Newspace parameters
Level: | \( N \) | \(=\) | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 414.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(24.4267907424\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 219x^{2} - 468x + 3240 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(16.3784\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 414.1 |
$q$-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 | ||||||||
\(5\) | 13.0601 | 1.16813 | 0.584066 | − | 0.811706i | \(-0.301461\pi\) | ||||
0.584066 | + | 0.811706i | \(0.301461\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.7067 | 1.01006 | 0.505032 | − | 0.863100i | \(-0.331481\pi\) | ||||
0.505032 | + | 0.863100i | \(0.331481\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 26.1202 | 0.825995 | ||||||||
\(11\) | 41.1103 | 1.12684 | 0.563419 | − | 0.826171i | \(-0.309486\pi\) | ||||
0.563419 | + | 0.826171i | \(0.309486\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 32.6366 | 0.696290 | 0.348145 | − | 0.937441i | \(-0.386812\pi\) | ||||
0.348145 | + | 0.937441i | \(0.386812\pi\) | |||||||
\(14\) | 37.4133 | 0.714224 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −76.8570 | −1.09650 | −0.548252 | − | 0.836313i | \(-0.684706\pi\) | ||||
−0.548252 | + | 0.836313i | \(0.684706\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −164.965 | −1.99187 | −0.995934 | − | 0.0900884i | \(-0.971285\pi\) | ||||
−0.995934 | + | 0.0900884i | \(0.971285\pi\) | |||||||
\(20\) | 52.2405 | 0.584066 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 82.2206 | 0.796795 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 45.5668 | 0.364534 | ||||||||
\(26\) | 65.2732 | 0.492351 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 74.8267 | 0.505032 | ||||||||
\(29\) | −42.5314 | −0.272341 | −0.136170 | − | 0.990685i | \(-0.543479\pi\) | ||||
−0.136170 | + | 0.990685i | \(0.543479\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 246.351 | 1.42729 | 0.713644 | − | 0.700508i | \(-0.247043\pi\) | ||||
0.713644 | + | 0.700508i | \(0.247043\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −153.714 | −0.775345 | ||||||||
\(35\) | 244.311 | 1.17989 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 281.671 | 1.25153 | 0.625763 | − | 0.780013i | \(-0.284788\pi\) | ||||
0.625763 | + | 0.780013i | \(0.284788\pi\) | |||||||
\(38\) | −329.929 | −1.40846 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 104.481 | 0.412997 | ||||||||
\(41\) | 330.365 | 1.25840 | 0.629200 | − | 0.777244i | \(-0.283383\pi\) | ||||
0.629200 | + | 0.777244i | \(0.283383\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −160.644 | −0.569721 | −0.284861 | − | 0.958569i | \(-0.591947\pi\) | ||||
−0.284861 | + | 0.958569i | \(0.591947\pi\) | |||||||
\(44\) | 164.441 | 0.563419 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | −578.490 | −1.79535 | −0.897675 | − | 0.440658i | \(-0.854745\pi\) | ||||
−0.897675 | + | 0.440658i | \(0.854745\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.93931 | 0.0202312 | ||||||||
\(50\) | 91.1336 | 0.257765 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 130.546 | 0.348145 | ||||||||
\(53\) | −621.131 | −1.60979 | −0.804895 | − | 0.593418i | \(-0.797778\pi\) | ||||
−0.804895 | + | 0.593418i | \(0.797778\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 536.906 | 1.31630 | ||||||||
\(56\) | 149.653 | 0.357112 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −85.0628 | −0.192574 | ||||||||
\(59\) | 347.432 | 0.766640 | 0.383320 | − | 0.923616i | \(-0.374781\pi\) | ||||
0.383320 | + | 0.923616i | \(0.374781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 372.119 | 0.781065 | 0.390532 | − | 0.920589i | \(-0.372291\pi\) | ||||
0.390532 | + | 0.920589i | \(0.372291\pi\) | |||||||
\(62\) | 492.702 | 1.00925 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 426.238 | 0.813359 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 884.432 | 1.61270 | 0.806348 | − | 0.591442i | \(-0.201441\pi\) | ||||
0.806348 | + | 0.591442i | \(0.201441\pi\) | |||||||
\(68\) | −307.428 | −0.548252 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 488.623 | 0.834308 | ||||||||
\(71\) | −777.672 | −1.29990 | −0.649948 | − | 0.759978i | \(-0.725209\pi\) | ||||
−0.649948 | + | 0.759978i | \(0.725209\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −188.099 | −0.301581 | −0.150790 | − | 0.988566i | \(-0.548182\pi\) | ||||
−0.150790 | + | 0.988566i | \(0.548182\pi\) | |||||||
\(74\) | 563.343 | 0.884963 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −659.859 | −0.995934 | ||||||||
\(77\) | 769.037 | 1.13818 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 200.062 | 0.284921 | 0.142461 | − | 0.989800i | \(-0.454499\pi\) | ||||
0.142461 | + | 0.989800i | \(0.454499\pi\) | |||||||
\(80\) | 208.962 | 0.292033 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 660.730 | 0.889823 | ||||||||
\(83\) | 49.9822 | 0.0660995 | 0.0330497 | − | 0.999454i | \(-0.489478\pi\) | ||||
0.0330497 | + | 0.999454i | \(0.489478\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1003.76 | −1.28086 | ||||||||
\(86\) | −321.288 | −0.402854 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 328.882 | 0.398398 | ||||||||
\(89\) | −767.598 | −0.914216 | −0.457108 | − | 0.889411i | \(-0.651115\pi\) | ||||
−0.457108 | + | 0.889411i | \(0.651115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 610.522 | 0.703298 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1156.98 | −1.26950 | ||||||||
\(95\) | −2154.46 | −2.32677 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1626.31 | 1.70234 | 0.851171 | − | 0.524888i | \(-0.175893\pi\) | ||||
0.851171 | + | 0.524888i | \(0.175893\pi\) | |||||||
\(98\) | 13.8786 | 0.0143056 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 182.267 | 0.182267 | ||||||||
\(101\) | −366.127 | −0.360703 | −0.180352 | − | 0.983602i | \(-0.557724\pi\) | ||||
−0.180352 | + | 0.983602i | \(0.557724\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1828.41 | 1.74911 | 0.874554 | − | 0.484928i | \(-0.161154\pi\) | ||||
0.874554 | + | 0.484928i | \(0.161154\pi\) | |||||||
\(104\) | 261.093 | 0.246176 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1242.26 | −1.13829 | ||||||||
\(107\) | −555.660 | −0.502034 | −0.251017 | − | 0.967983i | \(-0.580765\pi\) | ||||
−0.251017 | + | 0.967983i | \(0.580765\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −952.852 | −0.837309 | −0.418654 | − | 0.908146i | \(-0.637498\pi\) | ||||
−0.418654 | + | 0.908146i | \(0.637498\pi\) | |||||||
\(110\) | 1073.81 | 0.930763 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 299.307 | 0.252516 | ||||||||
