Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, 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("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 | ||||||||
\(3\) | −1.33333 | −0.769798 | −0.384899 | − | 0.922959i | \(-0.625764\pi\) | ||||
−0.384899 | + | 0.922959i | \(0.625764\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.98893 | 1.33669 | 0.668345 | − | 0.743852i | \(-0.267003\pi\) | ||||
0.668345 | + | 0.743852i | \(0.267003\pi\) | |||||||
\(6\) | 1.33333 | 0.544330 | ||||||||
\(7\) | 1.91777 | 0.724847 | 0.362424 | − | 0.932013i | \(-0.381949\pi\) | ||||
0.362424 | + | 0.932013i | \(0.381949\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.22223 | −0.407410 | ||||||||
\(10\) | −2.98893 | −0.945182 | ||||||||
\(11\) | 2.33413 | 0.703766 | 0.351883 | − | 0.936044i | \(-0.385541\pi\) | ||||
0.351883 | + | 0.936044i | \(0.385541\pi\) | |||||||
\(12\) | −1.33333 | −0.384899 | ||||||||
\(13\) | −1.24369 | −0.344937 | −0.172468 | − | 0.985015i | \(-0.555174\pi\) | ||||
−0.172468 | + | 0.985015i | \(0.555174\pi\) | |||||||
\(14\) | −1.91777 | −0.512545 | ||||||||
\(15\) | −3.98523 | −1.02898 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.75205 | 1.15254 | 0.576271 | − | 0.817259i | \(-0.304507\pi\) | ||||
0.576271 | + | 0.817259i | \(0.304507\pi\) | |||||||
\(18\) | 1.22223 | 0.288083 | ||||||||
\(19\) | −6.69664 | −1.53631 | −0.768157 | − | 0.640262i | \(-0.778826\pi\) | ||||
−0.768157 | + | 0.640262i | \(0.778826\pi\) | |||||||
\(20\) | 2.98893 | 0.668345 | ||||||||
\(21\) | −2.55702 | −0.557986 | ||||||||
\(22\) | −2.33413 | −0.497638 | ||||||||
\(23\) | 2.52597 | 0.526701 | 0.263351 | − | 0.964700i | \(-0.415172\pi\) | ||||
0.263351 | + | 0.964700i | \(0.415172\pi\) | |||||||
\(24\) | 1.33333 | 0.272165 | ||||||||
\(25\) | 3.93370 | 0.786739 | ||||||||
\(26\) | 1.24369 | 0.243907 | ||||||||
\(27\) | 5.62963 | 1.08342 | ||||||||
\(28\) | 1.91777 | 0.362424 | ||||||||
\(29\) | −4.11267 | −0.763703 | −0.381852 | − | 0.924224i | \(-0.624713\pi\) | ||||
−0.381852 | + | 0.924224i | \(0.624713\pi\) | |||||||
\(30\) | 3.98523 | 0.727600 | ||||||||
\(31\) | 0.469368 | 0.0843010 | 0.0421505 | − | 0.999111i | \(-0.486579\pi\) | ||||
0.0421505 | + | 0.999111i | \(0.486579\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.11216 | −0.541758 | ||||||||
\(34\) | −4.75205 | −0.814970 | ||||||||
\(35\) | 5.73207 | 0.968896 | ||||||||
\(36\) | −1.22223 | −0.203705 | ||||||||
\(37\) | −4.62422 | −0.760217 | −0.380109 | − | 0.924942i | \(-0.624113\pi\) | ||||
−0.380109 | + | 0.924942i | \(0.624113\pi\) | |||||||
\(38\) | 6.69664 | 1.08634 | ||||||||
\(39\) | 1.65825 | 0.265532 | ||||||||
\(40\) | −2.98893 | −0.472591 | ||||||||
\(41\) | 2.98791 | 0.466634 | 0.233317 | − | 0.972401i | \(-0.425042\pi\) | ||||
0.233317 | + | 0.972401i | \(0.425042\pi\) | |||||||
\(42\) | 2.55702 | 0.394556 | ||||||||
\(43\) | 2.32394 | 0.354397 | 0.177199 | − | 0.984175i | \(-0.443297\pi\) | ||||
0.177199 | + | 0.984175i | \(0.443297\pi\) | |||||||
\(44\) | 2.33413 | 0.351883 | ||||||||
\(45\) | −3.65316 | −0.544581 | ||||||||
\(46\) | −2.52597 | −0.372434 | ||||||||
\(47\) | 4.98057 | 0.726491 | 0.363245 | − | 0.931693i | \(-0.381669\pi\) | ||||
0.363245 | + | 0.931693i | \(0.381669\pi\) | |||||||
\(48\) | −1.33333 | −0.192450 | ||||||||
\(49\) | −3.32217 | −0.474596 | ||||||||
\(50\) | −3.93370 | −0.556309 | ||||||||
\(51\) | −6.33605 | −0.887225 | ||||||||
\(52\) | −1.24369 | −0.172468 | ||||||||
\(53\) | 9.38381 | 1.28897 | 0.644483 | − | 0.764619i | \(-0.277073\pi\) | ||||
0.644483 | + | 0.764619i | \(0.277073\pi\) | |||||||
\(54\) | −5.62963 | −0.766095 | ||||||||
\(55\) | 6.97654 | 0.940717 | ||||||||
\(56\) | −1.91777 | −0.256272 | ||||||||
\(57\) | 8.92883 | 1.18265 | ||||||||
\(58\) | 4.11267 | 0.540020 | ||||||||
\(59\) | 8.98826 | 1.17017 | 0.585086 | − | 0.810972i | \(-0.301061\pi\) | ||||
0.585086 | + | 0.810972i | \(0.301061\pi\) | |||||||
\(60\) | −3.98523 | −0.514491 | ||||||||
\(61\) | 4.47226 | 0.572614 | 0.286307 | − | 0.958138i | \(-0.407572\pi\) | ||||
0.286307 | + | 0.958138i | \(0.407572\pi\) | |||||||
\(62\) | −0.469368 | −0.0596098 | ||||||||
\(63\) | −2.34395 | −0.295310 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.71729 | −0.461074 | ||||||||
\(66\) | 3.11216 | 0.383081 | ||||||||
\(67\) | 10.1840 | 1.24418 | 0.622089 | − | 0.782947i | \(-0.286284\pi\) | ||||
0.622089 | + | 0.782947i | \(0.286284\pi\) | |||||||
\(68\) | 4.75205 | 0.576271 | ||||||||
\(69\) | −3.36795 | −0.405454 | ||||||||
\(70\) | −5.73207 | −0.685113 | ||||||||
\(71\) | 8.59830 | 1.02043 | 0.510215 | − | 0.860047i | \(-0.329566\pi\) | ||||
0.510215 | + | 0.860047i | \(0.329566\pi\) | |||||||
\(72\) | 1.22223 | 0.144041 | ||||||||
\(73\) | 1.10340 | 0.129143 | 0.0645714 | − | 0.997913i | \(-0.479432\pi\) | ||||
0.0645714 | + | 0.997913i | \(0.479432\pi\) | |||||||
\(74\) | 4.62422 | 0.537555 | ||||||||
\(75\) | −5.24492 | −0.605631 | ||||||||
\(76\) | −6.69664 | −0.768157 | ||||||||
\(77\) | 4.47631 | 0.510123 | ||||||||
\(78\) | −1.65825 | −0.187759 | ||||||||
\(79\) | −4.62998 | −0.520913 | −0.260457 | − | 0.965486i | \(-0.583873\pi\) | ||||
−0.260457 | + | 0.965486i | \(0.583873\pi\) | |||||||
\(80\) | 2.98893 | 0.334172 | ||||||||
\(81\) | −3.83946 | −0.426606 | ||||||||
\(82\) | −2.98791 | −0.329960 | ||||||||
\(83\) | −17.7455 | −1.94782 | −0.973912 | − | 0.226927i | \(-0.927132\pi\) | ||||
−0.973912 | + | 0.226927i | \(0.927132\pi\) | |||||||
\(84\) | −2.55702 | −0.278993 | ||||||||
\(85\) | 14.2036 | 1.54059 | ||||||||
\(86\) | −2.32394 | −0.250597 | ||||||||
\(87\) | 5.48354 | 0.587897 | ||||||||
\(88\) | −2.33413 | −0.248819 | ||||||||
\(89\) | 8.16173 | 0.865142 | 0.432571 | − | 0.901600i | \(-0.357607\pi\) | ||||
0.432571 | + | 0.901600i | \(0.357607\pi\) | |||||||
\(90\) | 3.65316 | 0.385077 | ||||||||
\(91\) | −2.38510 | −0.250027 | ||||||||
\(92\) | 2.52597 | 0.263351 | ||||||||
\(93\) | −0.625823 | −0.0648948 | ||||||||
\(94\) | −4.98057 | −0.513707 | ||||||||
\(95\) | −20.0158 | −2.05357 | ||||||||
\(96\) | 1.33333 | 0.136082 | ||||||||
\(97\) | 12.8159 | 1.30125 | 0.650627 | − | 0.759398i | \(-0.274506\pi\) | ||||
0.650627 | + | 0.759398i | \(0.274506\pi\) | |||||||
\(98\) | 3.32217 | 0.335590 | ||||||||
\(99\) | −2.85284 | −0.286722 | ||||||||
\(100\) | 3.93370 | 0.393370 | ||||||||
\(101\) | 7.41703 | 0.738022 | 0.369011 | − | 0.929425i | \(-0.379696\pi\) | ||||
0.369011 | + | 0.929425i | \(0.379696\pi\) | |||||||
\(102\) | 6.33605 | 0.627363 | ||||||||
\(103\) | 9.01476 | 0.888250 | 0.444125 | − | 0.895965i | \(-0.353515\pi\) | ||||
0.444125 | + | 0.895965i | \(0.353515\pi\) | |||||||
\(104\) | 1.24369 | 0.121954 | ||||||||
\(105\) | −7.64274 | −0.745855 | ||||||||
\(106\) | −9.38381 | −0.911436 | ||||||||
\(107\) | 5.10024 | 0.493059 | 0.246529 | − | 0.969135i | \(-0.420710\pi\) | ||||
0.246529 | + | 0.969135i | \(0.420710\pi\) | |||||||
\(108\) | 5.62963 | 0.541711 | ||||||||
\(109\) | −4.60448 | −0.441030 | −0.220515 | − | 0.975384i | \(-0.570774\pi\) | ||||
−0.220515 | + | 0.975384i | \(0.570774\pi\) | |||||||
\(110\) | −6.97654 | −0.665187 | ||||||||
