Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [208,4,Mod(81,208)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(208, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("208.81");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 208 = 2^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 208.i (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(12.2723972812\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Root | \(-0.780776 - 1.35234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 208.81 |
Dual form | 208.4.i.e.113.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/208\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.84233 | − | 3.19101i | −0.354556 | − | 0.614110i | 0.632486 | − | 0.774572i | \(-0.282035\pi\) |
−0.987042 | + | 0.160462i | \(0.948701\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −17.8078 | −1.59277 | −0.796387 | − | 0.604787i | \(-0.793258\pi\) | ||||
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.71922 | − | 4.70983i | 0.146824 | − | 0.254307i | −0.783228 | − | 0.621735i | \(-0.786428\pi\) |
0.930052 | + | 0.367428i | \(0.119761\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.71165 | − | 11.6249i | 0.248579 | − | 0.430552i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.2116 | − | 19.4191i | −0.307313 | − | 0.532281i | 0.670461 | − | 0.741945i | \(-0.266096\pi\) |
−0.977774 | + | 0.209664i | \(0.932763\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.9730 | + | 41.4027i | 0.468786 | + | 0.883312i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 32.8078 | + | 56.8247i | 0.564729 | + | 0.978139i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −33.9924 | + | 58.8766i | −0.484963 | + | 0.839981i | −0.999851 | − | 0.0172769i | \(-0.994500\pi\) |
0.514888 | + | 0.857258i | \(0.327834\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −40.4039 | + | 69.9816i | −0.487857 | + | 0.844993i | −0.999902 | − | 0.0139650i | \(-0.995555\pi\) |
0.512045 | + | 0.858958i | \(0.328888\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −20.0388 | −0.208230 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 70.2656 | + | 121.704i | 0.637017 | + | 1.10335i | 0.986084 | + | 0.166248i | \(0.0531653\pi\) |
−0.349067 | + | 0.937098i | \(0.613501\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 192.116 | 1.53693 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −148.946 | −1.06165 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 53.3466 | + | 92.3990i | 0.341594 | + | 0.591657i | 0.984729 | − | 0.174095i | \(-0.0557001\pi\) |
−0.643135 | + | 0.765753i | \(0.722367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 276.155 | 1.59997 | 0.799983 | − | 0.600023i | \(-0.204842\pi\) | ||||
0.799983 | + | 0.600023i | \(0.204842\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −41.3111 | + | 71.5529i | −0.217919 | + | 0.377447i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −48.4233 | + | 83.8716i | −0.233858 | + | 0.405054i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.14584 | + | 3.71670i | 0.00953442 | + | 0.0165141i | 0.870753 | − | 0.491720i | \(-0.163632\pi\) |
−0.861219 | + | 0.508234i | \(0.830298\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 91.6349 | − | 146.394i | 0.376239 | − | 0.601070i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −113.884 | − | 197.254i | −0.433799 | − | 0.751362i | 0.563398 | − | 0.826186i | \(-0.309494\pi\) |
−0.997197 | + | 0.0748237i | \(0.976161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13.7647 | − | 23.8411i | 0.0488162 | − | 0.0845521i | −0.840585 | − | 0.541680i | \(-0.817788\pi\) |
0.889401 | + | 0.457128i | \(0.151122\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −119.519 | + | 207.014i | −0.395931 | + | 0.685773i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −318.617 | −0.988832 | −0.494416 | − | 0.869225i | \(-0.664618\pi\) | ||||
−0.494416 | + | 0.869225i | \(0.664618\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 156.712 | + | 271.433i | 0.456885 | + | 0.791348i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 250.501 | 0.687787 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −67.6562 | −0.175345 | −0.0876726 | − | 0.996149i | \(-0.527943\pi\) | ||||
−0.0876726 | + | 0.996149i | \(0.527943\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 199.654 | + | 345.811i | 0.489480 | + | 0.847804i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 297.749 | 0.691892 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −145.557 | + | 252.113i | −0.321186 | + | 0.556310i | −0.980733 | − | 0.195353i | \(-0.937415\pi\) |
0.659547 | + | 0.751663i | \(0.270748\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −331.655 | + | 574.444i | −0.696133 | + | 1.20574i | 0.273664 | + | 0.961825i | \(0.411764\pi\) |
−0.969797 | + | 0.243912i | \(0.921569\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −36.5009 | − | 63.2215i | −0.0729950 | − | 0.126431i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −391.290 | − | 737.290i | −0.746670 | − | 1.40692i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −212.551 | − | 368.149i | −0.387570 | − | 0.671291i | 0.604552 | − | 0.796566i | \(-0.293352\pi\) |
−0.992122 | + | 0.125275i | \(0.960019\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 258.905 | − | 448.436i | 0.451717 | − | 0.782397i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −76.4815 | + | 132.470i | −0.127841 | + | 0.221427i | −0.922840 | − | 0.385184i | \(-0.874138\pi\) |
0.794999 | + | 0.606611i | \(0.207471\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 117.268 | 0.188016 | 0.0940081 | − | 0.995571i | \(-0.470032\pi\) | ||||
0.0940081 | + | 0.995571i | \(0.470032\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −353.942 | − | 613.045i | −0.544929 | − | 0.943845i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −121.948 | −0.180484 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −202.462 | −0.288339 | −0.144169 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144169 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 93.1932 | + | 161.415i | 0.127837 | + | 0.221420i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −336.155 | −0.444552 | −0.222276 | − | 0.974984i | \(-0.571349\pi\) | ||||
−0.222276 | + | 0.974984i | \(0.571349\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 605.329 | − | 1048.46i | 0.772437 | − | 1.33790i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 196.564 | − | 340.459i | 0.242228 | − | 0.419552i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −359.097 | − | 621.974i | −0.427688 | − | 0.740777i | 0.568979 | − | 0.822352i | \(-0.307338\pi\) |
−0.996667 | + | 0.0815748i | \(0.974005\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 254.750 | + | 9.09407i | 0.293462 | + | 0.0104760i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −508.769 | − | 881.214i | −0.567278 | − | 0.982555i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 719.503 | − | 1246.22i | 0.777047 | − | 1.34588i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −379.684 | + | 657.632i | −0.397434 | + | 0.688376i | −0.993409 | − | 0.114628i | \(-0.963433\pi\) |
0.595975 | + | 0.803003i | \(0.296766\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −300.994 | −0.305566 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 174.348 | + | 301.980i | 0.171766 | + | 0.297507i | 0.939037 | − | 0.343816i | \(-0.111720\pi\) |
−0.767272 | + | 0.641322i | \(0.778386\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 580.303 | 0.555136 | 0.277568 | − | 0.960706i | \(-0.410472\pi\) | ||||
0.277568 | + | 0.960706i | \(0.410472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 356.847 | 0.331663 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 285.747 | + | 494.928i | 0.258170 | + | 0.447163i | 0.965752 | − | 0.259468i | \(-0.0835473\pi\) |
−0.707582 | + | 0.706631i | \(0.750214\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 176.004 | 0.154661 | 0.0773307 | − | 0.997005i | \(-0.475360\pi\) | ||||
