Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1100,2,Mod(749,1100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1100.749");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1100.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.78354422234\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{21})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 11x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 749.4 | ||
Root | \(2.79129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1100.749 |
Dual form | 1100.2.b.d.749.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(551\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.79129i | 1.61155i | 0.592221 | + | 0.805775i | \(0.298251\pi\) | ||||
−0.592221 | + | 0.805775i | \(0.701749\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.208712i | − 0.0788858i | −0.999222 | − | 0.0394429i | \(-0.987442\pi\) | ||||
0.999222 | − | 0.0394429i | \(-0.0125583\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.79129 | −1.59710 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | 0.990338 | + | 0.138675i | \(0.0442844\pi\) | ||||
−0.990338 | + | 0.138675i | \(0.955716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.791288i | 0.191915i | 0.995385 | + | 0.0959577i | \(0.0305914\pi\) | ||||
−0.995385 | + | 0.0959577i | \(0.969409\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.58258 | −1.51015 | −0.755073 | − | 0.655640i | \(-0.772399\pi\) | ||||
−0.755073 | + | 0.655640i | \(0.772399\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.582576 | 0.127128 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.79129i | 0.790538i | 0.918565 | + | 0.395269i | \(0.129349\pi\) | ||||
−0.918565 | + | 0.395269i | \(0.870651\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.00000i | − 0.962250i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.79129 | −1.26111 | −0.630555 | − | 0.776144i | \(-0.717173\pi\) | ||||
−0.630555 | + | 0.776144i | \(0.717173\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.58258 | −1.54148 | −0.770738 | − | 0.637152i | \(-0.780112\pi\) | ||||
−0.770738 | + | 0.637152i | \(0.780112\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 2.79129i | − 0.485901i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.58258i | − 0.424573i | −0.977207 | − | 0.212286i | \(-0.931909\pi\) | ||||
0.977207 | − | 0.212286i | \(-0.0680910\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.79129 | −0.446964 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.41742 | −0.221364 | −0.110682 | − | 0.993856i | \(-0.535304\pi\) | ||||
−0.110682 | + | 0.993856i | \(0.535304\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0000i | 1.52499i | 0.646997 | + | 0.762493i | \(0.276025\pi\) | ||||
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1.41742i | − 0.206753i | −0.994642 | − | 0.103376i | \(-0.967035\pi\) | ||||
0.994642 | − | 0.103376i | \(-0.0329646\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.95644 | 0.993777 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.20871 | −0.309282 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 11.3739i | − 1.56232i | −0.624331 | − | 0.781160i | \(-0.714628\pi\) | ||||
0.624331 | − | 0.781160i | \(-0.285372\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 18.3739i | − 2.43368i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.5826 | 1.37773 | 0.688867 | − | 0.724888i | \(-0.258108\pi\) | ||||
0.688867 | + | 0.724888i | \(0.258108\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.20871 | 0.538870 | 0.269435 | − | 0.963019i | \(-0.413163\pi\) | ||||
0.269435 | + | 0.963019i | \(0.413163\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 4.00000i | − 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.5826 | −1.27399 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7477 | −1.27552 | −0.637760 | − | 0.770235i | \(-0.720139\pi\) | ||||
−0.637760 | + | 0.770235i | \(0.720139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.79129i | 0.911901i | 0.890005 | + | 0.455951i | \(0.150701\pi\) | ||||
−0.890005 | + | 0.455951i | \(0.849299\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.208712i | 0.0237850i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.5390 | 1.74828 | 0.874138 | − | 0.485678i | \(-0.161427\pi\) | ||||
0.874138 | + | 0.485678i | \(0.161427\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.417424 | −0.0463805 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.95644i | 1.09286i | 0.837504 | + | 0.546431i | \(0.184014\pi\) | ||||
−0.837504 | + | 0.546431i | \(0.815986\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 18.9564i | − 2.03234i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.791288 | 0.0838763 | 0.0419382 | − | 0.999120i | \(-0.486647\pi\) | ||||
0.0419382 | + | 0.999120i | \(0.486647\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.208712 | 0.0218790 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 23.9564i | − 2.48417i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 6.20871i | − 0.630399i | −0.949025 | − | 0.315200i | \(-0.897929\pi\) | ||||
0.949025 | − | 0.315200i | \(-0.102071\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.79129 | 0.481543 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.3739 | −1.72876 | −0.864382 | − | 0.502836i | \(-0.832290\pi\) | ||||
−0.864382 | + | 0.502836i | \(0.832290\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 5.95644i | − 0.586905i | −0.955974 | − | 0.293453i | \(-0.905196\pi\) | ||||
0.955974 | − | 0.293453i | \(-0.0948043\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.7477i | 1.90908i | 0.298075 | + | 0.954542i | \(0.403655\pi\) | ||||
