Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(1,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.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: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.7459857.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 3x^{5} - 6x^{4} + 13x^{3} + 12x^{2} - 12x - 8 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.77773\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 729.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.12503 | −1.50262 | −0.751311 | − | 0.659948i | \(-0.770578\pi\) | ||||
−0.751311 | + | 0.659948i | \(0.770578\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.51575 | 1.25787 | ||||||||
\(5\) | −2.07094 | −0.926153 | −0.463076 | − | 0.886318i | \(-0.653254\pi\) | ||||
−0.463076 | + | 0.886318i | \(0.653254\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.84867 | 1.83263 | 0.916313 | − | 0.400463i | \(-0.131151\pi\) | ||||
0.916313 | + | 0.400463i | \(0.131151\pi\) | |||||||
\(8\) | −1.09598 | −0.387487 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.40081 | 1.39166 | ||||||||
\(11\) | 4.14949 | 1.25112 | 0.625559 | − | 0.780177i | \(-0.284871\pi\) | ||||
0.625559 | + | 0.780177i | \(0.284871\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.21602 | −0.337262 | −0.168631 | − | 0.985679i | \(-0.553935\pi\) | ||||
−0.168631 | + | 0.985679i | \(0.553935\pi\) | |||||||
\(14\) | −10.3036 | −2.75374 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.70251 | −0.675628 | ||||||||
\(17\) | 2.36364 | 0.573266 | 0.286633 | − | 0.958040i | \(-0.407464\pi\) | ||||
0.286633 | + | 0.958040i | \(0.407464\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.83801 | −0.421668 | −0.210834 | − | 0.977522i | \(-0.567618\pi\) | ||||
−0.210834 | + | 0.977522i | \(0.567618\pi\) | |||||||
\(20\) | −5.20996 | −1.16498 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.81778 | −1.87996 | ||||||||
\(23\) | −4.30357 | −0.897356 | −0.448678 | − | 0.893693i | \(-0.648105\pi\) | ||||
−0.448678 | + | 0.893693i | \(0.648105\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.711206 | −0.142241 | ||||||||
\(26\) | 2.58407 | 0.506777 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 12.1980 | 2.30521 | ||||||||
\(29\) | 2.98182 | 0.553710 | 0.276855 | − | 0.960912i | \(-0.410708\pi\) | ||||
0.276855 | + | 0.960912i | \(0.410708\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.47359 | 0.264664 | 0.132332 | − | 0.991205i | \(-0.457754\pi\) | ||||
0.132332 | + | 0.991205i | \(0.457754\pi\) | |||||||
\(32\) | 7.93487 | 1.40270 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.02280 | −0.861403 | ||||||||
\(35\) | −10.0413 | −1.69729 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.97108 | 1.47484 | 0.737418 | − | 0.675436i | \(-0.236045\pi\) | ||||
0.737418 | + | 0.675436i | \(0.236045\pi\) | |||||||
\(38\) | 3.90582 | 0.633607 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.26970 | 0.358872 | ||||||||
\(41\) | 2.26052 | 0.353035 | 0.176517 | − | 0.984298i | \(-0.443517\pi\) | ||||
0.176517 | + | 0.984298i | \(0.443517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.48486 | −0.836433 | −0.418216 | − | 0.908347i | \(-0.637345\pi\) | ||||
−0.418216 | + | 0.908347i | \(0.637345\pi\) | |||||||
\(44\) | 10.4391 | 1.57375 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.14521 | 1.34839 | ||||||||
\(47\) | 7.18313 | 1.04777 | 0.523884 | − | 0.851790i | \(-0.324483\pi\) | ||||
0.523884 | + | 0.851790i | \(0.324483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.5096 | 2.35852 | ||||||||
\(50\) | 1.51133 | 0.213735 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.05919 | −0.424233 | ||||||||
\(53\) | −6.32803 | −0.869222 | −0.434611 | − | 0.900618i | \(-0.643114\pi\) | ||||
−0.434611 | + | 0.900618i | \(0.643114\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.59334 | −1.15873 | ||||||||
\(56\) | −5.31404 | −0.710118 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.33645 | −0.832017 | ||||||||
\(59\) | 0.262257 | 0.0341429 | 0.0170715 | − | 0.999854i | \(-0.494566\pi\) | ||||
0.0170715 | + | 0.999854i | \(0.494566\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.45561 | −0.570482 | −0.285241 | − | 0.958456i | \(-0.592074\pi\) | ||||
−0.285241 | + | 0.958456i | \(0.592074\pi\) | |||||||
\(62\) | −3.13141 | −0.397690 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.4568 | −1.43210 | ||||||||
\(65\) | 2.51830 | 0.312356 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.13110 | 0.504695 | 0.252347 | − | 0.967637i | \(-0.418797\pi\) | ||||
0.252347 | + | 0.967637i | \(0.418797\pi\) | |||||||
\(68\) | 5.94632 | 0.721097 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 21.3381 | 2.55039 | ||||||||
\(71\) | 3.08551 | 0.366183 | 0.183091 | − | 0.983096i | \(-0.441390\pi\) | ||||
0.183091 | + | 0.983096i | \(0.441390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.7601 | 1.49345 | 0.746726 | − | 0.665132i | \(-0.231625\pi\) | ||||
0.746726 | + | 0.665132i | \(0.231625\pi\) | |||||||
\(74\) | −19.0638 | −2.21612 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.62396 | −0.530405 | ||||||||
\(77\) | 20.1195 | 2.29283 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.55241 | 0.512186 | 0.256093 | − | 0.966652i | \(-0.417565\pi\) | ||||
0.256093 | + | 0.966652i | \(0.417565\pi\) | |||||||
\(80\) | 5.59674 | 0.625734 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.80368 | −0.530478 | ||||||||
\(83\) | −8.45306 | −0.927844 | −0.463922 | − | 0.885876i | \(-0.653558\pi\) | ||||
−0.463922 | + | 0.885876i | \(0.653558\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.89495 | −0.530932 | ||||||||
\(86\) | 11.6555 | 1.25684 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.54775 | −0.484791 | ||||||||
\(89\) | 16.9632 | 1.79809 | 0.899046 | − | 0.437854i | \(-0.144261\pi\) | ||||
0.899046 | + | 0.437854i | \(0.144261\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.89606 | −0.618075 | ||||||||
\(92\) | −10.8267 | −1.12876 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −15.2644 | −1.57440 | ||||||||
\(95\) | 3.80640 | 0.390529 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.10977 | −0.518819 | −0.259409 | − | 0.965767i | \(-0.583528\pi\) | ||||
−0.259409 | + | 0.965767i | \(0.583528\pi\) | |||||||
\(98\) | −35.0834 | −3.54396 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.78921 | −0.178921 | ||||||||
\(101\) | 18.5799 | 1.84877 | 0.924384 | − | 0.381464i | \(-0.124580\pi\) | ||||
0.924384 | + | 0.381464i | \(0.124580\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.00577 | 0.887365 | 0.443682 | − | 0.896184i | \(-0.353672\pi\) | ||||
0.443682 | + | 0.896184i | \(0.353672\pi\) | |||||||
\(104\) | 1.33273 | 0.130684 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.4472 | 1.30611 | ||||||||
\(107\) | 7.42680 | 0.717976 | 0.358988 | − | 0.933342i | \(-0.383122\pi\) | ||||
