Newspace parameters
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(122.133953712\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 60x^{2} - 45x + 108 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-6.12571\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.6431 | −1.33060 | −0.665301 | − | 0.746575i | \(-0.731697\pi\) | ||||
−0.665301 | + | 0.746575i | \(0.731697\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.0000 | 0.316228 | ||||||||
\(11\) | 17.3867 | 0.476572 | 0.238286 | − | 0.971195i | \(-0.423414\pi\) | ||||
0.238286 | + | 0.971195i | \(0.423414\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00699 | 0.0854876 | 0.0427438 | − | 0.999086i | \(-0.486390\pi\) | ||||
0.0427438 | + | 0.999086i | \(0.486390\pi\) | |||||||
\(14\) | 49.2862 | 0.940877 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −48.2740 | −0.688716 | −0.344358 | − | 0.938838i | \(-0.611903\pi\) | ||||
−0.344358 | + | 0.938838i | \(0.611903\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 79.3172 | 0.957717 | 0.478859 | − | 0.877892i | \(-0.341051\pi\) | ||||
0.478859 | + | 0.877892i | \(0.341051\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −34.7734 | −0.336987 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −8.01398 | −0.0604488 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −98.5723 | −0.665301 | ||||||||
\(29\) | 254.267 | 1.62815 | 0.814074 | − | 0.580761i | \(-0.197245\pi\) | ||||
0.814074 | + | 0.580761i | \(0.197245\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −220.696 | −1.27865 | −0.639325 | − | 0.768937i | \(-0.720786\pi\) | ||||
−0.639325 | + | 0.768937i | \(0.720786\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 96.5480 | 0.486996 | ||||||||
\(35\) | 123.215 | 0.595063 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −422.904 | −1.87905 | −0.939527 | − | 0.342476i | \(-0.888735\pi\) | ||||
−0.939527 | + | 0.342476i | \(0.888735\pi\) | |||||||
\(38\) | −158.634 | −0.677208 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 40.0000 | 0.158114 | ||||||||
\(41\) | 170.251 | 0.648505 | 0.324252 | − | 0.945971i | \(-0.394887\pi\) | ||||
0.324252 | + | 0.945971i | \(0.394887\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −228.920 | −0.811860 | −0.405930 | − | 0.913904i | \(-0.633052\pi\) | ||||
−0.405930 | + | 0.913904i | \(0.633052\pi\) | |||||||
\(44\) | 69.5468 | 0.238286 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | −580.087 | −1.80031 | −0.900154 | − | 0.435572i | \(-0.856546\pi\) | ||||
−0.900154 | + | 0.435572i | \(0.856546\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 264.282 | 0.770500 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16.0280 | 0.0427438 | ||||||||
\(53\) | 260.354 | 0.674762 | 0.337381 | − | 0.941368i | \(-0.390459\pi\) | ||||
0.337381 | + | 0.941368i | \(0.390459\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −86.9335 | −0.213129 | ||||||||
\(56\) | 197.145 | 0.470439 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −508.535 | −1.15127 | ||||||||
\(59\) | −353.130 | −0.779215 | −0.389607 | − | 0.920981i | \(-0.627389\pi\) | ||||
−0.389607 | + | 0.920981i | \(0.627389\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −80.6108 | −0.169199 | −0.0845996 | − | 0.996415i | \(-0.526961\pi\) | ||||
−0.0845996 | + | 0.996415i | \(0.526961\pi\) | |||||||
\(62\) | 441.392 | 0.904142 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −20.0349 | −0.0382312 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −820.011 | −1.49523 | −0.747614 | − | 0.664133i | \(-0.768801\pi\) | ||||
−0.747614 | + | 0.664133i | \(0.768801\pi\) | |||||||
\(68\) | −193.096 | −0.344358 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −246.431 | −0.420773 | ||||||||
\(71\) | −614.845 | −1.02773 | −0.513864 | − | 0.857872i | \(-0.671786\pi\) | ||||
−0.513864 | + | 0.857872i | \(0.671786\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 511.586 | 0.820228 | 0.410114 | − | 0.912034i | \(-0.365489\pi\) | ||||
0.410114 | + | 0.912034i | \(0.365489\pi\) | |||||||
\(74\) | 845.808 | 1.32869 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 317.269 | 0.478859 | ||||||||
\(77\) | −428.462 | −0.634127 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 160.464 | 0.228526 | 0.114263 | − | 0.993451i | \(-0.463549\pi\) | ||||
0.114263 | + | 0.993451i | \(0.463549\pi\) | |||||||
\(80\) | −80.0000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −340.502 | −0.458562 | ||||||||
\(83\) | 32.5646 | 0.0430654 | 0.0215327 | − | 0.999768i | \(-0.493145\pi\) | ||||
0.0215327 | + | 0.999768i | \(0.493145\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 241.370 | 0.308003 | ||||||||
\(86\) | 457.840 | 0.574072 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −139.094 | −0.168494 | ||||||||
\(89\) | 25.0375 | 0.0298199 | 0.0149100 | − | 0.999889i | \(-0.495254\pi\) | ||||
0.0149100 | + | 0.999889i | \(0.495254\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −98.7445 | −0.113750 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1160.17 | 1.27301 | ||||||||
\(95\) | −396.586 | −0.428304 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −249.798 | −0.261476 | −0.130738 | − | 0.991417i | \(-0.541735\pi\) | ||||
−0.130738 | + | 0.991417i | \(0.541735\pi\) | |||||||
\(98\) | −528.563 | −0.544826 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | −620.493 | −0.611300 | −0.305650 | − | 0.952144i | \(-0.598874\pi\) | ||||
−0.305650 | + | 0.952144i | \(0.598874\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1473.24 | 1.40935 | 0.704673 | − | 0.709532i | \(-0.251094\pi\) | ||||
0.704673 | + | 0.709532i | \(0.251094\pi\) | |||||||
\(104\) | −32.0559 | −0.0302244 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −520.708 | −0.477129 | ||||||||
\(107\) | 940.141 | 0.849410 | 0.424705 | − | 0.905332i | \(-0.360378\pi\) | ||||
0.424705 | + | 0.905332i | \(0.360378\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −636.264 | −0.559111 | −0.279555 | − | 0.960130i | \(-0.590187\pi\) | ||||
−0.279555 | + | 0.960130i | \(0.590187\pi\) | |||||||
\(110\) | 173.867 | 0.150705 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −394.289 | −0.332650 | ||||||||
\(113\) | −832.451 | −0.693013 | −0.346506 | − | 0.938048i | \(-0.612632\pi\) | ||||
−0.346506 | + | 0.938048i | \(0.612632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −115.000 | −0.0932505 | ||||||||
\(116\) | 1017.07 | 0.814074 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 706.261 | 0.550988 | ||||||||
\(119\) | 1189.62 | 0.916406 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1028.70 | −0.772879 | ||||||||
