Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-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 | ||||||||
\(3\) | 2.26689 | 1.30879 | 0.654394 | − | 0.756154i | \(-0.272924\pi\) | ||||
0.654394 | + | 0.756154i | \(0.272924\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.31390 | −1.92924 | −0.964618 | − | 0.263650i | \(-0.915074\pi\) | ||||
−0.964618 | + | 0.263650i | \(0.915074\pi\) | |||||||
\(6\) | 2.26689 | 0.925453 | ||||||||
\(7\) | 1.45520 | 0.550014 | 0.275007 | − | 0.961442i | \(-0.411320\pi\) | ||||
0.275007 | + | 0.961442i | \(0.411320\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.13877 | 0.712925 | ||||||||
\(10\) | −4.31390 | −1.36418 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.26689 | 0.654394 | ||||||||
\(13\) | 5.78539 | 1.60458 | 0.802289 | − | 0.596935i | \(-0.203615\pi\) | ||||
0.802289 | + | 0.596935i | \(0.203615\pi\) | |||||||
\(14\) | 1.45520 | 0.388919 | ||||||||
\(15\) | −9.77913 | −2.52496 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.84797 | 0.933270 | 0.466635 | − | 0.884450i | \(-0.345466\pi\) | ||||
0.466635 | + | 0.884450i | \(0.345466\pi\) | |||||||
\(18\) | 2.13877 | 0.504114 | ||||||||
\(19\) | −4.96345 | −1.13869 | −0.569346 | − | 0.822098i | \(-0.692804\pi\) | ||||
−0.569346 | + | 0.822098i | \(0.692804\pi\) | |||||||
\(20\) | −4.31390 | −0.964618 | ||||||||
\(21\) | 3.29878 | 0.719852 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −2.20643 | −0.460072 | −0.230036 | − | 0.973182i | \(-0.573884\pi\) | ||||
−0.230036 | + | 0.973182i | \(0.573884\pi\) | |||||||
\(24\) | 2.26689 | 0.462726 | ||||||||
\(25\) | 13.6098 | 2.72196 | ||||||||
\(26\) | 5.78539 | 1.13461 | ||||||||
\(27\) | −1.95230 | −0.375721 | ||||||||
\(28\) | 1.45520 | 0.275007 | ||||||||
\(29\) | 0.634230 | 0.117774 | 0.0588868 | − | 0.998265i | \(-0.481245\pi\) | ||||
0.0588868 | + | 0.998265i | \(0.481245\pi\) | |||||||
\(30\) | −9.77913 | −1.78542 | ||||||||
\(31\) | 5.25012 | 0.942950 | 0.471475 | − | 0.881880i | \(-0.343722\pi\) | ||||
0.471475 | + | 0.881880i | \(0.343722\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.26689 | 0.394614 | ||||||||
\(34\) | 3.84797 | 0.659922 | ||||||||
\(35\) | −6.27760 | −1.06111 | ||||||||
\(36\) | 2.13877 | 0.356462 | ||||||||
\(37\) | 2.91592 | 0.479374 | 0.239687 | − | 0.970850i | \(-0.422955\pi\) | ||||
0.239687 | + | 0.970850i | \(0.422955\pi\) | |||||||
\(38\) | −4.96345 | −0.805178 | ||||||||
\(39\) | 13.1148 | 2.10005 | ||||||||
\(40\) | −4.31390 | −0.682088 | ||||||||
\(41\) | −5.56125 | −0.868522 | −0.434261 | − | 0.900787i | \(-0.642990\pi\) | ||||
−0.434261 | + | 0.900787i | \(0.642990\pi\) | |||||||
\(42\) | 3.29878 | 0.509012 | ||||||||
\(43\) | 1.21278 | 0.184947 | 0.0924736 | − | 0.995715i | \(-0.470523\pi\) | ||||
0.0924736 | + | 0.995715i | \(0.470523\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −9.22647 | −1.37540 | ||||||||
\(46\) | −2.20643 | −0.325320 | ||||||||
\(47\) | −4.07168 | −0.593916 | −0.296958 | − | 0.954890i | \(-0.595972\pi\) | ||||
−0.296958 | + | 0.954890i | \(0.595972\pi\) | |||||||
\(48\) | 2.26689 | 0.327197 | ||||||||
\(49\) | −4.88239 | −0.697484 | ||||||||
\(50\) | 13.6098 | 1.92471 | ||||||||
\(51\) | 8.72291 | 1.22145 | ||||||||
\(52\) | 5.78539 | 0.802289 | ||||||||
\(53\) | −5.37607 | −0.738460 | −0.369230 | − | 0.929338i | \(-0.620379\pi\) | ||||
−0.369230 | + | 0.929338i | \(0.620379\pi\) | |||||||
\(54\) | −1.95230 | −0.265675 | ||||||||
\(55\) | −4.31390 | −0.581687 | ||||||||
\(56\) | 1.45520 | 0.194459 | ||||||||
\(57\) | −11.2516 | −1.49031 | ||||||||
\(58\) | 0.634230 | 0.0832784 | ||||||||
\(59\) | 15.1544 | 1.97294 | 0.986469 | − | 0.163946i | \(-0.0524223\pi\) | ||||
0.986469 | + | 0.163946i | \(0.0524223\pi\) | |||||||
\(60\) | −9.77913 | −1.26248 | ||||||||
\(61\) | 12.8293 | 1.64262 | 0.821311 | − | 0.570480i | \(-0.193243\pi\) | ||||
0.821311 | + | 0.570480i | \(0.193243\pi\) | |||||||
\(62\) | 5.25012 | 0.666766 | ||||||||
\(63\) | 3.11235 | 0.392119 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −24.9576 | −3.09561 | ||||||||
\(66\) | 2.26689 | 0.279034 | ||||||||
\(67\) | 11.6941 | 1.42866 | 0.714329 | − | 0.699810i | \(-0.246732\pi\) | ||||
0.714329 | + | 0.699810i | \(0.246732\pi\) | |||||||
\(68\) | 3.84797 | 0.466635 | ||||||||
\(69\) | −5.00172 | −0.602136 | ||||||||
\(70\) | −6.27760 | −0.750317 | ||||||||
\(71\) | 4.92023 | 0.583924 | 0.291962 | − | 0.956430i | \(-0.405692\pi\) | ||||
0.291962 | + | 0.956430i | \(0.405692\pi\) | |||||||
\(72\) | 2.13877 | 0.252057 | ||||||||
\(73\) | 16.7710 | 1.96290 | 0.981448 | − | 0.191729i | \(-0.0614094\pi\) | ||||
0.981448 | + | 0.191729i | \(0.0614094\pi\) | |||||||
\(74\) | 2.91592 | 0.338969 | ||||||||
\(75\) | 30.8518 | 3.56246 | ||||||||
\(76\) | −4.96345 | −0.569346 | ||||||||
\(77\) | 1.45520 | 0.165836 | ||||||||
\(78\) | 13.1148 | 1.48496 | ||||||||
\(79\) | 4.21494 | 0.474218 | 0.237109 | − | 0.971483i | \(-0.423800\pi\) | ||||
0.237109 | + | 0.971483i | \(0.423800\pi\) | |||||||
\(80\) | −4.31390 | −0.482309 | ||||||||
\(81\) | −10.8420 | −1.20466 | ||||||||
\(82\) | −5.56125 | −0.614138 | ||||||||
\(83\) | −4.59201 | −0.504039 | −0.252019 | − | 0.967722i | \(-0.581095\pi\) | ||||
−0.252019 | + | 0.967722i | \(0.581095\pi\) | |||||||
\(84\) | 3.29878 | 0.359926 | ||||||||
\(85\) | −16.5998 | −1.80050 | ||||||||
\(86\) | 1.21278 | 0.130777 | ||||||||
\(87\) | 1.43773 | 0.154140 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 6.56639 | 0.696036 | 0.348018 | − | 0.937488i | \(-0.386855\pi\) | ||||
0.348018 | + | 0.937488i | \(0.386855\pi\) | |||||||
\(90\) | −9.22647 | −0.972555 | ||||||||
\(91\) | 8.41891 | 0.882541 | ||||||||
\(92\) | −2.20643 | −0.230036 | ||||||||
\(93\) | 11.9014 | 1.23412 | ||||||||
\(94\) | −4.07168 | −0.419962 | ||||||||
\(95\) | 21.4118 | 2.19681 | ||||||||
\(96\) | 2.26689 | 0.231363 | ||||||||
\(97\) | −1.64673 | −0.167200 | −0.0835998 | − | 0.996499i | \(-0.526642\pi\) | ||||
−0.0835998 | + | 0.996499i | \(0.526642\pi\) | |||||||
\(98\) | −4.88239 | −0.493196 | ||||||||
\(99\) | 2.13877 | 0.214955 | ||||||||
\(100\) | 13.6098 | 1.36098 | ||||||||
\(101\) | 2.12355 | 0.211301 | 0.105650 | − | 0.994403i | \(-0.466308\pi\) | ||||
0.105650 | + | 0.994403i | \(0.466308\pi\) | |||||||
\(102\) | 8.72291 | 0.863697 | ||||||||
\(103\) | −6.81012 | −0.671021 | −0.335510 | − | 0.942037i | \(-0.608909\pi\) | ||||
−0.335510 | + | 0.942037i | \(0.608909\pi\) | |||||||
\(104\) | 5.78539 | 0.567304 | ||||||||
\(105\) | −14.2306 | −1.38876 | ||||||||
\(106\) | −5.37607 | −0.522170 | ||||||||
\(107\) | 4.19419 | 0.405468 | 0.202734 | − | 0.979234i | \(-0.435017\pi\) | ||||
0.202734 | + | 0.979234i | \(0.435017\pi\) | |||||||
\(108\) | −1.95230 | −0.187860 | ||||||||
\(109\) | 10.4686 | 1.00271 | 0.501354 | − | 0.865242i | \(-0.332835\pi\) | ||||
0.501354 | + | 0.865242i | \(0.332835\pi\) | |||||||
\(110\) | −4.31390 | −0.411315 | ||||||||
\(111\) | 6.61006 | 0.627399 | ||||||||
\(112\) | 1.45520 | 0.137504 | ||||||||
\(113\) | −18.0135 | −1.69457 | −0.847285 | − | 0.531138i | \(-0.821765\pi\) | ||||
