Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6864,2,Mod(1,6864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("6864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6864.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: | \(54.8093159474\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3432) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6864.1 |
$q$-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 | ||||||||
\(5\) | −0.732051 | −0.327383 | −0.163692 | − | 0.986512i | \(-0.552340\pi\) | ||||
−0.163692 | + | 0.986512i | \(0.552340\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410 | 1.30931 | 0.654654 | − | 0.755929i | \(-0.272814\pi\) | ||||
0.654654 | + | 0.755929i | \(0.272814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.732051 | −0.189015 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.73205 | −0.662620 | −0.331310 | − | 0.943522i | \(-0.607491\pi\) | ||||
−0.331310 | + | 0.943522i | \(0.607491\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.46410 | 0.755929 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.00000 | −1.25109 | −0.625543 | − | 0.780189i | \(-0.715123\pi\) | ||||
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.46410 | −0.892820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.73205 | −1.25011 | −0.625055 | − | 0.780581i | \(-0.714924\pi\) | ||||
−0.625055 | + | 0.780581i | \(0.714924\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.26795 | −0.946152 | −0.473076 | − | 0.881022i | \(-0.656856\pi\) | ||||
−0.473076 | + | 0.881022i | \(0.656856\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.53590 | −0.428645 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.9282 | −1.70670 | −0.853349 | − | 0.521340i | \(-0.825432\pi\) | ||||
−0.853349 | + | 0.521340i | \(0.825432\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.26795 | −0.498358 | −0.249179 | − | 0.968458i | \(-0.580161\pi\) | ||||
−0.249179 | + | 0.968458i | \(0.580161\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.732051 | −0.109128 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.46410 | 0.213561 | 0.106781 | − | 0.994283i | \(-0.465946\pi\) | ||||
0.106781 | + | 0.994283i | \(0.465946\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.73205 | −0.382564 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.732051 | 0.0987097 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.46410 | −0.711365 | −0.355683 | − | 0.934607i | \(-0.615752\pi\) | ||||
−0.355683 | + | 0.934607i | \(0.615752\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92820 | 0.630992 | 0.315496 | − | 0.948927i | \(-0.397829\pi\) | ||||
0.315496 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.46410 | 0.436436 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.732051 | −0.0907997 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.19615 | −1.00132 | −0.500660 | − | 0.865644i | \(-0.666909\pi\) | ||||
−0.500660 | + | 0.865644i | \(0.666909\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.46410 | −0.515470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.46410 | −0.394771 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.26795 | 0.367673 | 0.183837 | − | 0.982957i | \(-0.441148\pi\) | ||||
0.183837 | + | 0.982957i | \(0.441148\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.9282 | −1.19953 | −0.599763 | − | 0.800178i | \(-0.704739\pi\) | ||||
−0.599763 | + | 0.800178i | \(0.704739\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.73205 | −0.721752 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.6603 | 1.23598 | 0.617992 | − | 0.786184i | \(-0.287946\pi\) | ||||
0.617992 | + | 0.786184i | \(0.287946\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.46410 | 0.363137 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.26795 | −0.546261 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.46410 | −0.150214 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8564 | 1.60997 | 0.804987 | − | 0.593292i | \(-0.202172\pi\) | ||||
0.804987 | + | 0.593292i | \(0.202172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.7321 | 1.06788 | 0.533939 | − | 0.845523i | \(-0.320711\pi\) | ||||
0.533939 | + | 0.845523i | \(0.320711\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.46410 | 0.538394 | 0.269197 | − | 0.963085i | \(-0.413242\pi\) | ||||
0.269197 | + | 0.963085i | \(0.413242\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.53590 | −0.247478 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.39230 | −0.424620 | −0.212310 | − | 0.977202i | \(-0.568099\pi\) | ||||
−0.212310 | + | 0.977202i | \(0.568099\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.8564 | −1.71033 | −0.855167 | − | 0.518353i | \(-0.826545\pi\) | ||||
−0.855167 | + | 0.518353i | \(0.826545\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.39230 | 0.409585 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.46410 | −0.867573 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.9282 | −0.985363 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.5885 | −0.939574 | −0.469787 | − | 0.882780i | \(-0.655669\pi\) | ||||
−0.469787 | + | 0.882780i | \(0.655669\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.26795 | −0.287727 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.07180 | −0.0936433 | −0.0468217 | − | 0.998903i | \(-0.514909\pi\) | ||||
−0.0468217 | + | 0.998903i | \(0.514909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.92820 | 0.600751 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.732051 | −0.0630049 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.80385 | 0.154113 | 0.0770565 | − | 0.997027i | \(-0.475448\pi\) | ||||
0.0770565 | + | 0.997027i | \(0.475448\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0526 | 1.70084 | 0.850418 | − | 0.526108i | \(-0.176349\pi\) | ||||
