Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50021 | −1.06081 | −0.530406 | − | 0.847744i | \(-0.677960\pi\) | ||||
−0.530406 | + | 0.847744i | \(0.677960\pi\) | |||||||
\(3\) | 0.266806 | 0.154041 | 0.0770204 | − | 0.997030i | \(-0.475459\pi\) | ||||
0.0770204 | + | 0.997030i | \(0.475459\pi\) | |||||||
\(4\) | 0.250644 | 0.125322 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.400267 | −0.163408 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.62441 | 0.927869 | ||||||||
\(9\) | −2.92881 | −0.976271 | ||||||||
\(10\) | −1.50021 | −0.474409 | ||||||||
\(11\) | −2.55030 | −0.768943 | −0.384472 | − | 0.923137i | \(-0.625616\pi\) | ||||
−0.384472 | + | 0.923137i | \(0.625616\pi\) | |||||||
\(12\) | 0.0668733 | 0.0193047 | ||||||||
\(13\) | 6.27542 | 1.74049 | 0.870244 | − | 0.492620i | \(-0.163961\pi\) | ||||
0.870244 | + | 0.492620i | \(0.163961\pi\) | |||||||
\(14\) | 1.50021 | 0.400949 | ||||||||
\(15\) | 0.266806 | 0.0688891 | ||||||||
\(16\) | −4.43846 | −1.10962 | ||||||||
\(17\) | 0.504865 | 0.122448 | 0.0612239 | − | 0.998124i | \(-0.480500\pi\) | ||||
0.0612239 | + | 0.998124i | \(0.480500\pi\) | |||||||
\(18\) | 4.39385 | 1.03564 | ||||||||
\(19\) | 3.47987 | 0.798337 | 0.399169 | − | 0.916877i | \(-0.369299\pi\) | ||||
0.399169 | + | 0.916877i | \(0.369299\pi\) | |||||||
\(20\) | 0.250644 | 0.0560456 | ||||||||
\(21\) | −0.266806 | −0.0582219 | ||||||||
\(22\) | 3.82599 | 0.815704 | ||||||||
\(23\) | −7.56441 | −1.57729 | −0.788645 | − | 0.614849i | \(-0.789217\pi\) | ||||
−0.788645 | + | 0.614849i | \(0.789217\pi\) | |||||||
\(24\) | 0.700209 | 0.142930 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −9.41448 | −1.84633 | ||||||||
\(27\) | −1.58185 | −0.304426 | ||||||||
\(28\) | −0.250644 | −0.0473672 | ||||||||
\(29\) | −5.18542 | −0.962908 | −0.481454 | − | 0.876471i | \(-0.659891\pi\) | ||||
−0.481454 | + | 0.876471i | \(0.659891\pi\) | |||||||
\(30\) | −0.400267 | −0.0730784 | ||||||||
\(31\) | 2.19885 | 0.394924 | 0.197462 | − | 0.980310i | \(-0.436730\pi\) | ||||
0.197462 | + | 0.980310i | \(0.436730\pi\) | |||||||
\(32\) | 1.40983 | 0.249225 | ||||||||
\(33\) | −0.680435 | −0.118449 | ||||||||
\(34\) | −0.757406 | −0.129894 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −0.734088 | −0.122348 | ||||||||
\(37\) | 5.38561 | 0.885389 | 0.442694 | − | 0.896673i | \(-0.354023\pi\) | ||||
0.442694 | + | 0.896673i | \(0.354023\pi\) | |||||||
\(38\) | −5.22055 | −0.846886 | ||||||||
\(39\) | 1.67432 | 0.268106 | ||||||||
\(40\) | 2.62441 | 0.414956 | ||||||||
\(41\) | −6.93512 | −1.08308 | −0.541542 | − | 0.840674i | \(-0.682159\pi\) | ||||
−0.541542 | + | 0.840674i | \(0.682159\pi\) | |||||||
\(42\) | 0.400267 | 0.0617625 | ||||||||
\(43\) | 5.47623 | 0.835117 | 0.417559 | − | 0.908650i | \(-0.362886\pi\) | ||||
0.417559 | + | 0.908650i | \(0.362886\pi\) | |||||||
\(44\) | −0.639215 | −0.0963653 | ||||||||
\(45\) | −2.92881 | −0.436602 | ||||||||
\(46\) | 11.3482 | 1.67321 | ||||||||
\(47\) | 8.38893 | 1.22365 | 0.611825 | − | 0.790993i | \(-0.290435\pi\) | ||||
0.611825 | + | 0.790993i | \(0.290435\pi\) | |||||||
\(48\) | −1.18421 | −0.170926 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.50021 | −0.212162 | ||||||||
\(51\) | 0.134701 | 0.0188619 | ||||||||
\(52\) | 1.57289 | 0.218121 | ||||||||
\(53\) | −4.09118 | −0.561967 | −0.280983 | − | 0.959713i | \(-0.590661\pi\) | ||||
−0.280983 | + | 0.959713i | \(0.590661\pi\) | |||||||
\(54\) | 2.37311 | 0.322939 | ||||||||
\(55\) | −2.55030 | −0.343882 | ||||||||
\(56\) | −2.62441 | −0.350702 | ||||||||
\(57\) | 0.928452 | 0.122976 | ||||||||
\(58\) | 7.77924 | 1.02146 | ||||||||
\(59\) | −6.46570 | −0.841762 | −0.420881 | − | 0.907116i | \(-0.638279\pi\) | ||||
−0.420881 | + | 0.907116i | \(0.638279\pi\) | |||||||
\(60\) | 0.0668733 | 0.00863330 | ||||||||
\(61\) | 1.98590 | 0.254268 | 0.127134 | − | 0.991886i | \(-0.459422\pi\) | ||||
0.127134 | + | 0.991886i | \(0.459422\pi\) | |||||||
\(62\) | −3.29874 | −0.418941 | ||||||||
\(63\) | 2.92881 | 0.368996 | ||||||||
\(64\) | 6.76188 | 0.845235 | ||||||||
\(65\) | 6.27542 | 0.778370 | ||||||||
\(66\) | 1.02080 | 0.125652 | ||||||||
\(67\) | 8.62225 | 1.05338 | 0.526688 | − | 0.850059i | \(-0.323434\pi\) | ||||
0.526688 | + | 0.850059i | \(0.323434\pi\) | |||||||
\(68\) | 0.126541 | 0.0153454 | ||||||||
\(69\) | −2.01823 | −0.242967 | ||||||||
\(70\) | 1.50021 | 0.179310 | ||||||||
\(71\) | −9.38322 | −1.11358 | −0.556792 | − | 0.830652i | \(-0.687968\pi\) | ||||
−0.556792 | + | 0.830652i | \(0.687968\pi\) | |||||||
\(72\) | −7.68641 | −0.905852 | ||||||||
\(73\) | 3.60124 | 0.421493 | 0.210747 | − | 0.977541i | \(-0.432410\pi\) | ||||
0.210747 | + | 0.977541i | \(0.432410\pi\) | |||||||
\(74\) | −8.07957 | −0.939231 | ||||||||
\(75\) | 0.266806 | 0.0308081 | ||||||||
\(76\) | 0.872207 | 0.100049 | ||||||||
\(77\) | 2.55030 | 0.290633 | ||||||||
\(78\) | −2.51184 | −0.284410 | ||||||||
\(79\) | −5.42500 | −0.610361 | −0.305180 | − | 0.952295i | \(-0.598717\pi\) | ||||
−0.305180 | + | 0.952295i | \(0.598717\pi\) | |||||||
\(80\) | −4.43846 | −0.496235 | ||||||||
\(81\) | 8.36440 | 0.929377 | ||||||||
\(82\) | 10.4042 | 1.14895 | ||||||||
\(83\) | 1.16863 | 0.128274 | 0.0641372 | − | 0.997941i | \(-0.479570\pi\) | ||||
0.0641372 | + | 0.997941i | \(0.479570\pi\) | |||||||
\(84\) | −0.0668733 | −0.00729647 | ||||||||
\(85\) | 0.504865 | 0.0547603 | ||||||||
\(86\) | −8.21552 | −0.885902 | ||||||||
\(87\) | −1.38350 | −0.148327 | ||||||||
\(88\) | −6.69302 | −0.713478 | ||||||||
\(89\) | 1.25561 | 0.133094 | 0.0665471 | − | 0.997783i | \(-0.478802\pi\) | ||||
0.0665471 | + | 0.997783i | \(0.478802\pi\) | |||||||
\(90\) | 4.39385 | 0.463152 | ||||||||
\(91\) | −6.27542 | −0.657843 | ||||||||
\(92\) | −1.89597 | −0.197669 | ||||||||
\(93\) | 0.586666 | 0.0608344 | ||||||||
\(94\) | −12.5852 | −1.29806 | ||||||||
\(95\) | 3.47987 | 0.357027 | ||||||||
\(96\) | 0.376151 | 0.0383908 | ||||||||
\(97\) | 18.1951 | 1.84744 | 0.923718 | − | 0.383072i | \(-0.125134\pi\) | ||||
0.923718 | + | 0.383072i | \(0.125134\pi\) | |||||||
\(98\) | −1.50021 | −0.151545 | ||||||||
\(99\) | 7.46934 | 0.750697 | ||||||||
\(100\) | 0.250644 | 0.0250644 | ||||||||
\(101\) | 3.60580 | 0.358791 | 0.179395 | − | 0.983777i | \(-0.442586\pi\) | ||||
0.179395 | + | 0.983777i | \(0.442586\pi\) | |||||||
\(102\) | −0.202081 | −0.0200090 | ||||||||
\(103\) | −0.693412 | −0.0683240 | −0.0341620 | − | 0.999416i | \(-0.510876\pi\) | ||||
−0.0341620 | + | 0.999416i | \(0.510876\pi\) | |||||||
\(104\) | 16.4693 | 1.61495 | ||||||||
\(105\) | −0.266806 | −0.0260376 | ||||||||
\(106\) | 6.13765 | 0.596141 | ||||||||
\(107\) | 8.05582 | 0.778786 | 0.389393 | − | 0.921072i | \(-0.372685\pi\) | ||||
0.389393 | + | 0.921072i | \(0.372685\pi\) | |||||||
\(108\) | −0.396479 | −0.0381512 | ||||||||
\(109\) | −15.0474 | −1.44128 | −0.720638 | − | 0.693312i | \(-0.756151\pi\) | ||||
−0.720638 | + | 0.693312i | \(0.756151\pi\) | |||||||
\(110\) | 3.82599 | 0.364794 | ||||||||
\(111\) | 1.43691 | 0.136386 | ||||||||
\(112\) | 4.43846 | 0.419396 | ||||||||
\(113\) | −14.4370 | −1.35812 | −0.679062 | − | 0.734081i | \(-0.737613\pi\) | ||||