\(111\) | 6.16561 | 0.585214 | ||||||||
\(112\) | 1.91777 | 0.181212 | ||||||||
\(113\) | 19.0022 | 1.78758 | 0.893790 | − | 0.448487i | \(-0.148037\pi\) | ||||
0.893790 | + | 0.448487i | \(0.148037\pi\) | |||||||
\(114\) | −8.92883 | −0.836261 | ||||||||
\(115\) | 7.54995 | 0.704036 | ||||||||
\(116\) | −4.11267 | −0.381852 | ||||||||
\(117\) | 1.52007 | 0.140531 | ||||||||
\(118\) | −8.98826 | −0.827436 | ||||||||
\(119\) | 9.11333 | 0.835417 | ||||||||
\(120\) | 3.98523 | 0.363800 | ||||||||
\(121\) | −5.55185 | −0.504713 | ||||||||
\(122\) | −4.47226 | −0.404899 | ||||||||
\(123\) | −3.98388 | −0.359214 | ||||||||
\(124\) | 0.469368 | 0.0421505 | ||||||||
\(125\) | −3.18710 | −0.285063 | ||||||||
\(126\) | 2.34395 | 0.208816 | ||||||||
\(127\) | −17.8145 | −1.58079 | −0.790393 | − | 0.612601i | \(-0.790123\pi\) | ||||
−0.790393 | + | 0.612601i | \(0.790123\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.09857 | −0.272814 | ||||||||
\(130\) | 3.71729 | 0.326028 | ||||||||
\(131\) | −15.2437 | −1.33185 | −0.665923 | − | 0.746020i | \(-0.731962\pi\) | ||||
−0.665923 | + | 0.746020i | \(0.731962\pi\) | |||||||
\(132\) | −3.11216 | −0.270879 | ||||||||
\(133\) | −12.8426 | −1.11359 | ||||||||
\(134\) | −10.1840 | −0.879767 | ||||||||
\(135\) | 16.8266 | 1.44820 | ||||||||
\(136\) | −4.75205 | −0.407485 | ||||||||
\(137\) | −19.6421 | −1.67814 | −0.839068 | − | 0.544026i | \(-0.816899\pi\) | ||||
−0.839068 | + | 0.544026i | \(0.816899\pi\) | |||||||
\(138\) | 3.36795 | 0.286699 | ||||||||
\(139\) | 1.71462 | 0.145432 | 0.0727162 | − | 0.997353i | \(-0.476833\pi\) | ||||
0.0727162 | + | 0.997353i | \(0.476833\pi\) | |||||||
\(140\) | 5.73207 | 0.484448 | ||||||||
\(141\) | −6.64074 | −0.559251 | ||||||||
\(142\) | −8.59830 | −0.721553 | ||||||||
\(143\) | −2.90293 | −0.242755 | ||||||||
\(144\) | −1.22223 | −0.101853 | ||||||||
\(145\) | −12.2925 | −1.02083 | ||||||||
\(146\) | −1.10340 | −0.0913178 | ||||||||
\(147\) | 4.42955 | 0.365343 | ||||||||
\(148\) | −4.62422 | −0.380109 | ||||||||
\(149\) | −17.0292 | −1.39509 | −0.697543 | − | 0.716542i | \(-0.745724\pi\) | ||||
−0.697543 | + | 0.716542i | \(0.745724\pi\) | |||||||
\(150\) | 5.24492 | 0.428246 | ||||||||
\(151\) | 23.9792 | 1.95140 | 0.975698 | − | 0.219118i | \(-0.0703181\pi\) | ||||
0.975698 | + | 0.219118i | \(0.0703181\pi\) | |||||||
\(152\) | 6.69664 | 0.543169 | ||||||||
\(153\) | −5.80811 | −0.469558 | ||||||||
\(154\) | −4.47631 | −0.360711 | ||||||||
\(155\) | 1.40291 | 0.112684 | ||||||||
\(156\) | 1.65825 | 0.132766 | ||||||||
\(157\) | −7.85769 | −0.627112 | −0.313556 | − | 0.949570i | \(-0.601520\pi\) | ||||
−0.313556 | + | 0.949570i | \(0.601520\pi\) | |||||||
\(158\) | 4.62998 | 0.368341 | ||||||||
\(159\) | −12.5117 | −0.992244 | ||||||||
\(160\) | −2.98893 | −0.236296 | ||||||||
\(161\) | 4.84422 | 0.381778 | ||||||||
\(162\) | 3.83946 | 0.301656 | ||||||||
\(163\) | −12.6697 | −0.992367 | −0.496183 | − | 0.868218i | \(-0.665266\pi\) | ||||
−0.496183 | + | 0.868218i | \(0.665266\pi\) | |||||||
\(164\) | 2.98791 | 0.233317 | ||||||||
\(165\) | −9.30203 | −0.724162 | ||||||||
\(166\) | 17.7455 | 1.37732 | ||||||||
\(167\) | 10.8427 | 0.839031 | 0.419515 | − | 0.907748i | \(-0.362200\pi\) | ||||
0.419515 | + | 0.907748i | \(0.362200\pi\) | |||||||
\(168\) | 2.55702 | 0.197278 | ||||||||
\(169\) | −11.4532 | −0.881019 | ||||||||
\(170\) | −14.2036 | −1.08936 | ||||||||
\(171\) | 8.18484 | 0.625910 | ||||||||
\(172\) | 2.32394 | 0.177199 | ||||||||
\(173\) | −15.9526 | −1.21285 | −0.606425 | − | 0.795141i | \(-0.707397\pi\) | ||||
−0.606425 | + | 0.795141i | \(0.707397\pi\) | |||||||
\(174\) | −5.48354 | −0.415706 | ||||||||
\(175\) | 7.54391 | 0.570266 | ||||||||
\(176\) | 2.33413 | 0.175941 | ||||||||
\(177\) | −11.9843 | −0.900796 | ||||||||
\(178\) | −8.16173 | −0.611748 | ||||||||
\(179\) | 19.9609 | 1.49195 | 0.745973 | − | 0.665976i | \(-0.231985\pi\) | ||||
0.745973 | + | 0.665976i | \(0.231985\pi\) | |||||||
\(180\) | −3.65316 | −0.272291 | ||||||||
\(181\) | −14.5803 | −1.08375 | −0.541874 | − | 0.840460i | \(-0.682285\pi\) | ||||
−0.541874 | + | 0.840460i | \(0.682285\pi\) | |||||||
\(182\) | 2.38510 | 0.176796 | ||||||||
\(183\) | −5.96300 | −0.440798 | ||||||||
\(184\) | −2.52597 | −0.186217 | ||||||||
\(185\) | −13.8215 | −1.01617 | ||||||||
\(186\) | 0.625823 | 0.0458875 | ||||||||
\(187\) | 11.0919 | 0.811120 | ||||||||
\(188\) | 4.98057 | 0.363245 | ||||||||
\(189\) | 10.7963 | 0.785316 | ||||||||
\(190\) | 20.0158 | 1.45210 | ||||||||
\(191\) | 17.0309 | 1.23231 | 0.616157 | − | 0.787623i | \(-0.288689\pi\) | ||||
0.616157 | + | 0.787623i | \(0.288689\pi\) | |||||||
\(192\) | −1.33333 | −0.0962248 | ||||||||
\(193\) | 23.7253 | 1.70779 | 0.853893 | − | 0.520448i | \(-0.174235\pi\) | ||||
0.853893 | + | 0.520448i | \(0.174235\pi\) | |||||||
\(194\) | −12.8159 | −0.920125 | ||||||||
\(195\) | 4.95638 | 0.354934 | ||||||||
\(196\) | −3.32217 | −0.237298 | ||||||||
\(197\) | 22.1157 | 1.57568 | 0.787838 | − | 0.615882i | \(-0.211200\pi\) | ||||
0.787838 | + | 0.615882i | \(0.211200\pi\) | |||||||
\(198\) | 2.85284 | 0.202743 | ||||||||
\(199\) | 26.2679 | 1.86208 | 0.931041 | − | 0.364916i | \(-0.118902\pi\) | ||||
0.931041 | + | 0.364916i | \(0.118902\pi\) | |||||||
\(200\) | −3.93370 | −0.278154 | ||||||||
\(201\) | −13.5787 | −0.957766 | ||||||||
\(202\) | −7.41703 | −0.521860 | ||||||||
\(203\) | −7.88713 | −0.553568 | ||||||||
\(204\) | −6.33605 | −0.443613 | ||||||||
\(205\) | 8.93066 | 0.623745 | ||||||||
\(206\) | −9.01476 | −0.628088 | ||||||||
\(207\) | −3.08732 | −0.214584 | ||||||||
\(208\) | −1.24369 | −0.0862342 | ||||||||
\(209\) | −15.6308 | −1.08121 | ||||||||
\(210\) | 7.64274 | 0.527399 | ||||||||
\(211\) | 21.1043 | 1.45288 | 0.726439 | − | 0.687230i | \(-0.241174\pi\) | ||||
0.726439 | + | 0.687230i | \(0.241174\pi\) | |||||||
\(212\) | 9.38381 | 0.644483 | ||||||||
\(213\) | −11.4644 | −0.785525 | ||||||||
\(214\) | −5.10024 | −0.348645 | ||||||||
\(215\) | 6.94608 | 0.473719 | ||||||||
\(216\) | −5.62963 | −0.383048 | ||||||||
\(217\) | 0.900138 | 0.0611054 | ||||||||
\(218\) | 4.60448 | 0.311855 | ||||||||
\(219\) | −1.47119 | −0.0994140 | ||||||||
\(220\) | 6.97654 | 0.470358 | ||||||||
\(221\) | −5.91007 | −0.397554 | ||||||||
\(222\) | −6.16561 | −0.413809 | ||||||||
\(223\) | 12.5620 | 0.841213 | 0.420607 | − | 0.907243i | \(-0.361817\pi\) | ||||
0.420607 | + | 0.907243i | \(0.361817\pi\) | |||||||
\(224\) | −1.91777 | −0.128136 | ||||||||
\(225\) | −4.80789 | −0.320526 | ||||||||
\(226\) | −19.0022 | −1.26401 | ||||||||
\(227\) | −0.728356 | −0.0483427 | −0.0241713 | − | 0.999708i | \(-0.507695\pi\) | ||||
−0.0241713 | + | 0.999708i | \(0.507695\pi\) | |||||||
\(228\) | 8.92883 | 0.591326 | ||||||||
\(229\) | 3.37043 | 0.222724 | 0.111362 | − | 0.993780i | \(-0.464479\pi\) | ||||
0.111362 | + | 0.993780i | \(0.464479\pi\) | |||||||
\(230\) | −7.54995 | −0.497829 | ||||||||
\(231\) | −5.96840 | −0.392692 | ||||||||
\(232\) | 4.11267 | 0.270010 | ||||||||
\(233\) | −4.65253 | −0.304797 | −0.152399 | − | 0.988319i | \(-0.548700\pi\) | ||||
−0.152399 | + | 0.988319i | \(0.548700\pi\) | |||||||
