Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - x^{12} - 40 x^{11} + 34 x^{10} + 604 x^{9} - 381 x^{8} - 4352 x^{7} + 1474 x^{6} + 15809 x^{5} + \cdots + 8832 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.54523\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.54523 | −1.58547 | −0.792737 | − | 0.609564i | \(-0.791345\pi\) | ||||
−0.792737 | + | 0.609564i | \(0.791345\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.166701 | 0.0630071 | 0.0315036 | − | 0.999504i | \(-0.489970\pi\) | ||||
0.0315036 | + | 0.999504i | \(0.489970\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.54523 | 1.12110 | ||||||||
\(11\) | 4.41321 | 1.33063 | 0.665317 | − | 0.746561i | \(-0.268297\pi\) | ||||
0.665317 | + | 0.746561i | \(0.268297\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −0.166701 | −0.0445528 | ||||||||
\(15\) | −3.54523 | −0.915374 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.92847 | 1.43786 | 0.718932 | − | 0.695080i | \(-0.244631\pi\) | ||||
0.718932 | + | 0.695080i | \(0.244631\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.45439 | 1.25132 | 0.625662 | − | 0.780094i | \(-0.284829\pi\) | ||||
0.625662 | + | 0.780094i | \(0.284829\pi\) | |||||||
\(20\) | −3.54523 | −0.792737 | ||||||||
\(21\) | 0.166701 | 0.0363772 | ||||||||
\(22\) | −4.41321 | −0.940900 | ||||||||
\(23\) | 6.44327 | 1.34352 | 0.671758 | − | 0.740771i | \(-0.265540\pi\) | ||||
0.671758 | + | 0.740771i | \(0.265540\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 7.56864 | 1.51373 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.166701 | 0.0315036 | ||||||||
\(29\) | 0.584971 | 0.108626 | 0.0543132 | − | 0.998524i | \(-0.482703\pi\) | ||||
0.0543132 | + | 0.998524i | \(0.482703\pi\) | |||||||
\(30\) | 3.54523 | 0.647267 | ||||||||
\(31\) | −4.19458 | −0.753369 | −0.376684 | − | 0.926342i | \(-0.622936\pi\) | ||||
−0.376684 | + | 0.926342i | \(0.622936\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.41321 | 0.768242 | ||||||||
\(34\) | −5.92847 | −1.01672 | ||||||||
\(35\) | −0.590994 | −0.0998962 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.59476 | 1.41297 | 0.706485 | − | 0.707728i | \(-0.250280\pi\) | ||||
0.706485 | + | 0.707728i | \(0.250280\pi\) | |||||||
\(38\) | −5.45439 | −0.884819 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 3.54523 | 0.560550 | ||||||||
\(41\) | −7.73673 | −1.20827 | −0.604137 | − | 0.796880i | \(-0.706482\pi\) | ||||
−0.604137 | + | 0.796880i | \(0.706482\pi\) | |||||||
\(42\) | −0.166701 | −0.0257226 | ||||||||
\(43\) | −7.36207 | −1.12270 | −0.561352 | − | 0.827577i | \(-0.689719\pi\) | ||||
−0.561352 | + | 0.827577i | \(0.689719\pi\) | |||||||
\(44\) | 4.41321 | 0.665317 | ||||||||
\(45\) | −3.54523 | −0.528491 | ||||||||
\(46\) | −6.44327 | −0.950009 | ||||||||
\(47\) | 12.7766 | 1.86366 | 0.931829 | − | 0.362899i | \(-0.118213\pi\) | ||||
0.931829 | + | 0.362899i | \(0.118213\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.97221 | −0.996030 | ||||||||
\(50\) | −7.56864 | −1.07037 | ||||||||
\(51\) | 5.92847 | 0.830151 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 1.83140 | 0.251563 | 0.125781 | − | 0.992058i | \(-0.459856\pi\) | ||||
0.125781 | + | 0.992058i | \(0.459856\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −15.6458 | −2.10969 | ||||||||
\(56\) | −0.166701 | −0.0222764 | ||||||||
\(57\) | 5.45439 | 0.722452 | ||||||||
\(58\) | −0.584971 | −0.0768105 | ||||||||
\(59\) | 15.1468 | 1.97194 | 0.985972 | − | 0.166911i | \(-0.0533793\pi\) | ||||
0.985972 | + | 0.166911i | \(0.0533793\pi\) | |||||||
\(60\) | −3.54523 | −0.457687 | ||||||||
\(61\) | 10.5545 | 1.35137 | 0.675684 | − | 0.737192i | \(-0.263848\pi\) | ||||
0.675684 | + | 0.737192i | \(0.263848\pi\) | |||||||
\(62\) | 4.19458 | 0.532712 | ||||||||
\(63\) | 0.166701 | 0.0210024 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.54523 | −0.439731 | ||||||||
\(66\) | −4.41321 | −0.543229 | ||||||||
\(67\) | −14.3239 | −1.74994 | −0.874970 | − | 0.484178i | \(-0.839119\pi\) | ||||
−0.874970 | + | 0.484178i | \(0.839119\pi\) | |||||||
\(68\) | 5.92847 | 0.718932 | ||||||||
\(69\) | 6.44327 | 0.775679 | ||||||||
\(70\) | 0.590994 | 0.0706373 | ||||||||
\(71\) | 1.93330 | 0.229440 | 0.114720 | − | 0.993398i | \(-0.463403\pi\) | ||||
0.114720 | + | 0.993398i | \(0.463403\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −13.3410 | −1.56145 | −0.780724 | − | 0.624876i | \(-0.785149\pi\) | ||||
−0.780724 | + | 0.624876i | \(0.785149\pi\) | |||||||
\(74\) | −8.59476 | −0.999121 | ||||||||
\(75\) | 7.56864 | 0.873952 | ||||||||
\(76\) | 5.45439 | 0.625662 | ||||||||
\(77\) | 0.735688 | 0.0838394 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −5.41863 | −0.609644 | −0.304822 | − | 0.952409i | \(-0.598597\pi\) | ||||
−0.304822 | + | 0.952409i | \(0.598597\pi\) | |||||||
\(80\) | −3.54523 | −0.396369 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.73673 | 0.854379 | ||||||||
\(83\) | 0.0310976 | 0.00341341 | 0.00170670 | − | 0.999999i | \(-0.499457\pi\) | ||||
0.00170670 | + | 0.999999i | \(0.499457\pi\) | |||||||
\(84\) | 0.166701 | 0.0181886 | ||||||||
\(85\) | −21.0178 | −2.27970 | ||||||||
\(86\) | 7.36207 | 0.793872 | ||||||||
\(87\) | 0.584971 | 0.0627155 | ||||||||
\(88\) | −4.41321 | −0.470450 | ||||||||
\(89\) | −1.88292 | −0.199589 | −0.0997947 | − | 0.995008i | \(-0.531819\pi\) | ||||
−0.0997947 | + | 0.995008i | \(0.531819\pi\) | |||||||
\(90\) | 3.54523 | 0.373700 | ||||||||
\(91\) | 0.166701 | 0.0174750 | ||||||||
\(92\) | 6.44327 | 0.671758 | ||||||||
\(93\) | −4.19458 | −0.434958 | ||||||||
\(94\) | −12.7766 | −1.31780 | ||||||||
\(95\) | −19.3371 | −1.98394 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 1.26550 | 0.128493 | 0.0642463 | − | 0.997934i | \(-0.479536\pi\) | ||||
0.0642463 | + | 0.997934i | \(0.479536\pi\) | |||||||
\(98\) | 6.97221 | 0.704300 | ||||||||
\(99\) | 4.41321 | 0.443544 | ||||||||
\(100\) | 7.56864 | 0.756864 | ||||||||
\(101\) | 11.4085 | 1.13519 | 0.567596 | − | 0.823307i | \(-0.307874\pi\) | ||||
0.567596 | + | 0.823307i | \(0.307874\pi\) | |||||||
\(102\) | −5.92847 | −0.587006 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −0.590994 | −0.0576751 | ||||||||
\(106\) | −1.83140 | −0.177882 | ||||||||
\(107\) | −7.43278 | −0.718554 | −0.359277 | − | 0.933231i | \(-0.616977\pi\) | ||||
−0.359277 | + | 0.933231i | \(0.616977\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −6.41750 | −0.614685 | −0.307343 | − | 0.951599i | \(-0.599440\pi\) | ||||
−0.307343 | + | 0.951599i | \(0.599440\pi\) | |||||||
\(110\) | 15.6458 | 1.49177 | ||||||||
\(111\) | 8.59476 | 0.815779 | ||||||||
\(112\) | 0.166701 | 0.0157518 | ||||||||
\(113\) | 0.936328 | 0.0880823 | 0.0440412 | − | 0.999030i | \(-0.485977\pi\) | ||||
0.0440412 | + | 0.999030i | \(0.485977\pi\) | |||||||
\(114\) | −5.45439 | −0.510851 | ||||||||
\(115\) | −22.8429 | −2.13011 | ||||||||
\(116\) | 0.584971 | 0.0543132 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −15.1468 | −1.39437 | ||||||||
\(119\) | 0.988283 | 0.0905957 | ||||||||
