 | −0.0825090 | ||||||||
\(993\) | 73.3873 | 2.32888 | ||||||||
\(994\) | −8.07129 | −0.256006 | ||||||||
\(995\) | −9.29350 | −0.294624 | ||||||||
\(996\) | 37.7305 | 1.19554 | ||||||||
\(997\) | −49.3544 | −1.56307 | −0.781535 | − | 0.623862i | \(-0.785563\pi\) | ||||
−0.781535 | + | 0.623862i | \(0.785563\pi\) | |||||||
\(998\) | −22.0407 | −0.697686 | ||||||||
\(999\) | −5.00951 | −0.158494 |
(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 | 4015.2.a.c.1.16 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.c.1.16 | ✓ | 23 | 1.1 | even | 1 | trivial |