Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,2,Mod(1,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, 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("1143.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.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: | \(9.12690095103\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.456850\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1143.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | −1.22474 | −0.612372 | − | 0.790569i | \(-0.709785\pi\) | ||||
−0.612372 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.456850 | −0.204310 | −0.102155 | − | 0.994769i | \(-0.532574\pi\) | ||||
−0.102155 | + | 0.994769i | \(0.532574\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.79129 | −1.43297 | −0.716486 | − | 0.697601i | \(-0.754251\pi\) | ||||
−0.716486 | + | 0.697601i | \(0.754251\pi\) | |||||||
\(8\) | 1.73205 | 0.612372 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.791288 | 0.250227 | ||||||||
\(11\) | 2.18890 | 0.659979 | 0.329989 | − | 0.943985i | \(-0.392955\pi\) | ||||
0.329989 | + | 0.943985i | \(0.392955\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.20871 | −0.335236 | −0.167618 | − | 0.985852i | \(-0.553608\pi\) | ||||
−0.167618 | + | 0.985852i | \(0.553608\pi\) | |||||||
\(14\) | 6.56670 | 1.75503 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 4.37780 | 1.06177 | 0.530886 | − | 0.847443i | \(-0.321859\pi\) | ||||
0.530886 | + | 0.847443i | \(0.321859\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.58258 | 0.821899 | 0.410950 | − | 0.911658i | \(-0.365197\pi\) | ||||
0.410950 | + | 0.911658i | \(0.365197\pi\) | |||||||
\(20\) | −0.456850 | −0.102155 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.79129 | −0.808305 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.79129 | −0.958258 | ||||||||
\(26\) | 2.09355 | 0.410579 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.79129 | −0.716486 | ||||||||
\(29\) | 3.10260 | 0.576139 | 0.288069 | − | 0.957610i | \(-0.406987\pi\) | ||||
0.288069 | + | 0.957610i | \(0.406987\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.58258 | 0.643450 | 0.321725 | − | 0.946833i | \(-0.395737\pi\) | ||||
0.321725 | + | 0.946833i | \(0.395737\pi\) | |||||||
\(32\) | 5.19615 | 0.918559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.58258 | −1.30040 | ||||||||
\(35\) | 1.73205 | 0.292770 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.79129 | −0.458885 | −0.229442 | − | 0.973322i | \(-0.573690\pi\) | ||||
−0.229442 | + | 0.973322i | \(0.573690\pi\) | |||||||
\(38\) | −6.20520 | −1.00662 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.791288 | −0.125114 | ||||||||
\(41\) | −9.66930 | −1.51009 | −0.755046 | − | 0.655672i | \(-0.772385\pi\) | ||||
−0.755046 | + | 0.655672i | \(0.772385\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.37386 | −1.27700 | −0.638501 | − | 0.769621i | \(-0.720445\pi\) | ||||
−0.638501 | + | 0.769621i | \(0.720445\pi\) | |||||||
\(44\) | 2.18890 | 0.329989 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.456850 | 0.0666385 | 0.0333192 | − | 0.999445i | \(-0.489392\pi\) | ||||
0.0333192 | + | 0.999445i | \(0.489392\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.37386 | 1.05341 | ||||||||
\(50\) | 8.29875 | 1.17362 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.20871 | −0.167618 | ||||||||
\(53\) | 3.10260 | 0.426175 | 0.213088 | − | 0.977033i | \(-0.431648\pi\) | ||||
0.213088 | + | 0.977033i | \(0.431648\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −6.56670 | −0.877513 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.37386 | −0.705623 | ||||||||
\(59\) | −8.75560 | −1.13988 | −0.569941 | − | 0.821685i | \(-0.693034\pi\) | ||||
−0.569941 | + | 0.821685i | \(0.693034\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.79129 | 0.229351 | 0.114675 | − | 0.993403i | \(-0.463417\pi\) | ||||
0.114675 | + | 0.993403i | \(0.463417\pi\) | |||||||
\(62\) | −6.20520 | −0.788062 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.552200 | 0.0684920 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.20871 | −0.147668 | −0.0738338 | − | 0.997271i | \(-0.523523\pi\) | ||||
−0.0738338 | + | 0.997271i | \(0.523523\pi\) | |||||||
\(68\) | 4.37780 | 0.530886 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.00000 | −0.358569 | ||||||||
\(71\) | 0.361500 | 0.0429022 | 0.0214511 | − | 0.999770i | \(-0.493171\pi\) | ||||
0.0214511 | + | 0.999770i | \(0.493171\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.3739 | −1.56529 | −0.782646 | − | 0.622467i | \(-0.786131\pi\) | ||||
−0.782646 | + | 0.622467i | \(0.786131\pi\) | |||||||
\(74\) | 4.83465 | 0.562017 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.58258 | 0.410950 | ||||||||
\(77\) | −8.29875 | −0.945731 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.58258 | 0.628089 | 0.314044 | − | 0.949408i | \(-0.398316\pi\) | ||||
0.314044 | + | 0.949408i | \(0.398316\pi\) | |||||||
\(80\) | 2.28425 | 0.255387 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 16.7477 | 1.84948 | ||||||||
\(83\) | −0.723000 | −0.0793596 | −0.0396798 | − | 0.999212i | \(-0.512634\pi\) | ||||
−0.0396798 | + | 0.999212i | \(0.512634\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 14.5040 | 1.56400 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.79129 | 0.404153 | ||||||||
\(89\) | 8.29875 | 0.879666 | 0.439833 | − | 0.898080i | \(-0.355038\pi\) | ||||
0.439833 | + | 0.898080i | \(0.355038\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.58258 | 0.480384 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.791288 | −0.0816151 | ||||||||
\(95\) | −1.63670 | −0.167922 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | −12.7719 | −1.29016 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.79129 | −0.479129 | ||||||||
\(101\) | −17.5112 | −1.74243 | −0.871215 | − | 0.490901i | \(-0.836668\pi\) | ||||
−0.871215 | + | 0.490901i | \(0.836668\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.58258 | −0.747133 | −0.373567 | − | 0.927603i | \(-0.621865\pi\) | ||||
−0.373567 | + | 0.927603i | \(0.621865\pi\) | |||||||
\(104\) | −2.09355 | −0.205290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.37386 | −0.521956 | ||||||||
\(107\) | −11.0399 | −1.06726 | −0.533632 | − | 0.845717i | \(-0.679173\pi\) | ||||
