Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.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: | \(31.6926245622\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 22 x^{10} + 92 x^{9} + 125 x^{8} - 620 x^{7} - 94 x^{6} + 1280 x^{5} - 234 x^{4} + \cdots - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 441) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.51703\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.10281 | 0.779807 | 0.389903 | − | 0.920856i | \(-0.372508\pi\) | ||||
0.389903 | + | 0.920856i | \(0.372508\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.783802 | −0.391901 | ||||||||
\(5\) | −0.105466 | −0.0471659 | −0.0235829 | − | 0.999722i | \(-0.507507\pi\) | ||||
−0.0235829 | + | 0.999722i | \(0.507507\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.07001 | −1.08541 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.116309 | −0.0367803 | ||||||||
\(11\) | −3.33731 | −1.00624 | −0.503119 | − | 0.864217i | \(-0.667814\pi\) | ||||
−0.503119 | + | 0.864217i | \(0.667814\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.47995 | 0.687814 | 0.343907 | − | 0.939004i | \(-0.388250\pi\) | ||||
0.343907 | + | 0.939004i | \(0.388250\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.81805 | −0.454512 | ||||||||
\(17\) | −1.61319 | −0.391255 | −0.195628 | − | 0.980678i | \(-0.562674\pi\) | ||||
−0.195628 | + | 0.980678i | \(0.562674\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.68266 | −1.76252 | −0.881262 | − | 0.472629i | \(-0.843305\pi\) | ||||
−0.881262 | + | 0.472629i | \(0.843305\pi\) | |||||||
\(20\) | 0.0826646 | 0.0184844 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.68044 | −0.784672 | ||||||||
\(23\) | 1.89719 | 0.395591 | 0.197795 | − | 0.980243i | \(-0.436622\pi\) | ||||
0.197795 | + | 0.980243i | \(0.436622\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.98888 | −0.997775 | ||||||||
\(26\) | 2.73492 | 0.536362 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.29042 | 1.72519 | 0.862594 | − | 0.505896i | \(-0.168838\pi\) | ||||
0.862594 | + | 0.505896i | \(0.168838\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.26162 | 1.66344 | 0.831718 | − | 0.555199i | \(-0.187358\pi\) | ||||
0.831718 | + | 0.555199i | \(0.187358\pi\) | |||||||
\(32\) | 4.13506 | 0.730982 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.77905 | −0.305104 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.98254 | −0.325927 | −0.162963 | − | 0.986632i | \(-0.552105\pi\) | ||||
−0.162963 | + | 0.986632i | \(0.552105\pi\) | |||||||
\(38\) | −8.47254 | −1.37443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.323782 | 0.0511945 | ||||||||
\(41\) | 7.48537 | 1.16902 | 0.584509 | − | 0.811387i | \(-0.301287\pi\) | ||||
0.584509 | + | 0.811387i | \(0.301287\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.54776 | 1.15102 | 0.575512 | − | 0.817794i | \(-0.304803\pi\) | ||||
0.575512 | + | 0.817794i | \(0.304803\pi\) | |||||||
\(44\) | 2.61579 | 0.394346 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.09224 | 0.308484 | ||||||||
\(47\) | 3.19560 | 0.466127 | 0.233063 | − | 0.972462i | \(-0.425125\pi\) | ||||
0.233063 | + | 0.972462i | \(0.425125\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.50180 | −0.778072 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.94379 | −0.269555 | ||||||||
\(53\) | 9.97679 | 1.37042 | 0.685209 | − | 0.728347i | \(-0.259711\pi\) | ||||
0.685209 | + | 0.728347i | \(0.259711\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.351974 | 0.0474601 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.2456 | 1.34531 | ||||||||
\(59\) | −4.45986 | −0.580625 | −0.290312 | − | 0.956932i | \(-0.593759\pi\) | ||||
−0.290312 | + | 0.956932i | \(0.593759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.67100 | −0.726097 | −0.363048 | − | 0.931770i | \(-0.618264\pi\) | ||||
−0.363048 | + | 0.931770i | \(0.618264\pi\) | |||||||
\(62\) | 10.2138 | 1.29716 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.19630 | 1.02454 | ||||||||
\(65\) | −0.261550 | −0.0324413 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.97141 | 1.21820 | 0.609101 | − | 0.793093i | \(-0.291530\pi\) | ||||
0.609101 | + | 0.793093i | \(0.291530\pi\) | |||||||
\(68\) | 1.26442 | 0.153333 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.29042 | −0.390502 | −0.195251 | − | 0.980753i | \(-0.562552\pi\) | ||||
−0.195251 | + | 0.980753i | \(0.562552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.72378 | −0.552877 | −0.276438 | − | 0.961032i | \(-0.589154\pi\) | ||||
−0.276438 | + | 0.961032i | \(0.589154\pi\) | |||||||
\(74\) | −2.18637 | −0.254160 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.02169 | 0.690735 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.69409 | 0.865653 | 0.432827 | − | 0.901477i | \(-0.357516\pi\) | ||||
0.432827 | + | 0.901477i | \(0.357516\pi\) | |||||||
\(80\) | 0.191743 | 0.0214375 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.25496 | 0.911608 | ||||||||
\(83\) | −1.16886 | −0.128299 | −0.0641493 | − | 0.997940i | \(-0.520433\pi\) | ||||
−0.0641493 | + | 0.997940i | \(0.520433\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.170137 | 0.0184539 | ||||||||
\(86\) | 8.32378 | 0.897576 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.2456 | 1.09219 | ||||||||
\(89\) | −6.02954 | −0.639130 | −0.319565 | − | 0.947564i | \(-0.603537\pi\) | ||||
−0.319565 | + | 0.947564i | \(0.603537\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.48702 | −0.155032 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.52415 | 0.363489 | ||||||||
\(95\) | 0.810260 | 0.0831309 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.80255 | 0.386090 | 0.193045 | − | 0.981190i | \(-0.438164\pi\) | ||||
0.193045 | + | 0.981190i | \(0.438164\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.91029 | 0.391029 | ||||||||
\(101\) | −17.4702 | −1.73835 | −0.869177 | − | 0.494501i | \(-0.835351\pi\) | ||||
−0.869177 | + | 0.494501i | \(0.835351\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.73204 | −0.860394 | −0.430197 | − | 0.902735i | \(-0.641556\pi\) | ||||
−0.430197 | + | 0.902735i | \(0.641556\pi\) | |||||||
\(104\) | −7.61347 | −0.746563 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.0025 | 1.06866 | ||||||||
\(107\) | 18.1463 | 1.75427 | 0.877135 | − | 0.480244i | \(-0.159452\pi\) | ||||
0.877135 | + | 0.480244i | \(0.159452\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.22248 | −0.404440 | −0.202220 | − | 0.979340i | \(-0.564816\pi\) | ||||