\(122\) | 161.222 | 0.119642 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −882.783 | −0.639325 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1614.60 | 1.12813 | 0.564067 | − | 0.825729i | \(-0.309236\pi\) | ||||
0.564067 | + | 0.825729i | \(0.309236\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 40.0699 | 0.0270335 | ||||||||
\(131\) | 1974.56 | 1.31693 | 0.658464 | − | 0.752612i | \(-0.271206\pi\) | ||||
0.658464 | + | 0.752612i | \(0.271206\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1954.62 | −1.27434 | ||||||||
\(134\) | 1640.02 | 1.05729 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 386.192 | 0.243498 | ||||||||
\(137\) | −753.805 | −0.470087 | −0.235044 | − | 0.971985i | \(-0.575523\pi\) | ||||
−0.235044 | + | 0.971985i | \(0.575523\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1014.10 | 0.618810 | 0.309405 | − | 0.950930i | \(-0.399870\pi\) | ||||
0.309405 | + | 0.950930i | \(0.399870\pi\) | |||||||
\(140\) | 492.862 | 0.297532 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1229.69 | 0.726714 | ||||||||
\(143\) | 69.6683 | 0.0407410 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1271.34 | −0.728130 | ||||||||
\(146\) | −1023.17 | −0.579989 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1691.62 | −0.939527 | ||||||||
\(149\) | 2771.80 | 1.52399 | 0.761995 | − | 0.647583i | \(-0.224220\pi\) | ||||
0.761995 | + | 0.647583i | \(0.224220\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3108.62 | 1.67534 | 0.837668 | − | 0.546180i | \(-0.183918\pi\) | ||||
0.837668 | + | 0.546180i | \(0.183918\pi\) | |||||||
\(152\) | −634.538 | −0.338604 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 856.924 | 0.448396 | ||||||||
\(155\) | 1103.48 | 0.571830 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3712.87 | 1.88739 | 0.943693 | − | 0.330822i | \(-0.107326\pi\) | ||||
0.943693 | + | 0.330822i | \(0.107326\pi\) | |||||||
\(158\) | −320.928 | −0.161593 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 160.000 | 0.0790569 | ||||||||
\(161\) | −566.791 | −0.277450 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 915.791 | 0.440063 | 0.220032 | − | 0.975493i | \(-0.429384\pi\) | ||||
0.220032 | + | 0.975493i | \(0.429384\pi\) | |||||||
\(164\) | 681.003 | 0.324252 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −65.1292 | −0.0304518 | ||||||||
\(167\) | −1432.32 | −0.663688 | −0.331844 | − | 0.943334i | \(-0.607671\pi\) | ||||
−0.331844 | + | 0.943334i | \(0.607671\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2180.94 | −0.992692 | ||||||||
\(170\) | −482.740 | −0.217791 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −915.680 | −0.405930 | ||||||||
\(173\) | 3479.54 | 1.52916 | 0.764580 | − | 0.644529i | \(-0.222946\pi\) | ||||
0.764580 | + | 0.644529i | \(0.222946\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −616.077 | −0.266120 | ||||||||
\(176\) | 278.187 | 0.119143 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −50.0751 | −0.0210859 | ||||||||
\(179\) | −3642.71 | −1.52105 | −0.760527 | − | 0.649307i | \(-0.775059\pi\) | ||||
−0.760527 | + | 0.649307i | \(0.775059\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2409.15 | 0.989342 | 0.494671 | − | 0.869080i | \(-0.335289\pi\) | ||||
0.494671 | + | 0.869080i | \(0.335289\pi\) | |||||||
\(182\) | 197.489 | 0.0804333 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 2114.52 | 0.840338 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −839.326 | −0.328223 | ||||||||
\(188\) | −2320.35 | −0.900154 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 793.172 | 0.302857 | ||||||||
\(191\) | 189.608 | 0.0718299 | 0.0359150 | − | 0.999355i | \(-0.488565\pi\) | ||||
0.0359150 | + | 0.999355i | \(0.488565\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1855.45 | −0.692012 | −0.346006 | − | 0.938232i | \(-0.612462\pi\) | ||||
−0.346006 | + | 0.938232i | \(0.612462\pi\) | |||||||
\(194\) | 499.597 | 0.184891 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1057.13 | 0.385250 | ||||||||
\(197\) | −2429.85 | −0.878779 | −0.439390 | − | 0.898297i | \(-0.644805\pi\) | ||||
−0.439390 | + | 0.898297i | \(0.644805\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4333.49 | 1.54368 | 0.771842 | − | 0.635815i | \(-0.219336\pi\) | ||||
0.771842 | + | 0.635815i | \(0.219336\pi\) | |||||||
\(200\) | −200.000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1240.99 | 0.432255 | ||||||||
\(203\) | −6265.94 | −2.16642 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −851.254 | −0.290020 | ||||||||
\(206\) | −2946.48 | −0.996558 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 64.1118 | 0.0213719 | ||||||||
\(209\) | 1379.07 | 0.456421 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −816.788 | −0.266493 | −0.133247 | − | 0.991083i | \(-0.542540\pi\) | ||||
−0.133247 | + | 0.991083i | \(0.542540\pi\) | |||||||
\(212\) | 1041.42 | 0.337381 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1880.28 | −0.600624 | ||||||||
\(215\) | 1144.60 | 0.363075 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5438.63 | 1.70137 | ||||||||
\(218\) | 1272.53 | 0.395351 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −347.734 | −0.106565 | ||||||||
\(221\) | −193.433 | −0.0588767 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4513.80 | −1.35546 | −0.677728 | − | 0.735313i | \(-0.737035\pi\) | ||||
−0.677728 | + | 0.735313i | \(0.737035\pi\) | |||||||
\(224\) | 788.579 | 0.235219 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1664.90 | 0.490034 | ||||||||
\(227\) | −2792.85 | −0.816599 | −0.408300 | − | 0.912848i | \(-0.633878\pi\) | ||||
−0.408300 | + | 0.912848i | \(0.633878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1404.50 | 0.405292 | 0.202646 | − | 0.979252i | \(-0.435046\pi\) | ||||
0.202646 | + | 0.979252i | \(0.435046\pi\) | |||||||
\(230\) | 230.000 | 0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2034.14 | −0.575637 | ||||||||
\(233\) | −1073.79 | −0.301916 | −0.150958 | − | 0.988540i | \(-0.548236\pi\) | ||||
−0.150958 | + | 0.988540i | \(0.548236\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2900.44 | 0.805122 | ||||||||
\(236\) | −1412.52 | −0.389607 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2379.24 | −0.647997 | ||||||||
\(239\) | 2573.18 | 0.696423 | 0.348212 | − | 0.937416i | \(-0.386789\pi\) | ||||
0.348212 | + | 0.937416i | \(0.386789\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −696.127 | −0.186064 | −0.0930321 | − | 0.995663i | \(-0.529656\pi\) | ||||
−0.0930321 | + | 0.995663i | \(0.529656\pi\) | |||||||
\(242\) | 2057.40 | 0.546508 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −322.443 | −0.0845996 | ||||||||
