Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(41,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([0, 33, 53]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.ba (of order \(66\), degree \(20\), minimal) |
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: | no |
Analytic conductor: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{66}]$ |
Embedding invariants
Embedding label | 197.1 | ||
Root | \(0.0475819 - 0.998867i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.197 |
Dual form | 804.2.ba.a.653.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{35}{66}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.936417 | + | 1.45709i | −0.540641 | + | 0.841254i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.614593 | − | 0.437650i | −0.232294 | − | 0.165416i | 0.457983 | − | 0.888961i | \(-0.348572\pi\) |
−0.690277 | + | 0.723545i | \(0.742511\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.24625 | − | 2.72890i | −0.415415 | − | 0.909632i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.618159 | − | 0.786053i | \(-0.712121\pi\) | ||||
0.618159 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.32224 | − | 0.563370i | −0.644074 | − | 0.156251i | −0.0995988 | − | 0.995028i | \(-0.531756\pi\) |
−0.544475 | + | 0.838777i | \(0.683271\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.99015 | − | 7.00769i | −1.14482 | − | 1.60767i | −0.704245 | − | 0.709957i | \(-0.748714\pi\) |
−0.440574 | − | 0.897716i | \(-0.645225\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.21321 | − | 0.485697i | 0.264745 | − | 0.105988i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.79746 | − | 1.40866i | 0.959493 | − | 0.281733i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.14326 | + | 0.739490i | 0.989821 | + | 0.142315i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.3416 | + | 2.50884i | −1.85740 | + | 0.450601i | −0.998141 | − | 0.0609393i | \(-0.980590\pi\) |
−0.859260 | + | 0.511540i | \(0.829075\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.77342 | − | 9.99985i | 0.949144 | − | 1.64396i | 0.201909 | − | 0.979404i | \(-0.435285\pi\) |
0.747234 | − | 0.664561i | \(-0.231381\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.99547 | − | 2.85617i | 0.479659 | − | 0.457354i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.945001 | − | 0.327068i | \(-0.893939\pi\) | ||||
0.945001 | + | 0.327068i | \(0.106061\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.51198 | − | 1.31014i | 0.230574 | − | 0.199794i | −0.531909 | − | 0.846801i | \(-0.678525\pi\) |
0.762484 | + | 0.647008i | \(0.223980\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.10329 | − | 6.07705i | −0.300470 | − | 0.868150i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.8837 | − | 0.708999i | 1.97140 | − | 0.0939092i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.44064 | − | 10.7332i | 1.08071 | − | 1.37424i | 0.158590 | − | 0.987345i | \(-0.449305\pi\) |
0.922124 | − | 0.386895i | \(-0.126452\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.428367 | + | 2.22258i | −0.0539692 | + | 0.280019i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.98512 | + | 4.26709i | 0.853369 | + | 0.521308i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.3456 | − | 8.92225i | −1.32790 | − | 1.04427i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
−0.333048 | − | 0.942910i | \(-0.608077\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.43988 | + | 8.30945i | −0.281733 | + | 0.959493i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50042 | + | 5.76867i | −0.618846 | + | 0.649027i | −0.956325 | − | 0.292306i | \(-0.905577\pi\) |
0.337479 | + | 0.941333i | \(0.390426\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.89375 | + | 6.80175i | −0.654861 | + | 0.755750i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.18067 | + | 1.36257i | 0.123768 | + | 0.142836i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.02841 | − | 17.4180i | 0.625117 | − | 1.80616i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.2217 | − | 9.36562i | −1.64707 | − | 0.950934i | −0.978230 | − | 0.207526i | \(-0.933459\pi\) |
−0.668837 | − | 0.743409i | \(-0.733208\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.0950560 | − | 0.995472i | \(-0.530303\pi\) | ||||
0.0950560 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.70165 | − | 11.1363i | −0.266201 | − | 1.09730i | −0.935225 | − | 0.354055i | \(-0.884803\pi\) |
