Newspace parameters
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
Defining polynomial: |
\( x^{2} - 3 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-expansion
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.46410 | −1.22474 | −0.612372 | − | 0.790569i | \(-0.709785\pi\) | ||||
−0.612372 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −13.8564 | −1.23935 | −0.619677 | − | 0.784857i | \(-0.712737\pi\) | ||||
−0.619677 | + | 0.784857i | \(0.712737\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −22.5167 | −1.21579 | −0.607893 | − | 0.794019i | \(-0.707985\pi\) | ||||
−0.607893 | + | 0.794019i | \(0.707985\pi\) | |||||||
\(8\) | 13.8564 | 0.612372 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 48.0000 | 1.51789 | ||||||||
\(11\) | 22.5167 | 0.617184 | 0.308592 | − | 0.951194i | \(-0.400142\pi\) | ||||
0.308592 | + | 0.951194i | \(0.400142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 78.0000 | 1.48903 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −80.0000 | −1.25000 | ||||||||
\(17\) | 27.0000 | 0.385204 | 0.192602 | − | 0.981277i | \(-0.438307\pi\) | ||||
0.192602 | + | 0.981277i | \(0.438307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −88.3346 | −1.06660 | −0.533299 | − | 0.845927i | \(-0.679048\pi\) | ||||
−0.533299 | + | 0.845927i | \(0.679048\pi\) | |||||||
\(20\) | −55.4256 | −0.619677 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −78.0000 | −0.755893 | ||||||||
\(23\) | 57.0000 | 0.516753 | 0.258377 | − | 0.966044i | \(-0.416812\pi\) | ||||
0.258377 | + | 0.966044i | \(0.416812\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 67.0000 | 0.536000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −90.0666 | −0.607893 | ||||||||
\(29\) | 69.0000 | 0.441827 | 0.220913 | − | 0.975293i | \(-0.429096\pi\) | ||||
0.220913 | + | 0.975293i | \(0.429096\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −72.7461 | −0.421471 | −0.210735 | − | 0.977543i | \(-0.567586\pi\) | ||||
−0.210735 | + | 0.977543i | \(0.567586\pi\) | |||||||
\(32\) | 166.277 | 0.918559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −93.5307 | −0.471776 | ||||||||
\(35\) | 312.000 | 1.50679 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −39.8372 | −0.177005 | −0.0885026 | − | 0.996076i | \(-0.528208\pi\) | ||||
−0.0885026 | + | 0.996076i | \(0.528208\pi\) | |||||||
\(38\) | 306.000 | 1.30631 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −192.000 | −0.758947 | ||||||||
\(41\) | −393.176 | −1.49765 | −0.748826 | − | 0.662767i | \(-0.769382\pi\) | ||||
−0.748826 | + | 0.662767i | \(0.769382\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 85.0000 | 0.301451 | 0.150725 | − | 0.988576i | \(-0.451839\pi\) | ||||
0.150725 | + | 0.988576i | \(0.451839\pi\) | |||||||
\(44\) | 90.0666 | 0.308592 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −197.454 | −0.632891 | ||||||||
\(47\) | −342.946 | −1.06434 | −0.532168 | − | 0.846639i | \(-0.678623\pi\) | ||||
−0.532168 | + | 0.846639i | \(0.678623\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 164.000 | 0.478134 | ||||||||
\(50\) | −232.095 | −0.656463 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −426.000 | −1.10407 | −0.552034 | − | 0.833822i | \(-0.686148\pi\) | ||||
−0.552034 | + | 0.833822i | \(0.686148\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −312.000 | −0.764910 | ||||||||
\(56\) | −312.000 | −0.744513 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −239.023 | −0.541125 | ||||||||
\(59\) | −19.0526 | −0.0420412 | −0.0210206 | − | 0.999779i | \(-0.506692\pi\) | ||||
−0.0210206 | + | 0.999779i | \(0.506692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17.0000 | −0.0356824 | −0.0178412 | − | 0.999841i | \(-0.505679\pi\) | ||||
−0.0178412 | + | 0.999841i | \(0.505679\pi\) | |||||||
\(62\) | 252.000 | 0.516194 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −164.545 | −0.300035 | −0.150018 | − | 0.988683i | \(-0.547933\pi\) | ||||
−0.150018 | + | 0.988683i | \(0.547933\pi\) | |||||||
\(68\) | 108.000 | 0.192602 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1080.80 | −1.84543 | ||||||||
\(71\) | −583.701 | −0.975670 | −0.487835 | − | 0.872936i | \(-0.662213\pi\) | ||||
−0.487835 | + | 0.872936i | \(0.662213\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1004.59 | −1.61066 | −0.805331 | − | 0.592826i | \(-0.798012\pi\) | ||||
−0.805331 | + | 0.592826i | \(0.798012\pi\) | |||||||
\(74\) | 138.000 | 0.216786 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −353.338 | −0.533299 | ||||||||
\(77\) | −507.000 | −0.750364 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1244.00 | −1.77166 | −0.885829 | − | 0.464012i | \(-0.846409\pi\) | ||||
−0.885829 | + | 0.464012i | \(0.846409\pi\) | |||||||
\(80\) | 1108.51 | 1.54919 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1362.00 | 1.83424 | ||||||||
\(83\) | 426.084 | 0.563480 | 0.281740 | − | 0.959491i | \(-0.409088\pi\) | ||||
0.281740 | + | 0.959491i | \(0.409088\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −374.123 | −0.477404 | ||||||||
\(86\) | −294.449 | −0.369200 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 312.000 | 0.377947 | ||||||||
\(89\) | −306.573 | −0.365131 | −0.182566 | − | 0.983194i | \(-0.558440\pi\) | ||||
−0.182566 | + | 0.983194i | \(0.558440\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 228.000 | 0.258377 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1188.00 | 1.30354 | ||||||||
\(95\) | 1224.00 | 1.32189 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1234.95 | 1.29268 | 0.646342 | − | 0.763048i | \(-0.276298\pi\) | ||||
0.646342 | + | 0.763048i | \(0.276298\pi\) | |||||||
\(98\) | −568.113 | −0.585592 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 268.000 | 0.268000 | ||||||||
\(101\) | 1959.00 | 1.92998 | 0.964989 | − | 0.262290i | \(-0.0844778\pi\) | ||||
0.964989 | + | 0.262290i | \(0.0844778\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1856.00 | −1.77551 | −0.887753 | − | 0.460320i | \(-0.847735\pi\) | ||||
−0.887753 | + | 0.460320i | \(0.847735\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1475.71 | 1.35220 | ||||||||
\(107\) | 255.000 | 0.230390 | 0.115195 | − | 0.993343i | \(-0.463251\pi\) | ||||
0.115195 | + | 0.993343i | \(0.463251\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −609.682 | −0.535752 | −0.267876 | − | 0.963453i | \(-0.586322\pi\) | ||||
−0.267876 | + | 0.963453i | \(0.586322\pi\) | |||||||
\(110\) | 1080.80 | 0.936820 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1801.33 | 1.51973 | ||||||||
\(113\) | −411.000 | −0.342156 | −0.171078 | − | 0.985257i | \(-0.554725\pi\) | ||||