0.0773307 | + | 0.997005i | \(0.475360\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.90668 | − | 13.6948i | 0.00676098 | − | 0.0117104i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −632.441 | + | 1095.42i | −0.526505 | + | 0.911933i | 0.473018 | + | 0.881053i | \(0.343165\pi\) |
−0.999523 | + | 0.0308807i | \(0.990169\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1251.27 | − | 2167.27i | −1.01462 | − | 1.75738i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 628.778 | + | 22.4462i | 0.496842 | + | 0.0177363i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 184.866 | + | 320.197i | 0.142409 | + | 0.246659i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 414.098 | − | 717.239i | 0.311118 | − | 0.538872i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −419.625 | + | 726.812i | −0.307613 | + | 0.532801i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1195.19 | −0.855211 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1302.05 | + | 2255.22i | 0.909752 | + | 1.57574i | 0.814408 | + | 0.580293i | \(0.197062\pi\) |
0.0953448 | + | 0.995444i | \(0.469605\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −101.436 | −0.0692323 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2131.70 | −1.42174 | −0.710870 | − | 0.703324i | \(-0.751698\pi\) | ||||
−0.710870 | + | 0.703324i | \(0.751698\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 219.734 | + | 380.591i | 0.143259 | + | 0.248131i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2652.40 | 1.69098 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −343.992 | + | 595.812i | −0.214520 | + | 0.371560i | −0.953124 | − | 0.302580i | \(-0.902152\pi\) |
0.738604 | + | 0.674140i | \(0.235485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −339.790 | + | 588.534i | −0.207343 | + | 0.359128i | −0.950877 | − | 0.309570i | \(-0.899815\pi\) |
0.743534 | + | 0.668698i | \(0.233148\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 586.998 | + | 1016.71i | 0.350597 | + | 0.607252i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 557.652 | − | 890.890i | 0.326106 | − | 0.520979i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −949.983 | − | 1645.42i | −0.544082 | − | 0.942377i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 577.429 | − | 1000.14i | 0.323983 | − | 0.561155i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 987.731 | − | 1710.80i | 0.543074 | − | 0.940632i | −0.455651 | − | 0.890159i | \(-0.650593\pi\) |
0.998725 | − | 0.0504739i | \(-0.0160732\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1803.24 | −0.971824 | −0.485912 | − | 0.874008i | \(-0.661513\pi\) | ||||
−0.485912 | + | 0.874008i | \(0.661513\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 456.290 | + | 790.318i | 0.241104 | + | 0.417604i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4917.71 | −2.54839 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −397.168 | −0.201894 | −0.100947 | − | 0.994892i | \(-0.532187\pi\) | ||||
−0.100947 | + | 0.994892i | \(0.532187\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 124.645 | + | 215.892i | 0.0621698 | + | 0.107681i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 764.272 | 0.374118 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 470.696 | − | 815.270i | 0.226183 | − | 0.391760i | −0.730491 | − | 0.682922i | \(-0.760709\pi\) |
0.956674 | + | 0.291162i | \(0.0940420\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 735.658 | − | 1274.20i | 0.347096 | − | 0.601189i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1840.22 | + | 3187.35i | 0.852696 | + | 1.47691i | 0.878766 | + | 0.477252i | \(0.158367\pi\) |
−0.0260704 | + | 0.999660i | \(0.508299\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1231.37 | + | 1819.49i | −0.560479 | + | 0.828168i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 542.353 | + | 939.383i | 0.242543 | + | 0.420096i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −711.387 | + | 1232.16i | −0.312634 | + | 0.541499i | −0.978932 | − | 0.204187i | \(-0.934545\pi\) |
0.666297 | + | 0.745686i | \(0.267878\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 522.408 | − | 904.837i | 0.225659 | − | 0.390853i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1072.66 | 0.455514 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 583.946 | + | 1011.42i | 0.243833 | + | 0.422331i | 0.961803 | − | 0.273743i | \(-0.0882617\pi\) |
−0.717970 | + | 0.696074i | \(0.754928\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1133.96 | −0.465673 | −0.232836 | − | 0.972516i | \(-0.574801\pi\) | ||||
−0.232836 | + | 0.972516i | \(0.574801\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2444.07 | 0.987274 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −38.2126 | − | 66.1861i | −0.0151862 | − | 0.0263032i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1524.44 | 0.596141 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −405.018 | + | 701.511i | −0.155877 | + | 0.269986i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1341.06 | − | 2322.78i | 0.508040 | − | 0.879952i | −0.491916 | − | 0.870642i | \(-0.663703\pi\) |
0.999957 | − | 0.00930919i | \(-0.00296325\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 985.333 | + | 1706.65i | 0.367491 | + | 0.636514i | 0.989173 | − | 0.146757i | \(-0.0468834\pi\) |
−0.621681 | + | 0.783270i | \(0.713550\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1631.81 | + | 2606.94i | −0.599265 | + | 0.957369i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2008.02 | + | 3478.00i | 0.726222 | + | 1.25785i | 0.958469 | + | 0.285197i | \(0.0920590\pi\) |
−0.232247 | + | 0.972657i | \(0.574608\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2113.03 | + | 3659.87i | −0.752707 | + | 1.30373i | 0.193800 | + | 0.981041i | \(0.437919\pi\) |
−0.946506 | + | 0.322685i | \(0.895415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −783.177 | + | 1356.50i | −0.274831 | + | 0.476021i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 580.245 | 0.200617 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2028.03 | + | 3512.65i | 0.690944 | + | 1.19675i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1886.39 | 0.633398 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1811.98 | 0.599699 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 682.334 | + | 1181.84i | 0.222625 | + | 0.385597i | 0.955604 | − | 0.294654i | \(-0.0952043\pi\) |
−0.732980 | + | 0.680251i | \(0.761871\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 563.617 | 0.181307 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −245.118 | + | 424.557i | −0.0777532 | + | 0.134672i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 750.928 | − | 1300.65i | 0.234914 | − | 0.406883i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −216.046 | − | 374.203i | −0.0666624 | − | 0.115463i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3184.57 | − | 113.683i | −0.969309 | − | 0.0346025i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −529.734 | − | 917.527i | −0.159075 | − | 0.275525i | 0.775461 | − | 0.631396i | \(-0.217518\pi\) |
−0.934535 | + | 0.355871i | \(0.884184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1289.42 | − | 2233.34i | 0.382050 | − | 0.661729i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1732.10 | − | 3000.08i | 0.506446 | − | 0.877190i | −0.493526 | − | 0.869731i | \(-0.664292\pi\) |
0.999972 | − | 0.00745930i | \(-0.00237439\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2324.64 | −0.670815 | −0.335407 | − | 0.942073i | \(-0.608874\pi\) | ||||
−0.335407 | + | 0.942073i | \(0.608874\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 224.668 | + | 389.137i | 0.0639917 | + | 0.110837i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3731.01 | −1.04904 | −0.524521 | − | 0.851398i | \(-0.675755\pi\) | ||||
