Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8035,2,Mod(1,8035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8035, 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("8035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8035 = 5 \cdot 1607 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8035.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1597980241\) |
Analytic rank: | \(0\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8035.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.27555 | −1.60906 | −0.804529 | − | 0.593913i | \(-0.797582\pi\) | ||||
−0.804529 | + | 0.593913i | \(0.797582\pi\) | |||||||
\(3\) | 1.50447 | 0.868605 | 0.434303 | − | 0.900767i | \(-0.356995\pi\) | ||||
0.434303 | + | 0.900767i | \(0.356995\pi\) | |||||||
\(4\) | 3.17814 | 1.58907 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −3.42350 | −1.39764 | ||||||||
\(7\) | 2.50382 | 0.946357 | 0.473178 | − | 0.880967i | \(-0.343107\pi\) | ||||
0.473178 | + | 0.880967i | \(0.343107\pi\) | |||||||
\(8\) | −2.68091 | −0.947846 | ||||||||
\(9\) | −0.736575 | −0.245525 | ||||||||
\(10\) | −2.27555 | −0.719593 | ||||||||
\(11\) | −5.24727 | −1.58211 | −0.791056 | − | 0.611744i | \(-0.790468\pi\) | ||||
−0.791056 | + | 0.611744i | \(0.790468\pi\) | |||||||
\(12\) | 4.78141 | 1.38027 | ||||||||
\(13\) | −3.80317 | −1.05481 | −0.527405 | − | 0.849614i | \(-0.676835\pi\) | ||||
−0.527405 | + | 0.849614i | \(0.676835\pi\) | |||||||
\(14\) | −5.69758 | −1.52274 | ||||||||
\(15\) | 1.50447 | 0.388452 | ||||||||
\(16\) | −0.255719 | −0.0639296 | ||||||||
\(17\) | −4.81056 | −1.16673 | −0.583366 | − | 0.812210i | \(-0.698264\pi\) | ||||
−0.583366 | + | 0.812210i | \(0.698264\pi\) | |||||||
\(18\) | 1.67612 | 0.395064 | ||||||||
\(19\) | −6.96879 | −1.59875 | −0.799375 | − | 0.600832i | \(-0.794836\pi\) | ||||
−0.799375 | + | 0.600832i | \(0.794836\pi\) | |||||||
\(20\) | 3.17814 | 0.710653 | ||||||||
\(21\) | 3.76692 | 0.822010 | ||||||||
\(22\) | 11.9404 | 2.54571 | ||||||||
\(23\) | 7.29962 | 1.52208 | 0.761038 | − | 0.648707i | \(-0.224690\pi\) | ||||
0.761038 | + | 0.648707i | \(0.224690\pi\) | |||||||
\(24\) | −4.03335 | −0.823304 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 8.65432 | 1.69725 | ||||||||
\(27\) | −5.62156 | −1.08187 | ||||||||
\(28\) | 7.95750 | 1.50383 | ||||||||
\(29\) | 4.20392 | 0.780649 | 0.390324 | − | 0.920677i | \(-0.372363\pi\) | ||||
0.390324 | + | 0.920677i | \(0.372363\pi\) | |||||||
\(30\) | −3.42350 | −0.625042 | ||||||||
\(31\) | 1.55323 | 0.278969 | 0.139484 | − | 0.990224i | \(-0.455456\pi\) | ||||
0.139484 | + | 0.990224i | \(0.455456\pi\) | |||||||
\(32\) | 5.94373 | 1.05071 | ||||||||
\(33\) | −7.89435 | −1.37423 | ||||||||
\(34\) | 10.9467 | 1.87734 | ||||||||
\(35\) | 2.50382 | 0.423224 | ||||||||
\(36\) | −2.34094 | −0.390156 | ||||||||
\(37\) | −2.66575 | −0.438247 | −0.219124 | − | 0.975697i | \(-0.570320\pi\) | ||||
−0.219124 | + | 0.975697i | \(0.570320\pi\) | |||||||
\(38\) | 15.8579 | 2.57248 | ||||||||
\(39\) | −5.72175 | −0.916214 | ||||||||
\(40\) | −2.68091 | −0.423889 | ||||||||
\(41\) | −1.82214 | −0.284570 | −0.142285 | − | 0.989826i | \(-0.545445\pi\) | ||||
−0.142285 | + | 0.989826i | \(0.545445\pi\) | |||||||
\(42\) | −8.57183 | −1.32266 | ||||||||
\(43\) | 6.25569 | 0.953984 | 0.476992 | − | 0.878908i | \(-0.341727\pi\) | ||||
0.476992 | + | 0.878908i | \(0.341727\pi\) | |||||||
\(44\) | −16.6765 | −2.51408 | ||||||||
\(45\) | −0.736575 | −0.109802 | ||||||||
\(46\) | −16.6107 | −2.44911 | ||||||||
\(47\) | 9.31783 | 1.35915 | 0.679573 | − | 0.733608i | \(-0.262165\pi\) | ||||
0.679573 | + | 0.733608i | \(0.262165\pi\) | |||||||
\(48\) | −0.384720 | −0.0555296 | ||||||||
\(49\) | −0.730862 | −0.104409 | ||||||||
\(50\) | −2.27555 | −0.321812 | ||||||||
\(51\) | −7.23733 | −1.01343 | ||||||||
\(52\) | −12.0870 | −1.67617 | ||||||||
\(53\) | 10.0844 | 1.38520 | 0.692599 | − | 0.721323i | \(-0.256466\pi\) | ||||
0.692599 | + | 0.721323i | \(0.256466\pi\) | |||||||
\(54\) | 12.7921 | 1.74079 | ||||||||
\(55\) | −5.24727 | −0.707542 | ||||||||
\(56\) | −6.71253 | −0.897000 | ||||||||
\(57\) | −10.4843 | −1.38868 | ||||||||
\(58\) | −9.56624 | −1.25611 | ||||||||
\(59\) | −14.1232 | −1.83869 | −0.919343 | − | 0.393458i | \(-0.871279\pi\) | ||||
−0.919343 | + | 0.393458i | \(0.871279\pi\) | |||||||
\(60\) | 4.78141 | 0.617277 | ||||||||
\(61\) | 4.75049 | 0.608237 | 0.304119 | − | 0.952634i | \(-0.401638\pi\) | ||||
0.304119 | + | 0.952634i | \(0.401638\pi\) | |||||||
\(62\) | −3.53446 | −0.448877 | ||||||||
\(63\) | −1.84426 | −0.232354 | ||||||||
\(64\) | −13.0138 | −1.62673 | ||||||||
\(65\) | −3.80317 | −0.471726 | ||||||||
\(66\) | 17.9640 | 2.21122 | ||||||||
\(67\) | 14.3978 | 1.75897 | 0.879484 | − | 0.475928i | \(-0.157888\pi\) | ||||
0.879484 | + | 0.475928i | \(0.157888\pi\) | |||||||
\(68\) | −15.2886 | −1.85402 | ||||||||
\(69\) | 10.9820 | 1.32208 | ||||||||
\(70\) | −5.69758 | −0.680991 | ||||||||
\(71\) | −4.86014 | −0.576793 | −0.288396 | − | 0.957511i | \(-0.593122\pi\) | ||||
−0.288396 | + | 0.957511i | \(0.593122\pi\) | |||||||
\(72\) | 1.97469 | 0.232720 | ||||||||
\(73\) | −6.55155 | −0.766801 | −0.383401 | − | 0.923582i | \(-0.625247\pi\) | ||||
−0.383401 | + | 0.923582i | \(0.625247\pi\) | |||||||
\(74\) | 6.06606 | 0.705165 | ||||||||
\(75\) | 1.50447 | 0.173721 | ||||||||
\(76\) | −22.1478 | −2.54052 | ||||||||
\(77\) | −13.1382 | −1.49724 | ||||||||
\(78\) | 13.0201 | 1.47424 | ||||||||
\(79\) | 9.02603 | 1.01551 | 0.507754 | − | 0.861502i | \(-0.330476\pi\) | ||||
0.507754 | + | 0.861502i | \(0.330476\pi\) | |||||||
\(80\) | −0.255719 | −0.0285902 | ||||||||
\(81\) | −6.24773 | −0.694192 | ||||||||
\(82\) | 4.14637 | 0.457890 | ||||||||
\(83\) | −3.79250 | −0.416281 | −0.208141 | − | 0.978099i | \(-0.566741\pi\) | ||||
−0.208141 | + | 0.978099i | \(0.566741\pi\) | |||||||
\(84\) | 11.9718 | 1.30623 | ||||||||
\(85\) | −4.81056 | −0.521778 | ||||||||
\(86\) | −14.2351 | −1.53502 | ||||||||
\(87\) | 6.32467 | 0.678075 | ||||||||
\(88\) | 14.0675 | 1.49960 | ||||||||
\(89\) | −16.5487 | −1.75416 | −0.877079 | − | 0.480347i | \(-0.840511\pi\) | ||||
−0.877079 | + | 0.480347i | \(0.840511\pi\) | |||||||
\(90\) | 1.67612 | 0.176678 | ||||||||
\(91\) | −9.52248 | −0.998227 | ||||||||
\(92\) | 23.1992 | 2.41868 | ||||||||
\(93\) | 2.33679 | 0.242314 | ||||||||
\(94\) | −21.2032 | −2.18694 | ||||||||
\(95\) | −6.96879 | −0.714983 | ||||||||
\(96\) | 8.94215 | 0.912654 | ||||||||
\(97\) | 2.97990 | 0.302563 | 0.151281 | − | 0.988491i | \(-0.451660\pi\) | ||||
0.151281 | + | 0.988491i | \(0.451660\pi\) | |||||||
\(98\) | 1.66312 | 0.168000 | ||||||||
\(99\) | 3.86501 | 0.388448 | ||||||||
\(100\) | 3.17814 | 0.317814 | ||||||||
\(101\) | 13.8701 | 1.38013 | 0.690066 | − | 0.723747i | \(-0.257582\pi\) | ||||
0.690066 | + | 0.723747i | \(0.257582\pi\) | |||||||
\(102\) | 16.4689 | 1.63067 | ||||||||
\(103\) | −11.7824 | −1.16095 | −0.580476 | − | 0.814277i | \(-0.697134\pi\) | ||||
−0.580476 | + | 0.814277i | \(0.697134\pi\) | |||||||
\(104\) | 10.1960 | 0.999797 | ||||||||
\(105\) | 3.76692 | 0.367614 | ||||||||