−0.847285 | + | 0.531138i | \(0.821765\pi\) | |||||||
\(114\) | −11.2516 | −1.05381 | ||||||||
\(115\) | 9.51831 | 0.887587 | ||||||||
\(116\) | 0.634230 | 0.0588868 | ||||||||
\(117\) | 12.3736 | 1.14394 | ||||||||
\(118\) | 15.1544 | 1.39508 | ||||||||
\(119\) | 5.59957 | 0.513312 | ||||||||
\(120\) | −9.77913 | −0.892709 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 12.8293 | 1.16151 | ||||||||
\(123\) | −12.6067 | −1.13671 | ||||||||
\(124\) | 5.25012 | 0.471475 | ||||||||
\(125\) | −37.1418 | −3.32206 | ||||||||
\(126\) | 3.11235 | 0.277270 | ||||||||
\(127\) | 12.4888 | 1.10820 | 0.554100 | − | 0.832450i | \(-0.313063\pi\) | ||||
0.554100 | + | 0.832450i | \(0.313063\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.74923 | 0.242057 | ||||||||
\(130\) | −24.9576 | −2.18893 | ||||||||
\(131\) | 3.47476 | 0.303591 | 0.151796 | − | 0.988412i | \(-0.451494\pi\) | ||||
0.151796 | + | 0.988412i | \(0.451494\pi\) | |||||||
\(132\) | 2.26689 | 0.197307 | ||||||||
\(133\) | −7.22281 | −0.626297 | ||||||||
\(134\) | 11.6941 | 1.01021 | ||||||||
\(135\) | 8.42204 | 0.724854 | ||||||||
\(136\) | 3.84797 | 0.329961 | ||||||||
\(137\) | −4.01709 | −0.343203 | −0.171602 | − | 0.985166i | \(-0.554894\pi\) | ||||
−0.171602 | + | 0.985166i | \(0.554894\pi\) | |||||||
\(138\) | −5.00172 | −0.425775 | ||||||||
\(139\) | −5.28021 | −0.447862 | −0.223931 | − | 0.974605i | \(-0.571889\pi\) | ||||
−0.223931 | + | 0.974605i | \(0.571889\pi\) | |||||||
\(140\) | −6.27760 | −0.530554 | ||||||||
\(141\) | −9.23005 | −0.777310 | ||||||||
\(142\) | 4.92023 | 0.412897 | ||||||||
\(143\) | 5.78539 | 0.483799 | ||||||||
\(144\) | 2.13877 | 0.178231 | ||||||||
\(145\) | −2.73601 | −0.227213 | ||||||||
\(146\) | 16.7710 | 1.38798 | ||||||||
\(147\) | −11.0678 | −0.912859 | ||||||||
\(148\) | 2.91592 | 0.239687 | ||||||||
\(149\) | 2.22890 | 0.182598 | 0.0912992 | − | 0.995824i | \(-0.470898\pi\) | ||||
0.0912992 | + | 0.995824i | \(0.470898\pi\) | |||||||
\(150\) | 30.8518 | 2.51904 | ||||||||
\(151\) | 14.5914 | 1.18743 | 0.593716 | − | 0.804675i | \(-0.297660\pi\) | ||||
0.593716 | + | 0.804675i | \(0.297660\pi\) | |||||||
\(152\) | −4.96345 | −0.402589 | ||||||||
\(153\) | 8.22994 | 0.665351 | ||||||||
\(154\) | 1.45520 | 0.117263 | ||||||||
\(155\) | −22.6485 | −1.81917 | ||||||||
\(156\) | 13.1148 | 1.05003 | ||||||||
\(157\) | 1.69825 | 0.135535 | 0.0677674 | − | 0.997701i | \(-0.478412\pi\) | ||||
0.0677674 | + | 0.997701i | \(0.478412\pi\) | |||||||
\(158\) | 4.21494 | 0.335323 | ||||||||
\(159\) | −12.1869 | −0.966487 | ||||||||
\(160\) | −4.31390 | −0.341044 | ||||||||
\(161\) | −3.21079 | −0.253046 | ||||||||
\(162\) | −10.8420 | −0.851825 | ||||||||
\(163\) | −22.7432 | −1.78138 | −0.890691 | − | 0.454609i | \(-0.849779\pi\) | ||||
−0.890691 | + | 0.454609i | \(0.849779\pi\) | |||||||
\(164\) | −5.56125 | −0.434261 | ||||||||
\(165\) | −9.77913 | −0.761304 | ||||||||
\(166\) | −4.59201 | −0.356409 | ||||||||
\(167\) | 1.19080 | 0.0921470 | 0.0460735 | − | 0.998938i | \(-0.485329\pi\) | ||||
0.0460735 | + | 0.998938i | \(0.485329\pi\) | |||||||
\(168\) | 3.29878 | 0.254506 | ||||||||
\(169\) | 20.4708 | 1.57467 | ||||||||
\(170\) | −16.5998 | −1.27315 | ||||||||
\(171\) | −10.6157 | −0.811802 | ||||||||
\(172\) | 1.21278 | 0.0924736 | ||||||||
\(173\) | 17.4792 | 1.32892 | 0.664458 | − | 0.747326i | \(-0.268662\pi\) | ||||
0.664458 | + | 0.747326i | \(0.268662\pi\) | |||||||
\(174\) | 1.43773 | 0.108994 | ||||||||
\(175\) | 19.8050 | 1.49711 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 34.3534 | 2.58216 | ||||||||
\(178\) | 6.56639 | 0.492172 | ||||||||
\(179\) | −16.6632 | −1.24547 | −0.622733 | − | 0.782434i | \(-0.713978\pi\) | ||||
−0.622733 | + | 0.782434i | \(0.713978\pi\) | |||||||
\(180\) | −9.22647 | −0.687700 | ||||||||
\(181\) | −24.0436 | −1.78715 | −0.893573 | − | 0.448919i | \(-0.851809\pi\) | ||||
−0.893573 | + | 0.448919i | \(0.851809\pi\) | |||||||
\(182\) | 8.41891 | 0.624051 | ||||||||
\(183\) | 29.0825 | 2.14984 | ||||||||
\(184\) | −2.20643 | −0.162660 | ||||||||
\(185\) | −12.5790 | −0.924826 | ||||||||
\(186\) | 11.9014 | 0.872655 | ||||||||
\(187\) | 3.84797 | 0.281392 | ||||||||
\(188\) | −4.07168 | −0.296958 | ||||||||
\(189\) | −2.84099 | −0.206652 | ||||||||
\(190\) | 21.4118 | 1.55338 | ||||||||
\(191\) | 16.7007 | 1.20842 | 0.604210 | − | 0.796825i | \(-0.293489\pi\) | ||||
0.604210 | + | 0.796825i | \(0.293489\pi\) | |||||||
\(192\) | 2.26689 | 0.163598 | ||||||||
\(193\) | −3.90861 | −0.281348 | −0.140674 | − | 0.990056i | \(-0.544927\pi\) | ||||
−0.140674 | + | 0.990056i | \(0.544927\pi\) | |||||||
\(194\) | −1.64673 | −0.118228 | ||||||||
\(195\) | −56.5761 | −4.05150 | ||||||||
\(196\) | −4.88239 | −0.348742 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | 2.13877 | 0.151996 | ||||||||
\(199\) | −6.01298 | −0.426249 | −0.213124 | − | 0.977025i | \(-0.568364\pi\) | ||||
−0.213124 | + | 0.977025i | \(0.568364\pi\) | |||||||
\(200\) | 13.6098 | 0.962356 | ||||||||
\(201\) | 26.5091 | 1.86981 | ||||||||
\(202\) | 2.12355 | 0.149412 | ||||||||
\(203\) | 0.922932 | 0.0647771 | ||||||||
\(204\) | 8.72291 | 0.610726 | ||||||||
\(205\) | 23.9907 | 1.67558 | ||||||||
\(206\) | −6.81012 | −0.474483 | ||||||||
\(207\) | −4.71905 | −0.327997 | ||||||||
\(208\) | 5.78539 | 0.401145 | ||||||||
\(209\) | −4.96345 | −0.343329 | ||||||||
\(210\) | −14.2306 | −0.982005 | ||||||||
\(211\) | −11.5594 | −0.795779 | −0.397889 | − | 0.917433i | \(-0.630257\pi\) | ||||
−0.397889 | + | 0.917433i | \(0.630257\pi\) | |||||||
\(212\) | −5.37607 | −0.369230 | ||||||||
\(213\) | 11.1536 | 0.764233 | ||||||||
\(214\) | 4.19419 | 0.286709 | ||||||||
\(215\) | −5.23182 | −0.356807 | ||||||||
\(216\) | −1.95230 | −0.132837 | ||||||||
\(217\) | 7.63998 | 0.518636 | ||||||||
\(218\) | 10.4686 | 0.709022 | ||||||||
\(219\) | 38.0179 | 2.56901 | ||||||||
\(220\) | −4.31390 | −0.290843 | ||||||||
\(221\) | 22.2620 | 1.49751 | ||||||||
\(222\) | 6.61006 | 0.443638 | ||||||||
\(223\) | −21.3160 | −1.42743 | −0.713713 | − | 0.700438i | \(-0.752988\pi\) | ||||
−0.713713 | + | 0.700438i | \(0.752988\pi\) | |||||||
\(224\) | 1.45520 | 0.0972297 | ||||||||
\(225\) | 29.1082 | 1.94055 | ||||||||
\(226\) | −18.0135 | −1.19824 | ||||||||
\(227\) | −11.1150 | −0.737726 | −0.368863 | − | 0.929484i | \(-0.620253\pi\) | ||||
−0.368863 | + | 0.929484i | \(0.620253\pi\) | |||||||
\(228\) | −11.2516 | −0.745154 | ||||||||
\(229\) | −25.1307 | −1.66069 | −0.830343 | − | 0.557253i | \(-0.811855\pi\) | ||||
−0.830343 | + | 0.557253i | \(0.811855\pi\) | |||||||
\(230\) | 9.51831 | 0.627619 | ||||||||
\(231\) | 3.29878 | 0.217043 | ||||||||
\(232\) | 0.634230 | 0.0416392 | ||||||||
\(233\) | −8.50901 | −0.557444 | −0.278722 | − | 0.960372i | \(-0.589911\pi\) | ||||
−0.278722 | + | 0.960372i | \(0.589911\pi\) | |||||||
\(234\) | 12.3736 | 0.808891 | ||||||||
\(235\) | 17.5649 | 1.14581 | ||||||||
\(236\) | 15.1544 | 0.986469 | ||||||||
\(237\) | 9.55479 | 0.620651 | ||||||||
\(238\) | 5.59957 | 0.362966 | ||||||||
