Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(1\) |
Dimension: | \(149\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62536 | −1.85641 | −0.928205 | − | 0.372069i | \(-0.878649\pi\) | ||||
−0.928205 | + | 0.372069i | \(0.878649\pi\) | |||||||
\(3\) | 1.08746 | 0.627846 | 0.313923 | − | 0.949448i | \(-0.398357\pi\) | ||||
0.313923 | + | 0.949448i | \(0.398357\pi\) | |||||||
\(4\) | 4.89252 | 2.44626 | ||||||||
\(5\) | 0.733437 | 0.328003 | 0.164001 | − | 0.986460i | \(-0.447560\pi\) | ||||
0.164001 | + | 0.986460i | \(0.447560\pi\) | |||||||
\(6\) | −2.85498 | −1.16554 | ||||||||
\(7\) | −4.12609 | −1.55952 | −0.779759 | − | 0.626080i | \(-0.784658\pi\) | ||||
−0.779759 | + | 0.626080i | \(0.784658\pi\) | |||||||
\(8\) | −7.59390 | −2.68485 | ||||||||
\(9\) | −1.81743 | −0.605809 | ||||||||
\(10\) | −1.92554 | −0.608908 | ||||||||
\(11\) | −1.44851 | −0.436742 | −0.218371 | − | 0.975866i | \(-0.570074\pi\) | ||||
−0.218371 | + | 0.975866i | \(0.570074\pi\) | |||||||
\(12\) | 5.32042 | 1.53587 | ||||||||
\(13\) | 4.28374 | 1.18810 | 0.594048 | − | 0.804429i | \(-0.297529\pi\) | ||||
0.594048 | + | 0.804429i | \(0.297529\pi\) | |||||||
\(14\) | 10.8325 | 2.89510 | ||||||||
\(15\) | 0.797584 | 0.205935 | ||||||||
\(16\) | 10.1517 | 2.53792 | ||||||||
\(17\) | 1.99209 | 0.483152 | 0.241576 | − | 0.970382i | \(-0.422336\pi\) | ||||
0.241576 | + | 0.970382i | \(0.422336\pi\) | |||||||
\(18\) | 4.77140 | 1.12463 | ||||||||
\(19\) | 0.597631 | 0.137106 | 0.0685530 | − | 0.997647i | \(-0.478162\pi\) | ||||
0.0685530 | + | 0.997647i | \(0.478162\pi\) | |||||||
\(20\) | 3.58835 | 0.802380 | ||||||||
\(21\) | −4.48697 | −0.979137 | ||||||||
\(22\) | 3.80286 | 0.810772 | ||||||||
\(23\) | 1.41089 | 0.294190 | 0.147095 | − | 0.989122i | \(-0.453008\pi\) | ||||
0.147095 | + | 0.989122i | \(0.453008\pi\) | |||||||
\(24\) | −8.25807 | −1.68567 | ||||||||
\(25\) | −4.46207 | −0.892414 | ||||||||
\(26\) | −11.2464 | −2.20559 | ||||||||
\(27\) | −5.23877 | −1.00820 | ||||||||
\(28\) | −20.1870 | −3.81498 | ||||||||
\(29\) | 4.25595 | 0.790311 | 0.395155 | − | 0.918614i | \(-0.370691\pi\) | ||||
0.395155 | + | 0.918614i | \(0.370691\pi\) | |||||||
\(30\) | −2.09395 | −0.382300 | ||||||||
\(31\) | −0.639790 | −0.114910 | −0.0574548 | − | 0.998348i | \(-0.518299\pi\) | ||||
−0.0574548 | + | 0.998348i | \(0.518299\pi\) | |||||||
\(32\) | −11.4641 | −2.02658 | ||||||||
\(33\) | −1.57520 | −0.274207 | ||||||||
\(34\) | −5.22995 | −0.896929 | ||||||||
\(35\) | −3.02623 | −0.511526 | ||||||||
\(36\) | −8.89180 | −1.48197 | ||||||||
\(37\) | 10.0922 | 1.65915 | 0.829577 | − | 0.558392i | \(-0.188581\pi\) | ||||
0.829577 | + | 0.558392i | \(0.188581\pi\) | |||||||
\(38\) | −1.56900 | −0.254525 | ||||||||
\(39\) | 4.65840 | 0.745942 | ||||||||
\(40\) | −5.56965 | −0.880638 | ||||||||
\(41\) | −1.23998 | −0.193652 | −0.0968259 | − | 0.995301i | \(-0.530869\pi\) | ||||
−0.0968259 | + | 0.995301i | \(0.530869\pi\) | |||||||
\(42\) | 11.7799 | 1.81768 | ||||||||
\(43\) | −10.4464 | −1.59306 | −0.796530 | − | 0.604600i | \(-0.793333\pi\) | ||||
−0.796530 | + | 0.604600i | \(0.793333\pi\) | |||||||
\(44\) | −7.08686 | −1.06838 | ||||||||
\(45\) | −1.33297 | −0.198707 | ||||||||
\(46\) | −3.70409 | −0.546138 | ||||||||
\(47\) | 6.42172 | 0.936704 | 0.468352 | − | 0.883542i | \(-0.344848\pi\) | ||||
0.468352 | + | 0.883542i | \(0.344848\pi\) | |||||||
\(48\) | 11.0396 | 1.59343 | ||||||||
\(49\) | 10.0247 | 1.43209 | ||||||||
\(50\) | 11.7145 | 1.65669 | ||||||||
\(51\) | 2.16632 | 0.303345 | ||||||||
\(52\) | 20.9583 | 2.90639 | ||||||||
\(53\) | 6.12751 | 0.841678 | 0.420839 | − | 0.907135i | \(-0.361736\pi\) | ||||
0.420839 | + | 0.907135i | \(0.361736\pi\) | |||||||
\(54\) | 13.7536 | 1.87163 | ||||||||
\(55\) | −1.06239 | −0.143253 | ||||||||
\(56\) | 31.3332 | 4.18707 | ||||||||
\(57\) | 0.649900 | 0.0860814 | ||||||||
\(58\) | −11.1734 | −1.46714 | ||||||||
\(59\) | −13.2345 | −1.72298 | −0.861492 | − | 0.507771i | \(-0.830470\pi\) | ||||
−0.861492 | + | 0.507771i | \(0.830470\pi\) | |||||||
\(60\) | 3.90219 | 0.503771 | ||||||||
\(61\) | 10.1737 | 1.30261 | 0.651303 | − | 0.758818i | \(-0.274223\pi\) | ||||
0.651303 | + | 0.758818i | \(0.274223\pi\) | |||||||
\(62\) | 1.67968 | 0.213320 | ||||||||
\(63\) | 7.49888 | 0.944770 | ||||||||
\(64\) | 9.79389 | 1.22424 | ||||||||
\(65\) | 3.14185 | 0.389699 | ||||||||
\(66\) | 4.13546 | 0.509040 | ||||||||
\(67\) | −14.3855 | −1.75747 | −0.878734 | − | 0.477312i | \(-0.841611\pi\) | ||||
−0.878734 | + | 0.477312i | \(0.841611\pi\) | |||||||
\(68\) | 9.74633 | 1.18192 | ||||||||
\(69\) | 1.53428 | 0.184706 | ||||||||
\(70\) | 7.94494 | 0.949602 | ||||||||
\(71\) | 11.0048 | 1.30603 | 0.653015 | − | 0.757345i | \(-0.273504\pi\) | ||||
0.653015 | + | 0.757345i | \(0.273504\pi\) | |||||||
\(72\) | 13.8014 | 1.62651 | ||||||||
\(73\) | 13.2009 | 1.54505 | 0.772523 | − | 0.634987i | \(-0.218995\pi\) | ||||
0.772523 | + | 0.634987i | \(0.218995\pi\) | |||||||
\(74\) | −26.4958 | −3.08007 | ||||||||
\(75\) | −4.85233 | −0.560299 | ||||||||
\(76\) | 2.92392 | 0.335397 | ||||||||
\(77\) | 5.97669 | 0.681107 | ||||||||
\(78\) | −12.2300 | −1.38477 | ||||||||
\(79\) | −14.1339 | −1.59019 | −0.795093 | − | 0.606488i | \(-0.792578\pi\) | ||||
−0.795093 | + | 0.606488i | \(0.792578\pi\) | |||||||
\(80\) | 7.44563 | 0.832446 | ||||||||
\(81\) | −0.244671 | −0.0271856 | ||||||||
\(82\) | 3.25538 | 0.359497 | ||||||||
\(83\) | 1.26751 | 0.139128 | 0.0695639 | − | 0.997577i | \(-0.477839\pi\) | ||||
0.0695639 | + | 0.997577i | \(0.477839\pi\) | |||||||
\(84\) | −21.9526 | −2.39522 | ||||||||
\(85\) | 1.46107 | 0.158475 | ||||||||
\(86\) | 27.4255 | 2.95737 | ||||||||
\(87\) | 4.62819 | 0.496194 | ||||||||
\(88\) | 10.9998 | 1.17259 | ||||||||
\(89\) | −2.34175 | −0.248225 | −0.124113 | − | 0.992268i | \(-0.539608\pi\) | ||||
−0.124113 | + | 0.992268i | \(0.539608\pi\) | |||||||
\(90\) | 3.49952 | 0.368882 | ||||||||
\(91\) | −17.6751 | −1.85286 | ||||||||
\(92\) | 6.90279 | 0.719665 | ||||||||
\(93\) | −0.695747 | −0.0721456 | ||||||||
\(94\) | −16.8593 | −1.73891 | ||||||||
\(95\) | 0.438324 | 0.0449711 | ||||||||
\(96\) | −12.4667 | −1.27238 | ||||||||
\(97\) | −6.34090 | −0.643820 | −0.321910 | − | 0.946770i | \(-0.604325\pi\) | ||||
−0.321910 | + | 0.946770i | \(0.604325\pi\) | |||||||
\(98\) | −26.3183 | −2.65855 | ||||||||
\(99\) | 2.63256 | 0.264582 | ||||||||
\(100\) | −21.8308 | −2.18308 | ||||||||
\(101\) | 14.9900 | 1.49156 | 0.745781 | − | 0.666192i | \(-0.232077\pi\) | ||||
0.745781 | + | 0.666192i | \(0.232077\pi\) | |||||||
\(102\) | −5.68737 | −0.563133 | ||||||||
\(103\) | −9.59391 | −0.945316 | −0.472658 | − | 0.881246i | \(-0.656705\pi\) | ||||
−0.472658 | + | 0.881246i | \(0.656705\pi\) | |||||||
\(104\) | −32.5303 | −3.18986 | ||||||||
\(105\) | −3.29091 | −0.321160 | ||||||||
\(106\) | −16.0869 | −1.56250 | ||||||||
\(107\) | 2.66701 | 0.257830 | 0.128915 | − | 0.991656i | \(-0.458851\pi\) | ||||
0.128915 | + | 0.991656i | \(0.458851\pi\) | |||||||
\(108\) | −25.6308 | −2.46632 | ||||||||
\(109\) | 2.89810 | 0.277588 | 0.138794 | − | 0.990321i | \(-0.455677\pi\) | ||||