−0.202220 | + | 0.979340i | \(0.564816\pi\) | |||||||
\(110\) | 0.388161 | 0.0370097 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.05648 | 0.193457 | 0.0967285 | − | 0.995311i | \(-0.469162\pi\) | ||||
0.0967285 | + | 0.995311i | \(0.469162\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.200089 | −0.0186584 | ||||||||
\(116\) | −7.28186 | −0.676103 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.91840 | −0.452775 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.137670 | 0.0125155 | ||||||||
\(122\) | −6.25405 | −0.566215 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.25928 | −0.651902 | ||||||||
\(125\) | 1.05349 | 0.0942268 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.317159 | 0.0281433 | 0.0140717 | − | 0.999901i | \(-0.495521\pi\) | ||||
0.0140717 | + | 0.999901i | \(0.495521\pi\) | |||||||
\(128\) | 0.768871 | 0.0679592 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.288441 | −0.0252980 | ||||||||
\(131\) | 14.9563 | 1.30674 | 0.653370 | − | 0.757039i | \(-0.273355\pi\) | ||||
0.653370 | + | 0.757039i | \(0.273355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.9966 | 0.949962 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.95251 | 0.424674 | ||||||||
\(137\) | 15.2473 | 1.30267 | 0.651334 | − | 0.758791i | \(-0.274210\pi\) | ||||
0.651334 | + | 0.758791i | \(0.274210\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.11886 | 0.688633 | 0.344316 | − | 0.938854i | \(-0.388111\pi\) | ||||
0.344316 | + | 0.938854i | \(0.388111\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.62872 | −0.304516 | ||||||||
\(143\) | −8.27636 | −0.692104 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.979825 | −0.0813700 | ||||||||
\(146\) | −5.20945 | −0.431137 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.55392 | 0.127731 | ||||||||
\(149\) | 11.1486 | 0.913329 | 0.456664 | − | 0.889639i | \(-0.349044\pi\) | ||||
0.456664 | + | 0.889639i | \(0.349044\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.2735 | −0.917425 | −0.458713 | − | 0.888585i | \(-0.651689\pi\) | ||||
−0.458713 | + | 0.888585i | \(0.651689\pi\) | |||||||
\(152\) | 23.5859 | 1.91307 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.976786 | −0.0784574 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.2064 | −0.974173 | −0.487087 | − | 0.873354i | \(-0.661940\pi\) | ||||
−0.487087 | + | 0.873354i | \(0.661940\pi\) | |||||||
\(158\) | 8.48515 | 0.675042 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.436109 | −0.0344774 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.96264 | 0.702008 | 0.351004 | − | 0.936374i | \(-0.385840\pi\) | ||||
0.351004 | + | 0.936374i | \(0.385840\pi\) | |||||||
\(164\) | −5.86705 | −0.458139 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.28903 | −0.100048 | ||||||||
\(167\) | 17.4167 | 1.34774 | 0.673871 | − | 0.738849i | \(-0.264630\pi\) | ||||
0.673871 | + | 0.738849i | \(0.264630\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.84986 | −0.526913 | ||||||||
\(170\) | 0.187629 | 0.0143905 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.91595 | −0.451087 | ||||||||
\(173\) | 2.82933 | 0.215110 | 0.107555 | − | 0.994199i | \(-0.465698\pi\) | ||||
0.107555 | + | 0.994199i | \(0.465698\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.06740 | 0.457348 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.64946 | −0.498398 | ||||||||
\(179\) | 10.1627 | 0.759595 | 0.379798 | − | 0.925070i | \(-0.375994\pi\) | ||||
0.379798 | + | 0.925070i | \(0.375994\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0870 | 1.27006 | 0.635032 | − | 0.772486i | \(-0.280987\pi\) | ||||
0.635032 | + | 0.772486i | \(0.280987\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.82439 | −0.429380 | ||||||||
\(185\) | 0.209090 | 0.0153726 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.38371 | 0.393696 | ||||||||
\(188\) | −2.50472 | −0.182676 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.893566 | 0.0648261 | ||||||||
\(191\) | 22.4000 | 1.62081 | 0.810404 | − | 0.585872i | \(-0.199248\pi\) | ||||
0.810404 | + | 0.585872i | \(0.199248\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.256786 | −0.0184839 | −0.00924194 | − | 0.999957i | \(-0.502942\pi\) | ||||
−0.00924194 | + | 0.999957i | \(0.502942\pi\) | |||||||
\(194\) | 4.19350 | 0.301076 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.763370 | 0.0543878 | 0.0271939 | − | 0.999630i | \(-0.491343\pi\) | ||||
0.0271939 | + | 0.999630i | \(0.491343\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.03121 | 0.356653 | 0.178327 | − | 0.983971i | \(-0.442932\pi\) | ||||
0.178327 | + | 0.983971i | \(0.442932\pi\) | |||||||
\(200\) | 15.3159 | 1.08300 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −19.2664 | −1.35558 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.789452 | −0.0551377 | ||||||||
\(206\) | −9.62981 | −0.670941 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.50867 | −0.312620 | ||||||||
\(209\) | 25.6395 | 1.77352 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.21074 | 0.496407 | 0.248204 | − | 0.968708i | \(-0.420160\pi\) | ||||
0.248204 | + | 0.968708i | \(0.420160\pi\) | |||||||
\(212\) | −7.81983 | −0.537068 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.0120 | 1.36799 | ||||||||
\(215\) | −0.796033 | −0.0542890 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.65661 | −0.315385 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.275878 | −0.0185997 | ||||||||
\(221\) | −4.00062 | −0.269111 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1821 | 0.748810 | 0.374405 | − | 0.927265i | \(-0.377847\pi\) | ||||
0.374405 | + | 0.927265i | \(0.377847\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.26791 | 0.150859 | ||||||||
\(227\) | 23.7706 | 1.57771 | 0.788857 | − | 0.614577i | \(-0.210673\pi\) | ||||
0.788857 | + | 0.614577i | \(0.210673\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.90547 | 0.125917 | 0.0629586 | − | 0.998016i | \(-0.479946\pi\) | ||||
0.0629586 | + | 0.998016i | \(0.479946\pi\) | |||||||
\(230\) | −0.220661 | −0.0145499 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −28.5217 | −1.87254 | ||||||||
\(233\) | −6.54184 | −0.428570 | −0.214285 | − | 0.976771i | \(-0.568742\pi\) | ||||
−0.214285 | + | 0.976771i | \(0.568742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.337028 | −0.0219853 | ||||||||
\(236\) | 3.49565 | 0.227547 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3469 | 1.38082 | 0.690409 | − | 0.723419i | \(-0.257431\pi\) | ||||