−0.298075 | + | 0.954542i | \(0.596345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.79129 | 0.458922 | 0.229461 | − | 0.973318i | \(-0.426304\pi\) | ||||
0.229461 | + | 0.973318i | \(0.426304\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.20871 | 0.684221 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1.41742i | − 0.133340i | −0.997775 | − | 0.0666700i | \(-0.978763\pi\) | ||||
0.997775 | − | 0.0666700i | \(-0.0212375\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 4.79129i | − 0.442955i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.165151 | 0.0151394 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 3.95644i | − 0.356740i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.3739i | 1.45295i | 0.687195 | + | 0.726473i | \(0.258842\pi\) | ||||
−0.687195 | + | 0.726473i | \(0.741158\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −27.9129 | −2.45759 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.626136 | −0.0547058 | −0.0273529 | − | 0.999626i | \(-0.508708\pi\) | ||||
−0.0273529 | + | 0.999626i | \(0.508708\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.37386i | 0.119129i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 11.5390i | − 0.985845i | −0.870073 | − | 0.492922i | \(-0.835929\pi\) | ||||
0.870073 | − | 0.492922i | \(-0.164071\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.74773 | −0.826791 | −0.413396 | − | 0.910551i | \(-0.635657\pi\) | ||||
−0.413396 | + | 0.910551i | \(0.635657\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.95644 | 0.333192 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1.00000i | − 0.0836242i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.4174i | 1.60152i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.16515 | −0.259299 | −0.129650 | − | 0.991560i | \(-0.541385\pi\) | ||||
−0.129650 | + | 0.991560i | \(0.541385\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | 0.406894 | 0.203447 | − | 0.979086i | \(-0.434786\pi\) | ||||
0.203447 | + | 0.979086i | \(0.434786\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 3.79129i | − 0.306507i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.1652i | 1.36993i | 0.728577 | + | 0.684964i | \(0.240182\pi\) | ||||
−0.728577 | + | 0.684964i | \(0.759818\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 31.7477 | 2.51776 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.791288 | 0.0623622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.3739i | 1.67413i | 0.547103 | + | 0.837065i | \(0.315730\pi\) | ||||
−0.547103 | + | 0.837065i | \(0.684270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 16.5826i | − 1.28320i | −0.767040 | − | 0.641599i | \(-0.778271\pi\) | ||||
0.767040 | − | 0.641599i | \(-0.221729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 31.5390 | 2.41185 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.7477i | 1.04522i | 0.852572 | + | 0.522610i | \(0.175042\pi\) | ||||
−0.852572 | + | 0.522610i | \(0.824958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 29.5390i | 2.22029i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.1216 | −1.65345 | −0.826723 | − | 0.562610i | \(-0.809797\pi\) | ||||
−0.826723 | + | 0.562610i | \(0.809797\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.37386 | −0.250777 | −0.125389 | − | 0.992108i | \(-0.540018\pi\) | ||||
−0.125389 | + | 0.992108i | \(0.540018\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.7477i | 0.868417i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 0.791288i | − 0.0578647i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.04356 | −0.0759079 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.2087 | 1.24518 | 0.622589 | − | 0.782549i | \(-0.286081\pi\) | ||||
0.622589 | + | 0.782549i | \(0.286081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.16515i | 0.515759i | 0.966177 | + | 0.257879i | \(0.0830237\pi\) | ||||
−0.966177 | + | 0.257879i | \(0.916976\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.5390i | 1.89083i | 0.325874 | + | 0.945413i | \(0.394342\pi\) | ||||
−0.325874 | + | 0.945413i | \(0.605658\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.62614 | 0.115274 | 0.0576369 | − | 0.998338i | \(-0.481643\pi\) | ||||
0.0576369 | + | 0.998338i | \(0.481643\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.1652 | 0.787529 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.41742i | 0.0994837i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 18.1652i | − 1.26257i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.58258 | 0.455326 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.00000 | 0.344214 | 0.172107 | − | 0.985078i | \(-0.444942\pi\) | ||||
0.172107 | + | 0.985078i | \(0.444942\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 30.0000i | − 2.05557i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.79129i | 0.121601i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.7477 | −1.46958 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.791288 | −0.0532278 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.5826i | 1.37831i | 0.724613 | + | 0.689156i | \(0.242018\pi\) | ||||
−0.724613 | + | 0.689156i | \(0.757982\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.5390i | 0.765871i | 0.923775 | + | 0.382936i | \(0.125087\pi\) | ||||
−0.923775 | + | 0.382936i | \(0.874913\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.62614 | 0.503949 | 0.251975 | − | 0.967734i | \(-0.418920\pi\) | ||||
0.251975 | + | 0.967734i | \(0.418920\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.582576 | −0.0383307 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 15.7913i | − 1.03452i | −0.855828 | − | 0.517261i | \(-0.826952\pi\) | ||||