\(234\) | −1.52007 | −0.0993703 | ||||||||
\(235\) | 14.8866 | 0.971093 | ||||||||
\(236\) | 8.98826 | 0.585086 | ||||||||
\(237\) | 6.17329 | 0.400998 | ||||||||
\(238\) | −9.11333 | −0.590729 | ||||||||
\(239\) | −11.4546 | −0.740935 | −0.370467 | − | 0.928845i | \(-0.620802\pi\) | ||||
−0.370467 | + | 0.928845i | \(0.620802\pi\) | |||||||
\(240\) | −3.98523 | −0.257245 | ||||||||
\(241\) | −18.7577 | −1.20829 | −0.604145 | − | 0.796874i | \(-0.706485\pi\) | ||||
−0.604145 | + | 0.796874i | \(0.706485\pi\) | |||||||
\(242\) | 5.55185 | 0.356886 | ||||||||
\(243\) | −11.7696 | −0.755021 | ||||||||
\(244\) | 4.47226 | 0.286307 | ||||||||
\(245\) | −9.92974 | −0.634388 | ||||||||
\(246\) | 3.98388 | 0.254003 | ||||||||
\(247\) | 8.32852 | 0.529931 | ||||||||
\(248\) | −0.469368 | −0.0298049 | ||||||||
\(249\) | 23.6606 | 1.49943 | ||||||||
\(250\) | 3.18710 | 0.201570 | ||||||||
\(251\) | 15.4862 | 0.977480 | 0.488740 | − | 0.872429i | \(-0.337457\pi\) | ||||
0.488740 | + | 0.872429i | \(0.337457\pi\) | |||||||
\(252\) | −2.34395 | −0.147655 | ||||||||
\(253\) | 5.89594 | 0.370674 | ||||||||
\(254\) | 17.8145 | 1.11778 | ||||||||
\(255\) | −18.9380 | −1.18594 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.0194 | −1.24878 | −0.624389 | − | 0.781114i | \(-0.714652\pi\) | ||||
−0.624389 | + | 0.781114i | \(0.714652\pi\) | |||||||
\(258\) | 3.09857 | 0.192909 | ||||||||
\(259\) | −8.86818 | −0.551042 | ||||||||
\(260\) | −3.71729 | −0.230537 | ||||||||
\(261\) | 5.02663 | 0.311141 | ||||||||
\(262\) | 15.2437 | 0.941758 | ||||||||
\(263\) | −17.1130 | −1.05523 | −0.527617 | − | 0.849483i | \(-0.676914\pi\) | ||||
−0.527617 | + | 0.849483i | \(0.676914\pi\) | |||||||
\(264\) | 3.11216 | 0.191540 | ||||||||
\(265\) | 28.0475 | 1.72295 | ||||||||
\(266\) | 12.8426 | 0.787429 | ||||||||
\(267\) | −10.8823 | −0.665985 | ||||||||
\(268\) | 10.1840 | 0.622089 | ||||||||
\(269\) | −2.57418 | −0.156950 | −0.0784752 | − | 0.996916i | \(-0.525005\pi\) | ||||
−0.0784752 | + | 0.996916i | \(0.525005\pi\) | |||||||
\(270\) | −16.8266 | −1.02403 | ||||||||
\(271\) | −1.71085 | −0.103926 | −0.0519632 | − | 0.998649i | \(-0.516548\pi\) | ||||
−0.0519632 | + | 0.998649i | \(0.516548\pi\) | |||||||
\(272\) | 4.75205 | 0.288136 | ||||||||
\(273\) | 3.18013 | 0.192470 | ||||||||
\(274\) | 19.6421 | 1.18662 | ||||||||
\(275\) | 9.18175 | 0.553680 | ||||||||
\(276\) | −3.36795 | −0.202727 | ||||||||
\(277\) | 20.8412 | 1.25222 | 0.626112 | − | 0.779733i | \(-0.284645\pi\) | ||||
0.626112 | + | 0.779733i | \(0.284645\pi\) | |||||||
\(278\) | −1.71462 | −0.102836 | ||||||||
\(279\) | −0.573677 | −0.0343451 | ||||||||
\(280\) | −5.73207 | −0.342557 | ||||||||
\(281\) | 12.3990 | 0.739665 | 0.369832 | − | 0.929098i | \(-0.379415\pi\) | ||||
0.369832 | + | 0.929098i | \(0.379415\pi\) | |||||||
\(282\) | 6.64074 | 0.395451 | ||||||||
\(283\) | −13.2924 | −0.790151 | −0.395076 | − | 0.918649i | \(-0.629282\pi\) | ||||
−0.395076 | + | 0.918649i | \(0.629282\pi\) | |||||||
\(284\) | 8.59830 | 0.510215 | ||||||||
\(285\) | 26.6876 | 1.58084 | ||||||||
\(286\) | 2.90293 | 0.171654 | ||||||||
\(287\) | 5.73012 | 0.338238 | ||||||||
\(288\) | 1.22223 | 0.0720207 | ||||||||
\(289\) | 5.58201 | 0.328354 | ||||||||
\(290\) | 12.2925 | 0.721839 | ||||||||
\(291\) | −17.0878 | −1.00170 | ||||||||
\(292\) | 1.10340 | 0.0645714 | ||||||||
\(293\) | −11.6140 | −0.678498 | −0.339249 | − | 0.940697i | \(-0.610173\pi\) | ||||
−0.339249 | + | 0.940697i | \(0.610173\pi\) | |||||||
\(294\) | −4.42955 | −0.258337 | ||||||||
\(295\) | 26.8653 | 1.56416 | ||||||||
\(296\) | 4.62422 | 0.268777 | ||||||||
\(297\) | 13.1403 | 0.762476 | ||||||||
\(298\) | 17.0292 | 0.986475 | ||||||||
\(299\) | −3.14152 | −0.181679 | ||||||||
\(300\) | −5.24492 | −0.302815 | ||||||||
\(301\) | 4.45677 | 0.256884 | ||||||||
\(302\) | −23.9792 | −1.37985 | ||||||||
\(303\) | −9.88934 | −0.568128 | ||||||||
\(304\) | −6.69664 | −0.384078 | ||||||||
\(305\) | 13.3673 | 0.765408 | ||||||||
\(306\) | 5.80811 | 0.332027 | ||||||||
\(307\) | 16.2335 | 0.926495 | 0.463247 | − | 0.886229i | \(-0.346684\pi\) | ||||
0.463247 | + | 0.886229i | \(0.346684\pi\) | |||||||
\(308\) | 4.47631 | 0.255061 | ||||||||
\(309\) | −12.0196 | −0.683774 | ||||||||
\(310\) | −1.40291 | −0.0796798 | ||||||||
\(311\) | 26.0622 | 1.47785 | 0.738925 | − | 0.673788i | \(-0.235334\pi\) | ||||
0.738925 | + | 0.673788i | \(0.235334\pi\) | |||||||
\(312\) | −1.65825 | −0.0938797 | ||||||||
\(313\) | 5.14258 | 0.290676 | 0.145338 | − | 0.989382i | \(-0.453573\pi\) | ||||
0.145338 | + | 0.989382i | \(0.453573\pi\) | |||||||
\(314\) | 7.85769 | 0.443435 | ||||||||
\(315\) | −7.00591 | −0.394738 | ||||||||
\(316\) | −4.62998 | −0.260457 | ||||||||
\(317\) | 9.06819 | 0.509321 | 0.254660 | − | 0.967031i | \(-0.418036\pi\) | ||||
0.254660 | + | 0.967031i | \(0.418036\pi\) | |||||||
\(318\) | 12.5117 | 0.701622 | ||||||||
\(319\) | −9.59949 | −0.537468 | ||||||||
\(320\) | 2.98893 | 0.167086 | ||||||||
\(321\) | −6.80030 | −0.379556 | ||||||||
\(322\) | −4.84422 | −0.269958 | ||||||||
\(323\) | −31.8228 | −1.77067 | ||||||||
\(324\) | −3.83946 | −0.213303 | ||||||||
\(325\) | −4.89229 | −0.271375 | ||||||||
\(326\) | 12.6697 | 0.701709 | ||||||||
\(327\) | 6.13930 | 0.339504 | ||||||||
\(328\) | −2.98791 | −0.164980 | ||||||||
\(329\) | 9.55157 | 0.526595 | ||||||||
\(330\) | 9.30203 | 0.512060 | ||||||||
\(331\) | 17.7206 | 0.974013 | 0.487006 | − | 0.873398i | \(-0.338089\pi\) | ||||
0.487006 | + | 0.873398i | \(0.338089\pi\) | |||||||
\(332\) | −17.7455 | −0.973912 | ||||||||
\(333\) | 5.65187 | 0.309720 | ||||||||
\(334\) | −10.8427 | −0.593284 | ||||||||
\(335\) | 30.4394 | 1.66308 | ||||||||
\(336\) | −2.55702 | −0.139497 | ||||||||
\(337\) | −1.10289 | −0.0600782 | −0.0300391 | − | 0.999549i | \(-0.509563\pi\) | ||||
−0.0300391 | + | 0.999549i | \(0.509563\pi\) | |||||||
\(338\) | 11.4532 | 0.622974 | ||||||||
\(339\) | −25.3362 | −1.37608 | ||||||||
\(340\) | 14.2036 | 0.770296 | ||||||||
\(341\) | 1.09557 | 0.0593282 | ||||||||
\(342\) | −8.18484 | −0.442585 | ||||||||
\(343\) | −19.7955 | −1.06886 | ||||||||
\(344\) | −2.32394 | −0.125298 | ||||||||
\(345\) | −10.0666 | −0.541966 | ||||||||
\(346\) | 15.9526 | 0.857615 | ||||||||
\(347\) | 18.1744 | 0.975654 | 0.487827 | − | 0.872940i | \(-0.337790\pi\) | ||||
0.487827 | + | 0.872940i | \(0.337790\pi\) | |||||||
\(348\) | 5.48354 | 0.293949 | ||||||||
\(349\) | 18.0704 | 0.967288 | 0.483644 | − | 0.875265i | \(-0.339313\pi\) | ||||
0.483644 | + | 0.875265i | \(0.339313\pi\) | |||||||
\(350\) | −7.54391 | −0.403239 | ||||||||
\(351\) | −7.00150 | −0.373712 | ||||||||
\(352\) | −2.33413 | −0.124409 | ||||||||
\(353\) | −16.6377 | −0.885536 | −0.442768 | − | 0.896636i | \(-0.646003\pi\) | ||||
−0.442768 | + | 0.896636i | \(0.646003\pi\) | |||||||
\(354\) | 11.9843 | 0.636959 | ||||||||
\(355\) | 25.6997 | 1.36400 | ||||||||
\(356\) | 8.16173 | 0.432571 | ||||||||
\(357\) | −12.1511 | −0.643103 | ||||||||
\(358\) | −19.9609 | −1.05496 | ||||||||
\(359\) | 20.5853 | 1.08645 | 0.543226 | − | 0.839586i | \(-0.317203\pi\) | ||||
0.543226 | + | 0.839586i | \(0.317203\pi\) | |||||||
