Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(1,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(45.3134668844\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 384) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 768.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.00000 | 0.715542 | 0.357771 | − | 0.933809i | \(-0.383537\pi\) | ||||
0.357771 | + | 0.933809i | \(0.383537\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.0000 | −0.647939 | −0.323970 | − | 0.946068i | \(-0.605018\pi\) | ||||
−0.323970 | + | 0.946068i | \(0.605018\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.0000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.0000 | −0.426692 | −0.213346 | − | 0.976977i | \(-0.568436\pi\) | ||||
−0.213346 | + | 0.976977i | \(0.568436\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −24.0000 | −0.413118 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 62.0000 | 0.884542 | 0.442271 | − | 0.896882i | \(-0.354173\pi\) | ||||
0.442271 | + | 0.896882i | \(0.354173\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −108.000 | −1.30405 | −0.652024 | − | 0.758199i | \(-0.726080\pi\) | ||||
−0.652024 | + | 0.758199i | \(0.726080\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 36.0000 | 0.374088 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 72.0000 | 0.652741 | 0.326370 | − | 0.945242i | \(-0.394174\pi\) | ||||
0.326370 | + | 0.945242i | \(0.394174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −61.0000 | −0.488000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 128.000 | 0.819621 | 0.409810 | − | 0.912171i | \(-0.365595\pi\) | ||||
0.409810 | + | 0.912171i | \(0.365595\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −204.000 | −1.18192 | −0.590959 | − | 0.806701i | \(-0.701251\pi\) | ||||
−0.590959 | + | 0.806701i | \(0.701251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −36.0000 | −0.189903 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −96.0000 | −0.463627 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 228.000 | 1.01305 | 0.506527 | − | 0.862224i | \(-0.330929\pi\) | ||||
0.506527 | + | 0.862224i | \(0.330929\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 60.0000 | 0.246351 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 22.0000 | 0.0838006 | 0.0419003 | − | 0.999122i | \(-0.486659\pi\) | ||||
0.0419003 | + | 0.999122i | \(0.486659\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 204.000 | 0.723482 | 0.361741 | − | 0.932279i | \(-0.382183\pi\) | ||||
0.361741 | + | 0.932279i | \(0.382183\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 72.0000 | 0.238514 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −600.000 | −1.86211 | −0.931053 | − | 0.364884i | \(-0.881109\pi\) | ||||
−0.931053 | + | 0.364884i | \(0.881109\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −199.000 | −0.580175 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −186.000 | −0.510690 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −256.000 | −0.663477 | −0.331739 | − | 0.943371i | \(-0.607635\pi\) | ||||
−0.331739 | + | 0.943371i | \(0.607635\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 96.0000 | 0.235357 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 324.000 | 0.752892 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 828.000 | 1.82706 | 0.913529 | − | 0.406774i | \(-0.133346\pi\) | ||||
0.913529 | + | 0.406774i | \(0.133346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 84.0000 | 0.176313 | 0.0881565 | − | 0.996107i | \(-0.471902\pi\) | ||||
0.0881565 | + | 0.996107i | \(0.471902\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −108.000 | −0.215980 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −160.000 | −0.305316 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −348.000 | −0.634552 | −0.317276 | − | 0.948333i | \(-0.602768\pi\) | ||||
−0.317276 | + | 0.948333i | \(0.602768\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −456.000 | −0.762215 | −0.381107 | − | 0.924531i | \(-0.624457\pi\) | ||||
−0.381107 | + | 0.924531i | \(0.624457\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −822.000 | −1.31792 | −0.658958 | − | 0.752180i | \(-0.729002\pi\) | ||||
−0.658958 | + | 0.752180i | \(0.729002\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 183.000 | 0.281747 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −144.000 | −0.213121 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1356.00 | −1.93116 | −0.965582 | − | 0.260100i | \(-0.916245\pi\) | ||||
−0.965582 | + | 0.260100i | \(0.916245\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −108.000 | −0.142826 | −0.0714129 | − | 0.997447i | \(-0.522751\pi\) | ||||
−0.0714129 | + | 0.997447i | \(0.522751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 496.000 | 0.632927 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −384.000 | −0.473208 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 938.000 | 1.11717 | 0.558583 | − | 0.829449i | \(-0.311345\pi\) | ||||
0.558583 | + | 0.829449i | \(0.311345\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 240.000 | 0.276471 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 612.000 | 0.682381 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −864.000 | −0.933100 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1278.00 | 1.33774 | 0.668872 | − | 0.743377i | \(-0.266777\pi\) | ||||
0.668872 | + | 0.743377i | \(0.266777\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 108.000 | 0.109640 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −608.000 | −0.598993 | −0.299496 | − | 0.954097i | \(-0.596819\pi\) | ||||
−0.299496 | + | 0.954097i | \(0.596819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −948.000 | −0.906886 | −0.453443 | − | 0.891285i | \(-0.649804\pi\) | ||||
−0.453443 | + | 0.891285i | \(0.649804\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 288.000 | 0.267675 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1044.00 | −0.943246 | −0.471623 | − | 0.881800i | \(-0.656332\pi\) | ||||
−0.471623 | + | 0.881800i | \(0.656332\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1780.00 | −1.56416 | −0.782078 | − | 0.623180i | \(-0.785840\pi\) | ||||
−0.782078 | + | 0.623180i | \(0.785840\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −684.000 | −0.584887 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −622.000 | −0.517813 | −0.258906 | − | 0.965902i | \(-0.583362\pi\) | ||||