\(113\) | −255.634 | −0.212815 | −0.106407 | − | 0.994323i | \(-0.533935\pi\) | ||||
−0.106407 | + | 0.994323i | \(0.533935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 300.383 | 0.243573 | ||||||||
\(116\) | −170.126 | −0.136170 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 694.864 | 0.542096 | ||||||||
\(119\) | −1437.74 | −1.10754 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 359.058 | 0.269765 | ||||||||
\(122\) | 744.238 | 0.552296 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 985.404 | 0.713644 | ||||||||
\(125\) | −1037.41 | −0.742308 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1543.83 | −1.07868 | −0.539341 | − | 0.842088i | \(-0.681327\pi\) | ||||
−0.539341 | + | 0.842088i | \(0.681327\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 852.476 | 0.575132 | ||||||||
\(131\) | −116.906 | −0.0779702 | −0.0389851 | − | 0.999240i | \(-0.512412\pi\) | ||||
−0.0389851 | + | 0.999240i | \(0.512412\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3085.94 | −2.01192 | ||||||||
\(134\) | 1768.86 | 1.14035 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −614.856 | −0.387672 | ||||||||
\(137\) | −2770.00 | −1.72742 | −0.863712 | − | 0.503986i | \(-0.831866\pi\) | ||||
−0.863712 | + | 0.503986i | \(0.831866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1296.27 | −0.790992 | −0.395496 | − | 0.918468i | \(-0.629427\pi\) | ||||
−0.395496 | + | 0.918468i | \(0.629427\pi\) | |||||||
\(140\) | 977.245 | 0.589945 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1555.34 | −0.919166 | ||||||||
\(143\) | 1341.70 | 0.784606 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −555.466 | −0.318130 | ||||||||
\(146\) | −376.199 | −0.213250 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1126.69 | 0.625763 | ||||||||
\(149\) | −200.699 | −0.110348 | −0.0551742 | − | 0.998477i | \(-0.517571\pi\) | ||||
−0.0551742 | + | 0.998477i | \(0.517571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −109.209 | −0.0588564 | −0.0294282 | − | 0.999567i | \(-0.509369\pi\) | ||||
−0.0294282 | + | 0.999567i | \(0.509369\pi\) | |||||||
\(152\) | −1319.72 | −0.704232 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1538.07 | 0.804815 | ||||||||
\(155\) | 3217.38 | 1.66726 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3299.65 | −1.67733 | −0.838665 | − | 0.544647i | \(-0.816664\pi\) | ||||
−0.838665 | + | 0.544647i | \(0.816664\pi\) | |||||||
\(158\) | 400.125 | 0.201470 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 417.924 | 0.206499 | ||||||||
\(161\) | 430.253 | 0.210613 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 238.673 | 0.114689 | 0.0573446 | − | 0.998354i | \(-0.481737\pi\) | ||||
0.0573446 | + | 0.998354i | \(0.481737\pi\) | |||||||
\(164\) | 1321.46 | 0.629200 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 99.9644 | 0.0467394 | ||||||||
\(167\) | 3124.43 | 1.44776 | 0.723880 | − | 0.689926i | \(-0.242357\pi\) | ||||
0.723880 | + | 0.689926i | \(0.242357\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1131.85 | −0.515181 | ||||||||
\(170\) | −2007.52 | −0.905706 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −642.577 | −0.284861 | ||||||||
\(173\) | −2732.43 | −1.20083 | −0.600413 | − | 0.799690i | \(-0.704997\pi\) | ||||
−0.600413 | + | 0.799690i | \(0.704997\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 852.403 | 0.368203 | ||||||||
\(176\) | 657.765 | 0.281710 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1535.20 | −0.646449 | ||||||||
\(179\) | 2350.95 | 0.981665 | 0.490833 | − | 0.871254i | \(-0.336693\pi\) | ||||
0.490833 | + | 0.871254i | \(0.336693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2224.83 | −0.913650 | −0.456825 | − | 0.889557i | \(-0.651013\pi\) | ||||
−0.456825 | + | 0.889557i | \(0.651013\pi\) | |||||||
\(182\) | 1221.04 | 0.497307 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 3678.66 | 1.46195 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3159.61 | −1.23558 | ||||||||
\(188\) | −2313.96 | −0.897675 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4308.92 | −1.64527 | ||||||||
\(191\) | 3099.04 | 1.17403 | 0.587013 | − | 0.809577i | \(-0.300304\pi\) | ||||
0.587013 | + | 0.809577i | \(0.300304\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −679.935 | −0.253590 | −0.126795 | − | 0.991929i | \(-0.540469\pi\) | ||||
−0.126795 | + | 0.991929i | \(0.540469\pi\) | |||||||
\(194\) | 3252.63 | 1.20374 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 27.7573 | 0.0101156 | ||||||||
\(197\) | −49.9118 | −0.0180511 | −0.00902555 | − | 0.999959i | \(-0.502873\pi\) | ||||
−0.00902555 | + | 0.999959i | \(0.502873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4052.80 | −1.44369 | −0.721847 | − | 0.692052i | \(-0.756707\pi\) | ||||
−0.721847 | + | 0.692052i | \(0.756707\pi\) | |||||||
\(200\) | 364.534 | 0.128882 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −732.255 | −0.255056 | ||||||||
\(203\) | −795.621 | −0.275082 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4314.61 | 1.46998 | ||||||||
\(206\) | 3656.81 | 1.23681 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 522.186 | 0.174072 | ||||||||
\(209\) | −6781.75 | −2.24451 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −864.141 | −0.281943 | −0.140971 | − | 0.990014i | \(-0.545023\pi\) | ||||
−0.140971 | + | 0.990014i | \(0.545023\pi\) | |||||||
\(212\) | −2484.52 | −0.804895 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1111.32 | −0.354992 | ||||||||
\(215\) | −2098.03 | −0.665510 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4608.41 | 1.44165 | ||||||||
\(218\) | −1905.70 | −0.592067 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2147.62 | 0.658149 | ||||||||
\(221\) | −2508.35 | −0.763484 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5682.45 | 1.70639 | 0.853196 | − | 0.521591i | \(-0.174661\pi\) | ||||
0.853196 | + | 0.521591i | \(0.174661\pi\) | |||||||
\(224\) | 598.613 | 0.178556 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −511.269 | −0.150483 | ||||||||
\(227\) | −158.099 | −0.0462263 | −0.0231132 | − | 0.999733i | \(-0.507358\pi\) | ||||
−0.0231132 | + | 0.999733i | \(0.507358\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2744.94 | 0.792100 | 0.396050 | − | 0.918229i | \(-0.370381\pi\) | ||||
0.396050 | + | 0.918229i | \(0.370381\pi\) | |||||||
\(230\) | 600.766 | 0.172232 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −340.251 | −0.0962871 | ||||||||
\(233\) | 3647.63 | 1.02560 | 0.512798 | − | 0.858509i | \(-0.328609\pi\) | ||||
0.512798 | + | 0.858509i | \(0.328609\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7555.15 | −2.09721 | ||||||||