0.669024 | − | 0.743241i | \(-0.266712\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.64566 | + | 19.2274i | 0.540757 | + | 1.84165i | 0.540027 | + | 0.841648i | \(0.318414\pi\) |
0.000729916 | 1.00000i | \(0.499768\pi\) | ||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.16439 | + | 17.7764i | 0.869846 | + | 1.68726i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.371662 | − | 0.928368i | \(-0.621212\pi\) | ||||
0.371662 | + | 0.928368i | \(0.378788\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.35670 | + | 7.03925i | 0.125427 | + | 0.650779i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.59335 | + | 10.6899i | −0.235759 | + | 0.971812i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.5560 | + | 17.6325i | −1.11417 | + | 1.56463i | −0.330107 | + | 0.943944i | \(0.607085\pi\) |
−0.784060 | + | 0.620685i | \(0.786855\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.493149 | + | 3.42993i | 0.0434193 | + | 0.301988i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.49081i | 0.562825i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.98138 | + | 1.14755i | −0.676972 | + | 0.0973339i | −0.472221 | − | 0.881480i | \(-0.656548\pi\) |
−0.204751 | + | 0.978814i | \(0.565638\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.8244 | + | 2.62597i | 0.892781 | + | 0.216586i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.6313 | + | 2.24175i | −0.946541 | + | 0.182431i | −0.639089 | − | 0.769133i | \(-0.720688\pi\) |
−0.307452 | + | 0.951564i | \(0.599476\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6353 | − | 5.99843i | 0.928601 | − | 0.478727i | 0.0735617 | − | 0.997291i | \(-0.476563\pi\) |
0.855039 | + | 0.518564i | \(0.173533\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.22226 | − | 10.7773i | −0.487365 | − | 0.844142i | 0.512529 | − | 0.858670i | \(-0.328709\pi\) |
−0.999894 | + | 0.0145283i | \(0.995375\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.47944 | − | 3.34038i | −0.498419 | − | 0.256953i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.9043 | + | 22.3509i | −0.986816 | + | 1.70922i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.56499 | − | 1.23385i | −0.269488 | − | 0.0932706i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.25066 | + | 26.2546i | −0.0929610 | + | 1.95149i | 0.167192 | + | 0.985924i | \(0.446530\pi\) |
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.73524 | + | 22.3495i | 0.571806 | + | 1.65212i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.83738 | − | 2.70543i | −0.206389 | − | 0.196791i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.998867 | − | 0.0475819i | \(-0.0151515\pi\) | ||||
−0.998867 | + | 0.0475819i | \(0.984848\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.617267 | − | 0.181246i | −0.0444319 | − | 0.0130464i | 0.259441 | − | 0.965759i | \(-0.416462\pi\) |
−0.303873 | + | 0.952713i | \(0.598280\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.189251 | − | 0.981929i | \(-0.439394\pi\) | ||||
−0.189251 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.85768 | + | 0.559341i | 0.415240 | + | 0.0396506i | 0.300586 | − | 0.953755i | \(-0.402818\pi\) |
0.114654 | + | 0.993405i | \(0.463424\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.7585 | + | 6.18221i | −0.899918 | + | 0.436059i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.277952 | + | 5.83493i | 0.0191350 | + | 0.401693i | 0.988034 | + | 0.154237i | \(0.0492918\pi\) |
−0.968899 | + | 0.247457i | \(0.920405\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.45385 | + | 2.98407i | 0.506000 | + | 0.202572i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23.6247 | − | 8.17660i | 1.59641 | − | 0.552524i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.9305 | − | 10.8806i | 1.13375 | − | 0.728618i | 0.167412 | − | 0.985887i | \(-0.446459\pi\) |
0.966340 | + | 0.257269i | \(0.0828225\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.82291 | − | 11.3362i | −0.654861 | − | 0.755750i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3723 | + | 11.9269i | 0.751502 | + | 0.788153i | 0.982789 | − | 0.184733i | \(-0.0591420\pi\) |
−0.231287 | + | 0.972886i | \(0.574293\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.458227 | − | 0.888835i | \(-0.348485\pi\) | ||||