\(245\) | −1321.41 | −0.344578 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 317.823 | 0.0818729 | ||||||||
\(248\) | 1765.57 | 0.452071 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 250.000 | 0.0632456 | ||||||||
\(251\) | −6467.81 | −1.62647 | −0.813236 | − | 0.581934i | \(-0.802296\pi\) | ||||
−0.813236 | + | 0.581934i | \(0.802296\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 399.894 | 0.0993721 | ||||||||
\(254\) | −3229.21 | −0.797711 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5332.72 | −1.29434 | −0.647172 | − | 0.762344i | \(-0.724048\pi\) | ||||
−0.647172 | + | 0.762344i | \(0.724048\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10421.7 | 2.50027 | ||||||||
\(260\) | −80.1398 | −0.0191156 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3949.11 | −0.931209 | ||||||||
\(263\) | 6872.85 | 1.61140 | 0.805699 | − | 0.592325i | \(-0.201790\pi\) | ||||
0.805699 | + | 0.592325i | \(0.201790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1301.77 | −0.301763 | ||||||||
\(266\) | 3909.24 | 0.901094 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3280.04 | −0.747614 | ||||||||
\(269\) | 1926.13 | 0.436572 | 0.218286 | − | 0.975885i | \(-0.429953\pi\) | ||||
0.218286 | + | 0.975885i | \(0.429953\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3653.06 | −0.818847 | −0.409423 | − | 0.912344i | \(-0.634270\pi\) | ||||
−0.409423 | + | 0.912344i | \(0.634270\pi\) | |||||||
\(272\) | −772.384 | −0.172179 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1507.61 | 0.332402 | ||||||||
\(275\) | 434.668 | 0.0953144 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1047.37 | −0.227185 | −0.113592 | − | 0.993527i | \(-0.536236\pi\) | ||||
−0.113592 | + | 0.993527i | \(0.536236\pi\) | |||||||
\(278\) | −2028.19 | −0.437565 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −985.723 | −0.210387 | ||||||||
\(281\) | 2758.90 | 0.585701 | 0.292851 | − | 0.956158i | \(-0.405396\pi\) | ||||
0.292851 | + | 0.956158i | \(0.405396\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3355.58 | 0.704837 | 0.352418 | − | 0.935843i | \(-0.385359\pi\) | ||||
0.352418 | + | 0.935843i | \(0.385359\pi\) | |||||||
\(284\) | −2459.38 | −0.513864 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −139.337 | −0.0288082 | ||||||||
\(287\) | −4195.50 | −0.862902 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2582.62 | −0.525670 | ||||||||
\(290\) | 2542.67 | 0.514866 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2046.35 | 0.410114 | ||||||||
\(293\) | −419.625 | −0.0836681 | −0.0418341 | − | 0.999125i | \(-0.513320\pi\) | ||||
−0.0418341 | + | 0.999125i | \(0.513320\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1765.65 | 0.348475 | ||||||||
\(296\) | 3383.23 | 0.664346 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5543.59 | −1.07762 | ||||||||
\(299\) | 92.1607 | 0.0178254 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5641.30 | 1.08026 | ||||||||
\(302\) | −6217.24 | −1.18464 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1269.08 | 0.239429 | ||||||||
\(305\) | 403.054 | 0.0756682 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4133.41 | −0.768425 | −0.384212 | − | 0.923245i | \(-0.625527\pi\) | ||||
−0.384212 | + | 0.923245i | \(0.625527\pi\) | |||||||
\(308\) | −1713.85 | −0.317064 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2206.96 | −0.404345 | ||||||||
\(311\) | 6991.03 | 1.27468 | 0.637339 | − | 0.770584i | \(-0.280035\pi\) | ||||
0.637339 | + | 0.770584i | \(0.280035\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9380.53 | 1.69399 | 0.846996 | − | 0.531600i | \(-0.178409\pi\) | ||||
0.846996 | + | 0.531600i | \(0.178409\pi\) | |||||||
\(314\) | −7425.75 | −1.33458 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 641.855 | 0.114263 | ||||||||
\(317\) | 7995.35 | 1.41660 | 0.708302 | − | 0.705910i | \(-0.249462\pi\) | ||||
0.708302 | + | 0.705910i | \(0.249462\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4420.87 | 0.775929 | ||||||||
\(320\) | −320.000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1133.58 | 0.196186 | ||||||||
\(323\) | −3828.96 | −0.659595 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 100.175 | 0.0170975 | ||||||||
\(326\) | −1831.58 | −0.311172 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1362.01 | −0.229281 | ||||||||
\(329\) | 14295.1 | 2.39549 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4798.86 | −0.796886 | −0.398443 | − | 0.917193i | \(-0.630449\pi\) | ||||
−0.398443 | + | 0.917193i | \(0.630449\pi\) | |||||||
\(332\) | 130.258 | 0.0215327 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2864.63 | 0.469298 | ||||||||
\(335\) | 4100.06 | 0.668687 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6895.51 | 1.11461 | 0.557303 | − | 0.830309i | \(-0.311836\pi\) | ||||
0.557303 | + | 0.830309i | \(0.311836\pi\) | |||||||
\(338\) | 4361.89 | 0.701939 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 965.480 | 0.154002 | ||||||||
\(341\) | −3837.17 | −0.609368 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1939.86 | 0.305372 | ||||||||
\(344\) | 1831.36 | 0.287036 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6959.08 | −1.08128 | ||||||||
\(347\) | 8744.17 | 1.35277 | 0.676386 | − | 0.736548i | \(-0.263545\pi\) | ||||
0.676386 | + | 0.736548i | \(0.263545\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6387.08 | −0.979635 | −0.489818 | − | 0.871825i | \(-0.662937\pi\) | ||||
−0.489818 | + | 0.871825i | \(0.662937\pi\) | |||||||
\(350\) | 1232.15 | 0.188175 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −556.375 | −0.0842468 | ||||||||
\(353\) | 589.384 | 0.0888661 | 0.0444331 | − | 0.999012i | \(-0.485852\pi\) | ||||
0.0444331 | + | 0.999012i | \(0.485852\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3074.23 | 0.459614 | ||||||||
\(356\) | 100.150 | 0.0149100 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7285.41 | 1.07555 | ||||||||
\(359\) | −7214.13 | −1.06058 | −0.530289 | − | 0.847817i | \(-0.677917\pi\) | ||||
−0.530289 | + | 0.847817i | \(0.677917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −567.774 | −0.0827780 | ||||||||
\(362\) | −4818.30 | −0.699570 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −394.978 | −0.0568749 | ||||||||
\(365\) | −2557.93 | −0.366817 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12356.4 | 1.75750 | 0.878748 | − | 0.477286i | \(-0.158379\pi\) | ||||
0.878748 | + | 0.477286i | \(0.158379\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4229.04 | −0.594209 | ||||||||