−0.258906 | + | 0.965902i | \(0.583362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 576.000 | 0.467063 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −180.000 | −0.142231 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −744.000 | −0.573129 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −66.0000 | −0.0483823 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1488.00 | −1.06473 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 204.000 | 0.142536 | 0.0712680 | − | 0.997457i | \(-0.477295\pi\) | ||||
0.0712680 | + | 0.997457i | \(0.477295\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −612.000 | −0.417702 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −348.000 | −0.232098 | −0.116049 | − | 0.993243i | \(-0.537023\pi\) | ||||
−0.116049 | + | 0.993243i | \(0.537023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1296.00 | 0.844943 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −216.000 | −0.137706 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −106.000 | −0.0661036 | −0.0330518 | − | 0.999454i | \(-0.510523\pi\) | ||||
−0.0330518 | + | 0.999454i | \(0.510523\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1188.00 | −0.724927 | −0.362463 | − | 0.931998i | \(-0.618064\pi\) | ||||
−0.362463 | + | 0.931998i | \(0.618064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1800.00 | 1.07509 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −240.000 | −0.140348 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1024.00 | 0.586473 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 597.000 | 0.334964 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2648.00 | −1.45592 | −0.727962 | − | 0.685618i | \(-0.759532\pi\) | ||||
−0.727962 | + | 0.685618i | \(0.759532\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3420.00 | −1.84315 | −0.921575 | − | 0.388200i | \(-0.873097\pi\) | ||||
−0.921575 | + | 0.388200i | \(0.873097\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 558.000 | 0.294847 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1632.00 | −0.845712 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −60.0000 | −0.0305001 | −0.0152501 | − | 0.999884i | \(-0.504854\pi\) | ||||
−0.0152501 | + | 0.999884i | \(0.504854\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 768.000 | 0.383059 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −864.000 | −0.422936 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 228.000 | 0.109560 | 0.0547802 | − | 0.998498i | \(-0.482554\pi\) | ||||
0.0547802 | + | 0.998498i | \(0.482554\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −288.000 | −0.135883 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4128.00 | −1.91278 | −0.956390 | − | 0.292093i | \(-0.905648\pi\) | ||||
−0.956390 | + | 0.292093i | \(0.905648\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1797.00 | −0.817934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −972.000 | −0.434682 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1352.00 | 0.594166 | 0.297083 | − | 0.954852i | \(-0.403986\pi\) | ||||
0.297083 | + | 0.954852i | \(0.403986\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 732.000 | 0.316194 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2484.00 | −1.05485 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1716.00 | 0.716536 | 0.358268 | − | 0.933619i | \(-0.383367\pi\) | ||||
0.358268 | + | 0.933619i | \(0.383367\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3692.00 | 1.51616 | 0.758078 | − | 0.652164i | \(-0.226139\pi\) | ||||
0.758078 | + | 0.652164i | \(0.226139\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −252.000 | −0.101794 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1824.00 | 0.724882 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 744.000 | 0.290945 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 324.000 | 0.124696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 48.0000 | 0.0181841 | 0.00909204 | − | 0.999959i | \(-0.497106\pi\) | ||||
0.00909204 | + | 0.999959i | \(0.497106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2414.00 | 0.900329 | 0.450165 | − | 0.892946i | \(-0.351365\pi\) | ||||
0.450165 | + | 0.892946i | \(0.351365\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 480.000 | 0.176274 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4304.00 | −1.55659 | −0.778293 | − | 0.627902i | \(-0.783914\pi\) | ||||
−0.778293 | + | 0.627902i | \(0.783914\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 204.000 | 0.0726692 | 0.0363346 | − | 0.999340i | \(-0.488432\pi\) | ||||
0.0363346 | + | 0.999340i | \(0.488432\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1044.00 | 0.366359 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1536.00 | −0.531064 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 176.000 | 0.0599628 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 648.000 | 0.217580 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1296.00 | −0.428929 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4020.00 | 1.31160 | 0.655801 | − | 0.754933i | \(-0.272331\pi\) | ||||
0.655801 | + | 0.754933i | \(0.272331\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1368.00 | 0.440065 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1632.00 | 0.517681 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2448.00 | 0.765811 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2466.00 | 0.760899 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1240.00 | −0.377427 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −516.000 | −0.154950 | −0.0774751 | − | 0.996994i | \(-0.524686\pi\) | ||||
−0.0774751 | + | 0.996994i | \(0.524686\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −549.000 | −0.162667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1428.00 | 0.417532 | 0.208766 | − | 0.977966i | \(-0.433055\pi\) | ||||
0.208766 | + | 0.977966i | \(0.433055\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6028.00 | 1.73948 | 0.869741 | − | 0.493508i | \(-0.164286\pi\) | ||||
0.869741 | + | 0.493508i | \(0.164286\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 432.000 | 0.123046 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2630.00 | −0.739472 | −0.369736 | − | 0.929137i | \(-0.620552\pi\) | ||||
−0.369736 | + | 0.929137i | \(0.620552\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4800.00 | −1.33241 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4068.00 | 1.11496 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4416.00 | 1.19518 | 0.597588 | − | 0.801803i | \(-0.296126\pi\) | ||||
0.597588 | + | 0.801803i | \(0.296126\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4830.00 | 1.29099 | 0.645493 | − | 0.763766i | \(-0.276652\pi\) | ||||