−0.524521 | + | 0.851398i | \(0.675755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5673.86 | 1.57499 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 373.002 | + | 646.058i | 0.102232 | + | 0.177072i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6044.47 | −1.63592 | −0.817958 | − | 0.575278i | \(-0.804894\pi\) | ||||
−0.817958 | + | 0.575278i | \(0.804894\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2586.98 | − | 4480.78i | 0.691461 | − | 1.19765i | −0.279898 | − | 0.960030i | \(-0.590301\pi\) |
0.971359 | − | 0.237616i | \(-0.0763659\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1667.39 | + | 2888.00i | −0.440176 | + | 0.762408i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2790.68 | − | 4833.61i | −0.727715 | − | 1.26044i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3785.22 | − | 135.125i | −0.975093 | − | 0.0348090i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 619.309 | + | 1072.67i | 0.157619 | + | 0.273004i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2810.37 | − | 4867.70i | 0.706728 | − | 1.22409i | −0.259337 | − | 0.965787i | \(-0.583504\pi\) |
0.966064 | − | 0.258301i | \(-0.0831628\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1575.59 | − | 2729.00i | 0.391527 | − | 0.678144i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4460.86 | −1.09549 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 837.070 | + | 1449.85i | 0.203171 | + | 0.351903i | 0.949549 | − | 0.313620i | \(-0.101542\pi\) |
−0.746377 | + | 0.665523i | \(0.768209\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.3401 | 0.00559954 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1432.17 | 0.339653 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3154.59 | − | 5463.91i | −0.739622 | − | 1.28106i | −0.952666 | − | 0.304020i | \(-0.901671\pi\) |
0.213044 | − | 0.977043i | \(-0.431662\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1204.81 | 0.279285 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1323.15 | + | 2291.76i | −0.303279 | + | 0.525294i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1241.37 | − | 2150.11i | 0.281366 | − | 0.487340i | −0.690356 | − | 0.723470i | \(-0.742546\pi\) |
0.971721 | + | 0.236131i | \(0.0758793\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1417.86 | + | 2455.81i | 0.317819 | + | 0.550478i | 0.980033 | − | 0.198837i | \(-0.0637163\pi\) |
−0.662214 | + | 0.749315i | \(0.730383\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −440.313 | − | 829.662i | −0.0976153 | − | 0.183932i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2153.94 | − | 3730.74i | −0.472318 | − | 0.818080i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1918.76 | − | 3323.38i | 0.416198 | − | 0.720876i | −0.579355 | − | 0.815075i | \(-0.696696\pi\) |
0.995553 | + | 0.0941989i | \(0.0300290\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1853.46 | − | 3210.28i | 0.397719 | − | 0.688869i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9122.13 | −1.93659 | −0.968293 | − | 0.249819i | \(-0.919629\pi\) | ||||
−0.968293 | + | 0.249819i | \(0.919629\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1063.92 | + | 1842.77i | 0.223476 | + | 0.387072i | 0.955861 | − | 0.293819i | \(-0.0949262\pi\) |
−0.732385 | + | 0.680891i | \(0.761593\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5302.24 | −1.10203 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1238.71 | −0.254769 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 145.530 | + | 252.066i | 0.0296215 | + | 0.0513059i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2798.01 | 0.563651 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4137.38 | + | 7166.16i | −0.824944 | + | 1.42884i | 0.0770183 | + | 0.997030i | \(0.475460\pi\) |
−0.901962 | + | 0.431815i | \(0.857873\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2592.05 | − | 4489.56i | 0.511576 | − | 0.886076i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1669.93 | + | 2892.40i | 0.326260 | + | 0.565099i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3494.92 | + | 5583.38i | −0.675974 | + | 1.07992i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −74.8585 | − | 129.659i | −0.0143348 | − | 0.0248286i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 642.414 | − | 1112.69i | 0.121801 | − | 0.210966i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5906.04 | − | 10229.6i | 1.10878 | − | 1.92047i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3610.49 | 0.671211 | 0.335605 | − | 0.942003i | \(-0.391059\pi\) | ||||
0.335605 | + | 0.942003i | \(0.391059\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1069.11 | − | 1851.75i | −0.196827 | − | 0.340914i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3331.06 | −0.607354 | −0.303677 | − | 0.952775i | \(-0.598214\pi\) | ||||
−0.303677 | + | 0.952775i | \(0.598214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −358.125 | −0.0646724 | −0.0323362 | − | 0.999477i | \(-0.510295\pi\) | ||||
−0.0323362 | + | 0.999477i | \(0.510295\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 650.000 | + | 1125.83i | 0.116265 | + | 0.201376i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3047.46 | 0.539944 | 0.269972 | − | 0.962868i | \(-0.412986\pi\) | ||||
0.269972 | + | 0.962868i | \(0.412986\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1196.21 | − | 2071.89i | 0.209952 | − | 0.363647i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1052.88 | − | 1823.64i | 0.183072 | − | 0.317089i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2746.85 | − | 4757.69i | −0.473185 | − | 0.819581i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4221.38 | + | 7954.15i | 0.720492 | + | 1.35759i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −324.257 | − | 561.629i | −0.0548362 | − | 0.0949791i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −866.392 | + | 1500.63i | −0.145185 | + | 0.251467i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3847.39 | − | 6663.87i | 0.638887 | − | 1.10658i | −0.346791 | − | 0.937942i | \(-0.612729\pi\) |
0.985677 | − | 0.168641i | \(-0.0539380\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 57.6084 | 0.00948025 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3785.05 | + | 6555.90i | 0.617312 | + | 1.06922i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4712.21 | 0.761693 | 0.380846 | − | 0.924638i | \(-0.375633\pi\) | ||||
0.380846 | + | 0.924638i | \(0.375633\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4660.66 | 0.746703 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3096.16 | − | 5362.70i | −0.491690 | − | 0.851632i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3569.92 | 0.561976 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4610.52 | + | 7985.65i | −0.719484 | + | 1.24618i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2630.99 | + | 4557.01i | −0.407029 | + | 0.704995i | −0.994555 | − | 0.104210i | \(-0.966768\pi\) |
0.587526 | + | 0.809205i | \(0.300102\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.1672 | − | 43.5909i | −0.00386009 | − | 0.00668587i | 0.864089 | − | 0.503339i | \(-0.167895\pi\) |
−0.867949 | + | 0.496653i | \(0.834562\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3272.79 | − | 6166.77i | −0.497689 | − | 0.937772i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4528.82 | − | 7844.14i | −0.682846 | − | 1.18272i | −0.974109 | − | 0.226081i | \(-0.927409\pi\) |
0.291263 | − | 0.956643i | \(-0.405925\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1361.96 | − | 2358.99i | 0.203621 | − | 0.352683i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 681.168 | − | 1179.82i | 0.100984 | − | 0.174909i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7177.86 | −1.05525 | −0.527623 | − | 0.849479i | \(-0.676917\pi\) | ||||
−0.527623 | + | 0.849479i | \(0.676917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 164.553 | + | 285.014i | 0.0239908 | + | 0.0415532i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3051.62 | −0.441235 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2088.28 | −0.299467 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2002.07 | + | 3467.69i | 0.284761 | + | 0.493221i | 0.972551 | − | 0.232689i | \(-0.0747524\pi\) |
