Newspace parameters
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(81.7766472680\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 462) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1386.1 |
$q$-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 | ||||||||
\(5\) | 7.00000 | 0.626099 | 0.313050 | − | 0.949737i | \(-0.398649\pi\) | ||||
0.313050 | + | 0.949737i | \(0.398649\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 14.0000 | 0.442719 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −67.0000 | −1.42942 | −0.714710 | − | 0.699421i | \(-0.753441\pi\) | ||||
−0.714710 | + | 0.699421i | \(0.753441\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −30.0000 | −0.428004 | −0.214002 | − | 0.976833i | \(-0.568650\pi\) | ||||
−0.214002 | + | 0.976833i | \(0.568650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.00000 | −0.0845216 | −0.0422608 | − | 0.999107i | \(-0.513456\pi\) | ||||
−0.0422608 | + | 0.999107i | \(0.513456\pi\) | |||||||
\(20\) | 28.0000 | 0.313050 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −22.0000 | −0.213201 | ||||||||
\(23\) | −28.0000 | −0.253844 | −0.126922 | − | 0.991913i | \(-0.540510\pi\) | ||||
−0.126922 | + | 0.991913i | \(0.540510\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −76.0000 | −0.608000 | ||||||||
\(26\) | −134.000 | −1.01075 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | −121.000 | −0.774798 | −0.387399 | − | 0.921912i | \(-0.626626\pi\) | ||||
−0.387399 | + | 0.921912i | \(0.626626\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −310.000 | −1.79605 | −0.898027 | − | 0.439941i | \(-0.854999\pi\) | ||||
−0.898027 | + | 0.439941i | \(0.854999\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −60.0000 | −0.302645 | ||||||||
\(35\) | 49.0000 | 0.236643 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −71.0000 | −0.315468 | −0.157734 | − | 0.987482i | \(-0.550419\pi\) | ||||
−0.157734 | + | 0.987482i | \(0.550419\pi\) | |||||||
\(38\) | −14.0000 | −0.0597658 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 56.0000 | 0.221359 | ||||||||
\(41\) | 180.000 | 0.685641 | 0.342820 | − | 0.939401i | \(-0.388618\pi\) | ||||
0.342820 | + | 0.939401i | \(0.388618\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −108.000 | −0.383020 | −0.191510 | − | 0.981491i | \(-0.561338\pi\) | ||||
−0.191510 | + | 0.981491i | \(0.561338\pi\) | |||||||
\(44\) | −44.0000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −56.0000 | −0.179495 | ||||||||
\(47\) | −71.0000 | −0.220349 | −0.110175 | − | 0.993912i | \(-0.535141\pi\) | ||||
−0.110175 | + | 0.993912i | \(0.535141\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −152.000 | −0.429921 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −268.000 | −0.714710 | ||||||||
\(53\) | −128.000 | −0.331739 | −0.165869 | − | 0.986148i | \(-0.553043\pi\) | ||||
−0.165869 | + | 0.986148i | \(0.553043\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −77.0000 | −0.188776 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −242.000 | −0.547865 | ||||||||
\(59\) | 429.000 | 0.946628 | 0.473314 | − | 0.880894i | \(-0.343058\pi\) | ||||
0.473314 | + | 0.880894i | \(0.343058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 22.0000 | 0.0461772 | 0.0230886 | − | 0.999733i | \(-0.492650\pi\) | ||||
0.0230886 | + | 0.999733i | \(0.492650\pi\) | |||||||
\(62\) | −620.000 | −1.27000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −469.000 | −0.894958 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −803.000 | −1.46421 | −0.732105 | − | 0.681192i | \(-0.761462\pi\) | ||||
−0.732105 | + | 0.681192i | \(0.761462\pi\) | |||||||
\(68\) | −120.000 | −0.214002 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 98.0000 | 0.167332 | ||||||||
\(71\) | −468.000 | −0.782273 | −0.391136 | − | 0.920333i | \(-0.627918\pi\) | ||||
−0.391136 | + | 0.920333i | \(0.627918\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −117.000 | −0.187586 | −0.0937932 | − | 0.995592i | \(-0.529899\pi\) | ||||
−0.0937932 | + | 0.995592i | \(0.529899\pi\) | |||||||
\(74\) | −142.000 | −0.223070 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −28.0000 | −0.0422608 | ||||||||
\(77\) | −77.0000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −96.0000 | −0.136720 | −0.0683598 | − | 0.997661i | \(-0.521777\pi\) | ||||
−0.0683598 | + | 0.997661i | \(0.521777\pi\) | |||||||
\(80\) | 112.000 | 0.156525 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 360.000 | 0.484821 | ||||||||
\(83\) | 1122.00 | 1.48380 | 0.741901 | − | 0.670510i | \(-0.233925\pi\) | ||||
0.741901 | + | 0.670510i | \(0.233925\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −210.000 | −0.267973 | ||||||||
\(86\) | −216.000 | −0.270836 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −88.0000 | −0.106600 | ||||||||
\(89\) | 1146.00 | 1.36490 | 0.682448 | − | 0.730934i | \(-0.260915\pi\) | ||||
0.682448 | + | 0.730934i | \(0.260915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −469.000 | −0.540270 | ||||||||
\(92\) | −112.000 | −0.126922 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −142.000 | −0.155810 | ||||||||
\(95\) | −49.0000 | −0.0529189 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −92.0000 | −0.0963009 | −0.0481504 | − | 0.998840i | \(-0.515333\pi\) | ||||
−0.0481504 | + | 0.998840i | \(0.515333\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −304.000 | −0.304000 | ||||||||
\(101\) | 202.000 | 0.199007 | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1798.00 | −1.72002 | −0.860011 | − | 0.510276i | \(-0.829543\pi\) | ||||
−0.860011 | + | 0.510276i | \(0.829543\pi\) | |||||||
\(104\) | −536.000 | −0.505376 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −256.000 | −0.234575 | ||||||||
\(107\) | 1431.00 | 1.29290 | 0.646449 | − | 0.762958i | \(-0.276253\pi\) | ||||
0.646449 | + | 0.762958i | \(0.276253\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −278.000 | −0.244290 | −0.122145 | − | 0.992512i | \(-0.538977\pi\) | ||||
−0.122145 | + | 0.992512i | \(0.538977\pi\) | |||||||
\(110\) | −154.000 | −0.133485 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | 2322.00 | 1.93306 | 0.966528 | − | 0.256560i | \(-0.0825892\pi\) | ||||
0.966528 | + | 0.256560i | \(0.0825892\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −196.000 | −0.158931 | ||||||||
\(116\) | −484.000 | −0.387399 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 858.000 | 0.669367 | ||||||||
\(119\) | −210.000 | −0.161770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 44.0000 | 0.0326522 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1240.00 | −0.898027 | ||||||||