−0.458227 | + | 0.888835i | \(0.651515\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.25481 | − | 13.4165i | −0.211423 | − | 0.871496i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.36304 | − | 23.3905i | 0.216633 | − | 1.50671i | −0.533712 | − | 0.845666i | \(-0.679203\pi\) |
0.750345 | − | 0.661047i | \(-0.229888\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.39178 | − | 14.9570i | −0.281733 | − | 0.959493i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.64042 | + | 19.0848i | 0.486148 | + | 1.21434i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.189251 | − | 0.981929i | \(-0.560606\pi\) | ||||
0.189251 | + | 0.981929i | \(0.439394\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.92473 | + | 3.61910i | −0.492419 | + | 0.224880i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7607 | + | 16.7440i | −0.653667 | + | 1.01713i | 0.343294 | + | 0.939228i | \(0.388457\pi\) |
−0.996961 | + | 0.0778984i | \(0.975179\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.09100 | + | 0.444418i | −0.187076 | + | 0.0268974i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.2396 | − | 26.8011i | −0.735409 | − | 1.61032i | −0.790962 | − | 0.611866i | \(-0.790419\pi\) |
0.0555527 | − | 0.998456i | \(-0.482308\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.7345 | + | 25.0944i | 1.18147 | + | 1.50237i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.971812 | − | 0.235759i | \(-0.924242\pi\) | ||||
0.971812 | + | 0.235759i | \(0.0757576\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.16501 | + | 13.4995i | −0.366472 | + | 0.802461i | 0.633125 | + | 0.774050i | \(0.281772\pi\) |
−0.999596 | + | 0.0284112i | \(0.990955\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.7823 | − | 6.31826i | 0.928368 | − | 0.371662i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.8369 | − | 14.8665i | 1.69045 | − | 0.871487i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.50263 | + | 0.143484i | −0.0866102 | + | 0.00827027i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.1102 | − | 23.9425i | 1.43311 | − | 1.36647i | 0.619610 | − | 0.784910i | \(-0.287291\pi\) |
0.813503 | − | 0.581560i | \(-0.197558\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.7566 | + | 6.49171i | 1.06702 | + | 0.369300i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.59522 | − | 7.15031i | −0.259737 | − | 0.404159i | 0.686753 | − | 0.726891i | \(-0.259035\pi\) |
−0.946491 | + | 0.322731i | \(0.895399\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.9345 | + | 0.568509i | −0.662005 | + | 0.0315352i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −33.3028 | − | 9.77858i | −1.84165 | − | 0.540757i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.20515 | − | 32.1954i | 0.341066 | − | 1.76962i | −0.255257 | − | 0.966873i | \(-0.582160\pi\) |
0.596323 | − | 0.802745i | \(-0.296628\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −34.4836 | − | 3.29279i | −1.88969 | − | 0.180444i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.18353 | + | 33.3394i | −0.173418 | + | 1.81611i | 0.321211 | + | 0.947008i | \(0.395910\pi\) |
−0.494628 | + | 0.869105i | \(0.664696\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.85491 | + | 9.72294i | −0.154151 | + | 0.524989i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.690079 | − | 0.723734i | \(-0.257576\pi\) | ||||
−0.690079 | + | 0.723734i | \(0.742424\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.7967 | − | 27.4628i | 1.27381 | − | 1.47005i | 0.461136 | − | 0.887330i | \(-0.347442\pi\) |
0.812672 | − | 0.582722i | \(-0.198012\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.5273 | − | 4.61483i | −0.615281 | − | 0.246321i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.945001 | − | 0.327068i | \(-0.106061\pi\) | ||||
−0.945001 | + | 0.327068i | \(0.893939\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9918 | + | 51.9838i | −0.946935 | + | 2.73599i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.1478 | − | 13.7890i | −0.690079 | − | 0.723734i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.29918 | − | 8.33924i | 0.224415 | − | 0.435305i | −0.749567 | − | 0.661928i | \(-0.769738\pi\) |
0.973982 | + | 0.226623i | \(0.0727687\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.10103 | − | 5.25448i | 0.471233 | − | 0.272067i | −0.245523 | − | 0.969391i | \(-0.578960\pi\) |