0.855828 | − | 0.517261i | \(-0.173048\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 43.3739i | 2.81744i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.20871 | 0.142870 | 0.0714349 | − | 0.997445i | \(-0.477242\pi\) | ||||
0.0714349 | + | 0.997445i | \(0.477242\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.1216 | −1.48939 | −0.744696 | − | 0.667404i | \(-0.767406\pi\) | ||||
−0.744696 | + | 0.667404i | \(0.767406\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 16.1652i | − 1.03699i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 6.58258i | − 0.418839i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27.7913 | −1.76120 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.5390 | −0.728336 | −0.364168 | − | 0.931333i | \(-0.618647\pi\) | ||||
−0.364168 | + | 0.931333i | \(0.618647\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 3.79129i | − 0.238356i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.0000i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.539015 | −0.0334928 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 32.5390 | 2.01411 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 24.1652i | − 1.49009i | −0.667016 | − | 0.745044i | \(-0.732429\pi\) | ||||
0.667016 | − | 0.745044i | \(-0.267571\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.20871i | 0.135171i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.7042 | 1.26236 | 0.631178 | − | 0.775638i | \(-0.282572\pi\) | ||||
0.631178 | + | 0.775638i | \(0.282572\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.7477 | 0.956606 | 0.478303 | − | 0.878195i | \(-0.341252\pi\) | ||||
0.478303 | + | 0.878195i | \(0.341252\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.582576i | 0.0352591i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 8.58258i | − 0.515677i | −0.966188 | − | 0.257838i | \(-0.916990\pi\) | ||||
0.966188 | − | 0.257838i | \(-0.0830102\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 41.1216 | 2.46189 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.7477 | −0.820121 | −0.410060 | − | 0.912058i | \(-0.634492\pi\) | ||||
−0.410060 | + | 0.912058i | \(0.634492\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.7042i | 1.82517i | 0.408883 | + | 0.912587i | \(0.365918\pi\) | ||||
−0.408883 | + | 0.912587i | \(0.634082\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.295834i | 0.0174625i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3739 | 0.963168 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.3303 | 1.01592 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.83485i | 0.165614i | 0.996566 | + | 0.0828068i | \(0.0263884\pi\) | ||||
−0.996566 | + | 0.0828068i | \(0.973612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.00000i | 0.290129i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.79129 | −0.219256 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.08712 | 0.120300 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 48.4955i | − 2.78599i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 27.2087i | − 1.55288i | −0.630189 | − | 0.776442i | \(-0.717023\pi\) | ||||
0.630189 | − | 0.776442i | \(-0.282977\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.6261 | 0.945828 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.83485 | −0.330864 | −0.165432 | − | 0.986221i | \(-0.552902\pi\) | ||||
−0.165432 | + | 0.986221i | \(0.552902\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 6.74773i | − 0.381404i | −0.981648 | − | 0.190702i | \(-0.938924\pi\) | ||||
0.981648 | − | 0.190702i | \(-0.0610764\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 8.37386i | − 0.470323i | −0.971956 | − | 0.235162i | \(-0.924438\pi\) | ||||
0.971956 | − | 0.235162i | \(-0.0755619\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.79129 | 0.380239 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −55.1216 | −3.07659 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 5.20871i | − 0.289820i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.3739i | 0.739576i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.295834 | −0.0163098 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3303 | 0.952560 | 0.476280 | − | 0.879294i | \(-0.341985\pi\) | ||||
0.476280 | + | 0.879294i | \(0.341985\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.3739i | 0.678084i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 22.0000i | − 1.19842i | −0.800593 | − | 0.599208i | \(-0.795482\pi\) | ||||
0.800593 | − | 0.599208i | \(-0.204518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.95644 | 0.214884 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.58258 | 0.464773 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 2.91288i | − 0.157281i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.6261i | 0.677807i | 0.940821 | + | 0.338903i | \(0.110056\pi\) | ||||
−0.940821 | + | 0.338903i | \(0.889944\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.5826 | 0.780587 | 0.390294 | − | 0.920690i | \(-0.372373\pi\) | ||||
0.390294 | + | 0.920690i | \(0.372373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 18.1652i | − 0.966833i | −0.875390 | − | 0.483417i | \(-0.839396\pi\) | ||||
0.875390 | − | 0.483417i | \(-0.160604\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.460985i | 0.0243979i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.00000 | 0.316668 | 0.158334 | − | 0.987386i | \(-0.449388\pi\) | ||||
0.158334 | + | 0.987386i | \(0.449388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.3303 | 1.28054 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.79129i | 0.146505i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.62614i | 0.450281i | 0.974326 | + | 0.225140i | \(0.0722841\pi\) | ||||