\(360\) | 3.65316 | 0.192539 | ||||||||
\(361\) | 25.8449 | 1.36026 | ||||||||
\(362\) | 14.5803 | 0.766326 | ||||||||
\(363\) | 7.40245 | 0.388528 | ||||||||
\(364\) | −2.38510 | −0.125013 | ||||||||
\(365\) | 3.29798 | 0.172624 | ||||||||
\(366\) | 5.96300 | 0.311691 | ||||||||
\(367\) | 5.46990 | 0.285526 | 0.142763 | − | 0.989757i | \(-0.454401\pi\) | ||||
0.142763 | + | 0.989757i | \(0.454401\pi\) | |||||||
\(368\) | 2.52597 | 0.131675 | ||||||||
\(369\) | −3.65192 | −0.190111 | ||||||||
\(370\) | 13.8215 | 0.718544 | ||||||||
\(371\) | 17.9960 | 0.934304 | ||||||||
\(372\) | −0.625823 | −0.0324474 | ||||||||
\(373\) | −33.7563 | −1.74784 | −0.873918 | − | 0.486073i | \(-0.838429\pi\) | ||||
−0.873918 | + | 0.486073i | \(0.838429\pi\) | |||||||
\(374\) | −11.0919 | −0.573548 | ||||||||
\(375\) | 4.24946 | 0.219441 | ||||||||
\(376\) | −4.98057 | −0.256853 | ||||||||
\(377\) | 5.11487 | 0.263429 | ||||||||
\(378\) | −10.7963 | −0.555302 | ||||||||
\(379\) | 15.1793 | 0.779707 | 0.389854 | − | 0.920877i | \(-0.372526\pi\) | ||||
0.389854 | + | 0.920877i | \(0.372526\pi\) | |||||||
\(380\) | −20.0158 | −1.02679 | ||||||||
\(381\) | 23.7527 | 1.21689 | ||||||||
\(382\) | −17.0309 | −0.871378 | ||||||||
\(383\) | 17.7641 | 0.907705 | 0.453852 | − | 0.891077i | \(-0.350049\pi\) | ||||
0.453852 | + | 0.891077i | \(0.350049\pi\) | |||||||
\(384\) | 1.33333 | 0.0680412 | ||||||||
\(385\) | 13.3794 | 0.681876 | ||||||||
\(386\) | −23.7253 | −1.20759 | ||||||||
\(387\) | −2.84039 | −0.144385 | ||||||||
\(388\) | 12.8159 | 0.650627 | ||||||||
\(389\) | 15.3930 | 0.780456 | 0.390228 | − | 0.920718i | \(-0.372396\pi\) | ||||
0.390228 | + | 0.920718i | \(0.372396\pi\) | |||||||
\(390\) | −4.95638 | −0.250976 | ||||||||
\(391\) | 12.0035 | 0.607045 | ||||||||
\(392\) | 3.32217 | 0.167795 | ||||||||
\(393\) | 20.3249 | 1.02525 | ||||||||
\(394\) | −22.1157 | −1.11417 | ||||||||
\(395\) | −13.8387 | −0.696299 | ||||||||
\(396\) | −2.85284 | −0.143361 | ||||||||
\(397\) | 26.4279 | 1.32638 | 0.663189 | − | 0.748452i | \(-0.269202\pi\) | ||||
0.663189 | + | 0.748452i | \(0.269202\pi\) | |||||||
\(398\) | −26.2679 | −1.31669 | ||||||||
\(399\) | 17.1234 | 0.857242 | ||||||||
\(400\) | 3.93370 | 0.196685 | ||||||||
\(401\) | −3.16838 | −0.158221 | −0.0791106 | − | 0.996866i | \(-0.525208\pi\) | ||||
−0.0791106 | + | 0.996866i | \(0.525208\pi\) | |||||||
\(402\) | 13.5787 | 0.677243 | ||||||||
\(403\) | −0.583747 | −0.0290785 | ||||||||
\(404\) | 7.41703 | 0.369011 | ||||||||
\(405\) | −11.4759 | −0.570240 | ||||||||
\(406\) | 7.88713 | 0.391432 | ||||||||
\(407\) | −10.7935 | −0.535015 | ||||||||
\(408\) | 6.33605 | 0.313681 | ||||||||
\(409\) | −35.3341 | −1.74716 | −0.873579 | − | 0.486682i | \(-0.838207\pi\) | ||||
−0.873579 | + | 0.486682i | \(0.838207\pi\) | |||||||
\(410\) | −8.93066 | −0.441054 | ||||||||
\(411\) | 26.1894 | 1.29183 | ||||||||
\(412\) | 9.01476 | 0.444125 | ||||||||
\(413\) | 17.2374 | 0.848196 | ||||||||
\(414\) | 3.08732 | 0.151734 | ||||||||
\(415\) | −53.0401 | −2.60364 | ||||||||
\(416\) | 1.24369 | 0.0609768 | ||||||||
\(417\) | −2.28616 | −0.111954 | ||||||||
\(418\) | 15.6308 | 0.764528 | ||||||||
\(419\) | −2.86936 | −0.140177 | −0.0700887 | − | 0.997541i | \(-0.522328\pi\) | ||||
−0.0700887 | + | 0.997541i | \(0.522328\pi\) | |||||||
\(420\) | −7.64274 | −0.372927 | ||||||||
\(421\) | −4.13528 | −0.201541 | −0.100771 | − | 0.994910i | \(-0.532131\pi\) | ||||
−0.100771 | + | 0.994910i | \(0.532131\pi\) | |||||||
\(422\) | −21.1043 | −1.02734 | ||||||||
\(423\) | −6.08741 | −0.295980 | ||||||||
\(424\) | −9.38381 | −0.455718 | ||||||||
\(425\) | 18.6931 | 0.906750 | ||||||||
\(426\) | 11.4644 | 0.555450 | ||||||||
\(427\) | 8.57675 | 0.415058 | ||||||||
\(428\) | 5.10024 | 0.246529 | ||||||||
\(429\) | 3.87056 | 0.186872 | ||||||||
\(430\) | −6.94608 | −0.334970 | ||||||||
\(431\) | −13.1289 | −0.632398 | −0.316199 | − | 0.948693i | \(-0.602407\pi\) | ||||
−0.316199 | + | 0.948693i | \(0.602407\pi\) | |||||||
\(432\) | 5.62963 | 0.270856 | ||||||||
\(433\) | 22.7745 | 1.09447 | 0.547236 | − | 0.836978i | \(-0.315680\pi\) | ||||
0.547236 | + | 0.836978i | \(0.315680\pi\) | |||||||
\(434\) | −0.900138 | −0.0432080 | ||||||||
\(435\) | 16.3899 | 0.785836 | ||||||||
\(436\) | −4.60448 | −0.220515 | ||||||||
\(437\) | −16.9155 | −0.809178 | ||||||||
\(438\) | 1.47119 | 0.0702963 | ||||||||
\(439\) | 33.3151 | 1.59004 | 0.795021 | − | 0.606583i | \(-0.207460\pi\) | ||||
0.795021 | + | 0.606583i | \(0.207460\pi\) | |||||||
\(440\) | −6.97654 | −0.332594 | ||||||||
\(441\) | 4.06046 | 0.193355 | ||||||||
\(442\) | 5.91007 | 0.281113 | ||||||||
\(443\) | −30.4373 | −1.44612 | −0.723059 | − | 0.690786i | \(-0.757265\pi\) | ||||
−0.723059 | + | 0.690786i | \(0.757265\pi\) | |||||||
\(444\) | 6.16561 | 0.292607 | ||||||||
\(445\) | 24.3948 | 1.15643 | ||||||||
\(446\) | −12.5620 | −0.594828 | ||||||||
\(447\) | 22.7055 | 1.07394 | ||||||||
\(448\) | 1.91777 | 0.0906059 | ||||||||
\(449\) | 6.34738 | 0.299551 | 0.149776 | − | 0.988720i | \(-0.452145\pi\) | ||||
0.149776 | + | 0.988720i | \(0.452145\pi\) | |||||||
\(450\) | 4.80789 | 0.226646 | ||||||||
\(451\) | 6.97417 | 0.328401 | ||||||||
\(452\) | 19.0022 | 0.893790 | ||||||||
\(453\) | −31.9721 | −1.50218 | ||||||||
\(454\) | 0.728356 | 0.0341834 | ||||||||
\(455\) | −7.12890 | −0.334208 | ||||||||
\(456\) | −8.92883 | −0.418131 | ||||||||
\(457\) | −1.55505 | −0.0727423 | −0.0363711 | − | 0.999338i | \(-0.511580\pi\) | ||||
−0.0363711 | + | 0.999338i | \(0.511580\pi\) | |||||||
\(458\) | −3.37043 | −0.157490 | ||||||||
\(459\) | 26.7523 | 1.24869 | ||||||||
\(460\) | 7.54995 | 0.352018 | ||||||||
\(461\) | 30.9703 | 1.44243 | 0.721215 | − | 0.692712i | \(-0.243584\pi\) | ||||
0.721215 | + | 0.692712i | \(0.243584\pi\) | |||||||
\(462\) | 5.96840 | 0.277675 | ||||||||
\(463\) | 28.2842 | 1.31448 | 0.657239 | − | 0.753682i | \(-0.271724\pi\) | ||||
0.657239 | + | 0.753682i | \(0.271724\pi\) | |||||||
\(464\) | −4.11267 | −0.190926 | ||||||||
\(465\) | −1.87054 | −0.0867442 | ||||||||
\(466\) | 4.65253 | 0.215524 | ||||||||
\(467\) | 14.0223 | 0.648873 | 0.324436 | − | 0.945908i | \(-0.394825\pi\) | ||||
0.324436 | + | 0.945908i | \(0.394825\pi\) | |||||||
\(468\) | 1.52007 | 0.0702654 | ||||||||
\(469\) | 19.5306 | 0.901839 | ||||||||
\(470\) | −14.8866 | −0.686666 | ||||||||
\(471\) | 10.4769 | 0.482750 | ||||||||
\(472\) | −8.98826 | −0.413718 | ||||||||
\(473\) | 5.42437 | 0.249413 | ||||||||
\(474\) | −6.17329 | −0.283549 | ||||||||
\(475\) | −26.3425 | −1.20868 | ||||||||
\(476\) | 9.11333 | 0.417709 | ||||||||
\(477\) | −11.4692 | −0.525138 | ||||||||
\(478\) | 11.4546 | 0.523920 | ||||||||
\(479\) | 1.21117 | 0.0553400 | 0.0276700 | − | 0.999617i | \(-0.491191\pi\) | ||||
0.0276700 | + | 0.999617i | \(0.491191\pi\) | |||||||
\(480\) | 3.98523 | 0.181900 | ||||||||
\(481\) | 5.75109 | 0.262227 | ||||||||
\(482\) | 18.7577 | 0.854390 | ||||||||
\(483\) | −6.45894 | −0.293892 | ||||||||
\(484\) | −5.55185 | −0.252357 | ||||||||
\(485\) | 38.3057 | 1.73937 | ||||||||
\(486\) | 11.7696 | 0.533881 | ||||||||
