Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5586,2,Mod(1,5586)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5586, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5586.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5586.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: | \(44.6044345691\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.29268.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 5x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 798) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.83719\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5586.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.49248 | 1.11467 | 0.557335 | − | 0.830288i | \(-0.311824\pi\) | ||||
0.557335 | + | 0.830288i | \(0.311824\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.49248 | −0.788191 | ||||||||
\(11\) | −3.46193 | −1.04381 | −0.521906 | − | 0.853003i | \(-0.674779\pi\) | ||||
−0.521906 | + | 0.853003i | \(0.674779\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.98496 | −1.38258 | −0.691289 | − | 0.722578i | \(-0.742957\pi\) | ||||
−0.691289 | + | 0.722578i | \(0.742957\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.49248 | −0.643555 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.24299 | 0.544006 | 0.272003 | − | 0.962296i | \(-0.412314\pi\) | ||||
0.272003 | + | 0.962296i | \(0.412314\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.49248 | 0.557335 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.46193 | 0.738086 | ||||||||
\(23\) | 6.00404 | 1.25193 | 0.625964 | − | 0.779852i | \(-0.284705\pi\) | ||||
0.625964 | + | 0.779852i | \(0.284705\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.21245 | 0.242489 | ||||||||
\(26\) | 4.98496 | 0.977630 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.51156 | −1.02347 | −0.511736 | − | 0.859143i | \(-0.670997\pi\) | ||||
−0.511736 | + | 0.859143i | \(0.670997\pi\) | |||||||
\(30\) | 2.49248 | 0.455062 | ||||||||
\(31\) | −7.28407 | −1.30826 | −0.654129 | − | 0.756383i | \(-0.726965\pi\) | ||||
−0.654129 | + | 0.756383i | \(0.726965\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.46193 | 0.602645 | ||||||||
\(34\) | −2.24299 | −0.384670 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.16685 | −1.50702 | −0.753511 | − | 0.657436i | \(-0.771641\pi\) | ||||
−0.753511 | + | 0.657436i | \(0.771641\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 4.98496 | 0.798232 | ||||||||
\(40\) | −2.49248 | −0.394095 | ||||||||
\(41\) | 4.64383 | 0.725244 | 0.362622 | − | 0.931936i | \(-0.381882\pi\) | ||||
0.362622 | + | 0.931936i | \(0.381882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.54211 | 1.45516 | 0.727579 | − | 0.686024i | \(-0.240645\pi\) | ||||
0.727579 | + | 0.686024i | \(0.240645\pi\) | |||||||
\(44\) | −3.46193 | −0.521906 | ||||||||
\(45\) | 2.49248 | 0.371557 | ||||||||
\(46\) | −6.00404 | −0.885247 | ||||||||
\(47\) | 5.36021 | 0.781868 | 0.390934 | − | 0.920419i | \(-0.372152\pi\) | ||||
0.390934 | + | 0.920419i | \(0.372152\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.21245 | −0.171466 | ||||||||
\(51\) | −2.24299 | −0.314082 | ||||||||
\(52\) | −4.98496 | −0.691289 | ||||||||
\(53\) | −5.87423 | −0.806887 | −0.403443 | − | 0.915005i | \(-0.632187\pi\) | ||||
−0.403443 | + | 0.915005i | \(0.632187\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −8.62878 | −1.16350 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 5.51156 | 0.723704 | ||||||||
\(59\) | −8.67842 | −1.12983 | −0.564917 | − | 0.825148i | \(-0.691092\pi\) | ||||
−0.564917 | + | 0.825148i | \(0.691092\pi\) | |||||||
\(60\) | −2.49248 | −0.321778 | ||||||||
\(61\) | 4.37526 | 0.560194 | 0.280097 | − | 0.959972i | \(-0.409633\pi\) | ||||
0.280097 | + | 0.959972i | \(0.409633\pi\) | |||||||
\(62\) | 7.28407 | 0.925078 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.4249 | −1.54112 | ||||||||
\(66\) | −3.46193 | −0.426134 | ||||||||
\(67\) | 15.1583 | 1.85188 | 0.925940 | − | 0.377670i | \(-0.123274\pi\) | ||||
0.925940 | + | 0.377670i | \(0.123274\pi\) | |||||||
\(68\) | 2.24299 | 0.272003 | ||||||||
\(69\) | −6.00404 | −0.722802 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0907 | 1.43490 | 0.717452 | − | 0.696608i | \(-0.245308\pi\) | ||||
0.717452 | + | 0.696608i | \(0.245308\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 14.4204 | 1.68778 | 0.843889 | − | 0.536518i | \(-0.180261\pi\) | ||||
0.843889 | + | 0.536518i | \(0.180261\pi\) | |||||||
\(74\) | 9.16685 | 1.06563 | ||||||||
\(75\) | −1.21245 | −0.140001 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.98496 | −0.564435 | ||||||||
\(79\) | −7.08667 | −0.797313 | −0.398656 | − | 0.917100i | \(-0.630523\pi\) | ||||
−0.398656 | + | 0.917100i | \(0.630523\pi\) | |||||||
\(80\) | 2.49248 | 0.278667 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.64383 | −0.512825 | ||||||||
\(83\) | −5.59823 | −0.614486 | −0.307243 | − | 0.951631i | \(-0.599406\pi\) | ||||
−0.307243 | + | 0.951631i | \(0.599406\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.59061 | 0.606387 | ||||||||
\(86\) | −9.54211 | −1.02895 | ||||||||
\(87\) | 5.51156 | 0.590902 | ||||||||
\(88\) | 3.46193 | 0.369043 | ||||||||
\(89\) | 7.52952 | 0.798127 | 0.399064 | − | 0.916923i | \(-0.369335\pi\) | ||||
0.399064 | + | 0.916923i | \(0.369335\pi\) | |||||||
\(90\) | −2.49248 | −0.262730 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00404 | 0.625964 | ||||||||
\(93\) | 7.28407 | 0.755323 | ||||||||
\(94\) | −5.36021 | −0.552864 | ||||||||
\(95\) | 2.49248 | 0.255723 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 7.00404 | 0.711153 | 0.355576 | − | 0.934647i | \(-0.384285\pi\) | ||||
0.355576 | + | 0.934647i | \(0.384285\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.46193 | −0.347937 | ||||||||
\(100\) | 1.21245 | 0.121245 | ||||||||
\(101\) | 7.09569 | 0.706047 | 0.353024 | − | 0.935614i | \(-0.385154\pi\) | ||||
0.353024 | + | 0.935614i | \(0.385154\pi\) | |||||||
\(102\) | 2.24299 | 0.222089 | ||||||||
\(103\) | 7.15135 | 0.704643 | 0.352322 | − | 0.935879i | \(-0.385392\pi\) | ||||
0.352322 | + | 0.935879i | \(0.385392\pi\) | |||||||
\(104\) | 4.98496 | 0.488815 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.87423 | 0.570555 | ||||||||
\(107\) | −15.7305 | −1.52072 | −0.760362 | − | 0.649499i | \(-0.774979\pi\) | ||||
−0.760362 | + | 0.649499i | \(0.774979\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 8.31707 | 0.796631 | 0.398315 | − | 0.917249i | \(-0.369595\pi\) | ||||
0.398315 | + | 0.917249i | \(0.369595\pi\) | |||||||
\(110\) | 8.62878 | 0.822722 | ||||||||
\(111\) | 9.16685 | 0.870079 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3643 | 1.25720 | 0.628602 | − | 0.777727i | \(-0.283628\pi\) | ||||
0.628602 | + | 0.777727i | \(0.283628\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | 14.9649 | 1.39549 | ||||||||
