Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4851,2,Mod(1,4851)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4851, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4851.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4851 = 3^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4851.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: | \(38.7354300205\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1617) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.11491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4851.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.11491 | −1.49547 | −0.747733 | − | 0.664000i | \(-0.768858\pi\) | ||||
−0.747733 | + | 0.664000i | \(0.768858\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.47283 | 1.23642 | ||||||||
\(5\) | 1.64207 | 0.734358 | 0.367179 | − | 0.930150i | \(-0.380324\pi\) | ||||
0.367179 | + | 0.930150i | \(0.380324\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.47283 | −1.09821 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.58774 | −1.27241 | −0.636205 | − | 0.771520i | \(-0.719497\pi\) | ||||
−0.636205 | + | 0.771520i | \(0.719497\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.83076 | −0.707690 | ||||||||
\(17\) | 0.715853 | 0.173620 | 0.0868099 | − | 0.996225i | \(-0.472333\pi\) | ||||
0.0868099 | + | 0.996225i | \(0.472333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.64207 | −0.376718 | −0.188359 | − | 0.982100i | \(-0.560317\pi\) | ||||
−0.188359 | + | 0.982100i | \(0.560317\pi\) | |||||||
\(20\) | 4.06058 | 0.907972 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.11491 | 0.450900 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.30359 | −0.460719 | ||||||||
\(26\) | 9.70265 | 1.90285 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.53341 | 1.02753 | 0.513764 | − | 0.857931i | \(-0.328251\pi\) | ||||
0.513764 | + | 0.857931i | \(0.328251\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.17548 | 0.929544 | 0.464772 | − | 0.885430i | \(-0.346136\pi\) | ||||
0.464772 | + | 0.885430i | \(0.346136\pi\) | |||||||
\(32\) | 7.98680 | 1.41188 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.51396 | −0.259642 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.58774 | −1.08302 | −0.541509 | − | 0.840695i | \(-0.682147\pi\) | ||||
−0.541509 | + | 0.840695i | \(0.682147\pi\) | |||||||
\(38\) | 3.47283 | 0.563368 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.64207 | −0.259635 | ||||||||
\(41\) | 5.17548 | 0.808275 | 0.404137 | − | 0.914698i | \(-0.367572\pi\) | ||||
0.404137 | + | 0.914698i | \(0.367572\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.17548 | 0.789254 | 0.394627 | − | 0.918841i | \(-0.370874\pi\) | ||||
0.394627 | + | 0.918841i | \(0.370874\pi\) | |||||||
\(44\) | −2.47283 | −0.372794 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.87189 | 1.14823 | 0.574116 | − | 0.818774i | \(-0.305346\pi\) | ||||
0.574116 | + | 0.818774i | \(0.305346\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.87189 | 0.688989 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −11.3447 | −1.57323 | ||||||||
\(53\) | −2.71585 | −0.373051 | −0.186526 | − | 0.982450i | \(-0.559723\pi\) | ||||
−0.186526 | + | 0.982450i | \(0.559723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.64207 | −0.221417 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.7026 | −1.53663 | ||||||||
\(59\) | −3.15604 | −0.410881 | −0.205440 | − | 0.978670i | \(-0.565863\pi\) | ||||
−0.205440 | + | 0.978670i | \(0.565863\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.1755 | −1.68695 | −0.843474 | − | 0.537170i | \(-0.819493\pi\) | ||||
−0.843474 | + | 0.537170i | \(0.819493\pi\) | |||||||
\(62\) | −10.9457 | −1.39010 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.2298 | −1.40373 | ||||||||
\(65\) | −7.53341 | −0.934404 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.21037 | 0.514378 | 0.257189 | − | 0.966361i | \(-0.417204\pi\) | ||||
0.257189 | + | 0.966361i | \(0.417204\pi\) | |||||||
\(68\) | 1.77018 | 0.214666 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.85244 | 0.219844 | 0.109922 | − | 0.993940i | \(-0.464940\pi\) | ||||
0.109922 | + | 0.993940i | \(0.464940\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4791 | 1.22648 | 0.613242 | − | 0.789895i | \(-0.289865\pi\) | ||||
0.613242 | + | 0.789895i | \(0.289865\pi\) | |||||||
\(74\) | 13.9325 | 1.61962 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.06058 | −0.465780 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.4596 | −1.40182 | −0.700909 | − | 0.713251i | \(-0.747222\pi\) | ||||
−0.700909 | + | 0.713251i | \(0.747222\pi\) | |||||||
\(80\) | −4.64832 | −0.519698 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.9457 | −1.20875 | ||||||||
\(83\) | −9.17548 | −1.00714 | −0.503570 | − | 0.863954i | \(-0.667980\pi\) | ||||
−0.503570 | + | 0.863954i | \(0.667980\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.17548 | 0.127499 | ||||||||
\(86\) | −10.9457 | −1.18030 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 4.71585 | 0.499879 | 0.249940 | − | 0.968261i | \(-0.419589\pi\) | ||||
0.249940 | + | 0.968261i | \(0.419589\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −16.6483 | −1.71714 | ||||||||
\(95\) | −2.69641 | −0.276645 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.6351 | 1.38444 | 0.692218 | − | 0.721688i | \(-0.256634\pi\) | ||||
0.692218 | + | 0.721688i | \(0.256634\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.69641 | −0.569641 | ||||||||
\(101\) | −14.6072 | −1.45347 | −0.726735 | − | 0.686918i | \(-0.758963\pi\) | ||||
−0.726735 | + | 0.686918i | \(0.758963\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.8913 | −1.76289 | −0.881443 | − | 0.472291i | \(-0.843427\pi\) | ||||
−0.881443 | + | 0.472291i | \(0.843427\pi\) | |||||||
\(104\) | 4.58774 | 0.449865 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.74378 | 0.557885 | ||||||||
\(107\) | −11.1560 | −1.07849 | −0.539247 | − | 0.842147i | \(-0.681291\pi\) | ||||