\(487\) | 4.85559 | 0.220028 | 0.110014 | − | 0.993930i | \(-0.464910\pi\) | ||||
0.110014 | + | 0.993930i | \(0.464910\pi\) | |||||||
\(488\) | −4.47226 | −0.202450 | ||||||||
\(489\) | 16.8929 | 0.763922 | ||||||||
\(490\) | 9.92974 | 0.448580 | ||||||||
\(491\) | −2.42603 | −0.109485 | −0.0547425 | − | 0.998501i | \(-0.517434\pi\) | ||||
−0.0547425 | + | 0.998501i | \(0.517434\pi\) | |||||||
\(492\) | −3.98388 | −0.179607 | ||||||||
\(493\) | −19.5436 | −0.880200 | ||||||||
\(494\) | −8.32852 | −0.374718 | ||||||||
\(495\) | −8.52695 | −0.383258 | ||||||||
\(496\) | 0.469368 | 0.0210753 | ||||||||
\(497\) | 16.4895 | 0.739656 | ||||||||
\(498\) | −23.6606 | −1.06026 | ||||||||
\(499\) | −8.45826 | −0.378644 | −0.189322 | − | 0.981915i | \(-0.560629\pi\) | ||||
−0.189322 | + | 0.981915i | \(0.560629\pi\) | |||||||
\(500\) | −3.18710 | −0.142532 | ||||||||
\(501\) | −14.4569 | −0.645885 | ||||||||
\(502\) | −15.4862 | −0.691183 | ||||||||
\(503\) | −15.1942 | −0.677476 | −0.338738 | − | 0.940881i | \(-0.610000\pi\) | ||||
−0.338738 | + | 0.940881i | \(0.610000\pi\) | |||||||
\(504\) | 2.34395 | 0.104408 | ||||||||
\(505\) | 22.1690 | 0.986506 | ||||||||
\(506\) | −5.89594 | −0.262106 | ||||||||
\(507\) | 15.2709 | 0.678207 | ||||||||
\(508\) | −17.8145 | −0.790393 | ||||||||
\(509\) | −36.3495 | −1.61116 | −0.805582 | − | 0.592485i | \(-0.798147\pi\) | ||||
−0.805582 | + | 0.592485i | \(0.798147\pi\) | |||||||
\(510\) | 18.9380 | 0.838590 | ||||||||
\(511\) | 2.11606 | 0.0936089 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −37.6996 | −1.66448 | ||||||||
\(514\) | 20.0194 | 0.883019 | ||||||||
\(515\) | 26.9445 | 1.18732 | ||||||||
\(516\) | −3.09857 | −0.136407 | ||||||||
\(517\) | 11.6253 | 0.511280 | ||||||||
\(518\) | 8.86818 | 0.389645 | ||||||||
\(519\) | 21.2700 | 0.933650 | ||||||||
\(520\) | 3.71729 | 0.163014 | ||||||||
\(521\) | 10.5858 | 0.463773 | 0.231887 | − | 0.972743i | \(-0.425510\pi\) | ||||
0.231887 | + | 0.972743i | \(0.425510\pi\) | |||||||
\(522\) | −5.02663 | −0.220010 | ||||||||
\(523\) | −1.45737 | −0.0637263 | −0.0318631 | − | 0.999492i | \(-0.510144\pi\) | ||||
−0.0318631 | + | 0.999492i | \(0.510144\pi\) | |||||||
\(524\) | −15.2437 | −0.665923 | ||||||||
\(525\) | −10.0585 | −0.438990 | ||||||||
\(526\) | 17.1130 | 0.746163 | ||||||||
\(527\) | 2.23046 | 0.0971605 | ||||||||
\(528\) | −3.11216 | −0.135439 | ||||||||
\(529\) | −16.6195 | −0.722586 | ||||||||
\(530\) | −28.0475 | −1.21831 | ||||||||
\(531\) | −10.9857 | −0.476740 | ||||||||
\(532\) | −12.8426 | −0.556797 | ||||||||
\(533\) | −3.71603 | −0.160959 | ||||||||
\(534\) | 10.8823 | 0.470922 | ||||||||
\(535\) | 15.2443 | 0.659067 | ||||||||
\(536\) | −10.1840 | −0.439883 | ||||||||
\(537\) | −26.6144 | −1.14850 | ||||||||
\(538\) | 2.57418 | 0.110981 | ||||||||
\(539\) | −7.75438 | −0.334005 | ||||||||
\(540\) | 16.8266 | 0.724100 | ||||||||
\(541\) | −28.1078 | −1.20845 | −0.604225 | − | 0.796814i | \(-0.706517\pi\) | ||||
−0.604225 | + | 0.796814i | \(0.706517\pi\) | |||||||
\(542\) | 1.71085 | 0.0734871 | ||||||||
\(543\) | 19.4404 | 0.834267 | ||||||||
\(544\) | −4.75205 | −0.203743 | ||||||||
\(545\) | −13.7625 | −0.589520 | ||||||||
\(546\) | −3.18013 | −0.136097 | ||||||||
\(547\) | −32.4409 | −1.38707 | −0.693536 | − | 0.720422i | \(-0.743948\pi\) | ||||
−0.693536 | + | 0.720422i | \(0.743948\pi\) | |||||||
\(548\) | −19.6421 | −0.839068 | ||||||||
\(549\) | −5.46614 | −0.233289 | ||||||||
\(550\) | −9.18175 | −0.391511 | ||||||||
\(551\) | 27.5410 | 1.17329 | ||||||||
\(552\) | 3.36795 | 0.143350 | ||||||||
\(553\) | −8.87922 | −0.377583 | ||||||||
\(554\) | −20.8412 | −0.885456 | ||||||||
\(555\) | 18.4286 | 0.782250 | ||||||||
\(556\) | 1.71462 | 0.0727162 | ||||||||
\(557\) | −39.2749 | −1.66413 | −0.832066 | − | 0.554677i | \(-0.812842\pi\) | ||||
−0.832066 | + | 0.554677i | \(0.812842\pi\) | |||||||
\(558\) | 0.573677 | 0.0242857 | ||||||||
\(559\) | −2.89025 | −0.122245 | ||||||||
\(560\) | 5.73207 | 0.242224 | ||||||||
\(561\) | −14.7892 | −0.624399 | ||||||||
\(562\) | −12.3990 | −0.523022 | ||||||||
\(563\) | 46.3256 | 1.95239 | 0.976195 | − | 0.216896i | \(-0.0695931\pi\) | ||||
0.976195 | + | 0.216896i | \(0.0695931\pi\) | |||||||
\(564\) | −6.64074 | −0.279626 | ||||||||
\(565\) | 56.7963 | 2.38944 | ||||||||
\(566\) | 13.2924 | 0.558721 | ||||||||
\(567\) | −7.36318 | −0.309224 | ||||||||
\(568\) | −8.59830 | −0.360777 | ||||||||
\(569\) | −1.90580 | −0.0798952 | −0.0399476 | − | 0.999202i | \(-0.512719\pi\) | ||||
−0.0399476 | + | 0.999202i | \(0.512719\pi\) | |||||||
\(570\) | −26.6876 | −1.11782 | ||||||||
\(571\) | 26.0415 | 1.08980 | 0.544901 | − | 0.838500i | \(-0.316567\pi\) | ||||
0.544901 | + | 0.838500i | \(0.316567\pi\) | |||||||
\(572\) | −2.90293 | −0.121377 | ||||||||
\(573\) | −22.7078 | −0.948634 | ||||||||
\(574\) | −5.73012 | −0.239171 | ||||||||
\(575\) | 9.93640 | 0.414377 | ||||||||
\(576\) | −1.22223 | −0.0509263 | ||||||||
\(577\) | −10.5560 | −0.439451 | −0.219725 | − | 0.975562i | \(-0.570516\pi\) | ||||
−0.219725 | + | 0.975562i | \(0.570516\pi\) | |||||||
\(578\) | −5.58201 | −0.232181 | ||||||||
\(579\) | −31.6337 | −1.31465 | ||||||||
\(580\) | −12.2925 | −0.510417 | ||||||||
\(581\) | −34.0318 | −1.41188 | ||||||||
\(582\) | 17.0878 | 0.708311 | ||||||||
\(583\) | 21.9030 | 0.907130 | ||||||||
\(584\) | −1.10340 | −0.0456589 | ||||||||
\(585\) | 4.54339 | 0.187846 | ||||||||
\(586\) | 11.6140 | 0.479771 | ||||||||
\(587\) | −31.2569 | −1.29011 | −0.645054 | − | 0.764137i | \(-0.723165\pi\) | ||||
−0.645054 | + | 0.764137i | \(0.723165\pi\) | |||||||
\(588\) | 4.42955 | 0.182672 | ||||||||
\(589\) | −3.14319 | −0.129513 | ||||||||
\(590\) | −26.8653 | −1.10603 | ||||||||
\(591\) | −29.4875 | −1.21295 | ||||||||
\(592\) | −4.62422 | −0.190054 | ||||||||
\(593\) | −4.17751 | −0.171550 | −0.0857748 | − | 0.996315i | \(-0.527337\pi\) | ||||
−0.0857748 | + | 0.996315i | \(0.527337\pi\) | |||||||
\(594\) | −13.1403 | −0.539152 | ||||||||
\(595\) | 27.2391 | 1.11669 | ||||||||
\(596\) | −17.0292 | −0.697543 | ||||||||
\(597\) | −35.0238 | −1.43343 | ||||||||
\(598\) | 3.14152 | 0.128466 | ||||||||
\(599\) | 16.8143 | 0.687015 | 0.343507 | − | 0.939150i | \(-0.388385\pi\) | ||||
0.343507 | + | 0.939150i | \(0.388385\pi\) | |||||||
\(600\) | 5.24492 | 0.214123 | ||||||||
\(601\) | 31.8830 | 1.30053 | 0.650267 | − | 0.759706i | \(-0.274657\pi\) | ||||
0.650267 | + | 0.759706i | \(0.274657\pi\) | |||||||
\(602\) | −4.45677 | −0.181644 | ||||||||
\(603\) | −12.4472 | −0.506891 | ||||||||
\(604\) | 23.9792 | 0.975698 | ||||||||
\(605\) | −16.5941 | −0.674645 | ||||||||
\(606\) | 9.88934 | 0.401727 | ||||||||
\(607\) | −32.0830 | −1.30221 | −0.651105 | − | 0.758988i | \(-0.725694\pi\) | ||||
−0.651105 | + | 0.758988i | \(0.725694\pi\) | |||||||
\(608\) | 6.69664 | 0.271584 | ||||||||
\(609\) | 10.5162 | 0.426136 | ||||||||
\(610\) | −13.3673 | −0.541225 | ||||||||
\(611\) | −6.19427 | −0.250593 | ||||||||
\(612\) | −5.80811 | −0.234779 | ||||||||
\(613\) | 26.5795 | 1.07354 | 0.536769 | − | 0.843729i | \(-0.319645\pi\) | ||||
0.536769 | + | 0.843729i | \(0.319645\pi\) | |||||||