\(116\) | −5.51156 | −0.511736 | ||||||||
\(117\) | −4.98496 | −0.460859 | ||||||||
\(118\) | 8.67842 | 0.798913 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.49248 | 0.227531 | ||||||||
\(121\) | 0.984956 | 0.0895414 | ||||||||
\(122\) | −4.37526 | −0.396117 | ||||||||
\(123\) | −4.64383 | −0.418720 | ||||||||
\(124\) | −7.28407 | −0.654129 | ||||||||
\(125\) | −9.44040 | −0.844375 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.09569 | 0.540905 | 0.270452 | − | 0.962733i | \(-0.412827\pi\) | ||||
0.270452 | + | 0.962733i | \(0.412827\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −9.54211 | −0.840136 | ||||||||
\(130\) | 12.4249 | 1.08974 | ||||||||
\(131\) | 9.31416 | 0.813782 | 0.406891 | − | 0.913477i | \(-0.366613\pi\) | ||||
0.406891 | + | 0.913477i | \(0.366613\pi\) | |||||||
\(132\) | 3.46193 | 0.301322 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −15.1583 | −1.30948 | ||||||||
\(135\) | −2.49248 | −0.214518 | ||||||||
\(136\) | −2.24299 | −0.192335 | ||||||||
\(137\) | −7.78510 | −0.665126 | −0.332563 | − | 0.943081i | \(-0.607913\pi\) | ||||
−0.332563 | + | 0.943081i | \(0.607913\pi\) | |||||||
\(138\) | 6.00404 | 0.511098 | ||||||||
\(139\) | 12.5882 | 1.06771 | 0.533857 | − | 0.845575i | \(-0.320742\pi\) | ||||
0.533857 | + | 0.845575i | \(0.320742\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.36021 | −0.451411 | ||||||||
\(142\) | −12.0907 | −1.01463 | ||||||||
\(143\) | 17.2576 | 1.44315 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −13.7374 | −1.14083 | ||||||||
\(146\) | −14.4204 | −1.19344 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.16685 | −0.753511 | ||||||||
\(149\) | 16.2922 | 1.33471 | 0.667353 | − | 0.744742i | \(-0.267427\pi\) | ||||
0.667353 | + | 0.744742i | \(0.267427\pi\) | |||||||
\(150\) | 1.21245 | 0.0989958 | ||||||||
\(151\) | 19.9735 | 1.62542 | 0.812710 | − | 0.582669i | \(-0.197991\pi\) | ||||
0.812710 | + | 0.582669i | \(0.197991\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 2.24299 | 0.181335 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.1554 | −1.45828 | ||||||||
\(156\) | 4.98496 | 0.399116 | ||||||||
\(157\) | −0.739053 | −0.0589828 | −0.0294914 | − | 0.999565i | \(-0.509389\pi\) | ||||
−0.0294914 | + | 0.999565i | \(0.509389\pi\) | |||||||
\(158\) | 7.08667 | 0.563785 | ||||||||
\(159\) | 5.87423 | 0.465856 | ||||||||
\(160\) | −2.49248 | −0.197048 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −5.79808 | −0.454141 | −0.227071 | − | 0.973878i | \(-0.572915\pi\) | ||||
−0.227071 | + | 0.973878i | \(0.572915\pi\) | |||||||
\(164\) | 4.64383 | 0.362622 | ||||||||
\(165\) | 8.62878 | 0.671750 | ||||||||
\(166\) | 5.59823 | 0.434507 | ||||||||
\(167\) | 17.1058 | 1.32368 | 0.661842 | − | 0.749644i | \(-0.269775\pi\) | ||||
0.661842 | + | 0.749644i | \(0.269775\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8498 | 0.911522 | ||||||||
\(170\) | −5.59061 | −0.428780 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 9.54211 | 0.727579 | ||||||||
\(173\) | −2.58412 | −0.196467 | −0.0982336 | − | 0.995163i | \(-0.531319\pi\) | ||||
−0.0982336 | + | 0.995163i | \(0.531319\pi\) | |||||||
\(174\) | −5.51156 | −0.417830 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.46193 | −0.260953 | ||||||||
\(177\) | 8.67842 | 0.652310 | ||||||||
\(178\) | −7.52952 | −0.564361 | ||||||||
\(179\) | −3.24948 | −0.242878 | −0.121439 | − | 0.992599i | \(-0.538751\pi\) | ||||
−0.121439 | + | 0.992599i | \(0.538751\pi\) | |||||||
\(180\) | 2.49248 | 0.185778 | ||||||||
\(181\) | 12.4559 | 0.925840 | 0.462920 | − | 0.886400i | \(-0.346802\pi\) | ||||
0.462920 | + | 0.886400i | \(0.346802\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.37526 | −0.323428 | ||||||||
\(184\) | −6.00404 | −0.442624 | ||||||||
\(185\) | −22.8482 | −1.67983 | ||||||||
\(186\) | −7.28407 | −0.534094 | ||||||||
\(187\) | −7.76509 | −0.567839 | ||||||||
\(188\) | 5.36021 | 0.390934 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.49248 | −0.180823 | ||||||||
\(191\) | −16.4444 | −1.18988 | −0.594939 | − | 0.803771i | \(-0.702824\pi\) | ||||
−0.594939 | + | 0.803771i | \(0.702824\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −18.6854 | −1.34500 | −0.672501 | − | 0.740096i | \(-0.734780\pi\) | ||||
−0.672501 | + | 0.740096i | \(0.734780\pi\) | |||||||
\(194\) | −7.00404 | −0.502861 | ||||||||
\(195\) | 12.4249 | 0.889765 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.4965 | −1.10408 | −0.552041 | − | 0.833817i | \(-0.686151\pi\) | ||||
−0.552041 | + | 0.833817i | \(0.686151\pi\) | |||||||
\(198\) | 3.46193 | 0.246029 | ||||||||
\(199\) | −1.45948 | −0.103460 | −0.0517299 | − | 0.998661i | \(-0.516473\pi\) | ||||
−0.0517299 | + | 0.998661i | \(0.516473\pi\) | |||||||
\(200\) | −1.21245 | −0.0857329 | ||||||||
\(201\) | −15.1583 | −1.06918 | ||||||||
\(202\) | −7.09569 | −0.499251 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.24299 | −0.157041 | ||||||||
\(205\) | 11.5746 | 0.808408 | ||||||||
\(206\) | −7.15135 | −0.498258 | ||||||||
\(207\) | 6.00404 | 0.417310 | ||||||||
\(208\) | −4.98496 | −0.345644 | ||||||||
\(209\) | −3.46193 | −0.239467 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.3953 | −1.61060 | −0.805298 | − | 0.592870i | \(-0.797995\pi\) | ||||
−0.805298 | + | 0.592870i | \(0.797995\pi\) | |||||||
\(212\) | −5.87423 | −0.403443 | ||||||||
\(213\) | −12.0907 | −0.828442 | ||||||||
\(214\) | 15.7305 | 1.07531 | ||||||||
\(215\) | 23.7835 | 1.62202 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.31707 | −0.563303 | ||||||||
\(219\) | −14.4204 | −0.974439 | ||||||||
\(220\) | −8.62878 | −0.581752 | ||||||||
\(221\) | −11.1812 | −0.752131 | ||||||||
\(222\) | −9.16685 | −0.615239 | ||||||||
\(223\) | 14.8221 | 0.992564 | 0.496282 | − | 0.868161i | \(-0.334698\pi\) | ||||
0.496282 | + | 0.868161i | \(0.334698\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.21245 | 0.0808297 | ||||||||
\(226\) | −13.3643 | −0.888977 | ||||||||
\(227\) | 16.2295 | 1.07719 | 0.538594 | − | 0.842566i | \(-0.318956\pi\) | ||||
0.538594 | + | 0.842566i | \(0.318956\pi\) | |||||||
\(228\) | −1.00000 | −0.0662266 | ||||||||
\(229\) | −6.39480 | −0.422580 | −0.211290 | − | 0.977423i | \(-0.567767\pi\) | ||||
−0.211290 | + | 0.977423i | \(0.567767\pi\) | |||||||
\(230\) | −14.9649 | −0.986759 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.51156 | 0.361852 | ||||||||
\(233\) | −21.3798 | −1.40063 | −0.700317 | − | 0.713832i | \(-0.746958\pi\) | ||||
−0.700317 | + | 0.713832i | \(0.746958\pi\) | |||||||
\(234\) | 4.98496 | 0.325877 | ||||||||
\(235\) | 13.3602 | 0.871524 | ||||||||
\(236\) | −8.67842 | −0.564917 | ||||||||
\(237\) | 7.08667 | 0.460329 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.8938 | 1.22214 | 0.611068 | − | 0.791578i | \(-0.290740\pi\) | ||||
