Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + 678 x^{6} - 39390 x^{5} - 3280 x^{4} + 42456 x^{3} + 10816 x^{2} + \cdots - 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-1.34813\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.34813 | 0.602901 | 0.301450 | − | 0.953482i | \(-0.402529\pi\) | ||||
0.301450 | + | 0.953482i | \(0.402529\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.71387 | 1.02575 | 0.512873 | − | 0.858465i | \(-0.328581\pi\) | ||||
0.512873 | + | 0.858465i | \(0.328581\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.34813 | −0.426315 | ||||||||
\(11\) | −2.39135 | −0.721020 | −0.360510 | − | 0.932755i | \(-0.617397\pi\) | ||||
−0.360510 | + | 0.932755i | \(0.617397\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −2.71387 | −0.725312 | ||||||||
\(15\) | 1.34813 | 0.348085 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.50957 | −1.57880 | −0.789402 | − | 0.613877i | \(-0.789609\pi\) | ||||
−0.789402 | + | 0.613877i | \(0.789609\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −0.431762 | −0.0990531 | −0.0495265 | − | 0.998773i | \(-0.515771\pi\) | ||||
−0.0495265 | + | 0.998773i | \(0.515771\pi\) | |||||||
\(20\) | 1.34813 | 0.301450 | ||||||||
\(21\) | 2.71387 | 0.592215 | ||||||||
\(22\) | 2.39135 | 0.509838 | ||||||||
\(23\) | −4.50549 | −0.939460 | −0.469730 | − | 0.882810i | \(-0.655649\pi\) | ||||
−0.469730 | + | 0.882810i | \(0.655649\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.18255 | −0.636511 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.71387 | 0.512873 | ||||||||
\(29\) | −1.56456 | −0.290531 | −0.145266 | − | 0.989393i | \(-0.546404\pi\) | ||||
−0.145266 | + | 0.989393i | \(0.546404\pi\) | |||||||
\(30\) | −1.34813 | −0.246133 | ||||||||
\(31\) | 10.2484 | 1.84067 | 0.920336 | − | 0.391128i | \(-0.127915\pi\) | ||||
0.920336 | + | 0.391128i | \(0.127915\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.39135 | −0.416281 | ||||||||
\(34\) | 6.50957 | 1.11638 | ||||||||
\(35\) | 3.65864 | 0.618423 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.36996 | −1.04721 | −0.523607 | − | 0.851960i | \(-0.675414\pi\) | ||||
−0.523607 | + | 0.851960i | \(0.675414\pi\) | |||||||
\(38\) | 0.431762 | 0.0700411 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −1.34813 | −0.213158 | ||||||||
\(41\) | −5.06676 | −0.791295 | −0.395647 | − | 0.918403i | \(-0.629480\pi\) | ||||
−0.395647 | + | 0.918403i | \(0.629480\pi\) | |||||||
\(42\) | −2.71387 | −0.418759 | ||||||||
\(43\) | 5.51257 | 0.840660 | 0.420330 | − | 0.907371i | \(-0.361914\pi\) | ||||
0.420330 | + | 0.907371i | \(0.361914\pi\) | |||||||
\(44\) | −2.39135 | −0.360510 | ||||||||
\(45\) | 1.34813 | 0.200967 | ||||||||
\(46\) | 4.50549 | 0.664298 | ||||||||
\(47\) | −1.41946 | −0.207050 | −0.103525 | − | 0.994627i | \(-0.533012\pi\) | ||||
−0.103525 | + | 0.994627i | \(0.533012\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0.365083 | 0.0521547 | ||||||||
\(50\) | 3.18255 | 0.450081 | ||||||||
\(51\) | −6.50957 | −0.911522 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −8.06106 | −1.10727 | −0.553636 | − | 0.832759i | \(-0.686760\pi\) | ||||
−0.553636 | + | 0.832759i | \(0.686760\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.22385 | −0.434703 | ||||||||
\(56\) | −2.71387 | −0.362656 | ||||||||
\(57\) | −0.431762 | −0.0571883 | ||||||||
\(58\) | 1.56456 | 0.205436 | ||||||||
\(59\) | 6.88037 | 0.895747 | 0.447874 | − | 0.894097i | \(-0.352181\pi\) | ||||
0.447874 | + | 0.894097i | \(0.352181\pi\) | |||||||
\(60\) | 1.34813 | 0.174042 | ||||||||
\(61\) | −11.9507 | −1.53013 | −0.765064 | − | 0.643954i | \(-0.777293\pi\) | ||||
−0.765064 | + | 0.643954i | \(0.777293\pi\) | |||||||
\(62\) | −10.2484 | −1.30155 | ||||||||
\(63\) | 2.71387 | 0.341915 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.34813 | −0.167215 | ||||||||
\(66\) | 2.39135 | 0.294355 | ||||||||
\(67\) | 8.38179 | 1.02400 | 0.511999 | − | 0.858986i | \(-0.328905\pi\) | ||||
0.511999 | + | 0.858986i | \(0.328905\pi\) | |||||||
\(68\) | −6.50957 | −0.789402 | ||||||||
\(69\) | −4.50549 | −0.542397 | ||||||||
\(70\) | −3.65864 | −0.437291 | ||||||||
\(71\) | 12.9886 | 1.54146 | 0.770732 | − | 0.637160i | \(-0.219891\pi\) | ||||
0.770732 | + | 0.637160i | \(0.219891\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −1.57753 | −0.184636 | −0.0923182 | − | 0.995730i | \(-0.529428\pi\) | ||||
−0.0923182 | + | 0.995730i | \(0.529428\pi\) | |||||||
\(74\) | 6.36996 | 0.740492 | ||||||||
\(75\) | −3.18255 | −0.367490 | ||||||||
\(76\) | −0.431762 | −0.0495265 | ||||||||
\(77\) | −6.48982 | −0.739583 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 11.4119 | 1.28394 | 0.641969 | − | 0.766730i | \(-0.278118\pi\) | ||||
0.641969 | + | 0.766730i | \(0.278118\pi\) | |||||||
\(80\) | 1.34813 | 0.150725 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.06676 | 0.559530 | ||||||||
\(83\) | −5.72642 | −0.628556 | −0.314278 | − | 0.949331i | \(-0.601762\pi\) | ||||
−0.314278 | + | 0.949331i | \(0.601762\pi\) | |||||||
\(84\) | 2.71387 | 0.296107 | ||||||||
\(85\) | −8.77573 | −0.951861 | ||||||||
\(86\) | −5.51257 | −0.594436 | ||||||||
\(87\) | −1.56456 | −0.167738 | ||||||||
\(88\) | 2.39135 | 0.254919 | ||||||||
\(89\) | −11.4913 | −1.21808 | −0.609039 | − | 0.793140i | \(-0.708445\pi\) | ||||
−0.609039 | + | 0.793140i | \(0.708445\pi\) | |||||||
\(90\) | −1.34813 | −0.142105 | ||||||||
\(91\) | −2.71387 | −0.284491 | ||||||||
\(92\) | −4.50549 | −0.469730 | ||||||||
\(93\) | 10.2484 | 1.06271 | ||||||||
\(94\) | 1.41946 | 0.146407 | ||||||||
\(95\) | −0.582070 | −0.0597192 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −6.79470 | −0.689897 | −0.344949 | − | 0.938622i | \(-0.612104\pi\) | ||||
−0.344949 | + | 0.938622i | \(0.612104\pi\) | |||||||
\(98\) | −0.365083 | −0.0368790 | ||||||||
\(99\) | −2.39135 | −0.240340 | ||||||||
\(100\) | −3.18255 | −0.318255 | ||||||||
\(101\) | −14.9341 | −1.48599 | −0.742997 | − | 0.669295i | \(-0.766596\pi\) | ||||
−0.742997 | + | 0.669295i | \(0.766596\pi\) | |||||||
\(102\) | 6.50957 | 0.644544 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 3.65864 | 0.357047 | ||||||||
\(106\) | 8.06106 | 0.782959 | ||||||||
\(107\) | 8.05560 | 0.778764 | 0.389382 | − | 0.921076i | \(-0.372689\pi\) | ||||
0.389382 | + | 0.921076i | \(0.372689\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −3.57732 | −0.342645 | −0.171322 | − | 0.985215i | \(-0.554804\pi\) | ||||
−0.171322 | + | 0.985215i | \(0.554804\pi\) | |||||||
\(110\) | 3.22385 | 0.307382 | ||||||||
\(111\) | −6.36996 | −0.604610 | ||||||||
\(112\) | 2.71387 | 0.256436 | ||||||||
\(113\) | −10.1751 | −0.957192 | −0.478596 | − | 0.878035i | \(-0.658854\pi\) | ||||
−0.478596 | + | 0.878035i | \(0.658854\pi\) | |||||||
\(114\) | 0.431762 | 0.0404383 | ||||||||
\(115\) | −6.07397 | −0.566401 | ||||||||
\(116\) | −1.56456 | −0.145266 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −6.88037 | −0.633389 | ||||||||
\(119\) | −17.6661 | −1.61945 | ||||||||
