Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(71,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.71");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.36 | ||
Character | \(\chi\) | \(=\) | 252.71 |
Dual form | 252.4.e.a.71.35 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82720 | + | 0.0833946i | 0.999565 | + | 0.0294844i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.98609 | + | 0.471546i | 0.998261 | + | 0.0589432i | ||||
\(5\) | 8.62666i | 0.771592i | 0.922584 | + | 0.385796i | \(0.126073\pi\) | ||||
−0.922584 | + | 0.385796i | \(0.873927\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.00000i | − | 0.377964i | ||||||
\(8\) | 22.5389 | + | 1.99915i | 0.996089 | + | 0.0883508i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.719417 | + | 24.3893i | −0.0227500 | + | 0.771257i | ||||
\(11\) | 44.2558 | 1.21306 | 0.606529 | − | 0.795062i | \(-0.292562\pi\) | ||||
0.606529 | + | 0.795062i | \(0.292562\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.70463 | −0.0790368 | −0.0395184 | − | 0.999219i | \(-0.512582\pi\) | ||||
−0.0395184 | + | 0.999219i | \(0.512582\pi\) | |||||||
\(14\) | 0.583762 | − | 19.7904i | 0.0111441 | − | 0.377800i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 63.5553 | + | 7.53161i | 0.993051 | + | 0.117681i | ||||
\(17\) | 35.8211i | 0.511052i | 0.966802 | + | 0.255526i | \(0.0822486\pi\) | ||||
−0.966802 | + | 0.255526i | \(0.917751\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 88.8088i | 1.07232i | 0.844115 | + | 0.536162i | \(0.180126\pi\) | ||||
−0.844115 | + | 0.536162i | \(0.819874\pi\) | |||||||
\(20\) | −4.06787 | + | 68.8933i | −0.0454801 | + | 0.770251i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 125.120 | + | 3.69069i | 1.21253 | + | 0.0357663i | ||||
\(23\) | 41.2086 | 0.373591 | 0.186796 | − | 0.982399i | \(-0.440190\pi\) | ||||
0.186796 | + | 0.982399i | \(0.440190\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 50.5807 | 0.404646 | ||||||||
\(26\) | −10.4737 | − | 0.308946i | −0.0790024 | − | 0.00233035i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.30082 | − | 55.9026i | 0.0222784 | − | 0.377307i | ||||
\(29\) | 12.7794i | 0.0818299i | 0.999163 | + | 0.0409149i | \(0.0130273\pi\) | ||||
−0.999163 | + | 0.0409149i | \(0.986973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 67.8021i | 0.392826i | 0.980521 | + | 0.196413i | \(0.0629293\pi\) | ||||
−0.980521 | + | 0.196413i | \(0.937071\pi\) | |||||||
\(32\) | 179.055 | + | 26.5935i | 0.989150 | + | 0.146910i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.98728 | + | 101.273i | −0.0150681 | + | 0.510830i | ||||
\(35\) | 60.3866 | 0.291634 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −339.755 | −1.50961 | −0.754803 | − | 0.655951i | \(-0.772268\pi\) | ||||
−0.754803 | + | 0.655951i | \(0.772268\pi\) | |||||||
\(38\) | −7.40617 | + | 251.080i | −0.0316168 | + | 1.07186i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −17.2460 | + | 194.436i | −0.0681707 | + | 0.768575i | ||||
\(41\) | − | 450.831i | − | 1.71727i | −0.512590 | − | 0.858634i | \(-0.671314\pi\) | ||
0.512590 | − | 0.858634i | \(-0.328686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 60.2125i | − | 0.213542i | −0.994284 | − | 0.106771i | \(-0.965949\pi\) | ||
0.994284 | − | 0.106771i | \(-0.0340512\pi\) | |||||||
\(44\) | 353.431 | + | 20.8686i | 1.21095 | + | 0.0715015i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 116.505 | + | 3.43658i | 0.373429 | + | 0.0110151i | ||||
\(47\) | 243.426 | 0.755474 | 0.377737 | − | 0.925913i | \(-0.376702\pi\) | ||||
0.377737 | + | 0.925913i | \(0.376702\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 143.002 | + | 4.21816i | 0.404470 | + | 0.0119307i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −29.5855 | − | 1.74690i | −0.0788994 | − | 0.00465868i | ||||
\(53\) | − | 587.360i | − | 1.52227i | −0.648596 | − | 0.761133i | \(-0.724644\pi\) | ||
0.648596 | − | 0.761133i | \(-0.275356\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 381.780i | 0.935985i | ||||||||
\(56\) | 13.9940 | − | 157.773i | 0.0333934 | − | 0.376486i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.06573 | + | 36.1298i | −0.00241271 | + | 0.0817943i | ||||
\(59\) | 393.669 | 0.868667 | 0.434333 | − | 0.900752i | \(-0.356984\pi\) | ||||
0.434333 | + | 0.900752i | \(0.356984\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −890.660 | −1.86946 | −0.934732 | − | 0.355353i | \(-0.884361\pi\) | ||||
−0.934732 | + | 0.355353i | \(0.884361\pi\) | |||||||