\(236\) | 1389.73 | 0.383320 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2875.48 | −0.783149 | ||||||||
\(239\) | −2580.14 | −0.698306 | −0.349153 | − | 0.937066i | \(-0.613531\pi\) | ||||
−0.349153 | + | 0.937066i | \(0.613531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4498.59 | 1.20240 | 0.601202 | − | 0.799097i | \(-0.294689\pi\) | ||||
0.601202 | + | 0.799097i | \(0.294689\pi\) | |||||||
\(242\) | 718.115 | 0.190753 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1488.48 | 0.390532 | ||||||||
\(245\) | 90.6283 | 0.0236328 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5383.89 | −1.38692 | ||||||||
\(248\) | 1970.81 | 0.504623 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2074.81 | −0.524891 | ||||||||
\(251\) | 1285.33 | 0.323223 | 0.161612 | − | 0.986854i | \(-0.448331\pi\) | ||||
0.161612 | + | 0.986854i | \(0.448331\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 945.537 | 0.234962 | ||||||||
\(254\) | −3087.66 | −0.762743 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 768.793 | 0.186599 | 0.0932996 | − | 0.995638i | \(-0.470259\pi\) | ||||
0.0932996 | + | 0.995638i | \(0.470259\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5269.13 | 1.26412 | ||||||||
\(260\) | 1704.95 | 0.406679 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −233.811 | −0.0551333 | ||||||||
\(263\) | −3454.27 | −0.809883 | −0.404942 | − | 0.914342i | \(-0.632708\pi\) | ||||
−0.404942 | + | 0.914342i | \(0.632708\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8112.04 | −1.88045 | ||||||||
\(266\) | −6171.88 | −1.42264 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3537.73 | 0.806348 | ||||||||
\(269\) | −4348.89 | −0.985712 | −0.492856 | − | 0.870111i | \(-0.664047\pi\) | ||||
−0.492856 | + | 0.870111i | \(0.664047\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4876.35 | 1.09305 | 0.546527 | − | 0.837442i | \(-0.315950\pi\) | ||||
0.546527 | + | 0.837442i | \(0.315950\pi\) | |||||||
\(272\) | −1229.71 | −0.274126 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5540.00 | −1.22147 | ||||||||
\(275\) | 1873.27 | 0.410771 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −757.557 | −0.164322 | −0.0821610 | − | 0.996619i | \(-0.526182\pi\) | ||||
−0.0821610 | + | 0.996619i | \(0.526182\pi\) | |||||||
\(278\) | −2592.53 | −0.559316 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1954.49 | 0.417154 | ||||||||
\(281\) | −8407.74 | −1.78492 | −0.892462 | − | 0.451122i | \(-0.851024\pi\) | ||||
−0.892462 | + | 0.451122i | \(0.851024\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2522.06 | −0.529757 | −0.264878 | − | 0.964282i | \(-0.585332\pi\) | ||||
−0.264878 | + | 0.964282i | \(0.585332\pi\) | |||||||
\(284\) | −3110.69 | −0.649948 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2683.40 | 0.554800 | ||||||||
\(287\) | 6180.03 | 1.27106 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 993.996 | 0.202319 | ||||||||
\(290\) | −1110.93 | −0.224952 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −752.398 | −0.150790 | ||||||||
\(293\) | 3357.13 | 0.669372 | 0.334686 | − | 0.942330i | \(-0.391370\pi\) | ||||
0.334686 | + | 0.942330i | \(0.391370\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4537.50 | 0.895537 | ||||||||
\(296\) | 2253.37 | 0.442481 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −401.399 | −0.0780282 | ||||||||
\(299\) | 750.642 | 0.145186 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3005.12 | −0.575455 | ||||||||
\(302\) | −218.418 | −0.0416177 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2639.43 | −0.497967 | ||||||||
\(305\) | 4859.92 | 0.912387 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7660.19 | −1.42407 | −0.712036 | − | 0.702143i | \(-0.752227\pi\) | ||||
−0.712036 | + | 0.702143i | \(0.752227\pi\) | |||||||
\(308\) | 3076.15 | 0.569090 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6434.75 | 1.17893 | ||||||||
\(311\) | 344.406 | 0.0627958 | 0.0313979 | − | 0.999507i | \(-0.490004\pi\) | ||||
0.0313979 | + | 0.999507i | \(0.490004\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3403.84 | 0.614685 | 0.307343 | − | 0.951599i | \(-0.400560\pi\) | ||||
0.307343 | + | 0.951599i | \(0.400560\pi\) | |||||||
\(314\) | −6599.30 | −1.18605 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 800.249 | 0.142461 | ||||||||
\(317\) | −5801.37 | −1.02788 | −0.513939 | − | 0.857827i | \(-0.671814\pi\) | ||||
−0.513939 | + | 0.857827i | \(0.671814\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1748.48 | −0.306884 | ||||||||
\(320\) | 835.848 | 0.146017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 860.507 | 0.148926 | ||||||||
\(323\) | 12678.7 | 2.18409 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1487.15 | 0.253822 | ||||||||
\(326\) | 477.347 | 0.0810975 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2642.92 | 0.444911 | ||||||||
\(329\) | −10821.6 | −1.81342 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8400.66 | 1.39499 | 0.697495 | − | 0.716589i | \(-0.254298\pi\) | ||||
0.697495 | + | 0.716589i | \(0.254298\pi\) | |||||||
\(332\) | 199.929 | 0.0330497 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6248.87 | 1.02372 | ||||||||
\(335\) | 11550.8 | 1.88384 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4144.17 | 0.669873 | 0.334937 | − | 0.942241i | \(-0.391285\pi\) | ||||
0.334937 | + | 0.942241i | \(0.391285\pi\) | |||||||
\(338\) | −2263.70 | −0.364288 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4015.05 | −0.640431 | ||||||||
\(341\) | 10127.6 | 1.60832 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6286.57 | −0.989630 | ||||||||
\(344\) | −1285.15 | −0.201427 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5464.87 | −0.849113 | ||||||||
\(347\) | 3851.70 | 0.595880 | 0.297940 | − | 0.954585i | \(-0.403701\pi\) | ||||
0.297940 | + | 0.954585i | \(0.403701\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2581.17 | 0.395893 | 0.197947 | − | 0.980213i | \(-0.436573\pi\) | ||||
0.197947 | + | 0.980213i | \(0.436573\pi\) | |||||||
\(350\) | 1704.81 | 0.260359 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1315.53 | 0.199199 | ||||||||
\(353\) | 7748.76 | 1.16834 | 0.584171 | − | 0.811630i | \(-0.301420\pi\) | ||||
0.584171 | + | 0.811630i | \(0.301420\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10156.5 | −1.51845 | ||||||||
\(356\) | −3070.39 | −0.457108 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4701.90 | 0.694142 | ||||||||
\(359\) | 1957.02 | 0.287709 | 0.143855 | − | 0.989599i | \(-0.454050\pi\) | ||||
0.143855 | + | 0.989599i | \(0.454050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20354.3 | 2.96754 | ||||||||
