Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, 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("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.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: | \(64.2156933055\) |
Analytic rank: | \(0\) |
Dimension: | \(86\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.19026 | −1.26455 | −0.632275 | − | 0.774744i | \(-0.717879\pi\) | ||||
−0.632275 | + | 0.774744i | \(0.717879\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.77068 | −1.23908 | −0.619542 | − | 0.784963i | \(-0.712682\pi\) | ||||
−0.619542 | + | 0.784963i | \(0.712682\pi\) | |||||||
\(6\) | 2.19026 | 0.894172 | ||||||||
\(7\) | 3.06919 | 1.16004 | 0.580022 | − | 0.814601i | \(-0.303044\pi\) | ||||
0.580022 | + | 0.814601i | \(0.303044\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.79726 | 0.599086 | ||||||||
\(10\) | 2.77068 | 0.876165 | ||||||||
\(11\) | −4.27619 | −1.28932 | −0.644660 | − | 0.764469i | \(-0.723001\pi\) | ||||
−0.644660 | + | 0.764469i | \(0.723001\pi\) | |||||||
\(12\) | −2.19026 | −0.632275 | ||||||||
\(13\) | 6.31398 | 1.75118 | 0.875592 | − | 0.483051i | \(-0.160472\pi\) | ||||
0.875592 | + | 0.483051i | \(0.160472\pi\) | |||||||
\(14\) | −3.06919 | −0.820275 | ||||||||
\(15\) | 6.06852 | 1.56688 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.67143 | −1.37552 | −0.687762 | − | 0.725936i | \(-0.741407\pi\) | ||||
−0.687762 | + | 0.725936i | \(0.741407\pi\) | |||||||
\(18\) | −1.79726 | −0.423618 | ||||||||
\(19\) | 3.05034 | 0.699797 | 0.349898 | − | 0.936788i | \(-0.386216\pi\) | ||||
0.349898 | + | 0.936788i | \(0.386216\pi\) | |||||||
\(20\) | −2.77068 | −0.619542 | ||||||||
\(21\) | −6.72234 | −1.46693 | ||||||||
\(22\) | 4.27619 | 0.911687 | ||||||||
\(23\) | −3.16331 | −0.659595 | −0.329797 | − | 0.944052i | \(-0.606980\pi\) | ||||
−0.329797 | + | 0.944052i | \(0.606980\pi\) | |||||||
\(24\) | 2.19026 | 0.447086 | ||||||||
\(25\) | 2.67665 | 0.535331 | ||||||||
\(26\) | −6.31398 | −1.23827 | ||||||||
\(27\) | 2.63432 | 0.506975 | ||||||||
\(28\) | 3.06919 | 0.580022 | ||||||||
\(29\) | −5.56146 | −1.03274 | −0.516368 | − | 0.856367i | \(-0.672716\pi\) | ||||
−0.516368 | + | 0.856367i | \(0.672716\pi\) | |||||||
\(30\) | −6.06852 | −1.10795 | ||||||||
\(31\) | 1.42455 | 0.255857 | 0.127928 | − | 0.991783i | \(-0.459167\pi\) | ||||
0.127928 | + | 0.991783i | \(0.459167\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 9.36599 | 1.63041 | ||||||||
\(34\) | 5.67143 | 0.972642 | ||||||||
\(35\) | −8.50374 | −1.43739 | ||||||||
\(36\) | 1.79726 | 0.299543 | ||||||||
\(37\) | 0.630865 | 0.103714 | 0.0518568 | − | 0.998655i | \(-0.483486\pi\) | ||||
0.0518568 | + | 0.998655i | \(0.483486\pi\) | |||||||
\(38\) | −3.05034 | −0.494831 | ||||||||
\(39\) | −13.8293 | −2.21446 | ||||||||
\(40\) | 2.77068 | 0.438083 | ||||||||
\(41\) | 8.42078 | 1.31510 | 0.657552 | − | 0.753409i | \(-0.271592\pi\) | ||||
0.657552 | + | 0.753409i | \(0.271592\pi\) | |||||||
\(42\) | 6.72234 | 1.03728 | ||||||||
\(43\) | −9.98240 | −1.52230 | −0.761151 | − | 0.648575i | \(-0.775365\pi\) | ||||
−0.761151 | + | 0.648575i | \(0.775365\pi\) | |||||||
\(44\) | −4.27619 | −0.644660 | ||||||||
\(45\) | −4.97963 | −0.742319 | ||||||||
\(46\) | 3.16331 | 0.466404 | ||||||||
\(47\) | 4.60486 | 0.671688 | 0.335844 | − | 0.941918i | \(-0.390978\pi\) | ||||
0.335844 | + | 0.941918i | \(0.390978\pi\) | |||||||
\(48\) | −2.19026 | −0.316137 | ||||||||
\(49\) | 2.41992 | 0.345704 | ||||||||
\(50\) | −2.67665 | −0.378536 | ||||||||
\(51\) | 12.4219 | 1.73942 | ||||||||
\(52\) | 6.31398 | 0.875592 | ||||||||
\(53\) | 6.71274 | 0.922066 | 0.461033 | − | 0.887383i | \(-0.347479\pi\) | ||||
0.461033 | + | 0.887383i | \(0.347479\pi\) | |||||||
\(54\) | −2.63432 | −0.358486 | ||||||||
\(55\) | 11.8479 | 1.59758 | ||||||||
\(56\) | −3.06919 | −0.410138 | ||||||||
\(57\) | −6.68106 | −0.884928 | ||||||||
\(58\) | 5.56146 | 0.730255 | ||||||||
\(59\) | 10.9137 | 1.42084 | 0.710422 | − | 0.703776i | \(-0.248504\pi\) | ||||
0.710422 | + | 0.703776i | \(0.248504\pi\) | |||||||
\(60\) | 6.06852 | 0.783442 | ||||||||
\(61\) | 3.67051 | 0.469961 | 0.234981 | − | 0.972000i | \(-0.424497\pi\) | ||||
0.234981 | + | 0.972000i | \(0.424497\pi\) | |||||||
\(62\) | −1.42455 | −0.180918 | ||||||||
\(63\) | 5.51613 | 0.694967 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −17.4940 | −2.16987 | ||||||||
\(66\) | −9.36599 | −1.15287 | ||||||||
\(67\) | −5.77000 | −0.704918 | −0.352459 | − | 0.935827i | \(-0.614654\pi\) | ||||
−0.352459 | + | 0.935827i | \(0.614654\pi\) | |||||||
\(68\) | −5.67143 | −0.687762 | ||||||||
\(69\) | 6.92848 | 0.834091 | ||||||||
\(70\) | 8.50374 | 1.01639 | ||||||||
\(71\) | 4.19250 | 0.497558 | 0.248779 | − | 0.968560i | \(-0.419971\pi\) | ||||
0.248779 | + | 0.968560i | \(0.419971\pi\) | |||||||
\(72\) | −1.79726 | −0.211809 | ||||||||
\(73\) | −6.91203 | −0.808992 | −0.404496 | − | 0.914540i | \(-0.632553\pi\) | ||||
−0.404496 | + | 0.914540i | \(0.632553\pi\) | |||||||
\(74\) | −0.630865 | −0.0733365 | ||||||||
\(75\) | −5.86258 | −0.676953 | ||||||||
\(76\) | 3.05034 | 0.349898 | ||||||||
\(77\) | −13.1244 | −1.49567 | ||||||||
\(78\) | 13.8293 | 1.56586 | ||||||||
\(79\) | −17.2341 | −1.93899 | −0.969496 | − | 0.245107i | \(-0.921177\pi\) | ||||
−0.969496 | + | 0.245107i | \(0.921177\pi\) | |||||||
\(80\) | −2.77068 | −0.309771 | ||||||||
\(81\) | −11.1616 | −1.24018 | ||||||||
\(82\) | −8.42078 | −0.929920 | ||||||||
\(83\) | 4.21083 | 0.462199 | 0.231099 | − | 0.972930i | \(-0.425768\pi\) | ||||
0.231099 | + | 0.972930i | \(0.425768\pi\) | |||||||
\(84\) | −6.72234 | −0.733467 | ||||||||
\(85\) | 15.7137 | 1.70439 | ||||||||
\(86\) | 9.98240 | 1.07643 | ||||||||
\(87\) | 12.1811 | 1.30595 | ||||||||
\(88\) | 4.27619 | 0.455844 | ||||||||
\(89\) | −5.49270 | −0.582225 | −0.291112 | − | 0.956689i | \(-0.594025\pi\) | ||||
−0.291112 | + | 0.956689i | \(0.594025\pi\) | |||||||
\(90\) | 4.97963 | 0.524899 | ||||||||
\(91\) | 19.3788 | 2.03145 | ||||||||
\(92\) | −3.16331 | −0.329797 | ||||||||
\(93\) | −3.12014 | −0.323543 | ||||||||
\(94\) | −4.60486 | −0.474955 | ||||||||
\(95\) | −8.45152 | −0.867107 | ||||||||
\(96\) | 2.19026 | 0.223543 | ||||||||
\(97\) | 5.15491 | 0.523402 | 0.261701 | − | 0.965149i | \(-0.415717\pi\) | ||||
0.261701 | + | 0.965149i | \(0.415717\pi\) | |||||||
\(98\) | −2.41992 | −0.244449 | ||||||||
\(99\) | −7.68542 | −0.772414 | ||||||||
\(100\) | 2.67665 | 0.267665 | ||||||||
\(101\) | 0.0775340 | 0.00771492 | 0.00385746 | − | 0.999993i | \(-0.498772\pi\) | ||||
0.00385746 | + | 0.999993i | \(0.498772\pi\) | |||||||
\(102\) | −12.4219 | −1.22995 | ||||||||
\(103\) | 14.7092 | 1.44934 | 0.724670 | − | 0.689096i | \(-0.241992\pi\) | ||||
0.724670 | + | 0.689096i | \(0.241992\pi\) | |||||||
\(104\) | −6.31398 | −0.619137 | ||||||||
\(105\) | 18.6254 | 1.81766 | ||||||||
\(106\) | −6.71274 | −0.651999 | ||||||||
\(107\) | 9.78969 | 0.946405 | 0.473202 | − | 0.880954i | \(-0.343098\pi\) | ||||
0.473202 | + | 0.880954i | \(0.343098\pi\) | |||||||
\(108\) | 2.63432 | 0.253488 | ||||||||
\(109\) | 4.28813 | 0.410728 | 0.205364 | − | 0.978686i | \(-0.434162\pi\) | ||||