\(614\) | −16.2335 | −0.655131 | ||||||||
\(615\) | −11.9075 | −0.480158 | ||||||||
\(616\) | −4.47631 | −0.180356 | ||||||||
\(617\) | −15.9268 | −0.641191 | −0.320595 | − | 0.947216i | \(-0.603883\pi\) | ||||
−0.320595 | + | 0.947216i | \(0.603883\pi\) | |||||||
\(618\) | 12.0196 | 0.483501 | ||||||||
\(619\) | −18.3398 | −0.737138 | −0.368569 | − | 0.929600i | \(-0.620152\pi\) | ||||
−0.368569 | + | 0.929600i | \(0.620152\pi\) | |||||||
\(620\) | 1.40291 | 0.0563422 | ||||||||
\(621\) | 14.2203 | 0.570640 | ||||||||
\(622\) | −26.0622 | −1.04500 | ||||||||
\(623\) | 15.6523 | 0.627096 | ||||||||
\(624\) | 1.65825 | 0.0663830 | ||||||||
\(625\) | −29.1945 | −1.16778 | ||||||||
\(626\) | −5.14258 | −0.205539 | ||||||||
\(627\) | 20.8410 | 0.832310 | ||||||||
\(628\) | −7.85769 | −0.313556 | ||||||||
\(629\) | −21.9745 | −0.876183 | ||||||||
\(630\) | 7.00591 | 0.279122 | ||||||||
\(631\) | −42.4574 | −1.69020 | −0.845102 | − | 0.534605i | \(-0.820460\pi\) | ||||
−0.845102 | + | 0.534605i | \(0.820460\pi\) | |||||||
\(632\) | 4.62998 | 0.184171 | ||||||||
\(633\) | −28.1390 | −1.11842 | ||||||||
\(634\) | −9.06819 | −0.360144 | ||||||||
\(635\) | −53.2464 | −2.11302 | ||||||||
\(636\) | −12.5117 | −0.496122 | ||||||||
\(637\) | 4.13174 | 0.163706 | ||||||||
\(638\) | 9.59949 | 0.380047 | ||||||||
\(639\) | −10.5091 | −0.415734 | ||||||||
\(640\) | −2.98893 | −0.118148 | ||||||||
\(641\) | 20.3819 | 0.805035 | 0.402518 | − | 0.915412i | \(-0.368135\pi\) | ||||
0.402518 | + | 0.915412i | \(0.368135\pi\) | |||||||
\(642\) | 6.80030 | 0.268387 | ||||||||
\(643\) | 7.82337 | 0.308524 | 0.154262 | − | 0.988030i | \(-0.450700\pi\) | ||||
0.154262 | + | 0.988030i | \(0.450700\pi\) | |||||||
\(644\) | 4.84422 | 0.190889 | ||||||||
\(645\) | −9.26142 | −0.364668 | ||||||||
\(646\) | 31.8228 | 1.25205 | ||||||||
\(647\) | −14.7223 | −0.578793 | −0.289397 | − | 0.957209i | \(-0.593455\pi\) | ||||
−0.289397 | + | 0.957209i | \(0.593455\pi\) | |||||||
\(648\) | 3.83946 | 0.150828 | ||||||||
\(649\) | 20.9797 | 0.823527 | ||||||||
\(650\) | 4.89229 | 0.191891 | ||||||||
\(651\) | −1.20018 | −0.0470388 | ||||||||
\(652\) | −12.6697 | −0.496183 | ||||||||
\(653\) | −2.22868 | −0.0872151 | −0.0436075 | − | 0.999049i | \(-0.513885\pi\) | ||||
−0.0436075 | + | 0.999049i | \(0.513885\pi\) | |||||||
\(654\) | −6.13930 | −0.240065 | ||||||||
\(655\) | −45.5623 | −1.78027 | ||||||||
\(656\) | 2.98791 | 0.116658 | ||||||||
\(657\) | −1.34861 | −0.0526142 | ||||||||
\(658\) | −9.55157 | −0.372359 | ||||||||
\(659\) | −28.1050 | −1.09481 | −0.547407 | − | 0.836866i | \(-0.684385\pi\) | ||||
−0.547407 | + | 0.836866i | \(0.684385\pi\) | |||||||
\(660\) | −9.30203 | −0.362081 | ||||||||
\(661\) | 37.1058 | 1.44325 | 0.721625 | − | 0.692285i | \(-0.243396\pi\) | ||||
0.721625 | + | 0.692285i | \(0.243396\pi\) | |||||||
\(662\) | −17.7206 | −0.688731 | ||||||||
\(663\) | 7.88007 | 0.306037 | ||||||||
\(664\) | 17.7455 | 0.688660 | ||||||||
\(665\) | −38.3856 | −1.48853 | ||||||||
\(666\) | −5.65187 | −0.219005 | ||||||||
\(667\) | −10.3885 | −0.402243 | ||||||||
\(668\) | 10.8427 | 0.419515 | ||||||||
\(669\) | −16.7493 | −0.647565 | ||||||||
\(670\) | −30.4394 | −1.17598 | ||||||||
\(671\) | 10.4388 | 0.402986 | ||||||||
\(672\) | 2.55702 | 0.0986390 | ||||||||
\(673\) | 39.0990 | 1.50716 | 0.753579 | − | 0.657358i | \(-0.228326\pi\) | ||||
0.753579 | + | 0.657358i | \(0.228326\pi\) | |||||||
\(674\) | 1.10289 | 0.0424817 | ||||||||
\(675\) | 22.1452 | 0.852371 | ||||||||
\(676\) | −11.4532 | −0.440509 | ||||||||
\(677\) | 10.5775 | 0.406526 | 0.203263 | − | 0.979124i | \(-0.434845\pi\) | ||||
0.203263 | + | 0.979124i | \(0.434845\pi\) | |||||||
\(678\) | 25.3362 | 0.973032 | ||||||||
\(679\) | 24.5778 | 0.943210 | ||||||||
\(680\) | −14.2036 | −0.544681 | ||||||||
\(681\) | 0.971139 | 0.0372141 | ||||||||
\(682\) | −1.09557 | −0.0419514 | ||||||||
\(683\) | 15.0524 | 0.575965 | 0.287983 | − | 0.957636i | \(-0.407015\pi\) | ||||
0.287983 | + | 0.957636i | \(0.407015\pi\) | |||||||
\(684\) | 8.18484 | 0.312955 | ||||||||
\(685\) | −58.7088 | −2.24315 | ||||||||
\(686\) | 19.7955 | 0.755796 | ||||||||
\(687\) | −4.49389 | −0.171453 | ||||||||
\(688\) | 2.32394 | 0.0885993 | ||||||||
\(689\) | −11.6705 | −0.444612 | ||||||||
\(690\) | 10.0666 | 0.383228 | ||||||||
\(691\) | 13.8069 | 0.525238 | 0.262619 | − | 0.964900i | \(-0.415414\pi\) | ||||
0.262619 | + | 0.964900i | \(0.415414\pi\) | |||||||
\(692\) | −15.9526 | −0.606425 | ||||||||
\(693\) | −5.47109 | −0.207829 | ||||||||
\(694\) | −18.1744 | −0.689892 | ||||||||
\(695\) | 5.12488 | 0.194398 | ||||||||
\(696\) | −5.48354 | −0.207853 | ||||||||
\(697\) | 14.1987 | 0.537815 | ||||||||
\(698\) | −18.0704 | −0.683976 | ||||||||
\(699\) | 6.20335 | 0.234632 | ||||||||
\(700\) | 7.54391 | 0.285133 | ||||||||
\(701\) | −46.0681 | −1.73997 | −0.869985 | − | 0.493079i | \(-0.835871\pi\) | ||||
−0.869985 | + | 0.493079i | \(0.835871\pi\) | |||||||
\(702\) | 7.00150 | 0.264254 | ||||||||
\(703\) | 30.9667 | 1.16793 | ||||||||
\(704\) | 2.33413 | 0.0879707 | ||||||||
\(705\) | −19.8487 | −0.747546 | ||||||||
\(706\) | 16.6377 | 0.626168 | ||||||||
\(707\) | 14.2241 | 0.534953 | ||||||||
\(708\) | −11.9843 | −0.450398 | ||||||||
\(709\) | 14.0797 | 0.528775 | 0.264387 | − | 0.964417i | \(-0.414830\pi\) | ||||
0.264387 | + | 0.964417i | \(0.414830\pi\) | |||||||
\(710\) | −25.6997 | −0.964493 | ||||||||
\(711\) | 5.65890 | 0.212225 | ||||||||
\(712\) | −8.16173 | −0.305874 | ||||||||
\(713\) | 1.18561 | 0.0444015 | ||||||||
\(714\) | 12.1511 | 0.454742 | ||||||||
\(715\) | −8.67664 | −0.324488 | ||||||||
\(716\) | 19.9609 | 0.745973 | ||||||||
\(717\) | 15.2727 | 0.570370 | ||||||||
\(718\) | −20.5853 | −0.768238 | ||||||||
\(719\) | −43.8233 | −1.63433 | −0.817166 | − | 0.576402i | \(-0.804456\pi\) | ||||
−0.817166 | + | 0.576402i | \(0.804456\pi\) | |||||||
\(720\) | −3.65316 | −0.136145 | ||||||||
\(721\) | 17.2882 | 0.643846 | ||||||||
\(722\) | −25.8449 | −0.961849 | ||||||||
\(723\) | 25.0102 | 0.930140 | ||||||||
\(724\) | −14.5803 | −0.541874 | ||||||||
\(725\) | −16.1780 | −0.600835 | ||||||||
\(726\) | −7.40245 | −0.274731 | ||||||||
\(727\) | 24.3603 | 0.903475 | 0.451737 | − | 0.892151i | \(-0.350804\pi\) | ||||
0.451737 | + | 0.892151i | \(0.350804\pi\) | |||||||
\(728\) | 2.38510 | 0.0883978 | ||||||||
\(729\) | 27.2112 | 1.00782 | ||||||||
\(730\) | −3.29798 | −0.122064 | ||||||||
\(731\) | 11.0435 | 0.408458 | ||||||||
\(732\) | −5.96300 | −0.220399 | ||||||||
\(733\) | −10.7654 | −0.397630 | −0.198815 | − | 0.980037i | \(-0.563709\pi\) | ||||
−0.198815 | + | 0.980037i | \(0.563709\pi\) | |||||||
\(734\) | −5.46990 | −0.201898 | ||||||||
\(735\) | 13.2396 | 0.488351 | ||||||||
\(736\) | −2.52597 | −0.0931085 | ||||||||
\(737\) | 23.7708 | 0.875610 | ||||||||
\(738\) | 3.65192 | 0.134429 | ||||||||
\(739\) | −12.5874 | −0.463034 | −0.231517 | − | 0.972831i | \(-0.574369\pi\) | ||||
−0.231517 | + | 0.972831i | \(0.574369\pi\) | |||||||
\(740\) | −13.8215 | −0.508087 | ||||||||
\(741\) | −11.1047 | −0.407940 | ||||||||
\(742\) | −17.9960 | −0.660652 | ||||||||