\(120\) | 3.54523 | 0.323634 | ||||||||
\(121\) | 8.47644 | 0.770585 | ||||||||
\(122\) | −10.5545 | −0.955561 | ||||||||
\(123\) | −7.73673 | −0.697598 | ||||||||
\(124\) | −4.19458 | −0.376684 | ||||||||
\(125\) | −9.10643 | −0.814504 | ||||||||
\(126\) | −0.166701 | −0.0148509 | ||||||||
\(127\) | 20.8839 | 1.85315 | 0.926575 | − | 0.376111i | \(-0.122739\pi\) | ||||
0.926575 | + | 0.376111i | \(0.122739\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.36207 | −0.648194 | ||||||||
\(130\) | 3.54523 | 0.310937 | ||||||||
\(131\) | 0.957541 | 0.0836607 | 0.0418304 | − | 0.999125i | \(-0.486681\pi\) | ||||
0.0418304 | + | 0.999125i | \(0.486681\pi\) | |||||||
\(132\) | 4.41321 | 0.384121 | ||||||||
\(133\) | 0.909254 | 0.0788423 | ||||||||
\(134\) | 14.3239 | 1.23739 | ||||||||
\(135\) | −3.54523 | −0.305125 | ||||||||
\(136\) | −5.92847 | −0.508362 | ||||||||
\(137\) | −13.0164 | −1.11207 | −0.556035 | − | 0.831159i | \(-0.687678\pi\) | ||||
−0.556035 | + | 0.831159i | \(0.687678\pi\) | |||||||
\(138\) | −6.44327 | −0.548488 | ||||||||
\(139\) | −1.41313 | −0.119860 | −0.0599301 | − | 0.998203i | \(-0.519088\pi\) | ||||
−0.0599301 | + | 0.998203i | \(0.519088\pi\) | |||||||
\(140\) | −0.590994 | −0.0499481 | ||||||||
\(141\) | 12.7766 | 1.07598 | ||||||||
\(142\) | −1.93330 | −0.162239 | ||||||||
\(143\) | 4.41321 | 0.369051 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.07386 | −0.172224 | ||||||||
\(146\) | 13.3410 | 1.10411 | ||||||||
\(147\) | −6.97221 | −0.575058 | ||||||||
\(148\) | 8.59476 | 0.706485 | ||||||||
\(149\) | −7.00440 | −0.573823 | −0.286912 | − | 0.957957i | \(-0.592629\pi\) | ||||
−0.286912 | + | 0.957957i | \(0.592629\pi\) | |||||||
\(150\) | −7.56864 | −0.617977 | ||||||||
\(151\) | 17.6617 | 1.43729 | 0.718643 | − | 0.695379i | \(-0.244764\pi\) | ||||
0.718643 | + | 0.695379i | \(0.244764\pi\) | |||||||
\(152\) | −5.45439 | −0.442410 | ||||||||
\(153\) | 5.92847 | 0.479288 | ||||||||
\(154\) | −0.735688 | −0.0592834 | ||||||||
\(155\) | 14.8707 | 1.19445 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −12.5859 | −1.00446 | −0.502231 | − | 0.864734i | \(-0.667487\pi\) | ||||
−0.502231 | + | 0.864734i | \(0.667487\pi\) | |||||||
\(158\) | 5.41863 | 0.431083 | ||||||||
\(159\) | 1.83140 | 0.145240 | ||||||||
\(160\) | 3.54523 | 0.280275 | ||||||||
\(161\) | 1.07410 | 0.0846511 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −22.7916 | −1.78518 | −0.892589 | − | 0.450872i | \(-0.851113\pi\) | ||||
−0.892589 | + | 0.450872i | \(0.851113\pi\) | |||||||
\(164\) | −7.73673 | −0.604137 | ||||||||
\(165\) | −15.6458 | −1.21803 | ||||||||
\(166\) | −0.0310976 | −0.00241364 | ||||||||
\(167\) | −3.49484 | −0.270439 | −0.135220 | − | 0.990816i | \(-0.543174\pi\) | ||||
−0.135220 | + | 0.990816i | \(0.543174\pi\) | |||||||
\(168\) | −0.166701 | −0.0128613 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 21.0178 | 1.61199 | ||||||||
\(171\) | 5.45439 | 0.417108 | ||||||||
\(172\) | −7.36207 | −0.561352 | ||||||||
\(173\) | 13.3786 | 1.01716 | 0.508578 | − | 0.861016i | \(-0.330171\pi\) | ||||
0.508578 | + | 0.861016i | \(0.330171\pi\) | |||||||
\(174\) | −0.584971 | −0.0443465 | ||||||||
\(175\) | 1.26170 | 0.0953757 | ||||||||
\(176\) | 4.41321 | 0.332658 | ||||||||
\(177\) | 15.1468 | 1.13850 | ||||||||
\(178\) | 1.88292 | 0.141131 | ||||||||
\(179\) | 1.33946 | 0.100116 | 0.0500580 | − | 0.998746i | \(-0.484059\pi\) | ||||
0.0500580 | + | 0.998746i | \(0.484059\pi\) | |||||||
\(180\) | −3.54523 | −0.264246 | ||||||||
\(181\) | −5.60284 | −0.416456 | −0.208228 | − | 0.978080i | \(-0.566770\pi\) | ||||
−0.208228 | + | 0.978080i | \(0.566770\pi\) | |||||||
\(182\) | −0.166701 | −0.0123567 | ||||||||
\(183\) | 10.5545 | 0.780212 | ||||||||
\(184\) | −6.44327 | −0.475005 | ||||||||
\(185\) | −30.4704 | −2.24023 | ||||||||
\(186\) | 4.19458 | 0.307562 | ||||||||
\(187\) | 26.1636 | 1.91327 | ||||||||
\(188\) | 12.7766 | 0.931829 | ||||||||
\(189\) | 0.166701 | 0.0121257 | ||||||||
\(190\) | 19.3371 | 1.40286 | ||||||||
\(191\) | 8.01970 | 0.580285 | 0.290143 | − | 0.956983i | \(-0.406297\pi\) | ||||
0.290143 | + | 0.956983i | \(0.406297\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 16.5029 | 1.18790 | 0.593952 | − | 0.804501i | \(-0.297567\pi\) | ||||
0.593952 | + | 0.804501i | \(0.297567\pi\) | |||||||
\(194\) | −1.26550 | −0.0908579 | ||||||||
\(195\) | −3.54523 | −0.253879 | ||||||||
\(196\) | −6.97221 | −0.498015 | ||||||||
\(197\) | −21.0006 | −1.49623 | −0.748114 | − | 0.663570i | \(-0.769040\pi\) | ||||
−0.748114 | + | 0.663570i | \(0.769040\pi\) | |||||||
\(198\) | −4.41321 | −0.313633 | ||||||||
\(199\) | −22.0758 | −1.56491 | −0.782455 | − | 0.622707i | \(-0.786033\pi\) | ||||
−0.782455 | + | 0.622707i | \(0.786033\pi\) | |||||||
\(200\) | −7.56864 | −0.535184 | ||||||||
\(201\) | −14.3239 | −1.01033 | ||||||||
\(202\) | −11.4085 | −0.802702 | ||||||||
\(203\) | 0.0975154 | 0.00684424 | ||||||||
\(204\) | 5.92847 | 0.415076 | ||||||||
\(205\) | 27.4285 | 1.91569 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 6.44327 | 0.447839 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 24.0714 | 1.66505 | ||||||||
\(210\) | 0.590994 | 0.0407825 | ||||||||
\(211\) | 17.8887 | 1.23151 | 0.615755 | − | 0.787937i | \(-0.288851\pi\) | ||||
0.615755 | + | 0.787937i | \(0.288851\pi\) | |||||||
\(212\) | 1.83140 | 0.125781 | ||||||||
\(213\) | 1.93330 | 0.132467 | ||||||||
\(214\) | 7.43278 | 0.508095 | ||||||||
\(215\) | 26.1002 | 1.78002 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −0.699242 | −0.0474676 | ||||||||
\(218\) | 6.41750 | 0.434648 | ||||||||
\(219\) | −13.3410 | −0.901502 | ||||||||
\(220\) | −15.6458 | −1.05484 | ||||||||
\(221\) | 5.92847 | 0.398792 | ||||||||
\(222\) | −8.59476 | −0.576843 | ||||||||
\(223\) | −16.1109 | −1.07887 | −0.539433 | − | 0.842029i | \(-0.681361\pi\) | ||||
−0.539433 | + | 0.842029i | \(0.681361\pi\) | |||||||
\(224\) | −0.166701 | −0.0111382 | ||||||||
\(225\) | 7.56864 | 0.504576 | ||||||||
\(226\) | −0.936328 | −0.0622836 | ||||||||
\(227\) | −14.0683 | −0.933749 | −0.466874 | − | 0.884324i | \(-0.654620\pi\) | ||||
−0.466874 | + | 0.884324i | \(0.654620\pi\) | |||||||
\(228\) | 5.45439 | 0.361226 | ||||||||
\(229\) | 9.68824 | 0.640217 | 0.320109 | − | 0.947381i | \(-0.396281\pi\) | ||||
0.320109 | + | 0.947381i | \(0.396281\pi\) | |||||||
\(230\) | 22.8429 | 1.50621 | ||||||||
\(231\) | 0.735688 | 0.0484047 | ||||||||
\(232\) | −0.584971 | −0.0384052 | ||||||||
\(233\) | 15.9605 | 1.04561 | 0.522804 | − | 0.852453i | \(-0.324886\pi\) | ||||
0.522804 | + | 0.852453i | \(0.324886\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −45.2959 | −2.95478 | ||||||||
\(236\) | 15.1468 | 0.985972 | ||||||||
\(237\) | −5.41863 | −0.351978 | ||||||||
\(238\) | −0.988283 | −0.0640608 | ||||||||
\(239\) | −22.7497 | −1.47156 | −0.735779 | − | 0.677222i | \(-0.763184\pi\) | ||||
−0.735779 | + | 0.677222i | \(0.763184\pi\) | |||||||
\(240\) | −3.54523 | −0.228844 | ||||||||
