Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.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: | \(31.6926245622\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.59351616.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 12x^{4} + 21x^{2} - 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 441) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.820103\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.46050 | 1.73984 | 0.869920 | − | 0.493193i | \(-0.164170\pi\) | ||||
0.869920 | + | 0.493193i | \(0.164170\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.05408 | 2.02704 | ||||||||
\(5\) | −3.65808 | −1.63594 | −0.817970 | − | 0.575260i | \(-0.804901\pi\) | ||||
−0.817970 | + | 0.575260i | \(0.804901\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 5.05408 | 1.78689 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9.00071 | −2.84628 | ||||||||
\(11\) | 0.406421 | 0.122540 | 0.0612702 | − | 0.998121i | \(-0.480485\pi\) | ||||
0.0612702 | + | 0.998121i | \(0.480485\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.486796 | −0.135013 | −0.0675065 | − | 0.997719i | \(-0.521504\pi\) | ||||
−0.0675065 | + | 0.997719i | \(0.521504\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.32743 | 1.08186 | ||||||||
\(17\) | 4.85584 | 1.17771 | 0.588857 | − | 0.808237i | \(-0.299578\pi\) | ||||
0.588857 | + | 0.808237i | \(0.299578\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.97351 | −0.452755 | −0.226378 | − | 0.974040i | \(-0.572688\pi\) | ||||
−0.226378 | + | 0.974040i | \(0.572688\pi\) | |||||||
\(20\) | −14.8301 | −3.31612 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 4.64766 | 0.969105 | 0.484552 | − | 0.874762i | \(-0.338982\pi\) | ||||
0.484552 | + | 0.874762i | \(0.338982\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.38151 | 1.67630 | ||||||||
\(26\) | −1.19777 | −0.234901 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.64766 | 1.42014 | 0.710068 | − | 0.704133i | \(-0.248664\pi\) | ||||
0.710068 | + | 0.704133i | \(0.248664\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.02720 | 1.26212 | 0.631061 | − | 0.775733i | \(-0.282620\pi\) | ||||
0.631061 | + | 0.775733i | \(0.282620\pi\) | |||||||
\(32\) | 0.539495 | 0.0953702 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.9478 | 2.04903 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.32743 | 0.382627 | 0.191314 | − | 0.981529i | \(-0.438725\pi\) | ||||
0.191314 | + | 0.981529i | \(0.438725\pi\) | |||||||
\(38\) | −4.85584 | −0.787721 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −18.4882 | −2.92324 | ||||||||
\(41\) | 7.51399 | 1.17349 | 0.586744 | − | 0.809772i | \(-0.300409\pi\) | ||||
0.586744 | + | 0.809772i | \(0.300409\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.32743 | −0.354930 | −0.177465 | − | 0.984127i | \(-0.556790\pi\) | ||||
−0.177465 | + | 0.984127i | \(0.556790\pi\) | |||||||
\(44\) | 1.64766 | 0.248395 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.4356 | 1.68609 | ||||||||
\(47\) | −6.31623 | −0.921317 | −0.460658 | − | 0.887578i | \(-0.652387\pi\) | ||||
−0.460658 | + | 0.887578i | \(0.652387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 20.6228 | 2.91650 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.97351 | −0.273677 | ||||||||
\(53\) | −3.56867 | −0.490195 | −0.245097 | − | 0.969498i | \(-0.578820\pi\) | ||||
−0.245097 | + | 0.969498i | \(0.578820\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.48672 | −0.200469 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 18.8171 | 2.47081 | ||||||||
\(59\) | 6.11839 | 0.796546 | 0.398273 | − | 0.917267i | \(-0.369610\pi\) | ||||
0.398273 | + | 0.917267i | \(0.369610\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.02712 | −1.02777 | −0.513884 | − | 0.857860i | \(-0.671794\pi\) | ||||
−0.513884 | + | 0.857860i | \(0.671794\pi\) | |||||||
\(62\) | 17.2905 | 2.19589 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.32743 | −0.915929 | ||||||||
\(65\) | 1.78074 | 0.220873 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.60078 | 0.439905 | 0.219952 | − | 0.975511i | \(-0.429410\pi\) | ||||
0.219952 | + | 0.975511i | \(0.429410\pi\) | |||||||
\(68\) | 19.6860 | 2.38728 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.46050 | 1.00408 | 0.502039 | − | 0.864845i | \(-0.332584\pi\) | ||||
0.502039 | + | 0.864845i | \(0.332584\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.97351 | 0.230982 | 0.115491 | − | 0.993309i | \(-0.463156\pi\) | ||||
0.115491 | + | 0.993309i | \(0.463156\pi\) | |||||||
\(74\) | 5.72665 | 0.665710 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.00079 | −0.917754 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.16225 | 0.918325 | 0.459163 | − | 0.888352i | \(-0.348150\pi\) | ||||
0.459163 | + | 0.888352i | \(0.348150\pi\) | |||||||
\(80\) | −15.8301 | −1.76986 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18.4882 | 2.04168 | ||||||||
\(83\) | 12.1720 | 1.33605 | 0.668025 | − | 0.744139i | \(-0.267140\pi\) | ||||
0.668025 | + | 0.744139i | \(0.267140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.7630 | −1.92667 | ||||||||
\(86\) | −5.72665 | −0.617521 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.05408 | 0.218966 | ||||||||
\(89\) | 14.8301 | 1.57199 | 0.785996 | − | 0.618231i | \(-0.212151\pi\) | ||||
0.785996 | + | 0.618231i | \(0.212151\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 18.8420 | 1.96442 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −15.5411 | −1.60294 | ||||||||
\(95\) | 7.21926 | 0.740681 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.48751 | −0.963311 | −0.481655 | − | 0.876361i | \(-0.659964\pi\) | ||||
−0.481655 | + | 0.876361i | \(0.659964\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 33.9794 | 3.39794 | ||||||||
\(101\) | 8.71176 | 0.866852 | 0.433426 | − | 0.901189i | \(-0.357304\pi\) | ||||
0.433426 | + | 0.901189i | \(0.357304\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.02712 | 0.790936 | 0.395468 | − | 0.918480i | \(-0.370582\pi\) | ||||
0.395468 | + | 0.918480i | \(0.370582\pi\) | |||||||
\(104\) | −2.46031 | −0.241253 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.78074 | −0.852861 | ||||||||
\(107\) | 12.8420 | 1.24148 | 0.620742 | − | 0.784015i | \(-0.286831\pi\) | ||||
0.620742 | + | 0.784015i | \(0.286831\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.60078 | 0.249109 | 0.124555 | − | 0.992213i | \(-0.460250\pi\) | ||||
0.124555 | + | 0.992213i | \(0.460250\pi\) | |||||||