0.690409 | + | 0.723419i | \(0.257431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0662 | 1.29258 | 0.646288 | − | 0.763094i | \(-0.276321\pi\) | ||||
0.646288 | + | 0.763094i | \(0.276321\pi\) | |||||||
\(242\) | 0.151825 | 0.00975967 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.44494 | 0.284558 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.0526 | −1.21229 | ||||||||
\(248\) | −28.4333 | −1.80552 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.16180 | 0.0734787 | ||||||||
\(251\) | −6.81467 | −0.430138 | −0.215069 | − | 0.976599i | \(-0.568998\pi\) | ||||
−0.215069 | + | 0.976599i | \(0.568998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.33151 | −0.398059 | ||||||||
\(254\) | 0.349767 | 0.0219464 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.5447 | −0.971542 | ||||||||
\(257\) | −14.3883 | −0.897518 | −0.448759 | − | 0.893653i | \(-0.648134\pi\) | ||||
−0.448759 | + | 0.893653i | \(0.648134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.205004 | 0.0127138 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.4940 | 1.01900 | ||||||||
\(263\) | 1.53901 | 0.0948992 | 0.0474496 | − | 0.998874i | \(-0.484891\pi\) | ||||
0.0474496 | + | 0.998874i | \(0.484891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.05221 | −0.0646369 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.81562 | −0.477415 | ||||||||
\(269\) | −26.2571 | −1.60092 | −0.800461 | − | 0.599385i | \(-0.795412\pi\) | ||||
−0.800461 | + | 0.599385i | \(0.795412\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.9335 | −1.08938 | −0.544690 | − | 0.838637i | \(-0.683353\pi\) | ||||
−0.544690 | + | 0.838637i | \(0.683353\pi\) | |||||||
\(272\) | 2.93286 | 0.177830 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.8150 | 1.01583 | ||||||||
\(275\) | 16.6495 | 1.00400 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.8713 | −1.13386 | −0.566932 | − | 0.823764i | \(-0.691870\pi\) | ||||
−0.566932 | + | 0.823764i | \(0.691870\pi\) | |||||||
\(278\) | 8.95359 | 0.537001 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.99157 | −0.297772 | −0.148886 | − | 0.988854i | \(-0.547569\pi\) | ||||
−0.148886 | + | 0.988854i | \(0.547569\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.3927 | −0.915000 | −0.457500 | − | 0.889210i | \(-0.651255\pi\) | ||||
−0.457500 | + | 0.889210i | \(0.651255\pi\) | |||||||
\(284\) | 2.57904 | 0.153038 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.12729 | −0.539708 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3976 | −0.846919 | ||||||||
\(290\) | −1.08056 | −0.0634529 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.70251 | 0.216673 | ||||||||
\(293\) | −25.8025 | −1.50740 | −0.753700 | − | 0.657219i | \(-0.771733\pi\) | ||||
−0.753700 | + | 0.657219i | \(0.771733\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.470364 | 0.0273857 | ||||||||
\(296\) | 6.08642 | 0.353766 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.2948 | 0.712220 | ||||||||
\(299\) | 4.70492 | 0.272093 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.4326 | −0.715415 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 13.9675 | 0.801089 | ||||||||
\(305\) | 0.598098 | 0.0342470 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.2914 | −1.27224 | −0.636120 | − | 0.771590i | \(-0.719462\pi\) | ||||
−0.636120 | + | 0.771590i | \(0.719462\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.07721 | −0.0611816 | ||||||||
\(311\) | 1.30986 | 0.0742755 | 0.0371377 | − | 0.999310i | \(-0.488176\pi\) | ||||
0.0371377 | + | 0.999310i | \(0.488176\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.5770 | 1.21960 | 0.609802 | − | 0.792554i | \(-0.291249\pi\) | ||||
0.609802 | + | 0.792554i | \(0.291249\pi\) | |||||||
\(314\) | −13.4613 | −0.759667 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.03065 | −0.339250 | ||||||||
\(317\) | 24.7819 | 1.39189 | 0.695946 | − | 0.718094i | \(-0.254985\pi\) | ||||
0.695946 | + | 0.718094i | \(0.254985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −31.0051 | −1.73595 | ||||||||
\(320\) | −0.864432 | −0.0483232 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.3936 | 0.689597 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.3722 | −0.686283 | ||||||||
\(326\) | 9.88412 | 0.547431 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −22.9802 | −1.26887 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.8451 | 0.760996 | 0.380498 | − | 0.924782i | \(-0.375753\pi\) | ||||
0.380498 | + | 0.924782i | \(0.375753\pi\) | |||||||
\(332\) | 0.916151 | 0.0502803 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.2073 | 1.05098 | ||||||||
\(335\) | −1.05165 | −0.0574576 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.38887 | −0.184604 | −0.0923018 | − | 0.995731i | \(-0.529422\pi\) | ||||
−0.0923018 | + | 0.995731i | \(0.529422\pi\) | |||||||
\(338\) | −7.55412 | −0.410890 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.133353 | −0.00723210 | ||||||||
\(341\) | −30.9089 | −1.67381 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −23.1717 | −1.24934 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.12022 | 0.167744 | ||||||||
\(347\) | 14.5148 | 0.779195 | 0.389597 | − | 0.920985i | \(-0.372614\pi\) | ||||
0.389597 | + | 0.920985i | \(0.372614\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.7282 | −0.841914 | −0.420957 | − | 0.907081i | \(-0.638306\pi\) | ||||
−0.420957 | + | 0.907081i | \(0.638306\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13.8000 | −0.735542 | ||||||||
\(353\) | 4.14423 | 0.220575 | 0.110287 | − | 0.993900i | \(-0.464823\pi\) | ||||
0.110287 | + | 0.993900i | \(0.464823\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.347028 | 0.0184183 | ||||||||
\(356\) | 4.72597 | 0.250476 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.2076 | 0.592338 | ||||||||
\(359\) | −7.93988 | −0.419051 | −0.209525 | − | 0.977803i | \(-0.567192\pi\) | ||||
−0.209525 | + | 0.977803i | \(0.567192\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.0233 | 2.10649 | ||||||||
\(362\) | 18.8437 | 0.990405 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.498199 | 0.0260769 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.1491 | −0.686377 | −0.343189 | − | 0.939266i | \(-0.611507\pi\) | ||||
−0.343189 | + | 0.939266i | \(0.611507\pi\) | |||||||
\(368\) | −3.44918 | −0.179801 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.230588 | 0.0119877 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.81086 | 0.404431 | 0.202216 | − | 0.979341i | \(-0.435186\pi\) | ||||
