Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.744786576.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - x^{5} - 17x^{4} + 13x^{3} + 69x^{2} - 21x - 30 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 836) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.82559\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.82559 | −1.63135 | −0.815677 | − | 0.578508i | \(-0.803635\pi\) | ||||
−0.815677 | + | 0.578508i | \(0.803635\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.343563 | −0.153646 | −0.0768231 | − | 0.997045i | \(-0.524478\pi\) | ||||
−0.0768231 | + | 0.997045i | \(0.524478\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.77460 | −1.80463 | −0.902314 | − | 0.431079i | \(-0.858133\pi\) | ||||
−0.902314 | + | 0.431079i | \(0.858133\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.98394 | 1.66131 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.86340 | 0.516815 | 0.258407 | − | 0.966036i | \(-0.416802\pi\) | ||||
0.258407 | + | 0.966036i | \(0.416802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.970768 | 0.250651 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.69469 | −1.38116 | −0.690582 | − | 0.723254i | \(-0.742646\pi\) | ||||
−0.690582 | + | 0.723254i | \(0.742646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.4910 | 2.94399 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.06385 | 0.221829 | 0.110914 | − | 0.993830i | \(-0.464622\pi\) | ||||
0.110914 | + | 0.993830i | \(0.464622\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88196 | −0.976393 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.60580 | −1.07884 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.31093 | −1.72900 | −0.864498 | − | 0.502636i | \(-0.832364\pi\) | ||||
−0.864498 | + | 0.502636i | \(0.832364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.97077 | −0.533566 | −0.266783 | − | 0.963757i | \(-0.585961\pi\) | ||||
−0.266783 | + | 0.963757i | \(0.585961\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.82559 | −0.491872 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.64038 | 0.277274 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.54764 | −0.583229 | −0.291614 | − | 0.956536i | \(-0.594192\pi\) | ||||
−0.291614 | + | 0.956536i | \(0.594192\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.26521 | −0.843108 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.82372 | 0.440992 | 0.220496 | − | 0.975388i | \(-0.429232\pi\) | ||||
0.220496 | + | 0.975388i | \(0.429232\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.09454 | −1.23441 | −0.617203 | − | 0.786804i | \(-0.711734\pi\) | ||||
−0.617203 | + | 0.786804i | \(0.711734\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.71230 | −0.255255 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00756 | −0.438698 | −0.219349 | − | 0.975646i | \(-0.570393\pi\) | ||||
−0.219349 | + | 0.975646i | \(0.570393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.7968 | 2.25668 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.0908 | 2.25317 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.33830 | −0.595911 | −0.297956 | − | 0.954580i | \(-0.596305\pi\) | ||||
−0.297956 | + | 0.954580i | \(0.596305\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.343563 | −0.0463261 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.82559 | −0.374258 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.6566 | −1.90812 | −0.954061 | − | 0.299613i | \(-0.903143\pi\) | ||||
−0.954061 | + | 0.299613i | \(0.903143\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.03595 | 0.132640 | 0.0663201 | − | 0.997798i | \(-0.478874\pi\) | ||||
0.0663201 | + | 0.997798i | \(0.478874\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −23.7963 | −2.99805 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.640197 | −0.0794067 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.93109 | −0.968937 | −0.484468 | − | 0.874809i | \(-0.660987\pi\) | ||||
−0.484468 | + | 0.874809i | \(0.660987\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.00601 | −0.361881 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4107 | 1.35421 | 0.677103 | − | 0.735889i | \(-0.263235\pi\) | ||||
0.677103 | + | 0.735889i | \(0.263235\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.3062 | −1.90849 | −0.954247 | − | 0.299019i | \(-0.903341\pi\) | ||||
−0.954247 | + | 0.299019i | \(0.903341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.7944 | 1.59284 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.77460 | −0.544116 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.3459 | 1.50153 | 0.750763 | − | 0.660571i | \(-0.229686\pi\) | ||||
0.750763 | + | 0.660571i | \(0.229686\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.887845 | 0.0986494 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.40742 | 0.374012 | 0.187006 | − | 0.982359i | \(-0.440122\pi\) | ||||
0.187006 | + | 0.982359i | \(0.440122\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.95649 | 0.212211 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 26.3088 | 2.82060 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.0562918 | 0.00596692 | 0.00298346 | − | 0.999996i | \(-0.499050\pi\) | ||||
0.00298346 | + | 0.999996i | \(0.499050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.89700 | −0.932659 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.39416 | 0.870434 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.343563 | −0.0352489 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.4778 | 1.16539 | 0.582696 | − | 0.812690i | \(-0.301998\pi\) | ||||
0.582696 | + | 0.812690i | \(0.301998\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.98394 | 0.500905 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.64361 | 0.462057 | 0.231028 | − | 0.972947i | \(-0.425791\pi\) | ||||
0.231028 | + | 0.972947i | \(0.425791\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.73334 | −0.959055 | −0.479527 | − | 0.877527i | \(-0.659192\pi\) | ||||
−0.479527 | + | 0.877527i | \(0.659192\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.63503 | −0.452333 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.06541 | 0.876386 | 0.438193 | − | 0.898881i | \(-0.355619\pi\) | ||||
0.438193 | + | 0.898881i | \(0.355619\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.74943 | 0.550695 | 0.275348 | − | 0.961345i | \(-0.411207\pi\) | ||||