−0.679062 | + | 0.734081i | \(0.737613\pi\) | |||||||
\(114\) | −1.39288 | −0.130455 | ||||||||
\(115\) | −7.56441 | −0.705385 | ||||||||
\(116\) | −1.29969 | −0.120673 | ||||||||
\(117\) | −18.3795 | −1.69919 | ||||||||
\(118\) | 9.69993 | 0.892951 | ||||||||
\(119\) | −0.504865 | −0.0462809 | ||||||||
\(120\) | 0.700209 | 0.0639201 | ||||||||
\(121\) | −4.49599 | −0.408727 | ||||||||
\(122\) | −2.97927 | −0.269730 | ||||||||
\(123\) | −1.85033 | −0.166839 | ||||||||
\(124\) | 0.551127 | 0.0494926 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.39385 | −0.391435 | ||||||||
\(127\) | 12.9788 | 1.15168 | 0.575840 | − | 0.817562i | \(-0.304675\pi\) | ||||
0.575840 | + | 0.817562i | \(0.304675\pi\) | |||||||
\(128\) | −12.9639 | −1.14586 | ||||||||
\(129\) | 1.46109 | 0.128642 | ||||||||
\(130\) | −9.41448 | −0.825704 | ||||||||
\(131\) | −13.9304 | −1.21711 | −0.608553 | − | 0.793513i | \(-0.708250\pi\) | ||||
−0.608553 | + | 0.793513i | \(0.708250\pi\) | |||||||
\(132\) | −0.170547 | −0.0148442 | ||||||||
\(133\) | −3.47987 | −0.301743 | ||||||||
\(134\) | −12.9352 | −1.11743 | ||||||||
\(135\) | −1.58185 | −0.136144 | ||||||||
\(136\) | 1.32497 | 0.113615 | ||||||||
\(137\) | 1.96693 | 0.168046 | 0.0840231 | − | 0.996464i | \(-0.473223\pi\) | ||||
0.0840231 | + | 0.996464i | \(0.473223\pi\) | |||||||
\(138\) | 3.02778 | 0.257742 | ||||||||
\(139\) | 19.5592 | 1.65899 | 0.829496 | − | 0.558513i | \(-0.188628\pi\) | ||||
0.829496 | + | 0.558513i | \(0.188628\pi\) | |||||||
\(140\) | −0.250644 | −0.0211832 | ||||||||
\(141\) | 2.23822 | 0.188492 | ||||||||
\(142\) | 14.0768 | 1.18130 | ||||||||
\(143\) | −16.0042 | −1.33834 | ||||||||
\(144\) | 12.9994 | 1.08329 | ||||||||
\(145\) | −5.18542 | −0.430626 | ||||||||
\(146\) | −5.40263 | −0.447125 | ||||||||
\(147\) | 0.266806 | 0.0220058 | ||||||||
\(148\) | 1.34987 | 0.110958 | ||||||||
\(149\) | −8.31376 | −0.681090 | −0.340545 | − | 0.940228i | \(-0.610612\pi\) | ||||
−0.340545 | + | 0.940228i | \(0.610612\pi\) | |||||||
\(150\) | −0.400267 | −0.0326816 | ||||||||
\(151\) | 1.71856 | 0.139854 | 0.0699272 | − | 0.997552i | \(-0.477723\pi\) | ||||
0.0699272 | + | 0.997552i | \(0.477723\pi\) | |||||||
\(152\) | 9.13261 | 0.740753 | ||||||||
\(153\) | −1.47866 | −0.119542 | ||||||||
\(154\) | −3.82599 | −0.308307 | ||||||||
\(155\) | 2.19885 | 0.176616 | ||||||||
\(156\) | 0.419658 | 0.0335995 | ||||||||
\(157\) | −1.72011 | −0.137279 | −0.0686397 | − | 0.997642i | \(-0.521866\pi\) | ||||
−0.0686397 | + | 0.997642i | \(0.521866\pi\) | |||||||
\(158\) | 8.13867 | 0.647478 | ||||||||
\(159\) | −1.09155 | −0.0865658 | ||||||||
\(160\) | 1.40983 | 0.111457 | ||||||||
\(161\) | 7.56441 | 0.596159 | ||||||||
\(162\) | −12.5484 | −0.985895 | ||||||||
\(163\) | −24.6303 | −1.92920 | −0.964598 | − | 0.263726i | \(-0.915049\pi\) | ||||
−0.964598 | + | 0.263726i | \(0.915049\pi\) | |||||||
\(164\) | −1.73824 | −0.135734 | ||||||||
\(165\) | −0.680435 | −0.0529718 | ||||||||
\(166\) | −1.75320 | −0.136075 | ||||||||
\(167\) | −13.3179 | −1.03057 | −0.515285 | − | 0.857019i | \(-0.672314\pi\) | ||||
−0.515285 | + | 0.857019i | \(0.672314\pi\) | |||||||
\(168\) | −0.700209 | −0.0540223 | ||||||||
\(169\) | 26.3809 | 2.02930 | ||||||||
\(170\) | −0.757406 | −0.0580904 | ||||||||
\(171\) | −10.1919 | −0.779394 | ||||||||
\(172\) | 1.37258 | 0.104658 | ||||||||
\(173\) | −2.50942 | −0.190788 | −0.0953940 | − | 0.995440i | \(-0.530411\pi\) | ||||
−0.0953940 | + | 0.995440i | \(0.530411\pi\) | |||||||
\(174\) | 2.07555 | 0.157347 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 11.3194 | 0.853232 | ||||||||
\(177\) | −1.72509 | −0.129666 | ||||||||
\(178\) | −1.88368 | −0.141188 | ||||||||
\(179\) | 20.2006 | 1.50986 | 0.754932 | − | 0.655803i | \(-0.227670\pi\) | ||||
0.754932 | + | 0.655803i | \(0.227670\pi\) | |||||||
\(180\) | −0.734088 | −0.0547157 | ||||||||
\(181\) | 13.9823 | 1.03930 | 0.519649 | − | 0.854380i | \(-0.326063\pi\) | ||||
0.519649 | + | 0.854380i | \(0.326063\pi\) | |||||||
\(182\) | 9.41448 | 0.697848 | ||||||||
\(183\) | 0.529849 | 0.0391676 | ||||||||
\(184\) | −19.8521 | −1.46352 | ||||||||
\(185\) | 5.38561 | 0.395958 | ||||||||
\(186\) | −0.880125 | −0.0645339 | ||||||||
\(187\) | −1.28755 | −0.0941553 | ||||||||
\(188\) | 2.10263 | 0.153350 | ||||||||
\(189\) | 1.58185 | 0.115062 | ||||||||
\(190\) | −5.22055 | −0.378739 | ||||||||
\(191\) | −16.3439 | −1.18261 | −0.591303 | − | 0.806450i | \(-0.701386\pi\) | ||||
−0.591303 | + | 0.806450i | \(0.701386\pi\) | |||||||
\(192\) | 1.80411 | 0.130201 | ||||||||
\(193\) | 12.0381 | 0.866519 | 0.433260 | − | 0.901269i | \(-0.357363\pi\) | ||||
0.433260 | + | 0.901269i | \(0.357363\pi\) | |||||||
\(194\) | −27.2966 | −1.95978 | ||||||||
\(195\) | 1.67432 | 0.119901 | ||||||||
\(196\) | 0.250644 | 0.0179031 | ||||||||
\(197\) | 20.7841 | 1.48081 | 0.740403 | − | 0.672164i | \(-0.234635\pi\) | ||||
0.740403 | + | 0.672164i | \(0.234635\pi\) | |||||||
\(198\) | −11.2056 | −0.796348 | ||||||||
\(199\) | −19.1145 | −1.35499 | −0.677496 | − | 0.735527i | \(-0.736935\pi\) | ||||
−0.677496 | + | 0.735527i | \(0.736935\pi\) | |||||||
\(200\) | 2.62441 | 0.185574 | ||||||||
\(201\) | 2.30047 | 0.162263 | ||||||||
\(202\) | −5.40948 | −0.380609 | ||||||||
\(203\) | 5.18542 | 0.363945 | ||||||||
\(204\) | 0.0337620 | 0.00236381 | ||||||||
\(205\) | −6.93512 | −0.484370 | ||||||||
\(206\) | 1.04027 | 0.0724789 | ||||||||
\(207\) | 22.1548 | 1.53986 | ||||||||
\(208\) | −27.8532 | −1.93127 | ||||||||
\(209\) | −8.87470 | −0.613876 | ||||||||
\(210\) | 0.400267 | 0.0276210 | ||||||||
\(211\) | 17.0273 | 1.17221 | 0.586104 | − | 0.810236i | \(-0.300661\pi\) | ||||
0.586104 | + | 0.810236i | \(0.300661\pi\) | |||||||
\(212\) | −1.02543 | −0.0704267 | ||||||||
\(213\) | −2.50350 | −0.171537 | ||||||||
\(214\) | −12.0855 | −0.826145 | ||||||||
\(215\) | 5.47623 | 0.373476 | ||||||||
\(216\) | −4.15141 | −0.282468 | ||||||||
\(217\) | −2.19885 | −0.149267 | ||||||||
\(218\) | 22.5743 | 1.52892 | ||||||||
\(219\) | 0.960834 | 0.0649271 | ||||||||
\(220\) | −0.639215 | −0.0430959 | ||||||||
\(221\) | 3.16824 | 0.213119 | ||||||||
\(222\) | −2.15568 | −0.144680 | ||||||||
\(223\) | 15.6832 | 1.05022 | 0.525112 | − | 0.851033i | \(-0.324023\pi\) | ||||
0.525112 | + | 0.851033i | \(0.324023\pi\) | |||||||
\(224\) | −1.40983 | −0.0941982 | ||||||||
\(225\) | −2.92881 | −0.195254 | ||||||||
\(226\) | 21.6587 | 1.44071 | ||||||||
\(227\) | 11.0446 | 0.733059 | 0.366529 | − | 0.930406i | \(-0.380546\pi\) | ||||
0.366529 | + | 0.930406i | \(0.380546\pi\) | |||||||
\(228\) | 0.232710 | 0.0154116 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | 11.3482 | 0.748281 | ||||||||
\(231\) | 0.680435 | 0.0447693 | ||||||||
\(232\) | −13.6087 | −0.893453 | ||||||||
\(233\) | 6.05794 | 0.396869 | 0.198434 | − | 0.980114i | \(-0.436414\pi\) | ||||
0.198434 | + | 0.980114i | \(0.436414\pi\) | |||||||
\(234\) | 27.5733 | 1.80252 | ||||||||
\(235\) | 8.38893 | 0.547233 | ||||||||
\(236\) | −1.62058 | −0.105491 | ||||||||
\(237\) | −1.44743 | −0.0940204 | ||||||||
\(238\) | 0.757406 | 0.0490953 | ||||||||