−0.533632 | + | 0.845717i | \(0.679173\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.74773 | −0.646315 | −0.323158 | − | 0.946345i | \(-0.604744\pi\) | ||||
−0.323158 | + | 0.946345i | \(0.604744\pi\) | |||||||
\(110\) | 1.73205 | 0.165145 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 18.9564 | 1.79122 | ||||||||
\(113\) | −9.47860 | −0.891672 | −0.445836 | − | 0.895115i | \(-0.647094\pi\) | ||||
−0.445836 | + | 0.895115i | \(0.647094\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.10260 | 0.288069 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.1652 | 1.39607 | ||||||||
\(119\) | −16.5975 | −1.52149 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.20871 | −0.564428 | ||||||||
\(122\) | −3.10260 | −0.280896 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.58258 | 0.321725 | ||||||||
\(125\) | 4.47315 | 0.400091 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −12.1244 | −1.07165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.956439 | −0.0838853 | ||||||||
\(131\) | 7.38505 | 0.645235 | 0.322618 | − | 0.946529i | \(-0.395437\pi\) | ||||
0.322618 | + | 0.946529i | \(0.395437\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.5826 | −1.17776 | ||||||||
\(134\) | 2.09355 | 0.180855 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.58258 | 0.650201 | ||||||||
\(137\) | −5.10080 | −0.435791 | −0.217895 | − | 0.975972i | \(-0.569919\pi\) | ||||
−0.217895 | + | 0.975972i | \(0.569919\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.1652 | −0.947016 | −0.473508 | − | 0.880790i | \(-0.657012\pi\) | ||||
−0.473508 | + | 0.880790i | \(0.657012\pi\) | |||||||
\(140\) | 1.73205 | 0.146385 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.626136 | −0.0525442 | ||||||||
\(143\) | −2.64575 | −0.221249 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.41742 | −0.117711 | ||||||||
\(146\) | 23.1642 | 1.91708 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.79129 | −0.229442 | ||||||||
\(149\) | 11.4967 | 0.941847 | 0.470923 | − | 0.882174i | \(-0.343921\pi\) | ||||
0.470923 | + | 0.882174i | \(0.343921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.37386 | 0.600077 | 0.300038 | − | 0.953927i | \(-0.403001\pi\) | ||||
0.300038 | + | 0.953927i | \(0.403001\pi\) | |||||||
\(152\) | 6.20520 | 0.503308 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.3739 | 1.15828 | ||||||||
\(155\) | −1.63670 | −0.131463 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.3739 | −1.06735 | −0.533675 | − | 0.845689i | \(-0.679190\pi\) | ||||
−0.533675 | + | 0.845689i | \(0.679190\pi\) | |||||||
\(158\) | −9.66930 | −0.769249 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.37386 | −0.187670 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | −9.66930 | −0.755046 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.25227 | 0.0971952 | ||||||||
\(167\) | 7.84190 | 0.606825 | 0.303412 | − | 0.952859i | \(-0.401874\pi\) | ||||
0.303412 | + | 0.952859i | \(0.401874\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5390 | −0.887617 | ||||||||
\(170\) | 3.46410 | 0.265684 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.37386 | −0.638501 | ||||||||
\(173\) | −17.9681 | −1.36609 | −0.683043 | − | 0.730378i | \(-0.739344\pi\) | ||||
−0.683043 | + | 0.730378i | \(0.739344\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.1652 | 1.37316 | ||||||||
\(176\) | −10.9445 | −0.824973 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.3739 | −1.07737 | ||||||||
\(179\) | −18.8818 | −1.41129 | −0.705644 | − | 0.708566i | \(-0.749342\pi\) | ||||
−0.705644 | + | 0.708566i | \(0.749342\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.1652 | −1.42453 | −0.712267 | − | 0.701908i | \(-0.752332\pi\) | ||||
−0.712267 | + | 0.701908i | \(0.752332\pi\) | |||||||
\(182\) | −7.93725 | −0.588348 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.27520 | 0.0937546 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.58258 | 0.700747 | ||||||||
\(188\) | 0.456850 | 0.0333192 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.83485 | 0.205662 | ||||||||
\(191\) | 8.94630 | 0.647332 | 0.323666 | − | 0.946171i | \(-0.395085\pi\) | ||||
0.323666 | + | 0.946171i | \(0.395085\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.0000 | −1.15171 | −0.575853 | − | 0.817554i | \(-0.695330\pi\) | ||||
−0.575853 | + | 0.817554i | \(0.695330\pi\) | |||||||
\(194\) | 13.8564 | 0.994832 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.37386 | 0.526705 | ||||||||
\(197\) | 25.1624 | 1.79275 | 0.896374 | − | 0.443299i | \(-0.146192\pi\) | ||||
0.896374 | + | 0.443299i | \(0.146192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.7477 | 1.04544 | 0.522719 | − | 0.852505i | \(-0.324918\pi\) | ||||
0.522719 | + | 0.852505i | \(0.324918\pi\) | |||||||
\(200\) | −8.29875 | −0.586811 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 30.3303 | 2.13403 | ||||||||
\(203\) | −11.7629 | −0.825591 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.41742 | 0.308526 | ||||||||
\(206\) | 13.1334 | 0.915048 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.04356 | 0.419046 | ||||||||
\(209\) | 7.84190 | 0.542436 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 3.10260 | 0.213088 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.1216 | 1.30713 | ||||||||
\(215\) | 3.82560 | 0.260904 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.5826 | −0.922045 | ||||||||
\(218\) | 11.6874 | 0.791571 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −5.29150 | −0.355945 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.5390 | 1.30843 | 0.654215 | − | 0.756309i | \(-0.272999\pi\) | ||||
0.654215 | + | 0.756309i | \(0.272999\pi\) | |||||||
\(224\) | −19.7001 | −1.31627 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.4174 | 1.09207 | ||||||||
\(227\) | 2.18890 | 0.145282 | 0.0726412 | − | 0.997358i | \(-0.476857\pi\) | ||||
0.0726412 | + | 0.997358i | \(0.476857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.5826 | 1.16189 | 0.580945 | − | 0.813943i | \(-0.302683\pi\) | ||||
0.580945 | + | 0.813943i | \(0.302683\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.37386 | 0.352811 | ||||||||
\(233\) | −19.7955 | −1.29684 | −0.648422 | − | 0.761281i | \(-0.724571\pi\) | ||||
−0.648422 | + | 0.761281i | \(0.724571\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.208712 | −0.0136149 | ||||||||
\(236\) | −8.75560 | −0.569941 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 28.7477 | 1.86344 | ||||||||
