Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, 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("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.78585 | −0.798654 | −0.399327 | − | 0.916809i | \(-0.630756\pi\) | ||||
−0.399327 | + | 0.916809i | \(0.630756\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.07926 | −0.785885 | −0.392942 | − | 0.919563i | \(-0.628543\pi\) | ||||
−0.392942 | + | 0.919563i | \(0.628543\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.20363 | 0.664419 | 0.332209 | − | 0.943206i | \(-0.392206\pi\) | ||||
0.332209 | + | 0.943206i | \(0.392206\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.61519 | −1.83472 | −0.917362 | − | 0.398055i | \(-0.869685\pi\) | ||||
−0.917362 | + | 0.398055i | \(0.869685\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.78585 | 0.461103 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.93993 | −1.68318 | −0.841590 | − | 0.540117i | \(-0.818380\pi\) | ||||
−0.841590 | + | 0.540117i | \(0.818380\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.40790 | −0.781827 | −0.390913 | − | 0.920427i | \(-0.627841\pi\) | ||||
−0.390913 | + | 0.920427i | \(0.627841\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.07926 | 0.453731 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.31931 | 0.483609 | 0.241804 | − | 0.970325i | \(-0.422261\pi\) | ||||
0.241804 | + | 0.970325i | \(0.422261\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.81076 | −0.362151 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.77508 | −0.329624 | −0.164812 | − | 0.986325i | \(-0.552702\pi\) | ||||
−0.164812 | + | 0.986325i | \(0.552702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.22504 | 0.938444 | 0.469222 | − | 0.883080i | \(-0.344534\pi\) | ||||
0.469222 | + | 0.883080i | \(0.344534\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.20363 | −0.383602 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.71323 | 0.627650 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.8349 | −1.78125 | −0.890625 | − | 0.454739i | \(-0.849732\pi\) | ||||
−0.890625 | + | 0.454739i | \(0.849732\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.61519 | 1.05928 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.10677 | 0.485197 | 0.242598 | − | 0.970127i | \(-0.422000\pi\) | ||||
0.242598 | + | 0.970127i | \(0.422000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.95587 | −0.603264 | −0.301632 | − | 0.953424i | \(-0.597531\pi\) | ||||
−0.301632 | + | 0.953424i | \(0.597531\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.78585 | −0.266218 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.71070 | 0.978857 | 0.489428 | − | 0.872044i | \(-0.337205\pi\) | ||||
0.489428 | + | 0.872044i | \(0.337205\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.67669 | −0.382385 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.93993 | 0.971784 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.33131 | −1.28175 | −0.640877 | − | 0.767644i | \(-0.721429\pi\) | ||||
−0.640877 | + | 0.767644i | \(0.721429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.93534 | −0.530641 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.40790 | 0.451388 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.55552 | −1.11383 | −0.556917 | − | 0.830568i | \(-0.688016\pi\) | ||||
−0.556917 | + | 0.830568i | \(0.688016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.78763 | 1.12514 | 0.562571 | − | 0.826749i | \(-0.309812\pi\) | ||||
0.562571 | + | 0.826749i | \(0.309812\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.07926 | −0.261962 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.8137 | 1.46531 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.71231 | −1.06438 | −0.532189 | − | 0.846626i | \(-0.678630\pi\) | ||||
−0.532189 | + | 0.846626i | \(0.678630\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.31931 | −0.279212 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1955 | −1.20998 | −0.604989 | − | 0.796234i | \(-0.706823\pi\) | ||||
−0.604989 | + | 0.796234i | \(0.706823\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.60865 | −1.12461 | −0.562304 | − | 0.826931i | \(-0.690085\pi\) | ||||
−0.562304 | + | 0.826931i | \(0.690085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.81076 | 0.209088 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.58191 | −0.522157 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9198 | 1.45359 | 0.726794 | − | 0.686855i | \(-0.241009\pi\) | ||||
0.726794 | + | 0.686855i | \(0.241009\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.56790 | 0.391628 | 0.195814 | − | 0.980641i | \(-0.437265\pi\) | ||||
0.195814 | + | 0.980641i | \(0.437265\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.3936 | 1.34428 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.77508 | 0.190309 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.0077 | 1.16682 | 0.583408 | − | 0.812179i | \(-0.301719\pi\) | ||||
0.583408 | + | 0.812179i | \(0.301719\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.7547 | 1.44188 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.22504 | −0.541811 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.08599 | 0.624409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1768 | 1.33790 | 0.668950 | − | 0.743308i | \(-0.266744\pi\) | ||||
0.668950 | + | 0.743308i | \(0.266744\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.20363 | 0.221473 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.21326 | 0.120723 | 0.0603617 | − | 0.998177i | \(-0.480775\pi\) | ||||
0.0603617 | + | 0.998177i | \(0.480775\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8674 | 1.56346 | 0.781728 | − | 0.623619i | \(-0.214338\pi\) | ||||
0.781728 | + | 0.623619i | \(0.214338\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.71323 | −0.362374 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.6627 | −1.70751 | −0.853757 | − | 0.520671i | \(-0.825682\pi\) | ||||
−0.853757 | + | 0.520671i | \(0.825682\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.2491 | −1.46060 | −0.730301 | − | 0.683126i | \(-0.760620\pi\) | ||||
−0.730301 | + | 0.683126i | \(0.760620\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.8349 | 1.02840 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.21830 | 0.490896 | 0.245448 | − | 0.969410i | \(-0.421065\pi\) | ||||