−0.171078 | + | 0.985257i | \(0.554725\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −789.815 | −0.640440 | ||||||||
\(116\) | 276.000 | 0.220913 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 66.0000 | 0.0514898 | ||||||||
\(119\) | −607.950 | −0.468325 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −824.000 | −0.619083 | ||||||||
\(122\) | 58.8897 | 0.0437018 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −290.985 | −0.210735 | ||||||||
\(125\) | 803.672 | 0.575061 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2243.00 | 1.56720 | 0.783599 | − | 0.621267i | \(-0.213382\pi\) | ||||
0.783599 | + | 0.621267i | \(0.213382\pi\) | |||||||
\(128\) | −1551.92 | −1.07165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 372.000 | 0.248105 | 0.124053 | − | 0.992276i | \(-0.460411\pi\) | ||||
0.124053 | + | 0.992276i | \(0.460411\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1989.00 | 1.29675 | ||||||||
\(134\) | 570.000 | 0.367466 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 374.123 | 0.235888 | ||||||||
\(137\) | −1189.92 | −0.742056 | −0.371028 | − | 0.928622i | \(-0.620995\pi\) | ||||
−0.371028 | + | 0.928622i | \(0.620995\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2545.00 | −1.55298 | −0.776490 | − | 0.630130i | \(-0.783002\pi\) | ||||
−0.776490 | + | 0.630130i | \(0.783002\pi\) | |||||||
\(140\) | 1248.00 | 0.753395 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2022.00 | 1.19495 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −956.092 | −0.547580 | ||||||||
\(146\) | 3480.00 | 1.97265 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −159.349 | −0.0885026 | ||||||||
\(149\) | −1304.23 | −0.717094 | −0.358547 | − | 0.933512i | \(-0.616728\pi\) | ||||
−0.358547 | + | 0.933512i | \(0.616728\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 86.6025 | 0.0466729 | 0.0233365 | − | 0.999728i | \(-0.492571\pi\) | ||||
0.0233365 | + | 0.999728i | \(0.492571\pi\) | |||||||
\(152\) | −1224.00 | −0.653155 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1756.30 | 0.919004 | ||||||||
\(155\) | 1008.00 | 0.522352 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1534.00 | −0.779787 | −0.389893 | − | 0.920860i | \(-0.627488\pi\) | ||||
−0.389893 | + | 0.920860i | \(0.627488\pi\) | |||||||
\(158\) | 4309.34 | 2.16983 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2304.00 | −1.13842 | ||||||||
\(161\) | −1283.45 | −0.628261 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1633.32 | 0.784858 | 0.392429 | − | 0.919782i | \(-0.371635\pi\) | ||||
0.392429 | + | 0.919782i | \(0.371635\pi\) | |||||||
\(164\) | −1572.70 | −0.748826 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1476.00 | −0.690119 | ||||||||
\(167\) | −1626.40 | −0.753618 | −0.376809 | − | 0.926291i | \(-0.622979\pi\) | ||||
−0.376809 | + | 0.926291i | \(0.622979\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1296.00 | 0.584698 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 340.000 | 0.150725 | ||||||||
\(173\) | −873.000 | −0.383659 | −0.191829 | − | 0.981428i | \(-0.561442\pi\) | ||||
−0.191829 | + | 0.981428i | \(0.561442\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1508.62 | −0.651661 | ||||||||
\(176\) | −1801.33 | −0.771481 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1062.00 | 0.447193 | ||||||||
\(179\) | −1287.00 | −0.537402 | −0.268701 | − | 0.963224i | \(-0.586594\pi\) | ||||
−0.268701 | + | 0.963224i | \(0.586594\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.000821319 0 | −0.000410660 | − | 1.00000i | \(-0.500131\pi\) | ||||
−0.000410660 | 1.00000i | \(0.500131\pi\) | ||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 789.815 | 0.316445 | ||||||||
\(185\) | 552.000 | 0.219372 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 607.950 | 0.237742 | ||||||||
\(188\) | −1371.78 | −0.532168 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4240.06 | −1.61898 | ||||||||
\(191\) | 2841.00 | 1.07627 | 0.538135 | − | 0.842859i | \(-0.319129\pi\) | ||||
0.538135 | + | 0.842859i | \(0.319129\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4245.26 | −1.58332 | −0.791659 | − | 0.610964i | \(-0.790782\pi\) | ||||
−0.791659 | + | 0.610964i | \(0.790782\pi\) | |||||||
\(194\) | −4278.00 | −1.58321 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 656.000 | 0.239067 | ||||||||
\(197\) | 2752.23 | 0.995371 | 0.497686 | − | 0.867357i | \(-0.334183\pi\) | ||||
0.497686 | + | 0.867357i | \(0.334183\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1685.00 | 0.600234 | 0.300117 | − | 0.953902i | \(-0.402974\pi\) | ||||
0.300117 | + | 0.953902i | \(0.402974\pi\) | |||||||
\(200\) | 928.379 | 0.328232 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6786.18 | −2.36373 | ||||||||
\(203\) | −1553.65 | −0.537167 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5448.00 | 1.85612 | ||||||||
\(206\) | 6429.37 | 2.17454 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1989.00 | −0.658287 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1681.00 | 0.548459 | 0.274229 | − | 0.961664i | \(-0.411577\pi\) | ||||
0.274229 | + | 0.961664i | \(0.411577\pi\) | |||||||
\(212\) | −1704.00 | −0.552034 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −883.346 | −0.282170 | ||||||||
\(215\) | −1177.79 | −0.373604 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1638.00 | 0.512418 | ||||||||
\(218\) | 2112.00 | 0.656159 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1248.00 | −0.382455 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4096.30 | 1.23008 | 0.615042 | − | 0.788495i | \(-0.289139\pi\) | ||||
0.615042 | + | 0.788495i | \(0.289139\pi\) | |||||||
\(224\) | −3744.00 | −1.11677 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1423.75 | 0.419054 | ||||||||
\(227\) | −438.209 | −0.128128 | −0.0640638 | − | 0.997946i | \(-0.520406\pi\) | ||||
−0.0640638 | + | 0.997946i | \(0.520406\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −180.133 | −0.0519805 | −0.0259903 | − | 0.999662i | \(-0.508274\pi\) | ||||
−0.0259903 | + | 0.999662i | \(0.508274\pi\) | |||||||
\(230\) | 2736.00 | 0.784376 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 956.092 | 0.270563 | ||||||||
\(233\) | −5778.00 | −1.62459 | −0.812295 | − | 0.583247i | \(-0.801782\pi\) | ||||
−0.812295 | + | 0.583247i | \(0.801782\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4752.00 | 1.31909 | ||||||||
\(236\) | −76.2102 | −0.0210206 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2106.00 | 0.573579 | ||||||||
\(239\) | 1860.22 | 0.503464 | 0.251732 | − | 0.967797i | \(-0.419000\pi\) | ||||