\(62\) | −5.65432 | + | 191.690i | −0.0115823 | + | 0.392655i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 504.007 | + | 90.1174i | 0.984388 | + | 0.176011i | ||||
\(65\) | − | 31.9586i | − | 0.0609842i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 497.143i | 0.906502i | 0.891383 | + | 0.453251i | \(0.149736\pi\) | ||||
−0.891383 | + | 0.453251i | \(0.850264\pi\) | |||||||
\(68\) | −16.8913 | + | 286.070i | −0.0301231 | + | 0.510163i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 170.725 | + | 5.03592i | 0.291508 | + | 0.00859867i | ||||
\(71\) | 94.3384 | 0.157689 | 0.0788444 | − | 0.996887i | \(-0.474877\pi\) | ||||
0.0788444 | + | 0.996887i | \(0.474877\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −636.939 | −1.02121 | −0.510603 | − | 0.859817i | \(-0.670578\pi\) | ||||
−0.510603 | + | 0.859817i | \(0.670578\pi\) | |||||||
\(74\) | −960.556 | − | 28.3338i | −1.50895 | − | 0.0445099i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −41.8774 | + | 709.235i | −0.0632062 | + | 1.07046i | ||||
\(77\) | − | 309.791i | − | 0.458492i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1118.13i | − | 1.59240i | −0.605036 | − | 0.796198i | \(-0.706841\pi\) | ||
0.605036 | − | 0.796198i | \(-0.293159\pi\) | |||||||
\(80\) | −64.9727 | + | 548.270i | −0.0908021 | + | 0.766231i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 37.5968 | − | 1274.59i | 0.0506326 | − | 1.71652i | ||||
\(83\) | −1167.84 | −1.54442 | −0.772209 | − | 0.635369i | \(-0.780848\pi\) | ||||
−0.772209 | + | 0.635369i | \(0.780848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −309.016 | −0.394324 | ||||||||
\(86\) | 5.02139 | − | 170.233i | 0.00629617 | − | 0.213449i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 997.479 | + | 88.4740i | 1.20831 | + | 0.107175i | ||||
\(89\) | 328.229i | 0.390923i | 0.980711 | + | 0.195462i | \(0.0626205\pi\) | ||||
−0.980711 | + | 0.195462i | \(0.937380\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.9324i | 0.0298731i | ||||||||
\(92\) | 329.096 | + | 19.4318i | 0.372942 | + | 0.0220207i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 688.213 | + | 20.3004i | 0.755146 | + | 0.0222747i | ||||
\(95\) | −766.124 | −0.827396 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −467.361 | −0.489209 | −0.244605 | − | 0.969623i | \(-0.578658\pi\) | ||||
−0.244605 | + | 0.969623i | \(0.578658\pi\) | |||||||
\(98\) | −138.533 | − | 4.08633i | −0.142795 | − | 0.00421206i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 403.942 | + | 23.8511i | 0.403942 | + | 0.0238511i | ||||
\(101\) | − | 162.896i | − | 0.160483i | −0.996775 | − | 0.0802414i | \(-0.974431\pi\) | ||
0.996775 | − | 0.0802414i | \(-0.0255691\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 973.199i | − | 0.930991i | −0.885050 | − | 0.465496i | \(-0.845876\pi\) | ||
0.885050 | − | 0.465496i | \(-0.154124\pi\) | |||||||
\(104\) | −83.4983 | − | 7.40610i | −0.0787277 | − | 0.00698296i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 48.9826 | − | 1660.58i | 0.0448831 | − | 1.52160i | ||||
\(107\) | −940.544 | −0.849774 | −0.424887 | − | 0.905246i | \(-0.639686\pi\) | ||||
−0.424887 | + | 0.905246i | \(0.639686\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 35.7699 | 0.0314324 | 0.0157162 | − | 0.999876i | \(-0.494997\pi\) | ||||
0.0157162 | + | 0.999876i | \(0.494997\pi\) | |||||||
\(110\) | −31.8384 | + | 1079.37i | −0.0275970 | + | 0.935578i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 52.7213 | − | 444.887i | 0.0444794 | − | 0.375338i | ||||
\(113\) | − | 466.240i | − | 0.388143i | −0.980987 | − | 0.194071i | \(-0.937831\pi\) | ||
0.980987 | − | 0.194071i | \(-0.0621693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 355.493i | 0.288260i | ||||||||
\(116\) | −6.02605 | + | 102.057i | −0.00482332 | + | 0.0816876i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1112.98 | + | 32.8298i | 0.868289 | + | 0.0256121i | ||||
\(119\) | 250.747 | 0.193159 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 627.577 | 0.471508 | ||||||||
\(122\) | −2518.07 | − | 74.2762i | −1.86865 | − | 0.0551201i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −31.9718 | + | 541.473i | −0.0231544 | + | 0.392143i | ||||
\(125\) | 1514.68i | 1.08381i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1364.63i | − | 0.953475i | −0.879046 | − | 0.476737i | \(-0.841819\pi\) | ||
0.879046 | − | 0.476737i | \(-0.158181\pi\) | |||||||
\(128\) | 1417.41 | + | 296.811i | 0.978771 | + | 0.204958i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.66517 | − | 90.3531i | 0.00179808 | − | 0.0609576i | ||||
\(131\) | 1237.31 | 0.825220 | 0.412610 | − | 0.910908i | \(-0.364617\pi\) | ||||