−0.974326 | + | 0.225140i | \(0.927716\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.79129 | 0.353540 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.37386 | −0.123245 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.3303i | 1.00089i | 0.865770 | + | 0.500443i | \(0.166829\pi\) | ||||
−0.865770 | + | 0.500443i | \(0.833171\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 6.79129i | − 0.349769i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.0000 | 1.59236 | 0.796182 | − | 0.605058i | \(-0.206850\pi\) | ||||
0.796182 | + | 0.605058i | \(0.206850\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −45.7042 | −2.34150 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.0000i | 0.919757i | 0.887982 | + | 0.459879i | \(0.152107\pi\) | ||||
−0.887982 | + | 0.459879i | \(0.847893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 47.9129i | − 2.43555i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.0000 | 0.608424 | 0.304212 | − | 0.952604i | \(-0.401607\pi\) | ||||
0.304212 | + | 0.952604i | \(0.401607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.00000 | −0.151717 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 1.74773i | − 0.0881612i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.20871i | 0.361795i | 0.983502 | + | 0.180897i | \(0.0579002\pi\) | ||||
−0.983502 | + | 0.180897i | \(0.942100\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.83485 | −0.191983 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.8348 | −0.740817 | −0.370408 | − | 0.928869i | \(-0.620782\pi\) | ||||
−0.370408 | + | 0.928869i | \(0.620782\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 8.58258i | − 0.427529i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.58258i | 0.128014i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.0000 | −0.840596 | −0.420298 | − | 0.907386i | \(-0.638074\pi\) | ||||
−0.420298 | + | 0.907386i | \(0.638074\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.2087 | 1.58874 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.20871i | − 0.108684i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 27.2087i | − 1.33242i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.0000 | −1.31904 | −0.659518 | − | 0.751689i | \(-0.729240\pi\) | ||||
−0.659518 | + | 0.751689i | \(0.729240\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.3739 | 1.23665 | 0.618323 | − | 0.785924i | \(-0.287812\pi\) | ||||
0.618323 | + | 0.785924i | \(0.287812\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.79129i | 0.330204i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 0.878409i | − 0.0425092i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.79129 | 0.134765 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.9129 | 0.525655 | 0.262827 | − | 0.964843i | \(-0.415345\pi\) | ||||
0.262827 | + | 0.964843i | \(0.415345\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.3303i | 0.640613i | 0.947314 | + | 0.320307i | \(0.103786\pi\) | ||||
−0.947314 | + | 0.320307i | \(0.896214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 24.9564i | − 1.19383i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.9564 | −0.570650 | −0.285325 | − | 0.958431i | \(-0.592101\pi\) | ||||
−0.285325 | + | 0.958431i | \(0.592101\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −33.3303 | −1.58716 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 22.4174i | − 1.06508i | −0.846404 | − | 0.532542i | \(-0.821237\pi\) | ||||
0.846404 | − | 0.532542i | \(-0.178763\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 8.83485i | − 0.417874i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.2087 | −1.23687 | −0.618433 | − | 0.785838i | \(-0.712232\pi\) | ||||
−0.618433 | + | 0.785838i | \(0.712232\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.41742 | 0.0667439 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.9564i | 0.655731i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.3739i | 0.625603i | 0.949819 | + | 0.312801i | \(0.101267\pi\) | ||||
−0.949819 | + | 0.312801i | \(0.898733\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.95644 | 0.184671 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.4955 | −1.14087 | −0.570434 | − | 0.821344i | \(-0.693225\pi\) | ||||
−0.570434 | + | 0.821344i | \(0.693225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.25227i | 0.104672i | 0.998630 | + | 0.0523360i | \(0.0166667\pi\) | ||||
−0.998630 | + | 0.0523360i | \(0.983333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.5826i | 0.489703i | 0.969561 | + | 0.244852i | \(0.0787392\pi\) | ||||
−0.969561 | + | 0.244852i | \(0.921261\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.834849 | −0.0385497 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −47.9129 | −2.20771 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 10.0000i | − 0.459800i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 54.4955i | 2.49518i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.165151 | −0.00754596 | −0.00377298 | − | 0.999993i | \(-0.501201\pi\) | ||||
−0.00377298 | + | 0.999993i | \(0.501201\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.58258 | 0.117755 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.20871i | 0.100500i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 29.7477i | − 1.34800i | −0.738732 | − | 0.673999i | \(-0.764575\pi\) | ||||
0.738732 | − | 0.673999i | \(-0.235425\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −59.6606 | −2.69795 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.41742 | −0.334744 | −0.167372 | − | 0.985894i | \(-0.553528\pi\) | ||||