0.251732 | + | 0.967797i | \(0.419000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2059.41 | −0.550449 | −0.275224 | − | 0.961380i | \(-0.588752\pi\) | ||||
−0.275224 | + | 0.961380i | \(0.588752\pi\) | |||||||
\(242\) | 2854.42 | 0.758219 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −68.0000 | −0.0178412 | ||||||||
\(245\) | −2272.45 | −0.592578 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1008.00 | −0.258097 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2784.00 | −0.704302 | ||||||||
\(251\) | 4491.00 | 1.12936 | 0.564680 | − | 0.825310i | \(-0.309000\pi\) | ||||
0.564680 | + | 0.825310i | \(0.309000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1283.45 | 0.318932 | ||||||||
\(254\) | −7769.98 | −1.91942 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4864.00 | 1.18750 | ||||||||
\(257\) | 5451.00 | 1.32305 | 0.661525 | − | 0.749923i | \(-0.269909\pi\) | ||||
0.661525 | + | 0.749923i | \(0.269909\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 897.000 | 0.215200 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1288.65 | −0.303866 | ||||||||
\(263\) | 783.000 | 0.183581 | 0.0917906 | − | 0.995778i | \(-0.470741\pi\) | ||||
0.0917906 | + | 0.995778i | \(0.470741\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5902.83 | 1.36833 | ||||||||
\(266\) | −6890.10 | −1.58819 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −658.179 | −0.150018 | ||||||||
\(269\) | 5085.00 | 1.15256 | 0.576279 | − | 0.817253i | \(-0.304504\pi\) | ||||
0.576279 | + | 0.817253i | \(0.304504\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1325.02 | −0.297008 | −0.148504 | − | 0.988912i | \(-0.547446\pi\) | ||||
−0.148504 | + | 0.988912i | \(0.547446\pi\) | |||||||
\(272\) | −2160.00 | −0.481505 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4122.00 | 0.908829 | ||||||||
\(275\) | 1508.62 | 0.330811 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3421.00 | 0.742050 | 0.371025 | − | 0.928623i | \(-0.379006\pi\) | ||||
0.371025 | + | 0.928623i | \(0.379006\pi\) | |||||||
\(278\) | 8816.14 | 1.90200 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4323.20 | 0.922716 | ||||||||
\(281\) | 810.600 | 0.172087 | 0.0860433 | − | 0.996291i | \(-0.472578\pi\) | ||||
0.0860433 | + | 0.996291i | \(0.472578\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7177.00 | −1.50752 | −0.753760 | − | 0.657149i | \(-0.771762\pi\) | ||||
−0.753760 | + | 0.657149i | \(0.771762\pi\) | |||||||
\(284\) | −2334.80 | −0.487835 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8853.00 | 1.82082 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4184.00 | −0.851618 | ||||||||
\(290\) | 3312.00 | 0.670646 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4018.36 | −0.805331 | ||||||||
\(293\) | 9313.24 | 1.85695 | 0.928473 | − | 0.371400i | \(-0.121122\pi\) | ||||
0.928473 | + | 0.371400i | \(0.121122\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 264.000 | 0.0521040 | ||||||||
\(296\) | −552.000 | −0.108393 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4518.00 | 0.878257 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1913.92 | −0.366499 | ||||||||
\(302\) | −300.000 | −0.0571625 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7066.77 | 1.33325 | ||||||||
\(305\) | 235.559 | 0.0442232 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4777.00 | 0.888070 | 0.444035 | − | 0.896009i | \(-0.353547\pi\) | ||||
0.444035 | + | 0.896009i | \(0.353547\pi\) | |||||||
\(308\) | −2028.00 | −0.375182 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3491.81 | −0.639748 | ||||||||
\(311\) | 6192.00 | 1.12899 | 0.564495 | − | 0.825436i | \(-0.309071\pi\) | ||||
0.564495 | + | 0.825436i | \(0.309071\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −770.000 | −0.139051 | −0.0695255 | − | 0.997580i | \(-0.522149\pi\) | ||||
−0.0695255 | + | 0.997580i | \(0.522149\pi\) | |||||||
\(314\) | 5313.93 | 0.955040 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4976.00 | −0.885829 | ||||||||
\(317\) | −8057.50 | −1.42762 | −0.713808 | − | 0.700341i | \(-0.753031\pi\) | ||||
−0.713808 | + | 0.700341i | \(0.753031\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1553.65 | 0.272689 | ||||||||
\(320\) | −886.810 | −0.154919 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4446.00 | 0.769459 | ||||||||
\(323\) | −2385.03 | −0.410857 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5658.00 | −0.961250 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5448.00 | −0.917120 | ||||||||
\(329\) | 7722.00 | 1.29400 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5277.56 | −0.876377 | −0.438189 | − | 0.898883i | \(-0.644380\pi\) | ||||
−0.438189 | + | 0.898883i | \(0.644380\pi\) | |||||||
\(332\) | 1704.34 | 0.281740 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5634.00 | 0.922990 | ||||||||
\(335\) | 2280.00 | 0.371850 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8278.00 | −1.33808 | −0.669038 | − | 0.743228i | \(-0.733294\pi\) | ||||
−0.669038 | + | 0.743228i | \(0.733294\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1496.49 | −0.238702 | ||||||||
\(341\) | −1638.00 | −0.260125 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4030.48 | 0.634477 | ||||||||
\(344\) | 1177.79 | 0.184600 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3024.16 | 0.469884 | ||||||||
\(347\) | −6867.00 | −1.06236 | −0.531181 | − | 0.847258i | \(-0.678252\pi\) | ||||
−0.531181 | + | 0.847258i | \(0.678252\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12153.8 | 1.86412 | 0.932060 | − | 0.362303i | \(-0.118010\pi\) | ||||
0.932060 | + | 0.362303i | \(0.118010\pi\) | |||||||
\(350\) | 5226.00 | 0.798118 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3744.00 | 0.566920 | ||||||||
\(353\) | 5807.57 | 0.875653 | 0.437827 | − | 0.899059i | \(-0.355748\pi\) | ||||
0.437827 | + | 0.899059i | \(0.355748\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8088.00 | 1.20920 | ||||||||
\(356\) | −1226.29 | −0.182566 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4458.30 | 0.658180 | ||||||||
\(359\) | 1340.61 | 0.197088 | 0.0985439 | − | 0.995133i | \(-0.468581\pi\) | ||||
0.0985439 | + | 0.995133i | \(0.468581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 944.000 | 0.137629 | ||||||||
\(362\) | 6.92820 | 0.00100591 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13920.0 | 1.99618 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3665.00 | 0.521285 | 0.260642 | − | 0.965435i | \(-0.416066\pi\) | ||||
0.260642 | + | 0.965435i | \(0.416066\pi\) | |||||||
\(368\) | −4560.00 | −0.645941 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1912.18 | −0.268675 | ||||||||