\(241\) | −4.90865 | −0.316194 | −0.158097 | − | 0.987424i | \(-0.550536\pi\) | ||||
−0.158097 | + | 0.987424i | \(0.550536\pi\) | |||||||
\(242\) | −8.47644 | −0.544886 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 10.5545 | 0.675684 | ||||||||
\(245\) | 24.7181 | 1.57918 | ||||||||
\(246\) | 7.73673 | 0.493276 | ||||||||
\(247\) | 5.45439 | 0.347055 | ||||||||
\(248\) | 4.19458 | 0.266356 | ||||||||
\(249\) | 0.0310976 | 0.00197073 | ||||||||
\(250\) | 9.10643 | 0.575941 | ||||||||
\(251\) | −18.4284 | −1.16319 | −0.581594 | − | 0.813479i | \(-0.697571\pi\) | ||||
−0.581594 | + | 0.813479i | \(0.697571\pi\) | |||||||
\(252\) | 0.166701 | 0.0105012 | ||||||||
\(253\) | 28.4355 | 1.78773 | ||||||||
\(254\) | −20.8839 | −1.31037 | ||||||||
\(255\) | −21.0178 | −1.31618 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.7453 | 1.85546 | 0.927730 | − | 0.373253i | \(-0.121758\pi\) | ||||
0.927730 | + | 0.373253i | \(0.121758\pi\) | |||||||
\(258\) | 7.36207 | 0.458342 | ||||||||
\(259\) | 1.43276 | 0.0890272 | ||||||||
\(260\) | −3.54523 | −0.219866 | ||||||||
\(261\) | 0.584971 | 0.0362088 | ||||||||
\(262\) | −0.957541 | −0.0591571 | ||||||||
\(263\) | 20.2991 | 1.25170 | 0.625849 | − | 0.779944i | \(-0.284752\pi\) | ||||
0.625849 | + | 0.779944i | \(0.284752\pi\) | |||||||
\(264\) | −4.41321 | −0.271614 | ||||||||
\(265\) | −6.49274 | −0.398846 | ||||||||
\(266\) | −0.909254 | −0.0557499 | ||||||||
\(267\) | −1.88292 | −0.115233 | ||||||||
\(268\) | −14.3239 | −0.874970 | ||||||||
\(269\) | 6.33144 | 0.386035 | 0.193017 | − | 0.981195i | \(-0.438173\pi\) | ||||
0.193017 | + | 0.981195i | \(0.438173\pi\) | |||||||
\(270\) | 3.54523 | 0.215756 | ||||||||
\(271\) | −29.3163 | −1.78084 | −0.890418 | − | 0.455143i | \(-0.849588\pi\) | ||||
−0.890418 | + | 0.455143i | \(0.849588\pi\) | |||||||
\(272\) | 5.92847 | 0.359466 | ||||||||
\(273\) | 0.166701 | 0.0100892 | ||||||||
\(274\) | 13.0164 | 0.786352 | ||||||||
\(275\) | 33.4020 | 2.01422 | ||||||||
\(276\) | 6.44327 | 0.387840 | ||||||||
\(277\) | 27.2323 | 1.63623 | 0.818114 | − | 0.575056i | \(-0.195020\pi\) | ||||
0.818114 | + | 0.575056i | \(0.195020\pi\) | |||||||
\(278\) | 1.41313 | 0.0847540 | ||||||||
\(279\) | −4.19458 | −0.251123 | ||||||||
\(280\) | 0.590994 | 0.0353186 | ||||||||
\(281\) | −22.5088 | −1.34276 | −0.671382 | − | 0.741111i | \(-0.734299\pi\) | ||||
−0.671382 | + | 0.741111i | \(0.734299\pi\) | |||||||
\(282\) | −12.7766 | −0.760835 | ||||||||
\(283\) | 14.8017 | 0.879872 | 0.439936 | − | 0.898029i | \(-0.355001\pi\) | ||||
0.439936 | + | 0.898029i | \(0.355001\pi\) | |||||||
\(284\) | 1.93330 | 0.114720 | ||||||||
\(285\) | −19.3371 | −1.14543 | ||||||||
\(286\) | −4.41321 | −0.260959 | ||||||||
\(287\) | −1.28972 | −0.0761299 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 18.1467 | 1.06745 | ||||||||
\(290\) | 2.07386 | 0.121781 | ||||||||
\(291\) | 1.26550 | 0.0741852 | ||||||||
\(292\) | −13.3410 | −0.780724 | ||||||||
\(293\) | 2.36229 | 0.138007 | 0.0690033 | − | 0.997616i | \(-0.478018\pi\) | ||||
0.0690033 | + | 0.997616i | \(0.478018\pi\) | |||||||
\(294\) | 6.97221 | 0.406628 | ||||||||
\(295\) | −53.6988 | −3.12647 | ||||||||
\(296\) | −8.59476 | −0.499560 | ||||||||
\(297\) | 4.41321 | 0.256081 | ||||||||
\(298\) | 7.00440 | 0.405754 | ||||||||
\(299\) | 6.44327 | 0.372624 | ||||||||
\(300\) | 7.56864 | 0.436976 | ||||||||
\(301\) | −1.22727 | −0.0707384 | ||||||||
\(302\) | −17.6617 | −1.01631 | ||||||||
\(303\) | 11.4085 | 0.655403 | ||||||||
\(304\) | 5.45439 | 0.312831 | ||||||||
\(305\) | −37.4182 | −2.14256 | ||||||||
\(306\) | −5.92847 | −0.338908 | ||||||||
\(307\) | 33.3405 | 1.90284 | 0.951422 | − | 0.307889i | \(-0.0996224\pi\) | ||||
0.951422 | + | 0.307889i | \(0.0996224\pi\) | |||||||
\(308\) | 0.735688 | 0.0419197 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −14.8707 | −0.844602 | ||||||||
\(311\) | 26.8070 | 1.52008 | 0.760042 | − | 0.649874i | \(-0.225178\pi\) | ||||
0.760042 | + | 0.649874i | \(0.225178\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 10.1194 | 0.571985 | 0.285993 | − | 0.958232i | \(-0.407677\pi\) | ||||
0.285993 | + | 0.958232i | \(0.407677\pi\) | |||||||
\(314\) | 12.5859 | 0.710261 | ||||||||
\(315\) | −0.590994 | −0.0332987 | ||||||||
\(316\) | −5.41863 | −0.304822 | ||||||||
\(317\) | 12.7234 | 0.714615 | 0.357307 | − | 0.933987i | \(-0.383695\pi\) | ||||
0.357307 | + | 0.933987i | \(0.383695\pi\) | |||||||
\(318\) | −1.83140 | −0.102700 | ||||||||
\(319\) | 2.58160 | 0.144542 | ||||||||
\(320\) | −3.54523 | −0.198184 | ||||||||
\(321\) | −7.43278 | −0.414858 | ||||||||
\(322\) | −1.07410 | −0.0598574 | ||||||||
\(323\) | 32.3362 | 1.79923 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 7.56864 | 0.419833 | ||||||||
\(326\) | 22.7916 | 1.26231 | ||||||||
\(327\) | −6.41750 | −0.354889 | ||||||||
\(328\) | 7.73673 | 0.427190 | ||||||||
\(329\) | 2.12987 | 0.117424 | ||||||||
\(330\) | 15.6458 | 0.861275 | ||||||||
\(331\) | −18.0998 | −0.994854 | −0.497427 | − | 0.867506i | \(-0.665722\pi\) | ||||
−0.497427 | + | 0.867506i | \(0.665722\pi\) | |||||||
\(332\) | 0.0310976 | 0.00170670 | ||||||||
\(333\) | 8.59476 | 0.470990 | ||||||||
\(334\) | 3.49484 | 0.191229 | ||||||||
\(335\) | 50.7814 | 2.77448 | ||||||||
\(336\) | 0.166701 | 0.00909430 | ||||||||
\(337\) | −13.9374 | −0.759216 | −0.379608 | − | 0.925147i | \(-0.623941\pi\) | ||||
−0.379608 | + | 0.925147i | \(0.623941\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 0.936328 | 0.0508544 | ||||||||
\(340\) | −21.0178 | −1.13985 | ||||||||
\(341\) | −18.5116 | −1.00246 | ||||||||
\(342\) | −5.45439 | −0.294940 | ||||||||
\(343\) | −2.32918 | −0.125764 | ||||||||
\(344\) | 7.36207 | 0.396936 | ||||||||
\(345\) | −22.8429 | −1.22982 | ||||||||
\(346\) | −13.3786 | −0.719238 | ||||||||
\(347\) | −2.89499 | −0.155411 | −0.0777056 | − | 0.996976i | \(-0.524759\pi\) | ||||
−0.0777056 | + | 0.996976i | \(0.524759\pi\) | |||||||
\(348\) | 0.584971 | 0.0313577 | ||||||||
\(349\) | 3.83614 | 0.205344 | 0.102672 | − | 0.994715i | \(-0.467261\pi\) | ||||
0.102672 | + | 0.994715i | \(0.467261\pi\) | |||||||
\(350\) | −1.26170 | −0.0674408 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −4.41321 | −0.235225 | ||||||||
\(353\) | 14.3426 | 0.763378 | 0.381689 | − | 0.924291i | \(-0.375343\pi\) | ||||
0.381689 | + | 0.924291i | \(0.375343\pi\) | |||||||
\(354\) | −15.1468 | −0.805043 | ||||||||
\(355\) | −6.85399 | −0.363772 | ||||||||
\(356\) | −1.88292 | −0.0997947 | ||||||||
\(357\) | 0.988283 | 0.0523055 | ||||||||
\(358\) | −1.33946 | −0.0707926 | ||||||||
\(359\) | 29.9911 | 1.58287 | 0.791434 | − | 0.611255i | \(-0.209335\pi\) | ||||
0.791434 | + | 0.611255i | \(0.209335\pi\) | |||||||
\(360\) | 3.54523 | 0.186850 | ||||||||
\(361\) | 10.7504 | 0.565810 | ||||||||
\(362\) | 5.60284 | 0.294479 | ||||||||
\(363\) | 8.47644 | 0.444898 | ||||||||
\(364\) | 0.166701 | 0.00873752 | ||||||||
\(365\) | 47.2969 | 2.47563 | ||||||||
\(366\) | −10.5545 | −0.551694 | ||||||||
\(367\) | −2.25358 | −0.117636 | −0.0588180 | − | 0.998269i | \(-0.518733\pi\) | ||||