\(106\) | −22.9476 | −2.22886 | ||||||||
\(107\) | −1.28361 | −0.124091 | −0.0620454 | − | 0.998073i | \(-0.519762\pi\) | ||||
−0.0620454 | + | 0.998073i | \(0.519762\pi\) | |||||||
\(108\) | −17.8661 | −1.71916 | ||||||||
\(109\) | 18.6045 | 1.78198 | 0.890992 | − | 0.454018i | \(-0.150010\pi\) | ||||
0.890992 | + | 0.454018i | \(0.150010\pi\) | |||||||
\(110\) | 11.9404 | 1.13848 | ||||||||
\(111\) | −4.01054 | −0.380664 | ||||||||
\(112\) | −0.640274 | −0.0605002 | ||||||||
\(113\) | 11.1810 | 1.05182 | 0.525909 | − | 0.850541i | \(-0.323725\pi\) | ||||
0.525909 | + | 0.850541i | \(0.323725\pi\) | |||||||
\(114\) | 23.8576 | 2.23447 | ||||||||
\(115\) | 7.29962 | 0.680693 | ||||||||
\(116\) | 13.3606 | 1.24050 | ||||||||
\(117\) | 2.80132 | 0.258982 | ||||||||
\(118\) | 32.1381 | 2.95855 | ||||||||
\(119\) | −12.0448 | −1.10414 | ||||||||
\(120\) | −4.03335 | −0.368193 | ||||||||
\(121\) | 16.5338 | 1.50308 | ||||||||
\(122\) | −10.8100 | −0.978690 | ||||||||
\(123\) | −2.74135 | −0.247179 | ||||||||
\(124\) | 4.93638 | 0.443300 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 4.19670 | 0.373872 | ||||||||
\(127\) | −0.734058 | −0.0651371 | −0.0325685 | − | 0.999470i | \(-0.510369\pi\) | ||||
−0.0325685 | + | 0.999470i | \(0.510369\pi\) | |||||||
\(128\) | 17.7262 | 1.56679 | ||||||||
\(129\) | 9.41148 | 0.828635 | ||||||||
\(130\) | 8.65432 | 0.759034 | ||||||||
\(131\) | 14.5580 | 1.27194 | 0.635971 | − | 0.771713i | \(-0.280600\pi\) | ||||
0.635971 | + | 0.771713i | \(0.280600\pi\) | |||||||
\(132\) | −25.0893 | −2.18375 | ||||||||
\(133\) | −17.4486 | −1.51299 | ||||||||
\(134\) | −32.7629 | −2.83028 | ||||||||
\(135\) | −5.62156 | −0.483827 | ||||||||
\(136\) | 12.8967 | 1.10588 | ||||||||
\(137\) | 16.8803 | 1.44218 | 0.721089 | − | 0.692842i | \(-0.243642\pi\) | ||||
0.721089 | + | 0.692842i | \(0.243642\pi\) | |||||||
\(138\) | −24.9902 | −2.12731 | ||||||||
\(139\) | 12.6496 | 1.07292 | 0.536462 | − | 0.843925i | \(-0.319761\pi\) | ||||
0.536462 | + | 0.843925i | \(0.319761\pi\) | |||||||
\(140\) | 7.95750 | 0.672531 | ||||||||
\(141\) | 14.0184 | 1.18056 | ||||||||
\(142\) | 11.0595 | 0.928093 | ||||||||
\(143\) | 19.9563 | 1.66883 | ||||||||
\(144\) | 0.188356 | 0.0156963 | ||||||||
\(145\) | 4.20392 | 0.349117 | ||||||||
\(146\) | 14.9084 | 1.23383 | ||||||||
\(147\) | −1.09956 | −0.0906901 | ||||||||
\(148\) | −8.47213 | −0.696405 | ||||||||
\(149\) | 6.26500 | 0.513249 | 0.256624 | − | 0.966511i | \(-0.417390\pi\) | ||||
0.256624 | + | 0.966511i | \(0.417390\pi\) | |||||||
\(150\) | −3.42350 | −0.279527 | ||||||||
\(151\) | −4.22092 | −0.343493 | −0.171747 | − | 0.985141i | \(-0.554941\pi\) | ||||
−0.171747 | + | 0.985141i | \(0.554941\pi\) | |||||||
\(152\) | 18.6827 | 1.51537 | ||||||||
\(153\) | 3.54334 | 0.286462 | ||||||||
\(154\) | 29.8968 | 2.40915 | ||||||||
\(155\) | 1.55323 | 0.124759 | ||||||||
\(156\) | −18.1845 | −1.45593 | ||||||||
\(157\) | 8.69378 | 0.693839 | 0.346919 | − | 0.937895i | \(-0.387228\pi\) | ||||
0.346919 | + | 0.937895i | \(0.387228\pi\) | |||||||
\(158\) | −20.5392 | −1.63401 | ||||||||
\(159\) | 15.1716 | 1.20319 | ||||||||
\(160\) | 5.94373 | 0.469893 | ||||||||
\(161\) | 18.2770 | 1.44043 | ||||||||
\(162\) | 14.2170 | 1.11700 | ||||||||
\(163\) | −12.8601 | −1.00728 | −0.503642 | − | 0.863913i | \(-0.668007\pi\) | ||||
−0.503642 | + | 0.863913i | \(0.668007\pi\) | |||||||
\(164\) | −5.79100 | −0.452201 | ||||||||
\(165\) | −7.89435 | −0.614574 | ||||||||
\(166\) | 8.63004 | 0.669821 | ||||||||
\(167\) | 7.17778 | 0.555434 | 0.277717 | − | 0.960663i | \(-0.410422\pi\) | ||||
0.277717 | + | 0.960663i | \(0.410422\pi\) | |||||||
\(168\) | −10.0988 | −0.779139 | ||||||||
\(169\) | 1.46412 | 0.112625 | ||||||||
\(170\) | 10.9467 | 0.839571 | ||||||||
\(171\) | 5.13304 | 0.392534 | ||||||||
\(172\) | 19.8814 | 1.51595 | ||||||||
\(173\) | 8.54652 | 0.649780 | 0.324890 | − | 0.945752i | \(-0.394673\pi\) | ||||
0.324890 | + | 0.945752i | \(0.394673\pi\) | |||||||
\(174\) | −14.3921 | −1.09106 | ||||||||
\(175\) | 2.50382 | 0.189271 | ||||||||
\(176\) | 1.34182 | 0.101144 | ||||||||
\(177\) | −21.2479 | −1.59709 | ||||||||
\(178\) | 37.6574 | 2.82254 | ||||||||
\(179\) | 12.3954 | 0.926478 | 0.463239 | − | 0.886233i | \(-0.346687\pi\) | ||||
0.463239 | + | 0.886233i | \(0.346687\pi\) | |||||||
\(180\) | −2.34094 | −0.174483 | ||||||||
\(181\) | −22.3674 | −1.66256 | −0.831279 | − | 0.555855i | \(-0.812391\pi\) | ||||
−0.831279 | + | 0.555855i | \(0.812391\pi\) | |||||||
\(182\) | 21.6689 | 1.60621 | ||||||||
\(183\) | 7.14696 | 0.528318 | ||||||||
\(184\) | −19.5696 | −1.44269 | ||||||||
\(185\) | −2.66575 | −0.195990 | ||||||||
\(186\) | −5.31748 | −0.389897 | ||||||||
\(187\) | 25.2423 | 1.84590 | ||||||||
\(188\) | 29.6133 | 2.15978 | ||||||||
\(189\) | −14.0754 | −1.02383 | ||||||||
\(190\) | 15.8579 | 1.15045 | ||||||||
\(191\) | 9.59032 | 0.693931 | 0.346965 | − | 0.937878i | \(-0.387212\pi\) | ||||
0.346965 | + | 0.937878i | \(0.387212\pi\) | |||||||
\(192\) | −19.5789 | −1.41298 | ||||||||
\(193\) | −21.0726 | −1.51684 | −0.758421 | − | 0.651765i | \(-0.774029\pi\) | ||||
−0.758421 | + | 0.651765i | \(0.774029\pi\) | |||||||
\(194\) | −6.78091 | −0.486841 | ||||||||
\(195\) | −5.72175 | −0.409743 | ||||||||
\(196\) | −2.32278 | −0.165913 | ||||||||
\(197\) | −24.4357 | −1.74097 | −0.870485 | − | 0.492196i | \(-0.836194\pi\) | ||||
−0.870485 | + | 0.492196i | \(0.836194\pi\) | |||||||
\(198\) | −8.79503 | −0.625036 | ||||||||
\(199\) | −21.0865 | −1.49478 | −0.747391 | − | 0.664384i | \(-0.768694\pi\) | ||||
−0.747391 | + | 0.664384i | \(0.768694\pi\) | |||||||
\(200\) | −2.68091 | −0.189569 | ||||||||
\(201\) | 21.6610 | 1.52785 | ||||||||
\(202\) | −31.5622 | −2.22071 | ||||||||
\(203\) | 10.5259 | 0.738772 | ||||||||
\(204\) | −23.0012 | −1.61041 | ||||||||
\(205\) | −1.82214 | −0.127264 | ||||||||
\(206\) | 26.8114 | 1.86804 | ||||||||
\(207\) | −5.37672 | −0.373708 | ||||||||
\(208\) | 0.972542 | 0.0674336 | ||||||||
\(209\) | 36.5671 | 2.52940 | ||||||||
\(210\) | −8.57183 | −0.591513 | ||||||||
\(211\) | 23.1396 | 1.59300 | 0.796498 | − | 0.604642i | \(-0.206684\pi\) | ||||
0.796498 | + | 0.604642i | \(0.206684\pi\) | |||||||
\(212\) | 32.0496 | 2.20117 | ||||||||
\(213\) | −7.31193 | −0.501005 | ||||||||
\(214\) | 2.92091 | 0.199669 | ||||||||
\(215\) | 6.25569 | 0.426634 | ||||||||
\(216\) | 15.0709 | 1.02545 | ||||||||
\(217\) | 3.88902 | 0.264004 | ||||||||
\(218\) | −42.3354 | −2.86732 | ||||||||
\(219\) | −9.85660 | −0.666048 | ||||||||
\(220\) | −16.6765 | −1.12433 | ||||||||
\(221\) | 18.2954 | 1.23068 | ||||||||
\(222\) | 9.12620 | 0.612510 | ||||||||
\(223\) | 24.1681 | 1.61841 | 0.809207 | − | 0.587523i | \(-0.199897\pi\) | ||||
0.809207 | + | 0.587523i | \(0.199897\pi\) | |||||||
\(224\) | 14.8820 | 0.994349 | ||||||||
\(225\) | −0.736575 | −0.0491050 | ||||||||
\(226\) | −25.4429 | −1.69244 | ||||||||
\(227\) | 23.2897 | 1.54579 | 0.772895 | − | 0.634533i | \(-0.218808\pi\) | ||||
0.772895 | + | 0.634533i | \(0.218808\pi\) | |||||||
\(228\) | −33.3206 | −2.20671 | ||||||||
\(229\) | −15.2617 | −1.00852 | −0.504262 | − | 0.863551i | \(-0.668236\pi\) | ||||