−0.687790 | + | 0.725910i | \(0.741419\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3057.41 | −0.431334 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −183.972 | + | 318.649i | −0.0257449 | + | 0.0445915i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5007.09 | − | 8672.53i | 0.695060 | − | 1.20388i | −0.275101 | − | 0.961415i | \(-0.588711\pi\) |
0.970161 | − | 0.242464i | \(-0.0779555\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2201.94 | + | 3813.87i | 0.303221 | + | 0.525194i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2653.39 | + | 4238.98i | −0.362484 | + | 0.579094i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4084.56 | − | 7074.66i | −0.553587 | − | 0.958842i | −0.998012 | − | 0.0630252i | \(-0.979925\pi\) |
0.444425 | − | 0.895816i | \(-0.353408\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4797.62 | − | 8309.73i | 0.645117 | − | 1.11738i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3655.12 | + | 6330.86i | −0.487645 | + | 0.844626i | −0.999899 | − | 0.0142079i | \(-0.995477\pi\) |
0.512254 | + | 0.858834i | \(0.328811\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2171.62 | 0.287470 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −184.767 | − | 320.027i | −0.0242694 | − | 0.0420358i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8785.47 | 1.14509 | 0.572546 | − | 0.819872i | \(-0.305956\pi\) | ||||
0.572546 | + | 0.819872i | \(0.305956\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9553.99 | −1.23572 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3927.30 | + | 6802.29i | 0.504087 | + | 0.873104i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3605.40 | 0.459259 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5633.40 | + | 9757.33i | −0.712171 | + | 1.23352i | 0.251869 | + | 0.967761i | \(0.418955\pi\) |
−0.964040 | + | 0.265756i | \(0.914379\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 809.646 | − | 1402.35i | 0.101586 | − | 0.175953i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −788.117 | − | 1365.06i | −0.0981464 | − | 0.169995i | 0.812771 | − | 0.582583i | \(-0.197958\pi\) |
−0.910917 | + | 0.412589i | \(0.864625\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6067.96 | + | 11433.6i | 0.750042 | + | 1.41327i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1659.56 | − | 2874.45i | −0.203616 | − | 0.352672i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.1168 | − | 83.3407i | 0.00586010 | − | 0.0101500i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3377.89 | + | 5850.68i | −0.408377 | + | 0.707329i | −0.994708 | − | 0.102742i | \(-0.967238\pi\) |
0.586331 | + | 0.810071i | \(0.300572\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2534.99 | 0.304238 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 791.606 | + | 1371.10i | 0.0943157 | + | 0.163360i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5986.17 | 0.708072 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2504.02 | 0.294059 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5378.09 | + | 9315.13i | 0.627057 | + | 1.08610i | 0.988139 | + | 0.153561i | \(0.0490742\pi\) |
−0.361082 | + | 0.932534i | \(0.617592\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7886.03 | 0.912925 | 0.456463 | − | 0.889743i | \(-0.349116\pi\) | ||||
0.456463 | + | 0.889743i | \(0.349116\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2138.45 | + | 3703.90i | −0.245803 | + | 0.425744i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6530.50 | + | 11311.2i | −0.745355 | + | 1.29099i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1803.69 | + | 3124.08i | 0.204418 | + | 0.354063i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3870.22 | − | 138.159i | −0.435561 | − | 0.0155487i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7042.31 | − | 12197.6i | −0.787044 | − | 1.36320i | −0.927770 | − | 0.373152i | \(-0.878277\pi\) |
0.140726 | − | 0.990049i | \(-0.455056\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −932.072 | + | 1614.40i | −0.103447 | + | 0.179175i | −0.913103 | − | 0.407730i | \(-0.866321\pi\) |
0.809656 | + | 0.586905i | \(0.199654\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3500.36 | + | 6062.81i | −0.385815 | + | 0.668252i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11356.0 | −1.24309 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3077.24 | + | 5329.94i | 0.334553 | + | 0.579463i | 0.983399 | − | 0.181457i | \(-0.0580813\pi\) |
−0.648846 | + | 0.760920i | \(0.724748\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4207.17 | 0.454289 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14539.3 | 1.55933 | 0.779663 | − | 0.626200i | \(-0.215391\pi\) | ||||
0.779663 | + | 0.626200i | \(0.215391\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6394.72 | + | 11076.0i | 0.681210 | + | 1.17989i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7278.90 | −0.770202 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3521.93 | − | 6100.17i | 0.370179 | − | 0.641169i | −0.619414 | − | 0.785065i | \(-0.712630\pi\) |
0.989593 | + | 0.143896i | \(0.0459630\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2553.66 | + | 4423.08i | −0.266624 | + | 0.461806i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3322.16 | + | 5754.15i | 0.344567 | + | 0.596807i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4536.52 | − | 161.945i | −0.467418 | − | 0.0166859i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7049.43 | − | 12210.0i | −0.721572 | − | 1.24980i | −0.960370 | − | 0.278730i | \(-0.910087\pi\) |
0.238798 | − | 0.971069i | \(-0.423247\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5063.04 | − | 8769.44i | 0.514863 | − | 0.891770i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7224.85 | + | 12513.8i | −0.729924 | + | 1.26426i | 0.226991 | + | 0.973897i | \(0.427111\pi\) |
−0.956915 | + | 0.290368i | \(0.906222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15806.5 | −1.58659 | −0.793293 | − | 0.608840i | \(-0.791635\pi\) | ||||
−0.793293 | + | 0.608840i | \(0.791635\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9060.04 | + | 15692.4i | 0.903547 | + | 1.56499i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15071.3 | 1.49340 | 0.746699 | − | 0.665162i | \(-0.231638\pi\) | ||||
0.746699 | + | 0.665162i | \(0.231638\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2311.89 | −0.227619 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 731.713 | + | 1267.36i | 0.0715830 | + | 0.123985i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −617.299 | −0.0600073 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7762.25 | + | 13444.6i | −0.749803 | + | 1.29870i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −454.085 | + | 786.498i | −0.0435872 | + | 0.0754953i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −196.272 | − | 339.954i | −0.0187222 | − | 0.0324277i | 0.856513 | − | 0.516126i | \(-0.172626\pi\) |
−0.875235 | + | 0.483698i | \(0.839293\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −106.731 | + | 170.511i | −0.0101175 | + | 0.0161634i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1408.04 | − | 2438.80i | −0.132646 | − | 0.229750i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6761.33 | − | 11711.0i | 0.633023 | − | 1.09643i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4748.94 | − | 8225.41i | 0.441879 | − | 0.765357i | −0.555950 | − | 0.831216i | \(-0.687645\pi\) |
0.997829 | + | 0.0658588i | \(0.0209787\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3468.71 | −0.320778 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −946.912 | − | 1640.10i | −0.0870337 | − | 0.150747i | 0.819222 | − | 0.573476i | \(-0.194405\pi\) |