\(125\) | −1407.00 | −1.00677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2254.00 | 1.57488 | 0.787442 | − | 0.616389i | \(-0.211405\pi\) | ||||
0.787442 | + | 0.616389i | \(0.211405\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −938.000 | −0.632831 | ||||||||
\(131\) | −2196.00 | −1.46462 | −0.732311 | − | 0.680971i | \(-0.761558\pi\) | ||||
−0.732311 | + | 0.680971i | \(0.761558\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −49.0000 | −0.0319462 | ||||||||
\(134\) | −1606.00 | −1.03535 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −240.000 | −0.151322 | ||||||||
\(137\) | −766.000 | −0.477692 | −0.238846 | − | 0.971057i | \(-0.576769\pi\) | ||||
−0.238846 | + | 0.971057i | \(0.576769\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1080.00 | −0.659024 | −0.329512 | − | 0.944151i | \(-0.606884\pi\) | ||||
−0.329512 | + | 0.944151i | \(0.606884\pi\) | |||||||
\(140\) | 196.000 | 0.118322 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −936.000 | −0.553151 | ||||||||
\(143\) | 737.000 | 0.430986 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −847.000 | −0.485100 | ||||||||
\(146\) | −234.000 | −0.132644 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −284.000 | −0.157734 | ||||||||
\(149\) | −1373.00 | −0.754903 | −0.377451 | − | 0.926029i | \(-0.623200\pi\) | ||||
−0.377451 | + | 0.926029i | \(0.623200\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3210.00 | −1.72997 | −0.864987 | − | 0.501794i | \(-0.832673\pi\) | ||||
−0.864987 | + | 0.501794i | \(0.832673\pi\) | |||||||
\(152\) | −56.0000 | −0.0298829 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −154.000 | −0.0805823 | ||||||||
\(155\) | −2170.00 | −1.12451 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 452.000 | 0.229768 | 0.114884 | − | 0.993379i | \(-0.463350\pi\) | ||||
0.114884 | + | 0.993379i | \(0.463350\pi\) | |||||||
\(158\) | −192.000 | −0.0966753 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 224.000 | 0.110680 | ||||||||
\(161\) | −196.000 | −0.0959439 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.0000 | −0.00528581 | −0.00264290 | − | 0.999997i | \(-0.500841\pi\) | ||||
−0.00264290 | + | 0.999997i | \(0.500841\pi\) | |||||||
\(164\) | 720.000 | 0.342820 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2244.00 | 1.04921 | ||||||||
\(167\) | −504.000 | −0.233537 | −0.116769 | − | 0.993159i | \(-0.537254\pi\) | ||||
−0.116769 | + | 0.993159i | \(0.537254\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2292.00 | 1.04324 | ||||||||
\(170\) | −420.000 | −0.189485 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −432.000 | −0.191510 | ||||||||
\(173\) | −1688.00 | −0.741828 | −0.370914 | − | 0.928667i | \(-0.620956\pi\) | ||||
−0.370914 | + | 0.928667i | \(0.620956\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −532.000 | −0.229802 | ||||||||
\(176\) | −176.000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2292.00 | 0.965127 | ||||||||
\(179\) | −460.000 | −0.192078 | −0.0960391 | − | 0.995378i | \(-0.530617\pi\) | ||||
−0.0960391 | + | 0.995378i | \(0.530617\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2296.00 | 0.942875 | 0.471437 | − | 0.881900i | \(-0.343735\pi\) | ||||
0.471437 | + | 0.881900i | \(0.343735\pi\) | |||||||
\(182\) | −938.000 | −0.382028 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −224.000 | −0.0897473 | ||||||||
\(185\) | −497.000 | −0.197514 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 330.000 | 0.129048 | ||||||||
\(188\) | −284.000 | −0.110175 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −98.0000 | −0.0374193 | ||||||||
\(191\) | −878.000 | −0.332617 | −0.166309 | − | 0.986074i | \(-0.553185\pi\) | ||||
−0.166309 | + | 0.986074i | \(0.553185\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2268.00 | −0.845877 | −0.422938 | − | 0.906158i | \(-0.639001\pi\) | ||||
−0.422938 | + | 0.906158i | \(0.639001\pi\) | |||||||
\(194\) | −184.000 | −0.0680950 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −5298.00 | −1.91608 | −0.958038 | − | 0.286642i | \(-0.907461\pi\) | ||||
−0.958038 | + | 0.286642i | \(0.907461\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1044.00 | 0.371895 | 0.185948 | − | 0.982560i | \(-0.440464\pi\) | ||||
0.185948 | + | 0.982560i | \(0.440464\pi\) | |||||||
\(200\) | −608.000 | −0.214960 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 404.000 | 0.140720 | ||||||||
\(203\) | −847.000 | −0.292846 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1260.00 | 0.429279 | ||||||||
\(206\) | −3596.00 | −1.21624 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1072.00 | −0.357355 | ||||||||
\(209\) | 77.0000 | 0.0254842 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4566.00 | 1.48975 | 0.744873 | − | 0.667206i | \(-0.232510\pi\) | ||||
0.744873 | + | 0.667206i | \(0.232510\pi\) | |||||||
\(212\) | −512.000 | −0.165869 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2862.00 | 0.914216 | ||||||||
\(215\) | −756.000 | −0.239808 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2170.00 | −0.678844 | ||||||||
\(218\) | −556.000 | −0.172739 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −308.000 | −0.0943880 | ||||||||
\(221\) | 2010.00 | 0.611797 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 198.000 | 0.0594577 | 0.0297288 | − | 0.999558i | \(-0.490536\pi\) | ||||
0.0297288 | + | 0.999558i | \(0.490536\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4644.00 | 1.36688 | ||||||||
\(227\) | −3762.00 | −1.09997 | −0.549984 | − | 0.835175i | \(-0.685366\pi\) | ||||
−0.549984 | + | 0.835175i | \(0.685366\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −704.000 | −0.203151 | −0.101576 | − | 0.994828i | \(-0.532388\pi\) | ||||
−0.101576 | + | 0.994828i | \(0.532388\pi\) | |||||||
\(230\) | −392.000 | −0.112381 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −968.000 | −0.273932 | ||||||||
\(233\) | −2210.00 | −0.621382 | −0.310691 | − | 0.950511i | \(-0.600560\pi\) | ||||
−0.310691 | + | 0.950511i | \(0.600560\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −497.000 | −0.137960 | ||||||||
\(236\) | 1716.00 | 0.473314 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −420.000 | −0.114389 | ||||||||
\(239\) | −2451.00 | −0.663356 | −0.331678 | − | 0.943393i | \(-0.607615\pi\) | ||||
−0.331678 | + | 0.943393i | \(0.607615\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.0000 | 0.00668212 | 0.00334106 | − | 0.999994i | \(-0.498937\pi\) | ||||
0.00334106 | + | 0.999994i | \(0.498937\pi\) | |||||||