0.412610 | + | 0.910908i | \(0.364617\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 621.662 | 0.405300 | ||||||||
\(134\) | −41.4590 | + | 1405.52i | −0.0267277 | + | 0.906108i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −71.6117 | + | 807.368i | −0.0451518 | + | 0.509053i | ||||
\(137\) | − | 425.810i | − | 0.265543i | −0.991147 | − | 0.132772i | \(-0.957612\pi\) | ||
0.991147 | − | 0.132772i | \(-0.0423877\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1410.05i | 0.860421i | 0.902729 | + | 0.430211i | \(0.141561\pi\) | ||||
−0.902729 | + | 0.430211i | \(0.858439\pi\) | |||||||
\(140\) | 482.253 | + | 28.4751i | 0.291127 | + | 0.0171899i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 266.713 | + | 7.86731i | 0.157620 | + | 0.00464937i | ||||
\(143\) | −163.951 | −0.0958761 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −110.243 | −0.0631393 | ||||||||
\(146\) | −1800.75 | − | 53.1172i | −1.02076 | − | 0.0301097i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2713.32 | − | 160.210i | −1.50698 | − | 0.0889811i | ||||
\(149\) | − | 2815.26i | − | 1.54789i | −0.633255 | − | 0.773943i | \(-0.718282\pi\) | ||
0.633255 | − | 0.773943i | \(-0.281718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1650.97i | 0.889762i | 0.895590 | + | 0.444881i | \(0.146754\pi\) | ||||
−0.895590 | + | 0.444881i | \(0.853246\pi\) | |||||||
\(152\) | −177.542 | + | 2001.66i | −0.0947406 | + | 1.06813i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 25.8349 | − | 875.839i | 0.0135184 | − | 0.458293i | ||||
\(155\) | −584.905 | −0.303102 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1773.44 | 0.901500 | 0.450750 | − | 0.892650i | \(-0.351157\pi\) | ||||
0.450750 | + | 0.892650i | \(0.351157\pi\) | |||||||
\(158\) | 93.2459 | − | 3161.17i | 0.0469509 | − | 1.59170i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −229.413 | + | 1544.65i | −0.113354 | + | 0.763220i | ||||
\(161\) | − | 288.461i | − | 0.141204i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2642.80i | − | 1.26994i | −0.772536 | − | 0.634971i | \(-0.781012\pi\) | ||
0.772536 | − | 0.634971i | \(-0.218988\pi\) | |||||||
\(164\) | 212.587 | − | 3600.38i | 0.101221 | − | 1.71428i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3301.70 | − | 97.3912i | −1.54375 | − | 0.0455363i | ||||
\(167\) | −2462.44 | −1.14101 | −0.570507 | − | 0.821293i | \(-0.693253\pi\) | ||||
−0.570507 | + | 0.821293i | \(0.693253\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2183.28 | −0.993753 | ||||||||
\(170\) | −873.650 | − | 25.7703i | −0.394152 | − | 0.0116264i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 28.3929 | − | 480.862i | 0.0125869 | − | 0.213171i | ||||
\(173\) | 3762.50i | 1.65351i | 0.562560 | + | 0.826756i | \(0.309816\pi\) | ||||
−0.562560 | + | 0.826756i | \(0.690184\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 354.065i | − | 0.152942i | ||||||
\(176\) | 2812.69 | + | 333.318i | 1.20463 | + | 0.142754i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −27.3725 | + | 927.967i | −0.0115261 | + | 0.390753i | ||||
\(179\) | 449.960 | 0.187886 | 0.0939429 | − | 0.995578i | \(-0.470053\pi\) | ||||
0.0939429 | + | 0.995578i | \(0.470053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −728.531 | −0.299178 | −0.149589 | − | 0.988748i | \(-0.547795\pi\) | ||||
−0.149589 | + | 0.988748i | \(0.547795\pi\) | |||||||
\(182\) | −2.16262 | + | 73.3160i | −0.000880791 | + | 0.0298601i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 928.799 | + | 82.3823i | 0.372130 | + | 0.0330071i | ||||
\(185\) | − | 2930.95i | − | 1.16480i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1585.29i | 0.619935i | ||||||||
\(188\) | 1944.02 | + | 114.786i | 0.754161 | + | 0.0445301i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2165.98 | − | 63.8905i | −0.827036 | − | 0.0243953i | ||||
\(191\) | 3611.80 | 1.36827 | 0.684137 | − | 0.729353i | \(-0.260179\pi\) | ||||
0.684137 | + | 0.729353i | \(0.260179\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1871.03 | 0.697823 | 0.348912 | − | 0.937156i | \(-0.386551\pi\) | ||||
0.348912 | + | 0.937156i | \(0.386551\pi\) | |||||||
\(194\) | −1321.32 | − | 38.9754i | −0.488997 | − | 0.0144241i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −391.318 | − | 23.1057i | −0.142609 | − | 0.00842046i | ||||
\(197\) | 3659.98i | 1.32367i | 0.749650 | + | 0.661835i | \(0.230222\pi\) | ||||
−0.749650 | + | 0.661835i | \(0.769778\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3946.37i | − | 1.40578i | −0.711297 | − | 0.702892i | \(-0.751892\pi\) | ||