0.205364 | + | 0.978686i | \(0.434162\pi\) | |||||||
\(110\) | −11.8479 | −1.12966 | ||||||||
\(111\) | −1.38176 | −0.131151 | ||||||||
\(112\) | 3.06919 | 0.290011 | ||||||||
\(113\) | −10.1591 | −0.955688 | −0.477844 | − | 0.878445i | \(-0.658581\pi\) | ||||
−0.477844 | + | 0.878445i | \(0.658581\pi\) | |||||||
\(114\) | 6.68106 | 0.625738 | ||||||||
\(115\) | 8.76450 | 0.817294 | ||||||||
\(116\) | −5.56146 | −0.516368 | ||||||||
\(117\) | 11.3479 | 1.04911 | ||||||||
\(118\) | −10.9137 | −1.00469 | ||||||||
\(119\) | −17.4067 | −1.59567 | ||||||||
\(120\) | −6.06852 | −0.553977 | ||||||||
\(121\) | 7.28581 | 0.662347 | ||||||||
\(122\) | −3.67051 | −0.332313 | ||||||||
\(123\) | −18.4437 | −1.66302 | ||||||||
\(124\) | 1.42455 | 0.127928 | ||||||||
\(125\) | 6.43724 | 0.575764 | ||||||||
\(126\) | −5.51613 | −0.491416 | ||||||||
\(127\) | −17.1035 | −1.51769 | −0.758845 | − | 0.651271i | \(-0.774236\pi\) | ||||
−0.758845 | + | 0.651271i | \(0.774236\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 21.8641 | 1.92503 | ||||||||
\(130\) | 17.4940 | 1.53433 | ||||||||
\(131\) | −1.46655 | −0.128133 | −0.0640667 | − | 0.997946i | \(-0.520407\pi\) | ||||
−0.0640667 | + | 0.997946i | \(0.520407\pi\) | |||||||
\(132\) | 9.36599 | 0.815205 | ||||||||
\(133\) | 9.36208 | 0.811795 | ||||||||
\(134\) | 5.77000 | 0.498452 | ||||||||
\(135\) | −7.29886 | −0.628185 | ||||||||
\(136\) | 5.67143 | 0.486321 | ||||||||
\(137\) | −9.74768 | −0.832801 | −0.416400 | − | 0.909181i | \(-0.636709\pi\) | ||||
−0.416400 | + | 0.909181i | \(0.636709\pi\) | |||||||
\(138\) | −6.92848 | −0.589791 | ||||||||
\(139\) | −22.3524 | −1.89591 | −0.947954 | − | 0.318407i | \(-0.896852\pi\) | ||||
−0.947954 | + | 0.318407i | \(0.896852\pi\) | |||||||
\(140\) | −8.50374 | −0.718697 | ||||||||
\(141\) | −10.0859 | −0.849383 | ||||||||
\(142\) | −4.19250 | −0.351827 | ||||||||
\(143\) | −26.9998 | −2.25784 | ||||||||
\(144\) | 1.79726 | 0.149772 | ||||||||
\(145\) | 15.4090 | 1.27965 | ||||||||
\(146\) | 6.91203 | 0.572044 | ||||||||
\(147\) | −5.30027 | −0.437159 | ||||||||
\(148\) | 0.630865 | 0.0518568 | ||||||||
\(149\) | −13.6798 | −1.12069 | −0.560346 | − | 0.828259i | \(-0.689332\pi\) | ||||
−0.560346 | + | 0.828259i | \(0.689332\pi\) | |||||||
\(150\) | 5.86258 | 0.478678 | ||||||||
\(151\) | −10.9167 | −0.888390 | −0.444195 | − | 0.895930i | \(-0.646510\pi\) | ||||
−0.444195 | + | 0.895930i | \(0.646510\pi\) | |||||||
\(152\) | −3.05034 | −0.247415 | ||||||||
\(153\) | −10.1930 | −0.824058 | ||||||||
\(154\) | 13.1244 | 1.05760 | ||||||||
\(155\) | −3.94697 | −0.317028 | ||||||||
\(156\) | −13.8293 | −1.10723 | ||||||||
\(157\) | −0.191486 | −0.0152823 | −0.00764113 | − | 0.999971i | \(-0.502432\pi\) | ||||
−0.00764113 | + | 0.999971i | \(0.502432\pi\) | |||||||
\(158\) | 17.2341 | 1.37107 | ||||||||
\(159\) | −14.7027 | −1.16600 | ||||||||
\(160\) | 2.77068 | 0.219041 | ||||||||
\(161\) | −9.70879 | −0.765160 | ||||||||
\(162\) | 11.1616 | 0.876941 | ||||||||
\(163\) | −12.3496 | −0.967294 | −0.483647 | − | 0.875263i | \(-0.660688\pi\) | ||||
−0.483647 | + | 0.875263i | \(0.660688\pi\) | |||||||
\(164\) | 8.42078 | 0.657552 | ||||||||
\(165\) | −25.9501 | −2.02022 | ||||||||
\(166\) | −4.21083 | −0.326824 | ||||||||
\(167\) | −2.57759 | −0.199460 | −0.0997298 | − | 0.995015i | \(-0.531798\pi\) | ||||
−0.0997298 | + | 0.995015i | \(0.531798\pi\) | |||||||
\(168\) | 6.72234 | 0.518640 | ||||||||
\(169\) | 26.8664 | 2.06665 | ||||||||
\(170\) | −15.7137 | −1.20519 | ||||||||
\(171\) | 5.48225 | 0.419238 | ||||||||
\(172\) | −9.98240 | −0.761151 | ||||||||
\(173\) | 7.80926 | 0.593727 | 0.296863 | − | 0.954920i | \(-0.404059\pi\) | ||||
0.296863 | + | 0.954920i | \(0.404059\pi\) | |||||||
\(174\) | −12.1811 | −0.923444 | ||||||||
\(175\) | 8.21516 | 0.621008 | ||||||||
\(176\) | −4.27619 | −0.322330 | ||||||||
\(177\) | −23.9039 | −1.79673 | ||||||||
\(178\) | 5.49270 | 0.411695 | ||||||||
\(179\) | −13.1978 | −0.986451 | −0.493226 | − | 0.869901i | \(-0.664182\pi\) | ||||
−0.493226 | + | 0.869901i | \(0.664182\pi\) | |||||||
\(180\) | −4.97963 | −0.371159 | ||||||||
\(181\) | 10.7292 | 0.797499 | 0.398749 | − | 0.917060i | \(-0.369444\pi\) | ||||
0.398749 | + | 0.917060i | \(0.369444\pi\) | |||||||
\(182\) | −19.3788 | −1.43645 | ||||||||
\(183\) | −8.03940 | −0.594289 | ||||||||
\(184\) | 3.16331 | 0.233202 | ||||||||
\(185\) | −1.74792 | −0.128510 | ||||||||
\(186\) | 3.12014 | 0.228780 | ||||||||
\(187\) | 24.2521 | 1.77349 | ||||||||
\(188\) | 4.60486 | 0.335844 | ||||||||
\(189\) | 8.08523 | 0.588114 | ||||||||
\(190\) | 8.45152 | 0.613137 | ||||||||
\(191\) | 19.3721 | 1.40172 | 0.700858 | − | 0.713301i | \(-0.252801\pi\) | ||||
0.700858 | + | 0.713301i | \(0.252801\pi\) | |||||||
\(192\) | −2.19026 | −0.158069 | ||||||||
\(193\) | −22.3466 | −1.60855 | −0.804273 | − | 0.594260i | \(-0.797445\pi\) | ||||
−0.804273 | + | 0.594260i | \(0.797445\pi\) | |||||||
\(194\) | −5.15491 | −0.370101 | ||||||||
\(195\) | 38.3165 | 2.74390 | ||||||||
\(196\) | 2.41992 | 0.172852 | ||||||||
\(197\) | −17.1642 | −1.22290 | −0.611448 | − | 0.791285i | \(-0.709413\pi\) | ||||
−0.611448 | + | 0.791285i | \(0.709413\pi\) | |||||||
\(198\) | 7.68542 | 0.546179 | ||||||||
\(199\) | 12.8124 | 0.908246 | 0.454123 | − | 0.890939i | \(-0.349953\pi\) | ||||
0.454123 | + | 0.890939i | \(0.349953\pi\) | |||||||
\(200\) | −2.67665 | −0.189268 | ||||||||
\(201\) | 12.6378 | 0.891404 | ||||||||
\(202\) | −0.0775340 | −0.00545527 | ||||||||
\(203\) | −17.0692 | −1.19802 | ||||||||
\(204\) | 12.4219 | 0.869709 | ||||||||
\(205\) | −23.3313 | −1.62953 | ||||||||
\(206\) | −14.7092 | −1.02484 | ||||||||
\(207\) | −5.68528 | −0.395154 | ||||||||
\(208\) | 6.31398 | 0.437796 | ||||||||
\(209\) | −13.0438 | −0.902262 | ||||||||
\(210\) | −18.6254 | −1.28528 | ||||||||
\(211\) | 22.8910 | 1.57588 | 0.787939 | − | 0.615753i | \(-0.211148\pi\) | ||||
0.787939 | + | 0.615753i | \(0.211148\pi\) | |||||||
\(212\) | 6.71274 | 0.461033 | ||||||||
\(213\) | −9.18269 | −0.629187 | ||||||||
\(214\) | −9.78969 | −0.669209 | ||||||||
\(215\) | 27.6580 | 1.88626 | ||||||||
\(216\) | −2.63432 | −0.179243 | ||||||||
\(217\) | 4.37221 | 0.296805 | ||||||||
\(218\) | −4.28813 | −0.290429 | ||||||||
\(219\) | 15.1392 | 1.02301 | ||||||||
\(220\) | 11.8479 | 0.798789 | ||||||||
\(221\) | −35.8093 | −2.40880 | ||||||||
\(222\) | 1.38176 | 0.0927377 | ||||||||
\(223\) | 6.58421 | 0.440911 | 0.220456 | − | 0.975397i | \(-0.429246\pi\) | ||||
0.220456 | + | 0.975397i | \(0.429246\pi\) | |||||||
\(224\) | −3.06919 | −0.205069 | ||||||||
\(225\) | 4.81064 | 0.320709 | ||||||||
\(226\) | 10.1591 | 0.675773 | ||||||||
\(227\) | −5.96504 | −0.395914 | −0.197957 | − | 0.980211i | \(-0.563431\pi\) | ||||
−0.197957 | + | 0.980211i | \(0.563431\pi\) | |||||||
\(228\) | −6.68106 | −0.442464 | ||||||||
\(229\) | −5.79620 | −0.383024 | −0.191512 | − | 0.981490i | \(-0.561339\pi\) | ||||
−0.191512 | + | 0.981490i | \(0.561339\pi\) | |||||||
\(230\) | −8.76450 | −0.577914 | ||||||||
\(231\) | 28.7460 | 1.89135 | ||||||||
\(232\) | 5.56146 | 0.365128 | ||||||||