0.358988 | + | 0.933342i | \(0.383122\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.62396 | −0.538678 | −0.269339 | − | 0.963045i | \(-0.586805\pi\) | ||||
−0.269339 | + | 0.963045i | \(0.586805\pi\) | |||||||
\(110\) | 18.2611 | 1.74113 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13.1036 | −1.23817 | ||||||||
\(113\) | −2.40267 | −0.226024 | −0.113012 | − | 0.993594i | \(-0.536050\pi\) | ||||
−0.113012 | + | 0.993594i | \(0.536050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.91243 | 0.831089 | ||||||||
\(116\) | 7.50150 | 0.696497 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.557303 | −0.0513039 | ||||||||
\(119\) | 11.4605 | 1.05058 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.21826 | 0.565296 | ||||||||
\(122\) | 9.46829 | 0.857219 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.70717 | 0.332914 | ||||||||
\(125\) | 11.8276 | 1.05789 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.23469 | −0.819447 | −0.409723 | − | 0.912210i | \(-0.634375\pi\) | ||||
−0.409723 | + | 0.912210i | \(0.634375\pi\) | |||||||
\(128\) | 8.47629 | 0.749206 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.35145 | −0.469353 | ||||||||
\(131\) | −15.3390 | −1.34018 | −0.670088 | − | 0.742282i | \(-0.733743\pi\) | ||||
−0.670088 | + | 0.742282i | \(0.733743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.91189 | −0.772759 | ||||||||
\(134\) | −8.77871 | −0.758365 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.59049 | −0.222133 | ||||||||
\(137\) | −3.64397 | −0.311325 | −0.155663 | − | 0.987810i | \(-0.549751\pi\) | ||||
−0.155663 | + | 0.987810i | \(0.549751\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.2755 | 1.12602 | 0.563008 | − | 0.826451i | \(-0.309644\pi\) | ||||
0.563008 | + | 0.826451i | \(0.309644\pi\) | |||||||
\(140\) | −25.2614 | −2.13498 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.55680 | −0.550234 | ||||||||
\(143\) | −5.04584 | −0.421954 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.17517 | −0.512820 | ||||||||
\(146\) | −27.1155 | −2.24409 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 22.5690 | 1.85516 | ||||||||
\(149\) | 8.91098 | 0.730016 | 0.365008 | − | 0.931004i | \(-0.381066\pi\) | ||||
0.365008 | + | 0.931004i | \(0.381066\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.712404 | −0.0579746 | −0.0289873 | − | 0.999580i | \(-0.509228\pi\) | ||||
−0.0289873 | + | 0.999580i | \(0.509228\pi\) | |||||||
\(152\) | 2.01441 | 0.163391 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −42.7545 | −3.44526 | ||||||||
\(155\) | −3.05171 | −0.245119 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.8181 | −1.10280 | −0.551400 | − | 0.834241i | \(-0.685906\pi\) | ||||
−0.551400 | + | 0.834241i | \(0.685906\pi\) | |||||||
\(158\) | −9.67399 | −0.769622 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.4326 | −1.29911 | ||||||||
\(161\) | −20.8666 | −1.64452 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.19321 | −0.0934597 | −0.0467298 | − | 0.998908i | \(-0.514880\pi\) | ||||
−0.0467298 | + | 0.998908i | \(0.514880\pi\) | |||||||
\(164\) | 5.68691 | 0.444073 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.9630 | 1.39420 | ||||||||
\(167\) | −23.9363 | −1.85225 | −0.926124 | − | 0.377219i | \(-0.876880\pi\) | ||||
−0.926124 | + | 0.377219i | \(0.876880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5213 | −0.886254 | ||||||||
\(170\) | 10.4019 | 0.797791 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.7985 | −1.05213 | ||||||||
\(173\) | −9.14000 | −0.694902 | −0.347451 | − | 0.937698i | \(-0.612953\pi\) | ||||
−0.347451 | + | 0.937698i | \(0.612953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.44841 | −0.260675 | ||||||||
\(176\) | −11.2140 | −0.845290 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −36.0472 | −2.70185 | ||||||||
\(179\) | 10.6008 | 0.792337 | 0.396169 | − | 0.918178i | \(-0.370340\pi\) | ||||
0.396169 | + | 0.918178i | \(0.370340\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.46292 | −0.108738 | −0.0543690 | − | 0.998521i | \(-0.517315\pi\) | ||||
−0.0543690 | + | 0.998521i | \(0.517315\pi\) | |||||||
\(182\) | 12.5293 | 0.928733 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.71661 | 0.347713 | ||||||||
\(185\) | −18.5786 | −1.36592 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.80789 | 0.717224 | ||||||||
\(188\) | 18.0709 | 1.31796 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.08871 | −0.586817 | ||||||||
\(191\) | 12.4223 | 0.898844 | 0.449422 | − | 0.893320i | \(-0.351630\pi\) | ||||
0.449422 | + | 0.893320i | \(0.351630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.7733 | 1.49529 | 0.747647 | − | 0.664096i | \(-0.231183\pi\) | ||||
0.747647 | + | 0.664096i | \(0.231183\pi\) | |||||||
\(194\) | 10.8584 | 0.779588 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 41.5340 | 2.96672 | ||||||||
\(197\) | −14.1887 | −1.01090 | −0.505450 | − | 0.862856i | \(-0.668674\pi\) | ||||
−0.505450 | + | 0.862856i | \(0.668674\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.3286 | 1.44106 | 0.720529 | − | 0.693424i | \(-0.243899\pi\) | ||||
0.720529 | + | 0.693424i | \(0.243899\pi\) | |||||||
\(200\) | 0.779466 | 0.0551165 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −39.4828 | −2.77800 | ||||||||
\(203\) | 14.4579 | 1.01474 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.68141 | −0.326964 | ||||||||
\(206\) | −19.1375 | −1.33337 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.28629 | 0.227864 | ||||||||
\(209\) | −7.62679 | −0.527556 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.86332 | −0.679019 | −0.339509 | − | 0.940603i | \(-0.610261\pi\) | ||||
−0.339509 | + | 0.940603i | \(0.610261\pi\) | |||||||
\(212\) | −15.9197 | −1.09337 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.7822 | −1.07885 | ||||||||
\(215\) | 11.3588 | 0.774665 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.14494 | 0.485030 | ||||||||
\(218\) | 11.9511 | 0.809429 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −21.6187 | −1.45753 | ||||||||
\(221\) | −2.87422 | −0.193341 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.0714 | 1.00925 | 0.504627 | − | 0.863337i | \(-0.331630\pi\) | ||||
0.504627 | + | 0.863337i | \(0.331630\pi\) | |||||||
\(224\) | 38.4736 | 2.57062 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.10574 | 0.339629 | ||||||||
\(227\) | −22.6926 | −1.50616 | −0.753079 | − | 0.657930i | \(-0.771432\pi\) | ||||
−0.753079 | + | 0.657930i | \(0.771432\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.71670 | 0.576016 | 0.288008 | − | 0.957628i | \(-0.407007\pi\) | ||||
0.288008 | + | 0.957628i | \(0.407007\pi\) | |||||||
\(230\) | −18.9392 | −1.24881 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.26801 | −0.214555 | ||||||||
\(233\) | −23.5890 | −1.54536 | −0.772682 | − | 0.634793i | \(-0.781085\pi\) | ||||
