Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(1,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.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: | \(6.53974792554\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.81361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.81361 | 1.28241 | 0.641207 | − | 0.767368i | \(-0.278434\pi\) | ||||
0.641207 | + | 0.767368i | \(0.278434\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.28917 | 0.644584 | ||||||||
\(5\) | −2.81361 | −1.25828 | −0.629142 | − | 0.777291i | \(-0.716593\pi\) | ||||
−0.629142 | + | 0.777291i | \(0.716593\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.28917 | −0.455790 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.10278 | −1.61364 | ||||||||
\(11\) | −3.10278 | −0.935522 | −0.467761 | − | 0.883855i | \(-0.654939\pi\) | ||||
−0.467761 | + | 0.883855i | \(0.654939\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −1.81361 | −0.484707 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.91638 | −1.22910 | ||||||||
\(17\) | 0.524438 | 0.127195 | 0.0635974 | − | 0.997976i | \(-0.479743\pi\) | ||||
0.0635974 | + | 0.997976i | \(0.479743\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.813607 | 0.186654 | 0.0933271 | − | 0.995636i | \(-0.470250\pi\) | ||||
0.0933271 | + | 0.995636i | \(0.470250\pi\) | |||||||
\(20\) | −3.62721 | −0.811069 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.62721 | −1.19973 | ||||||||
\(23\) | −7.33804 | −1.53009 | −0.765044 | − | 0.643978i | \(-0.777283\pi\) | ||||
−0.765044 | + | 0.643978i | \(0.777283\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.91638 | 0.583276 | ||||||||
\(26\) | 1.81361 | 0.355677 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.28917 | −0.243630 | ||||||||
\(29\) | −8.28917 | −1.53926 | −0.769630 | − | 0.638490i | \(-0.779559\pi\) | ||||
−0.769630 | + | 0.638490i | \(0.779559\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.39194 | 0.250000 | 0.125000 | − | 0.992157i | \(-0.460107\pi\) | ||||
0.125000 | + | 0.992157i | \(0.460107\pi\) | |||||||
\(32\) | −6.33804 | −1.12042 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.951124 | 0.163116 | ||||||||
\(35\) | 2.81361 | 0.475586 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.15165 | −1.01133 | −0.505663 | − | 0.862731i | \(-0.668752\pi\) | ||||
−0.505663 | + | 0.862731i | \(0.668752\pi\) | |||||||
\(38\) | 1.47556 | 0.239368 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.62721 | 0.573513 | ||||||||
\(41\) | 4.20555 | 0.656797 | 0.328398 | − | 0.944539i | \(-0.393491\pi\) | ||||
0.328398 | + | 0.944539i | \(0.393491\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.75971 | 1.03085 | 0.515423 | − | 0.856936i | \(-0.327635\pi\) | ||||
0.515423 | + | 0.856936i | \(0.327635\pi\) | |||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.3083 | −1.96221 | ||||||||
\(47\) | 5.97028 | 0.870855 | 0.435427 | − | 0.900224i | \(-0.356597\pi\) | ||||
0.435427 | + | 0.900224i | \(0.356597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.28917 | 0.748001 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.28917 | 0.178776 | ||||||||
\(53\) | 2.49472 | 0.342676 | 0.171338 | − | 0.985212i | \(-0.445191\pi\) | ||||
0.171338 | + | 0.985212i | \(0.445191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.72999 | 1.17715 | ||||||||
\(56\) | 1.28917 | 0.172272 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −15.0333 | −1.97397 | ||||||||
\(59\) | 4.47054 | 0.582015 | 0.291007 | − | 0.956721i | \(-0.406010\pi\) | ||||
0.291007 | + | 0.956721i | \(0.406010\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 2.52444 | 0.320604 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.66196 | −0.207744 | ||||||||
\(65\) | −2.81361 | −0.348985 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0383 | 1.22638 | 0.613188 | − | 0.789937i | \(-0.289887\pi\) | ||||
0.613188 | + | 0.789937i | \(0.289887\pi\) | |||||||
\(68\) | 0.676089 | 0.0819878 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.10278 | 0.609898 | ||||||||
\(71\) | 8.72999 | 1.03606 | 0.518029 | − | 0.855363i | \(-0.326666\pi\) | ||||
0.518029 | + | 0.855363i | \(0.326666\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.34307 | −0.274235 | −0.137118 | − | 0.990555i | \(-0.543784\pi\) | ||||
−0.137118 | + | 0.990555i | \(0.543784\pi\) | |||||||
\(74\) | −11.1567 | −1.29694 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.04888 | 0.120314 | ||||||||
\(77\) | 3.10278 | 0.353594 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.5436 | −1.52377 | −0.761887 | − | 0.647710i | \(-0.775727\pi\) | ||||
−0.761887 | + | 0.647710i | \(0.775727\pi\) | |||||||
\(80\) | 13.8328 | 1.54655 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.62721 | 0.842285 | ||||||||
\(83\) | −16.4791 | −1.80882 | −0.904410 | − | 0.426665i | \(-0.859688\pi\) | ||||
−0.904410 | + | 0.426665i | \(0.859688\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.47556 | −0.160047 | ||||||||
\(86\) | 12.2594 | 1.32197 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.00000 | 0.426401 | ||||||||
\(89\) | 10.6464 | 1.12851 | 0.564256 | − | 0.825600i | \(-0.309163\pi\) | ||||
0.564256 | + | 0.825600i | \(0.309163\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | −9.45998 | −0.986271 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.8277 | 1.11680 | ||||||||
\(95\) | −2.28917 | −0.234864 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.18639 | −0.120460 | −0.0602300 | − | 0.998185i | \(-0.519183\pi\) | ||||
−0.0602300 | + | 0.998185i | \(0.519183\pi\) | |||||||
\(98\) | 1.81361 | 0.183202 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.75971 | 0.375971 | ||||||||
\(101\) | −13.1028 | −1.30377 | −0.651887 | − | 0.758316i | \(-0.726023\pi\) | ||||
−0.651887 | + | 0.758316i | \(0.726023\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.41110 | 0.434639 | 0.217319 | − | 0.976101i | \(-0.430269\pi\) | ||||
0.217319 | + | 0.976101i | \(0.430269\pi\) | |||||||
\(104\) | −1.28917 | −0.126413 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.52444 | 0.439452 | ||||||||
\(107\) | −0.578337 | −0.0559100 | −0.0279550 | − | 0.999609i | \(-0.508900\pi\) | ||||
−0.0279550 | + | 0.999609i | \(0.508900\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.57331 | 0.533827 | 0.266913 | − | 0.963721i | \(-0.413996\pi\) | ||||
0.266913 | + | 0.963721i | \(0.413996\pi\) | |||||||
\(110\) | 15.8328 | 1.50959 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.91638 | 0.464554 | ||||||||
\(113\) | −5.44584 | −0.512302 | −0.256151 | − | 0.966637i | \(-0.582454\pi\) | ||||
−0.256151 | + | 0.966637i | \(0.582454\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.6464 | 1.92528 | ||||||||