0.138794 | + | 0.990321i | \(0.455677\pi\) | |||||||
\(110\) | 2.78916 | 0.265936 | ||||||||
\(111\) | 10.9749 | 1.04169 | ||||||||
\(112\) | −41.8869 | −3.95794 | ||||||||
\(113\) | −20.1989 | −1.90015 | −0.950077 | − | 0.312017i | \(-0.898995\pi\) | ||||
−0.950077 | + | 0.312017i | \(0.898995\pi\) | |||||||
\(114\) | −1.70622 | −0.159802 | ||||||||
\(115\) | 1.03480 | 0.0964952 | ||||||||
\(116\) | 20.8223 | 1.93331 | ||||||||
\(117\) | −7.78539 | −0.719760 | ||||||||
\(118\) | 34.7453 | 3.19857 | ||||||||
\(119\) | −8.21954 | −0.753484 | ||||||||
\(120\) | −6.05677 | −0.552905 | ||||||||
\(121\) | −8.90182 | −0.809256 | ||||||||
\(122\) | −26.7096 | −2.41817 | ||||||||
\(123\) | −1.34843 | −0.121583 | ||||||||
\(124\) | −3.13018 | −0.281099 | ||||||||
\(125\) | −6.93983 | −0.620717 | ||||||||
\(126\) | −19.6873 | −1.75388 | ||||||||
\(127\) | −12.6383 | −1.12147 | −0.560734 | − | 0.827996i | \(-0.689481\pi\) | ||||
−0.560734 | + | 0.827996i | \(0.689481\pi\) | |||||||
\(128\) | −2.78438 | −0.246106 | ||||||||
\(129\) | −11.3600 | −1.00020 | ||||||||
\(130\) | −8.24850 | −0.723441 | ||||||||
\(131\) | −11.3099 | −0.988149 | −0.494075 | − | 0.869419i | \(-0.664493\pi\) | ||||
−0.494075 | + | 0.869419i | \(0.664493\pi\) | |||||||
\(132\) | −7.70668 | −0.670781 | ||||||||
\(133\) | −2.46588 | −0.213819 | ||||||||
\(134\) | 37.7671 | 3.26258 | ||||||||
\(135\) | −3.84230 | −0.330693 | ||||||||
\(136\) | −15.1277 | −1.29719 | ||||||||
\(137\) | −11.1111 | −0.949282 | −0.474641 | − | 0.880179i | \(-0.657422\pi\) | ||||
−0.474641 | + | 0.880179i | \(0.657422\pi\) | |||||||
\(138\) | −4.02805 | −0.342890 | ||||||||
\(139\) | −11.2859 | −0.957259 | −0.478630 | − | 0.878017i | \(-0.658866\pi\) | ||||
−0.478630 | + | 0.878017i | \(0.658866\pi\) | |||||||
\(140\) | −14.8059 | −1.25133 | ||||||||
\(141\) | 6.98337 | 0.588106 | ||||||||
\(142\) | −28.8916 | −2.42453 | ||||||||
\(143\) | −6.20504 | −0.518892 | ||||||||
\(144\) | −18.4500 | −1.53750 | ||||||||
\(145\) | 3.12147 | 0.259224 | ||||||||
\(146\) | −34.6570 | −2.86824 | ||||||||
\(147\) | 10.9014 | 0.899134 | ||||||||
\(148\) | 49.3765 | 4.05872 | ||||||||
\(149\) | −12.4674 | −1.02137 | −0.510686 | − | 0.859767i | \(-0.670609\pi\) | ||||
−0.510686 | + | 0.859767i | \(0.670609\pi\) | |||||||
\(150\) | 12.7391 | 1.04014 | ||||||||
\(151\) | 2.73646 | 0.222690 | 0.111345 | − | 0.993782i | \(-0.464484\pi\) | ||||
0.111345 | + | 0.993782i | \(0.464484\pi\) | |||||||
\(152\) | −4.53835 | −0.368109 | ||||||||
\(153\) | −3.62048 | −0.292698 | ||||||||
\(154\) | −15.6910 | −1.26441 | ||||||||
\(155\) | −0.469245 | −0.0376907 | ||||||||
\(156\) | 22.7913 | 1.82477 | ||||||||
\(157\) | −23.7635 | −1.89654 | −0.948269 | − | 0.317469i | \(-0.897167\pi\) | ||||
−0.948269 | + | 0.317469i | \(0.897167\pi\) | |||||||
\(158\) | 37.1065 | 2.95204 | ||||||||
\(159\) | 6.66343 | 0.528444 | ||||||||
\(160\) | −8.40816 | −0.664723 | ||||||||
\(161\) | −5.82145 | −0.458795 | ||||||||
\(162\) | 0.642349 | 0.0504677 | ||||||||
\(163\) | 18.4864 | 1.44796 | 0.723982 | − | 0.689819i | \(-0.242310\pi\) | ||||
0.723982 | + | 0.689819i | \(0.242310\pi\) | |||||||
\(164\) | −6.06660 | −0.473722 | ||||||||
\(165\) | −1.15531 | −0.0899406 | ||||||||
\(166\) | −3.32768 | −0.258278 | ||||||||
\(167\) | 19.8629 | 1.53704 | 0.768520 | − | 0.639826i | \(-0.220994\pi\) | ||||
0.768520 | + | 0.639826i | \(0.220994\pi\) | |||||||
\(168\) | 34.0736 | 2.62883 | ||||||||
\(169\) | 5.35045 | 0.411573 | ||||||||
\(170\) | −3.83584 | −0.294195 | ||||||||
\(171\) | −1.08615 | −0.0830601 | ||||||||
\(172\) | −51.1091 | −3.89704 | ||||||||
\(173\) | 14.5017 | 1.10254 | 0.551271 | − | 0.834326i | \(-0.314143\pi\) | ||||
0.551271 | + | 0.834326i | \(0.314143\pi\) | |||||||
\(174\) | −12.1507 | −0.921139 | ||||||||
\(175\) | 18.4109 | 1.39174 | ||||||||
\(176\) | −14.7048 | −1.10842 | ||||||||
\(177\) | −14.3920 | −1.08177 | ||||||||
\(178\) | 6.14794 | 0.460808 | ||||||||
\(179\) | 0.933072 | 0.0697411 | 0.0348706 | − | 0.999392i | \(-0.488898\pi\) | ||||
0.0348706 | + | 0.999392i | \(0.488898\pi\) | |||||||
\(180\) | −6.52157 | −0.486089 | ||||||||
\(181\) | 15.3228 | 1.13894 | 0.569468 | − | 0.822014i | \(-0.307149\pi\) | ||||
0.569468 | + | 0.822014i | \(0.307149\pi\) | |||||||
\(182\) | 46.4036 | 3.43966 | ||||||||
\(183\) | 11.0635 | 0.817836 | ||||||||
\(184\) | −10.7141 | −0.789856 | ||||||||
\(185\) | 7.40202 | 0.544207 | ||||||||
\(186\) | 1.82659 | 0.133932 | ||||||||
\(187\) | −2.88556 | −0.211013 | ||||||||
\(188\) | 31.4184 | 2.29142 | ||||||||
\(189\) | 21.6156 | 1.57231 | ||||||||
\(190\) | −1.15076 | −0.0834849 | ||||||||
\(191\) | −18.7002 | −1.35310 | −0.676549 | − | 0.736398i | \(-0.736525\pi\) | ||||
−0.676549 | + | 0.736398i | \(0.736525\pi\) | |||||||
\(192\) | 10.6505 | 0.768632 | ||||||||
\(193\) | −1.22566 | −0.0882250 | −0.0441125 | − | 0.999027i | \(-0.514046\pi\) | ||||
−0.0441125 | + | 0.999027i | \(0.514046\pi\) | |||||||
\(194\) | 16.6471 | 1.19519 | ||||||||
\(195\) | 3.41664 | 0.244671 | ||||||||
\(196\) | 49.0458 | 3.50327 | ||||||||
\(197\) | 11.8434 | 0.843807 | 0.421904 | − | 0.906641i | \(-0.361362\pi\) | ||||
0.421904 | + | 0.906641i | \(0.361362\pi\) | |||||||
\(198\) | −6.91142 | −0.491173 | ||||||||
\(199\) | −14.7180 | −1.04333 | −0.521665 | − | 0.853150i | \(-0.674689\pi\) | ||||
−0.521665 | + | 0.853150i | \(0.674689\pi\) | |||||||
\(200\) | 33.8845 | 2.39600 | ||||||||
\(201\) | −15.6437 | −1.10342 | ||||||||
\(202\) | −39.3542 | −2.76895 | ||||||||
\(203\) | −17.5605 | −1.23250 | ||||||||
\(204\) | 10.5988 | 0.742061 | ||||||||
\(205\) | −0.909444 | −0.0635183 | ||||||||
\(206\) | 25.1875 | 1.75489 | ||||||||
\(207\) | −2.56418 | −0.178223 | ||||||||
\(208\) | 43.4872 | 3.01530 | ||||||||
\(209\) | −0.865674 | −0.0598799 | ||||||||
\(210\) | 8.63982 | 0.596204 | ||||||||
\(211\) | −28.1994 | −1.94132 | −0.970662 | − | 0.240447i | \(-0.922706\pi\) | ||||
−0.970662 | + | 0.240447i | \(0.922706\pi\) | |||||||
\(212\) | 29.9789 | 2.05896 | ||||||||
\(213\) | 11.9673 | 0.819985 | ||||||||
\(214\) | −7.00187 | −0.478638 | ||||||||
\(215\) | −7.66176 | −0.522528 | ||||||||
\(216\) | 39.7827 | 2.70687 | ||||||||
\(217\) | 2.63983 | 0.179204 | ||||||||
\(218\) | −7.60857 | −0.515317 | ||||||||
\(219\) | 14.3554 | 0.970050 | ||||||||
\(220\) | −5.19776 | −0.350433 | ||||||||
\(221\) | 8.53359 | 0.574031 | ||||||||
\(222\) | −28.8131 | −1.93381 | ||||||||
\(223\) | −0.455850 | −0.0305260 | −0.0152630 | − | 0.999884i | \(-0.504859\pi\) | ||||
−0.0152630 | + | 0.999884i | \(0.504859\pi\) | |||||||
\(224\) | 47.3018 | 3.16048 | ||||||||
\(225\) | 8.10949 | 0.540633 | ||||||||
\(226\) | 53.0294 | 3.52746 | ||||||||
\(227\) | 14.7658 | 0.980040 | 0.490020 | − | 0.871711i | \(-0.336989\pi\) | ||||
0.490020 | + | 0.871711i | \(0.336989\pi\) | |||||||
\(228\) | 3.17965 | 0.210577 | ||||||||
\(229\) | 10.8749 | 0.718631 | 0.359316 | − | 0.933216i | \(-0.383010\pi\) | ||||
0.359316 | + | 0.933216i | \(0.383010\pi\) | |||||||
\(230\) | −2.71671 | −0.179135 | ||||||||
\(231\) | 6.49941 | 0.427630 | ||||||||
\(232\) | −32.3193 | −2.12187 | ||||||||