−0.504262 | + | 0.863551i | \(0.668236\pi\) | |||||||
\(230\) | −16.6107 | −1.09527 | ||||||||
\(231\) | −19.7661 | −1.30051 | ||||||||
\(232\) | −11.2703 | −0.739934 | ||||||||
\(233\) | 14.9388 | 0.978676 | 0.489338 | − | 0.872094i | \(-0.337238\pi\) | ||||
0.489338 | + | 0.872094i | \(0.337238\pi\) | |||||||
\(234\) | −6.37456 | −0.416718 | ||||||||
\(235\) | 9.31783 | 0.607828 | ||||||||
\(236\) | −44.8855 | −2.92180 | ||||||||
\(237\) | 13.5794 | 0.882075 | ||||||||
\(238\) | 27.4085 | 1.77663 | ||||||||
\(239\) | −18.0666 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(240\) | −0.384720 | −0.0248336 | ||||||||
\(241\) | 1.29823 | 0.0836264 | 0.0418132 | − | 0.999125i | \(-0.486687\pi\) | ||||
0.0418132 | + | 0.999125i | \(0.486687\pi\) | |||||||
\(242\) | −37.6236 | −2.41854 | ||||||||
\(243\) | 7.46517 | 0.478891 | ||||||||
\(244\) | 15.0977 | 0.966531 | ||||||||
\(245\) | −0.730862 | −0.0466931 | ||||||||
\(246\) | 6.23808 | 0.397725 | ||||||||
\(247\) | 26.5035 | 1.68638 | ||||||||
\(248\) | −4.16408 | −0.264419 | ||||||||
\(249\) | −5.70570 | −0.361584 | ||||||||
\(250\) | −2.27555 | −0.143919 | ||||||||
\(251\) | 21.8057 | 1.37636 | 0.688182 | − | 0.725538i | \(-0.258409\pi\) | ||||
0.688182 | + | 0.725538i | \(0.258409\pi\) | |||||||
\(252\) | −5.86130 | −0.369227 | ||||||||
\(253\) | −38.3031 | −2.40809 | ||||||||
\(254\) | 1.67039 | 0.104809 | ||||||||
\(255\) | −7.23733 | −0.453219 | ||||||||
\(256\) | −14.3092 | −0.894324 | ||||||||
\(257\) | 3.37353 | 0.210435 | 0.105217 | − | 0.994449i | \(-0.466446\pi\) | ||||
0.105217 | + | 0.994449i | \(0.466446\pi\) | |||||||
\(258\) | −21.4163 | −1.33332 | ||||||||
\(259\) | −6.67458 | −0.414738 | ||||||||
\(260\) | −12.0870 | −0.749604 | ||||||||
\(261\) | −3.09651 | −0.191669 | ||||||||
\(262\) | −33.1276 | −2.04663 | ||||||||
\(263\) | 25.2581 | 1.55748 | 0.778740 | − | 0.627346i | \(-0.215859\pi\) | ||||
0.778740 | + | 0.627346i | \(0.215859\pi\) | |||||||
\(264\) | 21.1641 | 1.30256 | ||||||||
\(265\) | 10.0844 | 0.619479 | ||||||||
\(266\) | 39.7053 | 2.43449 | ||||||||
\(267\) | −24.8970 | −1.52367 | ||||||||
\(268\) | 45.7581 | 2.79512 | ||||||||
\(269\) | −18.2060 | −1.11004 | −0.555019 | − | 0.831837i | \(-0.687289\pi\) | ||||
−0.555019 | + | 0.831837i | \(0.687289\pi\) | |||||||
\(270\) | 12.7921 | 0.778505 | ||||||||
\(271\) | 7.11004 | 0.431904 | 0.215952 | − | 0.976404i | \(-0.430714\pi\) | ||||
0.215952 | + | 0.976404i | \(0.430714\pi\) | |||||||
\(272\) | 1.23015 | 0.0745887 | ||||||||
\(273\) | −14.3263 | −0.867065 | ||||||||
\(274\) | −38.4119 | −2.32055 | ||||||||
\(275\) | −5.24727 | −0.316422 | ||||||||
\(276\) | 34.9025 | 2.10088 | ||||||||
\(277\) | −11.3819 | −0.683873 | −0.341937 | − | 0.939723i | \(-0.611083\pi\) | ||||
−0.341937 | + | 0.939723i | \(0.611083\pi\) | |||||||
\(278\) | −28.7848 | −1.72640 | ||||||||
\(279\) | −1.14407 | −0.0684938 | ||||||||
\(280\) | −6.71253 | −0.401151 | ||||||||
\(281\) | −7.36784 | −0.439529 | −0.219764 | − | 0.975553i | \(-0.570529\pi\) | ||||
−0.219764 | + | 0.975553i | \(0.570529\pi\) | |||||||
\(282\) | −31.8996 | −1.89959 | ||||||||
\(283\) | −16.9802 | −1.00937 | −0.504683 | − | 0.863305i | \(-0.668391\pi\) | ||||
−0.504683 | + | 0.863305i | \(0.668391\pi\) | |||||||
\(284\) | −15.4462 | −0.916564 | ||||||||
\(285\) | −10.4843 | −0.621038 | ||||||||
\(286\) | −45.4115 | −2.68524 | ||||||||
\(287\) | −4.56231 | −0.269305 | ||||||||
\(288\) | −4.37800 | −0.257976 | ||||||||
\(289\) | 6.14144 | 0.361261 | ||||||||
\(290\) | −9.56624 | −0.561749 | ||||||||
\(291\) | 4.48316 | 0.262807 | ||||||||
\(292\) | −20.8217 | −1.21850 | ||||||||
\(293\) | 25.2249 | 1.47365 | 0.736826 | − | 0.676083i | \(-0.236324\pi\) | ||||
0.736826 | + | 0.676083i | \(0.236324\pi\) | |||||||
\(294\) | 2.50210 | 0.145926 | ||||||||
\(295\) | −14.1232 | −0.822285 | ||||||||
\(296\) | 7.14665 | 0.415391 | ||||||||
\(297\) | 29.4978 | 1.71164 | ||||||||
\(298\) | −14.2563 | −0.825847 | ||||||||
\(299\) | −27.7617 | −1.60550 | ||||||||
\(300\) | 4.78141 | 0.276055 | ||||||||
\(301\) | 15.6631 | 0.902809 | ||||||||
\(302\) | 9.60491 | 0.552701 | ||||||||
\(303\) | 20.8672 | 1.19879 | ||||||||
\(304\) | 1.78205 | 0.102208 | ||||||||
\(305\) | 4.75049 | 0.272012 | ||||||||
\(306\) | −8.06305 | −0.460934 | ||||||||
\(307\) | −4.82295 | −0.275260 | −0.137630 | − | 0.990484i | \(-0.543949\pi\) | ||||
−0.137630 | + | 0.990484i | \(0.543949\pi\) | |||||||
\(308\) | −41.7551 | −2.37922 | ||||||||
\(309\) | −17.7262 | −1.00841 | ||||||||
\(310\) | −3.53446 | −0.200744 | ||||||||
\(311\) | −8.97997 | −0.509208 | −0.254604 | − | 0.967045i | \(-0.581945\pi\) | ||||
−0.254604 | + | 0.967045i | \(0.581945\pi\) | |||||||
\(312\) | 15.3395 | 0.868429 | ||||||||
\(313\) | 21.2719 | 1.20236 | 0.601180 | − | 0.799114i | \(-0.294698\pi\) | ||||
0.601180 | + | 0.799114i | \(0.294698\pi\) | |||||||
\(314\) | −19.7831 | −1.11643 | ||||||||
\(315\) | −1.84426 | −0.103912 | ||||||||
\(316\) | 28.6860 | 1.61371 | ||||||||
\(317\) | 7.44384 | 0.418088 | 0.209044 | − | 0.977906i | \(-0.432965\pi\) | ||||
0.209044 | + | 0.977906i | \(0.432965\pi\) | |||||||
\(318\) | −34.5239 | −1.93600 | ||||||||
\(319\) | −22.0591 | −1.23507 | ||||||||
\(320\) | −13.0138 | −0.727495 | ||||||||
\(321\) | −1.93114 | −0.107786 | ||||||||
\(322\) | −41.5902 | −2.31773 | ||||||||
\(323\) | 33.5238 | 1.86531 | ||||||||
\(324\) | −19.8561 | −1.10312 | ||||||||
\(325\) | −3.80317 | −0.210962 | ||||||||
\(326\) | 29.2639 | 1.62078 | ||||||||
\(327\) | 27.9898 | 1.54784 | ||||||||
\(328\) | 4.88499 | 0.269728 | ||||||||
\(329\) | 23.3302 | 1.28624 | ||||||||
\(330\) | 17.9640 | 0.988886 | ||||||||
\(331\) | 7.76416 | 0.426757 | 0.213378 | − | 0.976970i | \(-0.431553\pi\) | ||||
0.213378 | + | 0.976970i | \(0.431553\pi\) | |||||||
\(332\) | −12.0531 | −0.661499 | ||||||||
\(333\) | 1.96353 | 0.107601 | ||||||||
\(334\) | −16.3334 | −0.893725 | ||||||||
\(335\) | 14.3978 | 0.786635 | ||||||||
\(336\) | −0.963272 | −0.0525508 | ||||||||
\(337\) | 8.30367 | 0.452330 | 0.226165 | − | 0.974089i | \(-0.427381\pi\) | ||||
0.226165 | + | 0.974089i | \(0.427381\pi\) | |||||||
\(338\) | −3.33169 | −0.181220 | ||||||||
\(339\) | 16.8214 | 0.913615 | ||||||||
\(340\) | −15.2886 | −0.829141 | ||||||||
\(341\) | −8.15022 | −0.441359 | ||||||||
\(342\) | −11.6805 | −0.631609 | ||||||||
\(343\) | −19.3567 | −1.04516 | ||||||||
\(344\) | −16.7710 | −0.904229 | ||||||||
\(345\) | 10.9820 | 0.591254 | ||||||||
\(346\) | −19.4481 | −1.04553 | ||||||||
\(347\) | 34.0457 | 1.82767 | 0.913834 | − | 0.406089i | \(-0.133108\pi\) | ||||
0.913834 | + | 0.406089i | \(0.133108\pi\) | |||||||
\(348\) | 20.1007 | 1.07751 | ||||||||
\(349\) | 20.7211 | 1.10918 | 0.554589 | − | 0.832125i | \(-0.312876\pi\) | ||||
0.554589 | + | 0.832125i | \(0.312876\pi\) | |||||||
\(350\) | −5.69758 | −0.304549 | ||||||||
\(351\) | 21.3798 | 1.14117 | ||||||||
\(352\) | −31.1883 | −1.66234 | ||||||||
\(353\) | 4.76457 | 0.253593 | 0.126796 | − | 0.991929i | \(-0.459531\pi\) | ||||
0.126796 | + | 0.991929i | \(0.459531\pi\) | |||||||
\(354\) | 48.3507 | 2.56981 | ||||||||
\(355\) | −4.86014 | −0.257950 | ||||||||