0.645493 | + | 0.763766i | \(0.276652\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1592.00 | −0.415139 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2160.00 | 0.556427 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 324.000 | 0.0824605 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5532.00 | 1.39114 | 0.695571 | − | 0.718457i | \(-0.255151\pi\) | ||||
0.695571 | + | 0.718457i | \(0.255151\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 864.000 | 0.214700 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1488.00 | −0.365420 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −254.000 | −0.0616501 | −0.0308251 | − | 0.999525i | \(-0.509813\pi\) | ||||
−0.0308251 | + | 0.999525i | \(0.509813\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2736.00 | −0.656397 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1152.00 | 0.273207 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4272.00 | 1.00161 | 0.500804 | − | 0.865561i | \(-0.333038\pi\) | ||||
0.500804 | + | 0.865561i | \(0.333038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2048.00 | −0.474746 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2814.00 | −0.644996 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4544.00 | −1.02994 | −0.514968 | − | 0.857210i | \(-0.672196\pi\) | ||||
−0.514968 | + | 0.857210i | \(0.672196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2076.00 | 0.465343 | 0.232672 | − | 0.972555i | \(-0.425253\pi\) | ||||
0.232672 | + | 0.972555i | \(0.425253\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −720.000 | −0.159620 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −732.000 | −0.160514 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −484.000 | −0.104985 | −0.0524923 | − | 0.998621i | \(-0.516717\pi\) | ||||
−0.0524923 | + | 0.998621i | \(0.516717\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1836.00 | −0.393973 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −406.000 | −0.0861919 | −0.0430960 | − | 0.999071i | \(-0.513722\pi\) | ||||
−0.0430960 | + | 0.999071i | \(0.513722\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8172.00 | 1.71652 | 0.858260 | − | 0.513216i | \(-0.171546\pi\) | ||||
0.858260 | + | 0.513216i | \(0.171546\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2592.00 | 0.538726 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −264.000 | −0.0542977 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1069.00 | −0.217586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3834.00 | −0.772347 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4960.00 | −0.988963 | −0.494482 | − | 0.869188i | \(-0.664642\pi\) | ||||
−0.494482 | + | 0.869188i | \(0.664642\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6624.00 | 1.30734 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −324.000 | −0.0633010 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1440.00 | −0.278520 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2448.00 | −0.468772 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1824.00 | 0.345829 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 672.000 | 0.126159 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6684.00 | −1.24259 | −0.621296 | − | 0.783576i | \(-0.713394\pi\) | ||||
−0.621296 | + | 0.783576i | \(0.713394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2844.00 | 0.523591 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4992.00 | 0.910194 | 0.455097 | − | 0.890442i | \(-0.349605\pi\) | ||||
0.455097 | + | 0.890442i | \(0.349605\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5402.00 | −0.975524 | −0.487762 | − | 0.872977i | \(-0.662187\pi\) | ||||
−0.487762 | + | 0.872977i | \(0.662187\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −864.000 | −0.154542 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7856.00 | −1.39191 | −0.695957 | − | 0.718083i | \(-0.745020\pi\) | ||||
−0.695957 | + | 0.718083i | \(0.745020\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1536.00 | 0.269591 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3132.00 | 0.544583 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6696.00 | −1.15348 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1220.00 | 0.208226 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5340.00 | 0.903066 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7200.00 | 1.20653 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3732.00 | −0.619726 | −0.309863 | − | 0.950781i | \(-0.600283\pi\) | ||||
−0.309863 | + | 0.950781i | \(0.600283\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2052.00 | 0.337684 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2784.00 | −0.454048 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5598.00 | −0.904874 | −0.452437 | − | 0.891796i | \(-0.649445\pi\) | ||||
−0.452437 | + | 0.891796i | \(0.649445\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1866.00 | 0.298959 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2448.00 | −0.388758 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6504.00 | 1.02386 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1728.00 | −0.269659 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8220.00 | 1.27168 | 0.635840 | − | 0.771821i | \(-0.280654\pi\) | ||||
0.635840 | + | 0.771821i | \(0.280654\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11844.0 | 1.81660 | 0.908302 | − | 0.418315i | \(-0.137379\pi\) | ||||
0.908302 | + | 0.418315i | \(0.137379\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 540.000 | 0.0821170 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7006.00 | −1.05635 | −0.528175 | − | 0.849135i | \(-0.677124\pi\) | ||||
−0.528175 | + | 0.849135i | \(0.677124\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3648.00 | −0.545396 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2232.00 | 0.330896 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7512.00 | 1.10437 | 0.552184 | − | 0.833722i | \(-0.313795\pi\) | ||||
0.552184 | + | 0.833722i | \(0.313795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4805.00 | 0.700539 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3561.00 | 0.514887 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6576.00 | −0.943023 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5076.00 | 0.721976 | 0.360988 | − | 0.932571i | \(-0.382440\pi\) | ||||
0.360988 | + | 0.932571i | \(0.382440\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 198.000 | 0.0279335 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3072.00 | 0.429893 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4860.00 | −0.674641 | −0.337321 | − | 0.941390i | \(-0.609521\pi\) | ||||