\(371\) | −6415.92 | −0.897839 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7145.98 | 0.991969 | 0.495985 | − | 0.868331i | \(-0.334807\pi\) | ||||
0.495985 | + | 0.868331i | \(0.334807\pi\) | |||||||
\(374\) | 1678.65 | 0.232088 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4640.70 | 0.636505 | ||||||||
\(377\) | 1018.85 | 0.139186 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2170.69 | 0.294197 | 0.147099 | − | 0.989122i | \(-0.453007\pi\) | ||||
0.147099 | + | 0.989122i | \(0.453007\pi\) | |||||||
\(380\) | −1586.34 | −0.214152 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −379.215 | −0.0507914 | ||||||||
\(383\) | 7967.21 | 1.06294 | 0.531469 | − | 0.847078i | \(-0.321640\pi\) | ||||
0.531469 | + | 0.847078i | \(0.321640\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2142.31 | 0.283590 | ||||||||
\(386\) | 3710.90 | 0.489326 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −999.193 | −0.130738 | ||||||||
\(389\) | 568.951 | 0.0741567 | 0.0370783 | − | 0.999312i | \(-0.488195\pi\) | ||||
0.0370783 | + | 0.999312i | \(0.488195\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1110.30 | −0.143607 | ||||||||
\(392\) | −2114.25 | −0.272413 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4859.70 | 0.621391 | ||||||||
\(395\) | −802.319 | −0.102200 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8564.88 | 1.08277 | 0.541384 | − | 0.840775i | \(-0.317900\pi\) | ||||
0.541384 | + | 0.840775i | \(0.317900\pi\) | |||||||
\(398\) | −8666.98 | −1.09155 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 12455.6 | 1.55113 | 0.775563 | − | 0.631270i | \(-0.217466\pi\) | ||||
0.775563 | + | 0.631270i | \(0.217466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −884.325 | −0.109309 | ||||||||
\(404\) | −2481.97 | −0.305650 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12531.9 | 1.53189 | ||||||||
\(407\) | −7352.91 | −0.895504 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11838.9 | 1.43129 | 0.715645 | − | 0.698465i | \(-0.246133\pi\) | ||||
0.715645 | + | 0.698465i | \(0.246133\pi\) | |||||||
\(410\) | 1702.51 | 0.205075 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5892.96 | 0.704673 | ||||||||
\(413\) | 8702.22 | 1.03682 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −162.823 | −0.0192594 | ||||||||
\(416\) | −128.224 | −0.0151122 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2758.13 | −0.322738 | ||||||||
\(419\) | 1531.77 | 0.178596 | 0.0892981 | − | 0.996005i | \(-0.471538\pi\) | ||||
0.0892981 | + | 0.996005i | \(0.471538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9985.06 | −1.15592 | −0.577959 | − | 0.816066i | \(-0.696151\pi\) | ||||
−0.577959 | + | 0.816066i | \(0.696151\pi\) | |||||||
\(422\) | 1633.58 | 0.188439 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2082.83 | −0.238564 | ||||||||
\(425\) | −1206.85 | −0.137743 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1986.50 | 0.225137 | ||||||||
\(428\) | 3760.56 | 0.424705 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2289.20 | −0.256733 | ||||||||
\(431\) | 13786.7 | 1.54079 | 0.770396 | − | 0.637566i | \(-0.220059\pi\) | ||||
0.770396 | + | 0.637566i | \(0.220059\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2621.92 | −0.290996 | −0.145498 | − | 0.989359i | \(-0.546478\pi\) | ||||
−0.145498 | + | 0.989359i | \(0.546478\pi\) | |||||||
\(434\) | −10877.3 | −1.20305 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2545.06 | −0.279555 | ||||||||
\(437\) | 1824.30 | 0.199698 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12062.7 | 1.31143 | 0.655717 | − | 0.755007i | \(-0.272367\pi\) | ||||
0.655717 | + | 0.755007i | \(0.272367\pi\) | |||||||
\(440\) | 695.468 | 0.0753526 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 386.867 | 0.0416321 | ||||||||
\(443\) | −3659.26 | −0.392453 | −0.196227 | − | 0.980559i | \(-0.562869\pi\) | ||||
−0.196227 | + | 0.980559i | \(0.562869\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −125.188 | −0.0133359 | ||||||||
\(446\) | 9027.60 | 0.958452 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1577.16 | −0.166325 | ||||||||
\(449\) | 10529.6 | 1.10674 | 0.553368 | − | 0.832937i | \(-0.313342\pi\) | ||||
0.553368 | + | 0.832937i | \(0.313342\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2960.10 | 0.309059 | ||||||||
\(452\) | −3329.81 | −0.346506 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5585.70 | 0.577423 | ||||||||
\(455\) | 493.723 | 0.0508705 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6443.23 | 0.659522 | 0.329761 | − | 0.944064i | \(-0.393032\pi\) | ||||
0.329761 | + | 0.944064i | \(0.393032\pi\) | |||||||
\(458\) | −2809.00 | −0.286585 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −460.000 | −0.0466252 | ||||||||
\(461\) | 3263.86 | 0.329747 | 0.164873 | − | 0.986315i | \(-0.447278\pi\) | ||||
0.164873 | + | 0.986315i | \(0.447278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9518.12 | 0.955388 | 0.477694 | − | 0.878526i | \(-0.341473\pi\) | ||||
0.477694 | + | 0.878526i | \(0.341473\pi\) | |||||||
\(464\) | 4068.28 | 0.407037 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2147.59 | 0.213487 | ||||||||
\(467\) | −19092.6 | −1.89187 | −0.945934 | − | 0.324360i | \(-0.894851\pi\) | ||||
−0.945934 | + | 0.324360i | \(0.894851\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20207.6 | 1.98955 | ||||||||
\(470\) | −5800.87 | −0.569307 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2825.04 | 0.275494 | ||||||||
\(473\) | −3980.17 | −0.386910 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1982.93 | 0.191543 | ||||||||
\(476\) | 4758.48 | 0.458203 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5146.36 | −0.492446 | ||||||||
\(479\) | 6324.81 | 0.603315 | 0.301658 | − | 0.953416i | \(-0.402460\pi\) | ||||
0.301658 | + | 0.953416i | \(0.402460\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1694.57 | −0.160636 | ||||||||
\(482\) | 1392.25 | 0.131567 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4114.81 | −0.386440 | ||||||||
\(485\) | 1248.99 | 0.116936 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7873.07 | −0.732573 | −0.366286 | − | 0.930502i | \(-0.619371\pi\) | ||||
−0.366286 | + | 0.930502i | \(0.619371\pi\) | |||||||
\(488\) | 644.886 | 0.0598209 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2642.82 | 0.243654 | ||||||||
\(491\) | 3556.82 | 0.326918 | 0.163459 | − | 0.986550i | \(-0.447735\pi\) | ||||
0.163459 | + | 0.986550i | \(0.447735\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12274.5 | −1.12133 | ||||||||