−0.0588180 | + | 0.998269i | \(0.518733\pi\) | |||||||
\(368\) | 6.44327 | 0.335879 | ||||||||
\(369\) | −7.73673 | −0.402758 | ||||||||
\(370\) | 30.4704 | 1.58408 | ||||||||
\(371\) | 0.305297 | 0.0158502 | ||||||||
\(372\) | −4.19458 | −0.217479 | ||||||||
\(373\) | 26.3702 | 1.36540 | 0.682700 | − | 0.730699i | \(-0.260806\pi\) | ||||
0.682700 | + | 0.730699i | \(0.260806\pi\) | |||||||
\(374\) | −26.1636 | −1.35289 | ||||||||
\(375\) | −9.10643 | −0.470254 | ||||||||
\(376\) | −12.7766 | −0.658902 | ||||||||
\(377\) | 0.584971 | 0.0301275 | ||||||||
\(378\) | −0.166701 | −0.00857419 | ||||||||
\(379\) | 7.86050 | 0.403767 | 0.201883 | − | 0.979410i | \(-0.435294\pi\) | ||||
0.201883 | + | 0.979410i | \(0.435294\pi\) | |||||||
\(380\) | −19.3371 | −0.991971 | ||||||||
\(381\) | 20.8839 | 1.06992 | ||||||||
\(382\) | −8.01970 | −0.410324 | ||||||||
\(383\) | 4.79907 | 0.245221 | 0.122611 | − | 0.992455i | \(-0.460873\pi\) | ||||
0.122611 | + | 0.992455i | \(0.460873\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −2.60818 | −0.132925 | ||||||||
\(386\) | −16.5029 | −0.839975 | ||||||||
\(387\) | −7.36207 | −0.374235 | ||||||||
\(388\) | 1.26550 | 0.0642463 | ||||||||
\(389\) | −6.03796 | −0.306137 | −0.153068 | − | 0.988216i | \(-0.548915\pi\) | ||||
−0.153068 | + | 0.988216i | \(0.548915\pi\) | |||||||
\(390\) | 3.54523 | 0.179520 | ||||||||
\(391\) | 38.1987 | 1.93179 | ||||||||
\(392\) | 6.97221 | 0.352150 | ||||||||
\(393\) | 0.957541 | 0.0483015 | ||||||||
\(394\) | 21.0006 | 1.05799 | ||||||||
\(395\) | 19.2103 | 0.966574 | ||||||||
\(396\) | 4.41321 | 0.221772 | ||||||||
\(397\) | 8.58208 | 0.430722 | 0.215361 | − | 0.976534i | \(-0.430907\pi\) | ||||
0.215361 | + | 0.976534i | \(0.430907\pi\) | |||||||
\(398\) | 22.0758 | 1.10656 | ||||||||
\(399\) | 0.909254 | 0.0455196 | ||||||||
\(400\) | 7.56864 | 0.378432 | ||||||||
\(401\) | −8.93961 | −0.446423 | −0.223211 | − | 0.974770i | \(-0.571654\pi\) | ||||
−0.223211 | + | 0.974770i | \(0.571654\pi\) | |||||||
\(402\) | 14.3239 | 0.714410 | ||||||||
\(403\) | −4.19458 | −0.208947 | ||||||||
\(404\) | 11.4085 | 0.567596 | ||||||||
\(405\) | −3.54523 | −0.176164 | ||||||||
\(406\) | −0.0975154 | −0.00483961 | ||||||||
\(407\) | 37.9305 | 1.88015 | ||||||||
\(408\) | −5.92847 | −0.293503 | ||||||||
\(409\) | −12.8873 | −0.637237 | −0.318619 | − | 0.947883i | \(-0.603219\pi\) | ||||
−0.318619 | + | 0.947883i | \(0.603219\pi\) | |||||||
\(410\) | −27.4285 | −1.35460 | ||||||||
\(411\) | −13.0164 | −0.642054 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | 2.52499 | 0.124247 | ||||||||
\(414\) | −6.44327 | −0.316670 | ||||||||
\(415\) | −0.110248 | −0.00541187 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −1.41313 | −0.0692013 | ||||||||
\(418\) | −24.0714 | −1.17737 | ||||||||
\(419\) | 37.2192 | 1.81828 | 0.909138 | − | 0.416495i | \(-0.136742\pi\) | ||||
0.909138 | + | 0.416495i | \(0.136742\pi\) | |||||||
\(420\) | −0.590994 | −0.0288376 | ||||||||
\(421\) | 19.7551 | 0.962803 | 0.481402 | − | 0.876500i | \(-0.340128\pi\) | ||||
0.481402 | + | 0.876500i | \(0.340128\pi\) | |||||||
\(422\) | −17.8887 | −0.870810 | ||||||||
\(423\) | 12.7766 | 0.621219 | ||||||||
\(424\) | −1.83140 | −0.0889408 | ||||||||
\(425\) | 44.8705 | 2.17654 | ||||||||
\(426\) | −1.93330 | −0.0936687 | ||||||||
\(427\) | 1.75945 | 0.0851458 | ||||||||
\(428\) | −7.43278 | −0.359277 | ||||||||
\(429\) | 4.41321 | 0.213072 | ||||||||
\(430\) | −26.1002 | −1.25866 | ||||||||
\(431\) | −9.88375 | −0.476084 | −0.238042 | − | 0.971255i | \(-0.576506\pi\) | ||||
−0.238042 | + | 0.971255i | \(0.576506\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −6.36387 | −0.305828 | −0.152914 | − | 0.988239i | \(-0.548866\pi\) | ||||
−0.152914 | + | 0.988239i | \(0.548866\pi\) | |||||||
\(434\) | 0.699242 | 0.0335647 | ||||||||
\(435\) | −2.07386 | −0.0994338 | ||||||||
\(436\) | −6.41750 | −0.307343 | ||||||||
\(437\) | 35.1441 | 1.68117 | ||||||||
\(438\) | 13.3410 | 0.637458 | ||||||||
\(439\) | 19.3688 | 0.924421 | 0.462210 | − | 0.886770i | \(-0.347057\pi\) | ||||
0.462210 | + | 0.886770i | \(0.347057\pi\) | |||||||
\(440\) | 15.6458 | 0.745886 | ||||||||
\(441\) | −6.97221 | −0.332010 | ||||||||
\(442\) | −5.92847 | −0.281988 | ||||||||
\(443\) | 7.47721 | 0.355253 | 0.177626 | − | 0.984098i | \(-0.443158\pi\) | ||||
0.177626 | + | 0.984098i | \(0.443158\pi\) | |||||||
\(444\) | 8.59476 | 0.407889 | ||||||||
\(445\) | 6.67539 | 0.316444 | ||||||||
\(446\) | 16.1109 | 0.762873 | ||||||||
\(447\) | −7.00440 | −0.331297 | ||||||||
\(448\) | 0.166701 | 0.00787589 | ||||||||
\(449\) | 15.5110 | 0.732010 | 0.366005 | − | 0.930613i | \(-0.380725\pi\) | ||||
0.366005 | + | 0.930613i | \(0.380725\pi\) | |||||||
\(450\) | −7.56864 | −0.356789 | ||||||||
\(451\) | −34.1438 | −1.60777 | ||||||||
\(452\) | 0.936328 | 0.0440412 | ||||||||
\(453\) | 17.6617 | 0.829817 | ||||||||
\(454\) | 14.0683 | 0.660260 | ||||||||
\(455\) | −0.590994 | −0.0277062 | ||||||||
\(456\) | −5.45439 | −0.255425 | ||||||||
\(457\) | −15.0435 | −0.703707 | −0.351853 | − | 0.936055i | \(-0.614448\pi\) | ||||
−0.351853 | + | 0.936055i | \(0.614448\pi\) | |||||||
\(458\) | −9.68824 | −0.452702 | ||||||||
\(459\) | 5.92847 | 0.276717 | ||||||||
\(460\) | −22.8429 | −1.06505 | ||||||||
\(461\) | −3.44551 | −0.160473 | −0.0802367 | − | 0.996776i | \(-0.525568\pi\) | ||||
−0.0802367 | + | 0.996776i | \(0.525568\pi\) | |||||||
\(462\) | −0.735688 | −0.0342273 | ||||||||
\(463\) | −7.48545 | −0.347878 | −0.173939 | − | 0.984756i | \(-0.555650\pi\) | ||||
−0.173939 | + | 0.984756i | \(0.555650\pi\) | |||||||
\(464\) | 0.584971 | 0.0271566 | ||||||||
\(465\) | 14.8707 | 0.689614 | ||||||||
\(466\) | −15.9605 | −0.739357 | ||||||||
\(467\) | −12.9657 | −0.599982 | −0.299991 | − | 0.953942i | \(-0.596984\pi\) | ||||
−0.299991 | + | 0.953942i | \(0.596984\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −2.38781 | −0.110259 | ||||||||
\(470\) | 45.2959 | 2.08935 | ||||||||
\(471\) | −12.5859 | −0.579926 | ||||||||
\(472\) | −15.1468 | −0.697187 | ||||||||
\(473\) | −32.4904 | −1.49391 | ||||||||
\(474\) | 5.41863 | 0.248886 | ||||||||
\(475\) | 41.2824 | 1.89416 | ||||||||
\(476\) | 0.988283 | 0.0452979 | ||||||||
\(477\) | 1.83140 | 0.0838542 | ||||||||
\(478\) | 22.7497 | 1.04055 | ||||||||
\(479\) | −6.53720 | −0.298692 | −0.149346 | − | 0.988785i | \(-0.547717\pi\) | ||||
−0.149346 | + | 0.988785i | \(0.547717\pi\) | |||||||
\(480\) | 3.54523 | 0.161817 | ||||||||
\(481\) | 8.59476 | 0.391887 | ||||||||
\(482\) | 4.90865 | 0.223583 | ||||||||
\(483\) | 1.07410 | 0.0488733 | ||||||||
\(484\) | 8.47644 | 0.385293 | ||||||||
\(485\) | −4.48650 | −0.203722 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −20.2434 | −0.917314 | −0.458657 | − | 0.888613i | \(-0.651669\pi\) | ||||
−0.458657 | + | 0.888613i | \(0.651669\pi\) | |||||||
\(488\) | −10.5545 | −0.477781 | ||||||||
\(489\) | −22.7916 | −1.03067 | ||||||||
\(490\) | −24.7181 | −1.11665 | ||||||||