0.711297 | − | 0.702892i | \(-0.248108\pi\) | |||||||
\(200\) | 1140.04 | + | 101.118i | 0.403063 | + | 0.0357508i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.5846 | − | 460.539i | 0.00473174 | − | 0.160413i | ||||
\(203\) | 89.4555 | 0.0309288 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3889.17 | 1.32503 | ||||||||
\(206\) | 81.1595 | − | 2751.42i | 0.0274498 | − | 0.930587i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −235.449 | − | 27.9018i | −0.0784876 | − | 0.00930117i | ||||
\(209\) | 3930.31i | 1.30079i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4492.02i | 1.46561i | 0.680440 | + | 0.732804i | \(0.261789\pi\) | ||||
−0.680440 | + | 0.732804i | \(0.738211\pi\) | |||||||
\(212\) | 276.967 | − | 4690.71i | 0.0897272 | − | 1.51962i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2659.10 | − | 78.4363i | −0.849405 | − | 0.0250551i | ||||
\(215\) | 519.433 | 0.164768 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 474.614 | 0.148474 | ||||||||
\(218\) | 101.129 | + | 2.98301i | 0.0314188 | + | 0.000926767i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −180.027 | + | 3048.93i | −0.0551700 | + | 0.934358i | ||||
\(221\) | − | 132.704i | − | 0.0403919i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5398.26i | 1.62105i | 0.585704 | + | 0.810525i | \(0.300818\pi\) | ||||
−0.585704 | + | 0.810525i | \(0.699182\pi\) | |||||||
\(224\) | 186.155 | − | 1253.39i | 0.0555267 | − | 0.373864i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 38.8819 | − | 1318.15i | 0.0114442 | − | 0.387974i | ||||
\(227\) | 5620.96 | 1.64351 | 0.821754 | − | 0.569843i | \(-0.192996\pi\) | ||||
0.821754 | + | 0.569843i | \(0.192996\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1480.78 | −0.427305 | −0.213652 | − | 0.976910i | \(-0.568536\pi\) | ||||
−0.213652 | + | 0.976910i | \(0.568536\pi\) | |||||||
\(230\) | −29.6462 | + | 1005.05i | −0.00849918 | + | 0.288135i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −25.5478 | + | 288.033i | −0.00722973 | + | 0.0815099i | ||||
\(233\) | − | 42.8997i | − | 0.0120620i | −0.999982 | − | 0.00603102i | \(-0.998080\pi\) | ||
0.999982 | − | 0.00603102i | \(-0.00191974\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2099.95i | 0.582918i | ||||||||
\(236\) | 3143.88 | + | 185.633i | 0.867156 | + | 0.0512020i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 708.913 | + | 20.9110i | 0.193076 | + | 0.00569520i | ||||
\(239\) | 162.709 | 0.0440367 | 0.0220184 | − | 0.999758i | \(-0.492991\pi\) | ||||
0.0220184 | + | 0.999758i | \(0.492991\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4633.53 | 1.23847 | 0.619236 | − | 0.785205i | \(-0.287443\pi\) | ||||
0.619236 | + | 0.785205i | \(0.287443\pi\) | |||||||
\(242\) | 1774.28 | + | 52.3365i | 0.471303 | + | 0.0139021i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7112.89 | − | 419.987i | −1.86621 | − | 0.110192i | ||||
\(245\) | − | 422.706i | − | 0.110227i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 329.003i | − | 0.0847530i | ||||||
\(248\) | −135.546 | + | 1528.19i | −0.0347065 | + | 0.391290i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −126.316 | + | 4282.29i | −0.0319556 | + | 1.08334i | ||||
\(251\) | 4459.19 | 1.12136 | 0.560680 | − | 0.828032i | \(-0.310540\pi\) | ||||
0.560680 | + | 0.828032i | \(0.310540\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1823.72 | 0.453187 | ||||||||
\(254\) | 113.803 | − | 3858.08i | 0.0281127 | − | 0.953060i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3982.55 | + | 957.348i | 0.972302 | + | 0.233728i | ||||
\(257\) | 6877.12i | 1.66919i | 0.550861 | + | 0.834597i | \(0.314299\pi\) | ||||
−0.550861 | + | 0.834597i | \(0.685701\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2378.29i | 0.570578i | ||||||||
\(260\) | 15.0699 | − | 255.224i | 0.00359460 | − | 0.0608781i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3498.11 | + | 103.185i | 0.824862 | + | 0.0243312i | ||||
\(263\) | −5906.74 | −1.38489 | −0.692443 | − | 0.721473i | \(-0.743466\pi\) | ||||
−0.692443 | + | 0.721473i | \(0.743466\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5066.95 | 1.17457 | ||||||||
\(266\) | 1757.56 | + | 51.8432i | 0.405124 | + | 0.0119500i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −234.426 | + | 3970.23i | −0.0534322 | + | 0.904926i | ||||
\(269\) | − | 1366.13i | − | 0.309645i | −0.987942 | − | 0.154823i | \(-0.950519\pi\) | ||
0.987942 | − | 0.154823i | \(-0.0494806\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5728.00i | − | 1.28395i | −0.766724 | − | 0.641977i | \(-0.778114\pi\) | ||
