Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.37902897.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 15x^{4} - x^{3} + 60x^{2} - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.14945\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-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 | ||||||||
\(3\) | −3.14945 | −1.81834 | −0.909168 | − | 0.416431i | \(-0.863281\pi\) | ||||
−0.909168 | + | 0.416431i | \(0.863281\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.53209 | 0.685171 | 0.342585 | − | 0.939487i | \(-0.388697\pi\) | ||||
0.342585 | + | 0.939487i | \(0.388697\pi\) | |||||||
\(6\) | −3.14945 | −1.28576 | ||||||||
\(7\) | −4.82524 | −1.82377 | −0.911884 | − | 0.410448i | \(-0.865372\pi\) | ||||
−0.911884 | + | 0.410448i | \(0.865372\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.91903 | 2.30634 | ||||||||
\(10\) | 1.53209 | 0.484489 | ||||||||
\(11\) | −1.09379 | −0.329791 | −0.164895 | − | 0.986311i | \(-0.552729\pi\) | ||||
−0.164895 | + | 0.986311i | \(0.552729\pi\) | |||||||
\(12\) | −3.14945 | −0.909168 | ||||||||
\(13\) | 1.76958 | 0.490793 | 0.245396 | − | 0.969423i | \(-0.421082\pi\) | ||||
0.245396 | + | 0.969423i | \(0.421082\pi\) | |||||||
\(14\) | −4.82524 | −1.28960 | ||||||||
\(15\) | −4.82524 | −1.24587 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.94585 | 0.714474 | 0.357237 | − | 0.934014i | \(-0.383719\pi\) | ||||
0.357237 | + | 0.934014i | \(0.383719\pi\) | |||||||
\(18\) | 6.91903 | 1.63083 | ||||||||
\(19\) | −0.825235 | −0.189322 | −0.0946610 | − | 0.995510i | \(-0.530177\pi\) | ||||
−0.0946610 | + | 0.995510i | \(0.530177\pi\) | |||||||
\(20\) | 1.53209 | 0.342585 | ||||||||
\(21\) | 15.1968 | 3.31622 | ||||||||
\(22\) | −1.09379 | −0.233197 | ||||||||
\(23\) | −0.243241 | −0.0507192 | −0.0253596 | − | 0.999678i | \(-0.508073\pi\) | ||||
−0.0253596 | + | 0.999678i | \(0.508073\pi\) | |||||||
\(24\) | −3.14945 | −0.642879 | ||||||||
\(25\) | −2.65270 | −0.530541 | ||||||||
\(26\) | 1.76958 | 0.347043 | ||||||||
\(27\) | −12.3428 | −2.37537 | ||||||||
\(28\) | −4.82524 | −0.911884 | ||||||||
\(29\) | −5.57173 | −1.03464 | −0.517322 | − | 0.855791i | \(-0.673071\pi\) | ||||
−0.517322 | + | 0.855791i | \(0.673071\pi\) | |||||||
\(30\) | −4.82524 | −0.880963 | ||||||||
\(31\) | −5.73495 | −1.03003 | −0.515013 | − | 0.857182i | \(-0.672213\pi\) | ||||
−0.515013 | + | 0.857182i | \(0.672213\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.44484 | 0.599670 | ||||||||
\(34\) | 2.94585 | 0.505209 | ||||||||
\(35\) | −7.39269 | −1.24959 | ||||||||
\(36\) | 6.91903 | 1.15317 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | −0.825235 | −0.133871 | ||||||||
\(39\) | −5.57320 | −0.892426 | ||||||||
\(40\) | 1.53209 | 0.242245 | ||||||||
\(41\) | 2.91194 | 0.454768 | 0.227384 | − | 0.973805i | \(-0.426983\pi\) | ||||
0.227384 | + | 0.973805i | \(0.426983\pi\) | |||||||
\(42\) | 15.1968 | 2.34492 | ||||||||
\(43\) | 4.37987 | 0.667924 | 0.333962 | − | 0.942587i | \(-0.391614\pi\) | ||||
0.333962 | + | 0.942587i | \(0.391614\pi\) | |||||||
\(44\) | −1.09379 | −0.164895 | ||||||||
\(45\) | 10.6006 | 1.58024 | ||||||||
\(46\) | −0.243241 | −0.0358639 | ||||||||
\(47\) | 2.26498 | 0.330382 | 0.165191 | − | 0.986262i | \(-0.447176\pi\) | ||||
0.165191 | + | 0.986262i | \(0.447176\pi\) | |||||||
\(48\) | −3.14945 | −0.454584 | ||||||||
\(49\) | 16.2829 | 2.32613 | ||||||||
\(50\) | −2.65270 | −0.375149 | ||||||||
\(51\) | −9.27780 | −1.29915 | ||||||||
\(52\) | 1.76958 | 0.245396 | ||||||||
\(53\) | 6.14945 | 0.844692 | 0.422346 | − | 0.906435i | \(-0.361207\pi\) | ||||
0.422346 | + | 0.906435i | \(0.361207\pi\) | |||||||
\(54\) | −12.3428 | −1.67964 | ||||||||
\(55\) | −1.67579 | −0.225963 | ||||||||
\(56\) | −4.82524 | −0.644799 | ||||||||
\(57\) | 2.59904 | 0.344251 | ||||||||
\(58\) | −5.57173 | −0.731604 | ||||||||
\(59\) | 8.82524 | 1.14895 | 0.574474 | − | 0.818523i | \(-0.305207\pi\) | ||||
0.574474 | + | 0.818523i | \(0.305207\pi\) | |||||||
\(60\) | −4.82524 | −0.622935 | ||||||||
\(61\) | −11.7522 | −1.50472 | −0.752360 | − | 0.658752i | \(-0.771085\pi\) | ||||
−0.752360 | + | 0.658752i | \(0.771085\pi\) | |||||||
\(62\) | −5.73495 | −0.728339 | ||||||||
\(63\) | −33.3859 | −4.20623 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.71115 | 0.336277 | ||||||||
\(66\) | 3.44484 | 0.424031 | ||||||||
\(67\) | 8.98400 | 1.09757 | 0.548785 | − | 0.835963i | \(-0.315091\pi\) | ||||
0.548785 | + | 0.835963i | \(0.315091\pi\) | |||||||
\(68\) | 2.94585 | 0.357237 | ||||||||
\(69\) | 0.766075 | 0.0922245 | ||||||||
\(70\) | −7.39269 | −0.883595 | ||||||||
\(71\) | −1.21864 | −0.144626 | −0.0723132 | − | 0.997382i | \(-0.523038\pi\) | ||||
−0.0723132 | + | 0.997382i | \(0.523038\pi\) | |||||||
\(72\) | 6.91903 | 0.815415 | ||||||||
\(73\) | 8.79418 | 1.02928 | 0.514640 | − | 0.857406i | \(-0.327925\pi\) | ||||
0.514640 | + | 0.857406i | \(0.327925\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.35455 | 0.964701 | ||||||||
\(76\) | −0.825235 | −0.0946610 | ||||||||
\(77\) | 5.27780 | 0.601462 | ||||||||
\(78\) | −5.57320 | −0.631040 | ||||||||
\(79\) | 2.15367 | 0.242307 | 0.121153 | − | 0.992634i | \(-0.461341\pi\) | ||||
0.121153 | + | 0.992634i | \(0.461341\pi\) | |||||||
\(80\) | 1.53209 | 0.171293 | ||||||||
\(81\) | 18.1159 | 2.01287 | ||||||||
\(82\) | 2.91194 | 0.321570 | ||||||||
\(83\) | 5.09379 | 0.559116 | 0.279558 | − | 0.960129i | \(-0.409812\pi\) | ||||
0.279558 | + | 0.960129i | \(0.409812\pi\) | |||||||
\(84\) | 15.1968 | 1.65811 | ||||||||
\(85\) | 4.51330 | 0.489537 | ||||||||
\(86\) | 4.37987 | 0.472294 | ||||||||
\(87\) | 17.5479 | 1.88133 | ||||||||
\(88\) | −1.09379 | −0.116599 | ||||||||
\(89\) | 8.97619 | 0.951474 | 0.475737 | − | 0.879587i | \(-0.342181\pi\) | ||||
0.475737 | + | 0.879587i | \(0.342181\pi\) | |||||||
\(90\) | 10.6006 | 1.11740 | ||||||||
\(91\) | −8.53863 | −0.895092 | ||||||||
\(92\) | −0.243241 | −0.0253596 | ||||||||
\(93\) | 18.0619 | 1.87293 | ||||||||
\(94\) | 2.26498 | 0.233615 | ||||||||
\(95\) | −1.26433 | −0.129718 | ||||||||
\(96\) | −3.14945 | −0.321439 | ||||||||
\(97\) | 4.35907 | 0.442597 | 0.221298 | − | 0.975206i | \(-0.428971\pi\) | ||||
0.221298 | + | 0.975206i | \(0.428971\pi\) | |||||||
\(98\) | 16.2829 | 1.64482 | ||||||||
\(99\) | −7.56798 | −0.760610 | ||||||||
\(100\) | −2.65270 | −0.265270 | ||||||||
\(101\) | −4.38889 | −0.436711 | −0.218355 | − | 0.975869i | \(-0.570069\pi\) | ||||
−0.218355 | + | 0.975869i | \(0.570069\pi\) | |||||||
\(102\) | −9.27780 | −0.918640 | ||||||||
\(103\) | 12.6452 | 1.24597 | 0.622987 | − | 0.782233i | \(-0.285919\pi\) | ||||
0.622987 | + | 0.782233i | \(0.285919\pi\) | |||||||
\(104\) | 1.76958 | 0.173521 | ||||||||
\(105\) | 23.2829 | 2.27218 | ||||||||
\(106\) | 6.14945 | 0.597287 | ||||||||
\(107\) | 18.8597 | 1.82323 | 0.911616 | − | 0.411042i | \(-0.134835\pi\) | ||||
0.911616 | + | 0.411042i | \(0.134835\pi\) | |||||||
\(108\) | −12.3428 | −1.18768 | ||||||||
\(109\) | −8.41432 | −0.805946 | −0.402973 | − | 0.915212i | \(-0.632023\pi\) | ||||
−0.402973 | + | 0.915212i | \(0.632023\pi\) | |||||||
\(110\) | −1.67579 | −0.159780 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.82524 | −0.455942 | ||||||||