\(233\) | −24.1947 | −1.58505 | −0.792524 | − | 0.609841i | \(-0.791233\pi\) | ||||
−0.792524 | + | 0.609841i | \(0.791233\pi\) | |||||||
\(234\) | 20.4395 | 1.33617 | ||||||||
\(235\) | 4.70992 | 0.307241 | ||||||||
\(236\) | −64.7500 | −4.21487 | ||||||||
\(237\) | −15.3700 | −0.998392 | ||||||||
\(238\) | 21.5793 | 1.39878 | ||||||||
\(239\) | −18.7835 | −1.21500 | −0.607502 | − | 0.794318i | \(-0.707828\pi\) | ||||
−0.607502 | + | 0.794318i | \(0.707828\pi\) | |||||||
\(240\) | 8.09683 | 0.522648 | ||||||||
\(241\) | −24.7403 | −1.59366 | −0.796831 | − | 0.604203i | \(-0.793492\pi\) | ||||
−0.796831 | + | 0.604203i | \(0.793492\pi\) | |||||||
\(242\) | 23.3705 | 1.50231 | ||||||||
\(243\) | 15.4502 | 0.991133 | ||||||||
\(244\) | 49.7749 | 3.18651 | ||||||||
\(245\) | 7.35245 | 0.469731 | ||||||||
\(246\) | 3.54010 | 0.225709 | ||||||||
\(247\) | 2.56010 | 0.162895 | ||||||||
\(248\) | 4.85850 | 0.308515 | ||||||||
\(249\) | 1.37837 | 0.0873508 | ||||||||
\(250\) | 18.2196 | 1.15231 | ||||||||
\(251\) | −6.55742 | −0.413901 | −0.206950 | − | 0.978351i | \(-0.566354\pi\) | ||||
−0.206950 | + | 0.978351i | \(0.566354\pi\) | |||||||
\(252\) | 36.6884 | 2.31115 | ||||||||
\(253\) | −2.04368 | −0.128485 | ||||||||
\(254\) | 33.1801 | 2.08190 | ||||||||
\(255\) | 1.58886 | 0.0994981 | ||||||||
\(256\) | −12.2778 | −0.767362 | ||||||||
\(257\) | −12.5523 | −0.782988 | −0.391494 | − | 0.920181i | \(-0.628042\pi\) | ||||
−0.391494 | + | 0.920181i | \(0.628042\pi\) | |||||||
\(258\) | 29.8242 | 1.85677 | ||||||||
\(259\) | −41.6415 | −2.58748 | ||||||||
\(260\) | 15.3716 | 0.953305 | ||||||||
\(261\) | −7.73489 | −0.478778 | ||||||||
\(262\) | 29.6925 | 1.83441 | ||||||||
\(263\) | 21.0005 | 1.29494 | 0.647472 | − | 0.762089i | \(-0.275826\pi\) | ||||
0.647472 | + | 0.762089i | \(0.275826\pi\) | |||||||
\(264\) | 11.9619 | 0.736204 | ||||||||
\(265\) | 4.49414 | 0.276073 | ||||||||
\(266\) | 6.47383 | 0.396936 | ||||||||
\(267\) | −2.54656 | −0.155847 | ||||||||
\(268\) | −70.3813 | −4.29922 | ||||||||
\(269\) | −18.9122 | −1.15310 | −0.576550 | − | 0.817062i | \(-0.695601\pi\) | ||||
−0.576550 | + | 0.817062i | \(0.695601\pi\) | |||||||
\(270\) | 10.0874 | 0.613901 | ||||||||
\(271\) | −13.2394 | −0.804239 | −0.402120 | − | 0.915587i | \(-0.631726\pi\) | ||||
−0.402120 | + | 0.915587i | \(0.631726\pi\) | |||||||
\(272\) | 20.2231 | 1.22620 | ||||||||
\(273\) | −19.2210 | −1.16331 | ||||||||
\(274\) | 29.1706 | 1.76226 | ||||||||
\(275\) | 6.46335 | 0.389755 | ||||||||
\(276\) | 7.50651 | 0.451839 | ||||||||
\(277\) | −28.4071 | −1.70682 | −0.853409 | − | 0.521242i | \(-0.825469\pi\) | ||||
−0.853409 | + | 0.521242i | \(0.825469\pi\) | |||||||
\(278\) | 29.6296 | 1.77707 | ||||||||
\(279\) | 1.16277 | 0.0696134 | ||||||||
\(280\) | 22.9809 | 1.37337 | ||||||||
\(281\) | 4.02100 | 0.239873 | 0.119936 | − | 0.992782i | \(-0.461731\pi\) | ||||
0.119936 | + | 0.992782i | \(0.461731\pi\) | |||||||
\(282\) | −18.3339 | −1.09177 | ||||||||
\(283\) | 32.1318 | 1.91004 | 0.955018 | − | 0.296547i | \(-0.0958351\pi\) | ||||
0.955018 | + | 0.296547i | \(0.0958351\pi\) | |||||||
\(284\) | 53.8412 | 3.19489 | ||||||||
\(285\) | 0.476661 | 0.0282350 | ||||||||
\(286\) | 16.2905 | 0.963276 | ||||||||
\(287\) | 5.11626 | 0.302003 | ||||||||
\(288\) | 20.8351 | 1.22772 | ||||||||
\(289\) | −13.0316 | −0.766564 | ||||||||
\(290\) | −8.19499 | −0.481226 | ||||||||
\(291\) | −6.89548 | −0.404220 | ||||||||
\(292\) | 64.5855 | 3.77958 | ||||||||
\(293\) | −15.7469 | −0.919944 | −0.459972 | − | 0.887934i | \(-0.652140\pi\) | ||||
−0.459972 | + | 0.887934i | \(0.652140\pi\) | |||||||
\(294\) | −28.6202 | −1.66916 | ||||||||
\(295\) | −9.70666 | −0.565144 | ||||||||
\(296\) | −76.6395 | −4.45458 | ||||||||
\(297\) | 7.58840 | 0.440324 | ||||||||
\(298\) | 32.7315 | 1.89609 | ||||||||
\(299\) | 6.04387 | 0.349526 | ||||||||
\(300\) | −23.7401 | −1.37064 | ||||||||
\(301\) | 43.1028 | 2.48440 | ||||||||
\(302\) | −7.18419 | −0.413403 | ||||||||
\(303\) | 16.3010 | 0.936471 | ||||||||
\(304\) | 6.06697 | 0.347964 | ||||||||
\(305\) | 7.46175 | 0.427259 | ||||||||
\(306\) | 9.50506 | 0.543368 | ||||||||
\(307\) | 14.1736 | 0.808928 | 0.404464 | − | 0.914554i | \(-0.367458\pi\) | ||||
0.404464 | + | 0.914554i | \(0.367458\pi\) | |||||||
\(308\) | 29.2410 | 1.66616 | ||||||||
\(309\) | −10.4330 | −0.593513 | ||||||||
\(310\) | 1.23194 | 0.0699694 | ||||||||
\(311\) | 6.64208 | 0.376638 | 0.188319 | − | 0.982108i | \(-0.439696\pi\) | ||||
0.188319 | + | 0.982108i | \(0.439696\pi\) | |||||||
\(312\) | −35.3755 | −2.00274 | ||||||||
\(313\) | −19.0713 | −1.07797 | −0.538987 | − | 0.842314i | \(-0.681193\pi\) | ||||
−0.538987 | + | 0.842314i | \(0.681193\pi\) | |||||||
\(314\) | 62.3879 | 3.52075 | ||||||||
\(315\) | 5.49995 | 0.309887 | ||||||||
\(316\) | −69.1502 | −3.89001 | ||||||||
\(317\) | 8.46312 | 0.475336 | 0.237668 | − | 0.971346i | \(-0.423617\pi\) | ||||
0.237668 | + | 0.971346i | \(0.423617\pi\) | |||||||
\(318\) | −17.4939 | −0.981009 | ||||||||
\(319\) | −6.16479 | −0.345162 | ||||||||
\(320\) | 7.18320 | 0.401553 | ||||||||
\(321\) | 2.90027 | 0.161877 | ||||||||
\(322\) | 15.2834 | 0.851711 | ||||||||
\(323\) | 1.19053 | 0.0662430 | ||||||||
\(324\) | −1.19706 | −0.0665031 | ||||||||
\(325\) | −19.1144 | −1.06027 | ||||||||
\(326\) | −48.5334 | −2.68801 | ||||||||
\(327\) | 3.15158 | 0.174283 | ||||||||
\(328\) | 9.41626 | 0.519926 | ||||||||
\(329\) | −26.4966 | −1.46081 | ||||||||
\(330\) | 3.03310 | 0.166967 | ||||||||
\(331\) | −1.71062 | −0.0940244 | −0.0470122 | − | 0.998894i | \(-0.514970\pi\) | ||||
−0.0470122 | + | 0.998894i | \(0.514970\pi\) | |||||||
\(332\) | 6.20133 | 0.340342 | ||||||||
\(333\) | −18.3419 | −1.00513 | ||||||||
\(334\) | −52.1474 | −2.85338 | ||||||||
\(335\) | −10.5508 | −0.576454 | ||||||||
\(336\) | −45.5503 | −2.48497 | ||||||||
\(337\) | 12.1880 | 0.663924 | 0.331962 | − | 0.943293i | \(-0.392289\pi\) | ||||
0.331962 | + | 0.943293i | \(0.392289\pi\) | |||||||
\(338\) | −14.0469 | −0.764048 | ||||||||
\(339\) | −21.9655 | −1.19300 | ||||||||
\(340\) | 7.14831 | 0.387672 | ||||||||
\(341\) | 0.926742 | 0.0501859 | ||||||||
\(342\) | 2.85154 | 0.154194 | ||||||||
\(343\) | −12.4800 | −0.673858 | ||||||||
\(344\) | 79.3288 | 4.27712 | ||||||||
\(345\) | 1.12530 | 0.0605841 | ||||||||
\(346\) | −38.0721 | −2.04677 | ||||||||
\(347\) | −15.8787 | −0.852415 | −0.426208 | − | 0.904625i | \(-0.640151\pi\) | ||||
−0.426208 | + | 0.904625i | \(0.640151\pi\) | |||||||
\(348\) | 22.6435 | 1.21382 | ||||||||
\(349\) | −18.0671 | −0.967110 | −0.483555 | − | 0.875314i | \(-0.660655\pi\) | ||||
−0.483555 | + | 0.875314i | \(0.660655\pi\) | |||||||
\(350\) | −48.3353 | −2.58363 | ||||||||
\(351\) | −22.4415 | −1.19784 | ||||||||
\(352\) | 16.6058 | 0.885092 | ||||||||
\(353\) | 19.2972 | 1.02709 | 0.513543 | − | 0.858064i | \(-0.328333\pi\) | ||||
0.513543 | + | 0.858064i | \(0.328333\pi\) | |||||||
\(354\) | 37.7842 | 2.00821 | ||||||||
\(355\) | 8.07132 | 0.428381 | ||||||||
\(356\) | −11.4571 | −0.607223 | ||||||||
\(357\) | −8.93843 | −0.473072 | ||||||||
\(358\) | −2.44965 | −0.129468 | ||||||||