−0.337321 | + | 0.941390i | \(0.609521\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4464.00 | 0.614720 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2560.00 | −0.349726 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5964.00 | 0.808312 | 0.404156 | − | 0.914690i | \(-0.367565\pi\) | ||||
0.404156 | + | 0.914690i | \(0.367565\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −612.000 | −0.0822932 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −432.000 | −0.0576349 | −0.0288175 | − | 0.999585i | \(-0.509174\pi\) | ||||
−0.0288175 | + | 0.999585i | \(0.509174\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1152.00 | −0.152497 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1836.00 | 0.241161 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8888.00 | −1.15846 | −0.579228 | − | 0.815165i | \(-0.696646\pi\) | ||||
−0.579228 | + | 0.815165i | \(0.696646\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4464.00 | 0.577376 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1044.00 | 0.134002 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10848.0 | −1.38183 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2676.00 | 0.338299 | 0.169149 | − | 0.985590i | \(-0.445898\pi\) | ||||
0.169149 | + | 0.985590i | \(0.445898\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3888.00 | −0.487828 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13790.0 | 1.71731 | 0.858653 | − | 0.512557i | \(-0.171302\pi\) | ||||
0.858653 | + | 0.512557i | \(0.171302\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4080.00 | 0.504316 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 648.000 | 0.0795046 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2736.00 | 0.333215 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1974.00 | 0.238650 | 0.119325 | − | 0.992855i | \(-0.461927\pi\) | ||||
0.119325 | + | 0.992855i | \(0.461927\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 318.000 | 0.0381649 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9936.00 | −1.18382 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −864.000 | −0.102198 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3564.00 | 0.418537 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4764.00 | −0.555457 | −0.277729 | − | 0.960660i | \(-0.589582\pi\) | ||||
−0.277729 | + | 0.960660i | \(0.589582\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 92.0000 | 0.0106504 | 0.00532518 | − | 0.999986i | \(-0.498305\pi\) | ||||
0.00532518 | + | 0.999986i | \(0.498305\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5400.00 | −0.620702 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3782.00 | −0.431656 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1008.00 | −0.114240 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 720.000 | 0.0810301 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10488.0 | 1.17213 | 0.586066 | − | 0.810263i | \(-0.300676\pi\) | ||||
0.586066 | + | 0.810263i | \(0.300676\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13138.0 | −1.45813 | −0.729067 | − | 0.684442i | \(-0.760046\pi\) | ||||
−0.729067 | + | 0.684442i | \(0.760046\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3072.00 | −0.338600 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7776.00 | −0.851205 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3612.00 | 0.392691 | 0.196346 | − | 0.980535i | \(-0.437093\pi\) | ||||
0.196346 | + | 0.980535i | \(0.437093\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1791.00 | −0.193392 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12972.0 | 1.39124 | 0.695619 | − | 0.718411i | \(-0.255130\pi\) | ||||
0.695619 | + | 0.718411i | \(0.255130\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7504.00 | 0.799379 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7944.00 | 0.840578 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5998.00 | 0.630430 | 0.315215 | − | 0.949020i | \(-0.397923\pi\) | ||||
0.315215 | + | 0.949020i | \(0.397923\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 264.000 | 0.0275638 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10260.0 | 1.06414 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1920.00 | 0.197826 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8934.00 | 0.914475 | 0.457237 | − | 0.889345i | \(-0.348839\pi\) | ||||
0.457237 | + | 0.889345i | \(0.348839\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1674.00 | −0.170230 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7448.00 | −0.752468 | −0.376234 | − | 0.926525i | \(-0.622781\pi\) | ||||
−0.376234 | + | 0.926525i | \(0.622781\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4356.00 | −0.437236 | −0.218618 | − | 0.975810i | \(-0.570155\pi\) | ||||
−0.218618 | + | 0.975810i | \(0.570155\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4896.00 | 0.488272 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8580.00 | 0.850182 | 0.425091 | − | 0.905151i | \(-0.360242\pi\) | ||||
0.425091 | + | 0.905151i | \(0.360242\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4176.00 | 0.411151 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 180.000 | 0.0176093 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2448.00 | 0.237969 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6588.00 | 0.636375 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2304.00 | −0.221159 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12648.0 | 1.20648 | 0.603238 | − | 0.797561i | \(-0.293877\pi\) | ||||
0.603238 | + | 0.797561i | \(0.293877\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4560.00 | −0.432262 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2592.00 | 0.244182 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10224.0 | 0.957212 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15036.0 | −1.39907 | −0.699534 | − | 0.714599i | \(-0.746609\pi\) | ||||
−0.699534 | + | 0.714599i | \(0.746609\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −684.000 | −0.0632547 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15684.0 | −1.44157 | −0.720783 | − | 0.693161i | \(-0.756218\pi\) | ||||
−0.720783 | + | 0.693161i | \(0.756218\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7936.00 | 0.724989 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 864.000 | 0.0784523 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5472.00 | 0.493869 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16308.0 | 1.46302 | 0.731509 | − | 0.681831i | \(-0.238816\pi\) | ||||