\(242\) | 242.000 | 0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 88.0000 | 0.0230886 | ||||||||
\(245\) | 343.000 | 0.0894427 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 469.000 | 0.120817 | ||||||||
\(248\) | −2480.00 | −0.635001 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2814.00 | −0.711892 | ||||||||
\(251\) | 5267.00 | 1.32450 | 0.662251 | − | 0.749282i | \(-0.269601\pi\) | ||||
0.662251 | + | 0.749282i | \(0.269601\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 308.000 | 0.0765367 | ||||||||
\(254\) | 4508.00 | 1.11361 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 1623.00 | 0.393930 | 0.196965 | − | 0.980411i | \(-0.436891\pi\) | ||||
0.196965 | + | 0.980411i | \(0.436891\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −497.000 | −0.119236 | ||||||||
\(260\) | −1876.00 | −0.447479 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4392.00 | −1.03564 | ||||||||
\(263\) | 2475.00 | 0.580285 | 0.290143 | − | 0.956983i | \(-0.406297\pi\) | ||||
0.290143 | + | 0.956983i | \(0.406297\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −896.000 | −0.207701 | ||||||||
\(266\) | −98.0000 | −0.0225893 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3212.00 | −0.732105 | ||||||||
\(269\) | −1746.00 | −0.395745 | −0.197873 | − | 0.980228i | \(-0.563403\pi\) | ||||
−0.197873 | + | 0.980228i | \(0.563403\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1653.00 | 0.370526 | 0.185263 | − | 0.982689i | \(-0.440686\pi\) | ||||
0.185263 | + | 0.982689i | \(0.440686\pi\) | |||||||
\(272\) | −480.000 | −0.107001 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1532.00 | −0.337779 | ||||||||
\(275\) | 836.000 | 0.183319 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2056.00 | −0.445968 | −0.222984 | − | 0.974822i | \(-0.571580\pi\) | ||||
−0.222984 | + | 0.974822i | \(0.571580\pi\) | |||||||
\(278\) | −2160.00 | −0.466001 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 392.000 | 0.0836660 | ||||||||
\(281\) | −837.000 | −0.177691 | −0.0888456 | − | 0.996045i | \(-0.528318\pi\) | ||||
−0.0888456 | + | 0.996045i | \(0.528318\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8969.00 | 1.88393 | 0.941964 | − | 0.335713i | \(-0.108977\pi\) | ||||
0.941964 | + | 0.335713i | \(0.108977\pi\) | |||||||
\(284\) | −1872.00 | −0.391136 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1474.00 | 0.304753 | ||||||||
\(287\) | 1260.00 | 0.259148 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4013.00 | −0.816813 | ||||||||
\(290\) | −1694.00 | −0.343018 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −468.000 | −0.0937932 | ||||||||
\(293\) | −5120.00 | −1.02087 | −0.510433 | − | 0.859918i | \(-0.670515\pi\) | ||||
−0.510433 | + | 0.859918i | \(0.670515\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3003.00 | 0.592683 | ||||||||
\(296\) | −568.000 | −0.111535 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2746.00 | −0.533797 | ||||||||
\(299\) | 1876.00 | 0.362849 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −756.000 | −0.144768 | ||||||||
\(302\) | −6420.00 | −1.22328 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −112.000 | −0.0211304 | ||||||||
\(305\) | 154.000 | 0.0289115 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2892.00 | −0.537639 | −0.268819 | − | 0.963191i | \(-0.586634\pi\) | ||||
−0.268819 | + | 0.963191i | \(0.586634\pi\) | |||||||
\(308\) | −308.000 | −0.0569803 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4340.00 | −0.795147 | ||||||||
\(311\) | −3208.00 | −0.584916 | −0.292458 | − | 0.956278i | \(-0.594473\pi\) | ||||
−0.292458 | + | 0.956278i | \(0.594473\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3550.00 | 0.641079 | 0.320540 | − | 0.947235i | \(-0.396136\pi\) | ||||
0.320540 | + | 0.947235i | \(0.396136\pi\) | |||||||
\(314\) | 904.000 | 0.162470 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −384.000 | −0.0683598 | ||||||||
\(317\) | 5524.00 | 0.978734 | 0.489367 | − | 0.872078i | \(-0.337228\pi\) | ||||
0.489367 | + | 0.872078i | \(0.337228\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1331.00 | 0.233610 | ||||||||
\(320\) | 448.000 | 0.0782624 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −392.000 | −0.0678426 | ||||||||
\(323\) | 210.000 | 0.0361756 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5092.00 | 0.869087 | ||||||||
\(326\) | −22.0000 | −0.00373763 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1440.00 | 0.242411 | ||||||||
\(329\) | −497.000 | −0.0832842 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2144.00 | −0.356027 | −0.178013 | − | 0.984028i | \(-0.556967\pi\) | ||||
−0.178013 | + | 0.984028i | \(0.556967\pi\) | |||||||
\(332\) | 4488.00 | 0.741901 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1008.00 | −0.165136 | ||||||||
\(335\) | −5621.00 | −0.916740 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −884.000 | −0.142892 | −0.0714459 | − | 0.997444i | \(-0.522761\pi\) | ||||
−0.0714459 | + | 0.997444i | \(0.522761\pi\) | |||||||
\(338\) | 4584.00 | 0.737683 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −840.000 | −0.133986 | ||||||||
\(341\) | 3410.00 | 0.541530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −864.000 | −0.135418 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3376.00 | −0.524552 | ||||||||
\(347\) | 4040.00 | 0.625010 | 0.312505 | − | 0.949916i | \(-0.398832\pi\) | ||||
0.312505 | + | 0.949916i | \(0.398832\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1225.00 | 0.187888 | 0.0939438 | − | 0.995578i | \(-0.470053\pi\) | ||||
0.0939438 | + | 0.995578i | \(0.470053\pi\) | |||||||
\(350\) | −1064.00 | −0.162495 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −352.000 | −0.0533002 | ||||||||
\(353\) | −2483.00 | −0.374382 | −0.187191 | − | 0.982324i | \(-0.559938\pi\) | ||||
−0.187191 | + | 0.982324i | \(0.559938\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3276.00 | −0.489780 | ||||||||
\(356\) | 4584.00 | 0.682448 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −920.000 | −0.135820 | ||||||||
\(359\) | −7804.00 | −1.14730 | −0.573648 | − | 0.819102i | \(-0.694472\pi\) | ||||
−0.573648 | + | 0.819102i | \(0.694472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6810.00 | −0.992856 | ||||||||
\(362\) | 4592.00 | 0.666713 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1876.00 | −0.270135 | ||||||||
\(365\) | −819.000 | −0.117448 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3074.00 | 0.437225 | 0.218612 | − | 0.975812i | \(-0.429847\pi\) | ||||
0.218612 | + | 0.975812i | \(0.429847\pi\) | |||||||