\(113\) | −6.38461 | −0.600614 | −0.300307 | − | 0.953843i | \(-0.597089\pi\) | ||||
−0.300307 | + | 0.953843i | \(0.597089\pi\) | |||||||
\(114\) | 2.59904 | 0.243422 | ||||||||
\(115\) | −0.372667 | −0.0347513 | ||||||||
\(116\) | −5.57173 | −0.517322 | ||||||||
\(117\) | 12.2438 | 1.13194 | ||||||||
\(118\) | 8.82524 | 0.812429 | ||||||||
\(119\) | −14.2144 | −1.30303 | ||||||||
\(120\) | −4.82524 | −0.440482 | ||||||||
\(121\) | −9.80362 | −0.891238 | ||||||||
\(122\) | −11.7522 | −1.06400 | ||||||||
\(123\) | −9.17100 | −0.826921 | ||||||||
\(124\) | −5.73495 | −0.515013 | ||||||||
\(125\) | −11.7246 | −1.04868 | ||||||||
\(126\) | −33.3859 | −2.97426 | ||||||||
\(127\) | −4.75254 | −0.421719 | −0.210860 | − | 0.977516i | \(-0.567626\pi\) | ||||
−0.210860 | + | 0.977516i | \(0.567626\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −13.7942 | −1.21451 | ||||||||
\(130\) | 2.71115 | 0.237784 | ||||||||
\(131\) | 17.9870 | 1.57153 | 0.785765 | − | 0.618525i | \(-0.212270\pi\) | ||||
0.785765 | + | 0.618525i | \(0.212270\pi\) | |||||||
\(132\) | 3.44484 | 0.299835 | ||||||||
\(133\) | 3.98196 | 0.345279 | ||||||||
\(134\) | 8.98400 | 0.776099 | ||||||||
\(135\) | −18.9102 | −1.62753 | ||||||||
\(136\) | 2.94585 | 0.252605 | ||||||||
\(137\) | 22.1091 | 1.88891 | 0.944456 | − | 0.328639i | \(-0.106590\pi\) | ||||
0.944456 | + | 0.328639i | \(0.106590\pi\) | |||||||
\(138\) | 0.766075 | 0.0652126 | ||||||||
\(139\) | −2.66547 | −0.226082 | −0.113041 | − | 0.993590i | \(-0.536059\pi\) | ||||
−0.113041 | + | 0.993590i | \(0.536059\pi\) | |||||||
\(140\) | −7.39269 | −0.624796 | ||||||||
\(141\) | −7.13345 | −0.600745 | ||||||||
\(142\) | −1.21864 | −0.102266 | ||||||||
\(143\) | −1.93555 | −0.161859 | ||||||||
\(144\) | 6.91903 | 0.576586 | ||||||||
\(145\) | −8.53639 | −0.708908 | ||||||||
\(146\) | 8.79418 | 0.727811 | ||||||||
\(147\) | −51.2822 | −4.22968 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.13622 | 0.502699 | 0.251349 | − | 0.967896i | \(-0.419126\pi\) | ||||
0.251349 | + | 0.967896i | \(0.419126\pi\) | |||||||
\(150\) | 8.35455 | 0.682146 | ||||||||
\(151\) | −0.436768 | −0.0355437 | −0.0177719 | − | 0.999842i | \(-0.505657\pi\) | ||||
−0.0177719 | + | 0.999842i | \(0.505657\pi\) | |||||||
\(152\) | −0.825235 | −0.0669354 | ||||||||
\(153\) | 20.3824 | 1.64782 | ||||||||
\(154\) | 5.27780 | 0.425298 | ||||||||
\(155\) | −8.78645 | −0.705745 | ||||||||
\(156\) | −5.57320 | −0.446213 | ||||||||
\(157\) | 6.06139 | 0.483751 | 0.241876 | − | 0.970307i | \(-0.422237\pi\) | ||||
0.241876 | + | 0.970307i | \(0.422237\pi\) | |||||||
\(158\) | 2.15367 | 0.171337 | ||||||||
\(159\) | −19.3674 | −1.53593 | ||||||||
\(160\) | 1.53209 | 0.121122 | ||||||||
\(161\) | 1.17369 | 0.0925001 | ||||||||
\(162\) | 18.1159 | 1.42332 | ||||||||
\(163\) | 13.7349 | 1.07580 | 0.537902 | − | 0.843007i | \(-0.319217\pi\) | ||||
0.537902 | + | 0.843007i | \(0.319217\pi\) | |||||||
\(164\) | 2.91194 | 0.227384 | ||||||||
\(165\) | 5.27780 | 0.410877 | ||||||||
\(166\) | 5.09379 | 0.395355 | ||||||||
\(167\) | 23.8199 | 1.84324 | 0.921621 | − | 0.388091i | \(-0.126865\pi\) | ||||
0.921621 | + | 0.388091i | \(0.126865\pi\) | |||||||
\(168\) | 15.1968 | 1.17246 | ||||||||
\(169\) | −9.86859 | −0.759122 | ||||||||
\(170\) | 4.51330 | 0.346155 | ||||||||
\(171\) | −5.70983 | −0.436641 | ||||||||
\(172\) | 4.37987 | 0.333962 | ||||||||
\(173\) | 21.4452 | 1.63045 | 0.815223 | − | 0.579147i | \(-0.196614\pi\) | ||||
0.815223 | + | 0.579147i | \(0.196614\pi\) | |||||||
\(174\) | 17.5479 | 1.33030 | ||||||||
\(175\) | 12.7999 | 0.967583 | ||||||||
\(176\) | −1.09379 | −0.0824477 | ||||||||
\(177\) | −27.7946 | −2.08917 | ||||||||
\(178\) | 8.97619 | 0.672794 | ||||||||
\(179\) | 11.5247 | 0.861400 | 0.430700 | − | 0.902495i | \(-0.358267\pi\) | ||||
0.430700 | + | 0.902495i | \(0.358267\pi\) | |||||||
\(180\) | 10.6006 | 0.790119 | ||||||||
\(181\) | −17.7689 | −1.32075 | −0.660374 | − | 0.750937i | \(-0.729602\pi\) | ||||
−0.660374 | + | 0.750937i | \(0.729602\pi\) | |||||||
\(182\) | −8.53863 | −0.632926 | ||||||||
\(183\) | 37.0131 | 2.73609 | ||||||||
\(184\) | −0.243241 | −0.0179320 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 18.0619 | 1.32436 | ||||||||
\(187\) | −3.22215 | −0.235627 | ||||||||
\(188\) | 2.26498 | 0.165191 | ||||||||
\(189\) | 59.5568 | 4.33212 | ||||||||
\(190\) | −1.26433 | −0.0917244 | ||||||||
\(191\) | −25.9113 | −1.87487 | −0.937437 | − | 0.348155i | \(-0.886808\pi\) | ||||
−0.937437 | + | 0.348155i | \(0.886808\pi\) | |||||||
\(192\) | −3.14945 | −0.227292 | ||||||||
\(193\) | 10.9030 | 0.784813 | 0.392407 | − | 0.919792i | \(-0.371643\pi\) | ||||
0.392407 | + | 0.919792i | \(0.371643\pi\) | |||||||
\(194\) | 4.35907 | 0.312963 | ||||||||
\(195\) | −8.53863 | −0.611464 | ||||||||
\(196\) | 16.2829 | 1.16306 | ||||||||
\(197\) | −6.44314 | −0.459055 | −0.229527 | − | 0.973302i | \(-0.573718\pi\) | ||||
−0.229527 | + | 0.973302i | \(0.573718\pi\) | |||||||
\(198\) | −7.56798 | −0.537833 | ||||||||
\(199\) | 18.8556 | 1.33664 | 0.668318 | − | 0.743876i | \(-0.267014\pi\) | ||||
0.668318 | + | 0.743876i | \(0.267014\pi\) | |||||||
\(200\) | −2.65270 | −0.187574 | ||||||||
\(201\) | −28.2946 | −1.99575 | ||||||||
\(202\) | −4.38889 | −0.308801 | ||||||||
\(203\) | 26.8849 | 1.88695 | ||||||||
\(204\) | −9.27780 | −0.649576 | ||||||||
\(205\) | 4.46135 | 0.311594 | ||||||||
\(206\) | 12.6452 | 0.881036 | ||||||||
\(207\) | −1.68299 | −0.116976 | ||||||||
\(208\) | 1.76958 | 0.122698 | ||||||||
\(209\) | 0.902636 | 0.0624366 | ||||||||
\(210\) | 23.2829 | 1.60667 | ||||||||
\(211\) | −1.41450 | −0.0973783 | −0.0486891 | − | 0.998814i | \(-0.515504\pi\) | ||||
−0.0486891 | + | 0.998814i | \(0.515504\pi\) | |||||||
\(212\) | 6.14945 | 0.422346 | ||||||||
\(213\) | 3.83806 | 0.262979 | ||||||||
\(214\) | 18.8597 | 1.28922 | ||||||||
\(215\) | 6.71035 | 0.457642 | ||||||||
\(216\) | −12.3428 | −0.839820 | ||||||||
\(217\) | 27.6725 | 1.87853 | ||||||||
\(218\) | −8.41432 | −0.569890 | ||||||||
\(219\) | −27.6968 | −1.87158 | ||||||||
\(220\) | −1.67579 | −0.112982 | ||||||||
\(221\) | 5.21291 | 0.350659 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.1750 | −0.815302 | −0.407651 | − | 0.913138i | \(-0.633652\pi\) | ||||
−0.407651 | + | 0.913138i | \(0.633652\pi\) | |||||||
\(224\) | −4.82524 | −0.322400 | ||||||||
\(225\) | −18.3541 | −1.22361 | ||||||||
\(226\) | −6.38461 | −0.424698 | ||||||||
\(227\) | −21.2999 | −1.41373 | −0.706863 | − | 0.707350i | \(-0.749890\pi\) | ||||
−0.706863 | + | 0.707350i | \(0.749890\pi\) | |||||||
\(228\) | 2.59904 | 0.172125 | ||||||||
\(229\) | −2.84960 | −0.188307 | −0.0941535 | − | 0.995558i | \(-0.530014\pi\) | ||||
−0.0941535 | + | 0.995558i | \(0.530014\pi\) | |||||||
\(230\) | −0.372667 | −0.0245729 | ||||||||
\(231\) | −16.6222 | −1.09366 | ||||||||
\(232\) | −5.57173 | −0.365802 | ||||||||
\(233\) | 23.5165 | 1.54062 | 0.770310 | − | 0.637670i | \(-0.220101\pi\) | ||||
0.770310 | + | 0.637670i | \(0.220101\pi\) | |||||||
\(234\) | 12.2438 | 0.800400 | ||||||||
\(235\) | 3.47016 | 0.226368 | ||||||||
\(236\) | 8.82524 | 0.574474 | ||||||||