0.766724 | − | 0.641977i | \(-0.221886\pi\) | |||||||
\(272\) | −269.790 | + | 2276.62i | −0.0601414 | + | 0.507501i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 35.5102 | − | 1203.85i | 0.00782939 | − | 0.265428i | ||||
\(275\) | 2238.49 | 0.490858 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6438.08 | 1.39649 | 0.698243 | − | 0.715860i | \(-0.253965\pi\) | ||||
0.698243 | + | 0.715860i | \(0.253965\pi\) | |||||||
\(278\) | −117.590 | + | 3986.48i | −0.0253690 | + | 0.860047i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1361.05 | + | 120.722i | 0.290494 | + | 0.0257661i | ||||
\(281\) | 8186.44i | 1.73794i | 0.494861 | + | 0.868972i | \(0.335219\pi\) | ||||
−0.494861 | + | 0.868972i | \(0.664781\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 6518.84i | − | 1.36928i | −0.728884 | − | 0.684638i | \(-0.759960\pi\) | ||
0.728884 | − | 0.684638i | \(-0.240040\pi\) | |||||||
\(284\) | 753.395 | + | 44.4849i | 0.157415 | + | 0.00929469i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −463.522 | − | 13.6726i | −0.0958345 | − | 0.00282685i | ||||
\(287\) | −3155.82 | −0.649066 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3629.85 | 0.738826 | ||||||||
\(290\) | −311.679 | − | 9.19368i | −0.0631118 | − | 0.00186163i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5086.65 | − | 300.346i | −1.01943 | − | 0.0601932i | ||||
\(293\) | − | 5776.02i | − | 1.15167i | −0.817567 | − | 0.575834i | \(-0.804678\pi\) | ||
0.817567 | − | 0.575834i | \(-0.195322\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3396.05i | 0.670256i | ||||||||
\(296\) | −7657.72 | − | 679.222i | −1.50370 | − | 0.133375i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 234.777 | − | 7959.29i | 0.0456385 | − | 1.54721i | ||||
\(299\) | −152.663 | −0.0295274 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −421.487 | −0.0807114 | ||||||||
\(302\) | −137.682 | + | 4667.62i | −0.0262341 | + | 0.889375i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −668.874 | + | 5644.27i | −0.126193 | + | 1.06487i | ||||
\(305\) | − | 7683.42i | − | 1.44246i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7138.73i | − | 1.32713i | −0.748119 | − | 0.663564i | \(-0.769043\pi\) | ||
0.748119 | − | 0.663564i | \(-0.230957\pi\) | |||||||
\(308\) | 146.080 | − | 2474.02i | 0.0270250 | − | 0.457695i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1653.64 | − | 48.7779i | −0.302970 | − | 0.00893678i | ||||
\(311\) | −2455.56 | −0.447724 | −0.223862 | − | 0.974621i | \(-0.571867\pi\) | ||||
−0.223862 | + | 0.974621i | \(0.571867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9841.00 | −1.77715 | −0.888573 | − | 0.458736i | \(-0.848302\pi\) | ||||
−0.888573 | + | 0.458736i | \(0.848302\pi\) | |||||||
\(314\) | 5013.85 | + | 147.895i | 0.901109 | + | 0.0265802i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 527.249 | − | 8929.48i | 0.0938610 | − | 1.58963i | ||||
\(317\) | 220.937i | 0.0391453i | 0.999808 | + | 0.0195727i | \(0.00623057\pi\) | ||||
−0.999808 | + | 0.0195727i | \(0.993769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 565.561i | 0.0992643i | ||||||||
\(320\) | −777.412 | + | 4347.90i | −0.135808 | + | 0.759546i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 24.0560 | − | 815.535i | 0.00416333 | − | 0.141143i | ||||
\(323\) | −3181.23 | −0.548013 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −187.383 | −0.0319819 | ||||||||
\(326\) | 220.396 | − | 7471.73i | 0.0374435 | − | 1.26939i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 901.278 | − | 10161.2i | 0.151722 | − | 1.71055i | ||||
\(329\) | − | 1703.98i | − | 0.285542i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5852.38i | 0.971831i | 0.874006 | + | 0.485916i | \(0.161514\pi\) | ||||
−0.874006 | + | 0.485916i | \(0.838486\pi\) | |||||||
\(332\) | −9326.44 | − | 550.688i | −1.54173 | − | 0.0910329i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6961.80 | − | 205.354i | −1.14052 | − | 0.0336421i | ||||
\(335\) | −4288.68 | −0.699450 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −336.910 | −0.0544589 | −0.0272294 | − | 0.999629i | \(-0.508668\pi\) | ||||
−0.0272294 | + | 0.999629i | \(0.508668\pi\) | |||||||
\(338\) | −6172.55 | − | 182.073i | −0.993321 | − | 0.0293002i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2467.83 | − | 145.715i | −0.393638 | − | 0.0232427i | ||||
\(341\) | 3000.63i | 0.476520i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 120.374 | − | 1357.13i | 0.0188666 | − | 0.212707i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −313.772 | + | 10637.3i | −0.0487529 | + | 1.65279i | ||||