\(233\) | 7.47164 | 0.489483 | 0.244742 | − | 0.969588i | \(-0.421297\pi\) | ||||
0.244742 | + | 0.969588i | \(0.421297\pi\) | |||||||
\(234\) | −11.3479 | −0.741833 | ||||||||
\(235\) | −12.7586 | −0.832278 | ||||||||
\(236\) | 10.9137 | 0.710422 | ||||||||
\(237\) | 37.7473 | 2.45195 | ||||||||
\(238\) | 17.4067 | 1.12831 | ||||||||
\(239\) | −0.953242 | −0.0616601 | −0.0308301 | − | 0.999525i | \(-0.509815\pi\) | ||||
−0.0308301 | + | 0.999525i | \(0.509815\pi\) | |||||||
\(240\) | 6.06852 | 0.391721 | ||||||||
\(241\) | 8.63373 | 0.556147 | 0.278074 | − | 0.960560i | \(-0.410304\pi\) | ||||
0.278074 | + | 0.960560i | \(0.410304\pi\) | |||||||
\(242\) | −7.28581 | −0.468350 | ||||||||
\(243\) | 16.5440 | 1.06130 | ||||||||
\(244\) | 3.67051 | 0.234981 | ||||||||
\(245\) | −6.70483 | −0.428356 | ||||||||
\(246\) | 18.4437 | 1.17593 | ||||||||
\(247\) | 19.2598 | 1.22547 | ||||||||
\(248\) | −1.42455 | −0.0904590 | ||||||||
\(249\) | −9.22283 | −0.584473 | ||||||||
\(250\) | −6.43724 | −0.407127 | ||||||||
\(251\) | −11.3676 | −0.717519 | −0.358760 | − | 0.933430i | \(-0.616800\pi\) | ||||
−0.358760 | + | 0.933430i | \(0.616800\pi\) | |||||||
\(252\) | 5.51613 | 0.347483 | ||||||||
\(253\) | 13.5269 | 0.850429 | ||||||||
\(254\) | 17.1035 | 1.07317 | ||||||||
\(255\) | −34.4172 | −2.15529 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.3223 | −0.831025 | −0.415512 | − | 0.909587i | \(-0.636398\pi\) | ||||
−0.415512 | + | 0.909587i | \(0.636398\pi\) | |||||||
\(258\) | −21.8641 | −1.36120 | ||||||||
\(259\) | 1.93624 | 0.120312 | ||||||||
\(260\) | −17.4940 | −1.08493 | ||||||||
\(261\) | −9.99538 | −0.618698 | ||||||||
\(262\) | 1.46655 | 0.0906040 | ||||||||
\(263\) | 7.66856 | 0.472864 | 0.236432 | − | 0.971648i | \(-0.424022\pi\) | ||||
0.236432 | + | 0.971648i | \(0.424022\pi\) | |||||||
\(264\) | −9.36599 | −0.576437 | ||||||||
\(265\) | −18.5989 | −1.14252 | ||||||||
\(266\) | −9.36208 | −0.574026 | ||||||||
\(267\) | 12.0305 | 0.736252 | ||||||||
\(268\) | −5.77000 | −0.352459 | ||||||||
\(269\) | −3.02964 | −0.184720 | −0.0923601 | − | 0.995726i | \(-0.529441\pi\) | ||||
−0.0923601 | + | 0.995726i | \(0.529441\pi\) | |||||||
\(270\) | 7.29886 | 0.444194 | ||||||||
\(271\) | 13.0886 | 0.795076 | 0.397538 | − | 0.917586i | \(-0.369865\pi\) | ||||
0.397538 | + | 0.917586i | \(0.369865\pi\) | |||||||
\(272\) | −5.67143 | −0.343881 | ||||||||
\(273\) | −42.4447 | −2.56887 | ||||||||
\(274\) | 9.74768 | 0.588879 | ||||||||
\(275\) | −11.4459 | −0.690213 | ||||||||
\(276\) | 6.92848 | 0.417045 | ||||||||
\(277\) | −0.588778 | −0.0353762 | −0.0176881 | − | 0.999844i | \(-0.505631\pi\) | ||||
−0.0176881 | + | 0.999844i | \(0.505631\pi\) | |||||||
\(278\) | 22.3524 | 1.34061 | ||||||||
\(279\) | 2.56028 | 0.153280 | ||||||||
\(280\) | 8.50374 | 0.508195 | ||||||||
\(281\) | 10.0168 | 0.597554 | 0.298777 | − | 0.954323i | \(-0.403421\pi\) | ||||
0.298777 | + | 0.954323i | \(0.403421\pi\) | |||||||
\(282\) | 10.0859 | 0.600605 | ||||||||
\(283\) | 21.7789 | 1.29462 | 0.647309 | − | 0.762227i | \(-0.275894\pi\) | ||||
0.647309 | + | 0.762227i | \(0.275894\pi\) | |||||||
\(284\) | 4.19250 | 0.248779 | ||||||||
\(285\) | 18.5111 | 1.09650 | ||||||||
\(286\) | 26.9998 | 1.59653 | ||||||||
\(287\) | 25.8450 | 1.52558 | ||||||||
\(288\) | −1.79726 | −0.105904 | ||||||||
\(289\) | 15.1651 | 0.892066 | ||||||||
\(290\) | −15.4090 | −0.904848 | ||||||||
\(291\) | −11.2906 | −0.661868 | ||||||||
\(292\) | −6.91203 | −0.404496 | ||||||||
\(293\) | −12.2822 | −0.717532 | −0.358766 | − | 0.933427i | \(-0.616802\pi\) | ||||
−0.358766 | + | 0.933427i | \(0.616802\pi\) | |||||||
\(294\) | 5.30027 | 0.309118 | ||||||||
\(295\) | −30.2384 | −1.76055 | ||||||||
\(296\) | −0.630865 | −0.0366683 | ||||||||
\(297\) | −11.2649 | −0.653654 | ||||||||
\(298\) | 13.6798 | 0.792448 | ||||||||
\(299\) | −19.9731 | −1.15507 | ||||||||
\(300\) | −5.86258 | −0.338476 | ||||||||
\(301\) | −30.6379 | −1.76594 | ||||||||
\(302\) | 10.9167 | 0.628187 | ||||||||
\(303\) | −0.169820 | −0.00975591 | ||||||||
\(304\) | 3.05034 | 0.174949 | ||||||||
\(305\) | −10.1698 | −0.582322 | ||||||||
\(306\) | 10.1930 | 0.582697 | ||||||||
\(307\) | −7.09108 | −0.404709 | −0.202355 | − | 0.979312i | \(-0.564859\pi\) | ||||
−0.202355 | + | 0.979312i | \(0.564859\pi\) | |||||||
\(308\) | −13.1244 | −0.747835 | ||||||||
\(309\) | −32.2170 | −1.83276 | ||||||||
\(310\) | 3.94697 | 0.224173 | ||||||||
\(311\) | −20.4211 | −1.15798 | −0.578988 | − | 0.815336i | \(-0.696552\pi\) | ||||
−0.578988 | + | 0.815336i | \(0.696552\pi\) | |||||||
\(312\) | 13.8293 | 0.782930 | ||||||||
\(313\) | 31.4280 | 1.77642 | 0.888209 | − | 0.459440i | \(-0.151950\pi\) | ||||
0.888209 | + | 0.459440i | \(0.151950\pi\) | |||||||
\(314\) | 0.191486 | 0.0108062 | ||||||||
\(315\) | −15.2834 | −0.861123 | ||||||||
\(316\) | −17.2341 | −0.969496 | ||||||||
\(317\) | 7.66928 | 0.430750 | 0.215375 | − | 0.976531i | \(-0.430903\pi\) | ||||
0.215375 | + | 0.976531i | \(0.430903\pi\) | |||||||
\(318\) | 14.7027 | 0.824486 | ||||||||
\(319\) | 23.7819 | 1.33153 | ||||||||
\(320\) | −2.77068 | −0.154886 | ||||||||
\(321\) | −21.4420 | −1.19678 | ||||||||
\(322\) | 9.70879 | 0.541050 | ||||||||
\(323\) | −17.2998 | −0.962587 | ||||||||
\(324\) | −11.1616 | −0.620091 | ||||||||
\(325\) | 16.9004 | 0.937463 | ||||||||
\(326\) | 12.3496 | 0.683980 | ||||||||
\(327\) | −9.39213 | −0.519386 | ||||||||
\(328\) | −8.42078 | −0.464960 | ||||||||
\(329\) | 14.1332 | 0.779188 | ||||||||
\(330\) | 25.9501 | 1.42851 | ||||||||
\(331\) | −22.4770 | −1.23545 | −0.617724 | − | 0.786395i | \(-0.711945\pi\) | ||||
−0.617724 | + | 0.786395i | \(0.711945\pi\) | |||||||
\(332\) | 4.21083 | 0.231099 | ||||||||
\(333\) | 1.13383 | 0.0621333 | ||||||||
\(334\) | 2.57759 | 0.141039 | ||||||||
\(335\) | 15.9868 | 0.873453 | ||||||||
\(336\) | −6.72234 | −0.366734 | ||||||||
\(337\) | −32.4632 | −1.76838 | −0.884191 | − | 0.467126i | \(-0.845289\pi\) | ||||
−0.884191 | + | 0.467126i | \(0.845289\pi\) | |||||||
\(338\) | −26.8664 | −1.46134 | ||||||||
\(339\) | 22.2511 | 1.20851 | ||||||||
\(340\) | 15.7137 | 0.852195 | ||||||||
\(341\) | −6.09164 | −0.329881 | ||||||||
\(342\) | −5.48225 | −0.296446 | ||||||||
\(343\) | −14.0571 | −0.759013 | ||||||||
\(344\) | 9.98240 | 0.538215 | ||||||||
\(345\) | −19.1966 | −1.03351 | ||||||||
\(346\) | −7.80926 | −0.419828 | ||||||||
\(347\) | 3.93027 | 0.210988 | 0.105494 | − | 0.994420i | \(-0.466358\pi\) | ||||
0.105494 | + | 0.994420i | \(0.466358\pi\) | |||||||
\(348\) | 12.1811 | 0.652973 | ||||||||
\(349\) | 35.1030 | 1.87902 | 0.939509 | − | 0.342523i | \(-0.111281\pi\) | ||||
0.939509 | + | 0.342523i | \(0.111281\pi\) | |||||||
\(350\) | −8.21516 | −0.439119 | ||||||||
\(351\) | 16.6331 | 0.887807 | ||||||||
\(352\) | 4.27619 | 0.227922 | ||||||||
\(353\) | −6.16529 | −0.328145 | −0.164073 | − | 0.986448i | \(-0.552463\pi\) | ||||
−0.164073 | + | 0.986448i | \(0.552463\pi\) | |||||||
\(354\) | 23.9039 | 1.27048 | ||||||||
\(355\) | −11.6161 | −0.616517 | ||||||||
\(356\) | −5.49270 | −0.291112 | ||||||||
\(357\) | 38.1253 | 2.01780 | ||||||||