\(120\) | −1.34813 | −0.123067 | ||||||||
\(121\) | −5.28143 | −0.480130 | ||||||||
\(122\) | 11.9507 | 1.08196 | ||||||||
\(123\) | −5.06676 | −0.456854 | ||||||||
\(124\) | 10.2484 | 0.920336 | ||||||||
\(125\) | −11.0311 | −0.986653 | ||||||||
\(126\) | −2.71387 | −0.241771 | ||||||||
\(127\) | −9.58182 | −0.850249 | −0.425124 | − | 0.905135i | \(-0.639770\pi\) | ||||
−0.425124 | + | 0.905135i | \(0.639770\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.51257 | 0.485355 | ||||||||
\(130\) | 1.34813 | 0.118239 | ||||||||
\(131\) | −9.94744 | −0.869112 | −0.434556 | − | 0.900645i | \(-0.643095\pi\) | ||||
−0.434556 | + | 0.900645i | \(0.643095\pi\) | |||||||
\(132\) | −2.39135 | −0.208140 | ||||||||
\(133\) | −1.17175 | −0.101603 | ||||||||
\(134\) | −8.38179 | −0.724076 | ||||||||
\(135\) | 1.34813 | 0.116028 | ||||||||
\(136\) | 6.50957 | 0.558191 | ||||||||
\(137\) | 3.56849 | 0.304877 | 0.152438 | − | 0.988313i | \(-0.451287\pi\) | ||||
0.152438 | + | 0.988313i | \(0.451287\pi\) | |||||||
\(138\) | 4.50549 | 0.383533 | ||||||||
\(139\) | −16.3086 | −1.38327 | −0.691637 | − | 0.722245i | \(-0.743110\pi\) | ||||
−0.691637 | + | 0.722245i | \(0.743110\pi\) | |||||||
\(140\) | 3.65864 | 0.309211 | ||||||||
\(141\) | −1.41946 | −0.119540 | ||||||||
\(142\) | −12.9886 | −1.08998 | ||||||||
\(143\) | 2.39135 | 0.199975 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.10922 | −0.175161 | ||||||||
\(146\) | 1.57753 | 0.130558 | ||||||||
\(147\) | 0.365083 | 0.0301115 | ||||||||
\(148\) | −6.36996 | −0.523607 | ||||||||
\(149\) | −1.55123 | −0.127082 | −0.0635409 | − | 0.997979i | \(-0.520239\pi\) | ||||
−0.0635409 | + | 0.997979i | \(0.520239\pi\) | |||||||
\(150\) | 3.18255 | 0.259854 | ||||||||
\(151\) | −14.3699 | −1.16941 | −0.584703 | − | 0.811247i | \(-0.698789\pi\) | ||||
−0.584703 | + | 0.811247i | \(0.698789\pi\) | |||||||
\(152\) | 0.431762 | 0.0350206 | ||||||||
\(153\) | −6.50957 | −0.526268 | ||||||||
\(154\) | 6.48982 | 0.522964 | ||||||||
\(155\) | 13.8162 | 1.10974 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 8.54243 | 0.681760 | 0.340880 | − | 0.940107i | \(-0.389275\pi\) | ||||
0.340880 | + | 0.940107i | \(0.389275\pi\) | |||||||
\(158\) | −11.4119 | −0.907882 | ||||||||
\(159\) | −8.06106 | −0.639283 | ||||||||
\(160\) | −1.34813 | −0.106579 | ||||||||
\(161\) | −12.2273 | −0.963647 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −0.232060 | −0.0181763 | −0.00908816 | − | 0.999959i | \(-0.502893\pi\) | ||||
−0.00908816 | + | 0.999959i | \(0.502893\pi\) | |||||||
\(164\) | −5.06676 | −0.395647 | ||||||||
\(165\) | −3.22385 | −0.250976 | ||||||||
\(166\) | 5.72642 | 0.444456 | ||||||||
\(167\) | −1.99495 | −0.154374 | −0.0771868 | − | 0.997017i | \(-0.524594\pi\) | ||||
−0.0771868 | + | 0.997017i | \(0.524594\pi\) | |||||||
\(168\) | −2.71387 | −0.209380 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 8.77573 | 0.673068 | ||||||||
\(171\) | −0.431762 | −0.0330177 | ||||||||
\(172\) | 5.51257 | 0.420330 | ||||||||
\(173\) | 24.4936 | 1.86222 | 0.931108 | − | 0.364743i | \(-0.118843\pi\) | ||||
0.931108 | + | 0.364743i | \(0.118843\pi\) | |||||||
\(174\) | 1.56456 | 0.118609 | ||||||||
\(175\) | −8.63703 | −0.652898 | ||||||||
\(176\) | −2.39135 | −0.180255 | ||||||||
\(177\) | 6.88037 | 0.517160 | ||||||||
\(178\) | 11.4913 | 0.861312 | ||||||||
\(179\) | −24.9563 | −1.86532 | −0.932660 | − | 0.360758i | \(-0.882518\pi\) | ||||
−0.932660 | + | 0.360758i | \(0.882518\pi\) | |||||||
\(180\) | 1.34813 | 0.100483 | ||||||||
\(181\) | 19.7726 | 1.46968 | 0.734842 | − | 0.678238i | \(-0.237256\pi\) | ||||
0.734842 | + | 0.678238i | \(0.237256\pi\) | |||||||
\(182\) | 2.71387 | 0.201165 | ||||||||
\(183\) | −11.9507 | −0.883420 | ||||||||
\(184\) | 4.50549 | 0.332149 | ||||||||
\(185\) | −8.58751 | −0.631366 | ||||||||
\(186\) | −10.2484 | −0.751451 | ||||||||
\(187\) | 15.5667 | 1.13835 | ||||||||
\(188\) | −1.41946 | −0.103525 | ||||||||
\(189\) | 2.71387 | 0.197405 | ||||||||
\(190\) | 0.582070 | 0.0422278 | ||||||||
\(191\) | 4.73569 | 0.342662 | 0.171331 | − | 0.985214i | \(-0.445193\pi\) | ||||
0.171331 | + | 0.985214i | \(0.445193\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −6.52330 | −0.469558 | −0.234779 | − | 0.972049i | \(-0.575437\pi\) | ||||
−0.234779 | + | 0.972049i | \(0.575437\pi\) | |||||||
\(194\) | 6.79470 | 0.487831 | ||||||||
\(195\) | −1.34813 | −0.0965414 | ||||||||
\(196\) | 0.365083 | 0.0260774 | ||||||||
\(197\) | −8.88078 | −0.632729 | −0.316365 | − | 0.948638i | \(-0.602462\pi\) | ||||
−0.316365 | + | 0.948638i | \(0.602462\pi\) | |||||||
\(198\) | 2.39135 | 0.169946 | ||||||||
\(199\) | −23.6494 | −1.67646 | −0.838231 | − | 0.545315i | \(-0.816410\pi\) | ||||
−0.838231 | + | 0.545315i | \(0.816410\pi\) | |||||||
\(200\) | 3.18255 | 0.225041 | ||||||||
\(201\) | 8.38179 | 0.591206 | ||||||||
\(202\) | 14.9341 | 1.05076 | ||||||||
\(203\) | −4.24600 | −0.298011 | ||||||||
\(204\) | −6.50957 | −0.455761 | ||||||||
\(205\) | −6.83063 | −0.477072 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −4.50549 | −0.313153 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 1.03250 | 0.0714192 | ||||||||
\(210\) | −3.65864 | −0.252470 | ||||||||
\(211\) | −11.2030 | −0.771249 | −0.385625 | − | 0.922656i | \(-0.626014\pi\) | ||||
−0.385625 | + | 0.922656i | \(0.626014\pi\) | |||||||
\(212\) | −8.06106 | −0.553636 | ||||||||
\(213\) | 12.9886 | 0.889964 | ||||||||
\(214\) | −8.05560 | −0.550670 | ||||||||
\(215\) | 7.43165 | 0.506834 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 27.8129 | 1.88806 | ||||||||
\(218\) | 3.57732 | 0.242287 | ||||||||
\(219\) | −1.57753 | −0.106600 | ||||||||
\(220\) | −3.22385 | −0.217352 | ||||||||
\(221\) | 6.50957 | 0.437881 | ||||||||
\(222\) | 6.36996 | 0.427524 | ||||||||
\(223\) | 27.5336 | 1.84379 | 0.921893 | − | 0.387445i | \(-0.126642\pi\) | ||||
0.921893 | + | 0.387445i | \(0.126642\pi\) | |||||||
\(224\) | −2.71387 | −0.181328 | ||||||||
\(225\) | −3.18255 | −0.212170 | ||||||||
\(226\) | 10.1751 | 0.676837 | ||||||||
\(227\) | 23.3657 | 1.55083 | 0.775416 | − | 0.631450i | \(-0.217540\pi\) | ||||
0.775416 | + | 0.631450i | \(0.217540\pi\) | |||||||
\(228\) | −0.431762 | −0.0285942 | ||||||||
\(229\) | −13.7682 | −0.909831 | −0.454916 | − | 0.890535i | \(-0.650331\pi\) | ||||
−0.454916 | + | 0.890535i | \(0.650331\pi\) | |||||||
\(230\) | 6.07397 | 0.400506 | ||||||||
\(231\) | −6.48982 | −0.426999 | ||||||||
\(232\) | 1.56456 | 0.102718 | ||||||||
\(233\) | 22.0201 | 1.44259 | 0.721294 | − | 0.692629i | \(-0.243548\pi\) | ||||
0.721294 | + | 0.692629i | \(0.243548\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −1.91362 | −0.124831 | ||||||||
\(236\) | 6.88037 | 0.447874 | ||||||||
\(237\) | 11.4119 | 0.741282 | ||||||||
\(238\) | 17.6661 | 1.14512 | ||||||||
\(239\) | −23.6471 | −1.52960 | −0.764800 | − | 0.644267i | \(-0.777162\pi\) | ||||
−0.764800 | + | 0.644267i | \(0.777162\pi\) | |||||||
\(240\) | 1.34813 | 0.0870212 | ||||||||
\(241\) | −13.2240 | −0.851830 | −0.425915 | − | 0.904763i | \(-0.640048\pi\) | ||||