\(494\) | −635.646 | −0.0578929 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3531.13 | −0.319662 | ||||||||
\(497\) | 15151.7 | 1.36750 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1933.37 | −0.173446 | −0.0867231 | − | 0.996232i | \(-0.527640\pi\) | ||||
−0.0867231 | + | 0.996232i | \(0.527640\pi\) | |||||||
\(500\) | −500.000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12935.6 | 1.15009 | ||||||||
\(503\) | −2114.36 | −0.187425 | −0.0937123 | − | 0.995599i | \(-0.529873\pi\) | ||||
−0.0937123 | + | 0.995599i | \(0.529873\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3102.46 | 0.273382 | ||||||||
\(506\) | −799.789 | −0.0702667 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6458.42 | 0.564067 | ||||||||
\(509\) | 316.452 | 0.0275570 | 0.0137785 | − | 0.999905i | \(-0.495614\pi\) | ||||
0.0137785 | + | 0.999905i | \(0.495614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12607.1 | −1.09140 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10665.4 | 0.915239 | ||||||||
\(515\) | −7366.20 | −0.630279 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10085.8 | −0.857976 | ||||||||
\(518\) | −20843.3 | −1.76796 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 160.280 | 0.0135168 | ||||||||
\(521\) | 309.041 | 0.0259872 | 0.0129936 | − | 0.999916i | \(-0.495864\pi\) | ||||
0.0129936 | + | 0.999916i | \(0.495864\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5892.46 | −0.492656 | −0.246328 | − | 0.969186i | \(-0.579224\pi\) | ||||
−0.246328 | + | 0.969186i | \(0.579224\pi\) | |||||||
\(524\) | 7898.22 | 0.658464 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13745.7 | −1.13943 | ||||||||
\(527\) | 10653.9 | 0.880626 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 2603.54 | 0.213378 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7818.49 | −0.637170 | ||||||||
\(533\) | 682.193 | 0.0554391 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4700.71 | −0.379868 | ||||||||
\(536\) | 6560.09 | 0.528643 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3852.25 | −0.308703 | ||||||||
\(539\) | 4594.99 | 0.367199 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1560.55 | 0.124017 | 0.0620085 | − | 0.998076i | \(-0.480249\pi\) | ||||
0.0620085 | + | 0.998076i | \(0.480249\pi\) | |||||||
\(542\) | 7306.12 | 0.579012 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1544.77 | 0.121749 | ||||||||
\(545\) | 3181.32 | 0.250042 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17756.3 | 1.38795 | 0.693973 | − | 0.720001i | \(-0.255859\pi\) | ||||
0.693973 | + | 0.720001i | \(0.255859\pi\) | |||||||
\(548\) | −3015.22 | −0.235044 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −869.335 | −0.0673974 | ||||||||
\(551\) | 20167.8 | 1.55930 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3954.32 | −0.304078 | ||||||||
\(554\) | 2094.73 | 0.160644 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4056.39 | 0.309405 | ||||||||
\(557\) | −1212.77 | −0.0922559 | −0.0461280 | − | 0.998936i | \(-0.514688\pi\) | ||||
−0.0461280 | + | 0.998936i | \(0.514688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −917.280 | −0.0694040 | ||||||||
\(560\) | 1971.45 | 0.148766 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5517.80 | −0.414153 | ||||||||
\(563\) | −12558.2 | −0.940078 | −0.470039 | − | 0.882646i | \(-0.655760\pi\) | ||||
−0.470039 | + | 0.882646i | \(0.655760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4162.26 | 0.309925 | ||||||||
\(566\) | −6711.17 | −0.498395 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4918.76 | 0.363357 | ||||||||
\(569\) | −9776.72 | −0.720319 | −0.360159 | − | 0.932891i | \(-0.617278\pi\) | ||||
−0.360159 | + | 0.932891i | \(0.617278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18733.9 | −1.37301 | −0.686505 | − | 0.727125i | \(-0.740856\pi\) | ||||
−0.686505 | + | 0.727125i | \(0.740856\pi\) | |||||||
\(572\) | 278.673 | 0.0203705 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8391.01 | 0.610164 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5113.58 | 0.368944 | 0.184472 | − | 0.982838i | \(-0.440942\pi\) | ||||
0.184472 | + | 0.982838i | \(0.440942\pi\) | |||||||
\(578\) | 5165.24 | 0.371705 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5085.35 | −0.364065 | ||||||||
\(581\) | −802.492 | −0.0573029 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4526.70 | 0.321572 | ||||||||
\(584\) | −4092.69 | −0.289995 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 839.250 | 0.0591623 | ||||||||
\(587\) | 5379.95 | 0.378287 | 0.189143 | − | 0.981949i | \(-0.439429\pi\) | ||||
0.189143 | + | 0.981949i | \(0.439429\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17505.0 | −1.22458 | ||||||||
\(590\) | −3531.30 | −0.246409 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6766.46 | −0.469763 | ||||||||
\(593\) | 15060.3 | 1.04292 | 0.521461 | − | 0.853275i | \(-0.325387\pi\) | ||||
0.521461 | + | 0.853275i | \(0.325387\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5948.10 | −0.409829 | ||||||||
\(596\) | 11087.2 | 0.761995 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −184.321 | −0.0126045 | ||||||||
\(599\) | 3772.04 | 0.257298 | 0.128649 | − | 0.991690i | \(-0.458936\pi\) | ||||
0.128649 | + | 0.991690i | \(0.458936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14663.9 | −0.995261 | −0.497631 | − | 0.867389i | \(-0.665796\pi\) | ||||
−0.497631 | + | 0.867389i | \(0.665796\pi\) | |||||||
\(602\) | −11282.6 | −0.763861 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12434.5 | 0.837668 | ||||||||
\(605\) | 5143.51 | 0.345642 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24514.5 | −1.63923 | −0.819614 | − | 0.572915i | \(-0.805812\pi\) | ||||
−0.819614 | + | 0.572915i | \(0.805812\pi\) | |||||||
\(608\) | −2538.15 | −0.169302 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −806.108 | −0.0535055 | ||||||||
\(611\) | −2324.40 | −0.153904 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14451.2 | 0.952167 | 0.476084 | − | 0.879400i | \(-0.342056\pi\) | ||||
0.476084 | + | 0.879400i | \(0.342056\pi\) | |||||||
\(614\) | 8266.83 | 0.543358 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3427.70 | 0.224198 | ||||||||
\(617\) | −3292.19 | −0.214811 | −0.107406 | − | 0.994215i | \(-0.534254\pi\) | ||||
−0.107406 | + | 0.994215i | \(0.534254\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12595.5 | −0.817858 | −0.408929 | − | 0.912566i | \(-0.634098\pi\) | ||||
−0.408929 | + | 0.912566i | \(0.634098\pi\) | |||||||
\(620\) | 4413.92 | 0.285915 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13982.1 | −0.901333 | ||||||||