−0.906256 | + | 0.422729i | \(0.861072\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7253.52 | −0.662641 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5360.04 | 0.486699 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 415.941 | + | 720.430i | 0.0375402 | + | 0.0650216i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13370.1 | 1.19945 | 0.599727 | − | 0.800205i | \(-0.295276\pi\) | ||||
0.599727 | + | 0.800205i | \(0.295276\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6780.57 | − | 11744.3i | 0.604658 | − | 1.04730i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2777.36 | − | 4810.52i | 0.246195 | − | 0.426423i | −0.716272 | − | 0.697822i | \(-0.754153\pi\) |
0.962467 | + | 0.271399i | \(0.0874862\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3104.76 | − | 5377.60i | −0.273584 | − | 0.473861i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8074.59 | + | 577.231i | 0.707308 | + | 0.0505635i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1098.78 | − | 1903.13i | −0.0956824 | − | 0.165727i | 0.814211 | − | 0.580569i | \(-0.197170\pi\) |
−0.909893 | + | 0.414843i | \(0.863837\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 318.878 | − | 552.313i | 0.0276053 | − | 0.0478139i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6018.00 | − | 10423.5i | 0.517936 | − | 0.897091i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10333.9 | −0.884206 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3572.23 | + | 6187.28i | 0.303881 | + | 0.526337i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5242.44 | 0.443386 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17005.2 | 1.42997 | 0.714983 | − | 0.699142i | \(-0.246435\pi\) | ||||
0.714983 | + | 0.699142i | \(0.246435\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7243.11 | − | 12545.4i | −0.605581 | − | 1.04890i | −0.991959 | − | 0.126557i | \(-0.959607\pi\) |
0.386378 | − | 0.922341i | \(-0.373726\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3849.79 | −0.320035 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9387.19 | + | 16259.1i | −0.775925 | + | 1.34394i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3791.02 | + | 6566.23i | −0.311582 | + | 0.539675i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1953.86 | + | 3384.18i | 0.159680 | + | 0.276574i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5664.46 | − | 9049.39i | 0.460328 | − | 0.735408i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5088.51 | − | 8813.56i | −0.411206 | − | 0.712230i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2151.64 | − | 3726.75i | 0.172905 | − | 0.299481i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3513.99 | − | 6086.41i | 0.280813 | − | 0.486383i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15266.7 | −1.21325 | −0.606623 | − | 0.794990i | \(-0.707476\pi\) | ||||
−0.606623 | + | 0.794990i | \(0.707476\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2089.13 | + | 3618.48i | 0.165107 | + | 0.285974i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3134.23 | −0.246341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15260.5 | −1.19286 | −0.596430 | − | 0.802665i | \(-0.703414\pi\) | ||||
−0.596430 | + | 0.802665i | \(0.703414\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4451.91 | + | 7710.93i | 0.346089 | + | 0.599443i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8621.64 | −0.666595 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −550.540 | + | 953.563i | −0.0423351 | + | 0.0733266i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −140.800 | + | 243.873i | −0.0107687 | + | 0.0186520i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5221.05 | + | 9043.12i | 0.397169 | + | 0.687916i | 0.993375 | − | 0.114915i | \(-0.0366595\pi\) |
−0.596207 | + | 0.802831i | \(0.703326\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1289.54 | + | 46.0341i | 0.0975702 | + | 0.00348307i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2808.53 | − | 4864.51i | −0.211366 | − | 0.366096i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3572.63 | − | 6187.98i | 0.267440 | − | 0.463219i | −0.700760 | − | 0.713397i | \(-0.747156\pi\) |
0.968200 | + | 0.250178i | \(0.0804891\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11262.4 | − | 19507.0i | 0.838604 | − | 1.45250i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1013.65 | 0.0750783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2219.43 | − | 3844.17i | −0.163521 | − | 0.283226i | 0.772608 | − | 0.634883i | \(-0.218952\pi\) |
−0.936129 | + | 0.351657i | \(0.885618\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10117.3 | −0.741497 | −0.370748 | − | 0.928733i | \(-0.620899\pi\) | ||||
−0.370748 | + | 0.928733i | \(0.620899\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9882.70 | −0.720516 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13499.2 | + | 23381.3i | 0.979052 | + | 1.69577i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3105.60 | 0.224069 | 0.112035 | − | 0.993704i | \(-0.464263\pi\) | ||||
0.112035 | + | 0.993704i | \(0.464263\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3630.62 | − | 6288.41i | 0.260593 | − | 0.451360i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −914.081 | + | 1583.24i | −0.0652711 | + | 0.113053i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 758.538 | + | 1313.83i | 0.0538858 | + | 0.0933329i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11197.1 | − | 399.716i | −0.791358 | − | 0.0282500i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9831.16 | + | 17028.1i | 0.691270 | + | 1.19731i | 0.971422 | + | 0.237359i | \(0.0762818\pi\) |
−0.280152 | + | 0.959956i | \(0.590385\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11157.7 | + | 19325.8i | −0.780555 | + | 1.35196i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7398.88 | − | 12815.2i | 0.514974 | − | 0.891960i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6395.51 | 0.442888 | 0.221444 | − | 0.975173i | \(-0.428923\pi\) | ||||
0.221444 | + | 0.975173i | \(0.428923\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3292.05 | − | 5702.00i | −0.226825 | − | 0.392872i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15571.6 | 1.06751 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8878.48 | −0.605618 | −0.302809 | − | 0.953051i | \(-0.597924\pi\) | ||||
−0.302809 | + | 0.953051i | \(0.597924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9550.29 | − | 16541.6i | −0.648194 | − | 1.12270i | −0.983554 | − | 0.180615i | \(-0.942191\pi\) |
0.335360 | − | 0.942090i | \(-0.391142\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5706.26 | −0.385368 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7374.16 | + | 12772.4i | −0.495541 | + | 0.858302i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8297.88 | − | 14372.4i | 0.554861 | − | 0.961047i | −0.443053 | − | 0.896495i | \(-0.646105\pi\) |
0.997914 | − | 0.0645522i | \(-0.0205619\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1069.00 | − | 1851.57i | −0.0711300 | − | 0.123201i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7000.98 | − | 13191.6i | −0.463551 | − | 0.873447i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8234.58 | − | 14262.7i | −0.542564 | − | 0.939748i | −0.998756 | − | 0.0498668i | \(-0.984120\pi\) |
0.456192 | − | 0.889881i | \(-0.349213\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7472.59 | − | 12942.9i | 0.489958 | − | 0.848631i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5057.99 | + | 8760.69i | −0.330027 | + | 0.571624i | −0.982517 | − | 0.186174i | \(-0.940391\pi\) |
0.652489 | + | 0.757798i | \(0.273725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18854.8 | −1.22430 | −0.612148 | − | 0.790743i | \(-0.709694\pi\) | ||||
−0.612148 | + | 0.790743i | \(0.709694\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10465.8 | − | 18127.3i | −0.676292 | − | 1.17137i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3905.86 | −0.251180 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2730.82 | −0.174773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3338.26 | − | 5782.03i | −0.212627 | − | 0.368281i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −291.769 | −0.0184954 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9473.12 | − | 16407.9i | 0.597653 | − | 1.03517i | −0.395514 | − | 0.918460i | \(-0.629433\pi\) |