0.731509 | + | 0.681831i | \(0.238816\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12384.0 | 1.10434 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10344.0 | −0.916931 | −0.458465 | − | 0.888712i | \(-0.651601\pi\) | ||||
−0.458465 | + | 0.888712i | \(0.651601\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4864.00 | −0.428604 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5391.00 | 0.472234 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5648.00 | 0.491833 | 0.245917 | − | 0.969291i | \(-0.420911\pi\) | ||||
0.245917 | + | 0.969291i | \(0.420911\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9864.00 | 0.853929 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2916.00 | 0.250964 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7584.00 | −0.648915 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7200.00 | −0.612487 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4056.00 | −0.343042 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19498.0 | −1.63958 | −0.819792 | − | 0.572662i | \(-0.805911\pi\) | ||||
−0.819792 | + | 0.572662i | \(0.805911\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22596.0 | −1.88920 | −0.944602 | − | 0.328217i | \(-0.893552\pi\) | ||||
−0.944602 | + | 0.328217i | \(0.893552\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2196.00 | −0.182555 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12648.0 | −1.04546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7452.00 | 0.609019 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −440.000 | −0.0357571 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8352.00 | −0.674932 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5148.00 | −0.413692 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2388.00 | −0.190832 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 812.000 | 0.0645298 | 0.0322649 | − | 0.999479i | \(-0.489728\pi\) | ||||
0.0322649 | + | 0.999479i | \(0.489728\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11076.0 | −0.875353 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14240.0 | −1.11922 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6132.00 | 0.479315 | 0.239658 | − | 0.970857i | \(-0.422965\pi\) | ||||
0.239658 | + | 0.970857i | \(0.422965\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 756.000 | 0.0587710 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13824.0 | −1.06882 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16272.0 | 1.25128 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5472.00 | −0.418511 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2792.00 | −0.212389 | −0.106195 | − | 0.994345i | \(-0.533867\pi\) | ||||
−0.106195 | + | 0.994345i | \(0.533867\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4080.00 | −0.308704 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2232.00 | −0.167977 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6468.00 | 0.484181 | 0.242090 | − | 0.970254i | \(-0.422167\pi\) | ||||
0.242090 | + | 0.970254i | \(0.422167\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4976.00 | −0.370517 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −972.000 | −0.0719932 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10522.0 | −0.775229 | −0.387614 | − | 0.921822i | \(-0.626701\pi\) | ||||
−0.387614 | + | 0.921822i | \(0.626701\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1068.00 | 0.0782739 | 0.0391370 | − | 0.999234i | \(-0.487539\pi\) | ||||
0.0391370 | + | 0.999234i | \(0.487539\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −144.000 | −0.0104986 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4392.00 | −0.318537 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3602.00 | 0.259884 | 0.129942 | − | 0.991522i | \(-0.458521\pi\) | ||||
0.129942 | + | 0.991522i | \(0.458521\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7242.00 | −0.519805 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1296.00 | 0.0925424 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3072.00 | −0.218232 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1440.00 | −0.101772 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17940.0 | −1.26144 | −0.630718 | − | 0.776012i | \(-0.717240\pi\) | ||||
−0.630718 | + | 0.776012i | \(0.717240\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22032.0 | 1.54128 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12912.0 | 0.898695 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18034.0 | 1.24885 | 0.624425 | − | 0.781085i | \(-0.285334\pi\) | ||||
0.624425 | + | 0.781085i | \(0.285334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5952.00 | −0.410098 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −612.000 | −0.0419556 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12264.0 | −0.836550 | −0.418275 | − | 0.908320i | \(-0.637365\pi\) | ||||
−0.418275 | + | 0.908320i | \(0.637365\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12634.0 | 0.857490 | 0.428745 | − | 0.903426i | \(-0.358956\pi\) | ||||
0.428745 | + | 0.903426i | \(0.358956\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3132.00 | −0.211517 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9496.00 | −0.638128 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2796.00 | 0.186962 | 0.0934812 | − | 0.995621i | \(-0.470201\pi\) | ||||
0.0934812 | + | 0.995621i | \(0.470201\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4608.00 | 0.306610 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12000.0 | 0.794547 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13788.0 | −0.908470 | −0.454235 | − | 0.890882i | \(-0.650087\pi\) | ||||
−0.454235 | + | 0.890882i | \(0.650087\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −528.000 | −0.0346195 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18074.0 | 1.17931 | 0.589653 | − | 0.807657i | \(-0.299264\pi\) | ||||
0.589653 | + | 0.807657i | \(0.299264\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5940.00 | −0.385701 | −0.192850 | − | 0.981228i | \(-0.561773\pi\) | ||||
−0.192850 | + | 0.981228i | \(0.561773\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1944.00 | −0.125620 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11256.0 | −0.723856 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4279.00 | −0.273856 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3888.00 | 0.247642 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14136.0 | 0.896088 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8700.00 | −0.548877 | −0.274439 | − | 0.961605i | \(-0.588492\pi\) | ||||