0.850418 | + | 0.526108i | \(0.176349\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.46410 | 0.123300 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.92820 | 0.409265 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.00000 | 0.412393 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.53590 | 0.207749 | 0.103874 | − | 0.994590i | \(-0.466876\pi\) | ||||
0.103874 | + | 0.994590i | \(0.466876\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8564 | −1.29038 | −0.645188 | − | 0.764024i | \(-0.723221\pi\) | ||||
−0.645188 | + | 0.764024i | \(0.723221\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.73205 | −0.220873 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.85641 | 0.309754 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.3205 | 1.86118 | 0.930590 | − | 0.366064i | \(-0.119295\pi\) | ||||
0.930590 | + | 0.366064i | \(0.119295\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.7846 | −1.63806 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.66025 | 0.443345 | 0.221673 | − | 0.975121i | \(-0.428848\pi\) | ||||
0.221673 | + | 0.975121i | \(0.428848\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.732051 | 0.0569901 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.8564 | −1.38177 | −0.690885 | − | 0.722965i | \(-0.742779\pi\) | ||||
−0.690885 | + | 0.722965i | \(0.742779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.66025 | 0.430341 | 0.215171 | − | 0.976576i | \(-0.430969\pi\) | ||||
0.215171 | + | 0.976576i | \(0.430969\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.4641 | −1.16898 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.46410 | −0.410707 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.00000 | −0.149487 | −0.0747435 | − | 0.997203i | \(-0.523814\pi\) | ||||
−0.0747435 | + | 0.997203i | \(0.523814\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.46410 | 0.406143 | 0.203072 | − | 0.979164i | \(-0.434908\pi\) | ||||
0.203072 | + | 0.979164i | \(0.434908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.92820 | 0.364303 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.46410 | 0.107643 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.73205 | 0.199787 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.46410 | 0.251976 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.9282 | −1.94846 | −0.974228 | − | 0.225565i | \(-0.927577\pi\) | ||||
−0.974228 | + | 0.225565i | \(0.927577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.9282 | −0.786629 | −0.393315 | − | 0.919404i | \(-0.628672\pi\) | ||||
−0.393315 | + | 0.919404i | \(0.628672\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.732051 | −0.0524232 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.3205 | 1.37653 | 0.688265 | − | 0.725460i | \(-0.258373\pi\) | ||||
0.688265 | + | 0.725460i | \(0.258373\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.3205 | 1.36959 | 0.684797 | − | 0.728734i | \(-0.259891\pi\) | ||||
0.684797 | + | 0.728734i | \(0.259891\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.19615 | −0.578112 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.3205 | −1.63678 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.00000 | 0.558744 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.00000 | −0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.80385 | −0.674925 | −0.337462 | − | 0.941339i | \(-0.609569\pi\) | ||||
−0.337462 | + | 0.941339i | \(0.609569\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.00000 | −0.274075 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.39230 | 0.163154 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.2487 | −1.23880 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.00000 | −0.270295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.73205 | −0.183778 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.80385 | −0.254724 | −0.127362 | − | 0.991856i | \(-0.540651\pi\) | ||||
−0.127362 | + | 0.991856i | \(0.540651\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.46410 | −0.297607 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.535898 | −0.0355688 | −0.0177844 | − | 0.999842i | \(-0.505661\pi\) | ||||
−0.0177844 | + | 0.999842i | \(0.505661\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5359 | −0.828395 | −0.414198 | − | 0.910187i | \(-0.635938\pi\) | ||||
−0.414198 | + | 0.910187i | \(0.635938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.46410 | −0.227921 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.1244 | −0.728781 | −0.364390 | − | 0.931246i | \(-0.618723\pi\) | ||||
−0.364390 | + | 0.931246i | \(0.618723\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.07180 | −0.0699163 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.26795 | 0.212276 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3923 | 0.672222 | 0.336111 | − | 0.941822i | \(-0.390888\pi\) | ||||
0.336111 | + | 0.941822i | \(0.390888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.7846 | 1.21002 | 0.605012 | − | 0.796217i | \(-0.293168\pi\) | ||||
0.605012 | + | 0.796217i | \(0.293168\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.66025 | −0.233845 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.00000 | 0.127257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.9282 | −0.692547 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.07180 | 0.0676512 | 0.0338256 | − | 0.999428i | \(-0.489231\pi\) | ||||
0.0338256 | + | 0.999428i | \(0.489231\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.00000 | 0.125245 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.4641 | 0.715111 | 0.357556 | − | 0.933892i | \(-0.383610\pi\) | ||||
0.357556 | + | 0.933892i | \(0.383610\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.92820 | −0.430498 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.73205 | −0.416703 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.3205 | 1.43800 | 0.719002 | − | 0.695008i | \(-0.244599\pi\) | ||||