0.202216 | + | 0.979341i | \(0.435186\pi\) | |||||||
\(374\) | 5.93723 | 0.307007 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.81055 | −0.505940 | ||||||||
\(377\) | 23.0398 | 1.18661 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.6147 | −1.62394 | −0.811968 | − | 0.583702i | \(-0.801604\pi\) | ||||
−0.811968 | + | 0.583702i | \(0.801604\pi\) | |||||||
\(380\) | −0.635084 | −0.0325791 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24.7030 | 1.26392 | ||||||||
\(383\) | 10.7319 | 0.548373 | 0.274186 | − | 0.961677i | \(-0.411592\pi\) | ||||
0.274186 | + | 0.961677i | \(0.411592\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.283187 | −0.0144139 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.98045 | −0.151309 | ||||||||
\(389\) | −24.1468 | −1.22429 | −0.612147 | − | 0.790744i | \(-0.709694\pi\) | ||||
−0.612147 | + | 0.790744i | \(0.709694\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.06052 | −0.154777 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.841854 | 0.0424120 | ||||||||
\(395\) | −0.811466 | −0.0408293 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.0569 | 1.20738 | 0.603691 | − | 0.797218i | \(-0.293696\pi\) | ||||
0.603691 | + | 0.797218i | \(0.293696\pi\) | |||||||
\(398\) | 5.54849 | 0.278121 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.07003 | 0.453501 | ||||||||
\(401\) | 1.56232 | 0.0780183 | 0.0390092 | − | 0.999239i | \(-0.487580\pi\) | ||||
0.0390092 | + | 0.999239i | \(0.487580\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.9683 | 1.14413 | ||||||||
\(404\) | 13.6932 | 0.681263 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.61635 | 0.327960 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.3456 | −1.10492 | −0.552460 | − | 0.833539i | \(-0.686311\pi\) | ||||
−0.552460 | + | 0.833539i | \(0.686311\pi\) | |||||||
\(410\) | −0.870619 | −0.0429968 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.84419 | 0.337189 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.123275 | 0.00605131 | ||||||||
\(416\) | 10.2547 | 0.502779 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 28.2755 | 1.38300 | ||||||||
\(419\) | 5.97295 | 0.291798 | 0.145899 | − | 0.989299i | \(-0.453393\pi\) | ||||
0.145899 | + | 0.989299i | \(0.453393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.6319 | −0.713114 | −0.356557 | − | 0.934273i | \(-0.616050\pi\) | ||||
−0.356557 | + | 0.934273i | \(0.616050\pi\) | |||||||
\(422\) | 7.95210 | 0.387102 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30.6289 | −1.48747 | ||||||||
\(425\) | 8.04799 | 0.390385 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14.2231 | −0.687500 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.877876 | −0.0423349 | ||||||||
\(431\) | 19.4034 | 0.934628 | 0.467314 | − | 0.884091i | \(-0.345222\pi\) | ||||
0.467314 | + | 0.884091i | \(0.345222\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.35217 | 0.0649810 | 0.0324905 | − | 0.999472i | \(-0.489656\pi\) | ||||
0.0324905 | + | 0.999472i | \(0.489656\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.30959 | 0.158501 | ||||||||
\(437\) | −14.5754 | −0.697238 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.3412 | 0.827650 | 0.413825 | − | 0.910356i | \(-0.364193\pi\) | ||||
0.413825 | + | 0.910356i | \(0.364193\pi\) | |||||||
\(440\) | −1.08056 | −0.0515139 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.41194 | −0.209854 | ||||||||
\(443\) | −19.6100 | −0.931698 | −0.465849 | − | 0.884864i | \(-0.654251\pi\) | ||||
−0.465849 | + | 0.884864i | \(0.654251\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.635912 | 0.0301451 | ||||||||
\(446\) | 12.3318 | 0.583927 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.7345 | 0.836942 | 0.418471 | − | 0.908230i | \(-0.362566\pi\) | ||||
0.418471 | + | 0.908230i | \(0.362566\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.9810 | −1.17631 | ||||||||
\(452\) | −1.61187 | −0.0758160 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 26.2146 | 1.23031 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.485451 | 0.0227084 | 0.0113542 | − | 0.999936i | \(-0.496386\pi\) | ||||
0.0113542 | + | 0.999936i | \(0.496386\pi\) | |||||||
\(458\) | 2.10138 | 0.0981912 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.156830 | 0.00731224 | ||||||||
\(461\) | 7.99375 | 0.372306 | 0.186153 | − | 0.982521i | \(-0.440398\pi\) | ||||
0.186153 | + | 0.982521i | \(0.440398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.4856 | −0.487308 | −0.243654 | − | 0.969862i | \(-0.578346\pi\) | ||||
−0.243654 | + | 0.969862i | \(0.578346\pi\) | |||||||
\(464\) | −16.8905 | −0.784120 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.21443 | −0.334202 | ||||||||
\(467\) | −21.8977 | −1.01331 | −0.506653 | − | 0.862150i | \(-0.669117\pi\) | ||||
−0.506653 | + | 0.862150i | \(0.669117\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.371679 | −0.0171443 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.6918 | 0.630218 | ||||||||
\(473\) | −25.1893 | −1.15820 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38.3278 | 1.75860 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 23.5417 | 1.07677 | ||||||||
\(479\) | −4.00169 | −0.182842 | −0.0914210 | − | 0.995812i | \(-0.529141\pi\) | ||||
−0.0914210 | + | 0.995812i | \(0.529141\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.91658 | −0.224177 | ||||||||
\(482\) | 22.1292 | 1.00796 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.107906 | −0.00490483 | ||||||||
\(485\) | −0.401040 | −0.0182103 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.4755 | −1.19972 | −0.599859 | − | 0.800106i | \(-0.704777\pi\) | ||||
−0.599859 | + | 0.800106i | \(0.704777\pi\) | |||||||
\(488\) | 17.4100 | 0.788116 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.4299 | 1.28302 | 0.641511 | − | 0.767114i | \(-0.278308\pi\) | ||||
0.641511 | + | 0.767114i | \(0.278308\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.9872 | −0.674989 | ||||||||
\(494\) | −21.0115 | −0.945350 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.8381 | −0.756052 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.43118 | −0.332665 | −0.166333 | − | 0.986070i | \(-0.553193\pi\) | ||||
−0.166333 | + | 0.986070i | \(0.553193\pi\) | |||||||
\(500\) | −0.825726 | −0.0369276 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.51531 | −0.335425 | ||||||||
\(503\) | 10.1610 | 0.453057 | 0.226529 | − | 0.974004i | \(-0.427262\pi\) | ||||