\(116\) | −10.6861 | −0.992183 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.10780 | 0.746383 | ||||||||
\(119\) | −0.524438 | −0.0480751 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.37279 | −0.124799 | ||||||||
\(122\) | −3.62721 | −0.328392 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.79445 | 0.161146 | ||||||||
\(125\) | 5.86248 | 0.524356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8816 | −1.14306 | −0.571530 | − | 0.820581i | \(-0.693650\pi\) | ||||
−0.571530 | + | 0.820581i | \(0.693650\pi\) | |||||||
\(128\) | 9.66196 | 0.854004 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.10278 | −0.447543 | ||||||||
\(131\) | −9.04888 | −0.790604 | −0.395302 | − | 0.918551i | \(-0.629360\pi\) | ||||
−0.395302 | + | 0.918551i | \(0.629360\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.813607 | −0.0705486 | ||||||||
\(134\) | 18.2056 | 1.57272 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.676089 | −0.0579741 | ||||||||
\(137\) | 6.25945 | 0.534781 | 0.267390 | − | 0.963588i | \(-0.413839\pi\) | ||||
0.267390 | + | 0.963588i | \(0.413839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.5733 | −0.981636 | −0.490818 | − | 0.871262i | \(-0.663302\pi\) | ||||
−0.490818 | + | 0.871262i | \(0.663302\pi\) | |||||||
\(140\) | 3.62721 | 0.306555 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.8328 | 1.32866 | ||||||||
\(143\) | −3.10278 | −0.259467 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23.3225 | 1.93682 | ||||||||
\(146\) | −4.24940 | −0.351683 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.93051 | −0.651884 | ||||||||
\(149\) | −8.52444 | −0.698349 | −0.349175 | − | 0.937058i | \(-0.613538\pi\) | ||||
−0.349175 | + | 0.937058i | \(0.613538\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9844 | −0.975278 | −0.487639 | − | 0.873045i | \(-0.662142\pi\) | ||||
−0.487639 | + | 0.873045i | \(0.662142\pi\) | |||||||
\(152\) | −1.04888 | −0.0850751 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.62721 | 0.453454 | ||||||||
\(155\) | −3.91638 | −0.314571 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.8277 | −1.02377 | −0.511883 | − | 0.859055i | \(-0.671052\pi\) | ||||
−0.511883 | + | 0.859055i | \(0.671052\pi\) | |||||||
\(158\) | −24.5628 | −1.95411 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 17.8328 | 1.40980 | ||||||||
\(161\) | 7.33804 | 0.578319 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.4600 | −1.05427 | −0.527133 | − | 0.849783i | \(-0.676733\pi\) | ||||
−0.527133 | + | 0.849783i | \(0.676733\pi\) | |||||||
\(164\) | 5.42166 | 0.423361 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −29.8867 | −2.31965 | ||||||||
\(167\) | 2.02972 | 0.157064 | 0.0785322 | − | 0.996912i | \(-0.474977\pi\) | ||||
0.0785322 | + | 0.996912i | \(0.474977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.67609 | −0.205247 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.71440 | 0.664467 | ||||||||
\(173\) | −20.2978 | −1.54321 | −0.771605 | − | 0.636102i | \(-0.780546\pi\) | ||||
−0.771605 | + | 0.636102i | \(0.780546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.91638 | −0.220458 | ||||||||
\(176\) | 15.2544 | 1.14985 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 19.3083 | 1.44722 | ||||||||
\(179\) | 11.0036 | 0.822445 | 0.411223 | − | 0.911535i | \(-0.365102\pi\) | ||||
0.411223 | + | 0.911535i | \(0.365102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.691675 | 0.0514118 | 0.0257059 | − | 0.999670i | \(-0.491817\pi\) | ||||
0.0257059 | + | 0.999670i | \(0.491817\pi\) | |||||||
\(182\) | −1.81361 | −0.134433 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.45998 | 0.697399 | ||||||||
\(185\) | 17.3083 | 1.27253 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.62721 | −0.118994 | ||||||||
\(188\) | 7.69670 | 0.561339 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.15165 | −0.301192 | ||||||||
\(191\) | −7.83276 | −0.566759 | −0.283379 | − | 0.959008i | \(-0.591456\pi\) | ||||
−0.283379 | + | 0.959008i | \(0.591456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.2056 | −0.878575 | −0.439287 | − | 0.898347i | \(-0.644769\pi\) | ||||
−0.439287 | + | 0.898347i | \(0.644769\pi\) | |||||||
\(194\) | −2.15165 | −0.154480 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.28917 | 0.0920835 | ||||||||
\(197\) | 18.8222 | 1.34103 | 0.670513 | − | 0.741898i | \(-0.266074\pi\) | ||||
0.670513 | + | 0.741898i | \(0.266074\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.6116 | 1.53201 | 0.766004 | − | 0.642836i | \(-0.222242\pi\) | ||||
0.766004 | + | 0.642836i | \(0.222242\pi\) | |||||||
\(200\) | −3.75971 | −0.265851 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −23.7633 | −1.67198 | ||||||||
\(203\) | 8.28917 | 0.581786 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.8328 | −0.826436 | ||||||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.91638 | −0.340890 | ||||||||
\(209\) | −2.52444 | −0.174619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.3764 | −1.19624 | −0.598119 | − | 0.801407i | \(-0.704085\pi\) | ||||
−0.598119 | + | 0.801407i | \(0.704085\pi\) | |||||||
\(212\) | 3.21611 | 0.220884 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.04888 | −0.0716997 | ||||||||
\(215\) | −19.0192 | −1.29710 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.39194 | −0.0944913 | ||||||||
\(218\) | 10.1078 | 0.684586 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.2544 | 0.758773 | ||||||||
\(221\) | 0.524438 | 0.0352775 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.5486 | −0.706388 | −0.353194 | − | 0.935550i | \(-0.614904\pi\) | ||||
−0.353194 | + | 0.935550i | \(0.614904\pi\) | |||||||
\(224\) | 6.33804 | 0.423478 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.87662 | −0.656983 | ||||||||
\(227\) | 6.95112 | 0.461362 | 0.230681 | − | 0.973029i | \(-0.425905\pi\) | ||||
0.230681 | + | 0.973029i | \(0.425905\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.0872 | −1.39348 | −0.696740 | − | 0.717323i | \(-0.745367\pi\) | ||||
−0.696740 | + | 0.717323i | \(0.745367\pi\) | |||||||
\(230\) | 37.4444 | 2.46901 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.6861 | 0.701579 | ||||||||
\(233\) | −6.08362 | −0.398551 | −0.199276 | − | 0.979943i | \(-0.563859\pi\) | ||||
−0.199276 | + | 0.979943i | \(0.563859\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.7980 | −1.09578 | ||||||||
\(236\) | 5.76328 | 0.375157 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.951124 | −0.0616522 | ||||||||
\(239\) | 14.2056 | 0.918881 | 0.459440 | − | 0.888209i | \(-0.348050\pi\) | ||||
0.459440 | + | 0.888209i | \(0.348050\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.44082 | 0.543721 | 0.271860 | − | 0.962337i | \(-0.412361\pi\) | ||||