−0.772682 | + | 0.634793i | \(0.781085\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.8758 | −0.970393 | ||||||||
\(236\) | 0.659772 | 0.0429475 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −24.3539 | −1.57863 | ||||||||
\(239\) | 9.95452 | 0.643904 | 0.321952 | − | 0.946756i | \(-0.395661\pi\) | ||||
0.321952 | + | 0.946756i | \(0.395661\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.71345 | 0.368036 | 0.184018 | − | 0.982923i | \(-0.441090\pi\) | ||||
0.184018 | + | 0.982923i | \(0.441090\pi\) | |||||||
\(242\) | −13.2140 | −0.849427 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.2092 | −0.717594 | ||||||||
\(245\) | −34.1905 | −2.18435 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.23504 | 0.142212 | ||||||||
\(248\) | −1.61502 | −0.102554 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −25.1339 | −1.58961 | ||||||||
\(251\) | −7.28966 | −0.460120 | −0.230060 | − | 0.973176i | \(-0.573892\pi\) | ||||
−0.230060 | + | 0.973176i | \(0.573892\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.8576 | −1.12270 | ||||||||
\(254\) | 19.6240 | 1.23132 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.90123 | 0.306327 | ||||||||
\(257\) | −23.2431 | −1.44986 | −0.724932 | − | 0.688821i | \(-0.758129\pi\) | ||||
−0.724932 | + | 0.688821i | \(0.758129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 43.4978 | 2.70282 | ||||||||
\(260\) | 6.33539 | 0.392904 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 32.5958 | 2.01378 | ||||||||
\(263\) | −27.3996 | −1.68953 | −0.844766 | − | 0.535136i | \(-0.820260\pi\) | ||||
−0.844766 | + | 0.535136i | \(0.820260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.1050 | 0.805032 | ||||||||
\(266\) | 18.9380 | 1.16116 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.3928 | 0.634842 | ||||||||
\(269\) | 9.41973 | 0.574331 | 0.287166 | − | 0.957881i | \(-0.407287\pi\) | ||||
0.287166 | + | 0.957881i | \(0.407287\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.2797 | 1.59638 | 0.798189 | − | 0.602408i | \(-0.205792\pi\) | ||||
0.798189 | + | 0.602408i | \(0.205792\pi\) | |||||||
\(272\) | −6.38776 | −0.387315 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.74354 | 0.467804 | ||||||||
\(275\) | −2.95114 | −0.177961 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.374812 | 0.0225203 | 0.0112601 | − | 0.999937i | \(-0.496416\pi\) | ||||
0.0112601 | + | 0.999937i | \(0.496416\pi\) | |||||||
\(278\) | −28.2109 | −1.69198 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.0051 | 0.657678 | ||||||||
\(281\) | 13.9816 | 0.834071 | 0.417036 | − | 0.908890i | \(-0.363069\pi\) | ||||
0.417036 | + | 0.908890i | \(0.363069\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5619 | 0.925058 | 0.462529 | − | 0.886604i | \(-0.346942\pi\) | ||||
0.462529 | + | 0.886604i | \(0.346942\pi\) | |||||||
\(284\) | 7.76236 | 0.460612 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.7226 | 0.634038 | ||||||||
\(287\) | 10.9605 | 0.646980 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.4132 | −0.671366 | ||||||||
\(290\) | 13.1224 | 0.770575 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 32.1011 | 1.87857 | ||||||||
\(293\) | 24.6242 | 1.43856 | 0.719281 | − | 0.694719i | \(-0.244471\pi\) | ||||
0.719281 | + | 0.694719i | \(0.244471\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.543118 | −0.0316216 | ||||||||
\(296\) | −9.83210 | −0.571479 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.9361 | −1.09694 | ||||||||
\(299\) | 5.23321 | 0.302644 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.5943 | −1.53287 | ||||||||
\(302\) | 1.51388 | 0.0871139 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.96723 | 0.284890 | ||||||||
\(305\) | 9.22729 | 0.528353 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.3912 | −1.16379 | −0.581893 | − | 0.813265i | \(-0.697688\pi\) | ||||
−0.581893 | + | 0.813265i | \(0.697688\pi\) | |||||||
\(308\) | 50.6156 | 2.88409 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.48497 | 0.368322 | ||||||||
\(311\) | 22.1790 | 1.25766 | 0.628828 | − | 0.777544i | \(-0.283535\pi\) | ||||
0.628828 | + | 0.777544i | \(0.283535\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.1720 | −0.631481 | −0.315740 | − | 0.948846i | \(-0.602253\pi\) | ||||
−0.315740 | + | 0.948846i | \(0.602253\pi\) | |||||||
\(314\) | 29.3638 | 1.65709 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.4527 | 0.644265 | ||||||||
\(317\) | 25.2167 | 1.41631 | 0.708154 | − | 0.706058i | \(-0.249528\pi\) | ||||
0.708154 | + | 0.706058i | \(0.249528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.3730 | 0.692757 | ||||||||
\(320\) | 23.7264 | 1.32634 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 44.3421 | 2.47109 | ||||||||
\(323\) | −4.34438 | −0.241728 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.864837 | 0.0479725 | ||||||||
\(326\) | 2.53561 | 0.140435 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.47748 | −0.136796 | ||||||||
\(329\) | 34.8287 | 1.92017 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.1657 | −1.43820 | −0.719098 | − | 0.694908i | \(-0.755445\pi\) | ||||
−0.719098 | + | 0.694908i | \(0.755445\pi\) | |||||||
\(332\) | −21.2658 | −1.16711 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 50.8654 | 2.78323 | ||||||||
\(335\) | −8.55527 | −0.467424 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.9460 | 0.596269 | 0.298135 | − | 0.954524i | \(-0.403636\pi\) | ||||
0.298135 | + | 0.954524i | \(0.403636\pi\) | |||||||
\(338\) | 24.4831 | 1.33171 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.3145 | −0.667846 | ||||||||
\(341\) | 6.11463 | 0.331126 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 46.1091 | 2.48966 | ||||||||
\(344\) | 6.01128 | 0.324106 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.4228 | 1.04417 | ||||||||
\(347\) | 3.51338 | 0.188608 | 0.0943040 | − | 0.995543i | \(-0.469937\pi\) | ||||
0.0943040 | + | 0.995543i | \(0.469937\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.1968 | −1.56287 | −0.781436 | − | 0.623986i | \(-0.785512\pi\) | ||||
−0.781436 | + | 0.623986i | \(0.785512\pi\) | |||||||
\(350\) | 7.32796 | 0.391696 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 32.9256 | 1.75494 | ||||||||
\(353\) | −25.0768 | −1.33470 | −0.667352 | − | 0.744742i | \(-0.732572\pi\) | ||||
−0.667352 | + | 0.744742i | \(0.732572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.38991 | −0.339141 | ||||||||
\(356\) | 42.6750 | 2.26177 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.5269 | −1.19058 | ||||||||
\(359\) | 4.20724 | 0.222050 | 0.111025 | − | 0.993818i | \(-0.464587\pi\) | ||||
0.111025 | + | 0.993818i | \(0.464587\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6217 | −0.822196 | ||||||||
\(362\) | 3.10875 | 0.163392 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.8330 | −0.777460 | ||||||||