\(239\) | 18.9076 | 1.22303 | 0.611514 | − | 0.791234i | \(-0.290561\pi\) | ||||
0.611514 | + | 0.791234i | \(0.290561\pi\) | |||||||
\(240\) | −9.77913 | −0.631240 | ||||||||
\(241\) | 1.93068 | 0.124366 | 0.0621830 | − | 0.998065i | \(-0.480194\pi\) | ||||
0.0621830 | + | 0.998065i | \(0.480194\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −18.7206 | −1.20093 | ||||||||
\(244\) | 12.8293 | 0.821311 | ||||||||
\(245\) | 21.0622 | 1.34561 | ||||||||
\(246\) | −12.6067 | −0.803776 | ||||||||
\(247\) | −28.7155 | −1.82712 | ||||||||
\(248\) | 5.25012 | 0.333383 | ||||||||
\(249\) | −10.4096 | −0.659680 | ||||||||
\(250\) | −37.1418 | −2.34905 | ||||||||
\(251\) | 8.94751 | 0.564762 | 0.282381 | − | 0.959302i | \(-0.408876\pi\) | ||||
0.282381 | + | 0.959302i | \(0.408876\pi\) | |||||||
\(252\) | 3.11235 | 0.196059 | ||||||||
\(253\) | −2.20643 | −0.138717 | ||||||||
\(254\) | 12.4888 | 0.783615 | ||||||||
\(255\) | −37.6298 | −2.35647 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.42717 | −0.463294 | −0.231647 | − | 0.972800i | \(-0.574411\pi\) | ||||
−0.231647 | + | 0.972800i | \(0.574411\pi\) | |||||||
\(258\) | 2.74923 | 0.171160 | ||||||||
\(259\) | 4.24325 | 0.263663 | ||||||||
\(260\) | −24.9576 | −1.54781 | ||||||||
\(261\) | 1.35647 | 0.0839636 | ||||||||
\(262\) | 3.47476 | 0.214672 | ||||||||
\(263\) | −4.07400 | −0.251214 | −0.125607 | − | 0.992080i | \(-0.540088\pi\) | ||||
−0.125607 | + | 0.992080i | \(0.540088\pi\) | |||||||
\(264\) | 2.26689 | 0.139517 | ||||||||
\(265\) | 23.1919 | 1.42466 | ||||||||
\(266\) | −7.22281 | −0.442859 | ||||||||
\(267\) | 14.8853 | 0.910963 | ||||||||
\(268\) | 11.6941 | 0.714329 | ||||||||
\(269\) | 12.8855 | 0.785645 | 0.392823 | − | 0.919614i | \(-0.371499\pi\) | ||||
0.392823 | + | 0.919614i | \(0.371499\pi\) | |||||||
\(270\) | 8.42204 | 0.512549 | ||||||||
\(271\) | −1.31221 | −0.0797108 | −0.0398554 | − | 0.999205i | \(-0.512690\pi\) | ||||
−0.0398554 | + | 0.999205i | \(0.512690\pi\) | |||||||
\(272\) | 3.84797 | 0.233318 | ||||||||
\(273\) | 19.0847 | 1.15506 | ||||||||
\(274\) | −4.01709 | −0.242681 | ||||||||
\(275\) | 13.6098 | 0.820700 | ||||||||
\(276\) | −5.00172 | −0.301068 | ||||||||
\(277\) | 4.52523 | 0.271895 | 0.135947 | − | 0.990716i | \(-0.456592\pi\) | ||||
0.135947 | + | 0.990716i | \(0.456592\pi\) | |||||||
\(278\) | −5.28021 | −0.316686 | ||||||||
\(279\) | 11.2288 | 0.672252 | ||||||||
\(280\) | −6.27760 | −0.375158 | ||||||||
\(281\) | −30.2456 | −1.80430 | −0.902151 | − | 0.431420i | \(-0.858013\pi\) | ||||
−0.902151 | + | 0.431420i | \(0.858013\pi\) | |||||||
\(282\) | −9.23005 | −0.549641 | ||||||||
\(283\) | 9.95702 | 0.591884 | 0.295942 | − | 0.955206i | \(-0.404367\pi\) | ||||
0.295942 | + | 0.955206i | \(0.404367\pi\) | |||||||
\(284\) | 4.92023 | 0.291962 | ||||||||
\(285\) | 48.5382 | 2.87516 | ||||||||
\(286\) | 5.78539 | 0.342097 | ||||||||
\(287\) | −8.09274 | −0.477699 | ||||||||
\(288\) | 2.13877 | 0.126028 | ||||||||
\(289\) | −2.19312 | −0.129007 | ||||||||
\(290\) | −2.73601 | −0.160664 | ||||||||
\(291\) | −3.73294 | −0.218829 | ||||||||
\(292\) | 16.7710 | 0.981448 | ||||||||
\(293\) | −0.204412 | −0.0119419 | −0.00597095 | − | 0.999982i | \(-0.501901\pi\) | ||||
−0.00597095 | + | 0.999982i | \(0.501901\pi\) | |||||||
\(294\) | −11.0678 | −0.645489 | ||||||||
\(295\) | −65.3748 | −3.80627 | ||||||||
\(296\) | 2.91592 | 0.169484 | ||||||||
\(297\) | −1.95230 | −0.113284 | ||||||||
\(298\) | 2.22890 | 0.129117 | ||||||||
\(299\) | −12.7650 | −0.738221 | ||||||||
\(300\) | 30.8518 | 1.78123 | ||||||||
\(301\) | 1.76484 | 0.101724 | ||||||||
\(302\) | 14.5914 | 0.839641 | ||||||||
\(303\) | 4.81384 | 0.276548 | ||||||||
\(304\) | −4.96345 | −0.284673 | ||||||||
\(305\) | −55.3443 | −3.16901 | ||||||||
\(306\) | 8.22994 | 0.470474 | ||||||||
\(307\) | 5.99190 | 0.341976 | 0.170988 | − | 0.985273i | \(-0.445304\pi\) | ||||
0.170988 | + | 0.985273i | \(0.445304\pi\) | |||||||
\(308\) | 1.45520 | 0.0829178 | ||||||||
\(309\) | −15.4378 | −0.878224 | ||||||||
\(310\) | −22.6485 | −1.28635 | ||||||||
\(311\) | 29.6779 | 1.68288 | 0.841441 | − | 0.540349i | \(-0.181708\pi\) | ||||
0.841441 | + | 0.540349i | \(0.181708\pi\) | |||||||
\(312\) | 13.1148 | 0.742481 | ||||||||
\(313\) | −2.08952 | −0.118106 | −0.0590532 | − | 0.998255i | \(-0.518808\pi\) | ||||
−0.0590532 | + | 0.998255i | \(0.518808\pi\) | |||||||
\(314\) | 1.69825 | 0.0958375 | ||||||||
\(315\) | −13.4264 | −0.756490 | ||||||||
\(316\) | 4.21494 | 0.237109 | ||||||||
\(317\) | 30.7875 | 1.72920 | 0.864598 | − | 0.502464i | \(-0.167573\pi\) | ||||
0.864598 | + | 0.502464i | \(0.167573\pi\) | |||||||
\(318\) | −12.1869 | −0.683410 | ||||||||
\(319\) | 0.634230 | 0.0355100 | ||||||||
\(320\) | −4.31390 | −0.241155 | ||||||||
\(321\) | 9.50775 | 0.530671 | ||||||||
\(322\) | −3.21079 | −0.178931 | ||||||||
\(323\) | −19.0992 | −1.06271 | ||||||||
\(324\) | −10.8420 | −0.602332 | ||||||||
\(325\) | 78.7379 | 4.36759 | ||||||||
\(326\) | −22.7432 | −1.25963 | ||||||||
\(327\) | 23.7311 | 1.31233 | ||||||||
\(328\) | −5.56125 | −0.307069 | ||||||||
\(329\) | −5.92512 | −0.326662 | ||||||||
\(330\) | −9.77913 | −0.538324 | ||||||||
\(331\) | −25.5382 | −1.40371 | −0.701853 | − | 0.712322i | \(-0.747644\pi\) | ||||
−0.701853 | + | 0.712322i | \(0.747644\pi\) | |||||||
\(332\) | −4.59201 | −0.252019 | ||||||||
\(333\) | 6.23649 | 0.341758 | ||||||||
\(334\) | 1.19080 | 0.0651578 | ||||||||
\(335\) | −50.4471 | −2.75622 | ||||||||
\(336\) | 3.29878 | 0.179963 | ||||||||
\(337\) | −0.00855933 | −0.000466257 0 | −0.000233128 | − | 1.00000i | \(-0.500074\pi\) | ||||
−0.000233128 | 1.00000i | \(0.500074\pi\) | ||||||||
\(338\) | 20.4708 | 1.11346 | ||||||||
\(339\) | −40.8346 | −2.21783 | ||||||||
\(340\) | −16.5998 | −0.900250 | ||||||||
\(341\) | 5.25012 | 0.284310 | ||||||||
\(342\) | −10.6157 | −0.574031 | ||||||||
\(343\) | −17.2913 | −0.933641 | ||||||||
\(344\) | 1.21278 | 0.0653887 | ||||||||
\(345\) | 21.5769 | 1.16166 | ||||||||
\(346\) | 17.4792 | 0.939685 | ||||||||
\(347\) | −25.4319 | −1.36525 | −0.682627 | − | 0.730767i | \(-0.739163\pi\) | ||||
−0.682627 | + | 0.730767i | \(0.739163\pi\) | |||||||
\(348\) | 1.43773 | 0.0770702 | ||||||||
\(349\) | 4.87428 | 0.260914 | 0.130457 | − | 0.991454i | \(-0.458356\pi\) | ||||
0.130457 | + | 0.991454i | \(0.458356\pi\) | |||||||
\(350\) | 19.8050 | 1.05862 | ||||||||
\(351\) | −11.2948 | −0.602873 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −13.5161 | −0.719391 | −0.359696 | − | 0.933070i | \(-0.617119\pi\) | ||||
−0.359696 | + | 0.933070i | \(0.617119\pi\) | |||||||
\(354\) | 34.3534 | 1.82586 | ||||||||
\(355\) | −21.2254 | −1.12653 | ||||||||
\(356\) | 6.56639 | 0.348018 | ||||||||
\(357\) | 12.6936 | 0.671816 | ||||||||
\(358\) | −16.6632 | −0.880677 | ||||||||
\(359\) | 17.8409 | 0.941607 | 0.470803 | − | 0.882238i | \(-0.343964\pi\) | ||||
0.470803 | + | 0.882238i | \(0.343964\pi\) | |||||||
\(360\) | −9.22647 | −0.486278 | ||||||||
\(361\) | 5.63581 | 0.296622 | ||||||||
\(362\) | −24.0436 | −1.26370 | ||||||||
\(363\) | 2.26689 | 0.118981 | ||||||||