0.275348 | + | 0.961345i | \(0.411207\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.0242 | 0.951452 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.68930 | 0.252988 | 0.126494 | − | 0.991967i | \(-0.459628\pi\) | ||||
0.126494 | + | 0.991967i | \(0.459628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.365501 | −0.0340831 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.28709 | 0.858592 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 27.1898 | 2.49249 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.97868 | −0.719413 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.39508 | 0.303665 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.1746 | 1.16906 | 0.584530 | − | 0.811372i | \(-0.301279\pi\) | ||||
0.584530 | + | 0.811372i | \(0.301279\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 22.8718 | 2.01375 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.6659 | −1.71822 | −0.859110 | − | 0.511791i | \(-0.828982\pi\) | ||||
−0.859110 | + | 0.511791i | \(0.828982\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.77460 | −0.414010 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.92595 | 0.165759 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00937 | 0.769722 | 0.384861 | − | 0.922974i | \(-0.374249\pi\) | ||||
0.384861 | + | 0.922974i | \(0.374249\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.8943 | 1.68741 | 0.843707 | − | 0.536804i | \(-0.180369\pi\) | ||||
0.843707 | + | 0.536804i | \(0.180369\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.49812 | 0.715671 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.86340 | 0.155826 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.19890 | 0.265654 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −44.6352 | −3.68145 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.0292 | −1.06739 | −0.533695 | − | 0.845677i | \(-0.679197\pi\) | ||||
−0.533695 | + | 0.845677i | \(0.679197\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.73820 | 0.141453 | 0.0707264 | − | 0.997496i | \(-0.477468\pi\) | ||||
0.0707264 | + | 0.997496i | \(0.477468\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −28.3820 | −2.29455 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.02065 | 0.0819804 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.95506 | −0.555074 | −0.277537 | − | 0.960715i | \(-0.589518\pi\) | ||||
−0.277537 | + | 0.960715i | \(0.589518\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.2582 | 0.972142 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.07947 | −0.400318 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.7201 | −1.15297 | −0.576484 | − | 0.817108i | \(-0.695576\pi\) | ||||
−0.576484 | + | 0.817108i | \(0.695576\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.970768 | 0.0755742 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.95276 | 0.460638 | 0.230319 | − | 0.973115i | \(-0.426023\pi\) | ||||
0.230319 | + | 0.973115i | \(0.426023\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.52773 | −0.732902 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.98394 | 0.381131 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.925392 | −0.0703563 | −0.0351781 | − | 0.999381i | \(-0.511200\pi\) | ||||
−0.0351781 | + | 0.999381i | \(0.511200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.3094 | 1.76203 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 41.4134 | 3.11282 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.9602 | −1.41716 | −0.708578 | − | 0.705633i | \(-0.750663\pi\) | ||||
−0.708578 | + | 0.705633i | \(0.750663\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.27828 | 0.466661 | 0.233331 | − | 0.972397i | \(-0.425038\pi\) | ||||
0.233331 | + | 0.972397i | \(0.425038\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.92718 | −0.216383 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.21884 | 0.0896109 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.69469 | −0.416437 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 26.7654 | 1.94690 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.2273 | 1.31888 | 0.659440 | − | 0.751758i | \(-0.270794\pi\) | ||||
0.659440 | + | 0.751758i | \(0.270794\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.51799 | −0.397194 | −0.198597 | − | 0.980081i | \(-0.563638\pi\) | ||||
−0.198597 | + | 0.980081i | \(0.563638\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.80893 | 0.129540 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.5897 | 1.75195 | 0.875973 | − | 0.482359i | \(-0.160220\pi\) | ||||
0.875973 | + | 0.482359i | \(0.160220\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.1425 | 1.21520 | 0.607601 | − | 0.794243i | \(-0.292132\pi\) | ||||
0.607601 | + | 0.794243i | \(0.292132\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.4100 | 1.58068 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 44.4560 | 3.12020 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.970128 | −0.0677567 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.30218 | 0.368527 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.10198 | −0.282392 | −0.141196 | − | 0.989982i | \(-0.545095\pi\) | ||||
−0.141196 | + | 0.989982i | \(0.545095\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −32.2420 | −2.20919 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.78099 | 0.189662 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.1842 | 0.962888 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 46.0745 | 3.11343 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.6115 | −0.713806 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.2530 | −1.75803 | −0.879015 | − | 0.476793i | \(-0.841799\pi\) | ||||
−0.879015 | + | 0.476793i | \(0.841799\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −24.3314 | −1.62209 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.54225 | 0.168735 | 0.0843677 | − | 0.996435i | \(-0.473113\pi\) | ||||
0.0843677 | + | 0.996435i | \(0.473113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.23905 | −0.478370 | −0.239185 | − | 0.970974i | \(-0.576880\pi\) | ||||
−0.239185 | + | 0.970974i | \(0.576880\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.4910 | 0.887645 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.6807 | 1.61689 | 0.808444 | − | 0.588573i | \(-0.200310\pi\) | ||||