0.716756 | + | 0.697324i | \(0.245626\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.7302 | − | 34.3917i | −0.910738 | − | 1.76658i | −0.554481 | − | 0.832196i | \(-0.687083\pi\) |
−0.356257 | − | 0.934388i | \(-0.615947\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.9345 | − | 34.8067i | −0.713885 | − | 1.78320i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.814576 | − | 0.580057i | \(-0.196970\pi\) | ||||
−0.814576 | + | 0.580057i | \(0.803030\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.45952 | − | 2.49328i | −0.277523 | − | 0.126740i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.21269 | − | 8.43443i | −0.0608631 | − | 0.423312i | −0.997359 | − | 0.0726328i | \(-0.976860\pi\) |
0.936496 | − | 0.350679i | \(-0.114049\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.45772 | − | 6.07811i | −0.473478 | − | 0.304286i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.4290 | 1.26671 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.2451 | − | 22.9617i | −1.59442 | − | 1.13538i | −0.916346 | − | 0.400387i | \(-0.868876\pi\) |
−0.678073 | − | 0.734994i | \(-0.737185\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.80182 | − | 12.7042i | 0.284116 | − | 0.622128i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.1020 | + | 32.4423i | 1.12592 | + | 1.58114i | 0.759262 | + | 0.650785i | \(0.225560\pi\) |
0.366663 | + | 0.930354i | \(0.380500\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.88492 | + | 2.90247i | −0.478365 | + | 0.140461i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.3086 | − | 9.53618i | 1.88905 | − | 0.458279i | 0.889053 | − | 0.457804i | \(-0.151364\pi\) |
1.00000 | 0.000475561i | \(-0.000151376\pi\) | ||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.7969 | + | 18.7007i | −0.515306 | + | 0.892537i | 0.484536 | + | 0.874771i | \(0.338989\pi\) |
−0.999842 | + | 0.0177654i | \(0.994345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.9624 | + | 13.3132i | −0.664878 | + | 0.633960i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.945001 | − | 0.327068i | \(-0.893939\pi\) | ||||
0.945001 | + | 0.327068i | \(0.106061\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.62530 | − | 19.0471i | 0.358268 | − | 0.894910i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.3085 | + | 19.3641i | 0.949991 | + | 0.905815i | 0.995653 | − | 0.0931420i | \(-0.0296911\pi\) |
−0.0456614 | + | 0.998957i | \(0.514540\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.0311 | − | 26.7432i | 0.977396 | − | 1.24286i | 0.00734134 | − | 0.999973i | \(-0.497663\pi\) |
0.970055 | − | 0.242887i | \(-0.0780944\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.42552 | − | 5.67956i | −0.112000 | − | 0.262258i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.15525 | + | 22.5708i | −0.0993087 | + | 1.04001i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.8115 | − | 26.5897i | −1.55138 | − | 1.22002i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.0409 | + | 19.9695i | −0.868189 | + | 0.910530i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0835 | − | 3.83603i | 0.502241 | − | 0.173827i | −0.0641880 | − | 0.997938i | \(-0.520446\pi\) |
0.566429 | + | 0.824110i | \(0.308325\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.5301 | + | 1.02561i | 0.973627 | + | 0.0463796i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.0987 | − | 10.4493i | −0.810209 | − | 0.467775i | 0.0368191 | − | 0.999322i | \(-0.488277\pi\) |
−0.847029 | + | 0.531547i | \(0.821611\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.0950560 | − | 0.995472i | \(-0.530303\pi\) | ||||
0.0950560 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.9347 | − | 6.31316i | 0.485628 | − | 0.280377i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.06808 | + | 10.4489i | 0.135724 | + | 0.462234i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.4835 | − | 39.7325i | −0.904371 | − | 1.75423i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.87407 | − | 36.5794i | 0.388036 | − | 1.59951i | −0.358081 | − | 0.933691i | \(-0.616569\pi\) |
0.746117 | − | 0.665815i | \(-0.231916\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.13616 | − | 4.03912i | 0.224160 | − | 0.176282i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.3413 | − | 18.7352i | 0.580057 | − | 0.814576i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.88319 | − | 0.270762i | 0.0809647 | − | 0.0116410i | −0.101713 | − | 0.994814i | \(-0.532432\pi\) |