\(359\) | 8.53872 | 0.450656 | 0.225328 | − | 0.974283i | \(-0.427655\pi\) | ||||
0.225328 | + | 0.974283i | \(0.427655\pi\) | |||||||
\(360\) | 10.1224 | 0.533499 | ||||||||
\(361\) | −18.6428 | −0.981202 | ||||||||
\(362\) | −40.2279 | −2.11433 | ||||||||
\(363\) | −9.68038 | −0.508088 | ||||||||
\(364\) | −86.4759 | −4.53257 | ||||||||
\(365\) | 9.68200 | 0.506779 | ||||||||
\(366\) | −29.0456 | −1.51824 | ||||||||
\(367\) | −15.1636 | −0.791533 | −0.395766 | − | 0.918351i | \(-0.629521\pi\) | ||||
−0.395766 | + | 0.918351i | \(0.629521\pi\) | |||||||
\(368\) | 14.3229 | 0.746632 | ||||||||
\(369\) | 2.25357 | 0.117316 | ||||||||
\(370\) | −19.4330 | −1.01027 | ||||||||
\(371\) | −25.2827 | −1.31261 | ||||||||
\(372\) | −3.40395 | −0.176487 | ||||||||
\(373\) | 2.17168 | 0.112445 | 0.0562225 | − | 0.998418i | \(-0.482094\pi\) | ||||
0.0562225 | + | 0.998418i | \(0.482094\pi\) | |||||||
\(374\) | 7.57563 | 0.391726 | ||||||||
\(375\) | −7.54680 | −0.389715 | ||||||||
\(376\) | −48.7659 | −2.51491 | ||||||||
\(377\) | 18.2314 | 0.938965 | ||||||||
\(378\) | −56.7489 | −2.91885 | ||||||||
\(379\) | −21.5504 | −1.10697 | −0.553485 | − | 0.832859i | \(-0.686702\pi\) | ||||
−0.553485 | + | 0.832859i | \(0.686702\pi\) | |||||||
\(380\) | 2.14451 | 0.110011 | ||||||||
\(381\) | −13.7437 | −0.704109 | ||||||||
\(382\) | 49.0947 | 2.51191 | ||||||||
\(383\) | 11.5508 | 0.590216 | 0.295108 | − | 0.955464i | \(-0.404644\pi\) | ||||
0.295108 | + | 0.955464i | \(0.404644\pi\) | |||||||
\(384\) | −3.02790 | −0.154517 | ||||||||
\(385\) | 4.38352 | 0.223405 | ||||||||
\(386\) | 3.21780 | 0.163782 | ||||||||
\(387\) | 18.9856 | 0.965090 | ||||||||
\(388\) | −31.0229 | −1.57495 | ||||||||
\(389\) | 13.1413 | 0.666289 | 0.333144 | − | 0.942876i | \(-0.391890\pi\) | ||||
0.333144 | + | 0.942876i | \(0.391890\pi\) | |||||||
\(390\) | −8.96992 | −0.454210 | ||||||||
\(391\) | 2.81061 | 0.142139 | ||||||||
\(392\) | −76.1263 | −3.84496 | ||||||||
\(393\) | −12.2991 | −0.620406 | ||||||||
\(394\) | −31.0932 | −1.56645 | ||||||||
\(395\) | −10.3663 | −0.521585 | ||||||||
\(396\) | 12.8799 | 0.647237 | ||||||||
\(397\) | 3.76584 | 0.189002 | 0.0945011 | − | 0.995525i | \(-0.469874\pi\) | ||||
0.0945011 | + | 0.995525i | \(0.469874\pi\) | |||||||
\(398\) | 38.6400 | 1.93685 | ||||||||
\(399\) | −2.68155 | −0.134245 | ||||||||
\(400\) | −45.2976 | −2.26488 | ||||||||
\(401\) | 21.6231 | 1.07980 | 0.539902 | − | 0.841728i | \(-0.318461\pi\) | ||||
0.539902 | + | 0.841728i | \(0.318461\pi\) | |||||||
\(402\) | 41.0703 | 2.04840 | ||||||||
\(403\) | −2.74070 | −0.136524 | ||||||||
\(404\) | 73.3389 | 3.64874 | ||||||||
\(405\) | −0.179450 | −0.00891696 | ||||||||
\(406\) | 46.1026 | 2.28803 | ||||||||
\(407\) | −14.6187 | −0.724622 | ||||||||
\(408\) | −16.4508 | −0.814436 | ||||||||
\(409\) | 5.32155 | 0.263134 | 0.131567 | − | 0.991307i | \(-0.457999\pi\) | ||||
0.131567 | + | 0.991307i | \(0.457999\pi\) | |||||||
\(410\) | 2.38762 | 0.117916 | ||||||||
\(411\) | −12.0829 | −0.596003 | ||||||||
\(412\) | −46.9384 | −2.31249 | ||||||||
\(413\) | 54.6068 | 2.68702 | ||||||||
\(414\) | 6.73191 | 0.330855 | ||||||||
\(415\) | 0.929641 | 0.0456343 | ||||||||
\(416\) | −49.1091 | −2.40777 | ||||||||
\(417\) | −12.2730 | −0.601011 | ||||||||
\(418\) | 2.27271 | 0.111162 | ||||||||
\(419\) | 31.1047 | 1.51957 | 0.759783 | − | 0.650177i | \(-0.225305\pi\) | ||||
0.759783 | + | 0.650177i | \(0.225305\pi\) | |||||||
\(420\) | −16.1008 | −0.785640 | ||||||||
\(421\) | −0.523219 | −0.0255001 | −0.0127501 | − | 0.999919i | \(-0.504059\pi\) | ||||
−0.0127501 | + | 0.999919i | \(0.504059\pi\) | |||||||
\(422\) | 74.0335 | 3.60389 | ||||||||
\(423\) | −11.6710 | −0.567464 | ||||||||
\(424\) | −46.5317 | −2.25978 | ||||||||
\(425\) | −8.88884 | −0.431172 | ||||||||
\(426\) | −31.4185 | −1.52223 | ||||||||
\(427\) | −41.9776 | −2.03144 | ||||||||
\(428\) | 13.0484 | 0.630718 | ||||||||
\(429\) | −6.74774 | −0.325784 | ||||||||
\(430\) | 20.1149 | 0.970026 | ||||||||
\(431\) | 25.3742 | 1.22223 | 0.611116 | − | 0.791541i | \(-0.290721\pi\) | ||||
0.611116 | + | 0.791541i | \(0.290721\pi\) | |||||||
\(432\) | −53.1824 | −2.55874 | ||||||||
\(433\) | 31.0150 | 1.49049 | 0.745243 | − | 0.666793i | \(-0.232334\pi\) | ||||
0.745243 | + | 0.666793i | \(0.232334\pi\) | |||||||
\(434\) | −6.93052 | −0.332675 | ||||||||
\(435\) | 3.39448 | 0.162753 | ||||||||
\(436\) | 14.1790 | 0.679052 | ||||||||
\(437\) | 0.843189 | 0.0403352 | ||||||||
\(438\) | −37.6882 | −1.80081 | ||||||||
\(439\) | −29.1319 | −1.39039 | −0.695195 | − | 0.718821i | \(-0.744682\pi\) | ||||
−0.695195 | + | 0.718821i | \(0.744682\pi\) | |||||||
\(440\) | 8.06768 | 0.384612 | ||||||||
\(441\) | −18.2191 | −0.867576 | ||||||||
\(442\) | −22.4038 | −1.06564 | ||||||||
\(443\) | −6.88182 | −0.326965 | −0.163483 | − | 0.986546i | \(-0.552273\pi\) | ||||
−0.163483 | + | 0.986546i | \(0.552273\pi\) | |||||||
\(444\) | 53.6950 | 2.54825 | ||||||||
\(445\) | −1.71753 | −0.0814186 | ||||||||
\(446\) | 1.19677 | 0.0566687 | ||||||||
\(447\) | −13.5579 | −0.641265 | ||||||||
\(448\) | −40.4105 | −1.90922 | ||||||||
\(449\) | −29.6542 | −1.39947 | −0.699735 | − | 0.714402i | \(-0.746699\pi\) | ||||
−0.699735 | + | 0.714402i | \(0.746699\pi\) | |||||||
\(450\) | −21.2903 | −1.00364 | ||||||||
\(451\) | 1.79612 | 0.0845758 | ||||||||
\(452\) | −98.8235 | −4.64827 | ||||||||
\(453\) | 2.97579 | 0.139815 | ||||||||
\(454\) | −38.7655 | −1.81936 | ||||||||
\(455\) | −12.9636 | −0.607742 | ||||||||
\(456\) | −4.93528 | −0.231116 | ||||||||
\(457\) | 14.7253 | 0.688820 | 0.344410 | − | 0.938819i | \(-0.388079\pi\) | ||||
0.344410 | + | 0.938819i | \(0.388079\pi\) | |||||||
\(458\) | −28.5504 | −1.33407 | ||||||||
\(459\) | −10.4361 | −0.487115 | ||||||||
\(460\) | 5.06276 | 0.236052 | ||||||||
\(461\) | −14.6573 | −0.682658 | −0.341329 | − | 0.939944i | \(-0.610877\pi\) | ||||
−0.341329 | + | 0.939944i | \(0.610877\pi\) | |||||||
\(462\) | −17.0633 | −0.793857 | ||||||||
\(463\) | −27.9279 | −1.29792 | −0.648960 | − | 0.760822i | \(-0.724796\pi\) | ||||
−0.648960 | + | 0.760822i | \(0.724796\pi\) | |||||||
\(464\) | 43.2052 | 2.00575 | ||||||||
\(465\) | −0.510286 | −0.0236640 | ||||||||
\(466\) | 63.5198 | 2.94250 | ||||||||
\(467\) | −37.5168 | −1.73607 | −0.868035 | − | 0.496504i | \(-0.834617\pi\) | ||||
−0.868035 | + | 0.496504i | \(0.834617\pi\) | |||||||
\(468\) | −38.0902 | −1.76072 | ||||||||
\(469\) | 59.3559 | 2.74080 | ||||||||
\(470\) | −12.3652 | −0.570366 | ||||||||
\(471\) | −25.8419 | −1.19073 | ||||||||
\(472\) | 100.501 | 4.62595 | ||||||||
\(473\) | 15.1317 | 0.695756 | ||||||||
\(474\) | 40.3519 | 1.85342 | ||||||||
\(475\) | −2.66667 | −0.122355 | ||||||||
\(476\) | −40.2143 | −1.84322 | ||||||||
\(477\) | −11.1363 | −0.509896 | ||||||||
\(478\) | 49.3135 | 2.25555 | ||||||||
\(479\) | 15.1993 | 0.694475 | 0.347238 | − | 0.937777i | \(-0.387120\pi\) | ||||
0.347238 | + | 0.937777i | \(0.387120\pi\) | |||||||
\(480\) | −9.14355 | −0.417344 | ||||||||
\(481\) | 43.2326 | 1.97124 | ||||||||
\(482\) | 64.9521 | 2.95849 | ||||||||
\(483\) | −6.33060 | −0.288052 | ||||||||