−0.539247 | + | 0.842147i | \(0.681291\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.108664 | −0.0104082 | −0.00520408 | − | 0.999986i | \(-0.501657\pi\) | ||||
−0.00520408 | + | 0.999986i | \(0.501657\pi\) | |||||||
\(110\) | 3.47283 | 0.331122 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0668 | 1.22922 | 0.614611 | − | 0.788830i | \(-0.289313\pi\) | ||||
0.614611 | + | 0.788830i | \(0.289313\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 13.6832 | 1.27045 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.67472 | 0.614458 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 27.8649 | 2.52277 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.7981 | 1.14930 | ||||||||
\(125\) | −11.9930 | −1.07269 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.4596 | −1.81550 | −0.907749 | − | 0.419513i | \(-0.862201\pi\) | ||||
−0.907749 | + | 0.419513i | \(0.862201\pi\) | |||||||
\(128\) | 7.77643 | 0.687346 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 15.9325 | 1.39737 | ||||||||
\(131\) | −15.0668 | −1.31639 | −0.658197 | − | 0.752846i | \(-0.728681\pi\) | ||||
−0.658197 | + | 0.752846i | \(0.728681\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.90454 | −0.769235 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.715853 | −0.0613839 | ||||||||
\(137\) | 14.4596 | 1.23537 | 0.617685 | − | 0.786426i | \(-0.288071\pi\) | ||||
0.617685 | + | 0.786426i | \(0.288071\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.13659 | 0.435680 | 0.217840 | − | 0.975985i | \(-0.430099\pi\) | ||||
0.217840 | + | 0.975985i | \(0.430099\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.91774 | −0.328770 | ||||||||
\(143\) | 4.58774 | 0.383646 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.08627 | 0.754573 | ||||||||
\(146\) | −22.1623 | −1.83416 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −16.2904 | −1.33906 | ||||||||
\(149\) | −16.8176 | −1.37775 | −0.688874 | − | 0.724881i | \(-0.741895\pi\) | ||||
−0.688874 | + | 0.724881i | \(0.741895\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.71585 | 0.383771 | 0.191885 | − | 0.981417i | \(-0.438540\pi\) | ||||
0.191885 | + | 0.981417i | \(0.438540\pi\) | |||||||
\(152\) | 1.64207 | 0.133190 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.49852 | 0.682618 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0279 | 0.880124 | 0.440062 | − | 0.897967i | \(-0.354956\pi\) | ||||
0.440062 | + | 0.897967i | \(0.354956\pi\) | |||||||
\(158\) | 26.3510 | 2.09637 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.1149 | 1.03682 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.64207 | 0.441921 | 0.220961 | − | 0.975283i | \(-0.429081\pi\) | ||||
0.220961 | + | 0.975283i | \(0.429081\pi\) | |||||||
\(164\) | 12.7981 | 0.999364 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.4053 | 1.50614 | ||||||||
\(167\) | 16.0000 | 1.23812 | 0.619059 | − | 0.785345i | \(-0.287514\pi\) | ||||
0.619059 | + | 0.785345i | \(0.287514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.04737 | 0.619029 | ||||||||
\(170\) | −2.48604 | −0.190670 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.7981 | 0.975847 | ||||||||
\(173\) | −15.0279 | −1.14255 | −0.571276 | − | 0.820758i | \(-0.693551\pi\) | ||||
−0.571276 | + | 0.820758i | \(0.693551\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.83076 | 0.213377 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.97359 | −0.747552 | ||||||||
\(179\) | −9.89134 | −0.739313 | −0.369657 | − | 0.929168i | \(-0.620525\pi\) | ||||
−0.369657 | + | 0.929168i | \(0.620525\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.82452 | −0.507262 | −0.253631 | − | 0.967301i | \(-0.581625\pi\) | ||||
−0.253631 | + | 0.967301i | \(0.581625\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.8176 | −0.795323 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.715853 | −0.0523483 | ||||||||
\(188\) | 19.4659 | 1.41969 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.70265 | 0.413714 | ||||||||
\(191\) | −11.0279 | −0.797953 | −0.398976 | − | 0.916961i | \(-0.630634\pi\) | ||||
−0.398976 | + | 0.916961i | \(0.630634\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.85244 | −0.565231 | −0.282616 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282616 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(194\) | −28.8370 | −2.07038 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.8913 | −1.41720 | −0.708599 | − | 0.705611i | \(-0.750673\pi\) | ||||
−0.708599 | + | 0.705611i | \(0.750673\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.5264 | −1.66775 | −0.833873 | − | 0.551957i | \(-0.813881\pi\) | ||||
−0.833873 | + | 0.551957i | \(0.813881\pi\) | |||||||
\(200\) | 2.30359 | 0.162889 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 30.8929 | 2.17361 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.49852 | 0.593563 | ||||||||
\(206\) | 37.8385 | 2.63633 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.9868 | 0.900472 | ||||||||
\(209\) | 1.64207 | 0.113585 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.25622 | −0.293010 | −0.146505 | − | 0.989210i | \(-0.546803\pi\) | ||||
−0.146505 | + | 0.989210i | \(0.546803\pi\) | |||||||
\(212\) | −6.71585 | −0.461247 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23.5940 | 1.61285 | ||||||||
\(215\) | 8.49852 | 0.579595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.229815 | 0.0155650 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.06058 | −0.273764 | ||||||||
\(221\) | −3.28415 | −0.220916 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.74378 | 0.250702 | 0.125351 | − | 0.992112i | \(-0.459994\pi\) | ||||
0.125351 | + | 0.992112i | \(0.459994\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.6351 | −1.83826 | ||||||||
\(227\) | −15.4876 | −1.02795 | −0.513973 | − | 0.857807i | \(-0.671827\pi\) | ||||
−0.513973 | + | 0.857807i | \(0.671827\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | 0.528655 | 0.264327 | − | 0.964433i | \(-0.414850\pi\) | ||||
0.264327 | + | 0.964433i | \(0.414850\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.53341 | −0.363286 | ||||||||