−0.167372 | + | 0.985894i | \(0.553528\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.37386i | − 0.242027i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.24318i | 0.100620i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.9564 | −0.669542 | −0.334771 | − | 0.942299i | \(-0.608659\pi\) | ||||
−0.334771 | + | 0.942299i | \(0.608659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 46.2867 | 2.06794 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 16.4174i | − 0.732017i | −0.930612 | − | 0.366008i | \(-0.880724\pi\) | ||||
0.930612 | − | 0.366008i | \(-0.119276\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.4955i | 1.48759i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.1216 | −0.448632 | −0.224316 | − | 0.974517i | \(-0.572015\pi\) | ||||
−0.224316 | + | 0.974517i | \(0.572015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.62614 | 0.0719360 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.9129i | 1.45314i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.41742i | 0.0623382i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −38.3739 | −1.68443 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.58258 | 0.0693339 | 0.0346670 | − | 0.999399i | \(-0.488963\pi\) | ||||
0.0346670 | + | 0.999399i | \(0.488963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.1652i | 1.10040i | 0.835034 | + | 0.550198i | \(0.185448\pi\) | ||||
−0.835034 | + | 0.550198i | \(0.814552\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 6.79129i | − 0.295833i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.62614 | 0.375049 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −50.7042 | −2.20037 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.41742i | − 0.0613955i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 61.7477i | − 2.66461i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.95644 | −0.299635 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6261 | −0.456853 | −0.228427 | − | 0.973561i | \(-0.573358\pi\) | ||||
−0.228427 | + | 0.973561i | \(0.573358\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 9.41742i | − 0.404140i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.37386i | 0.315284i | 0.987496 | + | 0.157642i | \(0.0503891\pi\) | ||||
−0.987496 | + | 0.157642i | \(0.949611\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.1652 | −0.860628 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 44.7042 | 1.90446 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 3.24318i | − 0.137914i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 45.6606i | − 1.93470i | −0.253441 | − | 0.967351i | \(-0.581562\pi\) | ||||
0.253441 | − | 0.967351i | \(-0.418438\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.0000 | −0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.20871 | 0.0932519 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.1216i | 1.69092i | 0.534036 | + | 0.845462i | \(0.320675\pi\) | ||||
−0.534036 | + | 0.845462i | \(0.679325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.0871215i | 0.00365876i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.9564 | −0.794695 | −0.397348 | − | 0.917668i | \(-0.630069\pi\) | ||||
−0.397348 | + | 0.917668i | \(0.630069\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.2867 | 1.14191 | 0.570957 | − | 0.820980i | \(-0.306572\pi\) | ||||
0.570957 | + | 0.820980i | \(0.306572\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 48.0345i | 2.00667i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.9564i | 0.497753i | 0.968535 | + | 0.248877i | \(0.0800613\pi\) | ||||
−0.968535 | + | 0.248877i | \(0.919939\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.0000 | −0.831172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.07803 | 0.0862112 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.3739i | 0.471057i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.9564i | 0.658593i | 0.944227 | + | 0.329296i | \(0.106812\pi\) | ||||
−0.944227 | + | 0.329296i | \(0.893188\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 56.4955 | 2.32785 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −74.0780 | −3.04716 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.5826i | 0.927355i | 0.886004 | + | 0.463678i | \(0.153470\pi\) | ||||
−0.886004 | + | 0.463678i | \(0.846530\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.53901i | 0.185770i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.7042 | −1.82656 | −0.913281 | − | 0.407329i | \(-0.866460\pi\) | ||||
−0.913281 | + | 0.407329i | \(0.866460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.5390 | 1.16413 | 0.582065 | − | 0.813142i | \(-0.302245\pi\) | ||||
0.582065 | + | 0.813142i | \(0.302245\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.1652i | 0.780465i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 34.0000i | − 1.38002i | −0.723801 | − | 0.690009i | \(-0.757607\pi\) | ||||
0.723801 | − | 0.690009i | \(-0.242393\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.95644 | −0.160323 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.41742 | 0.0573428 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 33.4519i | − 1.35111i | −0.737310 | − | 0.675555i | \(-0.763904\pi\) | ||||
0.737310 | − | 0.675555i | \(-0.236096\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 28.7477i | − 1.15734i | −0.815562 | − | 0.578670i | \(-0.803572\pi\) | ||||
0.815562 | − | 0.578670i | \(-0.196428\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.25227 | −0.251300 | −0.125650 | − | 0.992075i | \(-0.540102\pi\) | ||||
−0.125650 | + | 0.992075i | \(0.540102\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.9564 | 0.760696 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 0.165151i | − 0.00661665i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.3739i | 0.733781i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.04356 | 0.0814821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.1216 | 0.721409 | 0.360705 | − | 0.932680i | \(-0.382536\pi\) | ||||