\(239\) | 20.8162 | 1.34649 | 0.673244 | − | 0.739421i | \(-0.264900\pi\) | ||||
0.673244 | + | 0.739421i | \(0.264900\pi\) | |||||||
\(240\) | −1.18421 | −0.0764405 | ||||||||
\(241\) | −4.38625 | −0.282543 | −0.141272 | − | 0.989971i | \(-0.545119\pi\) | ||||
−0.141272 | + | 0.989971i | \(0.545119\pi\) | |||||||
\(242\) | 6.74495 | 0.433582 | ||||||||
\(243\) | 6.97721 | 0.447588 | ||||||||
\(244\) | 0.497752 | 0.0318653 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 2.77590 | 0.176985 | ||||||||
\(247\) | 21.8377 | 1.38950 | ||||||||
\(248\) | 5.77067 | 0.366438 | ||||||||
\(249\) | 0.311799 | 0.0197595 | ||||||||
\(250\) | −1.50021 | −0.0948819 | ||||||||
\(251\) | −4.60395 | −0.290599 | −0.145299 | − | 0.989388i | \(-0.546415\pi\) | ||||
−0.145299 | + | 0.989388i | \(0.546415\pi\) | |||||||
\(252\) | 0.734088 | 0.0462432 | ||||||||
\(253\) | 19.2915 | 1.21285 | ||||||||
\(254\) | −19.4709 | −1.22172 | ||||||||
\(255\) | 0.134701 | 0.00843531 | ||||||||
\(256\) | 5.92492 | 0.370307 | ||||||||
\(257\) | 23.5742 | 1.47052 | 0.735259 | − | 0.677786i | \(-0.237061\pi\) | ||||
0.735259 | + | 0.677786i | \(0.237061\pi\) | |||||||
\(258\) | −2.19195 | −0.136465 | ||||||||
\(259\) | −5.38561 | −0.334646 | ||||||||
\(260\) | 1.57289 | 0.0975467 | ||||||||
\(261\) | 15.1871 | 0.940060 | ||||||||
\(262\) | 20.8986 | 1.29112 | ||||||||
\(263\) | 3.54528 | 0.218611 | 0.109306 | − | 0.994008i | \(-0.465137\pi\) | ||||
0.109306 | + | 0.994008i | \(0.465137\pi\) | |||||||
\(264\) | −1.78574 | −0.109905 | ||||||||
\(265\) | −4.09118 | −0.251319 | ||||||||
\(266\) | 5.22055 | 0.320093 | ||||||||
\(267\) | 0.335004 | 0.0205019 | ||||||||
\(268\) | 2.16111 | 0.132011 | ||||||||
\(269\) | −5.26431 | −0.320971 | −0.160485 | − | 0.987038i | \(-0.551306\pi\) | ||||
−0.160485 | + | 0.987038i | \(0.551306\pi\) | |||||||
\(270\) | 2.37311 | 0.144423 | ||||||||
\(271\) | −2.88615 | −0.175321 | −0.0876605 | − | 0.996150i | \(-0.527939\pi\) | ||||
−0.0876605 | + | 0.996150i | \(0.527939\pi\) | |||||||
\(272\) | −2.24083 | −0.135870 | ||||||||
\(273\) | −1.67432 | −0.101335 | ||||||||
\(274\) | −2.95082 | −0.178265 | ||||||||
\(275\) | −2.55030 | −0.153789 | ||||||||
\(276\) | −0.505857 | −0.0304490 | ||||||||
\(277\) | 1.36957 | 0.0822892 | 0.0411446 | − | 0.999153i | \(-0.486900\pi\) | ||||
0.0411446 | + | 0.999153i | \(0.486900\pi\) | |||||||
\(278\) | −29.3430 | −1.75988 | ||||||||
\(279\) | −6.44001 | −0.385553 | ||||||||
\(280\) | −2.62441 | −0.156838 | ||||||||
\(281\) | 13.5515 | 0.808416 | 0.404208 | − | 0.914667i | \(-0.367547\pi\) | ||||
0.404208 | + | 0.914667i | \(0.367547\pi\) | |||||||
\(282\) | −3.35781 | −0.199955 | ||||||||
\(283\) | −6.77186 | −0.402545 | −0.201273 | − | 0.979535i | \(-0.564508\pi\) | ||||
−0.201273 | + | 0.979535i | \(0.564508\pi\) | |||||||
\(284\) | −2.35184 | −0.139556 | ||||||||
\(285\) | 0.928452 | 0.0549967 | ||||||||
\(286\) | 24.0097 | 1.41972 | ||||||||
\(287\) | 6.93512 | 0.409367 | ||||||||
\(288\) | −4.12913 | −0.243311 | ||||||||
\(289\) | −16.7451 | −0.985007 | ||||||||
\(290\) | 7.77924 | 0.456813 | ||||||||
\(291\) | 4.85458 | 0.284580 | ||||||||
\(292\) | 0.902628 | 0.0528223 | ||||||||
\(293\) | −7.32664 | −0.428027 | −0.214013 | − | 0.976831i | \(-0.568654\pi\) | ||||
−0.214013 | + | 0.976831i | \(0.568654\pi\) | |||||||
\(294\) | −0.400267 | −0.0233440 | ||||||||
\(295\) | −6.46570 | −0.376447 | ||||||||
\(296\) | 14.1340 | 0.821525 | ||||||||
\(297\) | 4.03417 | 0.234086 | ||||||||
\(298\) | 12.4724 | 0.722508 | ||||||||
\(299\) | −47.4699 | −2.74525 | ||||||||
\(300\) | 0.0668733 | 0.00386093 | ||||||||
\(301\) | −5.47623 | −0.315645 | ||||||||
\(302\) | −2.57821 | −0.148359 | ||||||||
\(303\) | 0.962051 | 0.0552684 | ||||||||
\(304\) | −15.4453 | −0.885848 | ||||||||
\(305\) | 1.98590 | 0.113712 | ||||||||
\(306\) | 2.21830 | 0.126812 | ||||||||
\(307\) | −10.8411 | −0.618736 | −0.309368 | − | 0.950942i | \(-0.600117\pi\) | ||||
−0.309368 | + | 0.950942i | \(0.600117\pi\) | |||||||
\(308\) | 0.639215 | 0.0364227 | ||||||||
\(309\) | −0.185007 | −0.0105247 | ||||||||
\(310\) | −3.29874 | −0.187356 | ||||||||
\(311\) | −11.4789 | −0.650907 | −0.325454 | − | 0.945558i | \(-0.605517\pi\) | ||||
−0.325454 | + | 0.945558i | \(0.605517\pi\) | |||||||
\(312\) | 4.39411 | 0.248767 | ||||||||
\(313\) | −23.4091 | −1.32316 | −0.661581 | − | 0.749874i | \(-0.730114\pi\) | ||||
−0.661581 | + | 0.749874i | \(0.730114\pi\) | |||||||
\(314\) | 2.58053 | 0.145628 | ||||||||
\(315\) | 2.92881 | 0.165020 | ||||||||
\(316\) | −1.35974 | −0.0764915 | ||||||||
\(317\) | 15.7970 | 0.887248 | 0.443624 | − | 0.896213i | \(-0.353693\pi\) | ||||
0.443624 | + | 0.896213i | \(0.353693\pi\) | |||||||
\(318\) | 1.63756 | 0.0918300 | ||||||||
\(319\) | 13.2244 | 0.740422 | ||||||||
\(320\) | 6.76188 | 0.378001 | ||||||||
\(321\) | 2.14934 | 0.119965 | ||||||||
\(322\) | −11.3482 | −0.632413 | ||||||||
\(323\) | 1.75687 | 0.0977546 | ||||||||
\(324\) | 2.09648 | 0.116471 | ||||||||
\(325\) | 6.27542 | 0.348098 | ||||||||
\(326\) | 36.9508 | 2.04651 | ||||||||
\(327\) | −4.01473 | −0.222015 | ||||||||
\(328\) | −18.2006 | −1.00496 | ||||||||
\(329\) | −8.38893 | −0.462497 | ||||||||
\(330\) | 1.02080 | 0.0561931 | ||||||||
\(331\) | 16.1759 | 0.889110 | 0.444555 | − | 0.895751i | \(-0.353362\pi\) | ||||
0.444555 | + | 0.895751i | \(0.353362\pi\) | |||||||
\(332\) | 0.292911 | 0.0160756 | ||||||||
\(333\) | −15.7735 | −0.864380 | ||||||||
\(334\) | 19.9797 | 1.09324 | ||||||||
\(335\) | 8.62225 | 0.471084 | ||||||||
\(336\) | 1.18421 | 0.0646040 | ||||||||
\(337\) | 24.6685 | 1.34378 | 0.671890 | − | 0.740651i | \(-0.265483\pi\) | ||||
0.671890 | + | 0.740651i | \(0.265483\pi\) | |||||||
\(338\) | −39.5770 | −2.15271 | ||||||||
\(339\) | −3.85190 | −0.209206 | ||||||||
\(340\) | 0.126541 | 0.00686266 | ||||||||
\(341\) | −5.60771 | −0.303674 | ||||||||
\(342\) | 15.2900 | 0.826790 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 14.3719 | 0.774879 | ||||||||
\(345\) | −2.01823 | −0.108658 | ||||||||
\(346\) | 3.76468 | 0.202390 | ||||||||
\(347\) | −5.07605 | −0.272497 | −0.136248 | − | 0.990675i | \(-0.543504\pi\) | ||||
−0.136248 | + | 0.990675i | \(0.543504\pi\) | |||||||
\(348\) | −0.346766 | −0.0185886 | ||||||||
\(349\) | 0.670535 | 0.0358929 | 0.0179465 | − | 0.999839i | \(-0.494287\pi\) | ||||
0.0179465 | + | 0.999839i | \(0.494287\pi\) | |||||||
\(350\) | 1.50021 | 0.0801898 | ||||||||
\(351\) | −9.92674 | −0.529850 | ||||||||
\(352\) | −3.59548 | −0.191640 | ||||||||
\(353\) | 24.4851 | 1.30321 | 0.651605 | − | 0.758558i | \(-0.274096\pi\) | ||||
0.651605 | + | 0.758558i | \(0.274096\pi\) | |||||||
\(354\) | 2.58800 | 0.137551 | ||||||||
\(355\) | −9.38322 | −0.498010 | ||||||||
\(356\) | 0.314710 | 0.0166796 | ||||||||
\(357\) | −0.134701 | −0.00712914 | ||||||||
\(358\) | −30.3052 | −1.60168 | ||||||||
\(359\) | 32.6609 | 1.72378 | 0.861889 | − | 0.507097i | \(-0.169281\pi\) | ||||
0.861889 | + | 0.507097i | \(0.169281\pi\) | |||||||
\(360\) | −7.68641 | −0.405109 | ||||||||
\(361\) | −6.89049 | −0.362657 | ||||||||
\(362\) | −20.9765 | −1.10250 | ||||||||