0.245448 | + | 0.969410i | \(0.421065\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.14192 | −0.386236 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.61519 | −0.611574 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.4299 | 1.32279 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.14402 | −0.558547 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.10677 | −0.280128 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1630 | 1.08789 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.3938 | −1.27724 | −0.638620 | − | 0.769522i | \(-0.720495\pi\) | ||||
−0.638620 | + | 0.769522i | \(0.720495\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.95587 | 0.348295 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5082 | −0.918110 | −0.459055 | − | 0.888408i | \(-0.651812\pi\) | ||||
−0.459055 | + | 0.888408i | \(0.651812\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.08591 | 0.614426 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.78585 | 0.153701 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.5382 | −0.985771 | −0.492886 | − | 0.870094i | \(-0.664058\pi\) | ||||
−0.492886 | + | 0.870094i | \(0.664058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.2200 | 1.29094 | 0.645472 | − | 0.763784i | \(-0.276661\pi\) | ||||
0.645472 | + | 0.763784i | \(0.276661\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.71070 | −0.565143 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.5774 | −1.21902 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.17002 | 0.263256 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.67669 | 0.220770 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.0350 | 0.985945 | 0.492973 | − | 0.870045i | \(-0.335910\pi\) | ||||
0.492973 | + | 0.870045i | \(0.335910\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.9197 | −1.29553 | −0.647763 | − | 0.761842i | \(-0.724295\pi\) | ||||
−0.647763 | + | 0.761842i | \(0.724295\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.93993 | −0.561060 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.33110 | −0.749492 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.08167 | −0.0863263 | −0.0431632 | − | 0.999068i | \(-0.513744\pi\) | ||||
−0.0431632 | + | 0.999068i | \(0.513744\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.33131 | 0.740021 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.82243 | −0.380061 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.26307 | 0.412235 | 0.206118 | − | 0.978527i | \(-0.433917\pi\) | ||||
0.206118 | + | 0.978527i | \(0.433917\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.93534 | 0.306366 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.0357 | −1.55041 | −0.775206 | − | 0.631708i | \(-0.782354\pi\) | ||||
−0.775206 | + | 0.631708i | \(0.782354\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.7607 | 2.36621 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.40790 | −0.260609 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.63384 | 0.352305 | 0.176152 | − | 0.984363i | \(-0.443635\pi\) | ||||
0.176152 | + | 0.984363i | \(0.443635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.76503 | 0.284609 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.55552 | 0.643072 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.0524 | 1.42404 | 0.712021 | − | 0.702158i | \(-0.247780\pi\) | ||||
0.712021 | + | 0.702158i | \(0.247780\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.45601 | 0.702860 | 0.351430 | − | 0.936214i | \(-0.385696\pi\) | ||||
0.351430 | + | 0.936214i | \(0.385696\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.78763 | −0.649600 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.3495 | 1.42260 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.2930 | −1.11834 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.07926 | 0.151244 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.54585 | −0.545999 | −0.272999 | − | 0.962014i | \(-0.588016\pi\) | ||||
−0.272999 | + | 0.962014i | \(0.588016\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.5660 | 0.832541 | 0.416271 | − | 0.909241i | \(-0.363337\pi\) | ||||
0.416271 | + | 0.909241i | \(0.363337\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.8137 | −0.845997 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.50436 | −0.605910 | −0.302955 | − | 0.953005i | \(-0.597973\pi\) | ||||
−0.302955 | + | 0.953005i | \(0.597973\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.92204 | 0.419802 | 0.209901 | − | 0.977723i | \(-0.432686\pi\) | ||||
0.209901 | + | 0.977723i | \(0.432686\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.71231 | 0.614519 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.69085 | 0.259047 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.54822 | −0.387504 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.31931 | 0.161203 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.50975 | −0.519461 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.66403 | −0.183399 | −0.0916996 | − | 0.995787i | \(-0.529230\pi\) | ||||
−0.0916996 | + | 0.995787i | \(0.529230\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.1955 | 0.698581 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.06457 | 0.481800 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.8642 | −0.737509 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.60865 | 0.649292 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 45.9089 | 3.08817 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.6207 | 0.778178 | 0.389089 | − | 0.921200i | \(-0.372790\pi\) | ||||
0.389089 | + | 0.921200i | \(0.372790\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.81076 | −0.120717 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.73829 | −0.380864 | −0.190432 | − | 0.981700i | \(-0.560989\pi\) | ||||
−0.190432 | + | 0.981700i | \(0.560989\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.94839 | −0.194835 | −0.0974177 | − | 0.995244i | \(-0.531058\pi\) | ||||
−0.0974177 | + | 0.995244i | \(0.531058\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.58191 | 0.301467 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0655 | 1.05249 | 0.526243 | − | 0.850334i | \(-0.323600\pi\) | ||||