0.271860 | + | 0.962337i | \(0.412361\pi\) | |||||||
\(242\) | −2.48970 | −0.160044 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.57834 | −0.165061 | ||||||||
\(245\) | −2.81361 | −0.179755 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.813607 | 0.0517685 | ||||||||
\(248\) | −1.79445 | −0.113948 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.6322 | 0.672442 | ||||||||
\(251\) | 23.9844 | 1.51388 | 0.756941 | − | 0.653483i | \(-0.226693\pi\) | ||||
0.756941 | + | 0.653483i | \(0.226693\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.7683 | 1.43143 | ||||||||
\(254\) | −23.3622 | −1.46588 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.8469 | 1.30293 | ||||||||
\(257\) | −15.6116 | −0.973827 | −0.486913 | − | 0.873450i | \(-0.661877\pi\) | ||||
−0.486913 | + | 0.873450i | \(0.661877\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.15165 | 0.382245 | ||||||||
\(260\) | −3.62721 | −0.224950 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.4111 | −1.01388 | ||||||||
\(263\) | 15.1708 | 0.935472 | 0.467736 | − | 0.883868i | \(-0.345070\pi\) | ||||
0.467736 | + | 0.883868i | \(0.345070\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.01916 | −0.431183 | ||||||||
\(266\) | −1.47556 | −0.0904725 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.9411 | 0.790502 | ||||||||
\(269\) | −23.2927 | −1.42018 | −0.710092 | − | 0.704109i | \(-0.751347\pi\) | ||||
−0.710092 | + | 0.704109i | \(0.751347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.7456 | 0.774238 | 0.387119 | − | 0.922030i | \(-0.373470\pi\) | ||||
0.387119 | + | 0.922030i | \(0.373470\pi\) | |||||||
\(272\) | −2.57834 | −0.156335 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.3522 | 0.685810 | ||||||||
\(275\) | −9.04888 | −0.545668 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.12193 | 0.488000 | 0.244000 | − | 0.969775i | \(-0.421540\pi\) | ||||
0.244000 | + | 0.969775i | \(0.421540\pi\) | |||||||
\(278\) | −20.9894 | −1.25886 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.62721 | −0.216767 | ||||||||
\(281\) | −19.0333 | −1.13543 | −0.567715 | − | 0.823225i | \(-0.692173\pi\) | ||||
−0.567715 | + | 0.823225i | \(0.692173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.1466 | 0.662598 | 0.331299 | − | 0.943526i | \(-0.392513\pi\) | ||||
0.331299 | + | 0.943526i | \(0.392513\pi\) | |||||||
\(284\) | 11.2544 | 0.667827 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.62721 | −0.332744 | ||||||||
\(287\) | −4.20555 | −0.248246 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7250 | −0.983821 | ||||||||
\(290\) | 42.2978 | 2.48381 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.02061 | −0.176768 | ||||||||
\(293\) | 14.1758 | 0.828161 | 0.414080 | − | 0.910240i | \(-0.364103\pi\) | ||||
0.414080 | + | 0.910240i | \(0.364103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.5783 | −0.732339 | ||||||||
\(296\) | 7.93051 | 0.460952 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.4600 | −0.895572 | ||||||||
\(299\) | −7.33804 | −0.424370 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.75971 | −0.389623 | ||||||||
\(302\) | −21.7350 | −1.25071 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | 5.62721 | 0.322213 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.5592 | 0.773863 | 0.386932 | − | 0.922108i | \(-0.373535\pi\) | ||||
0.386932 | + | 0.922108i | \(0.373535\pi\) | |||||||
\(308\) | 4.00000 | 0.227921 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.10278 | −0.403411 | ||||||||
\(311\) | −0.426686 | −0.0241952 | −0.0120976 | − | 0.999927i | \(-0.503851\pi\) | ||||
−0.0120976 | + | 0.999927i | \(0.503851\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.1517 | −1.02599 | −0.512996 | − | 0.858391i | \(-0.671464\pi\) | ||||
−0.512996 | + | 0.858391i | \(0.671464\pi\) | |||||||
\(314\) | −23.2645 | −1.31289 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.4600 | −0.982200 | ||||||||
\(317\) | −9.42166 | −0.529173 | −0.264587 | − | 0.964362i | \(-0.585236\pi\) | ||||
−0.264587 | + | 0.964362i | \(0.585236\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.7194 | 1.44001 | ||||||||
\(320\) | 4.67609 | 0.261401 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.3083 | 0.741644 | ||||||||
\(323\) | 0.426686 | 0.0237415 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.91638 | 0.161772 | ||||||||
\(326\) | −24.4111 | −1.35201 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.42166 | −0.299361 | ||||||||
\(329\) | −5.97028 | −0.329152 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.4005 | −0.956420 | −0.478210 | − | 0.878246i | \(-0.658714\pi\) | ||||
−0.478210 | + | 0.878246i | \(0.658714\pi\) | |||||||
\(332\) | −21.2444 | −1.16594 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.68111 | 0.201421 | ||||||||
\(335\) | −28.2439 | −1.54313 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0524 | 1.20127 | 0.600637 | − | 0.799522i | \(-0.294914\pi\) | ||||
0.600637 | + | 0.799522i | \(0.294914\pi\) | |||||||
\(338\) | 1.81361 | 0.0986472 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.90225 | −0.103164 | ||||||||
\(341\) | −4.31889 | −0.233881 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −8.71440 | −0.469849 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −36.8122 | −1.97903 | ||||||||
\(347\) | −25.3522 | −1.36098 | −0.680488 | − | 0.732759i | \(-0.738232\pi\) | ||||
−0.680488 | + | 0.732759i | \(0.738232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.70529 | −0.305397 | −0.152699 | − | 0.988273i | \(-0.548796\pi\) | ||||
−0.152699 | + | 0.988273i | \(0.548796\pi\) | |||||||
\(350\) | −5.28917 | −0.282718 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 19.6655 | 1.04818 | ||||||||
\(353\) | 28.6761 | 1.52627 | 0.763137 | − | 0.646237i | \(-0.223658\pi\) | ||||
0.763137 | + | 0.646237i | \(0.223658\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.5628 | −1.30366 | ||||||||
\(356\) | 13.7250 | 0.727422 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.9561 | 1.05472 | ||||||||
\(359\) | −11.0433 | −0.582845 | −0.291423 | − | 0.956594i | \(-0.594129\pi\) | ||||
−0.291423 | + | 0.956594i | \(0.594129\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3380 | −0.965160 | ||||||||
\(362\) | 1.25443 | 0.0659312 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.28917 | −0.0675708 | ||||||||
\(365\) | 6.59247 | 0.345066 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.3466 | 1.42748 | 0.713741 | − | 0.700409i | \(-0.246999\pi\) | ||||
0.713741 | + | 0.700409i | \(0.246999\pi\) | |||||||
\(368\) | 36.0766 | 1.88062 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 31.3905 | 1.63191 | ||||||||
\(371\) | −2.49472 | −0.129519 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.1461 | 0.836014 | 0.418007 | − | 0.908444i | \(-0.362729\pi\) | ||||