\(358\) | 13.1978 | 0.697527 | ||||||||
\(359\) | 8.39889 | 0.443277 | 0.221638 | − | 0.975129i | \(-0.428860\pi\) | ||||
0.221638 | + | 0.975129i | \(0.428860\pi\) | |||||||
\(360\) | 4.97963 | 0.262449 | ||||||||
\(361\) | −9.69541 | −0.510285 | ||||||||
\(362\) | −10.7292 | −0.563917 | ||||||||
\(363\) | −15.9579 | −0.837570 | ||||||||
\(364\) | 19.3788 | 1.01573 | ||||||||
\(365\) | 19.1510 | 1.00241 | ||||||||
\(366\) | 8.03940 | 0.420226 | ||||||||
\(367\) | −17.7449 | −0.926277 | −0.463139 | − | 0.886286i | \(-0.653277\pi\) | ||||
−0.463139 | + | 0.886286i | \(0.653277\pi\) | |||||||
\(368\) | −3.16331 | −0.164899 | ||||||||
\(369\) | 15.1343 | 0.787861 | ||||||||
\(370\) | 1.74792 | 0.0908702 | ||||||||
\(371\) | 20.6027 | 1.06964 | ||||||||
\(372\) | −3.12014 | −0.161772 | ||||||||
\(373\) | 9.17792 | 0.475215 | 0.237607 | − | 0.971361i | \(-0.423637\pi\) | ||||
0.237607 | + | 0.971361i | \(0.423637\pi\) | |||||||
\(374\) | −24.2521 | −1.25405 | ||||||||
\(375\) | −14.0993 | −0.728083 | ||||||||
\(376\) | −4.60486 | −0.237478 | ||||||||
\(377\) | −35.1149 | −1.80851 | ||||||||
\(378\) | −8.08523 | −0.415859 | ||||||||
\(379\) | −15.6763 | −0.805239 | −0.402619 | − | 0.915367i | \(-0.631900\pi\) | ||||
−0.402619 | + | 0.915367i | \(0.631900\pi\) | |||||||
\(380\) | −8.45152 | −0.433554 | ||||||||
\(381\) | 37.4612 | 1.91919 | ||||||||
\(382\) | −19.3721 | −0.991163 | ||||||||
\(383\) | −24.9315 | −1.27394 | −0.636971 | − | 0.770888i | \(-0.719813\pi\) | ||||
−0.636971 | + | 0.770888i | \(0.719813\pi\) | |||||||
\(384\) | 2.19026 | 0.111771 | ||||||||
\(385\) | 36.3636 | 1.85326 | ||||||||
\(386\) | 22.3466 | 1.13741 | ||||||||
\(387\) | −17.9410 | −0.911990 | ||||||||
\(388\) | 5.15491 | 0.261701 | ||||||||
\(389\) | 5.71843 | 0.289936 | 0.144968 | − | 0.989436i | \(-0.453692\pi\) | ||||
0.144968 | + | 0.989436i | \(0.453692\pi\) | |||||||
\(390\) | −38.3165 | −1.94023 | ||||||||
\(391\) | 17.9405 | 0.907289 | ||||||||
\(392\) | −2.41992 | −0.122225 | ||||||||
\(393\) | 3.21214 | 0.162031 | ||||||||
\(394\) | 17.1642 | 0.864718 | ||||||||
\(395\) | 47.7502 | 2.40258 | ||||||||
\(396\) | −7.68542 | −0.386207 | ||||||||
\(397\) | 24.0531 | 1.20719 | 0.603596 | − | 0.797290i | \(-0.293734\pi\) | ||||
0.603596 | + | 0.797290i | \(0.293734\pi\) | |||||||
\(398\) | −12.8124 | −0.642227 | ||||||||
\(399\) | −20.5054 | −1.02656 | ||||||||
\(400\) | 2.67665 | 0.133833 | ||||||||
\(401\) | −26.0036 | −1.29856 | −0.649278 | − | 0.760551i | \(-0.724929\pi\) | ||||
−0.649278 | + | 0.760551i | \(0.724929\pi\) | |||||||
\(402\) | −12.6378 | −0.630318 | ||||||||
\(403\) | 8.99458 | 0.448052 | ||||||||
\(404\) | 0.0775340 | 0.00385746 | ||||||||
\(405\) | 30.9253 | 1.53669 | ||||||||
\(406\) | 17.0692 | 0.847128 | ||||||||
\(407\) | −2.69770 | −0.133720 | ||||||||
\(408\) | −12.4219 | −0.614977 | ||||||||
\(409\) | −6.36860 | −0.314907 | −0.157454 | − | 0.987526i | \(-0.550328\pi\) | ||||
−0.157454 | + | 0.987526i | \(0.550328\pi\) | |||||||
\(410\) | 23.3313 | 1.15225 | ||||||||
\(411\) | 21.3500 | 1.05312 | ||||||||
\(412\) | 14.7092 | 0.724670 | ||||||||
\(413\) | 33.4963 | 1.64824 | ||||||||
\(414\) | 5.68528 | 0.279416 | ||||||||
\(415\) | −11.6669 | −0.572703 | ||||||||
\(416\) | −6.31398 | −0.309569 | ||||||||
\(417\) | 48.9577 | 2.39747 | ||||||||
\(418\) | 13.0438 | 0.637995 | ||||||||
\(419\) | 12.7030 | 0.620582 | 0.310291 | − | 0.950642i | \(-0.399574\pi\) | ||||
0.310291 | + | 0.950642i | \(0.399574\pi\) | |||||||
\(420\) | 18.6254 | 0.908828 | ||||||||
\(421\) | −10.1853 | −0.496400 | −0.248200 | − | 0.968709i | \(-0.579839\pi\) | ||||
−0.248200 | + | 0.968709i | \(0.579839\pi\) | |||||||
\(422\) | −22.8910 | −1.11431 | ||||||||
\(423\) | 8.27613 | 0.402399 | ||||||||
\(424\) | −6.71274 | −0.326000 | ||||||||
\(425\) | −15.1805 | −0.736361 | ||||||||
\(426\) | 9.18269 | 0.444903 | ||||||||
\(427\) | 11.2655 | 0.545176 | ||||||||
\(428\) | 9.78969 | 0.473202 | ||||||||
\(429\) | 59.1367 | 2.85515 | ||||||||
\(430\) | −27.6580 | −1.33379 | ||||||||
\(431\) | 26.0235 | 1.25351 | 0.626754 | − | 0.779217i | \(-0.284383\pi\) | ||||
0.626754 | + | 0.779217i | \(0.284383\pi\) | |||||||
\(432\) | 2.63432 | 0.126744 | ||||||||
\(433\) | 19.3961 | 0.932119 | 0.466059 | − | 0.884753i | \(-0.345673\pi\) | ||||
0.466059 | + | 0.884753i | \(0.345673\pi\) | |||||||
\(434\) | −4.37221 | −0.209873 | ||||||||
\(435\) | −33.7498 | −1.61818 | ||||||||
\(436\) | 4.28813 | 0.205364 | ||||||||
\(437\) | −9.64917 | −0.461582 | ||||||||
\(438\) | −15.1392 | −0.723378 | ||||||||
\(439\) | 32.7508 | 1.56311 | 0.781556 | − | 0.623835i | \(-0.214426\pi\) | ||||
0.781556 | + | 0.623835i | \(0.214426\pi\) | |||||||
\(440\) | −11.8479 | −0.564829 | ||||||||
\(441\) | 4.34923 | 0.207106 | ||||||||
\(442\) | 35.8093 | 1.70328 | ||||||||
\(443\) | 26.6685 | 1.26706 | 0.633529 | − | 0.773719i | \(-0.281606\pi\) | ||||
0.633529 | + | 0.773719i | \(0.281606\pi\) | |||||||
\(444\) | −1.38176 | −0.0655754 | ||||||||
\(445\) | 15.2185 | 0.721426 | ||||||||
\(446\) | −6.58421 | −0.311771 | ||||||||
\(447\) | 29.9623 | 1.41717 | ||||||||
\(448\) | 3.06919 | 0.145006 | ||||||||
\(449\) | 34.5933 | 1.63256 | 0.816279 | − | 0.577657i | \(-0.196033\pi\) | ||||
0.816279 | + | 0.577657i | \(0.196033\pi\) | |||||||
\(450\) | −4.81064 | −0.226776 | ||||||||
\(451\) | −36.0089 | −1.69559 | ||||||||
\(452\) | −10.1591 | −0.477844 | ||||||||
\(453\) | 23.9105 | 1.12341 | ||||||||
\(454\) | 5.96504 | 0.279953 | ||||||||
\(455\) | −53.6924 | −2.51714 | ||||||||
\(456\) | 6.68106 | 0.312869 | ||||||||
\(457\) | 4.18826 | 0.195919 | 0.0979594 | − | 0.995190i | \(-0.468768\pi\) | ||||
0.0979594 | + | 0.995190i | \(0.468768\pi\) | |||||||
\(458\) | 5.79620 | 0.270839 | ||||||||
\(459\) | −14.9404 | −0.697357 | ||||||||
\(460\) | 8.76450 | 0.408647 | ||||||||
\(461\) | 1.84749 | 0.0860461 | 0.0430230 | − | 0.999074i | \(-0.486301\pi\) | ||||
0.0430230 | + | 0.999074i | \(0.486301\pi\) | |||||||
\(462\) | −28.7460 | −1.33739 | ||||||||
\(463\) | 3.11585 | 0.144806 | 0.0724030 | − | 0.997375i | \(-0.476933\pi\) | ||||
0.0724030 | + | 0.997375i | \(0.476933\pi\) | |||||||
\(464\) | −5.56146 | −0.258184 | ||||||||
\(465\) | 8.64490 | 0.400898 | ||||||||
\(466\) | −7.47164 | −0.346117 | ||||||||
\(467\) | 36.8552 | 1.70546 | 0.852729 | − | 0.522354i | \(-0.174946\pi\) | ||||
0.852729 | + | 0.522354i | \(0.174946\pi\) | |||||||
\(468\) | 11.3479 | 0.524555 | ||||||||
\(469\) | −17.7092 | −0.817737 | ||||||||
\(470\) | 12.7586 | 0.588510 | ||||||||
\(471\) | 0.419405 | 0.0193252 | ||||||||
\(472\) | −10.9137 | −0.502344 | ||||||||
\(473\) | 42.6867 | 1.96273 | ||||||||
\(474\) | −37.7473 | −1.73379 | ||||||||
\(475\) | 8.16471 | 0.374623 | ||||||||
\(476\) | −17.4067 | −0.797835 | ||||||||
\(477\) | 12.0645 | 0.552397 | ||||||||
\(478\) | 0.953242 | 0.0436003 | ||||||||
\(479\) | −15.7315 | −0.718791 | −0.359396 | − | 0.933185i | \(-0.617017\pi\) | ||||
−0.359396 | + | 0.933185i | \(0.617017\pi\) | |||||||
\(480\) | −6.06852 | −0.276989 | ||||||||
\(481\) | 3.98327 | 0.181621 | ||||||||
\(482\) | −8.63373 | −0.393256 | ||||||||
\(483\) | 21.2648 | 0.967582 | ||||||||