\(362\) | −4449.67 | −0.646048 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2442.09 | 0.351649 | ||||||||
\(365\) | −2456.60 | −0.352286 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5825.76 | 0.828616 | 0.414308 | − | 0.910137i | \(-0.364024\pi\) | ||||
0.414308 | + | 0.910137i | \(0.364024\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7357.32 | 1.03375 | ||||||||
\(371\) | −11619.3 | −1.62599 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2339.75 | 0.324793 | 0.162396 | − | 0.986726i | \(-0.448078\pi\) | ||||
0.162396 | + | 0.986726i | \(0.448078\pi\) | |||||||
\(374\) | −6319.23 | −0.873689 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4627.92 | −0.634752 | ||||||||
\(377\) | −1388.08 | −0.189628 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10381.9 | 1.40707 | 0.703537 | − | 0.710658i | \(-0.251603\pi\) | ||||
0.703537 | + | 0.710658i | \(0.251603\pi\) | |||||||
\(380\) | −8617.83 | −1.16338 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6198.09 | 0.830162 | ||||||||
\(383\) | −4681.97 | −0.624641 | −0.312320 | − | 0.949977i | \(-0.601106\pi\) | ||||
−0.312320 | + | 0.949977i | \(0.601106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10043.7 | 1.32955 | ||||||||
\(386\) | −1359.87 | −0.179315 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6505.26 | 0.851171 | ||||||||
\(389\) | −2896.26 | −0.377497 | −0.188748 | − | 0.982025i | \(-0.560443\pi\) | ||||
−0.188748 | + | 0.982025i | \(0.560443\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1767.71 | −0.228637 | ||||||||
\(392\) | 55.5145 | 0.00715282 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −99.8235 | −0.0127641 | ||||||||
\(395\) | 2612.84 | 0.332826 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1599.60 | −0.202221 | −0.101111 | − | 0.994875i | \(-0.532240\pi\) | ||||
−0.101111 | + | 0.994875i | \(0.532240\pi\) | |||||||
\(398\) | −8105.60 | −1.02085 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 729.069 | 0.0911336 | ||||||||
\(401\) | −2132.80 | −0.265603 | −0.132802 | − | 0.991143i | \(-0.542397\pi\) | ||||
−0.132802 | + | 0.991143i | \(0.542397\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8040.06 | 0.993807 | ||||||||
\(404\) | −1464.51 | −0.180352 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1591.24 | −0.194512 | ||||||||
\(407\) | 11579.6 | 1.41027 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4181.61 | −0.505544 | −0.252772 | − | 0.967526i | \(-0.581342\pi\) | ||||
−0.252772 | + | 0.967526i | \(0.581342\pi\) | |||||||
\(410\) | 8629.22 | 1.03943 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7313.62 | 0.874554 | ||||||||
\(413\) | 6499.29 | 0.774356 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 652.773 | 0.0772130 | ||||||||
\(416\) | 1044.37 | 0.123088 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13563.5 | −1.58711 | ||||||||
\(419\) | 3866.07 | 0.450763 | 0.225381 | − | 0.974271i | \(-0.427637\pi\) | ||||
0.225381 | + | 0.974271i | \(0.427637\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6888.69 | −0.797469 | −0.398734 | − | 0.917066i | \(-0.630550\pi\) | ||||
−0.398734 | + | 0.917066i | \(0.630550\pi\) | |||||||
\(422\) | −1728.28 | −0.199364 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4969.04 | −0.569147 | ||||||||
\(425\) | −3502.13 | −0.399713 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6961.10 | 0.788926 | ||||||||
\(428\) | −2222.64 | −0.251017 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4196.07 | −0.470587 | ||||||||
\(431\) | −12349.8 | −1.38021 | −0.690105 | − | 0.723709i | \(-0.742436\pi\) | ||||
−0.690105 | + | 0.723709i | \(0.742436\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12531.1 | −1.39078 | −0.695391 | − | 0.718632i | \(-0.744769\pi\) | ||||
−0.695391 | + | 0.718632i | \(0.744769\pi\) | |||||||
\(434\) | 9216.81 | 1.01940 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3811.41 | −0.418654 | ||||||||
\(437\) | −3794.19 | −0.415333 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11534.2 | −1.25398 | −0.626988 | − | 0.779029i | \(-0.715713\pi\) | ||||
−0.626988 | + | 0.779029i | \(0.715713\pi\) | |||||||
\(440\) | 4295.25 | 0.465381 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5016.70 | −0.539865 | ||||||||
\(443\) | 2982.50 | 0.319871 | 0.159935 | − | 0.987127i | \(-0.448871\pi\) | ||||
0.159935 | + | 0.987127i | \(0.448871\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10024.9 | −1.06793 | ||||||||
\(446\) | 11364.9 | 1.20660 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1197.23 | 0.126258 | ||||||||
\(449\) | 12630.8 | 1.32759 | 0.663793 | − | 0.747917i | \(-0.268946\pi\) | ||||
0.663793 | + | 0.747917i | \(0.268946\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13581.4 | 1.41801 | ||||||||
\(452\) | −1022.54 | −0.106407 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −316.197 | −0.0326869 | ||||||||
\(455\) | 7973.49 | 0.821545 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13693.1 | −1.40161 | −0.700804 | − | 0.713354i | \(-0.747175\pi\) | ||||
−0.700804 | + | 0.713354i | \(0.747175\pi\) | |||||||
\(458\) | 5489.88 | 0.560099 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1201.53 | 0.121786 | ||||||||
\(461\) | 4588.64 | 0.463588 | 0.231794 | − | 0.972765i | \(-0.425540\pi\) | ||||
0.231794 | + | 0.972765i | \(0.425540\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6110.84 | 0.613380 | 0.306690 | − | 0.951809i | \(-0.400778\pi\) | ||||
0.306690 | + | 0.951809i | \(0.400778\pi\) | |||||||
\(464\) | −680.503 | −0.0680852 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7295.25 | 0.725206 | ||||||||
\(467\) | 2078.48 | 0.205954 | 0.102977 | − | 0.994684i | \(-0.467163\pi\) | ||||
0.102977 | + | 0.994684i | \(0.467163\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16544.8 | 1.62893 | ||||||||
\(470\) | −15110.3 | −1.48295 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2779.45 | 0.271048 | ||||||||
\(473\) | −6604.13 | −0.641984 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7516.91 | −0.726104 | ||||||||
\(476\) | −5750.95 | −0.553770 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5160.27 | −0.493777 | ||||||||
\(479\) | 13245.4 | 1.26346 | 0.631730 | − | 0.775189i | \(-0.282345\pi\) | ||||
0.631730 | + | 0.775189i | \(0.282345\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9192.80 | 0.871425 | ||||||||
\(482\) | 8997.17 | 0.850228 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1436.23 | 0.134883 | ||||||||
\(485\) | 21239.9 | 1.98856 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8327.36 | 0.774843 | 0.387421 | − | 0.921903i | \(-0.373366\pi\) | ||||