\(363\) | −1.19956 | −0.0629605 | ||||||||
\(364\) | −1.57289 | −0.0824420 | ||||||||
\(365\) | 3.60124 | 0.188498 | ||||||||
\(366\) | −0.794888 | −0.0415494 | ||||||||
\(367\) | −18.0468 | −0.942033 | −0.471017 | − | 0.882124i | \(-0.656113\pi\) | ||||
−0.471017 | + | 0.882124i | \(0.656113\pi\) | |||||||
\(368\) | 33.5744 | 1.75019 | ||||||||
\(369\) | 20.3117 | 1.05738 | ||||||||
\(370\) | −8.07957 | −0.420037 | ||||||||
\(371\) | 4.09118 | 0.212404 | ||||||||
\(372\) | 0.147044 | 0.00762388 | ||||||||
\(373\) | −1.39975 | −0.0724763 | −0.0362381 | − | 0.999343i | \(-0.511537\pi\) | ||||
−0.0362381 | + | 0.999343i | \(0.511537\pi\) | |||||||
\(374\) | 1.93161 | 0.0998811 | ||||||||
\(375\) | 0.266806 | 0.0137778 | ||||||||
\(376\) | 22.0160 | 1.13539 | ||||||||
\(377\) | −32.5407 | −1.67593 | ||||||||
\(378\) | −2.37311 | −0.122059 | ||||||||
\(379\) | −6.54587 | −0.336239 | −0.168120 | − | 0.985767i | \(-0.553769\pi\) | ||||
−0.168120 | + | 0.985767i | \(0.553769\pi\) | |||||||
\(380\) | 0.872207 | 0.0447433 | ||||||||
\(381\) | 3.46282 | 0.177406 | ||||||||
\(382\) | 24.5194 | 1.25452 | ||||||||
\(383\) | −20.0299 | −1.02348 | −0.511741 | − | 0.859140i | \(-0.670999\pi\) | ||||
−0.511741 | + | 0.859140i | \(0.670999\pi\) | |||||||
\(384\) | −3.45886 | −0.176509 | ||||||||
\(385\) | 2.55030 | 0.129975 | ||||||||
\(386\) | −18.0597 | −0.919214 | ||||||||
\(387\) | −16.0389 | −0.815301 | ||||||||
\(388\) | 4.56049 | 0.231524 | ||||||||
\(389\) | −0.889458 | −0.0450973 | −0.0225486 | − | 0.999746i | \(-0.507178\pi\) | ||||
−0.0225486 | + | 0.999746i | \(0.507178\pi\) | |||||||
\(390\) | −2.51184 | −0.127192 | ||||||||
\(391\) | −3.81901 | −0.193136 | ||||||||
\(392\) | 2.62441 | 0.132553 | ||||||||
\(393\) | −3.71672 | −0.187484 | ||||||||
\(394\) | −31.1806 | −1.57086 | ||||||||
\(395\) | −5.42500 | −0.272962 | ||||||||
\(396\) | 1.87214 | 0.0940787 | ||||||||
\(397\) | −4.67200 | −0.234481 | −0.117240 | − | 0.993104i | \(-0.537405\pi\) | ||||
−0.117240 | + | 0.993104i | \(0.537405\pi\) | |||||||
\(398\) | 28.6759 | 1.43739 | ||||||||
\(399\) | −0.928452 | −0.0464807 | ||||||||
\(400\) | −4.43846 | −0.221923 | ||||||||
\(401\) | 8.54573 | 0.426753 | 0.213377 | − | 0.976970i | \(-0.431554\pi\) | ||||
0.213377 | + | 0.976970i | \(0.431554\pi\) | |||||||
\(402\) | −3.45120 | −0.172130 | ||||||||
\(403\) | 13.7987 | 0.687362 | ||||||||
\(404\) | 0.903771 | 0.0449643 | ||||||||
\(405\) | 8.36440 | 0.415630 | ||||||||
\(406\) | −7.77924 | −0.386077 | ||||||||
\(407\) | −13.7349 | −0.680814 | ||||||||
\(408\) | 0.353511 | 0.0175014 | ||||||||
\(409\) | −15.5282 | −0.767821 | −0.383911 | − | 0.923370i | \(-0.625423\pi\) | ||||
−0.383911 | + | 0.923370i | \(0.625423\pi\) | |||||||
\(410\) | 10.4042 | 0.513825 | ||||||||
\(411\) | 0.524789 | 0.0258859 | ||||||||
\(412\) | −0.173799 | −0.00856248 | ||||||||
\(413\) | 6.46570 | 0.318156 | ||||||||
\(414\) | −33.2369 | −1.63350 | ||||||||
\(415\) | 1.16863 | 0.0573660 | ||||||||
\(416\) | 8.84727 | 0.433773 | ||||||||
\(417\) | 5.21852 | 0.255552 | ||||||||
\(418\) | 13.3140 | 0.651207 | ||||||||
\(419\) | 36.5913 | 1.78760 | 0.893802 | − | 0.448461i | \(-0.148028\pi\) | ||||
0.893802 | + | 0.448461i | \(0.148028\pi\) | |||||||
\(420\) | −0.0668733 | −0.00326308 | ||||||||
\(421\) | 27.5923 | 1.34477 | 0.672384 | − | 0.740203i | \(-0.265271\pi\) | ||||
0.672384 | + | 0.740203i | \(0.265271\pi\) | |||||||
\(422\) | −25.5446 | −1.24349 | ||||||||
\(423\) | −24.5696 | −1.19462 | ||||||||
\(424\) | −10.7369 | −0.521432 | ||||||||
\(425\) | 0.504865 | 0.0244895 | ||||||||
\(426\) | 3.75579 | 0.181969 | ||||||||
\(427\) | −1.98590 | −0.0961042 | ||||||||
\(428\) | 2.01914 | 0.0975988 | ||||||||
\(429\) | −4.27002 | −0.206158 | ||||||||
\(430\) | −8.21552 | −0.396188 | ||||||||
\(431\) | 20.0442 | 0.965495 | 0.482748 | − | 0.875759i | \(-0.339639\pi\) | ||||
0.482748 | + | 0.875759i | \(0.339639\pi\) | |||||||
\(432\) | 7.02096 | 0.337796 | ||||||||
\(433\) | −1.00206 | −0.0481560 | −0.0240780 | − | 0.999710i | \(-0.507665\pi\) | ||||
−0.0240780 | + | 0.999710i | \(0.507665\pi\) | |||||||
\(434\) | 3.29874 | 0.158345 | ||||||||
\(435\) | −1.38350 | −0.0663339 | ||||||||
\(436\) | −3.77152 | −0.180623 | ||||||||
\(437\) | −26.3232 | −1.25921 | ||||||||
\(438\) | −1.44146 | −0.0688755 | ||||||||
\(439\) | 7.65740 | 0.365468 | 0.182734 | − | 0.983162i | \(-0.441505\pi\) | ||||
0.182734 | + | 0.983162i | \(0.441505\pi\) | |||||||
\(440\) | −6.69302 | −0.319077 | ||||||||
\(441\) | −2.92881 | −0.139467 | ||||||||
\(442\) | −4.75304 | −0.226079 | ||||||||
\(443\) | −4.54703 | −0.216036 | −0.108018 | − | 0.994149i | \(-0.534450\pi\) | ||||
−0.108018 | + | 0.994149i | \(0.534450\pi\) | |||||||
\(444\) | 0.360153 | 0.0170921 | ||||||||
\(445\) | 1.25561 | 0.0595215 | ||||||||
\(446\) | −23.5282 | −1.11409 | ||||||||
\(447\) | −2.21816 | −0.104916 | ||||||||
\(448\) | −6.76188 | −0.319469 | ||||||||
\(449\) | 11.7624 | 0.555100 | 0.277550 | − | 0.960711i | \(-0.410478\pi\) | ||||
0.277550 | + | 0.960711i | \(0.410478\pi\) | |||||||
\(450\) | 4.39385 | 0.207128 | ||||||||
\(451\) | 17.6866 | 0.832830 | ||||||||
\(452\) | −3.61855 | −0.170202 | ||||||||
\(453\) | 0.458523 | 0.0215433 | ||||||||
\(454\) | −16.5693 | −0.777638 | ||||||||
\(455\) | −6.27542 | −0.294196 | ||||||||
\(456\) | 2.43664 | 0.114106 | ||||||||
\(457\) | −0.717119 | −0.0335454 | −0.0167727 | − | 0.999859i | \(-0.505339\pi\) | ||||
−0.0167727 | + | 0.999859i | \(0.505339\pi\) | |||||||
\(458\) | 1.50021 | 0.0701004 | ||||||||
\(459\) | −0.798618 | −0.0372763 | ||||||||
\(460\) | −1.89597 | −0.0884001 | ||||||||
\(461\) | 39.9072 | 1.85866 | 0.929331 | − | 0.369247i | \(-0.120385\pi\) | ||||
0.929331 | + | 0.369247i | \(0.120385\pi\) | |||||||
\(462\) | −1.02080 | −0.0474918 | ||||||||
\(463\) | −34.9321 | −1.62343 | −0.811716 | − | 0.584053i | \(-0.801466\pi\) | ||||
−0.811716 | + | 0.584053i | \(0.801466\pi\) | |||||||
\(464\) | 23.0153 | 1.06846 | ||||||||
\(465\) | 0.586666 | 0.0272060 | ||||||||
\(466\) | −9.08821 | −0.421003 | ||||||||
\(467\) | 13.5806 | 0.628434 | 0.314217 | − | 0.949351i | \(-0.398258\pi\) | ||||
0.314217 | + | 0.949351i | \(0.398258\pi\) | |||||||
\(468\) | −4.60671 | −0.212945 | ||||||||
\(469\) | −8.62225 | −0.398139 | ||||||||
\(470\) | −12.5852 | −0.580512 | ||||||||
\(471\) | −0.458935 | −0.0211466 | ||||||||
\(472\) | −16.9686 | −0.781045 | ||||||||
\(473\) | −13.9660 | −0.642158 | ||||||||
\(474\) | 2.17145 | 0.0997379 | ||||||||
\(475\) | 3.47987 | 0.159667 | ||||||||
\(476\) | −0.126541 | −0.00580000 | ||||||||
\(477\) | 11.9823 | 0.548632 | ||||||||
\(478\) | −31.2288 | −1.42837 | ||||||||
\(479\) | −34.2006 | −1.56266 | −0.781332 | − | 0.624116i | \(-0.785459\pi\) | ||||
−0.781332 | + | 0.624116i | \(0.785459\pi\) | |||||||
\(480\) | 0.376151 | 0.0171689 | ||||||||
\(481\) | 33.7970 | 1.54101 | ||||||||
\(482\) | 6.58032 | 0.299725 | ||||||||
\(483\) | 2.01823 | 0.0918328 | ||||||||
\(484\) | −1.12689 | −0.0512223 | ||||||||
\(485\) | 18.1951 | 0.826199 | ||||||||
\(486\) | −10.4673 | −0.474807 | ||||||||
\(487\) | −38.5276 | −1.74585 | −0.872925 | − | 0.487854i | \(-0.837780\pi\) | ||||