0.719002 | + | 0.695008i | \(0.244599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.39230 | 0.269817 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.6603 | 0.713596 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.3923 | −0.877514 | −0.438757 | − | 0.898606i | \(-0.644581\pi\) | ||||
−0.438757 | + | 0.898606i | \(0.644581\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.9282 | −0.785332 | −0.392666 | − | 0.919681i | \(-0.628447\pi\) | ||||
−0.392666 | + | 0.919681i | \(0.628447\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.46410 | 0.209657 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.46410 | 0.269195 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.26795 | −0.315384 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.8564 | 1.54246 | 0.771232 | − | 0.636554i | \(-0.219641\pi\) | ||||
0.771232 | + | 0.636554i | \(0.219641\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.80385 | 0.107228 | 0.0536138 | − | 0.998562i | \(-0.482926\pi\) | ||||
0.0536138 | + | 0.998562i | \(0.482926\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.46410 | −0.0867259 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −37.8564 | −2.23459 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.53590 | −0.560935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.8564 | 0.929519 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.4641 | 1.25395 | 0.626973 | − | 0.779041i | \(-0.284294\pi\) | ||||
0.626973 | + | 0.779041i | \(0.284294\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00000 | −0.346989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.3205 | −0.652503 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.7321 | 0.616540 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.60770 | −0.206576 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.7846 | 1.75697 | 0.878485 | − | 0.477769i | \(-0.158555\pi\) | ||||
0.878485 | + | 0.477769i | \(0.158555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.46410 | 0.310842 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.9282 | −0.733091 | −0.366546 | − | 0.930400i | \(-0.619460\pi\) | ||||
−0.366546 | + | 0.930400i | \(0.619460\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.46410 | −0.0827559 | −0.0413780 | − | 0.999144i | \(-0.513175\pi\) | ||||
−0.0413780 | + | 0.999144i | \(0.513175\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.53590 | −0.142882 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.26795 | −0.183546 | −0.0917732 | − | 0.995780i | \(-0.529253\pi\) | ||||
−0.0917732 | + | 0.995780i | \(0.529253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.73205 | 0.376922 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.39230 | −0.245155 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.46410 | −0.304031 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.46410 | −0.247624 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.8564 | −0.987462 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.07180 | 0.279617 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.7321 | 1.02961 | 0.514803 | − | 0.857308i | \(-0.327865\pi\) | ||||
0.514803 | + | 0.857308i | \(0.327865\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.00000 | 0.327815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.1769 | −1.48042 | −0.740210 | − | 0.672375i | \(-0.765274\pi\) | ||||
−0.740210 | + | 0.672375i | \(0.765274\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.0000 | 0.543125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.26795 | 0.285275 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.92820 | −0.374088 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.39230 | 0.236474 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.39230 | 0.235791 | 0.117896 | − | 0.993026i | \(-0.462385\pi\) | ||||
0.117896 | + | 0.993026i | \(0.462385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.928203 | 0.0496856 | 0.0248428 | − | 0.999691i | \(-0.492091\pi\) | ||||
0.0248428 | + | 0.999691i | \(0.492091\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.9808 | −1.43604 | −0.718021 | − | 0.696022i | \(-0.754952\pi\) | ||||
−0.718021 | + | 0.696022i | \(0.754952\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.92820 | 0.155413 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.46410 | −0.500893 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.46410 | −0.393940 | −0.196970 | − | 0.980409i | \(-0.563110\pi\) | ||||
−0.196970 | + | 0.980409i | \(0.563110\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.92820 | 0.153269 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.7846 | −1.50254 | −0.751272 | − | 0.659992i | \(-0.770559\pi\) | ||||
−0.751272 | + | 0.659992i | \(0.770559\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.9282 | −0.568900 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.7846 | −1.07908 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.4641 | −0.593589 | −0.296794 | − | 0.954941i | \(-0.595918\pi\) | ||||
−0.296794 | + | 0.954941i | \(0.595918\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.92820 | 0.357771 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.73205 | −0.346718 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.58846 | −0.441159 | −0.220580 | − | 0.975369i | \(-0.570795\pi\) | ||||
−0.220580 | + | 0.975369i | \(0.570795\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.5885 | −0.542463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −36.3923 | −1.85956 | −0.929780 | − | 0.368116i | \(-0.880003\pi\) | ||||
−0.929780 | + | 0.368116i | \(0.880003\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.53590 | 0.129241 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.26795 | −0.166119 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.39230 | 0.324103 | 0.162051 | − | 0.986782i | \(-0.448189\pi\) | ||||