\(364\) | 8.41891 | 0.441271 | ||||||||
\(365\) | −72.3485 | −3.78689 | ||||||||
\(366\) | 29.0825 | 1.52017 | ||||||||
\(367\) | −0.856582 | −0.0447132 | −0.0223566 | − | 0.999750i | \(-0.507117\pi\) | ||||
−0.0223566 | + | 0.999750i | \(0.507117\pi\) | |||||||
\(368\) | −2.20643 | −0.115018 | ||||||||
\(369\) | −11.8943 | −0.619191 | ||||||||
\(370\) | −12.5790 | −0.653951 | ||||||||
\(371\) | −7.82326 | −0.406164 | ||||||||
\(372\) | 11.9014 | 0.617060 | ||||||||
\(373\) | −21.9814 | −1.13815 | −0.569077 | − | 0.822284i | \(-0.692699\pi\) | ||||
−0.569077 | + | 0.822284i | \(0.692699\pi\) | |||||||
\(374\) | 3.84797 | 0.198974 | ||||||||
\(375\) | −84.1961 | −4.34787 | ||||||||
\(376\) | −4.07168 | −0.209981 | ||||||||
\(377\) | 3.66927 | 0.188977 | ||||||||
\(378\) | −2.84099 | −0.146125 | ||||||||
\(379\) | −10.5077 | −0.539744 | −0.269872 | − | 0.962896i | \(-0.586981\pi\) | ||||
−0.269872 | + | 0.962896i | \(0.586981\pi\) | |||||||
\(380\) | 21.4118 | 1.09840 | ||||||||
\(381\) | 28.3106 | 1.45040 | ||||||||
\(382\) | 16.7007 | 0.854482 | ||||||||
\(383\) | −29.0826 | −1.48605 | −0.743026 | − | 0.669263i | \(-0.766610\pi\) | ||||
−0.743026 | + | 0.669263i | \(0.766610\pi\) | |||||||
\(384\) | 2.26689 | 0.115682 | ||||||||
\(385\) | −6.27760 | −0.319936 | ||||||||
\(386\) | −3.90861 | −0.198943 | ||||||||
\(387\) | 2.59386 | 0.131853 | ||||||||
\(388\) | −1.64673 | −0.0835998 | ||||||||
\(389\) | −12.5211 | −0.634846 | −0.317423 | − | 0.948284i | \(-0.602817\pi\) | ||||
−0.317423 | + | 0.948284i | \(0.602817\pi\) | |||||||
\(390\) | −56.5761 | −2.86484 | ||||||||
\(391\) | −8.49027 | −0.429371 | ||||||||
\(392\) | −4.88239 | −0.246598 | ||||||||
\(393\) | 7.87689 | 0.397337 | ||||||||
\(394\) | 1.00000 | 0.0503793 | ||||||||
\(395\) | −18.1829 | −0.914879 | ||||||||
\(396\) | 2.13877 | 0.107477 | ||||||||
\(397\) | −1.48312 | −0.0744354 | −0.0372177 | − | 0.999307i | \(-0.511850\pi\) | ||||
−0.0372177 | + | 0.999307i | \(0.511850\pi\) | |||||||
\(398\) | −6.01298 | −0.301403 | ||||||||
\(399\) | −16.3733 | −0.819690 | ||||||||
\(400\) | 13.6098 | 0.680489 | ||||||||
\(401\) | −20.3461 | −1.01604 | −0.508018 | − | 0.861347i | \(-0.669622\pi\) | ||||
−0.508018 | + | 0.861347i | \(0.669622\pi\) | |||||||
\(402\) | 26.5091 | 1.32216 | ||||||||
\(403\) | 30.3740 | 1.51304 | ||||||||
\(404\) | 2.12355 | 0.105650 | ||||||||
\(405\) | 46.7712 | 2.32408 | ||||||||
\(406\) | 0.922932 | 0.0458043 | ||||||||
\(407\) | 2.91592 | 0.144537 | ||||||||
\(408\) | 8.72291 | 0.431849 | ||||||||
\(409\) | −33.7304 | −1.66786 | −0.833929 | − | 0.551871i | \(-0.813914\pi\) | ||||
−0.833929 | + | 0.551871i | \(0.813914\pi\) | |||||||
\(410\) | 23.9907 | 1.18482 | ||||||||
\(411\) | −9.10629 | −0.449180 | ||||||||
\(412\) | −6.81012 | −0.335510 | ||||||||
\(413\) | 22.0527 | 1.08514 | ||||||||
\(414\) | −4.71905 | −0.231929 | ||||||||
\(415\) | 19.8095 | 0.972410 | ||||||||
\(416\) | 5.78539 | 0.283652 | ||||||||
\(417\) | −11.9696 | −0.586156 | ||||||||
\(418\) | −4.96345 | −0.242770 | ||||||||
\(419\) | −13.6430 | −0.666505 | −0.333253 | − | 0.942838i | \(-0.608146\pi\) | ||||
−0.333253 | + | 0.942838i | \(0.608146\pi\) | |||||||
\(420\) | −14.2306 | −0.694382 | ||||||||
\(421\) | 1.96082 | 0.0955646 | 0.0477823 | − | 0.998858i | \(-0.484785\pi\) | ||||
0.0477823 | + | 0.998858i | \(0.484785\pi\) | |||||||
\(422\) | −11.5594 | −0.562700 | ||||||||
\(423\) | −8.70841 | −0.423418 | ||||||||
\(424\) | −5.37607 | −0.261085 | ||||||||
\(425\) | 52.3700 | 2.54032 | ||||||||
\(426\) | 11.1536 | 0.540394 | ||||||||
\(427\) | 18.6692 | 0.903466 | ||||||||
\(428\) | 4.19419 | 0.202734 | ||||||||
\(429\) | 13.1148 | 0.633190 | ||||||||
\(430\) | −5.23182 | −0.252301 | ||||||||
\(431\) | −39.2100 | −1.88868 | −0.944339 | − | 0.328973i | \(-0.893298\pi\) | ||||
−0.944339 | + | 0.328973i | \(0.893298\pi\) | |||||||
\(432\) | −1.95230 | −0.0939301 | ||||||||
\(433\) | 1.79869 | 0.0864395 | 0.0432198 | − | 0.999066i | \(-0.486238\pi\) | ||||
0.0432198 | + | 0.999066i | \(0.486238\pi\) | |||||||
\(434\) | 7.63998 | 0.366731 | ||||||||
\(435\) | −6.20222 | −0.297374 | ||||||||
\(436\) | 10.4686 | 0.501354 | ||||||||
\(437\) | 10.9515 | 0.523880 | ||||||||
\(438\) | 38.0179 | 1.81657 | ||||||||
\(439\) | −18.5939 | −0.887439 | −0.443719 | − | 0.896166i | \(-0.646341\pi\) | ||||
−0.443719 | + | 0.896166i | \(0.646341\pi\) | |||||||
\(440\) | −4.31390 | −0.205657 | ||||||||
\(441\) | −10.4423 | −0.497254 | ||||||||
\(442\) | 22.2620 | 1.05890 | ||||||||
\(443\) | 14.9630 | 0.710912 | 0.355456 | − | 0.934693i | \(-0.384326\pi\) | ||||
0.355456 | + | 0.934693i | \(0.384326\pi\) | |||||||
\(444\) | 6.61006 | 0.313699 | ||||||||
\(445\) | −28.3268 | −1.34282 | ||||||||
\(446\) | −21.3160 | −1.00934 | ||||||||
\(447\) | 5.05266 | 0.238983 | ||||||||
\(448\) | 1.45520 | 0.0687518 | ||||||||
\(449\) | 4.22845 | 0.199553 | 0.0997764 | − | 0.995010i | \(-0.468187\pi\) | ||||
0.0997764 | + | 0.995010i | \(0.468187\pi\) | |||||||
\(450\) | 29.1082 | 1.37218 | ||||||||
\(451\) | −5.56125 | −0.261869 | ||||||||
\(452\) | −18.0135 | −0.847285 | ||||||||
\(453\) | 33.0771 | 1.55410 | ||||||||
\(454\) | −11.1150 | −0.521651 | ||||||||
\(455\) | −36.3184 | −1.70263 | ||||||||
\(456\) | −11.2516 | −0.526903 | ||||||||
\(457\) | 14.5478 | 0.680519 | 0.340259 | − | 0.940332i | \(-0.389485\pi\) | ||||
0.340259 | + | 0.940332i | \(0.389485\pi\) | |||||||
\(458\) | −25.1307 | −1.17428 | ||||||||
\(459\) | −7.51240 | −0.350649 | ||||||||
\(460\) | 9.51831 | 0.443794 | ||||||||
\(461\) | 25.1335 | 1.17058 | 0.585291 | − | 0.810823i | \(-0.300980\pi\) | ||||
0.585291 | + | 0.810823i | \(0.300980\pi\) | |||||||
\(462\) | 3.29878 | 0.153473 | ||||||||
\(463\) | −11.4002 | −0.529812 | −0.264906 | − | 0.964274i | \(-0.585341\pi\) | ||||
−0.264906 | + | 0.964274i | \(0.585341\pi\) | |||||||
\(464\) | 0.634230 | 0.0294434 | ||||||||
\(465\) | −51.3416 | −2.38091 | ||||||||
\(466\) | −8.50901 | −0.394172 | ||||||||
\(467\) | 9.45646 | 0.437593 | 0.218796 | − | 0.975771i | \(-0.429787\pi\) | ||||
0.218796 | + | 0.975771i | \(0.429787\pi\) | |||||||
\(468\) | 12.3736 | 0.571972 | ||||||||
\(469\) | 17.0172 | 0.785783 | ||||||||
\(470\) | 17.5649 | 0.810207 | ||||||||
\(471\) | 3.84973 | 0.177386 | ||||||||
\(472\) | 15.1544 | 0.697539 | ||||||||
\(473\) | 1.21278 | 0.0557637 | ||||||||
\(474\) | 9.55479 | 0.438866 | ||||||||
\(475\) | −67.5514 | −3.09947 | ||||||||
\(476\) | 5.59957 | 0.256656 | ||||||||
\(477\) | −11.4982 | −0.526466 | ||||||||
\(478\) | 18.9076 | 0.864811 | ||||||||
\(479\) | −28.4335 | −1.29916 | −0.649580 | − | 0.760294i | \(-0.725055\pi\) | ||||
−0.649580 | + | 0.760294i | \(0.725055\pi\) | |||||||
\(480\) | −9.77913 | −0.446354 | ||||||||
\(481\) | 16.8697 | 0.769194 | ||||||||
\(482\) | 1.93068 | 0.0879400 | ||||||||
\(483\) | −7.27851 | −0.331184 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 7.10382 | 0.322568 | ||||||||
\(486\) | −18.7206 | −0.849184 | ||||||||
\(487\) | −10.1848 | −0.461516 | −0.230758 | − | 0.973011i | \(-0.574121\pi\) | ||||