\(356\) | −52.5940 | −2.78748 | ||||||||
\(357\) | −18.1210 | −0.959065 | ||||||||
\(358\) | −28.2064 | −1.49076 | ||||||||
\(359\) | 14.2631 | 0.752780 | 0.376390 | − | 0.926461i | \(-0.377165\pi\) | ||||
0.376390 | + | 0.926461i | \(0.377165\pi\) | |||||||
\(360\) | 1.97469 | 0.104076 | ||||||||
\(361\) | 29.5641 | 1.55600 | ||||||||
\(362\) | 50.8983 | 2.67515 | ||||||||
\(363\) | 24.8746 | 1.30558 | ||||||||
\(364\) | −30.2637 | −1.58625 | ||||||||
\(365\) | −6.55155 | −0.342924 | ||||||||
\(366\) | −16.2633 | −0.850095 | ||||||||
\(367\) | −21.6388 | −1.12954 | −0.564769 | − | 0.825249i | \(-0.691035\pi\) | ||||
−0.564769 | + | 0.825249i | \(0.691035\pi\) | |||||||
\(368\) | −1.86665 | −0.0973058 | ||||||||
\(369\) | 1.34214 | 0.0698691 | ||||||||
\(370\) | 6.06606 | 0.315360 | ||||||||
\(371\) | 25.2496 | 1.31089 | ||||||||
\(372\) | 7.42663 | 0.385053 | ||||||||
\(373\) | 4.14912 | 0.214833 | 0.107417 | − | 0.994214i | \(-0.465742\pi\) | ||||
0.107417 | + | 0.994214i | \(0.465742\pi\) | |||||||
\(374\) | −57.4401 | −2.97016 | ||||||||
\(375\) | 1.50447 | 0.0776904 | ||||||||
\(376\) | −24.9803 | −1.28826 | ||||||||
\(377\) | −15.9882 | −0.823436 | ||||||||
\(378\) | 32.0293 | 1.64741 | ||||||||
\(379\) | −6.72024 | −0.345196 | −0.172598 | − | 0.984992i | \(-0.555216\pi\) | ||||
−0.172598 | + | 0.984992i | \(0.555216\pi\) | |||||||
\(380\) | −22.1478 | −1.13616 | ||||||||
\(381\) | −1.10437 | −0.0565784 | ||||||||
\(382\) | −21.8233 | −1.11658 | ||||||||
\(383\) | −6.70720 | −0.342722 | −0.171361 | − | 0.985208i | \(-0.554816\pi\) | ||||
−0.171361 | + | 0.985208i | \(0.554816\pi\) | |||||||
\(384\) | 26.6685 | 1.36092 | ||||||||
\(385\) | −13.1382 | −0.669587 | ||||||||
\(386\) | 47.9519 | 2.44069 | ||||||||
\(387\) | −4.60779 | −0.234227 | ||||||||
\(388\) | 9.47052 | 0.480793 | ||||||||
\(389\) | 6.34437 | 0.321672 | 0.160836 | − | 0.986981i | \(-0.448581\pi\) | ||||
0.160836 | + | 0.986981i | \(0.448581\pi\) | |||||||
\(390\) | 13.0201 | 0.659301 | ||||||||
\(391\) | −35.1152 | −1.77585 | ||||||||
\(392\) | 1.95938 | 0.0989635 | ||||||||
\(393\) | 21.9021 | 1.10481 | ||||||||
\(394\) | 55.6046 | 2.80132 | ||||||||
\(395\) | 9.02603 | 0.454149 | ||||||||
\(396\) | 12.2835 | 0.617271 | ||||||||
\(397\) | −14.8646 | −0.746034 | −0.373017 | − | 0.927825i | \(-0.621677\pi\) | ||||
−0.373017 | + | 0.927825i | \(0.621677\pi\) | |||||||
\(398\) | 47.9834 | 2.40519 | ||||||||
\(399\) | −26.2509 | −1.31419 | ||||||||
\(400\) | −0.255719 | −0.0127859 | ||||||||
\(401\) | 20.4359 | 1.02052 | 0.510260 | − | 0.860020i | \(-0.329549\pi\) | ||||
0.510260 | + | 0.860020i | \(0.329549\pi\) | |||||||
\(402\) | −49.2907 | −2.45840 | ||||||||
\(403\) | −5.90721 | −0.294259 | ||||||||
\(404\) | 44.0812 | 2.19312 | ||||||||
\(405\) | −6.24773 | −0.310452 | ||||||||
\(406\) | −23.9522 | −1.18873 | ||||||||
\(407\) | 13.9879 | 0.693356 | ||||||||
\(408\) | 19.4026 | 0.960574 | ||||||||
\(409\) | 14.2914 | 0.706663 | 0.353332 | − | 0.935498i | \(-0.385049\pi\) | ||||
0.353332 | + | 0.935498i | \(0.385049\pi\) | |||||||
\(410\) | 4.14637 | 0.204774 | ||||||||
\(411\) | 25.3958 | 1.25268 | ||||||||
\(412\) | −37.4460 | −1.84483 | ||||||||
\(413\) | −35.3620 | −1.74005 | ||||||||
\(414\) | 12.2350 | 0.601318 | ||||||||
\(415\) | −3.79250 | −0.186167 | ||||||||
\(416\) | −22.6050 | −1.10830 | ||||||||
\(417\) | 19.0309 | 0.931947 | ||||||||
\(418\) | −83.2104 | −4.06995 | ||||||||
\(419\) | −2.01427 | −0.0984036 | −0.0492018 | − | 0.998789i | \(-0.515668\pi\) | ||||
−0.0492018 | + | 0.998789i | \(0.515668\pi\) | |||||||
\(420\) | 11.9718 | 0.584164 | ||||||||
\(421\) | −9.92116 | −0.483528 | −0.241764 | − | 0.970335i | \(-0.577726\pi\) | ||||
−0.241764 | + | 0.970335i | \(0.577726\pi\) | |||||||
\(422\) | −52.6553 | −2.56322 | ||||||||
\(423\) | −6.86329 | −0.333704 | ||||||||
\(424\) | −27.0354 | −1.31295 | ||||||||
\(425\) | −4.81056 | −0.233346 | ||||||||
\(426\) | 16.6387 | 0.806147 | ||||||||
\(427\) | 11.8944 | 0.575610 | ||||||||
\(428\) | −4.07947 | −0.197189 | ||||||||
\(429\) | 30.0236 | 1.44955 | ||||||||
\(430\) | −14.2351 | −0.686480 | ||||||||
\(431\) | 30.9377 | 1.49022 | 0.745108 | − | 0.666943i | \(-0.232398\pi\) | ||||
0.745108 | + | 0.666943i | \(0.232398\pi\) | |||||||
\(432\) | 1.43754 | 0.0691635 | ||||||||
\(433\) | 1.62121 | 0.0779104 | 0.0389552 | − | 0.999241i | \(-0.487597\pi\) | ||||
0.0389552 | + | 0.999241i | \(0.487597\pi\) | |||||||
\(434\) | −8.84966 | −0.424797 | ||||||||
\(435\) | 6.32467 | 0.303245 | ||||||||
\(436\) | 59.1275 | 2.83170 | ||||||||
\(437\) | −50.8695 | −2.43342 | ||||||||
\(438\) | 22.4292 | 1.07171 | ||||||||
\(439\) | 3.37600 | 0.161128 | 0.0805638 | − | 0.996749i | \(-0.474328\pi\) | ||||
0.0805638 | + | 0.996749i | \(0.474328\pi\) | |||||||
\(440\) | 14.0675 | 0.670640 | ||||||||
\(441\) | 0.538335 | 0.0256350 | ||||||||
\(442\) | −41.6321 | −1.98024 | ||||||||
\(443\) | −3.11412 | −0.147956 | −0.0739781 | − | 0.997260i | \(-0.523569\pi\) | ||||
−0.0739781 | + | 0.997260i | \(0.523569\pi\) | |||||||
\(444\) | −12.7461 | −0.604901 | ||||||||
\(445\) | −16.5487 | −0.784483 | ||||||||
\(446\) | −54.9957 | −2.60412 | ||||||||
\(447\) | 9.42549 | 0.445810 | ||||||||
\(448\) | −32.5843 | −1.53946 | ||||||||
\(449\) | 24.2005 | 1.14209 | 0.571047 | − | 0.820917i | \(-0.306537\pi\) | ||||
0.571047 | + | 0.820917i | \(0.306537\pi\) | |||||||
\(450\) | 1.67612 | 0.0790129 | ||||||||
\(451\) | 9.56124 | 0.450221 | ||||||||
\(452\) | 35.5347 | 1.67141 | ||||||||
\(453\) | −6.35023 | −0.298360 | ||||||||
\(454\) | −52.9969 | −2.48727 | ||||||||
\(455\) | −9.52248 | −0.446421 | ||||||||
\(456\) | 28.1076 | 1.31626 | ||||||||
\(457\) | −26.2123 | −1.22616 | −0.613079 | − | 0.790022i | \(-0.710069\pi\) | ||||
−0.613079 | + | 0.790022i | \(0.710069\pi\) | |||||||
\(458\) | 34.7289 | 1.62278 | ||||||||
\(459\) | 27.0428 | 1.26225 | ||||||||
\(460\) | 23.1992 | 1.08167 | ||||||||
\(461\) | 22.2314 | 1.03542 | 0.517709 | − | 0.855557i | \(-0.326785\pi\) | ||||
0.517709 | + | 0.855557i | \(0.326785\pi\) | |||||||
\(462\) | 44.9787 | 2.09260 | ||||||||
\(463\) | −10.6473 | −0.494821 | −0.247411 | − | 0.968911i | \(-0.579580\pi\) | ||||
−0.247411 | + | 0.968911i | \(0.579580\pi\) | |||||||
\(464\) | −1.07502 | −0.0499066 | ||||||||
\(465\) | 2.33679 | 0.108366 | ||||||||
\(466\) | −33.9941 | −1.57475 | ||||||||
\(467\) | −36.7629 | −1.70119 | −0.850593 | − | 0.525825i | \(-0.823757\pi\) | ||||
−0.850593 | + | 0.525825i | \(0.823757\pi\) | |||||||
\(468\) | 8.90299 | 0.411541 | ||||||||
\(469\) | 36.0495 | 1.66461 | ||||||||
\(470\) | −21.2032 | −0.978031 | ||||||||
\(471\) | 13.0795 | 0.602672 | ||||||||
\(472\) | 37.8631 | 1.74279 | ||||||||
\(473\) | −32.8253 | −1.50931 | ||||||||
\(474\) | −30.9006 | −1.41931 | ||||||||
\(475\) | −6.96879 | −0.319750 | ||||||||
\(476\) | −38.2800 | −1.75456 | ||||||||
\(477\) | −7.42792 | −0.340101 | ||||||||
\(478\) | 41.1116 | 1.88040 | ||||||||
\(479\) | 27.2857 | 1.24672 | 0.623358 | − | 0.781936i | \(-0.285768\pi\) | ||||
0.623358 | + | 0.781936i | \(0.285768\pi\) | |||||||
\(480\) | 8.94215 | 0.408151 | ||||||||
\(481\) | 10.1383 | 0.462268 | ||||||||