−0.872925 | + | 0.487854i | \(0.837780\pi\) | |||||||
\(488\) | 5.21180 | 0.235927 | ||||||||
\(489\) | −6.57152 | −0.297175 | ||||||||
\(490\) | −1.50021 | −0.0677728 | ||||||||
\(491\) | −3.60129 | −0.162524 | −0.0812619 | − | 0.996693i | \(-0.525895\pi\) | ||||
−0.0812619 | + | 0.996693i | \(0.525895\pi\) | |||||||
\(492\) | −0.463774 | −0.0209086 | ||||||||
\(493\) | −2.61794 | −0.117906 | ||||||||
\(494\) | −32.7612 | −1.47400 | ||||||||
\(495\) | 7.46934 | 0.335722 | ||||||||
\(496\) | −9.75950 | −0.438215 | ||||||||
\(497\) | 9.38322 | 0.420895 | ||||||||
\(498\) | −0.467766 | −0.0209611 | ||||||||
\(499\) | 7.90035 | 0.353668 | 0.176834 | − | 0.984241i | \(-0.443414\pi\) | ||||
0.176834 | + | 0.984241i | \(0.443414\pi\) | |||||||
\(500\) | 0.250644 | 0.0112091 | ||||||||
\(501\) | −3.55330 | −0.158750 | ||||||||
\(502\) | 6.90691 | 0.308270 | ||||||||
\(503\) | 4.07786 | 0.181823 | 0.0909113 | − | 0.995859i | \(-0.471022\pi\) | ||||
0.0909113 | + | 0.995859i | \(0.471022\pi\) | |||||||
\(504\) | 7.68641 | 0.342380 | ||||||||
\(505\) | 3.60580 | 0.160456 | ||||||||
\(506\) | −28.9414 | −1.28660 | ||||||||
\(507\) | 7.03859 | 0.312595 | ||||||||
\(508\) | 3.25305 | 0.144331 | ||||||||
\(509\) | 28.1655 | 1.24842 | 0.624208 | − | 0.781259i | \(-0.285422\pi\) | ||||
0.624208 | + | 0.781259i | \(0.285422\pi\) | |||||||
\(510\) | −0.202081 | −0.00894828 | ||||||||
\(511\) | −3.60124 | −0.159309 | ||||||||
\(512\) | 17.0392 | 0.753034 | ||||||||
\(513\) | −5.50462 | −0.243035 | ||||||||
\(514\) | −35.3663 | −1.55994 | ||||||||
\(515\) | −0.693412 | −0.0305554 | ||||||||
\(516\) | 0.366213 | 0.0161216 | ||||||||
\(517\) | −21.3942 | −0.940918 | ||||||||
\(518\) | 8.07957 | 0.354996 | ||||||||
\(519\) | −0.669530 | −0.0293891 | ||||||||
\(520\) | 16.4693 | 0.722226 | ||||||||
\(521\) | 4.45422 | 0.195143 | 0.0975715 | − | 0.995229i | \(-0.468893\pi\) | ||||
0.0975715 | + | 0.995229i | \(0.468893\pi\) | |||||||
\(522\) | −22.7840 | −0.997227 | ||||||||
\(523\) | 14.1787 | 0.619992 | 0.309996 | − | 0.950738i | \(-0.399672\pi\) | ||||
0.309996 | + | 0.950738i | \(0.399672\pi\) | |||||||
\(524\) | −3.49157 | −0.152530 | ||||||||
\(525\) | −0.266806 | −0.0116444 | ||||||||
\(526\) | −5.31868 | −0.231905 | ||||||||
\(527\) | 1.11012 | 0.0483576 | ||||||||
\(528\) | 3.02009 | 0.131432 | ||||||||
\(529\) | 34.2204 | 1.48784 | ||||||||
\(530\) | 6.13765 | 0.266602 | ||||||||
\(531\) | 18.9368 | 0.821788 | ||||||||
\(532\) | −0.872207 | −0.0378150 | ||||||||
\(533\) | −43.5208 | −1.88510 | ||||||||
\(534\) | −0.502578 | −0.0217487 | ||||||||
\(535\) | 8.05582 | 0.348284 | ||||||||
\(536\) | 22.6283 | 0.977395 | ||||||||
\(537\) | 5.38965 | 0.232581 | ||||||||
\(538\) | 7.89760 | 0.340490 | ||||||||
\(539\) | −2.55030 | −0.109849 | ||||||||
\(540\) | −0.396479 | −0.0170617 | ||||||||
\(541\) | −7.84973 | −0.337486 | −0.168743 | − | 0.985660i | \(-0.553971\pi\) | ||||
−0.168743 | + | 0.985660i | \(0.553971\pi\) | |||||||
\(542\) | 4.32984 | 0.185983 | ||||||||
\(543\) | 3.73057 | 0.160094 | ||||||||
\(544\) | 0.711773 | 0.0305170 | ||||||||
\(545\) | −15.0474 | −0.644558 | ||||||||
\(546\) | 2.51184 | 0.107497 | ||||||||
\(547\) | −8.17810 | −0.349670 | −0.174835 | − | 0.984598i | \(-0.555939\pi\) | ||||
−0.174835 | + | 0.984598i | \(0.555939\pi\) | |||||||
\(548\) | 0.492998 | 0.0210598 | ||||||||
\(549\) | −5.81632 | −0.248234 | ||||||||
\(550\) | 3.82599 | 0.163141 | ||||||||
\(551\) | −18.0446 | −0.768726 | ||||||||
\(552\) | −5.29667 | −0.225441 | ||||||||
\(553\) | 5.42500 | 0.230695 | ||||||||
\(554\) | −2.05464 | −0.0872934 | ||||||||
\(555\) | 1.43691 | 0.0609936 | ||||||||
\(556\) | 4.90239 | 0.207908 | ||||||||
\(557\) | 46.3539 | 1.96408 | 0.982039 | − | 0.188677i | \(-0.0604200\pi\) | ||||
0.982039 | + | 0.188677i | \(0.0604200\pi\) | |||||||
\(558\) | 9.66140 | 0.409000 | ||||||||
\(559\) | 34.3656 | 1.45351 | ||||||||
\(560\) | 4.43846 | 0.187559 | ||||||||
\(561\) | −0.343528 | −0.0145038 | ||||||||
\(562\) | −20.3302 | −0.857577 | ||||||||
\(563\) | 16.7672 | 0.706654 | 0.353327 | − | 0.935500i | \(-0.385050\pi\) | ||||
0.353327 | + | 0.935500i | \(0.385050\pi\) | |||||||
\(564\) | 0.560995 | 0.0236222 | ||||||||
\(565\) | −14.4370 | −0.607371 | ||||||||
\(566\) | 10.1592 | 0.427025 | ||||||||
\(567\) | −8.36440 | −0.351272 | ||||||||
\(568\) | −24.6254 | −1.03326 | ||||||||
\(569\) | 27.8896 | 1.16919 | 0.584597 | − | 0.811324i | \(-0.301253\pi\) | ||||
0.584597 | + | 0.811324i | \(0.301253\pi\) | |||||||
\(570\) | −1.39288 | −0.0583412 | ||||||||
\(571\) | 20.3398 | 0.851195 | 0.425597 | − | 0.904913i | \(-0.360064\pi\) | ||||
0.425597 | + | 0.904913i | \(0.360064\pi\) | |||||||
\(572\) | −4.01134 | −0.167723 | ||||||||
\(573\) | −4.36066 | −0.182169 | ||||||||
\(574\) | −10.4042 | −0.434262 | ||||||||
\(575\) | −7.56441 | −0.315458 | ||||||||
\(576\) | −19.8043 | −0.825179 | ||||||||
\(577\) | 8.06791 | 0.335872 | 0.167936 | − | 0.985798i | \(-0.446290\pi\) | ||||
0.167936 | + | 0.985798i | \(0.446290\pi\) | |||||||
\(578\) | 25.1213 | 1.04491 | ||||||||
\(579\) | 3.21183 | 0.133479 | ||||||||
\(580\) | −1.29969 | −0.0539668 | ||||||||
\(581\) | −1.16863 | −0.0484831 | ||||||||
\(582\) | −7.28291 | −0.301886 | ||||||||
\(583\) | 10.4337 | 0.432121 | ||||||||
\(584\) | 9.45113 | 0.391091 | ||||||||
\(585\) | −18.3795 | −0.759901 | ||||||||
\(586\) | 10.9915 | 0.454056 | ||||||||
\(587\) | 13.9056 | 0.573945 | 0.286972 | − | 0.957939i | \(-0.407351\pi\) | ||||
0.286972 | + | 0.957939i | \(0.407351\pi\) | |||||||
\(588\) | 0.0668733 | 0.00275781 | ||||||||
\(589\) | 7.65170 | 0.315283 | ||||||||
\(590\) | 9.69993 | 0.399340 | ||||||||
\(591\) | 5.54533 | 0.228104 | ||||||||
\(592\) | −23.9038 | −0.982442 | ||||||||
\(593\) | 25.1526 | 1.03289 | 0.516447 | − | 0.856319i | \(-0.327254\pi\) | ||||
0.516447 | + | 0.856319i | \(0.327254\pi\) | |||||||
\(594\) | −6.05212 | −0.248322 | ||||||||
\(595\) | −0.504865 | −0.0206974 | ||||||||
\(596\) | −2.08379 | −0.0853554 | ||||||||
\(597\) | −5.09987 | −0.208724 | ||||||||
\(598\) | 71.2150 | 2.91220 | ||||||||
\(599\) | 36.0591 | 1.47333 | 0.736667 | − | 0.676256i | \(-0.236399\pi\) | ||||
0.736667 | + | 0.676256i | \(0.236399\pi\) | |||||||
\(600\) | 0.700209 | 0.0285859 | ||||||||
\(601\) | 41.8375 | 1.70659 | 0.853294 | − | 0.521430i | \(-0.174601\pi\) | ||||
0.853294 | + | 0.521430i | \(0.174601\pi\) | |||||||
\(602\) | 8.21552 | 0.334840 | ||||||||
\(603\) | −25.2530 | −1.02838 | ||||||||
\(604\) | 0.430746 | 0.0175268 | ||||||||
\(605\) | −4.49599 | −0.182788 | ||||||||
\(606\) | −1.44328 | −0.0586293 | ||||||||
\(607\) | −37.5804 | −1.52534 | −0.762670 | − | 0.646788i | \(-0.776112\pi\) | ||||
−0.762670 | + | 0.646788i | \(0.776112\pi\) | |||||||
\(608\) | 4.90603 | 0.198966 | ||||||||
\(609\) | 1.38350 | 0.0560624 | ||||||||
\(610\) | −2.97927 | −0.120627 | ||||||||
\(611\) | 52.6441 | 2.12975 | ||||||||
\(612\) | −0.370615 | −0.0149812 | ||||||||
\(613\) | 42.0722 | 1.69928 | 0.849641 | − | 0.527362i | \(-0.176819\pi\) | ||||
0.849641 | + | 0.527362i | \(0.176819\pi\) | |||||||
\(614\) | 16.2640 | 0.656362 | ||||||||