0.162051 | + | 0.986782i | \(0.448189\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.3923 | 0.828994 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.07180 | −0.0540650 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.39230 | −0.120370 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.9282 | 1.65262 | 0.826310 | − | 0.563216i | \(-0.190436\pi\) | ||||
0.826310 | + | 0.563216i | \(0.190436\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.92820 | 0.346844 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.7321 | 1.03531 | 0.517655 | − | 0.855590i | \(-0.326805\pi\) | ||||
0.517655 | + | 0.855590i | \(0.326805\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.26795 | −0.262415 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.732051 | −0.0363759 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.00000 | 0.0991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.07180 | 0.0529969 | 0.0264985 | − | 0.999649i | \(-0.491564\pi\) | ||||
0.0264985 | + | 0.999649i | \(0.491564\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.80385 | 0.0889772 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.9282 | −0.931396 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.0526 | 0.981978 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.7128 | 0.865328 | 0.432664 | − | 0.901555i | \(-0.357574\pi\) | ||||
0.432664 | + | 0.901555i | \(0.357574\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.46410 | 0.0711871 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.1962 | 0.591600 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.0718 | 0.826162 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.00000 | −0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.7846 | −1.00116 | −0.500580 | − | 0.865690i | \(-0.666880\pi\) | ||||
−0.500580 | + | 0.865690i | \(0.666880\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.85641 | −0.185327 | −0.0926635 | − | 0.995697i | \(-0.529538\pi\) | ||||
−0.0926635 | + | 0.995697i | \(0.529538\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.92820 | 0.236289 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.0000 | −0.574038 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.73205 | 0.225848 | 0.112924 | − | 0.993604i | \(-0.463978\pi\) | ||||
0.112924 | + | 0.993604i | \(0.463978\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000 | 0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.85641 | 0.0882005 | 0.0441003 | − | 0.999027i | \(-0.485958\pi\) | ||||
0.0441003 | + | 0.999027i | \(0.485958\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.53590 | −0.404640 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.53590 | 0.119944 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.1962 | 0.669958 | 0.334979 | − | 0.942226i | \(-0.391271\pi\) | ||||
0.334979 | + | 0.942226i | \(0.391271\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.9282 | 0.514589 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.8564 | −0.744999 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.53590 | −0.118885 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.7846 | 0.691595 | 0.345797 | − | 0.938309i | \(-0.387608\pi\) | ||||
0.345797 | + | 0.938309i | \(0.387608\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.73205 | −0.127521 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.7128 | 1.84961 | 0.924805 | − | 0.380441i | \(-0.124228\pi\) | ||||
0.924805 | + | 0.380441i | \(0.124228\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.0526 | −1.02487 | −0.512435 | − | 0.858726i | \(-0.671256\pi\) | ||||
−0.512435 | + | 0.858726i | \(0.671256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.85641 | 0.178837 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.0000 | −0.832941 | −0.416470 | − | 0.909149i | \(-0.636733\pi\) | ||||
−0.416470 | + | 0.909149i | \(0.636733\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.3923 | −1.31103 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.3205 | 1.07455 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.26795 | 0.150260 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.92820 | −0.409654 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.32051 | −0.243100 | −0.121550 | − | 0.992585i | \(-0.538787\pi\) | ||||
−0.121550 | + | 0.992585i | \(0.538787\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.7846 | −0.945732 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.6077 | −0.527078 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.4449 | −1.56085 | −0.780423 | − | 0.625252i | \(-0.784996\pi\) | ||||
−0.780423 | + | 0.625252i | \(0.784996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.66025 | 0.255966 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.46410 | −0.0660740 | −0.0330370 | − | 0.999454i | \(-0.510518\pi\) | ||||
−0.0330370 | + | 0.999454i | \(0.510518\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.3923 | 0.828348 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.732051 | 0.0329032 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.8564 | −0.621545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.8038 | 1.06561 | 0.532803 | − | 0.846239i | \(-0.321139\pi\) | ||||
0.532803 | + | 0.846239i | \(0.321139\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.8564 | −0.797765 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.5359 | −1.36153 | −0.680764 | − | 0.732503i | \(-0.738352\pi\) | ||||
−0.680764 | + | 0.732503i | \(0.738352\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.85641 | −0.349605 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.5885 | −0.823919 | −0.411959 | − | 0.911202i | \(-0.635155\pi\) | ||||