\(368\) | −448.000 | −0.0634609 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −994.000 | −0.139664 | ||||||||
\(371\) | −896.000 | −0.125385 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 674.000 | 0.0935614 | 0.0467807 | − | 0.998905i | \(-0.485104\pi\) | ||||
0.0467807 | + | 0.998905i | \(0.485104\pi\) | |||||||
\(374\) | 660.000 | 0.0912508 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −568.000 | −0.0779052 | ||||||||
\(377\) | 8107.00 | 1.10751 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12051.0 | 1.63329 | 0.816647 | − | 0.577138i | \(-0.195830\pi\) | ||||
0.816647 | + | 0.577138i | \(0.195830\pi\) | |||||||
\(380\) | −196.000 | −0.0264594 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1756.00 | −0.235196 | ||||||||
\(383\) | 12664.0 | 1.68956 | 0.844778 | − | 0.535116i | \(-0.179732\pi\) | ||||
0.844778 | + | 0.535116i | \(0.179732\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −539.000 | −0.0713506 | ||||||||
\(386\) | −4536.00 | −0.598125 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −368.000 | −0.0481504 | ||||||||
\(389\) | −264.000 | −0.0344096 | −0.0172048 | − | 0.999852i | \(-0.505477\pi\) | ||||
−0.0172048 | + | 0.999852i | \(0.505477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 840.000 | 0.108646 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10596.0 | −1.35487 | ||||||||
\(395\) | −672.000 | −0.0856000 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14394.0 | −1.81968 | −0.909842 | − | 0.414956i | \(-0.863797\pi\) | ||||
−0.909842 | + | 0.414956i | \(0.863797\pi\) | |||||||
\(398\) | 2088.00 | 0.262970 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1216.00 | −0.152000 | ||||||||
\(401\) | 12304.0 | 1.53225 | 0.766125 | − | 0.642691i | \(-0.222182\pi\) | ||||
0.766125 | + | 0.642691i | \(0.222182\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20770.0 | 2.56731 | ||||||||
\(404\) | 808.000 | 0.0995037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1694.00 | −0.207073 | ||||||||
\(407\) | 781.000 | 0.0951173 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3154.00 | −0.381309 | −0.190654 | − | 0.981657i | \(-0.561061\pi\) | ||||
−0.190654 | + | 0.981657i | \(0.561061\pi\) | |||||||
\(410\) | 2520.00 | 0.303546 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7192.00 | −0.860011 | ||||||||
\(413\) | 3003.00 | 0.357792 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7854.00 | 0.929006 | ||||||||
\(416\) | −2144.00 | −0.252688 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 154.000 | 0.0180201 | ||||||||
\(419\) | 4635.00 | 0.540417 | 0.270208 | − | 0.962802i | \(-0.412907\pi\) | ||||
0.270208 | + | 0.962802i | \(0.412907\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7265.00 | −0.841032 | −0.420516 | − | 0.907285i | \(-0.638151\pi\) | ||||
−0.420516 | + | 0.907285i | \(0.638151\pi\) | |||||||
\(422\) | 9132.00 | 1.05341 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1024.00 | −0.117287 | ||||||||
\(425\) | 2280.00 | 0.260226 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 154.000 | 0.0174534 | ||||||||
\(428\) | 5724.00 | 0.646449 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1512.00 | −0.169570 | ||||||||
\(431\) | −7589.00 | −0.848142 | −0.424071 | − | 0.905629i | \(-0.639399\pi\) | ||||
−0.424071 | + | 0.905629i | \(0.639399\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5164.00 | 0.573132 | 0.286566 | − | 0.958061i | \(-0.407486\pi\) | ||||
0.286566 | + | 0.958061i | \(0.407486\pi\) | |||||||
\(434\) | −4340.00 | −0.480015 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1112.00 | −0.122145 | ||||||||
\(437\) | 196.000 | 0.0214553 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14221.0 | 1.54608 | 0.773042 | − | 0.634354i | \(-0.218734\pi\) | ||||
0.773042 | + | 0.634354i | \(0.218734\pi\) | |||||||
\(440\) | −616.000 | −0.0667424 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4020.00 | 0.432606 | ||||||||
\(443\) | −6924.00 | −0.742594 | −0.371297 | − | 0.928514i | \(-0.621087\pi\) | ||||
−0.371297 | + | 0.928514i | \(0.621087\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8022.00 | 0.854560 | ||||||||
\(446\) | 396.000 | 0.0420429 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | −2524.00 | −0.265289 | −0.132645 | − | 0.991164i | \(-0.542347\pi\) | ||||
−0.132645 | + | 0.991164i | \(0.542347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1980.00 | −0.206729 | ||||||||
\(452\) | 9288.00 | 0.966528 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7524.00 | −0.777795 | ||||||||
\(455\) | −3283.00 | −0.338262 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1928.00 | 0.197348 | 0.0986740 | − | 0.995120i | \(-0.468540\pi\) | ||||
0.0986740 | + | 0.995120i | \(0.468540\pi\) | |||||||
\(458\) | −1408.00 | −0.143650 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −784.000 | −0.0794656 | ||||||||
\(461\) | 12852.0 | 1.29843 | 0.649216 | − | 0.760604i | \(-0.275097\pi\) | ||||
0.649216 | + | 0.760604i | \(0.275097\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4741.00 | 0.475881 | 0.237941 | − | 0.971280i | \(-0.423528\pi\) | ||||
0.237941 | + | 0.971280i | \(0.423528\pi\) | |||||||
\(464\) | −1936.00 | −0.193699 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4420.00 | −0.439383 | ||||||||
\(467\) | 6809.00 | 0.674696 | 0.337348 | − | 0.941380i | \(-0.390470\pi\) | ||||
0.337348 | + | 0.941380i | \(0.390470\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5621.00 | −0.553419 | ||||||||
\(470\) | −994.000 | −0.0975528 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3432.00 | 0.334683 | ||||||||
\(473\) | 1188.00 | 0.115485 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 532.000 | 0.0513891 | ||||||||
\(476\) | −840.000 | −0.0808852 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4902.00 | −0.469063 | ||||||||
\(479\) | −1734.00 | −0.165404 | −0.0827020 | − | 0.996574i | \(-0.526355\pi\) | ||||
−0.0827020 | + | 0.996574i | \(0.526355\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4757.00 | 0.450937 | ||||||||
\(482\) | 50.0000 | 0.00472497 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 484.000 | 0.0454545 | ||||||||
\(485\) | −644.000 | −0.0602939 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7368.00 | −0.685577 | −0.342788 | − | 0.939413i | \(-0.611371\pi\) | ||||
−0.342788 | + | 0.939413i | \(0.611371\pi\) | |||||||
\(488\) | 176.000 | 0.0163261 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 686.000 | 0.0632456 | ||||||||
\(491\) | −13201.0 | −1.21335 | −0.606673 | − | 0.794952i | \(-0.707496\pi\) | ||||