\(484\) | 7.28581 | 0.331173 | ||||||||
\(485\) | −14.2826 | −0.648539 | ||||||||
\(486\) | −16.5440 | −0.750450 | ||||||||
\(487\) | 30.6542 | 1.38907 | 0.694537 | − | 0.719457i | \(-0.255609\pi\) | ||||
0.694537 | + | 0.719457i | \(0.255609\pi\) | |||||||
\(488\) | −3.67051 | −0.166156 | ||||||||
\(489\) | 27.0489 | 1.22319 | ||||||||
\(490\) | 6.70483 | 0.302893 | ||||||||
\(491\) | 23.6703 | 1.06822 | 0.534112 | − | 0.845414i | \(-0.320646\pi\) | ||||
0.534112 | + | 0.845414i | \(0.320646\pi\) | |||||||
\(492\) | −18.4437 | −0.831508 | ||||||||
\(493\) | 31.5414 | 1.42055 | ||||||||
\(494\) | −19.2598 | −0.866540 | ||||||||
\(495\) | 21.2938 | 0.957087 | ||||||||
\(496\) | 1.42455 | 0.0639641 | ||||||||
\(497\) | 12.8676 | 0.577190 | ||||||||
\(498\) | 9.22283 | 0.413285 | ||||||||
\(499\) | 6.01488 | 0.269263 | 0.134631 | − | 0.990896i | \(-0.457015\pi\) | ||||
0.134631 | + | 0.990896i | \(0.457015\pi\) | |||||||
\(500\) | 6.43724 | 0.287882 | ||||||||
\(501\) | 5.64559 | 0.252227 | ||||||||
\(502\) | 11.3676 | 0.507363 | ||||||||
\(503\) | 1.13420 | 0.0505715 | 0.0252857 | − | 0.999680i | \(-0.491950\pi\) | ||||
0.0252857 | + | 0.999680i | \(0.491950\pi\) | |||||||
\(504\) | −5.51613 | −0.245708 | ||||||||
\(505\) | −0.214822 | −0.00955944 | ||||||||
\(506\) | −13.5269 | −0.601344 | ||||||||
\(507\) | −58.8445 | −2.61338 | ||||||||
\(508\) | −17.1035 | −0.758845 | ||||||||
\(509\) | 26.0814 | 1.15604 | 0.578019 | − | 0.816023i | \(-0.303826\pi\) | ||||
0.578019 | + | 0.816023i | \(0.303826\pi\) | |||||||
\(510\) | 34.4172 | 1.52402 | ||||||||
\(511\) | −21.2143 | −0.938467 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 8.03558 | 0.354780 | ||||||||
\(514\) | 13.3223 | 0.587623 | ||||||||
\(515\) | −40.7545 | −1.79586 | ||||||||
\(516\) | 21.8641 | 0.962513 | ||||||||
\(517\) | −19.6913 | −0.866021 | ||||||||
\(518\) | −1.93624 | −0.0850736 | ||||||||
\(519\) | −17.1043 | −0.750797 | ||||||||
\(520\) | 17.4940 | 0.767163 | ||||||||
\(521\) | −40.7469 | −1.78515 | −0.892577 | − | 0.450896i | \(-0.851105\pi\) | ||||
−0.892577 | + | 0.450896i | \(0.851105\pi\) | |||||||
\(522\) | 9.99538 | 0.437486 | ||||||||
\(523\) | −0.222001 | −0.00970744 | −0.00485372 | − | 0.999988i | \(-0.501545\pi\) | ||||
−0.00485372 | + | 0.999988i | \(0.501545\pi\) | |||||||
\(524\) | −1.46655 | −0.0640667 | ||||||||
\(525\) | −17.9934 | −0.785295 | ||||||||
\(526\) | −7.66856 | −0.334365 | ||||||||
\(527\) | −8.07923 | −0.351937 | ||||||||
\(528\) | 9.36599 | 0.407602 | ||||||||
\(529\) | −12.9935 | −0.564935 | ||||||||
\(530\) | 18.5989 | 0.807882 | ||||||||
\(531\) | 19.6148 | 0.851208 | ||||||||
\(532\) | 9.36208 | 0.405898 | ||||||||
\(533\) | 53.1687 | 2.30299 | ||||||||
\(534\) | −12.0305 | −0.520609 | ||||||||
\(535\) | −27.1241 | −1.17268 | ||||||||
\(536\) | 5.77000 | 0.249226 | ||||||||
\(537\) | 28.9067 | 1.24742 | ||||||||
\(538\) | 3.02964 | 0.130617 | ||||||||
\(539\) | −10.3481 | −0.445723 | ||||||||
\(540\) | −7.29886 | −0.314093 | ||||||||
\(541\) | 22.0086 | 0.946224 | 0.473112 | − | 0.881002i | \(-0.343131\pi\) | ||||
0.473112 | + | 0.881002i | \(0.343131\pi\) | |||||||
\(542\) | −13.0886 | −0.562203 | ||||||||
\(543\) | −23.4999 | −1.00848 | ||||||||
\(544\) | 5.67143 | 0.243161 | ||||||||
\(545\) | −11.8810 | −0.508927 | ||||||||
\(546\) | 42.4447 | 1.81647 | ||||||||
\(547\) | 43.2481 | 1.84916 | 0.924578 | − | 0.380992i | \(-0.124418\pi\) | ||||
0.924578 | + | 0.380992i | \(0.124418\pi\) | |||||||
\(548\) | −9.74768 | −0.416400 | ||||||||
\(549\) | 6.59686 | 0.281547 | ||||||||
\(550\) | 11.4459 | 0.488054 | ||||||||
\(551\) | −16.9643 | −0.722705 | ||||||||
\(552\) | −6.92848 | −0.294896 | ||||||||
\(553\) | −52.8948 | −2.24932 | ||||||||
\(554\) | 0.588778 | 0.0250148 | ||||||||
\(555\) | 3.82841 | 0.162507 | ||||||||
\(556\) | −22.3524 | −0.947954 | ||||||||
\(557\) | 20.2941 | 0.859889 | 0.429945 | − | 0.902855i | \(-0.358533\pi\) | ||||
0.429945 | + | 0.902855i | \(0.358533\pi\) | |||||||
\(558\) | −2.56028 | −0.108385 | ||||||||
\(559\) | −63.0287 | −2.66583 | ||||||||
\(560\) | −8.50374 | −0.359348 | ||||||||
\(561\) | −53.1186 | −2.24267 | ||||||||
\(562\) | −10.0168 | −0.422534 | ||||||||
\(563\) | −15.9327 | −0.671483 | −0.335741 | − | 0.941954i | \(-0.608987\pi\) | ||||
−0.335741 | + | 0.941954i | \(0.608987\pi\) | |||||||
\(564\) | −10.0859 | −0.424692 | ||||||||
\(565\) | 28.1476 | 1.18418 | ||||||||
\(566\) | −21.7789 | −0.915434 | ||||||||
\(567\) | −34.2572 | −1.43867 | ||||||||
\(568\) | −4.19250 | −0.175913 | ||||||||
\(569\) | 14.1002 | 0.591109 | 0.295555 | − | 0.955326i | \(-0.404496\pi\) | ||||
0.295555 | + | 0.955326i | \(0.404496\pi\) | |||||||
\(570\) | −18.5111 | −0.775343 | ||||||||
\(571\) | −12.6378 | −0.528874 | −0.264437 | − | 0.964403i | \(-0.585186\pi\) | ||||
−0.264437 | + | 0.964403i | \(0.585186\pi\) | |||||||
\(572\) | −26.9998 | −1.12892 | ||||||||
\(573\) | −42.4300 | −1.77254 | ||||||||
\(574\) | −25.8450 | −1.07875 | ||||||||
\(575\) | −8.46708 | −0.353102 | ||||||||
\(576\) | 1.79726 | 0.0748858 | ||||||||
\(577\) | −20.7629 | −0.864369 | −0.432184 | − | 0.901785i | \(-0.642257\pi\) | ||||
−0.432184 | + | 0.901785i | \(0.642257\pi\) | |||||||
\(578\) | −15.1651 | −0.630786 | ||||||||
\(579\) | 48.9451 | 2.03409 | ||||||||
\(580\) | 15.4090 | 0.639824 | ||||||||
\(581\) | 12.9238 | 0.536171 | ||||||||
\(582\) | 11.2906 | 0.468011 | ||||||||
\(583\) | −28.7050 | −1.18884 | ||||||||
\(584\) | 6.91203 | 0.286022 | ||||||||
\(585\) | −31.4413 | −1.29994 | ||||||||
\(586\) | 12.2822 | 0.507372 | ||||||||
\(587\) | 24.5443 | 1.01305 | 0.506527 | − | 0.862224i | \(-0.330929\pi\) | ||||
0.506527 | + | 0.862224i | \(0.330929\pi\) | |||||||
\(588\) | −5.30027 | −0.218580 | ||||||||
\(589\) | 4.34536 | 0.179048 | ||||||||
\(590\) | 30.2384 | 1.24489 | ||||||||
\(591\) | 37.5940 | 1.54641 | ||||||||
\(592\) | 0.630865 | 0.0259284 | ||||||||
\(593\) | 21.9320 | 0.900638 | 0.450319 | − | 0.892868i | \(-0.351310\pi\) | ||||
0.450319 | + | 0.892868i | \(0.351310\pi\) | |||||||
\(594\) | 11.2649 | 0.462203 | ||||||||
\(595\) | 48.2283 | 1.97717 | ||||||||
\(596\) | −13.6798 | −0.560346 | ||||||||
\(597\) | −28.0625 | −1.14852 | ||||||||
\(598\) | 19.9731 | 0.816759 | ||||||||
\(599\) | 37.3098 | 1.52444 | 0.762219 | − | 0.647320i | \(-0.224110\pi\) | ||||
0.762219 | + | 0.647320i | \(0.224110\pi\) | |||||||
\(600\) | 5.86258 | 0.239339 | ||||||||
\(601\) | 10.0699 | 0.410758 | 0.205379 | − | 0.978683i | \(-0.434157\pi\) | ||||
0.205379 | + | 0.978683i | \(0.434157\pi\) | |||||||
\(602\) | 30.6379 | 1.24871 | ||||||||
\(603\) | −10.3702 | −0.422307 | ||||||||
\(604\) | −10.9167 | −0.444195 | ||||||||
\(605\) | −20.1866 | −0.820704 | ||||||||
\(606\) | 0.169820 | 0.00689847 | ||||||||
\(607\) | −1.02591 | −0.0416404 | −0.0208202 | − | 0.999783i | \(-0.506628\pi\) | ||||
−0.0208202 | + | 0.999783i | \(0.506628\pi\) | |||||||
\(608\) | −3.05034 | −0.123708 | ||||||||
\(609\) | 37.3860 | 1.51496 | ||||||||
\(610\) | 10.1698 | 0.411764 | ||||||||
\(611\) | 29.0750 | 1.17625 | ||||||||
\(612\) | −10.1930 | −0.412029 | ||||||||
\(613\) | 6.06510 | 0.244967 | 0.122484 | − | 0.992471i | \(-0.460914\pi\) | ||||