\(371\) | 9592.10 | 1.34231 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5371.00 | 0.745576 | 0.372788 | − | 0.927917i | \(-0.378402\pi\) | ||||
0.372788 | + | 0.927917i | \(0.378402\pi\) | |||||||
\(374\) | −2106.00 | −0.291173 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4752.00 | −0.651770 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11509.5 | 1.55990 | 0.779950 | − | 0.625842i | \(-0.215244\pi\) | ||||
0.779950 | + | 0.625842i | \(0.215244\pi\) | |||||||
\(380\) | 4896.00 | 0.660946 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9841.51 | −1.31816 | ||||||||
\(383\) | −2419.67 | −0.322819 | −0.161409 | − | 0.986888i | \(-0.551604\pi\) | ||||
−0.161409 | + | 0.986888i | \(0.551604\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7025.20 | 0.929967 | ||||||||
\(386\) | 14706.0 | 1.93916 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4939.81 | 0.646342 | ||||||||
\(389\) | −9858.00 | −1.28489 | −0.642443 | − | 0.766334i | \(-0.722079\pi\) | ||||
−0.642443 | + | 0.766334i | \(0.722079\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1539.00 | 0.199055 | ||||||||
\(392\) | 2272.45 | 0.292796 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9534.00 | −1.21908 | ||||||||
\(395\) | 17237.4 | 2.19571 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8720.88 | 1.10249 | 0.551245 | − | 0.834344i | \(-0.314153\pi\) | ||||
0.551245 | + | 0.834344i | \(0.314153\pi\) | |||||||
\(398\) | −5837.01 | −0.735133 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5360.00 | −0.670000 | ||||||||
\(401\) | 7584.65 | 0.944537 | 0.472269 | − | 0.881455i | \(-0.343435\pi\) | ||||
0.472269 | + | 0.881455i | \(0.343435\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 7836.00 | 0.964989 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5382.00 | 0.657892 | ||||||||
\(407\) | −897.000 | −0.109245 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4304.15 | 0.520358 | 0.260179 | − | 0.965560i | \(-0.416218\pi\) | ||||
0.260179 | + | 0.965560i | \(0.416218\pi\) | |||||||
\(410\) | −18872.4 | −2.27327 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7424.00 | −0.887753 | ||||||||
\(413\) | 429.000 | 0.0511131 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5904.00 | −0.698352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6890.10 | 0.806234 | ||||||||
\(419\) | −5397.00 | −0.629262 | −0.314631 | − | 0.949214i | \(-0.601881\pi\) | ||||
−0.314631 | + | 0.949214i | \(0.601881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7260.76 | 0.840541 | 0.420270 | − | 0.907399i | \(-0.361935\pi\) | ||||
0.420270 | + | 0.907399i | \(0.361935\pi\) | |||||||
\(422\) | −5823.15 | −0.671722 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5902.83 | −0.676101 | ||||||||
\(425\) | 1809.00 | 0.206469 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 382.783 | 0.0433822 | ||||||||
\(428\) | 1020.00 | 0.115195 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4080.00 | 0.457570 | ||||||||
\(431\) | −486.706 | −0.0543940 | −0.0271970 | − | 0.999630i | \(-0.508658\pi\) | ||||
−0.0271970 | + | 0.999630i | \(0.508658\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12139.0 | −1.34726 | −0.673629 | − | 0.739069i | \(-0.735266\pi\) | ||||
−0.673629 | + | 0.739069i | \(0.735266\pi\) | |||||||
\(434\) | −5674.20 | −0.627581 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2438.73 | −0.267876 | ||||||||
\(437\) | −5035.07 | −0.551167 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −461.000 | −0.0501192 | −0.0250596 | − | 0.999686i | \(-0.507978\pi\) | ||||
−0.0250596 | + | 0.999686i | \(0.507978\pi\) | |||||||
\(440\) | −4323.20 | −0.468410 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12156.0 | −1.30372 | −0.651861 | − | 0.758338i | \(-0.726012\pi\) | ||||
−0.651861 | + | 0.758338i | \(0.726012\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4248.00 | 0.452527 | ||||||||
\(446\) | −14190.0 | −1.50654 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1441.07 | −0.151973 | ||||||||
\(449\) | −296.181 | −0.0311306 | −0.0155653 | − | 0.999879i | \(-0.504955\pi\) | ||||
−0.0155653 | + | 0.999879i | \(0.504955\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8853.00 | −0.924327 | ||||||||
\(452\) | −1644.00 | −0.171078 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1518.00 | 0.156924 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −611.414 | −0.0625837 | −0.0312918 | − | 0.999510i | \(-0.509962\pi\) | ||||
−0.0312918 | + | 0.999510i | \(0.509962\pi\) | |||||||
\(458\) | 624.000 | 0.0636629 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3159.26 | −0.320220 | ||||||||
\(461\) | 13127.2 | 1.32624 | 0.663119 | − | 0.748514i | \(-0.269233\pi\) | ||||
0.663119 | + | 0.748514i | \(0.269233\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 834.848 | 0.0837985 | 0.0418992 | − | 0.999122i | \(-0.486659\pi\) | ||||
0.0418992 | + | 0.999122i | \(0.486659\pi\) | |||||||
\(464\) | −5520.00 | −0.552284 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20015.6 | 1.98971 | ||||||||
\(467\) | 14496.0 | 1.43639 | 0.718196 | − | 0.695841i | \(-0.244968\pi\) | ||||
0.718196 | + | 0.695841i | \(0.244968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3705.00 | 0.364778 | ||||||||
\(470\) | −16461.4 | −1.61555 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −264.000 | −0.0257449 | ||||||||
\(473\) | 1913.92 | 0.186051 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5918.42 | −0.571696 | ||||||||
\(476\) | −2431.80 | −0.234162 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6444.00 | −0.616614 | ||||||||
\(479\) | 8897.54 | 0.848725 | 0.424362 | − | 0.905492i | \(-0.360498\pi\) | ||||
0.424362 | + | 0.905492i | \(0.360498\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7134.00 | 0.674159 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3296.00 | −0.309542 | ||||||||
\(485\) | −17112.0 | −1.60209 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4754.48 | 0.442394 | 0.221197 | − | 0.975229i | \(-0.429004\pi\) | ||||
0.221197 | + | 0.975229i | \(0.429004\pi\) | |||||||
\(488\) | −235.559 | −0.0218509 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7872.00 | 0.725757 | ||||||||
\(491\) | −1635.00 | −0.150278 | −0.0751390 | − | 0.997173i | \(-0.523940\pi\) | ||||
−0.0751390 | + | 0.997173i | \(0.523940\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1863.00 | 0.170193 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5819.69 | 0.526838 | ||||||||
\(497\) | 13143.0 | 1.18621 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14434.9 | −1.29498 | −0.647490 | − | 0.762074i | \(-0.724181\pi\) | ||||