\(347\) | 1531.16 | 0.236878 | 0.118439 | − | 0.992961i | \(-0.462211\pi\) | ||||
0.118439 | + | 0.992961i | \(0.462211\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7302.37 | −1.12002 | −0.560010 | − | 0.828486i | \(-0.689203\pi\) | ||||
−0.560010 | + | 0.828486i | \(0.689203\pi\) | |||||||
\(350\) | 29.5271 | − | 1001.01i | 0.00450940 | − | 0.152875i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7924.24 | + | 1176.92i | 1.19990 | + | 0.178210i | ||||
\(353\) | 2246.03i | 0.338651i | 0.985560 | + | 0.169326i | \(0.0541589\pi\) | ||||
−0.985560 | + | 0.169326i | \(0.945841\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 813.826i | 0.121671i | ||||||||
\(356\) | −154.775 | + | 2621.26i | −0.0230423 | + | 0.390243i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1272.13 | + | 37.5242i | 0.187804 | + | 0.00553971i | ||||
\(359\) | 8.54625 | 0.00125642 | 0.000628208 | − | 1.00000i | \(-0.499800\pi\) | ||||
0.000628208 | 1.00000i | \(0.499800\pi\) | ||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1028.01 | −0.149877 | ||||||||
\(362\) | −2059.70 | − | 60.7555i | −0.299048 | − | 0.00882111i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.2283 | + | 207.098i | −0.00176082 | + | 0.0298212i | ||||
\(365\) | − | 5494.65i | − | 0.787954i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 12889.8i | − | 1.83336i | −0.399621 | − | 0.916681i | \(-0.630858\pi\) | ||
0.399621 | − | 0.916681i | \(-0.369142\pi\) | |||||||
\(368\) | 2619.03 | + | 310.368i | 0.370995 | + | 0.0439648i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 244.426 | − | 8286.39i | 0.0343435 | − | 1.16429i | ||||
\(371\) | −4111.52 | −0.575362 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12579.3 | −1.74620 | −0.873101 | − | 0.487540i | \(-0.837894\pi\) | ||||
−0.873101 | + | 0.487540i | \(0.837894\pi\) | |||||||
\(374\) | −132.205 | + | 4481.93i | −0.0182784 | + | 0.619666i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5486.55 | + | 486.644i | 0.752520 | + | 0.0667467i | ||||
\(377\) | − | 47.3427i | − | 0.00646757i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9627.78i | 1.30487i | 0.757845 | + | 0.652435i | \(0.226252\pi\) | ||||
−0.757845 | + | 0.652435i | \(0.773748\pi\) | |||||||
\(380\) | −6118.33 | − | 361.262i | −0.825957 | − | 0.0487694i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10211.3 | + | 301.204i | 1.36768 | + | 0.0403428i | ||||
\(383\) | −6174.08 | −0.823710 | −0.411855 | − | 0.911249i | \(-0.635119\pi\) | ||||
−0.411855 | + | 0.911249i | \(0.635119\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2672.46 | 0.353769 | ||||||||
\(386\) | 5289.78 | + | 156.034i | 0.697520 | + | 0.0205749i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3732.39 | − | 220.382i | −0.488359 | − | 0.0288356i | ||||
\(389\) | − | 2164.47i | − | 0.282116i | −0.990001 | − | 0.141058i | \(-0.954950\pi\) | ||
0.990001 | − | 0.141058i | \(-0.0450503\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1476.14i | 0.190925i | ||||||||
\(392\) | −1104.41 | − | 97.9583i | −0.142298 | − | 0.0126215i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −305.223 | + | 10347.5i | −0.0390276 | + | 1.32309i | ||||
\(395\) | 9645.72 | 1.22868 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −739.413 | −0.0934762 | −0.0467381 | − | 0.998907i | \(-0.514883\pi\) | ||||
−0.0467381 | + | 0.998907i | \(0.514883\pi\) | |||||||
\(398\) | 329.106 | − | 11157.2i | 0.0414487 | − | 1.40517i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3214.67 | + | 380.954i | 0.401834 | + | 0.0476193i | ||||
\(401\) | − | 9286.61i | − | 1.15649i | −0.815864 | − | 0.578243i | \(-0.803738\pi\) | ||
0.815864 | − | 0.578243i | \(-0.196262\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 251.181i | − | 0.0310477i | ||||||
\(404\) | 76.8130 | − | 1300.90i | 0.00945937 | − | 0.160204i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 252.908 | + | 7.46010i | 0.0309153 | + | 0.000911918i | ||||
\(407\) | −15036.1 | −1.83124 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11569.9 | −1.39877 | −0.699383 | − | 0.714747i | \(-0.746542\pi\) | ||||
−0.699383 | + | 0.714747i | \(0.746542\pi\) | |||||||
\(410\) | 10995.4 | + | 324.335i | 1.32445 | + | 0.0390677i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 458.908 | − | 7772.05i | 0.0548756 | − | 0.929373i | ||||
\(413\) | − | 2755.68i | − | 0.328325i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 10074.5i | − | 1.19166i | ||||||