\(110\) | −3.65808 | −0.348784 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.9502 | −1.31232 | −0.656162 | − | 0.754620i | \(-0.727821\pi\) | ||||
−0.656162 | + | 0.754620i | \(0.727821\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.0015 | −1.58540 | ||||||||
\(116\) | 31.0043 | 2.87867 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.0543 | 1.38586 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8348 | −0.984984 | ||||||||
\(122\) | −19.7508 | −1.78815 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 28.4889 | 2.55837 | ||||||||
\(125\) | −12.3698 | −1.10639 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.5438 | −1.37929 | −0.689643 | − | 0.724149i | \(-0.742233\pi\) | ||||
−0.689643 | + | 0.724149i | \(0.742233\pi\) | |||||||
\(128\) | −19.1082 | −1.68894 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.38151 | 0.384284 | ||||||||
\(131\) | −8.51392 | −0.743864 | −0.371932 | − | 0.928260i | \(-0.621305\pi\) | ||||
−0.371932 | + | 0.928260i | \(0.621305\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.85973 | 0.765364 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 24.5418 | 2.10444 | ||||||||
\(137\) | 0.377242 | 0.0322300 | 0.0161150 | − | 0.999870i | \(-0.494870\pi\) | ||||
0.0161150 | + | 0.999870i | \(0.494870\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.0013 | −1.61167 | −0.805837 | − | 0.592138i | \(-0.798284\pi\) | ||||
−0.805837 | + | 0.592138i | \(0.798284\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 20.8171 | 1.74693 | ||||||||
\(143\) | −0.197844 | −0.0165446 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −27.9757 | −2.32326 | ||||||||
\(146\) | 4.85584 | 0.401872 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.43560 | 0.775601 | ||||||||
\(149\) | −9.70175 | −0.794798 | −0.397399 | − | 0.917646i | \(-0.630087\pi\) | ||||
−0.397399 | + | 0.917646i | \(0.630087\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.8348 | −1.04448 | −0.522242 | − | 0.852798i | \(-0.674904\pi\) | ||||
−0.522242 | + | 0.852798i | \(0.674904\pi\) | |||||||
\(152\) | −9.97430 | −0.809023 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −25.7060 | −2.06476 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.9485 | 1.67187 | 0.835937 | − | 0.548825i | \(-0.184925\pi\) | ||||
0.835937 | + | 0.548825i | \(0.184925\pi\) | |||||||
\(158\) | 20.0833 | 1.59774 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.97351 | −0.156020 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.1623 | −0.874295 | −0.437148 | − | 0.899390i | \(-0.644011\pi\) | ||||
−0.437148 | + | 0.899390i | \(0.644011\pi\) | |||||||
\(164\) | 30.4624 | 2.37871 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 29.9492 | 2.32451 | ||||||||
\(167\) | 3.46023 | 0.267761 | 0.133880 | − | 0.990998i | \(-0.457256\pi\) | ||||
0.133880 | + | 0.990998i | \(0.457256\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7630 | −0.981771 | ||||||||
\(170\) | −43.7060 | −3.35210 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.43560 | −0.719458 | ||||||||
\(173\) | −6.05361 | −0.460247 | −0.230124 | − | 0.973161i | \(-0.573913\pi\) | ||||
−0.230124 | + | 0.973161i | \(0.573913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.75876 | 0.132571 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 36.4896 | 2.73501 | ||||||||
\(179\) | 9.13307 | 0.682638 | 0.341319 | − | 0.939948i | \(-0.389126\pi\) | ||||
0.341319 | + | 0.939948i | \(0.389126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.9478 | 0.888074 | 0.444037 | − | 0.896008i | \(-0.353546\pi\) | ||||
0.444037 | + | 0.896008i | \(0.353546\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 23.4897 | 1.73168 | ||||||||
\(185\) | −8.51392 | −0.625956 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.97351 | 0.144318 | ||||||||
\(188\) | −25.6065 | −1.86755 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.7630 | 1.28867 | ||||||||
\(191\) | 9.14027 | 0.661367 | 0.330683 | − | 0.943742i | \(-0.392721\pi\) | ||||
0.330683 | + | 0.943742i | \(0.392721\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.9430 | 1.21958 | 0.609792 | − | 0.792562i | \(-0.291253\pi\) | ||||
0.609792 | + | 0.792562i | \(0.291253\pi\) | |||||||
\(194\) | −23.3441 | −1.67601 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.3173 | −1.51880 | −0.759398 | − | 0.650627i | \(-0.774506\pi\) | ||||
−0.759398 | + | 0.650627i | \(0.774506\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.97430 | 0.707060 | 0.353530 | − | 0.935423i | \(-0.384981\pi\) | ||||
0.353530 | + | 0.935423i | \(0.384981\pi\) | |||||||
\(200\) | 42.3609 | 2.99537 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 21.4353 | 1.50818 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −27.4868 | −1.91976 | ||||||||
\(206\) | 19.7508 | 1.37610 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.10658 | −0.146065 | ||||||||
\(209\) | −0.802077 | −0.0554808 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.89183 | 0.336768 | 0.168384 | − | 0.985722i | \(-0.446145\pi\) | ||||
0.168384 | + | 0.985722i | \(0.446145\pi\) | |||||||
\(212\) | −14.4677 | −0.993646 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 31.5979 | 2.15998 | ||||||||
\(215\) | 8.51392 | 0.580644 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.39922 | 0.433410 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.02728 | −0.406359 | ||||||||
\(221\) | −2.36381 | −0.159007 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.4088 | −1.56757 | −0.783786 | − | 0.621031i | \(-0.786714\pi\) | ||||
−0.783786 | + | 0.621031i | \(0.786714\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −34.3245 | −2.28323 | ||||||||
\(227\) | −6.11839 | −0.406092 | −0.203046 | − | 0.979169i | \(-0.565084\pi\) | ||||
−0.203046 | + | 0.979169i | \(0.565084\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.46039 | 0.0965052 | 0.0482526 | − | 0.998835i | \(-0.484635\pi\) | ||||
0.0482526 | + | 0.998835i | \(0.484635\pi\) | |||||||
\(230\) | −41.8323 | −2.75834 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 38.6519 | 2.53762 | ||||||||
\(233\) | −13.2484 | −0.867934 | −0.433967 | − | 0.900929i | \(-0.642887\pi\) | ||||
−0.433967 | + | 0.900929i | \(0.642887\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.1052 | 1.50722 | ||||||||
\(236\) | 24.8045 | 1.61463 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.3887 | 1.25415 | 0.627076 | − | 0.778958i | \(-0.284252\pi\) | ||||