0.226529 | + | 0.974004i | \(0.427262\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.84252 | 0.0819910 | ||||||||
\(506\) | −6.98247 | −0.310409 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.248590 | −0.0110294 | ||||||||
\(509\) | −28.9063 | −1.28125 | −0.640625 | − | 0.767854i | \(-0.721325\pi\) | ||||
−0.640625 | + | 0.767854i | \(0.721325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −18.6806 | −0.825575 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.8676 | −0.699891 | ||||||||
\(515\) | 0.920934 | 0.0405812 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.6647 | −0.469034 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.802963 | 0.0352123 | ||||||||
\(521\) | 33.7990 | 1.48076 | 0.740381 | − | 0.672187i | \(-0.234645\pi\) | ||||
0.740381 | + | 0.672187i | \(0.234645\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.3779 | 0.628701 | 0.314351 | − | 0.949307i | \(-0.398213\pi\) | ||||
0.314351 | + | 0.949307i | \(0.398213\pi\) | |||||||
\(524\) | −11.7228 | −0.512113 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.69724 | 0.0740030 | ||||||||
\(527\) | −14.9407 | −0.650828 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.4007 | −0.843508 | ||||||||
\(530\) | −1.16039 | −0.0504043 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.5633 | 0.804066 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.91382 | −0.0827417 | ||||||||
\(536\) | −30.6124 | −1.32225 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −28.9567 | −1.24841 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.1764 | −1.08242 | −0.541210 | − | 0.840888i | \(-0.682034\pi\) | ||||
−0.541210 | + | 0.840888i | \(0.682034\pi\) | |||||||
\(542\) | −19.7773 | −0.849506 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.67063 | −0.286001 | ||||||||
\(545\) | 0.445329 | 0.0190758 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.18023 | −0.135977 | −0.0679883 | − | 0.997686i | \(-0.521658\pi\) | ||||
−0.0679883 | + | 0.997686i | \(0.521658\pi\) | |||||||
\(548\) | −11.9509 | −0.510517 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.3612 | 0.782926 | ||||||||
\(551\) | −71.3752 | −3.04068 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −20.8115 | −0.884195 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.36358 | −0.269876 | ||||||||
\(557\) | −20.0459 | −0.849371 | −0.424686 | − | 0.905341i | \(-0.639615\pi\) | ||||
−0.424686 | + | 0.905341i | \(0.639615\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.7181 | 0.791689 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.50477 | −0.232205 | ||||||||
\(563\) | 39.8013 | 1.67743 | 0.838713 | − | 0.544574i | \(-0.183309\pi\) | ||||
0.838713 | + | 0.544574i | \(0.183309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.216888 | −0.00912457 | ||||||||
\(566\) | −16.9753 | −0.713523 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.1017 | 0.423856 | ||||||||
\(569\) | −13.8159 | −0.579194 | −0.289597 | − | 0.957149i | \(-0.593521\pi\) | ||||
−0.289597 | + | 0.957149i | \(0.593521\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.4387 | 0.436846 | 0.218423 | − | 0.975854i | \(-0.429909\pi\) | ||||
0.218423 | + | 0.975854i | \(0.429909\pi\) | |||||||
\(572\) | 6.48703 | 0.271236 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.46483 | −0.394711 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.4923 | 1.06126 | 0.530628 | − | 0.847605i | \(-0.321956\pi\) | ||||
0.530628 | + | 0.847605i | \(0.321956\pi\) | |||||||
\(578\) | −15.8779 | −0.660433 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.767989 | 0.0318890 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −33.2957 | −1.37897 | ||||||||
\(584\) | 14.5021 | 0.600100 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.4554 | −1.17548 | ||||||||
\(587\) | −35.0337 | −1.44600 | −0.722998 | − | 0.690850i | \(-0.757236\pi\) | ||||
−0.722998 | + | 0.690850i | \(0.757236\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −71.1539 | −2.93184 | ||||||||
\(590\) | 0.518724 | 0.0213555 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.60435 | 0.148138 | ||||||||
\(593\) | 36.1292 | 1.48365 | 0.741824 | − | 0.670594i | \(-0.233961\pi\) | ||||
0.741824 | + | 0.670594i | \(0.233961\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.73830 | −0.357935 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.18865 | 0.212180 | ||||||||
\(599\) | 40.9484 | 1.67310 | 0.836552 | − | 0.547887i | \(-0.184568\pi\) | ||||
0.836552 | + | 0.547887i | \(0.184568\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.7094 | −1.04871 | −0.524354 | − | 0.851501i | \(-0.675693\pi\) | ||||
−0.524354 | + | 0.851501i | \(0.675693\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.83620 | 0.359540 | ||||||||
\(605\) | −0.0145196 | −0.000590304 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.84516 | 0.277836 | 0.138918 | − | 0.990304i | \(-0.455638\pi\) | ||||
0.138918 | + | 0.990304i | \(0.455638\pi\) | |||||||
\(608\) | −31.7683 | −1.28837 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.659590 | 0.0267060 | ||||||||
\(611\) | 7.92493 | 0.320608 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.1297 | −1.17654 | −0.588269 | − | 0.808666i | \(-0.700190\pi\) | ||||
−0.588269 | + | 0.808666i | \(0.700190\pi\) | |||||||
\(614\) | −24.5833 | −0.992101 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.6789 | −0.832503 | −0.416252 | − | 0.909250i | \(-0.636656\pi\) | ||||
−0.416252 | + | 0.909250i | \(0.636656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.86355 | −0.356256 | −0.178128 | − | 0.984007i | \(-0.557004\pi\) | ||||
−0.178128 | + | 0.984007i | \(0.557004\pi\) | |||||||
\(620\) | 0.765607 | 0.0307475 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.44453 | 0.0579205 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8333 | 0.993331 | ||||||||
\(626\) | 23.7954 | 0.951055 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.56737 | 0.381779 | ||||||||
\(629\) | 3.19820 | 0.127521 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4661 | 1.05360 | 0.526799 | − | 0.849990i | \(-0.323392\pi\) | ||||
0.526799 | + | 0.849990i | \(0.323392\pi\) | |||||||
\(632\) | −23.6210 | −0.939592 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27.3299 | 1.08541 | ||||||||
\(635\) | −0.0334495 | −0.00132740 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −34.1928 | −1.35371 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.0810898 | −0.00320536 | ||||||||
\(641\) | 16.5319 | 0.652971 | 0.326486 | − | 0.945202i | \(-0.394136\pi\) | ||||