0.611068 | + | 0.791578i | \(0.290740\pi\) | |||||||
\(240\) | −2.49248 | −0.160889 | ||||||||
\(241\) | 4.05009 | 0.260889 | 0.130445 | − | 0.991456i | \(-0.458359\pi\) | ||||
0.130445 | + | 0.991456i | \(0.458359\pi\) | |||||||
\(242\) | −0.984956 | −0.0633153 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.37526 | 0.280097 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.64383 | 0.296080 | ||||||||
\(247\) | −4.98496 | −0.317185 | ||||||||
\(248\) | 7.28407 | 0.462539 | ||||||||
\(249\) | 5.59823 | 0.354774 | ||||||||
\(250\) | 9.44040 | 0.597063 | ||||||||
\(251\) | 6.59917 | 0.416536 | 0.208268 | − | 0.978072i | \(-0.433217\pi\) | ||||
0.208268 | + | 0.978072i | \(0.433217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.7856 | −1.30678 | ||||||||
\(254\) | −6.09569 | −0.382477 | ||||||||
\(255\) | −5.59061 | −0.350098 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.65125 | −0.165380 | −0.0826902 | − | 0.996575i | \(-0.526351\pi\) | ||||
−0.0826902 | + | 0.996575i | \(0.526351\pi\) | |||||||
\(258\) | 9.54211 | 0.594066 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −12.4249 | −0.770559 | ||||||||
\(261\) | −5.51156 | −0.341157 | ||||||||
\(262\) | −9.31416 | −0.575431 | ||||||||
\(263\) | −1.45544 | −0.0897463 | −0.0448731 | − | 0.998993i | \(-0.514288\pi\) | ||||
−0.0448731 | + | 0.998993i | \(0.514288\pi\) | |||||||
\(264\) | −3.46193 | −0.213067 | ||||||||
\(265\) | −14.6414 | −0.899413 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.52952 | −0.460799 | ||||||||
\(268\) | 15.1583 | 0.925940 | ||||||||
\(269\) | 14.3232 | 0.873299 | 0.436650 | − | 0.899632i | \(-0.356165\pi\) | ||||
0.436650 | + | 0.899632i | \(0.356165\pi\) | |||||||
\(270\) | 2.49248 | 0.151687 | ||||||||
\(271\) | 20.6658 | 1.25536 | 0.627680 | − | 0.778472i | \(-0.284005\pi\) | ||||
0.627680 | + | 0.778472i | \(0.284005\pi\) | |||||||
\(272\) | 2.24299 | 0.136001 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.78510 | 0.470315 | ||||||||
\(275\) | −4.19740 | −0.253113 | ||||||||
\(276\) | −6.00404 | −0.361401 | ||||||||
\(277\) | −28.5421 | −1.71493 | −0.857464 | − | 0.514544i | \(-0.827961\pi\) | ||||
−0.857464 | + | 0.514544i | \(0.827961\pi\) | |||||||
\(278\) | −12.5882 | −0.754988 | ||||||||
\(279\) | −7.28407 | −0.436086 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.6443 | −0.813950 | −0.406975 | − | 0.913439i | \(-0.633416\pi\) | ||||
−0.406975 | + | 0.913439i | \(0.633416\pi\) | |||||||
\(282\) | 5.36021 | 0.319196 | ||||||||
\(283\) | −1.53403 | −0.0911886 | −0.0455943 | − | 0.998960i | \(-0.514518\pi\) | ||||
−0.0455943 | + | 0.998960i | \(0.514518\pi\) | |||||||
\(284\) | 12.0907 | 0.717452 | ||||||||
\(285\) | −2.49248 | −0.147642 | ||||||||
\(286\) | −17.2576 | −1.02046 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −11.9690 | −0.704058 | ||||||||
\(290\) | 13.7374 | 0.806691 | ||||||||
\(291\) | −7.00404 | −0.410584 | ||||||||
\(292\) | 14.4204 | 0.843889 | ||||||||
\(293\) | −33.3773 | −1.94992 | −0.974962 | − | 0.222373i | \(-0.928620\pi\) | ||||
−0.974962 | + | 0.222373i | \(0.928620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.6308 | −1.25939 | ||||||||
\(296\) | 9.16685 | 0.532813 | ||||||||
\(297\) | 3.46193 | 0.200882 | ||||||||
\(298\) | −16.2922 | −0.943779 | ||||||||
\(299\) | −29.9299 | −1.73089 | ||||||||
\(300\) | −1.21245 | −0.0700006 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −19.9735 | −1.14935 | ||||||||
\(303\) | −7.09569 | −0.407636 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 10.9052 | 0.624432 | ||||||||
\(306\) | −2.24299 | −0.128223 | ||||||||
\(307\) | 9.52952 | 0.543878 | 0.271939 | − | 0.962314i | \(-0.412335\pi\) | ||||
0.271939 | + | 0.962314i | \(0.412335\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.15135 | −0.406826 | ||||||||
\(310\) | 18.1554 | 1.03116 | ||||||||
\(311\) | 16.4404 | 0.932249 | 0.466125 | − | 0.884719i | \(-0.345650\pi\) | ||||
0.466125 | + | 0.884719i | \(0.345650\pi\) | |||||||
\(312\) | −4.98496 | −0.282218 | ||||||||
\(313\) | 10.9940 | 0.621416 | 0.310708 | − | 0.950505i | \(-0.399434\pi\) | ||||
0.310708 | + | 0.950505i | \(0.399434\pi\) | |||||||
\(314\) | 0.739053 | 0.0417072 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.08667 | −0.398656 | ||||||||
\(317\) | 6.66291 | 0.374226 | 0.187113 | − | 0.982338i | \(-0.440087\pi\) | ||||
0.187113 | + | 0.982338i | \(0.440087\pi\) | |||||||
\(318\) | −5.87423 | −0.329410 | ||||||||
\(319\) | 19.0806 | 1.06831 | ||||||||
\(320\) | 2.49248 | 0.139334 | ||||||||
\(321\) | 15.7305 | 0.877991 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.24299 | 0.124804 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −6.04399 | −0.335260 | ||||||||
\(326\) | 5.79808 | 0.321126 | ||||||||
\(327\) | −8.31707 | −0.459935 | ||||||||
\(328\) | −4.64383 | −0.256412 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −8.62878 | −0.474999 | ||||||||
\(331\) | 25.8102 | 1.41866 | 0.709329 | − | 0.704878i | \(-0.248998\pi\) | ||||
0.709329 | + | 0.704878i | \(0.248998\pi\) | |||||||
\(332\) | −5.59823 | −0.307243 | ||||||||
\(333\) | −9.16685 | −0.502340 | ||||||||
\(334\) | −17.1058 | −0.935985 | ||||||||
\(335\) | 37.7817 | 2.06424 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0932 | 0.549810 | 0.274905 | − | 0.961471i | \(-0.411354\pi\) | ||||
0.274905 | + | 0.961471i | \(0.411354\pi\) | |||||||
\(338\) | −11.8498 | −0.644543 | ||||||||
\(339\) | −13.3643 | −0.725847 | ||||||||
\(340\) | 5.59061 | 0.303194 | ||||||||
\(341\) | 25.2169 | 1.36557 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.54211 | −0.514476 | ||||||||
\(345\) | −14.9649 | −0.805685 | ||||||||
\(346\) | 2.58412 | 0.138923 | ||||||||
\(347\) | −0.369228 | −0.0198212 | −0.00991059 | − | 0.999951i | \(-0.503155\pi\) | ||||
−0.00991059 | + | 0.999951i | \(0.503155\pi\) | |||||||
\(348\) | 5.51156 | 0.295451 | ||||||||
\(349\) | 31.3643 | 1.67889 | 0.839445 | − | 0.543445i | \(-0.182880\pi\) | ||||
0.839445 | + | 0.543445i | \(0.182880\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.98496 | 0.266077 | ||||||||
\(352\) | 3.46193 | 0.184521 | ||||||||
\(353\) | −22.8192 | −1.21454 | −0.607272 | − | 0.794494i | \(-0.707736\pi\) | ||||
−0.607272 | + | 0.794494i | \(0.707736\pi\) | |||||||
\(354\) | −8.67842 | −0.461253 | ||||||||
\(355\) | 30.1358 | 1.59944 | ||||||||
\(356\) | 7.52952 | 0.399064 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.24948 | 0.171741 | ||||||||
\(359\) | 24.0276 | 1.26813 | 0.634065 | − | 0.773280i | \(-0.281385\pi\) | ||||
0.634065 | + | 0.773280i | \(0.281385\pi\) | |||||||
\(360\) | −2.49248 | −0.131365 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −12.4559 | −0.654668 | ||||||||
\(363\) | −0.984956 | −0.0516968 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 35.9425 | 1.88131 | ||||||||
\(366\) | 4.37526 | 0.228698 | ||||||||