0.627076 | + | 0.778958i | \(0.284252\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.05368 | −0.325536 | −0.162768 | − | 0.986664i | \(-0.552042\pi\) | ||||
−0.162768 | + | 0.986664i | \(0.552042\pi\) | |||||||
\(242\) | −26.6591 | −1.71371 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −32.5426 | −2.08333 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.960699 | 0.0611278 | ||||||||
\(248\) | 35.5161 | 2.25527 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −30.4360 | −1.92494 | ||||||||
\(251\) | −15.0928 | −0.952647 | −0.476324 | − | 0.879270i | \(-0.658031\pi\) | ||||
−0.476324 | + | 0.879270i | \(0.658031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.88891 | 0.118755 | ||||||||
\(254\) | −38.2455 | −2.39974 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.3609 | −2.02256 | ||||||||
\(257\) | −7.71184 | −0.481051 | −0.240526 | − | 0.970643i | \(-0.577320\pi\) | ||||
−0.240526 | + | 0.970643i | \(0.577320\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.21926 | 0.447720 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.9485 | −1.29420 | ||||||||
\(263\) | 4.21206 | 0.259727 | 0.129864 | − | 0.991532i | \(-0.458546\pi\) | ||||
0.129864 | + | 0.991532i | \(0.458546\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.0545 | 0.801930 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.5979 | 0.891706 | ||||||||
\(269\) | −20.7507 | −1.26519 | −0.632596 | − | 0.774482i | \(-0.718011\pi\) | ||||
−0.632596 | + | 0.774482i | \(0.718011\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.4889 | 1.73057 | 0.865287 | − | 0.501276i | \(-0.167136\pi\) | ||||
0.865287 | + | 0.501276i | \(0.167136\pi\) | |||||||
\(272\) | 21.0133 | 1.27412 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.928207 | 0.0560750 | ||||||||
\(275\) | 3.40642 | 0.205415 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.1623 | 1.03118 | 0.515590 | − | 0.856835i | \(-0.327573\pi\) | ||||
0.515590 | + | 0.856835i | \(0.327573\pi\) | |||||||
\(278\) | −46.7529 | −2.80405 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.44280 | 0.563310 | 0.281655 | − | 0.959516i | \(-0.409117\pi\) | ||||
0.281655 | + | 0.959516i | \(0.409117\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.8684 | −1.00272 | −0.501362 | − | 0.865237i | \(-0.667168\pi\) | ||||
−0.501362 | + | 0.865237i | \(0.667168\pi\) | |||||||
\(284\) | 34.2996 | 2.03531 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.486796 | −0.0287849 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.57918 | 0.387011 | ||||||||
\(290\) | −68.8344 | −4.04210 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.00079 | 0.468211 | ||||||||
\(293\) | 3.72286 | 0.217492 | 0.108746 | − | 0.994070i | \(-0.465317\pi\) | ||||
0.108746 | + | 0.994070i | \(0.465317\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.3815 | −1.30310 | ||||||||
\(296\) | 11.7630 | 0.683712 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −23.8712 | −1.38282 | ||||||||
\(299\) | −2.26247 | −0.130842 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −31.5801 | −1.81723 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.54024 | −0.489817 | ||||||||
\(305\) | 29.3638 | 1.68137 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.5691 | −1.74467 | −0.872335 | − | 0.488908i | \(-0.837395\pi\) | ||||
−0.872335 | + | 0.488908i | \(0.837395\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −63.2498 | −3.59235 | ||||||||
\(311\) | 10.4348 | 0.591702 | 0.295851 | − | 0.955234i | \(-0.404397\pi\) | ||||
0.295851 | + | 0.955234i | \(0.404397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.619860 | 0.0350366 | 0.0175183 | − | 0.999847i | \(-0.494423\pi\) | ||||
0.0175183 | + | 0.999847i | \(0.494423\pi\) | |||||||
\(314\) | 51.5440 | 2.90879 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.0905 | 1.86148 | ||||||||
\(317\) | 10.2484 | 0.575610 | 0.287805 | − | 0.957689i | \(-0.407075\pi\) | ||||
0.287805 | + | 0.957689i | \(0.407075\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.10817 | 0.174024 | ||||||||
\(320\) | 26.8043 | 1.49841 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.58307 | −0.533216 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.08009 | −0.226323 | ||||||||
\(326\) | −27.4648 | −1.52113 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 37.9764 | 2.09689 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.3638 | −1.11930 | −0.559648 | − | 0.828730i | \(-0.689064\pi\) | ||||
−0.559648 | + | 0.828730i | \(0.689064\pi\) | |||||||
\(332\) | 49.3463 | 2.70823 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.51392 | 0.465861 | ||||||||
\(335\) | −13.1719 | −0.719658 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.71187 | −0.311145 | −0.155573 | − | 0.987824i | \(-0.549722\pi\) | ||||
−0.155573 | + | 0.987824i | \(0.549722\pi\) | |||||||
\(338\) | −31.4035 | −1.70812 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −72.0128 | −3.90544 | ||||||||
\(341\) | 2.85600 | 0.154661 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.7630 | −0.634220 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.8949 | −0.800756 | ||||||||
\(347\) | 8.88132 | 0.476774 | 0.238387 | − | 0.971170i | \(-0.423381\pi\) | ||||
0.238387 | + | 0.971170i | \(0.423381\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.9749 | 1.12276 | 0.561379 | − | 0.827559i | \(-0.310271\pi\) | ||||
0.561379 | + | 0.827559i | \(0.310271\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.219262 | 0.0116867 | ||||||||
\(353\) | −14.7654 | −0.785881 | −0.392941 | − | 0.919564i | \(-0.628542\pi\) | ||||
−0.392941 | + | 0.919564i | \(0.628542\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.9492 | −1.64261 | ||||||||
\(356\) | 60.1227 | 3.18649 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.4720 | 1.18768 | ||||||||
\(359\) | 7.21206 | 0.380638 | 0.190319 | − | 0.981722i | \(-0.439048\pi\) | ||||
0.190319 | + | 0.981722i | \(0.439048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.1052 | −0.795013 | ||||||||
\(362\) | 29.3977 | 1.54511 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.21926 | −0.377873 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.9742 | −0.572850 | −0.286425 | − | 0.958103i | \(-0.592467\pi\) | ||||
−0.286425 | + | 0.958103i | \(0.592467\pi\) | |||||||
\(368\) | 20.1124 | 1.04843 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −20.9485 | −1.08906 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.543767 | −0.0281552 | −0.0140776 | − | 0.999901i | \(-0.504481\pi\) | ||||