0.387421 | + | 0.921903i | \(0.373366\pi\) | |||||||
\(488\) | 2976.95 | 0.276148 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 181.257 | 0.0167109 | ||||||||
\(491\) | 10585.9 | 0.972984 | 0.486492 | − | 0.873685i | \(-0.338276\pi\) | ||||
0.486492 | + | 0.873685i | \(0.338276\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3268.84 | 0.298623 | ||||||||
\(494\) | −10767.8 | −0.980698 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3941.62 | 0.356822 | ||||||||
\(497\) | −14547.6 | −1.31298 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2630.88 | −0.236021 | −0.118011 | − | 0.993012i | \(-0.537652\pi\) | ||||
−0.118011 | + | 0.993012i | \(0.537652\pi\) | |||||||
\(500\) | −4149.63 | −0.371154 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2570.65 | 0.228553 | ||||||||
\(503\) | −8978.08 | −0.795851 | −0.397925 | − | 0.917418i | \(-0.630270\pi\) | ||||
−0.397925 | + | 0.917418i | \(0.630270\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4781.67 | −0.421349 | ||||||||
\(506\) | 1891.07 | 0.166143 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6175.31 | −0.539341 | ||||||||
\(509\) | −10656.1 | −0.927942 | −0.463971 | − | 0.885850i | \(-0.653576\pi\) | ||||
−0.463971 | + | 0.885850i | \(0.653576\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3518.71 | −0.304616 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1537.59 | 0.131946 | ||||||||
\(515\) | 23879.2 | 2.04319 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23781.9 | −2.02307 | ||||||||
\(518\) | 10538.3 | 0.893870 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3409.90 | 0.287566 | ||||||||
\(521\) | −15732.0 | −1.32290 | −0.661449 | − | 0.749990i | \(-0.730058\pi\) | ||||
−0.661449 | + | 0.749990i | \(0.730058\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3937.97 | 0.329245 | 0.164623 | − | 0.986357i | \(-0.447359\pi\) | ||||
0.164623 | + | 0.986357i | \(0.447359\pi\) | |||||||
\(524\) | −467.623 | −0.0389851 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6908.54 | −0.572674 | ||||||||
\(527\) | −18933.8 | −1.56503 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −16224.1 | −1.32968 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12343.8 | −1.00596 | ||||||||
\(533\) | 10782.0 | 0.876210 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7256.98 | −0.586442 | ||||||||
\(536\) | 7075.46 | 0.570174 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8697.78 | −0.697003 | ||||||||
\(539\) | 285.277 | 0.0227973 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7886.04 | −0.626704 | −0.313352 | − | 0.949637i | \(-0.601452\pi\) | ||||
−0.313352 | + | 0.949637i | \(0.601452\pi\) | |||||||
\(542\) | 9752.71 | 0.772905 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2459.42 | −0.193836 | ||||||||
\(545\) | −12444.4 | −0.978088 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20947.1 | 1.63735 | 0.818677 | − | 0.574255i | \(-0.194708\pi\) | ||||
0.818677 | + | 0.574255i | \(0.194708\pi\) | |||||||
\(548\) | −11080.0 | −0.863712 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3746.53 | 0.290459 | ||||||||
\(551\) | 7016.18 | 0.542467 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3742.50 | 0.287789 | ||||||||
\(554\) | −1515.11 | −0.116193 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5185.07 | −0.395496 | ||||||||
\(557\) | −14249.9 | −1.08400 | −0.542001 | − | 0.840378i | \(-0.682333\pi\) | ||||
−0.542001 | + | 0.840378i | \(0.682333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5242.88 | −0.396691 | ||||||||
\(560\) | 3908.98 | 0.294973 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16815.5 | −1.26213 | ||||||||
\(563\) | 20886.4 | 1.56351 | 0.781755 | − | 0.623586i | \(-0.214325\pi\) | ||||
0.781755 | + | 0.623586i | \(0.214325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3338.62 | −0.248596 | ||||||||
\(566\) | −5044.13 | −0.374594 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6221.37 | −0.459583 | ||||||||
\(569\) | −18602.8 | −1.37060 | −0.685299 | − | 0.728262i | \(-0.740328\pi\) | ||||
−0.685299 | + | 0.728262i | \(0.740328\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13118.5 | −0.961456 | −0.480728 | − | 0.876870i | \(-0.659628\pi\) | ||||
−0.480728 | + | 0.876870i | \(0.659628\pi\) | |||||||
\(572\) | 5366.80 | 0.392303 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12360.1 | 0.898779 | ||||||||
\(575\) | 1048.04 | 0.0760107 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15596.4 | 1.12528 | 0.562640 | − | 0.826702i | \(-0.309786\pi\) | ||||
0.562640 | + | 0.826702i | \(0.309786\pi\) | |||||||
\(578\) | 1987.99 | 0.143061 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2221.86 | −0.159065 | ||||||||
\(581\) | 935.000 | 0.0667648 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25534.9 | −1.81397 | ||||||||
\(584\) | −1504.80 | −0.106625 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6714.27 | 0.473317 | ||||||||
\(587\) | −15569.7 | −1.09477 | −0.547385 | − | 0.836881i | \(-0.684377\pi\) | ||||
−0.547385 | + | 0.836881i | \(0.684377\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40639.2 | −2.84297 | ||||||||
\(590\) | 9075.00 | 0.633241 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4506.74 | 0.312882 | ||||||||
\(593\) | −1616.91 | −0.111971 | −0.0559854 | − | 0.998432i | \(-0.517830\pi\) | ||||
−0.0559854 | + | 0.998432i | \(0.517830\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18777.0 | −1.29375 | ||||||||
\(596\) | −802.797 | −0.0551742 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1501.28 | 0.102662 | ||||||||
\(599\) | 10595.7 | 0.722752 | 0.361376 | − | 0.932420i | \(-0.382307\pi\) | ||||
0.361376 | + | 0.932420i | \(0.382307\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5699.09 | −0.386806 | −0.193403 | − | 0.981119i | \(-0.561953\pi\) | ||||
−0.193403 | + | 0.981119i | \(0.561953\pi\) | |||||||
\(602\) | −6010.23 | −0.406908 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −436.836 | −0.0294282 | ||||||||
\(605\) | 4689.34 | 0.315122 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15513.1 | 1.03733 | 0.518664 | − | 0.854978i | \(-0.326430\pi\) | ||||
0.518664 | + | 0.854978i | \(0.326430\pi\) | |||||||
\(608\) | −5278.87 | −0.352116 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9719.84 | 0.645155 | ||||||||
\(611\) | −18880.0 | −1.25008 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5817.04 | 0.383276 | 0.191638 | − | 0.981466i | \(-0.438620\pi\) | ||||
0.191638 | + | 0.981466i | \(0.438620\pi\) | |||||||
\(614\) | −15320.4 | −1.00697 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6152.29 | 0.402407 | ||||||||