0.326486 | + | 0.945202i | \(0.394136\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.8920 | 1.21826 | 0.609130 | − | 0.793070i | \(-0.291519\pi\) | ||||
0.609130 | + | 0.793070i | \(0.291519\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.6678 | 0.537752 | ||||||||
\(647\) | 1.29981 | 0.0511007 | 0.0255503 | − | 0.999674i | \(-0.491866\pi\) | ||||
0.0255503 | + | 0.999674i | \(0.491866\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.8840 | 0.584247 | ||||||||
\(650\) | −13.6442 | −0.535169 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.02494 | −0.275118 | ||||||||
\(653\) | 44.8870 | 1.75656 | 0.878281 | − | 0.478144i | \(-0.158690\pi\) | ||||
0.878281 | + | 0.478144i | \(0.158690\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.57738 | −0.0616335 | ||||||||
\(656\) | −13.6088 | −0.531333 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.9233 | 0.698195 | 0.349097 | − | 0.937086i | \(-0.386488\pi\) | ||||
0.349097 | + | 0.937086i | \(0.386488\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.0256 | 1.28455 | 0.642274 | − | 0.766475i | \(-0.277991\pi\) | ||||
0.642274 | + | 0.766475i | \(0.277991\pi\) | |||||||
\(662\) | 15.2686 | 0.593430 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.58840 | 0.139257 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.6257 | 0.682469 | ||||||||
\(668\) | −13.6512 | −0.528182 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.15977 | −0.0448058 | ||||||||
\(671\) | 18.9259 | 0.730626 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.3515 | 0.823040 | 0.411520 | − | 0.911401i | \(-0.364998\pi\) | ||||
0.411520 | + | 0.911401i | \(0.364998\pi\) | |||||||
\(674\) | −3.73729 | −0.143955 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.36894 | 0.206498 | ||||||||
\(677\) | −8.30167 | −0.319059 | −0.159530 | − | 0.987193i | \(-0.550998\pi\) | ||||
−0.159530 | + | 0.987193i | \(0.550998\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.522322 | −0.0200301 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −34.0868 | −1.30525 | ||||||||
\(683\) | −2.49456 | −0.0954518 | −0.0477259 | − | 0.998860i | \(-0.515197\pi\) | ||||
−0.0477259 | + | 0.998860i | \(0.515197\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.60808 | −0.0614414 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13.7222 | −0.523154 | ||||||||
\(689\) | 24.7419 | 0.942591 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.8691 | −0.641731 | −0.320865 | − | 0.947125i | \(-0.603974\pi\) | ||||
−0.320865 | + | 0.947125i | \(0.603974\pi\) | |||||||
\(692\) | −2.21763 | −0.0843017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.0071 | 0.607621 | ||||||||
\(695\) | −0.856265 | −0.0324800 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0753 | −0.457385 | ||||||||
\(698\) | −17.3453 | −0.656530 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.4806 | −0.622465 | −0.311232 | − | 0.950334i | \(-0.600742\pi\) | ||||
−0.311232 | + | 0.950334i | \(0.600742\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.2312 | 0.574454 | ||||||||
\(704\) | −27.3536 | −1.03093 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.57031 | 0.172006 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.4925 | −1.10761 | −0.553807 | − | 0.832645i | \(-0.686825\pi\) | ||||
−0.553807 | + | 0.832645i | \(0.686825\pi\) | |||||||
\(710\) | 0.382707 | 0.0143628 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 18.5108 | 0.693721 | ||||||||
\(713\) | 17.5710 | 0.658040 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.872876 | 0.0326437 | ||||||||
\(716\) | −7.96554 | −0.297686 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.75620 | −0.326779 | ||||||||
\(719\) | 0.434622 | 0.0162087 | 0.00810433 | − | 0.999967i | \(-0.497420\pi\) | ||||
0.00810433 | + | 0.999967i | \(0.497420\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 44.1382 | 1.64265 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.3928 | −0.497740 | ||||||||
\(725\) | −46.3488 | −1.72135 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.1678 | −1.00760 | −0.503799 | − | 0.863821i | \(-0.668065\pi\) | ||||
−0.503799 | + | 0.863821i | \(0.668065\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.549420 | 0.0203350 | ||||||||
\(731\) | −12.1760 | −0.450344 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.66614 | −0.209284 | −0.104642 | − | 0.994510i | \(-0.533370\pi\) | ||||
−0.104642 | + | 0.994510i | \(0.533370\pi\) | |||||||
\(734\) | −14.5010 | −0.535242 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.84498 | 0.289170 | ||||||||
\(737\) | −33.2777 | −1.22580 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.6108 | −0.500681 | −0.250341 | − | 0.968158i | \(-0.580543\pi\) | ||||
−0.250341 | + | 0.968158i | \(0.580543\pi\) | |||||||
\(740\) | −0.163885 | −0.00602455 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.6684 | −0.464759 | −0.232380 | − | 0.972625i | \(-0.574651\pi\) | ||||
−0.232380 | + | 0.972625i | \(0.574651\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.17580 | −0.0430779 | ||||||||
\(746\) | 8.61393 | 0.315378 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.21977 | −0.154290 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.14538 | −0.260739 | −0.130369 | − | 0.991465i | \(-0.541616\pi\) | ||||
−0.130369 | + | 0.991465i | \(0.541616\pi\) | |||||||
\(752\) | −5.80977 | −0.211860 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 25.4086 | 0.925325 | ||||||||
\(755\) | 1.18897 | 0.0432712 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.6446 | 1.36822 | 0.684108 | − | 0.729381i | \(-0.260192\pi\) | ||||
0.684108 | + | 0.729381i | \(0.260192\pi\) | |||||||
\(758\) | −34.8651 | −1.26636 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.48751 | −0.0902315 | ||||||||
\(761\) | −10.0472 | −0.364209 | −0.182104 | − | 0.983279i | \(-0.558291\pi\) | ||||
−0.182104 | + | 0.983279i | \(0.558291\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −17.5572 | −0.635196 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.8352 | 0.427625 | ||||||||
\(767\) | −11.0602 | −0.399361 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.2927 | −1.16450 | −0.582252 | − | 0.813008i | \(-0.697828\pi\) | ||||
−0.582252 | + | 0.813008i | \(0.697828\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.201270 | 0.00724385 | ||||||||
\(773\) | 48.5878 | 1.74758 | 0.873792 | − | 0.486300i | \(-0.161654\pi\) | ||||
0.873792 | + | 0.486300i | \(0.161654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −46.2051 | −1.65973 | ||||||||