\(367\) | 15.8096 | 0.825256 | 0.412628 | − | 0.910900i | \(-0.364611\pi\) | ||||
0.412628 | + | 0.910900i | \(0.364611\pi\) | |||||||
\(368\) | 6.00404 | 0.312982 | ||||||||
\(369\) | 4.64383 | 0.241748 | ||||||||
\(370\) | 22.8482 | 1.18782 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.28407 | 0.377662 | ||||||||
\(373\) | 30.8507 | 1.59739 | 0.798694 | − | 0.601737i | \(-0.205524\pi\) | ||||
0.798694 | + | 0.601737i | \(0.205524\pi\) | |||||||
\(374\) | 7.76509 | 0.401523 | ||||||||
\(375\) | 9.44040 | 0.487500 | ||||||||
\(376\) | −5.36021 | −0.276432 | ||||||||
\(377\) | 27.4749 | 1.41503 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.5450 | 1.20943 | 0.604713 | − | 0.796443i | \(-0.293288\pi\) | ||||
0.604713 | + | 0.796443i | \(0.293288\pi\) | |||||||
\(380\) | 2.49248 | 0.127861 | ||||||||
\(381\) | −6.09569 | −0.312291 | ||||||||
\(382\) | 16.4444 | 0.841371 | ||||||||
\(383\) | 4.87271 | 0.248984 | 0.124492 | − | 0.992221i | \(-0.460270\pi\) | ||||
0.124492 | + | 0.992221i | \(0.460270\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.6854 | 0.951060 | ||||||||
\(387\) | 9.54211 | 0.485053 | ||||||||
\(388\) | 7.00404 | 0.355576 | ||||||||
\(389\) | −28.2856 | −1.43414 | −0.717068 | − | 0.697003i | \(-0.754516\pi\) | ||||
−0.717068 | + | 0.697003i | \(0.754516\pi\) | |||||||
\(390\) | −12.4249 | −0.629159 | ||||||||
\(391\) | 13.4670 | 0.681057 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.31416 | −0.469837 | ||||||||
\(394\) | 15.4965 | 0.780703 | ||||||||
\(395\) | −17.6634 | −0.888741 | ||||||||
\(396\) | −3.46193 | −0.173969 | ||||||||
\(397\) | 2.65125 | 0.133062 | 0.0665312 | − | 0.997784i | \(-0.478807\pi\) | ||||
0.0665312 | + | 0.997784i | \(0.478807\pi\) | |||||||
\(398\) | 1.45948 | 0.0731571 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.21245 | 0.0606223 | ||||||||
\(401\) | −7.45292 | −0.372181 | −0.186090 | − | 0.982533i | \(-0.559582\pi\) | ||||
−0.186090 | + | 0.982533i | \(0.559582\pi\) | |||||||
\(402\) | 15.1583 | 0.756027 | ||||||||
\(403\) | 36.3108 | 1.80877 | ||||||||
\(404\) | 7.09569 | 0.353024 | ||||||||
\(405\) | 2.49248 | 0.123852 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.7350 | 1.57305 | ||||||||
\(408\) | 2.24299 | 0.111045 | ||||||||
\(409\) | 17.4037 | 0.860560 | 0.430280 | − | 0.902696i | \(-0.358415\pi\) | ||||
0.430280 | + | 0.902696i | \(0.358415\pi\) | |||||||
\(410\) | −11.5746 | −0.571630 | ||||||||
\(411\) | 7.78510 | 0.384011 | ||||||||
\(412\) | 7.15135 | 0.352322 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.00404 | −0.295082 | ||||||||
\(415\) | −13.9535 | −0.684949 | ||||||||
\(416\) | 4.98496 | 0.244408 | ||||||||
\(417\) | −12.5882 | −0.616445 | ||||||||
\(418\) | 3.46193 | 0.169329 | ||||||||
\(419\) | −3.76105 | −0.183739 | −0.0918696 | − | 0.995771i | \(-0.529284\pi\) | ||||
−0.0918696 | + | 0.995771i | \(0.529284\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.6343 | 1.54176 | 0.770882 | − | 0.636978i | \(-0.219816\pi\) | ||||
0.770882 | + | 0.636978i | \(0.219816\pi\) | |||||||
\(422\) | 23.3953 | 1.13886 | ||||||||
\(423\) | 5.36021 | 0.260623 | ||||||||
\(424\) | 5.87423 | 0.285278 | ||||||||
\(425\) | 2.71951 | 0.131916 | ||||||||
\(426\) | 12.0907 | 0.585797 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −15.7305 | −0.760362 | ||||||||
\(429\) | −17.2576 | −0.833203 | ||||||||
\(430\) | −23.7835 | −1.14694 | ||||||||
\(431\) | −1.66582 | −0.0802398 | −0.0401199 | − | 0.999195i | \(-0.512774\pi\) | ||||
−0.0401199 | + | 0.999195i | \(0.512774\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 16.1062 | 0.774015 | 0.387008 | − | 0.922076i | \(-0.373509\pi\) | ||||
0.387008 | + | 0.922076i | \(0.373509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.7374 | 0.658660 | ||||||||
\(436\) | 8.31707 | 0.398315 | ||||||||
\(437\) | 6.00404 | 0.287212 | ||||||||
\(438\) | 14.4204 | 0.689032 | ||||||||
\(439\) | 21.0867 | 1.00641 | 0.503206 | − | 0.864167i | \(-0.332154\pi\) | ||||
0.503206 | + | 0.864167i | \(0.332154\pi\) | |||||||
\(440\) | 8.62878 | 0.411361 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.1812 | 0.531837 | ||||||||
\(443\) | −18.5958 | −0.883512 | −0.441756 | − | 0.897135i | \(-0.645644\pi\) | ||||
−0.441756 | + | 0.897135i | \(0.645644\pi\) | |||||||
\(444\) | 9.16685 | 0.435040 | ||||||||
\(445\) | 18.7672 | 0.889648 | ||||||||
\(446\) | −14.8221 | −0.701849 | ||||||||
\(447\) | −16.2922 | −0.770592 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.7410 | 0.931637 | 0.465818 | − | 0.884880i | \(-0.345760\pi\) | ||||
0.465818 | + | 0.884880i | \(0.345760\pi\) | |||||||
\(450\) | −1.21245 | −0.0571552 | ||||||||
\(451\) | −16.0766 | −0.757018 | ||||||||
\(452\) | 13.3643 | 0.628602 | ||||||||
\(453\) | −19.9735 | −0.938437 | ||||||||
\(454\) | −16.2295 | −0.761687 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 0.468893 | 0.0219339 | 0.0109669 | − | 0.999940i | \(-0.496509\pi\) | ||||
0.0109669 | + | 0.999940i | \(0.496509\pi\) | |||||||
\(458\) | 6.39480 | 0.298809 | ||||||||
\(459\) | −2.24299 | −0.104694 | ||||||||
\(460\) | 14.9649 | 0.697744 | ||||||||
\(461\) | −19.0556 | −0.887510 | −0.443755 | − | 0.896148i | \(-0.646354\pi\) | ||||
−0.443755 | + | 0.896148i | \(0.646354\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.65575 | −0.448741 | −0.224370 | − | 0.974504i | \(-0.572033\pi\) | ||||
−0.224370 | + | 0.974504i | \(0.572033\pi\) | |||||||
\(464\) | −5.51156 | −0.255868 | ||||||||
\(465\) | 18.1554 | 0.841936 | ||||||||
\(466\) | 21.3798 | 0.990398 | ||||||||
\(467\) | −9.16281 | −0.424004 | −0.212002 | − | 0.977269i | \(-0.567998\pi\) | ||||
−0.212002 | + | 0.977269i | \(0.567998\pi\) | |||||||
\(468\) | −4.98496 | −0.230430 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −13.3602 | −0.616261 | ||||||||
\(471\) | 0.739053 | 0.0340537 | ||||||||
\(472\) | 8.67842 | 0.399456 | ||||||||
\(473\) | −33.0341 | −1.51891 | ||||||||
\(474\) | −7.08667 | −0.325502 | ||||||||
\(475\) | 1.21245 | 0.0556308 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.87423 | −0.268962 | ||||||||
\(478\) | −18.8938 | −0.864181 | ||||||||
\(479\) | 42.8212 | 1.95655 | 0.978276 | − | 0.207309i | \(-0.0664706\pi\) | ||||
0.978276 | + | 0.207309i | \(0.0664706\pi\) | |||||||
\(480\) | 2.49248 | 0.113766 | ||||||||
\(481\) | 45.6964 | 2.08357 | ||||||||
\(482\) | −4.05009 | −0.184477 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.984956 | 0.0447707 | ||||||||
\(485\) | 17.4574 | 0.792700 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −26.3153 | −1.19246 | −0.596230 | − | 0.802814i | \(-0.703335\pi\) | ||||
−0.596230 | + | 0.802814i | \(0.703335\pi\) | |||||||
\(488\) | −4.37526 | −0.198059 | ||||||||
\(489\) | 5.79808 | 0.262198 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.2064 | −0.641127 | −0.320563 | − | 0.947227i | \(-0.603872\pi\) | ||||