−0.606673 | + | 0.794952i | \(0.707496\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3630.00 | 0.331617 | ||||||||
\(494\) | 938.000 | 0.0854304 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4960.00 | −0.449013 | ||||||||
\(497\) | −3276.00 | −0.295671 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16539.0 | 1.48374 | 0.741871 | − | 0.670543i | \(-0.233939\pi\) | ||||
0.741871 | + | 0.670543i | \(0.233939\pi\) | |||||||
\(500\) | −5628.00 | −0.503384 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10534.0 | 0.936565 | ||||||||
\(503\) | 14780.0 | 1.31015 | 0.655077 | − | 0.755562i | \(-0.272636\pi\) | ||||
0.655077 | + | 0.755562i | \(0.272636\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1414.00 | 0.124598 | ||||||||
\(506\) | 616.000 | 0.0541196 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9016.00 | 0.787442 | ||||||||
\(509\) | 11766.0 | 1.02459 | 0.512297 | − | 0.858808i | \(-0.328795\pi\) | ||||
0.512297 | + | 0.858808i | \(0.328795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −819.000 | −0.0709010 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3246.00 | 0.278550 | ||||||||
\(515\) | −12586.0 | −1.07690 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 781.000 | 0.0664378 | ||||||||
\(518\) | −994.000 | −0.0843125 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3752.00 | −0.316416 | ||||||||
\(521\) | 13503.0 | 1.13546 | 0.567732 | − | 0.823213i | \(-0.307821\pi\) | ||||
0.567732 | + | 0.823213i | \(0.307821\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18681.0 | −1.56188 | −0.780940 | − | 0.624606i | \(-0.785259\pi\) | ||||
−0.780940 | + | 0.624606i | \(0.785259\pi\) | |||||||
\(524\) | −8784.00 | −0.732311 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4950.00 | 0.410324 | ||||||||
\(527\) | 9300.00 | 0.768718 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11383.0 | −0.935563 | ||||||||
\(530\) | −1792.00 | −0.146867 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −196.000 | −0.0159731 | ||||||||
\(533\) | −12060.0 | −0.980069 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10017.0 | 0.809482 | ||||||||
\(536\) | −6424.00 | −0.517676 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3492.00 | −0.279834 | ||||||||
\(539\) | −539.000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2000.00 | −0.158940 | −0.0794702 | − | 0.996837i | \(-0.525323\pi\) | ||||
−0.0794702 | + | 0.996837i | \(0.525323\pi\) | |||||||
\(542\) | 3306.00 | 0.262002 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −960.000 | −0.0756611 | ||||||||
\(545\) | −1946.00 | −0.152950 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19368.0 | 1.51392 | 0.756961 | − | 0.653459i | \(-0.226683\pi\) | ||||
0.756961 | + | 0.653459i | \(0.226683\pi\) | |||||||
\(548\) | −3064.00 | −0.238846 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1672.00 | 0.129626 | ||||||||
\(551\) | 847.000 | 0.0654871 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −672.000 | −0.0516751 | ||||||||
\(554\) | −4112.00 | −0.315347 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4320.00 | −0.329512 | ||||||||
\(557\) | −4669.00 | −0.355174 | −0.177587 | − | 0.984105i | \(-0.556829\pi\) | ||||
−0.177587 | + | 0.984105i | \(0.556829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7236.00 | 0.547496 | ||||||||
\(560\) | 784.000 | 0.0591608 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1674.00 | −0.125647 | ||||||||
\(563\) | 9324.00 | 0.697975 | 0.348987 | − | 0.937127i | \(-0.386526\pi\) | ||||
0.348987 | + | 0.937127i | \(0.386526\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16254.0 | 1.21028 | ||||||||
\(566\) | 17938.0 | 1.33214 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3744.00 | −0.276575 | ||||||||
\(569\) | −25646.0 | −1.88952 | −0.944759 | − | 0.327765i | \(-0.893705\pi\) | ||||
−0.944759 | + | 0.327765i | \(0.893705\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12928.0 | −0.947496 | −0.473748 | − | 0.880661i | \(-0.657099\pi\) | ||||
−0.473748 | + | 0.880661i | \(0.657099\pi\) | |||||||
\(572\) | 2948.00 | 0.215493 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2520.00 | 0.183245 | ||||||||
\(575\) | 2128.00 | 0.154337 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14862.0 | −1.07229 | −0.536147 | − | 0.844125i | \(-0.680121\pi\) | ||||
−0.536147 | + | 0.844125i | \(0.680121\pi\) | |||||||
\(578\) | −8026.00 | −0.577574 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3388.00 | −0.242550 | ||||||||
\(581\) | 7854.00 | 0.560824 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1408.00 | 0.100023 | ||||||||
\(584\) | −936.000 | −0.0663218 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10240.0 | −0.721861 | ||||||||
\(587\) | 13383.0 | 0.941015 | 0.470507 | − | 0.882396i | \(-0.344071\pi\) | ||||
0.470507 | + | 0.882396i | \(0.344071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2170.00 | 0.151805 | ||||||||
\(590\) | 6006.00 | 0.419090 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1136.00 | −0.0788671 | ||||||||
\(593\) | 10152.0 | 0.703023 | 0.351512 | − | 0.936184i | \(-0.385668\pi\) | ||||
0.351512 | + | 0.936184i | \(0.385668\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1470.00 | −0.101284 | ||||||||
\(596\) | −5492.00 | −0.377451 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3752.00 | 0.256573 | ||||||||
\(599\) | −16592.0 | −1.13177 | −0.565885 | − | 0.824484i | \(-0.691466\pi\) | ||||
−0.565885 | + | 0.824484i | \(0.691466\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1001.00 | −0.0679395 | −0.0339698 | − | 0.999423i | \(-0.510815\pi\) | ||||
−0.0339698 | + | 0.999423i | \(0.510815\pi\) | |||||||
\(602\) | −1512.00 | −0.102366 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12840.0 | −0.864987 | ||||||||
\(605\) | 847.000 | 0.0569181 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18427.0 | −1.23217 | −0.616086 | − | 0.787679i | \(-0.711283\pi\) | ||||
−0.616086 | + | 0.787679i | \(0.711283\pi\) | |||||||
\(608\) | −224.000 | −0.0149414 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 308.000 | 0.0204435 | ||||||||
\(611\) | 4757.00 | 0.314972 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5606.00 | 0.369371 | 0.184685 | − | 0.982798i | \(-0.440873\pi\) | ||||
0.184685 | + | 0.982798i | \(0.440873\pi\) | |||||||
\(614\) | −5784.00 | −0.380168 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −616.000 | −0.0402911 | ||||||||
\(617\) | −6378.00 | −0.416157 | −0.208078 | − | 0.978112i | \(-0.566721\pi\) | ||||