−0.230758 | + | 0.973011i | \(0.574121\pi\) | |||||||
\(488\) | 12.8293 | 0.580755 | ||||||||
\(489\) | −51.5562 | −2.33145 | ||||||||
\(490\) | 21.0622 | 0.951492 | ||||||||
\(491\) | 20.8722 | 0.941951 | 0.470975 | − | 0.882146i | \(-0.343902\pi\) | ||||
0.470975 | + | 0.882146i | \(0.343902\pi\) | |||||||
\(492\) | −12.6067 | −0.568355 | ||||||||
\(493\) | 2.44050 | 0.109914 | ||||||||
\(494\) | −28.7155 | −1.29197 | ||||||||
\(495\) | −9.22647 | −0.414699 | ||||||||
\(496\) | 5.25012 | 0.235737 | ||||||||
\(497\) | 7.15993 | 0.321167 | ||||||||
\(498\) | −10.4096 | −0.466464 | ||||||||
\(499\) | 25.4661 | 1.14002 | 0.570010 | − | 0.821638i | \(-0.306939\pi\) | ||||
0.570010 | + | 0.821638i | \(0.306939\pi\) | |||||||
\(500\) | −37.1418 | −1.66103 | ||||||||
\(501\) | 2.69941 | 0.120601 | ||||||||
\(502\) | 8.94751 | 0.399347 | ||||||||
\(503\) | −23.8748 | −1.06453 | −0.532263 | − | 0.846579i | \(-0.678658\pi\) | ||||
−0.532263 | + | 0.846579i | \(0.678658\pi\) | |||||||
\(504\) | 3.11235 | 0.138635 | ||||||||
\(505\) | −9.16077 | −0.407649 | ||||||||
\(506\) | −2.20643 | −0.0980876 | ||||||||
\(507\) | 46.4049 | 2.06091 | ||||||||
\(508\) | 12.4888 | 0.554100 | ||||||||
\(509\) | −10.8474 | −0.480801 | −0.240401 | − | 0.970674i | \(-0.577279\pi\) | ||||
−0.240401 | + | 0.970674i | \(0.577279\pi\) | |||||||
\(510\) | −37.6298 | −1.66628 | ||||||||
\(511\) | 24.4052 | 1.07962 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 9.69014 | 0.427830 | ||||||||
\(514\) | −7.42717 | −0.327599 | ||||||||
\(515\) | 29.3782 | 1.29456 | ||||||||
\(516\) | 2.74923 | 0.121028 | ||||||||
\(517\) | −4.07168 | −0.179072 | ||||||||
\(518\) | 4.24325 | 0.186438 | ||||||||
\(519\) | 39.6233 | 1.73927 | ||||||||
\(520\) | −24.9576 | −1.09446 | ||||||||
\(521\) | 0.434079 | 0.0190174 | 0.00950868 | − | 0.999955i | \(-0.496973\pi\) | ||||
0.00950868 | + | 0.999955i | \(0.496973\pi\) | |||||||
\(522\) | 1.35647 | 0.0593713 | ||||||||
\(523\) | 17.3608 | 0.759137 | 0.379568 | − | 0.925164i | \(-0.376073\pi\) | ||||
0.379568 | + | 0.925164i | \(0.376073\pi\) | |||||||
\(524\) | 3.47476 | 0.151796 | ||||||||
\(525\) | 44.8956 | 1.95940 | ||||||||
\(526\) | −4.07400 | −0.177635 | ||||||||
\(527\) | 20.2023 | 0.880027 | ||||||||
\(528\) | 2.26689 | 0.0986536 | ||||||||
\(529\) | −18.1317 | −0.788334 | ||||||||
\(530\) | 23.1919 | 1.00739 | ||||||||
\(531\) | 32.4119 | 1.40656 | ||||||||
\(532\) | −7.22281 | −0.313149 | ||||||||
\(533\) | −32.1740 | −1.39361 | ||||||||
\(534\) | 14.8853 | 0.644148 | ||||||||
\(535\) | −18.0933 | −0.782243 | ||||||||
\(536\) | 11.6941 | 0.505107 | ||||||||
\(537\) | −37.7736 | −1.63005 | ||||||||
\(538\) | 12.8855 | 0.555535 | ||||||||
\(539\) | −4.88239 | −0.210299 | ||||||||
\(540\) | 8.42204 | 0.362427 | ||||||||
\(541\) | −30.1307 | −1.29542 | −0.647709 | − | 0.761887i | \(-0.724273\pi\) | ||||
−0.647709 | + | 0.761887i | \(0.724273\pi\) | |||||||
\(542\) | −1.31221 | −0.0563641 | ||||||||
\(543\) | −54.5041 | −2.33899 | ||||||||
\(544\) | 3.84797 | 0.164980 | ||||||||
\(545\) | −45.1605 | −1.93446 | ||||||||
\(546\) | 19.0847 | 0.816750 | ||||||||
\(547\) | −17.1020 | −0.731227 | −0.365614 | − | 0.930767i | \(-0.619141\pi\) | ||||
−0.365614 | + | 0.930767i | \(0.619141\pi\) | |||||||
\(548\) | −4.01709 | −0.171602 | ||||||||
\(549\) | 27.4390 | 1.17107 | ||||||||
\(550\) | 13.6098 | 0.580323 | ||||||||
\(551\) | −3.14797 | −0.134108 | ||||||||
\(552\) | −5.00172 | −0.212887 | ||||||||
\(553\) | 6.13359 | 0.260827 | ||||||||
\(554\) | 4.52523 | 0.192259 | ||||||||
\(555\) | −28.5152 | −1.21040 | ||||||||
\(556\) | −5.28021 | −0.223931 | ||||||||
\(557\) | −15.0213 | −0.636475 | −0.318237 | − | 0.948011i | \(-0.603091\pi\) | ||||
−0.318237 | + | 0.948011i | \(0.603091\pi\) | |||||||
\(558\) | 11.2288 | 0.475354 | ||||||||
\(559\) | 7.01641 | 0.296762 | ||||||||
\(560\) | −6.27760 | −0.265277 | ||||||||
\(561\) | 8.72291 | 0.368282 | ||||||||
\(562\) | −30.2456 | −1.27583 | ||||||||
\(563\) | 4.90766 | 0.206833 | 0.103417 | − | 0.994638i | \(-0.467023\pi\) | ||||
0.103417 | + | 0.994638i | \(0.467023\pi\) | |||||||
\(564\) | −9.23005 | −0.388655 | ||||||||
\(565\) | 77.7087 | 3.26923 | ||||||||
\(566\) | 9.95702 | 0.418525 | ||||||||
\(567\) | −15.7772 | −0.662582 | ||||||||
\(568\) | 4.92023 | 0.206448 | ||||||||
\(569\) | 20.6479 | 0.865605 | 0.432803 | − | 0.901489i | \(-0.357525\pi\) | ||||
0.432803 | + | 0.901489i | \(0.357525\pi\) | |||||||
\(570\) | 48.5382 | 2.03304 | ||||||||
\(571\) | −24.0233 | −1.00535 | −0.502673 | − | 0.864477i | \(-0.667650\pi\) | ||||
−0.502673 | + | 0.864477i | \(0.667650\pi\) | |||||||
\(572\) | 5.78539 | 0.241899 | ||||||||
\(573\) | 37.8586 | 1.58157 | ||||||||
\(574\) | −8.09274 | −0.337785 | ||||||||
\(575\) | −30.0290 | −1.25229 | ||||||||
\(576\) | 2.13877 | 0.0891156 | ||||||||
\(577\) | 2.40841 | 0.100264 | 0.0501318 | − | 0.998743i | \(-0.484036\pi\) | ||||
0.0501318 | + | 0.998743i | \(0.484036\pi\) | |||||||
\(578\) | −2.19312 | −0.0912216 | ||||||||
\(579\) | −8.86038 | −0.368225 | ||||||||
\(580\) | −2.73601 | −0.113606 | ||||||||
\(581\) | −6.68230 | −0.277229 | ||||||||
\(582\) | −3.73294 | −0.154735 | ||||||||
\(583\) | −5.37607 | −0.222654 | ||||||||
\(584\) | 16.7710 | 0.693988 | ||||||||
\(585\) | −53.3787 | −2.20694 | ||||||||
\(586\) | −0.204412 | −0.00844419 | ||||||||
\(587\) | 43.6735 | 1.80260 | 0.901298 | − | 0.433199i | \(-0.142615\pi\) | ||||
0.901298 | + | 0.433199i | \(0.142615\pi\) | |||||||
\(588\) | −11.0678 | −0.456429 | ||||||||
\(589\) | −26.0587 | −1.07373 | ||||||||
\(590\) | −65.3748 | −2.69144 | ||||||||
\(591\) | 2.26689 | 0.0932472 | ||||||||
\(592\) | 2.91592 | 0.119844 | ||||||||
\(593\) | −45.1466 | −1.85395 | −0.926974 | − | 0.375126i | \(-0.877599\pi\) | ||||
−0.926974 | + | 0.375126i | \(0.877599\pi\) | |||||||
\(594\) | −1.95230 | −0.0801039 | ||||||||
\(595\) | −24.1560 | −0.990300 | ||||||||
\(596\) | 2.22890 | 0.0912992 | ||||||||
\(597\) | −13.6307 | −0.557869 | ||||||||
\(598\) | −12.7650 | −0.522001 | ||||||||
\(599\) | 32.3828 | 1.32313 | 0.661563 | − | 0.749890i | \(-0.269894\pi\) | ||||
0.661563 | + | 0.749890i | \(0.269894\pi\) | |||||||
\(600\) | 30.8518 | 1.25952 | ||||||||
\(601\) | 10.2594 | 0.418490 | 0.209245 | − | 0.977863i | \(-0.432899\pi\) | ||||
0.209245 | + | 0.977863i | \(0.432899\pi\) | |||||||
\(602\) | 1.76484 | 0.0719294 | ||||||||
\(603\) | 25.0110 | 1.01853 | ||||||||
\(604\) | 14.5914 | 0.593716 | ||||||||
\(605\) | −4.31390 | −0.175385 | ||||||||
\(606\) | 4.81384 | 0.195549 | ||||||||
\(607\) | 9.92230 | 0.402734 | 0.201367 | − | 0.979516i | \(-0.435462\pi\) | ||||
0.201367 | + | 0.979516i | \(0.435462\pi\) | |||||||
\(608\) | −4.96345 | −0.201294 | ||||||||
\(609\) | 2.09218 | 0.0847795 | ||||||||
\(610\) | −55.3443 | −2.24083 | ||||||||
\(611\) | −23.5563 | −0.952986 | ||||||||
\(612\) | 8.22994 | 0.332676 | ||||||||
\(613\) | 41.2583 | 1.66641 | 0.833204 | − | 0.552966i | \(-0.186504\pi\) | ||||
0.833204 | + | 0.552966i | \(0.186504\pi\) | |||||||
\(614\) | 5.99190 | 0.241813 | ||||||||
\(615\) | 54.3842 | 2.19298 | ||||||||