\(233\) | 5.54037 | 0.362962 | 0.181481 | − | 0.983394i | \(-0.441911\pi\) | ||||
0.181481 | + | 0.983394i | \(0.441911\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.9262 | 0.843214 | ||||||||
\(236\) | −7.80435 | −0.508020 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.26470 | 0.0818067 | 0.0409033 | − | 0.999163i | \(-0.486976\pi\) | ||||
0.0409033 | + | 0.999163i | \(0.486976\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.8719 | 1.53772 | 0.768862 | − | 0.639415i | \(-0.220823\pi\) | ||||
0.768862 | + | 0.639415i | \(0.220823\pi\) | |||||||
\(242\) | −2.11491 | −0.135951 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −32.5808 | −2.08577 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.53341 | 0.479339 | ||||||||
\(248\) | −5.17548 | −0.328643 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 25.3642 | 1.60417 | ||||||||
\(251\) | 22.0194 | 1.38986 | 0.694928 | − | 0.719080i | \(-0.255436\pi\) | ||||
0.694928 | + | 0.719080i | \(0.255436\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 43.2702 | 2.71502 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.01320 | 0.375825 | ||||||||
\(257\) | 27.3161 | 1.70393 | 0.851965 | − | 0.523599i | \(-0.175411\pi\) | ||||
0.851965 | + | 0.523599i | \(0.175411\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −18.6289 | −1.15531 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 31.8649 | 1.96862 | ||||||||
\(263\) | 11.8719 | 0.732052 | 0.366026 | − | 0.930605i | \(-0.380718\pi\) | ||||
0.366026 | + | 0.930605i | \(0.380718\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.45963 | −0.273953 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.4115 | 0.635986 | ||||||||
\(269\) | 5.63511 | 0.343579 | 0.171789 | − | 0.985134i | \(-0.445045\pi\) | ||||
0.171789 | + | 0.985134i | \(0.445045\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.68097 | 0.345094 | 0.172547 | − | 0.985001i | \(-0.444800\pi\) | ||||
0.172547 | + | 0.985001i | \(0.444800\pi\) | |||||||
\(272\) | −2.02641 | −0.122869 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −30.5808 | −1.84745 | ||||||||
\(275\) | 2.30359 | 0.138912 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.4876 | −1.53140 | −0.765699 | − | 0.643199i | \(-0.777607\pi\) | ||||
−0.765699 | + | 0.643199i | \(0.777607\pi\) | |||||||
\(278\) | −10.8634 | −0.651544 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.5723 | −1.04828 | −0.524138 | − | 0.851633i | \(-0.675612\pi\) | ||||
−0.524138 | + | 0.851633i | \(0.675612\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.1296 | −1.49380 | −0.746901 | − | 0.664936i | \(-0.768459\pi\) | ||||
−0.746901 | + | 0.664936i | \(0.768459\pi\) | |||||||
\(284\) | 4.58078 | 0.271819 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.70265 | −0.573730 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4876 | −0.969856 | ||||||||
\(290\) | −19.2166 | −1.12844 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 25.9130 | 1.51644 | ||||||||
\(293\) | −14.3510 | −0.838392 | −0.419196 | − | 0.907896i | \(-0.637688\pi\) | ||||
−0.419196 | + | 0.907896i | \(0.637688\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.18244 | −0.301734 | ||||||||
\(296\) | 6.58774 | 0.382905 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 35.5676 | 2.06037 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.97359 | −0.573916 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.64832 | 0.266599 | ||||||||
\(305\) | −21.6351 | −1.23882 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.1366 | −0.749745 | −0.374872 | − | 0.927076i | \(-0.622313\pi\) | ||||
−0.374872 | + | 0.927076i | \(0.622313\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.9736 | −1.02083 | ||||||||
\(311\) | −14.3510 | −0.813769 | −0.406884 | − | 0.913480i | \(-0.633385\pi\) | ||||
−0.406884 | + | 0.913480i | \(0.633385\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.7438 | −1.34208 | −0.671039 | − | 0.741422i | \(-0.734152\pi\) | ||||
−0.671039 | + | 0.741422i | \(0.734152\pi\) | |||||||
\(314\) | −23.3230 | −1.31620 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −30.8106 | −1.73323 | ||||||||
\(317\) | 6.45963 | 0.362809 | 0.181404 | − | 0.983409i | \(-0.441936\pi\) | ||||
0.181404 | + | 0.983409i | \(0.441936\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.53341 | −0.309811 | ||||||||
\(320\) | −18.4402 | −1.03084 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.17548 | −0.0654056 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.5683 | 0.586224 | ||||||||
\(326\) | −11.9325 | −0.660878 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.17548 | −0.285768 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.2702 | 1.71877 | 0.859384 | − | 0.511332i | \(-0.170848\pi\) | ||||
0.859384 | + | 0.511332i | \(0.170848\pi\) | |||||||
\(332\) | −22.6894 | −1.24525 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −33.8385 | −1.85156 | ||||||||
\(335\) | 6.91373 | 0.377738 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.3121 | −0.888575 | −0.444288 | − | 0.895884i | \(-0.646543\pi\) | ||||
−0.444288 | + | 0.895884i | \(0.646543\pi\) | |||||||
\(338\) | −17.0194 | −0.925736 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.90677 | 0.157642 | ||||||||
\(341\) | −5.17548 | −0.280268 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.17548 | −0.279043 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.7827 | 1.70865 | ||||||||
\(347\) | 6.86341 | 0.368447 | 0.184224 | − | 0.982884i | \(-0.441023\pi\) | ||||
0.184224 | + | 0.982884i | \(0.441023\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.8580 | −1.27709 | −0.638544 | − | 0.769585i | \(-0.720463\pi\) | ||||
−0.638544 | + | 0.769585i | \(0.720463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.98680 | −0.425698 | ||||||||
\(353\) | 11.7368 | 0.624688 | 0.312344 | − | 0.949969i | \(-0.398886\pi\) | ||||
0.312344 | + | 0.949969i | \(0.398886\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.04185 | 0.161444 | ||||||||