\(484\) | −43.5523 | −1.97965 | ||||||||
\(485\) | −4.65064 | −0.211175 | ||||||||
\(486\) | −40.5624 | −1.83995 | ||||||||
\(487\) | −21.9599 | −0.995099 | −0.497550 | − | 0.867435i | \(-0.665767\pi\) | ||||
−0.497550 | + | 0.867435i | \(0.665767\pi\) | |||||||
\(488\) | −77.2579 | −3.49730 | ||||||||
\(489\) | 20.1032 | 0.909098 | ||||||||
\(490\) | −19.3028 | −0.872013 | ||||||||
\(491\) | 10.9171 | 0.492680 | 0.246340 | − | 0.969183i | \(-0.420772\pi\) | ||||
0.246340 | + | 0.969183i | \(0.420772\pi\) | |||||||
\(492\) | −6.59720 | −0.297425 | ||||||||
\(493\) | 8.47823 | 0.381840 | ||||||||
\(494\) | −6.72118 | −0.302400 | ||||||||
\(495\) | 1.93082 | 0.0867838 | ||||||||
\(496\) | −6.49495 | −0.291632 | ||||||||
\(497\) | −45.4068 | −2.03678 | ||||||||
\(498\) | −3.61872 | −0.162159 | ||||||||
\(499\) | −32.0158 | −1.43322 | −0.716612 | − | 0.697472i | \(-0.754308\pi\) | ||||
−0.716612 | + | 0.697472i | \(0.754308\pi\) | |||||||
\(500\) | −33.9532 | −1.51843 | ||||||||
\(501\) | 21.6002 | 0.965024 | ||||||||
\(502\) | 17.2156 | 0.768370 | ||||||||
\(503\) | 29.5367 | 1.31698 | 0.658488 | − | 0.752591i | \(-0.271196\pi\) | ||||
0.658488 | + | 0.752591i | \(0.271196\pi\) | |||||||
\(504\) | −56.9458 | −2.53657 | ||||||||
\(505\) | 10.9942 | 0.489236 | ||||||||
\(506\) | 5.36540 | 0.238521 | ||||||||
\(507\) | 5.81840 | 0.258404 | ||||||||
\(508\) | −61.8331 | −2.74340 | ||||||||
\(509\) | −32.0629 | −1.42116 | −0.710581 | − | 0.703615i | \(-0.751568\pi\) | ||||
−0.710581 | + | 0.703615i | \(0.751568\pi\) | |||||||
\(510\) | −4.17132 | −0.184709 | ||||||||
\(511\) | −54.4680 | −2.40952 | ||||||||
\(512\) | 37.8024 | 1.67064 | ||||||||
\(513\) | −3.13085 | −0.138230 | ||||||||
\(514\) | 32.9542 | 1.45355 | ||||||||
\(515\) | −7.03652 | −0.310066 | ||||||||
\(516\) | −55.5792 | −2.44674 | ||||||||
\(517\) | −9.30192 | −0.409098 | ||||||||
\(518\) | 109.324 | 4.80342 | ||||||||
\(519\) | 15.7700 | 0.692227 | ||||||||
\(520\) | −23.8589 | −1.04628 | ||||||||
\(521\) | 32.3202 | 1.41598 | 0.707988 | − | 0.706225i | \(-0.249603\pi\) | ||||
0.707988 | + | 0.706225i | \(0.249603\pi\) | |||||||
\(522\) | 20.3069 | 0.888808 | ||||||||
\(523\) | −18.8329 | −0.823504 | −0.411752 | − | 0.911296i | \(-0.635083\pi\) | ||||
−0.411752 | + | 0.911296i | \(0.635083\pi\) | |||||||
\(524\) | −55.3338 | −2.41727 | ||||||||
\(525\) | 20.0212 | 0.873795 | ||||||||
\(526\) | −55.1338 | −2.40395 | ||||||||
\(527\) | −1.27452 | −0.0555189 | ||||||||
\(528\) | −15.9909 | −0.695916 | ||||||||
\(529\) | −21.0094 | −0.913452 | ||||||||
\(530\) | −11.7987 | −0.512504 | ||||||||
\(531\) | 24.0527 | 1.04380 | ||||||||
\(532\) | −12.0644 | −0.523057 | ||||||||
\(533\) | −5.31174 | −0.230077 | ||||||||
\(534\) | 6.68565 | 0.289316 | ||||||||
\(535\) | 1.95608 | 0.0845689 | ||||||||
\(536\) | 109.242 | 4.71854 | ||||||||
\(537\) | 1.01468 | 0.0437867 | ||||||||
\(538\) | 49.6515 | 2.14063 | ||||||||
\(539\) | −14.5208 | −0.625455 | ||||||||
\(540\) | −18.7985 | −0.808960 | ||||||||
\(541\) | 19.3724 | 0.832883 | 0.416442 | − | 0.909162i | \(-0.363277\pi\) | ||||
0.416442 | + | 0.909162i | \(0.363277\pi\) | |||||||
\(542\) | 34.7583 | 1.49300 | ||||||||
\(543\) | 16.6630 | 0.715076 | ||||||||
\(544\) | −22.8374 | −0.979146 | ||||||||
\(545\) | 2.12558 | 0.0910497 | ||||||||
\(546\) | 50.4621 | 2.15958 | ||||||||
\(547\) | 28.3258 | 1.21112 | 0.605561 | − | 0.795799i | \(-0.292949\pi\) | ||||
0.605561 | + | 0.795799i | \(0.292949\pi\) | |||||||
\(548\) | −54.3611 | −2.32219 | ||||||||
\(549\) | −18.4899 | −0.789131 | ||||||||
\(550\) | −16.9686 | −0.723545 | ||||||||
\(551\) | 2.54349 | 0.108356 | ||||||||
\(552\) | −11.6512 | −0.495908 | ||||||||
\(553\) | 58.3177 | 2.47992 | ||||||||
\(554\) | 74.5789 | 3.16855 | ||||||||
\(555\) | 8.04941 | 0.341678 | ||||||||
\(556\) | −55.2166 | −2.34170 | ||||||||
\(557\) | −3.53402 | −0.149741 | −0.0748706 | − | 0.997193i | \(-0.523854\pi\) | ||||
−0.0748706 | + | 0.997193i | \(0.523854\pi\) | |||||||
\(558\) | −3.05270 | −0.129231 | ||||||||
\(559\) | −44.7496 | −1.89271 | ||||||||
\(560\) | −30.7214 | −1.29821 | ||||||||
\(561\) | −3.13793 | −0.132484 | ||||||||
\(562\) | −10.5566 | −0.445302 | ||||||||
\(563\) | 6.88783 | 0.290287 | 0.145144 | − | 0.989411i | \(-0.453636\pi\) | ||||
0.145144 | + | 0.989411i | \(0.453636\pi\) | |||||||
\(564\) | 34.1663 | 1.43866 | ||||||||
\(565\) | −14.8146 | −0.623256 | ||||||||
\(566\) | −84.3575 | −3.54581 | ||||||||
\(567\) | 1.00953 | 0.0423965 | ||||||||
\(568\) | −83.5694 | −3.50649 | ||||||||
\(569\) | −38.2911 | −1.60525 | −0.802623 | − | 0.596486i | \(-0.796563\pi\) | ||||
−0.802623 | + | 0.596486i | \(0.796563\pi\) | |||||||
\(570\) | −1.25141 | −0.0524157 | ||||||||
\(571\) | −21.1785 | −0.886294 | −0.443147 | − | 0.896449i | \(-0.646138\pi\) | ||||
−0.443147 | + | 0.896449i | \(0.646138\pi\) | |||||||
\(572\) | −30.3583 | −1.26934 | ||||||||
\(573\) | −20.3357 | −0.849537 | ||||||||
\(574\) | −13.4320 | −0.560642 | ||||||||
\(575\) | −6.29547 | −0.262539 | ||||||||
\(576\) | −17.7997 | −0.741654 | ||||||||
\(577\) | −27.9086 | −1.16185 | −0.580925 | − | 0.813957i | \(-0.697309\pi\) | ||||
−0.580925 | + | 0.813957i | \(0.697309\pi\) | |||||||
\(578\) | 34.2126 | 1.42306 | ||||||||
\(579\) | −1.33286 | −0.0553917 | ||||||||
\(580\) | 15.2719 | 0.634130 | ||||||||
\(581\) | −5.22988 | −0.216972 | ||||||||
\(582\) | 18.1031 | 0.750398 | ||||||||
\(583\) | −8.87575 | −0.367596 | ||||||||
\(584\) | −100.246 | −4.14821 | ||||||||
\(585\) | −5.71009 | −0.236083 | ||||||||
\(586\) | 41.3413 | 1.70779 | ||||||||
\(587\) | −7.26336 | −0.299791 | −0.149895 | − | 0.988702i | \(-0.547894\pi\) | ||||
−0.149895 | + | 0.988702i | \(0.547894\pi\) | |||||||
\(588\) | 53.3354 | 2.19952 | ||||||||
\(589\) | −0.382358 | −0.0157548 | ||||||||
\(590\) | 25.4835 | 1.04914 | ||||||||
\(591\) | 12.8792 | 0.529781 | ||||||||
\(592\) | 102.453 | 4.21081 | ||||||||
\(593\) | 19.0796 | 0.783507 | 0.391754 | − | 0.920070i | \(-0.371869\pi\) | ||||
0.391754 | + | 0.920070i | \(0.371869\pi\) | |||||||
\(594\) | −19.9223 | −0.817421 | ||||||||
\(595\) | −6.02851 | −0.247145 | ||||||||
\(596\) | −60.9972 | −2.49854 | ||||||||
\(597\) | −16.0052 | −0.655051 | ||||||||
\(598\) | −15.8673 | −0.648864 | ||||||||
\(599\) | 30.4303 | 1.24335 | 0.621674 | − | 0.783276i | \(-0.286453\pi\) | ||||
0.621674 | + | 0.783276i | \(0.286453\pi\) | |||||||
\(600\) | 36.8481 | 1.50432 | ||||||||
\(601\) | −35.0202 | −1.42850 | −0.714252 | − | 0.699888i | \(-0.753233\pi\) | ||||
−0.714252 | + | 0.699888i | \(0.753233\pi\) | |||||||
\(602\) | −113.160 | −4.61207 | ||||||||
\(603\) | 26.1446 | 1.06469 | ||||||||
\(604\) | 13.3882 | 0.544757 | ||||||||
\(605\) | −6.52892 | −0.265438 | ||||||||
\(606\) | −42.7961 | −1.73847 | ||||||||
\(607\) | 19.6820 | 0.798869 | 0.399434 | − | 0.916762i | \(-0.369207\pi\) | ||||
0.399434 | + | 0.916762i | \(0.369207\pi\) | |||||||
\(608\) | −6.85127 | −0.277856 | ||||||||
\(609\) | −19.0963 | −0.773822 | ||||||||
\(610\) | −19.5898 | −0.793167 | ||||||||
\(611\) | 27.5090 | 1.11289 | ||||||||
\(612\) | −17.7132 | −0.716016 | ||||||||