−0.411959 | + | 0.911202i | \(0.635155\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8564 | −0.612971 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.00000 | 0.0883022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.00000 | −0.176261 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.46410 | −0.0643911 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.66025 | 0.248458 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.7846 | 0.822969 | 0.411484 | − | 0.911417i | \(-0.365010\pi\) | ||||
0.411484 | + | 0.911417i | \(0.365010\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.58846 | −0.288093 | −0.144047 | − | 0.989571i | \(-0.546012\pi\) | ||||
−0.144047 | + | 0.989571i | \(0.546012\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15.4641 | −0.674909 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.3923 | 0.626939 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.46410 | −0.237122 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.9282 | −0.473353 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.21539 | 0.139013 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.00000 | −0.0863064 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.00000 | −0.215365 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.7846 | −0.807613 | −0.403807 | − | 0.914844i | \(-0.632313\pi\) | ||||
−0.403807 | + | 0.914844i | \(0.632313\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.46410 | 0.234487 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.0718 | 0.559934 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.7321 | 0.886438 | 0.443219 | − | 0.896413i | \(-0.353836\pi\) | ||||
0.443219 | + | 0.896413i | \(0.353836\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.92820 | 0.210331 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.4641 | −0.573590 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.3205 | 0.481397 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.46410 | 0.0621477 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.60770 | −0.322348 | −0.161174 | − | 0.986926i | \(-0.551528\pi\) | ||||
−0.161174 | + | 0.986926i | \(0.551528\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.26795 | −0.138220 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.73205 | 0.115347 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.8564 | −0.583978 | −0.291989 | − | 0.956422i | \(-0.594317\pi\) | ||||
−0.291989 | + | 0.956422i | \(0.594317\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.32051 | −0.307976 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.46410 | 0.145479 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −40.9808 | −1.71800 | −0.859001 | − | 0.511973i | \(-0.828915\pi\) | ||||
−0.859001 | + | 0.511973i | \(0.828915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.2679 | 0.973733 | 0.486867 | − | 0.873476i | \(-0.338140\pi\) | ||||
0.486867 | + | 0.873476i | \(0.338140\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.9282 | −1.12494 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.7846 | 1.11700 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.78461 | 0.115925 | 0.0579624 | − | 0.998319i | \(-0.481540\pi\) | ||||
0.0579624 | + | 0.998319i | \(0.481540\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.9282 | −0.454161 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.8564 | −1.57055 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | 0.248495 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.732051 | −0.0302666 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.6077 | 0.809296 | 0.404648 | − | 0.914472i | \(-0.367394\pi\) | ||||
0.404648 | + | 0.914472i | \(0.367394\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.5359 | −0.434124 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.3205 | 0.794740 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.4641 | 1.37421 | 0.687103 | − | 0.726560i | \(-0.258882\pi\) | ||||
0.687103 | + | 0.726560i | \(0.258882\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.92820 | 0.284029 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.3205 | 0.790736 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.6410 | 0.925087 | 0.462543 | − | 0.886597i | \(-0.346937\pi\) | ||||
0.462543 | + | 0.886597i | \(0.346937\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.19615 | −0.333773 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.732051 | −0.0297621 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.3731 | −1.11104 | −0.555519 | − | 0.831504i | \(-0.687480\pi\) | ||||
−0.555519 | + | 0.831504i | \(0.687480\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.3205 | −0.944995 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.46410 | 0.0592312 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.78461 | 0.354807 | 0.177404 | − | 0.984138i | \(-0.443230\pi\) | ||||
0.177404 | + | 0.984138i | \(0.443230\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.00000 | 0.322591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.73205 | −0.351539 | −0.175770 | − | 0.984431i | \(-0.556241\pi\) | ||||
−0.175770 | + | 0.984431i | \(0.556241\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.3397 | 0.737137 | 0.368568 | − | 0.929601i | \(-0.379848\pi\) | ||||
0.368568 | + | 0.929601i | \(0.379848\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.00000 | −0.240772 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 40.3923 | 1.61828 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.00000 | −0.0798723 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.46410 | 0.217868 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.4449 | 0.734278 | 0.367139 | − | 0.930166i | \(-0.380337\pi\) | ||||