0.526243 | + | 0.850334i | \(0.323600\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.9843 | −0.781768 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.9198 | −0.839229 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.3794 | −1.12418 | −0.562091 | − | 0.827076i | \(-0.690003\pi\) | ||||
−0.562091 | + | 0.827076i | \(0.690003\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3416 | −1.31031 | −0.655157 | − | 0.755493i | \(-0.727398\pi\) | ||||
−0.655157 | + | 0.755493i | \(0.727398\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.78016 | 0.305393 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.5439 | 1.43444 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.56790 | −0.226107 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.3382 | −1.47310 | −0.736548 | − | 0.676386i | \(-0.763545\pi\) | ||||
−0.736548 | + | 0.676386i | \(0.763545\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.11089 | 0.321319 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.3936 | −0.776119 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.27427 | 0.141865 | 0.0709326 | − | 0.997481i | \(-0.477402\pi\) | ||||
0.0709326 | + | 0.997481i | \(0.477402\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.5286 | 1.39986 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.77508 | −0.109875 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.3925 | 0.887477 | 0.443738 | − | 0.896156i | \(-0.353652\pi\) | ||||
0.443738 | + | 0.896156i | \(0.353652\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.6643 | 1.02368 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.0077 | −0.673661 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.1315 | 0.739673 | 0.369837 | − | 0.929097i | \(-0.379414\pi\) | ||||
0.369837 | + | 0.929097i | \(0.379414\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.5739 | −1.61425 | −0.807126 | − | 0.590380i | \(-0.798978\pi\) | ||||
−0.807126 | + | 0.590380i | \(0.798978\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.7547 | −0.832471 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.99023 | −0.240620 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.6649 | 1.00130 | 0.500649 | − | 0.865650i | \(-0.333095\pi\) | ||||
0.500649 | + | 0.865650i | \(0.333095\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.22504 | 0.312815 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0299 | 1.07558 | 0.537788 | − | 0.843080i | \(-0.319260\pi\) | ||||
0.537788 | + | 0.843080i | \(0.319260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.0846 | 1.31280 | 0.656398 | − | 0.754415i | \(-0.272079\pi\) | ||||
0.656398 | + | 0.754415i | \(0.272079\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.08599 | −0.360503 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.45978 | −0.381309 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.1626 | 1.83309 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.1768 | −0.772436 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.24011 | 0.130869 | 0.0654344 | − | 0.997857i | \(-0.479157\pi\) | ||||
0.0654344 | + | 0.997857i | \(0.479157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.2788 | 0.889568 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.20363 | −0.127867 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.3427 | −0.887288 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.22526 | 0.474096 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.21326 | −0.0696997 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.6934 | −0.898599 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.0330 | 1.20041 | 0.600207 | − | 0.799845i | \(-0.295085\pi\) | ||||
0.600207 | + | 0.799845i | \(0.295085\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.8674 | −0.902662 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.7129 | 1.34464 | 0.672319 | − | 0.740262i | \(-0.265298\pi\) | ||||
0.672319 | + | 0.740262i | \(0.265298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.7181 | 0.944963 | 0.472482 | − | 0.881341i | \(-0.343358\pi\) | ||||
0.472482 | + | 0.881341i | \(0.343358\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.71323 | 0.209217 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.17881 | −0.459368 | −0.229684 | − | 0.973265i | \(-0.573769\pi\) | ||||
−0.229684 | + | 0.973265i | \(0.573769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.91162 | −0.219008 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.6627 | 0.985834 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.6506 | 1.31595 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.9785 | 0.664447 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.2491 | 0.843279 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.9533 | −0.769269 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.5580 | 1.34983 | 0.674915 | − | 0.737895i | \(-0.264180\pi\) | ||||
0.674915 | + | 0.737895i | \(0.264180\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.8349 | −0.593750 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.5588 | 0.850070 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.14991 | −0.443954 | −0.221977 | − | 0.975052i | \(-0.571251\pi\) | ||||
−0.221977 | + | 0.975052i | \(0.571251\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.21830 | −0.283419 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.5140 | 0.623520 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1203 | 1.08640 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.14192 | 0.222994 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.4526 | −0.936903 | −0.468451 | − | 0.883489i | \(-0.655188\pi\) | ||||
−0.468451 | + | 0.883489i | \(0.655188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.2331 | 1.51129 | 0.755643 | − | 0.654984i | \(-0.227325\pi\) | ||||
0.755643 | + | 0.654984i | \(0.227325\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.61519 | 0.353093 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.5433 | −1.73211 | −0.866053 | − | 0.499953i | \(-0.833351\pi\) | ||||
−0.866053 | + | 0.499953i | \(0.833351\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.2075 | 0.966354 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.4299 | −0.763710 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.1755 | 0.537042 | 0.268521 | − | 0.963274i | \(-0.413465\pi\) | ||||