−0.320563 | + | 0.947227i | \(0.603872\pi\) | |||||||
\(492\) | −4.64383 | −0.209360 | ||||||||
\(493\) | −12.3624 | −0.556775 | ||||||||
\(494\) | 4.98496 | 0.224284 | ||||||||
\(495\) | −8.62878 | −0.387835 | ||||||||
\(496\) | −7.28407 | −0.327065 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5.59823 | −0.250863 | ||||||||
\(499\) | 34.0325 | 1.52351 | 0.761753 | − | 0.647868i | \(-0.224339\pi\) | ||||
0.761753 | + | 0.647868i | \(0.224339\pi\) | |||||||
\(500\) | −9.44040 | −0.422187 | ||||||||
\(501\) | −17.1058 | −0.764229 | ||||||||
\(502\) | −6.59917 | −0.294535 | ||||||||
\(503\) | 18.2003 | 0.811512 | 0.405756 | − | 0.913981i | \(-0.367008\pi\) | ||||
0.405756 | + | 0.913981i | \(0.367008\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.6858 | 0.787009 | ||||||||
\(506\) | 20.7856 | 0.924031 | ||||||||
\(507\) | −11.8498 | −0.526267 | ||||||||
\(508\) | 6.09569 | 0.270452 | ||||||||
\(509\) | −4.56478 | −0.202330 | −0.101165 | − | 0.994870i | \(-0.532257\pi\) | ||||
−0.101165 | + | 0.994870i | \(0.532257\pi\) | |||||||
\(510\) | 5.59061 | 0.247556 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 2.65125 | 0.116942 | ||||||||
\(515\) | 17.8246 | 0.785445 | ||||||||
\(516\) | −9.54211 | −0.420068 | ||||||||
\(517\) | −18.5567 | −0.816122 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.58412 | 0.113430 | ||||||||
\(520\) | 12.4249 | 0.544868 | ||||||||
\(521\) | −40.5160 | −1.77504 | −0.887520 | − | 0.460769i | \(-0.847574\pi\) | ||||
−0.887520 | + | 0.460769i | \(0.847574\pi\) | |||||||
\(522\) | 5.51156 | 0.241235 | ||||||||
\(523\) | −29.4644 | −1.28839 | −0.644195 | − | 0.764861i | \(-0.722807\pi\) | ||||
−0.644195 | + | 0.764861i | \(0.722807\pi\) | |||||||
\(524\) | 9.31416 | 0.406891 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.45544 | 0.0634602 | ||||||||
\(527\) | −16.3381 | −0.711700 | ||||||||
\(528\) | 3.46193 | 0.150661 | ||||||||
\(529\) | 13.0485 | 0.567326 | ||||||||
\(530\) | 14.6414 | 0.635981 | ||||||||
\(531\) | −8.67842 | −0.376611 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.1493 | −1.00271 | ||||||||
\(534\) | 7.52952 | 0.325834 | ||||||||
\(535\) | −39.2079 | −1.69511 | ||||||||
\(536\) | −15.1583 | −0.654739 | ||||||||
\(537\) | 3.24948 | 0.140226 | ||||||||
\(538\) | −14.3232 | −0.617516 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.49248 | −0.107259 | ||||||||
\(541\) | −5.52800 | −0.237667 | −0.118834 | − | 0.992914i | \(-0.537916\pi\) | ||||
−0.118834 | + | 0.992914i | \(0.537916\pi\) | |||||||
\(542\) | −20.6658 | −0.887673 | ||||||||
\(543\) | −12.4559 | −0.534534 | ||||||||
\(544\) | −2.24299 | −0.0961676 | ||||||||
\(545\) | 20.7301 | 0.887980 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.7329 | −0.587178 | −0.293589 | − | 0.955932i | \(-0.594850\pi\) | ||||
−0.293589 | + | 0.955932i | \(0.594850\pi\) | |||||||
\(548\) | −7.78510 | −0.332563 | ||||||||
\(549\) | 4.37526 | 0.186731 | ||||||||
\(550\) | 4.19740 | 0.178978 | ||||||||
\(551\) | −5.51156 | −0.234800 | ||||||||
\(552\) | 6.00404 | 0.255549 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 28.5421 | 1.21264 | ||||||||
\(555\) | 22.8482 | 0.969851 | ||||||||
\(556\) | 12.5882 | 0.533857 | ||||||||
\(557\) | −0.399242 | −0.0169164 | −0.00845821 | − | 0.999964i | \(-0.502692\pi\) | ||||
−0.00845821 | + | 0.999964i | \(0.502692\pi\) | |||||||
\(558\) | 7.28407 | 0.308359 | ||||||||
\(559\) | −47.5670 | −2.01187 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.76509 | 0.327842 | ||||||||
\(562\) | 13.6443 | 0.575549 | ||||||||
\(563\) | 26.1242 | 1.10100 | 0.550501 | − | 0.834834i | \(-0.314437\pi\) | ||||
0.550501 | + | 0.834834i | \(0.314437\pi\) | |||||||
\(564\) | −5.36021 | −0.225706 | ||||||||
\(565\) | 33.3101 | 1.40137 | ||||||||
\(566\) | 1.53403 | 0.0644801 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0907 | −0.507315 | ||||||||
\(569\) | 3.06316 | 0.128414 | 0.0642072 | − | 0.997937i | \(-0.479548\pi\) | ||||
0.0642072 | + | 0.997937i | \(0.479548\pi\) | |||||||
\(570\) | 2.49248 | 0.104398 | ||||||||
\(571\) | 5.89066 | 0.246517 | 0.123258 | − | 0.992375i | \(-0.460666\pi\) | ||||
0.123258 | + | 0.992375i | \(0.460666\pi\) | |||||||
\(572\) | 17.2576 | 0.721575 | ||||||||
\(573\) | 16.4444 | 0.686976 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.27957 | 0.303579 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −25.7896 | −1.07364 | −0.536818 | − | 0.843698i | \(-0.680374\pi\) | ||||
−0.536818 | + | 0.843698i | \(0.680374\pi\) | |||||||
\(578\) | 11.9690 | 0.497844 | ||||||||
\(579\) | 18.6854 | 0.776537 | ||||||||
\(580\) | −13.7374 | −0.570416 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.00404 | 0.290327 | ||||||||
\(583\) | 20.3362 | 0.842237 | ||||||||
\(584\) | −14.4204 | −0.596719 | ||||||||
\(585\) | −12.4249 | −0.513706 | ||||||||
\(586\) | 33.3773 | 1.37880 | ||||||||
\(587\) | 0.822143 | 0.0339335 | 0.0169667 | − | 0.999856i | \(-0.494599\pi\) | ||||
0.0169667 | + | 0.999856i | \(0.494599\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.28407 | −0.300135 | ||||||||
\(590\) | 21.6308 | 0.890524 | ||||||||
\(591\) | 15.4965 | 0.637442 | ||||||||
\(592\) | −9.16685 | −0.376755 | ||||||||
\(593\) | −16.6407 | −0.683352 | −0.341676 | − | 0.939818i | \(-0.610995\pi\) | ||||
−0.341676 | + | 0.939818i | \(0.610995\pi\) | |||||||
\(594\) | −3.46193 | −0.142045 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.2922 | 0.667353 | ||||||||
\(597\) | 1.45948 | 0.0597325 | ||||||||
\(598\) | 29.9299 | 1.22392 | ||||||||
\(599\) | 8.57670 | 0.350434 | 0.175217 | − | 0.984530i | \(-0.443937\pi\) | ||||
0.175217 | + | 0.984530i | \(0.443937\pi\) | |||||||
\(600\) | 1.21245 | 0.0494979 | ||||||||
\(601\) | 13.6993 | 0.558805 | 0.279403 | − | 0.960174i | \(-0.409864\pi\) | ||||
0.279403 | + | 0.960174i | \(0.409864\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.1583 | 0.617294 | ||||||||
\(604\) | 19.9735 | 0.812710 | ||||||||
\(605\) | 2.45498 | 0.0998091 | ||||||||
\(606\) | 7.09569 | 0.288243 | ||||||||
\(607\) | 42.5405 | 1.72667 | 0.863333 | − | 0.504635i | \(-0.168373\pi\) | ||||
0.863333 | + | 0.504635i | \(0.168373\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.9052 | −0.441540 | ||||||||
\(611\) | −26.7204 | −1.08099 | ||||||||
\(612\) | 2.24299 | 0.0906677 | ||||||||
\(613\) | 14.5096 | 0.586036 | 0.293018 | − | 0.956107i | \(-0.405340\pi\) | ||||
0.293018 | + | 0.956107i | \(0.405340\pi\) | |||||||
\(614\) | −9.52952 | −0.384580 | ||||||||
\(615\) | −11.5746 | −0.466734 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.3468 | −1.02042 | −0.510211 | − | 0.860049i | \(-0.670433\pi\) | ||||
−0.510211 | + | 0.860049i | \(0.670433\pi\) | |||||||
\(618\) | 7.15135 | 0.287669 | ||||||||
\(619\) | −15.9944 | −0.642867 | −0.321434 | − | 0.946932i | \(-0.604165\pi\) | ||||