\(743\) | −35.8517 | −1.31527 | −0.657636 | − | 0.753335i | \(-0.728444\pi\) | ||||
−0.657636 | + | 0.753335i | \(0.728444\pi\) | |||||||
\(744\) | 0.625823 | 0.0229438 | ||||||||
\(745\) | −50.8991 | −1.86480 | ||||||||
\(746\) | 33.7563 | 1.23591 | ||||||||
\(747\) | 21.6891 | 0.793564 | ||||||||
\(748\) | 11.0919 | 0.405560 | ||||||||
\(749\) | 9.78107 | 0.357392 | ||||||||
\(750\) | −4.24946 | −0.155168 | ||||||||
\(751\) | 2.98977 | 0.109098 | 0.0545490 | − | 0.998511i | \(-0.482628\pi\) | ||||
0.0545490 | + | 0.998511i | \(0.482628\pi\) | |||||||
\(752\) | 4.98057 | 0.181623 | ||||||||
\(753\) | −20.6482 | −0.752463 | ||||||||
\(754\) | −5.11487 | −0.186273 | ||||||||
\(755\) | 71.6720 | 2.60841 | ||||||||
\(756\) | 10.7963 | 0.392658 | ||||||||
\(757\) | 4.15807 | 0.151127 | 0.0755637 | − | 0.997141i | \(-0.475924\pi\) | ||||
0.0755637 | + | 0.997141i | \(0.475924\pi\) | |||||||
\(758\) | −15.1793 | −0.551336 | ||||||||
\(759\) | −7.86123 | −0.285345 | ||||||||
\(760\) | 20.0158 | 0.726048 | ||||||||
\(761\) | −5.23507 | −0.189771 | −0.0948856 | − | 0.995488i | \(-0.530249\pi\) | ||||
−0.0948856 | + | 0.995488i | \(0.530249\pi\) | |||||||
\(762\) | −23.7527 | −0.860468 | ||||||||
\(763\) | −8.83032 | −0.319679 | ||||||||
\(764\) | 17.0309 | 0.616157 | ||||||||
\(765\) | −17.3600 | −0.627653 | ||||||||
\(766\) | −17.7641 | −0.641844 | ||||||||
\(767\) | −11.1786 | −0.403635 | ||||||||
\(768\) | −1.33333 | −0.0481124 | ||||||||
\(769\) | 17.8240 | 0.642751 | 0.321376 | − | 0.946952i | \(-0.395855\pi\) | ||||
0.321376 | + | 0.946952i | \(0.395855\pi\) | |||||||
\(770\) | −13.3794 | −0.482159 | ||||||||
\(771\) | 26.6925 | 0.961307 | ||||||||
\(772\) | 23.7253 | 0.853893 | ||||||||
\(773\) | −25.1551 | −0.904767 | −0.452384 | − | 0.891823i | \(-0.649426\pi\) | ||||
−0.452384 | + | 0.891823i | \(0.649426\pi\) | |||||||
\(774\) | 2.84039 | 0.102096 | ||||||||
\(775\) | 1.84635 | 0.0663229 | ||||||||
\(776\) | −12.8159 | −0.460063 | ||||||||
\(777\) | 11.8242 | 0.424191 | ||||||||
\(778\) | −15.3930 | −0.551866 | ||||||||
\(779\) | −20.0090 | −0.716896 | ||||||||
\(780\) | 4.95638 | 0.177467 | ||||||||
\(781\) | 20.0695 | 0.718144 | ||||||||
\(782\) | −12.0035 | −0.429246 | ||||||||
\(783\) | −23.1528 | −0.827413 | ||||||||
\(784\) | −3.32217 | −0.118649 | ||||||||
\(785\) | −23.4861 | −0.838254 | ||||||||
\(786\) | −20.3249 | −0.724964 | ||||||||
\(787\) | −26.0504 | −0.928596 | −0.464298 | − | 0.885679i | \(-0.653693\pi\) | ||||
−0.464298 | + | 0.885679i | \(0.653693\pi\) | |||||||
\(788\) | 22.1157 | 0.787838 | ||||||||
\(789\) | 22.8173 | 0.812317 | ||||||||
\(790\) | 13.8387 | 0.492358 | ||||||||
\(791\) | 36.4418 | 1.29572 | ||||||||
\(792\) | 2.85284 | 0.101371 | ||||||||
\(793\) | −5.56209 | −0.197516 | ||||||||
\(794\) | −26.4279 | −0.937891 | ||||||||
\(795\) | −37.3966 | −1.32632 | ||||||||
\(796\) | 26.2679 | 0.931041 | ||||||||
\(797\) | −8.88591 | −0.314755 | −0.157378 | − | 0.987539i | \(-0.550304\pi\) | ||||
−0.157378 | + | 0.987539i | \(0.550304\pi\) | |||||||
\(798\) | −17.1234 | −0.606162 | ||||||||
\(799\) | 23.6679 | 0.837311 | ||||||||
\(800\) | −3.93370 | −0.139077 | ||||||||
\(801\) | −9.97552 | −0.352468 | ||||||||
\(802\) | 3.16838 | 0.111879 | ||||||||
\(803\) | 2.57547 | 0.0908864 | ||||||||
\(804\) | −13.5787 | −0.478883 | ||||||||
\(805\) | 14.4790 | 0.510319 | ||||||||
\(806\) | 0.583747 | 0.0205616 | ||||||||
\(807\) | 3.43223 | 0.120820 | ||||||||
\(808\) | −7.41703 | −0.260930 | ||||||||
\(809\) | 46.2057 | 1.62451 | 0.812253 | − | 0.583305i | \(-0.198241\pi\) | ||||
0.812253 | + | 0.583305i | \(0.198241\pi\) | |||||||
\(810\) | 11.4759 | 0.403221 | ||||||||
\(811\) | 11.2100 | 0.393636 | 0.196818 | − | 0.980440i | \(-0.436939\pi\) | ||||
0.196818 | + | 0.980440i | \(0.436939\pi\) | |||||||
\(812\) | −7.88713 | −0.276784 | ||||||||
\(813\) | 2.28112 | 0.0800024 | ||||||||
\(814\) | 10.7935 | 0.378313 | ||||||||
\(815\) | −37.8688 | −1.32649 | ||||||||
\(816\) | −6.33605 | −0.221806 | ||||||||
\(817\) | −15.5626 | −0.544465 | ||||||||
\(818\) | 35.3341 | 1.23543 | ||||||||
\(819\) | 2.91515 | 0.101863 | ||||||||
\(820\) | 8.93066 | 0.311872 | ||||||||
\(821\) | 1.41021 | 0.0492165 | 0.0246083 | − | 0.999697i | \(-0.492166\pi\) | ||||
0.0246083 | + | 0.999697i | \(0.492166\pi\) | |||||||
\(822\) | −26.1894 | −0.913460 | ||||||||
\(823\) | −52.2846 | −1.82253 | −0.911263 | − | 0.411826i | \(-0.864891\pi\) | ||||
−0.911263 | + | 0.411826i | \(0.864891\pi\) | |||||||
\(824\) | −9.01476 | −0.314044 | ||||||||
\(825\) | −12.2423 | −0.426222 | ||||||||
\(826\) | −17.2374 | −0.599765 | ||||||||
\(827\) | 23.9394 | 0.832455 | 0.416228 | − | 0.909261i | \(-0.363352\pi\) | ||||
0.416228 | + | 0.909261i | \(0.363352\pi\) | |||||||
\(828\) | −3.08732 | −0.107292 | ||||||||
\(829\) | −27.7631 | −0.964254 | −0.482127 | − | 0.876101i | \(-0.660136\pi\) | ||||
−0.482127 | + | 0.876101i | \(0.660136\pi\) | |||||||
\(830\) | 53.0401 | 1.84105 | ||||||||
\(831\) | −27.7881 | −0.963960 | ||||||||
\(832\) | −1.24369 | −0.0431171 | ||||||||
\(833\) | −15.7871 | −0.546992 | ||||||||
\(834\) | 2.28616 | 0.0791632 | ||||||||
\(835\) | 32.4080 | 1.12152 | ||||||||
\(836\) | −15.6308 | −0.540603 | ||||||||
\(837\) | 2.64237 | 0.0913336 | ||||||||
\(838\) | 2.86936 | 0.0991203 | ||||||||
\(839\) | −43.7890 | −1.51177 | −0.755883 | − | 0.654707i | \(-0.772792\pi\) | ||||
−0.755883 | + | 0.654707i | \(0.772792\pi\) | |||||||
\(840\) | 7.64274 | 0.263699 | ||||||||
\(841\) | −12.0860 | −0.416758 | ||||||||
\(842\) | 4.13528 | 0.142511 | ||||||||
\(843\) | −16.5320 | −0.569393 | ||||||||
\(844\) | 21.1043 | 0.726439 | ||||||||
\(845\) | −34.2329 | −1.17765 | ||||||||
\(846\) | 6.08741 | 0.209289 | ||||||||
\(847\) | −10.6471 | −0.365840 | ||||||||
\(848\) | 9.38381 | 0.322241 | ||||||||
\(849\) | 17.7232 | 0.608257 | ||||||||
\(850\) | −18.6931 | −0.641169 | ||||||||
\(851\) | −11.6806 | −0.400407 | ||||||||
\(852\) | −11.4644 | −0.392763 | ||||||||
\(853\) | −16.7815 | −0.574587 | −0.287293 | − | 0.957843i | \(-0.592755\pi\) | ||||
−0.287293 | + | 0.957843i | \(0.592755\pi\) | |||||||
\(854\) | −8.57675 | −0.293490 | ||||||||
\(855\) | 24.4639 | 0.836648 | ||||||||
\(856\) | −5.10024 | −0.174323 | ||||||||
\(857\) | −26.6227 | −0.909413 | −0.454707 | − | 0.890641i | \(-0.650256\pi\) | ||||
−0.454707 | + | 0.890641i | \(0.650256\pi\) | |||||||
\(858\) | −3.87056 | −0.132139 | ||||||||
\(859\) | 24.4541 | 0.834364 | 0.417182 | − | 0.908823i | \(-0.363018\pi\) | ||||
0.417182 | + | 0.908823i | \(0.363018\pi\) | |||||||
\(860\) | 6.94608 | 0.236859 | ||||||||
\(861\) | −7.64014 | −0.260375 | ||||||||
\(862\) | 13.1289 | 0.447173 | ||||||||
\(863\) | 9.65292 | 0.328589 | 0.164295 | − | 0.986411i | \(-0.447465\pi\) | ||||
0.164295 | + | 0.986411i | \(0.447465\pi\) | |||||||
\(864\) | −5.62963 | −0.191524 | ||||||||
\(865\) | −47.6810 | −1.62120 | ||||||||
\(866\) | −22.7745 | −0.773909 | ||||||||
\(867\) | −7.44266 | −0.252766 | ||||||||
\(868\) | 0.900138 | 0.0305527 | ||||||||
\(869\) | −10.8070 | −0.366601 | ||||||||
\(870\) | −16.3899 | −0.555670 | ||||||||
\(871\) | −12.6658 | −0.429163 | ||||||||