0.360705 | + | 0.932680i | \(0.382536\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.9564i | 0.554719i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.95644i | 0.275624i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 51.4955 | 2.03713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.8348 | −0.941420 | −0.470710 | − | 0.882288i | \(-0.656002\pi\) | ||||
−0.470710 | + | 0.882288i | \(0.656002\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.4955i | 1.71529i | 0.514239 | + | 0.857647i | \(0.328074\pi\) | ||||
−0.514239 | + | 0.857647i | \(0.671926\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.3303i | 0.838581i | 0.907852 | + | 0.419290i | \(0.137721\pi\) | ||||
−0.907852 | + | 0.419290i | \(0.862279\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.5826 | −0.415402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.00000 | −0.195965 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 26.7042i | − 1.04501i | −0.852635 | − | 0.522507i | \(-0.824997\pi\) | ||||
0.852635 | − | 0.522507i | \(-0.175003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 37.3303i | − 1.45639i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.460985 | −0.0179574 | −0.00897871 | − | 0.999960i | \(-0.502858\pi\) | ||||
−0.00897871 | + | 0.999960i | \(0.502858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.5826 | 1.18952 | 0.594762 | − | 0.803902i | \(-0.297246\pi\) | ||||
0.594762 | + | 0.803902i | \(0.297246\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2.20871i | − 0.0857793i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 25.7477i | − 0.996956i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −57.4519 | −2.22122 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.20871 | −0.162476 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.9129i | 1.49998i | 0.661448 | + | 0.749991i | \(0.269942\pi\) | ||||
−0.661448 | + | 0.749991i | \(0.730058\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.58258i | − 0.0608233i | −0.999537 | − | 0.0304117i | \(-0.990318\pi\) | ||||
0.999537 | − | 0.0304117i | \(-0.00968183\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.29583 | −0.0497295 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.2087 | −1.23424 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 34.9129i | − 1.33590i | −0.744204 | − | 0.667952i | \(-0.767171\pi\) | ||||
0.744204 | − | 0.667952i | \(-0.232829\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.2867i | 0.812140i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.3739 | 0.433310 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.1216 | −1.22196 | −0.610981 | − | 0.791645i | \(-0.709225\pi\) | ||||
−0.610981 | + | 0.791645i | \(0.709225\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.00000i | − 0.0379869i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.12159i | − 0.0424833i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 44.0780 | 1.66718 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.8348 | 0.786921 | 0.393461 | − | 0.919341i | \(-0.371278\pi\) | ||||
0.393461 | + | 0.919341i | \(0.371278\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.0000i | 0.641167i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.62614i | 0.136375i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.4955 | −1.10773 | −0.553863 | − | 0.832608i | \(-0.686847\pi\) | ||||
−0.553863 | + | 0.832608i | \(0.686847\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −74.4519 | −2.79216 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 32.5390i | − 1.21860i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.16515i | 0.230242i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.49545 | −0.242240 | −0.121120 | − | 0.992638i | \(-0.538649\pi\) | ||||
−0.121120 | + | 0.992638i | \(0.538649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.24318 | −0.0462985 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 64.5390i | − 2.40023i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 23.1216i | − 0.857532i | −0.903416 | − | 0.428766i | \(-0.858948\pi\) | ||||
0.903416 | − | 0.428766i | \(-0.141052\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.8693 | 1.62479 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.91288 | −0.292668 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 31.2432i | − 1.15399i | −0.816747 | − | 0.576997i | \(-0.804225\pi\) | ||||
0.816747 | − | 0.576997i | \(-0.195775\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.00000i | 0.147342i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.1216 | −1.54947 | −0.774734 | − | 0.632287i | \(-0.782116\pi\) | ||||
−0.774734 | + | 0.632287i | \(0.782116\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.3739 | 0.674981 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 39.7913i | − 1.45980i | −0.683554 | − | 0.729900i | \(-0.739566\pi\) | ||||
0.683554 | − | 0.729900i | \(-0.260434\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 47.7042i | − 1.74540i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.12159 | 0.150600 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.2087 | 0.481993 | 0.240996 | − | 0.970526i | \(-0.422526\pi\) | ||||
0.240996 | + | 0.970526i | \(0.422526\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 32.2087i | − 1.17375i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 7.33030i | − 0.266424i | −0.991088 | − | 0.133212i | \(-0.957471\pi\) | ||||