−0.274439 | + | 0.961605i | \(0.588492\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12060.0 | −0.757254 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1632.00 | 0.101990 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3980.00 | 0.247556 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4104.00 | −0.254072 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16306.0 | −1.00476 | −0.502378 | − | 0.864648i | \(-0.667541\pi\) | ||||
−0.502378 | + | 0.864648i | \(0.667541\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22668.0 | −1.39026 | −0.695131 | − | 0.718883i | \(-0.744654\pi\) | ||||
−0.695131 | + | 0.718883i | \(0.744654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4896.00 | −0.298883 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11928.0 | −0.724788 | −0.362394 | − | 0.932025i | \(-0.618041\pi\) | ||||
−0.362394 | + | 0.932025i | \(0.618041\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9936.00 | 0.600959 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7344.00 | −0.442141 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2552.00 | 0.152936 | 0.0764682 | − | 0.997072i | \(-0.475636\pi\) | ||||
0.0764682 | + | 0.997072i | \(0.475636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2784.00 | −0.166076 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7398.00 | −0.439305 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2196.00 | 0.129809 | 0.0649044 | − | 0.997891i | \(-0.479326\pi\) | ||||
0.0649044 | + | 0.997891i | \(0.479326\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4260.00 | 0.250673 | 0.125336 | − | 0.992114i | \(-0.459999\pi\) | ||||
0.125336 | + | 0.992114i | \(0.459999\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3720.00 | 0.217908 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10368.0 | 0.604592 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9216.00 | 0.535000 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1548.00 | 0.0894606 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1008.00 | 0.0579932 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2018.00 | −0.115584 | −0.0577921 | − | 0.998329i | \(-0.518406\pi\) | ||||
−0.0577921 | + | 0.998329i | \(0.518406\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1647.00 | 0.0939156 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9256.00 | −0.525461 | −0.262730 | − | 0.964869i | \(-0.584623\pi\) | ||||
−0.262730 | + | 0.964869i | \(0.584623\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15336.0 | −0.866777 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4284.00 | −0.241062 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29244.0 | 1.63835 | 0.819173 | − | 0.573546i | \(-0.194433\pi\) | ||||
0.819173 | + | 0.573546i | \(0.194433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −848.000 | −0.0472999 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18084.0 | −1.00429 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5120.00 | 0.283101 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3684.00 | 0.202816 | 0.101408 | − | 0.994845i | \(-0.467665\pi\) | ||||
0.101408 | + | 0.994845i | \(0.467665\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1296.00 | −0.0710404 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9504.00 | −0.518715 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1364.00 | 0.0741251 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7890.00 | 0.426934 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13456.0 | −0.725002 | −0.362501 | − | 0.931983i | \(-0.618077\pi\) | ||||
−0.362501 | + | 0.931983i | \(0.618077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24624.0 | −1.32107 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14400.0 | 0.769270 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7296.00 | 0.388111 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6460.00 | 0.342187 | 0.171093 | − | 0.985255i | \(-0.445270\pi\) | ||||
0.171093 | + | 0.985255i | \(0.445270\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12204.0 | −0.643721 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14688.0 | −0.771487 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1920.00 | −0.100425 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13248.0 | −0.690036 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17160.0 | −0.890070 | −0.445035 | − | 0.895513i | \(-0.646809\pi\) | ||||
−0.445035 | + | 0.895513i | \(0.646809\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11376.0 | 0.587607 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14490.0 | −0.745351 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7808.00 | −0.399975 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11820.0 | −0.602998 | −0.301499 | − | 0.953466i | \(-0.597487\pi\) | ||||
−0.301499 | + | 0.953466i | \(0.597487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12648.0 | 0.639950 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23924.0 | −1.20553 | −0.602765 | − | 0.797919i | \(-0.705934\pi\) | ||||
−0.602765 | + | 0.797919i | \(0.705934\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4776.00 | 0.239681 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4176.00 | −0.208718 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11796.0 | 0.587176 | 0.293588 | − | 0.955932i | \(-0.405151\pi\) | ||||
0.293588 | + | 0.955932i | \(0.405151\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6480.00 | −0.321253 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27024.0 | 1.33434 | 0.667170 | − | 0.744906i | \(-0.267506\pi\) | ||||
0.667170 | + | 0.744906i | \(0.267506\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21184.0 | −1.04177 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −972.000 | −0.0476086 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12528.0 | 0.611166 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17340.0 | −0.842537 | −0.421269 | − | 0.906936i | \(-0.638415\pi\) | ||||
−0.421269 | + | 0.906936i | \(0.638415\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16596.0 | −0.803176 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27360.0 | −1.31885 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27236.0 | −1.30767 | −0.653837 | − | 0.756635i | \(-0.726842\pi\) | ||||
−0.653837 | + | 0.756635i | \(0.726842\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2592.00 | −0.123957 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14758.0 | 0.702992 | 0.351496 | − | 0.936189i | \(-0.385673\pi\) | ||||