\(491\) | 7.77786 | 0.351010 | 0.175505 | − | 0.984479i | \(-0.443844\pi\) | ||||
0.175505 | + | 0.984479i | \(0.443844\pi\) | |||||||
\(492\) | −7.73673 | −0.348799 | ||||||||
\(493\) | 3.46798 | 0.156190 | ||||||||
\(494\) | −5.45439 | −0.245405 | ||||||||
\(495\) | −15.6458 | −0.703228 | ||||||||
\(496\) | −4.19458 | −0.188342 | ||||||||
\(497\) | 0.322283 | 0.0144564 | ||||||||
\(498\) | −0.0310976 | −0.00139352 | ||||||||
\(499\) | 8.02423 | 0.359214 | 0.179607 | − | 0.983738i | \(-0.442517\pi\) | ||||
0.179607 | + | 0.983738i | \(0.442517\pi\) | |||||||
\(500\) | −9.10643 | −0.407252 | ||||||||
\(501\) | −3.49484 | −0.156138 | ||||||||
\(502\) | 18.4284 | 0.822498 | ||||||||
\(503\) | −22.2740 | −0.993147 | −0.496574 | − | 0.867995i | \(-0.665409\pi\) | ||||
−0.496574 | + | 0.867995i | \(0.665409\pi\) | |||||||
\(504\) | −0.166701 | −0.00742546 | ||||||||
\(505\) | −40.4459 | −1.79982 | ||||||||
\(506\) | −28.4355 | −1.26411 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 20.8839 | 0.926575 | ||||||||
\(509\) | −26.1289 | −1.15814 | −0.579072 | − | 0.815276i | \(-0.696585\pi\) | ||||
−0.579072 | + | 0.815276i | \(0.696585\pi\) | |||||||
\(510\) | 21.0178 | 0.930682 | ||||||||
\(511\) | −2.22396 | −0.0983823 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.45439 | 0.240817 | ||||||||
\(514\) | −29.7453 | −1.31201 | ||||||||
\(515\) | −3.54523 | −0.156221 | ||||||||
\(516\) | −7.36207 | −0.324097 | ||||||||
\(517\) | 56.3858 | 2.47984 | ||||||||
\(518\) | −1.43276 | −0.0629518 | ||||||||
\(519\) | 13.3786 | 0.587256 | ||||||||
\(520\) | 3.54523 | 0.155469 | ||||||||
\(521\) | 38.1165 | 1.66991 | 0.834957 | − | 0.550315i | \(-0.185493\pi\) | ||||
0.834957 | + | 0.550315i | \(0.185493\pi\) | |||||||
\(522\) | −0.584971 | −0.0256035 | ||||||||
\(523\) | −40.0912 | −1.75307 | −0.876534 | − | 0.481341i | \(-0.840150\pi\) | ||||
−0.876534 | + | 0.481341i | \(0.840150\pi\) | |||||||
\(524\) | 0.957541 | 0.0418304 | ||||||||
\(525\) | 1.26170 | 0.0550652 | ||||||||
\(526\) | −20.2991 | −0.885085 | ||||||||
\(527\) | −24.8674 | −1.08324 | ||||||||
\(528\) | 4.41321 | 0.192060 | ||||||||
\(529\) | 18.5158 | 0.805034 | ||||||||
\(530\) | 6.49274 | 0.282027 | ||||||||
\(531\) | 15.1468 | 0.657315 | ||||||||
\(532\) | 0.909254 | 0.0394212 | ||||||||
\(533\) | −7.73673 | −0.335115 | ||||||||
\(534\) | 1.88292 | 0.0814820 | ||||||||
\(535\) | 26.3509 | 1.13925 | ||||||||
\(536\) | 14.3239 | 0.618697 | ||||||||
\(537\) | 1.33946 | 0.0578020 | ||||||||
\(538\) | −6.33144 | −0.272968 | ||||||||
\(539\) | −30.7698 | −1.32535 | ||||||||
\(540\) | −3.54523 | −0.152562 | ||||||||
\(541\) | 14.7556 | 0.634395 | 0.317197 | − | 0.948360i | \(-0.397258\pi\) | ||||
0.317197 | + | 0.948360i | \(0.397258\pi\) | |||||||
\(542\) | 29.3163 | 1.25924 | ||||||||
\(543\) | −5.60284 | −0.240441 | ||||||||
\(544\) | −5.92847 | −0.254181 | ||||||||
\(545\) | 22.7515 | 0.974567 | ||||||||
\(546\) | −0.166701 | −0.00713415 | ||||||||
\(547\) | −10.2583 | −0.438613 | −0.219307 | − | 0.975656i | \(-0.570380\pi\) | ||||
−0.219307 | + | 0.975656i | \(0.570380\pi\) | |||||||
\(548\) | −13.0164 | −0.556035 | ||||||||
\(549\) | 10.5545 | 0.450456 | ||||||||
\(550\) | −33.4020 | −1.42427 | ||||||||
\(551\) | 3.19066 | 0.135927 | ||||||||
\(552\) | −6.44327 | −0.274244 | ||||||||
\(553\) | −0.903293 | −0.0384119 | ||||||||
\(554\) | −27.2323 | −1.15699 | ||||||||
\(555\) | −30.4704 | −1.29340 | ||||||||
\(556\) | −1.41313 | −0.0599301 | ||||||||
\(557\) | 31.5065 | 1.33497 | 0.667486 | − | 0.744622i | \(-0.267370\pi\) | ||||
0.667486 | + | 0.744622i | \(0.267370\pi\) | |||||||
\(558\) | 4.19458 | 0.177571 | ||||||||
\(559\) | −7.36207 | −0.311382 | ||||||||
\(560\) | −0.590994 | −0.0249741 | ||||||||
\(561\) | 26.1636 | 1.10463 | ||||||||
\(562\) | 22.5088 | 0.949478 | ||||||||
\(563\) | −14.2498 | −0.600556 | −0.300278 | − | 0.953852i | \(-0.597079\pi\) | ||||
−0.300278 | + | 0.953852i | \(0.597079\pi\) | |||||||
\(564\) | 12.7766 | 0.537991 | ||||||||
\(565\) | −3.31950 | −0.139652 | ||||||||
\(566\) | −14.8017 | −0.622163 | ||||||||
\(567\) | 0.166701 | 0.00700079 | ||||||||
\(568\) | −1.93330 | −0.0811194 | ||||||||
\(569\) | −6.96402 | −0.291947 | −0.145973 | − | 0.989289i | \(-0.546631\pi\) | ||||
−0.145973 | + | 0.989289i | \(0.546631\pi\) | |||||||
\(570\) | 19.3371 | 0.809941 | ||||||||
\(571\) | −12.5116 | −0.523592 | −0.261796 | − | 0.965123i | \(-0.584315\pi\) | ||||
−0.261796 | + | 0.965123i | \(0.584315\pi\) | |||||||
\(572\) | 4.41321 | 0.184526 | ||||||||
\(573\) | 8.01970 | 0.335028 | ||||||||
\(574\) | 1.28972 | 0.0538320 | ||||||||
\(575\) | 48.7669 | 2.03372 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −0.602483 | −0.0250817 | −0.0125408 | − | 0.999921i | \(-0.503992\pi\) | ||||
−0.0125408 | + | 0.999921i | \(0.503992\pi\) | |||||||
\(578\) | −18.1467 | −0.754804 | ||||||||
\(579\) | 16.5029 | 0.685836 | ||||||||
\(580\) | −2.07386 | −0.0861122 | ||||||||
\(581\) | 0.00518401 | 0.000215069 0 | ||||||||
\(582\) | −1.26550 | −0.0524569 | ||||||||
\(583\) | 8.08237 | 0.334738 | ||||||||
\(584\) | 13.3410 | 0.552055 | ||||||||
\(585\) | −3.54523 | −0.146577 | ||||||||
\(586\) | −2.36229 | −0.0975854 | ||||||||
\(587\) | −32.4538 | −1.33951 | −0.669755 | − | 0.742582i | \(-0.733601\pi\) | ||||
−0.669755 | + | 0.742582i | \(0.733601\pi\) | |||||||
\(588\) | −6.97221 | −0.287529 | ||||||||
\(589\) | −22.8789 | −0.942708 | ||||||||
\(590\) | 53.6988 | 2.21075 | ||||||||
\(591\) | −21.0006 | −0.863848 | ||||||||
\(592\) | 8.59476 | 0.353243 | ||||||||
\(593\) | −0.494938 | −0.0203247 | −0.0101623 | − | 0.999948i | \(-0.503235\pi\) | ||||
−0.0101623 | + | 0.999948i | \(0.503235\pi\) | |||||||
\(594\) | −4.41321 | −0.181076 | ||||||||
\(595\) | −3.50369 | −0.143637 | ||||||||
\(596\) | −7.00440 | −0.286912 | ||||||||
\(597\) | −22.0758 | −0.903502 | ||||||||
\(598\) | −6.44327 | −0.263485 | ||||||||
\(599\) | −28.8497 | −1.17876 | −0.589382 | − | 0.807854i | \(-0.700629\pi\) | ||||
−0.589382 | + | 0.807854i | \(0.700629\pi\) | |||||||
\(600\) | −7.56864 | −0.308989 | ||||||||
\(601\) | 45.1024 | 1.83977 | 0.919883 | − | 0.392192i | \(-0.128283\pi\) | ||||
0.919883 | + | 0.392192i | \(0.128283\pi\) | |||||||
\(602\) | 1.22727 | 0.0500196 | ||||||||
\(603\) | −14.3239 | −0.583313 | ||||||||
\(604\) | 17.6617 | 0.718643 | ||||||||
\(605\) | −30.0509 | −1.22174 | ||||||||
\(606\) | −11.4085 | −0.463440 | ||||||||
\(607\) | −34.7633 | −1.41100 | −0.705500 | − | 0.708710i | \(-0.749277\pi\) | ||||
−0.705500 | + | 0.708710i | \(0.749277\pi\) | |||||||
\(608\) | −5.45439 | −0.221205 | ||||||||
\(609\) | 0.0975154 | 0.00395152 | ||||||||
\(610\) | 37.4182 | 1.51502 | ||||||||
\(611\) | 12.7766 | 0.516885 | ||||||||
\(612\) | 5.92847 | 0.239644 | ||||||||
\(613\) | −14.6854 | −0.593137 | −0.296569 | − | 0.955012i | \(-0.595842\pi\) | ||||
−0.296569 | + | 0.955012i | \(0.595842\pi\) | |||||||
\(614\) | −33.3405 | −1.34551 | ||||||||
\(615\) | 27.4285 | 1.10602 | ||||||||
\(616\) | −0.735688 | −0.0296417 | ||||||||
\(617\) | 24.2856 | 0.977702 | 0.488851 | − | 0.872367i | \(-0.337416\pi\) | ||||