\(617\) | −18218.6 | −1.18874 | −0.594370 | − | 0.804191i | \(-0.702599\pi\) | ||||
−0.594370 | + | 0.804191i | \(0.702599\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23581.8 | 1.53123 | 0.765617 | − | 0.643296i | \(-0.222434\pi\) | ||||
0.765617 | + | 0.643296i | \(0.222434\pi\) | |||||||
\(620\) | 12869.5 | 0.833632 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 688.812 | 0.0444033 | ||||||||
\(623\) | −14359.2 | −0.923418 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19244.5 | −1.23165 | ||||||||
\(626\) | 6807.68 | 0.434648 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13198.6 | −0.838665 | ||||||||
\(629\) | −21648.4 | −1.37230 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14989.0 | −0.945649 | −0.472825 | − | 0.881157i | \(-0.656766\pi\) | ||||
−0.472825 | + | 0.881157i | \(0.656766\pi\) | |||||||
\(632\) | 1600.50 | 0.100735 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11602.7 | −0.726820 | ||||||||
\(635\) | −20162.6 | −1.26004 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 226.476 | 0.0140868 | ||||||||
\(638\) | −3496.96 | −0.217000 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1671.70 | 0.103249 | ||||||||
\(641\) | 16769.0 | 1.03328 | 0.516642 | − | 0.856201i | \(-0.327182\pi\) | ||||
0.516642 | + | 0.856201i | \(0.327182\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15863.5 | −0.972933 | −0.486467 | − | 0.873699i | \(-0.661714\pi\) | ||||
−0.486467 | + | 0.873699i | \(0.661714\pi\) | |||||||
\(644\) | 1721.01 | 0.105307 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25357.4 | 1.54438 | ||||||||
\(647\) | 25100.0 | 1.52516 | 0.762582 | − | 0.646891i | \(-0.223931\pi\) | ||||
0.762582 | + | 0.646891i | \(0.223931\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14283.0 | 0.863880 | ||||||||
\(650\) | 2974.29 | 0.179479 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 954.693 | 0.0573446 | ||||||||
\(653\) | −7127.01 | −0.427108 | −0.213554 | − | 0.976931i | \(-0.568504\pi\) | ||||
−0.213554 | + | 0.976931i | \(0.568504\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1526.80 | −0.0910795 | ||||||||
\(656\) | 5285.84 | 0.314600 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −21643.2 | −1.28228 | ||||||||
\(659\) | 18985.3 | 1.12225 | 0.561124 | − | 0.827731i | \(-0.310369\pi\) | ||||
0.561124 | + | 0.827731i | \(0.310369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2780.35 | 0.163605 | 0.0818026 | − | 0.996649i | \(-0.473932\pi\) | ||||
0.0818026 | + | 0.996649i | \(0.473932\pi\) | |||||||
\(662\) | 16801.3 | 0.986407 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 399.857 | 0.0233697 | ||||||||
\(665\) | −40302.7 | −2.35018 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −978.223 | −0.0567870 | ||||||||
\(668\) | 12497.7 | 0.723880 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23101.6 | 1.33208 | ||||||||
\(671\) | 15297.9 | 0.880134 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9328.01 | −0.534277 | −0.267138 | − | 0.963658i | \(-0.586078\pi\) | ||||
−0.267138 | + | 0.963658i | \(0.586078\pi\) | |||||||
\(674\) | 8288.34 | 0.473672 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4527.41 | −0.257590 | ||||||||
\(677\) | −33535.6 | −1.90381 | −0.951905 | − | 0.306393i | \(-0.900878\pi\) | ||||
−0.951905 | + | 0.306393i | \(0.900878\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30422.9 | 1.71948 | ||||||||
\(680\) | −8030.09 | −0.452853 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 20255.1 | 1.13726 | ||||||||
\(683\) | 25507.4 | 1.42901 | 0.714506 | − | 0.699629i | \(-0.246652\pi\) | ||||
0.714506 | + | 0.699629i | \(0.246652\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36176.5 | −2.01786 | ||||||||
\(686\) | −12573.1 | −0.699774 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2570.31 | −0.142430 | ||||||||
\(689\) | −20271.6 | −1.12088 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3801.07 | −0.209261 | −0.104631 | − | 0.994511i | \(-0.533366\pi\) | ||||
−0.104631 | + | 0.994511i | \(0.533366\pi\) | |||||||
\(692\) | −10929.7 | −0.600413 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7703.41 | 0.421351 | ||||||||
\(695\) | −16929.4 | −0.923984 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25390.9 | −1.37984 | ||||||||
\(698\) | 5162.34 | 0.279939 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3409.61 | 0.184102 | ||||||||
\(701\) | 24101.5 | 1.29858 | 0.649289 | − | 0.760542i | \(-0.275067\pi\) | ||||
0.649289 | + | 0.760542i | \(0.275067\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −46465.8 | −2.49287 | ||||||||
\(704\) | 2631.06 | 0.140855 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15497.5 | 0.826143 | ||||||||
\(707\) | −6849.02 | −0.364334 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27015.2 | 1.43100 | 0.715498 | − | 0.698615i | \(-0.246200\pi\) | ||||
0.715498 | + | 0.698615i | \(0.246200\pi\) | |||||||
\(710\) | −20313.0 | −1.07371 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6140.79 | −0.323224 | ||||||||
\(713\) | 5666.07 | 0.297610 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17522.8 | 0.916524 | ||||||||
\(716\) | 9403.79 | 0.490833 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3914.04 | 0.203441 | ||||||||
\(719\) | −12022.5 | −0.623593 | −0.311797 | − | 0.950149i | \(-0.600931\pi\) | ||||
−0.311797 | + | 0.950149i | \(0.600931\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34203.4 | 1.76671 | ||||||||
\(722\) | 40708.7 | 2.09837 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8899.33 | −0.456825 | ||||||||
\(725\) | −1938.02 | −0.0992776 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20108.7 | 1.02585 | 0.512923 | − | 0.858435i | \(-0.328563\pi\) | ||||
0.512923 | + | 0.858435i | \(0.328563\pi\) | |||||||
\(728\) | 4884.18 | 0.248653 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4913.20 | −0.249104 | ||||||||
\(731\) | 12346.6 | 0.624701 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16026.4 | 0.807568 | 0.403784 | − | 0.914854i | \(-0.367695\pi\) | ||||
0.403784 | + | 0.914854i | \(0.367695\pi\) | |||||||
\(734\) | 11651.5 | 0.585920 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 36359.3 | 1.81725 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −121.045 | −0.00602532 | −0.00301266 | − | 0.999995i | \(-0.500959\pi\) | ||||
−0.00301266 | + | 0.999995i | \(0.500959\pi\) | |||||||
\(740\) | 14714.6 | 0.730975 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23238.6 | −1.14975 | ||||||||
\(743\) | 32902.8 | 1.62461 | 0.812306 | − | 0.583231i | \(-0.198212\pi\) | ||||