−0.0140776 | + | 0.999901i | \(0.504481\pi\) | |||||||
\(374\) | 4.85584 | 0.251090 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −31.9228 | −1.64629 | ||||||||
\(377\) | −3.72286 | −0.191737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6912 | −1.16557 | −0.582785 | − | 0.812626i | \(-0.698037\pi\) | ||||
−0.582785 | + | 0.812626i | \(0.698037\pi\) | |||||||
\(380\) | 29.2675 | 1.50139 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.4897 | 1.15067 | ||||||||
\(383\) | 35.7139 | 1.82489 | 0.912447 | − | 0.409194i | \(-0.134190\pi\) | ||||
0.912447 | + | 0.409194i | \(0.134190\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 41.6883 | 2.12188 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −38.4632 | −1.95267 | ||||||||
\(389\) | 38.6591 | 1.96010 | 0.980048 | − | 0.198761i | \(-0.0636919\pi\) | ||||
0.980048 | + | 0.198761i | \(0.0636919\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.5683 | 1.14133 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −52.4513 | −2.64246 | ||||||||
\(395\) | −29.8581 | −1.50233 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.9478 | −0.599644 | −0.299822 | − | 0.953995i | \(-0.596927\pi\) | ||||
−0.299822 | + | 0.953995i | \(0.596927\pi\) | |||||||
\(398\) | 24.5418 | 1.23017 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 36.2704 | 1.81352 | ||||||||
\(401\) | 32.3566 | 1.61581 | 0.807906 | − | 0.589311i | \(-0.200601\pi\) | ||||
0.807906 | + | 0.589311i | \(0.200601\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.42082 | −0.170403 | ||||||||
\(404\) | 35.3182 | 1.75715 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.945916 | 0.0468873 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.9750 | 0.938254 | 0.469127 | − | 0.883131i | \(-0.344569\pi\) | ||||
0.469127 | + | 0.883131i | \(0.344569\pi\) | |||||||
\(410\) | −67.6313 | −3.34007 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 32.5426 | 1.60326 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −44.5261 | −2.18570 | ||||||||
\(416\) | −0.262624 | −0.0128762 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.97351 | −0.0965277 | ||||||||
\(419\) | −17.2905 | −0.844694 | −0.422347 | − | 0.906434i | \(-0.638794\pi\) | ||||
−0.422347 | + | 0.906434i | \(0.638794\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6008 | 0.906546 | 0.453273 | − | 0.891372i | \(-0.350256\pi\) | ||||
0.453273 | + | 0.891372i | \(0.350256\pi\) | |||||||
\(422\) | 12.0364 | 0.585922 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.0364 | −0.875924 | ||||||||
\(425\) | 40.6993 | 1.97421 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 52.0626 | 2.51654 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 20.9485 | 1.01023 | ||||||||
\(431\) | −15.8784 | −0.764835 | −0.382418 | − | 0.923990i | \(-0.624908\pi\) | ||||
−0.382418 | + | 0.923990i | \(0.624908\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.4367 | 1.94326 | 0.971631 | − | 0.236501i | \(-0.0760007\pi\) | ||||
0.971631 | + | 0.236501i | \(0.0760007\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.5438 | 0.504955 | ||||||||
\(437\) | −9.17223 | −0.438767 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.4609 | 0.594728 | 0.297364 | − | 0.954764i | \(-0.403892\pi\) | ||||
0.297364 | + | 0.954764i | \(0.403892\pi\) | |||||||
\(440\) | −7.51399 | −0.358216 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.81616 | −0.276646 | ||||||||
\(443\) | −8.23073 | −0.391054 | −0.195527 | − | 0.980698i | \(-0.562642\pi\) | ||||
−0.195527 | + | 0.980698i | \(0.562642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −54.2498 | −2.57169 | ||||||||
\(446\) | −57.5976 | −2.72732 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.64474 | 0.266392 | 0.133196 | − | 0.991090i | \(-0.457476\pi\) | ||||
0.133196 | + | 0.991090i | \(0.457476\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.05384 | 0.143800 | ||||||||
\(452\) | −56.5552 | −2.66013 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.0543 | −0.706534 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.06887 | 0.237112 | 0.118556 | − | 0.992947i | \(-0.462174\pi\) | ||||
0.118556 | + | 0.992947i | \(0.462174\pi\) | |||||||
\(458\) | 3.59330 | 0.167904 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −68.9255 | −3.21367 | ||||||||
\(461\) | −7.77662 | −0.362193 | −0.181097 | − | 0.983465i | \(-0.557965\pi\) | ||||
−0.181097 | + | 0.983465i | \(0.557965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.17996 | −0.426629 | −0.213314 | − | 0.976984i | \(-0.568426\pi\) | ||||
−0.213314 | + | 0.976984i | \(0.568426\pi\) | |||||||
\(464\) | 33.0947 | 1.53638 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −32.5979 | −1.51007 | ||||||||
\(467\) | −13.7654 | −0.636989 | −0.318494 | − | 0.947925i | \(-0.603177\pi\) | ||||
−0.318494 | + | 0.947925i | \(0.603177\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 56.8506 | 2.62232 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 30.9228 | 1.42334 | ||||||||
\(473\) | −0.945916 | −0.0434933 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.5410 | −0.758955 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 47.7060 | 2.18202 | ||||||||
\(479\) | 8.71176 | 0.398050 | 0.199025 | − | 0.979994i | \(-0.436222\pi\) | ||||
0.199025 | + | 0.979994i | \(0.436222\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.13298 | −0.0516597 | ||||||||
\(482\) | −12.4346 | −0.566381 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −43.9253 | −1.99660 | ||||||||
\(485\) | 34.7060 | 1.57592 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.0364 | −0.817306 | −0.408653 | − | 0.912690i | \(-0.634001\pi\) | ||||
−0.408653 | + | 0.912690i | \(0.634001\pi\) | |||||||
\(488\) | −40.5697 | −1.83651 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.04689 | 0.0923747 | 0.0461874 | − | 0.998933i | \(-0.485293\pi\) | ||||
0.0461874 | + | 0.998933i | \(0.485293\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.1358 | 1.67251 | ||||||||
\(494\) | 2.36381 | 0.106353 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.4097 | 1.36544 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.0875 | −1.74980 | −0.874899 | − | 0.484305i | \(-0.839072\pi\) | ||||
−0.874899 | + | 0.484305i | \(0.839072\pi\) | |||||||
\(500\) | −50.1484 | −2.24270 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −37.1358 | −1.65745 | ||||||||
\(503\) | 5.11846 | 0.228221 | 0.114111 | − | 0.993468i | \(-0.463598\pi\) | ||||
0.114111 | + | 0.993468i | \(0.463598\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.8683 | −1.41812 | ||||||||