0.808444 | + | 0.588573i | \(0.200310\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.03329 | 0.0674043 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −37.7099 | −2.44952 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.3130 | 1.44331 | 0.721654 | − | 0.692254i | \(-0.243382\pi\) | ||||
0.721654 | + | 0.692254i | \(0.243382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.08973 | 0.585521 | 0.292760 | − | 0.956186i | \(-0.405426\pi\) | ||||
0.292760 | + | 0.956186i | \(0.405426\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.3087 | 0.917904 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.42720 | −0.346731 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.86340 | 0.118565 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.62795 | −0.610146 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.11865 | 0.133728 | 0.0668640 | − | 0.997762i | \(-0.478701\pi\) | ||||
0.0668640 | + | 0.997762i | \(0.478701\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.06385 | 0.0668838 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.52822 | −0.346191 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.83262 | −0.301450 | −0.150725 | − | 0.988576i | \(-0.548161\pi\) | ||||
−0.150725 | + | 0.988576i | \(0.548161\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.9386 | 1.05251 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −46.4051 | −2.87241 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.7931 | −0.665529 | −0.332764 | − | 0.943010i | \(-0.607981\pi\) | ||||
−0.332764 | + | 0.943010i | \(0.607981\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.49048 | 0.0915596 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.159057 | −0.00973415 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.0956 | −0.981365 | −0.490683 | − | 0.871338i | \(-0.663253\pi\) | ||||
−0.490683 | + | 0.871338i | \(0.663253\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.2262 | 1.35014 | 0.675072 | − | 0.737752i | \(-0.264113\pi\) | ||||
0.675072 | + | 0.737752i | \(0.264113\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.1392 | 1.52150 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.88196 | −0.294394 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.12740 | −0.0677392 | −0.0338696 | − | 0.999426i | \(-0.510783\pi\) | ||||
−0.0338696 | + | 0.999426i | \(0.510783\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.8061 | −0.886420 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.51489 | 0.0903705 | 0.0451852 | − | 0.998979i | \(-0.485612\pi\) | ||||
0.0451852 | + | 0.998979i | \(0.485612\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.74917 | −0.341753 | −0.170876 | − | 0.985292i | \(-0.554660\pi\) | ||||
−0.170876 | + | 0.985292i | \(0.554660\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.970768 | 0.0575034 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.4821 | −0.795826 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.4295 | 0.907615 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −32.4315 | −1.90117 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.00163269 | −9.53826e−5 0 | −4.76913e−5 | − | 1.00000i | \(-0.500015\pi\) | ||||
−4.76913e−5 | 1.00000i | \(0.500015\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.03546 | 0.293176 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.60580 | −0.325281 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.98238 | 0.114644 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.6482 | 2.22764 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.1209 | −0.753778 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.355916 | −0.0203797 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.0663 | 1.54475 | 0.772377 | − | 0.635164i | \(-0.219068\pi\) | ||||
0.772377 | + | 0.635164i | \(0.219068\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.5024 | 1.56456 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.8440 | −1.23866 | −0.619329 | − | 0.785131i | \(-0.712595\pi\) | ||||
−0.619329 | + | 0.785131i | \(0.712595\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.54317 | −0.256795 | −0.128398 | − | 0.991723i | \(-0.540983\pi\) | ||||
−0.128398 | + | 0.991723i | \(0.540983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.17554 | 0.460640 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.22001 | −0.461682 | −0.230841 | − | 0.972992i | \(-0.574148\pi\) | ||||
−0.230841 | + | 0.972992i | \(0.574148\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.31093 | −0.521312 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.6151 | −1.42969 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.69469 | −0.316861 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.09706 | −0.504614 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.2455 | −0.898378 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.3599 | 0.791687 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.5060 | 0.577463 | 0.288732 | − | 0.957410i | \(-0.406766\pi\) | ||||
0.288732 | + | 0.957410i | \(0.406766\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.6812 | −0.968926 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.72483 | 0.148874 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.5797 | 1.17552 | 0.587760 | − | 0.809035i | \(-0.300010\pi\) | ||||
0.587760 | + | 0.809035i | \(0.300010\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.59885 | −0.412713 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.97077 | −0.160876 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −42.0011 | −2.26785 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.03275 | 0.0556016 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.5171 | 1.15510 | 0.577549 | − | 0.816356i | \(-0.304009\pi\) | ||||
0.577549 | + | 0.816356i | \(0.304009\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.7204 | 1.26972 | 0.634862 | − | 0.772625i | \(-0.281057\pi\) | ||||
0.634862 | + | 0.772625i | \(0.281057\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.4459 | −0.557559 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.4757 | 0.717241 | 0.358621 | − | 0.933483i | \(-0.383247\pi\) | ||||
0.358621 | + | 0.933483i | \(0.383247\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.92031 | −0.208069 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −76.8273 | −4.06613 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.4579 | 0.763058 | 0.381529 | − | 0.924357i | \(-0.375398\pi\) | ||||