0.268521 | + | 0.963274i | \(0.413465\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.38619 | −0.388747 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.14402 | 0.322478 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.1596 | 0.898173 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.6754 | 1.65344 | 0.826721 | − | 0.562612i | \(-0.190204\pi\) | ||||
0.826721 | + | 0.562612i | \(0.190204\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.10677 | 0.161732 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.4022 | 1.00731 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.9400 | 0.670009 | 0.335004 | − | 0.942217i | \(-0.391262\pi\) | ||||
0.335004 | + | 0.942217i | \(0.391262\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1630 | −0.628092 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.7425 | 0.604769 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.8771 | 1.27785 | 0.638926 | − | 0.769269i | \(-0.279379\pi\) | ||||
0.638926 | + | 0.769269i | \(0.279379\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.3938 | 0.737415 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.0011 | −1.58408 | −0.792042 | − | 0.610467i | \(-0.790982\pi\) | ||||
−0.792042 | + | 0.610467i | \(0.790982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.18258 | 0.417023 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.95587 | −0.201088 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.84548 | −0.245676 | −0.122838 | − | 0.992427i | \(-0.539199\pi\) | ||||
−0.122838 | + | 0.992427i | \(0.539199\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0958 | −0.814000 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.5082 | 0.530071 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.0727 | −1.16091 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.9252 | 1.20077 | 0.600387 | − | 0.799710i | \(-0.295013\pi\) | ||||
0.600387 | + | 0.799710i | \(0.295013\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.08591 | −0.354739 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.03354 | −0.0516125 | −0.0258062 | − | 0.999667i | \(-0.508215\pi\) | ||||
−0.0258062 | + | 0.999667i | \(0.508215\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.5646 | −1.72179 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.78585 | −0.0887394 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.8761 | −1.18350 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.6327 | −0.921328 | −0.460664 | − | 0.887575i | \(-0.652389\pi\) | ||||
−0.460664 | + | 0.887575i | \(0.652389\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.5382 | 0.569135 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.7891 | 0.875345 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.37172 | −0.312775 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.2200 | −0.745327 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.19130 | −0.400171 | −0.200086 | − | 0.979778i | \(-0.564122\pi\) | ||||
−0.200086 | + | 0.979778i | \(0.564122\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.27517 | −0.208359 | −0.104180 | − | 0.994559i | \(-0.533222\pi\) | ||||
−0.104180 | + | 0.994559i | \(0.533222\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.71070 | 0.326286 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.5665 | 0.609566 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.2717 | −0.884231 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.5774 | 0.703804 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.0027 | 1.39701 | 0.698506 | − | 0.715604i | \(-0.253848\pi\) | ||||
0.698506 | + | 0.715604i | \(0.253848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.842181 | −0.0404727 | −0.0202363 | − | 0.999795i | \(-0.506442\pi\) | ||||
−0.0202363 | + | 0.999795i | \(0.506442\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.17002 | −0.151991 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.90398 | −0.378098 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.92802 | −0.378384 | −0.189192 | − | 0.981940i | \(-0.560587\pi\) | ||||
−0.189192 | + | 0.981940i | \(0.560587\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.67669 | −0.127462 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.3090 | −0.774862 | −0.387431 | − | 0.921899i | \(-0.626637\pi\) | ||||
−0.387431 | + | 0.921899i | \(0.626637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.6581 | −0.931882 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.0350 | −0.569236 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7992 | 0.604031 | 0.302015 | − | 0.953303i | \(-0.402341\pi\) | ||||
0.302015 | + | 0.953303i | \(0.402341\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.84617 | 0.322374 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.9197 | 0.747972 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24.5637 | −1.15156 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.1398 | 0.521097 | 0.260548 | − | 0.965461i | \(-0.416097\pi\) | ||||
0.260548 | + | 0.965461i | \(0.416097\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.93993 | 0.323928 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.5693 | −0.771710 | −0.385855 | − | 0.922559i | \(-0.626094\pi\) | ||||
−0.385855 | + | 0.922559i | \(0.626094\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.4349 | −1.41443 | −0.707215 | − | 0.706999i | \(-0.750049\pi\) | ||||
−0.707215 | + | 0.706999i | \(0.750049\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.33110 | 0.432720 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.7129 | 0.773379 | 0.386689 | − | 0.922210i | \(-0.373619\pi\) | ||||
0.386689 | + | 0.922210i | \(0.373619\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.1151 | 0.836478 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.08167 | 0.0498405 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.71726 | −0.400820 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.17089 | 0.283140 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.33131 | −0.427251 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.3321 | 0.472084 | 0.236042 | − | 0.971743i | \(-0.424150\pi\) | ||||
0.236042 | + | 0.971743i | \(0.424150\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 71.6750 | 3.26810 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.82243 | 0.219428 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.5317 | −1.06852 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.3555 | 1.23959 | 0.619797 | − | 0.784762i | \(-0.287215\pi\) | ||||