0.812306 | + | 0.583231i | \(0.198212\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2621.16 | −0.128902 | ||||||||
\(746\) | 4679.50 | 0.229663 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12638.5 | −0.617791 | ||||||||
\(749\) | −10394.5 | −0.507087 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8822.39 | −0.428673 | −0.214337 | − | 0.976760i | \(-0.568759\pi\) | ||||
−0.214337 | + | 0.976760i | \(0.568759\pi\) | |||||||
\(752\) | −9255.84 | −0.448838 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2776.16 | −0.134087 | ||||||||
\(755\) | −1426.28 | −0.0687520 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17256.9 | 0.828552 | 0.414276 | − | 0.910151i | \(-0.364035\pi\) | ||||
0.414276 | + | 0.910151i | \(0.364035\pi\) | |||||||
\(758\) | 20763.8 | 0.994952 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17235.7 | −0.822636 | ||||||||
\(761\) | 28563.8 | 1.36063 | 0.680313 | − | 0.732921i | \(-0.261844\pi\) | ||||
0.680313 | + | 0.732921i | \(0.261844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17824.7 | −0.845736 | ||||||||
\(764\) | 12396.2 | 0.587013 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9363.94 | −0.441688 | ||||||||
\(767\) | 11339.0 | 0.533804 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36869.9 | 1.72895 | 0.864475 | − | 0.502676i | \(-0.167651\pi\) | ||||
0.864475 | + | 0.502676i | \(0.167651\pi\) | |||||||
\(770\) | 20087.4 | 0.940131 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2719.74 | −0.126795 | ||||||||
\(773\) | −31615.1 | −1.47104 | −0.735520 | − | 0.677503i | \(-0.763062\pi\) | ||||
−0.735520 | + | 0.677503i | \(0.763062\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11225.4 | 0.520296 | ||||||||
\(776\) | 13010.5 | 0.601869 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5792.52 | −0.266931 | ||||||||
\(779\) | −54498.6 | −2.50656 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31970.3 | −1.46477 | ||||||||
\(782\) | −3535.42 | −0.161671 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 111.029 | 0.00505781 | ||||||||
\(785\) | −43093.9 | −1.95934 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22822.8 | −1.03373 | −0.516865 | − | 0.856067i | \(-0.672901\pi\) | ||||
−0.516865 | + | 0.856067i | \(0.672901\pi\) | |||||||
\(788\) | −199.647 | −0.00902555 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5225.68 | 0.235343 | ||||||||
\(791\) | −4782.07 | −0.214957 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12144.7 | 0.543847 | ||||||||
\(794\) | −3199.21 | −0.142992 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16211.2 | −0.721847 | ||||||||
\(797\) | 32080.5 | 1.42578 | 0.712892 | − | 0.701274i | \(-0.247385\pi\) | ||||
0.712892 | + | 0.701274i | \(0.247385\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44461.0 | 1.96861 | ||||||||
\(800\) | 1458.14 | 0.0644412 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4265.60 | −0.187810 | ||||||||
\(803\) | −7732.83 | −0.339833 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5619.16 | 0.246024 | ||||||||
\(806\) | 16080.1 | 0.702727 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2929.02 | −0.127528 | ||||||||
\(809\) | 12622.8 | 0.548570 | 0.274285 | − | 0.961649i | \(-0.411559\pi\) | ||||
0.274285 | + | 0.961649i | \(0.411559\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14725.4 | 0.637581 | 0.318791 | − | 0.947825i | \(-0.396723\pi\) | ||||
0.318791 | + | 0.947825i | \(0.396723\pi\) | |||||||
\(812\) | −3182.48 | −0.137541 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23159.2 | 0.997210 | ||||||||
\(815\) | 3117.10 | 0.133972 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26500.6 | 1.13481 | ||||||||
\(818\) | −8363.23 | −0.357474 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17258.4 | 0.734989 | ||||||||
\(821\) | −25304.1 | −1.07566 | −0.537832 | − | 0.843052i | \(-0.680756\pi\) | ||||
−0.537832 | + | 0.843052i | \(0.680756\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26359.2 | −1.11643 | −0.558217 | − | 0.829695i | \(-0.688514\pi\) | ||||
−0.558217 | + | 0.829695i | \(0.688514\pi\) | |||||||
\(824\) | 14627.2 | 0.618403 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12998.6 | 0.547553 | ||||||||
\(827\) | 23399.7 | 0.983902 | 0.491951 | − | 0.870623i | \(-0.336284\pi\) | ||||
0.491951 | + | 0.870623i | \(0.336284\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31965.7 | 1.33922 | 0.669612 | − | 0.742711i | \(-0.266461\pi\) | ||||
0.669612 | + | 0.742711i | \(0.266461\pi\) | |||||||
\(830\) | 1305.55 | 0.0545978 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2088.74 | 0.0870362 | ||||||||
\(833\) | −533.335 | −0.0221836 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40805.5 | 1.69118 | ||||||||
\(836\) | −27127.0 | −1.12226 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7732.13 | 0.318738 | ||||||||
\(839\) | 31922.9 | 1.31359 | 0.656793 | − | 0.754071i | \(-0.271912\pi\) | ||||
0.656793 | + | 0.754071i | \(0.271912\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22580.1 | −0.925830 | ||||||||
\(842\) | −13777.4 | −0.563896 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3456.57 | −0.140971 | ||||||||
\(845\) | −14782.1 | −0.601799 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6716.77 | 0.272481 | ||||||||
\(848\) | −9938.09 | −0.402447 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7004.25 | −0.282640 | ||||||||
\(851\) | 6478.44 | 0.260961 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23656.8 | 0.949583 | 0.474791 | − | 0.880098i | \(-0.342523\pi\) | ||||
0.474791 | + | 0.880098i | \(0.342523\pi\) | |||||||
\(854\) | 13922.2 | 0.557855 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4445.28 | −0.177496 | ||||||||
\(857\) | −31502.3 | −1.25566 | −0.627829 | − | 0.778351i | \(-0.716056\pi\) | ||||
−0.627829 | + | 0.778351i | \(0.716056\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4487.44 | −0.178242 | −0.0891208 | − | 0.996021i | \(-0.528406\pi\) | ||||
−0.0891208 | + | 0.996021i | \(0.528406\pi\) | |||||||
\(860\) | −8392.13 | −0.332755 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24699.7 | −0.975956 | ||||||||
\(863\) | −21730.6 | −0.857147 | −0.428574 | − | 0.903507i | \(-0.640984\pi\) | ||||
−0.428574 | + | 0.903507i | \(0.640984\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35685.9 | −1.40273 | ||||||||
\(866\) | −25062.3 | −0.983431 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18433.6 | 0.720827 | ||||||||
\(869\) | 8224.63 | 0.321060 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28864.9 | 1.12290 | ||||||||
\(872\) | −7622.82 | −0.296033 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7588.37 | −0.293685 | ||||||||