0.367139 | + | 0.930166i | \(0.380337\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.80385 | −0.389668 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.75129 | 0.307601 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.00000 | 0.198107 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.00000 | −0.158238 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.9282 | −1.45858 | −0.729288 | − | 0.684207i | \(-0.760149\pi\) | ||||
−0.729288 | + | 0.684207i | \(0.760149\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.73205 | −0.265486 | −0.132743 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132743 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.39230 | 0.0941969 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.85641 | 0.230239 | 0.115120 | − | 0.993352i | \(-0.463275\pi\) | ||||
0.115120 | + | 0.993352i | \(0.463275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.46410 | 0.214485 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.2487 | −0.715223 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.60770 | 0.0629140 | 0.0314570 | − | 0.999505i | \(-0.489985\pi\) | ||||
0.0314570 | + | 0.999505i | \(0.489985\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.784610 | 0.0306572 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.14359 | −0.239320 | −0.119660 | − | 0.992815i | \(-0.538181\pi\) | ||||
−0.119660 | + | 0.992815i | \(0.538181\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.2487 | −1.72108 | −0.860538 | − | 0.509387i | \(-0.829872\pi\) | ||||
−0.860538 | + | 0.509387i | \(0.829872\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.73205 | −0.106104 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.07180 | −0.196676 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.3923 | 1.56400 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.80385 | −0.147065 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.92820 | −0.190251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.60770 | 0.370349 | 0.185175 | − | 0.982706i | \(-0.440715\pi\) | ||||
0.185175 | + | 0.982706i | \(0.440715\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.46410 | −0.171823 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.2679 | −1.58606 | −0.793028 | − | 0.609185i | \(-0.791497\pi\) | ||||
−0.793028 | + | 0.609185i | \(0.791497\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 54.9282 | 2.10795 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.535898 | −0.0205357 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.7846 | 0.795301 | 0.397650 | − | 0.917537i | \(-0.369826\pi\) | ||||
0.397650 | + | 0.917537i | \(0.369826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.32051 | −0.0504540 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.5359 | −0.478274 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | −0.228582 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.6603 | 1.73700 | 0.868499 | − | 0.495691i | \(-0.165085\pi\) | ||||
0.868499 | + | 0.495691i | \(0.165085\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.46410 | −0.131590 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.6795 | −0.556825 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.8564 | 1.13089 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.1244 | −0.420762 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.1962 | −1.66927 | −0.834633 | − | 0.550807i | \(-0.814320\pi\) | ||||
−0.834633 | + | 0.550807i | \(0.814320\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.00000 | −0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.07180 | −0.0403662 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37.1769 | 1.39818 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.2487 | 1.66180 | 0.830898 | − | 0.556425i | \(-0.187827\pi\) | ||||
0.830898 | + | 0.556425i | \(0.187827\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.26795 | 0.122558 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.6077 | 1.18372 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.732051 | 0.0273771 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.3923 | 0.388108 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.9282 | 0.704923 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.7846 | 0.698607 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30.0526 | 1.11612 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.3205 | −1.45832 | −0.729158 | − | 0.684345i | \(-0.760088\pi\) | ||||
−0.729158 | + | 0.684345i | \(0.760088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.92820 | 0.330222 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.92820 | 0.108156 | 0.0540778 | − | 0.998537i | \(-0.482778\pi\) | ||||
0.0540778 | + | 0.998537i | \(0.482778\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.66025 | −0.135011 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.19615 | 0.301909 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.53590 | −0.166856 | −0.0834279 | − | 0.996514i | \(-0.526587\pi\) | ||||
−0.0834279 | + | 0.996514i | \(0.526587\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.00000 | 0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.0718 | 0.773049 | 0.386525 | − | 0.922279i | \(-0.373675\pi\) | ||||
0.386525 | + | 0.922279i | \(0.373675\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.85641 | −0.0680135 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.9282 | −0.399842 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.2154 | −0.555958 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.14359 | 0.224183 | 0.112091 | − | 0.993698i | \(-0.464245\pi\) | ||||
0.112091 | + | 0.993698i | \(0.464245\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.07180 | 0.0390584 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.6077 | 0.422447 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.53590 | −0.237551 | −0.118776 | − | 0.992921i | \(-0.537897\pi\) | ||||
−0.118776 | + | 0.992921i | \(0.537897\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.00000 | 0.217786 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.3205 | 0.990368 | 0.495184 | − | 0.868788i | \(-0.335101\pi\) | ||||