\(616\) | 1.45520 | 0.0586317 | ||||||||
\(617\) | 8.35400 | 0.336319 | 0.168160 | − | 0.985760i | \(-0.446218\pi\) | ||||
0.168160 | + | 0.985760i | \(0.446218\pi\) | |||||||
\(618\) | −15.4378 | −0.620998 | ||||||||
\(619\) | 46.5618 | 1.87148 | 0.935739 | − | 0.352694i | \(-0.114734\pi\) | ||||
0.935739 | + | 0.352694i | \(0.114734\pi\) | |||||||
\(620\) | −22.6485 | −0.909587 | ||||||||
\(621\) | 4.30761 | 0.172858 | ||||||||
\(622\) | 29.6779 | 1.18998 | ||||||||
\(623\) | 9.55542 | 0.382830 | ||||||||
\(624\) | 13.1148 | 0.525013 | ||||||||
\(625\) | 92.1771 | 3.68708 | ||||||||
\(626\) | −2.08952 | −0.0835139 | ||||||||
\(627\) | −11.2516 | −0.449344 | ||||||||
\(628\) | 1.69825 | 0.0677674 | ||||||||
\(629\) | 11.2204 | 0.447386 | ||||||||
\(630\) | −13.4264 | −0.534919 | ||||||||
\(631\) | 13.1496 | 0.523477 | 0.261738 | − | 0.965139i | \(-0.415704\pi\) | ||||
0.261738 | + | 0.965139i | \(0.415704\pi\) | |||||||
\(632\) | 4.21494 | 0.167661 | ||||||||
\(633\) | −26.2037 | −1.04151 | ||||||||
\(634\) | 30.7875 | 1.22273 | ||||||||
\(635\) | −53.8754 | −2.13798 | ||||||||
\(636\) | −12.1869 | −0.483244 | ||||||||
\(637\) | −28.2465 | −1.11917 | ||||||||
\(638\) | 0.634230 | 0.0251094 | ||||||||
\(639\) | 10.5233 | 0.416294 | ||||||||
\(640\) | −4.31390 | −0.170522 | ||||||||
\(641\) | −43.3331 | −1.71155 | −0.855777 | − | 0.517346i | \(-0.826920\pi\) | ||||
−0.855777 | + | 0.517346i | \(0.826920\pi\) | |||||||
\(642\) | 9.50775 | 0.375241 | ||||||||
\(643\) | 35.5339 | 1.40132 | 0.700660 | − | 0.713496i | \(-0.252889\pi\) | ||||
0.700660 | + | 0.713496i | \(0.252889\pi\) | |||||||
\(644\) | −3.21079 | −0.126523 | ||||||||
\(645\) | −11.8599 | −0.466984 | ||||||||
\(646\) | −19.0992 | −0.751448 | ||||||||
\(647\) | 1.39887 | 0.0549952 | 0.0274976 | − | 0.999622i | \(-0.491246\pi\) | ||||
0.0274976 | + | 0.999622i | \(0.491246\pi\) | |||||||
\(648\) | −10.8420 | −0.425913 | ||||||||
\(649\) | 15.1544 | 0.594863 | ||||||||
\(650\) | 78.7379 | 3.08835 | ||||||||
\(651\) | 17.3190 | 0.678784 | ||||||||
\(652\) | −22.7432 | −0.890691 | ||||||||
\(653\) | −45.6792 | −1.78756 | −0.893782 | − | 0.448502i | \(-0.851958\pi\) | ||||
−0.893782 | + | 0.448502i | \(0.851958\pi\) | |||||||
\(654\) | 23.7311 | 0.927960 | ||||||||
\(655\) | −14.9898 | −0.585700 | ||||||||
\(656\) | −5.56125 | −0.217130 | ||||||||
\(657\) | 35.8694 | 1.39940 | ||||||||
\(658\) | −5.92512 | −0.230985 | ||||||||
\(659\) | −16.8162 | −0.655064 | −0.327532 | − | 0.944840i | \(-0.606217\pi\) | ||||
−0.327532 | + | 0.944840i | \(0.606217\pi\) | |||||||
\(660\) | −9.77913 | −0.380652 | ||||||||
\(661\) | −5.46832 | −0.212693 | −0.106347 | − | 0.994329i | \(-0.533915\pi\) | ||||
−0.106347 | + | 0.994329i | \(0.533915\pi\) | |||||||
\(662\) | −25.5382 | −0.992570 | ||||||||
\(663\) | 50.4655 | 1.95992 | ||||||||
\(664\) | −4.59201 | −0.178205 | ||||||||
\(665\) | 31.1585 | 1.20828 | ||||||||
\(666\) | 6.23649 | 0.241659 | ||||||||
\(667\) | −1.39938 | −0.0541843 | ||||||||
\(668\) | 1.19080 | 0.0460735 | ||||||||
\(669\) | −48.3210 | −1.86820 | ||||||||
\(670\) | −50.4471 | −1.94894 | ||||||||
\(671\) | 12.8293 | 0.495269 | ||||||||
\(672\) | 3.29878 | 0.127253 | ||||||||
\(673\) | 40.1697 | 1.54843 | 0.774214 | − | 0.632923i | \(-0.218145\pi\) | ||||
0.774214 | + | 0.632923i | \(0.218145\pi\) | |||||||
\(674\) | −0.00855933 | −0.000329693 0 | ||||||||
\(675\) | −26.5704 | −1.02269 | ||||||||
\(676\) | 20.4708 | 0.787337 | ||||||||
\(677\) | −29.6833 | −1.14082 | −0.570411 | − | 0.821359i | \(-0.693216\pi\) | ||||
−0.570411 | + | 0.821359i | \(0.693216\pi\) | |||||||
\(678\) | −40.8346 | −1.56824 | ||||||||
\(679\) | −2.39632 | −0.0919622 | ||||||||
\(680\) | −16.5998 | −0.636573 | ||||||||
\(681\) | −25.1963 | −0.965526 | ||||||||
\(682\) | 5.25012 | 0.201038 | ||||||||
\(683\) | −23.5916 | −0.902707 | −0.451354 | − | 0.892345i | \(-0.649059\pi\) | ||||
−0.451354 | + | 0.892345i | \(0.649059\pi\) | |||||||
\(684\) | −10.6157 | −0.405901 | ||||||||
\(685\) | 17.3293 | 0.662120 | ||||||||
\(686\) | −17.2913 | −0.660184 | ||||||||
\(687\) | −56.9685 | −2.17348 | ||||||||
\(688\) | 1.21278 | 0.0462368 | ||||||||
\(689\) | −31.1027 | −1.18492 | ||||||||
\(690\) | 21.5769 | 0.821420 | ||||||||
\(691\) | −28.6987 | −1.09175 | −0.545874 | − | 0.837867i | \(-0.683802\pi\) | ||||
−0.545874 | + | 0.837867i | \(0.683802\pi\) | |||||||
\(692\) | 17.4792 | 0.664458 | ||||||||
\(693\) | 3.11235 | 0.118228 | ||||||||
\(694\) | −25.4319 | −0.965380 | ||||||||
\(695\) | 22.7783 | 0.864031 | ||||||||
\(696\) | 1.43773 | 0.0544969 | ||||||||
\(697\) | −21.3995 | −0.810566 | ||||||||
\(698\) | 4.87428 | 0.184494 | ||||||||
\(699\) | −19.2890 | −0.729575 | ||||||||
\(700\) | 19.8050 | 0.748557 | ||||||||
\(701\) | −37.6729 | −1.42288 | −0.711442 | − | 0.702745i | \(-0.751958\pi\) | ||||
−0.711442 | + | 0.702745i | \(0.751958\pi\) | |||||||
\(702\) | −11.2948 | −0.426296 | ||||||||
\(703\) | −14.4730 | −0.545860 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 39.8175 | 1.49962 | ||||||||
\(706\) | −13.5161 | −0.508686 | ||||||||
\(707\) | 3.09019 | 0.116218 | ||||||||
\(708\) | 34.3534 | 1.29108 | ||||||||
\(709\) | −45.2100 | −1.69790 | −0.848949 | − | 0.528475i | \(-0.822764\pi\) | ||||
−0.848949 | + | 0.528475i | \(0.822764\pi\) | |||||||
\(710\) | −21.2254 | −0.796576 | ||||||||
\(711\) | 9.01481 | 0.338082 | ||||||||
\(712\) | 6.56639 | 0.246086 | ||||||||
\(713\) | −11.5840 | −0.433825 | ||||||||
\(714\) | 12.6936 | 0.475046 | ||||||||
\(715\) | −24.9576 | −0.933362 | ||||||||
\(716\) | −16.6632 | −0.622733 | ||||||||
\(717\) | 42.8613 | 1.60068 | ||||||||
\(718\) | 17.8409 | 0.665816 | ||||||||
\(719\) | 5.75749 | 0.214718 | 0.107359 | − | 0.994220i | \(-0.465761\pi\) | ||||
0.107359 | + | 0.994220i | \(0.465761\pi\) | |||||||
\(720\) | −9.22647 | −0.343850 | ||||||||
\(721\) | −9.91009 | −0.369071 | ||||||||
\(722\) | 5.63581 | 0.209743 | ||||||||
\(723\) | 4.37663 | 0.162769 | ||||||||
\(724\) | −24.0436 | −0.893573 | ||||||||
\(725\) | 8.63172 | 0.320574 | ||||||||
\(726\) | 2.26689 | 0.0841320 | ||||||||
\(727\) | 30.2814 | 1.12308 | 0.561538 | − | 0.827451i | \(-0.310210\pi\) | ||||
0.561538 | + | 0.827451i | \(0.310210\pi\) | |||||||
\(728\) | 8.41891 | 0.312025 | ||||||||
\(729\) | −9.91159 | −0.367096 | ||||||||
\(730\) | −72.3485 | −2.67774 | ||||||||
\(731\) | 4.66674 | 0.172606 | ||||||||
\(732\) | 29.0825 | 1.07492 | ||||||||
\(733\) | 24.4091 | 0.901572 | 0.450786 | − | 0.892632i | \(-0.351144\pi\) | ||||
0.450786 | + | 0.892632i | \(0.351144\pi\) | |||||||
\(734\) | −0.856582 | −0.0316170 | ||||||||
\(735\) | 47.7455 | 1.76112 | ||||||||
\(736\) | −2.20643 | −0.0813300 | ||||||||
\(737\) | 11.6941 | 0.430757 | ||||||||
\(738\) | −11.8943 | −0.437834 | ||||||||
\(739\) | −48.9157 | −1.79939 | −0.899696 | − | 0.436517i | \(-0.856212\pi\) | ||||
−0.899696 | + | 0.436517i | \(0.856212\pi\) | |||||||
\(740\) | −12.5790 | −0.462413 | ||||||||
\(741\) | −65.0947 | −2.39132 | ||||||||
\(742\) | −7.82326 | −0.287201 | ||||||||
\(743\) | −31.3745 | −1.15102 | −0.575510 | − | 0.817795i | \(-0.695196\pi\) | ||||