0.182678 | + | 0.983173i | \(0.441523\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −37.0843 | − | 26.4076i | −1.59144 | − | 1.13326i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.3982 | + | 24.6668i | 0.829406 | + | 1.05468i | 0.997622 | + | 0.0689253i | \(0.0219570\pi\) |
−0.168216 | + | 0.985750i | \(0.553801\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −39.8088 | − | 9.65750i | −1.69900 | − | 0.412172i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.90518 | − | 1.13813i | 0.251114 | − | 0.0483982i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.24927 | + | 2.19065i | −0.179725 | + | 0.0926546i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.59904 | − | 1.60091i | 0.277133 | − | 0.0672318i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.6586 | + | 20.9609i | 1.70151 | + | 0.877188i | 0.983444 | + | 0.181210i | \(0.0580014\pi\) |
0.718063 | + | 0.695978i | \(0.245029\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.3125 | + | 9.79906i | 1.17867 | + | 0.407940i | 0.845008 | − | 0.534754i | \(-0.179596\pi\) |
0.333658 | + | 0.942694i | \(0.391717\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.842112 | − | 0.729694i | 0.0349970 | − | 0.0303251i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.371662 | − | 0.928368i | \(-0.378788\pi\) | ||||
−0.371662 | + | 0.928368i | \(0.621212\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 69.1871 | + | 59.9510i | 2.85081 | + | 2.47024i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.998867 | − | 0.0475819i | \(-0.0151515\pi\) | ||||
−0.998867 | + | 0.0475819i | \(0.984848\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.30024 | + | 8.01141i | −0.257852 | + | 0.327885i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.189251 | − | 0.981929i | \(-0.439394\pi\) | ||||
−0.189251 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.23519 | + | 0.499900i | 0.213548 | + | 0.0203914i | 0.201282 | − | 0.979533i | \(-0.435489\pi\) |
0.0122663 | + | 0.999925i | \(0.496095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.93926 | − | 24.3795i | 0.119696 | − | 0.992811i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.3463 | − | 2.95776i | −0.622888 | − | 0.120052i | −0.131964 | − | 0.991254i | \(-0.542128\pi\) |
−0.490923 | + | 0.871203i | \(0.663341\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.33631 | + | 49.0452i | 0.0943626 | + | 1.98092i | 0.176523 | + | 0.984297i | \(0.443515\pi\) |
−0.0821600 | + | 0.996619i | \(0.526182\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45.2196 | − | 18.1032i | −1.81753 | − | 0.727629i | −0.984738 | − | 0.174042i | \(-0.944317\pi\) |
−0.832792 | − | 0.553587i | \(-0.813259\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.0313 | − | 13.5160i | 0.841254 | − | 0.540641i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.4929 | + | 31.9800i | 1.21390 | + | 1.27310i | 0.951324 | + | 0.308193i | \(0.0997243\pi\) |
0.262578 | + | 0.964911i | \(0.415427\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.76233 | − | 5.05893i | −0.348271 | − | 0.201074i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.46072 | + | 15.2973i | 0.0578757 | + | 0.606102i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.08107 | − | 49.2499i | 0.279250 | − | 1.94223i | −0.0519076 | − | 0.998652i | \(-0.516530\pi\) |
0.331158 | − | 0.943575i | \(-0.392561\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.458227 | − | 0.888835i | \(-0.651515\pi\) | ||||
0.458227 | + | 0.888835i | \(0.348485\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.3280 | + | 8.06662i | −0.443979 | + | 0.316156i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.189251 | − | 0.981929i | \(-0.560606\pi\) | ||||
0.189251 | + | 0.981929i | \(0.439394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.2085 | + | 42.0802i | −0.398273 | + | 1.64170i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.4828 | + | 17.1178i | −1.45791 | + | 0.665806i | −0.977442 | − | 0.211205i | \(-0.932261\pi\) |
−0.480470 | + | 0.877011i | \(0.659534\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 34.8582i | 1.34769i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.5987 | − | 35.1642i | 0.871115 | − | 1.35548i | −0.0628142 | − | 0.998025i | \(-0.520008\pi\) |