0.495184 | + | 0.868788i | \(0.335101\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −61.8564 | −2.23935 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.00000 | 0.0723102 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.46410 | −0.197297 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.7846 | −0.533147 | −0.266573 | − | 0.963815i | \(-0.585891\pi\) | ||||
−0.266573 | + | 0.963815i | \(0.585891\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.4641 | 0.412870 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.5885 | 1.10019 | 0.550095 | − | 0.835102i | \(-0.314591\pi\) | ||||
0.550095 | + | 0.835102i | \(0.314591\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.5167 | 0.844743 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.92820 | −0.248548 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.8564 | −0.783087 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.73205 | −0.240584 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.0718 | −0.609319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.53590 | −0.161687 | −0.0808437 | − | 0.996727i | \(-0.525761\pi\) | ||||
−0.0808437 | + | 0.996727i | \(0.525761\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.3205 | 0.830232 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.6410 | 1.23169 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.92820 | 0.175006 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.39230 | 0.155779 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.3923 | −1.21824 | −0.609119 | − | 0.793079i | \(-0.708477\pi\) | ||||
−0.609119 | + | 0.793079i | \(0.708477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.00000 | −0.141510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.6603 | 0.411995 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.00000 | 0.141157 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.2154 | 0.536272 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.3923 | −0.506633 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5167 | 0.686169 | 0.343085 | − | 0.939304i | \(-0.388528\pi\) | ||||
0.343085 | + | 0.939304i | \(0.388528\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.0000 | 1.61528 | 0.807639 | − | 0.589677i | \(-0.200745\pi\) | ||||
0.807639 | + | 0.589677i | \(0.200745\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.9282 | −0.453412 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.14359 | −0.145144 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.53590 | −0.228662 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.46410 | 0.121046 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.0718 | 0.735411 | 0.367705 | − | 0.929942i | \(-0.380143\pi\) | ||||
0.367705 | + | 0.929942i | \(0.380143\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.2487 | 0.914973 | 0.457486 | − | 0.889217i | \(-0.348750\pi\) | ||||
0.457486 | + | 0.889217i | \(0.348750\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.46410 | 0.155420 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.46410 | −0.120459 | −0.0602293 | − | 0.998185i | \(-0.519183\pi\) | ||||
−0.0602293 | + | 0.998185i | \(0.519183\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.7128 | −0.476266 | −0.238133 | − | 0.971233i | \(-0.576535\pi\) | ||||
−0.238133 | + | 0.971233i | \(0.576535\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.00000 | 0.0693792 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.6603 | −0.473300 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.0718 | 0.452368 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.26795 | −0.182087 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.6410 | 1.05785 | 0.528923 | − | 0.848670i | \(-0.322596\pi\) | ||||
0.528923 | + | 0.848670i | \(0.322596\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.3205 | 0.562776 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.8564 | 0.890542 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.732051 | −0.0251833 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.46410 | 0.119028 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.80385 | 0.0619079 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000 | 0.411355 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.7846 | −0.780130 | −0.390065 | − | 0.920787i | \(-0.627547\pi\) | ||||
−0.390065 | + | 0.920787i | \(0.627547\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.46410 | −0.0500712 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.8372 | 1.46329 | 0.731645 | − | 0.681686i | \(-0.238753\pi\) | ||||
0.731645 | + | 0.681686i | \(0.238753\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.3205 | 0.659207 | 0.329604 | − | 0.944119i | \(-0.393085\pi\) | ||||
0.329604 | + | 0.944119i | \(0.393085\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −37.8564 | −1.29014 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.4641 | −1.13913 | −0.569566 | − | 0.821946i | \(-0.692889\pi\) | ||||
−0.569566 | + | 0.821946i | \(0.692889\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.14359 | −0.140886 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.53590 | −0.323856 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.26795 | −0.110858 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.19615 | −0.277716 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.8564 | 0.536658 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.0000 | 0.811348 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.9282 | −0.706695 | −0.353348 | − | 0.935492i | \(-0.614957\pi\) | ||||
−0.353348 | + | 0.935492i | \(0.614957\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.4641 | 0.723966 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.8564 | −0.938506 | −0.469253 | − | 0.883064i | \(-0.655477\pi\) | ||||