\(615\) | −1.85033 | −0.0746127 | ||||||||
\(616\) | 6.69302 | 0.269670 | ||||||||
\(617\) | −31.2591 | −1.25844 | −0.629222 | − | 0.777226i | \(-0.716626\pi\) | ||||
−0.629222 | + | 0.777226i | \(0.716626\pi\) | |||||||
\(618\) | 0.277550 | 0.0111647 | ||||||||
\(619\) | 16.0603 | 0.645517 | 0.322758 | − | 0.946481i | \(-0.395390\pi\) | ||||
0.322758 | + | 0.946481i | \(0.395390\pi\) | |||||||
\(620\) | 0.551127 | 0.0221338 | ||||||||
\(621\) | 11.9657 | 0.480168 | ||||||||
\(622\) | 17.2208 | 0.690490 | ||||||||
\(623\) | −1.25561 | −0.0503049 | ||||||||
\(624\) | −7.43142 | −0.297495 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 35.1187 | 1.40362 | ||||||||
\(627\) | −2.36783 | −0.0945619 | ||||||||
\(628\) | −0.431133 | −0.0172041 | ||||||||
\(629\) | 2.71901 | 0.108414 | ||||||||
\(630\) | −4.39385 | −0.175055 | ||||||||
\(631\) | 4.89969 | 0.195054 | 0.0975269 | − | 0.995233i | \(-0.468907\pi\) | ||||
0.0975269 | + | 0.995233i | \(0.468907\pi\) | |||||||
\(632\) | −14.2374 | −0.566335 | ||||||||
\(633\) | 4.54299 | 0.180568 | ||||||||
\(634\) | −23.6989 | −0.941203 | ||||||||
\(635\) | 12.9788 | 0.515047 | ||||||||
\(636\) | −0.273591 | −0.0108486 | ||||||||
\(637\) | 6.27542 | 0.248641 | ||||||||
\(638\) | −19.8394 | −0.785448 | ||||||||
\(639\) | 27.4817 | 1.08716 | ||||||||
\(640\) | −12.9639 | −0.512444 | ||||||||
\(641\) | −18.9168 | −0.747168 | −0.373584 | − | 0.927596i | \(-0.621871\pi\) | ||||
−0.373584 | + | 0.927596i | \(0.621871\pi\) | |||||||
\(642\) | −3.22448 | −0.127260 | ||||||||
\(643\) | −29.6676 | −1.16997 | −0.584987 | − | 0.811043i | \(-0.698900\pi\) | ||||
−0.584987 | + | 0.811043i | \(0.698900\pi\) | |||||||
\(644\) | 1.89597 | 0.0747117 | ||||||||
\(645\) | 1.46109 | 0.0575305 | ||||||||
\(646\) | −2.63567 | −0.103699 | ||||||||
\(647\) | −45.9479 | −1.80640 | −0.903199 | − | 0.429223i | \(-0.858788\pi\) | ||||
−0.903199 | + | 0.429223i | \(0.858788\pi\) | |||||||
\(648\) | 21.9516 | 0.862341 | ||||||||
\(649\) | 16.4894 | 0.647267 | ||||||||
\(650\) | −9.41448 | −0.369266 | ||||||||
\(651\) | −0.586666 | −0.0229933 | ||||||||
\(652\) | −6.17343 | −0.241770 | ||||||||
\(653\) | 32.7092 | 1.28001 | 0.640006 | − | 0.768370i | \(-0.278932\pi\) | ||||
0.640006 | + | 0.768370i | \(0.278932\pi\) | |||||||
\(654\) | 6.02296 | 0.235516 | ||||||||
\(655\) | −13.9304 | −0.544306 | ||||||||
\(656\) | 30.7813 | 1.20181 | ||||||||
\(657\) | −10.5474 | −0.411492 | ||||||||
\(658\) | 12.5852 | 0.490622 | ||||||||
\(659\) | −9.45410 | −0.368279 | −0.184140 | − | 0.982900i | \(-0.558950\pi\) | ||||
−0.184140 | + | 0.982900i | \(0.558950\pi\) | |||||||
\(660\) | −0.170547 | −0.00663852 | ||||||||
\(661\) | 32.4826 | 1.26343 | 0.631714 | − | 0.775202i | \(-0.282352\pi\) | ||||
0.631714 | + | 0.775202i | \(0.282352\pi\) | |||||||
\(662\) | −24.2674 | −0.943179 | ||||||||
\(663\) | 0.845306 | 0.0328290 | ||||||||
\(664\) | 3.06698 | 0.119022 | ||||||||
\(665\) | −3.47987 | −0.134944 | ||||||||
\(666\) | 23.6636 | 0.916944 | ||||||||
\(667\) | 39.2247 | 1.51879 | ||||||||
\(668\) | −3.33804 | −0.129153 | ||||||||
\(669\) | 4.18438 | 0.161777 | ||||||||
\(670\) | −12.9352 | −0.499732 | ||||||||
\(671\) | −5.06462 | −0.195517 | ||||||||
\(672\) | −0.376151 | −0.0145104 | ||||||||
\(673\) | 49.8803 | 1.92274 | 0.961371 | − | 0.275255i | \(-0.0887621\pi\) | ||||
0.961371 | + | 0.275255i | \(0.0887621\pi\) | |||||||
\(674\) | −37.0080 | −1.42550 | ||||||||
\(675\) | −1.58185 | −0.0608852 | ||||||||
\(676\) | 6.61220 | 0.254316 | ||||||||
\(677\) | −20.3386 | −0.781678 | −0.390839 | − | 0.920459i | \(-0.627815\pi\) | ||||
−0.390839 | + | 0.920459i | \(0.627815\pi\) | |||||||
\(678\) | 5.77867 | 0.221928 | ||||||||
\(679\) | −18.1951 | −0.698266 | ||||||||
\(680\) | 1.32497 | 0.0508104 | ||||||||
\(681\) | 2.94678 | 0.112921 | ||||||||
\(682\) | 8.41277 | 0.322141 | ||||||||
\(683\) | −20.7758 | −0.794965 | −0.397482 | − | 0.917610i | \(-0.630116\pi\) | ||||
−0.397482 | + | 0.917610i | \(0.630116\pi\) | |||||||
\(684\) | −2.55453 | −0.0976750 | ||||||||
\(685\) | 1.96693 | 0.0751525 | ||||||||
\(686\) | 1.50021 | 0.0572785 | ||||||||
\(687\) | −0.266806 | −0.0101793 | ||||||||
\(688\) | −24.3061 | −0.926660 | ||||||||
\(689\) | −25.6739 | −0.978097 | ||||||||
\(690\) | 3.02778 | 0.115266 | ||||||||
\(691\) | −21.4273 | −0.815133 | −0.407566 | − | 0.913176i | \(-0.633623\pi\) | ||||
−0.407566 | + | 0.913176i | \(0.633623\pi\) | |||||||
\(692\) | −0.628971 | −0.0239099 | ||||||||
\(693\) | −7.46934 | −0.283737 | ||||||||
\(694\) | 7.61516 | 0.289068 | ||||||||
\(695\) | 19.5592 | 0.741924 | ||||||||
\(696\) | −3.63088 | −0.137628 | ||||||||
\(697\) | −3.50130 | −0.132621 | ||||||||
\(698\) | −1.00595 | −0.0380756 | ||||||||
\(699\) | 1.61630 | 0.0611339 | ||||||||
\(700\) | −0.250644 | −0.00947343 | ||||||||
\(701\) | 24.5272 | 0.926380 | 0.463190 | − | 0.886259i | \(-0.346705\pi\) | ||||
0.463190 | + | 0.886259i | \(0.346705\pi\) | |||||||
\(702\) | 14.8922 | 0.562072 | ||||||||
\(703\) | 18.7412 | 0.706839 | ||||||||
\(704\) | −17.2448 | −0.649938 | ||||||||
\(705\) | 2.23822 | 0.0842962 | ||||||||
\(706\) | −36.7329 | −1.38246 | ||||||||
\(707\) | −3.60580 | −0.135610 | ||||||||
\(708\) | −0.432382 | −0.0162499 | ||||||||
\(709\) | 22.8344 | 0.857563 | 0.428782 | − | 0.903408i | \(-0.358943\pi\) | ||||
0.428782 | + | 0.903408i | \(0.358943\pi\) | |||||||
\(710\) | 14.0768 | 0.528295 | ||||||||
\(711\) | 15.8888 | 0.595878 | ||||||||
\(712\) | 3.29523 | 0.123494 | ||||||||
\(713\) | −16.6330 | −0.622910 | ||||||||
\(714\) | 0.202081 | 0.00756268 | ||||||||
\(715\) | −16.0042 | −0.598522 | ||||||||
\(716\) | 5.06315 | 0.189219 | ||||||||
\(717\) | 5.55389 | 0.207414 | ||||||||
\(718\) | −48.9984 | −1.82860 | ||||||||
\(719\) | 21.4181 | 0.798762 | 0.399381 | − | 0.916785i | \(-0.369225\pi\) | ||||
0.399381 | + | 0.916785i | \(0.369225\pi\) | |||||||
\(720\) | 12.9994 | 0.484461 | ||||||||
\(721\) | 0.693412 | 0.0258240 | ||||||||
\(722\) | 10.3372 | 0.384711 | ||||||||
\(723\) | −1.17028 | −0.0435232 | ||||||||
\(724\) | 3.50458 | 0.130247 | ||||||||
\(725\) | −5.18542 | −0.192582 | ||||||||
\(726\) | 1.79960 | 0.0667893 | ||||||||
\(727\) | 34.3606 | 1.27436 | 0.637182 | − | 0.770714i | \(-0.280100\pi\) | ||||
0.637182 | + | 0.770714i | \(0.280100\pi\) | |||||||
\(728\) | −16.4693 | −0.610392 | ||||||||
\(729\) | −23.2316 | −0.860431 | ||||||||
\(730\) | −5.40263 | −0.199960 | ||||||||
\(731\) | 2.76476 | 0.102258 | ||||||||
\(732\) | 0.132803 | 0.00490855 | ||||||||
\(733\) | 2.78415 | 0.102835 | 0.0514175 | − | 0.998677i | \(-0.483626\pi\) | ||||
0.0514175 | + | 0.998677i | \(0.483626\pi\) | |||||||
\(734\) | 27.0740 | 0.999320 | ||||||||
\(735\) | 0.266806 | 0.00984130 | ||||||||
\(736\) | −10.6645 | −0.393100 | ||||||||
\(737\) | −21.9893 | −0.809986 | ||||||||
\(738\) | −30.4719 | −1.12169 | ||||||||
\(739\) | 26.2525 | 0.965712 | 0.482856 | − | 0.875700i | \(-0.339599\pi\) | ||||
0.482856 | + | 0.875700i | \(0.339599\pi\) | |||||||
\(740\) | 1.34987 | 0.0496221 | ||||||||
\(741\) | 5.82643 | 0.214039 | ||||||||
\(742\) | −6.13765 | −0.225320 | ||||||||
\(743\) | −15.4977 | −0.568555 | −0.284278 | − | 0.958742i | \(-0.591754\pi\) | ||||