0.418007 | + | 0.908444i | \(0.362729\pi\) | |||||||
\(374\) | −2.95112 | −0.152599 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.69670 | −0.396927 | ||||||||
\(377\) | −8.28917 | −0.426914 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.1305 | 1.34223 | 0.671117 | − | 0.741351i | \(-0.265815\pi\) | ||||
0.671117 | + | 0.741351i | \(0.265815\pi\) | |||||||
\(380\) | −2.95112 | −0.151389 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.2056 | −0.726819 | ||||||||
\(383\) | 21.0489 | 1.07555 | 0.537774 | − | 0.843089i | \(-0.319265\pi\) | ||||
0.537774 | + | 0.843089i | \(0.319265\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.72999 | −0.444921 | ||||||||
\(386\) | −22.1361 | −1.12670 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.52946 | −0.0776466 | ||||||||
\(389\) | 21.6061 | 1.09547 | 0.547736 | − | 0.836651i | \(-0.315490\pi\) | ||||
0.547736 | + | 0.836651i | \(0.315490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.84835 | −0.194619 | ||||||||
\(392\) | −1.28917 | −0.0651128 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 34.1361 | 1.71975 | ||||||||
\(395\) | 38.1063 | 1.91734 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.6952 | −1.38998 | −0.694992 | − | 0.719017i | \(-0.744592\pi\) | ||||
−0.694992 | + | 0.719017i | \(0.744592\pi\) | |||||||
\(398\) | 39.1950 | 1.96467 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.3380 | −0.716902 | ||||||||
\(401\) | 2.57834 | 0.128756 | 0.0643780 | − | 0.997926i | \(-0.479494\pi\) | ||||
0.0643780 | + | 0.997926i | \(0.479494\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.39194 | 0.0693376 | ||||||||
\(404\) | −16.8917 | −0.840393 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.0333 | 0.746090 | ||||||||
\(407\) | 19.0872 | 0.946117 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1169 | 0.747483 | 0.373742 | − | 0.927533i | \(-0.378075\pi\) | ||||
0.373742 | + | 0.927533i | \(0.378075\pi\) | |||||||
\(410\) | −21.4600 | −1.05983 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.68665 | 0.280161 | ||||||||
\(413\) | −4.47054 | −0.219981 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 46.3658 | 2.27601 | ||||||||
\(416\) | −6.33804 | −0.310748 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.57834 | −0.223934 | ||||||||
\(419\) | 9.99446 | 0.488261 | 0.244131 | − | 0.969742i | \(-0.421497\pi\) | ||||
0.244131 | + | 0.969742i | \(0.421497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.9250 | −1.26351 | −0.631753 | − | 0.775170i | \(-0.717664\pi\) | ||||
−0.631753 | + | 0.775170i | \(0.717664\pi\) | |||||||
\(422\) | −31.5139 | −1.53407 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.21611 | −0.156188 | ||||||||
\(425\) | 1.52946 | 0.0741898 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.00000 | 0.0967868 | ||||||||
\(428\) | −0.745574 | −0.0360387 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −34.4933 | −1.66341 | ||||||||
\(431\) | −30.6761 | −1.47762 | −0.738808 | − | 0.673916i | \(-0.764611\pi\) | ||||
−0.738808 | + | 0.673916i | \(0.764611\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.51941 | −0.169132 | −0.0845661 | − | 0.996418i | \(-0.526950\pi\) | ||||
−0.0845661 | + | 0.996418i | \(0.526950\pi\) | |||||||
\(434\) | −2.52444 | −0.121177 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.18494 | 0.344096 | ||||||||
\(437\) | −5.97028 | −0.285597 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.3517 | 1.54406 | 0.772030 | − | 0.635586i | \(-0.219241\pi\) | ||||
0.772030 | + | 0.635586i | \(0.219241\pi\) | |||||||
\(440\) | −11.2544 | −0.536534 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.951124 | 0.0452404 | ||||||||
\(443\) | −15.4458 | −0.733854 | −0.366927 | − | 0.930250i | \(-0.619590\pi\) | ||||
−0.366927 | + | 0.930250i | \(0.619590\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.9547 | −1.41999 | ||||||||
\(446\) | −19.1310 | −0.905881 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.66196 | 0.0785200 | ||||||||
\(449\) | 14.4705 | 0.682907 | 0.341453 | − | 0.939899i | \(-0.389081\pi\) | ||||
0.341453 | + | 0.939899i | \(0.389081\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.0489 | −0.614448 | ||||||||
\(452\) | −7.02061 | −0.330222 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.6066 | 0.591657 | ||||||||
\(455\) | 2.81361 | 0.131904 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.6705 | −1.62182 | −0.810910 | − | 0.585171i | \(-0.801027\pi\) | ||||
−0.810910 | + | 0.585171i | \(0.801027\pi\) | |||||||
\(458\) | −38.2439 | −1.78702 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 26.6167 | 1.24101 | ||||||||
\(461\) | −12.5400 | −0.584047 | −0.292024 | − | 0.956411i | \(-0.594329\pi\) | ||||
−0.292024 | + | 0.956411i | \(0.594329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.1517 | 0.564735 | 0.282368 | − | 0.959306i | \(-0.408880\pi\) | ||||
0.282368 | + | 0.959306i | \(0.408880\pi\) | |||||||
\(464\) | 40.7527 | 1.89190 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.0333 | −0.511107 | ||||||||
\(467\) | 37.0333 | 1.71370 | 0.856848 | − | 0.515569i | \(-0.172419\pi\) | ||||
0.856848 | + | 0.515569i | \(0.172419\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0383 | −0.463526 | ||||||||
\(470\) | −30.4650 | −1.40525 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.76328 | −0.265276 | ||||||||
\(473\) | −20.9739 | −0.964379 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.37279 | 0.108871 | ||||||||
\(476\) | −0.676089 | −0.0309885 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.7633 | 1.17838 | ||||||||
\(479\) | −12.0086 | −0.548687 | −0.274343 | − | 0.961632i | \(-0.588460\pi\) | ||||
−0.274343 | + | 0.961632i | \(0.588460\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.15165 | −0.280491 | ||||||||
\(482\) | 15.3083 | 0.697275 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.76975 | −0.0804434 | ||||||||
\(485\) | 3.33804 | 0.151573 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.1184 | 0.503821 | 0.251911 | − | 0.967751i | \(-0.418941\pi\) | ||||
0.251911 | + | 0.967751i | \(0.418941\pi\) | |||||||
\(488\) | 2.57834 | 0.116716 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.10278 | −0.230520 | ||||||||
\(491\) | −0.0594386 | −0.00268243 | −0.00134121 | − | 0.999999i | \(-0.500427\pi\) | ||||
−0.00134121 | + | 0.999999i | \(0.500427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.34715 | −0.195786 | ||||||||
\(494\) | 1.47556 | 0.0663887 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.84333 | −0.307274 | ||||||||
\(497\) | −8.72999 | −0.391593 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.2978 | 0.460991 | 0.230496 | − | 0.973073i | \(-0.425965\pi\) | ||||