\(356\) | 11.6615 | 0.618059 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.9193 | 1.10562 | ||||||||
\(359\) | 27.7827 | 1.46631 | 0.733157 | − | 0.680060i | \(-0.238046\pi\) | ||||
0.733157 | + | 0.680060i | \(0.238046\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.3036 | −0.858084 | ||||||||
\(362\) | 14.4332 | 0.758593 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.2074 | 0.900677 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.5544 | 1.38613 | 0.693064 | − | 0.720877i | \(-0.256261\pi\) | ||||
0.693064 | + | 0.720877i | \(0.256261\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 22.8781 | 1.18938 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.06682 | 0.262350 | 0.131175 | − | 0.991359i | \(-0.458125\pi\) | ||||
0.131175 | + | 0.991359i | \(0.458125\pi\) | |||||||
\(374\) | 1.51396 | 0.0782851 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.87189 | −0.405962 | ||||||||
\(377\) | −25.3859 | −1.30744 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.5613 | −1.56983 | −0.784915 | − | 0.619603i | \(-0.787294\pi\) | ||||
−0.784915 | + | 0.619603i | \(0.787294\pi\) | |||||||
\(380\) | −6.66776 | −0.342049 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 23.3230 | 1.19331 | ||||||||
\(383\) | 9.13659 | 0.466858 | 0.233429 | − | 0.972374i | \(-0.425005\pi\) | ||||
0.233429 | + | 0.972374i | \(0.425005\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.6072 | 0.845284 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 33.7174 | 1.71174 | ||||||||
\(389\) | −21.2702 | −1.07844 | −0.539222 | − | 0.842164i | \(-0.681281\pi\) | ||||
−0.539222 | + | 0.842164i | \(0.681281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 42.0683 | 2.11937 | ||||||||
\(395\) | −20.4596 | −1.02944 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.9582 | −1.45337 | −0.726684 | − | 0.686972i | \(-0.758940\pi\) | ||||
−0.726684 | + | 0.686972i | \(0.758940\pi\) | |||||||
\(398\) | 49.7563 | 2.49406 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.52092 | 0.326046 | ||||||||
\(401\) | −32.3510 | −1.61553 | −0.807765 | − | 0.589505i | \(-0.799323\pi\) | ||||
−0.807765 | + | 0.589505i | \(0.799323\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.7438 | −1.18276 | ||||||||
\(404\) | −36.1212 | −1.79709 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.58774 | 0.326542 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.31207 | −0.114325 | −0.0571623 | − | 0.998365i | \(-0.518205\pi\) | ||||
−0.0571623 | + | 0.998365i | \(0.518205\pi\) | |||||||
\(410\) | −17.9736 | −0.887652 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −44.2423 | −2.17966 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.0668 | −0.739601 | ||||||||
\(416\) | −36.6414 | −1.79649 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.47283 | −0.169862 | ||||||||
\(419\) | 38.4263 | 1.87725 | 0.938623 | − | 0.344945i | \(-0.112102\pi\) | ||||
0.938623 | + | 0.344945i | \(0.112102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.5070 | 0.755765 | 0.377883 | − | 0.925854i | \(-0.376652\pi\) | ||||
0.377883 | + | 0.925854i | \(0.376652\pi\) | |||||||
\(422\) | 9.00152 | 0.438187 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.71585 | 0.131893 | ||||||||
\(425\) | −1.64903 | −0.0799899 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −27.5870 | −1.33347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.9736 | −0.866764 | ||||||||
\(431\) | −37.9666 | −1.82879 | −0.914394 | − | 0.404825i | \(-0.867332\pi\) | ||||
−0.914394 | + | 0.404825i | \(0.867332\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.1087 | −0.485791 | −0.242896 | − | 0.970052i | \(-0.578097\pi\) | ||||
−0.242896 | + | 0.970052i | \(0.578097\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.268709 | −0.0128688 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5224 | 1.07494 | 0.537469 | − | 0.843284i | \(-0.319381\pi\) | ||||
0.537469 | + | 0.843284i | \(0.319381\pi\) | |||||||
\(440\) | 1.64207 | 0.0782828 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.94567 | 0.330372 | ||||||||
\(443\) | −20.6630 | −0.981731 | −0.490865 | − | 0.871235i | \(-0.663319\pi\) | ||||
−0.490865 | + | 0.871235i | \(0.663319\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.74378 | 0.367090 | ||||||||
\(446\) | −7.91774 | −0.374916 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.8106 | −1.92597 | −0.962986 | − | 0.269553i | \(-0.913124\pi\) | ||||
−0.962986 | + | 0.269553i | \(0.913124\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.17548 | −0.243704 | ||||||||
\(452\) | 32.3121 | 1.51983 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 32.7547 | 1.53726 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.3899 | −1.32802 | −0.664011 | − | 0.747723i | \(-0.731147\pi\) | ||||
−0.664011 | + | 0.747723i | \(0.731147\pi\) | |||||||
\(458\) | −16.9193 | −0.790585 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.4178 | 0.997526 | 0.498763 | − | 0.866739i | \(-0.333788\pi\) | ||||
0.498763 | + | 0.866739i | \(0.333788\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.7478 | 0.964231 | 0.482116 | − | 0.876108i | \(-0.339868\pi\) | ||||
0.482116 | + | 0.876108i | \(0.339868\pi\) | |||||||
\(464\) | −15.6638 | −0.727172 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.7174 | −0.542797 | ||||||||
\(467\) | 26.8998 | 1.24477 | 0.622387 | − | 0.782709i | \(-0.286163\pi\) | ||||
0.622387 | + | 0.782709i | \(0.286163\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −27.3378 | −1.26100 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.15604 | 0.145268 | ||||||||
\(473\) | −5.17548 | −0.237969 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.78267 | 0.173561 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.67472 | −0.122339 | ||||||||
\(479\) | 30.8106 | 1.40777 | 0.703886 | − | 0.710313i | \(-0.251447\pi\) | ||||
0.703886 | + | 0.710313i | \(0.251447\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.2229 | 1.37804 | ||||||||
\(482\) | −50.4868 | −2.29961 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.47283 | 0.112402 | ||||||||