\(239\) | −14.2378 | −0.920967 | −0.460484 | − | 0.887668i | \(-0.652324\pi\) | ||||
−0.460484 | + | 0.887668i | \(0.652324\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.16515 | 0.0750540 | 0.0375270 | − | 0.999296i | \(-0.488052\pi\) | ||||
0.0375270 | + | 0.999296i | \(0.488052\pi\) | |||||||
\(242\) | 10.7538 | 0.691281 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.79129 | 0.114675 | ||||||||
\(245\) | −3.36875 | −0.215222 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.33030 | −0.275531 | ||||||||
\(248\) | 6.20520 | 0.394031 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.74773 | −0.490009 | ||||||||
\(251\) | 17.3205 | 1.09326 | 0.546630 | − | 0.837374i | \(-0.315910\pi\) | ||||
0.546630 | + | 0.837374i | \(0.315910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.73205 | 0.108679 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | 28.2650 | 1.76312 | 0.881562 | − | 0.472069i | \(-0.156493\pi\) | ||||
0.881562 | + | 0.472069i | \(0.156493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.5826 | 0.657569 | ||||||||
\(260\) | 0.552200 | 0.0342460 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.7913 | −0.790248 | ||||||||
\(263\) | −12.0489 | −0.742967 | −0.371484 | − | 0.928439i | \(-0.621151\pi\) | ||||
−0.371484 | + | 0.928439i | \(0.621151\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.41742 | −0.0870717 | ||||||||
\(266\) | 23.5257 | 1.44245 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.20871 | −0.0738338 | ||||||||
\(269\) | 12.4104 | 0.756676 | 0.378338 | − | 0.925668i | \(-0.376496\pi\) | ||||
0.378338 | + | 0.925668i | \(0.376496\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.5826 | 1.31105 | 0.655524 | − | 0.755174i | \(-0.272448\pi\) | ||||
0.655524 | + | 0.755174i | \(0.272448\pi\) | |||||||
\(272\) | −21.8890 | −1.32722 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.83485 | 0.533733 | ||||||||
\(275\) | −10.4877 | −0.632429 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.16515 | 0.310344 | 0.155172 | − | 0.987887i | \(-0.450407\pi\) | ||||
0.155172 | + | 0.987887i | \(0.450407\pi\) | |||||||
\(278\) | 19.3386 | 1.15985 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.00000 | 0.179284 | ||||||||
\(281\) | 13.3996 | 0.799351 | 0.399675 | − | 0.916657i | \(-0.369123\pi\) | ||||
0.399675 | + | 0.916657i | \(0.369123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.20871 | −0.487957 | −0.243979 | − | 0.969781i | \(-0.578453\pi\) | ||||
−0.243979 | + | 0.969781i | \(0.578453\pi\) | |||||||
\(284\) | 0.361500 | 0.0214511 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.58258 | 0.270973 | ||||||||
\(287\) | 36.6591 | 2.16392 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.16515 | 0.127362 | ||||||||
\(290\) | 2.45505 | 0.144166 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.3739 | −0.782646 | ||||||||
\(293\) | −1.99820 | −0.116736 | −0.0583681 | − | 0.998295i | \(-0.518590\pi\) | ||||
−0.0583681 | + | 0.998295i | \(0.518590\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | −4.83465 | −0.281008 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.9129 | −1.15352 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.7477 | 1.82991 | ||||||||
\(302\) | −12.7719 | −0.734941 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −17.9129 | −1.02737 | ||||||||
\(305\) | −0.818350 | −0.0468586 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.1216 | −1.03425 | −0.517127 | − | 0.855909i | \(-0.672998\pi\) | ||||
−0.517127 | + | 0.855909i | \(0.672998\pi\) | |||||||
\(308\) | −8.29875 | −0.472865 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.83485 | 0.161009 | ||||||||
\(311\) | 6.01450 | 0.341051 | 0.170526 | − | 0.985353i | \(-0.445453\pi\) | ||||
0.170526 | + | 0.985353i | \(0.445453\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4174 | −0.814921 | −0.407461 | − | 0.913223i | \(-0.633586\pi\) | ||||
−0.407461 | + | 0.913223i | \(0.633586\pi\) | |||||||
\(314\) | 23.1642 | 1.30723 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.58258 | 0.314044 | ||||||||
\(317\) | 24.4394 | 1.37265 | 0.686327 | − | 0.727293i | \(-0.259222\pi\) | ||||
0.686327 | + | 0.727293i | \(0.259222\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.79129 | 0.380239 | ||||||||
\(320\) | −0.456850 | −0.0255387 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.6838 | 0.872670 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.79129 | 0.321243 | ||||||||
\(326\) | 6.92820 | 0.383718 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −16.7477 | −0.924739 | ||||||||
\(329\) | −1.73205 | −0.0954911 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.7042 | −1.41283 | −0.706414 | − | 0.707799i | \(-0.749688\pi\) | ||||
−0.706414 | + | 0.707799i | \(0.749688\pi\) | |||||||
\(332\) | −0.723000 | −0.0396798 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.5826 | −0.743205 | ||||||||
\(335\) | 0.552200 | 0.0301699 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.9129 | 1.41156 | 0.705782 | − | 0.708429i | \(-0.250596\pi\) | ||||
0.705782 | + | 0.708429i | \(0.250596\pi\) | |||||||
\(338\) | 19.9862 | 1.08710 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.00000 | −0.108465 | ||||||||
\(341\) | 7.84190 | 0.424663 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.41742 | −0.0765337 | ||||||||
\(344\) | −14.5040 | −0.782001 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.1216 | 1.67311 | ||||||||
\(347\) | −15.8745 | −0.852188 | −0.426094 | − | 0.904679i | \(-0.640111\pi\) | ||||
−0.426094 | + | 0.904679i | \(0.640111\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.4174 | −0.557632 | −0.278816 | − | 0.960345i | \(-0.589942\pi\) | ||||
−0.278816 | + | 0.960345i | \(0.589942\pi\) | |||||||
\(350\) | −31.4630 | −1.68177 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.3739 | 0.606229 | ||||||||
\(353\) | −27.1805 | −1.44667 | −0.723336 | − | 0.690496i | \(-0.757392\pi\) | ||||
−0.723336 | + | 0.690496i | \(0.757392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.165151 | −0.00876533 | ||||||||
\(356\) | 8.29875 | 0.439833 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 32.7042 | 1.72847 | ||||||||
\(359\) | 12.4104 | 0.654996 | 0.327498 | − | 0.944852i | \(-0.393794\pi\) | ||||
0.327498 | + | 0.944852i | \(0.393794\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.16515 | −0.324482 | ||||||||