0.488851 | + | 0.872367i | \(0.337416\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −23.9388 | −0.962183 | −0.481092 | − | 0.876670i | \(-0.659760\pi\) | ||||
−0.481092 | + | 0.876670i | \(0.659760\pi\) | |||||||
\(620\) | 14.8707 | 0.597223 | ||||||||
\(621\) | 6.44327 | 0.258560 | ||||||||
\(622\) | −26.8070 | −1.07486 | ||||||||
\(623\) | −0.313886 | −0.0125756 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −5.55884 | −0.222354 | ||||||||
\(626\) | −10.1194 | −0.404454 | ||||||||
\(627\) | 24.0714 | 0.961319 | ||||||||
\(628\) | −12.5859 | −0.502231 | ||||||||
\(629\) | 50.9538 | 2.03166 | ||||||||
\(630\) | 0.590994 | 0.0235458 | ||||||||
\(631\) | 21.3458 | 0.849763 | 0.424881 | − | 0.905249i | \(-0.360316\pi\) | ||||
0.424881 | + | 0.905249i | \(0.360316\pi\) | |||||||
\(632\) | 5.41863 | 0.215542 | ||||||||
\(633\) | 17.8887 | 0.711013 | ||||||||
\(634\) | −12.7234 | −0.505309 | ||||||||
\(635\) | −74.0383 | −2.93812 | ||||||||
\(636\) | 1.83140 | 0.0726199 | ||||||||
\(637\) | −6.97221 | −0.276249 | ||||||||
\(638\) | −2.58160 | −0.102207 | ||||||||
\(639\) | 1.93330 | 0.0764801 | ||||||||
\(640\) | 3.54523 | 0.140137 | ||||||||
\(641\) | −9.82132 | −0.387919 | −0.193959 | − | 0.981010i | \(-0.562133\pi\) | ||||
−0.193959 | + | 0.981010i | \(0.562133\pi\) | |||||||
\(642\) | 7.43278 | 0.293349 | ||||||||
\(643\) | −35.6944 | −1.40765 | −0.703825 | − | 0.710373i | \(-0.748526\pi\) | ||||
−0.703825 | + | 0.710373i | \(0.748526\pi\) | |||||||
\(644\) | 1.07410 | 0.0423255 | ||||||||
\(645\) | 26.1002 | 1.02769 | ||||||||
\(646\) | −32.3362 | −1.27225 | ||||||||
\(647\) | −23.9578 | −0.941877 | −0.470938 | − | 0.882166i | \(-0.656085\pi\) | ||||
−0.470938 | + | 0.882166i | \(0.656085\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 66.8460 | 2.62393 | ||||||||
\(650\) | −7.56864 | −0.296867 | ||||||||
\(651\) | −0.699242 | −0.0274054 | ||||||||
\(652\) | −22.7916 | −0.892589 | ||||||||
\(653\) | −23.3322 | −0.913058 | −0.456529 | − | 0.889708i | \(-0.650908\pi\) | ||||
−0.456529 | + | 0.889708i | \(0.650908\pi\) | |||||||
\(654\) | 6.41750 | 0.250944 | ||||||||
\(655\) | −3.39470 | −0.132642 | ||||||||
\(656\) | −7.73673 | −0.302069 | ||||||||
\(657\) | −13.3410 | −0.520482 | ||||||||
\(658\) | −2.12987 | −0.0830311 | ||||||||
\(659\) | −18.8562 | −0.734533 | −0.367267 | − | 0.930116i | \(-0.619706\pi\) | ||||
−0.367267 | + | 0.930116i | \(0.619706\pi\) | |||||||
\(660\) | −15.6458 | −0.609014 | ||||||||
\(661\) | −8.21926 | −0.319692 | −0.159846 | − | 0.987142i | \(-0.551100\pi\) | ||||
−0.159846 | + | 0.987142i | \(0.551100\pi\) | |||||||
\(662\) | 18.0998 | 0.703468 | ||||||||
\(663\) | 5.92847 | 0.230243 | ||||||||
\(664\) | −0.0310976 | −0.00120682 | ||||||||
\(665\) | −3.22351 | −0.125002 | ||||||||
\(666\) | −8.59476 | −0.333040 | ||||||||
\(667\) | 3.76913 | 0.145941 | ||||||||
\(668\) | −3.49484 | −0.135220 | ||||||||
\(669\) | −16.1109 | −0.622883 | ||||||||
\(670\) | −50.7814 | −1.96186 | ||||||||
\(671\) | 46.5793 | 1.79817 | ||||||||
\(672\) | −0.166701 | −0.00643064 | ||||||||
\(673\) | 7.82248 | 0.301534 | 0.150767 | − | 0.988569i | \(-0.451826\pi\) | ||||
0.150767 | + | 0.988569i | \(0.451826\pi\) | |||||||
\(674\) | 13.9374 | 0.536847 | ||||||||
\(675\) | 7.56864 | 0.291317 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 0.944147 | 0.0362865 | 0.0181433 | − | 0.999835i | \(-0.494225\pi\) | ||||
0.0181433 | + | 0.999835i | \(0.494225\pi\) | |||||||
\(678\) | −0.936328 | −0.0359595 | ||||||||
\(679\) | 0.210961 | 0.00809595 | ||||||||
\(680\) | 21.0178 | 0.805995 | ||||||||
\(681\) | −14.0683 | −0.539100 | ||||||||
\(682\) | 18.5116 | 0.708845 | ||||||||
\(683\) | −13.5829 | −0.519736 | −0.259868 | − | 0.965644i | \(-0.583679\pi\) | ||||
−0.259868 | + | 0.965644i | \(0.583679\pi\) | |||||||
\(684\) | 5.45439 | 0.208554 | ||||||||
\(685\) | 46.1462 | 1.76316 | ||||||||
\(686\) | 2.32918 | 0.0889287 | ||||||||
\(687\) | 9.68824 | 0.369630 | ||||||||
\(688\) | −7.36207 | −0.280676 | ||||||||
\(689\) | 1.83140 | 0.0697709 | ||||||||
\(690\) | 22.8429 | 0.869614 | ||||||||
\(691\) | 6.10311 | 0.232173 | 0.116087 | − | 0.993239i | \(-0.462965\pi\) | ||||
0.116087 | + | 0.993239i | \(0.462965\pi\) | |||||||
\(692\) | 13.3786 | 0.508578 | ||||||||
\(693\) | 0.735688 | 0.0279465 | ||||||||
\(694\) | 2.89499 | 0.109892 | ||||||||
\(695\) | 5.00987 | 0.190035 | ||||||||
\(696\) | −0.584971 | −0.0221733 | ||||||||
\(697\) | −45.8670 | −1.73733 | ||||||||
\(698\) | −3.83614 | −0.145200 | ||||||||
\(699\) | 15.9605 | 0.603683 | ||||||||
\(700\) | 1.26170 | 0.0476879 | ||||||||
\(701\) | 9.00589 | 0.340148 | 0.170074 | − | 0.985431i | \(-0.445599\pi\) | ||||
0.170074 | + | 0.985431i | \(0.445599\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 46.8792 | 1.76808 | ||||||||
\(704\) | 4.41321 | 0.166329 | ||||||||
\(705\) | −45.2959 | −1.70594 | ||||||||
\(706\) | −14.3426 | −0.539789 | ||||||||
\(707\) | 1.90182 | 0.0715252 | ||||||||
\(708\) | 15.1468 | 0.569251 | ||||||||
\(709\) | −17.0731 | −0.641193 | −0.320597 | − | 0.947216i | \(-0.603883\pi\) | ||||
−0.320597 | + | 0.947216i | \(0.603883\pi\) | |||||||
\(710\) | 6.85399 | 0.257226 | ||||||||
\(711\) | −5.41863 | −0.203215 | ||||||||
\(712\) | 1.88292 | 0.0705655 | ||||||||
\(713\) | −27.0268 | −1.01216 | ||||||||
\(714\) | −0.988283 | −0.0369855 | ||||||||
\(715\) | −15.6458 | −0.585121 | ||||||||
\(716\) | 1.33946 | 0.0500580 | ||||||||
\(717\) | −22.7497 | −0.849604 | ||||||||
\(718\) | −29.9911 | −1.11926 | ||||||||
\(719\) | −50.5592 | −1.88554 | −0.942771 | − | 0.333441i | \(-0.891790\pi\) | ||||
−0.942771 | + | 0.333441i | \(0.891790\pi\) | |||||||
\(720\) | −3.54523 | −0.132123 | ||||||||
\(721\) | 0.166701 | 0.00620828 | ||||||||
\(722\) | −10.7504 | −0.400088 | ||||||||
\(723\) | −4.90865 | −0.182555 | ||||||||
\(724\) | −5.60284 | −0.208228 | ||||||||
\(725\) | 4.42744 | 0.164431 | ||||||||
\(726\) | −8.47644 | −0.314590 | ||||||||
\(727\) | 24.0375 | 0.891500 | 0.445750 | − | 0.895157i | \(-0.352937\pi\) | ||||
0.445750 | + | 0.895157i | \(0.352937\pi\) | |||||||
\(728\) | −0.166701 | −0.00617836 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −47.2969 | −1.75054 | ||||||||
\(731\) | −43.6458 | −1.61430 | ||||||||
\(732\) | 10.5545 | 0.390106 | ||||||||
\(733\) | −7.01068 | −0.258945 | −0.129473 | − | 0.991583i | \(-0.541328\pi\) | ||||
−0.129473 | + | 0.991583i | \(0.541328\pi\) | |||||||
\(734\) | 2.25358 | 0.0831812 | ||||||||
\(735\) | 24.7181 | 0.911740 | ||||||||
\(736\) | −6.44327 | −0.237502 | ||||||||
\(737\) | −63.2143 | −2.32853 | ||||||||
\(738\) | 7.73673 | 0.284793 | ||||||||
\(739\) | 37.0958 | 1.36459 | 0.682296 | − | 0.731076i | \(-0.260982\pi\) | ||||
0.682296 | + | 0.731076i | \(0.260982\pi\) | |||||||
\(740\) | −30.4704 | −1.12011 | ||||||||
\(741\) | 5.45439 | 0.200372 | ||||||||
\(742\) | −0.305297 | −0.0112078 | ||||||||
\(743\) | −12.5006 | −0.458604 | −0.229302 | − | 0.973355i | \(-0.573644\pi\) | ||||
−0.229302 | + | 0.973355i | \(0.573644\pi\) | |||||||