0.381529 | + | 0.924357i | \(0.375398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.82559 | −0.148305 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.60221 | 0.293233 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.692406 | 0.0361433 | 0.0180716 | − | 0.999837i | \(-0.494247\pi\) | ||||
0.0180716 | + | 0.999837i | \(0.494247\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.0733 | 0.732625 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.7136 | 1.07540 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.2174 | 0.787929 | 0.393964 | − | 0.919126i | \(-0.371103\pi\) | ||||
0.393964 | + | 0.919126i | \(0.371103\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.59310 | −0.495385 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.3500 | −0.893571 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.7668 | −1.58039 | −0.790193 | − | 0.612859i | \(-0.790020\pi\) | ||||
−0.790193 | + | 0.612859i | \(0.790020\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.2261 | −1.90715 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.1031 | −1.58929 | −0.794646 | − | 0.607073i | \(-0.792344\pi\) | ||||
−0.794646 | + | 0.607073i | \(0.792344\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.64038 | 0.0836014 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −40.3427 | −2.05074 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.8274 | 0.853181 | 0.426590 | − | 0.904445i | \(-0.359715\pi\) | ||||
0.426590 | + | 0.904445i | \(0.359715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.05831 | −0.306382 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 55.5678 | 2.80302 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.58515 | −0.230704 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.3895 | 0.922943 | 0.461472 | − | 0.887155i | \(-0.347322\pi\) | ||||
0.461472 | + | 0.887155i | \(0.347322\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.4910 | 0.675397 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.4034 | −0.919022 | −0.459511 | − | 0.888172i | \(-0.651975\pi\) | ||||
−0.459511 | + | 0.888172i | \(0.651975\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.53574 | −0.275755 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.305031 | −0.0151571 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.54764 | −0.175850 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −39.3705 | −1.94675 | −0.973373 | − | 0.229225i | \(-0.926381\pi\) | ||||
−0.973373 | + | 0.229225i | \(0.926381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.4568 | −1.25569 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 69.9792 | 3.44345 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.17066 | −0.0574656 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −56.2131 | −2.75277 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.2402 | −0.842237 | −0.421118 | − | 0.907006i | \(-0.638362\pi\) | ||||
−0.421118 | + | 0.907006i | \(0.638362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.86946 | 0.383534 | 0.191767 | − | 0.981440i | \(-0.438578\pi\) | ||||
0.191767 | + | 0.981440i | \(0.438578\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.9895 | −0.728815 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 27.8013 | 1.34856 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.94626 | −0.239366 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.26521 | −0.254207 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.9971 | 1.05957 | 0.529783 | − | 0.848133i | \(-0.322274\pi\) | ||||
0.529783 | + | 0.848133i | \(0.322274\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.7111 | 1.18754 | 0.593771 | − | 0.804634i | \(-0.297639\pi\) | ||||
0.593771 | + | 0.804634i | \(0.297639\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.03876 | −0.433375 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.06385 | 0.0508909 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.3096 | −1.30342 | −0.651708 | − | 0.758470i | \(-0.725947\pi\) | ||||
−0.651708 | + | 0.758470i | \(0.725947\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 78.7303 | 3.74906 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.0147 | 1.80613 | 0.903066 | − | 0.429501i | \(-0.141311\pi\) | ||||
0.903066 | + | 0.429501i | \(0.141311\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.0193398 | −0.000916795 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.8150 | 1.74129 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.1470 | 1.84746 | 0.923730 | − | 0.383043i | \(-0.125124\pi\) | ||||
0.923730 | + | 0.383043i | \(0.125124\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.82372 | 0.132964 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.91144 | −0.230759 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.05668 | 0.143300 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.72692 | 0.221116 | 0.110558 | − | 0.993870i | \(-0.464736\pi\) | ||||
0.110558 | + | 0.993870i | \(0.464736\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 31.9233 | 1.49005 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.1666 | −0.520079 | −0.260040 | − | 0.965598i | \(-0.583736\pi\) | ||||
−0.260040 | + | 0.965598i | \(0.583736\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.5320 | −1.41894 | −0.709470 | − | 0.704735i | \(-0.751066\pi\) | ||||
−0.709470 | + | 0.704735i | \(0.751066\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.88393 | −0.133739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.2216 | −0.519274 | −0.259637 | − | 0.965706i | \(-0.583603\pi\) | ||||
−0.259637 | + | 0.965706i | \(0.583603\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 37.8678 | 1.74857 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.6521 | 0.905522 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.09454 | −0.372187 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.88196 | −0.224000 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.6218 | −0.989996 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.0838 | −0.689197 | −0.344598 | − | 0.938750i | \(-0.611985\pi\) | ||||
−0.344598 | + | 0.938750i | \(0.611985\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.61069 | −0.301421 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.3525 | 0.653060 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.94335 | −0.179058 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.3598 | 1.10385 | 0.551925 | − | 0.833894i | \(-0.313894\pi\) | ||||