0.993167 | − | 0.116705i | \(-0.0372333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2514.17 | − | 4354.66i | 0.157866 | − | 0.273432i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23186.7 | − | 40160.5i | −1.44903 | − | 2.50979i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7794.62 | + | 12452.5i | −0.484826 | + | 0.774545i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1026.63 | + | 1778.18i | 0.0635571 | + | 0.110084i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11793.5 | − | 20426.9i | 0.726698 | − | 1.25868i | −0.231573 | − | 0.972818i | \(-0.574387\pi\) |
0.958271 | − | 0.285861i | \(-0.0922795\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13576.5 | + | 23515.2i | −0.832669 | + | 1.44222i | 0.0632461 | + | 0.997998i | \(0.479855\pi\) |
−0.895915 | + | 0.444226i | \(0.853479\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1806.35 | 0.110272 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3428.36 | + | 5938.09i | 0.208319 | + | 0.360820i | 0.951185 | − | 0.308620i | \(-0.0998673\pi\) |
−0.742866 | + | 0.669440i | \(0.766534\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6527.75 | 0.394817 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5533.83 | −0.333161 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4036.95 | + | 6992.20i | 0.241926 | + | 0.419029i | 0.961263 | − | 0.275633i | \(-0.0888874\pi\) |
−0.719337 | + | 0.694662i | \(0.755554\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37960.9 | 2.26451 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 787.061 | − | 1363.23i | 0.0467370 | − | 0.0809508i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2652.86 | − | 4594.89i | 0.156815 | − | 0.271611i | −0.776904 | − | 0.629620i | \(-0.783211\pi\) |
0.933718 | + | 0.358008i | \(0.116544\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12924.2 | − | 22385.3i | −0.760502 | − | 1.31723i | −0.942592 | − | 0.333946i | \(-0.891620\pi\) |
0.182091 | − | 0.983282i | \(-0.441714\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5504.26 | + | 10371.4i | 0.322425 | + | 0.607531i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3912.98 | − | 6777.48i | −0.228179 | − | 0.395217i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7496.86 | + | 12984.9i | −0.435202 | + | 0.753792i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1951.89 | + | 3380.77i | −0.112802 | + | 0.195379i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14873.6 | 0.855722 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7264.55 | + | 12582.6i | 0.416089 | + | 0.720687i | 0.995542 | − | 0.0943186i | \(-0.0300673\pi\) |
−0.579453 | + | 0.815005i | \(0.696734\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −28615.0 | −1.63169 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12058.1 | 0.684535 | 0.342267 | − | 0.939603i | \(-0.388805\pi\) | ||||
0.342267 | + | 0.939603i | \(0.388805\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2064.89 | + | 3576.50i | 0.116706 | + | 0.202140i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12764.4 | −0.718255 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15014.4 | − | 26005.7i | 0.841156 | − | 1.45693i | −0.0477615 | − | 0.998859i | \(-0.515209\pi\) |
0.888918 | − | 0.458067i | \(-0.151458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6125.74 | − | 10610.1i | 0.341682 | − | 0.591811i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4282.75 | + | 7417.94i | 0.237842 | + | 0.411954i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1486.61 | − | 2801.15i | −0.0821994 | − | 0.154884i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 224.848 | + | 389.448i | 0.0123786 | + | 0.0214404i | 0.872148 | − | 0.489241i | \(-0.162726\pi\) |
−0.859770 | + | 0.510682i | \(0.829393\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −818.471 | + | 1417.63i | −0.0448646 | + | 0.0777077i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6050.90 | − | 10480.5i | 0.330250 | − | 0.572010i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15484.8 | 0.841506 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6873.75 | + | 11905.7i | 0.371944 | + | 0.644227i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26986.0 | −1.45399 | −0.726994 | − | 0.686644i | \(-0.759083\pi\) | ||||
−0.726994 | + | 0.686644i | \(0.759083\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −346.801 | −0.0186057 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10453.1 | − | 18105.3i | −0.558422 | − | 0.967215i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1896.37 | 0.100877 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4549.44 | − | 7879.85i | 0.240984 | − | 0.417396i | −0.720011 | − | 0.693963i | \(-0.755863\pi\) |
0.960995 | + | 0.276566i | \(0.0891965\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1358.85 | + | 2353.60i | −0.0716751 | + | 0.124145i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19404.2 | + | 33609.1i | 1.01921 | + | 1.76532i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9930.53 | + | 15864.8i | −0.519414 | + | 0.829802i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11135.9 | + | 19287.9i | 0.580025 | + | 1.00463i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3146.78 | + | 5450.38i | −0.163220 | + | 0.282705i | −0.936022 | − | 0.351942i | \(-0.885521\pi\) |
0.772802 | + | 0.634647i | \(0.218855\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1577.97 | − | 2733.13i | 0.0815074 | − | 0.141175i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19064.3 | −0.980648 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10248.8 | + | 17751.4i | 0.525006 | + | 0.909337i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18070.7 | −0.921878 | −0.460939 | − | 0.887432i | \(-0.652487\pi\) | ||||
−0.460939 | + | 0.887432i | \(0.652487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17319.9 | 0.879944 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 935.790 | + | 1620.84i | 0.0473481 | + | 0.0820093i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34771.5 | 1.75214 | 0.876068 | − | 0.482188i | \(-0.160158\pi\) | ||||
0.876068 | + | 0.482188i | \(0.160158\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10282.7 | + | 17810.2i | −0.516032 | + | 0.893794i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4766.09 | + | 8255.10i | −0.238210 | + | 0.412592i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11815.7 | + | 20465.4i | 0.588158 | + | 1.01872i | 0.994474 | + | 0.104986i | \(0.0334799\pi\) |
−0.406316 | + | 0.913733i | \(0.633187\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6542.44 | + | 12327.6i | 0.324349 | + | 0.611156i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16251.4 | + | 28148.3i | 0.802431 | + | 1.38985i | 0.918012 | + | 0.396553i | \(0.129794\pi\) |
−0.115581 | + | 0.993298i | \(0.536873\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17589.3 | + | 30465.5i | −0.864995 | + | 1.49822i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2256.16 | + | 3907.78i | −0.110507 | + | 0.191403i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3108.04 | 0.151622 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1010.43 | + | 1750.12i | 0.0490960 | + | 0.0850368i | 0.889529 | − | 0.456879i | \(-0.151033\pi\) |
−0.840433 | + | 0.541915i | \(0.817699\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20710.5 | −1.00230 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32111.6 | 1.54790 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6284.11 | − | 10884.4i | −0.301717 | − | 0.522589i | 0.674808 | − | 0.737993i | \(-0.264226\pi\) |
−0.976525 | + | 0.215404i | \(0.930893\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11611.0 | −0.555273 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4352.40 | − | 7538.59i | 0.207325 | − | 0.359098i | −0.743546 | − | 0.668685i | \(-0.766857\pi\) |