\(237\) | −6.78288 | −0.440595 | ||||||||
\(238\) | −14.2144 | −0.921384 | ||||||||
\(239\) | 8.03813 | 0.519943 | 0.259972 | − | 0.965616i | \(-0.416287\pi\) | ||||
0.259972 | + | 0.965616i | \(0.416287\pi\) | |||||||
\(240\) | −4.82524 | −0.311468 | ||||||||
\(241\) | 18.4519 | 1.18859 | 0.594294 | − | 0.804248i | \(-0.297432\pi\) | ||||
0.594294 | + | 0.804248i | \(0.297432\pi\) | |||||||
\(242\) | −9.80362 | −0.630200 | ||||||||
\(243\) | −20.0266 | −1.28471 | ||||||||
\(244\) | −11.7522 | −0.752360 | ||||||||
\(245\) | 24.9468 | 1.59380 | ||||||||
\(246\) | −9.17100 | −0.584721 | ||||||||
\(247\) | −1.46032 | −0.0929179 | ||||||||
\(248\) | −5.73495 | −0.364170 | ||||||||
\(249\) | −16.0426 | −1.01666 | ||||||||
\(250\) | −11.7246 | −0.741530 | ||||||||
\(251\) | 23.2945 | 1.47033 | 0.735167 | − | 0.677886i | \(-0.237104\pi\) | ||||
0.735167 | + | 0.677886i | \(0.237104\pi\) | |||||||
\(252\) | −33.3859 | −2.10312 | ||||||||
\(253\) | 0.266055 | 0.0167267 | ||||||||
\(254\) | −4.75254 | −0.298201 | ||||||||
\(255\) | −14.2144 | −0.890142 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.25683 | −0.265534 | −0.132767 | − | 0.991147i | \(-0.542386\pi\) | ||||
−0.132767 | + | 0.991147i | \(0.542386\pi\) | |||||||
\(258\) | −13.7942 | −0.858788 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.71115 | 0.168139 | ||||||||
\(261\) | −38.5510 | −2.38624 | ||||||||
\(262\) | 17.9870 | 1.11124 | ||||||||
\(263\) | −6.88547 | −0.424576 | −0.212288 | − | 0.977207i | \(-0.568092\pi\) | ||||
−0.212288 | + | 0.977207i | \(0.568092\pi\) | |||||||
\(264\) | 3.44484 | 0.212015 | ||||||||
\(265\) | 9.42150 | 0.578758 | ||||||||
\(266\) | 3.98196 | 0.244149 | ||||||||
\(267\) | −28.2701 | −1.73010 | ||||||||
\(268\) | 8.98400 | 0.548785 | ||||||||
\(269\) | 9.67565 | 0.589935 | 0.294968 | − | 0.955507i | \(-0.404691\pi\) | ||||
0.294968 | + | 0.955507i | \(0.404691\pi\) | |||||||
\(270\) | −18.9102 | −1.15084 | ||||||||
\(271\) | 7.66277 | 0.465480 | 0.232740 | − | 0.972539i | \(-0.425231\pi\) | ||||
0.232740 | + | 0.972539i | \(0.425231\pi\) | |||||||
\(272\) | 2.94585 | 0.178618 | ||||||||
\(273\) | 26.8920 | 1.62758 | ||||||||
\(274\) | 22.1091 | 1.33566 | ||||||||
\(275\) | 2.90151 | 0.174967 | ||||||||
\(276\) | 0.766075 | 0.0461123 | ||||||||
\(277\) | 4.01957 | 0.241513 | 0.120756 | − | 0.992682i | \(-0.461468\pi\) | ||||
0.120756 | + | 0.992682i | \(0.461468\pi\) | |||||||
\(278\) | −2.66547 | −0.159864 | ||||||||
\(279\) | −39.6803 | −2.37560 | ||||||||
\(280\) | −7.39269 | −0.441798 | ||||||||
\(281\) | −6.99927 | −0.417542 | −0.208771 | − | 0.977965i | \(-0.566946\pi\) | ||||
−0.208771 | + | 0.977965i | \(0.566946\pi\) | |||||||
\(282\) | −7.13345 | −0.424791 | ||||||||
\(283\) | −4.70460 | −0.279660 | −0.139830 | − | 0.990176i | \(-0.544656\pi\) | ||||
−0.139830 | + | 0.990176i | \(0.544656\pi\) | |||||||
\(284\) | −1.21864 | −0.0723132 | ||||||||
\(285\) | 3.98196 | 0.235871 | ||||||||
\(286\) | −1.93555 | −0.114452 | ||||||||
\(287\) | −14.0508 | −0.829392 | ||||||||
\(288\) | 6.91903 | 0.407708 | ||||||||
\(289\) | −8.32197 | −0.489527 | ||||||||
\(290\) | −8.53639 | −0.501274 | ||||||||
\(291\) | −13.7287 | −0.804790 | ||||||||
\(292\) | 8.79418 | 0.514640 | ||||||||
\(293\) | −14.2310 | −0.831384 | −0.415692 | − | 0.909505i | \(-0.636461\pi\) | ||||
−0.415692 | + | 0.909505i | \(0.636461\pi\) | |||||||
\(294\) | −51.2822 | −2.99084 | ||||||||
\(295\) | 13.5210 | 0.787226 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5004 | 0.783374 | ||||||||
\(298\) | 6.13622 | 0.355462 | ||||||||
\(299\) | −0.430434 | −0.0248926 | ||||||||
\(300\) | 8.35455 | 0.482350 | ||||||||
\(301\) | −21.1339 | −1.21814 | ||||||||
\(302\) | −0.436768 | −0.0251332 | ||||||||
\(303\) | 13.8226 | 0.794086 | ||||||||
\(304\) | −0.825235 | −0.0473305 | ||||||||
\(305\) | −18.0055 | −1.03099 | ||||||||
\(306\) | 20.3824 | 1.16519 | ||||||||
\(307\) | 0.802616 | 0.0458077 | 0.0229039 | − | 0.999738i | \(-0.492709\pi\) | ||||
0.0229039 | + | 0.999738i | \(0.492709\pi\) | |||||||
\(308\) | 5.27780 | 0.300731 | ||||||||
\(309\) | −39.8256 | −2.26560 | ||||||||
\(310\) | −8.78645 | −0.499037 | ||||||||
\(311\) | −2.46944 | −0.140029 | −0.0700145 | − | 0.997546i | \(-0.522305\pi\) | ||||
−0.0700145 | + | 0.997546i | \(0.522305\pi\) | |||||||
\(312\) | −5.57320 | −0.315520 | ||||||||
\(313\) | −17.8439 | −1.00860 | −0.504298 | − | 0.863530i | \(-0.668249\pi\) | ||||
−0.504298 | + | 0.863530i | \(0.668249\pi\) | |||||||
\(314\) | 6.06139 | 0.342064 | ||||||||
\(315\) | −51.1502 | −2.88199 | ||||||||
\(316\) | 2.15367 | 0.121153 | ||||||||
\(317\) | 3.53955 | 0.198801 | 0.0994006 | − | 0.995047i | \(-0.468307\pi\) | ||||
0.0994006 | + | 0.995047i | \(0.468307\pi\) | |||||||
\(318\) | −19.3674 | −1.08607 | ||||||||
\(319\) | 6.09432 | 0.341216 | ||||||||
\(320\) | 1.53209 | 0.0856464 | ||||||||
\(321\) | −59.3976 | −3.31525 | ||||||||
\(322\) | 1.17369 | 0.0654074 | ||||||||
\(323\) | −2.43102 | −0.135266 | ||||||||
\(324\) | 18.1159 | 1.00644 | ||||||||
\(325\) | −4.69417 | −0.260386 | ||||||||
\(326\) | 13.7349 | 0.760708 | ||||||||
\(327\) | 26.5005 | 1.46548 | ||||||||
\(328\) | 2.91194 | 0.160785 | ||||||||
\(329\) | −10.9291 | −0.602540 | ||||||||
\(330\) | 5.27780 | 0.290534 | ||||||||
\(331\) | 3.82628 | 0.210311 | 0.105156 | − | 0.994456i | \(-0.466466\pi\) | ||||
0.105156 | + | 0.994456i | \(0.466466\pi\) | |||||||
\(332\) | 5.09379 | 0.279558 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.8199 | 1.30337 | ||||||||
\(335\) | 13.7643 | 0.752023 | ||||||||
\(336\) | 15.1968 | 0.829055 | ||||||||
\(337\) | −21.3962 | −1.16553 | −0.582764 | − | 0.812641i | \(-0.698029\pi\) | ||||
−0.582764 | + | 0.812641i | \(0.698029\pi\) | |||||||
\(338\) | −9.86859 | −0.536781 | ||||||||
\(339\) | 20.1080 | 1.09212 | ||||||||
\(340\) | 4.51330 | 0.244768 | ||||||||
\(341\) | 6.27284 | 0.339693 | ||||||||
\(342\) | −5.70983 | −0.308752 | ||||||||
\(343\) | −44.7922 | −2.41855 | ||||||||
\(344\) | 4.37987 | 0.236147 | ||||||||
\(345\) | 1.17369 | 0.0631896 | ||||||||
\(346\) | 21.4452 | 1.15290 | ||||||||
\(347\) | −25.6363 | −1.37623 | −0.688113 | − | 0.725603i | \(-0.741561\pi\) | ||||
−0.688113 | + | 0.725603i | \(0.741561\pi\) | |||||||
\(348\) | 17.5479 | 0.940665 | ||||||||
\(349\) | 15.5352 | 0.831578 | 0.415789 | − | 0.909461i | \(-0.363505\pi\) | ||||
0.415789 | + | 0.909461i | \(0.363505\pi\) | |||||||
\(350\) | 12.7999 | 0.684184 | ||||||||
\(351\) | −21.8415 | −1.16581 | ||||||||
\(352\) | −1.09379 | −0.0582993 | ||||||||
\(353\) | −1.35631 | −0.0721890 | −0.0360945 | − | 0.999348i | \(-0.511492\pi\) | ||||
−0.0360945 | + | 0.999348i | \(0.511492\pi\) | |||||||
\(354\) | −27.7946 | −1.47727 | ||||||||
\(355\) | −1.86707 | −0.0990938 | ||||||||
\(356\) | 8.97619 | 0.475737 | ||||||||
\(357\) | 44.7676 | 2.36935 | ||||||||
\(358\) | 11.5247 | 0.609102 | ||||||||
\(359\) | −22.3147 | −1.17772 | −0.588862 | − | 0.808233i | \(-0.700424\pi\) | ||||
−0.588862 | + | 0.808233i | \(0.700424\pi\) | |||||||
\(360\) | 10.6006 | 0.558699 | ||||||||
\(361\) | −18.3190 | −0.964157 | ||||||||
\(362\) | −17.7689 | −0.933910 | ||||||||