\(482\) | −2.95419 | −0.134560 | ||||||||
\(483\) | 27.4971 | 1.25116 | ||||||||
\(484\) | 52.5468 | 2.38849 | ||||||||
\(485\) | 2.97990 | 0.135310 | ||||||||
\(486\) | −16.9874 | −0.770563 | ||||||||
\(487\) | −19.0676 | −0.864036 | −0.432018 | − | 0.901865i | \(-0.642198\pi\) | ||||
−0.432018 | + | 0.901865i | \(0.642198\pi\) | |||||||
\(488\) | −12.7356 | −0.576515 | ||||||||
\(489\) | −19.3477 | −0.874932 | ||||||||
\(490\) | 1.66312 | 0.0751319 | ||||||||
\(491\) | −0.263944 | −0.0119116 | −0.00595581 | − | 0.999982i | \(-0.501896\pi\) | ||||
−0.00595581 | + | 0.999982i | \(0.501896\pi\) | |||||||
\(492\) | −8.71238 | −0.392784 | ||||||||
\(493\) | −20.2232 | −0.910807 | ||||||||
\(494\) | −60.3102 | −2.71348 | ||||||||
\(495\) | 3.86501 | 0.173719 | ||||||||
\(496\) | −0.397190 | −0.0178344 | ||||||||
\(497\) | −12.1689 | −0.545852 | ||||||||
\(498\) | 12.9836 | 0.581810 | ||||||||
\(499\) | −4.36997 | −0.195627 | −0.0978133 | − | 0.995205i | \(-0.531185\pi\) | ||||
−0.0978133 | + | 0.995205i | \(0.531185\pi\) | |||||||
\(500\) | 3.17814 | 0.142131 | ||||||||
\(501\) | 10.7987 | 0.482452 | ||||||||
\(502\) | −49.6201 | −2.21465 | ||||||||
\(503\) | 28.6997 | 1.27965 | 0.639827 | − | 0.768519i | \(-0.279006\pi\) | ||||
0.639827 | + | 0.768519i | \(0.279006\pi\) | |||||||
\(504\) | 4.94429 | 0.220236 | ||||||||
\(505\) | 13.8701 | 0.617213 | ||||||||
\(506\) | 87.1606 | 3.87476 | ||||||||
\(507\) | 2.20273 | 0.0978266 | ||||||||
\(508\) | −2.33294 | −0.103507 | ||||||||
\(509\) | −14.7584 | −0.654156 | −0.327078 | − | 0.944997i | \(-0.606064\pi\) | ||||
−0.327078 | + | 0.944997i | \(0.606064\pi\) | |||||||
\(510\) | 16.4689 | 0.729256 | ||||||||
\(511\) | −16.4039 | −0.725668 | ||||||||
\(512\) | −2.89104 | −0.127767 | ||||||||
\(513\) | 39.1755 | 1.72964 | ||||||||
\(514\) | −7.67664 | −0.338602 | ||||||||
\(515\) | −11.7824 | −0.519194 | ||||||||
\(516\) | 29.9110 | 1.31676 | ||||||||
\(517\) | −48.8932 | −2.15032 | ||||||||
\(518\) | 15.1884 | 0.667338 | ||||||||
\(519\) | 12.8580 | 0.564402 | ||||||||
\(520\) | 10.1960 | 0.447123 | ||||||||
\(521\) | −31.9970 | −1.40182 | −0.700908 | − | 0.713252i | \(-0.747222\pi\) | ||||
−0.700908 | + | 0.713252i | \(0.747222\pi\) | |||||||
\(522\) | 7.04626 | 0.308406 | ||||||||
\(523\) | −4.60845 | −0.201514 | −0.100757 | − | 0.994911i | \(-0.532126\pi\) | ||||
−0.100757 | + | 0.994911i | \(0.532126\pi\) | |||||||
\(524\) | 46.2674 | 2.02120 | ||||||||
\(525\) | 3.76692 | 0.164402 | ||||||||
\(526\) | −57.4761 | −2.50608 | ||||||||
\(527\) | −7.47190 | −0.325481 | ||||||||
\(528\) | 2.01873 | 0.0878540 | ||||||||
\(529\) | 30.2845 | 1.31672 | ||||||||
\(530\) | −22.9476 | −0.996778 | ||||||||
\(531\) | 10.4028 | 0.451443 | ||||||||
\(532\) | −55.4542 | −2.40424 | ||||||||
\(533\) | 6.92990 | 0.300167 | ||||||||
\(534\) | 56.6544 | 2.45167 | ||||||||
\(535\) | −1.28361 | −0.0554951 | ||||||||
\(536\) | −38.5992 | −1.66723 | ||||||||
\(537\) | 18.6485 | 0.804743 | ||||||||
\(538\) | 41.4287 | 1.78612 | ||||||||
\(539\) | 3.83503 | 0.165187 | ||||||||
\(540\) | −17.8661 | −0.768834 | ||||||||
\(541\) | 27.8353 | 1.19673 | 0.598366 | − | 0.801223i | \(-0.295817\pi\) | ||||
0.598366 | + | 0.801223i | \(0.295817\pi\) | |||||||
\(542\) | −16.1793 | −0.694959 | ||||||||
\(543\) | −33.6511 | −1.44411 | ||||||||
\(544\) | −28.5926 | −1.22590 | ||||||||
\(545\) | 18.6045 | 0.796928 | ||||||||
\(546\) | 32.6002 | 1.39516 | ||||||||
\(547\) | −44.5854 | −1.90633 | −0.953166 | − | 0.302448i | \(-0.902196\pi\) | ||||
−0.953166 | + | 0.302448i | \(0.902196\pi\) | |||||||
\(548\) | 53.6478 | 2.29172 | ||||||||
\(549\) | −3.49909 | −0.149338 | ||||||||
\(550\) | 11.9404 | 0.509142 | ||||||||
\(551\) | −29.2963 | −1.24806 | ||||||||
\(552\) | −29.4419 | −1.25313 | ||||||||
\(553\) | 22.5996 | 0.961033 | ||||||||
\(554\) | 25.9002 | 1.10039 | ||||||||
\(555\) | −4.01054 | −0.170238 | ||||||||
\(556\) | 40.2021 | 1.70495 | ||||||||
\(557\) | 9.70433 | 0.411186 | 0.205593 | − | 0.978638i | \(-0.434088\pi\) | ||||
0.205593 | + | 0.978638i | \(0.434088\pi\) | |||||||
\(558\) | 2.60340 | 0.110211 | ||||||||
\(559\) | −23.7915 | −1.00627 | ||||||||
\(560\) | −0.640274 | −0.0270565 | ||||||||
\(561\) | 37.9762 | 1.60336 | ||||||||
\(562\) | 16.7659 | 0.707227 | ||||||||
\(563\) | 31.4912 | 1.32719 | 0.663597 | − | 0.748090i | \(-0.269029\pi\) | ||||
0.663597 | + | 0.748090i | \(0.269029\pi\) | |||||||
\(564\) | 44.5523 | 1.87599 | ||||||||
\(565\) | 11.1810 | 0.470387 | ||||||||
\(566\) | 38.6392 | 1.62413 | ||||||||
\(567\) | −15.6432 | −0.656954 | ||||||||
\(568\) | 13.0296 | 0.546711 | ||||||||
\(569\) | −15.3630 | −0.644049 | −0.322025 | − | 0.946731i | \(-0.604363\pi\) | ||||
−0.322025 | + | 0.946731i | \(0.604363\pi\) | |||||||
\(570\) | 23.8576 | 0.999286 | ||||||||
\(571\) | −11.9601 | −0.500517 | −0.250258 | − | 0.968179i | \(-0.580516\pi\) | ||||
−0.250258 | + | 0.968179i | \(0.580516\pi\) | |||||||
\(572\) | 63.4238 | 2.65188 | ||||||||
\(573\) | 14.4283 | 0.602752 | ||||||||
\(574\) | 10.3818 | 0.433327 | ||||||||
\(575\) | 7.29962 | 0.304415 | ||||||||
\(576\) | 9.58566 | 0.399403 | ||||||||
\(577\) | 12.6390 | 0.526168 | 0.263084 | − | 0.964773i | \(-0.415260\pi\) | ||||
0.263084 | + | 0.964773i | \(0.415260\pi\) | |||||||
\(578\) | −13.9752 | −0.581291 | ||||||||
\(579\) | −31.7031 | −1.31754 | ||||||||
\(580\) | 13.3606 | 0.554770 | ||||||||
\(581\) | −9.49576 | −0.393951 | ||||||||
\(582\) | −10.2017 | −0.422872 | ||||||||
\(583\) | −52.9155 | −2.19154 | ||||||||
\(584\) | 17.5641 | 0.726809 | ||||||||
\(585\) | 2.80132 | 0.115820 | ||||||||
\(586\) | −57.4005 | −2.37119 | ||||||||
\(587\) | −20.0503 | −0.827566 | −0.413783 | − | 0.910376i | \(-0.635793\pi\) | ||||
−0.413783 | + | 0.910376i | \(0.635793\pi\) | |||||||
\(588\) | −3.49455 | −0.144113 | ||||||||
\(589\) | −10.8241 | −0.446001 | ||||||||
\(590\) | 32.1381 | 1.32310 | ||||||||
\(591\) | −36.7627 | −1.51221 | ||||||||
\(592\) | 0.681683 | 0.0280170 | ||||||||
\(593\) | −10.3794 | −0.426230 | −0.213115 | − | 0.977027i | \(-0.568361\pi\) | ||||
−0.213115 | + | 0.977027i | \(0.568361\pi\) | |||||||
\(594\) | −67.1239 | −2.75413 | ||||||||
\(595\) | −12.0448 | −0.493788 | ||||||||
\(596\) | 19.9110 | 0.815587 | ||||||||
\(597\) | −31.7240 | −1.29838 | ||||||||
\(598\) | 63.1732 | 2.58335 | ||||||||
\(599\) | −45.6014 | −1.86322 | −0.931611 | − | 0.363456i | \(-0.881597\pi\) | ||||
−0.931611 | + | 0.363456i | \(0.881597\pi\) | |||||||
\(600\) | −4.03335 | −0.164661 | ||||||||
\(601\) | −7.21630 | −0.294359 | −0.147179 | − | 0.989110i | \(-0.547019\pi\) | ||||
−0.147179 | + | 0.989110i | \(0.547019\pi\) | |||||||
\(602\) | −35.6423 | −1.45267 | ||||||||
\(603\) | −10.6051 | −0.431871 | ||||||||
\(604\) | −13.4146 | −0.545834 | ||||||||
\(605\) | 16.5338 | 0.672196 | ||||||||
\(606\) | −47.4844 | −1.92892 | ||||||||
\(607\) | 24.9637 | 1.01325 | 0.506623 | − | 0.862168i | \(-0.330894\pi\) | ||||
0.506623 | + | 0.862168i | \(0.330894\pi\) | |||||||
\(608\) | −41.4206 | −1.67983 | ||||||||
\(609\) | 15.8359 | 0.641701 | ||||||||
\(610\) | −10.8100 | −0.437683 | ||||||||
\(611\) | −35.4373 | −1.43364 | ||||||||