\(365\) | −26.4253 | −1.38316 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.4966 | 0.913317 | 0.456658 | − | 0.889642i | \(-0.349046\pi\) | ||||
0.456658 | + | 0.889642i | \(0.349046\pi\) | |||||||
\(368\) | 11.6304 | 0.606279 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 39.4800 | 2.05247 | ||||||||
\(371\) | −30.6825 | −1.59296 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.6546 | −1.53546 | −0.767728 | − | 0.640776i | \(-0.778613\pi\) | ||||
−0.767728 | + | 0.640776i | \(0.778613\pi\) | |||||||
\(374\) | −20.8420 | −1.07772 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.87255 | −0.405996 | ||||||||
\(377\) | −3.62594 | −0.186745 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.9523 | 1.07625 | 0.538124 | − | 0.842865i | \(-0.319133\pi\) | ||||
0.538124 | + | 0.842865i | \(0.319133\pi\) | |||||||
\(380\) | 9.57594 | 0.491236 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −26.3977 | −1.35062 | ||||||||
\(383\) | 9.89678 | 0.505702 | 0.252851 | − | 0.967505i | \(-0.418632\pi\) | ||||
0.252851 | + | 0.967505i | \(0.418632\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −41.6663 | −2.12351 | ||||||||
\(386\) | −44.1439 | −2.24686 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.8549 | −0.652608 | ||||||||
\(389\) | −21.1148 | −1.07056 | −0.535281 | − | 0.844674i | \(-0.679794\pi\) | ||||
−0.535281 | + | 0.844674i | \(0.679794\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.1721 | −0.514424 | ||||||||
\(392\) | −18.0942 | −0.913894 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 30.1513 | 1.51900 | ||||||||
\(395\) | −9.42776 | −0.474362 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.77909 | −0.490799 | −0.245399 | − | 0.969422i | \(-0.578919\pi\) | ||||
−0.245399 | + | 0.969422i | \(0.578919\pi\) | |||||||
\(398\) | −43.1989 | −2.16537 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.92204 | 0.0961021 | ||||||||
\(401\) | −19.1393 | −0.955773 | −0.477886 | − | 0.878422i | \(-0.658597\pi\) | ||||
−0.477886 | + | 0.878422i | \(0.658597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.79190 | −0.0892611 | ||||||||
\(404\) | 46.7423 | 2.32552 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −30.7234 | −1.52478 | ||||||||
\(407\) | 37.2254 | 1.84519 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9956 | 0.741483 | 0.370741 | − | 0.928736i | \(-0.379104\pi\) | ||||
0.370741 | + | 0.928736i | \(0.379104\pi\) | |||||||
\(410\) | 9.94813 | 0.491303 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 22.6562 | 1.11619 | ||||||||
\(413\) | 1.27160 | 0.0625712 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.5058 | 0.859325 | ||||||||
\(416\) | −9.64892 | −0.473077 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.2071 | 0.792717 | ||||||||
\(419\) | 5.81180 | 0.283925 | 0.141963 | − | 0.989872i | \(-0.454659\pi\) | ||||
0.141963 | + | 0.989872i | \(0.454659\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.3135 | −0.648861 | −0.324431 | − | 0.945910i | \(-0.605173\pi\) | ||||
−0.324431 | + | 0.945910i | \(0.605173\pi\) | |||||||
\(422\) | 20.9598 | 1.02031 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.93538 | 0.336812 | ||||||||
\(425\) | −1.68103 | −0.0815421 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.6038 | −1.04548 | ||||||||
\(428\) | 18.6840 | 0.903123 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.1378 | −1.16403 | ||||||||
\(431\) | −36.4166 | −1.75413 | −0.877064 | − | 0.480374i | \(-0.840501\pi\) | ||||
−0.877064 | + | 0.480374i | \(0.840501\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.8761 | −0.522674 | −0.261337 | − | 0.965248i | \(-0.584163\pi\) | ||||
−0.261337 | + | 0.965248i | \(0.584163\pi\) | |||||||
\(434\) | −15.1832 | −0.728817 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.1485 | −0.677589 | ||||||||
\(437\) | 7.90999 | 0.378386 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.45326 | 0.451180 | 0.225590 | − | 0.974222i | \(-0.427569\pi\) | ||||
0.225590 | + | 0.974222i | \(0.427569\pi\) | |||||||
\(440\) | 9.41811 | 0.448991 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.10780 | 0.290518 | ||||||||
\(443\) | 16.5239 | 0.785075 | 0.392537 | − | 0.919736i | \(-0.371597\pi\) | ||||
0.392537 | + | 0.919736i | \(0.371597\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −35.1297 | −1.66531 | ||||||||
\(446\) | −32.0271 | −1.51653 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −55.5503 | −2.62450 | ||||||||
\(449\) | −4.74362 | −0.223865 | −0.111933 | − | 0.993716i | \(-0.535704\pi\) | ||||
−0.111933 | + | 0.993716i | \(0.535704\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.38002 | 0.441688 | ||||||||
\(452\) | −6.04451 | −0.284310 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 48.2223 | 2.26319 | ||||||||
\(455\) | 12.2104 | 0.572432 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.4085 | −1.04823 | −0.524114 | − | 0.851648i | \(-0.675603\pi\) | ||||
−0.524114 | + | 0.851648i | \(0.675603\pi\) | |||||||
\(458\) | −18.5232 | −0.865534 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 22.4214 | 1.04540 | ||||||||
\(461\) | −14.9223 | −0.694999 | −0.347499 | − | 0.937680i | \(-0.612969\pi\) | ||||
−0.347499 | + | 0.937680i | \(0.612969\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.8472 | −0.690007 | −0.345003 | − | 0.938601i | \(-0.612122\pi\) | ||||
−0.345003 | + | 0.938601i | \(0.612122\pi\) | |||||||
\(464\) | −8.05840 | −0.374102 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 50.1272 | 2.32210 | ||||||||
\(467\) | −15.3514 | −0.710379 | −0.355190 | − | 0.934794i | \(-0.615584\pi\) | ||||
−0.355190 | + | 0.934794i | \(0.615584\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0304 | 0.924917 | ||||||||
\(470\) | 31.6116 | 1.45813 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.287427 | −0.0132299 | ||||||||
\(473\) | −22.7594 | −1.04648 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.30720 | 0.0599785 | ||||||||
\(476\) | 28.8317 | 1.32150 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −21.1536 | −0.967545 | ||||||||
\(479\) | 10.4486 | 0.477409 | 0.238705 | − | 0.971092i | \(-0.423277\pi\) | ||||
0.238705 | + | 0.971092i | \(0.423277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.9090 | −0.497406 | ||||||||
\(482\) | −12.1412 | −0.553018 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.6436 | 0.711071 | ||||||||
\(485\) | 10.5820 | 0.480505 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.1649 | −0.732500 | −0.366250 | − | 0.930516i | \(-0.619359\pi\) | ||||
−0.366250 | + | 0.930516i | \(0.619359\pi\) | |||||||
\(488\) | 4.88324 | 0.221054 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 72.6557 | 3.28225 | ||||||||
\(491\) | −10.7773 | −0.486375 | −0.243187 | − | 0.969979i | \(-0.578193\pi\) | ||||
−0.243187 | + | 0.969979i | \(0.578193\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.04794 | 0.317423 | ||||||||