\(485\) | 22.3899 | 1.01667 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.4876 | −1.06432 | −0.532161 | − | 0.846643i | \(-0.678620\pi\) | ||||
−0.532161 | + | 0.846643i | \(0.678620\pi\) | |||||||
\(488\) | 13.1755 | 0.596426 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.6266 | 0.750350 | 0.375175 | − | 0.926954i | \(-0.377583\pi\) | ||||
0.375175 | + | 0.926954i | \(0.377583\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.96111 | 0.178399 | ||||||||
\(494\) | −15.9325 | −0.716835 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.6506 | −0.657829 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.99304 | −0.357818 | −0.178909 | − | 0.983866i | \(-0.557257\pi\) | ||||
−0.178909 | + | 0.983866i | \(0.557257\pi\) | |||||||
\(500\) | −29.6568 | −1.32629 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −46.5691 | −2.07848 | ||||||||
\(503\) | 24.6630 | 1.09967 | 0.549835 | − | 0.835273i | \(-0.314690\pi\) | ||||
0.549835 | + | 0.835273i | \(0.314690\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.9861 | −1.06737 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −50.5933 | −2.24471 | ||||||||
\(509\) | 15.0668 | 0.667825 | 0.333912 | − | 0.942604i | \(-0.391631\pi\) | ||||
0.333912 | + | 0.942604i | \(0.391631\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −28.2702 | −1.24938 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −57.7710 | −2.54817 | ||||||||
\(515\) | −29.3789 | −1.29459 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.87189 | −0.346205 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.53341 | 0.330362 | ||||||||
\(521\) | −42.3051 | −1.85342 | −0.926710 | − | 0.375777i | \(-0.877376\pi\) | ||||
−0.926710 | + | 0.375777i | \(0.877376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.84548 | −0.255605 | −0.127803 | − | 0.991800i | \(-0.540792\pi\) | ||||
−0.127803 | + | 0.991800i | \(0.540792\pi\) | |||||||
\(524\) | −37.2577 | −1.62761 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25.1079 | −1.09476 | ||||||||
\(527\) | 3.70488 | 0.161387 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 9.43171 | 0.409687 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.7438 | −1.02846 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.3190 | −0.792001 | ||||||||
\(536\) | −4.21037 | −0.181860 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.9177 | −0.513810 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.2982 | −1.73255 | −0.866276 | − | 0.499565i | \(-0.833493\pi\) | ||||
−0.866276 | + | 0.499565i | \(0.833493\pi\) | |||||||
\(542\) | −12.0147 | −0.516076 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.71737 | 0.245130 | ||||||||
\(545\) | −0.178435 | −0.00764331 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.98903 | 0.127802 | 0.0639009 | − | 0.997956i | \(-0.479646\pi\) | ||||
0.0639009 | + | 0.997956i | \(0.479646\pi\) | |||||||
\(548\) | 35.7563 | 1.52743 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.87189 | −0.207738 | ||||||||
\(551\) | −9.08627 | −0.387088 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 53.9038 | 2.29015 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.7019 | 0.538682 | ||||||||
\(557\) | −21.1127 | −0.894573 | −0.447286 | − | 0.894391i | \(-0.647610\pi\) | ||||
−0.447286 | + | 0.894391i | \(0.647610\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.7438 | −1.00425 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 37.1638 | 1.56766 | ||||||||
\(563\) | 29.8774 | 1.25918 | 0.629591 | − | 0.776926i | \(-0.283222\pi\) | ||||
0.629591 | + | 0.776926i | \(0.283222\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.4567 | 0.902689 | ||||||||
\(566\) | 53.1468 | 2.23393 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.85244 | −0.0777267 | ||||||||
\(569\) | −0.186452 | −0.00781648 | −0.00390824 | − | 0.999992i | \(-0.501244\pi\) | ||||
−0.00390824 | + | 0.999992i | \(0.501244\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.06682 | 0.128342 | 0.0641712 | − | 0.997939i | \(-0.479560\pi\) | ||||
0.0641712 | + | 0.997939i | \(0.479560\pi\) | |||||||
\(572\) | 11.3447 | 0.474347 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.8495 | −0.784715 | −0.392357 | − | 0.919813i | \(-0.628340\pi\) | ||||
−0.392357 | + | 0.919813i | \(0.628340\pi\) | |||||||
\(578\) | 34.8697 | 1.45039 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 22.4688 | 0.932967 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.71585 | 0.112479 | ||||||||
\(584\) | −10.4791 | −0.433627 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.3510 | 1.25379 | ||||||||
\(587\) | −8.11419 | −0.334908 | −0.167454 | − | 0.985880i | \(-0.553555\pi\) | ||||
−0.167454 | + | 0.985880i | \(0.553555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.49852 | −0.350176 | ||||||||
\(590\) | 10.9604 | 0.451232 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18.6483 | 0.766441 | ||||||||
\(593\) | 6.36489 | 0.261375 | 0.130687 | − | 0.991424i | \(-0.458282\pi\) | ||||
0.130687 | + | 0.991424i | \(0.458282\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −41.5870 | −1.70347 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.676959 | −0.0276598 | −0.0138299 | − | 0.999904i | \(-0.504402\pi\) | ||||
−0.0138299 | + | 0.999904i | \(0.504402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.6964 | 0.925806 | 0.462903 | − | 0.886409i | \(-0.346808\pi\) | ||||
0.462903 | + | 0.886409i | \(0.346808\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.6615 | 0.474501 | ||||||||
\(605\) | 1.64207 | 0.0667598 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.6141 | −0.593170 | −0.296585 | − | 0.955006i | \(-0.595848\pi\) | ||||
−0.296585 | + | 0.955006i | \(0.595848\pi\) | |||||||
\(608\) | −13.1149 | −0.531880 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 45.7563 | 1.85262 | ||||||||
\(611\) | −36.1142 | −1.46102 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.3899 | −1.14666 | −0.573328 | − | 0.819326i | \(-0.694348\pi\) | ||||
−0.573328 | + | 0.819326i | \(0.694348\pi\) | |||||||