0.551925 | + | 0.833894i | \(0.313894\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 41.5930 | 1.88090 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.4105 | −0.695467 | −0.347734 | − | 0.937593i | \(-0.613049\pi\) | ||||
−0.347734 | + | 0.937593i | \(0.613049\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 53.0228 | 2.38803 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.71230 | −0.0769622 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −54.4817 | −2.44384 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.7733 | −0.527043 | −0.263522 | − | 0.964653i | \(-0.584884\pi\) | ||||
−0.263522 | + | 0.964653i | \(0.584884\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.8200 | −0.751464 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.6073 | 0.963421 | 0.481710 | − | 0.876330i | \(-0.340016\pi\) | ||||
0.481710 | + | 0.876330i | \(0.340016\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.59538 | −0.0709933 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 26.9214 | 1.19562 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.4087 | −1.34784 | −0.673921 | − | 0.738804i | \(-0.735391\pi\) | ||||
−0.673921 | + | 0.738804i | \(0.735391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 77.8555 | 3.44412 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.60580 | −0.247502 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.34402 | 0.147355 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.00756 | −0.132272 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.61478 | 0.114776 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.2167 | 1.10476 | 0.552381 | − | 0.833591i | \(-0.313719\pi\) | ||||
0.552381 | + | 0.833591i | \(0.313719\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.9677 | −1.22294 | −0.611472 | − | 0.791266i | \(-0.709422\pi\) | ||||
−0.611472 | + | 0.791266i | \(0.709422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −65.8628 | −2.87449 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.9176 | 0.736942 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8682 | −0.950792 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −73.0474 | −3.16999 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.26174 | 0.227911 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.11454 | −0.134653 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 53.5738 | 2.31188 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.7968 | 0.680416 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.8814 | 1.24171 | 0.620855 | − | 0.783926i | \(-0.286786\pi\) | ||||
0.620855 | + | 0.783926i | \(0.286786\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.7398 | −0.761289 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.97529 | −0.0846122 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.4332 | −0.702632 | −0.351316 | − | 0.936257i | \(-0.614266\pi\) | ||||
−0.351316 | + | 0.936257i | \(0.614266\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.16313 | 0.220357 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.31093 | −0.396659 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −63.7211 | −2.70970 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.44394 | −0.146187 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.814831 | 0.0345255 | 0.0172628 | − | 0.999851i | \(-0.494505\pi\) | ||||
0.0172628 | + | 0.999851i | \(0.494505\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.0834 | −0.637960 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.0908 | 0.679356 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.0662 | −1.01427 | −0.507134 | − | 0.861867i | \(-0.669295\pi\) | ||||
−0.507134 | + | 0.861867i | \(0.669295\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.923945 | −0.0388706 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.23910 | −0.178026 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.5082 | −0.901670 | −0.450835 | − | 0.892607i | \(-0.648874\pi\) | ||||
−0.450835 | + | 0.892607i | \(0.648874\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.6812 | −0.614388 | −0.307194 | − | 0.951647i | \(-0.599390\pi\) | ||||
−0.307194 | + | 0.951647i | \(0.599390\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −51.5027 | −2.15156 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.19369 | −0.216592 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.0271 | −0.917001 | −0.458501 | − | 0.888694i | \(-0.651613\pi\) | ||||
−0.458501 | + | 0.888694i | \(0.651613\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.5916 | 0.647963 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.2690 | −0.674954 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.33830 | −0.179674 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.19070 | −0.131919 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.9648 | −1.15423 | −0.577116 | − | 0.816663i | \(-0.695822\pi\) | ||||
−0.577116 | + | 0.816663i | \(0.695822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.97077 | −0.122408 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −69.4805 | −2.85804 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.4726 | −0.594317 | −0.297159 | − | 0.954828i | \(-0.596039\pi\) | ||||
−0.297159 | + | 0.954828i | \(0.596039\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.34144 | −0.382962 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −48.4377 | −1.98242 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.7403 | −0.520554 | −0.260277 | − | 0.965534i | \(-0.583814\pi\) | ||||
−0.260277 | + | 0.965534i | \(0.583814\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.00889305 | −0.000362755 0 | −0.000181378 | − | 1.00000i | \(-0.500058\pi\) | ||||
−0.000181378 | 1.00000i | \(0.500058\pi\) | ||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −39.5281 | −1.60971 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.343563 | −0.0139678 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0651 | −0.408530 | −0.204265 | − | 0.978916i | \(-0.565480\pi\) | ||||
−0.204265 | + | 0.978916i | \(0.565480\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −125.614 | −5.09014 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.60430 | −0.226726 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.0238 | −0.687584 | −0.343792 | − | 0.939046i | \(-0.611712\pi\) | ||||
−0.343792 | + | 0.939046i | \(0.611712\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.74118 | 0.110535 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.2503 | −1.58016 | −0.790078 | − | 0.613006i | \(-0.789960\pi\) | ||||