\(416\) | −663.333 | − | 98.5191i | −0.0781792 | − | 0.0116113i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −327.766 | + | 11111.8i | −0.0383530 | + | 1.30022i | ||||
\(419\) | 8586.92 | 1.00119 | 0.500595 | − | 0.865682i | \(-0.333115\pi\) | ||||
0.500595 | + | 0.865682i | \(0.333115\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5371.55 | −0.621837 | −0.310918 | − | 0.950437i | \(-0.600637\pi\) | ||||
−0.310918 | + | 0.950437i | \(0.600637\pi\) | |||||||
\(422\) | −374.610 | + | 12699.8i | −0.0432126 | + | 1.46497i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1174.22 | − | 13238.5i | 0.134493 | − | 1.51631i | ||||
\(425\) | 1811.85i | 0.206795i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6234.62i | 0.706591i | ||||||||
\(428\) | −7511.27 | − | 443.510i | −0.848297 | − | 0.0500884i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1468.54 | + | 43.3179i | 0.164696 | + | 0.00485808i | ||||
\(431\) | −11094.9 | −1.23996 | −0.619978 | − | 0.784619i | \(-0.712859\pi\) | ||||
−0.619978 | + | 0.784619i | \(0.712859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9455.94 | −1.04948 | −0.524738 | − | 0.851263i | \(-0.675837\pi\) | ||||
−0.524738 | + | 0.851263i | \(0.675837\pi\) | |||||||
\(434\) | 1341.83 | + | 39.5803i | 0.148410 | + | 0.00437768i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 285.662 | + | 16.8671i | 0.0313778 | + | 0.00185273i | ||||
\(437\) | 3659.69i | 0.400610i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1277.44i | − | 0.138881i | −0.997586 | − | 0.0694407i | \(-0.977879\pi\) | ||
0.997586 | − | 0.0694407i | \(-0.0221215\pi\) | |||||||
\(440\) | −763.235 | + | 8604.91i | −0.0826950 | + | 0.932325i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.0668 | − | 375.179i | 0.00119093 | − | 0.0403743i | ||||
\(443\) | 7948.67 | 0.852489 | 0.426245 | − | 0.904608i | \(-0.359836\pi\) | ||||
0.426245 | + | 0.904608i | \(0.359836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2831.52 | −0.301633 | ||||||||
\(446\) | −450.185 | + | 15261.9i | −0.0477957 | + | 1.62034i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 630.822 | − | 3528.05i | 0.0665257 | − | 0.372064i | ||||
\(449\) | − | 10690.8i | − | 1.12368i | −0.827247 | − | 0.561839i | \(-0.810094\pi\) | ||
0.827247 | − | 0.561839i | \(-0.189906\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 19951.9i | − | 2.08314i | ||||||
\(452\) | 219.853 | − | 3723.43i | 0.0228784 | − | 0.387468i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15891.6 | + | 468.757i | 1.64279 | + | 0.0484579i | ||||
\(455\) | −223.710 | −0.0230498 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11479.3 | 1.17500 | 0.587502 | − | 0.809222i | \(-0.300111\pi\) | ||||
0.587502 | + | 0.809222i | \(0.300111\pi\) | |||||||
\(458\) | −4186.46 | − | 123.489i | −0.427119 | − | 0.0125988i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −167.631 | + | 2839.00i | −0.0169910 | + | 0.287759i | ||||
\(461\) | 7324.06i | 0.739947i | 0.929042 | + | 0.369973i | \(0.120633\pi\) | ||||
−0.929042 | + | 0.369973i | \(0.879367\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11018.2i | 1.10596i | 0.833196 | + | 0.552978i | \(0.186509\pi\) | ||||
−0.833196 | + | 0.552978i | \(0.813491\pi\) | |||||||
\(464\) | −96.2492 | + | 812.196i | −0.00962986 | + | 0.0812613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.57760 | − | 121.286i | 0.000355642 | − | 0.0120568i | ||||
\(467\) | 11040.0 | 1.09394 | 0.546969 | − | 0.837153i | \(-0.315782\pi\) | ||||
0.546969 | + | 0.837153i | \(0.315782\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3480.00 | 0.342626 | ||||||||
\(470\) | −175.125 | + | 5936.98i | −0.0171870 | + | 0.582664i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8872.88 | + | 787.003i | 0.865270 | + | 0.0767474i | ||||
\(473\) | − | 2664.75i | − | 0.259039i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4492.01i | 0.433911i | ||||||||
\(476\) | 2002.49 | + | 118.239i | 0.192824 | + | 0.0113854i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 460.011 | + | 13.5691i | 0.0440176 | + | 0.00129840i | ||||
\(479\) | 16926.4 | 1.61459 | 0.807295 | − | 0.590148i | \(-0.200931\pi\) | ||||
0.807295 | + | 0.590148i | \(0.200931\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1258.67 | 0.119314 | ||||||||
\(482\) | 13099.9 | + | 386.411i | 1.23793 | + | 0.0365156i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5011.88 | + | 295.931i | 0.470688 | + | 0.0277922i | ||||
\(485\) | − | 4031.76i | − | 0.377470i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9639.43i | 0.896929i | 0.893801 | + | 0.448464i | \(0.148029\pi\) | ||||