\(506\) | 4.64766 | 0.206614 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −63.0157 | −2.79587 | ||||||||
\(509\) | −29.5272 | −1.30877 | −0.654386 | − | 0.756161i | \(-0.727073\pi\) | ||||
−0.654386 | + | 0.756161i | \(0.727073\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −41.4078 | −1.82998 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.9750 | −0.836952 | ||||||||
\(515\) | −29.3638 | −1.29392 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.56705 | −0.112899 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.00000 | 0.394676 | ||||||||
\(521\) | 1.06470 | 0.0466454 | 0.0233227 | − | 0.999728i | \(-0.492575\pi\) | ||||
0.0233227 | + | 0.999728i | \(0.492575\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.3819 | 0.585149 | 0.292574 | − | 0.956243i | \(-0.405488\pi\) | ||||
0.292574 | + | 0.956243i | \(0.405488\pi\) | |||||||
\(524\) | −34.5161 | −1.50784 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.3638 | 0.451883 | ||||||||
\(527\) | 34.1230 | 1.48642 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.39922 | −0.0608358 | ||||||||
\(530\) | 32.1206 | 1.39523 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.65779 | −0.158436 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −46.9771 | −2.03100 | ||||||||
\(536\) | 18.1986 | 0.786061 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −51.0572 | −2.20123 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.0875 | −1.46554 | −0.732769 | − | 0.680478i | \(-0.761772\pi\) | ||||
−0.732769 | + | 0.680478i | \(0.761772\pi\) | |||||||
\(542\) | 70.0970 | 3.01092 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.61970 | 0.112319 | ||||||||
\(545\) | −9.51384 | −0.407528 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.94299 | −0.254104 | −0.127052 | − | 0.991896i | \(-0.540551\pi\) | ||||
−0.127052 | + | 0.991896i | \(0.540551\pi\) | |||||||
\(548\) | 1.52937 | 0.0653316 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.38151 | 0.357389 | ||||||||
\(551\) | −15.0928 | −0.642974 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 42.2278 | 1.79409 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −77.0331 | −3.26693 | ||||||||
\(557\) | −30.0803 | −1.27454 | −0.637272 | − | 0.770639i | \(-0.719937\pi\) | ||||
−0.637272 | + | 0.770639i | \(0.719937\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.13298 | 0.0479202 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.2340 | 0.980069 | ||||||||
\(563\) | 19.6212 | 0.826935 | 0.413468 | − | 0.910519i | \(-0.364317\pi\) | ||||
0.413468 | + | 0.910519i | \(0.364317\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 51.0308 | 2.14688 | ||||||||
\(566\) | −41.5049 | −1.74458 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.7601 | 1.79417 | ||||||||
\(569\) | −1.37432 | −0.0576144 | −0.0288072 | − | 0.999585i | \(-0.509171\pi\) | ||||
−0.0288072 | + | 0.999585i | \(0.509171\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.3815 | 0.727394 | 0.363697 | − | 0.931517i | \(-0.381514\pi\) | ||||
0.363697 | + | 0.931517i | \(0.381514\pi\) | |||||||
\(572\) | −0.802077 | −0.0335365 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 38.9545 | 1.62451 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.0548 | 1.12631 | 0.563153 | − | 0.826353i | \(-0.309588\pi\) | ||||
0.563153 | + | 0.826353i | \(0.309588\pi\) | |||||||
\(578\) | 16.1881 | 0.673337 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −113.416 | −4.70934 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.45038 | −0.0600687 | ||||||||
\(584\) | 9.97430 | 0.412740 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.16010 | 0.378400 | ||||||||
\(587\) | −7.51399 | −0.310136 | −0.155068 | − | 0.987904i | \(-0.549560\pi\) | ||||
−0.155068 | + | 0.987904i | \(0.549560\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.8683 | −0.571432 | ||||||||
\(590\) | −55.0698 | −2.26719 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.0718 | 0.413948 | ||||||||
\(593\) | −35.5808 | −1.46113 | −0.730565 | − | 0.682843i | \(-0.760743\pi\) | ||||
−0.730565 | + | 0.682843i | \(0.760743\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −39.3317 | −1.61109 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.56681 | −0.227644 | ||||||||
\(599\) | −11.4821 | −0.469146 | −0.234573 | − | 0.972099i | \(-0.575369\pi\) | ||||
−0.234573 | + | 0.972099i | \(0.575369\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.380061 | 0.0155030 | 0.00775150 | − | 0.999970i | \(-0.497533\pi\) | ||||
0.00775150 | + | 0.999970i | \(0.497533\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −52.0335 | −2.11721 | ||||||||
\(605\) | 39.6346 | 1.61138 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.5409 | 0.752551 | 0.376275 | − | 0.926508i | \(-0.377205\pi\) | ||||
0.376275 | + | 0.926508i | \(0.377205\pi\) | |||||||
\(608\) | −1.06470 | −0.0431793 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 72.2498 | 2.92531 | ||||||||
\(611\) | 3.07472 | 0.124390 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.32451 | 0.295834 | 0.147917 | − | 0.989000i | \(-0.452743\pi\) | ||||
0.147917 | + | 0.989000i | \(0.452743\pi\) | |||||||
\(614\) | −75.2154 | −3.03545 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.4854 | −1.02600 | −0.513002 | − | 0.858387i | \(-0.671467\pi\) | ||||
−0.513002 | + | 0.858387i | \(0.671467\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.8963 | −1.32222 | −0.661108 | − | 0.750291i | \(-0.729913\pi\) | ||||
−0.661108 | + | 0.750291i | \(0.729913\pi\) | |||||||
\(620\) | −104.214 | −4.18535 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 25.6748 | 1.02947 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.34221 | 0.133689 | ||||||||
\(626\) | 1.52517 | 0.0609580 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 84.9271 | 3.38896 | ||||||||
\(629\) | 11.3016 | 0.450626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8683 | 1.18904 | 0.594519 | − | 0.804082i | \(-0.297343\pi\) | ||||
0.594519 | + | 0.804082i | \(0.297343\pi\) | |||||||
\(632\) | 41.2527 | 1.64094 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.2163 | 1.00147 | ||||||||
\(635\) | 56.8603 | 2.25643 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.64766 | 0.302774 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 69.8991 | 2.76301 | ||||||||
\(641\) | 11.4605 | 0.452663 | 0.226331 | − | 0.974050i | \(-0.427327\pi\) | ||||