0.619797 | + | 0.784762i | \(0.287215\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.26307 | −0.238004 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.46231 | 0.0659933 | 0.0329967 | − | 0.999455i | \(-0.489495\pi\) | ||||
0.0329967 | + | 0.999455i | \(0.489495\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.3189 | 0.554816 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.93534 | −0.176880 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.1990 | 0.950904 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.0351 | −0.449231 | −0.224616 | − | 0.974447i | \(-0.572113\pi\) | ||||
−0.224616 | + | 0.974447i | \(0.572113\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.0357 | 0.895131 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.16669 | −0.0964163 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −30.7607 | −1.36613 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.9267 | 0.661616 | 0.330808 | − | 0.943698i | \(-0.392679\pi\) | ||||
0.330808 | + | 0.943698i | \(0.392679\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.9788 | 0.883812 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.40790 | 0.150463 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28.3366 | −1.24866 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.7879 | 0.650371 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.63384 | −0.203403 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.4560 | 0.501896 | 0.250948 | − | 0.968001i | \(-0.419258\pi\) | ||||
0.250948 | + | 0.968001i | \(0.419258\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.2698 | −1.36733 | −0.683667 | − | 0.729794i | \(-0.739616\pi\) | ||||
−0.683667 | + | 0.729794i | \(0.739616\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.76503 | −0.164319 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.2614 | −1.57957 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.6208 | −0.766122 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.55552 | −0.371278 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.5519 | −0.890201 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.5428 | 1.36371 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.0524 | −0.822171 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.89844 | −0.254064 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.0403 | −1.11956 | −0.559780 | − | 0.828641i | \(-0.689114\pi\) | ||||
−0.559780 | + | 0.828641i | \(0.689114\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.45601 | −0.405796 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.2326 | 1.16652 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.18501 | 0.136181 | 0.0680907 | − | 0.997679i | \(-0.478309\pi\) | ||||
0.0680907 | + | 0.997679i | \(0.478309\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.78763 | 0.375047 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.04930 | 0.257709 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.8635 | −1.14235 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.3495 | −0.821340 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.3455 | −1.83661 | −0.918304 | − | 0.395876i | \(-0.870441\pi\) | ||||
−0.918304 | + | 0.395876i | \(0.870441\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.1688 | 1.10682 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.2930 | 0.645672 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.97360 | −0.251757 | −0.125879 | − | 0.992046i | \(-0.540175\pi\) | ||||
−0.125879 | + | 0.992046i | \(0.540175\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.31907 | −0.392056 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.07926 | −0.0873205 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.9243 | −1.42218 | −0.711090 | − | 0.703101i | \(-0.751798\pi\) | ||||
−0.711090 | + | 0.703101i | \(0.751798\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.50760 | 0.314183 | 0.157092 | − | 0.987584i | \(-0.449788\pi\) | ||||
0.157092 | + | 0.987584i | \(0.449788\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.54585 | 0.315232 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.19970 | −0.175140 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.765181 | −0.0318549 | −0.0159274 | − | 0.999873i | \(-0.505070\pi\) | ||||
−0.0159274 | + | 0.999873i | \(0.505070\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.5660 | −0.480668 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.41858 | −0.307775 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.5627 | −0.851622 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.8137 | 0.488437 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.1637 | −1.24499 | −0.622494 | − | 0.782624i | \(-0.713881\pi\) | ||||
−0.622494 | + | 0.782624i | \(0.713881\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.8064 | −0.733701 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.50436 | 0.349823 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.9808 | 1.23116 | 0.615581 | − | 0.788074i | \(-0.288921\pi\) | ||||
0.615581 | + | 0.788074i | \(0.288921\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.7695 | −1.05645 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.92204 | −0.242373 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.0064 | −0.531428 | −0.265714 | − | 0.964052i | \(-0.585608\pi\) | ||||
−0.265714 | + | 0.964052i | \(0.585608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.3763 | −0.749587 | −0.374793 | − | 0.927108i | \(-0.622286\pi\) | ||||
−0.374793 | + | 0.927108i | \(0.622286\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.71231 | −0.354793 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.9723 | 0.446086 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.30961 | −0.377866 | −0.188933 | − | 0.981990i | \(-0.560503\pi\) | ||||
−0.188933 | + | 0.981990i | \(0.560503\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.69085 | −0.149561 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −44.3926 | −1.79593 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.3076 | 1.66840 | 0.834200 | − | 0.551462i | \(-0.185930\pi\) | ||||