\(875\) | −19406.4 | −0.749780 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9754.59 | −0.375586 | −0.187793 | − | 0.982209i | \(-0.560133\pi\) | ||||
−0.187793 | + | 0.982209i | \(0.560133\pi\) | |||||||
\(878\) | −23068.3 | −0.886696 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8590.49 | 0.329074 | ||||||||
\(881\) | 25789.6 | 0.986235 | 0.493118 | − | 0.869963i | \(-0.335857\pi\) | ||||
0.493118 | + | 0.869963i | \(0.335857\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8851.25 | −0.337337 | −0.168668 | − | 0.985673i | \(-0.553947\pi\) | ||||
−0.168668 | + | 0.985673i | \(0.553947\pi\) | |||||||
\(884\) | −10033.4 | −0.381742 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5964.99 | 0.226183 | ||||||||
\(887\) | −13140.9 | −0.497439 | −0.248720 | − | 0.968576i | \(-0.580010\pi\) | ||||
−0.248720 | + | 0.968576i | \(0.580010\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28879.9 | −1.08954 | ||||||||
\(890\) | −20049.9 | −0.755138 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22729.8 | 0.853196 | ||||||||
\(893\) | 95430.4 | 3.57610 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30703.7 | 1.14672 | ||||||||
\(896\) | 2394.45 | 0.0892780 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25261.7 | 0.938744 | ||||||||
\(899\) | −10477.7 | −0.388709 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47738.2 | 1.76514 | ||||||||
\(902\) | 27162.8 | 1.00269 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2045.07 | −0.0752413 | ||||||||
\(905\) | −29056.6 | −1.06726 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12195.6 | −0.446471 | −0.223235 | − | 0.974765i | \(-0.571662\pi\) | ||||
−0.223235 | + | 0.974765i | \(0.571662\pi\) | |||||||
\(908\) | −632.394 | −0.0231132 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 15947.0 | 0.580920 | ||||||||
\(911\) | 23873.1 | 0.868223 | 0.434111 | − | 0.900859i | \(-0.357062\pi\) | ||||
0.434111 | + | 0.900859i | \(0.357062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2054.78 | 0.0744835 | ||||||||
\(914\) | −27386.1 | −0.991087 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10979.8 | 0.396050 | ||||||||
\(917\) | −2186.92 | −0.0787550 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25048.2 | −0.899092 | −0.449546 | − | 0.893257i | \(-0.648414\pi\) | ||||
−0.449546 | + | 0.893257i | \(0.648414\pi\) | |||||||
\(920\) | 2403.06 | 0.0861159 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9177.28 | 0.327806 | ||||||||
\(923\) | −25380.6 | −0.905105 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12834.9 | 0.456224 | ||||||||
\(926\) | 12221.7 | 0.433725 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1361.01 | −0.0481435 | ||||||||
\(929\) | 40641.7 | 1.43532 | 0.717660 | − | 0.696394i | \(-0.245213\pi\) | ||||
0.717660 | + | 0.696394i | \(0.245213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1144.74 | −0.0402979 | ||||||||
\(932\) | 14590.5 | 0.512798 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4156.96 | 0.145632 | ||||||||
\(935\) | −41265.0 | −1.44332 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39519.4 | 1.37785 | 0.688924 | − | 0.724833i | \(-0.258083\pi\) | ||||
0.688924 | + | 0.724833i | \(0.258083\pi\) | |||||||
\(938\) | 33089.6 | 1.15183 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −30220.6 | −1.04860 | ||||||||
\(941\) | 32189.2 | 1.11513 | 0.557566 | − | 0.830133i | \(-0.311735\pi\) | ||||
0.557566 | + | 0.830133i | \(0.311735\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7598.40 | 0.262394 | ||||||||
\(944\) | 5558.91 | 0.191660 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13208.3 | −0.453951 | ||||||||
\(947\) | 18703.2 | 0.641786 | 0.320893 | − | 0.947115i | \(-0.396017\pi\) | ||||
0.320893 | + | 0.947115i | \(0.396017\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6138.93 | −0.209987 | ||||||||
\(950\) | −15033.8 | −0.513433 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11501.9 | −0.391574 | ||||||||
\(953\) | −19901.0 | −0.676449 | −0.338224 | − | 0.941066i | \(-0.609826\pi\) | ||||
−0.338224 | + | 0.941066i | \(0.609826\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40473.9 | 1.37142 | ||||||||
\(956\) | −10320.5 | −0.349153 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26490.8 | 0.893401 | ||||||||
\(959\) | −51817.4 | −1.74481 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30897.9 | 1.03715 | ||||||||
\(962\) | 18385.6 | 0.616191 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17994.3 | 0.601202 | ||||||||
\(965\) | −8880.03 | −0.296226 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1654.58 | −0.0550236 | −0.0275118 | − | 0.999621i | \(-0.508758\pi\) | ||||
−0.0275118 | + | 0.999621i | \(0.508758\pi\) | |||||||
\(968\) | 2872.46 | 0.0953765 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 42479.7 | 1.40613 | ||||||||
\(971\) | −21532.9 | −0.711661 | −0.355831 | − | 0.934550i | \(-0.615802\pi\) | ||||
−0.355831 | + | 0.934550i | \(0.615802\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24248.8 | −0.798953 | ||||||||
\(974\) | 16654.7 | 0.547897 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5953.90 | 0.195266 | ||||||||
\(977\) | −28732.0 | −0.940856 | −0.470428 | − | 0.882438i | \(-0.655901\pi\) | ||||
−0.470428 | + | 0.882438i | \(0.655901\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31556.2 | −1.03017 | ||||||||
\(980\) | 362.513 | 0.0118164 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21171.8 | 0.688004 | ||||||||
\(983\) | 7497.77 | 0.243277 | 0.121639 | − | 0.992574i | \(-0.461185\pi\) | ||||
0.121639 | + | 0.992574i | \(0.461185\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −651.854 | −0.0210861 | ||||||||
\(986\) | 6537.67 | 0.211158 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21535.5 | −0.693458 | ||||||||
\(989\) | −3694.82 | −0.118795 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32374.5 | 1.03775 | 0.518874 | − | 0.854851i | \(-0.326351\pi\) | ||||
0.518874 | + | 0.854851i | \(0.326351\pi\) | |||||||
\(992\) | 7883.23 | 0.252311 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −29095.3 | −0.928417 | ||||||||
\(995\) | −52930.0 | −1.68643 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19368.9 | 0.615264 | 0.307632 | − | 0.951505i | \(-0.400463\pi\) | ||||
0.307632 | + | 0.951505i | \(0.400463\pi\) | |||||||
\(998\) | −5261.77 | −0.166892 | ||||||||
\(999\) | 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 | 414.4.a.n.1.3 | yes | 4 | |
3.2 | odd | 2 | 414.4.a.m.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.4.a.m.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
414.4.a.n.1.3 | yes | 4 | 1.1 | even | 1 | trivial |