\(744\) | 4.19458 | 0.153781 | ||||||||
\(745\) | 24.8322 | 0.909782 | ||||||||
\(746\) | −26.3702 | −0.965483 | ||||||||
\(747\) | 0.0310976 | 0.00113780 | ||||||||
\(748\) | 26.1636 | 0.956635 | ||||||||
\(749\) | −1.23905 | −0.0452741 | ||||||||
\(750\) | 9.10643 | 0.332520 | ||||||||
\(751\) | 39.4781 | 1.44058 | 0.720288 | − | 0.693675i | \(-0.244009\pi\) | ||||
0.720288 | + | 0.693675i | \(0.244009\pi\) | |||||||
\(752\) | 12.7766 | 0.465914 | ||||||||
\(753\) | −18.4284 | −0.671567 | ||||||||
\(754\) | −0.584971 | −0.0213034 | ||||||||
\(755\) | −62.6146 | −2.27878 | ||||||||
\(756\) | 0.166701 | 0.00606287 | ||||||||
\(757\) | −7.13120 | −0.259188 | −0.129594 | − | 0.991567i | \(-0.541367\pi\) | ||||
−0.129594 | + | 0.991567i | \(0.541367\pi\) | |||||||
\(758\) | −7.86050 | −0.285506 | ||||||||
\(759\) | 28.4355 | 1.03214 | ||||||||
\(760\) | 19.3371 | 0.701429 | ||||||||
\(761\) | −31.6705 | −1.14805 | −0.574026 | − | 0.818837i | \(-0.694619\pi\) | ||||
−0.574026 | + | 0.818837i | \(0.694619\pi\) | |||||||
\(762\) | −20.8839 | −0.756545 | ||||||||
\(763\) | −1.06981 | −0.0387295 | ||||||||
\(764\) | 8.01970 | 0.290143 | ||||||||
\(765\) | −21.0178 | −0.759899 | ||||||||
\(766\) | −4.79907 | −0.173397 | ||||||||
\(767\) | 15.1468 | 0.546919 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 23.1490 | 0.834775 | 0.417387 | − | 0.908729i | \(-0.362946\pi\) | ||||
0.417387 | + | 0.908729i | \(0.362946\pi\) | |||||||
\(770\) | 2.60818 | 0.0939923 | ||||||||
\(771\) | 29.7453 | 1.07125 | ||||||||
\(772\) | 16.5029 | 0.593952 | ||||||||
\(773\) | 34.1894 | 1.22971 | 0.614853 | − | 0.788642i | \(-0.289215\pi\) | ||||
0.614853 | + | 0.788642i | \(0.289215\pi\) | |||||||
\(774\) | 7.36207 | 0.264624 | ||||||||
\(775\) | −31.7473 | −1.14040 | ||||||||
\(776\) | −1.26550 | −0.0454290 | ||||||||
\(777\) | 1.43276 | 0.0513999 | ||||||||
\(778\) | 6.03796 | 0.216471 | ||||||||
\(779\) | −42.1992 | −1.51194 | ||||||||
\(780\) | −3.54523 | −0.126940 | ||||||||
\(781\) | 8.53206 | 0.305301 | ||||||||
\(782\) | −38.1987 | −1.36598 | ||||||||
\(783\) | 0.584971 | 0.0209052 | ||||||||
\(784\) | −6.97221 | −0.249008 | ||||||||
\(785\) | 44.6198 | 1.59255 | ||||||||
\(786\) | −0.957541 | −0.0341543 | ||||||||
\(787\) | −2.16408 | −0.0771411 | −0.0385705 | − | 0.999256i | \(-0.512280\pi\) | ||||
−0.0385705 | + | 0.999256i | \(0.512280\pi\) | |||||||
\(788\) | −21.0006 | −0.748114 | ||||||||
\(789\) | 20.2991 | 0.722669 | ||||||||
\(790\) | −19.2103 | −0.683471 | ||||||||
\(791\) | 0.156087 | 0.00554982 | ||||||||
\(792\) | −4.41321 | −0.156817 | ||||||||
\(793\) | 10.5545 | 0.374802 | ||||||||
\(794\) | −8.58208 | −0.304567 | ||||||||
\(795\) | −6.49274 | −0.230274 | ||||||||
\(796\) | −22.0758 | −0.782455 | ||||||||
\(797\) | 9.88873 | 0.350277 | 0.175138 | − | 0.984544i | \(-0.443963\pi\) | ||||
0.175138 | + | 0.984544i | \(0.443963\pi\) | |||||||
\(798\) | −0.909254 | −0.0321872 | ||||||||
\(799\) | 75.7456 | 2.67969 | ||||||||
\(800\) | −7.56864 | −0.267592 | ||||||||
\(801\) | −1.88292 | −0.0665298 | ||||||||
\(802\) | 8.93961 | 0.315668 | ||||||||
\(803\) | −58.8767 | −2.07771 | ||||||||
\(804\) | −14.3239 | −0.505164 | ||||||||
\(805\) | −3.80794 | −0.134212 | ||||||||
\(806\) | 4.19458 | 0.147748 | ||||||||
\(807\) | 6.33144 | 0.222877 | ||||||||
\(808\) | −11.4085 | −0.401351 | ||||||||
\(809\) | −26.1335 | −0.918805 | −0.459402 | − | 0.888228i | \(-0.651936\pi\) | ||||
−0.459402 | + | 0.888228i | \(0.651936\pi\) | |||||||
\(810\) | 3.54523 | 0.124567 | ||||||||
\(811\) | 12.2978 | 0.431834 | 0.215917 | − | 0.976412i | \(-0.430726\pi\) | ||||
0.215917 | + | 0.976412i | \(0.430726\pi\) | |||||||
\(812\) | 0.0975154 | 0.00342212 | ||||||||
\(813\) | −29.3163 | −1.02817 | ||||||||
\(814\) | −37.9305 | −1.32946 | ||||||||
\(815\) | 80.8015 | 2.83035 | ||||||||
\(816\) | 5.92847 | 0.207538 | ||||||||
\(817\) | −40.1556 | −1.40487 | ||||||||
\(818\) | 12.8873 | 0.450595 | ||||||||
\(819\) | 0.166701 | 0.00582501 | ||||||||
\(820\) | 27.4285 | 0.957844 | ||||||||
\(821\) | 51.1200 | 1.78410 | 0.892051 | − | 0.451935i | \(-0.149266\pi\) | ||||
0.892051 | + | 0.451935i | \(0.149266\pi\) | |||||||
\(822\) | 13.0164 | 0.454000 | ||||||||
\(823\) | 30.7770 | 1.07282 | 0.536409 | − | 0.843958i | \(-0.319781\pi\) | ||||
0.536409 | + | 0.843958i | \(0.319781\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 33.4020 | 1.16291 | ||||||||
\(826\) | −2.52499 | −0.0878556 | ||||||||
\(827\) | 31.3675 | 1.09075 | 0.545377 | − | 0.838191i | \(-0.316386\pi\) | ||||
0.545377 | + | 0.838191i | \(0.316386\pi\) | |||||||
\(828\) | 6.44327 | 0.223919 | ||||||||
\(829\) | −11.7624 | −0.408524 | −0.204262 | − | 0.978916i | \(-0.565479\pi\) | ||||
−0.204262 | + | 0.978916i | \(0.565479\pi\) | |||||||
\(830\) | 0.110248 | 0.00382677 | ||||||||
\(831\) | 27.2323 | 0.944677 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −41.3345 | −1.43216 | ||||||||
\(834\) | 1.41313 | 0.0489327 | ||||||||
\(835\) | 12.3900 | 0.428774 | ||||||||
\(836\) | 24.0714 | 0.832526 | ||||||||
\(837\) | −4.19458 | −0.144986 | ||||||||
\(838\) | −37.2192 | −1.28572 | ||||||||
\(839\) | 49.1695 | 1.69752 | 0.848760 | − | 0.528778i | \(-0.177350\pi\) | ||||
0.848760 | + | 0.528778i | \(0.177350\pi\) | |||||||
\(840\) | 0.590994 | 0.0203912 | ||||||||
\(841\) | −28.6578 | −0.988200 | ||||||||
\(842\) | −19.7551 | −0.680805 | ||||||||
\(843\) | −22.5088 | −0.775245 | ||||||||
\(844\) | 17.8887 | 0.615755 | ||||||||
\(845\) | −3.54523 | −0.121960 | ||||||||
\(846\) | −12.7766 | −0.439268 | ||||||||
\(847\) | 1.41303 | 0.0485524 | ||||||||
\(848\) | 1.83140 | 0.0628906 | ||||||||
\(849\) | 14.8017 | 0.507994 | ||||||||
\(850\) | −44.8705 | −1.53904 | ||||||||
\(851\) | 55.3784 | 1.89835 | ||||||||
\(852\) | 1.93330 | 0.0662337 | ||||||||
\(853\) | −52.5264 | −1.79847 | −0.899235 | − | 0.437466i | \(-0.855876\pi\) | ||||
−0.899235 | + | 0.437466i | \(0.855876\pi\) | |||||||
\(854\) | −1.75945 | −0.0602072 | ||||||||
\(855\) | −19.3371 | −0.661314 | ||||||||
\(856\) | 7.43278 | 0.254047 | ||||||||
\(857\) | 29.6276 | 1.01206 | 0.506030 | − | 0.862516i | \(-0.331112\pi\) | ||||
0.506030 | + | 0.862516i | \(0.331112\pi\) | |||||||
\(858\) | −4.41321 | −0.150665 | ||||||||
\(859\) | 12.5133 | 0.426948 | 0.213474 | − | 0.976949i | \(-0.431522\pi\) | ||||
0.213474 | + | 0.976949i | \(0.431522\pi\) | |||||||
\(860\) | 26.1002 | 0.890010 | ||||||||
\(861\) | −1.28972 | −0.0439536 | ||||||||
\(862\) | 9.88375 | 0.336642 | ||||||||
\(863\) | −14.7839 | −0.503251 | −0.251626 | − | 0.967825i | \(-0.580965\pi\) | ||||
−0.251626 | + | 0.967825i | \(0.580965\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −47.4302 | −1.61268 | ||||||||
\(866\) | 6.36387 | 0.216253 | ||||||||
\(867\) | 18.1467 | 0.616295 | ||||||||
\(868\) | −0.699242 | −0.0237338 | ||||||||
\(869\) | −23.9136 | −0.811212 | ||||||||
\(870\) | 2.07386 | 0.0703103 | ||||||||
\(871\) | −14.3239 | −0.485346 | ||||||||
\(872\) | 6.41750 | 0.217324 | ||||||||
\(873\) | 1.26550 | 0.0428308 | ||||||||