\(623\) | −617.002 | −0.0396785 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −18761.1 | −1.19783 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14851.5 | 0.943693 | ||||||||
\(629\) | 20415.3 | 1.29413 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19889.3 | 1.25480 | 0.627401 | − | 0.778697i | \(-0.284119\pi\) | ||||
0.627401 | + | 0.778697i | \(0.284119\pi\) | |||||||
\(632\) | −1283.71 | −0.0807963 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15990.7 | −1.00169 | ||||||||
\(635\) | −8073.02 | −0.504517 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1058.97 | 0.0658682 | ||||||||
\(638\) | −8841.75 | −0.548665 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 640.000 | 0.0395285 | ||||||||
\(641\) | 19276.0 | 1.18776 | 0.593880 | − | 0.804553i | \(-0.297595\pi\) | ||||
0.593880 | + | 0.804553i | \(0.297595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10219.2 | −0.626758 | −0.313379 | − | 0.949628i | \(-0.601461\pi\) | ||||
−0.313379 | + | 0.949628i | \(0.601461\pi\) | |||||||
\(644\) | −2267.16 | −0.138725 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7657.93 | 0.466404 | ||||||||
\(647\) | −20818.4 | −1.26500 | −0.632500 | − | 0.774560i | \(-0.717971\pi\) | ||||
−0.632500 | + | 0.774560i | \(0.717971\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6139.77 | −0.371352 | ||||||||
\(650\) | −200.349 | −0.0120898 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3663.17 | 0.220032 | ||||||||
\(653\) | 15135.3 | 0.907031 | 0.453516 | − | 0.891248i | \(-0.350170\pi\) | ||||
0.453516 | + | 0.891248i | \(0.350170\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9872.78 | −0.588949 | ||||||||
\(656\) | 2724.01 | 0.162126 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −28590.3 | −1.69387 | ||||||||
\(659\) | 13207.9 | 0.780737 | 0.390369 | − | 0.920659i | \(-0.372348\pi\) | ||||
0.390369 | + | 0.920659i | \(0.372348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6671.34 | 0.392564 | 0.196282 | − | 0.980547i | \(-0.437113\pi\) | ||||
0.196282 | + | 0.980547i | \(0.437113\pi\) | |||||||
\(662\) | 9597.72 | 0.563484 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −260.517 | −0.0152259 | ||||||||
\(665\) | 9773.11 | 0.569902 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5848.15 | 0.339492 | ||||||||
\(668\) | −5729.26 | −0.331844 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8200.11 | −0.472833 | ||||||||
\(671\) | −1401.56 | −0.0806355 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9534.41 | −0.546099 | −0.273049 | − | 0.962000i | \(-0.588032\pi\) | ||||
−0.273049 | + | 0.962000i | \(0.588032\pi\) | |||||||
\(674\) | −13791.0 | −0.788146 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8723.78 | −0.496346 | ||||||||
\(677\) | −17748.4 | −1.00757 | −0.503787 | − | 0.863828i | \(-0.668060\pi\) | ||||
−0.503787 | + | 0.863828i | \(0.668060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6155.80 | 0.347920 | ||||||||
\(680\) | −1930.96 | −0.108896 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7674.35 | 0.430888 | ||||||||
\(683\) | −9583.57 | −0.536904 | −0.268452 | − | 0.963293i | \(-0.586512\pi\) | ||||
−0.268452 | + | 0.963293i | \(0.586512\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3769.03 | 0.210229 | ||||||||
\(686\) | −3879.73 | −0.215931 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3662.72 | −0.202965 | ||||||||
\(689\) | 1043.24 | 0.0576837 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9410.74 | 0.518092 | 0.259046 | − | 0.965865i | \(-0.416592\pi\) | ||||
0.259046 | + | 0.965865i | \(0.416592\pi\) | |||||||
\(692\) | 13918.2 | 0.764580 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17488.3 | −0.956554 | ||||||||
\(695\) | −5070.48 | −0.276740 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8218.69 | −0.446636 | ||||||||
\(698\) | 12774.2 | 0.692707 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2464.31 | −0.133060 | ||||||||
\(701\) | 19517.9 | 1.05161 | 0.525806 | − | 0.850605i | \(-0.323764\pi\) | ||||
0.525806 | + | 0.850605i | \(0.323764\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33543.6 | −1.79960 | ||||||||
\(704\) | 1112.75 | 0.0595715 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1178.77 | −0.0628378 | ||||||||
\(707\) | 15290.9 | 0.813397 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28430.7 | −1.50598 | −0.752990 | − | 0.658033i | \(-0.771389\pi\) | ||||
−0.752990 | + | 0.658033i | \(0.771389\pi\) | |||||||
\(710\) | −6148.45 | −0.324996 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −200.300 | −0.0105429 | ||||||||
\(713\) | −5076.00 | −0.266617 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −348.342 | −0.0182199 | ||||||||
\(716\) | −14570.8 | −0.760527 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14428.3 | 0.749942 | ||||||||
\(719\) | −18716.0 | −0.970779 | −0.485390 | − | 0.874298i | \(-0.661322\pi\) | ||||
−0.485390 | + | 0.874298i | \(0.661322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36305.2 | −1.87528 | ||||||||
\(722\) | 1135.55 | 0.0585329 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9636.61 | 0.494671 | ||||||||
\(725\) | 6356.69 | 0.325630 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18419.5 | 0.939670 | 0.469835 | − | 0.882754i | \(-0.344313\pi\) | ||||
0.469835 | + | 0.882754i | \(0.344313\pi\) | |||||||
\(728\) | 789.956 | 0.0402167 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5115.86 | 0.259379 | ||||||||
\(731\) | 11050.9 | 0.559141 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21548.4 | −1.08582 | −0.542912 | − | 0.839790i | \(-0.682678\pi\) | ||||
−0.542912 | + | 0.839790i | \(0.682678\pi\) | |||||||
\(734\) | −24712.9 | −1.24274 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | −14257.3 | −0.712584 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12066.4 | 0.600636 | 0.300318 | − | 0.953839i | \(-0.402907\pi\) | ||||
0.300318 | + | 0.953839i | \(0.402907\pi\) | |||||||
\(740\) | 8458.08 | 0.420169 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12831.8 | 0.634868 | ||||||||
\(743\) | 21951.0 | 1.08385 | 0.541926 | − | 0.840426i | \(-0.317695\pi\) | ||||
0.541926 | + | 0.840426i | \(0.317695\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13859.0 | −0.681549 | ||||||||
\(746\) | −14292.0 | −0.701428 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3357.31 | −0.164111 | ||||||||
\(749\) | −23168.0 | −1.13023 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3112.43 | −0.151230 | −0.0756152 | − | 0.997137i | \(-0.524092\pi\) | ||||
−0.0756152 | + | 0.997137i | \(0.524092\pi\) | |||||||