0.351496 | + | 0.936189i | \(0.385673\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21360.0 | 1.01348 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4464.00 | 0.210976 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16560.0 | −0.779592 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25774.0 | 1.20863 | 0.604314 | − | 0.796747i | \(-0.293447\pi\) | ||||
0.604314 | + | 0.796747i | \(0.293447\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 762.000 | 0.0355937 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37424.0 | 1.74133 | 0.870665 | − | 0.491877i | \(-0.163689\pi\) | ||||
0.870665 | + | 0.491877i | \(0.163689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12444.0 | 0.576776 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8208.00 | 0.378971 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2376.00 | −0.109280 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5472.00 | −0.250709 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3456.00 | −0.157736 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −480.000 | −0.0218241 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12804.0 | 0.579941 | 0.289970 | − | 0.957036i | \(-0.406355\pi\) | ||||
0.289970 | + | 0.957036i | \(0.406355\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12816.0 | −0.578278 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7464.00 | 0.335511 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1680.00 | −0.0752315 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6144.00 | 0.274095 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32024.0 | 1.42327 | 0.711636 | − | 0.702548i | \(-0.247954\pi\) | ||||
0.711636 | + | 0.702548i | \(0.247954\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37200.0 | −1.64711 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8442.00 | 0.372389 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9864.00 | −0.433491 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6912.00 | −0.302629 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13632.0 | 0.594633 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38090.0 | −1.65534 | −0.827672 | − | 0.561212i | \(-0.810335\pi\) | ||||
−0.827672 | + | 0.561212i | \(0.810335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10428.0 | 0.451512 | 0.225756 | − | 0.974184i | \(-0.427515\pi\) | ||||
0.225756 | + | 0.974184i | \(0.427515\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6228.00 | −0.268666 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1824.00 | 0.0783950 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22032.0 | −0.943454 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2160.00 | 0.0921569 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7984.00 | 0.339395 | 0.169698 | − | 0.985496i | \(-0.445721\pi\) | ||||
0.169698 | + | 0.985496i | \(0.445721\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28788.0 | 1.21930 | 0.609652 | − | 0.792669i | \(-0.291309\pi\) | ||||
0.609652 | + | 0.792669i | \(0.291309\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2196.00 | 0.0926726 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −468.000 | −0.0196783 | −0.00983915 | − | 0.999952i | \(-0.503132\pi\) | ||||
−0.00983915 | + | 0.999952i | \(0.503132\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28852.0 | −1.20877 | −0.604386 | − | 0.796692i | \(-0.706581\pi\) | ||||
−0.604386 | + | 0.796692i | \(0.706581\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1452.00 | 0.0606129 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12338.0 | −0.513189 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33024.0 | −1.36867 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5508.00 | 0.227460 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1944.00 | −0.0799932 | −0.0399966 | − | 0.999200i | \(-0.512735\pi\) | ||||
−0.0399966 | + | 0.999200i | \(0.512735\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8005.00 | −0.328222 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1218.00 | 0.0497629 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14376.0 | −0.585266 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14244.0 | 0.577839 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24516.0 | −0.991033 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16416.0 | 0.661261 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37044.0 | 1.48694 | 0.743472 | − | 0.668768i | \(-0.233178\pi\) | ||||
0.743472 | + | 0.668768i | \(0.233178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7776.00 | −0.311033 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15046.0 | 0.599722 | 0.299861 | − | 0.953983i | \(-0.403060\pi\) | ||||
0.299861 | + | 0.953983i | \(0.403060\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12180.0 | −0.483791 | −0.241895 | − | 0.970302i | \(-0.577769\pi\) | ||||
−0.241895 | + | 0.970302i | \(0.577769\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 792.000 | 0.0313488 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28752.0 | −1.13410 | −0.567051 | − | 0.823683i | \(-0.691916\pi\) | ||||
−0.567051 | + | 0.823683i | \(0.691916\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10816.0 | 0.425150 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3207.00 | 0.125623 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16272.0 | −0.635201 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6960.00 | 0.270758 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11502.0 | 0.445915 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17856.0 | 0.689878 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31884.0 | −1.22765 | −0.613823 | − | 0.789443i | \(-0.710369\pi\) | ||||
−0.613823 | + | 0.789443i | \(0.710369\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14880.0 | 0.570978 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30802.0 | 1.17792 | 0.588959 | − | 0.808163i | \(-0.299538\pi\) | ||||
0.588959 | + | 0.808163i | \(0.299538\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32460.0 | −1.23711 | −0.618554 | − | 0.785742i | \(-0.712281\pi\) | ||||
−0.618554 | + | 0.785742i | \(0.712281\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19872.0 | −0.754791 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14832.0 | −0.561454 | −0.280727 | − | 0.959788i | \(-0.590576\pi\) | ||||