0.226331 | + | 0.974050i | \(0.427327\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.3816 | 0.685462 | 0.342731 | − | 0.939434i | \(-0.388648\pi\) | ||||
0.342731 | + | 0.939434i | \(0.388648\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −23.5792 | −0.927711 | ||||||||
\(647\) | −25.3439 | −0.996372 | −0.498186 | − | 0.867070i | \(-0.666000\pi\) | ||||
−0.498186 | + | 0.867070i | \(0.666000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.48664 | 0.0976091 | ||||||||
\(650\) | −10.0391 | −0.393765 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −45.2527 | −1.77223 | ||||||||
\(653\) | 14.0833 | 0.551121 | 0.275560 | − | 0.961284i | \(-0.411137\pi\) | ||||
0.275560 | + | 0.961284i | \(0.411137\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.1445 | 1.21692 | ||||||||
\(656\) | 32.5163 | 1.26955 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.1708 | 1.48692 | 0.743462 | − | 0.668779i | \(-0.233183\pi\) | ||||
0.743462 | + | 0.668779i | \(0.233183\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.353732 | 0.0137586 | 0.00687930 | − | 0.999976i | \(-0.497810\pi\) | ||||
0.00687930 | + | 0.999976i | \(0.497810\pi\) | |||||||
\(662\) | −50.1052 | −1.94740 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 61.5183 | 2.38737 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.5438 | 1.37626 | ||||||||
\(668\) | 14.0281 | 0.542762 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −32.4096 | −1.25209 | ||||||||
\(671\) | −3.26239 | −0.125943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.1111 | −0.813773 | −0.406886 | − | 0.913479i | \(-0.633386\pi\) | ||||
−0.406886 | + | 0.913479i | \(0.633386\pi\) | |||||||
\(674\) | −14.0541 | −0.541343 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −51.7424 | −1.99009 | ||||||||
\(677\) | −21.1464 | −0.812721 | −0.406361 | − | 0.913713i | \(-0.633202\pi\) | ||||
−0.406361 | + | 0.913713i | \(0.633202\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −89.7758 | −3.44275 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.02720 | 0.269085 | ||||||||
\(683\) | 34.7716 | 1.33050 | 0.665249 | − | 0.746622i | \(-0.268326\pi\) | ||||
0.665249 | + | 0.746622i | \(0.268326\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.37998 | −0.0527264 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.0718 | −0.383984 | ||||||||
\(689\) | 1.73722 | 0.0661827 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.6492 | −1.31812 | −0.659059 | − | 0.752091i | \(-0.729045\pi\) | ||||
−0.659059 | + | 0.752091i | \(0.729045\pi\) | |||||||
\(692\) | −24.5418 | −0.932940 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.8525 | 0.829511 | ||||||||
\(695\) | 69.5083 | 2.63660 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.4868 | 1.38203 | ||||||||
\(698\) | 51.6087 | 1.95342 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.6050 | −1.83579 | −0.917894 | − | 0.396826i | \(-0.870111\pi\) | ||||
−0.917894 | + | 0.396826i | \(0.870111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.59322 | −0.173236 | ||||||||
\(704\) | −2.97802 | −0.112238 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.3303 | −1.36731 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.10817 | 0.154286 | 0.0771428 | − | 0.997020i | \(-0.475420\pi\) | ||||
0.0771428 | + | 0.997020i | \(0.475420\pi\) | |||||||
\(710\) | −76.1506 | −2.85788 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 74.9528 | 2.80898 | ||||||||
\(713\) | 32.6601 | 1.22313 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.723729 | 0.0270659 | ||||||||
\(716\) | 37.0263 | 1.38374 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.7453 | 0.662249 | ||||||||
\(719\) | −48.2816 | −1.80060 | −0.900299 | − | 0.435271i | \(-0.856653\pi\) | ||||
−0.900299 | + | 0.435271i | \(0.856653\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −37.1665 | −1.38319 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 48.4375 | 1.80016 | ||||||||
\(725\) | 64.0990 | 2.38058 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.0302 | 1.52173 | 0.760863 | − | 0.648913i | \(-0.224776\pi\) | ||||
0.760863 | + | 0.648913i | \(0.224776\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.7630 | −0.657439 | ||||||||
\(731\) | −11.3016 | −0.418006 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.5428 | −1.12812 | −0.564062 | − | 0.825733i | \(-0.690762\pi\) | ||||
−0.564062 | + | 0.825733i | \(0.690762\pi\) | |||||||
\(734\) | −27.0021 | −0.996667 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.50739 | 0.0924237 | ||||||||
\(737\) | 1.46343 | 0.0539061 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.8200 | 0.876234 | 0.438117 | − | 0.898918i | \(-0.355646\pi\) | ||||
0.438117 | + | 0.898918i | \(0.355646\pi\) | |||||||
\(740\) | −34.5161 | −1.26884 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.5218 | 0.386007 | 0.193003 | − | 0.981198i | \(-0.438177\pi\) | ||||
0.193003 | + | 0.981198i | \(0.438177\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.4897 | 1.30024 | ||||||||
\(746\) | −1.33794 | −0.0489855 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.00079 | 0.292538 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.2704 | −0.374773 | −0.187386 | − | 0.982286i | \(-0.560002\pi\) | ||||
−0.187386 | + | 0.982286i | \(0.560002\pi\) | |||||||
\(752\) | −27.3330 | −0.996734 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.16010 | −0.333591 | ||||||||
\(755\) | 46.9507 | 1.70871 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.03930 | 0.292193 | 0.146097 | − | 0.989270i | \(-0.453329\pi\) | ||||
0.146097 | + | 0.989270i | \(0.453329\pi\) | |||||||
\(758\) | −55.8319 | −2.02791 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 36.4868 | 1.32351 | ||||||||
\(761\) | −27.6604 | −1.00269 | −0.501345 | − | 0.865247i | \(-0.667161\pi\) | ||||
−0.501345 | + | 0.865247i | \(0.667161\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 37.0554 | 1.34062 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 87.8742 | 3.17502 | ||||||||
\(767\) | −2.97841 | −0.107544 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.9226 | 1.22328 | 0.611640 | − | 0.791136i | \(-0.290510\pi\) | ||||
0.611640 | + | 0.791136i | \(0.290510\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 68.6883 | 2.47215 | ||||||||
\(773\) | 28.5956 | 1.02851 | 0.514256 | − | 0.857637i | \(-0.328068\pi\) | ||||
0.514256 | + | 0.857637i | \(0.328068\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 58.8986 | 2.11570 | ||||||||