\(362\) | 33.1950 | 1.74469 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.58258 | 0.240192 | ||||||||
\(365\) | 6.10985 | 0.319804 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.00000 | 0.104399 | 0.0521996 | − | 0.998637i | \(-0.483377\pi\) | ||||
0.0521996 | + | 0.998637i | \(0.483377\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.20871 | −0.114825 | ||||||||
\(371\) | −11.7629 | −0.610697 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.00000 | 0.207112 | 0.103556 | − | 0.994624i | \(-0.466978\pi\) | ||||
0.103556 | + | 0.994624i | \(0.466978\pi\) | |||||||
\(374\) | −16.5975 | −0.858237 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.791288 | 0.0408076 | ||||||||
\(377\) | −3.75015 | −0.193143 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.1216 | −1.49588 | −0.747938 | − | 0.663769i | \(-0.768956\pi\) | ||||
−0.747938 | + | 0.663769i | \(0.768956\pi\) | |||||||
\(380\) | −1.63670 | −0.0839610 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.4955 | −0.792816 | ||||||||
\(383\) | 17.1497 | 0.876309 | 0.438155 | − | 0.898900i | \(-0.355632\pi\) | ||||
0.438155 | + | 0.898900i | \(0.355632\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.79129 | 0.193222 | ||||||||
\(386\) | 27.7128 | 1.41055 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.00000 | −0.406138 | ||||||||
\(389\) | 0.723000 | 0.0366576 | 0.0183288 | − | 0.999832i | \(-0.494165\pi\) | ||||
0.0183288 | + | 0.999832i | \(0.494165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 12.7719 | 0.645079 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −43.5826 | −2.19566 | ||||||||
\(395\) | −2.55040 | −0.128325 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.0000 | −1.70641 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | −25.5438 | −1.28040 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 23.9564 | 1.19782 | ||||||||
\(401\) | −35.0224 | −1.74894 | −0.874468 | − | 0.485083i | \(-0.838789\pi\) | ||||
−0.874468 | + | 0.485083i | \(0.838789\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.33030 | −0.215708 | ||||||||
\(404\) | −17.5112 | −0.871215 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.3739 | 1.01114 | ||||||||
\(407\) | −6.10985 | −0.302854 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.1652 | −0.552081 | −0.276041 | − | 0.961146i | \(-0.589022\pi\) | ||||
−0.276041 | + | 0.961146i | \(0.589022\pi\) | |||||||
\(410\) | −7.65120 | −0.377866 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.58258 | −0.373567 | ||||||||
\(413\) | 33.1950 | 1.63342 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.330303 | 0.0162139 | ||||||||
\(416\) | −6.28065 | −0.307934 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.5826 | −0.664345 | ||||||||
\(419\) | 29.4648 | 1.43945 | 0.719724 | − | 0.694260i | \(-0.244268\pi\) | ||||
0.719724 | + | 0.694260i | \(0.244268\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1652 | −0.739104 | −0.369552 | − | 0.929210i | \(-0.620489\pi\) | ||||
−0.369552 | + | 0.929210i | \(0.620489\pi\) | |||||||
\(422\) | −27.7128 | −1.34904 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.37386 | 0.260978 | ||||||||
\(425\) | −20.9753 | −1.01745 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.79129 | −0.328653 | ||||||||
\(428\) | −11.0399 | −0.533632 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.62614 | −0.319541 | ||||||||
\(431\) | 27.6374 | 1.33124 | 0.665622 | − | 0.746289i | \(-0.268166\pi\) | ||||
0.665622 | + | 0.746289i | \(0.268166\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.7042 | 1.13915 | 0.569575 | − | 0.821940i | \(-0.307108\pi\) | ||||
0.569575 | + | 0.821940i | \(0.307108\pi\) | |||||||
\(434\) | 23.5257 | 1.12927 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.74773 | −0.323158 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.7913 | 1.08777 | 0.543884 | − | 0.839160i | \(-0.316953\pi\) | ||||
0.543884 | + | 0.839160i | \(0.316953\pi\) | |||||||
\(440\) | −1.73205 | −0.0825723 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.16515 | 0.435942 | ||||||||
\(443\) | 5.84370 | 0.277643 | 0.138821 | − | 0.990317i | \(-0.455669\pi\) | ||||
0.138821 | + | 0.990317i | \(0.455669\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.79129 | −0.179724 | ||||||||
\(446\) | −33.8426 | −1.60249 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.79129 | −0.179122 | ||||||||
\(449\) | −6.20520 | −0.292842 | −0.146421 | − | 0.989222i | \(-0.546775\pi\) | ||||
−0.146421 | + | 0.989222i | \(0.546775\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.1652 | −0.996628 | ||||||||
\(452\) | −9.47860 | −0.445836 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.79129 | −0.177934 | ||||||||
\(455\) | −2.09355 | −0.0981472 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.6261 | −0.497070 | −0.248535 | − | 0.968623i | \(-0.579949\pi\) | ||||
−0.248535 | + | 0.968623i | \(0.579949\pi\) | |||||||
\(458\) | −30.4539 | −1.42302 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.48040 | 0.348397 | 0.174199 | − | 0.984711i | \(-0.444267\pi\) | ||||
0.174199 | + | 0.984711i | \(0.444267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | −15.5130 | −0.720173 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 34.2867 | 1.58830 | ||||||||
\(467\) | −0.190700 | −0.00882456 | −0.00441228 | − | 0.999990i | \(-0.501404\pi\) | ||||
−0.00441228 | + | 0.999990i | \(0.501404\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.58258 | 0.211604 | ||||||||
\(470\) | 0.361500 | 0.0166748 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.1652 | −0.698033 | ||||||||
\(473\) | −18.3296 | −0.842794 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.1652 | −0.787591 | ||||||||
\(476\) | −16.5975 | −0.760746 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.6606 | 1.12795 | ||||||||
\(479\) | 16.5221 | 0.754912 | 0.377456 | − | 0.926027i | \(-0.376799\pi\) | ||||
0.377456 | + | 0.926027i | \(0.376799\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.37386 | 0.153835 | ||||||||
\(482\) | −2.01810 | −0.0919220 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.20871 | −0.282214 | ||||||||
\(485\) | 3.65480 | 0.165956 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.9564 | −0.632427 | −0.316213 | − | 0.948688i | \(-0.602412\pi\) | ||||
−0.316213 | + | 0.948688i | \(0.602412\pi\) | |||||||
\(488\) | 3.10260 | 0.140448 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.83485 | 0.263592 | ||||||||