−0.575510 | + | 0.817795i | \(0.695196\pi\) | |||||||
\(744\) | 11.9014 | 0.436328 | ||||||||
\(745\) | −9.61526 | −0.352276 | ||||||||
\(746\) | −21.9814 | −0.804796 | ||||||||
\(747\) | −9.82128 | −0.359342 | ||||||||
\(748\) | 3.84797 | 0.140696 | ||||||||
\(749\) | 6.10339 | 0.223013 | ||||||||
\(750\) | −84.1961 | −3.07441 | ||||||||
\(751\) | 7.64485 | 0.278965 | 0.139482 | − | 0.990225i | \(-0.455456\pi\) | ||||
0.139482 | + | 0.990225i | \(0.455456\pi\) | |||||||
\(752\) | −4.07168 | −0.148479 | ||||||||
\(753\) | 20.2830 | 0.739153 | ||||||||
\(754\) | 3.66927 | 0.133627 | ||||||||
\(755\) | −62.9459 | −2.29084 | ||||||||
\(756\) | −2.84099 | −0.103326 | ||||||||
\(757\) | 31.3139 | 1.13812 | 0.569062 | − | 0.822295i | \(-0.307306\pi\) | ||||
0.569062 | + | 0.822295i | \(0.307306\pi\) | |||||||
\(758\) | −10.5077 | −0.381657 | ||||||||
\(759\) | −5.00172 | −0.181551 | ||||||||
\(760\) | 21.4118 | 0.776689 | ||||||||
\(761\) | −32.4940 | −1.17791 | −0.588953 | − | 0.808167i | \(-0.700460\pi\) | ||||
−0.588953 | + | 0.808167i | \(0.700460\pi\) | |||||||
\(762\) | 28.3106 | 1.02559 | ||||||||
\(763\) | 15.2339 | 0.551504 | ||||||||
\(764\) | 16.7007 | 0.604210 | ||||||||
\(765\) | −35.5032 | −1.28362 | ||||||||
\(766\) | −29.0826 | −1.05080 | ||||||||
\(767\) | 87.6743 | 3.16574 | ||||||||
\(768\) | 2.26689 | 0.0817992 | ||||||||
\(769\) | 19.8357 | 0.715292 | 0.357646 | − | 0.933857i | \(-0.383579\pi\) | ||||
0.357646 | + | 0.933857i | \(0.383579\pi\) | |||||||
\(770\) | −6.27760 | −0.226229 | ||||||||
\(771\) | −16.8366 | −0.606354 | ||||||||
\(772\) | −3.90861 | −0.140674 | ||||||||
\(773\) | 43.3541 | 1.55934 | 0.779669 | − | 0.626192i | \(-0.215387\pi\) | ||||
0.779669 | + | 0.626192i | \(0.215387\pi\) | |||||||
\(774\) | 2.59386 | 0.0932344 | ||||||||
\(775\) | 71.4530 | 2.56667 | ||||||||
\(776\) | −1.64673 | −0.0591140 | ||||||||
\(777\) | 9.61896 | 0.345078 | ||||||||
\(778\) | −12.5211 | −0.448904 | ||||||||
\(779\) | 27.6030 | 0.988980 | ||||||||
\(780\) | −56.5761 | −2.02575 | ||||||||
\(781\) | 4.92023 | 0.176060 | ||||||||
\(782\) | −8.49027 | −0.303611 | ||||||||
\(783\) | −1.23821 | −0.0442499 | ||||||||
\(784\) | −4.88239 | −0.174371 | ||||||||
\(785\) | −7.32607 | −0.261479 | ||||||||
\(786\) | 7.87689 | 0.280959 | ||||||||
\(787\) | 47.1570 | 1.68097 | 0.840484 | − | 0.541837i | \(-0.182271\pi\) | ||||
0.840484 | + | 0.541837i | \(0.182271\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | −9.23530 | −0.328785 | ||||||||
\(790\) | −18.1829 | −0.646917 | ||||||||
\(791\) | −26.2133 | −0.932038 | ||||||||
\(792\) | 2.13877 | 0.0759980 | ||||||||
\(793\) | 74.2225 | 2.63572 | ||||||||
\(794\) | −1.48312 | −0.0526338 | ||||||||
\(795\) | 52.5733 | 1.86458 | ||||||||
\(796\) | −6.01298 | −0.213124 | ||||||||
\(797\) | 34.9366 | 1.23752 | 0.618759 | − | 0.785581i | \(-0.287636\pi\) | ||||
0.618759 | + | 0.785581i | \(0.287636\pi\) | |||||||
\(798\) | −16.3733 | −0.579609 | ||||||||
\(799\) | −15.6677 | −0.554284 | ||||||||
\(800\) | 13.6098 | 0.481178 | ||||||||
\(801\) | 14.0440 | 0.496221 | ||||||||
\(802\) | −20.3461 | −0.718446 | ||||||||
\(803\) | 16.7710 | 0.591835 | ||||||||
\(804\) | 26.5091 | 0.934905 | ||||||||
\(805\) | 13.8511 | 0.488186 | ||||||||
\(806\) | 30.3740 | 1.06988 | ||||||||
\(807\) | 29.2101 | 1.02824 | ||||||||
\(808\) | 2.12355 | 0.0747061 | ||||||||
\(809\) | 27.7986 | 0.977348 | 0.488674 | − | 0.872467i | \(-0.337481\pi\) | ||||
0.488674 | + | 0.872467i | \(0.337481\pi\) | |||||||
\(810\) | 46.7712 | 1.64337 | ||||||||
\(811\) | 26.8405 | 0.942496 | 0.471248 | − | 0.882001i | \(-0.343804\pi\) | ||||
0.471248 | + | 0.882001i | \(0.343804\pi\) | |||||||
\(812\) | 0.922932 | 0.0323886 | ||||||||
\(813\) | −2.97462 | −0.104325 | ||||||||
\(814\) | 2.91592 | 0.102203 | ||||||||
\(815\) | 98.1119 | 3.43671 | ||||||||
\(816\) | 8.72291 | 0.305363 | ||||||||
\(817\) | −6.01957 | −0.210598 | ||||||||
\(818\) | −33.7304 | −1.17935 | ||||||||
\(819\) | 18.0061 | 0.629186 | ||||||||
\(820\) | 23.9907 | 0.837792 | ||||||||
\(821\) | 52.7522 | 1.84106 | 0.920531 | − | 0.390668i | \(-0.127756\pi\) | ||||
0.920531 | + | 0.390668i | \(0.127756\pi\) | |||||||
\(822\) | −9.10629 | −0.317618 | ||||||||
\(823\) | 48.4851 | 1.69008 | 0.845042 | − | 0.534700i | \(-0.179575\pi\) | ||||
0.845042 | + | 0.534700i | \(0.179575\pi\) | |||||||
\(824\) | −6.81012 | −0.237242 | ||||||||
\(825\) | 30.8518 | 1.07412 | ||||||||
\(826\) | 22.0527 | 0.767313 | ||||||||
\(827\) | −9.75721 | −0.339292 | −0.169646 | − | 0.985505i | \(-0.554262\pi\) | ||||
−0.169646 | + | 0.985505i | \(0.554262\pi\) | |||||||
\(828\) | −4.71905 | −0.163998 | ||||||||
\(829\) | 53.5979 | 1.86153 | 0.930766 | − | 0.365615i | \(-0.119141\pi\) | ||||
0.930766 | + | 0.365615i | \(0.119141\pi\) | |||||||
\(830\) | 19.8095 | 0.687598 | ||||||||
\(831\) | 10.2582 | 0.355853 | ||||||||
\(832\) | 5.78539 | 0.200572 | ||||||||
\(833\) | −18.7873 | −0.650941 | ||||||||
\(834\) | −11.9696 | −0.414475 | ||||||||
\(835\) | −5.13701 | −0.177773 | ||||||||
\(836\) | −4.96345 | −0.171664 | ||||||||
\(837\) | −10.2498 | −0.354286 | ||||||||
\(838\) | −13.6430 | −0.471290 | ||||||||
\(839\) | 36.7945 | 1.27029 | 0.635143 | − | 0.772394i | \(-0.280941\pi\) | ||||
0.635143 | + | 0.772394i | \(0.280941\pi\) | |||||||
\(840\) | −14.2306 | −0.491002 | ||||||||
\(841\) | −28.5978 | −0.986129 | ||||||||
\(842\) | 1.96082 | 0.0675743 | ||||||||
\(843\) | −68.5634 | −2.36145 | ||||||||
\(844\) | −11.5594 | −0.397889 | ||||||||
\(845\) | −88.3089 | −3.03792 | ||||||||
\(846\) | −8.70841 | −0.299401 | ||||||||
\(847\) | 1.45520 | 0.0500013 | ||||||||
\(848\) | −5.37607 | −0.184615 | ||||||||
\(849\) | 22.5714 | 0.774650 | ||||||||
\(850\) | 52.3700 | 1.79628 | ||||||||
\(851\) | −6.43376 | −0.220547 | ||||||||
\(852\) | 11.1536 | 0.382116 | ||||||||
\(853\) | −0.761804 | −0.0260837 | −0.0130418 | − | 0.999915i | \(-0.504151\pi\) | ||||
−0.0130418 | + | 0.999915i | \(0.504151\pi\) | |||||||
\(854\) | 18.6692 | 0.638847 | ||||||||
\(855\) | 45.7951 | 1.56616 | ||||||||
\(856\) | 4.19419 | 0.143354 | ||||||||
\(857\) | 10.8886 | 0.371948 | 0.185974 | − | 0.982555i | \(-0.440456\pi\) | ||||
0.185974 | + | 0.982555i | \(0.440456\pi\) | |||||||
\(858\) | 13.1148 | 0.447733 | ||||||||
\(859\) | 28.6007 | 0.975844 | 0.487922 | − | 0.872887i | \(-0.337755\pi\) | ||||
0.487922 | + | 0.872887i | \(0.337755\pi\) | |||||||
\(860\) | −5.23182 | −0.178403 | ||||||||
\(861\) | −18.3453 | −0.625207 | ||||||||
\(862\) | −39.2100 | −1.33550 | ||||||||
\(863\) | −3.78122 | −0.128714 | −0.0643572 | − | 0.997927i | \(-0.520500\pi\) | ||||
−0.0643572 | + | 0.997927i | \(0.520500\pi\) | |||||||
\(864\) | −1.95230 | −0.0664186 | ||||||||
\(865\) | −75.4034 | −2.56379 | ||||||||
\(866\) | 1.79869 | 0.0611220 | ||||||||
\(867\) | −4.97155 | −0.168843 | ||||||||
\(868\) | 7.63998 | 0.259318 | ||||||||
\(869\) | 4.21494 | 0.142982 | ||||||||
\(870\) | −6.20222 | −0.210275 | ||||||||
\(871\) | 67.6548 | 2.29240 | ||||||||
\(872\) | 10.4686 | 0.354511 | ||||||||