−0.284278 | + | 0.958742i | \(0.591754\pi\) | |||||||
\(744\) | 1.53965 | 0.0564464 | ||||||||
\(745\) | −8.31376 | −0.304593 | ||||||||
\(746\) | 2.09992 | 0.0768837 | ||||||||
\(747\) | −3.42271 | −0.125231 | ||||||||
\(748\) | −0.322717 | −0.0117997 | ||||||||
\(749\) | −8.05582 | −0.294353 | ||||||||
\(750\) | −0.400267 | −0.0146157 | ||||||||
\(751\) | 20.0604 | 0.732014 | 0.366007 | − | 0.930612i | \(-0.380725\pi\) | ||||
0.366007 | + | 0.930612i | \(0.380725\pi\) | |||||||
\(752\) | −37.2340 | −1.35778 | ||||||||
\(753\) | −1.22836 | −0.0447640 | ||||||||
\(754\) | 48.8180 | 1.77785 | ||||||||
\(755\) | 1.71856 | 0.0625448 | ||||||||
\(756\) | 0.396479 | 0.0144198 | ||||||||
\(757\) | 42.7063 | 1.55219 | 0.776094 | − | 0.630617i | \(-0.217198\pi\) | ||||
0.776094 | + | 0.630617i | \(0.217198\pi\) | |||||||
\(758\) | 9.82022 | 0.356686 | ||||||||
\(759\) | 5.14709 | 0.186828 | ||||||||
\(760\) | 9.13261 | 0.331275 | ||||||||
\(761\) | −36.5625 | −1.32539 | −0.662696 | − | 0.748889i | \(-0.730588\pi\) | ||||
−0.662696 | + | 0.748889i | \(0.730588\pi\) | |||||||
\(762\) | −5.19497 | −0.188194 | ||||||||
\(763\) | 15.0474 | 0.544751 | ||||||||
\(764\) | −4.09650 | −0.148206 | ||||||||
\(765\) | −1.47866 | −0.0534609 | ||||||||
\(766\) | 30.0492 | 1.08572 | ||||||||
\(767\) | −40.5750 | −1.46508 | ||||||||
\(768\) | 1.58080 | 0.0570424 | ||||||||
\(769\) | 3.34947 | 0.120785 | 0.0603924 | − | 0.998175i | \(-0.480765\pi\) | ||||
0.0603924 | + | 0.998175i | \(0.480765\pi\) | |||||||
\(770\) | −3.82599 | −0.137879 | ||||||||
\(771\) | 6.28974 | 0.226520 | ||||||||
\(772\) | 3.01726 | 0.108594 | ||||||||
\(773\) | 35.7937 | 1.28741 | 0.643705 | − | 0.765274i | \(-0.277397\pi\) | ||||
0.643705 | + | 0.765274i | \(0.277397\pi\) | |||||||
\(774\) | 24.0617 | 0.864881 | ||||||||
\(775\) | 2.19885 | 0.0789849 | ||||||||
\(776\) | 47.7515 | 1.71418 | ||||||||
\(777\) | −1.43691 | −0.0515490 | ||||||||
\(778\) | 1.33438 | 0.0478397 | ||||||||
\(779\) | −24.1333 | −0.864667 | ||||||||
\(780\) | 0.419658 | 0.0150262 | ||||||||
\(781\) | 23.9300 | 0.856283 | ||||||||
\(782\) | 5.72933 | 0.204880 | ||||||||
\(783\) | 8.20253 | 0.293135 | ||||||||
\(784\) | −4.43846 | −0.158517 | ||||||||
\(785\) | −1.72011 | −0.0613932 | ||||||||
\(786\) | 5.57588 | 0.198885 | ||||||||
\(787\) | 31.4755 | 1.12198 | 0.560990 | − | 0.827822i | \(-0.310420\pi\) | ||||
0.560990 | + | 0.827822i | \(0.310420\pi\) | |||||||
\(788\) | 5.20940 | 0.185577 | ||||||||
\(789\) | 0.945902 | 0.0336750 | ||||||||
\(790\) | 8.13867 | 0.289561 | ||||||||
\(791\) | 14.4370 | 0.513322 | ||||||||
\(792\) | 19.6026 | 0.696549 | ||||||||
\(793\) | 12.4623 | 0.442550 | ||||||||
\(794\) | 7.00900 | 0.248740 | ||||||||
\(795\) | −1.09155 | −0.0387134 | ||||||||
\(796\) | −4.79093 | −0.169810 | ||||||||
\(797\) | 24.9451 | 0.883602 | 0.441801 | − | 0.897113i | \(-0.354340\pi\) | ||||
0.441801 | + | 0.897113i | \(0.354340\pi\) | |||||||
\(798\) | 1.39288 | 0.0493073 | ||||||||
\(799\) | 4.23528 | 0.149833 | ||||||||
\(800\) | 1.40983 | 0.0498450 | ||||||||
\(801\) | −3.67744 | −0.129936 | ||||||||
\(802\) | −12.8204 | −0.452705 | ||||||||
\(803\) | −9.18423 | −0.324104 | ||||||||
\(804\) | 0.576598 | 0.0203351 | ||||||||
\(805\) | 7.56441 | 0.266611 | ||||||||
\(806\) | −20.7010 | −0.729161 | ||||||||
\(807\) | −1.40455 | −0.0494426 | ||||||||
\(808\) | 9.46310 | 0.332911 | ||||||||
\(809\) | 54.2917 | 1.90880 | 0.954398 | − | 0.298537i | \(-0.0964987\pi\) | ||||
0.954398 | + | 0.298537i | \(0.0964987\pi\) | |||||||
\(810\) | −12.5484 | −0.440905 | ||||||||
\(811\) | −50.8645 | −1.78609 | −0.893047 | − | 0.449964i | \(-0.851437\pi\) | ||||
−0.893047 | + | 0.449964i | \(0.851437\pi\) | |||||||
\(812\) | 1.29969 | 0.0456102 | ||||||||
\(813\) | −0.770042 | −0.0270066 | ||||||||
\(814\) | 20.6053 | 0.722215 | ||||||||
\(815\) | −24.6303 | −0.862762 | ||||||||
\(816\) | −0.597866 | −0.0209295 | ||||||||
\(817\) | 19.0566 | 0.666705 | ||||||||
\(818\) | 23.2957 | 0.814514 | ||||||||
\(819\) | 18.3795 | 0.642233 | ||||||||
\(820\) | −1.73824 | −0.0607021 | ||||||||
\(821\) | −31.6110 | −1.10323 | −0.551615 | − | 0.834099i | \(-0.685988\pi\) | ||||
−0.551615 | + | 0.834099i | \(0.685988\pi\) | |||||||
\(822\) | −0.787296 | −0.0274601 | ||||||||
\(823\) | 48.6036 | 1.69422 | 0.847108 | − | 0.531420i | \(-0.178341\pi\) | ||||
0.847108 | + | 0.531420i | \(0.178341\pi\) | |||||||
\(824\) | −1.81980 | −0.0633957 | ||||||||
\(825\) | −0.680435 | −0.0236897 | ||||||||
\(826\) | −9.69993 | −0.337504 | ||||||||
\(827\) | 1.39817 | 0.0486192 | 0.0243096 | − | 0.999704i | \(-0.492261\pi\) | ||||
0.0243096 | + | 0.999704i | \(0.492261\pi\) | |||||||
\(828\) | 5.55295 | 0.192978 | ||||||||
\(829\) | 8.80210 | 0.305710 | 0.152855 | − | 0.988249i | \(-0.451153\pi\) | ||||
0.152855 | + | 0.988249i | \(0.451153\pi\) | |||||||
\(830\) | −1.75320 | −0.0608546 | ||||||||
\(831\) | 0.365409 | 0.0126759 | ||||||||
\(832\) | 42.4337 | 1.47112 | ||||||||
\(833\) | 0.504865 | 0.0174925 | ||||||||
\(834\) | −7.82890 | −0.271093 | ||||||||
\(835\) | −13.3179 | −0.460885 | ||||||||
\(836\) | −2.22439 | −0.0769320 | ||||||||
\(837\) | −3.47823 | −0.120225 | ||||||||
\(838\) | −54.8949 | −1.89631 | ||||||||
\(839\) | 15.6338 | 0.539739 | 0.269870 | − | 0.962897i | \(-0.413019\pi\) | ||||
0.269870 | + | 0.962897i | \(0.413019\pi\) | |||||||
\(840\) | −0.700209 | −0.0241595 | ||||||||
\(841\) | −2.11142 | −0.0728077 | ||||||||
\(842\) | −41.3944 | −1.42655 | ||||||||
\(843\) | 3.61563 | 0.124529 | ||||||||
\(844\) | 4.26778 | 0.146903 | ||||||||
\(845\) | 26.3809 | 0.907531 | ||||||||
\(846\) | 36.8597 | 1.26726 | ||||||||
\(847\) | 4.49599 | 0.154484 | ||||||||
\(848\) | 18.1586 | 0.623568 | ||||||||
\(849\) | −1.80677 | −0.0620083 | ||||||||
\(850\) | −0.757406 | −0.0259788 | ||||||||
\(851\) | −40.7390 | −1.39651 | ||||||||
\(852\) | −0.627487 | −0.0214973 | ||||||||
\(853\) | −37.9243 | −1.29850 | −0.649252 | − | 0.760573i | \(-0.724918\pi\) | ||||
−0.649252 | + | 0.760573i | \(0.724918\pi\) | |||||||
\(854\) | 2.97927 | 0.101948 | ||||||||
\(855\) | −10.1919 | −0.348556 | ||||||||
\(856\) | 21.1418 | 0.722611 | ||||||||
\(857\) | 2.05854 | 0.0703185 | 0.0351592 | − | 0.999382i | \(-0.488806\pi\) | ||||
0.0351592 | + | 0.999382i | \(0.488806\pi\) | |||||||
\(858\) | 6.40594 | 0.218695 | ||||||||
\(859\) | 21.0555 | 0.718403 | 0.359201 | − | 0.933260i | \(-0.383049\pi\) | ||||
0.359201 | + | 0.933260i | \(0.383049\pi\) | |||||||
\(860\) | 1.37258 | 0.0468046 | ||||||||
\(861\) | 1.85033 | 0.0630592 | ||||||||
\(862\) | −30.0706 | −1.02421 | ||||||||
\(863\) | −44.5512 | −1.51654 | −0.758270 | − | 0.651940i | \(-0.773955\pi\) | ||||
−0.758270 | + | 0.651940i | \(0.773955\pi\) | |||||||
\(864\) | −2.23013 | −0.0758706 | ||||||||
\(865\) | −2.50942 | −0.0853230 | ||||||||
\(866\) | 1.50331 | 0.0510844 | ||||||||
\(867\) | −4.46770 | −0.151731 | ||||||||
\(868\) | −0.551127 | −0.0187065 | ||||||||
\(869\) | 13.8354 | 0.469333 | ||||||||
\(870\) | 2.07555 | 0.0703678 | ||||||||
\(871\) | 54.1083 | 1.83339 | ||||||||
\(872\) | −39.4904 | −1.33731 | ||||||||