−0.321434 | + | 0.946932i | \(0.604165\pi\) | |||||||
\(620\) | −18.1554 | −0.729138 | ||||||||
\(621\) | −6.00404 | −0.240934 | ||||||||
\(622\) | −16.4404 | −0.659200 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.98496 | 0.199558 | ||||||||
\(625\) | −29.5922 | −1.18369 | ||||||||
\(626\) | −10.9940 | −0.439407 | ||||||||
\(627\) | 3.46193 | 0.138256 | ||||||||
\(628\) | −0.739053 | −0.0294914 | ||||||||
\(629\) | −20.5612 | −0.819829 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.6970 | −1.02298 | −0.511491 | − | 0.859288i | \(-0.670907\pi\) | ||||
−0.511491 | + | 0.859288i | \(0.670907\pi\) | |||||||
\(632\) | 7.08667 | 0.281893 | ||||||||
\(633\) | 23.3953 | 0.929878 | ||||||||
\(634\) | −6.66291 | −0.264618 | ||||||||
\(635\) | 15.1934 | 0.602930 | ||||||||
\(636\) | 5.87423 | 0.232928 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −19.0806 | −0.755410 | ||||||||
\(639\) | 12.0907 | 0.478301 | ||||||||
\(640\) | −2.49248 | −0.0985238 | ||||||||
\(641\) | 44.0747 | 1.74085 | 0.870424 | − | 0.492303i | \(-0.163845\pi\) | ||||
0.870424 | + | 0.492303i | \(0.163845\pi\) | |||||||
\(642\) | −15.7305 | −0.620833 | ||||||||
\(643\) | 22.7730 | 0.898078 | 0.449039 | − | 0.893512i | \(-0.351766\pi\) | ||||
0.449039 | + | 0.893512i | \(0.351766\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.7835 | −0.936474 | ||||||||
\(646\) | −2.24299 | −0.0882494 | ||||||||
\(647\) | 30.3678 | 1.19388 | 0.596941 | − | 0.802285i | \(-0.296382\pi\) | ||||
0.596941 | + | 0.802285i | \(0.296382\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 30.0441 | 1.17933 | ||||||||
\(650\) | 6.04399 | 0.237065 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.79808 | −0.227071 | ||||||||
\(653\) | −4.63535 | −0.181395 | −0.0906976 | − | 0.995878i | \(-0.528910\pi\) | ||||
−0.0906976 | + | 0.995878i | \(0.528910\pi\) | |||||||
\(654\) | 8.31707 | 0.325223 | ||||||||
\(655\) | 23.2153 | 0.907098 | ||||||||
\(656\) | 4.64383 | 0.181311 | ||||||||
\(657\) | 14.4204 | 0.562592 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.8998 | −0.736232 | −0.368116 | − | 0.929780i | \(-0.619997\pi\) | ||||
−0.368116 | + | 0.929780i | \(0.619997\pi\) | |||||||
\(660\) | 8.62878 | 0.335875 | ||||||||
\(661\) | 25.8042 | 1.00367 | 0.501833 | − | 0.864964i | \(-0.332659\pi\) | ||||
0.501833 | + | 0.864964i | \(0.332659\pi\) | |||||||
\(662\) | −25.8102 | −1.00314 | ||||||||
\(663\) | 11.1812 | 0.434243 | ||||||||
\(664\) | 5.59823 | 0.217254 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.16685 | 0.355208 | ||||||||
\(667\) | −33.0916 | −1.28131 | ||||||||
\(668\) | 17.1058 | 0.661842 | ||||||||
\(669\) | −14.8221 | −0.573057 | ||||||||
\(670\) | −37.7817 | −1.45964 | ||||||||
\(671\) | −15.1468 | −0.584737 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.7844 | 0.608445 | 0.304223 | − | 0.952601i | \(-0.401603\pi\) | ||||
0.304223 | + | 0.952601i | \(0.401603\pi\) | |||||||
\(674\) | −10.0932 | −0.388774 | ||||||||
\(675\) | −1.21245 | −0.0466671 | ||||||||
\(676\) | 11.8498 | 0.455761 | ||||||||
\(677\) | −24.0786 | −0.925415 | −0.462707 | − | 0.886511i | \(-0.653122\pi\) | ||||
−0.462707 | + | 0.886511i | \(0.653122\pi\) | |||||||
\(678\) | 13.3643 | 0.513251 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.59061 | −0.214390 | ||||||||
\(681\) | −16.2295 | −0.621914 | ||||||||
\(682\) | −25.2169 | −0.965607 | ||||||||
\(683\) | 14.8506 | 0.568243 | 0.284122 | − | 0.958788i | \(-0.408298\pi\) | ||||
0.284122 | + | 0.958788i | \(0.408298\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | −19.4042 | −0.741396 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.39480 | 0.243977 | ||||||||
\(688\) | 9.54211 | 0.363790 | ||||||||
\(689\) | 29.2828 | 1.11558 | ||||||||
\(690\) | 14.9649 | 0.569705 | ||||||||
\(691\) | 38.2941 | 1.45678 | 0.728389 | − | 0.685164i | \(-0.240269\pi\) | ||||
0.728389 | + | 0.685164i | \(0.240269\pi\) | |||||||
\(692\) | −2.58412 | −0.0982336 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.369228 | 0.0140157 | ||||||||
\(695\) | 31.3757 | 1.19015 | ||||||||
\(696\) | −5.51156 | −0.208915 | ||||||||
\(697\) | 10.4161 | 0.394537 | ||||||||
\(698\) | −31.3643 | −1.18715 | ||||||||
\(699\) | 21.3798 | 0.808657 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.6068 | −0.929385 | −0.464693 | − | 0.885472i | \(-0.653835\pi\) | ||||
−0.464693 | + | 0.885472i | \(0.653835\pi\) | |||||||
\(702\) | −4.98496 | −0.188145 | ||||||||
\(703\) | −9.16685 | −0.345734 | ||||||||
\(704\) | −3.46193 | −0.130476 | ||||||||
\(705\) | −13.3602 | −0.503175 | ||||||||
\(706\) | 22.8192 | 0.858813 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.67842 | 0.326155 | ||||||||
\(709\) | 17.2665 | 0.648457 | 0.324229 | − | 0.945979i | \(-0.394895\pi\) | ||||
0.324229 | + | 0.945979i | \(0.394895\pi\) | |||||||
\(710\) | −30.1358 | −1.13098 | ||||||||
\(711\) | −7.08667 | −0.265771 | ||||||||
\(712\) | −7.52952 | −0.282181 | ||||||||
\(713\) | −43.7339 | −1.63785 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 43.0141 | 1.60864 | ||||||||
\(716\) | −3.24948 | −0.121439 | ||||||||
\(717\) | −18.8938 | −0.705601 | ||||||||
\(718\) | −24.0276 | −0.896703 | ||||||||
\(719\) | 43.2527 | 1.61305 | 0.806526 | − | 0.591198i | \(-0.201345\pi\) | ||||
0.806526 | + | 0.591198i | \(0.201345\pi\) | |||||||
\(720\) | 2.49248 | 0.0928892 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −4.05009 | −0.150625 | ||||||||
\(724\) | 12.4559 | 0.462920 | ||||||||
\(725\) | −6.68247 | −0.248181 | ||||||||
\(726\) | 0.984956 | 0.0365551 | ||||||||
\(727\) | −26.0766 | −0.967127 | −0.483564 | − | 0.875309i | \(-0.660658\pi\) | ||||
−0.483564 | + | 0.875309i | \(0.660658\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −35.9425 | −1.33029 | ||||||||
\(731\) | 21.4029 | 0.791615 | ||||||||
\(732\) | −4.37526 | −0.161714 | ||||||||
\(733\) | −8.21894 | −0.303573 | −0.151787 | − | 0.988413i | \(-0.548503\pi\) | ||||
−0.151787 | + | 0.988413i | \(0.548503\pi\) | |||||||
\(734\) | −15.8096 | −0.583544 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00404 | −0.221312 | ||||||||
\(737\) | −52.4770 | −1.93301 | ||||||||
\(738\) | −4.64383 | −0.170942 | ||||||||
\(739\) | 38.5978 | 1.41984 | 0.709921 | − | 0.704282i | \(-0.248731\pi\) | ||||
0.709921 | + | 0.704282i | \(0.248731\pi\) | |||||||
\(740\) | −22.8482 | −0.839916 | ||||||||
\(741\) | 4.98496 | 0.183127 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.51309 | −0.202256 | −0.101128 | − | 0.994873i | \(-0.532245\pi\) | ||||
−0.101128 | + | 0.994873i | \(0.532245\pi\) | |||||||
\(744\) | −7.28407 | −0.267047 | ||||||||
\(745\) | 40.6078 | 1.48776 | ||||||||
\(746\) | −30.8507 | −1.12952 | ||||||||
\(747\) | −5.59823 | −0.204829 | ||||||||
\(748\) | −7.76509 | −0.283920 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −9.44040 | −0.344714 | ||||||||