0.230496 | + | 0.973073i | \(0.425965\pi\) | |||||||
\(500\) | 7.55773 | 0.337992 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 43.4983 | 1.94142 | ||||||||
\(503\) | 9.32391 | 0.415733 | 0.207866 | − | 0.978157i | \(-0.433348\pi\) | ||||
0.207866 | + | 0.978157i | \(0.433348\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.8661 | 1.64052 | ||||||||
\(506\) | 41.2927 | 1.83569 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.6066 | −0.736799 | ||||||||
\(509\) | −39.6952 | −1.75946 | −0.879730 | − | 0.475473i | \(-0.842277\pi\) | ||||
−0.879730 | + | 0.475473i | \(0.842277\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.34307 | 0.103651 | ||||||||
\(512\) | 18.4842 | 0.816892 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28.3133 | −1.24885 | ||||||||
\(515\) | −12.4111 | −0.546898 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.5244 | −0.814704 | ||||||||
\(518\) | 11.1567 | 0.490196 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.62721 | 0.159064 | ||||||||
\(521\) | −22.3627 | −0.979729 | −0.489865 | − | 0.871798i | \(-0.662954\pi\) | ||||
−0.489865 | + | 0.871798i | \(0.662954\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.6550 | −0.903178 | −0.451589 | − | 0.892226i | \(-0.649143\pi\) | ||||
−0.451589 | + | 0.892226i | \(0.649143\pi\) | |||||||
\(524\) | −11.6655 | −0.509611 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.5139 | 1.19966 | ||||||||
\(527\) | 0.729988 | 0.0317988 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.8469 | 1.34117 | ||||||||
\(530\) | −12.7300 | −0.552955 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.04888 | −0.0454745 | ||||||||
\(533\) | 4.20555 | 0.182163 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.62721 | 0.0703506 | ||||||||
\(536\) | −12.9411 | −0.558969 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −42.2439 | −1.82126 | ||||||||
\(539\) | −3.10278 | −0.133646 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.62167 | 0.241695 | 0.120847 | − | 0.992671i | \(-0.461439\pi\) | ||||
0.120847 | + | 0.992671i | \(0.461439\pi\) | |||||||
\(542\) | 23.1155 | 0.992894 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.32391 | −0.142512 | ||||||||
\(545\) | −15.6811 | −0.671705 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.3970 | −0.444542 | −0.222271 | − | 0.974985i | \(-0.571347\pi\) | ||||
−0.222271 | + | 0.974985i | \(0.571347\pi\) | |||||||
\(548\) | 8.06949 | 0.344711 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.4111 | −0.699772 | ||||||||
\(551\) | −6.74412 | −0.287309 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.5436 | 0.575932 | ||||||||
\(554\) | 14.7300 | 0.625817 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.9200 | −0.632747 | ||||||||
\(557\) | −14.6550 | −0.620951 | −0.310475 | − | 0.950581i | \(-0.600488\pi\) | ||||
−0.310475 | + | 0.950581i | \(0.600488\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.75971 | 0.285905 | ||||||||
\(560\) | −13.8328 | −0.584541 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −34.5189 | −1.45609 | ||||||||
\(563\) | 24.7456 | 1.04290 | 0.521451 | − | 0.853281i | \(-0.325391\pi\) | ||||
0.521451 | + | 0.853281i | \(0.325391\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.3225 | 0.644621 | ||||||||
\(566\) | 20.2156 | 0.849725 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.2544 | −0.472225 | ||||||||
\(569\) | 20.5330 | 0.860789 | 0.430395 | − | 0.902641i | \(-0.358374\pi\) | ||||
0.430395 | + | 0.902641i | \(0.358374\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.8953 | −1.75326 | −0.876631 | − | 0.481163i | \(-0.840214\pi\) | ||||
−0.876631 | + | 0.481163i | \(0.840214\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.62721 | −0.318354 | ||||||||
\(575\) | −21.4005 | −0.892464 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.1744 | −0.839870 | −0.419935 | − | 0.907554i | \(-0.637947\pi\) | ||||
−0.419935 | + | 0.907554i | \(0.637947\pi\) | |||||||
\(578\) | −30.3325 | −1.26167 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 30.0666 | 1.24845 | ||||||||
\(581\) | 16.4791 | 0.683670 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.74055 | −0.320581 | ||||||||
\(584\) | 3.02061 | 0.124994 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.7094 | 1.06204 | ||||||||
\(587\) | 18.7441 | 0.773653 | 0.386826 | − | 0.922153i | \(-0.373571\pi\) | ||||
0.386826 | + | 0.922153i | \(0.373571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.13249 | 0.0466636 | ||||||||
\(590\) | −22.8122 | −0.939162 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 30.2439 | 1.24302 | ||||||||
\(593\) | 2.98084 | 0.122409 | 0.0612043 | − | 0.998125i | \(-0.480506\pi\) | ||||
0.0612043 | + | 0.998125i | \(0.480506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.47556 | 0.0604921 | ||||||||
\(596\) | −10.9894 | −0.450145 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.3083 | −0.544218 | ||||||||
\(599\) | −7.47411 | −0.305384 | −0.152692 | − | 0.988274i | \(-0.548794\pi\) | ||||
−0.152692 | + | 0.988274i | \(0.548794\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.4700 | 0.875780 | 0.437890 | − | 0.899028i | \(-0.355726\pi\) | ||||
0.437890 | + | 0.899028i | \(0.355726\pi\) | |||||||
\(602\) | −12.2594 | −0.499658 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.4499 | −0.628649 | ||||||||
\(605\) | 3.86248 | 0.157032 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.9044 | −0.929660 | −0.464830 | − | 0.885400i | \(-0.653884\pi\) | ||||
−0.464830 | + | 0.885400i | \(0.653884\pi\) | |||||||
\(608\) | −5.15667 | −0.209131 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.2056 | 0.413211 | ||||||||
\(611\) | 5.97028 | 0.241532 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.1461 | −0.813694 | −0.406847 | − | 0.913496i | \(-0.633372\pi\) | ||||
−0.406847 | + | 0.913496i | \(0.633372\pi\) | |||||||
\(614\) | 24.5910 | 0.992413 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | 13.7844 | 0.554939 | 0.277470 | − | 0.960734i | \(-0.410504\pi\) | ||||
0.277470 | + | 0.960734i | \(0.410504\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.6655 | −0.790424 | −0.395212 | − | 0.918590i | \(-0.629329\pi\) | ||||
−0.395212 | + | 0.918590i | \(0.629329\pi\) | |||||||
\(620\) | −5.04888 | −0.202768 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.773841 | −0.0310282 | ||||||||
\(623\) | −10.6464 | −0.426538 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0766 | −1.24307 | ||||||||
\(626\) | −32.9200 | −1.31575 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.5371 | −0.659903 | ||||||||
\(629\) | −3.22616 | −0.128635 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.1672 | −0.643608 | −0.321804 | − | 0.946806i | \(-0.604289\pi\) | ||||