\(363\) | 30.8760 | 1.62057 | ||||||||
\(364\) | −8.53863 | −0.447546 | ||||||||
\(365\) | 13.4735 | 0.705233 | ||||||||
\(366\) | 37.0131 | 1.93470 | ||||||||
\(367\) | 7.22844 | 0.377321 | 0.188661 | − | 0.982042i | \(-0.439585\pi\) | ||||
0.188661 | + | 0.982042i | \(0.439585\pi\) | |||||||
\(368\) | −0.243241 | −0.0126798 | ||||||||
\(369\) | 20.1478 | 1.04885 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.6725 | −1.54052 | ||||||||
\(372\) | 18.0619 | 0.936467 | ||||||||
\(373\) | −11.7328 | −0.607504 | −0.303752 | − | 0.952751i | \(-0.598239\pi\) | ||||
−0.303752 | + | 0.952751i | \(0.598239\pi\) | |||||||
\(374\) | −3.22215 | −0.166613 | ||||||||
\(375\) | 36.9261 | 1.90686 | ||||||||
\(376\) | 2.26498 | 0.116808 | ||||||||
\(377\) | −9.85962 | −0.507796 | ||||||||
\(378\) | 59.5568 | 3.06327 | ||||||||
\(379\) | −2.76782 | −0.142173 | −0.0710866 | − | 0.997470i | \(-0.522647\pi\) | ||||
−0.0710866 | + | 0.997470i | \(0.522647\pi\) | |||||||
\(380\) | −1.26433 | −0.0648590 | ||||||||
\(381\) | 14.9679 | 0.766827 | ||||||||
\(382\) | −25.9113 | −1.32574 | ||||||||
\(383\) | 19.4717 | 0.994955 | 0.497478 | − | 0.867477i | \(-0.334260\pi\) | ||||
0.497478 | + | 0.867477i | \(0.334260\pi\) | |||||||
\(384\) | −3.14945 | −0.160720 | ||||||||
\(385\) | 8.08607 | 0.412104 | ||||||||
\(386\) | 10.9030 | 0.554947 | ||||||||
\(387\) | 30.3044 | 1.54046 | ||||||||
\(388\) | 4.35907 | 0.221298 | ||||||||
\(389\) | −2.34776 | −0.119036 | −0.0595181 | − | 0.998227i | \(-0.518956\pi\) | ||||
−0.0595181 | + | 0.998227i | \(0.518956\pi\) | |||||||
\(390\) | −8.53863 | −0.432371 | ||||||||
\(391\) | −0.716551 | −0.0362375 | ||||||||
\(392\) | 16.2829 | 0.822411 | ||||||||
\(393\) | −56.6491 | −2.85757 | ||||||||
\(394\) | −6.44314 | −0.324601 | ||||||||
\(395\) | 3.29962 | 0.166022 | ||||||||
\(396\) | −7.56798 | −0.380305 | ||||||||
\(397\) | 2.27548 | 0.114203 | 0.0571015 | − | 0.998368i | \(-0.481814\pi\) | ||||
0.0571015 | + | 0.998368i | \(0.481814\pi\) | |||||||
\(398\) | 18.8556 | 0.945145 | ||||||||
\(399\) | −12.5410 | −0.627834 | ||||||||
\(400\) | −2.65270 | −0.132635 | ||||||||
\(401\) | 17.5482 | 0.876316 | 0.438158 | − | 0.898898i | \(-0.355631\pi\) | ||||
0.438158 | + | 0.898898i | \(0.355631\pi\) | |||||||
\(402\) | −28.2946 | −1.41121 | ||||||||
\(403\) | −10.1484 | −0.505530 | ||||||||
\(404\) | −4.38889 | −0.218355 | ||||||||
\(405\) | 27.7551 | 1.37916 | ||||||||
\(406\) | 26.8849 | 1.33428 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −9.27780 | −0.459320 | ||||||||
\(409\) | 22.6789 | 1.12140 | 0.560699 | − | 0.828020i | \(-0.310532\pi\) | ||||
0.560699 | + | 0.828020i | \(0.310532\pi\) | |||||||
\(410\) | 4.46135 | 0.220330 | ||||||||
\(411\) | −69.6316 | −3.43467 | ||||||||
\(412\) | 12.6452 | 0.622987 | ||||||||
\(413\) | −42.5838 | −2.09541 | ||||||||
\(414\) | −1.68299 | −0.0827145 | ||||||||
\(415\) | 7.80414 | 0.383090 | ||||||||
\(416\) | 1.76958 | 0.0867607 | ||||||||
\(417\) | 8.39476 | 0.411093 | ||||||||
\(418\) | 0.902636 | 0.0441494 | ||||||||
\(419\) | 18.8213 | 0.919483 | 0.459741 | − | 0.888053i | \(-0.347942\pi\) | ||||
0.459741 | + | 0.888053i | \(0.347942\pi\) | |||||||
\(420\) | 23.2829 | 1.13609 | ||||||||
\(421\) | −17.9266 | −0.873689 | −0.436844 | − | 0.899537i | \(-0.643904\pi\) | ||||
−0.436844 | + | 0.899537i | \(0.643904\pi\) | |||||||
\(422\) | −1.41450 | −0.0688568 | ||||||||
\(423\) | 15.6715 | 0.761974 | ||||||||
\(424\) | 6.14945 | 0.298644 | ||||||||
\(425\) | −7.81447 | −0.379057 | ||||||||
\(426\) | 3.83806 | 0.185954 | ||||||||
\(427\) | 56.7073 | 2.74426 | ||||||||
\(428\) | 18.8597 | 0.911616 | ||||||||
\(429\) | 6.09592 | 0.294314 | ||||||||
\(430\) | 6.71035 | 0.323602 | ||||||||
\(431\) | 12.2609 | 0.590585 | 0.295293 | − | 0.955407i | \(-0.404583\pi\) | ||||
0.295293 | + | 0.955407i | \(0.404583\pi\) | |||||||
\(432\) | −12.3428 | −0.593842 | ||||||||
\(433\) | 21.1146 | 1.01470 | 0.507351 | − | 0.861740i | \(-0.330625\pi\) | ||||
0.507351 | + | 0.861740i | \(0.330625\pi\) | |||||||
\(434\) | 27.6725 | 1.32832 | ||||||||
\(435\) | 26.8849 | 1.28903 | ||||||||
\(436\) | −8.41432 | −0.402973 | ||||||||
\(437\) | 0.200731 | 0.00960226 | ||||||||
\(438\) | −27.6968 | −1.32340 | ||||||||
\(439\) | −24.0926 | −1.14988 | −0.574938 | − | 0.818197i | \(-0.694974\pi\) | ||||
−0.574938 | + | 0.818197i | \(0.694974\pi\) | |||||||
\(440\) | −1.67579 | −0.0798900 | ||||||||
\(441\) | 112.662 | 5.36485 | ||||||||
\(442\) | 5.21291 | 0.247953 | ||||||||
\(443\) | 19.2348 | 0.913871 | 0.456936 | − | 0.889500i | \(-0.348947\pi\) | ||||
0.456936 | + | 0.889500i | \(0.348947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.7523 | 0.651923 | ||||||||
\(446\) | −12.1750 | −0.576505 | ||||||||
\(447\) | −19.3257 | −0.914075 | ||||||||
\(448\) | −4.82524 | −0.227971 | ||||||||
\(449\) | −6.58735 | −0.310876 | −0.155438 | − | 0.987846i | \(-0.549679\pi\) | ||||
−0.155438 | + | 0.987846i | \(0.549679\pi\) | |||||||
\(450\) | −18.3541 | −0.865222 | ||||||||
\(451\) | −3.18505 | −0.149978 | ||||||||
\(452\) | −6.38461 | −0.300307 | ||||||||
\(453\) | 1.37558 | 0.0646304 | ||||||||
\(454\) | −21.2999 | −0.999656 | ||||||||
\(455\) | −13.0819 | −0.613291 | ||||||||
\(456\) | 2.59904 | 0.121711 | ||||||||
\(457\) | −28.9912 | −1.35615 | −0.678075 | − | 0.734992i | \(-0.737186\pi\) | ||||
−0.678075 | + | 0.734992i | \(0.737186\pi\) | |||||||
\(458\) | −2.84960 | −0.133153 | ||||||||
\(459\) | −36.3600 | −1.69714 | ||||||||
\(460\) | −0.372667 | −0.0173757 | ||||||||
\(461\) | 35.8514 | 1.66977 | 0.834883 | − | 0.550428i | \(-0.185535\pi\) | ||||
0.834883 | + | 0.550428i | \(0.185535\pi\) | |||||||
\(462\) | −16.6222 | −0.773334 | ||||||||
\(463\) | −18.5824 | −0.863599 | −0.431800 | − | 0.901970i | \(-0.642121\pi\) | ||||
−0.431800 | + | 0.901970i | \(0.642121\pi\) | |||||||
\(464\) | −5.57173 | −0.258661 | ||||||||
\(465\) | 27.6725 | 1.28328 | ||||||||
\(466\) | 23.5165 | 1.08938 | ||||||||
\(467\) | −1.64625 | −0.0761795 | −0.0380898 | − | 0.999274i | \(-0.512127\pi\) | ||||
−0.0380898 | + | 0.999274i | \(0.512127\pi\) | |||||||
\(468\) | 12.2438 | 0.565968 | ||||||||
\(469\) | −43.3499 | −2.00171 | ||||||||
\(470\) | 3.47016 | 0.160066 | ||||||||
\(471\) | −19.0900 | −0.879622 | ||||||||
\(472\) | 8.82524 | 0.406214 | ||||||||
\(473\) | −4.79067 | −0.220275 | ||||||||
\(474\) | −6.78288 | −0.311548 | ||||||||
\(475\) | 2.18911 | 0.100443 | ||||||||
\(476\) | −14.2144 | −0.651517 | ||||||||
\(477\) | 42.5482 | 1.94815 | ||||||||
\(478\) | 8.03813 | 0.367656 | ||||||||
\(479\) | −34.0714 | −1.55676 | −0.778381 | − | 0.627792i | \(-0.783959\pi\) | ||||
−0.778381 | + | 0.627792i | \(0.783959\pi\) | |||||||
\(480\) | −4.82524 | −0.220241 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 18.4519 | 0.840459 | ||||||||
\(483\) | −3.69649 | −0.168196 | ||||||||
\(484\) | −9.80362 | −0.445619 | ||||||||
\(485\) | 6.67849 | 0.303255 | ||||||||
\(486\) | −20.0266 | −0.908427 | ||||||||
\(487\) | −31.0898 | −1.40881 | −0.704407 | − | 0.709796i | \(-0.748787\pi\) | ||||
−0.704407 | + | 0.709796i | \(0.748787\pi\) | |||||||
\(488\) | −11.7522 | −0.531999 | ||||||||
\(489\) | −43.2575 | −1.95617 | ||||||||