−0.647490 | + | 0.762074i | \(0.724181\pi\) | |||||||
\(500\) | 3214.69 | 0.287530 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15557.3 | −1.38318 | ||||||||
\(503\) | −12687.0 | −1.12462 | −0.562312 | − | 0.826925i | \(-0.690088\pi\) | ||||
−0.562312 | + | 0.826925i | \(0.690088\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27144.7 | −2.39193 | ||||||||
\(506\) | −4446.00 | −0.390610 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8972.00 | 0.783599 | ||||||||
\(509\) | −5748.68 | −0.500600 | −0.250300 | − | 0.968168i | \(-0.580529\pi\) | ||||
−0.250300 | + | 0.968168i | \(0.580529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22620.0 | 1.95822 | ||||||||
\(512\) | −4434.05 | −0.382733 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18882.8 | −1.62040 | ||||||||
\(515\) | 25717.5 | 2.20048 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7722.00 | −0.656892 | ||||||||
\(518\) | −3107.30 | −0.263565 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6054.00 | −0.509080 | −0.254540 | − | 0.967062i | \(-0.581924\pi\) | ||||
−0.254540 | + | 0.967062i | \(0.581924\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14803.0 | −1.23765 | −0.618824 | − | 0.785530i | \(-0.712391\pi\) | ||||
−0.618824 | + | 0.785530i | \(0.712391\pi\) | |||||||
\(524\) | 1488.00 | 0.124053 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2712.39 | −0.224840 | ||||||||
\(527\) | −1964.15 | −0.162352 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8918.00 | −0.732966 | ||||||||
\(530\) | −20448.0 | −1.67586 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7956.00 | 0.648377 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3533.38 | −0.285536 | ||||||||
\(536\) | −2280.00 | −0.183733 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17615.0 | −1.41159 | ||||||||
\(539\) | 3692.73 | 0.295097 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21470.5 | 1.70626 | 0.853132 | − | 0.521695i | \(-0.174700\pi\) | ||||
0.853132 | + | 0.521695i | \(0.174700\pi\) | |||||||
\(542\) | 4590.00 | 0.363759 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4489.48 | 0.353832 | ||||||||
\(545\) | 8448.00 | 0.663986 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13516.0 | −1.05649 | −0.528247 | − | 0.849091i | \(-0.677151\pi\) | ||||
−0.528247 | + | 0.849091i | \(0.677151\pi\) | |||||||
\(548\) | −4759.68 | −0.371028 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5226.00 | −0.405159 | ||||||||
\(551\) | −6095.09 | −0.471251 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28010.7 | 2.15396 | ||||||||
\(554\) | −11850.7 | −0.908822 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10180.0 | −0.776490 | ||||||||
\(557\) | −2890.79 | −0.219905 | −0.109952 | − | 0.993937i | \(-0.535070\pi\) | ||||
−0.109952 | + | 0.993937i | \(0.535070\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −24960.0 | −1.88349 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2808.00 | −0.210762 | ||||||||
\(563\) | 11583.0 | 0.867079 | 0.433539 | − | 0.901135i | \(-0.357265\pi\) | ||||
0.433539 | + | 0.901135i | \(0.357265\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5694.98 | 0.424053 | ||||||||
\(566\) | 24861.9 | 1.84633 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8088.00 | −0.597473 | ||||||||
\(569\) | 12879.0 | 0.948885 | 0.474443 | − | 0.880286i | \(-0.342650\pi\) | ||||
0.474443 | + | 0.880286i | \(0.342650\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11636.0 | 0.852805 | 0.426402 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426402 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −30667.7 | −2.23004 | ||||||||
\(575\) | 3819.00 | 0.276980 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12311.4 | 0.888269 | 0.444134 | − | 0.895960i | \(-0.353511\pi\) | ||||
0.444134 | + | 0.895960i | \(0.353511\pi\) | |||||||
\(578\) | 14493.8 | 1.04301 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3824.37 | −0.273790 | ||||||||
\(581\) | −9594.00 | −0.685071 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9592.10 | −0.681414 | ||||||||
\(584\) | −13920.0 | −0.986325 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32262.0 | −2.27428 | ||||||||
\(587\) | −15645.6 | −1.10011 | −0.550054 | − | 0.835129i | \(-0.685393\pi\) | ||||
−0.550054 | + | 0.835129i | \(0.685393\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6426.00 | 0.449539 | ||||||||
\(590\) | −914.523 | −0.0638141 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3186.97 | 0.221256 | ||||||||
\(593\) | 25821.4 | 1.78813 | 0.894063 | − | 0.447942i | \(-0.147843\pi\) | ||||
0.894063 | + | 0.447942i | \(0.147843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8424.00 | 0.580421 | ||||||||
\(596\) | −5216.94 | −0.358547 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1668.00 | −0.113777 | −0.0568887 | − | 0.998381i | \(-0.518118\pi\) | ||||
−0.0568887 | + | 0.998381i | \(0.518118\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13699.0 | 0.929773 | 0.464887 | − | 0.885370i | \(-0.346095\pi\) | ||||
0.464887 | + | 0.885370i | \(0.346095\pi\) | |||||||
\(602\) | 6630.00 | 0.448868 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 346.410 | 0.0233365 | ||||||||
\(605\) | 11417.7 | 0.767264 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23173.0 | −1.54953 | −0.774764 | − | 0.632251i | \(-0.782131\pi\) | ||||
−0.774764 | + | 0.632251i | \(0.782131\pi\) | |||||||
\(608\) | −14688.0 | −0.979732 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −816.000 | −0.0541621 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16615.6 | −1.09477 | −0.547387 | − | 0.836880i | \(-0.684377\pi\) | ||||
−0.547387 | + | 0.836880i | \(0.684377\pi\) | |||||||
\(614\) | −16548.0 | −1.08766 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7025.20 | −0.459502 | ||||||||
\(617\) | −28393.5 | −1.85264 | −0.926321 | − | 0.376736i | \(-0.877046\pi\) | ||||
−0.926321 | + | 0.376736i | \(0.877046\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6245.78 | 0.405556 | 0.202778 | − | 0.979225i | \(-0.435003\pi\) | ||||
0.202778 | + | 0.979225i | \(0.435003\pi\) | |||||||
\(620\) | 4032.00 | 0.261176 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21449.7 | −1.38273 | ||||||||
\(623\) | 6903.00 | 0.443921 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19511.0 | −1.24870 | ||||||||
\(626\) | 2667.36 | 0.170302 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6136.00 | −0.389893 | ||||||||
\(629\) | −1075.60 | −0.0681830 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22379.8 | −1.41193 | −0.705964 | − | 0.708247i | \(-0.749486\pi\) | ||||