−0.321804 | + | 0.946806i | \(0.604289\pi\) | |||||||
\(632\) | 17.4600 | 0.694521 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.0872 | −0.678619 | ||||||||
\(635\) | 36.2439 | 1.43829 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 46.6449 | 1.84669 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −27.1849 | −1.07458 | ||||||||
\(641\) | 29.0036 | 1.14557 | 0.572786 | − | 0.819705i | \(-0.305863\pi\) | ||||
0.572786 | + | 0.819705i | \(0.305863\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.2233 | −1.54681 | −0.773407 | − | 0.633910i | \(-0.781449\pi\) | ||||
−0.773407 | + | 0.633910i | \(0.781449\pi\) | |||||||
\(644\) | 9.45998 | 0.372775 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.773841 | 0.0304464 | ||||||||
\(647\) | 11.9844 | 0.471156 | 0.235578 | − | 0.971855i | \(-0.424302\pi\) | ||||
0.235578 | + | 0.971855i | \(0.424302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.8711 | −0.544487 | ||||||||
\(650\) | 5.28917 | 0.207458 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.3522 | −0.679564 | ||||||||
\(653\) | −45.3311 | −1.77394 | −0.886971 | − | 0.461826i | \(-0.847194\pi\) | ||||
−0.886971 | + | 0.461826i | \(0.847194\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.4600 | 0.994804 | ||||||||
\(656\) | −20.6761 | −0.807266 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.8277 | −0.422109 | ||||||||
\(659\) | −6.12193 | −0.238477 | −0.119238 | − | 0.992866i | \(-0.538045\pi\) | ||||
−0.119238 | + | 0.992866i | \(0.538045\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.5280 | −1.07072 | −0.535358 | − | 0.844625i | \(-0.679823\pi\) | ||||
−0.535358 | + | 0.844625i | \(0.679823\pi\) | |||||||
\(662\) | −31.5577 | −1.22653 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21.2444 | 0.824442 | ||||||||
\(665\) | 2.28917 | 0.0887701 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 60.8263 | 2.35520 | ||||||||
\(668\) | 2.61665 | 0.101241 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −51.2233 | −1.97893 | ||||||||
\(671\) | 6.20555 | 0.239563 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.9547 | 1.07757 | 0.538787 | − | 0.842442i | \(-0.318883\pi\) | ||||
0.538787 | + | 0.842442i | \(0.318883\pi\) | |||||||
\(674\) | 39.9945 | 1.54053 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.28917 | 0.0495834 | ||||||||
\(677\) | 12.6605 | 0.486583 | 0.243291 | − | 0.969953i | \(-0.421773\pi\) | ||||
0.243291 | + | 0.969953i | \(0.421773\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.18639 | 0.0455296 | ||||||||
\(680\) | 1.90225 | 0.0729479 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.83276 | −0.299932 | ||||||||
\(683\) | 28.3033 | 1.08300 | 0.541498 | − | 0.840702i | \(-0.317857\pi\) | ||||
0.541498 | + | 0.840702i | \(0.317857\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.6116 | −0.672906 | ||||||||
\(686\) | −1.81361 | −0.0692438 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −33.2333 | −1.26701 | ||||||||
\(689\) | 2.49472 | 0.0950412 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.2353 | 0.465452 | 0.232726 | − | 0.972542i | \(-0.425236\pi\) | ||||
0.232726 | + | 0.972542i | \(0.425236\pi\) | |||||||
\(692\) | −26.1672 | −0.994729 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −45.9789 | −1.74533 | ||||||||
\(695\) | 32.5628 | 1.23518 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.20555 | 0.0835412 | ||||||||
\(698\) | −10.3472 | −0.391646 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.75971 | −0.142104 | ||||||||
\(701\) | −51.0419 | −1.92783 | −0.963913 | − | 0.266219i | \(-0.914226\pi\) | ||||
−0.963913 | + | 0.266219i | \(0.914226\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.00502 | −0.188768 | ||||||||
\(704\) | 5.15667 | 0.194349 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 52.0071 | 1.95731 | ||||||||
\(707\) | 13.1028 | 0.492781 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.5910 | 1.59954 | 0.799770 | − | 0.600307i | \(-0.204955\pi\) | ||||
0.799770 | + | 0.600307i | \(0.204955\pi\) | |||||||
\(710\) | −44.5472 | −1.67183 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.7250 | −0.514365 | ||||||||
\(713\) | −10.2141 | −0.382523 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.72999 | 0.326483 | ||||||||
\(716\) | 14.1855 | 0.530135 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.0283 | −0.747448 | ||||||||
\(719\) | 42.4933 | 1.58473 | 0.792366 | − | 0.610046i | \(-0.208849\pi\) | ||||
0.792366 | + | 0.610046i | \(0.208849\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.41110 | −0.164278 | ||||||||
\(722\) | −33.2580 | −1.23773 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.891685 | 0.0331392 | ||||||||
\(725\) | −24.1744 | −0.897814 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.75614 | −0.139307 | −0.0696537 | − | 0.997571i | \(-0.522189\pi\) | ||||
−0.0696537 | + | 0.997571i | \(0.522189\pi\) | |||||||
\(728\) | 1.28917 | 0.0477798 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.9561 | 0.442517 | ||||||||
\(731\) | 3.54505 | 0.131118 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.7819 | 1.69099 | 0.845497 | − | 0.533980i | \(-0.179304\pi\) | ||||
0.845497 | + | 0.533980i | \(0.179304\pi\) | |||||||
\(734\) | 49.5960 | 1.83062 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 46.5089 | 1.71434 | ||||||||
\(737\) | −31.1466 | −1.14730 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.0539 | −0.516981 | −0.258491 | − | 0.966014i | \(-0.583225\pi\) | ||||
−0.258491 | + | 0.966014i | \(0.583225\pi\) | |||||||
\(740\) | 22.3133 | 0.820255 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.52444 | −0.166097 | ||||||||
\(743\) | −4.74557 | −0.174098 | −0.0870491 | − | 0.996204i | \(-0.527744\pi\) | ||||
−0.0870491 | + | 0.996204i | \(0.527744\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.9844 | 0.878721 | ||||||||
\(746\) | 29.2827 | 1.07212 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.09775 | −0.0767014 | ||||||||
\(749\) | 0.578337 | 0.0211320 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.1008 | 1.31734 | 0.658669 | − | 0.752433i | \(-0.271120\pi\) | ||||
0.658669 | + | 0.752433i | \(0.271120\pi\) | |||||||
\(752\) | −29.3522 | −1.07036 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.0333 | −0.547480 | ||||||||
\(755\) | 33.7194 | 1.22718 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.03474 | −0.0376084 | −0.0188042 | − | 0.999823i | \(-0.505986\pi\) | ||||
−0.0188042 | + | 0.999823i | \(0.505986\pi\) | |||||||
\(758\) | 47.3905 | 1.72130 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.95112 | 0.107049 | ||||||||
\(761\) | −29.8414 | −1.08175 | −0.540874 | − | 0.841104i | \(-0.681906\pi\) | ||||