\(614\) | 27.7827 | 1.12122 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.5404 | 0.867183 | 0.433591 | − | 0.901110i | \(-0.357246\pi\) | ||||
0.433591 | + | 0.901110i | \(0.357246\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.7827 | −0.955906 | −0.477953 | − | 0.878385i | \(-0.658621\pi\) | ||||
−0.477953 | + | 0.878385i | \(0.658621\pi\) | |||||||
\(620\) | 21.0154 | 0.844000 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.3510 | 1.21696 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.17548 | −0.327019 | ||||||||
\(626\) | 50.2159 | 2.00703 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 27.2702 | 1.08820 | ||||||||
\(629\) | −4.71585 | −0.188033 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.4068 | −1.60857 | −0.804285 | − | 0.594244i | \(-0.797451\pi\) | ||||
−0.804285 | + | 0.594244i | \(0.797451\pi\) | |||||||
\(632\) | 12.4596 | 0.495617 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.6615 | −0.542568 | ||||||||
\(635\) | −33.5962 | −1.33323 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 11.7026 | 0.463312 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.7695 | 0.504758 | ||||||||
\(641\) | −13.4876 | −0.532726 | −0.266363 | − | 0.963873i | \(-0.585822\pi\) | ||||
−0.266363 | + | 0.963873i | \(0.585822\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.8245 | −1.05786 | −0.528928 | − | 0.848667i | \(-0.677406\pi\) | ||||
−0.528928 | + | 0.848667i | \(0.677406\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.48604 | 0.0978118 | ||||||||
\(647\) | 42.4791 | 1.67002 | 0.835012 | − | 0.550231i | \(-0.185460\pi\) | ||||
0.835012 | + | 0.550231i | \(0.185460\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.15604 | 0.123885 | ||||||||
\(650\) | −22.3510 | −0.876677 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.9519 | 0.546399 | ||||||||
\(653\) | −7.39281 | −0.289303 | −0.144652 | − | 0.989483i | \(-0.546206\pi\) | ||||
−0.144652 | + | 0.989483i | \(0.546206\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.7408 | −0.966704 | ||||||||
\(656\) | −14.6506 | −0.572008 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.2368 | −0.710404 | −0.355202 | − | 0.934790i | \(-0.615588\pi\) | ||||
−0.355202 | + | 0.934790i | \(0.615588\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.16451 | −0.317563 | −0.158781 | − | 0.987314i | \(-0.550757\pi\) | ||||
−0.158781 | + | 0.987314i | \(0.550757\pi\) | |||||||
\(662\) | −66.1336 | −2.57036 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.17548 | 0.356078 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 39.5653 | 1.53083 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.6219 | −0.564894 | ||||||||
\(671\) | 13.1755 | 0.508634 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.6212 | 1.68147 | 0.840737 | − | 0.541444i | \(-0.182122\pi\) | ||||
0.840737 | + | 0.541444i | \(0.182122\pi\) | |||||||
\(674\) | 34.4985 | 1.32883 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.8998 | 0.765377 | ||||||||
\(677\) | −23.1057 | −0.888025 | −0.444012 | − | 0.896021i | \(-0.646445\pi\) | ||||
−0.444012 | + | 0.896021i | \(0.646445\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.17548 | −0.0450777 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.9457 | 0.419131 | ||||||||
\(683\) | −27.5653 | −1.05476 | −0.527379 | − | 0.849630i | \(-0.676825\pi\) | ||||
−0.527379 | + | 0.849630i | \(0.676825\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.7438 | 0.907203 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.6506 | −0.558547 | ||||||||
\(689\) | 12.4596 | 0.474674 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.85244 | 0.222637 | 0.111319 | − | 0.993785i | \(-0.464493\pi\) | ||||
0.111319 | + | 0.993785i | \(0.464493\pi\) | |||||||
\(692\) | −37.1616 | −1.41267 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.5155 | −0.551000 | ||||||||
\(695\) | 8.43466 | 0.319945 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.70488 | 0.140332 | ||||||||
\(698\) | 50.4574 | 1.90984 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.32304 | −0.352126 | −0.176063 | − | 0.984379i | \(-0.556336\pi\) | ||||
−0.176063 | + | 0.984379i | \(0.556336\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.8176 | 0.407992 | ||||||||
\(704\) | 11.2298 | 0.423240 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.8223 | −0.934199 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.5629 | 1.56093 | 0.780463 | − | 0.625202i | \(-0.214983\pi\) | ||||
0.780463 | + | 0.625202i | \(0.214983\pi\) | |||||||
\(710\) | −6.43322 | −0.241435 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.71585 | −0.176734 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.53341 | 0.281734 | ||||||||
\(716\) | −24.4596 | −0.914099 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −58.7578 | −2.19282 | ||||||||
\(719\) | −31.4372 | −1.17241 | −0.586205 | − | 0.810162i | \(-0.699379\pi\) | ||||
−0.586205 | + | 0.810162i | \(0.699379\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 34.4806 | 1.28323 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.8759 | −0.627188 | ||||||||
\(725\) | −12.7467 | −0.473402 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.2732 | 0.529363 | 0.264681 | − | 0.964336i | \(-0.414733\pi\) | ||||
0.264681 | + | 0.964336i | \(0.414733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −36.3921 | −1.34693 | ||||||||
\(731\) | 3.70488 | 0.137030 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.31207 | 0.0853983 | 0.0426992 | − | 0.999088i | \(-0.486404\pi\) | ||||
0.0426992 | + | 0.999088i | \(0.486404\pi\) | |||||||
\(734\) | −56.1600 | −2.07291 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.21037 | −0.155091 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.0558 | −0.958480 | −0.479240 | − | 0.877684i | \(-0.659088\pi\) | ||||
−0.479240 | + | 0.877684i | \(0.659088\pi\) | |||||||
\(740\) | −26.7500 | −0.983350 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.04737 | −0.185170 | −0.0925851 | − | 0.995705i | \(-0.529513\pi\) | ||||