−0.425915 | + | 0.904763i | \(0.640048\pi\) | |||||||
\(242\) | 5.28143 | 0.339503 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.9507 | −0.765064 | ||||||||
\(245\) | 0.492178 | 0.0314441 | ||||||||
\(246\) | 5.06676 | 0.323045 | ||||||||
\(247\) | 0.431762 | 0.0274724 | ||||||||
\(248\) | −10.2484 | −0.650776 | ||||||||
\(249\) | −5.72642 | −0.362897 | ||||||||
\(250\) | 11.0311 | 0.697669 | ||||||||
\(251\) | 4.85647 | 0.306538 | 0.153269 | − | 0.988185i | \(-0.451020\pi\) | ||||
0.153269 | + | 0.988185i | \(0.451020\pi\) | |||||||
\(252\) | 2.71387 | 0.170958 | ||||||||
\(253\) | 10.7742 | 0.677369 | ||||||||
\(254\) | 9.58182 | 0.601217 | ||||||||
\(255\) | −8.77573 | −0.549557 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.7803 | −0.734834 | −0.367417 | − | 0.930056i | \(-0.619758\pi\) | ||||
−0.367417 | + | 0.930056i | \(0.619758\pi\) | |||||||
\(258\) | −5.51257 | −0.343198 | ||||||||
\(259\) | −17.2872 | −1.07418 | ||||||||
\(260\) | −1.34813 | −0.0836073 | ||||||||
\(261\) | −1.56456 | −0.0968437 | ||||||||
\(262\) | 9.94744 | 0.614555 | ||||||||
\(263\) | 6.54794 | 0.403763 | 0.201882 | − | 0.979410i | \(-0.435294\pi\) | ||||
0.201882 | + | 0.979410i | \(0.435294\pi\) | |||||||
\(264\) | 2.39135 | 0.147178 | ||||||||
\(265\) | −10.8673 | −0.667575 | ||||||||
\(266\) | 1.17175 | 0.0718444 | ||||||||
\(267\) | −11.4913 | −0.703258 | ||||||||
\(268\) | 8.38179 | 0.511999 | ||||||||
\(269\) | 4.08408 | 0.249011 | 0.124505 | − | 0.992219i | \(-0.460266\pi\) | ||||
0.124505 | + | 0.992219i | \(0.460266\pi\) | |||||||
\(270\) | −1.34813 | −0.0820444 | ||||||||
\(271\) | −9.81272 | −0.596080 | −0.298040 | − | 0.954553i | \(-0.596333\pi\) | ||||
−0.298040 | + | 0.954553i | \(0.596333\pi\) | |||||||
\(272\) | −6.50957 | −0.394701 | ||||||||
\(273\) | −2.71387 | −0.164251 | ||||||||
\(274\) | −3.56849 | −0.215580 | ||||||||
\(275\) | 7.61061 | 0.458937 | ||||||||
\(276\) | −4.50549 | −0.271199 | ||||||||
\(277\) | −10.6253 | −0.638413 | −0.319206 | − | 0.947685i | \(-0.603416\pi\) | ||||
−0.319206 | + | 0.947685i | \(0.603416\pi\) | |||||||
\(278\) | 16.3086 | 0.978122 | ||||||||
\(279\) | 10.2484 | 0.613558 | ||||||||
\(280\) | −3.65864 | −0.218645 | ||||||||
\(281\) | −11.0617 | −0.659884 | −0.329942 | − | 0.944001i | \(-0.607029\pi\) | ||||
−0.329942 | + | 0.944001i | \(0.607029\pi\) | |||||||
\(282\) | 1.41946 | 0.0845278 | ||||||||
\(283\) | 6.36457 | 0.378334 | 0.189167 | − | 0.981945i | \(-0.439421\pi\) | ||||
0.189167 | + | 0.981945i | \(0.439421\pi\) | |||||||
\(284\) | 12.9886 | 0.770732 | ||||||||
\(285\) | −0.582070 | −0.0344789 | ||||||||
\(286\) | −2.39135 | −0.141404 | ||||||||
\(287\) | −13.7505 | −0.811667 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 25.3745 | 1.49262 | ||||||||
\(290\) | 2.10922 | 0.123858 | ||||||||
\(291\) | −6.79470 | −0.398312 | ||||||||
\(292\) | −1.57753 | −0.0923182 | ||||||||
\(293\) | 7.74495 | 0.452465 | 0.226232 | − | 0.974073i | \(-0.427359\pi\) | ||||
0.226232 | + | 0.974073i | \(0.427359\pi\) | |||||||
\(294\) | −0.365083 | −0.0212921 | ||||||||
\(295\) | 9.27560 | 0.540047 | ||||||||
\(296\) | 6.36996 | 0.370246 | ||||||||
\(297\) | −2.39135 | −0.138760 | ||||||||
\(298\) | 1.55123 | 0.0898605 | ||||||||
\(299\) | 4.50549 | 0.260559 | ||||||||
\(300\) | −3.18255 | −0.183745 | ||||||||
\(301\) | 14.9604 | 0.862303 | ||||||||
\(302\) | 14.3699 | 0.826895 | ||||||||
\(303\) | −14.9341 | −0.857939 | ||||||||
\(304\) | −0.431762 | −0.0247633 | ||||||||
\(305\) | −16.1110 | −0.922516 | ||||||||
\(306\) | 6.50957 | 0.372127 | ||||||||
\(307\) | −12.8933 | −0.735857 | −0.367928 | − | 0.929854i | \(-0.619933\pi\) | ||||
−0.367928 | + | 0.929854i | \(0.619933\pi\) | |||||||
\(308\) | −6.48982 | −0.369792 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −13.8162 | −0.784707 | ||||||||
\(311\) | 22.5094 | 1.27639 | 0.638197 | − | 0.769873i | \(-0.279681\pi\) | ||||
0.638197 | + | 0.769873i | \(0.279681\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −14.2391 | −0.804843 | −0.402421 | − | 0.915455i | \(-0.631831\pi\) | ||||
−0.402421 | + | 0.915455i | \(0.631831\pi\) | |||||||
\(314\) | −8.54243 | −0.482077 | ||||||||
\(315\) | 3.65864 | 0.206141 | ||||||||
\(316\) | 11.4119 | 0.641969 | ||||||||
\(317\) | 7.36812 | 0.413835 | 0.206917 | − | 0.978358i | \(-0.433657\pi\) | ||||
0.206917 | + | 0.978358i | \(0.433657\pi\) | |||||||
\(318\) | 8.06106 | 0.452042 | ||||||||
\(319\) | 3.74141 | 0.209479 | ||||||||
\(320\) | 1.34813 | 0.0753626 | ||||||||
\(321\) | 8.05560 | 0.449620 | ||||||||
\(322\) | 12.2273 | 0.681401 | ||||||||
\(323\) | 2.81059 | 0.156385 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 3.18255 | 0.176536 | ||||||||
\(326\) | 0.232060 | 0.0128526 | ||||||||
\(327\) | −3.57732 | −0.197826 | ||||||||
\(328\) | 5.06676 | 0.279765 | ||||||||
\(329\) | −3.85224 | −0.212381 | ||||||||
\(330\) | 3.22385 | 0.177467 | ||||||||
\(331\) | 18.1845 | 0.999509 | 0.499755 | − | 0.866167i | \(-0.333424\pi\) | ||||
0.499755 | + | 0.866167i | \(0.333424\pi\) | |||||||
\(332\) | −5.72642 | −0.314278 | ||||||||
\(333\) | −6.36996 | −0.349072 | ||||||||
\(334\) | 1.99495 | 0.109159 | ||||||||
\(335\) | 11.2997 | 0.617369 | ||||||||
\(336\) | 2.71387 | 0.148054 | ||||||||
\(337\) | 30.5645 | 1.66496 | 0.832478 | − | 0.554059i | \(-0.186922\pi\) | ||||
0.832478 | + | 0.554059i | \(0.186922\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −10.1751 | −0.552635 | ||||||||
\(340\) | −8.77573 | −0.475931 | ||||||||
\(341\) | −24.5076 | −1.32716 | ||||||||
\(342\) | 0.431762 | 0.0233470 | ||||||||
\(343\) | −18.0063 | −0.972248 | ||||||||
\(344\) | −5.51257 | −0.297218 | ||||||||
\(345\) | −6.07397 | −0.327012 | ||||||||
\(346\) | −24.4936 | −1.31679 | ||||||||
\(347\) | −25.2946 | −1.35788 | −0.678941 | − | 0.734192i | \(-0.737561\pi\) | ||||
−0.678941 | + | 0.734192i | \(0.737561\pi\) | |||||||
\(348\) | −1.56456 | −0.0838691 | ||||||||
\(349\) | 14.5811 | 0.780510 | 0.390255 | − | 0.920707i | \(-0.372387\pi\) | ||||
0.390255 | + | 0.920707i | \(0.372387\pi\) | |||||||
\(350\) | 8.63703 | 0.461669 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 2.39135 | 0.127460 | ||||||||
\(353\) | −29.6881 | −1.58014 | −0.790069 | − | 0.613018i | \(-0.789955\pi\) | ||||
−0.790069 | + | 0.613018i | \(0.789955\pi\) | |||||||
\(354\) | −6.88037 | −0.365687 | ||||||||
\(355\) | 17.5103 | 0.929349 | ||||||||
\(356\) | −11.4913 | −0.609039 | ||||||||
\(357\) | −17.6661 | −0.934990 | ||||||||
\(358\) | 24.9563 | 1.31898 | ||||||||
\(359\) | −15.1234 | −0.798185 | −0.399092 | − | 0.916911i | \(-0.630675\pi\) | ||||
−0.399092 | + | 0.916911i | \(0.630675\pi\) | |||||||
\(360\) | −1.34813 | −0.0710525 | ||||||||
\(361\) | −18.8136 | −0.990188 | ||||||||
\(362\) | −19.7726 | −1.03922 | ||||||||
\(363\) | −5.28143 | −0.277203 | ||||||||
\(364\) | −2.71387 | −0.142245 | ||||||||
\(365\) | −2.12671 | −0.111317 | ||||||||
\(366\) | 11.9507 | 0.624673 | ||||||||
\(367\) | −10.8564 | −0.566701 | −0.283350 | − | 0.959016i | \(-0.591446\pi\) | ||||