\(613\) | 33.9941 | 1.37301 | 0.686505 | − | 0.727125i | \(-0.259144\pi\) | ||||
0.686505 | + | 0.727125i | \(0.259144\pi\) | |||||||
\(614\) | −37.2107 | −1.50170 | ||||||||
\(615\) | −0.988985 | −0.0398797 | ||||||||
\(616\) | −45.3864 | −1.82867 | ||||||||
\(617\) | 35.3575 | 1.42344 | 0.711720 | − | 0.702463i | \(-0.247916\pi\) | ||||
0.711720 | + | 0.702463i | \(0.247916\pi\) | |||||||
\(618\) | 27.3904 | 1.10180 | ||||||||
\(619\) | −42.6361 | −1.71369 | −0.856846 | − | 0.515573i | \(-0.827579\pi\) | ||||
−0.856846 | + | 0.515573i | \(0.827579\pi\) | |||||||
\(620\) | −2.29579 | −0.0922012 | ||||||||
\(621\) | −7.39130 | −0.296603 | ||||||||
\(622\) | −17.4378 | −0.699194 | ||||||||
\(623\) | 9.66229 | 0.387112 | ||||||||
\(624\) | 47.2907 | 1.89314 | ||||||||
\(625\) | 17.2204 | 0.688817 | ||||||||
\(626\) | 50.0691 | 2.00116 | ||||||||
\(627\) | −0.941387 | −0.0375954 | ||||||||
\(628\) | −116.264 | −4.63942 | ||||||||
\(629\) | 20.1046 | 0.801624 | ||||||||
\(630\) | −14.4394 | −0.575278 | ||||||||
\(631\) | 26.4466 | 1.05282 | 0.526412 | − | 0.850230i | \(-0.323537\pi\) | ||||
0.526412 | + | 0.850230i | \(0.323537\pi\) | |||||||
\(632\) | 107.331 | 4.26941 | ||||||||
\(633\) | −30.6657 | −1.21885 | ||||||||
\(634\) | −22.2187 | −0.882419 | ||||||||
\(635\) | −9.26939 | −0.367845 | ||||||||
\(636\) | 32.6009 | 1.29271 | ||||||||
\(637\) | 42.9430 | 1.70147 | ||||||||
\(638\) | 16.1848 | 0.640762 | ||||||||
\(639\) | −20.0004 | −0.791205 | ||||||||
\(640\) | −2.04216 | −0.0807236 | ||||||||
\(641\) | −9.25871 | −0.365697 | −0.182848 | − | 0.983141i | \(-0.558532\pi\) | ||||
−0.182848 | + | 0.983141i | \(0.558532\pi\) | |||||||
\(642\) | −7.61426 | −0.300511 | ||||||||
\(643\) | 16.0559 | 0.633181 | 0.316591 | − | 0.948562i | \(-0.397462\pi\) | ||||
0.316591 | + | 0.948562i | \(0.397462\pi\) | |||||||
\(644\) | −28.4815 | −1.12233 | ||||||||
\(645\) | −8.33187 | −0.328067 | ||||||||
\(646\) | −3.12558 | −0.122974 | ||||||||
\(647\) | −8.96477 | −0.352442 | −0.176221 | − | 0.984351i | \(-0.556387\pi\) | ||||
−0.176221 | + | 0.984351i | \(0.556387\pi\) | |||||||
\(648\) | 1.85801 | 0.0729893 | ||||||||
\(649\) | 19.1703 | 0.752500 | ||||||||
\(650\) | 50.1821 | 1.96830 | ||||||||
\(651\) | 2.87072 | 0.112512 | ||||||||
\(652\) | 90.4448 | 3.54209 | ||||||||
\(653\) | −27.5018 | −1.07623 | −0.538115 | − | 0.842872i | \(-0.680863\pi\) | ||||
−0.538115 | + | 0.842872i | \(0.680863\pi\) | |||||||
\(654\) | −8.27402 | −0.323540 | ||||||||
\(655\) | −8.29509 | −0.324116 | ||||||||
\(656\) | −12.5879 | −0.491473 | ||||||||
\(657\) | −23.9916 | −0.936003 | ||||||||
\(658\) | 69.5632 | 2.71185 | ||||||||
\(659\) | −11.5297 | −0.449135 | −0.224567 | − | 0.974459i | \(-0.572097\pi\) | ||||
−0.224567 | + | 0.974459i | \(0.572097\pi\) | |||||||
\(660\) | −5.65236 | −0.220018 | ||||||||
\(661\) | −27.2742 | −1.06084 | −0.530422 | − | 0.847734i | \(-0.677966\pi\) | ||||
−0.530422 | + | 0.847734i | \(0.677966\pi\) | |||||||
\(662\) | 4.49101 | 0.174548 | ||||||||
\(663\) | 9.27995 | 0.360403 | ||||||||
\(664\) | −9.62538 | −0.373537 | ||||||||
\(665\) | −1.80857 | −0.0701333 | ||||||||
\(666\) | 48.1542 | 1.86594 | ||||||||
\(667\) | 6.00467 | 0.232502 | ||||||||
\(668\) | 97.1797 | 3.76000 | ||||||||
\(669\) | −0.495719 | −0.0191656 | ||||||||
\(670\) | 27.6998 | 1.07014 | ||||||||
\(671\) | −14.7367 | −0.568903 | ||||||||
\(672\) | 51.4388 | 1.98430 | ||||||||
\(673\) | 29.2840 | 1.12881 | 0.564407 | − | 0.825497i | \(-0.309105\pi\) | ||||
0.564407 | + | 0.825497i | \(0.309105\pi\) | |||||||
\(674\) | −31.9979 | −1.23251 | ||||||||
\(675\) | 23.3757 | 0.899733 | ||||||||
\(676\) | 26.1772 | 1.00681 | ||||||||
\(677\) | 7.58709 | 0.291595 | 0.145798 | − | 0.989314i | \(-0.453425\pi\) | ||||
0.145798 | + | 0.989314i | \(0.453425\pi\) | |||||||
\(678\) | 57.6674 | 2.21470 | ||||||||
\(679\) | 26.1631 | 1.00405 | ||||||||
\(680\) | −11.0952 | −0.425482 | ||||||||
\(681\) | 16.0572 | 0.615314 | ||||||||
\(682\) | −2.43303 | −0.0931656 | ||||||||
\(683\) | 29.2676 | 1.11989 | 0.559947 | − | 0.828529i | \(-0.310822\pi\) | ||||
0.559947 | + | 0.828529i | \(0.310822\pi\) | |||||||
\(684\) | −5.31401 | −0.203186 | ||||||||
\(685\) | −8.14926 | −0.311367 | ||||||||
\(686\) | 32.7645 | 1.25096 | ||||||||
\(687\) | 11.8260 | 0.451190 | ||||||||
\(688\) | −106.049 | −4.04306 | ||||||||
\(689\) | 26.2487 | 0.999995 | ||||||||
\(690\) | −2.95432 | −0.112469 | ||||||||
\(691\) | −23.1378 | −0.880205 | −0.440103 | − | 0.897948i | \(-0.645058\pi\) | ||||
−0.440103 | + | 0.897948i | \(0.645058\pi\) | |||||||
\(692\) | 70.9497 | 2.69710 | ||||||||
\(693\) | −10.8622 | −0.412621 | ||||||||
\(694\) | 41.6874 | 1.58243 | ||||||||
\(695\) | −8.27751 | −0.313984 | ||||||||
\(696\) | −35.1460 | −1.33221 | ||||||||
\(697\) | −2.47014 | −0.0935633 | ||||||||
\(698\) | 47.4327 | 1.79535 | ||||||||
\(699\) | −26.3108 | −0.995165 | ||||||||
\(700\) | 90.0758 | 3.40454 | ||||||||
\(701\) | −9.53588 | −0.360165 | −0.180083 | − | 0.983652i | \(-0.557636\pi\) | ||||
−0.180083 | + | 0.983652i | \(0.557636\pi\) | |||||||
\(702\) | 58.9171 | 2.22368 | ||||||||
\(703\) | 6.03144 | 0.227480 | ||||||||
\(704\) | −14.1865 | −0.534675 | ||||||||
\(705\) | 5.12186 | 0.192900 | ||||||||
\(706\) | −50.6621 | −1.90669 | ||||||||
\(707\) | −61.8502 | −2.32612 | ||||||||
\(708\) | −70.4131 | −2.64629 | ||||||||
\(709\) | −26.2648 | −0.986395 | −0.493198 | − | 0.869917i | \(-0.664172\pi\) | ||||
−0.493198 | + | 0.869917i | \(0.664172\pi\) | |||||||
\(710\) | −21.1901 | −0.795251 | ||||||||
\(711\) | 25.6873 | 0.963349 | ||||||||
\(712\) | 17.7830 | 0.666448 | ||||||||
\(713\) | −0.902671 | −0.0338053 | ||||||||
\(714\) | 23.4666 | 0.878216 | ||||||||
\(715\) | −4.55100 | −0.170198 | ||||||||
\(716\) | 4.56507 | 0.170605 | ||||||||
\(717\) | −20.4263 | −0.762836 | ||||||||
\(718\) | −22.4172 | −0.836603 | ||||||||
\(719\) | 4.08826 | 0.152466 | 0.0762331 | − | 0.997090i | \(-0.475711\pi\) | ||||
0.0762331 | + | 0.997090i | \(0.475711\pi\) | |||||||
\(720\) | −13.5319 | −0.504304 | ||||||||
\(721\) | 39.5854 | 1.47424 | ||||||||
\(722\) | 48.9442 | 1.82151 | ||||||||
\(723\) | −26.9041 | −1.00057 | ||||||||
\(724\) | 74.9671 | 2.78613 | ||||||||
\(725\) | −18.9904 | −0.705285 | ||||||||
\(726\) | 25.4145 | 0.943221 | ||||||||
\(727\) | 28.2309 | 1.04703 | 0.523514 | − | 0.852017i | \(-0.324621\pi\) | ||||
0.523514 | + | 0.852017i | \(0.324621\pi\) | |||||||
\(728\) | 134.223 | 4.97464 | ||||||||
\(729\) | 17.5355 | 0.649464 | ||||||||
\(730\) | −25.4187 | −0.940790 | ||||||||
\(731\) | −20.8101 | −0.769690 | ||||||||
\(732\) | 54.1283 | 2.00064 | ||||||||
\(733\) | −46.2094 | −1.70678 | −0.853392 | − | 0.521270i | \(-0.825458\pi\) | ||||
−0.853392 | + | 0.521270i | \(0.825458\pi\) | |||||||
\(734\) | 39.8099 | 1.46941 | ||||||||
\(735\) | 7.99550 | 0.294919 | ||||||||
\(736\) | −16.1745 | −0.596199 | ||||||||
\(737\) | 20.8375 | 0.767560 | ||||||||
\(738\) | −5.91643 | −0.217787 | ||||||||
\(739\) | 10.8698 | 0.399853 | 0.199926 | − | 0.979811i | \(-0.435930\pi\) | ||||
0.199926 | + | 0.979811i | \(0.435930\pi\) | |||||||
\(740\) | 36.2145 | 1.33127 | ||||||||
\(741\) | 2.78401 | 0.102273 | ||||||||