−0.0925851 | + | 0.995705i | \(0.529513\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.6157 | −1.01176 | ||||||||
\(746\) | −10.7159 | −0.392335 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.77018 | −0.0647244 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.4387 | −1.47563 | −0.737815 | − | 0.675002i | \(-0.764143\pi\) | ||||
−0.737815 | + | 0.675002i | \(0.764143\pi\) | |||||||
\(752\) | −22.2834 | −0.812593 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 53.6887 | 1.95523 | ||||||||
\(755\) | 7.74378 | 0.281825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.4263 | −0.887788 | −0.443894 | − | 0.896079i | \(-0.646403\pi\) | ||||
−0.443894 | + | 0.896079i | \(0.646403\pi\) | |||||||
\(758\) | 64.6344 | 2.34763 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.69641 | 0.0978089 | ||||||||
\(761\) | 5.18940 | 0.188116 | 0.0940579 | − | 0.995567i | \(-0.470016\pi\) | ||||
0.0940579 | + | 0.995567i | \(0.470016\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −27.2702 | −0.986602 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.3230 | −0.698170 | ||||||||
\(767\) | 14.4791 | 0.522809 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.1670 | 1.01573 | 0.507864 | − | 0.861437i | \(-0.330435\pi\) | ||||
0.507864 | + | 0.861437i | \(0.330435\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.4178 | −0.698861 | ||||||||
\(773\) | 38.2662 | 1.37634 | 0.688170 | − | 0.725549i | \(-0.258414\pi\) | ||||
0.688170 | + | 0.725549i | \(0.258414\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.9222 | −0.428259 | ||||||||
\(776\) | −13.6351 | −0.489472 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 44.9846 | 1.61277 | ||||||||
\(779\) | −8.49852 | −0.304491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.85244 | −0.0662856 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.1087 | 0.646326 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.4247 | 0.478540 | 0.239270 | − | 0.970953i | \(-0.423092\pi\) | ||||
0.239270 | + | 0.970953i | \(0.423092\pi\) | |||||||
\(788\) | −49.1880 | −1.75225 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 43.2702 | 1.53949 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 60.4457 | 2.14649 | ||||||||
\(794\) | 61.2438 | 2.17346 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −58.1770 | −2.06203 | ||||||||
\(797\) | −22.3440 | −0.791465 | −0.395733 | − | 0.918366i | \(-0.629509\pi\) | ||||
−0.395733 | + | 0.918366i | \(0.629509\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.63511 | 0.199356 | ||||||||
\(800\) | −18.3983 | −0.650479 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 68.4193 | 2.41597 | ||||||||
\(803\) | −10.4791 | −0.369799 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 50.2159 | 1.76878 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.6072 | 0.513879 | ||||||||
\(809\) | −31.8455 | −1.11963 | −0.559814 | − | 0.828618i | \(-0.689127\pi\) | ||||
−0.559814 | + | 0.828618i | \(0.689127\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.70889 | −0.305811 | −0.152905 | − | 0.988241i | \(-0.548863\pi\) | ||||
−0.152905 | + | 0.988241i | \(0.548863\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.9325 | −0.488333 | ||||||||
\(815\) | 9.26470 | 0.324528 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.49852 | −0.297326 | ||||||||
\(818\) | 4.88982 | 0.170968 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 21.0154 | 0.733891 | ||||||||
\(821\) | −6.45267 | −0.225200 | −0.112600 | − | 0.993640i | \(-0.535918\pi\) | ||||
−0.112600 | + | 0.993640i | \(0.535918\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.3719 | 0.884410 | 0.442205 | − | 0.896914i | \(-0.354196\pi\) | ||||
0.442205 | + | 0.896914i | \(0.354196\pi\) | |||||||
\(824\) | 17.8913 | 0.623274 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.0194 | −0.487504 | −0.243752 | − | 0.969838i | \(-0.578378\pi\) | ||||
−0.243752 | + | 0.969838i | \(0.578378\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.9970 | 1.70174 | 0.850869 | − | 0.525378i | \(-0.176076\pi\) | ||||
0.850869 | + | 0.525378i | \(0.176076\pi\) | |||||||
\(830\) | 31.8649 | 1.10605 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 51.5195 | 1.78612 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.2732 | 0.909221 | ||||||||
\(836\) | 4.06058 | 0.140438 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −81.2680 | −2.80736 | ||||||||
\(839\) | −13.2647 | −0.457948 | −0.228974 | − | 0.973433i | \(-0.573537\pi\) | ||||
−0.228974 | + | 0.973433i | \(0.573537\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.61862 | 0.0558144 | ||||||||
\(842\) | −32.7959 | −1.13022 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.5249 | −0.362283 | ||||||||
\(845\) | 13.2144 | 0.454588 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.68793 | 0.264005 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.48755 | 0.119622 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.25622 | 0.145730 | 0.0728651 | − | 0.997342i | \(-0.476786\pi\) | ||||
0.0728651 | + | 0.997342i | \(0.476786\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.1560 | 0.381305 | ||||||||
\(857\) | −23.5264 | −0.803648 | −0.401824 | − | 0.915717i | \(-0.631624\pi\) | ||||
−0.401824 | + | 0.915717i | \(0.631624\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.0279 | 1.05866 | 0.529330 | − | 0.848416i | \(-0.322444\pi\) | ||||
0.529330 | + | 0.848416i | \(0.322444\pi\) | |||||||
\(860\) | 21.0154 | 0.716620 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 80.2959 | 2.73489 | ||||||||
\(863\) | 46.3121 | 1.57648 | 0.788241 | − | 0.615367i | \(-0.210992\pi\) | ||||
0.788241 | + | 0.615367i | \(0.210992\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.6770 | −0.839042 | ||||||||
\(866\) | 21.3789 | 0.726484 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.4596 | 0.422664 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.3161 | −0.654500 | ||||||||
\(872\) | 0.108664 | 0.00367984 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.8245 | −0.433053 | −0.216527 | − | 0.976277i | \(-0.569473\pi\) | ||||