\(490\) | 24.9468 | 1.12698 | ||||||||
\(491\) | 35.0539 | 1.58196 | 0.790981 | − | 0.611841i | \(-0.209571\pi\) | ||||
0.790981 | + | 0.611841i | \(0.209571\pi\) | |||||||
\(492\) | −9.17100 | −0.413461 | ||||||||
\(493\) | −16.4135 | −0.739226 | ||||||||
\(494\) | −1.46032 | −0.0657029 | ||||||||
\(495\) | −11.5948 | −0.521148 | ||||||||
\(496\) | −5.73495 | −0.257507 | ||||||||
\(497\) | 5.88024 | 0.263765 | ||||||||
\(498\) | −16.0426 | −0.718888 | ||||||||
\(499\) | −35.1712 | −1.57448 | −0.787239 | − | 0.616648i | \(-0.788490\pi\) | ||||
−0.787239 | + | 0.616648i | \(0.788490\pi\) | |||||||
\(500\) | −11.7246 | −0.524341 | ||||||||
\(501\) | −75.0197 | −3.35163 | ||||||||
\(502\) | 23.2945 | 1.03968 | ||||||||
\(503\) | 4.63236 | 0.206547 | 0.103273 | − | 0.994653i | \(-0.467068\pi\) | ||||
0.103273 | + | 0.994653i | \(0.467068\pi\) | |||||||
\(504\) | −33.3859 | −1.48713 | ||||||||
\(505\) | −6.72417 | −0.299221 | ||||||||
\(506\) | 0.266055 | 0.0118276 | ||||||||
\(507\) | 31.0806 | 1.38034 | ||||||||
\(508\) | −4.75254 | −0.210860 | ||||||||
\(509\) | −23.8507 | −1.05716 | −0.528581 | − | 0.848883i | \(-0.677276\pi\) | ||||
−0.528581 | + | 0.848883i | \(0.677276\pi\) | |||||||
\(510\) | −14.2144 | −0.629425 | ||||||||
\(511\) | −42.4340 | −1.87717 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 10.1857 | 0.449709 | ||||||||
\(514\) | −4.25683 | −0.187761 | ||||||||
\(515\) | 19.3736 | 0.853705 | ||||||||
\(516\) | −13.7942 | −0.607255 | ||||||||
\(517\) | −2.47742 | −0.108957 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −67.5405 | −2.96470 | ||||||||
\(520\) | 2.71115 | 0.118892 | ||||||||
\(521\) | 19.3996 | 0.849912 | 0.424956 | − | 0.905214i | \(-0.360290\pi\) | ||||
0.424956 | + | 0.905214i | \(0.360290\pi\) | |||||||
\(522\) | −38.5510 | −1.68733 | ||||||||
\(523\) | 1.93995 | 0.0848283 | 0.0424141 | − | 0.999100i | \(-0.486495\pi\) | ||||
0.0424141 | + | 0.999100i | \(0.486495\pi\) | |||||||
\(524\) | 17.9870 | 0.785765 | ||||||||
\(525\) | −40.3127 | −1.75939 | ||||||||
\(526\) | −6.88547 | −0.300221 | ||||||||
\(527\) | −16.8943 | −0.735927 | ||||||||
\(528\) | 3.44484 | 0.149918 | ||||||||
\(529\) | −22.9408 | −0.997428 | ||||||||
\(530\) | 9.42150 | 0.409244 | ||||||||
\(531\) | 61.0620 | 2.64987 | ||||||||
\(532\) | 3.98196 | 0.172640 | ||||||||
\(533\) | 5.15290 | 0.223197 | ||||||||
\(534\) | −28.2701 | −1.22336 | ||||||||
\(535\) | 28.8947 | 1.24923 | ||||||||
\(536\) | 8.98400 | 0.388050 | ||||||||
\(537\) | −36.2966 | −1.56631 | ||||||||
\(538\) | 9.67565 | 0.417147 | ||||||||
\(539\) | −17.8101 | −0.767135 | ||||||||
\(540\) | −18.9102 | −0.813767 | ||||||||
\(541\) | −4.31210 | −0.185392 | −0.0926958 | − | 0.995694i | \(-0.529548\pi\) | ||||
−0.0926958 | + | 0.995694i | \(0.529548\pi\) | |||||||
\(542\) | 7.66277 | 0.329144 | ||||||||
\(543\) | 55.9621 | 2.40156 | ||||||||
\(544\) | 2.94585 | 0.126302 | ||||||||
\(545\) | −12.8915 | −0.552211 | ||||||||
\(546\) | 26.8920 | 1.15087 | ||||||||
\(547\) | 17.5166 | 0.748956 | 0.374478 | − | 0.927236i | \(-0.377822\pi\) | ||||
0.374478 | + | 0.927236i | \(0.377822\pi\) | |||||||
\(548\) | 22.1091 | 0.944456 | ||||||||
\(549\) | −81.3141 | −3.47040 | ||||||||
\(550\) | 2.90151 | 0.123721 | ||||||||
\(551\) | 4.59799 | 0.195881 | ||||||||
\(552\) | 0.766075 | 0.0326063 | ||||||||
\(553\) | −10.3920 | −0.441912 | ||||||||
\(554\) | 4.01957 | 0.170775 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.66547 | −0.113041 | ||||||||
\(557\) | 22.8107 | 0.966521 | 0.483261 | − | 0.875477i | \(-0.339452\pi\) | ||||
0.483261 | + | 0.875477i | \(0.339452\pi\) | |||||||
\(558\) | −39.6803 | −1.67980 | ||||||||
\(559\) | 7.75052 | 0.327812 | ||||||||
\(560\) | −7.39269 | −0.312398 | ||||||||
\(561\) | 10.1480 | 0.428448 | ||||||||
\(562\) | −6.99927 | −0.295247 | ||||||||
\(563\) | −26.5842 | −1.12039 | −0.560195 | − | 0.828361i | \(-0.689274\pi\) | ||||
−0.560195 | + | 0.828361i | \(0.689274\pi\) | |||||||
\(564\) | −7.13345 | −0.300373 | ||||||||
\(565\) | −9.78179 | −0.411523 | ||||||||
\(566\) | −4.70460 | −0.197749 | ||||||||
\(567\) | −87.4133 | −3.67101 | ||||||||
\(568\) | −1.21864 | −0.0511331 | ||||||||
\(569\) | −13.9698 | −0.585646 | −0.292823 | − | 0.956167i | \(-0.594595\pi\) | ||||
−0.292823 | + | 0.956167i | \(0.594595\pi\) | |||||||
\(570\) | 3.98196 | 0.166786 | ||||||||
\(571\) | 21.9636 | 0.919148 | 0.459574 | − | 0.888140i | \(-0.348002\pi\) | ||||
0.459574 | + | 0.888140i | \(0.348002\pi\) | |||||||
\(572\) | −1.93555 | −0.0809295 | ||||||||
\(573\) | 81.6062 | 3.40915 | ||||||||
\(574\) | −14.0508 | −0.586468 | ||||||||
\(575\) | 0.645246 | 0.0269086 | ||||||||
\(576\) | 6.91903 | 0.288293 | ||||||||
\(577\) | 31.5119 | 1.31186 | 0.655929 | − | 0.754823i | \(-0.272277\pi\) | ||||
0.655929 | + | 0.754823i | \(0.272277\pi\) | |||||||
\(578\) | −8.32197 | −0.346148 | ||||||||
\(579\) | −34.3384 | −1.42705 | ||||||||
\(580\) | −8.53639 | −0.354454 | ||||||||
\(581\) | −24.5787 | −1.01970 | ||||||||
\(582\) | −13.7287 | −0.569072 | ||||||||
\(583\) | −6.72622 | −0.278572 | ||||||||
\(584\) | 8.79418 | 0.363906 | ||||||||
\(585\) | 18.7585 | 0.775570 | ||||||||
\(586\) | −14.2310 | −0.587877 | ||||||||
\(587\) | −41.8748 | −1.72836 | −0.864179 | − | 0.503185i | \(-0.832161\pi\) | ||||
−0.864179 | + | 0.503185i | \(0.832161\pi\) | |||||||
\(588\) | −51.2822 | −2.11484 | ||||||||
\(589\) | 4.73268 | 0.195007 | ||||||||
\(590\) | 13.5210 | 0.556653 | ||||||||
\(591\) | 20.2923 | 0.834715 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.7471 | −1.26263 | −0.631316 | − | 0.775525i | \(-0.717485\pi\) | ||||
−0.631316 | + | 0.775525i | \(0.717485\pi\) | |||||||
\(594\) | 13.5004 | 0.553929 | ||||||||
\(595\) | −21.7778 | −0.892801 | ||||||||
\(596\) | 6.13622 | 0.251349 | ||||||||
\(597\) | −59.3847 | −2.43045 | ||||||||
\(598\) | −0.430434 | −0.0176017 | ||||||||
\(599\) | 30.0843 | 1.22921 | 0.614605 | − | 0.788835i | \(-0.289315\pi\) | ||||
0.614605 | + | 0.788835i | \(0.289315\pi\) | |||||||
\(600\) | 8.35455 | 0.341073 | ||||||||
\(601\) | 30.3518 | 1.23808 | 0.619038 | − | 0.785361i | \(-0.287523\pi\) | ||||
0.619038 | + | 0.785361i | \(0.287523\pi\) | |||||||
\(602\) | −21.1339 | −0.861354 | ||||||||
\(603\) | 62.1605 | 2.53137 | ||||||||
\(604\) | −0.436768 | −0.0177719 | ||||||||
\(605\) | −15.0200 | −0.610650 | ||||||||
\(606\) | 13.8226 | 0.561504 | ||||||||
\(607\) | −1.15032 | −0.0466902 | −0.0233451 | − | 0.999727i | \(-0.507432\pi\) | ||||
−0.0233451 | + | 0.999727i | \(0.507432\pi\) | |||||||
\(608\) | −0.825235 | −0.0334677 | ||||||||
\(609\) | −84.6727 | −3.43111 | ||||||||
\(610\) | −18.0055 | −0.729020 | ||||||||
\(611\) | 4.00807 | 0.162149 | ||||||||
\(612\) | 20.3824 | 0.823910 | ||||||||
\(613\) | −15.4606 | −0.624448 | −0.312224 | − | 0.950008i | \(-0.601074\pi\) | ||||
−0.312224 | + | 0.950008i | \(0.601074\pi\) | |||||||
\(614\) | 0.802616 | 0.0323910 | ||||||||
\(615\) | −14.0508 | −0.566582 | ||||||||
\(616\) | 5.27780 | 0.212649 | ||||||||
\(617\) | 20.9822 | 0.844711 | 0.422356 | − | 0.906430i | \(-0.361203\pi\) | ||||
0.422356 | + | 0.906430i | \(0.361203\pi\) | |||||||
\(618\) | −39.8256 | −1.60202 | ||||||||