\(776\) | −11.6739 | −0.419068 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.6295 | −0.954713 | ||||||||
\(779\) | −57.5075 | −2.06042 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.9812 | 0.392938 | ||||||||
\(782\) | −3.37518 | −0.120696 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.28736 | 0.0459477 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.9551 | 1.74506 | 0.872531 | − | 0.488560i | \(-0.162478\pi\) | ||||
0.872531 | + | 0.488560i | \(0.162478\pi\) | |||||||
\(788\) | −0.598331 | −0.0213147 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.894896 | −0.0318390 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.0638 | −0.499419 | ||||||||
\(794\) | 26.5303 | 0.941525 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.94348 | −0.139773 | ||||||||
\(797\) | 2.88833 | 0.102310 | 0.0511550 | − | 0.998691i | \(-0.483710\pi\) | ||||
0.0511550 | + | 0.998691i | \(0.483710\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.15511 | −0.182375 | ||||||||
\(800\) | −20.6293 | −0.729356 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.72294 | 0.0608393 | ||||||||
\(803\) | 15.7647 | 0.556326 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25.3298 | 0.892203 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 53.6339 | 1.88683 | ||||||||
\(809\) | −11.6974 | −0.411258 | −0.205629 | − | 0.978630i | \(-0.565924\pi\) | ||||
−0.205629 | + | 0.978630i | \(0.565924\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.1780 | −0.603199 | −0.301600 | − | 0.953435i | \(-0.597521\pi\) | ||||
−0.301600 | + | 0.953435i | \(0.597521\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.29660 | 0.255746 | ||||||||
\(815\) | −0.945254 | −0.0331108 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −57.9869 | −2.02870 | ||||||||
\(818\) | −24.6431 | −0.861624 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.618775 | 0.0216085 | ||||||||
\(821\) | −34.0137 | −1.18709 | −0.593543 | − | 0.804803i | \(-0.702271\pi\) | ||||
−0.593543 | + | 0.804803i | \(0.702271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.3780 | 1.51206 | 0.756031 | − | 0.654536i | \(-0.227136\pi\) | ||||
0.756031 | + | 0.654536i | \(0.227136\pi\) | |||||||
\(824\) | 26.8075 | 0.933883 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.0909 | 1.18546 | 0.592728 | − | 0.805403i | \(-0.298051\pi\) | ||||
0.592728 | + | 0.805403i | \(0.298051\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.9167 | −0.587540 | −0.293770 | − | 0.955876i | \(-0.594910\pi\) | ||||
−0.293770 | + | 0.955876i | \(0.594910\pi\) | |||||||
\(830\) | 0.135949 | 0.00471885 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20.3264 | 0.704691 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.83687 | −0.0635674 | ||||||||
\(836\) | −20.0963 | −0.695044 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.58705 | 0.227546 | ||||||||
\(839\) | −16.3249 | −0.563597 | −0.281799 | − | 0.959474i | \(-0.590931\pi\) | ||||
−0.281799 | + | 0.959474i | \(0.590931\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.3120 | 1.97628 | ||||||||
\(842\) | −16.1362 | −0.556092 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.65179 | −0.194543 | ||||||||
\(845\) | 0.722428 | 0.0248523 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −18.1383 | −0.622872 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.87544 | 0.304425 | ||||||||
\(851\) | −3.76124 | −0.128934 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.9048 | 0.989681 | 0.494841 | − | 0.868984i | \(-0.335226\pi\) | ||||
0.494841 | + | 0.868984i | \(0.335226\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −55.7095 | −1.90411 | ||||||||
\(857\) | 29.0567 | 0.992559 | 0.496280 | − | 0.868163i | \(-0.334699\pi\) | ||||
0.496280 | + | 0.868163i | \(0.334699\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.5964 | −0.429783 | −0.214892 | − | 0.976638i | \(-0.568940\pi\) | ||||
−0.214892 | + | 0.976638i | \(0.568940\pi\) | |||||||
\(860\) | 0.623932 | 0.0212759 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.3983 | 0.728829 | ||||||||
\(863\) | 14.6662 | 0.499243 | 0.249621 | − | 0.968344i | \(-0.419694\pi\) | ||||
0.249621 | + | 0.968344i | \(0.419694\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.298398 | −0.0101458 | ||||||||
\(866\) | 1.49119 | 0.0506726 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.6776 | −0.871053 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.7286 | 0.837896 | ||||||||
\(872\) | 12.9631 | 0.438985 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.0740 | −0.543711 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.1902 | 1.12075 | 0.560376 | − | 0.828238i | \(-0.310657\pi\) | ||||
0.560376 | + | 0.828238i | \(0.310657\pi\) | |||||||
\(878\) | 19.1241 | 0.645407 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.639905 | −0.0215712 | ||||||||
\(881\) | 31.7179 | 1.06860 | 0.534301 | − | 0.845294i | \(-0.320575\pi\) | ||||
0.534301 | + | 0.845294i | \(0.320575\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.5231 | −1.33006 | −0.665029 | − | 0.746818i | \(-0.731581\pi\) | ||||
−0.665029 | + | 0.746818i | \(0.731581\pi\) | |||||||
\(884\) | 3.13569 | 0.105465 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.6262 | −0.726545 | ||||||||
\(887\) | −49.9026 | −1.67556 | −0.837782 | − | 0.546005i | \(-0.816148\pi\) | ||||
−0.837782 | + | 0.546005i | \(0.816148\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.701292 | 0.0235074 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.76457 | −0.293459 | ||||||||
\(893\) | −24.5507 | −0.821559 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.07182 | −0.0358270 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.5578 | 0.652653 | ||||||||
\(899\) | 86.0443 | 2.86974 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.0944 | −0.536183 | ||||||||
\(902\) | −27.5494 | −0.917295 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.31341 | −0.209981 | ||||||||
\(905\) | −1.80210 | −0.0599037 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.9216 | −0.462259 | −0.231129 | − | 0.972923i | \(-0.574242\pi\) | ||||
−0.231129 | + | 0.972923i | \(0.574242\pi\) | |||||||
\(908\) | −18.6315 | −0.618308 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.40855 | 0.179193 | 0.0895967 | − | 0.995978i | \(-0.471442\pi\) | ||||
0.0895967 | + | 0.995978i | \(0.471442\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.90084 | 0.129099 | ||||||||
\(914\) | 0.535362 | 0.0177082 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.49352 | −0.0493471 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.0283 | 1.12249 | 0.561245 | − | 0.827649i | \(-0.310322\pi\) | ||||