0.834200 | + | 0.551462i | \(0.185930\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.54822 | 0.223726 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.1629 | 1.49612 | 0.748062 | − | 0.663629i | \(-0.230985\pi\) | ||||
0.748062 | + | 0.663629i | \(0.230985\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.50754 | 0.0605932 | 0.0302966 | − | 0.999541i | \(-0.490355\pi\) | ||||
0.0302966 | + | 0.999541i | \(0.490355\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.31931 | −0.0930706 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.8879 | −0.916983 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.6674 | −0.506695 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.50975 | 0.299911 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 75.1935 | 2.99816 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0906 | −1.23770 | −0.618849 | − | 0.785510i | \(-0.712401\pi\) | ||||
−0.618849 | + | 0.785510i | \(0.712401\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.66403 | 0.105886 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.7050 | 1.02007 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.7068 | 0.701570 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.1955 | −0.403326 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.14338 | −0.242649 | −0.121324 | − | 0.992613i | \(-0.538714\pi\) | ||||
−0.121324 | + | 0.992613i | \(0.538714\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.2097 | 0.954739 | 0.477369 | − | 0.878703i | \(-0.341590\pi\) | ||||
0.477369 | + | 0.878703i | \(0.341590\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.06457 | −0.278167 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.2774 | 1.38690 | 0.693449 | − | 0.720506i | \(-0.256090\pi\) | ||||
0.693449 | + | 0.720506i | \(0.256090\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.8532 | −0.740052 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.8642 | 0.425801 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.6040 | −1.47156 | −0.735780 | − | 0.677221i | \(-0.763184\pi\) | ||||
−0.735780 | + | 0.677221i | \(0.763184\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.7661 | 0.733253 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.60865 | −0.374869 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.2872 | −1.76414 | −0.882070 | − | 0.471119i | \(-0.843850\pi\) | ||||
−0.882070 | + | 0.471119i | \(0.843850\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.3602 | 1.68652 | 0.843258 | − | 0.537510i | \(-0.180635\pi\) | ||||
0.843258 | + | 0.537510i | \(0.180635\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −45.9089 | −1.78295 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.6543 | −0.490714 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.11695 | −0.159409 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.6207 | −0.449282 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.3647 | 0.747565 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.4056 | −1.32624 | −0.663119 | − | 0.748514i | \(-0.730768\pi\) | ||||
−0.663119 | + | 0.748514i | \(0.730768\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.81076 | 0.0696961 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.1246 | −0.927184 | −0.463592 | − | 0.886049i | \(-0.653440\pi\) | ||||
−0.463592 | + | 0.886049i | \(0.653440\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.3979 | −1.05143 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.73829 | 0.219892 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.6435 | −1.13428 | −0.567139 | − | 0.823622i | \(-0.691950\pi\) | ||||
−0.567139 | + | 0.823622i | \(0.691950\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.6054 | 0.787290 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.94839 | 0.112488 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 61.7284 | 2.35166 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.9279 | −1.32872 | −0.664359 | − | 0.747414i | \(-0.731295\pi\) | ||||
−0.664359 | + | 0.747414i | \(0.731295\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.58191 | −0.174052 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.1806 | −1.03102 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.5608 | −0.816673 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.0655 | −0.607653 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.2776 | 1.29465 | 0.647323 | − | 0.762216i | \(-0.275889\pi\) | ||||
0.647323 | + | 0.762216i | \(0.275889\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.9244 | 1.39263 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.9843 | 0.451354 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.52267 | −0.0948747 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.3856 | −1.06605 | −0.533023 | − | 0.846101i | \(-0.678944\pi\) | ||||
−0.533023 | + | 0.846101i | \(0.678944\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.9198 | 0.484529 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.1185 | 0.453840 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.0330 | 0.973579 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.3794 | 0.649047 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.1303 | 0.974495 | 0.487247 | − | 0.873264i | \(-0.338001\pi\) | ||||
0.487247 | + | 0.873264i | \(0.338001\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.9923 | −1.22870 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.3416 | 0.756510 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.21424 | 0.119374 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.3997 | 0.904935 | 0.452467 | − | 0.891781i | \(-0.350544\pi\) | ||||
0.452467 | + | 0.891781i | \(0.350544\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.4534 | 1.01540 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.49438 | −0.129068 | −0.0645340 | − | 0.997916i | \(-0.520556\pi\) | ||||
−0.0645340 | + | 0.997916i | \(0.520556\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.78016 | −0.176319 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.1987 | −0.707193 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.0377 | 0.700312 | 0.350156 | − | 0.936691i | \(-0.386129\pi\) | ||||
0.350156 | + | 0.936691i | \(0.386129\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.5439 | −0.828172 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.2950 | 0.854611 | 0.427306 | − | 0.904107i | \(-0.359463\pi\) | ||||