0.933930 | − | 0.357457i | \(-0.116356\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.7163 | − | 3.69745i | 0.989821 | − | 0.142315i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.814576 | − | 0.580057i | \(-0.803030\pi\) | ||||
0.814576 | + | 0.580057i | \(0.196970\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.87090 | + | 12.8555i | 0.225304 | + | 0.493348i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.971812 | − | 0.235759i | \(-0.924242\pi\) | ||||
0.971812 | + | 0.235759i | \(0.0757576\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.0279 | + | 5.40193i | −1.06933 | + | 0.206096i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7167 | − | 8.29372i | 0.788101 | − | 0.315508i | 0.0575291 | − | 0.998344i | \(-0.481678\pi\) |
0.730572 | + | 0.682836i | \(0.239254\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.971812 | − | 0.235759i | \(-0.0757576\pi\) | ||||
−0.971812 | + | 0.235759i | \(0.924242\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −98.8860 | + | 9.44247i | −3.72956 | + | 0.356129i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.58152 | + | 5.32196i | −0.209618 | + | 0.199871i | −0.787614 | − | 0.616169i | \(-0.788684\pi\) |
0.577995 | + | 0.816040i | \(0.303835\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.5970 | + | 7.82089i | 0.847453 | + | 0.293306i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.21340 | + | 8.02669i | −0.119673 | + | 0.298929i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.9329 | + | 26.8035i | 1.15041 | + | 0.996834i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 51.7184 | − | 2.46365i | 1.91813 | − | 0.0913717i | 0.945766 | − | 0.324850i | \(-0.105314\pi\) |
0.972362 | + | 0.233478i | \(0.0750106\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.9063 | + | 7.60678i | 0.959493 | + | 0.281733i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.97341 | + | 36.1815i | −0.257569 | + | 1.33639i | 0.590727 | + | 0.806871i | \(0.298841\pi\) |
−0.848296 | + | 0.529522i | \(0.822371\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.178224 | + | 1.86645i | −0.00655608 | + | 0.0686584i | −0.998158 | − | 0.0606703i | \(-0.980676\pi\) |
0.991602 | + | 0.129329i | \(0.0412822\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −34.9630 | − | 6.73857i | −1.28440 | − | 0.247547i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.8719 | + | 35.6281i | −1.12653 | + | 1.30009i | −0.177779 | + | 0.984070i | \(0.556891\pi\) |
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0244 | − | 1.04915i | −0.800492 | − | 0.0381321i | −0.356651 | − | 0.934238i | \(-0.616081\pi\) |
−0.443841 | + | 0.896106i | \(0.646384\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.94506 | − | 14.2878i | 0.179023 | − | 0.517254i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.0135 | + | 36.8810i | −0.685643 | + | 1.32996i | 0.246949 | + | 0.969028i | \(0.420572\pi\) |
−0.932592 | + | 0.360933i | \(0.882458\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −46.0792 | + | 26.6038i | −1.65521 | + | 0.955638i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.14748 | − | 14.9361i | 0.0770405 | − | 0.535828i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.61485 | + | 18.7556i | 0.128856 | + | 0.668566i | 0.987704 | + | 0.156336i | \(0.0499683\pi\) |
−0.858848 | + | 0.512230i | \(0.828820\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.6479 | + | 20.1698i | −0.910785 | + | 0.716249i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.3262 | + | 32.9887i | 1.62673 | + | 1.15839i | 0.844969 | + | 0.534815i | \(0.179619\pi\) |
0.781763 | + | 0.623576i | \(0.214321\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.3211 | − | 31.3588i | −0.502262 | − | 1.09980i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.7260 | − | 4.05769i | −0.585169 | − | 0.141960i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.24690 | − | 4.92003i | 0.0785132 | − | 0.171920i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.6894 | − | 40.2886i | −1.00005 | − | 1.40437i | −0.912904 | − | 0.408175i | \(-0.866165\pi\) |
−0.0871445 | − | 0.996196i | \(-0.527774\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.0488 | + | 10.8785i | −1.28676 | + | 0.377826i | −0.852388 | − | 0.522909i | \(-0.824847\pi\) |