0.561245 | + | 0.827649i | \(0.310322\pi\) | |||||||
\(920\) | 0.614276 | 0.0202521 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.81561 | 0.290327 | ||||||||
\(923\) | −8.16008 | −0.268592 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.89063 | 0.325202 | ||||||||
\(926\) | −11.5637 | −0.380006 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 38.4165 | 1.26108 | ||||||||
\(929\) | −10.6329 | −0.348855 | −0.174427 | − | 0.984670i | \(-0.555807\pi\) | ||||
−0.174427 | + | 0.984670i | \(0.555807\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.12751 | 0.167957 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24.1491 | −0.790183 | ||||||||
\(935\) | −0.567799 | −0.0185690 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.6692 | 1.72063 | 0.860314 | − | 0.509765i | \(-0.170268\pi\) | ||||
0.860314 | + | 0.509765i | \(0.170268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.264163 | 0.00861605 | ||||||||
\(941\) | 34.3656 | 1.12029 | 0.560143 | − | 0.828396i | \(-0.310746\pi\) | ||||
0.560143 | + | 0.828396i | \(0.310746\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.2011 | 0.462453 | ||||||||
\(944\) | 8.10825 | 0.263901 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.7791 | −0.903175 | ||||||||
\(947\) | 40.5840 | 1.31880 | 0.659401 | − | 0.751791i | \(-0.270810\pi\) | ||||
0.659401 | + | 0.751791i | \(0.270810\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.7147 | −0.380276 | ||||||||
\(950\) | 42.2685 | 1.37137 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.6904 | 0.735013 | 0.367507 | − | 0.930021i | \(-0.380211\pi\) | ||||
0.367507 | + | 0.930021i | \(0.380211\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.36244 | −0.0764468 | ||||||||
\(956\) | −16.7318 | −0.541144 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.41312 | −0.142581 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54.7775 | 1.76702 | ||||||||
\(962\) | −5.42208 | −0.174815 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.7279 | −0.506562 | ||||||||
\(965\) | 0.0270822 | 0.000871808 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.2776 | 0.780714 | 0.390357 | − | 0.920664i | \(-0.372352\pi\) | ||||
0.390357 | + | 0.920664i | \(0.372352\pi\) | |||||||
\(968\) | −0.422650 | −0.0135845 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.442272 | −0.0142005 | ||||||||
\(971\) | −45.5771 | −1.46264 | −0.731319 | − | 0.682035i | \(-0.761095\pi\) | ||||
−0.731319 | + | 0.682035i | \(0.761095\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −29.1975 | −0.935549 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.3102 | 0.330020 | ||||||||
\(977\) | 14.6896 | 0.469963 | 0.234981 | − | 0.972000i | \(-0.424497\pi\) | ||||
0.234981 | + | 0.972000i | \(0.424497\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.1225 | 0.643117 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 31.3528 | 1.00051 | ||||||||
\(983\) | 44.5909 | 1.42223 | 0.711115 | − | 0.703076i | \(-0.248191\pi\) | ||||
0.711115 | + | 0.703076i | \(0.248191\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.0805096 | −0.00256525 | ||||||||
\(986\) | −16.5281 | −0.526361 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.9335 | 0.475097 | ||||||||
\(989\) | 14.3195 | 0.455334 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.1829 | 0.768196 | 0.384098 | − | 0.923292i | \(-0.374512\pi\) | ||||
0.384098 | + | 0.923292i | \(0.374512\pi\) | |||||||
\(992\) | 38.2973 | 1.21594 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.530622 | −0.0168219 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.8652 | −0.344105 | −0.172053 | − | 0.985088i | \(-0.555040\pi\) | ||||
−0.172053 | + | 0.985088i | \(0.555040\pi\) | |||||||
\(998\) | −8.19521 | −0.259415 | ||||||||
\(999\) | 0 | 0 |
(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 | 3969.2.a.bi.1.7 | 12 | ||
3.2 | odd | 2 | 3969.2.a.bh.1.6 | 12 | |||
7.6 | odd | 2 | inner | 3969.2.a.bi.1.8 | 12 | ||
9.2 | odd | 6 | 441.2.f.h.148.8 | yes | 24 | ||
9.4 | even | 3 | 1323.2.f.h.883.5 | 24 | |||
9.5 | odd | 6 | 441.2.f.h.295.8 | yes | 24 | ||
9.7 | even | 3 | 1323.2.f.h.442.5 | 24 | |||
21.20 | even | 2 | 3969.2.a.bh.1.5 | 12 | |||
63.2 | odd | 6 | 441.2.g.h.67.7 | 24 | |||
63.4 | even | 3 | 1323.2.g.h.667.5 | 24 | |||
63.5 | even | 6 | 441.2.h.h.214.6 | 24 | |||
63.11 | odd | 6 | 441.2.h.h.373.5 | 24 | |||
63.13 | odd | 6 | 1323.2.f.h.883.6 | 24 | |||
63.16 | even | 3 | 1323.2.g.h.361.5 | 24 | |||
63.20 | even | 6 | 441.2.f.h.148.7 | ✓ | 24 | ||
63.23 | odd | 6 | 441.2.h.h.214.5 | 24 | |||
63.25 | even | 3 | 1323.2.h.h.226.8 | 24 | |||
63.31 | odd | 6 | 1323.2.g.h.667.6 | 24 | |||
63.32 | odd | 6 | 441.2.g.h.79.7 | 24 | |||
63.34 | odd | 6 | 1323.2.f.h.442.6 | 24 | |||
63.38 | even | 6 | 441.2.h.h.373.6 | 24 | |||
63.40 | odd | 6 | 1323.2.h.h.802.7 | 24 | |||
63.41 | even | 6 | 441.2.f.h.295.7 | yes | 24 | ||
63.47 | even | 6 | 441.2.g.h.67.8 | 24 | |||
63.52 | odd | 6 | 1323.2.h.h.226.7 | 24 | |||
63.58 | even | 3 | 1323.2.h.h.802.8 | 24 | |||
63.59 | even | 6 | 441.2.g.h.79.8 | 24 | |||
63.61 | odd | 6 | 1323.2.g.h.361.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.7 | ✓ | 24 | 63.20 | even | 6 | ||
441.2.f.h.148.8 | yes | 24 | 9.2 | odd | 6 | ||
441.2.f.h.295.7 | yes | 24 | 63.41 | even | 6 | ||
441.2.f.h.295.8 | yes | 24 | 9.5 | odd | 6 | ||
441.2.g.h.67.7 | 24 | 63.2 | odd | 6 | |||
441.2.g.h.67.8 | 24 | 63.47 | even | 6 | |||
441.2.g.h.79.7 | 24 | 63.32 | odd | 6 | |||
441.2.g.h.79.8 | 24 | 63.59 | even | 6 | |||
441.2.h.h.214.5 | 24 | 63.23 | odd | 6 | |||
441.2.h.h.214.6 | 24 | 63.5 | even | 6 | |||
441.2.h.h.373.5 | 24 | 63.11 | odd | 6 | |||
441.2.h.h.373.6 | 24 | 63.38 | even | 6 | |||
1323.2.f.h.442.5 | 24 | 9.7 | even | 3 | |||
1323.2.f.h.442.6 | 24 | 63.34 | odd | 6 | |||
1323.2.f.h.883.5 | 24 | 9.4 | even | 3 | |||
1323.2.f.h.883.6 | 24 | 63.13 | odd | 6 | |||
1323.2.g.h.361.5 | 24 | 63.16 | even | 3 | |||
1323.2.g.h.361.6 | 24 | 63.61 | odd | 6 | |||
1323.2.g.h.667.5 | 24 | 63.4 | even | 3 | |||
1323.2.g.h.667.6 | 24 | 63.31 | odd | 6 | |||
1323.2.h.h.226.7 | 24 | 63.52 | odd | 6 | |||
1323.2.h.h.226.8 | 24 | 63.25 | even | 3 | |||
1323.2.h.h.802.7 | 24 | 63.40 | odd | 6 | |||
1323.2.h.h.802.8 | 24 | 63.58 | even | 3 | |||
3969.2.a.bh.1.5 | 12 | 21.20 | even | 2 | |||
3969.2.a.bh.1.6 | 12 | 3.2 | odd | 2 | |||
3969.2.a.bi.1.7 | 12 | 1.1 | even | 1 | trivial | ||
3969.2.a.bi.1.8 | 12 | 7.6 | odd | 2 | inner |