\(494\) | −4.74953 | −0.213692 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.98238 | −0.178814 | ||||||||
\(497\) | 14.9606 | 0.671076 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.1872 | −0.858936 | −0.429468 | − | 0.903082i | \(-0.641299\pi\) | ||||
−0.429468 | + | 0.903082i | \(0.641299\pi\) | |||||||
\(500\) | 29.7552 | 1.33069 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.4907 | 0.691386 | ||||||||
\(503\) | −12.0251 | −0.536171 | −0.268086 | − | 0.963395i | \(-0.586391\pi\) | ||||
−0.268086 | + | 0.963395i | \(0.586391\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.4778 | −1.71224 | ||||||||
\(506\) | 37.9479 | 1.68699 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.2322 | −1.03076 | ||||||||
\(509\) | −14.9530 | −0.662781 | −0.331391 | − | 0.943494i | \(-0.607518\pi\) | ||||
−0.331391 | + | 0.943494i | \(0.607518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 61.8694 | 2.73694 | ||||||||
\(512\) | −27.3678 | −1.20950 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 49.3922 | 2.17860 | ||||||||
\(515\) | −18.6504 | −0.821835 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.8063 | 1.31088 | ||||||||
\(518\) | −92.4342 | −4.06132 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.75999 | −0.121034 | ||||||||
\(521\) | 37.4188 | 1.63935 | 0.819673 | − | 0.572832i | \(-0.194155\pi\) | ||||
0.819673 | + | 0.572832i | \(0.194155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.44979 | −0.369483 | −0.184742 | − | 0.982787i | \(-0.559145\pi\) | ||||
−0.184742 | + | 0.982787i | \(0.559145\pi\) | |||||||
\(524\) | −38.5891 | −1.68577 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 58.2250 | 2.53873 | ||||||||
\(527\) | 3.48303 | 0.151723 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.47929 | −0.194752 | ||||||||
\(530\) | −27.8484 | −1.20966 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −22.4201 | −0.972033 | ||||||||
\(533\) | −2.74883 | −0.119065 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.3805 | −0.664956 | ||||||||
\(536\) | −4.52760 | −0.195562 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.0172 | −0.863003 | ||||||||
\(539\) | 68.5065 | 2.95078 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.6259 | 0.542828 | 0.271414 | − | 0.962463i | \(-0.412509\pi\) | ||||
0.271414 | + | 0.962463i | \(0.412509\pi\) | |||||||
\(542\) | −55.8451 | −2.39875 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.7552 | 0.804121 | ||||||||
\(545\) | 11.6469 | 0.498898 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.3951 | 1.34236 | 0.671178 | − | 0.741296i | \(-0.265789\pi\) | ||||
0.671178 | + | 0.741296i | \(0.265789\pi\) | |||||||
\(548\) | −9.16731 | −0.391608 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.27126 | 0.267407 | ||||||||
\(551\) | −5.48060 | −0.233482 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.0731 | 0.938645 | ||||||||
\(554\) | −0.796486 | −0.0338394 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 33.3979 | 1.41639 | ||||||||
\(557\) | −15.9303 | −0.674988 | −0.337494 | − | 0.941328i | \(-0.609579\pi\) | ||||
−0.337494 | + | 0.941328i | \(0.609579\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.66967 | 0.282097 | ||||||||
\(560\) | 27.1368 | 1.14674 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −29.7113 | −1.25329 | ||||||||
\(563\) | −24.8609 | −1.04776 | −0.523880 | − | 0.851792i | \(-0.675516\pi\) | ||||
−0.523880 | + | 0.851792i | \(0.675516\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.97578 | 0.209333 | ||||||||
\(566\) | −33.0695 | −1.39001 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.38165 | −0.141891 | ||||||||
\(569\) | 19.1900 | 0.804487 | 0.402243 | − | 0.915533i | \(-0.368231\pi\) | ||||
0.402243 | + | 0.915533i | \(0.368231\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.3792 | −0.852844 | −0.426422 | − | 0.904524i | \(-0.640226\pi\) | ||||
−0.426422 | + | 0.904524i | \(0.640226\pi\) | |||||||
\(572\) | −12.6941 | −0.530765 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −23.2915 | −0.972167 | ||||||||
\(575\) | 3.06072 | 0.127641 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.2991 | 0.969953 | 0.484976 | − | 0.874527i | \(-0.338828\pi\) | ||||
0.484976 | + | 0.874527i | \(0.338828\pi\) | |||||||
\(578\) | 24.2534 | 1.00881 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15.5352 | −0.645063 | ||||||||
\(581\) | −40.9861 | −1.70039 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.2581 | −1.08750 | ||||||||
\(584\) | −13.9847 | −0.578693 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −52.3272 | −2.16162 | ||||||||
\(587\) | −36.9093 | −1.52341 | −0.761704 | − | 0.647925i | \(-0.775637\pi\) | ||||
−0.761704 | + | 0.647925i | \(0.775637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.70846 | −0.111600 | ||||||||
\(590\) | 1.15414 | 0.0475153 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.2444 | −0.996440 | ||||||||
\(593\) | 4.36830 | 0.179385 | 0.0896923 | − | 0.995970i | \(-0.471412\pi\) | ||||
0.0896923 | + | 0.995970i | \(0.471412\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.7340 | −0.973000 | ||||||||
\(596\) | 22.4178 | 0.918268 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.1207 | −0.454760 | ||||||||
\(599\) | −31.2056 | −1.27503 | −0.637513 | − | 0.770439i | \(-0.720037\pi\) | ||||
−0.637513 | + | 0.770439i | \(0.720037\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.9371 | 1.79223 | 0.896116 | − | 0.443820i | \(-0.146377\pi\) | ||||
0.896116 | + | 0.443820i | \(0.146377\pi\) | |||||||
\(602\) | 56.5136 | 2.30332 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.79223 | −0.0729247 | ||||||||
\(605\) | −12.8776 | −0.523551 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3587 | 0.704566 | 0.352283 | − | 0.935894i | \(-0.385405\pi\) | ||||
0.352283 | + | 0.935894i | \(0.385405\pi\) | |||||||
\(608\) | −14.5843 | −0.591473 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.6083 | −0.793915 | ||||||||
\(611\) | −8.73480 | −0.353372 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.19805 | −0.0483887 | −0.0241944 | − | 0.999707i | \(-0.507702\pi\) | ||||
−0.0241944 | + | 0.999707i | \(0.507702\pi\) | |||||||
\(614\) | 43.3318 | 1.74873 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.0505 | −0.888441 | ||||||||
\(617\) | 26.0137 | 1.04727 | 0.523636 | − | 0.851942i | \(-0.324575\pi\) | ||||
0.523636 | + | 0.851942i | \(0.324575\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.63135 | 0.387117 | 0.193558 | − | 0.981089i | \(-0.437997\pi\) | ||||
0.193558 | + | 0.981089i | \(0.437997\pi\) | |||||||
\(620\) | −7.67733 | −0.308329 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −47.1311 | −1.88978 | ||||||||
\(623\) | 82.2488 | 3.29523 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.9382 | −0.837526 | ||||||||
\(626\) | 23.7409 | 0.948877 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −34.7627 | −1.38718 | ||||||||