\(619\) | 30.8550 | 1.24017 | 0.620084 | − | 0.784535i | \(-0.287098\pi\) | ||||
0.620084 | + | 0.784535i | \(0.287098\pi\) | |||||||
\(620\) | −8.78645 | −0.352872 | ||||||||
\(621\) | 3.00227 | 0.120477 | ||||||||
\(622\) | −2.46944 | −0.0990155 | ||||||||
\(623\) | −43.3122 | −1.73527 | ||||||||
\(624\) | −5.57320 | −0.223106 | ||||||||
\(625\) | −4.69965 | −0.187986 | ||||||||
\(626\) | −17.8439 | −0.713185 | ||||||||
\(627\) | −2.84281 | −0.113531 | ||||||||
\(628\) | 6.06139 | 0.241876 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −51.1502 | −2.03787 | ||||||||
\(631\) | 5.84354 | 0.232628 | 0.116314 | − | 0.993213i | \(-0.462892\pi\) | ||||
0.116314 | + | 0.993213i | \(0.462892\pi\) | |||||||
\(632\) | 2.15367 | 0.0856684 | ||||||||
\(633\) | 4.45490 | 0.177066 | ||||||||
\(634\) | 3.53955 | 0.140574 | ||||||||
\(635\) | −7.28131 | −0.288950 | ||||||||
\(636\) | −19.3674 | −0.767966 | ||||||||
\(637\) | 28.8139 | 1.14165 | ||||||||
\(638\) | 6.09432 | 0.241276 | ||||||||
\(639\) | −8.43183 | −0.333558 | ||||||||
\(640\) | 1.53209 | 0.0605611 | ||||||||
\(641\) | 29.8415 | 1.17867 | 0.589334 | − | 0.807889i | \(-0.299390\pi\) | ||||
0.589334 | + | 0.807889i | \(0.299390\pi\) | |||||||
\(642\) | −59.3976 | −2.34423 | ||||||||
\(643\) | 14.3623 | 0.566396 | 0.283198 | − | 0.959062i | \(-0.408605\pi\) | ||||
0.283198 | + | 0.959062i | \(0.408605\pi\) | |||||||
\(644\) | 1.17369 | 0.0462500 | ||||||||
\(645\) | −21.1339 | −0.832147 | ||||||||
\(646\) | −2.43102 | −0.0956472 | ||||||||
\(647\) | 9.29257 | 0.365329 | 0.182664 | − | 0.983175i | \(-0.441528\pi\) | ||||
0.182664 | + | 0.983175i | \(0.441528\pi\) | |||||||
\(648\) | 18.1159 | 0.711658 | ||||||||
\(649\) | −9.65297 | −0.378912 | ||||||||
\(650\) | −4.69417 | −0.184120 | ||||||||
\(651\) | −87.1530 | −3.41580 | ||||||||
\(652\) | 13.7349 | 0.537902 | ||||||||
\(653\) | −42.5566 | −1.66537 | −0.832684 | − | 0.553748i | \(-0.813197\pi\) | ||||
−0.832684 | + | 0.553748i | \(0.813197\pi\) | |||||||
\(654\) | 26.5005 | 1.03625 | ||||||||
\(655\) | 27.5577 | 1.07677 | ||||||||
\(656\) | 2.91194 | 0.113692 | ||||||||
\(657\) | 60.8471 | 2.37387 | ||||||||
\(658\) | −10.9291 | −0.426060 | ||||||||
\(659\) | 10.9819 | 0.427794 | 0.213897 | − | 0.976856i | \(-0.431384\pi\) | ||||
0.213897 | + | 0.976856i | \(0.431384\pi\) | |||||||
\(660\) | 5.27780 | 0.205438 | ||||||||
\(661\) | 33.5295 | 1.30415 | 0.652073 | − | 0.758156i | \(-0.273900\pi\) | ||||
0.652073 | + | 0.758156i | \(0.273900\pi\) | |||||||
\(662\) | 3.82628 | 0.148712 | ||||||||
\(663\) | −16.4178 | −0.637615 | ||||||||
\(664\) | 5.09379 | 0.197677 | ||||||||
\(665\) | 6.10071 | 0.236575 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.35527 | 0.0524764 | ||||||||
\(668\) | 23.8199 | 0.921621 | ||||||||
\(669\) | 38.3447 | 1.48249 | ||||||||
\(670\) | 13.7643 | 0.531761 | ||||||||
\(671\) | 12.8545 | 0.496243 | ||||||||
\(672\) | 15.1968 | 0.586231 | ||||||||
\(673\) | −43.8179 | −1.68905 | −0.844527 | − | 0.535513i | \(-0.820118\pi\) | ||||
−0.844527 | + | 0.535513i | \(0.820118\pi\) | |||||||
\(674\) | −21.3962 | −0.824153 | ||||||||
\(675\) | 32.7417 | 1.26023 | ||||||||
\(676\) | −9.86859 | −0.379561 | ||||||||
\(677\) | −2.17579 | −0.0836225 | −0.0418113 | − | 0.999126i | \(-0.513313\pi\) | ||||
−0.0418113 | + | 0.999126i | \(0.513313\pi\) | |||||||
\(678\) | 20.1080 | 0.772243 | ||||||||
\(679\) | −21.0336 | −0.807194 | ||||||||
\(680\) | 4.51330 | 0.173077 | ||||||||
\(681\) | 67.0831 | 2.57063 | ||||||||
\(682\) | 6.27284 | 0.240199 | ||||||||
\(683\) | −31.7054 | −1.21317 | −0.606586 | − | 0.795018i | \(-0.707462\pi\) | ||||
−0.606586 | + | 0.795018i | \(0.707462\pi\) | |||||||
\(684\) | −5.70983 | −0.218321 | ||||||||
\(685\) | 33.8732 | 1.29423 | ||||||||
\(686\) | −44.7922 | −1.71017 | ||||||||
\(687\) | 8.97468 | 0.342405 | ||||||||
\(688\) | 4.37987 | 0.166981 | ||||||||
\(689\) | 10.8819 | 0.414569 | ||||||||
\(690\) | 1.17369 | 0.0446818 | ||||||||
\(691\) | 25.4909 | 0.969718 | 0.484859 | − | 0.874592i | \(-0.338871\pi\) | ||||
0.484859 | + | 0.874592i | \(0.338871\pi\) | |||||||
\(692\) | 21.4452 | 0.815223 | ||||||||
\(693\) | 36.5173 | 1.38718 | ||||||||
\(694\) | −25.6363 | −0.973139 | ||||||||
\(695\) | −4.08374 | −0.154905 | ||||||||
\(696\) | 17.5479 | 0.665151 | ||||||||
\(697\) | 8.57813 | 0.324920 | ||||||||
\(698\) | 15.5352 | 0.588015 | ||||||||
\(699\) | −74.0642 | −2.80136 | ||||||||
\(700\) | 12.7999 | 0.483791 | ||||||||
\(701\) | −17.9887 | −0.679426 | −0.339713 | − | 0.940529i | \(-0.610330\pi\) | ||||
−0.339713 | + | 0.940529i | \(0.610330\pi\) | |||||||
\(702\) | −21.8415 | −0.824355 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.09379 | −0.0412238 | ||||||||
\(705\) | −10.9291 | −0.411613 | ||||||||
\(706\) | −1.35631 | −0.0510453 | ||||||||
\(707\) | 21.1774 | 0.796459 | ||||||||
\(708\) | −27.7946 | −1.04459 | ||||||||
\(709\) | 27.8902 | 1.04744 | 0.523719 | − | 0.851891i | \(-0.324544\pi\) | ||||
0.523719 | + | 0.851891i | \(0.324544\pi\) | |||||||
\(710\) | −1.86707 | −0.0700699 | ||||||||
\(711\) | 14.9013 | 0.558843 | ||||||||
\(712\) | 8.97619 | 0.336397 | ||||||||
\(713\) | 1.39497 | 0.0522422 | ||||||||
\(714\) | 44.7676 | 1.67538 | ||||||||
\(715\) | −2.96544 | −0.110901 | ||||||||
\(716\) | 11.5247 | 0.430700 | ||||||||
\(717\) | −25.3157 | −0.945431 | ||||||||
\(718\) | −22.3147 | −0.832777 | ||||||||
\(719\) | −27.4295 | −1.02295 | −0.511474 | − | 0.859299i | \(-0.670900\pi\) | ||||
−0.511474 | + | 0.859299i | \(0.670900\pi\) | |||||||
\(720\) | 10.6006 | 0.395060 | ||||||||
\(721\) | −61.0163 | −2.27237 | ||||||||
\(722\) | −18.3190 | −0.681762 | ||||||||
\(723\) | −58.1132 | −2.16125 | ||||||||
\(724\) | −17.7689 | −0.660374 | ||||||||
\(725\) | 14.7802 | 0.548921 | ||||||||
\(726\) | 30.8760 | 1.14592 | ||||||||
\(727\) | 10.1833 | 0.377679 | 0.188839 | − | 0.982008i | \(-0.439527\pi\) | ||||
0.188839 | + | 0.982008i | \(0.439527\pi\) | |||||||
\(728\) | −8.53863 | −0.316463 | ||||||||
\(729\) | 8.72530 | 0.323159 | ||||||||
\(730\) | 13.4735 | 0.498675 | ||||||||
\(731\) | 12.9024 | 0.477214 | ||||||||
\(732\) | 37.0131 | 1.36804 | ||||||||
\(733\) | −35.2114 | −1.30056 | −0.650282 | − | 0.759693i | \(-0.725349\pi\) | ||||
−0.650282 | + | 0.759693i | \(0.725349\pi\) | |||||||
\(734\) | 7.22844 | 0.266807 | ||||||||
\(735\) | −78.5688 | −2.89805 | ||||||||
\(736\) | −0.243241 | −0.00896598 | ||||||||
\(737\) | −9.82663 | −0.361968 | ||||||||
\(738\) | 20.1478 | 0.741650 | ||||||||
\(739\) | −8.78122 | −0.323022 | −0.161511 | − | 0.986871i | \(-0.551637\pi\) | ||||
−0.161511 | + | 0.986871i | \(0.551637\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.59920 | 0.168956 | ||||||||
\(742\) | −29.6725 | −1.08931 | ||||||||
\(743\) | 14.7448 | 0.540935 | 0.270467 | − | 0.962729i | \(-0.412822\pi\) | ||||
0.270467 | + | 0.962729i | \(0.412822\pi\) | |||||||
\(744\) | 18.0619 | 0.662182 | ||||||||
\(745\) | 9.40123 | 0.344434 | ||||||||
\(746\) | −11.7328 | −0.429570 | ||||||||
\(747\) | 35.2441 | 1.28951 | ||||||||
\(748\) | −3.22215 | −0.117813 | ||||||||
\(749\) | −91.0023 | −3.32515 | ||||||||
\(750\) | 36.9261 | 1.34835 | ||||||||