−0.280727 | + | 0.959788i | \(0.590576\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2448.00 | −0.0923547 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 972.000 | 0.0365468 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 64800.0 | 2.42827 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13728.0 | 0.512711 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4320.00 | 0.160803 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26112.0 | −0.968725 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15872.0 | −0.586873 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7344.00 | 0.270646 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29536.0 | 1.08487 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6900.00 | −0.252603 | −0.126301 | − | 0.991992i | \(-0.540311\pi\) | ||||
−0.126301 | + | 0.991992i | \(0.540311\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5472.00 | −0.199664 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32832.0 | 1.19404 | 0.597021 | − | 0.802225i | \(-0.296351\pi\) | ||||
0.597021 | + | 0.802225i | \(0.296351\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1296.00 | −0.0469785 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2016.00 | −0.0728381 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4176.00 | 0.150386 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8340.00 | 0.299359 | 0.149680 | − | 0.988735i | \(-0.452176\pi\) | ||||
0.149680 | + | 0.988735i | \(0.452176\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20052.0 | 0.717411 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9120.00 | 0.325231 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13908.0 | −0.494370 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8532.00 | −0.302295 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39826.0 | −1.40651 | −0.703255 | − | 0.710937i | \(-0.748271\pi\) | ||||
−0.703255 | + | 0.710937i | \(0.748271\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21492.0 | 0.756576 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14976.0 | −0.525501 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5952.00 | 0.208183 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28550.0 | −0.995398 | −0.497699 | − | 0.867350i | \(-0.665822\pi\) | ||||
−0.497699 | + | 0.867350i | \(0.665822\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16206.0 | 0.563219 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50632.0 | 1.75404 | 0.877022 | − | 0.480450i | \(-0.159527\pi\) | ||||
0.877022 | + | 0.480450i | \(0.159527\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1584.00 | 0.0547000 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2592.00 | 0.0892251 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18204.0 | −0.624657 | −0.312329 | − | 0.949974i | \(-0.601109\pi\) | ||||
−0.312329 | + | 0.949974i | \(0.601109\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16440.0 | 0.562345 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23568.0 | 0.803622 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4934.00 | 0.167710 | 0.0838552 | − | 0.996478i | \(-0.473277\pi\) | ||||
0.0838552 | + | 0.996478i | \(0.473277\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 384.000 | 0.0130115 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4608.00 | −0.155648 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1272.00 | 0.0428311 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11825.0 | 0.396932 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9396.00 | −0.314415 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19312.0 | 0.644223 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13284.0 | −0.441763 | −0.220881 | − | 0.975301i | \(-0.570893\pi\) | ||||
−0.220881 | + | 0.975301i | \(0.570893\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20088.0 | 0.665964 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50820.0 | −1.67960 | −0.839800 | − | 0.542896i | \(-0.817328\pi\) | ||||
−0.839800 | + | 0.542896i | \(0.817328\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14256.0 | 0.469709 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3660.00 | −0.120219 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11038.0 | 0.361450 | 0.180725 | − | 0.983534i | \(-0.442156\pi\) | ||||
0.180725 | + | 0.983534i | \(0.442156\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11256.0 | 0.367460 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16020.0 | −0.521386 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44112.0 | 1.43129 | 0.715643 | − | 0.698466i | \(-0.246134\pi\) | ||||
0.715643 | + | 0.698466i | \(0.246134\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34432.0 | −1.11380 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21600.0 | −0.696591 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14688.0 | 0.472246 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56196.0 | 1.80134 | 0.900668 | − | 0.434507i | \(-0.143077\pi\) | ||||
0.900668 | + | 0.434507i | \(0.143077\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11196.0 | 0.357799 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1632.00 | 0.0519979 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45588.0 | 1.44813 | 0.724065 | − | 0.689731i | \(-0.242271\pi\) | ||||
0.724065 | + | 0.689731i | \(0.242271\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6156.00 | −0.194962 |
(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 | 768.4.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 2304.4.a.e.1.1 | 1 | |||
4.3 | odd | 2 | 768.4.a.d.1.1 | 1 | |||
8.3 | odd | 2 | 768.4.a.a.1.1 | 1 | |||
8.5 | even | 2 | 768.4.a.c.1.1 | 1 | |||
12.11 | even | 2 | 2304.4.a.f.1.1 | 1 | |||
16.3 | odd | 4 | 384.4.d.a.193.2 | yes | 2 | ||
16.5 | even | 4 | 384.4.d.b.193.2 | yes | 2 | ||
16.11 | odd | 4 | 384.4.d.a.193.1 | ✓ | 2 | ||
16.13 | even | 4 | 384.4.d.b.193.1 | yes | 2 | ||
24.5 | odd | 2 | 2304.4.a.k.1.1 | 1 | |||
24.11 | even | 2 | 2304.4.a.l.1.1 | 1 | |||
48.5 | odd | 4 | 1152.4.d.g.577.1 | 2 | |||
48.11 | even | 4 | 1152.4.d.b.577.1 | 2 | |||
48.29 | odd | 4 | 1152.4.d.g.577.2 | 2 | |||
48.35 | even | 4 | 1152.4.d.b.577.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.d.a.193.1 | ✓ | 2 | 16.11 | odd | 4 | ||
384.4.d.a.193.2 | yes | 2 | 16.3 | odd | 4 | ||
384.4.d.b.193.1 | yes | 2 | 16.13 | even | 4 | ||
384.4.d.b.193.2 | yes | 2 | 16.5 | even | 4 | ||
768.4.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
768.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
768.4.a.c.1.1 | 1 | 8.5 | even | 2 | |||
768.4.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
1152.4.d.b.577.1 | 2 | 48.11 | even | 4 | |||
1152.4.d.b.577.2 | 2 | 48.35 | even | 4 | |||
1152.4.d.g.577.1 | 2 | 48.5 | odd | 4 | |||
1152.4.d.g.577.2 | 2 | 48.29 | odd | 4 | |||
2304.4.a.e.1.1 | 1 | 3.2 | odd | 2 | |||
2304.4.a.f.1.1 | 1 | 12.11 | even | 2 | |||
2304.4.a.k.1.1 | 1 | 24.5 | odd | 2 | |||
2304.4.a.l.1.1 | 1 | 24.11 | even | 2 |