0.427306 | + | 0.904107i | \(0.359463\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.4926 | −0.787429 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.56790 | 0.130543 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.7252 | 1.34191 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.79988 | 0.248131 | 0.124066 | − | 0.992274i | \(-0.460407\pi\) | ||||
0.124066 | + | 0.992274i | \(0.460407\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.3382 | 0.850492 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.4301 | 1.03468 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.7885 | −0.501151 | −0.250576 | − | 0.968097i | \(-0.580620\pi\) | ||||
−0.250576 | + | 0.968097i | \(0.580620\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.11089 | −0.185514 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.3678 | −1.24583 | −0.622916 | − | 0.782288i | \(-0.714052\pi\) | ||||
−0.622916 | + | 0.782288i | \(0.714052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.7068 | 1.14786 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.3936 | 0.448093 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 56.5964 | 2.04358 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.34192 | −0.192635 | −0.0963173 | − | 0.995351i | \(-0.530706\pi\) | ||||
−0.0963173 | + | 0.995351i | \(0.530706\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.27427 | −0.0819059 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.7999 | −0.424413 | −0.212206 | − | 0.977225i | \(-0.568065\pi\) | ||||
−0.212206 | + | 0.977225i | \(0.568065\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.46127 | −0.339859 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.5286 | −0.808208 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.5876 | −0.379340 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.4670 | −0.803932 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.77508 | 0.0634362 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.93169 | 0.0689449 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.7088 | −0.488667 | −0.244333 | − | 0.969691i | \(-0.578569\pi\) | ||||
−0.244333 | + | 0.969691i | \(0.578569\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.3925 | −0.512385 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.8502 | −0.385788 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −58.1318 | −2.06432 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.6643 | −0.591021 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.0602 | −0.923099 | −0.461549 | − | 0.887115i | \(-0.652706\pi\) | ||||
−0.461549 | + | 0.887115i | \(0.652706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.5718 | −1.64759 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.0077 | 0.388939 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.1739 | −0.747211 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.61212 | 0.303537 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.1315 | −0.427051 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.10703 | 0.179554 | 0.0897769 | − | 0.995962i | \(-0.471385\pi\) | ||||
0.0897769 | + | 0.995962i | \(0.471385\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.93796 | 0.103166 | 0.0515829 | − | 0.998669i | \(-0.483573\pi\) | ||||
0.0515829 | + | 0.998669i | \(0.483573\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.5739 | 0.931988 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.39902 | −0.329233 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.4812 | 0.471648 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.7547 | 0.480627 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.2615 | 1.05613 | 0.528066 | − | 0.849203i | \(-0.322917\pi\) | ||||
0.528066 | + | 0.849203i | \(0.322917\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.9510 | 1.46232 | 0.731160 | − | 0.682206i | \(-0.238979\pi\) | ||||
0.731160 | + | 0.682206i | \(0.238979\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.99023 | 0.138922 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.4416 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.8232 | −0.723220 | −0.361610 | − | 0.932330i | \(-0.617773\pi\) | ||||
−0.361610 | + | 0.932330i | \(0.617773\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.6649 | −0.578100 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.5761 | 0.643622 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.7807 | 1.23824 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.22504 | −0.180604 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.3513 | 0.875225 | 0.437613 | − | 0.899164i | \(-0.355824\pi\) | ||||
0.437613 | + | 0.899164i | \(0.355824\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8491 | −0.891348 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.0299 | −0.620984 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −54.9339 | −1.88978 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.7750 | 0.438954 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.0846 | −0.757943 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.1295 | −0.861428 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.1216 | 1.20254 | 0.601271 | − | 0.799045i | \(-0.294661\pi\) | ||||
0.601271 | + | 0.799045i | \(0.294661\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.08599 | 0.208136 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −50.0517 | −1.70973 | −0.854867 | − | 0.518848i | \(-0.826361\pi\) | ||||
−0.854867 | + | 0.518848i | \(0.826361\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.8713 | −0.575641 | −0.287820 | − | 0.957684i | \(-0.592931\pi\) | ||||
−0.287820 | + | 0.957684i | \(0.592931\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.45978 | 0.220149 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.616318 | 0.0209797 | 0.0104899 | − | 0.999945i | \(-0.496661\pi\) | ||||
0.0104899 | + | 0.999945i | \(0.496661\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.27533 | −0.281370 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −31.1626 | −1.05834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.4704 | 0.965791 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 57.6336 | 1.95284 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.1768 | 0.445966 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25.2899 | −0.854955 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.27092 | 0.177986 | 0.0889931 | − | 0.996032i | \(-0.471635\pi\) | ||||