−0.283350 | + | 0.959016i | \(0.591446\pi\) | |||||||
\(368\) | −4.50549 | −0.234865 | ||||||||
\(369\) | −5.06676 | −0.263765 | ||||||||
\(370\) | 8.58751 | 0.446443 | ||||||||
\(371\) | −21.8766 | −1.13578 | ||||||||
\(372\) | 10.2484 | 0.531356 | ||||||||
\(373\) | 7.66103 | 0.396673 | 0.198337 | − | 0.980134i | \(-0.436446\pi\) | ||||
0.198337 | + | 0.980134i | \(0.436446\pi\) | |||||||
\(374\) | −15.5667 | −0.804934 | ||||||||
\(375\) | −11.0311 | −0.569645 | ||||||||
\(376\) | 1.41946 | 0.0732033 | ||||||||
\(377\) | 1.56456 | 0.0805788 | ||||||||
\(378\) | −2.71387 | −0.139586 | ||||||||
\(379\) | 10.0157 | 0.514471 | 0.257236 | − | 0.966349i | \(-0.417188\pi\) | ||||
0.257236 | + | 0.966349i | \(0.417188\pi\) | |||||||
\(380\) | −0.582070 | −0.0298596 | ||||||||
\(381\) | −9.58182 | −0.490891 | ||||||||
\(382\) | −4.73569 | −0.242299 | ||||||||
\(383\) | 17.7480 | 0.906883 | 0.453441 | − | 0.891286i | \(-0.350196\pi\) | ||||
0.453441 | + | 0.891286i | \(0.350196\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −8.74909 | −0.445895 | ||||||||
\(386\) | 6.52330 | 0.332027 | ||||||||
\(387\) | 5.51257 | 0.280220 | ||||||||
\(388\) | −6.79470 | −0.344949 | ||||||||
\(389\) | 17.6122 | 0.892973 | 0.446486 | − | 0.894790i | \(-0.352675\pi\) | ||||
0.446486 | + | 0.894790i | \(0.352675\pi\) | |||||||
\(390\) | 1.34813 | 0.0682651 | ||||||||
\(391\) | 29.3288 | 1.48322 | ||||||||
\(392\) | −0.365083 | −0.0184395 | ||||||||
\(393\) | −9.94744 | −0.501782 | ||||||||
\(394\) | 8.88078 | 0.447407 | ||||||||
\(395\) | 15.3847 | 0.774087 | ||||||||
\(396\) | −2.39135 | −0.120170 | ||||||||
\(397\) | 15.9439 | 0.800199 | 0.400100 | − | 0.916472i | \(-0.368975\pi\) | ||||
0.400100 | + | 0.916472i | \(0.368975\pi\) | |||||||
\(398\) | 23.6494 | 1.18544 | ||||||||
\(399\) | −1.17175 | −0.0586607 | ||||||||
\(400\) | −3.18255 | −0.159128 | ||||||||
\(401\) | −13.5652 | −0.677414 | −0.338707 | − | 0.940892i | \(-0.609990\pi\) | ||||
−0.338707 | + | 0.940892i | \(0.609990\pi\) | |||||||
\(402\) | −8.38179 | −0.418046 | ||||||||
\(403\) | −10.2484 | −0.510511 | ||||||||
\(404\) | −14.9341 | −0.742997 | ||||||||
\(405\) | 1.34813 | 0.0669890 | ||||||||
\(406\) | 4.24600 | 0.210726 | ||||||||
\(407\) | 15.2328 | 0.755062 | ||||||||
\(408\) | 6.50957 | 0.322272 | ||||||||
\(409\) | 23.6532 | 1.16958 | 0.584788 | − | 0.811186i | \(-0.301178\pi\) | ||||
0.584788 | + | 0.811186i | \(0.301178\pi\) | |||||||
\(410\) | 6.83063 | 0.337341 | ||||||||
\(411\) | 3.56849 | 0.176021 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | 18.6724 | 0.918809 | ||||||||
\(414\) | 4.50549 | 0.221433 | ||||||||
\(415\) | −7.71994 | −0.378957 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −16.3086 | −0.798634 | ||||||||
\(418\) | −1.03250 | −0.0505010 | ||||||||
\(419\) | 30.1554 | 1.47319 | 0.736594 | − | 0.676336i | \(-0.236433\pi\) | ||||
0.736594 | + | 0.676336i | \(0.236433\pi\) | |||||||
\(420\) | 3.65864 | 0.178523 | ||||||||
\(421\) | 13.2847 | 0.647456 | 0.323728 | − | 0.946150i | \(-0.395064\pi\) | ||||
0.323728 | + | 0.946150i | \(0.395064\pi\) | |||||||
\(422\) | 11.2030 | 0.545356 | ||||||||
\(423\) | −1.41946 | −0.0690167 | ||||||||
\(424\) | 8.06106 | 0.391479 | ||||||||
\(425\) | 20.7171 | 1.00493 | ||||||||
\(426\) | −12.9886 | −0.629300 | ||||||||
\(427\) | −32.4326 | −1.56952 | ||||||||
\(428\) | 8.05560 | 0.389382 | ||||||||
\(429\) | 2.39135 | 0.115456 | ||||||||
\(430\) | −7.43165 | −0.358386 | ||||||||
\(431\) | −8.15311 | −0.392721 | −0.196361 | − | 0.980532i | \(-0.562912\pi\) | ||||
−0.196361 | + | 0.980532i | \(0.562912\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −1.67772 | −0.0806258 | −0.0403129 | − | 0.999187i | \(-0.512835\pi\) | ||||
−0.0403129 | + | 0.999187i | \(0.512835\pi\) | |||||||
\(434\) | −27.8129 | −1.33506 | ||||||||
\(435\) | −2.10922 | −0.101129 | ||||||||
\(436\) | −3.57732 | −0.171322 | ||||||||
\(437\) | 1.94530 | 0.0930564 | ||||||||
\(438\) | 1.57753 | 0.0753775 | ||||||||
\(439\) | 38.8832 | 1.85579 | 0.927897 | − | 0.372836i | \(-0.121615\pi\) | ||||
0.927897 | + | 0.372836i | \(0.121615\pi\) | |||||||
\(440\) | 3.22385 | 0.153691 | ||||||||
\(441\) | 0.365083 | 0.0173849 | ||||||||
\(442\) | −6.50957 | −0.309629 | ||||||||
\(443\) | −18.8022 | −0.893319 | −0.446659 | − | 0.894704i | \(-0.647386\pi\) | ||||
−0.446659 | + | 0.894704i | \(0.647386\pi\) | |||||||
\(444\) | −6.36996 | −0.302305 | ||||||||
\(445\) | −15.4918 | −0.734380 | ||||||||
\(446\) | −27.5336 | −1.30375 | ||||||||
\(447\) | −1.55123 | −0.0733708 | ||||||||
\(448\) | 2.71387 | 0.128218 | ||||||||
\(449\) | −4.65776 | −0.219813 | −0.109907 | − | 0.993942i | \(-0.535055\pi\) | ||||
−0.109907 | + | 0.993942i | \(0.535055\pi\) | |||||||
\(450\) | 3.18255 | 0.150027 | ||||||||
\(451\) | 12.1164 | 0.570539 | ||||||||
\(452\) | −10.1751 | −0.478596 | ||||||||
\(453\) | −14.3699 | −0.675157 | ||||||||
\(454\) | −23.3657 | −1.09660 | ||||||||
\(455\) | −3.65864 | −0.171520 | ||||||||
\(456\) | 0.431762 | 0.0202191 | ||||||||
\(457\) | 16.6855 | 0.780514 | 0.390257 | − | 0.920706i | \(-0.372386\pi\) | ||||
0.390257 | + | 0.920706i | \(0.372386\pi\) | |||||||
\(458\) | 13.7682 | 0.643348 | ||||||||
\(459\) | −6.50957 | −0.303841 | ||||||||
\(460\) | −6.07397 | −0.283200 | ||||||||
\(461\) | −10.4652 | −0.487413 | −0.243706 | − | 0.969849i | \(-0.578363\pi\) | ||||
−0.243706 | + | 0.969849i | \(0.578363\pi\) | |||||||
\(462\) | 6.48982 | 0.301934 | ||||||||
\(463\) | 31.2686 | 1.45318 | 0.726588 | − | 0.687073i | \(-0.241105\pi\) | ||||
0.726588 | + | 0.687073i | \(0.241105\pi\) | |||||||
\(464\) | −1.56456 | −0.0726328 | ||||||||
\(465\) | 13.8162 | 0.640710 | ||||||||
\(466\) | −22.0201 | −1.02006 | ||||||||
\(467\) | −15.9687 | −0.738942 | −0.369471 | − | 0.929242i | \(-0.620461\pi\) | ||||
−0.369471 | + | 0.929242i | \(0.620461\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 22.7471 | 1.05036 | ||||||||
\(470\) | 1.91362 | 0.0882686 | ||||||||
\(471\) | 8.54243 | 0.393614 | ||||||||
\(472\) | −6.88037 | −0.316694 | ||||||||
\(473\) | −13.1825 | −0.606132 | ||||||||
\(474\) | −11.4119 | −0.524166 | ||||||||
\(475\) | 1.37411 | 0.0630484 | ||||||||
\(476\) | −17.6661 | −0.809725 | ||||||||
\(477\) | −8.06106 | −0.369090 | ||||||||
\(478\) | 23.6471 | 1.08159 | ||||||||
\(479\) | 18.5527 | 0.847693 | 0.423846 | − | 0.905734i | \(-0.360680\pi\) | ||||
0.423846 | + | 0.905734i | \(0.360680\pi\) | |||||||
\(480\) | −1.34813 | −0.0615333 | ||||||||
\(481\) | 6.36996 | 0.290445 | ||||||||
\(482\) | 13.2240 | 0.602335 | ||||||||
\(483\) | −12.2273 | −0.556362 | ||||||||
\(484\) | −5.28143 | −0.240065 | ||||||||
\(485\) | −9.16011 | −0.415939 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −35.5161 | −1.60939 | −0.804695 | − | 0.593689i | \(-0.797671\pi\) | ||||
−0.804695 | + | 0.593689i | \(0.797671\pi\) | |||||||
\(488\) | 11.9507 | 0.540982 | ||||||||
\(489\) | −0.232060 | −0.0104941 | ||||||||
\(490\) | −0.492178 | −0.0222343 | ||||||||
\(491\) | 5.28868 | 0.238675 | 0.119337 | − | 0.992854i | \(-0.461923\pi\) | ||||