0.122484 | + | 0.992471i | \(0.460914\pi\) | |||||||
\(614\) | 7.09108 | 0.286173 | ||||||||
\(615\) | 51.1016 | 2.06062 | ||||||||
\(616\) | 13.1244 | 0.528799 | ||||||||
\(617\) | 24.0196 | 0.966993 | 0.483496 | − | 0.875346i | \(-0.339367\pi\) | ||||
0.483496 | + | 0.875346i | \(0.339367\pi\) | |||||||
\(618\) | 32.2170 | 1.29596 | ||||||||
\(619\) | 34.9878 | 1.40628 | 0.703138 | − | 0.711053i | \(-0.251781\pi\) | ||||
0.703138 | + | 0.711053i | \(0.251781\pi\) | |||||||
\(620\) | −3.94697 | −0.158514 | ||||||||
\(621\) | −8.33316 | −0.334398 | ||||||||
\(622\) | 20.4211 | 0.818813 | ||||||||
\(623\) | −16.8581 | −0.675407 | ||||||||
\(624\) | −13.8293 | −0.553615 | ||||||||
\(625\) | −31.2188 | −1.24875 | ||||||||
\(626\) | −31.4280 | −1.25612 | ||||||||
\(627\) | 28.5695 | 1.14096 | ||||||||
\(628\) | −0.191486 | −0.00764113 | ||||||||
\(629\) | −3.57790 | −0.142660 | ||||||||
\(630\) | 15.2834 | 0.608906 | ||||||||
\(631\) | 1.11155 | 0.0442501 | 0.0221250 | − | 0.999755i | \(-0.492957\pi\) | ||||
0.0221250 | + | 0.999755i | \(0.492957\pi\) | |||||||
\(632\) | 17.2341 | 0.685537 | ||||||||
\(633\) | −50.1372 | −1.99278 | ||||||||
\(634\) | −7.66928 | −0.304586 | ||||||||
\(635\) | 47.3883 | 1.88055 | ||||||||
\(636\) | −14.7027 | −0.582999 | ||||||||
\(637\) | 15.2794 | 0.605390 | ||||||||
\(638\) | −23.7819 | −0.941533 | ||||||||
\(639\) | 7.53501 | 0.298080 | ||||||||
\(640\) | 2.77068 | 0.109521 | ||||||||
\(641\) | −22.7019 | −0.896671 | −0.448335 | − | 0.893865i | \(-0.647983\pi\) | ||||
−0.448335 | + | 0.893865i | \(0.647983\pi\) | |||||||
\(642\) | 21.4420 | 0.846249 | ||||||||
\(643\) | 15.2835 | 0.602724 | 0.301362 | − | 0.953510i | \(-0.402559\pi\) | ||||
0.301362 | + | 0.953510i | \(0.402559\pi\) | |||||||
\(644\) | −9.70879 | −0.382580 | ||||||||
\(645\) | −60.5784 | −2.38527 | ||||||||
\(646\) | 17.2998 | 0.680652 | ||||||||
\(647\) | 1.68254 | 0.0661476 | 0.0330738 | − | 0.999453i | \(-0.489470\pi\) | ||||
0.0330738 | + | 0.999453i | \(0.489470\pi\) | |||||||
\(648\) | 11.1616 | 0.438471 | ||||||||
\(649\) | −46.6691 | −1.83192 | ||||||||
\(650\) | −16.9004 | −0.662886 | ||||||||
\(651\) | −9.57630 | −0.375325 | ||||||||
\(652\) | −12.3496 | −0.483647 | ||||||||
\(653\) | 34.4669 | 1.34879 | 0.674397 | − | 0.738369i | \(-0.264404\pi\) | ||||
0.674397 | + | 0.738369i | \(0.264404\pi\) | |||||||
\(654\) | 9.39213 | 0.367261 | ||||||||
\(655\) | 4.06335 | 0.158768 | ||||||||
\(656\) | 8.42078 | 0.328776 | ||||||||
\(657\) | −12.4227 | −0.484656 | ||||||||
\(658\) | −14.1332 | −0.550969 | ||||||||
\(659\) | 41.5462 | 1.61841 | 0.809205 | − | 0.587526i | \(-0.199898\pi\) | ||||
0.809205 | + | 0.587526i | \(0.199898\pi\) | |||||||
\(660\) | −25.9501 | −1.01011 | ||||||||
\(661\) | −12.0867 | −0.470120 | −0.235060 | − | 0.971981i | \(-0.575529\pi\) | ||||
−0.235060 | + | 0.971981i | \(0.575529\pi\) | |||||||
\(662\) | 22.4770 | 0.873593 | ||||||||
\(663\) | 78.4319 | 3.04604 | ||||||||
\(664\) | −4.21083 | −0.163412 | ||||||||
\(665\) | −25.9393 | −1.00588 | ||||||||
\(666\) | −1.13383 | −0.0439349 | ||||||||
\(667\) | 17.5926 | 0.681188 | ||||||||
\(668\) | −2.57759 | −0.0997298 | ||||||||
\(669\) | −14.4212 | −0.557555 | ||||||||
\(670\) | −15.9868 | −0.617625 | ||||||||
\(671\) | −15.6958 | −0.605930 | ||||||||
\(672\) | 6.72234 | 0.259320 | ||||||||
\(673\) | 20.7127 | 0.798416 | 0.399208 | − | 0.916860i | \(-0.369285\pi\) | ||||
0.399208 | + | 0.916860i | \(0.369285\pi\) | |||||||
\(674\) | 32.4632 | 1.25043 | ||||||||
\(675\) | 7.05117 | 0.271400 | ||||||||
\(676\) | 26.8664 | 1.03332 | ||||||||
\(677\) | −30.2979 | −1.16444 | −0.582222 | − | 0.813030i | \(-0.697816\pi\) | ||||
−0.582222 | + | 0.813030i | \(0.697816\pi\) | |||||||
\(678\) | −22.2511 | −0.854549 | ||||||||
\(679\) | 15.8214 | 0.607169 | ||||||||
\(680\) | −15.7137 | −0.602593 | ||||||||
\(681\) | 13.0650 | 0.500653 | ||||||||
\(682\) | 6.09164 | 0.233261 | ||||||||
\(683\) | −15.7487 | −0.602608 | −0.301304 | − | 0.953528i | \(-0.597422\pi\) | ||||
−0.301304 | + | 0.953528i | \(0.597422\pi\) | |||||||
\(684\) | 5.48225 | 0.209619 | ||||||||
\(685\) | 27.0077 | 1.03191 | ||||||||
\(686\) | 14.0571 | 0.536703 | ||||||||
\(687\) | 12.6952 | 0.484353 | ||||||||
\(688\) | −9.98240 | −0.380575 | ||||||||
\(689\) | 42.3842 | 1.61471 | ||||||||
\(690\) | 19.1966 | 0.730801 | ||||||||
\(691\) | −33.6615 | −1.28054 | −0.640272 | − | 0.768148i | \(-0.721179\pi\) | ||||
−0.640272 | + | 0.768148i | \(0.721179\pi\) | |||||||
\(692\) | 7.80926 | 0.296863 | ||||||||
\(693\) | −23.5880 | −0.896035 | ||||||||
\(694\) | −3.93027 | −0.149191 | ||||||||
\(695\) | 61.9314 | 2.34919 | ||||||||
\(696\) | −12.1811 | −0.461722 | ||||||||
\(697\) | −47.7579 | −1.80896 | ||||||||
\(698\) | −35.1030 | −1.32867 | ||||||||
\(699\) | −16.3649 | −0.618976 | ||||||||
\(700\) | 8.21516 | 0.310504 | ||||||||
\(701\) | 33.6404 | 1.27058 | 0.635290 | − | 0.772273i | \(-0.280880\pi\) | ||||
0.635290 | + | 0.772273i | \(0.280880\pi\) | |||||||
\(702\) | −16.6331 | −0.627774 | ||||||||
\(703\) | 1.92435 | 0.0725783 | ||||||||
\(704\) | −4.27619 | −0.161165 | ||||||||
\(705\) | 27.9447 | 1.05246 | ||||||||
\(706\) | 6.16529 | 0.232034 | ||||||||
\(707\) | 0.237967 | 0.00894966 | ||||||||
\(708\) | −23.9039 | −0.898364 | ||||||||
\(709\) | 4.46979 | 0.167867 | 0.0839333 | − | 0.996471i | \(-0.473252\pi\) | ||||
0.0839333 | + | 0.996471i | \(0.473252\pi\) | |||||||
\(710\) | 11.6161 | 0.435943 | ||||||||
\(711\) | −30.9742 | −1.16162 | ||||||||
\(712\) | 5.49270 | 0.205848 | ||||||||
\(713\) | −4.50628 | −0.168762 | ||||||||
\(714\) | −38.1253 | −1.42680 | ||||||||
\(715\) | 74.8078 | 2.79765 | ||||||||
\(716\) | −13.1978 | −0.493226 | ||||||||
\(717\) | 2.08785 | 0.0779723 | ||||||||
\(718\) | −8.39889 | −0.313444 | ||||||||
\(719\) | 6.61299 | 0.246623 | 0.123311 | − | 0.992368i | \(-0.460649\pi\) | ||||
0.123311 | + | 0.992368i | \(0.460649\pi\) | |||||||
\(720\) | −4.97963 | −0.185580 | ||||||||
\(721\) | 45.1453 | 1.68130 | ||||||||
\(722\) | 9.69541 | 0.360826 | ||||||||
\(723\) | −18.9102 | −0.703276 | ||||||||
\(724\) | 10.7292 | 0.398749 | ||||||||
\(725\) | −14.8861 | −0.552856 | ||||||||
\(726\) | 15.9579 | 0.592252 | ||||||||
\(727\) | −12.3702 | −0.458785 | −0.229392 | − | 0.973334i | \(-0.573674\pi\) | ||||
−0.229392 | + | 0.973334i | \(0.573674\pi\) | |||||||
\(728\) | −19.3788 | −0.718227 | ||||||||
\(729\) | −2.75077 | −0.101880 | ||||||||
\(730\) | −19.1510 | −0.708811 | ||||||||
\(731\) | 56.6145 | 2.09396 | ||||||||
\(732\) | −8.03940 | −0.297145 | ||||||||
\(733\) | −8.53985 | −0.315427 | −0.157713 | − | 0.987485i | \(-0.550412\pi\) | ||||
−0.157713 | + | 0.987485i | \(0.550412\pi\) | |||||||
\(734\) | 17.7449 | 0.654977 | ||||||||
\(735\) | 14.6854 | 0.541677 | ||||||||
\(736\) | 3.16331 | 0.116601 | ||||||||
\(737\) | 24.6736 | 0.908865 | ||||||||
\(738\) | −15.1343 | −0.557102 | ||||||||
\(739\) | 6.19418 | 0.227857 | 0.113928 | − | 0.993489i | \(-0.463657\pi\) | ||||
0.113928 | + | 0.993489i | \(0.463657\pi\) | |||||||
\(740\) | −1.74792 | −0.0642549 | ||||||||
\(741\) | −42.1841 | −1.54967 | ||||||||