\(751\) | 19.2600 | 0.702808 | 0.351404 | − | 0.936224i | \(-0.385704\pi\) | ||||
0.351404 | + | 0.936224i | \(0.385704\pi\) | |||||||
\(752\) | 5.36021 | 0.195467 | ||||||||
\(753\) | −6.59917 | −0.240487 | ||||||||
\(754\) | −27.4749 | −1.00058 | ||||||||
\(755\) | 49.7835 | 1.81181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.556024 | −0.0202090 | −0.0101045 | − | 0.999949i | \(-0.503216\pi\) | ||||
−0.0101045 | + | 0.999949i | \(0.503216\pi\) | |||||||
\(758\) | −23.5450 | −0.855194 | ||||||||
\(759\) | 20.7856 | 0.754468 | ||||||||
\(760\) | −2.49248 | −0.0904117 | ||||||||
\(761\) | 9.17692 | 0.332663 | 0.166332 | − | 0.986070i | \(-0.446808\pi\) | ||||
0.166332 | + | 0.986070i | \(0.446808\pi\) | |||||||
\(762\) | 6.09569 | 0.220823 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16.4444 | −0.594939 | ||||||||
\(765\) | 5.59061 | 0.202129 | ||||||||
\(766\) | −4.87271 | −0.176058 | ||||||||
\(767\) | 43.2615 | 1.56208 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 10.2515 | 0.369680 | 0.184840 | − | 0.982769i | \(-0.440823\pi\) | ||||
0.184840 | + | 0.982769i | \(0.440823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.65125 | 0.0954824 | ||||||||
\(772\) | −18.6854 | −0.672501 | ||||||||
\(773\) | −25.3728 | −0.912596 | −0.456298 | − | 0.889827i | \(-0.650825\pi\) | ||||
−0.456298 | + | 0.889827i | \(0.650825\pi\) | |||||||
\(774\) | −9.54211 | −0.342984 | ||||||||
\(775\) | −8.83154 | −0.317238 | ||||||||
\(776\) | −7.00404 | −0.251430 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.2856 | 1.01409 | ||||||||
\(779\) | 4.64383 | 0.166382 | ||||||||
\(780\) | 12.4249 | 0.444882 | ||||||||
\(781\) | −41.8572 | −1.49777 | ||||||||
\(782\) | −13.4670 | −0.481580 | ||||||||
\(783\) | 5.51156 | 0.196967 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.84207 | −0.0657464 | ||||||||
\(786\) | 9.31416 | 0.332225 | ||||||||
\(787\) | 21.2886 | 0.758856 | 0.379428 | − | 0.925221i | \(-0.376121\pi\) | ||||
0.379428 | + | 0.925221i | \(0.376121\pi\) | |||||||
\(788\) | −15.4965 | −0.552041 | ||||||||
\(789\) | 1.45544 | 0.0518150 | ||||||||
\(790\) | 17.6634 | 0.628435 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.46193 | 0.123014 | ||||||||
\(793\) | −21.8105 | −0.774512 | ||||||||
\(794\) | −2.65125 | −0.0940893 | ||||||||
\(795\) | 14.6414 | 0.519276 | ||||||||
\(796\) | −1.45948 | −0.0517299 | ||||||||
\(797\) | 41.1949 | 1.45920 | 0.729600 | − | 0.683874i | \(-0.239706\pi\) | ||||
0.729600 | + | 0.683874i | \(0.239706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0229 | 0.425341 | ||||||||
\(800\) | −1.21245 | −0.0428664 | ||||||||
\(801\) | 7.52952 | 0.266042 | ||||||||
\(802\) | 7.45292 | 0.263172 | ||||||||
\(803\) | −49.9223 | −1.76172 | ||||||||
\(804\) | −15.1583 | −0.534592 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.3108 | −1.27899 | ||||||||
\(807\) | −14.3232 | −0.504200 | ||||||||
\(808\) | −7.09569 | −0.249625 | ||||||||
\(809\) | −18.3968 | −0.646797 | −0.323398 | − | 0.946263i | \(-0.604825\pi\) | ||||
−0.323398 | + | 0.946263i | \(0.604825\pi\) | |||||||
\(810\) | −2.49248 | −0.0875767 | ||||||||
\(811\) | −18.8662 | −0.662482 | −0.331241 | − | 0.943546i | \(-0.607467\pi\) | ||||
−0.331241 | + | 0.943546i | \(0.607467\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.6658 | −0.724782 | ||||||||
\(814\) | −31.7350 | −1.11231 | ||||||||
\(815\) | −14.4516 | −0.506217 | ||||||||
\(816\) | −2.24299 | −0.0785205 | ||||||||
\(817\) | 9.54211 | 0.333836 | ||||||||
\(818\) | −17.4037 | −0.608508 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.5746 | 0.404204 | ||||||||
\(821\) | 16.6517 | 0.581149 | 0.290574 | − | 0.956852i | \(-0.406154\pi\) | ||||
0.290574 | + | 0.956852i | \(0.406154\pi\) | |||||||
\(822\) | −7.78510 | −0.271537 | ||||||||
\(823\) | −35.3894 | −1.23360 | −0.616798 | − | 0.787122i | \(-0.711570\pi\) | ||||
−0.616798 | + | 0.787122i | \(0.711570\pi\) | |||||||
\(824\) | −7.15135 | −0.249129 | ||||||||
\(825\) | 4.19740 | 0.146135 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.71432 | −0.0943862 | −0.0471931 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471931 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(828\) | 6.00404 | 0.208655 | ||||||||
\(829\) | 12.5291 | 0.435152 | 0.217576 | − | 0.976043i | \(-0.430185\pi\) | ||||
0.217576 | + | 0.976043i | \(0.430185\pi\) | |||||||
\(830\) | 13.9535 | 0.484332 | ||||||||
\(831\) | 28.5421 | 0.990114 | ||||||||
\(832\) | −4.98496 | −0.172822 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 12.5882 | 0.435892 | ||||||||
\(835\) | 42.6357 | 1.47547 | ||||||||
\(836\) | −3.46193 | −0.119733 | ||||||||
\(837\) | 7.28407 | 0.251774 | ||||||||
\(838\) | 3.76105 | 0.129923 | ||||||||
\(839\) | 5.50546 | 0.190070 | 0.0950348 | − | 0.995474i | \(-0.469704\pi\) | ||||
0.0950348 | + | 0.995474i | \(0.469704\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.37732 | 0.0474939 | ||||||||
\(842\) | −31.6343 | −1.09019 | ||||||||
\(843\) | 13.6443 | 0.469934 | ||||||||
\(844\) | −23.3953 | −0.805298 | ||||||||
\(845\) | 29.5353 | 1.01605 | ||||||||
\(846\) | −5.36021 | −0.184288 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.87423 | −0.201722 | ||||||||
\(849\) | 1.53403 | 0.0526478 | ||||||||
\(850\) | −2.71951 | −0.0932784 | ||||||||
\(851\) | −55.0382 | −1.88668 | ||||||||
\(852\) | −12.0907 | −0.414221 | ||||||||
\(853\) | −47.3276 | −1.62047 | −0.810233 | − | 0.586108i | \(-0.800660\pi\) | ||||
−0.810233 | + | 0.586108i | \(0.800660\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.49248 | 0.0852409 | ||||||||
\(856\) | 15.7305 | 0.537657 | ||||||||
\(857\) | 54.1773 | 1.85066 | 0.925331 | − | 0.379161i | \(-0.123787\pi\) | ||||
0.925331 | + | 0.379161i | \(0.123787\pi\) | |||||||
\(858\) | 17.2576 | 0.589164 | ||||||||
\(859\) | −51.7842 | −1.76685 | −0.883426 | − | 0.468570i | \(-0.844769\pi\) | ||||
−0.883426 | + | 0.468570i | \(0.844769\pi\) | |||||||
\(860\) | 23.7835 | 0.811011 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.66582 | 0.0567381 | ||||||||
\(863\) | −26.6679 | −0.907785 | −0.453893 | − | 0.891056i | \(-0.649965\pi\) | ||||
−0.453893 | + | 0.891056i | \(0.649965\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −6.44087 | −0.218996 | ||||||||
\(866\) | −16.1062 | −0.547311 | ||||||||
\(867\) | 11.9690 | 0.406488 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.5336 | 0.832244 | ||||||||
\(870\) | −13.7374 | −0.465743 | ||||||||
\(871\) | −75.5634 | −2.56037 | ||||||||
\(872\) | −8.31707 | −0.281652 | ||||||||
\(873\) | 7.00404 | 0.237051 | ||||||||
\(874\) | −6.00404 | −0.203090 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.4204 | −0.487219 | ||||||||
\(877\) | −11.7318 | −0.396155 | −0.198078 | − | 0.980186i | \(-0.563470\pi\) | ||||
−0.198078 | + | 0.980186i | \(0.563470\pi\) | |||||||