0.119337 | + | 0.992854i | \(0.461923\pi\) | |||||||
\(492\) | −5.06676 | −0.228427 | ||||||||
\(493\) | 10.1846 | 0.458691 | ||||||||
\(494\) | −0.431762 | −0.0194259 | ||||||||
\(495\) | −3.22385 | −0.144901 | ||||||||
\(496\) | 10.2484 | 0.460168 | ||||||||
\(497\) | 35.2494 | 1.58115 | ||||||||
\(498\) | 5.72642 | 0.256607 | ||||||||
\(499\) | −10.8970 | −0.487815 | −0.243908 | − | 0.969798i | \(-0.578429\pi\) | ||||
−0.243908 | + | 0.969798i | \(0.578429\pi\) | |||||||
\(500\) | −11.0311 | −0.493327 | ||||||||
\(501\) | −1.99495 | −0.0891276 | ||||||||
\(502\) | −4.85647 | −0.216755 | ||||||||
\(503\) | 5.95779 | 0.265645 | 0.132822 | − | 0.991140i | \(-0.457596\pi\) | ||||
0.132822 | + | 0.991140i | \(0.457596\pi\) | |||||||
\(504\) | −2.71387 | −0.120885 | ||||||||
\(505\) | −20.1330 | −0.895907 | ||||||||
\(506\) | −10.7742 | −0.478972 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −9.58182 | −0.425124 | ||||||||
\(509\) | −6.66761 | −0.295537 | −0.147768 | − | 0.989022i | \(-0.547209\pi\) | ||||
−0.147768 | + | 0.989022i | \(0.547209\pi\) | |||||||
\(510\) | 8.77573 | 0.388596 | ||||||||
\(511\) | −4.28122 | −0.189390 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.431762 | −0.0190628 | ||||||||
\(514\) | 11.7803 | 0.519606 | ||||||||
\(515\) | 1.34813 | 0.0594056 | ||||||||
\(516\) | 5.51257 | 0.242678 | ||||||||
\(517\) | 3.39444 | 0.149287 | ||||||||
\(518\) | 17.2872 | 0.759557 | ||||||||
\(519\) | 24.4936 | 1.07515 | ||||||||
\(520\) | 1.34813 | 0.0591193 | ||||||||
\(521\) | 9.06386 | 0.397095 | 0.198547 | − | 0.980091i | \(-0.436378\pi\) | ||||
0.198547 | + | 0.980091i | \(0.436378\pi\) | |||||||
\(522\) | 1.56456 | 0.0684788 | ||||||||
\(523\) | −21.9878 | −0.961460 | −0.480730 | − | 0.876869i | \(-0.659628\pi\) | ||||
−0.480730 | + | 0.876869i | \(0.659628\pi\) | |||||||
\(524\) | −9.94744 | −0.434556 | ||||||||
\(525\) | −8.63703 | −0.376951 | ||||||||
\(526\) | −6.54794 | −0.285504 | ||||||||
\(527\) | −66.7129 | −2.90606 | ||||||||
\(528\) | −2.39135 | −0.104070 | ||||||||
\(529\) | −2.70056 | −0.117416 | ||||||||
\(530\) | 10.8673 | 0.472046 | ||||||||
\(531\) | 6.88037 | 0.298582 | ||||||||
\(532\) | −1.17175 | −0.0508017 | ||||||||
\(533\) | 5.06676 | 0.219466 | ||||||||
\(534\) | 11.4913 | 0.497278 | ||||||||
\(535\) | 10.8600 | 0.469518 | ||||||||
\(536\) | −8.38179 | −0.362038 | ||||||||
\(537\) | −24.9563 | −1.07694 | ||||||||
\(538\) | −4.08408 | −0.176077 | ||||||||
\(539\) | −0.873042 | −0.0376046 | ||||||||
\(540\) | 1.34813 | 0.0580141 | ||||||||
\(541\) | −7.02793 | −0.302154 | −0.151077 | − | 0.988522i | \(-0.548274\pi\) | ||||
−0.151077 | + | 0.988522i | \(0.548274\pi\) | |||||||
\(542\) | 9.81272 | 0.421492 | ||||||||
\(543\) | 19.7726 | 0.848523 | ||||||||
\(544\) | 6.50957 | 0.279096 | ||||||||
\(545\) | −4.82268 | −0.206581 | ||||||||
\(546\) | 2.71387 | 0.116143 | ||||||||
\(547\) | −36.3334 | −1.55350 | −0.776752 | − | 0.629806i | \(-0.783134\pi\) | ||||
−0.776752 | + | 0.629806i | \(0.783134\pi\) | |||||||
\(548\) | 3.56849 | 0.152438 | ||||||||
\(549\) | −11.9507 | −0.510043 | ||||||||
\(550\) | −7.61061 | −0.324517 | ||||||||
\(551\) | 0.675517 | 0.0287780 | ||||||||
\(552\) | 4.50549 | 0.191766 | ||||||||
\(553\) | 30.9704 | 1.31699 | ||||||||
\(554\) | 10.6253 | 0.451426 | ||||||||
\(555\) | −8.58751 | −0.364519 | ||||||||
\(556\) | −16.3086 | −0.691637 | ||||||||
\(557\) | −19.8696 | −0.841902 | −0.420951 | − | 0.907083i | \(-0.638304\pi\) | ||||
−0.420951 | + | 0.907083i | \(0.638304\pi\) | |||||||
\(558\) | −10.2484 | −0.433851 | ||||||||
\(559\) | −5.51257 | −0.233157 | ||||||||
\(560\) | 3.65864 | 0.154606 | ||||||||
\(561\) | 15.5667 | 0.657226 | ||||||||
\(562\) | 11.0617 | 0.466608 | ||||||||
\(563\) | 13.2306 | 0.557602 | 0.278801 | − | 0.960349i | \(-0.410063\pi\) | ||||
0.278801 | + | 0.960349i | \(0.410063\pi\) | |||||||
\(564\) | −1.41946 | −0.0597702 | ||||||||
\(565\) | −13.7173 | −0.577092 | ||||||||
\(566\) | −6.36457 | −0.267523 | ||||||||
\(567\) | 2.71387 | 0.113972 | ||||||||
\(568\) | −12.9886 | −0.544990 | ||||||||
\(569\) | −7.31748 | −0.306765 | −0.153382 | − | 0.988167i | \(-0.549017\pi\) | ||||
−0.153382 | + | 0.988167i | \(0.549017\pi\) | |||||||
\(570\) | 0.582070 | 0.0243802 | ||||||||
\(571\) | 24.0308 | 1.00566 | 0.502828 | − | 0.864386i | \(-0.332293\pi\) | ||||
0.502828 | + | 0.864386i | \(0.332293\pi\) | |||||||
\(572\) | 2.39135 | 0.0999875 | ||||||||
\(573\) | 4.73569 | 0.197836 | ||||||||
\(574\) | 13.7505 | 0.573935 | ||||||||
\(575\) | 14.3390 | 0.597976 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 23.1047 | 0.961859 | 0.480930 | − | 0.876759i | \(-0.340299\pi\) | ||||
0.480930 | + | 0.876759i | \(0.340299\pi\) | |||||||
\(578\) | −25.3745 | −1.05544 | ||||||||
\(579\) | −6.52330 | −0.271099 | ||||||||
\(580\) | −2.10922 | −0.0875807 | ||||||||
\(581\) | −15.5408 | −0.644739 | ||||||||
\(582\) | 6.79470 | 0.281649 | ||||||||
\(583\) | 19.2768 | 0.798364 | ||||||||
\(584\) | 1.57753 | 0.0652788 | ||||||||
\(585\) | −1.34813 | −0.0557382 | ||||||||
\(586\) | −7.74495 | −0.319941 | ||||||||
\(587\) | 3.64806 | 0.150571 | 0.0752857 | − | 0.997162i | \(-0.476013\pi\) | ||||
0.0752857 | + | 0.997162i | \(0.476013\pi\) | |||||||
\(588\) | 0.365083 | 0.0150558 | ||||||||
\(589\) | −4.42489 | −0.182324 | ||||||||
\(590\) | −9.27560 | −0.381871 | ||||||||
\(591\) | −8.88078 | −0.365306 | ||||||||
\(592\) | −6.36996 | −0.261804 | ||||||||
\(593\) | −43.6328 | −1.79179 | −0.895893 | − | 0.444270i | \(-0.853463\pi\) | ||||
−0.895893 | + | 0.444270i | \(0.853463\pi\) | |||||||
\(594\) | 2.39135 | 0.0981184 | ||||||||
\(595\) | −23.8162 | −0.976368 | ||||||||
\(596\) | −1.55123 | −0.0635409 | ||||||||
\(597\) | −23.6494 | −0.967906 | ||||||||
\(598\) | −4.50549 | −0.184243 | ||||||||
\(599\) | 26.7488 | 1.09293 | 0.546463 | − | 0.837483i | \(-0.315974\pi\) | ||||
0.546463 | + | 0.837483i | \(0.315974\pi\) | |||||||
\(600\) | 3.18255 | 0.129927 | ||||||||
\(601\) | 17.5744 | 0.716873 | 0.358436 | − | 0.933554i | \(-0.383310\pi\) | ||||
0.358436 | + | 0.933554i | \(0.383310\pi\) | |||||||
\(602\) | −14.9604 | −0.609740 | ||||||||
\(603\) | 8.38179 | 0.341333 | ||||||||
\(604\) | −14.3699 | −0.584703 | ||||||||
\(605\) | −7.12004 | −0.289471 | ||||||||
\(606\) | 14.9341 | 0.606655 | ||||||||
\(607\) | 45.0663 | 1.82919 | 0.914593 | − | 0.404375i | \(-0.132511\pi\) | ||||
0.914593 | + | 0.404375i | \(0.132511\pi\) | |||||||
\(608\) | 0.431762 | 0.0175103 | ||||||||
\(609\) | −4.24600 | −0.172057 | ||||||||
\(610\) | 16.1110 | 0.652317 | ||||||||
\(611\) | 1.41946 | 0.0574254 | ||||||||
\(612\) | −6.50957 | −0.263134 | ||||||||
\(613\) | −10.3838 | −0.419399 | −0.209700 | − | 0.977766i | \(-0.567249\pi\) | ||||
−0.209700 | + | 0.977766i | \(0.567249\pi\) | |||||||
\(614\) | 12.8933 | 0.520329 | ||||||||
\(615\) | −6.83063 | −0.275438 | ||||||||
\(616\) | 6.48982 | 0.261482 | ||||||||
\(617\) | 30.9502 | 1.24601 | 0.623004 | − | 0.782218i | \(-0.285912\pi\) | ||||