0.0889931 | + | 0.996032i | \(0.471635\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.24011 | −0.0755571 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.7534 | −0.665508 | −0.332754 | − | 0.943014i | \(-0.607978\pi\) | ||||
−0.332754 | + | 0.943014i | \(0.607978\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.3820 | −0.921478 | −0.460739 | − | 0.887536i | \(-0.652416\pi\) | ||||
−0.460739 | + | 0.887536i | \(0.652416\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.2788 | −0.513592 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.3374 | 0.750017 | 0.375008 | − | 0.927021i | \(-0.377640\pi\) | ||||
0.375008 | + | 0.927021i | \(0.377640\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.9283 | 1.00376 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.20363 | 0.0738243 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.8694 | −0.765296 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.0246 | −1.13732 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.3427 | 0.512276 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.27485 | −0.309334 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 64.7586 | 2.15742 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.22526 | −0.273720 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.8870 | −0.561342 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.2716 | −1.47002 | −0.735008 | − | 0.678059i | \(-0.762821\pi\) | ||||
−0.735008 | + | 0.678059i | \(0.762821\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.21326 | 0.0402411 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.801055 | −0.0265401 | −0.0132701 | − | 0.999912i | \(-0.504224\pi\) | ||||
−0.0132701 | + | 0.999912i | \(0.504224\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.86233 | 0.260205 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.6934 | 0.518806 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.8493 | 0.721529 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.5873 | 0.679114 | 0.339557 | − | 0.940586i | \(-0.389723\pi\) | ||||
0.339557 | + | 0.940586i | \(0.389723\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.0330 | −0.693059 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.4449 | 2.21997 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.6194 | 0.645082 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.8674 | 0.521152 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.26242 | −0.107036 | −0.0535182 | − | 0.998567i | \(-0.517044\pi\) | ||||
−0.0535182 | + | 0.998567i | \(0.517044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.12192 | 0.298959 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.7129 | −0.776327 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27.3110 | 0.893164 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.1655 | −0.462766 | −0.231383 | − | 0.972863i | \(-0.574325\pi\) | ||||
−0.231383 | + | 0.972863i | \(0.574325\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.7181 | −0.545575 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.8614 | −1.29945 | −0.649723 | − | 0.760171i | \(-0.725115\pi\) | ||||
−0.649723 | + | 0.760171i | \(0.725115\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.20556 | 0.234645 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.71323 | −0.120791 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.00969 | −0.195289 | −0.0976444 | − | 0.995221i | \(-0.531131\pi\) | ||||
−0.0976444 | + | 0.995221i | \(0.531131\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 63.5630 | 2.06334 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.17881 | 0.265216 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.59841 | 0.246137 | 0.123068 | − | 0.992398i | \(-0.460727\pi\) | ||||
0.123068 | + | 0.992398i | \(0.460727\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.4757 | 0.436064 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.91162 | 0.126445 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.9908 | 0.774703 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.69901 | −0.119323 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.6627 | −0.569172 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.6551 | −0.664913 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.25446 | −0.233288 | −0.116644 | − | 0.993174i | \(-0.537214\pi\) | ||||
−0.116644 | + | 0.993174i | \(0.537214\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.6506 | −0.759767 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.6297 | −1.56060 | −0.780301 | − | 0.625404i | \(-0.784934\pi\) | ||||
−0.780301 | + | 0.625404i | \(0.784934\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.6463 | −1.01453 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.9785 | −0.383619 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.78591 | −0.153115 | −0.0765574 | − | 0.997065i | \(-0.524393\pi\) | ||||
−0.0765574 | + | 0.997065i | \(0.524393\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.2569 | 0.775254 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.2491 | −0.486867 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.9979 | 1.65848 | 0.829238 | − | 0.558896i | \(-0.188775\pi\) | ||||
0.829238 | + | 0.558896i | \(0.188775\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.1875 | 0.483913 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.9533 | 0.444138 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.17487 | −0.291744 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.61960 | −0.273811 | −0.136905 | − | 0.990584i | \(-0.543716\pi\) | ||||
−0.136905 | + | 0.990584i | \(0.543716\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.5580 | −0.779325 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.5759 | −0.335277 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.7783 | 1.22812 | 0.614060 | − | 0.789259i | \(-0.289535\pi\) | ||||
0.614060 | + | 0.789259i | \(0.289535\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.8349 | 0.342802 |
(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 | 6036.2.a.i.1.9 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.i.1.9 | ✓ | 26 | 1.1 | even | 1 | trivial |