−0.705964 | + | 0.708247i | \(0.749486\pi\) | |||||||
\(632\) | −17237.4 | −1.08491 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27912.0 | 1.74847 | ||||||||
\(635\) | −31079.9 | −1.94231 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5382.00 | −0.333974 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 21504.0 | 1.32816 | ||||||||
\(641\) | 19827.0 | 1.22172 | 0.610858 | − | 0.791740i | \(-0.290825\pi\) | ||||
0.610858 | + | 0.791740i | \(0.290825\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8450.68 | −0.518293 | −0.259146 | − | 0.965838i | \(-0.583441\pi\) | ||||
−0.259146 | + | 0.965838i | \(0.583441\pi\) | |||||||
\(644\) | −5133.80 | −0.314130 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8262.00 | 0.503195 | ||||||||
\(647\) | 2949.00 | 0.179192 | 0.0895959 | − | 0.995978i | \(-0.471442\pi\) | ||||
0.0895959 | + | 0.995978i | \(0.471442\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −429.000 | −0.0259472 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6533.30 | 0.392429 | ||||||||
\(653\) | −12039.0 | −0.721474 | −0.360737 | − | 0.932668i | \(-0.617475\pi\) | ||||
−0.360737 | + | 0.932668i | \(0.617475\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5154.58 | −0.307490 | ||||||||
\(656\) | 31454.0 | 1.87206 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −26749.8 | −1.58483 | ||||||||
\(659\) | −3363.00 | −0.198792 | −0.0993960 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993960 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10158.5 | 0.597759 | 0.298880 | − | 0.954291i | \(-0.403387\pi\) | ||||
0.298880 | + | 0.954291i | \(0.403387\pi\) | |||||||
\(662\) | 18282.0 | 1.07334 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5904.00 | 0.345060 | ||||||||
\(665\) | −27560.4 | −1.60714 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3933.00 | 0.228315 | ||||||||
\(668\) | −6505.58 | −0.376809 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7898.15 | −0.455421 | ||||||||
\(671\) | −382.783 | −0.0220226 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18169.0 | 1.04066 | 0.520329 | − | 0.853966i | \(-0.325809\pi\) | ||||
0.520329 | + | 0.853966i | \(0.325809\pi\) | |||||||
\(674\) | 28675.8 | 1.63880 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9042.00 | −0.513312 | −0.256656 | − | 0.966503i | \(-0.582621\pi\) | ||||
−0.256656 | + | 0.966503i | \(0.582621\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27807.0 | −1.57163 | ||||||||
\(680\) | −5184.00 | −0.292349 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5674.20 | 0.318587 | ||||||||
\(683\) | −12462.1 | −0.698169 | −0.349084 | − | 0.937091i | \(-0.613507\pi\) | ||||
−0.349084 | + | 0.937091i | \(0.613507\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16488.0 | 0.919670 | ||||||||
\(686\) | −13962.0 | −0.777072 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6800.00 | −0.376813 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4318.00 | 0.237720 | 0.118860 | − | 0.992911i | \(-0.462076\pi\) | ||||
0.118860 | + | 0.992911i | \(0.462076\pi\) | |||||||
\(692\) | −3492.00 | −0.191829 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23788.0 | 1.30112 | ||||||||
\(695\) | 35264.6 | 1.92469 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10615.7 | −0.576901 | ||||||||
\(698\) | −42102.0 | −2.28307 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6034.47 | −0.325830 | ||||||||
\(701\) | −18270.0 | −0.984377 | −0.492189 | − | 0.870489i | \(-0.663803\pi\) | ||||
−0.492189 | + | 0.870489i | \(0.663803\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3519.00 | 0.188793 | ||||||||
\(704\) | 1441.07 | 0.0771481 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20118.0 | −1.07245 | ||||||||
\(707\) | −44110.1 | −2.34644 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1629.86 | −0.0863338 | −0.0431669 | − | 0.999068i | \(-0.513745\pi\) | ||||
−0.0431669 | + | 0.999068i | \(0.513745\pi\) | |||||||
\(710\) | −28017.7 | −1.48096 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4248.00 | −0.223596 | ||||||||
\(713\) | −4146.53 | −0.217796 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5148.00 | −0.268701 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4644.00 | −0.241382 | ||||||||
\(719\) | 9831.00 | 0.509923 | 0.254961 | − | 0.966951i | \(-0.417937\pi\) | ||||
0.254961 | + | 0.966951i | \(0.417937\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41790.9 | 2.15863 | ||||||||
\(722\) | −3270.11 | −0.168561 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.00000 | −0.000410660 0 | ||||||||
\(725\) | 4623.00 | 0.236819 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15464.0 | 0.788897 | 0.394448 | − | 0.918918i | \(-0.370936\pi\) | ||||
0.394448 | + | 0.918918i | \(0.370936\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −48220.3 | −2.44481 | ||||||||
\(731\) | 2295.00 | 0.116120 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12616.3 | −0.635733 | −0.317866 | − | 0.948136i | \(-0.602966\pi\) | ||||
−0.317866 | + | 0.948136i | \(0.602966\pi\) | |||||||
\(734\) | −12695.9 | −0.638441 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9477.78 | 0.474668 | ||||||||
\(737\) | −3705.00 | −0.185177 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16283.0 | −0.810528 | −0.405264 | − | 0.914200i | \(-0.632820\pi\) | ||||
−0.405264 | + | 0.914200i | \(0.632820\pi\) | |||||||
\(740\) | 2208.00 | 0.109686 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −33228.0 | −1.64399 | ||||||||
\(743\) | 10806.3 | 0.533571 | 0.266786 | − | 0.963756i | \(-0.414038\pi\) | ||||
0.266786 | + | 0.963756i | \(0.414038\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18072.0 | 0.888734 | ||||||||
\(746\) | −18605.7 | −0.913140 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2431.80 | 0.118871 | ||||||||
\(749\) | −5741.75 | −0.280105 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13615.0 | 0.661542 | 0.330771 | − | 0.943711i | \(-0.392691\pi\) | ||||
0.330771 | + | 0.943711i | \(0.392691\pi\) | |||||||
\(752\) | 27435.7 | 1.33042 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1200.00 | −0.0578443 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5551.00 | 0.266519 | 0.133259 | − | 0.991081i | \(-0.457456\pi\) | ||||
0.133259 | + | 0.991081i | \(0.457456\pi\) | |||||||
\(758\) | −39870.0 | −1.91048 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16960.2 | 0.809490 | ||||||||
\(761\) | 10082.3 | 0.480265 | 0.240133 | − | 0.970740i | \(-0.422809\pi\) | ||||
0.240133 | + | 0.970740i | \(0.422809\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13728.0 | 0.651359 | ||||||||