\(873\) | −3.52197 | −0.119201 | ||||||||
\(874\) | 10.9515 | 0.370439 | ||||||||
\(875\) | −54.0487 | −1.82718 | ||||||||
\(876\) | 38.0179 | 1.28451 | ||||||||
\(877\) | 28.8019 | 0.972570 | 0.486285 | − | 0.873800i | \(-0.338352\pi\) | ||||
0.486285 | + | 0.873800i | \(0.338352\pi\) | |||||||
\(878\) | −18.5939 | −0.627514 | ||||||||
\(879\) | −0.463379 | −0.0156294 | ||||||||
\(880\) | −4.31390 | −0.145422 | ||||||||
\(881\) | −14.1829 | −0.477832 | −0.238916 | − | 0.971040i | \(-0.576792\pi\) | ||||
−0.238916 | + | 0.971040i | \(0.576792\pi\) | |||||||
\(882\) | −10.4423 | −0.351612 | ||||||||
\(883\) | −25.9406 | −0.872972 | −0.436486 | − | 0.899711i | \(-0.643777\pi\) | ||||
−0.436486 | + | 0.899711i | \(0.643777\pi\) | |||||||
\(884\) | 22.2620 | 0.748753 | ||||||||
\(885\) | −148.197 | −4.98159 | ||||||||
\(886\) | 14.9630 | 0.502691 | ||||||||
\(887\) | −1.39317 | −0.0467781 | −0.0233890 | − | 0.999726i | \(-0.507446\pi\) | ||||
−0.0233890 | + | 0.999726i | \(0.507446\pi\) | |||||||
\(888\) | 6.61006 | 0.221819 | ||||||||
\(889\) | 18.1737 | 0.609525 | ||||||||
\(890\) | −28.3268 | −0.949516 | ||||||||
\(891\) | −10.8420 | −0.363220 | ||||||||
\(892\) | −21.3160 | −0.713713 | ||||||||
\(893\) | 20.2096 | 0.676288 | ||||||||
\(894\) | 5.05266 | 0.168986 | ||||||||
\(895\) | 71.8834 | 2.40280 | ||||||||
\(896\) | 1.45520 | 0.0486149 | ||||||||
\(897\) | −28.9369 | −0.966175 | ||||||||
\(898\) | 4.22845 | 0.141105 | ||||||||
\(899\) | 3.32978 | 0.111054 | ||||||||
\(900\) | 29.1082 | 0.970275 | ||||||||
\(901\) | −20.6870 | −0.689183 | ||||||||
\(902\) | −5.56125 | −0.185169 | ||||||||
\(903\) | 4.00069 | 0.133135 | ||||||||
\(904\) | −18.0135 | −0.599121 | ||||||||
\(905\) | 103.722 | 3.44783 | ||||||||
\(906\) | 33.0771 | 1.09891 | ||||||||
\(907\) | 20.3460 | 0.675578 | 0.337789 | − | 0.941222i | \(-0.390321\pi\) | ||||
0.337789 | + | 0.941222i | \(0.390321\pi\) | |||||||
\(908\) | −11.1150 | −0.368863 | ||||||||
\(909\) | 4.54178 | 0.150641 | ||||||||
\(910\) | −36.3184 | −1.20394 | ||||||||
\(911\) | −51.3026 | −1.69973 | −0.849866 | − | 0.526999i | \(-0.823317\pi\) | ||||
−0.849866 | + | 0.526999i | \(0.823317\pi\) | |||||||
\(912\) | −11.2516 | −0.372577 | ||||||||
\(913\) | −4.59201 | −0.151973 | ||||||||
\(914\) | 14.5478 | 0.481199 | ||||||||
\(915\) | −125.459 | −4.14756 | ||||||||
\(916\) | −25.1307 | −0.830343 | ||||||||
\(917\) | 5.05648 | 0.166980 | ||||||||
\(918\) | −7.51240 | −0.247946 | ||||||||
\(919\) | −31.8043 | −1.04913 | −0.524563 | − | 0.851372i | \(-0.675771\pi\) | ||||
−0.524563 | + | 0.851372i | \(0.675771\pi\) | |||||||
\(920\) | 9.51831 | 0.313810 | ||||||||
\(921\) | 13.5830 | 0.447574 | ||||||||
\(922\) | 25.1335 | 0.827727 | ||||||||
\(923\) | 28.4655 | 0.936952 | ||||||||
\(924\) | 3.29878 | 0.108522 | ||||||||
\(925\) | 39.6850 | 1.30484 | ||||||||
\(926\) | −11.4002 | −0.374633 | ||||||||
\(927\) | −14.5653 | −0.478387 | ||||||||
\(928\) | 0.634230 | 0.0208196 | ||||||||
\(929\) | 27.2976 | 0.895606 | 0.447803 | − | 0.894132i | \(-0.352207\pi\) | ||||
0.447803 | + | 0.894132i | \(0.352207\pi\) | |||||||
\(930\) | −51.3416 | −1.68356 | ||||||||
\(931\) | 24.2335 | 0.794220 | ||||||||
\(932\) | −8.50901 | −0.278722 | ||||||||
\(933\) | 67.2765 | 2.20253 | ||||||||
\(934\) | 9.45646 | 0.309425 | ||||||||
\(935\) | −16.5998 | −0.542871 | ||||||||
\(936\) | 12.3736 | 0.404445 | ||||||||
\(937\) | −8.70177 | −0.284274 | −0.142137 | − | 0.989847i | \(-0.545397\pi\) | ||||
−0.142137 | + | 0.989847i | \(0.545397\pi\) | |||||||
\(938\) | 17.0172 | 0.555632 | ||||||||
\(939\) | −4.73670 | −0.154576 | ||||||||
\(940\) | 17.5649 | 0.572903 | ||||||||
\(941\) | 27.1491 | 0.885036 | 0.442518 | − | 0.896760i | \(-0.354085\pi\) | ||||
0.442518 | + | 0.896760i | \(0.354085\pi\) | |||||||
\(942\) | 3.84973 | 0.125431 | ||||||||
\(943\) | 12.2705 | 0.399582 | ||||||||
\(944\) | 15.1544 | 0.493235 | ||||||||
\(945\) | 12.2558 | 0.398680 | ||||||||
\(946\) | 1.21278 | 0.0394309 | ||||||||
\(947\) | 4.20252 | 0.136564 | 0.0682818 | − | 0.997666i | \(-0.478248\pi\) | ||||
0.0682818 | + | 0.997666i | \(0.478248\pi\) | |||||||
\(948\) | 9.55479 | 0.310325 | ||||||||
\(949\) | 97.0267 | 3.14962 | ||||||||
\(950\) | −67.5514 | −2.19166 | ||||||||
\(951\) | 69.7917 | 2.26315 | ||||||||
\(952\) | 5.59957 | 0.181483 | ||||||||
\(953\) | −14.9812 | −0.485290 | −0.242645 | − | 0.970115i | \(-0.578015\pi\) | ||||
−0.242645 | + | 0.970115i | \(0.578015\pi\) | |||||||
\(954\) | −11.4982 | −0.372268 | ||||||||
\(955\) | −72.0453 | −2.33133 | ||||||||
\(956\) | 18.9076 | 0.611514 | ||||||||
\(957\) | 1.43773 | 0.0464751 | ||||||||
\(958\) | −28.4335 | −0.918644 | ||||||||
\(959\) | −5.84567 | −0.188767 | ||||||||
\(960\) | −9.77913 | −0.315620 | ||||||||
\(961\) | −3.43622 | −0.110846 | ||||||||
\(962\) | 16.8697 | 0.543902 | ||||||||
\(963\) | 8.97043 | 0.289068 | ||||||||
\(964\) | 1.93068 | 0.0621830 | ||||||||
\(965\) | 16.8614 | 0.542787 | ||||||||
\(966\) | −7.27851 | −0.234182 | ||||||||
\(967\) | 35.7060 | 1.14823 | 0.574114 | − | 0.818776i | \(-0.305347\pi\) | ||||
0.574114 | + | 0.818776i | \(0.305347\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −43.2957 | −1.39086 | ||||||||
\(970\) | 7.10382 | 0.228090 | ||||||||
\(971\) | −43.2921 | −1.38931 | −0.694655 | − | 0.719343i | \(-0.744443\pi\) | ||||
−0.694655 | + | 0.719343i | \(0.744443\pi\) | |||||||
\(972\) | −18.7206 | −0.600464 | ||||||||
\(973\) | −7.68377 | −0.246330 | ||||||||
\(974\) | −10.1848 | −0.326341 | ||||||||
\(975\) | 178.490 | 5.71625 | ||||||||
\(976\) | 12.8293 | 0.410656 | ||||||||
\(977\) | 18.7437 | 0.599664 | 0.299832 | − | 0.953992i | \(-0.403069\pi\) | ||||
0.299832 | + | 0.953992i | \(0.403069\pi\) | |||||||
\(978\) | −51.5562 | −1.64859 | ||||||||
\(979\) | 6.56639 | 0.209863 | ||||||||
\(980\) | 21.0622 | 0.672806 | ||||||||
\(981\) | 22.3899 | 0.714856 | ||||||||
\(982\) | 20.8722 | 0.666060 | ||||||||
\(983\) | 18.4010 | 0.586900 | 0.293450 | − | 0.955974i | \(-0.405197\pi\) | ||||
0.293450 | + | 0.955974i | \(0.405197\pi\) | |||||||
\(984\) | −12.6067 | −0.401888 | ||||||||
\(985\) | −4.31390 | −0.137452 | ||||||||
\(986\) | 2.44050 | 0.0777213 | ||||||||
\(987\) | −13.4316 | −0.427532 | ||||||||
\(988\) | −28.7155 | −0.913561 | ||||||||
\(989\) | −2.67591 | −0.0850890 | ||||||||
\(990\) | −9.22647 | −0.293236 | ||||||||
\(991\) | −0.361599 | −0.0114866 | −0.00574329 | − | 0.999984i | \(-0.501828\pi\) | ||||
−0.00574329 | + | 0.999984i | \(0.501828\pi\) | |||||||
\(992\) | 5.25012 | 0.166692 | ||||||||
\(993\) | −57.8922 | −1.83715 | ||||||||
\(994\) | 7.15993 | 0.227099 | ||||||||
\(995\) | 25.9394 | 0.822334 | ||||||||
\(996\) | −10.4096 | −0.329840 | ||||||||
\(997\) | −61.1462 | −1.93652 | −0.968260 | − | 0.249944i | \(-0.919588\pi\) | ||||
−0.968260 | + | 0.249944i | \(0.919588\pi\) | |||||||
\(998\) | 25.4661 | 0.806116 | ||||||||
\(999\) | −5.69275 | −0.180111 |
(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 | 4334.2.a.g.1.20 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.g.1.20 | ✓ | 26 | 1.1 | even | 1 | trivial |