−0.208078 | + | 0.978112i | \(0.566721\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4070.00 | −0.264276 | −0.132138 | − | 0.991231i | \(-0.542184\pi\) | ||||
−0.132138 | + | 0.991231i | \(0.542184\pi\) | |||||||
\(620\) | −8680.00 | −0.562254 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6416.00 | −0.413598 | ||||||||
\(623\) | 8022.00 | 0.515882 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −349.000 | −0.0223360 | ||||||||
\(626\) | 7100.00 | 0.453312 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1808.00 | 0.114884 | ||||||||
\(629\) | 2130.00 | 0.135022 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23252.0 | 1.46695 | 0.733477 | − | 0.679715i | \(-0.237896\pi\) | ||||
0.733477 | + | 0.679715i | \(0.237896\pi\) | |||||||
\(632\) | −768.000 | −0.0483377 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11048.0 | 0.692070 | ||||||||
\(635\) | 15778.0 | 0.986033 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3283.00 | −0.204203 | ||||||||
\(638\) | 2662.00 | 0.165187 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 896.000 | 0.0553399 | ||||||||
\(641\) | −3758.00 | −0.231563 | −0.115782 | − | 0.993275i | \(-0.536937\pi\) | ||||
−0.115782 | + | 0.993275i | \(0.536937\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13068.0 | 0.801480 | 0.400740 | − | 0.916192i | \(-0.368753\pi\) | ||||
0.400740 | + | 0.916192i | \(0.368753\pi\) | |||||||
\(644\) | −784.000 | −0.0479719 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 420.000 | 0.0255800 | ||||||||
\(647\) | 31027.0 | 1.88531 | 0.942656 | − | 0.333765i | \(-0.108319\pi\) | ||||
0.942656 | + | 0.333765i | \(0.108319\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4719.00 | −0.285419 | ||||||||
\(650\) | 10184.0 | 0.614537 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −44.0000 | −0.00264290 | ||||||||
\(653\) | 18456.0 | 1.10603 | 0.553016 | − | 0.833171i | \(-0.313477\pi\) | ||||
0.553016 | + | 0.833171i | \(0.313477\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15372.0 | −0.916998 | ||||||||
\(656\) | 2880.00 | 0.171410 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −994.000 | −0.0588908 | ||||||||
\(659\) | −11141.0 | −0.658561 | −0.329281 | − | 0.944232i | \(-0.606806\pi\) | ||||
−0.329281 | + | 0.944232i | \(0.606806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5172.00 | 0.304338 | 0.152169 | − | 0.988354i | \(-0.451374\pi\) | ||||
0.152169 | + | 0.988354i | \(0.451374\pi\) | |||||||
\(662\) | −4288.00 | −0.251749 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8976.00 | 0.524603 | ||||||||
\(665\) | −343.000 | −0.0200015 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3388.00 | 0.196677 | ||||||||
\(668\) | −2016.00 | −0.116769 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11242.0 | −0.648233 | ||||||||
\(671\) | −242.000 | −0.0139230 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10460.0 | −0.599113 | −0.299557 | − | 0.954078i | \(-0.596839\pi\) | ||||
−0.299557 | + | 0.954078i | \(0.596839\pi\) | |||||||
\(674\) | −1768.00 | −0.101040 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9168.00 | 0.521620 | ||||||||
\(677\) | 15546.0 | 0.882543 | 0.441271 | − | 0.897374i | \(-0.354528\pi\) | ||||
0.441271 | + | 0.897374i | \(0.354528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −644.000 | −0.0363983 | ||||||||
\(680\) | −1680.00 | −0.0947427 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6820.00 | 0.382920 | ||||||||
\(683\) | −31138.0 | −1.74445 | −0.872227 | − | 0.489101i | \(-0.837325\pi\) | ||||
−0.872227 | + | 0.489101i | \(0.837325\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5362.00 | −0.299082 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1728.00 | −0.0957549 | ||||||||
\(689\) | 8576.00 | 0.474194 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21574.0 | 1.18772 | 0.593859 | − | 0.804569i | \(-0.297604\pi\) | ||||
0.593859 | + | 0.804569i | \(0.297604\pi\) | |||||||
\(692\) | −6752.00 | −0.370914 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8080.00 | 0.441949 | ||||||||
\(695\) | −7560.00 | −0.412615 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5400.00 | −0.293457 | ||||||||
\(698\) | 2450.00 | 0.132857 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2128.00 | −0.114901 | ||||||||
\(701\) | −2074.00 | −0.111746 | −0.0558730 | − | 0.998438i | \(-0.517794\pi\) | ||||
−0.0558730 | + | 0.998438i | \(0.517794\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 497.000 | 0.0266639 | ||||||||
\(704\) | −704.000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4966.00 | −0.264728 | ||||||||
\(707\) | 1414.00 | 0.0752177 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6829.00 | −0.361733 | −0.180866 | − | 0.983508i | \(-0.557890\pi\) | ||||
−0.180866 | + | 0.983508i | \(0.557890\pi\) | |||||||
\(710\) | −6552.00 | −0.346327 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9168.00 | 0.482564 | ||||||||
\(713\) | 8680.00 | 0.455917 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5159.00 | 0.269840 | ||||||||
\(716\) | −1840.00 | −0.0960391 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15608.0 | −0.811261 | ||||||||
\(719\) | −6921.00 | −0.358984 | −0.179492 | − | 0.983759i | \(-0.557445\pi\) | ||||
−0.179492 | + | 0.983759i | \(0.557445\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12586.0 | −0.650107 | ||||||||
\(722\) | −13620.0 | −0.702055 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9184.00 | 0.471437 | ||||||||
\(725\) | 9196.00 | 0.471077 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24064.0 | 1.22763 | 0.613813 | − | 0.789451i | \(-0.289635\pi\) | ||||
0.613813 | + | 0.789451i | \(0.289635\pi\) | |||||||
\(728\) | −3752.00 | −0.191014 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1638.00 | −0.0830481 | ||||||||
\(731\) | 3240.00 | 0.163934 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30262.0 | 1.52490 | 0.762451 | − | 0.647047i | \(-0.223996\pi\) | ||||
0.762451 | + | 0.647047i | \(0.223996\pi\) | |||||||
\(734\) | 6148.00 | 0.309165 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −896.000 | −0.0448736 | ||||||||
\(737\) | 8833.00 | 0.441476 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24024.0 | 1.19586 | 0.597928 | − | 0.801550i | \(-0.295991\pi\) | ||||
0.597928 | + | 0.801550i | \(0.295991\pi\) | |||||||
\(740\) | −1988.00 | −0.0987572 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1792.00 | −0.0886609 | ||||||||
\(743\) | 227.000 | 0.0112084 | 0.00560419 | − | 0.999984i | \(-0.498216\pi\) | ||||
0.00560419 | + | 0.999984i | \(0.498216\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9611.00 | −0.472644 | ||||||||