\(629\) | 21.2044 | 0.845474 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.1673 | −0.563992 | −0.281996 | − | 0.959416i | \(-0.590997\pi\) | ||||
−0.281996 | + | 0.959416i | \(0.590997\pi\) | |||||||
\(632\) | −4.98933 | −0.198465 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −53.5861 | −2.12818 | ||||||||
\(635\) | 19.1245 | 0.758933 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.0760 | −0.795438 | ||||||||
\(638\) | −26.2930 | −1.04095 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −17.5539 | −0.693879 | ||||||||
\(641\) | 22.2009 | 0.876883 | 0.438442 | − | 0.898760i | \(-0.355531\pi\) | ||||
0.438442 | + | 0.898760i | \(0.355531\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.5368 | 0.849328 | 0.424664 | − | 0.905351i | \(-0.360392\pi\) | ||||
0.424664 | + | 0.905351i | \(0.360392\pi\) | |||||||
\(644\) | −52.4951 | −2.06860 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.23194 | 0.363226 | ||||||||
\(647\) | 13.4037 | 0.526952 | 0.263476 | − | 0.964666i | \(-0.415131\pi\) | ||||
0.263476 | + | 0.964666i | \(0.415131\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.08823 | 0.0427168 | ||||||||
\(650\) | −1.83780 | −0.0720846 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.00182 | −0.117560 | ||||||||
\(653\) | −18.9109 | −0.740039 | −0.370020 | − | 0.929024i | \(-0.620649\pi\) | ||||
−0.370020 | + | 0.929024i | \(0.620649\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.7662 | 1.24121 | ||||||||
\(656\) | −6.10909 | −0.238520 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −74.0119 | −2.88528 | ||||||||
\(659\) | −0.0281814 | −0.00109779 | −0.000548897 | − | 1.00000i | \(-0.500175\pi\) | ||||
−0.000548897 | 1.00000i | \(0.500175\pi\) | ||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.0417 | −1.75192 | −0.875960 | − | 0.482383i | \(-0.839771\pi\) | ||||
−0.875960 | + | 0.482383i | \(0.839771\pi\) | |||||||
\(662\) | 55.6028 | 2.16107 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.26436 | 0.359527 | ||||||||
\(665\) | 18.4560 | 0.715693 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.8325 | −0.496875 | ||||||||
\(668\) | −60.2177 | −2.32989 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.1802 | 0.702362 | ||||||||
\(671\) | −18.4885 | −0.713740 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.75969 | −0.376208 | −0.188104 | − | 0.982149i | \(-0.560234\pi\) | ||||
−0.188104 | + | 0.982149i | \(0.560234\pi\) | |||||||
\(674\) | −23.2607 | −0.895968 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.9847 | −1.11480 | ||||||||
\(677\) | 40.8808 | 1.57118 | 0.785588 | − | 0.618750i | \(-0.212361\pi\) | ||||
0.785588 | + | 0.618750i | \(0.212361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.7756 | −0.950801 | ||||||||
\(680\) | 5.36476 | 0.205729 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.9938 | −0.497557 | ||||||||
\(683\) | −44.0251 | −1.68457 | −0.842287 | − | 0.539029i | \(-0.818791\pi\) | ||||
−0.842287 | + | 0.539029i | \(0.818791\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.54644 | 0.288335 | ||||||||
\(686\) | −97.9831 | −3.74101 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 14.8229 | 0.565117 | ||||||||
\(689\) | 7.69498 | 0.293155 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.5516 | 0.819862 | 0.409931 | − | 0.912117i | \(-0.365553\pi\) | ||||
0.409931 | + | 0.912117i | \(0.365553\pi\) | |||||||
\(692\) | −22.9939 | −0.874098 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.46603 | −0.283407 | ||||||||
\(695\) | −27.4928 | −1.04286 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.34306 | 0.202383 | ||||||||
\(698\) | 62.0441 | 2.34841 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.67532 | −0.327896 | ||||||||
\(701\) | −12.8521 | −0.485419 | −0.242709 | − | 0.970099i | \(-0.578036\pi\) | ||||
−0.242709 | + | 0.970099i | \(0.578036\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.4889 | −0.621891 | ||||||||
\(704\) | −47.5399 | −1.79173 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 53.2889 | 2.00556 | ||||||||
\(707\) | 90.0878 | 3.38810 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −49.7117 | −1.86696 | −0.933481 | − | 0.358627i | \(-0.883245\pi\) | ||||
−0.933481 | + | 0.358627i | \(0.883245\pi\) | |||||||
\(710\) | 13.5787 | 0.509601 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −18.5912 | −0.696737 | ||||||||
\(713\) | −6.34168 | −0.237498 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.4496 | 0.390794 | ||||||||
\(716\) | 26.6688 | 0.996660 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.94051 | −0.333657 | ||||||||
\(719\) | −5.63745 | −0.210242 | −0.105121 | − | 0.994459i | \(-0.533523\pi\) | ||||
−0.105121 | + | 0.994459i | \(0.533523\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.6660 | 1.62621 | ||||||||
\(722\) | 33.1966 | 1.23545 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.68034 | −0.136779 | ||||||||
\(725\) | −2.12069 | −0.0787604 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.4143 | −1.68432 | −0.842161 | − | 0.539226i | \(-0.818717\pi\) | ||||
−0.842161 | + | 0.539226i | \(0.818717\pi\) | |||||||
\(728\) | 6.46195 | 0.239496 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 56.1546 | 2.07837 | ||||||||
\(731\) | −12.9642 | −0.479499 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.6669 | −0.948027 | −0.474013 | − | 0.880518i | \(-0.657195\pi\) | ||||
−0.474013 | + | 0.880518i | \(0.657195\pi\) | |||||||
\(734\) | −37.1808 | −1.37237 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −34.1483 | −1.25872 | ||||||||
\(737\) | 17.1420 | 0.631433 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.4553 | −0.531745 | −0.265873 | − | 0.964008i | \(-0.585660\pi\) | ||||
−0.265873 | + | 0.964008i | \(0.585660\pi\) | |||||||
\(740\) | −46.7390 | −1.71816 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 65.2013 | 2.39361 | ||||||||
\(743\) | 34.7937 | 1.27646 | 0.638229 | − | 0.769846i | \(-0.279667\pi\) | ||||
0.638229 | + | 0.769846i | \(0.279667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.4541 | −0.676107 | ||||||||
\(746\) | 63.0168 | 2.30721 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 24.6742 | 0.902177 | ||||||||
\(749\) | 36.0101 | 1.31578 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.1184 | 0.661152 | 0.330576 | − | 0.943779i | \(-0.392757\pi\) | ||||
0.330576 | + | 0.943779i | \(0.392757\pi\) | |||||||
\(752\) | −19.4125 | −0.707901 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.70522 | 0.280608 | ||||||||
\(755\) | 1.47535 | 0.0536933 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.0045 | −1.34495 | −0.672475 | − | 0.740120i | \(-0.734769\pi\) | ||||
−0.672475 | + | 0.740120i | \(0.734769\pi\) | |||||||
\(758\) | −44.5243 | −1.61720 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.17173 | −0.151325 | ||||||||