−0.434369 | + | 0.900735i | \(0.643028\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 50.5131 | + | 7.26269i | 1.75228 | + | 0.251940i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −55.0447 | + | 5.25613i | −1.90262 | + | 0.181678i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | + | 25.1147i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.27230 | − | 5.43497i | 0.215519 | − | 0.186748i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.8970 | − | 21.6241i | −0.476944 | − | 0.742139i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.2929 | + | 44.1860i | 0.523619 | + | 1.51290i | 0.828212 | + | 0.560415i | \(0.189359\pi\) |
−0.304592 | + | 0.952483i | \(0.598520\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.6818 | + | 19.7201i | 0.705656 | + | 0.672841i | 0.955348 | − | 0.295484i | \(-0.0954809\pi\) |
−0.249692 | + | 0.968325i | \(0.580329\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.57248 | + | 28.9128i | −0.189251 | + | 0.981929i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.8172 | − | 13.8444i | −0.468178 | − | 0.469100i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.34155 | + | 55.9393i | −0.180784 | + | 1.89326i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.5504 | + | 12.2290i | 0.525100 | + | 0.412943i | 0.845208 | − | 0.534438i | \(-0.179477\pi\) |
−0.320108 | + | 0.947381i | \(0.603719\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.2027 | − | 32.7244i | 1.05005 | − | 1.10126i | 0.0553507 | − | 0.998467i | \(-0.482372\pi\) |
0.994702 | − | 0.102797i | \(-0.0327792\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.4337 | − | 5.34165i | 0.517629 | − | 0.179153i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.19802 | − | 2.32383i | 0.0398676 | − | 0.0773324i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.16686 | − | 37.7863i | −0.304381 | − | 1.25467i | −0.894394 | − | 0.447280i | \(-0.852393\pi\) |
0.590013 | − | 0.807394i | \(-0.299123\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.5410 | − | 32.4296i | 1.50226 | − | 1.06975i | 0.526692 | − | 0.850056i | \(-0.323432\pi\) |
0.975568 | − | 0.219698i | \(-0.0705073\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.3729 | + | 59.0080i | 0.374749 | + | 1.94438i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.6113 | − | 56.1067i | 0.447538 | − | 1.84478i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −27.0230 | + | 21.2511i | −0.887551 | + | 0.697978i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.0904 | + | 45.0646i | −1.05172 | + | 1.47693i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.44207i | 0.210453i | 0.994448 | + | 0.105227i | \(0.0335568\pi\) | ||||
−0.994448 | + | 0.105227i | \(0.966443\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.7217 | 0.480425 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.3206 | + | 27.1114i | 0.692096 | + | 0.880072i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.0999 | − | 37.6856i | 2.35806 | − | 1.21567i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.3808 | − | 38.7646i | −0.719717 | − | 1.24659i | −0.961112 | − | 0.276160i | \(-0.910938\pi\) |
0.241395 | − | 0.970427i | \(-0.422395\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.40753 | + | 2.78777i | 0.173357 | + | 0.0893719i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.3473 | − | 17.9220i | 0.331378 | − | 0.573963i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.4336 | − | 39.3684i | 1.45058 | − | 1.25694i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.0710 | + | 24.3236i | 0.891704 | + | 0.772666i | 0.974614 | − | 0.223891i | \(-0.0718760\pi\) |
−0.0829100 | + | 0.996557i | \(0.526421\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 41.1011 | + | 39.1898i | 1.30430 | + | 1.24365i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.4173 | − | 11.8676i | −1.28003 | − | 0.375850i | −0.430115 | − | 0.902774i | \(-0.641527\pi\) |
−0.849912 | + | 0.526924i | \(0.823345\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 37.0890 | − | 47.1625i | 1.17344 | − | 1.49215i |
(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 | 804.2.ba.a.197.1 | ✓ | 20 | |
3.2 | odd | 2 | CM | 804.2.ba.a.197.1 | ✓ | 20 | |
67.50 | odd | 66 | inner | 804.2.ba.a.653.1 | yes | 20 | |
201.50 | even | 66 | inner | 804.2.ba.a.653.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.ba.a.197.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
804.2.ba.a.197.1 | ✓ | 20 | 3.2 | odd | 2 | CM | |
804.2.ba.a.653.1 | yes | 20 | 67.50 | odd | 66 | inner | |
804.2.ba.a.653.1 | yes | 20 | 201.50 | even | 66 | inner |