\(878\) | −21.0867 | −0.711641 | ||||||||
\(879\) | 33.3773 | 1.12579 | ||||||||
\(880\) | −8.62878 | −0.290876 | ||||||||
\(881\) | −11.8406 | −0.398918 | −0.199459 | − | 0.979906i | \(-0.563919\pi\) | ||||
−0.199459 | + | 0.979906i | \(0.563919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.5167 | 1.19523 | 0.597616 | − | 0.801782i | \(-0.296115\pi\) | ||||
0.597616 | + | 0.801782i | \(0.296115\pi\) | |||||||
\(884\) | −11.1812 | −0.376065 | ||||||||
\(885\) | 21.6308 | 0.727110 | ||||||||
\(886\) | 18.5958 | 0.624738 | ||||||||
\(887\) | −38.9544 | −1.30796 | −0.653980 | − | 0.756512i | \(-0.726902\pi\) | ||||
−0.653980 | + | 0.756512i | \(0.726902\pi\) | |||||||
\(888\) | −9.16685 | −0.307619 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −18.7672 | −0.629076 | ||||||||
\(891\) | −3.46193 | −0.115979 | ||||||||
\(892\) | 14.8221 | 0.496282 | ||||||||
\(893\) | 5.36021 | 0.179373 | ||||||||
\(894\) | 16.2922 | 0.544891 | ||||||||
\(895\) | −8.09927 | −0.270729 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.9299 | 0.999329 | ||||||||
\(898\) | −19.7410 | −0.658767 | ||||||||
\(899\) | 40.1466 | 1.33896 | ||||||||
\(900\) | 1.21245 | 0.0404149 | ||||||||
\(901\) | −13.1759 | −0.438951 | ||||||||
\(902\) | 16.0766 | 0.535292 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.3643 | −0.444488 | ||||||||
\(905\) | 31.0461 | 1.03201 | ||||||||
\(906\) | 19.9735 | 0.663575 | ||||||||
\(907\) | 55.1428 | 1.83099 | 0.915493 | − | 0.402333i | \(-0.131801\pi\) | ||||
0.915493 | + | 0.402333i | \(0.131801\pi\) | |||||||
\(908\) | 16.2295 | 0.538594 | ||||||||
\(909\) | 7.09569 | 0.235349 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.9618 | 0.396313 | 0.198157 | − | 0.980170i | \(-0.436505\pi\) | ||||
0.198157 | + | 0.980170i | \(0.436505\pi\) | |||||||
\(912\) | −1.00000 | −0.0331133 | ||||||||
\(913\) | 19.3807 | 0.641407 | ||||||||
\(914\) | −0.468893 | −0.0155096 | ||||||||
\(915\) | −10.9052 | −0.360516 | ||||||||
\(916\) | −6.39480 | −0.211290 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.24299 | 0.0740298 | ||||||||
\(919\) | 36.9365 | 1.21842 | 0.609211 | − | 0.793008i | \(-0.291486\pi\) | ||||
0.609211 | + | 0.793008i | \(0.291486\pi\) | |||||||
\(920\) | −14.9649 | −0.493379 | ||||||||
\(921\) | −9.52952 | −0.314008 | ||||||||
\(922\) | 19.0556 | 0.627564 | ||||||||
\(923\) | −60.2717 | −1.98387 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.1143 | −0.365436 | ||||||||
\(926\) | 9.65575 | 0.317308 | ||||||||
\(927\) | 7.15135 | 0.234881 | ||||||||
\(928\) | 5.51156 | 0.180926 | ||||||||
\(929\) | −24.2806 | −0.796620 | −0.398310 | − | 0.917251i | \(-0.630403\pi\) | ||||
−0.398310 | + | 0.917251i | \(0.630403\pi\) | |||||||
\(930\) | −18.1554 | −0.595339 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −21.3798 | −0.700317 | ||||||||
\(933\) | −16.4404 | −0.538234 | ||||||||
\(934\) | 9.16281 | 0.299816 | ||||||||
\(935\) | −19.3543 | −0.632954 | ||||||||
\(936\) | 4.98496 | 0.162938 | ||||||||
\(937\) | −24.5823 | −0.803068 | −0.401534 | − | 0.915844i | \(-0.631523\pi\) | ||||
−0.401534 | + | 0.915844i | \(0.631523\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.9940 | −0.358775 | ||||||||
\(940\) | 13.3602 | 0.435762 | ||||||||
\(941\) | −7.35723 | −0.239839 | −0.119919 | − | 0.992784i | \(-0.538264\pi\) | ||||
−0.119919 | + | 0.992784i | \(0.538264\pi\) | |||||||
\(942\) | −0.739053 | −0.0240796 | ||||||||
\(943\) | 27.8817 | 0.907954 | ||||||||
\(944\) | −8.67842 | −0.282458 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 33.0341 | 1.07403 | ||||||||
\(947\) | −29.0462 | −0.943876 | −0.471938 | − | 0.881632i | \(-0.656445\pi\) | ||||
−0.471938 | + | 0.881632i | \(0.656445\pi\) | |||||||
\(948\) | 7.08667 | 0.230164 | ||||||||
\(949\) | −71.8849 | −2.33348 | ||||||||
\(950\) | −1.21245 | −0.0393369 | ||||||||
\(951\) | −6.66291 | −0.216060 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.84772 | −0.189426 | −0.0947131 | − | 0.995505i | \(-0.530193\pi\) | ||||
−0.0947131 | + | 0.995505i | \(0.530193\pi\) | |||||||
\(954\) | 5.87423 | 0.190185 | ||||||||
\(955\) | −40.9874 | −1.32632 | ||||||||
\(956\) | 18.8938 | 0.611068 | ||||||||
\(957\) | −19.0806 | −0.616790 | ||||||||
\(958\) | −42.8212 | −1.38349 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.49248 | −0.0804444 | ||||||||
\(961\) | 22.0577 | 0.711539 | ||||||||
\(962\) | −45.6964 | −1.47331 | ||||||||
\(963\) | −15.7305 | −0.506908 | ||||||||
\(964\) | 4.05009 | 0.130445 | ||||||||
\(965\) | −46.5729 | −1.49923 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.7775 | 0.378738 | 0.189369 | − | 0.981906i | \(-0.439356\pi\) | ||||
0.189369 | + | 0.981906i | \(0.439356\pi\) | |||||||
\(968\) | −0.984956 | −0.0316577 | ||||||||
\(969\) | −2.24299 | −0.0720553 | ||||||||
\(970\) | −17.4574 | −0.560524 | ||||||||
\(971\) | −33.4810 | −1.07446 | −0.537228 | − | 0.843437i | \(-0.680529\pi\) | ||||
−0.537228 | + | 0.843437i | \(0.680529\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 26.3153 | 0.843196 | ||||||||
\(975\) | 6.04399 | 0.193563 | ||||||||
\(976\) | 4.37526 | 0.140049 | ||||||||
\(977\) | −17.3969 | −0.556575 | −0.278288 | − | 0.960498i | \(-0.589767\pi\) | ||||
−0.278288 | + | 0.960498i | \(0.589767\pi\) | |||||||
\(978\) | −5.79808 | −0.185402 | ||||||||
\(979\) | −26.0667 | −0.833094 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.31707 | 0.265544 | ||||||||
\(982\) | 14.2064 | 0.453345 | ||||||||
\(983\) | 13.9218 | 0.444036 | 0.222018 | − | 0.975043i | \(-0.428736\pi\) | ||||
0.222018 | + | 0.975043i | \(0.428736\pi\) | |||||||
\(984\) | 4.64383 | 0.148040 | ||||||||
\(985\) | −38.6247 | −1.23069 | ||||||||
\(986\) | 12.3624 | 0.393699 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.98496 | −0.158593 | ||||||||
\(989\) | 57.2912 | 1.82175 | ||||||||
\(990\) | 8.62878 | 0.274241 | ||||||||
\(991\) | −39.9694 | −1.26967 | −0.634834 | − | 0.772648i | \(-0.718932\pi\) | ||||
−0.634834 | + | 0.772648i | \(0.718932\pi\) | |||||||
\(992\) | 7.28407 | 0.231270 | ||||||||
\(993\) | −25.8102 | −0.819062 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.63772 | −0.115324 | ||||||||
\(996\) | 5.59823 | 0.177387 | ||||||||
\(997\) | 35.3277 | 1.11884 | 0.559419 | − | 0.828885i | \(-0.311024\pi\) | ||||
0.559419 | + | 0.828885i | \(0.311024\pi\) | |||||||
\(998\) | −34.0325 | −1.07728 | ||||||||
\(999\) | 9.16685 | 0.290026 |
(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 | 5586.2.a.bw.1.4 | 4 | ||
7.2 | even | 3 | 798.2.j.l.571.1 | yes | 8 | ||
7.4 | even | 3 | 798.2.j.l.457.1 | ✓ | 8 | ||
7.6 | odd | 2 | 5586.2.a.bz.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.j.l.457.1 | ✓ | 8 | 7.4 | even | 3 | ||
798.2.j.l.571.1 | yes | 8 | 7.2 | even | 3 | ||
5586.2.a.bw.1.4 | 4 | 1.1 | even | 1 | trivial | ||
5586.2.a.bz.1.1 | 4 | 7.6 | odd | 2 |