\(761\) | −12.4444 | −0.451110 | −0.225555 | − | 0.974230i | \(-0.572420\pi\) | ||||
−0.225555 | + | 0.974230i | \(0.572420\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.2688 | −0.987195 | ||||||||
\(764\) | 31.2513 | 1.13063 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.0309 | −0.759878 | ||||||||
\(767\) | −0.318908 | −0.0115151 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.8856 | −1.47437 | −0.737186 | − | 0.675690i | \(-0.763846\pi\) | ||||
−0.737186 | + | 0.675690i | \(0.763846\pi\) | |||||||
\(770\) | 88.5421 | 3.19084 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 52.2604 | 1.88089 | ||||||||
\(773\) | −36.4162 | −1.30980 | −0.654900 | − | 0.755716i | \(-0.727289\pi\) | ||||
−0.654900 | + | 0.755716i | \(0.727289\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.04802 | −0.0376461 | ||||||||
\(776\) | 5.60019 | 0.201035 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 44.8695 | 1.60865 | ||||||||
\(779\) | −4.15486 | −0.148863 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.8033 | 0.458138 | ||||||||
\(782\) | 21.6160 | 0.772985 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −44.6174 | −1.59348 | ||||||||
\(785\) | 28.6164 | 1.02136 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.3472 | 0.654005 | 0.327003 | − | 0.945023i | \(-0.393961\pi\) | ||||
0.327003 | + | 0.945023i | \(0.393961\pi\) | |||||||
\(788\) | −35.6951 | −1.27158 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 20.0343 | 0.712787 | ||||||||
\(791\) | −11.6498 | −0.414218 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.41808 | 0.192402 | ||||||||
\(794\) | 20.7808 | 0.737485 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 51.1417 | 1.81267 | ||||||||
\(797\) | 3.46492 | 0.122734 | 0.0613670 | − | 0.998115i | \(-0.480454\pi\) | ||||
0.0613670 | + | 0.998115i | \(0.480454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.9783 | 0.600650 | ||||||||
\(800\) | −5.64333 | −0.199522 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 40.6716 | 1.43617 | ||||||||
\(803\) | 52.9477 | 1.86849 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 43.2135 | 1.52307 | ||||||||
\(806\) | 3.80785 | 0.134126 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.3631 | −0.716372 | ||||||||
\(809\) | −24.8406 | −0.873348 | −0.436674 | − | 0.899620i | \(-0.643844\pi\) | ||||
−0.436674 | + | 0.899620i | \(0.643844\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.3286 | −1.41613 | −0.708063 | − | 0.706149i | \(-0.750431\pi\) | ||||
−0.708063 | + | 0.706149i | \(0.750431\pi\) | |||||||
\(812\) | 36.3723 | 1.27642 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −79.1050 | −2.77263 | ||||||||
\(815\) | 2.47107 | 0.0865579 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.0812 | 0.352697 | ||||||||
\(818\) | −31.8660 | −1.11417 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.7772 | −0.411279 | ||||||||
\(821\) | 40.1816 | 1.40235 | 0.701174 | − | 0.712990i | \(-0.252659\pi\) | ||||
0.701174 | + | 0.712990i | \(0.252659\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.9554 | −1.67162 | −0.835810 | − | 0.549019i | \(-0.815001\pi\) | ||||
−0.835810 | + | 0.549019i | \(0.815001\pi\) | |||||||
\(824\) | −9.87012 | −0.343842 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.70218 | −0.0940209 | ||||||||
\(827\) | −5.00048 | −0.173884 | −0.0869419 | − | 0.996213i | \(-0.527709\pi\) | ||||
−0.0869419 | + | 0.996213i | \(0.527709\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.7037 | 1.03165 | 0.515826 | − | 0.856693i | \(-0.327485\pi\) | ||||
0.515826 | + | 0.856693i | \(0.327485\pi\) | |||||||
\(830\) | −37.2003 | −1.29124 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.9316 | 0.482993 | ||||||||
\(833\) | 39.0228 | 1.35206 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.5707 | 1.71546 | ||||||||
\(836\) | −19.1871 | −0.663599 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.3502 | −0.426632 | ||||||||
\(839\) | −25.9045 | −0.894323 | −0.447162 | − | 0.894453i | \(-0.647565\pi\) | ||||
−0.447162 | + | 0.894453i | \(0.647565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.1088 | −0.693405 | ||||||||
\(842\) | 28.2916 | 0.974993 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −24.8136 | −0.854120 | ||||||||
\(845\) | 23.8599 | 0.820807 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.1503 | 1.03598 | ||||||||
\(848\) | 17.1016 | 0.587270 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.57224 | 0.122527 | ||||||||
\(851\) | −38.6077 | −1.32345 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.99166 | −0.170911 | −0.0854556 | − | 0.996342i | \(-0.527235\pi\) | ||||
−0.0854556 | + | 0.996342i | \(0.527235\pi\) | |||||||
\(854\) | 45.9086 | 1.57096 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.13961 | −0.278206 | ||||||||
\(857\) | −14.6830 | −0.501562 | −0.250781 | − | 0.968044i | \(-0.580687\pi\) | ||||
−0.250781 | + | 0.968044i | \(0.580687\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.4849 | −0.596576 | −0.298288 | − | 0.954476i | \(-0.596416\pi\) | ||||
−0.298288 | + | 0.954476i | \(0.596416\pi\) | |||||||
\(860\) | 28.5759 | 0.974430 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 77.3864 | 2.63579 | ||||||||
\(863\) | 6.33263 | 0.215565 | 0.107783 | − | 0.994174i | \(-0.465625\pi\) | ||||
0.107783 | + | 0.994174i | \(0.465625\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.9284 | 0.643585 | ||||||||
\(866\) | 23.1121 | 0.785381 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 17.9749 | 0.610106 | ||||||||
\(869\) | 18.8902 | 0.640805 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.02349 | −0.170214 | ||||||||
\(872\) | 6.16374 | 0.208730 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.8090 | −0.568571 | ||||||||
\(875\) | 57.3480 | 1.93872 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.5310 | 1.09849 | 0.549247 | − | 0.835660i | \(-0.314915\pi\) | ||||
0.549247 | + | 0.835660i | \(0.314915\pi\) | |||||||
\(878\) | −20.0885 | −0.677953 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 23.2236 | 0.782868 | ||||||||
\(881\) | −33.3599 | −1.12393 | −0.561963 | − | 0.827163i | \(-0.689954\pi\) | ||||
−0.561963 | + | 0.827163i | \(0.689954\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.8511 | −1.84589 | −0.922944 | − | 0.384934i | \(-0.874224\pi\) | ||||
−0.922944 | + | 0.384934i | \(0.874224\pi\) | |||||||
\(884\) | −7.23081 | −0.243198 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −35.1138 | −1.17967 | ||||||||
\(887\) | 21.0477 | 0.706714 | 0.353357 | − | 0.935489i | \(-0.385040\pi\) | ||||
0.353357 | + | 0.935489i | \(0.385040\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44.7760 | −1.50174 | ||||||||
\(890\) | 74.6516 | 2.50233 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 37.9158 | 1.26951 | ||||||||
\(893\) | −13.2026 | −0.441810 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.9535 | −0.733825 | ||||||||