−0.216527 | + | 0.976277i | \(0.569473\pi\) | |||||||
\(878\) | −47.6329 | −1.60753 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.64832 | 0.156695 | ||||||||
\(881\) | −56.9512 | −1.91873 | −0.959367 | − | 0.282160i | \(-0.908949\pi\) | ||||
−0.959367 | + | 0.282160i | \(0.908949\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00696 | 0.269456 | 0.134728 | − | 0.990883i | \(-0.456984\pi\) | ||||
0.134728 | + | 0.990883i | \(0.456984\pi\) | |||||||
\(884\) | −8.12115 | −0.273144 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 43.7004 | 1.46814 | ||||||||
\(887\) | 35.7827 | 1.20146 | 0.600732 | − | 0.799450i | \(-0.294876\pi\) | ||||
0.600732 | + | 0.799450i | \(0.294876\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −16.3774 | −0.548971 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.25774 | 0.309972 | ||||||||
\(893\) | −12.9262 | −0.432559 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.2423 | −0.542920 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 86.3106 | 2.88022 | ||||||||
\(899\) | 28.6381 | 0.955133 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.94415 | −0.0647690 | ||||||||
\(902\) | 10.9457 | 0.364451 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.0668 | −0.434596 | ||||||||
\(905\) | −11.2064 | −0.372512 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.43171 | 0.180357 | 0.0901784 | − | 0.995926i | \(-0.471256\pi\) | ||||
0.0901784 | + | 0.995926i | \(0.471256\pi\) | |||||||
\(908\) | −38.2982 | −1.27097 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.6770 | −0.552532 | −0.276266 | − | 0.961081i | \(-0.589097\pi\) | ||||
−0.276266 | + | 0.961081i | \(0.589097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.17548 | 0.303664 | ||||||||
\(914\) | 60.0419 | 1.98601 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.7827 | 0.653638 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.4038 | 0.475137 | 0.237568 | − | 0.971371i | \(-0.423650\pi\) | ||||
0.237568 | + | 0.971371i | \(0.423650\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −45.2966 | −1.49177 | ||||||||
\(923\) | −8.49852 | −0.279732 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.1755 | 0.498967 | ||||||||
\(926\) | −43.8796 | −1.44197 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 44.1942 | 1.45075 | ||||||||
\(929\) | 1.89830 | 0.0622811 | 0.0311405 | − | 0.999515i | \(-0.490086\pi\) | ||||
0.0311405 | + | 0.999515i | \(0.490086\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 13.7004 | 0.448772 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −56.8906 | −1.86152 | ||||||||
\(935\) | −1.17548 | −0.0384424 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.1755 | 0.430424 | 0.215212 | − | 0.976567i | \(-0.430956\pi\) | ||||
0.215212 | + | 0.976567i | \(0.430956\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 31.9644 | 1.04256 | ||||||||
\(941\) | 0.381842 | 0.0124477 | 0.00622385 | − | 0.999981i | \(-0.498019\pi\) | ||||
0.00622385 | + | 0.999981i | \(0.498019\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 8.93398 | 0.290776 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.9457 | 0.355874 | ||||||||
\(947\) | 52.2284 | 1.69719 | 0.848597 | − | 0.529040i | \(-0.177448\pi\) | ||||
0.848597 | + | 0.529040i | \(0.177448\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.0753 | −1.56059 | ||||||||
\(950\) | −8.00000 | −0.259554 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.7757 | 1.48282 | 0.741410 | − | 0.671052i | \(-0.234157\pi\) | ||||
0.741410 | + | 0.671052i | \(0.234157\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.1087 | −0.585983 | ||||||||
\(956\) | 3.12739 | 0.101147 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −65.1616 | −2.10527 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.21438 | −0.135948 | ||||||||
\(962\) | −63.9185 | −2.06082 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 59.0312 | 1.90127 | ||||||||
\(965\) | −12.8943 | −0.415082 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.3230 | −0.492756 | −0.246378 | − | 0.969174i | \(-0.579240\pi\) | ||||
−0.246378 | + | 0.969174i | \(0.579240\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −47.3525 | −1.52040 | ||||||||
\(971\) | 12.0753 | 0.387515 | 0.193757 | − | 0.981049i | \(-0.437933\pi\) | ||||
0.193757 | + | 0.981049i | \(0.437933\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 49.6740 | 1.59166 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 37.2966 | 1.19384 | ||||||||
\(977\) | 39.3650 | 1.25940 | 0.629698 | − | 0.776840i | \(-0.283178\pi\) | ||||
0.629698 | + | 0.776840i | \(0.283178\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.71585 | −0.150719 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −35.1638 | −1.12212 | ||||||||
\(983\) | 10.5683 | 0.337076 | 0.168538 | − | 0.985695i | \(-0.446095\pi\) | ||||
0.168538 | + | 0.985695i | \(0.446095\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32.6630 | −1.04073 | ||||||||
\(986\) | −8.37737 | −0.266790 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.6289 | 0.592663 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.8036 | 1.35970 | 0.679851 | − | 0.733350i | \(-0.262044\pi\) | ||||
0.679851 | + | 0.733350i | \(0.262044\pi\) | |||||||
\(992\) | 41.3355 | 1.31240 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.6322 | −1.22472 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.3121 | 0.326587 | 0.163293 | − | 0.986578i | \(-0.447788\pi\) | ||||
0.163293 | + | 0.986578i | \(0.447788\pi\) | |||||||
\(998\) | 16.9045 | 0.535104 | ||||||||
\(999\) | 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 | 4851.2.a.bm.1.1 | 3 | ||
3.2 | odd | 2 | 1617.2.a.q.1.3 | ✓ | 3 | ||
7.6 | odd | 2 | 4851.2.a.bl.1.1 | 3 | |||
21.20 | even | 2 | 1617.2.a.r.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1617.2.a.q.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
1617.2.a.r.1.3 | yes | 3 | 21.20 | even | 2 | ||
4851.2.a.bl.1.1 | 3 | 7.6 | odd | 2 | |||
4851.2.a.bm.1.1 | 3 | 1.1 | even | 1 | trivial |