0.623004 | + | 0.782218i | \(0.285912\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 12.0955 | 0.486159 | 0.243080 | − | 0.970006i | \(-0.421842\pi\) | ||||
0.243080 | + | 0.970006i | \(0.421842\pi\) | |||||||
\(620\) | 13.8162 | 0.554871 | ||||||||
\(621\) | −4.50549 | −0.180799 | ||||||||
\(622\) | −22.5094 | −0.902547 | ||||||||
\(623\) | −31.1860 | −1.24944 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 1.04142 | 0.0416569 | ||||||||
\(626\) | 14.2391 | 0.569110 | ||||||||
\(627\) | 1.03250 | 0.0412339 | ||||||||
\(628\) | 8.54243 | 0.340880 | ||||||||
\(629\) | 41.4657 | 1.65335 | ||||||||
\(630\) | −3.65864 | −0.145764 | ||||||||
\(631\) | −42.2963 | −1.68379 | −0.841894 | − | 0.539643i | \(-0.818559\pi\) | ||||
−0.841894 | + | 0.539643i | \(0.818559\pi\) | |||||||
\(632\) | −11.4119 | −0.453941 | ||||||||
\(633\) | −11.2030 | −0.445281 | ||||||||
\(634\) | −7.36812 | −0.292625 | ||||||||
\(635\) | −12.9175 | −0.512616 | ||||||||
\(636\) | −8.06106 | −0.319642 | ||||||||
\(637\) | −0.365083 | −0.0144651 | ||||||||
\(638\) | −3.74141 | −0.148124 | ||||||||
\(639\) | 12.9886 | 0.513821 | ||||||||
\(640\) | −1.34813 | −0.0532894 | ||||||||
\(641\) | −3.38669 | −0.133766 | −0.0668832 | − | 0.997761i | \(-0.521305\pi\) | ||||
−0.0668832 | + | 0.997761i | \(0.521305\pi\) | |||||||
\(642\) | −8.05560 | −0.317929 | ||||||||
\(643\) | −26.1572 | −1.03154 | −0.515769 | − | 0.856728i | \(-0.672494\pi\) | ||||
−0.515769 | + | 0.856728i | \(0.672494\pi\) | |||||||
\(644\) | −12.2273 | −0.481823 | ||||||||
\(645\) | 7.43165 | 0.292621 | ||||||||
\(646\) | −2.81059 | −0.110581 | ||||||||
\(647\) | −35.2804 | −1.38702 | −0.693508 | − | 0.720449i | \(-0.743936\pi\) | ||||
−0.693508 | + | 0.720449i | \(0.743936\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −16.4534 | −0.645852 | ||||||||
\(650\) | −3.18255 | −0.124830 | ||||||||
\(651\) | 27.8129 | 1.09007 | ||||||||
\(652\) | −0.232060 | −0.00908816 | ||||||||
\(653\) | 9.91311 | 0.387930 | 0.193965 | − | 0.981008i | \(-0.437865\pi\) | ||||
0.193965 | + | 0.981008i | \(0.437865\pi\) | |||||||
\(654\) | 3.57732 | 0.139884 | ||||||||
\(655\) | −13.4104 | −0.523988 | ||||||||
\(656\) | −5.06676 | −0.197824 | ||||||||
\(657\) | −1.57753 | −0.0615454 | ||||||||
\(658\) | 3.85224 | 0.150176 | ||||||||
\(659\) | −43.4838 | −1.69389 | −0.846945 | − | 0.531680i | \(-0.821561\pi\) | ||||
−0.846945 | + | 0.531680i | \(0.821561\pi\) | |||||||
\(660\) | −3.22385 | −0.125488 | ||||||||
\(661\) | 17.9106 | 0.696640 | 0.348320 | − | 0.937376i | \(-0.386752\pi\) | ||||
0.348320 | + | 0.937376i | \(0.386752\pi\) | |||||||
\(662\) | −18.1845 | −0.706760 | ||||||||
\(663\) | 6.50957 | 0.252811 | ||||||||
\(664\) | 5.72642 | 0.222228 | ||||||||
\(665\) | −1.57966 | −0.0612567 | ||||||||
\(666\) | 6.36996 | 0.246831 | ||||||||
\(667\) | 7.04910 | 0.272942 | ||||||||
\(668\) | −1.99495 | −0.0771868 | ||||||||
\(669\) | 27.5336 | 1.06451 | ||||||||
\(670\) | −11.2997 | −0.436546 | ||||||||
\(671\) | 28.5783 | 1.10325 | ||||||||
\(672\) | −2.71387 | −0.104690 | ||||||||
\(673\) | −11.0858 | −0.427327 | −0.213663 | − | 0.976907i | \(-0.568540\pi\) | ||||
−0.213663 | + | 0.976907i | \(0.568540\pi\) | |||||||
\(674\) | −30.5645 | −1.17730 | ||||||||
\(675\) | −3.18255 | −0.122497 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 27.8562 | 1.07060 | 0.535300 | − | 0.844662i | \(-0.320198\pi\) | ||||
0.535300 | + | 0.844662i | \(0.320198\pi\) | |||||||
\(678\) | 10.1751 | 0.390772 | ||||||||
\(679\) | −18.4399 | −0.707659 | ||||||||
\(680\) | 8.77573 | 0.336534 | ||||||||
\(681\) | 23.3657 | 0.895374 | ||||||||
\(682\) | 24.5076 | 0.938445 | ||||||||
\(683\) | 25.9979 | 0.994783 | 0.497392 | − | 0.867526i | \(-0.334291\pi\) | ||||
0.497392 | + | 0.867526i | \(0.334291\pi\) | |||||||
\(684\) | −0.431762 | −0.0165088 | ||||||||
\(685\) | 4.81078 | 0.183810 | ||||||||
\(686\) | 18.0063 | 0.687483 | ||||||||
\(687\) | −13.7682 | −0.525291 | ||||||||
\(688\) | 5.51257 | 0.210165 | ||||||||
\(689\) | 8.06106 | 0.307102 | ||||||||
\(690\) | 6.07397 | 0.231232 | ||||||||
\(691\) | −26.2325 | −0.997931 | −0.498966 | − | 0.866622i | \(-0.666287\pi\) | ||||
−0.498966 | + | 0.866622i | \(0.666287\pi\) | |||||||
\(692\) | 24.4936 | 0.931108 | ||||||||
\(693\) | −6.48982 | −0.246528 | ||||||||
\(694\) | 25.2946 | 0.960168 | ||||||||
\(695\) | −21.9860 | −0.833977 | ||||||||
\(696\) | 1.56456 | 0.0593044 | ||||||||
\(697\) | 32.9824 | 1.24930 | ||||||||
\(698\) | −14.5811 | −0.551904 | ||||||||
\(699\) | 22.0201 | 0.832878 | ||||||||
\(700\) | −8.63703 | −0.326449 | ||||||||
\(701\) | −10.6850 | −0.403568 | −0.201784 | − | 0.979430i | \(-0.564674\pi\) | ||||
−0.201784 | + | 0.979430i | \(0.564674\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 2.75031 | 0.103730 | ||||||||
\(704\) | −2.39135 | −0.0901275 | ||||||||
\(705\) | −1.91362 | −0.0720710 | ||||||||
\(706\) | 29.6881 | 1.11733 | ||||||||
\(707\) | −40.5291 | −1.52425 | ||||||||
\(708\) | 6.88037 | 0.258580 | ||||||||
\(709\) | −3.50709 | −0.131712 | −0.0658558 | − | 0.997829i | \(-0.520978\pi\) | ||||
−0.0658558 | + | 0.997829i | \(0.520978\pi\) | |||||||
\(710\) | −17.5103 | −0.657149 | ||||||||
\(711\) | 11.4119 | 0.427980 | ||||||||
\(712\) | 11.4913 | 0.430656 | ||||||||
\(713\) | −46.1742 | −1.72924 | ||||||||
\(714\) | 17.6661 | 0.661138 | ||||||||
\(715\) | 3.22385 | 0.120565 | ||||||||
\(716\) | −24.9563 | −0.932660 | ||||||||
\(717\) | −23.6471 | −0.883115 | ||||||||
\(718\) | 15.1234 | 0.564402 | ||||||||
\(719\) | −3.78949 | −0.141324 | −0.0706621 | − | 0.997500i | \(-0.522511\pi\) | ||||
−0.0706621 | + | 0.997500i | \(0.522511\pi\) | |||||||
\(720\) | 1.34813 | 0.0502417 | ||||||||
\(721\) | 2.71387 | 0.101070 | ||||||||
\(722\) | 18.8136 | 0.700169 | ||||||||
\(723\) | −13.2240 | −0.491804 | ||||||||
\(724\) | 19.7726 | 0.734842 | ||||||||
\(725\) | 4.97929 | 0.184926 | ||||||||
\(726\) | 5.28143 | 0.196012 | ||||||||
\(727\) | 38.5644 | 1.43027 | 0.715137 | − | 0.698984i | \(-0.246364\pi\) | ||||
0.715137 | + | 0.698984i | \(0.246364\pi\) | |||||||
\(728\) | 2.71387 | 0.100583 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.12671 | 0.0787133 | ||||||||
\(731\) | −35.8845 | −1.32724 | ||||||||
\(732\) | −11.9507 | −0.441710 | ||||||||
\(733\) | −23.8425 | −0.880644 | −0.440322 | − | 0.897840i | \(-0.645136\pi\) | ||||
−0.440322 | + | 0.897840i | \(0.645136\pi\) | |||||||
\(734\) | 10.8564 | 0.400718 | ||||||||
\(735\) | 0.492178 | 0.0181543 | ||||||||
\(736\) | 4.50549 | 0.166075 | ||||||||
\(737\) | −20.0438 | −0.738323 | ||||||||
\(738\) | 5.06676 | 0.186510 | ||||||||
\(739\) | 33.6980 | 1.23960 | 0.619800 | − | 0.784760i | \(-0.287214\pi\) | ||||
0.619800 | + | 0.784760i | \(0.287214\pi\) | |||||||
\(740\) | −8.58751 | −0.315683 | ||||||||
\(741\) | 0.431762 | 0.0158612 | ||||||||
\(742\) | 21.8766 | 0.803117 | ||||||||
\(743\) | 2.63822 | 0.0967871 | 0.0483935 | − | 0.998828i | \(-0.484590\pi\) | ||||
0.0483935 | + | 0.998828i | \(0.484590\pi\) | |||||||
\(744\) | −10.2484 | −0.375726 | ||||||||