\(746\) | 1348.00 | 0.0661579 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1320.00 | 0.0645240 | ||||||||
\(749\) | 10017.0 | 0.488669 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23435.0 | −1.13869 | −0.569344 | − | 0.822099i | \(-0.692803\pi\) | ||||
−0.569344 | + | 0.822099i | \(0.692803\pi\) | |||||||
\(752\) | −1136.00 | −0.0550873 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16214.0 | 0.783129 | ||||||||
\(755\) | −22470.0 | −1.08314 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1609.00 | 0.0772524 | 0.0386262 | − | 0.999254i | \(-0.487702\pi\) | ||||
0.0386262 | + | 0.999254i | \(0.487702\pi\) | |||||||
\(758\) | 24102.0 | 1.15491 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −392.000 | −0.0187097 | ||||||||
\(761\) | −6976.00 | −0.332299 | −0.166150 | − | 0.986101i | \(-0.553133\pi\) | ||||
−0.166150 | + | 0.986101i | \(0.553133\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1946.00 | −0.0923328 | ||||||||
\(764\) | −3512.00 | −0.166309 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25328.0 | 1.19470 | ||||||||
\(767\) | −28743.0 | −1.35313 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36079.0 | −1.69186 | −0.845931 | − | 0.533292i | \(-0.820955\pi\) | ||||
−0.845931 | + | 0.533292i | \(0.820955\pi\) | |||||||
\(770\) | −1078.00 | −0.0504525 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9072.00 | −0.422938 | ||||||||
\(773\) | 23507.0 | 1.09377 | 0.546887 | − | 0.837206i | \(-0.315813\pi\) | ||||
0.546887 | + | 0.837206i | \(0.315813\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23560.0 | 1.09200 | ||||||||
\(776\) | −736.000 | −0.0340475 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −528.000 | −0.0243313 | ||||||||
\(779\) | −1260.00 | −0.0579515 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5148.00 | 0.235864 | ||||||||
\(782\) | 1680.00 | 0.0768244 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 3164.00 | 0.143857 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35145.0 | −1.59185 | −0.795924 | − | 0.605397i | \(-0.793014\pi\) | ||||
−0.795924 | + | 0.605397i | \(0.793014\pi\) | |||||||
\(788\) | −21192.0 | −0.958038 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1344.00 | −0.0605283 | ||||||||
\(791\) | 16254.0 | 0.730627 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1474.00 | −0.0660067 | ||||||||
\(794\) | −28788.0 | −1.28671 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4176.00 | 0.185948 | ||||||||
\(797\) | −34155.0 | −1.51798 | −0.758991 | − | 0.651101i | \(-0.774308\pi\) | ||||
−0.758991 | + | 0.651101i | \(0.774308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2130.00 | 0.0943104 | ||||||||
\(800\) | −2432.00 | −0.107480 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24608.0 | 1.08346 | ||||||||
\(803\) | 1287.00 | 0.0565595 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1372.00 | −0.0600704 | ||||||||
\(806\) | 41540.0 | 1.81536 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1616.00 | 0.0703598 | ||||||||
\(809\) | 3439.00 | 0.149455 | 0.0747273 | − | 0.997204i | \(-0.476191\pi\) | ||||
0.0747273 | + | 0.997204i | \(0.476191\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1625.00 | −0.0703594 | −0.0351797 | − | 0.999381i | \(-0.511200\pi\) | ||||
−0.0351797 | + | 0.999381i | \(0.511200\pi\) | |||||||
\(812\) | −3388.00 | −0.146423 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1562.00 | 0.0672581 | ||||||||
\(815\) | −77.0000 | −0.00330944 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 756.000 | 0.0323734 | ||||||||
\(818\) | −6308.00 | −0.269626 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5040.00 | 0.214640 | ||||||||
\(821\) | −31531.0 | −1.34036 | −0.670182 | − | 0.742196i | \(-0.733784\pi\) | ||||
−0.670182 | + | 0.742196i | \(0.733784\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31003.0 | −1.31312 | −0.656559 | − | 0.754274i | \(-0.727989\pi\) | ||||
−0.656559 | + | 0.754274i | \(0.727989\pi\) | |||||||
\(824\) | −14384.0 | −0.608119 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6006.00 | 0.252997 | ||||||||
\(827\) | 15015.0 | 0.631345 | 0.315673 | − | 0.948868i | \(-0.397770\pi\) | ||||
0.315673 | + | 0.948868i | \(0.397770\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12280.0 | 0.514478 | 0.257239 | − | 0.966348i | \(-0.417187\pi\) | ||||
0.257239 | + | 0.966348i | \(0.417187\pi\) | |||||||
\(830\) | 15708.0 | 0.656907 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4288.00 | −0.178677 | ||||||||
\(833\) | −1470.00 | −0.0611434 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3528.00 | −0.146217 | ||||||||
\(836\) | 308.000 | 0.0127421 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9270.00 | 0.382132 | ||||||||
\(839\) | −26599.0 | −1.09452 | −0.547258 | − | 0.836964i | \(-0.684328\pi\) | ||||
−0.547258 | + | 0.836964i | \(0.684328\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9748.00 | −0.399688 | ||||||||
\(842\) | −14530.0 | −0.594699 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18264.0 | 0.744873 | ||||||||
\(845\) | 16044.0 | 0.653172 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | −2048.00 | −0.0829347 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4560.00 | 0.184008 | ||||||||
\(851\) | 1988.00 | 0.0800796 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3798.00 | −0.152451 | −0.0762257 | − | 0.997091i | \(-0.524287\pi\) | ||||
−0.0762257 | + | 0.997091i | \(0.524287\pi\) | |||||||
\(854\) | 308.000 | 0.0123414 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11448.0 | 0.457108 | ||||||||
\(857\) | 38726.0 | 1.54359 | 0.771794 | − | 0.635873i | \(-0.219360\pi\) | ||||
0.771794 | + | 0.635873i | \(0.219360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3296.00 | 0.130917 | 0.0654587 | − | 0.997855i | \(-0.479149\pi\) | ||||
0.0654587 | + | 0.997855i | \(0.479149\pi\) | |||||||
\(860\) | −3024.00 | −0.119904 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15178.0 | −0.599727 | ||||||||
\(863\) | −13488.0 | −0.532024 | −0.266012 | − | 0.963970i | \(-0.585706\pi\) | ||||
−0.266012 | + | 0.963970i | \(0.585706\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11816.0 | −0.464458 | ||||||||
\(866\) | 10328.0 | 0.405265 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8680.00 | −0.339422 | ||||||||
\(869\) | 1056.00 | 0.0412225 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53801.0 | 2.09297 | ||||||||
\(872\) | −2224.00 | −0.0863694 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 392.000 | 0.0151712 | ||||||||