\(776\) | −47.9507 | −1.72133 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 95.1210 | 3.41025 | ||||||||
\(779\) | −14.8290 | −0.531303 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.43852 | 0.123040 | ||||||||
\(782\) | 55.5294 | 1.98573 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −76.6313 | −2.73509 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.0035 | −1.63985 | −0.819923 | − | 0.572473i | \(-0.805984\pi\) | ||||
−0.819923 | + | 0.572473i | \(0.805984\pi\) | |||||||
\(788\) | −86.4222 | −3.07866 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −73.4661 | −2.61381 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.90757 | 0.138762 | ||||||||
\(794\) | −29.3977 | −1.04328 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 40.4367 | 1.43324 | ||||||||
\(797\) | 36.9117 | 1.30748 | 0.653739 | − | 0.756720i | \(-0.273199\pi\) | ||||
0.653739 | + | 0.756720i | \(0.273199\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.6706 | −1.08505 | ||||||||
\(800\) | 4.52179 | 0.159869 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 79.6136 | 2.81125 | ||||||||
\(803\) | 0.802077 | 0.0283047 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.41693 | −0.296474 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 44.0300 | 1.54897 | ||||||||
\(809\) | 47.6887 | 1.67665 | 0.838323 | − | 0.545174i | \(-0.183537\pi\) | ||||
0.838323 | + | 0.545174i | \(0.183537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.02728 | 0.211646 | 0.105823 | − | 0.994385i | \(-0.466252\pi\) | ||||
0.105823 | + | 0.994385i | \(0.466252\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.32743 | 0.0815764 | ||||||||
\(815\) | 40.8324 | 1.43030 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.59322 | 0.160696 | ||||||||
\(818\) | 46.6881 | 1.63241 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −111.434 | −3.89143 | ||||||||
\(821\) | −39.2642 | −1.37033 | −0.685165 | − | 0.728388i | \(-0.740270\pi\) | ||||
−0.685165 | + | 0.728388i | \(0.740270\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.7630 | 0.793469 | 0.396735 | − | 0.917933i | \(-0.370143\pi\) | ||||
0.396735 | + | 0.917933i | \(0.370143\pi\) | |||||||
\(824\) | 40.5697 | 1.41331 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.9286 | −1.00595 | −0.502973 | − | 0.864302i | \(-0.667760\pi\) | ||||
−0.502973 | + | 0.864302i | \(0.667760\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.9767 | −1.18006 | −0.590029 | − | 0.807382i | \(-0.700884\pi\) | ||||
−0.590029 | + | 0.807382i | \(0.700884\pi\) | |||||||
\(830\) | −109.557 | −3.80276 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.56697 | 0.123662 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.6578 | −0.438041 | ||||||||
\(836\) | −3.25169 | −0.112462 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −42.5432 | −1.46963 | ||||||||
\(839\) | 38.0411 | 1.31333 | 0.656663 | − | 0.754184i | \(-0.271967\pi\) | ||||
0.656663 | + | 0.754184i | \(0.271967\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.4868 | 1.01678 | ||||||||
\(842\) | 45.7673 | 1.57725 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19.8319 | 0.682642 | ||||||||
\(845\) | 46.6881 | 1.60612 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15.4432 | −0.530321 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 100.141 | 3.43480 | ||||||||
\(851\) | 10.8171 | 0.370806 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.81491 | 0.336056 | 0.168028 | − | 0.985782i | \(-0.446260\pi\) | ||||
0.168028 | + | 0.985782i | \(0.446260\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 64.9046 | 2.21840 | ||||||||
\(857\) | 26.7360 | 0.913285 | 0.456642 | − | 0.889650i | \(-0.349052\pi\) | ||||
0.456642 | + | 0.889650i | \(0.349052\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.4882 | −0.630810 | −0.315405 | − | 0.948957i | \(-0.602140\pi\) | ||||
−0.315405 | + | 0.948957i | \(0.602140\pi\) | |||||||
\(860\) | 34.5161 | 1.17699 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −39.0689 | −1.33069 | ||||||||
\(863\) | −9.14786 | −0.311397 | −0.155698 | − | 0.987805i | \(-0.549763\pi\) | ||||
−0.155698 | + | 0.987805i | \(0.549763\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.1445 | 0.752937 | ||||||||
\(866\) | 99.4946 | 3.38097 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.31731 | 0.112532 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.75285 | −0.0593929 | ||||||||
\(872\) | 13.1445 | 0.445130 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −22.5683 | −0.763385 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.6883 | 0.766130 | 0.383065 | − | 0.923721i | \(-0.374869\pi\) | ||||
0.383065 | + | 0.923721i | \(0.374869\pi\) | |||||||
\(878\) | 30.6602 | 1.03473 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.43367 | −0.216879 | ||||||||
\(881\) | 15.3696 | 0.517815 | 0.258907 | − | 0.965902i | \(-0.416638\pi\) | ||||
0.258907 | + | 0.965902i | \(0.416638\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.6372 | 0.997370 | 0.498685 | − | 0.866783i | \(-0.333817\pi\) | ||||
0.498685 | + | 0.866783i | \(0.333817\pi\) | |||||||
\(884\) | −9.58307 | −0.322313 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.2518 | −0.680371 | ||||||||
\(887\) | −18.7650 | −0.630069 | −0.315034 | − | 0.949080i | \(-0.602016\pi\) | ||||
−0.315034 | + | 0.949080i | \(0.602016\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −133.482 | −4.47432 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −94.9014 | −3.17753 | ||||||||
\(893\) | 12.4652 | 0.417131 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.4095 | −1.11676 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.8889 | 0.463479 | ||||||||
\(899\) | 53.7416 | 1.79238 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.3289 | −0.577310 | ||||||||
\(902\) | 7.51399 | 0.250189 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −70.5054 | −2.34498 | ||||||||
\(905\) | −43.7060 | −1.45284 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.1082 | −1.03293 | −0.516465 | − | 0.856308i | \(-0.672752\pi\) | ||||
−0.516465 | + | 0.856308i | \(0.672752\pi\) | |||||||
\(908\) | −24.8045 | −0.823165 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.4753 | 0.578982 | 0.289491 | − | 0.957181i | \(-0.406514\pi\) | ||||
0.289491 | + | 0.957181i | \(0.406514\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.94695 | 0.163720 | ||||||||
\(914\) | 12.4720 | 0.412536 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.92054 | 0.195620 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.1986 | 1.39200 | 0.696002 | − | 0.718040i | \(-0.254960\pi\) | ||||