\(491\) | 19.8709 | 0.896762 | 0.448381 | − | 0.893843i | \(-0.352001\pi\) | ||||
0.448381 | + | 0.893843i | \(0.352001\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.5826 | 0.611728 | ||||||||
\(494\) | 7.50030 | 0.337455 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.9129 | −0.804312 | ||||||||
\(497\) | −1.37055 | −0.0614776 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.6261 | 1.10242 | 0.551209 | − | 0.834367i | \(-0.314167\pi\) | ||||
0.551209 | + | 0.834367i | \(0.314167\pi\) | |||||||
\(500\) | 4.47315 | 0.200045 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.0000 | −1.33897 | ||||||||
\(503\) | −38.4865 | −1.71603 | −0.858015 | − | 0.513625i | \(-0.828302\pi\) | ||||
−0.858015 | + | 0.513625i | \(0.828302\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.00000 | 0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.00000 | −0.0443678 | ||||||||
\(509\) | −42.8643 | −1.89993 | −0.949964 | − | 0.312360i | \(-0.898880\pi\) | ||||
−0.949964 | + | 0.312360i | \(0.898880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 50.7042 | 2.24302 | ||||||||
\(512\) | −8.66025 | −0.382733 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −48.9564 | −2.15938 | ||||||||
\(515\) | 3.46410 | 0.152647 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.00000 | 0.0439799 | ||||||||
\(518\) | −18.3296 | −0.805355 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.956439 | 0.0419426 | ||||||||
\(521\) | 18.9572 | 0.830530 | 0.415265 | − | 0.909700i | \(-0.363689\pi\) | ||||
0.415265 | + | 0.909700i | \(0.363689\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.8348 | −1.08595 | −0.542976 | − | 0.839748i | \(-0.682703\pi\) | ||||
−0.542976 | + | 0.839748i | \(0.682703\pi\) | |||||||
\(524\) | 7.38505 | 0.322618 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.8693 | 0.909945 | ||||||||
\(527\) | 15.6838 | 0.683197 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 2.45505 | 0.106641 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −13.5826 | −0.588879 | ||||||||
\(533\) | 11.6874 | 0.506238 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.04356 | 0.218052 | ||||||||
\(536\) | −2.09355 | −0.0904276 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −21.4955 | −0.926735 | ||||||||
\(539\) | 16.1407 | 0.695227 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.66970 | 0.157773 | 0.0788863 | − | 0.996884i | \(-0.474864\pi\) | ||||
0.0788863 | + | 0.996884i | \(0.474864\pi\) | |||||||
\(542\) | −37.3821 | −1.60570 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 22.7477 | 0.975301 | ||||||||
\(545\) | 3.08270 | 0.132048 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.04356 | 0.386675 | 0.193337 | − | 0.981132i | \(-0.438069\pi\) | ||||
0.193337 | + | 0.981132i | \(0.438069\pi\) | |||||||
\(548\) | −5.10080 | −0.217895 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.1652 | 0.774565 | ||||||||
\(551\) | 11.1153 | 0.473528 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.1652 | −0.900034 | ||||||||
\(554\) | −8.94630 | −0.380092 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.1652 | −0.473508 | ||||||||
\(557\) | 7.11890 | 0.301638 | 0.150819 | − | 0.988561i | \(-0.451809\pi\) | ||||
0.150819 | + | 0.988561i | \(0.451809\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.1216 | 0.428098 | ||||||||
\(560\) | −8.66025 | −0.365963 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.2087 | −0.979000 | ||||||||
\(563\) | −9.47860 | −0.399476 | −0.199738 | − | 0.979849i | \(-0.564009\pi\) | ||||
−0.199738 | + | 0.979849i | \(0.564009\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.33030 | 0.182177 | ||||||||
\(566\) | 14.2179 | 0.597623 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.626136 | 0.0262721 | ||||||||
\(569\) | −13.8564 | −0.580891 | −0.290445 | − | 0.956892i | \(-0.593803\pi\) | ||||
−0.290445 | + | 0.956892i | \(0.593803\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.8693 | 1.41739 | 0.708693 | − | 0.705517i | \(-0.249285\pi\) | ||||
0.708693 | + | 0.705517i | \(0.249285\pi\) | |||||||
\(572\) | −2.64575 | −0.110624 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −63.4955 | −2.65025 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | −3.75015 | −0.155986 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.41742 | −0.0588553 | ||||||||
\(581\) | 2.74110 | 0.113720 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.79129 | 0.281266 | ||||||||
\(584\) | −23.1642 | −0.958542 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.46099 | 0.142972 | ||||||||
\(587\) | −7.28970 | −0.300878 | −0.150439 | − | 0.988619i | \(-0.548069\pi\) | ||||
−0.150439 | + | 0.988619i | \(0.548069\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.8348 | 0.528851 | ||||||||
\(590\) | −6.92820 | −0.285230 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.9564 | 0.573606 | ||||||||
\(593\) | 16.2360 | 0.666733 | 0.333366 | − | 0.942797i | \(-0.391815\pi\) | ||||
0.333366 | + | 0.942797i | \(0.391815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.58258 | 0.310855 | ||||||||
\(596\) | 11.4967 | 0.470923 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.4865 | −1.57252 | −0.786258 | − | 0.617898i | \(-0.787984\pi\) | ||||
−0.786258 | + | 0.617898i | \(0.787984\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.7477 | −0.846317 | −0.423159 | − | 0.906056i | \(-0.639079\pi\) | ||||
−0.423159 | + | 0.906056i | \(0.639079\pi\) | |||||||
\(602\) | −54.9887 | −2.24117 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.37386 | 0.300038 | ||||||||
\(605\) | 2.83645 | 0.115318 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.4955 | −0.872474 | −0.436237 | − | 0.899832i | \(-0.643689\pi\) | ||||
−0.436237 | + | 0.899832i | \(0.643689\pi\) | |||||||
\(608\) | 18.6156 | 0.754963 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.41742 | 0.0573898 | ||||||||
\(611\) | −0.552200 | −0.0223396 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.7477 | −0.999551 | −0.499776 | − | 0.866155i | \(-0.666584\pi\) | ||||
−0.499776 | + | 0.866155i | \(0.666584\pi\) | |||||||
\(614\) | 31.3875 | 1.26670 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.3739 | −0.579139 | ||||||||
\(617\) | 42.7889 | 1.72262 | 0.861308 | − | 0.508084i | \(-0.169646\pi\) | ||||
0.861308 | + | 0.508084i | \(0.169646\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.79129 | −0.152385 | −0.0761924 | − | 0.997093i | \(-0.524276\pi\) | ||||