−0.790078 | + | 0.613006i | \(0.789960\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 49.2905 | 1.98115 | 0.990577 | − | 0.136960i | \(-0.0437331\pi\) | ||||
0.990577 | + | 0.136960i | \(0.0437331\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.96374 | −0.239317 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.268771 | −0.0107681 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.2434 | 0.929736 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.82559 | −0.112843 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.2027 | 0.805535 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.9741 | 1.31268 | 0.656340 | − | 0.754465i | \(-0.272104\pi\) | ||||
0.656340 | + | 0.754465i | \(0.272104\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.5905 | 0.460681 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.52633 | −0.179622 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.4358 | 1.16629 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 56.8704 | 2.24976 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.23839 | −0.206904 | −0.103452 | − | 0.994634i | \(-0.532989\pi\) | ||||
−0.103452 | + | 0.994634i | \(0.532989\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.3440 | −0.486799 | −0.243400 | − | 0.969926i | \(-0.578263\pi\) | ||||
−0.243400 | + | 0.969926i | \(0.578263\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.85793 | −0.309406 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.0492 | 1.22067 | 0.610334 | − | 0.792144i | \(-0.291035\pi\) | ||||
0.610334 | + | 0.792144i | \(0.291035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.6566 | −0.575320 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −40.0788 | −1.57081 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.2141 | −0.947570 | −0.473785 | − | 0.880640i | \(-0.657113\pi\) | ||||
−0.473785 | + | 0.880640i | \(0.657113\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.75650 | 0.263998 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −81.2691 | −3.17061 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.4592 | −1.42025 | −0.710124 | − | 0.704076i | \(-0.751361\pi\) | ||||
−0.710124 | + | 0.704076i | \(0.751361\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.0828 | 1.83131 | 0.915655 | − | 0.401965i | \(-0.131673\pi\) | ||||
0.915655 | + | 0.401965i | \(0.131673\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 29.9837 | 1.16447 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.64038 | 0.0636111 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.90545 | −0.383541 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 74.1801 | 2.86797 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.03595 | 0.0399925 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.4857 | 1.29078 | 0.645390 | − | 0.763853i | \(-0.276695\pi\) | ||||
0.645390 | + | 0.763853i | \(0.276695\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 27.3673 | 1.05337 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.8223 | −1.53050 | −0.765249 | − | 0.643735i | \(-0.777384\pi\) | ||||
−0.765249 | + | 0.643735i | \(0.777384\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −54.8018 | −2.10310 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.18336 | −0.275267 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.36966 | −0.0524085 | −0.0262043 | − | 0.999657i | \(-0.508342\pi\) | ||||
−0.0262043 | + | 0.999657i | \(0.508342\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.09529 | −0.118265 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.4546 | 0.780390 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.08400 | −0.307976 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.5333 | −1.12350 | −0.561751 | − | 0.827307i | \(-0.689872\pi\) | ||||
−0.561751 | + | 0.827307i | \(0.689872\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −23.7963 | −0.903947 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.83496 | −0.259265 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.0802 | −0.609082 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −69.7376 | −2.63772 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.5434 | 1.53130 | 0.765651 | − | 0.643256i | \(-0.222417\pi\) | ||||
0.765651 | + | 0.643256i | \(0.222417\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.54764 | −0.133802 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.91964 | −0.109960 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.1714 | −0.833841 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.1180 | 0.379991 | 0.189995 | − | 0.981785i | \(-0.439153\pi\) | ||||
0.189995 | + | 0.981785i | \(0.439153\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 66.5150 | 2.49451 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.16046 | −0.118360 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.640197 | −0.0239420 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −63.0473 | −2.35455 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5326 | 0.392799 | 0.196400 | − | 0.980524i | \(-0.437075\pi\) | ||||
0.196400 | + | 0.980524i | \(0.437075\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.4728 | 1.73074 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.6838 | −0.955191 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 45.4556 | 1.68818 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.8599 | 0.476947 | 0.238474 | − | 0.971149i | \(-0.423353\pi\) | ||||
0.238474 | + | 0.971149i | \(0.423353\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.0940 | −1.59608 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.0959 | 1.70492 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.3272 | −0.492252 | −0.246126 | − | 0.969238i | \(-0.579158\pi\) | ||||
−0.246126 | + | 0.969238i | \(0.579158\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15.3350 | 0.565641 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.93109 | −0.292145 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.7362 | 0.726009 | 0.363004 | − | 0.931787i | \(-0.381751\pi\) | ||||
0.363004 | + | 0.931787i | \(0.381751\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.26521 | −0.193422 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.9311 | −0.401022 | −0.200511 | − | 0.979691i | \(-0.564260\pi\) | ||||