0.991088 | − | 0.133212i | \(-0.0425292\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.5826 | 0.384123 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.3303 | 1.09947 | 0.549736 | − | 0.835338i | \(-0.314728\pi\) | ||||
0.549736 | + | 0.835338i | \(0.314728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.00000i | − 0.0362024i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.5826i | 0.382115i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.7477 | 1.50546 | 0.752731 | − | 0.658328i | \(-0.228736\pi\) | ||||
0.752731 | + | 0.658328i | \(0.228736\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −50.2432 | −1.80946 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 26.2087i | − 0.942662i | −0.881956 | − | 0.471331i | \(-0.843774\pi\) | ||||
0.881956 | − | 0.471331i | \(-0.156226\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 1.50455i | − 0.0539753i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.33030 | 0.334293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7477 | 0.384584 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.9564i | 1.21350i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 17.7477i | − 0.632638i | −0.948653 | − | 0.316319i | \(-0.897553\pi\) | ||||
0.948653 | − | 0.316319i | \(-0.102447\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 67.4519 | 2.40135 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.295834 | −0.0105186 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.20871i | 0.149456i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.2867i | 1.21450i | 0.794511 | + | 0.607249i | \(0.207727\pi\) | ||||
−0.794511 | + | 0.607249i | \(0.792273\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.12159 | 0.0396790 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.79129 | −0.133959 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7.79129i | − 0.274949i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 57.7913i | 2.03435i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.4955 | 1.59953 | 0.799767 | − | 0.600310i | \(-0.204956\pi\) | ||||
0.799767 | + | 0.600310i | \(0.204956\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −55.6606 | −1.95451 | −0.977254 | − | 0.212072i | \(-0.931979\pi\) | ||||
−0.977254 | + | 0.212072i | \(0.931979\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 43.9564i | 1.54162i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 65.8258i | − 2.30295i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.00000 | −0.0349428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.6606 | 1.69827 | 0.849133 | − | 0.528178i | \(-0.177125\pi\) | ||||
0.849133 | + | 0.528178i | \(0.177125\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 8.00000i | − 0.278862i | −0.990232 | − | 0.139431i | \(-0.955473\pi\) | ||||
0.990232 | − | 0.139431i | \(-0.0445274\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 10.4174i | − 0.362249i | −0.983460 | − | 0.181125i | \(-0.942026\pi\) | ||||
0.983460 | − | 0.181125i | \(-0.0579738\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.9564 | 1.31828 | 0.659141 | − | 0.752020i | \(-0.270920\pi\) | ||||
0.659141 | + | 0.752020i | \(0.270920\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.9564 | 0.831040 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.50455i | 0.190721i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 42.9129i | 1.48329i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.7042 | 0.818359 | 0.409179 | − | 0.912454i | \(-0.365815\pi\) | ||||
0.409179 | + | 0.912454i | \(0.365815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.1216 | 0.590400 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 38.3739i | − 1.32167i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 0.208712i | − 0.00717143i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −85.7042 | −2.94136 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.79129 | 0.335641 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 3.12159i | − 0.106881i | −0.998571 | − | 0.0534406i | \(-0.982981\pi\) | ||||
0.998571 | − | 0.0534406i | \(-0.0170188\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 30.4955i | − 1.04170i | −0.853647 | − | 0.520852i | \(-0.825614\pi\) | ||||
0.853647 | − | 0.520852i | \(-0.174386\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.08712 | 0.0712117 | 0.0356058 | − | 0.999366i | \(-0.488664\pi\) | ||||
0.0356058 | + | 0.999366i | \(0.488664\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.825757 | −0.0281417 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.3303i | 0.930334i | 0.885223 | + | 0.465167i | \(0.154006\pi\) | ||||
−0.885223 | + | 0.465167i | \(0.845994\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 45.7042i | 1.55219i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.5390 | −0.527125 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000 | 0.135535 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.7477i | 1.00681i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 16.6606i | − 0.562589i | −0.959622 | − | 0.281294i | \(-0.909236\pi\) | ||||
0.959622 | − | 0.281294i | \(-0.0907637\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.91288 | −0.266895 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.87841 | 0.0632852 | 0.0316426 | − | 0.999499i | \(-0.489926\pi\) | ||||
0.0316426 | + | 0.999499i | \(0.489926\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 26.1652i | − 0.880527i | −0.897869 | − | 0.440264i | \(-0.854885\pi\) | ||||
0.897869 | − | 0.440264i | \(-0.145115\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 39.3303i | − 1.32058i | −0.751010 | − | 0.660291i | \(-0.770433\pi\) | ||||