\(896\) | 41.0988 | 1.37301 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.0803 | 0.336385 | ||||||||
\(899\) | 4.39397 | 0.146547 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.9572 | −0.498296 | ||||||||
\(902\) | −19.9328 | −0.663690 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.63327 | 0.0875813 | ||||||||
\(905\) | 3.02962 | 0.100708 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.8380 | 0.492689 | 0.246344 | − | 0.969182i | \(-0.420771\pi\) | ||||
0.246344 | + | 0.969182i | \(0.420771\pi\) | |||||||
\(908\) | −57.0887 | −1.89456 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −25.9474 | −0.860149 | ||||||||
\(911\) | 18.0295 | 0.597345 | 0.298673 | − | 0.954356i | \(-0.403456\pi\) | ||||
0.298673 | + | 0.954356i | \(0.403456\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.0759 | −1.16084 | ||||||||
\(914\) | 47.6188 | 1.57509 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.9290 | 0.724555 | ||||||||
\(917\) | −74.3738 | −2.45604 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.4881 | 0.444932 | 0.222466 | − | 0.974940i | \(-0.428589\pi\) | ||||
0.222466 | + | 0.974940i | \(0.428589\pi\) | |||||||
\(920\) | −9.76783 | −0.322036 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.7102 | 1.04432 | ||||||||
\(923\) | −3.75203 | −0.123499 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.38029 | −0.209783 | ||||||||
\(926\) | 31.5507 | 1.03682 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23.6603 | 0.776689 | ||||||||
\(929\) | −37.6211 | −1.23431 | −0.617155 | − | 0.786842i | \(-0.711715\pi\) | ||||
−0.617155 | + | 0.786842i | \(0.711715\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.3448 | −0.994511 | ||||||||
\(932\) | −59.3439 | −1.94387 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32.6222 | 1.06743 | ||||||||
\(935\) | −20.3116 | −0.664259 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.14458 | 0.135398 | 0.0676988 | − | 0.997706i | \(-0.478434\pi\) | ||||
0.0676988 | + | 0.997706i | \(0.478434\pi\) | |||||||
\(938\) | −42.5651 | −1.38980 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −37.4238 | −1.22063 | ||||||||
\(941\) | −3.53033 | −0.115085 | −0.0575427 | − | 0.998343i | \(-0.518327\pi\) | ||||
−0.0575427 | + | 0.998343i | \(0.518327\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.72832 | −0.316798 | ||||||||
\(944\) | −0.708752 | −0.0230679 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 48.3643 | 1.57246 | ||||||||
\(947\) | −14.2551 | −0.463228 | −0.231614 | − | 0.972808i | \(-0.574401\pi\) | ||||
−0.231614 | + | 0.972808i | \(0.574401\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.5164 | −0.503685 | ||||||||
\(950\) | −2.77784 | −0.0901250 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.5605 | −0.407087 | ||||||||
\(953\) | 11.6426 | 0.377141 | 0.188570 | − | 0.982060i | \(-0.439615\pi\) | ||||
0.188570 | + | 0.982060i | \(0.439615\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.7258 | −0.832467 | ||||||||
\(956\) | 25.0430 | 0.809950 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.2036 | −0.717365 | ||||||||
\(959\) | −17.6684 | −0.570543 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8285 | −0.929953 | ||||||||
\(962\) | 23.1819 | 0.747414 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.3736 | 0.462942 | ||||||||
\(965\) | −43.0203 | −1.38487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.0681 | 0.934768 | 0.467384 | − | 0.884054i | \(-0.345197\pi\) | ||||
0.467384 | + | 0.884054i | \(0.345197\pi\) | |||||||
\(968\) | −6.81507 | −0.219045 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.4871 | −0.722018 | ||||||||
\(971\) | 47.5792 | 1.52689 | 0.763444 | − | 0.645874i | \(-0.223507\pi\) | ||||
0.763444 | + | 0.645874i | \(0.223507\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 64.3687 | 2.06357 | ||||||||
\(974\) | 34.3508 | 1.10067 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.0413 | 0.385433 | ||||||||
\(977\) | 6.11630 | 0.195678 | 0.0978389 | − | 0.995202i | \(-0.468807\pi\) | ||||
0.0978389 | + | 0.995202i | \(0.468807\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 70.3885 | 2.24963 | ||||||||
\(980\) | −86.0145 | −2.74763 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22.9022 | 0.730837 | ||||||||
\(983\) | 10.6518 | 0.339740 | 0.169870 | − | 0.985466i | \(-0.445665\pi\) | ||||
0.169870 | + | 0.985466i | \(0.445665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.3839 | 0.936248 | ||||||||
\(986\) | −14.9771 | −0.476967 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.62281 | 0.178885 | ||||||||
\(989\) | 23.6045 | 0.750578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.9856 | 0.761928 | 0.380964 | − | 0.924590i | \(-0.375592\pi\) | ||||
0.380964 | + | 0.924590i | \(0.375592\pi\) | |||||||
\(992\) | 11.6927 | 0.371244 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −31.7918 | −1.00837 | ||||||||
\(995\) | −42.0994 | −1.33464 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.31418 | 0.136631 | 0.0683157 | − | 0.997664i | \(-0.478237\pi\) | ||||
0.0683157 | + | 0.997664i | \(0.478237\pi\) | |||||||
\(998\) | 40.7733 | 1.29066 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 729.2.a.b.1.2 | ✓ | 6 | |
3.2 | odd | 2 | 729.2.a.e.1.5 | yes | 6 | ||
9.2 | odd | 6 | 729.2.c.a.244.2 | 12 | |||
9.4 | even | 3 | 729.2.c.d.487.5 | 12 | |||
9.5 | odd | 6 | 729.2.c.a.487.2 | 12 | |||
9.7 | even | 3 | 729.2.c.d.244.5 | 12 | |||
27.2 | odd | 18 | 729.2.e.l.568.1 | 12 | |||
27.4 | even | 9 | 729.2.e.t.406.1 | 12 | |||
27.5 | odd | 18 | 729.2.e.u.649.2 | 12 | |||
27.7 | even | 9 | 729.2.e.t.325.1 | 12 | |||
27.11 | odd | 18 | 729.2.e.u.82.2 | 12 | |||
27.13 | even | 9 | 729.2.e.s.163.2 | 12 | |||
27.14 | odd | 18 | 729.2.e.l.163.1 | 12 | |||
27.16 | even | 9 | 729.2.e.j.82.1 | 12 | |||
27.20 | odd | 18 | 729.2.e.k.325.2 | 12 | |||
27.22 | even | 9 | 729.2.e.j.649.1 | 12 | |||
27.23 | odd | 18 | 729.2.e.k.406.2 | 12 | |||
27.25 | even | 9 | 729.2.e.s.568.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
729.2.a.b.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
729.2.a.e.1.5 | yes | 6 | 3.2 | odd | 2 | ||
729.2.c.a.244.2 | 12 | 9.2 | odd | 6 | |||
729.2.c.a.487.2 | 12 | 9.5 | odd | 6 | |||
729.2.c.d.244.5 | 12 | 9.7 | even | 3 | |||
729.2.c.d.487.5 | 12 | 9.4 | even | 3 | |||
729.2.e.j.82.1 | 12 | 27.16 | even | 9 | |||
729.2.e.j.649.1 | 12 | 27.22 | even | 9 | |||
729.2.e.k.325.2 | 12 | 27.20 | odd | 18 | |||
729.2.e.k.406.2 | 12 | 27.23 | odd | 18 | |||
729.2.e.l.163.1 | 12 | 27.14 | odd | 18 | |||
729.2.e.l.568.1 | 12 | 27.2 | odd | 18 | |||
729.2.e.s.163.2 | 12 | 27.13 | even | 9 | |||
729.2.e.s.568.2 | 12 | 27.25 | even | 9 | |||
729.2.e.t.325.1 | 12 | 27.7 | even | 9 | |||
729.2.e.t.406.1 | 12 | 27.4 | even | 9 | |||
729.2.e.u.82.2 | 12 | 27.11 | odd | 18 | |||
729.2.e.u.649.2 | 12 | 27.5 | odd | 18 |