−0.200511 | + | 0.979691i | \(0.564260\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.47634 | 0.164000 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.9824 | 0.621352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −43.2837 | −1.58155 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.00491790 | 0.000179457 0 | 8.97284e−5 | − | 1.00000i | \(-0.499971\pi\) | ||||
8.97284e−5 | 1.00000i | \(0.499971\pi\) | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.98643 | −0.218158 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.597182 | −0.0217337 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.46494 | 0.125935 | 0.0629677 | − | 0.998016i | \(-0.479943\pi\) | ||||
0.0629677 | + | 0.998016i | \(0.479943\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.00601 | −0.109111 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.8298 | 0.392580 | 0.196290 | − | 0.980546i | \(-0.437111\pi\) | ||||
0.196290 | + | 0.980546i | \(0.437111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.4512 | −0.993800 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.75101 | 0.352549 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.3111 | −0.986146 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.55885 | −0.200457 | −0.100229 | − | 0.994964i | \(-0.531957\pi\) | ||||
−0.100229 | + | 0.994964i | \(0.531957\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.6550 | 0.491772 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.6807 | −0.743834 | −0.371917 | − | 0.928266i | \(-0.621299\pi\) | ||||
−0.371917 | + | 0.928266i | \(0.621299\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.5032 | 0.520970 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −47.8614 | −1.71702 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.82372 | 0.101170 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4107 | 0.408308 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 52.1952 | 1.86530 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.38950 | 0.0852851 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.09548 | −0.252926 | −0.126463 | − | 0.991971i | \(-0.540363\pi\) | ||||
−0.126463 | + | 0.991971i | \(0.540363\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30.4967 | 1.08571 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.8403 | −0.456549 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.93040 | 0.0685504 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.21149 | −0.149366 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.9429 | −0.777258 | −0.388629 | − | 0.921394i | \(-0.627051\pi\) | ||||
−0.388629 | + | 0.921394i | \(0.627051\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.1271 | 0.605914 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.280555 | 0.00991293 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.3062 | −0.575433 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.74512 | 0.0615074 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 45.4795 | 1.60095 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.89093 | 0.136798 | 0.0683990 | − | 0.997658i | \(-0.478211\pi\) | ||||
0.0683990 | + | 0.997658i | \(0.478211\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.09828 | 0.284369 | 0.142185 | − | 0.989840i | \(-0.454587\pi\) | ||||
0.142185 | + | 0.989840i | \(0.454587\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −62.8019 | −2.20256 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.05729 | 0.177149 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.09454 | −0.283192 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −44.3421 | −1.54944 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.0408 | −1.01353 | −0.506765 | − | 0.862084i | \(-0.669159\pi\) | ||||
−0.506765 | + | 0.862084i | \(0.669159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.6098 | 1.62471 | 0.812357 | − | 0.583160i | \(-0.198184\pi\) | ||||
0.812357 | + | 0.583160i | \(0.198184\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.7944 | 0.480260 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −55.5230 | −1.93072 | −0.965361 | − | 0.260917i | \(-0.915975\pi\) | ||||
−0.965361 | + | 0.260917i | \(0.915975\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.7515 | 0.581802 | 0.290901 | − | 0.956753i | \(-0.406045\pi\) | ||||
0.290901 | + | 0.956753i | \(0.406045\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.18558 | 0.110507 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −89.9578 | −3.11685 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.04515 | −0.0707754 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.6535 | 0.575630 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.4855 | −1.39771 | −0.698857 | − | 0.715261i | \(-0.746308\pi\) | ||||
−0.698857 | + | 0.715261i | \(0.746308\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.6934 | 1.98943 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.28044 | −0.147426 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.27338 | 0.112608 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.77460 | −0.164057 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.2448 | 0.557519 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.77417 | −0.129377 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.7573 | 1.77214 | 0.886068 | − | 0.463555i | \(-0.153426\pi\) | ||||
0.886068 | + | 0.463555i | \(0.153426\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.71230 | −0.0585594 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.8604 | −0.951693 | −0.475846 | − | 0.879528i | \(-0.657858\pi\) | ||||
−0.475846 | + | 0.879528i | \(0.657858\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.6139 | 1.76104 | 0.880521 | − | 0.474007i | \(-0.157193\pi\) | ||||
0.880521 | + | 0.474007i | \(0.157193\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 38.0950 | 1.29827 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.36733 | −0.0465444 | −0.0232722 | − | 0.999729i | \(-0.507408\pi\) | ||||
−0.0232722 | + | 0.999729i | \(0.507408\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.317931 | 0.0108100 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −43.5973 | −1.48064 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.3459 | 0.452727 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.7788 | −0.500761 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 57.2046 | 1.93608 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.2102 | −0.548003 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.25271 | −0.109836 | −0.0549181 | − | 0.998491i | \(-0.517490\pi\) | ||||