0.696002 | + | 0.718040i | \(0.254960\pi\) | |||||||
\(920\) | −85.9270 | −2.83293 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.1344 | −0.630158 | ||||||||
\(923\) | −4.11854 | −0.135564 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.5074 | 0.641399 | ||||||||
\(926\) | −22.5873 | −0.742266 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.12588 | 0.135439 | ||||||||
\(929\) | 48.4111 | 1.58832 | 0.794159 | − | 0.607710i | \(-0.207912\pi\) | ||||
0.794159 | + | 0.607710i | \(0.207912\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −53.7103 | −1.75934 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −33.8699 | −1.10826 | ||||||||
\(935\) | −7.21926 | −0.236095 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.6750 | −0.740762 | −0.370381 | − | 0.928880i | \(-0.620773\pi\) | ||||
−0.370381 | + | 0.928880i | \(0.620773\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 93.6706 | 3.05520 | ||||||||
\(941\) | −49.9505 | −1.62834 | −0.814170 | − | 0.580627i | \(-0.802808\pi\) | ||||
−0.814170 | + | 0.580627i | \(0.802808\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.9225 | 1.13723 | ||||||||
\(944\) | 26.4769 | 0.861749 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.32743 | −0.0756713 | ||||||||
\(947\) | 17.7123 | 0.575571 | 0.287786 | − | 0.957695i | \(-0.407081\pi\) | ||||
0.287786 | + | 0.957695i | \(0.407081\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.960699 | −0.0311856 | ||||||||
\(950\) | −40.6993 | −1.32046 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.0229 | 1.23168 | 0.615842 | − | 0.787870i | \(-0.288816\pi\) | ||||
0.615842 | + | 0.787870i | \(0.288816\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.4358 | −1.08196 | ||||||||
\(956\) | 78.6035 | 2.54222 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.4353 | 0.692544 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.3815 | 0.592952 | ||||||||
\(962\) | −2.78771 | −0.0898795 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.4881 | −0.659876 | ||||||||
\(965\) | −61.9787 | −1.99517 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.0128 | −0.997305 | −0.498652 | − | 0.866802i | \(-0.666172\pi\) | ||||
−0.498652 | + | 0.866802i | \(0.666172\pi\) | |||||||
\(968\) | −54.7601 | −1.76006 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 85.3943 | 2.74185 | ||||||||
\(971\) | −14.5675 | −0.467494 | −0.233747 | − | 0.972297i | \(-0.575099\pi\) | ||||
−0.233747 | + | 0.972297i | \(0.575099\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −44.3786 | −1.42198 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.7368 | −1.11190 | ||||||||
\(977\) | −47.8797 | −1.53181 | −0.765904 | − | 0.642955i | \(-0.777708\pi\) | ||||
−0.765904 | + | 0.642955i | \(0.777708\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.02728 | 0.192633 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.03638 | 0.160717 | ||||||||
\(983\) | −44.4257 | −1.41696 | −0.708479 | − | 0.705732i | \(-0.750618\pi\) | ||||
−0.708479 | + | 0.705732i | \(0.750618\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 77.9803 | 2.48466 | ||||||||
\(986\) | 91.3729 | 2.90991 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.89476 | 0.123909 | ||||||||
\(989\) | −10.8171 | −0.343964 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.6156 | −1.32196 | −0.660981 | − | 0.750403i | \(-0.729860\pi\) | ||||
−0.660981 | + | 0.750403i | \(0.729860\pi\) | |||||||
\(992\) | 3.79114 | 0.120369 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.4868 | −1.15671 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.0281 | 0.412606 | 0.206303 | − | 0.978488i | \(-0.433857\pi\) | ||||
0.206303 | + | 0.978488i | \(0.433857\pi\) | |||||||
\(998\) | −96.1751 | −3.04437 | ||||||||
\(999\) | 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 | 3969.2.a.be.1.5 | 6 | ||
3.2 | odd | 2 | 3969.2.a.bd.1.2 | 6 | |||
7.6 | odd | 2 | inner | 3969.2.a.be.1.6 | 6 | ||
9.2 | odd | 6 | 1323.2.f.g.442.5 | 12 | |||
9.4 | even | 3 | 441.2.f.g.295.2 | yes | 12 | ||
9.5 | odd | 6 | 1323.2.f.g.883.5 | 12 | |||
9.7 | even | 3 | 441.2.f.g.148.2 | yes | 12 | ||
21.20 | even | 2 | 3969.2.a.bd.1.1 | 6 | |||
63.2 | odd | 6 | 1323.2.g.g.361.6 | 12 | |||
63.4 | even | 3 | 441.2.g.g.79.1 | 12 | |||
63.5 | even | 6 | 1323.2.h.g.802.2 | 12 | |||
63.11 | odd | 6 | 1323.2.h.g.226.1 | 12 | |||
63.13 | odd | 6 | 441.2.f.g.295.1 | yes | 12 | ||
63.16 | even | 3 | 441.2.g.g.67.1 | 12 | |||
63.20 | even | 6 | 1323.2.f.g.442.6 | 12 | |||
63.23 | odd | 6 | 1323.2.h.g.802.1 | 12 | |||
63.25 | even | 3 | 441.2.h.g.373.5 | 12 | |||
63.31 | odd | 6 | 441.2.g.g.79.2 | 12 | |||
63.32 | odd | 6 | 1323.2.g.g.667.6 | 12 | |||
63.34 | odd | 6 | 441.2.f.g.148.1 | ✓ | 12 | ||
63.38 | even | 6 | 1323.2.h.g.226.2 | 12 | |||
63.40 | odd | 6 | 441.2.h.g.214.6 | 12 | |||
63.41 | even | 6 | 1323.2.f.g.883.6 | 12 | |||
63.47 | even | 6 | 1323.2.g.g.361.5 | 12 | |||
63.52 | odd | 6 | 441.2.h.g.373.6 | 12 | |||
63.58 | even | 3 | 441.2.h.g.214.5 | 12 | |||
63.59 | even | 6 | 1323.2.g.g.667.5 | 12 | |||
63.61 | odd | 6 | 441.2.g.g.67.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.g.148.1 | ✓ | 12 | 63.34 | odd | 6 | ||
441.2.f.g.148.2 | yes | 12 | 9.7 | even | 3 | ||
441.2.f.g.295.1 | yes | 12 | 63.13 | odd | 6 | ||
441.2.f.g.295.2 | yes | 12 | 9.4 | even | 3 | ||
441.2.g.g.67.1 | 12 | 63.16 | even | 3 | |||
441.2.g.g.67.2 | 12 | 63.61 | odd | 6 | |||
441.2.g.g.79.1 | 12 | 63.4 | even | 3 | |||
441.2.g.g.79.2 | 12 | 63.31 | odd | 6 | |||
441.2.h.g.214.5 | 12 | 63.58 | even | 3 | |||
441.2.h.g.214.6 | 12 | 63.40 | odd | 6 | |||
441.2.h.g.373.5 | 12 | 63.25 | even | 3 | |||
441.2.h.g.373.6 | 12 | 63.52 | odd | 6 | |||
1323.2.f.g.442.5 | 12 | 9.2 | odd | 6 | |||
1323.2.f.g.442.6 | 12 | 63.20 | even | 6 | |||
1323.2.f.g.883.5 | 12 | 9.5 | odd | 6 | |||
1323.2.f.g.883.6 | 12 | 63.41 | even | 6 | |||
1323.2.g.g.361.5 | 12 | 63.47 | even | 6 | |||
1323.2.g.g.361.6 | 12 | 63.2 | odd | 6 | |||
1323.2.g.g.667.5 | 12 | 63.59 | even | 6 | |||
1323.2.g.g.667.6 | 12 | 63.32 | odd | 6 | |||
1323.2.h.g.226.1 | 12 | 63.11 | odd | 6 | |||
1323.2.h.g.226.2 | 12 | 63.38 | even | 6 | |||
1323.2.h.g.802.1 | 12 | 63.23 | odd | 6 | |||
1323.2.h.g.802.2 | 12 | 63.5 | even | 6 | |||
3969.2.a.bd.1.1 | 6 | 21.20 | even | 2 | |||
3969.2.a.bd.1.2 | 6 | 3.2 | odd | 2 | |||
3969.2.a.be.1.5 | 6 | 1.1 | even | 1 | trivial | ||
3969.2.a.be.1.6 | 6 | 7.6 | odd | 2 | inner |