\(745\) | −2.09126 | −0.0766177 | ||||||||
\(746\) | −7.66103 | −0.280490 | ||||||||
\(747\) | −5.72642 | −0.209519 | ||||||||
\(748\) | 15.5667 | 0.569174 | ||||||||
\(749\) | 21.8618 | 0.798814 | ||||||||
\(750\) | 11.0311 | 0.402800 | ||||||||
\(751\) | −15.9161 | −0.580788 | −0.290394 | − | 0.956907i | \(-0.593786\pi\) | ||||
−0.290394 | + | 0.956907i | \(0.593786\pi\) | |||||||
\(752\) | −1.41946 | −0.0517625 | ||||||||
\(753\) | 4.85647 | 0.176980 | ||||||||
\(754\) | −1.56456 | −0.0569778 | ||||||||
\(755\) | −19.3725 | −0.705036 | ||||||||
\(756\) | 2.71387 | 0.0987024 | ||||||||
\(757\) | 13.2525 | 0.481670 | 0.240835 | − | 0.970566i | \(-0.422579\pi\) | ||||
0.240835 | + | 0.970566i | \(0.422579\pi\) | |||||||
\(758\) | −10.0157 | −0.363786 | ||||||||
\(759\) | 10.7742 | 0.391079 | ||||||||
\(760\) | 0.582070 | 0.0211139 | ||||||||
\(761\) | 1.63852 | 0.0593963 | 0.0296982 | − | 0.999559i | \(-0.490545\pi\) | ||||
0.0296982 | + | 0.999559i | \(0.490545\pi\) | |||||||
\(762\) | 9.58182 | 0.347113 | ||||||||
\(763\) | −9.70837 | −0.351467 | ||||||||
\(764\) | 4.73569 | 0.171331 | ||||||||
\(765\) | −8.77573 | −0.317287 | ||||||||
\(766\) | −17.7480 | −0.641263 | ||||||||
\(767\) | −6.88037 | −0.248436 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −49.4014 | −1.78146 | −0.890730 | − | 0.454533i | \(-0.849806\pi\) | ||||
−0.890730 | + | 0.454533i | \(0.849806\pi\) | |||||||
\(770\) | 8.74909 | 0.315295 | ||||||||
\(771\) | −11.7803 | −0.424257 | ||||||||
\(772\) | −6.52330 | −0.234779 | ||||||||
\(773\) | −30.0731 | −1.08165 | −0.540827 | − | 0.841134i | \(-0.681889\pi\) | ||||
−0.540827 | + | 0.841134i | \(0.681889\pi\) | |||||||
\(774\) | −5.51257 | −0.198145 | ||||||||
\(775\) | −32.6162 | −1.17161 | ||||||||
\(776\) | 6.79470 | 0.243915 | ||||||||
\(777\) | −17.2872 | −0.620176 | ||||||||
\(778\) | −17.6122 | −0.631427 | ||||||||
\(779\) | 2.18764 | 0.0783802 | ||||||||
\(780\) | −1.34813 | −0.0482707 | ||||||||
\(781\) | −31.0603 | −1.11143 | ||||||||
\(782\) | −29.3288 | −1.04880 | ||||||||
\(783\) | −1.56456 | −0.0559127 | ||||||||
\(784\) | 0.365083 | 0.0130387 | ||||||||
\(785\) | 11.5163 | 0.411033 | ||||||||
\(786\) | 9.94744 | 0.354813 | ||||||||
\(787\) | −43.4901 | −1.55025 | −0.775127 | − | 0.631806i | \(-0.782314\pi\) | ||||
−0.775127 | + | 0.631806i | \(0.782314\pi\) | |||||||
\(788\) | −8.88078 | −0.316365 | ||||||||
\(789\) | 6.54794 | 0.233113 | ||||||||
\(790\) | −15.3847 | −0.547362 | ||||||||
\(791\) | −27.6139 | −0.981836 | ||||||||
\(792\) | 2.39135 | 0.0849730 | ||||||||
\(793\) | 11.9507 | 0.424381 | ||||||||
\(794\) | −15.9439 | −0.565826 | ||||||||
\(795\) | −10.8673 | −0.385424 | ||||||||
\(796\) | −23.6494 | −0.838231 | ||||||||
\(797\) | 21.0117 | 0.744271 | 0.372136 | − | 0.928178i | \(-0.378626\pi\) | ||||
0.372136 | + | 0.928178i | \(0.378626\pi\) | |||||||
\(798\) | 1.17175 | 0.0414794 | ||||||||
\(799\) | 9.24010 | 0.326891 | ||||||||
\(800\) | 3.18255 | 0.112520 | ||||||||
\(801\) | −11.4913 | −0.406026 | ||||||||
\(802\) | 13.5652 | 0.479004 | ||||||||
\(803\) | 3.77244 | 0.133126 | ||||||||
\(804\) | 8.38179 | 0.295603 | ||||||||
\(805\) | −16.4840 | −0.580983 | ||||||||
\(806\) | 10.2484 | 0.360986 | ||||||||
\(807\) | 4.08408 | 0.143766 | ||||||||
\(808\) | 14.9341 | 0.525378 | ||||||||
\(809\) | −39.2784 | −1.38096 | −0.690478 | − | 0.723353i | \(-0.742600\pi\) | ||||
−0.690478 | + | 0.723353i | \(0.742600\pi\) | |||||||
\(810\) | −1.34813 | −0.0473683 | ||||||||
\(811\) | 3.38932 | 0.119015 | 0.0595075 | − | 0.998228i | \(-0.481047\pi\) | ||||
0.0595075 | + | 0.998228i | \(0.481047\pi\) | |||||||
\(812\) | −4.24600 | −0.149006 | ||||||||
\(813\) | −9.81272 | −0.344147 | ||||||||
\(814\) | −15.2328 | −0.533910 | ||||||||
\(815\) | −0.312846 | −0.0109585 | ||||||||
\(816\) | −6.50957 | −0.227881 | ||||||||
\(817\) | −2.38012 | −0.0832699 | ||||||||
\(818\) | −23.6532 | −0.827015 | ||||||||
\(819\) | −2.71387 | −0.0948302 | ||||||||
\(820\) | −6.83063 | −0.238536 | ||||||||
\(821\) | −4.00943 | −0.139930 | −0.0699651 | − | 0.997549i | \(-0.522289\pi\) | ||||
−0.0699651 | + | 0.997549i | \(0.522289\pi\) | |||||||
\(822\) | −3.56849 | −0.124465 | ||||||||
\(823\) | 28.8401 | 1.00530 | 0.502652 | − | 0.864489i | \(-0.332358\pi\) | ||||
0.502652 | + | 0.864489i | \(0.332358\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 7.61061 | 0.264967 | ||||||||
\(826\) | −18.6724 | −0.649696 | ||||||||
\(827\) | 43.1464 | 1.50035 | 0.750174 | − | 0.661240i | \(-0.229970\pi\) | ||||
0.750174 | + | 0.661240i | \(0.229970\pi\) | |||||||
\(828\) | −4.50549 | −0.156577 | ||||||||
\(829\) | −18.0415 | −0.626606 | −0.313303 | − | 0.949653i | \(-0.601435\pi\) | ||||
−0.313303 | + | 0.949653i | \(0.601435\pi\) | |||||||
\(830\) | 7.71994 | 0.267963 | ||||||||
\(831\) | −10.6253 | −0.368588 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −2.37653 | −0.0823420 | ||||||||
\(834\) | 16.3086 | 0.564719 | ||||||||
\(835\) | −2.68944 | −0.0930719 | ||||||||
\(836\) | 1.03250 | 0.0357096 | ||||||||
\(837\) | 10.2484 | 0.354238 | ||||||||
\(838\) | −30.1554 | −1.04170 | ||||||||
\(839\) | −3.49785 | −0.120759 | −0.0603796 | − | 0.998175i | \(-0.519231\pi\) | ||||
−0.0603796 | + | 0.998175i | \(0.519231\pi\) | |||||||
\(840\) | −3.65864 | −0.126235 | ||||||||
\(841\) | −26.5522 | −0.915592 | ||||||||
\(842\) | −13.2847 | −0.457821 | ||||||||
\(843\) | −11.0617 | −0.380984 | ||||||||
\(844\) | −11.2030 | −0.385625 | ||||||||
\(845\) | 1.34813 | 0.0463770 | ||||||||
\(846\) | 1.41946 | 0.0488022 | ||||||||
\(847\) | −14.3331 | −0.492492 | ||||||||
\(848\) | −8.06106 | −0.276818 | ||||||||
\(849\) | 6.36457 | 0.218431 | ||||||||
\(850\) | −20.7171 | −0.710589 | ||||||||
\(851\) | 28.6998 | 0.983816 | ||||||||
\(852\) | 12.9886 | 0.444982 | ||||||||
\(853\) | 40.2794 | 1.37914 | 0.689571 | − | 0.724218i | \(-0.257799\pi\) | ||||
0.689571 | + | 0.724218i | \(0.257799\pi\) | |||||||
\(854\) | 32.4326 | 1.10982 | ||||||||
\(855\) | −0.582070 | −0.0199064 | ||||||||
\(856\) | −8.05560 | −0.275335 | ||||||||
\(857\) | 27.3567 | 0.934486 | 0.467243 | − | 0.884129i | \(-0.345247\pi\) | ||||
0.467243 | + | 0.884129i | \(0.345247\pi\) | |||||||
\(858\) | −2.39135 | −0.0816394 | ||||||||
\(859\) | 9.68118 | 0.330317 | 0.165159 | − | 0.986267i | \(-0.447186\pi\) | ||||
0.165159 | + | 0.986267i | \(0.447186\pi\) | |||||||
\(860\) | 7.43165 | 0.253417 | ||||||||
\(861\) | −13.7505 | −0.468616 | ||||||||
\(862\) | 8.15311 | 0.277696 | ||||||||
\(863\) | 31.4569 | 1.07081 | 0.535403 | − | 0.844597i | \(-0.320160\pi\) | ||||
0.535403 | + | 0.844597i | \(0.320160\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 33.0205 | 1.12273 | ||||||||
\(866\) | 1.67772 | 0.0570111 | ||||||||
\(867\) | 25.3745 | 0.861764 | ||||||||
\(868\) | 27.8129 | 0.944031 | ||||||||
\(869\) | −27.2899 | −0.925745 | ||||||||
\(870\) | 2.10922 | 0.0715093 | ||||||||
\(871\) | −8.38179 | −0.284006 | ||||||||
\(872\) | 3.57732 | 0.121143 | ||||||||
\(873\) | −6.79470 | −0.229966 | ||||||||