\(751\) | −34.8856 | −1.27299 | −0.636496 | − | 0.771280i | \(-0.719617\pi\) | ||||
−0.636496 | + | 0.771280i | \(0.719617\pi\) | |||||||
\(752\) | 2.26498 | 0.0825955 | ||||||||
\(753\) | −73.3648 | −2.67356 | ||||||||
\(754\) | −9.85962 | −0.359066 | ||||||||
\(755\) | −0.669168 | −0.0243535 | ||||||||
\(756\) | 59.5568 | 2.16606 | ||||||||
\(757\) | 52.0167 | 1.89058 | 0.945289 | − | 0.326233i | \(-0.105780\pi\) | ||||
0.945289 | + | 0.326233i | \(0.105780\pi\) | |||||||
\(758\) | −2.76782 | −0.100532 | ||||||||
\(759\) | −0.837926 | −0.0304148 | ||||||||
\(760\) | −1.26433 | −0.0458622 | ||||||||
\(761\) | 5.96409 | 0.216198 | 0.108099 | − | 0.994140i | \(-0.465524\pi\) | ||||
0.108099 | + | 0.994140i | \(0.465524\pi\) | |||||||
\(762\) | 14.9679 | 0.542229 | ||||||||
\(763\) | 40.6011 | 1.46986 | ||||||||
\(764\) | −25.9113 | −0.937437 | ||||||||
\(765\) | 31.2277 | 1.12904 | ||||||||
\(766\) | 19.4717 | 0.703540 | ||||||||
\(767\) | 15.6169 | 0.563895 | ||||||||
\(768\) | −3.14945 | −0.113646 | ||||||||
\(769\) | 37.0902 | 1.33751 | 0.668753 | − | 0.743484i | \(-0.266828\pi\) | ||||
0.668753 | + | 0.743484i | \(0.266828\pi\) | |||||||
\(770\) | 8.08607 | 0.291402 | ||||||||
\(771\) | 13.4067 | 0.482830 | ||||||||
\(772\) | 10.9030 | 0.392407 | ||||||||
\(773\) | −3.17969 | −0.114366 | −0.0571828 | − | 0.998364i | \(-0.518212\pi\) | ||||
−0.0571828 | + | 0.998364i | \(0.518212\pi\) | |||||||
\(774\) | 30.3044 | 1.08927 | ||||||||
\(775\) | 15.2131 | 0.546471 | ||||||||
\(776\) | 4.35907 | 0.156482 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.34776 | −0.0841713 | ||||||||
\(779\) | −2.40303 | −0.0860976 | ||||||||
\(780\) | −8.53863 | −0.305732 | ||||||||
\(781\) | 1.33294 | 0.0476964 | ||||||||
\(782\) | −0.716551 | −0.0256238 | ||||||||
\(783\) | 68.7706 | 2.45766 | ||||||||
\(784\) | 16.2829 | 0.581532 | ||||||||
\(785\) | 9.28658 | 0.331452 | ||||||||
\(786\) | −56.6491 | −2.02061 | ||||||||
\(787\) | −5.25051 | −0.187160 | −0.0935802 | − | 0.995612i | \(-0.529831\pi\) | ||||
−0.0935802 | + | 0.995612i | \(0.529831\pi\) | |||||||
\(788\) | −6.44314 | −0.229527 | ||||||||
\(789\) | 21.6854 | 0.772022 | ||||||||
\(790\) | 3.29962 | 0.117395 | ||||||||
\(791\) | 30.8073 | 1.09538 | ||||||||
\(792\) | −7.56798 | −0.268916 | ||||||||
\(793\) | −20.7965 | −0.738506 | ||||||||
\(794\) | 2.27548 | 0.0807536 | ||||||||
\(795\) | −29.6725 | −1.05238 | ||||||||
\(796\) | 18.8556 | 0.668318 | ||||||||
\(797\) | 26.6310 | 0.943319 | 0.471660 | − | 0.881781i | \(-0.343655\pi\) | ||||
0.471660 | + | 0.881781i | \(0.343655\pi\) | |||||||
\(798\) | −12.5410 | −0.443945 | ||||||||
\(799\) | 6.67231 | 0.236049 | ||||||||
\(800\) | −2.65270 | −0.0937872 | ||||||||
\(801\) | 62.1065 | 2.19443 | ||||||||
\(802\) | 17.5482 | 0.619649 | ||||||||
\(803\) | −9.61900 | −0.339447 | ||||||||
\(804\) | −28.2946 | −0.997875 | ||||||||
\(805\) | 1.79820 | 0.0633784 | ||||||||
\(806\) | −10.1484 | −0.357464 | ||||||||
\(807\) | −30.4730 | −1.07270 | ||||||||
\(808\) | −4.38889 | −0.154401 | ||||||||
\(809\) | −15.5185 | −0.545600 | −0.272800 | − | 0.962071i | \(-0.587950\pi\) | ||||
−0.272800 | + | 0.962071i | \(0.587950\pi\) | |||||||
\(810\) | 27.7551 | 0.975215 | ||||||||
\(811\) | 32.7418 | 1.14972 | 0.574860 | − | 0.818252i | \(-0.305056\pi\) | ||||
0.574860 | + | 0.818252i | \(0.305056\pi\) | |||||||
\(812\) | 26.8849 | 0.943476 | ||||||||
\(813\) | −24.1335 | −0.846399 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.0432 | 0.737110 | ||||||||
\(816\) | −9.27780 | −0.324788 | ||||||||
\(817\) | −3.61442 | −0.126453 | ||||||||
\(818\) | 22.6789 | 0.792948 | ||||||||
\(819\) | −59.0790 | −2.06439 | ||||||||
\(820\) | 4.46135 | 0.155797 | ||||||||
\(821\) | −12.1639 | −0.424521 | −0.212261 | − | 0.977213i | \(-0.568083\pi\) | ||||
−0.212261 | + | 0.977213i | \(0.568083\pi\) | |||||||
\(822\) | −69.6316 | −2.42868 | ||||||||
\(823\) | 21.8103 | 0.760259 | 0.380130 | − | 0.924933i | \(-0.375879\pi\) | ||||
0.380130 | + | 0.924933i | \(0.375879\pi\) | |||||||
\(824\) | 12.6452 | 0.440518 | ||||||||
\(825\) | −9.13815 | −0.318149 | ||||||||
\(826\) | −42.5838 | −1.48168 | ||||||||
\(827\) | −11.5278 | −0.400860 | −0.200430 | − | 0.979708i | \(-0.564234\pi\) | ||||
−0.200430 | + | 0.979708i | \(0.564234\pi\) | |||||||
\(828\) | −1.68299 | −0.0584879 | ||||||||
\(829\) | −10.4937 | −0.364461 | −0.182230 | − | 0.983256i | \(-0.558332\pi\) | ||||
−0.182230 | + | 0.983256i | \(0.558332\pi\) | |||||||
\(830\) | 7.80414 | 0.270886 | ||||||||
\(831\) | −12.6594 | −0.439151 | ||||||||
\(832\) | 1.76958 | 0.0613491 | ||||||||
\(833\) | 47.9670 | 1.66196 | ||||||||
\(834\) | 8.39476 | 0.290687 | ||||||||
\(835\) | 36.4943 | 1.26294 | ||||||||
\(836\) | 0.902636 | 0.0312183 | ||||||||
\(837\) | 70.7852 | 2.44669 | ||||||||
\(838\) | 18.8213 | 0.650172 | ||||||||
\(839\) | −27.6168 | −0.953436 | −0.476718 | − | 0.879056i | \(-0.658174\pi\) | ||||
−0.476718 | + | 0.879056i | \(0.658174\pi\) | |||||||
\(840\) | 23.2829 | 0.803336 | ||||||||
\(841\) | 2.04419 | 0.0704893 | ||||||||
\(842\) | −17.9266 | −0.617791 | ||||||||
\(843\) | 22.0439 | 0.759231 | ||||||||
\(844\) | −1.41450 | −0.0486891 | ||||||||
\(845\) | −15.1196 | −0.520129 | ||||||||
\(846\) | 15.6715 | 0.538797 | ||||||||
\(847\) | 47.3048 | 1.62541 | ||||||||
\(848\) | 6.14945 | 0.211173 | ||||||||
\(849\) | 14.8169 | 0.508515 | ||||||||
\(850\) | −7.81447 | −0.268034 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 3.83806 | 0.131490 | ||||||||
\(853\) | 20.6389 | 0.706661 | 0.353330 | − | 0.935499i | \(-0.385049\pi\) | ||||
0.353330 | + | 0.935499i | \(0.385049\pi\) | |||||||
\(854\) | 56.7073 | 1.94048 | ||||||||
\(855\) | −8.74796 | −0.299174 | ||||||||
\(856\) | 18.8597 | 0.644610 | ||||||||
\(857\) | 31.3189 | 1.06983 | 0.534917 | − | 0.844905i | \(-0.320343\pi\) | ||||
0.534917 | + | 0.844905i | \(0.320343\pi\) | |||||||
\(858\) | 6.09592 | 0.208111 | ||||||||
\(859\) | 45.5472 | 1.55405 | 0.777025 | − | 0.629469i | \(-0.216728\pi\) | ||||
0.777025 | + | 0.629469i | \(0.216728\pi\) | |||||||
\(860\) | 6.71035 | 0.228821 | ||||||||
\(861\) | 44.2522 | 1.50811 | ||||||||
\(862\) | 12.2609 | 0.417607 | ||||||||
\(863\) | −50.2043 | −1.70897 | −0.854487 | − | 0.519473i | \(-0.826128\pi\) | ||||
−0.854487 | + | 0.519473i | \(0.826128\pi\) | |||||||
\(864\) | −12.3428 | −0.419910 | ||||||||
\(865\) | 32.8559 | 1.11713 | ||||||||
\(866\) | 21.1146 | 0.717503 | ||||||||
\(867\) | 26.2096 | 0.890125 | ||||||||
\(868\) | 27.6725 | 0.939265 | ||||||||
\(869\) | −2.35567 | −0.0799106 | ||||||||
\(870\) | 26.8849 | 0.911484 | ||||||||
\(871\) | 15.8979 | 0.538680 | ||||||||
\(872\) | −8.41432 | −0.284945 | ||||||||
\(873\) | 30.1606 | 1.02078 | ||||||||
\(874\) | 0.200731 | 0.00678983 | ||||||||
\(875\) | 56.5741 | 1.91255 | ||||||||
\(876\) | −27.6968 | −0.935788 | ||||||||
\(877\) | 31.7132 | 1.07088 | 0.535439 | − | 0.844574i | \(-0.320146\pi\) | ||||
0.535439 | + | 0.844574i | \(0.320146\pi\) | |||||||
\(878\) | −24.0926 | −0.813086 | ||||||||
\(879\) | 44.8198 | 1.51173 | ||||||||
\(880\) | −1.67579 | −0.0564908 | ||||||||
\(881\) | 29.7084 | 1.00090 | 0.500450 | − | 0.865765i | \(-0.333168\pi\) | ||||
0.500450 | + | 0.865765i | \(0.333168\pi\) | |||||||