0.751010 | − | 0.660291i | \(-0.229567\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.41742 | 0.114617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.417424 | 0.0139842 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.33030i | 0.312227i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 10.5826i | − 0.353342i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.2867 | 1.94397 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000 | 0.299833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.82576i | 0.193869i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.6606i | 1.08448i | 0.840224 | + | 0.542239i | \(0.182423\pi\) | ||||
−0.840224 | + | 0.542239i | \(0.817577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 83.2432 | 2.76100 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.3303 | −0.408521 | −0.204261 | − | 0.978917i | \(-0.565479\pi\) | ||||
−0.204261 | + | 0.978917i | \(0.565479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 9.95644i | − 0.329510i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.130682i | 0.00431551i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.8348 | −0.951174 | −0.475587 | − | 0.879669i | \(-0.657764\pi\) | ||||
−0.475587 | + | 0.879669i | \(0.657764\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 75.9473 | 2.50255 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 10.7477i | − 0.353766i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.5390i | 0.937344i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.7477 | −0.451048 | −0.225524 | − | 0.974238i | \(-0.572409\pi\) | ||||
−0.225524 | + | 0.974238i | \(0.572409\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.7913 | −1.50075 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 16.2867i | − 0.533204i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.1652i | 1.14880i | 0.818576 | + | 0.574398i | \(0.194764\pi\) | ||||
−0.818576 | + | 0.574398i | \(0.805236\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.8348 | 0.614652 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.0780 | −1.63250 | −0.816249 | − | 0.577701i | \(-0.803950\pi\) | ||||
−0.816249 | + | 0.577701i | \(0.803950\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 5.37386i | − 0.174997i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.91288i | − 0.159647i | −0.996809 | − | 0.0798235i | \(-0.974564\pi\) | ||||
0.996809 | − | 0.0798235i | \(-0.0254357\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.79129 | −0.252916 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.3739 | 0.757949 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.0000i | 1.36051i | 0.732974 | + | 0.680257i | \(0.238132\pi\) | ||||
−0.732974 | + | 0.680257i | \(0.761868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.9564i | 0.612775i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.40833 | −0.0777691 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 42.6606 | 1.37615 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 94.6170i | − 3.04899i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.5390i | 1.40012i | 0.714084 | + | 0.700060i | \(0.246844\pi\) | ||||
−0.714084 | + | 0.700060i | \(0.753156\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.5390 | 0.467060 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.9564 | 0.608341 | 0.304171 | − | 0.952618i | \(-0.401621\pi\) | ||||
0.304171 | + | 0.952618i | \(0.401621\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.03447i | 0.0652221i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 25.7477i | − 0.823743i | −0.911242 | − | 0.411871i | \(-0.864875\pi\) | ||||
0.911242 | − | 0.411871i | \(-0.135125\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.791288 | −0.0252897 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.9564 | −0.732943 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.6606i | 1.55203i | 0.630713 | + | 0.776016i | \(0.282763\pi\) | ||||
−0.630713 | + | 0.776016i | \(0.717237\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 0.825757i | − 0.0262841i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37.9129 | −1.20556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.8693 | 1.77475 | 0.887374 | − | 0.461051i | \(-0.152527\pi\) | ||||
0.887374 | + | 0.461051i | \(0.152527\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 48.3739i | 1.53510i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.3739i | 1.27865i | 0.768935 | + | 0.639327i | \(0.220787\pi\) | ||||
−0.768935 | + | 0.639327i | \(0.779213\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.9129 | −0.408545 |
(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 | 1100.2.b.d.749.4 | 4 | ||
3.2 | odd | 2 | 9900.2.c.x.5149.2 | 4 | |||
4.3 | odd | 2 | 4400.2.b.s.4049.1 | 4 | |||
5.2 | odd | 4 | 1100.2.a.h.1.2 | yes | 2 | ||
5.3 | odd | 4 | 1100.2.a.g.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 1100.2.b.d.749.1 | 4 | ||
15.2 | even | 4 | 9900.2.a.bz.1.1 | 2 | |||
15.8 | even | 4 | 9900.2.a.bh.1.2 | 2 | |||
15.14 | odd | 2 | 9900.2.c.x.5149.3 | 4 | |||
20.3 | even | 4 | 4400.2.a.bu.1.2 | 2 | |||
20.7 | even | 4 | 4400.2.a.bi.1.1 | 2 | |||
20.19 | odd | 2 | 4400.2.b.s.4049.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1100.2.a.g.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
1100.2.a.h.1.2 | yes | 2 | 5.2 | odd | 4 | ||
1100.2.b.d.749.1 | 4 | 5.4 | even | 2 | inner | ||
1100.2.b.d.749.4 | 4 | 1.1 | even | 1 | trivial | ||
4400.2.a.bi.1.1 | 2 | 20.7 | even | 4 | |||
4400.2.a.bu.1.2 | 2 | 20.3 | even | 4 | |||
4400.2.b.s.4049.1 | 4 | 4.3 | odd | 2 | |||
4400.2.b.s.4049.4 | 4 | 20.19 | odd | 2 | |||
9900.2.a.bh.1.2 | 2 | 15.8 | even | 4 | |||
9900.2.a.bz.1.1 | 2 | 15.2 | even | 4 | |||
9900.2.c.x.5149.2 | 4 | 3.2 | odd | 2 | |||
9900.2.c.x.5149.3 | 4 | 15.14 | odd | 2 |