−0.0761924 | + | 0.997093i | \(0.524276\pi\) | |||||||
\(620\) | −1.63670 | −0.0657315 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.4174 | −0.417701 | ||||||||
\(623\) | −31.4630 | −1.26054 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.9129 | 0.876515 | ||||||||
\(626\) | 24.9717 | 0.998070 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.3739 | −0.533675 | ||||||||
\(629\) | −12.2197 | −0.487232 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.7042 | −1.38155 | −0.690776 | − | 0.723069i | \(-0.742731\pi\) | ||||
−0.690776 | + | 0.723069i | \(0.742731\pi\) | |||||||
\(632\) | 9.66930 | 0.384624 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −42.3303 | −1.68115 | ||||||||
\(635\) | 0.456850 | 0.0181295 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.91288 | −0.353141 | ||||||||
\(638\) | −11.7629 | −0.465696 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.53901 | 0.218949 | ||||||||
\(641\) | −26.7237 | −1.05552 | −0.527761 | − | 0.849393i | \(-0.676968\pi\) | ||||
−0.527761 | + | 0.849393i | \(0.676968\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.00000 | −0.236617 | −0.118308 | − | 0.992977i | \(-0.537747\pi\) | ||||
−0.118308 | + | 0.992977i | \(0.537747\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.1652 | −1.06880 | ||||||||
\(647\) | −24.2487 | −0.953315 | −0.476658 | − | 0.879089i | \(-0.658152\pi\) | ||||
−0.476658 | + | 0.879089i | \(0.658152\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.1652 | −0.752298 | ||||||||
\(650\) | −10.0308 | −0.393441 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | −28.6265 | −1.12024 | −0.560121 | − | 0.828411i | \(-0.689245\pi\) | ||||
−0.560121 | + | 0.828411i | \(0.689245\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.37386 | −0.131828 | ||||||||
\(656\) | 48.3465 | 1.88761 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.00000 | 0.116952 | ||||||||
\(659\) | 45.0333 | 1.75425 | 0.877125 | − | 0.480263i | \(-0.159459\pi\) | ||||
0.877125 | + | 0.480263i | \(0.159459\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.7042 | −0.610821 | −0.305411 | − | 0.952221i | \(-0.598794\pi\) | ||||
−0.305411 | + | 0.952221i | \(0.598794\pi\) | |||||||
\(662\) | 44.5209 | 1.73035 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.25227 | −0.0485976 | ||||||||
\(665\) | 6.20520 | 0.240627 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 7.84190 | 0.303412 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.956439 | −0.0369505 | ||||||||
\(671\) | 3.92095 | 0.151367 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.7042 | −1.02937 | −0.514685 | − | 0.857379i | \(-0.672091\pi\) | ||||
−0.514685 | + | 0.857379i | \(0.672091\pi\) | |||||||
\(674\) | −44.8824 | −1.72881 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5390 | −0.443808 | ||||||||
\(677\) | 4.91010 | 0.188711 | 0.0943553 | − | 0.995539i | \(-0.469921\pi\) | ||||
0.0943553 | + | 0.995539i | \(0.469921\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30.3303 | 1.16397 | ||||||||
\(680\) | −3.46410 | −0.132842 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.5826 | −0.520104 | ||||||||
\(683\) | −41.7599 | −1.59790 | −0.798949 | − | 0.601398i | \(-0.794611\pi\) | ||||
−0.798949 | + | 0.601398i | \(0.794611\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.33030 | 0.0890363 | ||||||||
\(686\) | 2.45505 | 0.0937343 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 41.8693 | 1.59625 | ||||||||
\(689\) | −3.75015 | −0.142869 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.7913 | −0.867021 | −0.433511 | − | 0.901148i | \(-0.642725\pi\) | ||||
−0.433511 | + | 0.901148i | \(0.642725\pi\) | |||||||
\(692\) | −17.9681 | −0.683043 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.4955 | 1.04371 | ||||||||
\(695\) | 5.10080 | 0.193484 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.3303 | −1.60337 | ||||||||
\(698\) | 18.0435 | 0.682957 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 18.1652 | 0.686578 | ||||||||
\(701\) | 16.2360 | 0.613226 | 0.306613 | − | 0.951834i | \(-0.400804\pi\) | ||||
0.306613 | + | 0.951834i | \(0.400804\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.0000 | −0.377157 | ||||||||
\(704\) | 2.18890 | 0.0824973 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 47.0780 | 1.77181 | ||||||||
\(707\) | 66.3900 | 2.49685 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.1216 | 1.54435 | 0.772177 | − | 0.635408i | \(-0.219168\pi\) | ||||
0.772177 | + | 0.635408i | \(0.219168\pi\) | |||||||
\(710\) | 0.286051 | 0.0107353 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.3739 | 0.538683 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.20871 | 0.0452033 | ||||||||
\(716\) | −18.8818 | −0.705644 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.4955 | −0.802203 | ||||||||
\(719\) | −22.5366 | −0.840472 | −0.420236 | − | 0.907415i | \(-0.638053\pi\) | ||||
−0.420236 | + | 0.907415i | \(0.638053\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.7477 | 1.07062 | ||||||||
\(722\) | 10.6784 | 0.397407 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.1652 | −0.712267 | ||||||||
\(725\) | −14.8655 | −0.552089 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.2087 | −0.489884 | −0.244942 | − | 0.969538i | \(-0.578769\pi\) | ||||
−0.244942 | + | 0.969538i | \(0.578769\pi\) | |||||||
\(728\) | 7.93725 | 0.294174 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.5826 | −0.391679 | ||||||||
\(731\) | −36.6591 | −1.35589 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.0345 | 1.81113 | 0.905565 | − | 0.424208i | \(-0.139448\pi\) | ||||
0.905565 | + | 0.424208i | \(0.139448\pi\) | |||||||
\(734\) | −3.46410 | −0.127862 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.64575 | −0.0974575 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.9129 | 1.17393 | 0.586967 | − | 0.809611i | \(-0.300322\pi\) | ||||
0.586967 | + | 0.809611i | \(0.300322\pi\) | |||||||
\(740\) | 1.27520 | 0.0468773 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.3739 | 0.747948 | ||||||||
\(743\) | 10.5830 | 0.388253 | 0.194126 | − | 0.980977i | \(-0.437813\pi\) | ||||
0.194126 | + | 0.980977i | \(0.437813\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.25227 | −0.192428 | ||||||||
\(746\) | −6.92820 | −0.253660 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.58258 | 0.350374 | ||||||||