−0.540874 | + | 0.841104i | \(0.681906\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.57331 | −0.201768 | ||||||||
\(764\) | −10.0978 | −0.365324 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 38.1744 | 1.37930 | ||||||||
\(767\) | 4.47054 | 0.161422 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.6358 | 0.852329 | 0.426164 | − | 0.904646i | \(-0.359864\pi\) | ||||
0.426164 | + | 0.904646i | \(0.359864\pi\) | |||||||
\(770\) | −15.8328 | −0.570573 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.7350 | −0.566315 | ||||||||
\(773\) | −13.0278 | −0.468576 | −0.234288 | − | 0.972167i | \(-0.575276\pi\) | ||||
−0.234288 | + | 0.972167i | \(0.575276\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.05944 | 0.145819 | ||||||||
\(776\) | 1.52946 | 0.0549045 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39.1849 | 1.40485 | ||||||||
\(779\) | 3.42166 | 0.122594 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0872 | −0.969256 | ||||||||
\(782\) | −6.97939 | −0.249583 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.91638 | −0.175585 | ||||||||
\(785\) | 36.0922 | 1.28819 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.2141 | 1.64736 | 0.823678 | − | 0.567058i | \(-0.191918\pi\) | ||||
0.823678 | + | 0.567058i | \(0.191918\pi\) | |||||||
\(788\) | 24.2650 | 0.864404 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 69.1099 | 2.45882 | ||||||||
\(791\) | 5.44584 | 0.193632 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.00000 | −0.0710221 | ||||||||
\(794\) | −50.2283 | −1.78253 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27.8610 | 0.987508 | ||||||||
\(797\) | −53.1155 | −1.88145 | −0.940723 | − | 0.339176i | \(-0.889852\pi\) | ||||
−0.940723 | + | 0.339176i | \(0.889852\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.13104 | 0.110768 | ||||||||
\(800\) | −18.4842 | −0.653514 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.67609 | 0.165118 | ||||||||
\(803\) | 7.27001 | 0.256553 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.6464 | −0.727689 | ||||||||
\(806\) | 2.52444 | 0.0889195 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.8917 | 0.594247 | ||||||||
\(809\) | 54.4635 | 1.91484 | 0.957418 | − | 0.288705i | \(-0.0932246\pi\) | ||||
0.957418 | + | 0.288705i | \(0.0932246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.0978 | 1.33779 | 0.668897 | − | 0.743356i | \(-0.266767\pi\) | ||||
0.668897 | + | 0.743356i | \(0.266767\pi\) | |||||||
\(812\) | 10.6861 | 0.375010 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 34.6167 | 1.21331 | ||||||||
\(815\) | 37.8711 | 1.32657 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.49974 | 0.192412 | ||||||||
\(818\) | 27.4161 | 0.958582 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.2544 | −0.532708 | ||||||||
\(821\) | 2.30330 | 0.0803858 | 0.0401929 | − | 0.999192i | \(-0.487203\pi\) | ||||
0.0401929 | + | 0.999192i | \(0.487203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.6172 | 0.823243 | 0.411621 | − | 0.911355i | \(-0.364963\pi\) | ||||
0.411621 | + | 0.911355i | \(0.364963\pi\) | |||||||
\(824\) | −5.68665 | −0.198104 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.10780 | −0.282106 | ||||||||
\(827\) | 48.1643 | 1.67484 | 0.837419 | − | 0.546562i | \(-0.184064\pi\) | ||||
0.837419 | + | 0.546562i | \(0.184064\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0716 | 0.453996 | 0.226998 | − | 0.973895i | \(-0.427109\pi\) | ||||
0.226998 | + | 0.973895i | \(0.427109\pi\) | |||||||
\(830\) | 84.0893 | 2.91878 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.66196 | −0.0576179 | ||||||||
\(833\) | 0.524438 | 0.0181707 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.71083 | −0.197631 | ||||||||
\(836\) | −3.25443 | −0.112557 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.1260 | 0.626153 | ||||||||
\(839\) | 17.6756 | 0.610229 | 0.305114 | − | 0.952316i | \(-0.401305\pi\) | ||||
0.305114 | + | 0.952316i | \(0.401305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.7103 | 1.36932 | ||||||||
\(842\) | −47.0177 | −1.62034 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.4011 | −0.771076 | ||||||||
\(845\) | −2.81361 | −0.0967910 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.37279 | 0.0471695 | ||||||||
\(848\) | −12.2650 | −0.421181 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.77384 | 0.0951420 | ||||||||
\(851\) | 45.1411 | 1.54742 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.48970 | −0.187964 | −0.0939818 | − | 0.995574i | \(-0.529960\pi\) | ||||
−0.0939818 | + | 0.995574i | \(0.529960\pi\) | |||||||
\(854\) | 3.62721 | 0.124121 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.745574 | 0.0254832 | ||||||||
\(857\) | 11.0489 | 0.377422 | 0.188711 | − | 0.982033i | \(-0.439569\pi\) | ||||
0.188711 | + | 0.982033i | \(0.439569\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.2616 | 1.54430 | 0.772152 | − | 0.635437i | \(-0.219180\pi\) | ||||
0.772152 | + | 0.635437i | \(0.219180\pi\) | |||||||
\(860\) | −24.5189 | −0.836087 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −55.6344 | −1.89491 | ||||||||
\(863\) | 5.90225 | 0.200915 | 0.100457 | − | 0.994941i | \(-0.467969\pi\) | ||||
0.100457 | + | 0.994941i | \(0.467969\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 57.1099 | 1.94180 | ||||||||
\(866\) | −6.38283 | −0.216898 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.79445 | −0.0609076 | ||||||||
\(869\) | 42.0227 | 1.42552 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0383 | 0.340135 | ||||||||
\(872\) | −7.18494 | −0.243313 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.8277 | −0.366254 | ||||||||
\(875\) | −5.86248 | −0.198188 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.90727 | −0.165707 | −0.0828534 | − | 0.996562i | \(-0.526403\pi\) | ||||
−0.0828534 | + | 0.996562i | \(0.526403\pi\) | |||||||
\(878\) | 58.6732 | 1.98012 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −42.9200 | −1.44683 | ||||||||
\(881\) | −44.2822 | −1.49190 | −0.745952 | − | 0.665999i | \(-0.768005\pi\) | ||||
−0.745952 | + | 0.665999i | \(0.768005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −58.8605 | −1.98081 | −0.990407 | − | 0.138181i | \(-0.955874\pi\) | ||||
−0.990407 | + | 0.138181i | \(0.955874\pi\) | |||||||
\(884\) | 0.676089 | 0.0227393 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.0127 | −0.941104 | ||||||||
\(887\) | 10.1289 | 0.340096 | 0.170048 | − | 0.985436i | \(-0.445608\pi\) | ||||
0.170048 | + | 0.985436i | \(0.445608\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.8816 | 0.432036 | ||||||||
\(890\) | −54.3260 | −1.82101 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.5989 | −0.455326 | ||||||||