\(742\) | −20.6027 | −0.756348 | ||||||||
\(743\) | 22.0148 | 0.807646 | 0.403823 | − | 0.914837i | \(-0.367681\pi\) | ||||
0.403823 | + | 0.914837i | \(0.367681\pi\) | |||||||
\(744\) | 3.12014 | 0.114390 | ||||||||
\(745\) | 37.9023 | 1.38863 | ||||||||
\(746\) | −9.17792 | −0.336028 | ||||||||
\(747\) | 7.56795 | 0.276897 | ||||||||
\(748\) | 24.2521 | 0.886746 | ||||||||
\(749\) | 30.0464 | 1.09787 | ||||||||
\(750\) | 14.0993 | 0.514832 | ||||||||
\(751\) | −30.8343 | −1.12516 | −0.562580 | − | 0.826743i | \(-0.690191\pi\) | ||||
−0.562580 | + | 0.826743i | \(0.690191\pi\) | |||||||
\(752\) | 4.60486 | 0.167922 | ||||||||
\(753\) | 24.8981 | 0.907339 | ||||||||
\(754\) | 35.1149 | 1.27881 | ||||||||
\(755\) | 30.2467 | 1.10079 | ||||||||
\(756\) | 8.08523 | 0.294057 | ||||||||
\(757\) | 29.3128 | 1.06539 | 0.532696 | − | 0.846307i | \(-0.321179\pi\) | ||||
0.532696 | + | 0.846307i | \(0.321179\pi\) | |||||||
\(758\) | 15.6763 | 0.569390 | ||||||||
\(759\) | −29.6275 | −1.07541 | ||||||||
\(760\) | 8.45152 | 0.306569 | ||||||||
\(761\) | −45.8413 | −1.66175 | −0.830873 | − | 0.556462i | \(-0.812159\pi\) | ||||
−0.830873 | + | 0.556462i | \(0.812159\pi\) | |||||||
\(762\) | −37.4612 | −1.35708 | ||||||||
\(763\) | 13.1611 | 0.476463 | ||||||||
\(764\) | 19.3721 | 0.700858 | ||||||||
\(765\) | 28.2416 | 1.02108 | ||||||||
\(766\) | 24.9315 | 0.900813 | ||||||||
\(767\) | 68.9090 | 2.48816 | ||||||||
\(768\) | −2.19026 | −0.0790344 | ||||||||
\(769\) | −45.9403 | −1.65665 | −0.828324 | − | 0.560249i | \(-0.810705\pi\) | ||||
−0.828324 | + | 0.560249i | \(0.810705\pi\) | |||||||
\(770\) | −36.3636 | −1.31045 | ||||||||
\(771\) | 29.1795 | 1.05087 | ||||||||
\(772\) | −22.3466 | −0.804273 | ||||||||
\(773\) | 34.4048 | 1.23745 | 0.618727 | − | 0.785606i | \(-0.287649\pi\) | ||||
0.618727 | + | 0.785606i | \(0.287649\pi\) | |||||||
\(774\) | 17.9410 | 0.644874 | ||||||||
\(775\) | 3.81303 | 0.136968 | ||||||||
\(776\) | −5.15491 | −0.185050 | ||||||||
\(777\) | −4.24088 | −0.152141 | ||||||||
\(778\) | −5.71843 | −0.205016 | ||||||||
\(779\) | 25.6863 | 0.920306 | ||||||||
\(780\) | 38.3165 | 1.37195 | ||||||||
\(781\) | −17.9279 | −0.641512 | ||||||||
\(782\) | −17.9405 | −0.641550 | ||||||||
\(783\) | −14.6507 | −0.523572 | ||||||||
\(784\) | 2.41992 | 0.0864259 | ||||||||
\(785\) | 0.530547 | 0.0189360 | ||||||||
\(786\) | −3.21214 | −0.114573 | ||||||||
\(787\) | 5.47953 | 0.195324 | 0.0976621 | − | 0.995220i | \(-0.468864\pi\) | ||||
0.0976621 | + | 0.995220i | \(0.468864\pi\) | |||||||
\(788\) | −17.1642 | −0.611448 | ||||||||
\(789\) | −16.7962 | −0.597960 | ||||||||
\(790\) | −47.7502 | −1.69888 | ||||||||
\(791\) | −31.1802 | −1.10864 | ||||||||
\(792\) | 7.68542 | 0.273090 | ||||||||
\(793\) | 23.1756 | 0.822988 | ||||||||
\(794\) | −24.0531 | −0.853614 | ||||||||
\(795\) | 40.7364 | 1.44477 | ||||||||
\(796\) | 12.8124 | 0.454123 | ||||||||
\(797\) | 14.9007 | 0.527811 | 0.263905 | − | 0.964549i | \(-0.414989\pi\) | ||||
0.263905 | + | 0.964549i | \(0.414989\pi\) | |||||||
\(798\) | 20.5054 | 0.725884 | ||||||||
\(799\) | −26.1162 | −0.923923 | ||||||||
\(800\) | −2.67665 | −0.0946340 | ||||||||
\(801\) | −9.87180 | −0.348803 | ||||||||
\(802\) | 26.0036 | 0.918218 | ||||||||
\(803\) | 29.5572 | 1.04305 | ||||||||
\(804\) | 12.6378 | 0.445702 | ||||||||
\(805\) | 26.8999 | 0.948098 | ||||||||
\(806\) | −8.99458 | −0.316821 | ||||||||
\(807\) | 6.63571 | 0.233588 | ||||||||
\(808\) | −0.0775340 | −0.00272764 | ||||||||
\(809\) | −14.5812 | −0.512646 | −0.256323 | − | 0.966591i | \(-0.582511\pi\) | ||||
−0.256323 | + | 0.966591i | \(0.582511\pi\) | |||||||
\(810\) | −30.9253 | −1.08660 | ||||||||
\(811\) | 14.0382 | 0.492947 | 0.246473 | − | 0.969150i | \(-0.420728\pi\) | ||||
0.246473 | + | 0.969150i | \(0.420728\pi\) | |||||||
\(812\) | −17.0692 | −0.599010 | ||||||||
\(813\) | −28.6675 | −1.00541 | ||||||||
\(814\) | 2.69770 | 0.0945543 | ||||||||
\(815\) | 34.2167 | 1.19856 | ||||||||
\(816\) | 12.4219 | 0.434855 | ||||||||
\(817\) | −30.4497 | −1.06530 | ||||||||
\(818\) | 6.36860 | 0.222673 | ||||||||
\(819\) | 34.8287 | 1.21701 | ||||||||
\(820\) | −23.3313 | −0.814763 | ||||||||
\(821\) | −50.2071 | −1.75224 | −0.876119 | − | 0.482094i | \(-0.839876\pi\) | ||||
−0.876119 | + | 0.482094i | \(0.839876\pi\) | |||||||
\(822\) | −21.3500 | −0.744667 | ||||||||
\(823\) | −12.2022 | −0.425342 | −0.212671 | − | 0.977124i | \(-0.568216\pi\) | ||||
−0.212671 | + | 0.977124i | \(0.568216\pi\) | |||||||
\(824\) | −14.7092 | −0.512419 | ||||||||
\(825\) | 25.0695 | 0.872809 | ||||||||
\(826\) | −33.4963 | −1.16548 | ||||||||
\(827\) | −4.40461 | −0.153163 | −0.0765816 | − | 0.997063i | \(-0.524401\pi\) | ||||
−0.0765816 | + | 0.997063i | \(0.524401\pi\) | |||||||
\(828\) | −5.68528 | −0.197577 | ||||||||
\(829\) | 2.50953 | 0.0871596 | 0.0435798 | − | 0.999050i | \(-0.486124\pi\) | ||||
0.0435798 | + | 0.999050i | \(0.486124\pi\) | |||||||
\(830\) | 11.6669 | 0.404962 | ||||||||
\(831\) | 1.28958 | 0.0447350 | ||||||||
\(832\) | 6.31398 | 0.218898 | ||||||||
\(833\) | −13.7244 | −0.475523 | ||||||||
\(834\) | −48.9577 | −1.69527 | ||||||||
\(835\) | 7.14166 | 0.247147 | ||||||||
\(836\) | −13.0438 | −0.451131 | ||||||||
\(837\) | 3.75272 | 0.129713 | ||||||||
\(838\) | −12.7030 | −0.438817 | ||||||||
\(839\) | 12.8516 | 0.443686 | 0.221843 | − | 0.975082i | \(-0.428793\pi\) | ||||
0.221843 | + | 0.975082i | \(0.428793\pi\) | |||||||
\(840\) | −18.6254 | −0.642638 | ||||||||
\(841\) | 1.92980 | 0.0665449 | ||||||||
\(842\) | 10.1853 | 0.351008 | ||||||||
\(843\) | −21.9395 | −0.755637 | ||||||||
\(844\) | 22.8910 | 0.787939 | ||||||||
\(845\) | −74.4381 | −2.56075 | ||||||||
\(846\) | −8.27613 | −0.284539 | ||||||||
\(847\) | 22.3615 | 0.768352 | ||||||||
\(848\) | 6.71274 | 0.230517 | ||||||||
\(849\) | −47.7015 | −1.63711 | ||||||||
\(850\) | 15.1805 | 0.520686 | ||||||||
\(851\) | −1.99562 | −0.0684089 | ||||||||
\(852\) | −9.18269 | −0.314594 | ||||||||
\(853\) | 29.2685 | 1.00213 | 0.501067 | − | 0.865409i | \(-0.332941\pi\) | ||||
0.501067 | + | 0.865409i | \(0.332941\pi\) | |||||||
\(854\) | −11.2655 | −0.385498 | ||||||||
\(855\) | −15.1896 | −0.519472 | ||||||||
\(856\) | −9.78969 | −0.334605 | ||||||||
\(857\) | 23.1817 | 0.791870 | 0.395935 | − | 0.918279i | \(-0.370421\pi\) | ||||
0.395935 | + | 0.918279i | \(0.370421\pi\) | |||||||
\(858\) | −59.1367 | −2.01889 | ||||||||
\(859\) | 11.0145 | 0.375810 | 0.187905 | − | 0.982187i | \(-0.439830\pi\) | ||||
0.187905 | + | 0.982187i | \(0.439830\pi\) | |||||||
\(860\) | 27.6580 | 0.943130 | ||||||||
\(861\) | −56.6073 | −1.92917 | ||||||||
\(862\) | −26.0235 | −0.886365 | ||||||||
\(863\) | 1.22035 | 0.0415411 | 0.0207705 | − | 0.999784i | \(-0.493388\pi\) | ||||
0.0207705 | + | 0.999784i | \(0.493388\pi\) | |||||||
\(864\) | −2.63432 | −0.0896214 | ||||||||
\(865\) | −21.6369 | −0.735678 | ||||||||
\(866\) | −19.3961 | −0.659107 | ||||||||
\(867\) | −33.2156 | −1.12806 | ||||||||
\(868\) | 4.37221 | 0.148403 | ||||||||
\(869\) | 73.6965 | 2.49998 | ||||||||
\(870\) | 33.7498 | 1.14423 | ||||||||
\(871\) | −36.4317 | −1.23444 | ||||||||