\(764\) | 11364.0 | 0.538135 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8382.00 | 0.395371 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29758.4 | −1.39547 | −0.697733 | − | 0.716357i | \(-0.745808\pi\) | ||||
−0.697733 | + | 0.716357i | \(0.745808\pi\) | |||||||
\(770\) | −24336.0 | −1.13897 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16981.0 | −0.791659 | ||||||||
\(773\) | −27735.3 | −1.29052 | −0.645259 | − | 0.763964i | \(-0.723251\pi\) | ||||
−0.645259 | + | 0.763964i | \(0.723251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4873.99 | −0.225908 | ||||||||
\(776\) | 17112.0 | 0.791604 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34149.1 | 1.57366 | ||||||||
\(779\) | 34731.0 | 1.59739 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13143.0 | −0.602168 | ||||||||
\(782\) | −5331.25 | −0.243792 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13120.0 | −0.597668 | ||||||||
\(785\) | 21255.7 | 0.966432 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31549.3 | 1.42899 | 0.714493 | − | 0.699643i | \(-0.246658\pi\) | ||||
0.714493 | + | 0.699643i | \(0.246658\pi\) | |||||||
\(788\) | 11008.9 | 0.497686 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −59712.0 | −2.68919 | ||||||||
\(791\) | 9254.35 | 0.415988 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −30210.0 | −1.35027 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6740.00 | 0.300117 | ||||||||
\(797\) | 1455.00 | 0.0646659 | 0.0323330 | − | 0.999477i | \(-0.489706\pi\) | ||||
0.0323330 | + | 0.999477i | \(0.489706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9259.54 | −0.409986 | ||||||||
\(800\) | 11140.6 | 0.492347 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26274.0 | −1.15682 | ||||||||
\(803\) | −22620.0 | −0.994075 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17784.0 | 0.778638 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 27144.7 | 1.18187 | ||||||||
\(809\) | −1659.00 | −0.0720981 | −0.0360490 | − | 0.999350i | \(-0.511477\pi\) | ||||
−0.0360490 | + | 0.999350i | \(0.511477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4402.87 | 0.190636 | 0.0953180 | − | 0.995447i | \(-0.469613\pi\) | ||||
0.0953180 | + | 0.995447i | \(0.469613\pi\) | |||||||
\(812\) | −6214.60 | −0.268583 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3107.30 | 0.133797 | ||||||||
\(815\) | −22632.0 | −0.972717 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7508.44 | −0.321526 | ||||||||
\(818\) | −14910.0 | −0.637306 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 21792.0 | 0.928061 | ||||||||
\(821\) | −28701.8 | −1.22010 | −0.610049 | − | 0.792364i | \(-0.708850\pi\) | ||||
−0.610049 | + | 0.792364i | \(0.708850\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15779.0 | −0.668313 | −0.334156 | − | 0.942518i | \(-0.608451\pi\) | ||||
−0.334156 | + | 0.942518i | \(0.608451\pi\) | |||||||
\(824\) | −25717.5 | −1.08727 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1486.10 | −0.0626005 | ||||||||
\(827\) | −7354.29 | −0.309231 | −0.154615 | − | 0.987975i | \(-0.549414\pi\) | ||||
−0.154615 | + | 0.987975i | \(0.549414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17371.0 | −0.727768 | −0.363884 | − | 0.931444i | \(-0.618550\pi\) | ||||
−0.363884 | + | 0.931444i | \(0.618550\pi\) | |||||||
\(830\) | 20452.1 | 0.855303 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4428.00 | 0.184179 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22536.0 | 0.934001 | ||||||||
\(836\) | −7956.00 | −0.329144 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18695.8 | 0.770685 | ||||||||
\(839\) | 29474.3 | 1.21283 | 0.606416 | − | 0.795148i | \(-0.292607\pi\) | ||||
0.606416 | + | 0.795148i | \(0.292607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19628.0 | −0.804789 | ||||||||
\(842\) | −25152.0 | −1.02945 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6724.00 | 0.274229 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18553.7 | 0.752673 | ||||||||
\(848\) | 34080.0 | 1.38008 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6266.56 | −0.252872 | ||||||||
\(851\) | −2270.72 | −0.0914680 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2909.85 | −0.116801 | −0.0584005 | − | 0.998293i | \(-0.518600\pi\) | ||||
−0.0584005 | + | 0.998293i | \(0.518600\pi\) | |||||||
\(854\) | −1326.00 | −0.0531321 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3533.38 | 0.141085 | ||||||||
\(857\) | −5346.00 | −0.213087 | −0.106544 | − | 0.994308i | \(-0.533978\pi\) | ||||
−0.106544 | + | 0.994308i | \(0.533978\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24244.0 | 0.962974 | 0.481487 | − | 0.876453i | \(-0.340097\pi\) | ||||
0.481487 | + | 0.876453i | \(0.340097\pi\) | |||||||
\(860\) | −4711.18 | −0.186802 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1686.00 | 0.0666188 | ||||||||
\(863\) | −32780.8 | −1.29301 | −0.646507 | − | 0.762908i | \(-0.723771\pi\) | ||||
−0.646507 | + | 0.762908i | \(0.723771\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12096.6 | 0.475489 | ||||||||
\(866\) | 42050.7 | 1.65005 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6552.00 | 0.256209 | ||||||||
\(869\) | −28010.7 | −1.09344 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8448.00 | −0.328080 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17442.0 | 0.675039 | ||||||||
\(875\) | −18096.0 | −0.699150 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4543.17 | −0.174928 | −0.0874640 | − | 0.996168i | \(-0.527876\pi\) | ||||
−0.0874640 | + | 0.996168i | \(0.527876\pi\) | |||||||
\(878\) | 1596.95 | 0.0613832 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 24960.0 | 0.956138 | ||||||||
\(881\) | −20517.0 | −0.784603 | −0.392302 | − | 0.919837i | \(-0.628321\pi\) | ||||
−0.392302 | + | 0.919837i | \(0.628321\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23852.0 | 0.909042 | 0.454521 | − | 0.890736i | \(-0.349811\pi\) | ||||
0.454521 | + | 0.890736i | \(0.349811\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 42109.6 | 1.59673 | ||||||||
\(887\) | −38757.0 | −1.46712 | −0.733558 | − | 0.679626i | \(-0.762142\pi\) | ||||
−0.733558 | + | 0.679626i | \(0.762142\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50504.9 | −1.90538 | ||||||||
\(890\) | −14715.5 | −0.554230 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16385.2 | 0.615042 | ||||||||
\(893\) | 30294.0 | 1.13522 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17833.2 | 0.666031 | ||||||||
\(896\) | 34944.0 | 1.30290 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1026.00 | 0.0381270 | ||||||||