0.950871 | + | 0.309587i | \(0.100191\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 478.593 | − | 828.948i | 0.0227081 | − | 0.0393315i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8125.51 | − | 14073.8i | −0.384024 | − | 0.665149i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13636.5 | − | 486.797i | −0.641962 | − | 0.0229168i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10957.9 | + | 18979.7i | 0.513853 | + | 0.890020i | 0.999871 | + | 0.0160706i | \(0.00511566\pi\) |
−0.486018 | + | 0.873949i | \(0.661551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3084.32 | − | 5342.19i | 0.144071 | − | 0.249539i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11538.8 | − | 19985.7i | 0.536896 | − | 0.929930i | −0.462173 | − | 0.886790i | \(-0.652930\pi\) |
0.999069 | − | 0.0431408i | \(-0.0137364\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 53054.0 | 2.45904 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −43.0001 | − | 74.4783i | −0.00198535 | − | 0.00343873i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18405.5 | 0.846528 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3429.94 | 0.157148 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7945.76 | − | 13762.5i | −0.362654 | − | 0.628136i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7072.67 | 0.321572 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8261.21 | + | 14308.8i | −0.374181 | + | 0.648100i | −0.990204 | − | 0.139628i | \(-0.955409\pi\) |
0.616023 | + | 0.787728i | \(0.288743\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11623.6 | + | 20132.7i | −0.524475 | + | 0.908418i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3439.50 | + | 5957.39i | 0.154607 | + | 0.267788i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31071.0 | − | 1109.18i | −1.39138 | − | 0.0496696i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2219.65 | − | 3844.55i | −0.0990224 | − | 0.171512i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5859.68 | − | 10149.3i | 0.260427 | − | 0.451073i | −0.705928 | − | 0.708283i | \(-0.749470\pi\) |
0.966356 | + | 0.257210i | \(0.0828032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10830.6 | − | 18759.1i | 0.479547 | − | 0.830600i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9640.53 | −0.425258 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1314.77 | − | 2277.24i | −0.0577797 | − | 0.100077i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13610.0 | −0.595886 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9148.01 | −0.399040 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12048.0 | + | 20867.8i | 0.523592 | + | 0.906888i | 0.999623 | + | 0.0274594i | \(0.00874171\pi\) |
−0.476031 | + | 0.879429i | \(0.657925\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16622.6 | −0.719729 | −0.359864 | − | 0.933005i | \(-0.617177\pi\) | ||||
−0.359864 | + | 0.933005i | \(0.617177\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5224.33 | − | 9048.81i | 0.225369 | − | 0.390351i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8382.05 | + | 14518.1i | −0.360258 | + | 0.623985i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1112.29 | + | 1926.55i | 0.0476306 | + | 0.0824987i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1815.51 | − | 2900.40i | 0.0774590 | − | 0.123746i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19002.8 | + | 32913.8i | 0.807797 | + | 1.39915i | 0.914387 | + | 0.404842i | \(0.132674\pi\) |
−0.106590 | + | 0.994303i | \(0.533993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7929.75 | + | 13734.7i | −0.335861 | + | 0.581728i | −0.983650 | − | 0.180092i | \(-0.942361\pi\) |
0.647789 | + | 0.761820i | \(0.275694\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7936.54 | + | 13746.5i | −0.334927 | + | 0.580111i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12201.0 | −0.513023 | −0.256512 | − | 0.966541i | \(-0.582573\pi\) | ||||
−0.256512 | + | 0.966541i | \(0.582573\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2715.71 | + | 4703.74i | 0.113776 | + | 0.197066i | 0.917290 | − | 0.398220i | \(-0.130372\pi\) |
−0.803514 | + | 0.595286i | \(0.797039\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14139.9 | −0.590263 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21308.0 | −0.886290 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32770.1 | − | 56759.5i | −1.35815 | − | 2.35239i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −41132.2 | −1.69861 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3980.45 | + | 6894.34i | −0.163791 | + | 0.283694i | −0.936225 | − | 0.351401i | \(-0.885706\pi\) |
0.772434 | + | 0.635095i | \(0.219039\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6502.78 | − | 11263.2i | 0.266628 | − | 0.461813i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16806.0 | + | 29108.8i | 0.686629 | + | 1.18928i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21928.0 | − | 32401.0i | 0.892718 | − | 1.31909i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2252.05 | − | 3900.67i | −0.0913593 | − | 0.158239i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3920.20 | − | 6789.98i | 0.158470 | − | 0.274478i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −301.557 | + | 522.313i | −0.0121472 | + | 0.0210395i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13576.7 | 0.544969 | 0.272485 | − | 0.962160i | \(-0.412155\pi\) | ||||
0.272485 | + | 0.962160i | \(0.412155\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9658.10 | − | 16728.3i | −0.386316 | − | 0.669118i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31223.9 | −1.24456 | −0.622281 | − | 0.782794i | \(-0.713794\pi\) | ||||
−0.622281 | + | 0.782794i | \(0.713794\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11815.8 | 0.469323 | 0.234661 | − | 0.972077i | \(-0.424602\pi\) | ||||
0.234661 | + | 0.972077i | \(0.424602\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2282.11 | + | 3952.73i | 0.0903300 | + | 0.156456i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1790.84 | 0.0706384 | 0.0353192 | − | 0.999376i | \(-0.488755\pi\) | ||||
0.0353192 | + | 0.999376i | \(0.488755\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12668.2 | − | 21942.0i | 0.497956 | − | 0.862485i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 536.230 | − | 928.777i | 0.0210050 | − | 0.0363817i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2269.93 | + | 3931.64i | 0.0886102 | + | 0.153477i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10572.0 | − | 16889.5i | 0.411272 | − | 0.657037i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5096.61 | + | 8827.59i | 0.197588 | + | 0.342232i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3250.00 | + | 5629.17i | −0.125566 | + | 0.217486i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21771.2 | + | 37708.9i | −0.838270 | + | 1.45193i | 0.0530701 | + | 0.998591i | \(0.483099\pi\) |
−0.891340 | + | 0.453335i | \(0.850234\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30489.7 | 1.16996 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 510.020 | + | 883.380i | 0.0195040 | + | 0.0337819i | 0.875613 | − | 0.483014i | \(-0.160458\pi\) |
−0.856109 | + | 0.516796i | \(0.827125\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34781.9 | 1.32560 | 0.662800 | − | 0.748797i | \(-0.269368\pi\) | ||||
0.662800 | + | 0.748797i | \(0.269368\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19101.6 | −0.725531 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24892.5 | + | 43115.2i | 0.942288 | + | 1.63209i | 0.761091 | + | 0.648645i | \(0.224664\pi\) |