\(749\) | 41.8553 | 1.52936 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.3303 | −0.522920 | −0.261460 | − | 0.965214i | \(-0.584204\pi\) | ||||
−0.261460 | + | 0.965214i | \(0.584204\pi\) | |||||||
\(752\) | −2.28425 | −0.0832981 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.49545 | 0.236550 | ||||||||
\(755\) | −3.36875 | −0.122601 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.79129 | 0.355870 | 0.177935 | − | 0.984042i | \(-0.443058\pi\) | ||||
0.177935 | + | 0.984042i | \(0.443058\pi\) | |||||||
\(758\) | 50.4401 | 1.83207 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.83485 | −0.102831 | ||||||||
\(761\) | 51.6000 | 1.87050 | 0.935250 | − | 0.353989i | \(-0.115175\pi\) | ||||
0.935250 | + | 0.353989i | \(0.115175\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.5826 | 0.926151 | ||||||||
\(764\) | 8.94630 | 0.323666 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29.7042 | −1.07326 | ||||||||
\(767\) | 10.5830 | 0.382130 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.417424 | 0.0150527 | 0.00752635 | − | 0.999972i | \(-0.497604\pi\) | ||||
0.00752635 | + | 0.999972i | \(0.497604\pi\) | |||||||
\(770\) | −6.56670 | −0.236648 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.0000 | −0.575853 | ||||||||
\(773\) | −37.9542 | −1.36512 | −0.682559 | − | 0.730830i | \(-0.739133\pi\) | ||||
−0.682559 | + | 0.730830i | \(0.739133\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.1652 | −0.616590 | ||||||||
\(776\) | −13.8564 | −0.497416 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.25227 | −0.0448962 | ||||||||
\(779\) | −34.6410 | −1.24114 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.791288 | 0.0283145 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −36.8693 | −1.31676 | ||||||||
\(785\) | 6.10985 | 0.218070 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.58258 | 0.127705 | 0.0638525 | − | 0.997959i | \(-0.479661\pi\) | ||||
0.0638525 | + | 0.997959i | \(0.479661\pi\) | |||||||
\(788\) | 25.1624 | 0.896374 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.41742 | 0.157165 | ||||||||
\(791\) | 35.9361 | 1.27774 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.16515 | −0.0768868 | ||||||||
\(794\) | 58.8897 | 2.08992 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.7477 | 0.522719 | ||||||||
\(797\) | −12.4104 | −0.439599 | −0.219800 | − | 0.975545i | \(-0.570540\pi\) | ||||
−0.219800 | + | 0.975545i | \(0.570540\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.00000 | 0.0707549 | ||||||||
\(800\) | −24.8963 | −0.880216 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 60.6606 | 2.14200 | ||||||||
\(803\) | −29.2741 | −1.03306 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.50030 | 0.264187 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −30.3303 | −1.06702 | ||||||||
\(809\) | 28.2849 | 0.994445 | 0.497222 | − | 0.867623i | \(-0.334353\pi\) | ||||
0.497222 | + | 0.867623i | \(0.334353\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.0000 | 1.12367 | 0.561836 | − | 0.827249i | \(-0.310095\pi\) | ||||
0.561836 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(812\) | −11.7629 | −0.412795 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.5826 | 0.370919 | ||||||||
\(815\) | 1.82740 | 0.0640111 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.0000 | −1.04957 | ||||||||
\(818\) | 19.3386 | 0.676159 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.41742 | 0.154263 | ||||||||
\(821\) | −34.9470 | −1.21966 | −0.609829 | − | 0.792533i | \(-0.708762\pi\) | ||||
−0.609829 | + | 0.792533i | \(0.708762\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.5826 | 0.752321 | 0.376161 | − | 0.926554i | \(-0.377244\pi\) | ||||
0.376161 | + | 0.926554i | \(0.377244\pi\) | |||||||
\(824\) | −13.1334 | −0.457524 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −57.4955 | −2.00052 | ||||||||
\(827\) | −2.93180 | −0.101949 | −0.0509744 | − | 0.998700i | \(-0.516233\pi\) | ||||
−0.0509744 | + | 0.998700i | \(0.516233\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.1652 | −0.665633 | −0.332817 | − | 0.942992i | \(-0.607999\pi\) | ||||
−0.332817 | + | 0.942992i | \(0.607999\pi\) | |||||||
\(830\) | −0.572101 | −0.0198579 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.20871 | −0.0419046 | ||||||||
\(833\) | 32.2813 | 1.11848 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.58258 | −0.123980 | ||||||||
\(836\) | 7.84190 | 0.271218 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −51.0345 | −1.76296 | ||||||||
\(839\) | −3.46410 | −0.119594 | −0.0597970 | − | 0.998211i | \(-0.519045\pi\) | ||||
−0.0597970 | + | 0.998211i | \(0.519045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.3739 | −0.668064 | ||||||||
\(842\) | 26.2668 | 0.905214 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.0000 | 0.550743 | ||||||||
\(845\) | 5.27160 | 0.181349 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.5390 | 0.808810 | ||||||||
\(848\) | −15.5130 | −0.532719 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 36.3303 | 1.24612 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.7477 | 0.641910 | 0.320955 | − | 0.947094i | \(-0.395996\pi\) | ||||
0.320955 | + | 0.947094i | \(0.395996\pi\) | |||||||
\(854\) | 11.7629 | 0.402517 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.1216 | −0.653563 | ||||||||
\(857\) | 27.7128 | 0.946652 | 0.473326 | − | 0.880887i | \(-0.343053\pi\) | ||||
0.473326 | + | 0.880887i | \(0.343053\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.62614 | 0.157842 | 0.0789209 | − | 0.996881i | \(-0.474853\pi\) | ||||
0.0789209 | + | 0.996881i | \(0.474853\pi\) | |||||||
\(860\) | 3.82560 | 0.130452 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −47.8693 | −1.63044 | ||||||||
\(863\) | 32.4720 | 1.10536 | 0.552680 | − | 0.833393i | \(-0.313605\pi\) | ||||
0.552680 | + | 0.833393i | \(0.313605\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.20871 | 0.279105 | ||||||||
\(866\) | −41.0568 | −1.39517 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.5826 | −0.461023 | ||||||||
\(869\) | 12.2197 | 0.414525 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.46099 | 0.0495036 | ||||||||
\(872\) | −11.6874 | −0.395786 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.9590 | −0.573319 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.6170 | 1.67545 | 0.837724 | − | 0.546093i | \(-0.183886\pi\) | ||||