\(752\) | −9281.40 | −0.450077 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2037.69 | −0.0984197 | ||||||||
\(755\) | −15543.1 | −0.749233 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7684.64 | −0.368960 | −0.184480 | − | 0.982836i | \(-0.559060\pi\) | ||||
−0.184480 | + | 0.982836i | \(0.559060\pi\) | |||||||
\(758\) | −4341.38 | −0.208029 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3172.69 | 0.151428 | ||||||||
\(761\) | 36484.6 | 1.73793 | 0.868965 | − | 0.494874i | \(-0.164786\pi\) | ||||
0.868965 | + | 0.494874i | \(0.164786\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15679.5 | 0.743954 | ||||||||
\(764\) | 758.430 | 0.0359150 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15934.4 | −0.751611 | ||||||||
\(767\) | −1414.99 | −0.0666132 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2004.39 | 0.0939925 | 0.0469962 | − | 0.998895i | \(-0.485035\pi\) | ||||
0.0469962 | + | 0.998895i | \(0.485035\pi\) | |||||||
\(770\) | −4284.62 | −0.200529 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7421.81 | −0.346006 | ||||||||
\(773\) | −7716.17 | −0.359031 | −0.179516 | − | 0.983755i | \(-0.557453\pi\) | ||||
−0.179516 | + | 0.983755i | \(0.557453\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5517.40 | −0.255730 | ||||||||
\(776\) | 1998.39 | 0.0924457 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1137.90 | −0.0524367 | ||||||||
\(779\) | 13503.8 | 0.621084 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10690.1 | −0.489786 | ||||||||
\(782\) | 2220.61 | 0.101546 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4228.51 | 0.192625 | ||||||||
\(785\) | −18564.4 | −0.844065 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −57.0149 | −0.00258241 | −0.00129121 | − | 0.999999i | \(-0.500411\pi\) | ||||
−0.00129121 | + | 0.999999i | \(0.500411\pi\) | |||||||
\(788\) | −9719.39 | −0.439390 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1604.64 | 0.0722664 | ||||||||
\(791\) | 20514.2 | 0.922124 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −323.006 | −0.0144644 | ||||||||
\(794\) | −17129.8 | −0.765633 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17334.0 | 0.771842 | ||||||||
\(797\) | 15184.7 | 0.674870 | 0.337435 | − | 0.941349i | \(-0.390441\pi\) | ||||
0.337435 | + | 0.941349i | \(0.390441\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28003.2 | 1.23990 | ||||||||
\(800\) | −800.000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24911.1 | −1.09681 | ||||||||
\(803\) | 8894.80 | 0.390898 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2833.95 | 0.124079 | ||||||||
\(806\) | 1768.65 | 0.0772929 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4963.94 | 0.216127 | ||||||||
\(809\) | 30286.4 | 1.31621 | 0.658105 | − | 0.752926i | \(-0.271358\pi\) | ||||
0.658105 | + | 0.752926i | \(0.271358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43936.2 | −1.90235 | −0.951176 | − | 0.308650i | \(-0.900123\pi\) | ||||
−0.951176 | + | 0.308650i | \(0.900123\pi\) | |||||||
\(812\) | −25063.7 | −1.08321 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14705.8 | 0.633217 | ||||||||
\(815\) | −4578.96 | −0.196802 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18157.3 | −0.777532 | ||||||||
\(818\) | −23677.9 | −1.01207 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3405.02 | −0.145010 | ||||||||
\(821\) | 5245.69 | 0.222991 | 0.111496 | − | 0.993765i | \(-0.464436\pi\) | ||||
0.111496 | + | 0.993765i | \(0.464436\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10678.0 | 0.452260 | 0.226130 | − | 0.974097i | \(-0.427393\pi\) | ||||
0.226130 | + | 0.974097i | \(0.427393\pi\) | |||||||
\(824\) | −11785.9 | −0.498279 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17404.4 | −0.733145 | ||||||||
\(827\) | −3393.69 | −0.142697 | −0.0713484 | − | 0.997451i | \(-0.522730\pi\) | ||||
−0.0713484 | + | 0.997451i | \(0.522730\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9601.74 | 0.402270 | 0.201135 | − | 0.979564i | \(-0.435537\pi\) | ||||
0.201135 | + | 0.979564i | \(0.435537\pi\) | |||||||
\(830\) | 325.646 | 0.0136185 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 256.447 | 0.0106859 | ||||||||
\(833\) | −12757.9 | −0.530656 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7161.58 | 0.296810 | ||||||||
\(836\) | 5516.26 | 0.228210 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3063.54 | −0.126287 | ||||||||
\(839\) | −11992.8 | −0.493489 | −0.246744 | − | 0.969081i | \(-0.579361\pi\) | ||||
−0.246744 | + | 0.969081i | \(0.579361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40263.0 | 1.65087 | ||||||||
\(842\) | 19970.1 | 0.817358 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3267.15 | −0.133247 | ||||||||
\(845\) | 10904.7 | 0.443945 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25350.4 | 1.02839 | ||||||||
\(848\) | 4165.66 | 0.168690 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2413.70 | 0.0973991 | ||||||||
\(851\) | −9726.79 | −0.391810 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15441.5 | −0.619821 | −0.309911 | − | 0.950766i | \(-0.600299\pi\) | ||||
−0.309911 | + | 0.950766i | \(0.600299\pi\) | |||||||
\(854\) | −3973.00 | −0.159196 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7521.13 | −0.300312 | ||||||||
\(857\) | 44572.4 | 1.77662 | 0.888310 | − | 0.459244i | \(-0.151880\pi\) | ||||
0.888310 | + | 0.459244i | \(0.151880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2519.56 | 0.100077 | 0.0500386 | − | 0.998747i | \(-0.484066\pi\) | ||||
0.0500386 | + | 0.998747i | \(0.484066\pi\) | |||||||
\(860\) | 4578.40 | 0.181537 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27573.4 | −1.08950 | ||||||||
\(863\) | −28980.1 | −1.14310 | −0.571548 | − | 0.820568i | \(-0.693657\pi\) | ||||
−0.571548 | + | 0.820568i | \(0.693657\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17397.7 | −0.683861 | ||||||||
\(866\) | 5243.83 | 0.205765 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 21754.5 | 0.850687 | ||||||||
\(869\) | 2789.94 | 0.108909 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3285.77 | −0.127823 | ||||||||
\(872\) | 5090.11 | 0.197675 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3648.59 | −0.141208 | ||||||||
\(875\) | 3080.39 | 0.119013 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7955.28 | −0.306307 | −0.153153 | − | 0.988202i | \(-0.548943\pi\) | ||||
−0.153153 | + | 0.988202i | \(0.548943\pi\) | |||||||
\(878\) | −24125.3 | −0.927323 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1390.94 | −0.0532823 | ||||||||
\(881\) | −29722.0 | −1.13662 | −0.568309 | − | 0.822815i | \(-0.692402\pi\) | ||||