\(873\) | −53.2902 | −1.80360 | ||||||||
\(874\) | 39.4904 | 1.33578 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0.240827 | 0.00813678 | ||||||||
\(877\) | 33.1561 | 1.11960 | 0.559802 | − | 0.828627i | \(-0.310877\pi\) | ||||
0.559802 | + | 0.828627i | \(0.310877\pi\) | |||||||
\(878\) | −11.4877 | −0.387693 | ||||||||
\(879\) | −1.95479 | −0.0659335 | ||||||||
\(880\) | 11.3194 | 0.381577 | ||||||||
\(881\) | 3.18444 | 0.107287 | 0.0536433 | − | 0.998560i | \(-0.482917\pi\) | ||||
0.0536433 | + | 0.998560i | \(0.482917\pi\) | |||||||
\(882\) | 4.39385 | 0.147949 | ||||||||
\(883\) | −35.7053 | −1.20158 | −0.600790 | − | 0.799407i | \(-0.705147\pi\) | ||||
−0.600790 | + | 0.799407i | \(0.705147\pi\) | |||||||
\(884\) | 0.794099 | 0.0267084 | ||||||||
\(885\) | −1.72509 | −0.0579882 | ||||||||
\(886\) | 6.82152 | 0.229174 | ||||||||
\(887\) | 29.7558 | 0.999101 | 0.499551 | − | 0.866285i | \(-0.333498\pi\) | ||||
0.499551 | + | 0.866285i | \(0.333498\pi\) | |||||||
\(888\) | 3.77105 | 0.126548 | ||||||||
\(889\) | −12.9788 | −0.435294 | ||||||||
\(890\) | −1.88368 | −0.0631411 | ||||||||
\(891\) | −21.3317 | −0.714638 | ||||||||
\(892\) | 3.93089 | 0.131616 | ||||||||
\(893\) | 29.1924 | 0.976886 | ||||||||
\(894\) | 3.32772 | 0.111296 | ||||||||
\(895\) | 20.2006 | 0.675232 | ||||||||
\(896\) | 12.9639 | 0.433095 | ||||||||
\(897\) | −12.6653 | −0.422881 | ||||||||
\(898\) | −17.6461 | −0.588857 | ||||||||
\(899\) | −11.4019 | −0.380276 | ||||||||
\(900\) | −0.734088 | −0.0244696 | ||||||||
\(901\) | −2.06549 | −0.0688116 | ||||||||
\(902\) | −26.5337 | −0.883476 | ||||||||
\(903\) | −1.46109 | −0.0486221 | ||||||||
\(904\) | −37.8887 | −1.26016 | ||||||||
\(905\) | 13.9823 | 0.464788 | ||||||||
\(906\) | −0.687883 | −0.0228534 | ||||||||
\(907\) | 2.91199 | 0.0966910 | 0.0483455 | − | 0.998831i | \(-0.484605\pi\) | ||||
0.0483455 | + | 0.998831i | \(0.484605\pi\) | |||||||
\(908\) | 2.76827 | 0.0918682 | ||||||||
\(909\) | −10.5607 | −0.350277 | ||||||||
\(910\) | 9.41448 | 0.312087 | ||||||||
\(911\) | 40.4821 | 1.34123 | 0.670616 | − | 0.741805i | \(-0.266030\pi\) | ||||
0.670616 | + | 0.741805i | \(0.266030\pi\) | |||||||
\(912\) | −4.12090 | −0.136457 | ||||||||
\(913\) | −2.98036 | −0.0986356 | ||||||||
\(914\) | 1.07583 | 0.0355854 | ||||||||
\(915\) | 0.529849 | 0.0175163 | ||||||||
\(916\) | −0.250644 | −0.00828149 | ||||||||
\(917\) | 13.9304 | 0.460023 | ||||||||
\(918\) | 1.19810 | 0.0395431 | ||||||||
\(919\) | −33.0028 | −1.08866 | −0.544331 | − | 0.838870i | \(-0.683217\pi\) | ||||
−0.544331 | + | 0.838870i | \(0.683217\pi\) | |||||||
\(920\) | −19.8521 | −0.654505 | ||||||||
\(921\) | −2.89248 | −0.0953105 | ||||||||
\(922\) | −59.8693 | −1.97169 | ||||||||
\(923\) | −58.8837 | −1.93818 | ||||||||
\(924\) | 0.170547 | 0.00561057 | ||||||||
\(925\) | 5.38561 | 0.177078 | ||||||||
\(926\) | 52.4056 | 1.72216 | ||||||||
\(927\) | 2.03088 | 0.0667027 | ||||||||
\(928\) | −7.31056 | −0.239981 | ||||||||
\(929\) | 31.9297 | 1.04758 | 0.523789 | − | 0.851848i | \(-0.324518\pi\) | ||||
0.523789 | + | 0.851848i | \(0.324518\pi\) | |||||||
\(930\) | −0.880125 | −0.0288604 | ||||||||
\(931\) | 3.47987 | 0.114048 | ||||||||
\(932\) | 1.51838 | 0.0497363 | ||||||||
\(933\) | −3.06264 | −0.100266 | ||||||||
\(934\) | −20.3738 | −0.666651 | ||||||||
\(935\) | −1.28755 | −0.0421075 | ||||||||
\(936\) | −48.2355 | −1.57663 | ||||||||
\(937\) | 15.6006 | 0.509650 | 0.254825 | − | 0.966987i | \(-0.417982\pi\) | ||||
0.254825 | + | 0.966987i | \(0.417982\pi\) | |||||||
\(938\) | 12.9352 | 0.422350 | ||||||||
\(939\) | −6.24570 | −0.203821 | ||||||||
\(940\) | 2.10263 | 0.0685802 | ||||||||
\(941\) | −37.8710 | −1.23456 | −0.617280 | − | 0.786744i | \(-0.711765\pi\) | ||||
−0.617280 | + | 0.786744i | \(0.711765\pi\) | |||||||
\(942\) | 0.688501 | 0.0224326 | ||||||||
\(943\) | 52.4602 | 1.70834 | ||||||||
\(944\) | 28.6978 | 0.934033 | ||||||||
\(945\) | 1.58185 | 0.0514574 | ||||||||
\(946\) | 20.9520 | 0.681208 | ||||||||
\(947\) | 5.69975 | 0.185217 | 0.0926085 | − | 0.995703i | \(-0.470479\pi\) | ||||
0.0926085 | + | 0.995703i | \(0.470479\pi\) | |||||||
\(948\) | −0.362788 | −0.0117828 | ||||||||
\(949\) | 22.5993 | 0.733604 | ||||||||
\(950\) | −5.22055 | −0.169377 | ||||||||
\(951\) | 4.21474 | 0.136672 | ||||||||
\(952\) | −1.32497 | −0.0429426 | ||||||||
\(953\) | 38.5064 | 1.24735 | 0.623673 | − | 0.781685i | \(-0.285640\pi\) | ||||
0.623673 | + | 0.781685i | \(0.285640\pi\) | |||||||
\(954\) | −17.9760 | −0.581996 | ||||||||
\(955\) | −16.3439 | −0.528877 | ||||||||
\(956\) | 5.21744 | 0.168744 | ||||||||
\(957\) | 3.52834 | 0.114055 | ||||||||
\(958\) | 51.3082 | 1.65769 | ||||||||
\(959\) | −1.96693 | −0.0635155 | ||||||||
\(960\) | 1.80411 | 0.0582275 | ||||||||
\(961\) | −26.1651 | −0.844035 | ||||||||
\(962\) | −50.7027 | −1.63472 | ||||||||
\(963\) | −23.5940 | −0.760306 | ||||||||
\(964\) | −1.09939 | −0.0354088 | ||||||||
\(965\) | 12.0381 | 0.387519 | ||||||||
\(966\) | −3.02778 | −0.0974173 | ||||||||
\(967\) | 27.1018 | 0.871536 | 0.435768 | − | 0.900059i | \(-0.356477\pi\) | ||||
0.435768 | + | 0.900059i | \(0.356477\pi\) | |||||||
\(968\) | −11.7993 | −0.379245 | ||||||||
\(969\) | 0.468743 | 0.0150582 | ||||||||
\(970\) | −27.2966 | −0.876442 | ||||||||
\(971\) | −0.643820 | −0.0206612 | −0.0103306 | − | 0.999947i | \(-0.503288\pi\) | ||||
−0.0103306 | + | 0.999947i | \(0.503288\pi\) | |||||||
\(972\) | 1.74879 | 0.0560925 | ||||||||
\(973\) | −19.5592 | −0.627040 | ||||||||
\(974\) | 57.7996 | 1.85202 | ||||||||
\(975\) | 1.67432 | 0.0536212 | ||||||||
\(976\) | −8.81433 | −0.282140 | ||||||||
\(977\) | −38.9530 | −1.24622 | −0.623108 | − | 0.782136i | \(-0.714130\pi\) | ||||
−0.623108 | + | 0.782136i | \(0.714130\pi\) | |||||||
\(978\) | 9.85870 | 0.315246 | ||||||||
\(979\) | −3.20217 | −0.102342 | ||||||||
\(980\) | 0.250644 | 0.00800651 | ||||||||
\(981\) | 44.0709 | 1.40708 | ||||||||
\(982\) | 5.40270 | 0.172407 | ||||||||
\(983\) | 2.10401 | 0.0671076 | 0.0335538 | − | 0.999437i | \(-0.489317\pi\) | ||||
0.0335538 | + | 0.999437i | \(0.489317\pi\) | |||||||
\(984\) | −4.85604 | −0.154805 | ||||||||
\(985\) | 20.7841 | 0.662236 | ||||||||
\(986\) | 3.92747 | 0.125076 | ||||||||
\(987\) | −2.23822 | −0.0712433 | ||||||||
\(988\) | 5.47347 | 0.174134 | ||||||||
\(989\) | −41.4245 | −1.31722 | ||||||||
\(990\) | −11.2056 | −0.356138 | ||||||||
\(991\) | −8.43483 | −0.267941 | −0.133971 | − | 0.990985i | \(-0.542773\pi\) | ||||
−0.133971 | + | 0.990985i | \(0.542773\pi\) | |||||||
\(992\) | 3.10000 | 0.0984250 | ||||||||
\(993\) | 4.31584 | 0.136959 | ||||||||
\(994\) | −14.0768 | −0.446491 | ||||||||
\(995\) | −19.1145 | −0.605971 | ||||||||
\(996\) | 0.0781504 | 0.00247629 | ||||||||
\(997\) | 45.8934 | 1.45346 | 0.726729 | − | 0.686924i | \(-0.241039\pi\) | ||||
0.726729 | + | 0.686924i | \(0.241039\pi\) | |||||||
\(998\) | −11.8522 | −0.375176 | ||||||||
\(999\) | −8.51920 | −0.269536 |
(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 | 8015.2.a.m.1.18 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.m.1.18 | ✓ | 67 | 1.1 | even | 1 | trivial |