\(875\) | −9849.00 | −0.380522 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17144.0 | −0.660105 | −0.330052 | − | 0.943963i | \(-0.607066\pi\) | ||||
−0.330052 | + | 0.943963i | \(0.607066\pi\) | |||||||
\(878\) | 28442.0 | 1.09325 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1232.00 | −0.0471940 | ||||||||
\(881\) | −11993.0 | −0.458632 | −0.229316 | − | 0.973352i | \(-0.573649\pi\) | ||||
−0.229316 | + | 0.973352i | \(0.573649\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10483.0 | 0.399526 | 0.199763 | − | 0.979844i | \(-0.435983\pi\) | ||||
0.199763 | + | 0.979844i | \(0.435983\pi\) | |||||||
\(884\) | 8040.00 | 0.305899 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13848.0 | −0.525093 | ||||||||
\(887\) | −4562.00 | −0.172691 | −0.0863455 | − | 0.996265i | \(-0.527519\pi\) | ||||
−0.0863455 | + | 0.996265i | \(0.527519\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15778.0 | 0.595250 | ||||||||
\(890\) | 16044.0 | 0.604265 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 792.000 | 0.0297288 | ||||||||
\(893\) | 497.000 | 0.0186243 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3220.00 | −0.120260 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5048.00 | −0.187588 | ||||||||
\(899\) | 37510.0 | 1.39158 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3840.00 | 0.141986 | ||||||||
\(902\) | −3960.00 | −0.146179 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18576.0 | 0.683439 | ||||||||
\(905\) | 16072.0 | 0.590333 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18556.0 | 0.679318 | 0.339659 | − | 0.940549i | \(-0.389688\pi\) | ||||
0.339659 | + | 0.940549i | \(0.389688\pi\) | |||||||
\(908\) | −15048.0 | −0.549984 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6566.00 | −0.239188 | ||||||||
\(911\) | −5826.00 | −0.211881 | −0.105941 | − | 0.994372i | \(-0.533785\pi\) | ||||
−0.105941 | + | 0.994372i | \(0.533785\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12342.0 | −0.447383 | ||||||||
\(914\) | 3856.00 | 0.139546 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2816.00 | −0.101576 | ||||||||
\(917\) | −15372.0 | −0.553575 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41492.0 | 1.48933 | 0.744665 | − | 0.667438i | \(-0.232609\pi\) | ||||
0.744665 | + | 0.667438i | \(0.232609\pi\) | |||||||
\(920\) | −1568.00 | −0.0561907 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25704.0 | 0.918130 | ||||||||
\(923\) | 31356.0 | 1.11820 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5396.00 | 0.191805 | ||||||||
\(926\) | 9482.00 | 0.336499 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3872.00 | −0.136966 | ||||||||
\(929\) | 15381.0 | 0.543202 | 0.271601 | − | 0.962410i | \(-0.412447\pi\) | ||||
0.271601 | + | 0.962410i | \(0.412447\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −343.000 | −0.0120745 | ||||||||
\(932\) | −8840.00 | −0.310691 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13618.0 | 0.477082 | ||||||||
\(935\) | 2310.00 | 0.0807969 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −55054.0 | −1.91946 | −0.959731 | − | 0.280921i | \(-0.909360\pi\) | ||||
−0.959731 | + | 0.280921i | \(0.909360\pi\) | |||||||
\(938\) | −11242.0 | −0.391327 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1988.00 | −0.0689802 | ||||||||
\(941\) | 3892.00 | 0.134831 | 0.0674153 | − | 0.997725i | \(-0.478525\pi\) | ||||
0.0674153 | + | 0.997725i | \(0.478525\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5040.00 | −0.174046 | ||||||||
\(944\) | 6864.00 | 0.236657 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2376.00 | 0.0816601 | ||||||||
\(947\) | 36158.0 | 1.24074 | 0.620368 | − | 0.784311i | \(-0.286983\pi\) | ||||
0.620368 | + | 0.784311i | \(0.286983\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7839.00 | 0.268140 | ||||||||
\(950\) | 1064.00 | 0.0363376 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1680.00 | −0.0571944 | ||||||||
\(953\) | 23959.0 | 0.814384 | 0.407192 | − | 0.913343i | \(-0.366508\pi\) | ||||
0.407192 | + | 0.913343i | \(0.366508\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6146.00 | −0.208251 | ||||||||
\(956\) | −9804.00 | −0.331678 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3468.00 | −0.116958 | ||||||||
\(959\) | −5362.00 | −0.180551 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66309.0 | 2.22581 | ||||||||
\(962\) | 9514.00 | 0.318860 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 100.000 | 0.00334106 | ||||||||
\(965\) | −15876.0 | −0.529603 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56106.0 | −1.86582 | −0.932910 | − | 0.360110i | \(-0.882739\pi\) | ||||
−0.932910 | + | 0.360110i | \(0.882739\pi\) | |||||||
\(968\) | 968.000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1288.00 | −0.0426342 | ||||||||
\(971\) | 35079.0 | 1.15936 | 0.579680 | − | 0.814844i | \(-0.303178\pi\) | ||||
0.579680 | + | 0.814844i | \(0.303178\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7560.00 | −0.249088 | ||||||||
\(974\) | −14736.0 | −0.484776 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 352.000 | 0.0115443 | ||||||||
\(977\) | 26184.0 | 0.857421 | 0.428711 | − | 0.903442i | \(-0.358968\pi\) | ||||
0.428711 | + | 0.903442i | \(0.358968\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12606.0 | −0.411532 | ||||||||
\(980\) | 1372.00 | 0.0447214 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26402.0 | −0.857965 | ||||||||
\(983\) | 8584.00 | 0.278522 | 0.139261 | − | 0.990256i | \(-0.455527\pi\) | ||||
0.139261 | + | 0.990256i | \(0.455527\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37086.0 | −1.19965 | ||||||||
\(986\) | 7260.00 | 0.234488 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1876.00 | 0.0604084 | ||||||||
\(989\) | 3024.00 | 0.0972271 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51331.0 | −1.64539 | −0.822696 | − | 0.568482i | \(-0.807531\pi\) | ||||
−0.822696 | + | 0.568482i | \(0.807531\pi\) | |||||||
\(992\) | −9920.00 | −0.317500 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6552.00 | −0.209071 | ||||||||
\(995\) | 7308.00 | 0.232843 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38542.0 | −1.22431 | −0.612155 | − | 0.790738i | \(-0.709697\pi\) | ||||
−0.612155 | + | 0.790738i | \(0.709697\pi\) | |||||||
\(998\) | 33078.0 | 1.04916 | ||||||||
\(999\) | 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 | 1386.4.a.l.1.1 | 1 | ||
3.2 | odd | 2 | 462.4.a.d.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.4.a.d.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
1386.4.a.l.1.1 | 1 | 1.1 | even | 1 | trivial |