\(874\) | −1.94530 | −0.0658008 | ||||||||
\(875\) | −29.9370 | −1.01206 | ||||||||
\(876\) | −1.57753 | −0.0532999 | ||||||||
\(877\) | 27.4115 | 0.925621 | 0.462810 | − | 0.886457i | \(-0.346841\pi\) | ||||
0.462810 | + | 0.886457i | \(0.346841\pi\) | |||||||
\(878\) | −38.8832 | −1.31224 | ||||||||
\(879\) | 7.74495 | 0.261231 | ||||||||
\(880\) | −3.22385 | −0.108676 | ||||||||
\(881\) | 2.91785 | 0.0983048 | 0.0491524 | − | 0.998791i | \(-0.484348\pi\) | ||||
0.0491524 | + | 0.998791i | \(0.484348\pi\) | |||||||
\(882\) | −0.365083 | −0.0122930 | ||||||||
\(883\) | −27.9384 | −0.940203 | −0.470101 | − | 0.882612i | \(-0.655783\pi\) | ||||
−0.470101 | + | 0.882612i | \(0.655783\pi\) | |||||||
\(884\) | 6.50957 | 0.218941 | ||||||||
\(885\) | 9.27560 | 0.311796 | ||||||||
\(886\) | 18.8022 | 0.631672 | ||||||||
\(887\) | −10.3031 | −0.345943 | −0.172972 | − | 0.984927i | \(-0.555337\pi\) | ||||
−0.172972 | + | 0.984927i | \(0.555337\pi\) | |||||||
\(888\) | 6.36996 | 0.213762 | ||||||||
\(889\) | −26.0038 | −0.872139 | ||||||||
\(890\) | 15.4918 | 0.519285 | ||||||||
\(891\) | −2.39135 | −0.0801133 | ||||||||
\(892\) | 27.5336 | 0.921893 | ||||||||
\(893\) | 0.612871 | 0.0205090 | ||||||||
\(894\) | 1.55123 | 0.0518810 | ||||||||
\(895\) | −33.6442 | −1.12460 | ||||||||
\(896\) | −2.71387 | −0.0906640 | ||||||||
\(897\) | 4.50549 | 0.150434 | ||||||||
\(898\) | 4.65776 | 0.155431 | ||||||||
\(899\) | −16.0343 | −0.534772 | ||||||||
\(900\) | −3.18255 | −0.106085 | ||||||||
\(901\) | 52.4740 | 1.74816 | ||||||||
\(902\) | −12.1164 | −0.403432 | ||||||||
\(903\) | 14.9604 | 0.497851 | ||||||||
\(904\) | 10.1751 | 0.338418 | ||||||||
\(905\) | 26.6559 | 0.886074 | ||||||||
\(906\) | 14.3699 | 0.477408 | ||||||||
\(907\) | 19.1032 | 0.634310 | 0.317155 | − | 0.948374i | \(-0.397272\pi\) | ||||
0.317155 | + | 0.948374i | \(0.397272\pi\) | |||||||
\(908\) | 23.3657 | 0.775416 | ||||||||
\(909\) | −14.9341 | −0.495331 | ||||||||
\(910\) | 3.65864 | 0.121283 | ||||||||
\(911\) | −41.7725 | −1.38398 | −0.691992 | − | 0.721905i | \(-0.743267\pi\) | ||||
−0.691992 | + | 0.721905i | \(0.743267\pi\) | |||||||
\(912\) | −0.431762 | −0.0142971 | ||||||||
\(913\) | 13.6939 | 0.453202 | ||||||||
\(914\) | −16.6855 | −0.551907 | ||||||||
\(915\) | −16.1110 | −0.532615 | ||||||||
\(916\) | −13.7682 | −0.454916 | ||||||||
\(917\) | −26.9960 | −0.891488 | ||||||||
\(918\) | 6.50957 | 0.214848 | ||||||||
\(919\) | 53.3955 | 1.76135 | 0.880677 | − | 0.473717i | \(-0.157088\pi\) | ||||
0.880677 | + | 0.473717i | \(0.157088\pi\) | |||||||
\(920\) | 6.07397 | 0.200253 | ||||||||
\(921\) | −12.8933 | −0.424847 | ||||||||
\(922\) | 10.4652 | 0.344653 | ||||||||
\(923\) | −12.9886 | −0.427525 | ||||||||
\(924\) | −6.48982 | −0.213499 | ||||||||
\(925\) | 20.2727 | 0.666563 | ||||||||
\(926\) | −31.2686 | −1.02755 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 1.56456 | 0.0513591 | ||||||||
\(929\) | −4.38364 | −0.143823 | −0.0719113 | − | 0.997411i | \(-0.522910\pi\) | ||||
−0.0719113 | + | 0.997411i | \(0.522910\pi\) | |||||||
\(930\) | −13.8162 | −0.453051 | ||||||||
\(931\) | −0.157629 | −0.00516609 | ||||||||
\(932\) | 22.0201 | 0.721294 | ||||||||
\(933\) | 22.5094 | 0.736926 | ||||||||
\(934\) | 15.9687 | 0.522511 | ||||||||
\(935\) | 20.9859 | 0.686311 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −28.5199 | −0.931704 | −0.465852 | − | 0.884863i | \(-0.654252\pi\) | ||||
−0.465852 | + | 0.884863i | \(0.654252\pi\) | |||||||
\(938\) | −22.7471 | −0.742718 | ||||||||
\(939\) | −14.2391 | −0.464676 | ||||||||
\(940\) | −1.91362 | −0.0624153 | ||||||||
\(941\) | −12.7299 | −0.414982 | −0.207491 | − | 0.978237i | \(-0.566530\pi\) | ||||
−0.207491 | + | 0.978237i | \(0.566530\pi\) | |||||||
\(942\) | −8.54243 | −0.278327 | ||||||||
\(943\) | 22.8282 | 0.743389 | ||||||||
\(944\) | 6.88037 | 0.223937 | ||||||||
\(945\) | 3.65864 | 0.119016 | ||||||||
\(946\) | 13.1825 | 0.428600 | ||||||||
\(947\) | 53.4256 | 1.73610 | 0.868050 | − | 0.496477i | \(-0.165373\pi\) | ||||
0.868050 | + | 0.496477i | \(0.165373\pi\) | |||||||
\(948\) | 11.4119 | 0.370641 | ||||||||
\(949\) | 1.57753 | 0.0512089 | ||||||||
\(950\) | −1.37411 | −0.0445819 | ||||||||
\(951\) | 7.36812 | 0.238928 | ||||||||
\(952\) | 17.6661 | 0.572562 | ||||||||
\(953\) | −15.7274 | −0.509459 | −0.254730 | − | 0.967012i | \(-0.581986\pi\) | ||||
−0.254730 | + | 0.967012i | \(0.581986\pi\) | |||||||
\(954\) | 8.06106 | 0.260986 | ||||||||
\(955\) | 6.38431 | 0.206591 | ||||||||
\(956\) | −23.6471 | −0.764800 | ||||||||
\(957\) | 3.74141 | 0.120943 | ||||||||
\(958\) | −18.5527 | −0.599409 | ||||||||
\(959\) | 9.68441 | 0.312726 | ||||||||
\(960\) | 1.34813 | 0.0435106 | ||||||||
\(961\) | 74.0303 | 2.38808 | ||||||||
\(962\) | −6.36996 | −0.205376 | ||||||||
\(963\) | 8.05560 | 0.259588 | ||||||||
\(964\) | −13.2240 | −0.425915 | ||||||||
\(965\) | −8.79424 | −0.283097 | ||||||||
\(966\) | 12.2273 | 0.393407 | ||||||||
\(967\) | −7.42064 | −0.238632 | −0.119316 | − | 0.992856i | \(-0.538070\pi\) | ||||
−0.119316 | + | 0.992856i | \(0.538070\pi\) | |||||||
\(968\) | 5.28143 | 0.169752 | ||||||||
\(969\) | 2.81059 | 0.0902891 | ||||||||
\(970\) | 9.16011 | 0.294114 | ||||||||
\(971\) | −43.6841 | −1.40189 | −0.700945 | − | 0.713215i | \(-0.747238\pi\) | ||||
−0.700945 | + | 0.713215i | \(0.747238\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −44.2593 | −1.41889 | ||||||||
\(974\) | 35.5161 | 1.13801 | ||||||||
\(975\) | 3.18255 | 0.101923 | ||||||||
\(976\) | −11.9507 | −0.382532 | ||||||||
\(977\) | −5.79119 | −0.185277 | −0.0926383 | − | 0.995700i | \(-0.529530\pi\) | ||||
−0.0926383 | + | 0.995700i | \(0.529530\pi\) | |||||||
\(978\) | 0.232060 | 0.00742045 | ||||||||
\(979\) | 27.4798 | 0.878259 | ||||||||
\(980\) | 0.492178 | 0.0157221 | ||||||||
\(981\) | −3.57732 | −0.114215 | ||||||||
\(982\) | −5.28868 | −0.168769 | ||||||||
\(983\) | −24.9652 | −0.796267 | −0.398133 | − | 0.917328i | \(-0.630342\pi\) | ||||
−0.398133 | + | 0.917328i | \(0.630342\pi\) | |||||||
\(984\) | 5.06676 | 0.161522 | ||||||||
\(985\) | −11.9724 | −0.381473 | ||||||||
\(986\) | −10.1846 | −0.324344 | ||||||||
\(987\) | −3.85224 | −0.122618 | ||||||||
\(988\) | 0.431762 | 0.0137362 | ||||||||
\(989\) | −24.8368 | −0.789766 | ||||||||
\(990\) | 3.22385 | 0.102461 | ||||||||
\(991\) | 39.6768 | 1.26037 | 0.630187 | − | 0.776443i | \(-0.282978\pi\) | ||||
0.630187 | + | 0.776443i | \(0.282978\pi\) | |||||||
\(992\) | −10.2484 | −0.325388 | ||||||||
\(993\) | 18.1845 | 0.577067 | ||||||||
\(994\) | −35.2494 | −1.11804 | ||||||||
\(995\) | −31.8824 | −1.01074 | ||||||||
\(996\) | −5.72642 | −0.181449 | ||||||||
\(997\) | −12.4981 | −0.395818 | −0.197909 | − | 0.980220i | \(-0.563415\pi\) | ||||
−0.197909 | + | 0.980220i | \(0.563415\pi\) | |||||||
\(998\) | 10.8970 | 0.344937 | ||||||||
\(999\) | −6.36996 | −0.201537 |
(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 | 8034.2.a.bb.1.10 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bb.1.10 | ✓ | 14 | 1.1 | even | 1 | trivial |