−0.0549181 | + | 0.998491i | \(0.517490\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.00461330 | 0.000155603 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.48028 | 0.319399 | 0.159699 | − | 0.987166i | \(-0.448948\pi\) | ||||
0.159699 | + | 0.987166i | \(0.448948\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.3488 | −1.12228 | −0.561138 | − | 0.827722i | \(-0.689636\pi\) | ||||
−0.561138 | + | 0.827722i | \(0.689636\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.2281 | −0.478273 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.2336 | −1.28376 | −0.641880 | − | 0.766805i | \(-0.721845\pi\) | ||||
−0.641880 | + | 0.766805i | \(0.721845\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −62.9036 | −2.10972 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.887845 | 0.0297439 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.00756 | −0.100644 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.51405 | 0.217741 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.60140 | −0.187025 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.6606 | 0.922533 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.7053 | 0.823052 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −109.204 | −3.63408 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.15699 | −0.0717007 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.9937 | 1.75963 | 0.879814 | − | 0.475318i | \(-0.157667\pi\) | ||||
0.879814 | + | 0.475318i | \(0.157667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.1435 | 0.767621 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.4793 | −0.380325 | −0.190162 | − | 0.981753i | \(-0.560901\pi\) | ||||
−0.190162 | + | 0.981753i | \(0.560901\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.40742 | 0.112769 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.00567 | 0.0332464 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 93.8969 | 3.10075 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.7962 | 1.67561 | 0.837806 | − | 0.545968i | \(-0.183838\pi\) | ||||
0.837806 | + | 0.545968i | \(0.183838\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −76.4781 | −2.52004 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.2628 | 0.699874 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.3195 | 0.569461 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −48.5104 | −1.59329 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.5521 | 0.838339 | 0.419169 | − | 0.907908i | \(-0.362321\pi\) | ||||
0.419169 | + | 0.907908i | \(0.362321\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.7968 | 0.517719 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 61.7221 | 2.02069 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.95649 | 0.0639839 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.0081 | −1.07833 | −0.539164 | − | 0.842201i | \(-0.681260\pi\) | ||||
−0.539164 | + | 0.842201i | \(0.681260\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.8371 | 0.418924 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.2690 | −0.334761 | −0.167380 | − | 0.985892i | \(-0.553531\pi\) | ||||
−0.167380 | + | 0.985892i | \(0.553531\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.00403 | 0.0978245 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.19562 | −0.299134 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.4610 | 0.762379 | 0.381190 | − | 0.924497i | \(-0.375514\pi\) | ||||
0.381190 | + | 0.924497i | \(0.375514\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.3850 | −0.986338 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.2264 | 0.753166 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.9755 | 1.26254 | 0.631271 | − | 0.775563i | \(-0.282534\pi\) | ||||
0.631271 | + | 0.775563i | \(0.282534\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.26222 | −0.202641 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 26.3088 | 0.850444 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43.0161 | −1.38906 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.1745 | −0.715308 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 45.1814 | 1.45595 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.89578 | 0.0610273 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.3942 | 1.65273 | 0.826363 | − | 0.563137i | \(-0.190406\pi\) | ||||
0.826363 | + | 0.563137i | \(0.190406\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.0908 | 0.516912 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.66223 | −0.149618 | −0.0748090 | − | 0.997198i | \(-0.523835\pi\) | ||||
−0.0748090 | + | 0.997198i | \(0.523835\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −94.9874 | −3.04515 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 25.7045 | 0.823204 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.7991 | −1.65720 | −0.828600 | − | 0.559841i | \(-0.810862\pi\) | ||||
−0.828600 | + | 0.559841i | \(0.810862\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.0562918 | 0.00179909 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.6548 | 0.914877 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.7747 | −1.65136 | −0.825678 | − | 0.564142i | \(-0.809207\pi\) | ||||
−0.825678 | + | 0.564142i | \(0.809207\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.44814 | −0.269180 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −40.5751 | −1.29152 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.61140 | −0.273826 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.2223 | 0.674148 | 0.337074 | − | 0.941478i | \(-0.390563\pi\) | ||||
0.337074 | + | 0.941478i | \(0.390563\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29.6857 | −0.942047 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.88955 | −0.186711 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.7325 | 1.63839 | 0.819193 | − | 0.573518i | \(-0.194422\pi\) | ||||
0.819193 | + | 0.573518i | \(0.194422\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19.8874 | 0.629209 |
(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 | 3344.2.a.w.1.2 | 6 | ||
4.3 | odd | 2 | 836.2.a.e.1.5 | ✓ | 6 | ||
12.11 | even | 2 | 7524.2.a.q.1.5 | 6 | |||
44.43 | even | 2 | 9196.2.a.n.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
836.2.a.e.1.5 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.w.1.2 | 6 | 1.1 | even | 1 | trivial | ||
7524.2.a.q.1.5 | 6 | 12.11 | even | 2 | |||
9196.2.a.n.1.5 | 6 | 44.43 | even | 2 |