\(893\) | 4.85746 | 0.162549 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.9597 | −1.03487 | ||||||||
\(896\) | −9.66196 | −0.322783 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.2439 | 0.875769 | ||||||||
\(899\) | −11.5381 | −0.384816 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.30833 | 0.0435866 | ||||||||
\(902\) | −23.6655 | −0.787976 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.02061 | 0.233502 | ||||||||
\(905\) | −1.94610 | −0.0646906 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.9547 | 1.26026 | 0.630132 | − | 0.776488i | \(-0.283001\pi\) | ||||
0.630132 | + | 0.776488i | \(0.283001\pi\) | |||||||
\(908\) | 8.96117 | 0.297387 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.10278 | 0.169155 | ||||||||
\(911\) | −5.57477 | −0.184700 | −0.0923501 | − | 0.995727i | \(-0.529438\pi\) | ||||
−0.0923501 | + | 0.995727i | \(0.529438\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.1310 | 1.69219 | ||||||||
\(914\) | −62.8787 | −2.07984 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27.1849 | −0.898216 | ||||||||
\(917\) | 9.04888 | 0.298820 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.7844 | 0.520679 | 0.260340 | − | 0.965517i | \(-0.416165\pi\) | ||||
0.260340 | + | 0.965517i | \(0.416165\pi\) | |||||||
\(920\) | −26.6167 | −0.877525 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.7427 | −0.748990 | ||||||||
\(923\) | 8.72999 | 0.287351 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.9406 | −0.589882 | ||||||||
\(926\) | 22.0383 | 0.724224 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 52.5371 | 1.72462 | ||||||||
\(929\) | 45.2630 | 1.48503 | 0.742516 | − | 0.669829i | \(-0.233632\pi\) | ||||
0.742516 | + | 0.669829i | \(0.233632\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.813607 | 0.0266649 | ||||||||
\(932\) | −7.84281 | −0.256900 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 67.1638 | 2.19767 | ||||||||
\(935\) | 4.57834 | 0.149728 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.6188 | 1.75165 | 0.875824 | − | 0.482630i | \(-0.160318\pi\) | ||||
0.875824 | + | 0.482630i | \(0.160318\pi\) | |||||||
\(938\) | −18.2056 | −0.594432 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −21.6555 | −0.706324 | ||||||||
\(941\) | −20.7753 | −0.677255 | −0.338628 | − | 0.940920i | \(-0.609963\pi\) | ||||
−0.338628 | + | 0.940920i | \(0.609963\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.8605 | −1.00496 | ||||||||
\(944\) | −21.9789 | −0.715351 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.0383 | −1.23673 | ||||||||
\(947\) | 10.8605 | 0.352919 | 0.176460 | − | 0.984308i | \(-0.443535\pi\) | ||||
0.176460 | + | 0.984308i | \(0.443535\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.34307 | −0.0760592 | ||||||||
\(950\) | 4.30330 | 0.139618 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.676089 | 0.0219122 | ||||||||
\(953\) | 25.7180 | 0.833087 | 0.416543 | − | 0.909116i | \(-0.363241\pi\) | ||||
0.416543 | + | 0.909116i | \(0.363241\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.0383 | 0.713143 | ||||||||
\(956\) | 18.3133 | 0.592296 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.7789 | −0.703643 | ||||||||
\(959\) | −6.25945 | −0.202128 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0625 | −0.937500 | ||||||||
\(962\) | −11.1567 | −0.359706 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.8816 | 0.350474 | ||||||||
\(965\) | 34.3416 | 1.10550 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.5038 | 1.07741 | 0.538705 | − | 0.842494i | \(-0.318914\pi\) | ||||
0.538705 | + | 0.842494i | \(0.318914\pi\) | |||||||
\(968\) | 1.76975 | 0.0568820 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.05390 | 0.194379 | ||||||||
\(971\) | −2.03831 | −0.0654126 | −0.0327063 | − | 0.999465i | \(-0.510413\pi\) | ||||
−0.0327063 | + | 0.999465i | \(0.510413\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.5733 | 0.371023 | ||||||||
\(974\) | 20.1643 | 0.646107 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.83276 | 0.314739 | ||||||||
\(977\) | −15.1411 | −0.484406 | −0.242203 | − | 0.970226i | \(-0.577870\pi\) | ||||
−0.242203 | + | 0.970226i | \(0.577870\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.0333 | −1.05575 | ||||||||
\(980\) | −3.62721 | −0.115867 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.107798 | −0.00343998 | ||||||||
\(983\) | −49.3124 | −1.57282 | −0.786411 | − | 0.617704i | \(-0.788063\pi\) | ||||
−0.786411 | + | 0.617704i | \(0.788063\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.9583 | −1.68739 | ||||||||
\(986\) | −7.88403 | −0.251079 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.04888 | 0.0333692 | ||||||||
\(989\) | −49.6030 | −1.57728 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.43171 | 0.172544 | 0.0862720 | − | 0.996272i | \(-0.472505\pi\) | ||||
0.0862720 | + | 0.996272i | \(0.472505\pi\) | |||||||
\(992\) | −8.82220 | −0.280105 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15.8328 | −0.502185 | ||||||||
\(995\) | −60.8066 | −1.92770 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.6061 | −1.69772 | −0.848861 | − | 0.528616i | \(-0.822711\pi\) | ||||
−0.848861 | + | 0.528616i | \(0.822711\pi\) | |||||||
\(998\) | 18.6761 | 0.591181 | ||||||||
\(999\) | 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 | 819.2.a.i.1.3 | 3 | ||
3.2 | odd | 2 | 91.2.a.d.1.1 | ✓ | 3 | ||
7.6 | odd | 2 | 5733.2.a.x.1.3 | 3 | |||
12.11 | even | 2 | 1456.2.a.t.1.3 | 3 | |||
15.14 | odd | 2 | 2275.2.a.m.1.3 | 3 | |||
21.2 | odd | 6 | 637.2.e.j.508.3 | 6 | |||
21.5 | even | 6 | 637.2.e.i.508.3 | 6 | |||
21.11 | odd | 6 | 637.2.e.j.79.3 | 6 | |||
21.17 | even | 6 | 637.2.e.i.79.3 | 6 | |||
21.20 | even | 2 | 637.2.a.j.1.1 | 3 | |||
24.5 | odd | 2 | 5824.2.a.by.1.3 | 3 | |||
24.11 | even | 2 | 5824.2.a.bs.1.1 | 3 | |||
39.5 | even | 4 | 1183.2.c.f.337.5 | 6 | |||
39.8 | even | 4 | 1183.2.c.f.337.2 | 6 | |||
39.38 | odd | 2 | 1183.2.a.i.1.3 | 3 | |||
273.272 | even | 2 | 8281.2.a.bg.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.a.d.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
637.2.a.j.1.1 | 3 | 21.20 | even | 2 | |||
637.2.e.i.79.3 | 6 | 21.17 | even | 6 | |||
637.2.e.i.508.3 | 6 | 21.5 | even | 6 | |||
637.2.e.j.79.3 | 6 | 21.11 | odd | 6 | |||
637.2.e.j.508.3 | 6 | 21.2 | odd | 6 | |||
819.2.a.i.1.3 | 3 | 1.1 | even | 1 | trivial | ||
1183.2.a.i.1.3 | 3 | 39.38 | odd | 2 | |||
1183.2.c.f.337.2 | 6 | 39.8 | even | 4 | |||
1183.2.c.f.337.5 | 6 | 39.5 | even | 4 | |||
1456.2.a.t.1.3 | 3 | 12.11 | even | 2 | |||
2275.2.a.m.1.3 | 3 | 15.14 | odd | 2 | |||
5733.2.a.x.1.3 | 3 | 7.6 | odd | 2 | |||
5824.2.a.bs.1.1 | 3 | 24.11 | even | 2 | |||
5824.2.a.by.1.3 | 3 | 24.5 | odd | 2 | |||
8281.2.a.bg.1.3 | 3 | 273.272 | even | 2 |