\(612\) | 11.2612 | 0.455207 | ||||||||
\(613\) | −41.3282 | −1.66923 | −0.834616 | − | 0.550832i | \(-0.814310\pi\) | ||||
−0.834616 | + | 0.550832i | \(0.814310\pi\) | |||||||
\(614\) | 10.9749 | 0.442910 | ||||||||
\(615\) | −2.74135 | −0.110542 | ||||||||
\(616\) | 35.2225 | 1.41915 | ||||||||
\(617\) | −26.2962 | −1.05865 | −0.529323 | − | 0.848420i | \(-0.677554\pi\) | ||||
−0.529323 | + | 0.848420i | \(0.677554\pi\) | |||||||
\(618\) | 40.3369 | 1.62259 | ||||||||
\(619\) | −10.1084 | −0.406289 | −0.203145 | − | 0.979149i | \(-0.565116\pi\) | ||||
−0.203145 | + | 0.979149i | \(0.565116\pi\) | |||||||
\(620\) | 4.93638 | 0.198250 | ||||||||
\(621\) | −41.0352 | −1.64669 | ||||||||
\(622\) | 20.4344 | 0.819345 | ||||||||
\(623\) | −41.4350 | −1.66006 | ||||||||
\(624\) | 1.46316 | 0.0585732 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −48.4053 | −1.93467 | ||||||||
\(627\) | 55.0141 | 2.19705 | ||||||||
\(628\) | 27.6300 | 1.10256 | ||||||||
\(629\) | 12.8238 | 0.511317 | ||||||||
\(630\) | 4.19670 | 0.167201 | ||||||||
\(631\) | 24.4124 | 0.971844 | 0.485922 | − | 0.874002i | \(-0.338484\pi\) | ||||
0.485922 | + | 0.874002i | \(0.338484\pi\) | |||||||
\(632\) | −24.1980 | −0.962545 | ||||||||
\(633\) | 34.8128 | 1.38368 | ||||||||
\(634\) | −16.9388 | −0.672728 | ||||||||
\(635\) | −0.734058 | −0.0291302 | ||||||||
\(636\) | 48.2176 | 1.91195 | ||||||||
\(637\) | 2.77960 | 0.110132 | ||||||||
\(638\) | 50.1967 | 1.98730 | ||||||||
\(639\) | 3.57986 | 0.141617 | ||||||||
\(640\) | 17.7262 | 0.700689 | ||||||||
\(641\) | 36.7001 | 1.44957 | 0.724783 | − | 0.688977i | \(-0.241940\pi\) | ||||
0.724783 | + | 0.688977i | \(0.241940\pi\) | |||||||
\(642\) | 4.39442 | 0.173434 | ||||||||
\(643\) | −0.957989 | −0.0377794 | −0.0188897 | − | 0.999822i | \(-0.506013\pi\) | ||||
−0.0188897 | + | 0.999822i | \(0.506013\pi\) | |||||||
\(644\) | 58.0867 | 2.28894 | ||||||||
\(645\) | 9.41148 | 0.370577 | ||||||||
\(646\) | −76.2851 | −3.00140 | ||||||||
\(647\) | −6.76900 | −0.266117 | −0.133058 | − | 0.991108i | \(-0.542480\pi\) | ||||
−0.133058 | + | 0.991108i | \(0.542480\pi\) | |||||||
\(648\) | 16.7496 | 0.657987 | ||||||||
\(649\) | 74.1083 | 2.90900 | ||||||||
\(650\) | 8.65432 | 0.339450 | ||||||||
\(651\) | 5.85090 | 0.229315 | ||||||||
\(652\) | −40.8713 | −1.60064 | ||||||||
\(653\) | 9.30651 | 0.364192 | 0.182096 | − | 0.983281i | \(-0.441712\pi\) | ||||
0.182096 | + | 0.983281i | \(0.441712\pi\) | |||||||
\(654\) | −63.6923 | −2.49057 | ||||||||
\(655\) | 14.5580 | 0.568829 | ||||||||
\(656\) | 0.465954 | 0.0181925 | ||||||||
\(657\) | 4.82571 | 0.188269 | ||||||||
\(658\) | −53.0891 | −2.06963 | ||||||||
\(659\) | 27.3110 | 1.06389 | 0.531943 | − | 0.846780i | \(-0.321462\pi\) | ||||
0.531943 | + | 0.846780i | \(0.321462\pi\) | |||||||
\(660\) | −25.0893 | −0.976601 | ||||||||
\(661\) | 0.661490 | 0.0257290 | 0.0128645 | − | 0.999917i | \(-0.495905\pi\) | ||||
0.0128645 | + | 0.999917i | \(0.495905\pi\) | |||||||
\(662\) | −17.6677 | −0.686676 | ||||||||
\(663\) | 27.5248 | 1.06898 | ||||||||
\(664\) | 10.1674 | 0.394570 | ||||||||
\(665\) | −17.4486 | −0.676629 | ||||||||
\(666\) | −4.46811 | −0.173136 | ||||||||
\(667\) | 30.6870 | 1.18821 | ||||||||
\(668\) | 22.8120 | 0.882622 | ||||||||
\(669\) | 36.3601 | 1.40576 | ||||||||
\(670\) | −32.7629 | −1.26574 | ||||||||
\(671\) | −24.9271 | −0.962299 | ||||||||
\(672\) | 22.3896 | 0.863696 | ||||||||
\(673\) | 1.58588 | 0.0611313 | 0.0305657 | − | 0.999533i | \(-0.490269\pi\) | ||||
0.0305657 | + | 0.999533i | \(0.490269\pi\) | |||||||
\(674\) | −18.8954 | −0.727825 | ||||||||
\(675\) | −5.62156 | −0.216374 | ||||||||
\(676\) | 4.65319 | 0.178969 | ||||||||
\(677\) | 18.1146 | 0.696200 | 0.348100 | − | 0.937457i | \(-0.386827\pi\) | ||||
0.348100 | + | 0.937457i | \(0.386827\pi\) | |||||||
\(678\) | −38.2780 | −1.47006 | ||||||||
\(679\) | 7.46114 | 0.286332 | ||||||||
\(680\) | 12.8967 | 0.494565 | ||||||||
\(681\) | 35.0386 | 1.34268 | ||||||||
\(682\) | 18.5463 | 0.710173 | ||||||||
\(683\) | 9.70328 | 0.371286 | 0.185643 | − | 0.982617i | \(-0.440563\pi\) | ||||
0.185643 | + | 0.982617i | \(0.440563\pi\) | |||||||
\(684\) | 16.3135 | 0.623763 | ||||||||
\(685\) | 16.8803 | 0.644962 | ||||||||
\(686\) | 44.0472 | 1.68173 | ||||||||
\(687\) | −22.9608 | −0.876010 | ||||||||
\(688\) | −1.59970 | −0.0609878 | ||||||||
\(689\) | −38.3527 | −1.46112 | ||||||||
\(690\) | −24.9902 | −0.951361 | ||||||||
\(691\) | 45.9000 | 1.74612 | 0.873059 | − | 0.487615i | \(-0.162133\pi\) | ||||
0.873059 | + | 0.487615i | \(0.162133\pi\) | |||||||
\(692\) | 27.1620 | 1.03255 | ||||||||
\(693\) | 9.67731 | 0.367610 | ||||||||
\(694\) | −77.4727 | −2.94082 | ||||||||
\(695\) | 12.6496 | 0.479826 | ||||||||
\(696\) | −16.9559 | −0.642711 | ||||||||
\(697\) | 8.76549 | 0.332017 | ||||||||
\(698\) | −47.1521 | −1.78473 | ||||||||
\(699\) | 22.4750 | 0.850083 | ||||||||
\(700\) | 7.95750 | 0.300765 | ||||||||
\(701\) | 46.3137 | 1.74924 | 0.874621 | − | 0.484807i | \(-0.161110\pi\) | ||||
0.874621 | + | 0.484807i | \(0.161110\pi\) | |||||||
\(702\) | −48.6508 | −1.83620 | ||||||||
\(703\) | 18.5771 | 0.700648 | ||||||||
\(704\) | 68.2870 | 2.57366 | ||||||||
\(705\) | 14.0184 | 0.527963 | ||||||||
\(706\) | −10.8420 | −0.408045 | ||||||||
\(707\) | 34.7284 | 1.30610 | ||||||||
\(708\) | −67.5288 | −2.53789 | ||||||||
\(709\) | −32.1345 | −1.20684 | −0.603418 | − | 0.797425i | \(-0.706195\pi\) | ||||
−0.603418 | + | 0.797425i | \(0.706195\pi\) | |||||||
\(710\) | 11.0595 | 0.415056 | ||||||||
\(711\) | −6.64835 | −0.249333 | ||||||||
\(712\) | 44.3656 | 1.66267 | ||||||||
\(713\) | 11.3380 | 0.424611 | ||||||||
\(714\) | 41.2353 | 1.54319 | ||||||||
\(715\) | 19.9563 | 0.746322 | ||||||||
\(716\) | 39.3944 | 1.47224 | ||||||||
\(717\) | −27.1807 | −1.01508 | ||||||||
\(718\) | −32.4565 | −1.21127 | ||||||||
\(719\) | 6.24392 | 0.232859 | 0.116429 | − | 0.993199i | \(-0.462855\pi\) | ||||
0.116429 | + | 0.993199i | \(0.462855\pi\) | |||||||
\(720\) | 0.188356 | 0.00701961 | ||||||||
\(721\) | −29.5010 | −1.09868 | ||||||||
\(722\) | −67.2746 | −2.50370 | ||||||||
\(723\) | 1.95315 | 0.0726383 | ||||||||
\(724\) | −71.0868 | −2.64192 | ||||||||
\(725\) | 4.20392 | 0.156130 | ||||||||
\(726\) | −56.6035 | −2.10075 | ||||||||
\(727\) | −24.0601 | −0.892339 | −0.446170 | − | 0.894948i | \(-0.647212\pi\) | ||||
−0.446170 | + | 0.894948i | \(0.647212\pi\) | |||||||
\(728\) | 25.5289 | 0.946165 | ||||||||
\(729\) | 29.9743 | 1.11016 | ||||||||
\(730\) | 14.9084 | 0.551785 | ||||||||
\(731\) | −30.0933 | −1.11304 | ||||||||
\(732\) | 22.7140 | 0.839534 | ||||||||
\(733\) | −5.67735 | −0.209698 | −0.104849 | − | 0.994488i | \(-0.533436\pi\) | ||||
−0.104849 | + | 0.994488i | \(0.533436\pi\) | |||||||
\(734\) | 49.2403 | 1.81749 | ||||||||
\(735\) | −1.09956 | −0.0405579 | ||||||||
\(736\) | 43.3869 | 1.59926 | ||||||||
\(737\) | −75.5490 | −2.78288 | ||||||||
\(738\) | −3.05411 | −0.112423 | ||||||||
\(739\) | −5.58461 | −0.205433 | −0.102717 | − | 0.994711i | \(-0.532753\pi\) | ||||
−0.102717 | + | 0.994711i | \(0.532753\pi\) | |||||||
\(740\) | −8.47213 | −0.311442 | ||||||||