\(872\) | −4.28813 | −0.145214 | ||||||||
\(873\) | 9.26471 | 0.313563 | ||||||||
\(874\) | 9.64917 | 0.326388 | ||||||||
\(875\) | 19.7571 | 0.667912 | ||||||||
\(876\) | 15.1392 | 0.511505 | ||||||||
\(877\) | 18.1457 | 0.612736 | 0.306368 | − | 0.951913i | \(-0.400886\pi\) | ||||
0.306368 | + | 0.951913i | \(0.400886\pi\) | |||||||
\(878\) | −32.7508 | −1.10529 | ||||||||
\(879\) | 26.9012 | 0.907355 | ||||||||
\(880\) | 11.8479 | 0.399394 | ||||||||
\(881\) | −23.0693 | −0.777225 | −0.388613 | − | 0.921401i | \(-0.627046\pi\) | ||||
−0.388613 | + | 0.921401i | \(0.627046\pi\) | |||||||
\(882\) | −4.34923 | −0.146446 | ||||||||
\(883\) | 52.9051 | 1.78040 | 0.890199 | − | 0.455572i | \(-0.150565\pi\) | ||||
0.890199 | + | 0.455572i | \(0.150565\pi\) | |||||||
\(884\) | −35.8093 | −1.20440 | ||||||||
\(885\) | 66.2301 | 2.22630 | ||||||||
\(886\) | −26.6685 | −0.895945 | ||||||||
\(887\) | 22.7817 | 0.764935 | 0.382467 | − | 0.923969i | \(-0.375074\pi\) | ||||
0.382467 | + | 0.923969i | \(0.375074\pi\) | |||||||
\(888\) | 1.38176 | 0.0463688 | ||||||||
\(889\) | −52.4939 | −1.76059 | ||||||||
\(890\) | −15.2185 | −0.510125 | ||||||||
\(891\) | 47.7293 | 1.59899 | ||||||||
\(892\) | 6.58421 | 0.220456 | ||||||||
\(893\) | 14.0464 | 0.470045 | ||||||||
\(894\) | −29.9623 | −1.00209 | ||||||||
\(895\) | 36.5669 | 1.22230 | ||||||||
\(896\) | −3.06919 | −0.102534 | ||||||||
\(897\) | 43.7463 | 1.46065 | ||||||||
\(898\) | −34.5933 | −1.15439 | ||||||||
\(899\) | −7.92257 | −0.264232 | ||||||||
\(900\) | 4.81064 | 0.160355 | ||||||||
\(901\) | −38.0709 | −1.26832 | ||||||||
\(902\) | 36.0089 | 1.19896 | ||||||||
\(903\) | 67.1051 | 2.23312 | ||||||||
\(904\) | 10.1591 | 0.337887 | ||||||||
\(905\) | −29.7273 | −0.988168 | ||||||||
\(906\) | −23.9105 | −0.794373 | ||||||||
\(907\) | 27.6388 | 0.917731 | 0.458866 | − | 0.888506i | \(-0.348256\pi\) | ||||
0.458866 | + | 0.888506i | \(0.348256\pi\) | |||||||
\(908\) | −5.96504 | −0.197957 | ||||||||
\(909\) | 0.139349 | 0.00462190 | ||||||||
\(910\) | 53.6924 | 1.77989 | ||||||||
\(911\) | 1.81558 | 0.0601530 | 0.0300765 | − | 0.999548i | \(-0.490425\pi\) | ||||
0.0300765 | + | 0.999548i | \(0.490425\pi\) | |||||||
\(912\) | −6.68106 | −0.221232 | ||||||||
\(913\) | −18.0063 | −0.595922 | ||||||||
\(914\) | −4.18826 | −0.138535 | ||||||||
\(915\) | 22.2746 | 0.736375 | ||||||||
\(916\) | −5.79620 | −0.191512 | ||||||||
\(917\) | −4.50113 | −0.148640 | ||||||||
\(918\) | 14.9404 | 0.493106 | ||||||||
\(919\) | 22.5149 | 0.742699 | 0.371350 | − | 0.928493i | \(-0.378895\pi\) | ||||
0.371350 | + | 0.928493i | \(0.378895\pi\) | |||||||
\(920\) | −8.76450 | −0.288957 | ||||||||
\(921\) | 15.5313 | 0.511775 | ||||||||
\(922\) | −1.84749 | −0.0608438 | ||||||||
\(923\) | 26.4714 | 0.871316 | ||||||||
\(924\) | 28.7460 | 0.945674 | ||||||||
\(925\) | 1.68861 | 0.0555210 | ||||||||
\(926\) | −3.11585 | −0.102393 | ||||||||
\(927\) | 26.4362 | 0.868280 | ||||||||
\(928\) | 5.56146 | 0.182564 | ||||||||
\(929\) | −0.836070 | −0.0274306 | −0.0137153 | − | 0.999906i | \(-0.504366\pi\) | ||||
−0.0137153 | + | 0.999906i | \(0.504366\pi\) | |||||||
\(930\) | −8.64490 | −0.283477 | ||||||||
\(931\) | 7.38160 | 0.241922 | ||||||||
\(932\) | 7.47164 | 0.244742 | ||||||||
\(933\) | 44.7277 | 1.46432 | ||||||||
\(934\) | −36.8552 | −1.20594 | ||||||||
\(935\) | −67.1948 | −2.19751 | ||||||||
\(936\) | −11.3479 | −0.370917 | ||||||||
\(937\) | 39.1560 | 1.27917 | 0.639585 | − | 0.768721i | \(-0.279106\pi\) | ||||
0.639585 | + | 0.768721i | \(0.279106\pi\) | |||||||
\(938\) | 17.7092 | 0.578227 | ||||||||
\(939\) | −68.8357 | −2.24637 | ||||||||
\(940\) | −12.7586 | −0.416139 | ||||||||
\(941\) | 27.3600 | 0.891910 | 0.445955 | − | 0.895055i | \(-0.352864\pi\) | ||||
0.445955 | + | 0.895055i | \(0.352864\pi\) | |||||||
\(942\) | −0.419405 | −0.0136650 | ||||||||
\(943\) | −26.6375 | −0.867437 | ||||||||
\(944\) | 10.9137 | 0.355211 | ||||||||
\(945\) | −22.4016 | −0.728723 | ||||||||
\(946\) | −42.6867 | −1.38786 | ||||||||
\(947\) | −10.7260 | −0.348547 | −0.174273 | − | 0.984697i | \(-0.555758\pi\) | ||||
−0.174273 | + | 0.984697i | \(0.555758\pi\) | |||||||
\(948\) | 37.7473 | 1.22598 | ||||||||
\(949\) | −43.6424 | −1.41669 | ||||||||
\(950\) | −8.16471 | −0.264898 | ||||||||
\(951\) | −16.7978 | −0.544704 | ||||||||
\(952\) | 17.4067 | 0.564154 | ||||||||
\(953\) | 8.95474 | 0.290072 | 0.145036 | − | 0.989426i | \(-0.453670\pi\) | ||||
0.145036 | + | 0.989426i | \(0.453670\pi\) | |||||||
\(954\) | −12.0645 | −0.390604 | ||||||||
\(955\) | −53.6738 | −1.73684 | ||||||||
\(956\) | −0.953242 | −0.0308301 | ||||||||
\(957\) | −52.0886 | −1.68378 | ||||||||
\(958\) | 15.7315 | 0.508262 | ||||||||
\(959\) | −29.9175 | −0.966086 | ||||||||
\(960\) | 6.06852 | 0.195861 | ||||||||
\(961\) | −28.9707 | −0.934537 | ||||||||
\(962\) | −3.98327 | −0.128426 | ||||||||
\(963\) | 17.5946 | 0.566978 | ||||||||
\(964\) | 8.63373 | 0.278074 | ||||||||
\(965\) | 61.9153 | 1.99313 | ||||||||
\(966\) | −21.2648 | −0.684184 | ||||||||
\(967\) | 44.6121 | 1.43463 | 0.717313 | − | 0.696751i | \(-0.245372\pi\) | ||||
0.717313 | + | 0.696751i | \(0.245372\pi\) | |||||||
\(968\) | −7.28581 | −0.234175 | ||||||||
\(969\) | 37.8912 | 1.21724 | ||||||||
\(970\) | 14.2826 | 0.458586 | ||||||||
\(971\) | 34.1411 | 1.09564 | 0.547820 | − | 0.836596i | \(-0.315458\pi\) | ||||
0.547820 | + | 0.836596i | \(0.315458\pi\) | |||||||
\(972\) | 16.5440 | 0.530648 | ||||||||
\(973\) | −68.6038 | −2.19934 | ||||||||
\(974\) | −30.6542 | −0.982224 | ||||||||
\(975\) | −37.0162 | −1.18547 | ||||||||
\(976\) | 3.67051 | 0.117490 | ||||||||
\(977\) | −47.4945 | −1.51948 | −0.759742 | − | 0.650225i | \(-0.774675\pi\) | ||||
−0.759742 | + | 0.650225i | \(0.774675\pi\) | |||||||
\(978\) | −27.0489 | −0.864927 | ||||||||
\(979\) | 23.4878 | 0.750674 | ||||||||
\(980\) | −6.70483 | −0.214178 | ||||||||
\(981\) | 7.70687 | 0.246062 | ||||||||
\(982\) | −23.6703 | −0.755348 | ||||||||
\(983\) | 6.64117 | 0.211820 | 0.105910 | − | 0.994376i | \(-0.466224\pi\) | ||||
0.105910 | + | 0.994376i | \(0.466224\pi\) | |||||||
\(984\) | 18.4437 | 0.587965 | ||||||||
\(985\) | 47.5564 | 1.51527 | ||||||||
\(986\) | −31.5414 | −1.00448 | ||||||||
\(987\) | −30.9554 | −0.985322 | ||||||||
\(988\) | 19.2598 | 0.612736 | ||||||||
\(989\) | 31.5774 | 1.00410 | ||||||||
\(990\) | −21.2938 | −0.676762 | ||||||||
\(991\) | 3.10904 | 0.0987620 | 0.0493810 | − | 0.998780i | \(-0.484275\pi\) | ||||
0.0493810 | + | 0.998780i | \(0.484275\pi\) | |||||||
\(992\) | −1.42455 | −0.0452295 | ||||||||
\(993\) | 49.2306 | 1.56229 | ||||||||
\(994\) | −12.8676 | −0.408135 | ||||||||
\(995\) | −35.4990 | −1.12539 | ||||||||
\(996\) | −9.22283 | −0.292237 | ||||||||
\(997\) | −10.3976 | −0.329296 | −0.164648 | − | 0.986352i | \(-0.552649\pi\) | ||||
−0.164648 | + | 0.986352i | \(0.552649\pi\) | |||||||
\(998\) | −6.01488 | −0.190398 | ||||||||
\(999\) | 1.66190 | 0.0525802 |
(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 | 8042.2.a.c.1.13 | ✓ | 86 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.c.1.13 | ✓ | 86 | 1.1 | even | 1 | trivial |