\(872\) | 4.60448 | 0.155927 | ||||||||
\(873\) | −15.6639 | −0.530144 | ||||||||
\(874\) | 16.9155 | 0.572175 | ||||||||
\(875\) | −6.11212 | −0.206627 | ||||||||
\(876\) | −1.47119 | −0.0497070 | ||||||||
\(877\) | −40.0819 | −1.35347 | −0.676736 | − | 0.736226i | \(-0.736606\pi\) | ||||
−0.676736 | + | 0.736226i | \(0.736606\pi\) | |||||||
\(878\) | −33.3151 | −1.12433 | ||||||||
\(879\) | 15.4853 | 0.522307 | ||||||||
\(880\) | 6.97654 | 0.235179 | ||||||||
\(881\) | −33.4002 | −1.12528 | −0.562640 | − | 0.826702i | \(-0.690214\pi\) | ||||
−0.562640 | + | 0.826702i | \(0.690214\pi\) | |||||||
\(882\) | −4.06046 | −0.136723 | ||||||||
\(883\) | 24.7544 | 0.833052 | 0.416526 | − | 0.909124i | \(-0.363247\pi\) | ||||
0.416526 | + | 0.909124i | \(0.363247\pi\) | |||||||
\(884\) | −5.91007 | −0.198777 | ||||||||
\(885\) | −35.8203 | −1.20408 | ||||||||
\(886\) | 30.4373 | 1.02256 | ||||||||
\(887\) | −4.02929 | −0.135290 | −0.0676452 | − | 0.997709i | \(-0.521549\pi\) | ||||
−0.0676452 | + | 0.997709i | \(0.521549\pi\) | |||||||
\(888\) | −6.16561 | −0.206904 | ||||||||
\(889\) | −34.1641 | −1.14583 | ||||||||
\(890\) | −24.3948 | −0.817717 | ||||||||
\(891\) | −8.96178 | −0.300231 | ||||||||
\(892\) | 12.5620 | 0.420607 | ||||||||
\(893\) | −33.3531 | −1.11612 | ||||||||
\(894\) | −22.7055 | −0.759387 | ||||||||
\(895\) | 59.6616 | 1.99427 | ||||||||
\(896\) | −1.91777 | −0.0640681 | ||||||||
\(897\) | 4.18868 | 0.139856 | ||||||||
\(898\) | −6.34738 | −0.211815 | ||||||||
\(899\) | −1.93036 | −0.0643810 | ||||||||
\(900\) | −4.80789 | −0.160263 | ||||||||
\(901\) | 44.5924 | 1.48559 | ||||||||
\(902\) | −6.97417 | −0.232215 | ||||||||
\(903\) | −5.94234 | −0.197749 | ||||||||
\(904\) | −19.0022 | −0.632005 | ||||||||
\(905\) | −43.5796 | −1.44863 | ||||||||
\(906\) | 31.9721 | 1.06220 | ||||||||
\(907\) | 12.2518 | 0.406815 | 0.203408 | − | 0.979094i | \(-0.434798\pi\) | ||||
0.203408 | + | 0.979094i | \(0.434798\pi\) | |||||||
\(908\) | −0.728356 | −0.0241713 | ||||||||
\(909\) | −9.06532 | −0.300678 | ||||||||
\(910\) | 7.12890 | 0.236321 | ||||||||
\(911\) | 35.7827 | 1.18553 | 0.592767 | − | 0.805374i | \(-0.298036\pi\) | ||||
0.592767 | + | 0.805374i | \(0.298036\pi\) | |||||||
\(912\) | 8.92883 | 0.295663 | ||||||||
\(913\) | −41.4203 | −1.37081 | ||||||||
\(914\) | 1.55505 | 0.0514366 | ||||||||
\(915\) | −17.8230 | −0.589210 | ||||||||
\(916\) | 3.37043 | 0.111362 | ||||||||
\(917\) | −29.2338 | −0.965386 | ||||||||
\(918\) | −26.7523 | −0.882957 | ||||||||
\(919\) | 41.3168 | 1.36292 | 0.681458 | − | 0.731857i | \(-0.261346\pi\) | ||||
0.681458 | + | 0.731857i | \(0.261346\pi\) | |||||||
\(920\) | −7.54995 | −0.248914 | ||||||||
\(921\) | −21.6446 | −0.713214 | ||||||||
\(922\) | −30.9703 | −1.01995 | ||||||||
\(923\) | −10.6936 | −0.351984 | ||||||||
\(924\) | −5.96840 | −0.196346 | ||||||||
\(925\) | −18.1903 | −0.598093 | ||||||||
\(926\) | −28.2842 | −0.929477 | ||||||||
\(927\) | −11.0181 | −0.361882 | ||||||||
\(928\) | 4.11267 | 0.135005 | ||||||||
\(929\) | 0.0160974 | 0.000528139 0 | 0.000264069 | − | 1.00000i | \(-0.499916\pi\) | ||||
0.000264069 | 1.00000i | \(0.499916\pi\) | ||||||||
\(930\) | 1.87054 | 0.0613374 | ||||||||
\(931\) | 22.2474 | 0.729129 | ||||||||
\(932\) | −4.65253 | −0.152399 | ||||||||
\(933\) | −34.7495 | −1.13765 | ||||||||
\(934\) | −14.0223 | −0.458822 | ||||||||
\(935\) | 33.1529 | 1.08422 | ||||||||
\(936\) | −1.52007 | −0.0496852 | ||||||||
\(937\) | −27.2636 | −0.890664 | −0.445332 | − | 0.895366i | \(-0.646914\pi\) | ||||
−0.445332 | + | 0.895366i | \(0.646914\pi\) | |||||||
\(938\) | −19.5306 | −0.637697 | ||||||||
\(939\) | −6.85676 | −0.223762 | ||||||||
\(940\) | 14.8866 | 0.485546 | ||||||||
\(941\) | 40.9371 | 1.33451 | 0.667256 | − | 0.744828i | \(-0.267469\pi\) | ||||
0.667256 | + | 0.744828i | \(0.267469\pi\) | |||||||
\(942\) | −10.4769 | −0.341356 | ||||||||
\(943\) | 7.54738 | 0.245777 | ||||||||
\(944\) | 8.98826 | 0.292543 | ||||||||
\(945\) | 32.2694 | 1.04972 | ||||||||
\(946\) | −5.42437 | −0.176361 | ||||||||
\(947\) | 48.2814 | 1.56894 | 0.784468 | − | 0.620170i | \(-0.212936\pi\) | ||||
0.784468 | + | 0.620170i | \(0.212936\pi\) | |||||||
\(948\) | 6.17329 | 0.200499 | ||||||||
\(949\) | −1.37228 | −0.0445461 | ||||||||
\(950\) | 26.3425 | 0.854665 | ||||||||
\(951\) | −12.0909 | −0.392074 | ||||||||
\(952\) | −9.11333 | −0.295365 | ||||||||
\(953\) | 38.4500 | 1.24552 | 0.622758 | − | 0.782414i | \(-0.286012\pi\) | ||||
0.622758 | + | 0.782414i | \(0.286012\pi\) | |||||||
\(954\) | 11.4692 | 0.371329 | ||||||||
\(955\) | 50.9042 | 1.64722 | ||||||||
\(956\) | −11.4546 | −0.370467 | ||||||||
\(957\) | 12.7993 | 0.413742 | ||||||||
\(958\) | −1.21117 | −0.0391313 | ||||||||
\(959\) | −37.6689 | −1.21639 | ||||||||
\(960\) | −3.98523 | −0.128623 | ||||||||
\(961\) | −30.7797 | −0.992893 | ||||||||
\(962\) | −5.75109 | −0.185422 | ||||||||
\(963\) | −6.23367 | −0.200877 | ||||||||
\(964\) | −18.7577 | −0.604145 | ||||||||
\(965\) | 70.9133 | 2.28278 | ||||||||
\(966\) | 6.45894 | 0.207813 | ||||||||
\(967\) | −40.6779 | −1.30811 | −0.654057 | − | 0.756445i | \(-0.726934\pi\) | ||||
−0.654057 | + | 0.756445i | \(0.726934\pi\) | |||||||
\(968\) | 5.55185 | 0.178443 | ||||||||
\(969\) | 42.4303 | 1.36306 | ||||||||
\(970\) | −38.3057 | −1.22992 | ||||||||
\(971\) | 27.1185 | 0.870276 | 0.435138 | − | 0.900364i | \(-0.356700\pi\) | ||||
0.435138 | + | 0.900364i | \(0.356700\pi\) | |||||||
\(972\) | −11.7696 | −0.377511 | ||||||||
\(973\) | 3.28824 | 0.105416 | ||||||||
\(974\) | −4.85559 | −0.155583 | ||||||||
\(975\) | 6.52304 | 0.208904 | ||||||||
\(976\) | 4.47226 | 0.143154 | ||||||||
\(977\) | −37.4524 | −1.19821 | −0.599104 | − | 0.800671i | \(-0.704476\pi\) | ||||
−0.599104 | + | 0.800671i | \(0.704476\pi\) | |||||||
\(978\) | −16.8929 | −0.540175 | ||||||||
\(979\) | 19.0505 | 0.608857 | ||||||||
\(980\) | −9.92974 | −0.317194 | ||||||||
\(981\) | 5.62774 | 0.179680 | ||||||||
\(982\) | 2.42603 | 0.0774176 | ||||||||
\(983\) | −52.1576 | −1.66357 | −0.831785 | − | 0.555098i | \(-0.812681\pi\) | ||||
−0.831785 | + | 0.555098i | \(0.812681\pi\) | |||||||
\(984\) | 3.98388 | 0.127001 | ||||||||
\(985\) | 66.1022 | 2.10619 | ||||||||
\(986\) | 19.5436 | 0.622395 | ||||||||
\(987\) | −12.7354 | −0.405372 | ||||||||
\(988\) | 8.32852 | 0.264966 | ||||||||
\(989\) | 5.87020 | 0.186661 | ||||||||
\(990\) | 8.52695 | 0.271004 | ||||||||
\(991\) | −1.42256 | −0.0451892 | −0.0225946 | − | 0.999745i | \(-0.507193\pi\) | ||||
−0.0225946 | + | 0.999745i | \(0.507193\pi\) | |||||||
\(992\) | −0.469368 | −0.0149025 | ||||||||
\(993\) | −23.6274 | −0.749793 | ||||||||
\(994\) | −16.4895 | −0.523016 | ||||||||
\(995\) | 78.5128 | 2.48902 | ||||||||
\(996\) | 23.6606 | 0.749716 | ||||||||
\(997\) | 42.1691 | 1.33551 | 0.667755 | − | 0.744381i | \(-0.267255\pi\) | ||||
0.667755 | + | 0.744381i | \(0.267255\pi\) | |||||||
\(998\) | 8.45826 | 0.267742 | ||||||||
\(999\) | −26.0326 | −0.823636 |
(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 | 4034.2.a.c.1.15 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.c.1.15 | ✓ | 49 | 1.1 | even | 1 | trivial |