\(741\) | 39.8737 | 1.46480 | ||||||||
\(742\) | −57.4567 | −2.10930 | ||||||||
\(743\) | 15.0241 | 0.551181 | 0.275591 | − | 0.961275i | \(-0.411127\pi\) | ||||
0.275591 | + | 0.961275i | \(0.411127\pi\) | |||||||
\(744\) | −6.26472 | −0.229676 | ||||||||
\(745\) | 6.26500 | 0.229532 | ||||||||
\(746\) | −9.44153 | −0.345679 | ||||||||
\(747\) | 2.79346 | 0.102208 | ||||||||
\(748\) | 80.2234 | 2.93326 | ||||||||
\(749\) | −3.21392 | −0.117434 | ||||||||
\(750\) | −3.42350 | −0.125008 | ||||||||
\(751\) | 6.55352 | 0.239141 | 0.119571 | − | 0.992826i | \(-0.461848\pi\) | ||||
0.119571 | + | 0.992826i | \(0.461848\pi\) | |||||||
\(752\) | −2.38274 | −0.0868897 | ||||||||
\(753\) | 32.8060 | 1.19552 | ||||||||
\(754\) | 36.3821 | 1.32496 | ||||||||
\(755\) | −4.22092 | −0.153615 | ||||||||
\(756\) | −44.7335 | −1.62694 | ||||||||
\(757\) | −5.82641 | −0.211764 | −0.105882 | − | 0.994379i | \(-0.533767\pi\) | ||||
−0.105882 | + | 0.994379i | \(0.533767\pi\) | |||||||
\(758\) | 15.2923 | 0.555440 | ||||||||
\(759\) | −57.6258 | −2.09168 | ||||||||
\(760\) | 18.6827 | 0.677694 | ||||||||
\(761\) | −16.9781 | −0.615456 | −0.307728 | − | 0.951474i | \(-0.599569\pi\) | ||||
−0.307728 | + | 0.951474i | \(0.599569\pi\) | |||||||
\(762\) | 2.51304 | 0.0910380 | ||||||||
\(763\) | 46.5823 | 1.68639 | ||||||||
\(764\) | 30.4793 | 1.10270 | ||||||||
\(765\) | 3.54334 | 0.128110 | ||||||||
\(766\) | 15.2626 | 0.551459 | ||||||||
\(767\) | 53.7130 | 1.93946 | ||||||||
\(768\) | −21.5277 | −0.776815 | ||||||||
\(769\) | 24.1800 | 0.871953 | 0.435977 | − | 0.899958i | \(-0.356403\pi\) | ||||
0.435977 | + | 0.899958i | \(0.356403\pi\) | |||||||
\(770\) | 29.8968 | 1.07740 | ||||||||
\(771\) | 5.07537 | 0.182785 | ||||||||
\(772\) | −66.9718 | −2.41037 | ||||||||
\(773\) | −37.1179 | −1.33504 | −0.667519 | − | 0.744593i | \(-0.732644\pi\) | ||||
−0.667519 | + | 0.744593i | \(0.732644\pi\) | |||||||
\(774\) | 10.4853 | 0.376885 | ||||||||
\(775\) | 1.55323 | 0.0557937 | ||||||||
\(776\) | −7.98884 | −0.286783 | ||||||||
\(777\) | −10.0417 | −0.360244 | ||||||||
\(778\) | −14.4369 | −0.517589 | ||||||||
\(779\) | 12.6981 | 0.454957 | ||||||||
\(780\) | −18.1845 | −0.651110 | ||||||||
\(781\) | 25.5025 | 0.912551 | ||||||||
\(782\) | 79.9065 | 2.85745 | ||||||||
\(783\) | −23.6326 | −0.844560 | ||||||||
\(784\) | 0.186895 | 0.00667482 | ||||||||
\(785\) | 8.69378 | 0.310294 | ||||||||
\(786\) | −49.8394 | −1.77771 | ||||||||
\(787\) | −43.6677 | −1.55659 | −0.778293 | − | 0.627901i | \(-0.783914\pi\) | ||||
−0.778293 | + | 0.627901i | \(0.783914\pi\) | |||||||
\(788\) | −77.6599 | −2.76652 | ||||||||
\(789\) | 38.0000 | 1.35284 | ||||||||
\(790\) | −20.5392 | −0.730752 | ||||||||
\(791\) | 27.9952 | 0.995395 | ||||||||
\(792\) | −10.3618 | −0.368189 | ||||||||
\(793\) | −18.0669 | −0.641575 | ||||||||
\(794\) | 33.8252 | 1.20041 | ||||||||
\(795\) | 15.1716 | 0.538083 | ||||||||
\(796\) | −67.0158 | −2.37531 | ||||||||
\(797\) | 4.42656 | 0.156797 | 0.0783984 | − | 0.996922i | \(-0.475019\pi\) | ||||
0.0783984 | + | 0.996922i | \(0.475019\pi\) | |||||||
\(798\) | 59.7353 | 2.11461 | ||||||||
\(799\) | −44.8239 | −1.58576 | ||||||||
\(800\) | 5.94373 | 0.210142 | ||||||||
\(801\) | 12.1894 | 0.430690 | ||||||||
\(802\) | −46.5030 | −1.64208 | ||||||||
\(803\) | 34.3778 | 1.21317 | ||||||||
\(804\) | 68.8416 | 2.42786 | ||||||||
\(805\) | 18.2770 | 0.644179 | ||||||||
\(806\) | 13.4422 | 0.473480 | ||||||||
\(807\) | −27.3903 | −0.964186 | ||||||||
\(808\) | −37.1847 | −1.30815 | ||||||||
\(809\) | −34.2476 | −1.20408 | −0.602040 | − | 0.798466i | \(-0.705645\pi\) | ||||
−0.602040 | + | 0.798466i | \(0.705645\pi\) | |||||||
\(810\) | 14.2170 | 0.499536 | ||||||||
\(811\) | 9.05938 | 0.318118 | 0.159059 | − | 0.987269i | \(-0.449154\pi\) | ||||
0.159059 | + | 0.987269i | \(0.449154\pi\) | |||||||
\(812\) | 33.4527 | 1.17396 | ||||||||
\(813\) | 10.6968 | 0.375154 | ||||||||
\(814\) | −31.8303 | −1.11565 | ||||||||
\(815\) | −12.8601 | −0.450471 | ||||||||
\(816\) | 1.85072 | 0.0647881 | ||||||||
\(817\) | −43.5946 | −1.52518 | ||||||||
\(818\) | −32.5208 | −1.13706 | ||||||||
\(819\) | 7.01402 | 0.245090 | ||||||||
\(820\) | −5.79100 | −0.202231 | ||||||||
\(821\) | 9.69965 | 0.338520 | 0.169260 | − | 0.985571i | \(-0.445862\pi\) | ||||
0.169260 | + | 0.985571i | \(0.445862\pi\) | |||||||
\(822\) | −57.7895 | −2.01564 | ||||||||
\(823\) | 17.9811 | 0.626783 | 0.313391 | − | 0.949624i | \(-0.398535\pi\) | ||||
0.313391 | + | 0.949624i | \(0.398535\pi\) | |||||||
\(824\) | 31.5875 | 1.10040 | ||||||||
\(825\) | −7.89435 | −0.274846 | ||||||||
\(826\) | 80.4682 | 2.79985 | ||||||||
\(827\) | −1.06152 | −0.0369127 | −0.0184563 | − | 0.999830i | \(-0.505875\pi\) | ||||
−0.0184563 | + | 0.999830i | \(0.505875\pi\) | |||||||
\(828\) | −17.0880 | −0.593848 | ||||||||
\(829\) | 24.3000 | 0.843973 | 0.421986 | − | 0.906602i | \(-0.361333\pi\) | ||||
0.421986 | + | 0.906602i | \(0.361333\pi\) | |||||||
\(830\) | 8.63004 | 0.299553 | ||||||||
\(831\) | −17.1237 | −0.594016 | ||||||||
\(832\) | 49.4938 | 1.71589 | ||||||||
\(833\) | 3.51585 | 0.121817 | ||||||||
\(834\) | −43.3058 | −1.49956 | ||||||||
\(835\) | 7.17778 | 0.248397 | ||||||||
\(836\) | 116.215 | 4.01939 | ||||||||
\(837\) | −8.73158 | −0.301808 | ||||||||
\(838\) | 4.58358 | 0.158337 | ||||||||
\(839\) | 19.8474 | 0.685207 | 0.342604 | − | 0.939480i | \(-0.388691\pi\) | ||||
0.342604 | + | 0.939480i | \(0.388691\pi\) | |||||||
\(840\) | −10.0988 | −0.348442 | ||||||||
\(841\) | −11.3270 | −0.390588 | ||||||||
\(842\) | 22.5761 | 0.778024 | ||||||||
\(843\) | −11.0847 | −0.381777 | ||||||||
\(844\) | 73.5408 | 2.53138 | ||||||||
\(845\) | 1.46412 | 0.0503674 | ||||||||
\(846\) | 15.6178 | 0.536950 | ||||||||
\(847\) | 41.3978 | 1.42245 | ||||||||
\(848\) | −2.57877 | −0.0885552 | ||||||||
\(849\) | −25.5461 | −0.876740 | ||||||||
\(850\) | 10.9467 | 0.375468 | ||||||||
\(851\) | −19.4590 | −0.667046 | ||||||||
\(852\) | −23.2383 | −0.796132 | ||||||||
\(853\) | −50.5322 | −1.73019 | −0.865095 | − | 0.501608i | \(-0.832742\pi\) | ||||
−0.865095 | + | 0.501608i | \(0.832742\pi\) | |||||||
\(854\) | −27.0663 | −0.926189 | ||||||||
\(855\) | 5.13304 | 0.175546 | ||||||||
\(856\) | 3.44123 | 0.117619 | ||||||||
\(857\) | 37.7693 | 1.29017 | 0.645087 | − | 0.764109i | \(-0.276821\pi\) | ||||
0.645087 | + | 0.764109i | \(0.276821\pi\) | |||||||
\(858\) | −68.3202 | −2.33241 | ||||||||
\(859\) | 47.6612 | 1.62618 | 0.813089 | − | 0.582139i | \(-0.197784\pi\) | ||||
0.813089 | + | 0.582139i | \(0.197784\pi\) | |||||||
\(860\) | 19.8814 | 0.677951 | ||||||||
\(861\) | −6.86385 | −0.233919 | ||||||||
\(862\) | −70.4004 | −2.39785 | ||||||||
\(863\) | 5.82396 | 0.198250 | 0.0991249 | − | 0.995075i | \(-0.468396\pi\) | ||||
0.0991249 | + | 0.995075i | \(0.468396\pi\) | |||||||
\(864\) | −33.4130 | −1.13673 | ||||||||
\(865\) | 8.54652 | 0.290591 | ||||||||
\(866\) | −3.68915 | −0.125362 | ||||||||
\(867\) | 9.23961 | 0.313794 | ||||||||
\(868\) | 12.3598 | 0.419520 | ||||||||
\(869\) | −47.3620 | −1.60665 | ||||||||
\(870\) | −14.3921 | −0.487938 | ||||||||