0.181197 | + | 0.983447i | \(0.442003\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14162.3 | 0.534295 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2089.70 | − | 3619.46i | 0.0785718 | − | 0.136090i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12873.4 | − | 22297.3i | 0.482409 | − | 0.835557i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10398.8 | − | 18011.2i | −0.388371 | − | 0.672679i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24255.4 | + | 865.872i | 0.902859 | + | 0.0322304i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14731.9 | + | 25516.5i | 0.546538 | + | 0.946632i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2299.80 | − | 3983.37i | 0.0850360 | − | 0.147287i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −275.828 | + | 477.748i | −0.0101650 | + | 0.0176063i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20193.3 | 0.741712 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8694.93 | + | 15060.1i | 0.318314 | + | 0.551335i | 0.980136 | − | 0.198325i | \(-0.0635502\pi\) |
−0.661823 | + | 0.749660i | \(0.730217\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4680.66 | 0.170790 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20419.5 | −0.742621 | −0.371311 | − | 0.928509i | \(-0.621091\pi\) | ||||
−0.371311 | + | 0.928509i | \(0.621091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3768.85 | + | 6527.85i | 0.136616 | + | 0.236627i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −43523.5 | −1.57250 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5796.58 | + | 10040.0i | −0.208746 | + | 0.361558i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16615.9 | + | 28779.6i | −0.596417 | + | 1.03303i | 0.396928 | + | 0.917850i | \(0.370076\pi\) |
−0.993345 | + | 0.115175i | \(0.963257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6651.71 | − | 11521.1i | −0.237982 | − | 0.412197i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7165.15 | − | 255.782i | −0.255519 | − | 0.00912153i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 412.251 | + | 714.039i | 0.0146538 | + | 0.0253810i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3894.79 | − | 6745.97i | 0.137995 | − | 0.239015i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12611.4 | − | 21843.6i | 0.445390 | − | 0.771438i | −0.552689 | − | 0.833387i | \(-0.686398\pi\) |
0.998079 | + | 0.0619492i | \(0.0197317\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25327.0 | −0.891579 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6136.91 | + | 10629.4i | 0.215341 | + | 0.372982i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −27146.9 | −0.949519 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26979.4 | −0.940639 | −0.470319 | − | 0.882496i | \(-0.655861\pi\) | ||||
−0.470319 | + | 0.882496i | \(0.655861\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 659.785 | + | 1142.78i | 0.0229300 | + | 0.0397159i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7641.67 | 0.264730 | 0.132365 | − | 0.991201i | \(-0.457743\pi\) | ||||
0.132365 | + | 0.991201i | \(0.457743\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16004.3 | − | 27720.3i | 0.552675 | − | 0.957261i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7212.46 | − | 12492.3i | 0.248276 | − | 0.430027i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1434.66 | − | 2484.90i | −0.0492293 | − | 0.0852677i | 0.840361 | − | 0.542028i | \(-0.182343\pi\) |
−0.889590 | + | 0.456760i | \(0.849010\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2576.73 | + | 4855.22i | 0.0881393 | + | 0.166077i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5614.42 | − | 9724.46i | −0.191441 | − | 0.331585i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6156.79 | + | 10663.9i | −0.209274 | + | 0.362473i | −0.951486 | − | 0.307692i | \(-0.900443\pi\) |
0.742212 | + | 0.670165i | \(0.233777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23881.3 | + | 41363.6i | −0.809194 | + | 1.40156i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8815.22 | −0.297759 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1870.78 | + | 3240.29i | 0.0629935 | + | 0.109108i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46470.7 | 1.55989 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7671.32 | 0.256703 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17546.6 | − | 30391.6i | −0.585331 | − | 1.01382i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17838.0 | 0.593207 | 0.296603 | − | 0.955001i | \(-0.404146\pi\) | ||||
0.296603 | + | 0.955001i | \(0.404146\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10121.2 | + | 17530.5i | −0.335542 | + | 0.581176i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20762.7 | − | 35962.0i | 0.686206 | − | 1.18854i | −0.286851 | − | 0.957975i | \(-0.592608\pi\) |
0.973056 | − | 0.230568i | \(-0.0740584\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1847.93 | + | 3200.71i | 0.0608859 | + | 0.105457i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17604.6 | − | 28124.6i | 0.578254 | − | 0.923803i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15827.2 | + | 27413.5i | 0.518277 | + | 0.897682i | 0.999775 | + | 0.0212344i | \(0.00675962\pi\) |
−0.481498 | + | 0.876447i | \(0.659907\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8052.14 | + | 13946.7i | −0.262868 | + | 0.455300i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1181.27 | − | 2046.03i | 0.0384457 | − | 0.0665899i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39913.2 | 1.29505 | 0.647525 | − | 0.762045i | \(-0.275804\pi\) | ||||
0.647525 | + | 0.762045i | \(0.275804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35758.4 | − | 61935.4i | −1.15671 | − | 2.00348i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6384.72 | 0.205905 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3868.74 | 0.124387 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1350.47 | − | 2339.08i | −0.0432887 | − | 0.0749781i | 0.843569 | − | 0.537020i | \(-0.180450\pi\) |
−0.886858 | + | 0.462042i | \(0.847117\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28352.6 | −0.906085 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 37628.3 | − | 65174.2i | 1.19889 | − | 2.07654i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4864.54 | − | 8425.63i | 0.154525 | − | 0.267645i | −0.778361 | − | 0.627817i | \(-0.783949\pi\) |
0.932886 | + | 0.360172i | \(0.117282\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −319.614 | − | 553.588i | −0.0101223 | − | 0.0175323i |
(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 | 208.4.i.e.81.1 | 4 | ||
4.3 | odd | 2 | 13.4.c.b.3.1 | ✓ | 4 | ||
12.11 | even | 2 | 117.4.g.d.55.2 | 4 | |||
13.9 | even | 3 | inner | 208.4.i.e.113.1 | 4 | ||
52.3 | odd | 6 | 169.4.a.f.1.2 | 2 | |||
52.7 | even | 12 | 169.4.e.g.147.3 | 8 | |||
52.11 | even | 12 | 169.4.b.e.168.2 | 4 | |||
52.15 | even | 12 | 169.4.b.e.168.3 | 4 | |||
52.19 | even | 12 | 169.4.e.g.147.2 | 8 | |||
52.23 | odd | 6 | 169.4.a.j.1.1 | 2 | |||
52.31 | even | 4 | 169.4.e.g.23.3 | 8 | |||
52.35 | odd | 6 | 13.4.c.b.9.1 | yes | 4 | ||
52.43 | odd | 6 | 169.4.c.f.22.2 | 4 | |||
52.47 | even | 4 | 169.4.e.g.23.2 | 8 | |||
52.51 | odd | 2 | 169.4.c.f.146.2 | 4 | |||
156.23 | even | 6 | 1521.4.a.l.1.2 | 2 | |||
156.35 | even | 6 | 117.4.g.d.100.2 | 4 | |||
156.107 | even | 6 | 1521.4.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.c.b.3.1 | ✓ | 4 | 4.3 | odd | 2 | ||
13.4.c.b.9.1 | yes | 4 | 52.35 | odd | 6 | ||
117.4.g.d.55.2 | 4 | 12.11 | even | 2 | |||
117.4.g.d.100.2 | 4 | 156.35 | even | 6 | |||
169.4.a.f.1.2 | 2 | 52.3 | odd | 6 | |||
169.4.a.j.1.1 | 2 | 52.23 | odd | 6 | |||
169.4.b.e.168.2 | 4 | 52.11 | even | 12 | |||
169.4.b.e.168.3 | 4 | 52.15 | even | 12 | |||
169.4.c.f.22.2 | 4 | 52.43 | odd | 6 | |||
169.4.c.f.146.2 | 4 | 52.51 | odd | 2 | |||
169.4.e.g.23.2 | 8 | 52.47 | even | 4 | |||
169.4.e.g.23.3 | 8 | 52.31 | even | 4 | |||
169.4.e.g.147.2 | 8 | 52.19 | even | 12 | |||
169.4.e.g.147.3 | 8 | 52.7 | even | 12 | |||
208.4.i.e.81.1 | 4 | 1.1 | even | 1 | trivial | ||
208.4.i.e.113.1 | 4 | 13.9 | even | 3 | inner | ||
1521.4.a.l.1.2 | 2 | 156.23 | even | 6 | |||
1521.4.a.t.1.1 | 2 | 156.107 | even | 6 |