\(899\) | −5019.48 | −0.186217 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11502.0 | −0.425291 | ||||||||
\(902\) | 30667.7 | 1.13206 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5694.98 | −0.209527 | ||||||||
\(905\) | 27.7128 | 0.00101791 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39071.0 | 1.43035 | 0.715177 | − | 0.698943i | \(-0.246346\pi\) | ||||
0.715177 | + | 0.698943i | \(0.246346\pi\) | |||||||
\(908\) | −1752.84 | −0.0640638 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53040.0 | 1.92897 | 0.964486 | − | 0.264134i | \(-0.0850860\pi\) | ||||
0.964486 | + | 0.264134i | \(0.0850860\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9594.00 | 0.347771 | ||||||||
\(914\) | 2118.00 | 0.0766490 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −720.533 | −0.0259903 | ||||||||
\(917\) | −8376.20 | −0.301643 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 367.000 | 0.0131732 | 0.00658662 | − | 0.999978i | \(-0.497903\pi\) | ||||
0.00658662 | + | 0.999978i | \(0.497903\pi\) | |||||||
\(920\) | −10944.0 | −0.392188 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −45474.0 | −1.62430 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2669.09 | −0.0948748 | ||||||||
\(926\) | −2892.00 | −0.102632 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11473.1 | 0.405844 | ||||||||
\(929\) | 29935.0 | 1.05720 | 0.528599 | − | 0.848872i | \(-0.322718\pi\) | ||||
0.528599 | + | 0.848872i | \(0.322718\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14486.9 | −0.509976 | ||||||||
\(932\) | −23112.0 | −0.812295 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −50215.6 | −1.75921 | ||||||||
\(935\) | −8424.00 | −0.294646 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42166.0 | 1.47012 | 0.735060 | − | 0.678002i | \(-0.237154\pi\) | ||||
0.735060 | + | 0.678002i | \(0.237154\pi\) | |||||||
\(938\) | −12834.5 | −0.446760 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 19008.0 | 0.659545 | ||||||||
\(941\) | 35022.1 | 1.21327 | 0.606635 | − | 0.794981i | \(-0.292519\pi\) | ||||
0.606635 | + | 0.794981i | \(0.292519\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22411.0 | −0.773916 | ||||||||
\(944\) | 1524.20 | 0.0525515 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6630.00 | −0.227865 | ||||||||
\(947\) | 2599.81 | 0.0892106 | 0.0446053 | − | 0.999005i | \(-0.485797\pi\) | ||||
0.0446053 | + | 0.999005i | \(0.485797\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 20502.0 | 0.700182 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8424.00 | −0.286789 | ||||||||
\(953\) | 10623.0 | 0.361084 | 0.180542 | − | 0.983567i | \(-0.442215\pi\) | ||||
0.180542 | + | 0.983567i | \(0.442215\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39366.1 | −1.33388 | ||||||||
\(956\) | 7440.89 | 0.251732 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −30822.0 | −1.03947 | ||||||||
\(959\) | 26793.0 | 0.902180 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24499.0 | −0.822362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8237.63 | −0.275224 | ||||||||
\(965\) | 58824.0 | 1.96229 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20199.2 | 0.671729 | 0.335864 | − | 0.941910i | \(-0.390972\pi\) | ||||
0.335864 | + | 0.941910i | \(0.390972\pi\) | |||||||
\(968\) | −11417.7 | −0.379110 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 59277.7 | 1.96216 | ||||||||
\(971\) | 2325.00 | 0.0768412 | 0.0384206 | − | 0.999262i | \(-0.487767\pi\) | ||||
0.0384206 | + | 0.999262i | \(0.487767\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57304.9 | 1.88809 | ||||||||
\(974\) | −16470.0 | −0.541820 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1360.00 | 0.0446030 | ||||||||
\(977\) | 32938.4 | 1.07860 | 0.539300 | − | 0.842113i | \(-0.318689\pi\) | ||||
0.539300 | + | 0.842113i | \(0.318689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6903.00 | −0.225353 | ||||||||
\(980\) | −9089.80 | −0.296289 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5663.81 | 0.184052 | ||||||||
\(983\) | 42702.0 | 1.38554 | 0.692768 | − | 0.721161i | \(-0.256391\pi\) | ||||
0.692768 | + | 0.721161i | \(0.256391\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38136.0 | −1.23362 | ||||||||
\(986\) | −6453.62 | −0.208443 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4845.00 | 0.155776 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4843.00 | −0.155240 | −0.0776201 | − | 0.996983i | \(-0.524732\pi\) | ||||
−0.0776201 | + | 0.996983i | \(0.524732\pi\) | |||||||
\(992\) | −12096.0 | −0.387146 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −45528.7 | −1.45280 | ||||||||
\(995\) | −23348.0 | −0.743902 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10943.0 | 0.347611 | 0.173806 | − | 0.984780i | \(-0.444394\pi\) | ||||
0.173806 | + | 0.984780i | \(0.444394\pi\) | |||||||
\(998\) | 50004.0 | 1.58602 | ||||||||
\(999\) | 0 | 0 |
(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 | 1521.4.a.q.1.1 | 2 | ||
3.2 | odd | 2 | 169.4.a.h.1.2 | 2 | |||
13.6 | odd | 12 | 117.4.q.c.10.1 | 2 | |||
13.11 | odd | 12 | 117.4.q.c.82.1 | 2 | |||
13.12 | even | 2 | inner | 1521.4.a.q.1.2 | 2 | ||
39.2 | even | 12 | 169.4.e.b.147.1 | 2 | |||
39.5 | even | 4 | 169.4.b.b.168.1 | 2 | |||
39.8 | even | 4 | 169.4.b.b.168.2 | 2 | |||
39.11 | even | 12 | 13.4.e.a.4.1 | ✓ | 2 | ||
39.17 | odd | 6 | 169.4.c.i.146.2 | 4 | |||
39.20 | even | 12 | 169.4.e.b.23.1 | 2 | |||
39.23 | odd | 6 | 169.4.c.i.22.2 | 4 | |||
39.29 | odd | 6 | 169.4.c.i.22.1 | 4 | |||
39.32 | even | 12 | 13.4.e.a.10.1 | yes | 2 | ||
39.35 | odd | 6 | 169.4.c.i.146.1 | 4 | |||
39.38 | odd | 2 | 169.4.a.h.1.1 | 2 | |||
156.11 | odd | 12 | 208.4.w.a.17.1 | 2 | |||
156.71 | odd | 12 | 208.4.w.a.49.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.e.a.4.1 | ✓ | 2 | 39.11 | even | 12 | ||
13.4.e.a.10.1 | yes | 2 | 39.32 | even | 12 | ||
117.4.q.c.10.1 | 2 | 13.6 | odd | 12 | |||
117.4.q.c.82.1 | 2 | 13.11 | odd | 12 | |||
169.4.a.h.1.1 | 2 | 39.38 | odd | 2 | |||
169.4.a.h.1.2 | 2 | 3.2 | odd | 2 | |||
169.4.b.b.168.1 | 2 | 39.5 | even | 4 | |||
169.4.b.b.168.2 | 2 | 39.8 | even | 4 | |||
169.4.c.i.22.1 | 4 | 39.29 | odd | 6 | |||
169.4.c.i.22.2 | 4 | 39.23 | odd | 6 | |||
169.4.c.i.146.1 | 4 | 39.35 | odd | 6 | |||
169.4.c.i.146.2 | 4 | 39.17 | odd | 6 | |||
169.4.e.b.23.1 | 2 | 39.20 | even | 12 | |||
169.4.e.b.147.1 | 2 | 39.2 | even | 12 | |||
208.4.w.a.17.1 | 2 | 156.11 | odd | 12 | |||
208.4.w.a.49.1 | 2 | 156.71 | odd | 12 | |||
1521.4.a.q.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1521.4.a.q.1.2 | 2 | 13.12 | even | 2 | inner |