\(882\) | 112.662 | 3.79352 | ||||||||
\(883\) | 15.5877 | 0.524569 | 0.262285 | − | 0.964991i | \(-0.415524\pi\) | ||||
0.262285 | + | 0.964991i | \(0.415524\pi\) | |||||||
\(884\) | 5.21291 | 0.175329 | ||||||||
\(885\) | −42.5838 | −1.43144 | ||||||||
\(886\) | 19.2348 | 0.646205 | ||||||||
\(887\) | −39.8038 | −1.33648 | −0.668240 | − | 0.743946i | \(-0.732952\pi\) | ||||
−0.668240 | + | 0.743946i | \(0.732952\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.9321 | 0.769118 | ||||||||
\(890\) | 13.7523 | 0.460979 | ||||||||
\(891\) | −19.8150 | −0.663827 | ||||||||
\(892\) | −12.1750 | −0.407651 | ||||||||
\(893\) | −1.86915 | −0.0625486 | ||||||||
\(894\) | −19.3257 | −0.646348 | ||||||||
\(895\) | 17.6569 | 0.590206 | ||||||||
\(896\) | −4.82524 | −0.161200 | ||||||||
\(897\) | 1.35563 | 0.0452631 | ||||||||
\(898\) | −6.58735 | −0.219823 | ||||||||
\(899\) | 31.9536 | 1.06571 | ||||||||
\(900\) | −18.3541 | −0.611804 | ||||||||
\(901\) | 18.1154 | 0.603510 | ||||||||
\(902\) | −3.18505 | −0.106051 | ||||||||
\(903\) | 66.5601 | 2.21498 | ||||||||
\(904\) | −6.38461 | −0.212349 | ||||||||
\(905\) | −27.2235 | −0.904938 | ||||||||
\(906\) | 1.37558 | 0.0457006 | ||||||||
\(907\) | 44.9605 | 1.49289 | 0.746444 | − | 0.665448i | \(-0.231760\pi\) | ||||
0.746444 | + | 0.665448i | \(0.231760\pi\) | |||||||
\(908\) | −21.2999 | −0.706863 | ||||||||
\(909\) | −30.3668 | −1.00720 | ||||||||
\(910\) | −13.0819 | −0.433662 | ||||||||
\(911\) | −14.2042 | −0.470607 | −0.235304 | − | 0.971922i | \(-0.575608\pi\) | ||||
−0.235304 | + | 0.971922i | \(0.575608\pi\) | |||||||
\(912\) | 2.59904 | 0.0860627 | ||||||||
\(913\) | −5.57155 | −0.184391 | ||||||||
\(914\) | −28.9912 | −0.958943 | ||||||||
\(915\) | 56.7073 | 1.87469 | ||||||||
\(916\) | −2.84960 | −0.0941535 | ||||||||
\(917\) | −86.7914 | −2.86611 | ||||||||
\(918\) | −36.3600 | −1.20006 | ||||||||
\(919\) | 46.2177 | 1.52458 | 0.762291 | − | 0.647235i | \(-0.224075\pi\) | ||||
0.762291 | + | 0.647235i | \(0.224075\pi\) | |||||||
\(920\) | −0.372667 | −0.0122865 | ||||||||
\(921\) | −2.52780 | −0.0832938 | ||||||||
\(922\) | 35.8514 | 1.18070 | ||||||||
\(923\) | −2.15649 | −0.0709816 | ||||||||
\(924\) | −16.6222 | −0.546829 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.5824 | −0.610657 | ||||||||
\(927\) | 87.4928 | 2.87364 | ||||||||
\(928\) | −5.57173 | −0.182901 | ||||||||
\(929\) | −53.7917 | −1.76485 | −0.882424 | − | 0.470455i | \(-0.844090\pi\) | ||||
−0.882424 | + | 0.470455i | \(0.844090\pi\) | |||||||
\(930\) | 27.6725 | 0.907416 | ||||||||
\(931\) | −13.4372 | −0.440387 | ||||||||
\(932\) | 23.5165 | 0.770310 | ||||||||
\(933\) | 7.77737 | 0.254620 | ||||||||
\(934\) | −1.64625 | −0.0538671 | ||||||||
\(935\) | −4.93662 | −0.161445 | ||||||||
\(936\) | 12.2438 | 0.400200 | ||||||||
\(937\) | −40.2307 | −1.31428 | −0.657140 | − | 0.753768i | \(-0.728234\pi\) | ||||
−0.657140 | + | 0.753768i | \(0.728234\pi\) | |||||||
\(938\) | −43.3499 | −1.41542 | ||||||||
\(939\) | 56.1984 | 1.83397 | ||||||||
\(940\) | 3.47016 | 0.113184 | ||||||||
\(941\) | −1.75799 | −0.0573087 | −0.0286544 | − | 0.999589i | \(-0.509122\pi\) | ||||
−0.0286544 | + | 0.999589i | \(0.509122\pi\) | |||||||
\(942\) | −19.0900 | −0.621987 | ||||||||
\(943\) | −0.708302 | −0.0230655 | ||||||||
\(944\) | 8.82524 | 0.287237 | ||||||||
\(945\) | 91.2463 | 2.96824 | ||||||||
\(946\) | −4.79067 | −0.155758 | ||||||||
\(947\) | 50.7742 | 1.64994 | 0.824971 | − | 0.565176i | \(-0.191192\pi\) | ||||
0.824971 | + | 0.565176i | \(0.191192\pi\) | |||||||
\(948\) | −6.78288 | −0.220298 | ||||||||
\(949\) | 15.5620 | 0.505163 | ||||||||
\(950\) | 2.18911 | 0.0710239 | ||||||||
\(951\) | −11.1476 | −0.361487 | ||||||||
\(952\) | −14.2144 | −0.460692 | ||||||||
\(953\) | 24.6652 | 0.798983 | 0.399492 | − | 0.916737i | \(-0.369187\pi\) | ||||
0.399492 | + | 0.916737i | \(0.369187\pi\) | |||||||
\(954\) | 42.5482 | 1.37755 | ||||||||
\(955\) | −39.6984 | −1.28461 | ||||||||
\(956\) | 8.03813 | 0.259972 | ||||||||
\(957\) | −19.1937 | −0.620445 | ||||||||
\(958\) | −34.0714 | −1.10080 | ||||||||
\(959\) | −106.682 | −3.44494 | ||||||||
\(960\) | −4.82524 | −0.155734 | ||||||||
\(961\) | 1.88962 | 0.0609556 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 130.491 | 4.20500 | ||||||||
\(964\) | 18.4519 | 0.594294 | ||||||||
\(965\) | 16.7043 | 0.537731 | ||||||||
\(966\) | −3.69649 | −0.118933 | ||||||||
\(967\) | −31.1092 | −1.00040 | −0.500202 | − | 0.865909i | \(-0.666741\pi\) | ||||
−0.500202 | + | 0.865909i | \(0.666741\pi\) | |||||||
\(968\) | −9.80362 | −0.315100 | ||||||||
\(969\) | 7.65637 | 0.245958 | ||||||||
\(970\) | 6.67849 | 0.214433 | ||||||||
\(971\) | 20.7251 | 0.665099 | 0.332550 | − | 0.943086i | \(-0.392091\pi\) | ||||
0.332550 | + | 0.943086i | \(0.392091\pi\) | |||||||
\(972\) | −20.0266 | −0.642355 | ||||||||
\(973\) | 12.8615 | 0.412321 | ||||||||
\(974\) | −31.0898 | −0.996182 | ||||||||
\(975\) | 14.7840 | 0.473468 | ||||||||
\(976\) | −11.7522 | −0.376180 | ||||||||
\(977\) | −27.6243 | −0.883778 | −0.441889 | − | 0.897070i | \(-0.645692\pi\) | ||||
−0.441889 | + | 0.897070i | \(0.645692\pi\) | |||||||
\(978\) | −43.2575 | −1.38322 | ||||||||
\(979\) | −9.81809 | −0.313787 | ||||||||
\(980\) | 24.9468 | 0.796898 | ||||||||
\(981\) | −58.2189 | −1.85879 | ||||||||
\(982\) | 35.0539 | 1.11862 | ||||||||
\(983\) | −31.8355 | −1.01539 | −0.507697 | − | 0.861536i | \(-0.669503\pi\) | ||||
−0.507697 | + | 0.861536i | \(0.669503\pi\) | |||||||
\(984\) | −9.17100 | −0.292361 | ||||||||
\(985\) | −9.87146 | −0.314531 | ||||||||
\(986\) | −16.4135 | −0.522712 | ||||||||
\(987\) | 34.4206 | 1.09562 | ||||||||
\(988\) | −1.46032 | −0.0464589 | ||||||||
\(989\) | −1.06536 | −0.0338766 | ||||||||
\(990\) | −11.5948 | −0.368507 | ||||||||
\(991\) | 0.0903272 | 0.00286934 | 0.00143467 | − | 0.999999i | \(-0.499543\pi\) | ||||
0.00143467 | + | 0.999999i | \(0.499543\pi\) | |||||||
\(992\) | −5.73495 | −0.182085 | ||||||||
\(993\) | −12.0507 | −0.382416 | ||||||||
\(994\) | 5.88024 | 0.186510 | ||||||||
\(995\) | 28.8884 | 0.915824 | ||||||||
\(996\) | −16.0426 | −0.508330 | ||||||||
\(997\) | 46.6956 | 1.47886 | 0.739432 | − | 0.673231i | \(-0.235094\pi\) | ||||
0.739432 | + | 0.673231i | \(0.235094\pi\) | |||||||
\(998\) | −35.1712 | −1.11332 | ||||||||
\(999\) | 0 | 0 |
(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 | 2738.2.a.t.1.1 | 6 | ||
37.7 | even | 9 | 74.2.f.b.49.1 | ✓ | 12 | ||
37.16 | even | 9 | 74.2.f.b.71.1 | yes | 12 | ||
37.36 | even | 2 | 2738.2.a.q.1.1 | 6 | |||
111.44 | odd | 18 | 666.2.x.g.271.2 | 12 | |||
111.53 | odd | 18 | 666.2.x.g.145.2 | 12 | |||
148.7 | odd | 18 | 592.2.bc.d.49.2 | 12 | |||
148.127 | odd | 18 | 592.2.bc.d.145.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.f.b.49.1 | ✓ | 12 | 37.7 | even | 9 | ||
74.2.f.b.71.1 | yes | 12 | 37.16 | even | 9 | ||
592.2.bc.d.49.2 | 12 | 148.7 | odd | 18 | |||
592.2.bc.d.145.2 | 12 | 148.127 | odd | 18 | |||
666.2.x.g.145.2 | 12 | 111.53 | odd | 18 | |||
666.2.x.g.271.2 | 12 | 111.44 | odd | 18 | |||
2738.2.a.q.1.1 | 6 | 37.36 | even | 2 | |||
2738.2.a.t.1.1 | 6 | 1.1 | even | 1 | trivial |