\(871\) | −54.7573 | −1.85538 | ||||||||
\(872\) | −49.8769 | −1.68905 | ||||||||
\(873\) | −2.19492 | −0.0742867 | ||||||||
\(874\) | 115.756 | 3.91552 | ||||||||
\(875\) | 2.50382 | 0.0846447 | ||||||||
\(876\) | −31.3256 | −1.05840 | ||||||||
\(877\) | 41.2030 | 1.39133 | 0.695664 | − | 0.718367i | \(-0.255110\pi\) | ||||
0.695664 | + | 0.718367i | \(0.255110\pi\) | |||||||
\(878\) | −7.68226 | −0.259264 | ||||||||
\(879\) | 37.9500 | 1.28002 | ||||||||
\(880\) | 1.34182 | 0.0452329 | ||||||||
\(881\) | −43.7348 | −1.47346 | −0.736731 | − | 0.676185i | \(-0.763632\pi\) | ||||
−0.736731 | + | 0.676185i | \(0.763632\pi\) | |||||||
\(882\) | −1.22501 | −0.0412482 | ||||||||
\(883\) | 5.26972 | 0.177340 | 0.0886701 | − | 0.996061i | \(-0.471738\pi\) | ||||
0.0886701 | + | 0.996061i | \(0.471738\pi\) | |||||||
\(884\) | 58.1452 | 1.95564 | ||||||||
\(885\) | −21.2479 | −0.714241 | ||||||||
\(886\) | 7.08634 | 0.238070 | ||||||||
\(887\) | −16.2680 | −0.546227 | −0.273113 | − | 0.961982i | \(-0.588053\pi\) | ||||
−0.273113 | + | 0.961982i | \(0.588053\pi\) | |||||||
\(888\) | 10.7519 | 0.360811 | ||||||||
\(889\) | −1.83795 | −0.0616429 | ||||||||
\(890\) | 37.6574 | 1.26228 | ||||||||
\(891\) | 32.7835 | 1.09829 | ||||||||
\(892\) | 76.8095 | 2.57177 | ||||||||
\(893\) | −64.9340 | −2.17294 | ||||||||
\(894\) | −21.4482 | −0.717335 | ||||||||
\(895\) | 12.3954 | 0.414334 | ||||||||
\(896\) | 44.3832 | 1.48274 | ||||||||
\(897\) | −41.7666 | −1.39455 | ||||||||
\(898\) | −55.0696 | −1.83770 | ||||||||
\(899\) | 6.52966 | 0.217776 | ||||||||
\(900\) | −2.34094 | −0.0780313 | ||||||||
\(901\) | −48.5115 | −1.61615 | ||||||||
\(902\) | −21.7571 | −0.724432 | ||||||||
\(903\) | 23.5647 | 0.784184 | ||||||||
\(904\) | −29.9752 | −0.996961 | ||||||||
\(905\) | −22.3674 | −0.743519 | ||||||||
\(906\) | 14.4503 | 0.480079 | ||||||||
\(907\) | 4.99565 | 0.165878 | 0.0829388 | − | 0.996555i | \(-0.473569\pi\) | ||||
0.0829388 | + | 0.996555i | \(0.473569\pi\) | |||||||
\(908\) | 74.0178 | 2.45637 | ||||||||
\(909\) | −10.2164 | −0.338857 | ||||||||
\(910\) | 21.6689 | 0.718317 | ||||||||
\(911\) | −37.7436 | −1.25050 | −0.625251 | − | 0.780424i | \(-0.715003\pi\) | ||||
−0.625251 | + | 0.780424i | \(0.715003\pi\) | |||||||
\(912\) | 2.68104 | 0.0887780 | ||||||||
\(913\) | 19.9003 | 0.658603 | ||||||||
\(914\) | 59.6474 | 1.97296 | ||||||||
\(915\) | 7.14696 | 0.236271 | ||||||||
\(916\) | −48.5039 | −1.60261 | ||||||||
\(917\) | 36.4508 | 1.20371 | ||||||||
\(918\) | −61.5373 | −2.03104 | ||||||||
\(919\) | −2.66360 | −0.0878640 | −0.0439320 | − | 0.999035i | \(-0.513988\pi\) | ||||
−0.0439320 | + | 0.999035i | \(0.513988\pi\) | |||||||
\(920\) | −19.5696 | −0.645192 | ||||||||
\(921\) | −7.25597 | −0.239092 | ||||||||
\(922\) | −50.5886 | −1.66605 | ||||||||
\(923\) | 18.4840 | 0.608407 | ||||||||
\(924\) | −62.8193 | −2.06660 | ||||||||
\(925\) | −2.66575 | −0.0876495 | ||||||||
\(926\) | 24.2285 | 0.796196 | ||||||||
\(927\) | 8.67861 | 0.285043 | ||||||||
\(928\) | 24.9870 | 0.820237 | ||||||||
\(929\) | 42.7429 | 1.40235 | 0.701175 | − | 0.712989i | \(-0.252659\pi\) | ||||
0.701175 | + | 0.712989i | \(0.252659\pi\) | |||||||
\(930\) | −5.31748 | −0.174367 | ||||||||
\(931\) | 5.09323 | 0.166924 | ||||||||
\(932\) | 47.4777 | 1.55518 | ||||||||
\(933\) | −13.5101 | −0.442300 | ||||||||
\(934\) | 83.6560 | 2.73731 | ||||||||
\(935\) | 25.2423 | 0.825511 | ||||||||
\(936\) | −7.51010 | −0.245475 | ||||||||
\(937\) | −2.15757 | −0.0704848 | −0.0352424 | − | 0.999379i | \(-0.511220\pi\) | ||||
−0.0352424 | + | 0.999379i | \(0.511220\pi\) | |||||||
\(938\) | −82.0326 | −2.67846 | ||||||||
\(939\) | 32.0029 | 1.04438 | ||||||||
\(940\) | 29.6133 | 0.965881 | ||||||||
\(941\) | 12.0300 | 0.392165 | 0.196083 | − | 0.980587i | \(-0.437178\pi\) | ||||
0.196083 | + | 0.980587i | \(0.437178\pi\) | |||||||
\(942\) | −29.7631 | −0.969735 | ||||||||
\(943\) | −13.3009 | −0.433137 | ||||||||
\(944\) | 3.61157 | 0.117546 | ||||||||
\(945\) | −14.0754 | −0.457873 | ||||||||
\(946\) | 74.6956 | 2.42856 | ||||||||
\(947\) | 3.89171 | 0.126464 | 0.0632318 | − | 0.997999i | \(-0.479859\pi\) | ||||
0.0632318 | + | 0.997999i | \(0.479859\pi\) | |||||||
\(948\) | 43.1571 | 1.40168 | ||||||||
\(949\) | 24.9167 | 0.808830 | ||||||||
\(950\) | 15.8579 | 0.514497 | ||||||||
\(951\) | 11.1990 | 0.363153 | ||||||||
\(952\) | 32.2910 | 1.04656 | ||||||||
\(953\) | 11.9064 | 0.385685 | 0.192842 | − | 0.981230i | \(-0.438229\pi\) | ||||
0.192842 | + | 0.981230i | \(0.438229\pi\) | |||||||
\(954\) | 16.9026 | 0.547242 | ||||||||
\(955\) | 9.59032 | 0.310335 | ||||||||
\(956\) | −57.4183 | −1.85704 | ||||||||
\(957\) | −33.1872 | −1.07279 | ||||||||
\(958\) | −62.0901 | −2.00604 | ||||||||
\(959\) | 42.2652 | 1.36482 | ||||||||
\(960\) | −19.5789 | −0.631906 | ||||||||
\(961\) | −28.5875 | −0.922177 | ||||||||
\(962\) | −23.0703 | −0.743816 | ||||||||
\(963\) | 0.945472 | 0.0304674 | ||||||||
\(964\) | 4.12596 | 0.132888 | ||||||||
\(965\) | −21.0726 | −0.678353 | ||||||||
\(966\) | −62.5711 | −2.01319 | ||||||||
\(967\) | −4.05346 | −0.130351 | −0.0651753 | − | 0.997874i | \(-0.520761\pi\) | ||||
−0.0651753 | + | 0.997874i | \(0.520761\pi\) | |||||||
\(968\) | −44.3258 | −1.42468 | ||||||||
\(969\) | 50.4354 | 1.62022 | ||||||||
\(970\) | −6.78091 | −0.217722 | ||||||||
\(971\) | −35.5755 | −1.14167 | −0.570836 | − | 0.821064i | \(-0.693381\pi\) | ||||
−0.570836 | + | 0.821064i | \(0.693381\pi\) | |||||||
\(972\) | 23.7253 | 0.760990 | ||||||||
\(973\) | 31.6723 | 1.01537 | ||||||||
\(974\) | 43.3893 | 1.39028 | ||||||||
\(975\) | −5.72175 | −0.183243 | ||||||||
\(976\) | −1.21479 | −0.0388844 | ||||||||
\(977\) | −2.31298 | −0.0739988 | −0.0369994 | − | 0.999315i | \(-0.511780\pi\) | ||||
−0.0369994 | + | 0.999315i | \(0.511780\pi\) | |||||||
\(978\) | 44.0266 | 1.40782 | ||||||||
\(979\) | 86.8354 | 2.77527 | ||||||||
\(980\) | −2.32278 | −0.0741985 | ||||||||
\(981\) | −13.7036 | −0.437522 | ||||||||
\(982\) | 0.600618 | 0.0191665 | ||||||||
\(983\) | −24.5345 | −0.782527 | −0.391264 | − | 0.920279i | \(-0.627962\pi\) | ||||
−0.391264 | + | 0.920279i | \(0.627962\pi\) | |||||||
\(984\) | 7.34931 | 0.234287 | ||||||||
\(985\) | −24.4357 | −0.778585 | ||||||||
\(986\) | 46.0189 | 1.46554 | ||||||||
\(987\) | 35.0996 | 1.11723 | ||||||||
\(988\) | 84.2318 | 2.67977 | ||||||||
\(989\) | 45.6642 | 1.45204 | ||||||||
\(990\) | −8.79503 | −0.279524 | ||||||||
\(991\) | 36.3419 | 1.15444 | 0.577218 | − | 0.816590i | \(-0.304138\pi\) | ||||
0.577218 | + | 0.816590i | \(0.304138\pi\) | |||||||
\(992\) | 9.23198 | 0.293116 | ||||||||
\(993\) | 11.6809 | 0.370683 | ||||||||
\(994\) | 27.6911 | 0.878308 | ||||||||
\(995\) | −21.0865 | −0.668487 | ||||||||
\(996\) | −18.1335 | −0.574582 | ||||||||
\(997\) | 43.8370 | 1.38833 | 0.694166 | − | 0.719815i | \(-0.255773\pi\) | ||||
0.694166 | + | 0.719815i | \(0.255773\pi\) | |||||||
\(998\) | 9.94409 | 0.314775 | ||||||||
\(999\) | 14.9857 | 0.474126 |
(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 | 8035.2.a.e.1.20 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8035.2.a.e.1.20 | ✓ | 153 | 1.1 | even | 1 | trivial |