\(742\) | 66.3761 | 2.43675 | ||||||||
\(743\) | −34.5313 | −1.26683 | −0.633416 | − | 0.773812i | \(-0.718348\pi\) | ||||
−0.633416 | + | 0.773812i | \(0.718348\pi\) | |||||||
\(744\) | 5.28343 | 0.193700 | ||||||||
\(745\) | −9.14408 | −0.335013 | ||||||||
\(746\) | −5.70143 | −0.208744 | ||||||||
\(747\) | −2.30362 | −0.0842849 | ||||||||
\(748\) | −14.1176 | −0.516192 | ||||||||
\(749\) | −11.0043 | −0.402090 | ||||||||
\(750\) | 19.8131 | 0.723471 | ||||||||
\(751\) | 34.4642 | 1.25762 | 0.628809 | − | 0.777560i | \(-0.283543\pi\) | ||||
0.628809 | + | 0.777560i | \(0.283543\pi\) | |||||||
\(752\) | 65.1913 | 2.37728 | ||||||||
\(753\) | −7.13094 | −0.259866 | ||||||||
\(754\) | −47.8640 | −1.74311 | ||||||||
\(755\) | 2.00702 | 0.0730429 | ||||||||
\(756\) | 105.755 | 3.84627 | ||||||||
\(757\) | −22.1515 | −0.805109 | −0.402554 | − | 0.915396i | \(-0.631878\pi\) | ||||
−0.402554 | + | 0.915396i | \(0.631878\pi\) | |||||||
\(758\) | 56.5775 | 2.05499 | ||||||||
\(759\) | −2.22242 | −0.0806689 | ||||||||
\(760\) | −3.32859 | −0.120741 | ||||||||
\(761\) | −16.7417 | −0.606885 | −0.303443 | − | 0.952850i | \(-0.598136\pi\) | ||||
−0.303443 | + | 0.952850i | \(0.598136\pi\) | |||||||
\(762\) | 36.0821 | 1.30712 | ||||||||
\(763\) | −11.9579 | −0.432903 | ||||||||
\(764\) | −91.4910 | −3.31003 | ||||||||
\(765\) | −2.65539 | −0.0960058 | ||||||||
\(766\) | −30.3249 | −1.09568 | ||||||||
\(767\) | −56.6932 | −2.04707 | ||||||||
\(768\) | −13.3516 | −0.481785 | ||||||||
\(769\) | 22.0382 | 0.794719 | 0.397359 | − | 0.917663i | \(-0.369927\pi\) | ||||
0.397359 | + | 0.917663i | \(0.369927\pi\) | |||||||
\(770\) | −11.5083 | −0.414731 | ||||||||
\(771\) | −13.6501 | −0.491596 | ||||||||
\(772\) | −5.99656 | −0.215821 | ||||||||
\(773\) | −20.7072 | −0.744785 | −0.372393 | − | 0.928075i | \(-0.621463\pi\) | ||||
−0.372393 | + | 0.928075i | \(0.621463\pi\) | |||||||
\(774\) | −49.8439 | −1.79160 | ||||||||
\(775\) | 2.85479 | 0.102547 | ||||||||
\(776\) | 48.1521 | 1.72856 | ||||||||
\(777\) | −45.2836 | −1.62454 | ||||||||
\(778\) | −34.5006 | −1.23691 | ||||||||
\(779\) | −0.741048 | −0.0265508 | ||||||||
\(780\) | 16.7160 | 0.598528 | ||||||||
\(781\) | −15.9406 | −0.570398 | ||||||||
\(782\) | −7.37886 | −0.263868 | ||||||||
\(783\) | −22.2960 | −0.796792 | ||||||||
\(784\) | 101.767 | 3.63454 | ||||||||
\(785\) | −17.4291 | −0.622070 | ||||||||
\(786\) | 32.2895 | 1.15173 | ||||||||
\(787\) | 14.7571 | 0.526035 | 0.263018 | − | 0.964791i | \(-0.415282\pi\) | ||||
0.263018 | + | 0.964791i | \(0.415282\pi\) | |||||||
\(788\) | 57.9440 | 2.06417 | ||||||||
\(789\) | 22.8372 | 0.813026 | ||||||||
\(790\) | 27.2153 | 0.968276 | ||||||||
\(791\) | 83.3426 | 2.96332 | ||||||||
\(792\) | −19.9914 | −0.710364 | ||||||||
\(793\) | 43.5814 | 1.54762 | ||||||||
\(794\) | −9.88669 | −0.350865 | ||||||||
\(795\) | 4.88720 | 0.173331 | ||||||||
\(796\) | −72.0080 | −2.55226 | ||||||||
\(797\) | −17.2782 | −0.612026 | −0.306013 | − | 0.952027i | \(-0.598995\pi\) | ||||
−0.306013 | + | 0.952027i | \(0.598995\pi\) | |||||||
\(798\) | 7.04004 | 0.249215 | ||||||||
\(799\) | 12.7926 | 0.452570 | ||||||||
\(800\) | 51.1534 | 1.80855 | ||||||||
\(801\) | 4.25597 | 0.150377 | ||||||||
\(802\) | −56.7684 | −2.00456 | ||||||||
\(803\) | −19.1216 | −0.674786 | ||||||||
\(804\) | −76.5369 | −2.69925 | ||||||||
\(805\) | −4.26966 | −0.150486 | ||||||||
\(806\) | 7.19531 | 0.253444 | ||||||||
\(807\) | −20.5663 | −0.723969 | ||||||||
\(808\) | −113.833 | −4.00462 | ||||||||
\(809\) | −30.5611 | −1.07447 | −0.537235 | − | 0.843432i | \(-0.680531\pi\) | ||||
−0.537235 | + | 0.843432i | \(0.680531\pi\) | |||||||
\(810\) | 0.471122 | 0.0165535 | ||||||||
\(811\) | 1.40629 | 0.0493815 | 0.0246908 | − | 0.999695i | \(-0.492140\pi\) | ||||
0.0246908 | + | 0.999695i | \(0.492140\pi\) | |||||||
\(812\) | −85.9149 | −3.01502 | ||||||||
\(813\) | −14.3974 | −0.504938 | ||||||||
\(814\) | 38.3794 | 1.34520 | ||||||||
\(815\) | 13.5586 | 0.474936 | ||||||||
\(816\) | 21.9918 | 0.769867 | ||||||||
\(817\) | −6.24308 | −0.218418 | ||||||||
\(818\) | −13.9710 | −0.488485 | ||||||||
\(819\) | 32.1233 | 1.12248 | ||||||||
\(820\) | −4.44947 | −0.155382 | ||||||||
\(821\) | −2.56990 | −0.0896902 | −0.0448451 | − | 0.998994i | \(-0.514279\pi\) | ||||
−0.0448451 | + | 0.998994i | \(0.514279\pi\) | |||||||
\(822\) | 31.7218 | 1.10643 | ||||||||
\(823\) | 11.2393 | 0.391778 | 0.195889 | − | 0.980626i | \(-0.437241\pi\) | ||||
0.195889 | + | 0.980626i | \(0.437241\pi\) | |||||||
\(824\) | 72.8552 | 2.53803 | ||||||||
\(825\) | 7.02864 | 0.244706 | ||||||||
\(826\) | −143.362 | −4.98822 | ||||||||
\(827\) | −25.9668 | −0.902953 | −0.451477 | − | 0.892283i | \(-0.649103\pi\) | ||||
−0.451477 | + | 0.892283i | \(0.649103\pi\) | |||||||
\(828\) | −12.5453 | −0.435980 | ||||||||
\(829\) | 22.5883 | 0.784524 | 0.392262 | − | 0.919853i | \(-0.371693\pi\) | ||||
0.392262 | + | 0.919853i | \(0.371693\pi\) | |||||||
\(830\) | −2.44064 | −0.0847160 | ||||||||
\(831\) | −30.8916 | −1.07162 | ||||||||
\(832\) | 41.9545 | 1.45451 | ||||||||
\(833\) | 19.9700 | 0.691919 | ||||||||
\(834\) | 32.2211 | 1.11572 | ||||||||
\(835\) | 14.5682 | 0.504153 | ||||||||
\(836\) | −4.23533 | −0.146482 | ||||||||
\(837\) | 3.35171 | 0.115852 | ||||||||
\(838\) | −81.6611 | −2.82094 | ||||||||
\(839\) | 13.7761 | 0.475602 | 0.237801 | − | 0.971314i | \(-0.423573\pi\) | ||||
0.237801 | + | 0.971314i | \(0.423573\pi\) | |||||||
\(840\) | 24.9908 | 0.862265 | ||||||||
\(841\) | −10.8869 | −0.375409 | ||||||||
\(842\) | 1.37364 | 0.0473387 | ||||||||
\(843\) | 4.37268 | 0.150603 | ||||||||
\(844\) | −137.966 | −4.74898 | ||||||||
\(845\) | 3.92421 | 0.134997 | ||||||||
\(846\) | 30.6406 | 1.05345 | ||||||||
\(847\) | 36.7298 | 1.26205 | ||||||||
\(848\) | 62.2046 | 2.13611 | ||||||||
\(849\) | 34.9421 | 1.19921 | ||||||||
\(850\) | 23.3364 | 0.800432 | ||||||||
\(851\) | 14.2390 | 0.488107 | ||||||||
\(852\) | 58.5502 | 2.00590 | ||||||||
\(853\) | −1.35058 | −0.0462429 | −0.0231215 | − | 0.999733i | \(-0.507360\pi\) | ||||
−0.0231215 | + | 0.999733i | \(0.507360\pi\) | |||||||
\(854\) | 110.206 | 3.77118 | ||||||||
\(855\) | −0.796623 | −0.0272439 | ||||||||
\(856\) | −20.2530 | −0.692234 | ||||||||
\(857\) | 37.1394 | 1.26866 | 0.634329 | − | 0.773063i | \(-0.281277\pi\) | ||||
0.634329 | + | 0.773063i | \(0.281277\pi\) | |||||||
\(858\) | 17.7153 | 0.604789 | ||||||||
\(859\) | −43.1363 | −1.47179 | −0.735896 | − | 0.677095i | \(-0.763239\pi\) | ||||
−0.735896 | + | 0.677095i | \(0.763239\pi\) | |||||||
\(860\) | −37.4853 | −1.27824 | ||||||||
\(861\) | 5.56373 | 0.189611 | ||||||||
\(862\) | −66.6164 | −2.26897 | ||||||||
\(863\) | −1.23618 | −0.0420802 | −0.0210401 | − | 0.999779i | \(-0.506698\pi\) | ||||
−0.0210401 | + | 0.999779i | \(0.506698\pi\) | |||||||
\(864\) | 60.0575 | 2.04320 | ||||||||
\(865\) | 10.6361 | 0.361637 | ||||||||
\(866\) | −81.4256 | −2.76695 | ||||||||
\(867\) | −14.1713 | −0.481284 | ||||||||
\(868\) | 12.9154 | 0.438378 | ||||||||
\(869\) | 20.4731 | 0.694501 | ||||||||
\(870\) | −8.91174 | −0.302136 | ||||||||