−0.568309 | + | 0.822815i | \(0.692402\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19379.7 | −0.738596 | −0.369298 | − | 0.929311i | \(-0.620402\pi\) | ||||
−0.369298 | + | 0.929311i | \(0.620402\pi\) | |||||||
\(884\) | −773.734 | −0.0294383 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7318.53 | 0.277507 | ||||||||
\(887\) | −22901.7 | −0.866925 | −0.433463 | − | 0.901172i | \(-0.642708\pi\) | ||||
−0.433463 | + | 0.901172i | \(0.642708\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −39788.8 | −1.50110 | ||||||||
\(890\) | 250.375 | 0.00942989 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18055.2 | −0.677728 | ||||||||
\(893\) | −46010.9 | −1.72419 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18213.5 | 0.680236 | ||||||||
\(896\) | 3154.31 | 0.117610 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21059.3 | −0.782581 | ||||||||
\(899\) | −56115.8 | −2.08183 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12568.3 | −0.464719 | ||||||||
\(902\) | −5920.20 | −0.218538 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6659.61 | 0.245017 | ||||||||
\(905\) | −12045.8 | −0.442447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42542.2 | 1.55743 | 0.778716 | − | 0.627376i | \(-0.215871\pi\) | ||||
0.778716 | + | 0.627376i | \(0.215871\pi\) | |||||||
\(908\) | −11171.4 | −0.408300 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −987.445 | −0.0359709 | ||||||||
\(911\) | −220.864 | −0.00803243 | −0.00401622 | − | 0.999992i | \(-0.501278\pi\) | ||||
−0.00401622 | + | 0.999992i | \(0.501278\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 566.191 | 0.0205237 | ||||||||
\(914\) | −12886.5 | −0.466352 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5617.99 | 0.202646 | ||||||||
\(917\) | −48659.1 | −1.75231 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27835.4 | 0.999135 | 0.499567 | − | 0.866275i | \(-0.333492\pi\) | ||||
0.499567 | + | 0.866275i | \(0.333492\pi\) | |||||||
\(920\) | 920.000 | 0.0329690 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6527.72 | −0.233166 | ||||||||
\(923\) | −2463.68 | −0.0878580 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10572.6 | −0.375811 | ||||||||
\(926\) | −19036.2 | −0.675562 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8136.56 | −0.287819 | ||||||||
\(929\) | 2172.71 | 0.0767323 | 0.0383661 | − | 0.999264i | \(-0.487785\pi\) | ||||
0.0383661 | + | 0.999264i | \(0.487785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20962.1 | 0.737921 | ||||||||
\(932\) | −4295.17 | −0.150958 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 38185.3 | 1.33775 | ||||||||
\(935\) | 4196.63 | 0.146786 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54906.5 | 1.91432 | 0.957160 | − | 0.289560i | \(-0.0935090\pi\) | ||||
0.957160 | + | 0.289560i | \(0.0935090\pi\) | |||||||
\(938\) | −40415.2 | −1.40683 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11601.7 | 0.402561 | ||||||||
\(941\) | −5980.06 | −0.207167 | −0.103584 | − | 0.994621i | \(-0.533031\pi\) | ||||
−0.103584 | + | 0.994621i | \(0.533031\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3915.77 | 0.135223 | ||||||||
\(944\) | −5650.09 | −0.194804 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7960.33 | 0.273586 | ||||||||
\(947\) | 20268.6 | 0.695504 | 0.347752 | − | 0.937587i | \(-0.386945\pi\) | ||||
0.347752 | + | 0.937587i | \(0.386945\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2049.92 | 0.0701193 | ||||||||
\(950\) | −3965.86 | −0.135442 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9516.97 | −0.323999 | ||||||||
\(953\) | 21797.9 | 0.740925 | 0.370463 | − | 0.928847i | \(-0.379199\pi\) | ||||
0.370463 | + | 0.928847i | \(0.379199\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −948.038 | −0.0321233 | ||||||||
\(956\) | 10292.7 | 0.348212 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12649.6 | −0.426608 | ||||||||
\(959\) | 18576.1 | 0.625499 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18915.6 | 0.634945 | ||||||||
\(962\) | 3389.14 | 0.113587 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2784.51 | −0.0930321 | ||||||||
\(965\) | 9277.26 | 0.309477 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48950.6 | 1.62786 | 0.813932 | − | 0.580960i | \(-0.197323\pi\) | ||||
0.813932 | + | 0.580960i | \(0.197323\pi\) | |||||||
\(968\) | 8229.62 | 0.273254 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2497.98 | −0.0826860 | ||||||||
\(971\) | 26426.2 | 0.873386 | 0.436693 | − | 0.899611i | \(-0.356150\pi\) | ||||
0.436693 | + | 0.899611i | \(0.356150\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24990.5 | −0.823389 | ||||||||
\(974\) | 15746.1 | 0.518007 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1289.77 | −0.0422998 | ||||||||
\(977\) | −5770.09 | −0.188947 | −0.0944736 | − | 0.995527i | \(-0.530117\pi\) | ||||
−0.0944736 | + | 0.995527i | \(0.530117\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 435.320 | 0.0142113 | ||||||||
\(980\) | −5285.63 | −0.172289 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7113.64 | −0.231166 | ||||||||
\(983\) | 484.532 | 0.0157214 | 0.00786071 | − | 0.999969i | \(-0.497498\pi\) | ||||
0.00786071 | + | 0.999969i | \(0.497498\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12149.2 | 0.393002 | ||||||||
\(986\) | 24549.0 | 0.792901 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1271.29 | 0.0409365 | ||||||||
\(989\) | −5265.16 | −0.169285 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26511.5 | −0.849813 | −0.424907 | − | 0.905237i | \(-0.639693\pi\) | ||||
−0.424907 | + | 0.905237i | \(0.639693\pi\) | |||||||
\(992\) | 7062.27 | 0.226035 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −30303.4 | −0.966966 | ||||||||
\(995\) | −21667.4 | −0.690356 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4628.20 | −0.147018 | −0.0735088 | − | 0.997295i | \(-0.523420\pi\) | ||||
−0.0735088 | + | 0.997295i | \(0.523420\pi\) | |||||||
\(998\) | 3866.74 | 0.122645 | ||||||||
\(999\) | 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 | 2070.4.a.bg.1.1 | 4 | ||
3.2 | odd | 2 | 230.4.a.j.1.4 | ✓ | 4 | ||
12.11 | even | 2 | 1840.4.a.k.1.1 | 4 | |||
15.2 | even | 4 | 1150.4.b.o.599.5 | 8 | |||
15.8 | even | 4 | 1150.4.b.o.599.4 | 8 | |||
15.14 | odd | 2 | 1150.4.a.n.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.j.1.4 | ✓ | 4 | 3.2 | odd | 2 | ||
1150.4.a.n.1.1 | 4 | 15.14 | odd | 2 | |||
1150.4.b.o.599.4 | 8 | 15.8 | even | 4 | |||
1150.4.b.o.599.5 | 8 | 15.2 | even | 4 | |||
1840.4.a.k.1.1 | 4 | 12.11 | even | 2 | |||
2070.4.a.bg.1.1 | 4 | 1.1 | even | 1 | trivial |