\(874\) | −35.1441 | −1.18877 | ||||||||
\(875\) | −1.51805 | −0.0513196 | ||||||||
\(876\) | −13.3410 | −0.450751 | ||||||||
\(877\) | −23.8254 | −0.804528 | −0.402264 | − | 0.915524i | \(-0.631777\pi\) | ||||
−0.402264 | + | 0.915524i | \(0.631777\pi\) | |||||||
\(878\) | −19.3688 | −0.653664 | ||||||||
\(879\) | 2.36229 | 0.0796781 | ||||||||
\(880\) | −15.6458 | −0.527421 | ||||||||
\(881\) | −44.5646 | −1.50142 | −0.750709 | − | 0.660633i | \(-0.770288\pi\) | ||||
−0.750709 | + | 0.660633i | \(0.770288\pi\) | |||||||
\(882\) | 6.97221 | 0.234767 | ||||||||
\(883\) | −27.3495 | −0.920383 | −0.460192 | − | 0.887820i | \(-0.652219\pi\) | ||||
−0.460192 | + | 0.887820i | \(0.652219\pi\) | |||||||
\(884\) | 5.92847 | 0.199396 | ||||||||
\(885\) | −53.6988 | −1.80507 | ||||||||
\(886\) | −7.47721 | −0.251202 | ||||||||
\(887\) | −21.7534 | −0.730406 | −0.365203 | − | 0.930928i | \(-0.619000\pi\) | ||||
−0.365203 | + | 0.930928i | \(0.619000\pi\) | |||||||
\(888\) | −8.59476 | −0.288421 | ||||||||
\(889\) | 3.48138 | 0.116762 | ||||||||
\(890\) | −6.67539 | −0.223760 | ||||||||
\(891\) | 4.41321 | 0.147848 | ||||||||
\(892\) | −16.1109 | −0.539433 | ||||||||
\(893\) | 69.6885 | 2.33204 | ||||||||
\(894\) | 7.00440 | 0.234262 | ||||||||
\(895\) | −4.74869 | −0.158731 | ||||||||
\(896\) | −0.166701 | −0.00556910 | ||||||||
\(897\) | 6.44327 | 0.215135 | ||||||||
\(898\) | −15.5110 | −0.517609 | ||||||||
\(899\) | −2.45371 | −0.0818357 | ||||||||
\(900\) | 7.56864 | 0.252288 | ||||||||
\(901\) | 10.8574 | 0.361713 | ||||||||
\(902\) | 34.1438 | 1.13687 | ||||||||
\(903\) | −1.22727 | −0.0408408 | ||||||||
\(904\) | −0.936328 | −0.0311418 | ||||||||
\(905\) | 19.8633 | 0.660280 | ||||||||
\(906\) | −17.6617 | −0.586769 | ||||||||
\(907\) | −37.6797 | −1.25113 | −0.625567 | − | 0.780170i | \(-0.715132\pi\) | ||||
−0.625567 | + | 0.780170i | \(0.715132\pi\) | |||||||
\(908\) | −14.0683 | −0.466874 | ||||||||
\(909\) | 11.4085 | 0.378397 | ||||||||
\(910\) | 0.590994 | 0.0195913 | ||||||||
\(911\) | 3.70168 | 0.122642 | 0.0613211 | − | 0.998118i | \(-0.480469\pi\) | ||||
0.0613211 | + | 0.998118i | \(0.480469\pi\) | |||||||
\(912\) | 5.45439 | 0.180613 | ||||||||
\(913\) | 0.137240 | 0.00454199 | ||||||||
\(914\) | 15.0435 | 0.497596 | ||||||||
\(915\) | −37.4182 | −1.23701 | ||||||||
\(916\) | 9.68824 | 0.320109 | ||||||||
\(917\) | 0.159623 | 0.00527122 | ||||||||
\(918\) | −5.92847 | −0.195669 | ||||||||
\(919\) | 14.3948 | 0.474840 | 0.237420 | − | 0.971407i | \(-0.423698\pi\) | ||||
0.237420 | + | 0.971407i | \(0.423698\pi\) | |||||||
\(920\) | 22.8429 | 0.753107 | ||||||||
\(921\) | 33.3405 | 1.09861 | ||||||||
\(922\) | 3.44551 | 0.113472 | ||||||||
\(923\) | 1.93330 | 0.0636353 | ||||||||
\(924\) | 0.735688 | 0.0242024 | ||||||||
\(925\) | 65.0507 | 2.13885 | ||||||||
\(926\) | 7.48545 | 0.245987 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −0.584971 | −0.0192026 | ||||||||
\(929\) | 54.2687 | 1.78050 | 0.890248 | − | 0.455475i | \(-0.150531\pi\) | ||||
0.890248 | + | 0.455475i | \(0.150531\pi\) | |||||||
\(930\) | −14.8707 | −0.487631 | ||||||||
\(931\) | −38.0292 | −1.24636 | ||||||||
\(932\) | 15.9605 | 0.522804 | ||||||||
\(933\) | 26.8070 | 0.877621 | ||||||||
\(934\) | 12.9657 | 0.424251 | ||||||||
\(935\) | −92.7559 | −3.03344 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 46.9426 | 1.53355 | 0.766774 | − | 0.641917i | \(-0.221861\pi\) | ||||
0.766774 | + | 0.641917i | \(0.221861\pi\) | |||||||
\(938\) | 2.38781 | 0.0779647 | ||||||||
\(939\) | 10.1194 | 0.330236 | ||||||||
\(940\) | −45.2959 | −1.47739 | ||||||||
\(941\) | −50.9187 | −1.65990 | −0.829952 | − | 0.557835i | \(-0.811632\pi\) | ||||
−0.829952 | + | 0.557835i | \(0.811632\pi\) | |||||||
\(942\) | 12.5859 | 0.410070 | ||||||||
\(943\) | −49.8499 | −1.62334 | ||||||||
\(944\) | 15.1468 | 0.492986 | ||||||||
\(945\) | −0.590994 | −0.0192250 | ||||||||
\(946\) | 32.4904 | 1.05635 | ||||||||
\(947\) | 25.2555 | 0.820694 | 0.410347 | − | 0.911929i | \(-0.365408\pi\) | ||||
0.410347 | + | 0.911929i | \(0.365408\pi\) | |||||||
\(948\) | −5.41863 | −0.175989 | ||||||||
\(949\) | −13.3410 | −0.433068 | ||||||||
\(950\) | −41.2824 | −1.33938 | ||||||||
\(951\) | 12.7234 | 0.412583 | ||||||||
\(952\) | −0.988283 | −0.0320304 | ||||||||
\(953\) | −13.8384 | −0.448268 | −0.224134 | − | 0.974558i | \(-0.571955\pi\) | ||||
−0.224134 | + | 0.974558i | \(0.571955\pi\) | |||||||
\(954\) | −1.83140 | −0.0592939 | ||||||||
\(955\) | −28.4317 | −0.920027 | ||||||||
\(956\) | −22.7497 | −0.735779 | ||||||||
\(957\) | 2.58160 | 0.0834513 | ||||||||
\(958\) | 6.53720 | 0.211207 | ||||||||
\(959\) | −2.16986 | −0.0700683 | ||||||||
\(960\) | −3.54523 | −0.114422 | ||||||||
\(961\) | −13.4055 | −0.432435 | ||||||||
\(962\) | −8.59476 | −0.277106 | ||||||||
\(963\) | −7.43278 | −0.239518 | ||||||||
\(964\) | −4.90865 | −0.158097 | ||||||||
\(965\) | −58.5065 | −1.88339 | ||||||||
\(966\) | −1.07410 | −0.0345587 | ||||||||
\(967\) | −4.71481 | −0.151618 | −0.0758090 | − | 0.997122i | \(-0.524154\pi\) | ||||
−0.0758090 | + | 0.997122i | \(0.524154\pi\) | |||||||
\(968\) | −8.47644 | −0.272443 | ||||||||
\(969\) | 32.3362 | 1.03879 | ||||||||
\(970\) | 4.48650 | 0.144053 | ||||||||
\(971\) | 5.24617 | 0.168358 | 0.0841788 | − | 0.996451i | \(-0.473173\pi\) | ||||
0.0841788 | + | 0.996451i | \(0.473173\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −0.235571 | −0.00755205 | ||||||||
\(974\) | 20.2434 | 0.648639 | ||||||||
\(975\) | 7.56864 | 0.242391 | ||||||||
\(976\) | 10.5545 | 0.337842 | ||||||||
\(977\) | 38.5977 | 1.23485 | 0.617425 | − | 0.786630i | \(-0.288176\pi\) | ||||
0.617425 | + | 0.786630i | \(0.288176\pi\) | |||||||
\(978\) | 22.7916 | 0.728795 | ||||||||
\(979\) | −8.30974 | −0.265580 | ||||||||
\(980\) | 24.7181 | 0.789590 | ||||||||
\(981\) | −6.41750 | −0.204895 | ||||||||
\(982\) | −7.77786 | −0.248201 | ||||||||
\(983\) | 54.0601 | 1.72425 | 0.862124 | − | 0.506697i | \(-0.169134\pi\) | ||||
0.862124 | + | 0.506697i | \(0.169134\pi\) | |||||||
\(984\) | 7.73673 | 0.246638 | ||||||||
\(985\) | 74.4518 | 2.37223 | ||||||||
\(986\) | −3.46798 | −0.110443 | ||||||||
\(987\) | 2.12987 | 0.0677946 | ||||||||
\(988\) | 5.45439 | 0.173527 | ||||||||
\(989\) | −47.4358 | −1.50837 | ||||||||
\(990\) | 15.6458 | 0.497258 | ||||||||
\(991\) | 54.8753 | 1.74317 | 0.871586 | − | 0.490242i | \(-0.163092\pi\) | ||||
0.871586 | + | 0.490242i | \(0.163092\pi\) | |||||||
\(992\) | 4.19458 | 0.133178 | ||||||||
\(993\) | −18.0998 | −0.574379 | ||||||||
\(994\) | −0.322283 | −0.0102222 | ||||||||
\(995\) | 78.2637 | 2.48113 | ||||||||
\(996\) | 0.0310976 | 0.000985365 0 | ||||||||
\(997\) | −32.5661 | −1.03138 | −0.515690 | − | 0.856775i | \(-0.672464\pi\) | ||||
−0.515690 | + | 0.856775i | \(0.672464\pi\) | |||||||
\(998\) | −8.02423 | −0.254003 | ||||||||
\(999\) | 8.59476 | 0.271926 |
(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 | 8034.2.a.x.1.2 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.x.1.2 | ✓ | 13 | 1.1 | even | 1 | trivial |