−0.469253 | + | 0.883064i | \(0.655477\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.5359 | 0.758393 | 0.379197 | − | 0.925316i | \(-0.376200\pi\) | ||||
0.379197 | + | 0.925316i | \(0.376200\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.00000 | 0.134459 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.7128 | −0.930505 | −0.465253 | − | 0.885178i | \(-0.654037\pi\) | ||||
−0.465253 | + | 0.885178i | \(0.654037\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.6795 | −1.23019 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.92820 | 0.0979886 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.46410 | 0.0489395 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00000 | −0.200334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.4641 | 1.18279 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.3923 | 0.546107 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.3205 | −0.376723 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.00000 | −0.132964 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.7128 | −1.45146 | −0.725730 | − | 0.687980i | \(-0.758498\pi\) | ||||
−0.725730 | + | 0.687980i | \(0.758498\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.7321 | 0.355960 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.8564 | 1.25424 | 0.627119 | − | 0.778923i | \(-0.284234\pi\) | ||||
0.627119 | + | 0.778923i | \(0.284234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.9282 | 0.361671 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.60770 | −0.119267 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.71281 | −0.122608 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.5167 | −1.36951 | −0.684754 | − | 0.728774i | \(-0.740090\pi\) | ||||
−0.684754 | + | 0.728774i | \(0.740090\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.7846 | 1.01439 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.00000 | −0.131662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.92820 | 0.293558 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.46410 | 0.179465 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.6603 | 0.513796 | 0.256898 | − | 0.966438i | \(-0.417300\pi\) | ||||
0.256898 | + | 0.966438i | \(0.417300\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.0000 | 0.327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.9282 | −0.423250 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.00000 | −0.0654070 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.3923 | −1.25422 | −0.627111 | − | 0.778930i | \(-0.715763\pi\) | ||||
−0.627111 | + | 0.778930i | \(0.715763\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.46410 | −0.0477792 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.7846 | −1.45994 | −0.729968 | − | 0.683481i | \(-0.760465\pi\) | ||||
−0.729968 | + | 0.683481i | \(0.760465\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 65.5692 | 2.13523 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.53590 | −0.0824928 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.6795 | −0.542011 | −0.271005 | − | 0.962578i | \(-0.587356\pi\) | ||||
−0.271005 | + | 0.962578i | \(0.587356\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | −0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.26795 | −0.105971 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.9090 | 0.774487 | 0.387244 | − | 0.921977i | \(-0.373427\pi\) | ||||
0.387244 | + | 0.921977i | \(0.373427\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.7128 | 0.637892 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.73205 | 0.217616 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.24871 | 0.201781 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.24871 | −0.104797 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.39230 | −0.141540 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.00000 | 0.257529 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.3923 | 1.74914 | 0.874569 | − | 0.484901i | \(-0.161144\pi\) | ||||
0.874569 | + | 0.484901i | \(0.161144\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.46410 | −0.175532 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.21539 | 0.295736 | 0.147868 | − | 0.989007i | \(-0.452759\pi\) | ||||
0.147868 | + | 0.989007i | \(0.452759\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 69.4641 | 2.22692 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.46410 | −0.142966 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56.1577 | −1.79664 | −0.898322 | − | 0.439338i | \(-0.855213\pi\) | ||||
−0.898322 | + | 0.439338i | \(0.855213\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.6603 | −0.372663 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.8564 | −0.570111 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.1436 | 0.323530 | 0.161765 | − | 0.986829i | \(-0.448281\pi\) | ||||
0.161765 | + | 0.986829i | \(0.448281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.1436 | −0.450652 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.07180 | 0.161437 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.6077 | 0.623488 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.3205 | −1.63025 | −0.815125 | − | 0.579285i | \(-0.803332\pi\) | ||||
−0.815125 | + | 0.579285i | \(0.803332\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.7321 | 0.594444 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.1436 | −0.448382 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.6077 | 0.430960 | 0.215480 | − | 0.976508i | \(-0.430868\pi\) | ||||
0.215480 | + | 0.976508i | \(0.430868\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 6864.2.a.bm.1.1 | 2 | ||
4.3 | odd | 2 | 3432.2.a.l.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3432.2.a.l.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
6864.2.a.bm.1.1 | 2 | 1.1 | even | 1 | trivial |