0.837724 | + | 0.546093i | \(0.183886\pi\) | |||||||
\(878\) | −39.4757 | −1.33224 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.00000 | 0.168550 | ||||||||
\(881\) | −17.3404 | −0.584213 | −0.292107 | − | 0.956386i | \(-0.594356\pi\) | ||||
−0.292107 | + | 0.956386i | \(0.594356\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.417424 | −0.0140474 | −0.00702372 | − | 0.999975i | \(-0.502236\pi\) | ||||
−0.00702372 | + | 0.999975i | \(0.502236\pi\) | |||||||
\(884\) | −5.29150 | −0.177972 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.1216 | −0.340041 | ||||||||
\(887\) | 9.28790 | 0.311857 | 0.155929 | − | 0.987768i | \(-0.450163\pi\) | ||||
0.155929 | + | 0.987768i | \(0.450163\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.79129 | 0.127156 | ||||||||
\(890\) | 6.56670 | 0.220116 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.5390 | 0.654215 | ||||||||
\(893\) | 1.63670 | 0.0547701 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.62614 | 0.288340 | ||||||||
\(896\) | 45.9669 | 1.53565 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.7477 | 0.358656 | ||||||||
\(899\) | 11.1153 | 0.370716 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.5826 | 0.452501 | ||||||||
\(902\) | 36.6591 | 1.22062 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.4174 | −0.546035 | ||||||||
\(905\) | 8.75560 | 0.291046 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.3303 | 0.475830 | 0.237915 | − | 0.971286i | \(-0.423536\pi\) | ||||
0.237915 | + | 0.971286i | \(0.423536\pi\) | |||||||
\(908\) | 2.18890 | 0.0726412 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.62614 | 0.120205 | ||||||||
\(911\) | 7.00365 | 0.232041 | 0.116021 | − | 0.993247i | \(-0.462986\pi\) | ||||
0.116021 | + | 0.993247i | \(0.462986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.58258 | −0.0523756 | ||||||||
\(914\) | 18.4050 | 0.608784 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.5826 | 0.580945 | ||||||||
\(917\) | −27.9989 | −0.924604 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.7477 | 1.21220 | 0.606098 | − | 0.795390i | \(-0.292734\pi\) | ||||
0.606098 | + | 0.795390i | \(0.292734\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.9564 | −0.426698 | ||||||||
\(923\) | −0.436950 | −0.0143824 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.3739 | 0.439730 | ||||||||
\(926\) | 6.92820 | 0.227675 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.1216 | 0.529217 | ||||||||
\(929\) | 20.9554 | 0.687525 | 0.343762 | − | 0.939057i | \(-0.388299\pi\) | ||||
0.343762 | + | 0.939057i | \(0.388299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.4174 | 0.865796 | ||||||||
\(932\) | −19.7955 | −0.648422 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.330303 | 0.0108078 | ||||||||
\(935\) | −4.37780 | −0.143169 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.4083 | −1.67944 | −0.839719 | − | 0.543022i | \(-0.817280\pi\) | ||||
−0.839719 | + | 0.543022i | \(0.817280\pi\) | |||||||
\(938\) | −7.93725 | −0.259161 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.208712 | −0.00680744 | ||||||||
\(941\) | −24.0580 | −0.784269 | −0.392134 | − | 0.919908i | \(-0.628263\pi\) | ||||
−0.392134 | + | 0.919908i | \(0.628263\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 43.7780 | 1.42485 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.7477 | 1.03221 | ||||||||
\(947\) | 24.2487 | 0.787977 | 0.393989 | − | 0.919115i | \(-0.371095\pi\) | ||||
0.393989 | + | 0.919115i | \(0.371095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.1652 | 0.524743 | ||||||||
\(950\) | 29.7309 | 0.964598 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −28.7477 | −0.931719 | ||||||||
\(953\) | −24.2487 | −0.785493 | −0.392746 | − | 0.919647i | \(-0.628475\pi\) | ||||
−0.392746 | + | 0.919647i | \(0.628475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.08712 | −0.132256 | ||||||||
\(956\) | −14.2378 | −0.460484 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −28.6170 | −0.924575 | ||||||||
\(959\) | 19.3386 | 0.624476 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.1652 | −0.585973 | ||||||||
\(962\) | −5.84370 | −0.188409 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.16515 | 0.0375270 | ||||||||
\(965\) | 7.30960 | 0.235304 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.7913 | 1.63334 | 0.816669 | − | 0.577107i | \(-0.195818\pi\) | ||||
0.816669 | + | 0.577107i | \(0.195818\pi\) | |||||||
\(968\) | −10.7538 | −0.345640 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.33030 | −0.203254 | ||||||||
\(971\) | 39.7617 | 1.27601 | 0.638007 | − | 0.770030i | \(-0.279759\pi\) | ||||
0.638007 | + | 0.770030i | \(0.279759\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.3303 | 1.35705 | ||||||||
\(974\) | 24.1733 | 0.774561 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.95644 | −0.286689 | ||||||||
\(977\) | −17.1298 | −0.548031 | −0.274016 | − | 0.961725i | \(-0.588352\pi\) | ||||
−0.274016 | + | 0.961725i | \(0.588352\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.1652 | 0.580561 | ||||||||
\(980\) | −3.36875 | −0.107611 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −34.4174 | −1.09830 | ||||||||
\(983\) | 11.4213 | 0.364282 | 0.182141 | − | 0.983272i | \(-0.441697\pi\) | ||||
0.182141 | + | 0.983272i | \(0.441697\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.4955 | −0.366276 | ||||||||
\(986\) | −23.5257 | −0.749211 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.33030 | −0.137765 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.9564 | 0.856300 | 0.428150 | − | 0.903708i | \(-0.359166\pi\) | ||||
0.428150 | + | 0.903708i | \(0.359166\pi\) | |||||||
\(992\) | 18.6156 | 0.591046 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.37386 | 0.0752944 | ||||||||
\(995\) | −6.73750 | −0.213593 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.5826 | −0.366824 | −0.183412 | − | 0.983036i | \(-0.558714\pi\) | ||||
−0.183412 | + | 0.983036i | \(0.558714\pi\) | |||||||
\(998\) | −42.6537 | −1.35018 | ||||||||
\(999\) | 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 | 1143.2.a.f.1.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 1143.2.a.f.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.2.a.f.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1143.2.a.f.1.4 | yes | 4 | 3.2 | odd | 2 | inner |