\(871\) | −61.6237 | −2.08804 | ||||||||
\(872\) | −22.0079 | −0.745282 | ||||||||
\(873\) | 11.5241 | 0.390032 | ||||||||
\(874\) | −2.21368 | −0.0748787 | ||||||||
\(875\) | 28.6344 | 0.968019 | ||||||||
\(876\) | 70.2342 | 2.37299 | ||||||||
\(877\) | −11.8821 | −0.401229 | −0.200614 | − | 0.979670i | \(-0.564294\pi\) | ||||
−0.200614 | + | 0.979670i | \(0.564294\pi\) | |||||||
\(878\) | 76.4818 | 2.58114 | ||||||||
\(879\) | −17.1241 | −0.577583 | ||||||||
\(880\) | −10.7851 | −0.363564 | ||||||||
\(881\) | 12.8350 | 0.432422 | 0.216211 | − | 0.976347i | \(-0.430630\pi\) | ||||
0.216211 | + | 0.976347i | \(0.430630\pi\) | |||||||
\(882\) | 47.8317 | 1.61058 | ||||||||
\(883\) | 8.18532 | 0.275458 | 0.137729 | − | 0.990470i | \(-0.456020\pi\) | ||||
0.137729 | + | 0.990470i | \(0.456020\pi\) | |||||||
\(884\) | 41.7507 | 1.40423 | ||||||||
\(885\) | −10.5556 | −0.354823 | ||||||||
\(886\) | 18.0673 | 0.606981 | ||||||||
\(887\) | −7.41031 | −0.248814 | −0.124407 | − | 0.992231i | \(-0.539703\pi\) | ||||
−0.124407 | + | 0.992231i | \(0.539703\pi\) | |||||||
\(888\) | −83.3425 | −2.79679 | ||||||||
\(889\) | 52.1468 | 1.74895 | ||||||||
\(890\) | 4.50913 | 0.151146 | ||||||||
\(891\) | 0.354408 | 0.0118731 | ||||||||
\(892\) | −2.23025 | −0.0746744 | ||||||||
\(893\) | 3.83782 | 0.128428 | ||||||||
\(894\) | 35.5943 | 1.19045 | ||||||||
\(895\) | 0.684350 | 0.0228753 | ||||||||
\(896\) | 11.4886 | 0.383807 | ||||||||
\(897\) | 6.57248 | 0.219449 | ||||||||
\(898\) | 77.8531 | 2.59799 | ||||||||
\(899\) | −2.72292 | −0.0908144 | ||||||||
\(900\) | 39.6758 | 1.32253 | ||||||||
\(901\) | 12.2065 | 0.406659 | ||||||||
\(902\) | −4.71545 | −0.157007 | ||||||||
\(903\) | 46.8726 | 1.55982 | ||||||||
\(904\) | 153.389 | 5.10163 | ||||||||
\(905\) | 11.2383 | 0.373574 | ||||||||
\(906\) | −7.81252 | −0.259554 | ||||||||
\(907\) | 46.4019 | 1.54075 | 0.770375 | − | 0.637592i | \(-0.220069\pi\) | ||||
0.770375 | + | 0.637592i | \(0.220069\pi\) | |||||||
\(908\) | 72.2419 | 2.39743 | ||||||||
\(909\) | −27.2433 | −0.903602 | ||||||||
\(910\) | 34.0341 | 1.12822 | ||||||||
\(911\) | −57.6163 | −1.90891 | −0.954457 | − | 0.298350i | \(-0.903564\pi\) | ||||
−0.954457 | + | 0.298350i | \(0.903564\pi\) | |||||||
\(912\) | 6.59759 | 0.218468 | ||||||||
\(913\) | −1.83601 | −0.0607629 | ||||||||
\(914\) | −38.6592 | −1.27873 | ||||||||
\(915\) | 8.11436 | 0.268253 | ||||||||
\(916\) | 53.2055 | 1.75796 | ||||||||
\(917\) | 46.6657 | 1.54104 | ||||||||
\(918\) | 27.3985 | 0.904285 | ||||||||
\(919\) | 31.7158 | 1.04621 | 0.523104 | − | 0.852269i | \(-0.324774\pi\) | ||||
0.523104 | + | 0.852269i | \(0.324774\pi\) | |||||||
\(920\) | −7.85814 | −0.259075 | ||||||||
\(921\) | 15.4132 | 0.507882 | ||||||||
\(922\) | 38.4807 | 1.26729 | ||||||||
\(923\) | 47.1417 | 1.55169 | ||||||||
\(924\) | 31.7985 | 1.04609 | ||||||||
\(925\) | −45.0323 | −1.48065 | ||||||||
\(926\) | 73.3209 | 2.40947 | ||||||||
\(927\) | 17.4362 | 0.572681 | ||||||||
\(928\) | −48.7905 | −1.60163 | ||||||||
\(929\) | −7.50547 | −0.246246 | −0.123123 | − | 0.992391i | \(-0.539291\pi\) | ||||
−0.123123 | + | 0.992391i | \(0.539291\pi\) | |||||||
\(930\) | 1.33969 | 0.0439300 | ||||||||
\(931\) | 5.99104 | 0.196349 | ||||||||
\(932\) | −118.373 | −3.87744 | ||||||||
\(933\) | 7.22300 | 0.236470 | ||||||||
\(934\) | 98.4950 | 3.22286 | ||||||||
\(935\) | −2.11637 | −0.0692128 | ||||||||
\(936\) | 59.1215 | 1.93245 | ||||||||
\(937\) | 28.8016 | 0.940906 | 0.470453 | − | 0.882425i | \(-0.344091\pi\) | ||||
0.470453 | + | 0.882425i | \(0.344091\pi\) | |||||||
\(938\) | −155.831 | −5.08805 | ||||||||
\(939\) | −20.7393 | −0.676802 | ||||||||
\(940\) | 23.0434 | 0.751592 | ||||||||
\(941\) | 5.22681 | 0.170389 | 0.0851945 | − | 0.996364i | \(-0.472849\pi\) | ||||
0.0851945 | + | 0.996364i | \(0.472849\pi\) | |||||||
\(942\) | 67.8444 | 2.21049 | ||||||||
\(943\) | −1.74946 | −0.0569704 | ||||||||
\(944\) | −134.353 | −4.37280 | ||||||||
\(945\) | 15.8537 | 0.515721 | ||||||||
\(946\) | −39.7261 | −1.29161 | ||||||||
\(947\) | 1.56923 | 0.0509931 | 0.0254966 | − | 0.999675i | \(-0.491883\pi\) | ||||
0.0254966 | + | 0.999675i | \(0.491883\pi\) | |||||||
\(948\) | −75.1982 | −2.44232 | ||||||||
\(949\) | 56.5491 | 1.83566 | ||||||||
\(950\) | 7.00097 | 0.227142 | ||||||||
\(951\) | 9.20331 | 0.298438 | ||||||||
\(952\) | 62.4184 | 2.02299 | ||||||||
\(953\) | −45.1574 | −1.46279 | −0.731396 | − | 0.681953i | \(-0.761131\pi\) | ||||
−0.731396 | + | 0.681953i | \(0.761131\pi\) | |||||||
\(954\) | 29.2368 | 0.946577 | ||||||||
\(955\) | −13.7154 | −0.443820 | ||||||||
\(956\) | −91.8987 | −2.97222 | ||||||||
\(957\) | −6.70397 | −0.216709 | ||||||||
\(958\) | −39.9037 | −1.28923 | ||||||||
\(959\) | 45.8453 | 1.48042 | ||||||||
\(960\) | 7.81145 | 0.252113 | ||||||||
\(961\) | −30.5907 | −0.986796 | ||||||||
\(962\) | −113.501 | −3.65942 | ||||||||
\(963\) | −4.84710 | −0.156196 | ||||||||
\(964\) | −121.042 | −3.89851 | ||||||||
\(965\) | −0.898944 | −0.0289380 | ||||||||
\(966\) | 16.6201 | 0.534743 | ||||||||
\(967\) | −22.7568 | −0.731809 | −0.365905 | − | 0.930652i | \(-0.619240\pi\) | ||||
−0.365905 | + | 0.930652i | \(0.619240\pi\) | |||||||
\(968\) | 67.5996 | 2.17273 | ||||||||
\(969\) | 1.29466 | 0.0415904 | ||||||||
\(970\) | 12.2096 | 0.392027 | ||||||||
\(971\) | −48.2255 | −1.54763 | −0.773814 | − | 0.633412i | \(-0.781654\pi\) | ||||
−0.773814 | + | 0.633412i | \(0.781654\pi\) | |||||||
\(972\) | 75.5905 | 2.42457 | ||||||||
\(973\) | 46.5668 | 1.49286 | ||||||||
\(974\) | 57.6527 | 1.84731 | ||||||||
\(975\) | −20.7861 | −0.665689 | ||||||||
\(976\) | 103.280 | 3.30592 | ||||||||
\(977\) | 1.41093 | 0.0451395 | 0.0225698 | − | 0.999745i | \(-0.492815\pi\) | ||||
0.0225698 | + | 0.999745i | \(0.492815\pi\) | |||||||
\(978\) | −52.7781 | −1.68766 | ||||||||
\(979\) | 3.39205 | 0.108410 | ||||||||
\(980\) | 35.9720 | 1.14908 | ||||||||
\(981\) | −5.26710 | −0.168165 | ||||||||
\(982\) | −28.6612 | −0.914617 | ||||||||
\(983\) | −18.3208 | −0.584344 | −0.292172 | − | 0.956366i | \(-0.594378\pi\) | ||||
−0.292172 | + | 0.956366i | \(0.594378\pi\) | |||||||
\(984\) | 10.2398 | 0.326433 | ||||||||
\(985\) | 8.68638 | 0.276771 | ||||||||
\(986\) | −22.2584 | −0.708853 | ||||||||
\(987\) | −28.8140 | −0.917161 | ||||||||
\(988\) | 12.5253 | 0.398484 | ||||||||
\(989\) | −14.7387 | −0.468662 | ||||||||
\(990\) | −5.06909 | −0.161106 | ||||||||
\(991\) | 3.18882 | 0.101296 | 0.0506481 | − | 0.998717i | \(-0.483871\pi\) | ||||
0.0506481 | + | 0.998717i | \(0.483871\pi\) | |||||||
\(992\) | 7.33459 | 0.232873 | ||||||||
\(993\) | −1.86024 | −0.0590329 | ||||||||
\(994\) | 119.209 | 3.78109 | ||||||||
\(995\) | −10.7947 | −0.342215 | ||||||||
\(996\) | 6.74371 | 0.213683 | ||||||||
\(997\) | 24.4181 | 0.773328 | 0.386664 | − | 0.922221i | \(-0.373627\pi\) | ||||
0.386664 | + | 0.922221i | \(0.373627\pi\) | |||||||
\(998\) | 84.0530 | 2.66065 | ||||||||
\(999\) | −52.8709 | −1.67276 |
(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 | 4001.2.a.a.1.5 | ✓ | 149 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.a.1.5 | ✓ | 149 | 1.1 | even | 1 | trivial |