−0.893801 | + | 0.448464i | \(0.851971\pi\) | |||||||
\(488\) | −20074.5 | − | 1780.56i | −1.86215 | − | 0.165169i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 35.2514 | − | 1195.07i | 0.00324999 | − | 0.110180i | ||||
\(491\) | −4791.74 | −0.440424 | −0.220212 | − | 0.975452i | \(-0.570675\pi\) | ||||
−0.220212 | + | 0.975452i | \(0.570675\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −457.770 | −0.0418193 | ||||||||
\(494\) | 27.4371 | − | 930.158i | 0.00249889 | − | 0.0847161i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −510.659 | + | 4309.18i | −0.0462284 | + | 0.390097i | ||||
\(497\) | − | 660.369i | − | 0.0596008i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2224.16i | 0.199533i | 0.995011 | + | 0.0997664i | \(0.0318096\pi\) | ||||
−0.995011 | + | 0.0997664i | \(0.968190\pi\) | |||||||
\(500\) | −714.239 | + | 12096.3i | −0.0638835 | + | 1.08193i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12607.0 | + | 371.872i | 1.12087 | + | 0.0330627i | ||||
\(503\) | −9038.06 | −0.801167 | −0.400584 | − | 0.916260i | \(-0.631193\pi\) | ||||
−0.400584 | + | 0.916260i | \(0.631193\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1405.25 | 0.123827 | ||||||||
\(506\) | 5156.02 | + | 152.089i | 0.452990 | + | 0.0133620i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 643.485 | − | 10898.1i | 0.0562009 | − | 0.951817i | ||||
\(509\) | − | 4178.67i | − | 0.363883i | −0.983309 | − | 0.181942i | \(-0.941762\pi\) | ||
0.983309 | − | 0.181942i | \(-0.0582382\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4458.57i | 0.385980i | ||||||||
\(512\) | 11179.6 | + | 3038.73i | 0.964988 | + | 0.262294i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −573.514 | + | 19443.0i | −0.0492152 | + | 1.66847i | ||||
\(515\) | 8395.46 | 0.718346 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10773.0 | 0.916433 | ||||||||
\(518\) | −198.336 | + | 6723.89i | −0.0168232 | + | 0.570330i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 63.8899 | − | 720.312i | 0.00538800 | − | 0.0607457i | ||||
\(521\) | − | 15973.1i | − | 1.34317i | −0.740925 | − | 0.671587i | \(-0.765613\pi\) | ||
0.740925 | − | 0.671587i | \(-0.234387\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7772.55i | 0.649847i | 0.945740 | + | 0.324923i | \(0.105339\pi\) | ||||
−0.945740 | + | 0.324923i | \(0.894661\pi\) | |||||||
\(524\) | 9881.23 | + | 583.446i | 0.823786 | + | 0.0486412i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16699.5 | − | 492.590i | −1.38428 | − | 0.0408326i | ||||
\(527\) | −2428.74 | −0.200755 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10468.8 | −0.860430 | ||||||||
\(530\) | 14325.3 | + | 422.556i | 1.17406 | + | 0.0346315i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4964.65 | + | 293.142i | 0.404595 | + | 0.0238897i | ||||
\(533\) | 1670.16i | 0.135727i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 8113.76i | − | 0.655679i | ||||||
\(536\) | −993.863 | + | 11205.1i | −0.0800902 | + | 0.902957i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 113.928 | − | 3862.33i | 0.00912972 | − | 0.309511i | ||||
\(539\) | −2168.53 | −0.173294 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1207.74 | −0.0959793 | −0.0479897 | − | 0.998848i | \(-0.515281\pi\) | ||||
−0.0479897 | + | 0.998848i | \(0.515281\pi\) | |||||||
\(542\) | 477.684 | − | 16194.2i | 0.0378566 | − | 1.28340i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −952.608 | + | 6413.95i | −0.0750786 | + | 0.505507i | ||||
\(545\) | 308.575i | 0.0242530i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22972.7i | 1.79569i | 0.440315 | + | 0.897843i | \(0.354867\pi\) | ||||
−0.440315 | + | 0.897843i | \(0.645133\pi\) | |||||||
\(548\) | 200.789 | − | 3400.56i | 0.0156520 | − | 0.265081i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6328.65 | + | 186.678i | 0.490645 | + | 0.0144727i | ||||
\(551\) | −1134.92 | −0.0877481 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7826.90 | −0.601869 | ||||||||
\(554\) | 18201.7 | + | 536.901i | 1.39588 | + | 0.0411746i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −664.901 | + | 11260.8i | −0.0507160 | + | 0.858925i | ||||
\(557\) | 3082.31i | 0.234473i | 0.993104 | + | 0.117237i | \(0.0374036\pi\) | ||||
−0.993104 | + | 0.117237i | \(0.962596\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 223.065i | 0.0168777i | ||||||||
\(560\) | 3837.89 | + | 454.809i | 0.289608 | + | 0.0343200i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −682.705 | + | 23144.7i | −0.0512423 | + | 1.73719i | ||||
\(563\) | 23690.8 | 1.77344 | 0.886721 | − | 0.462306i | \(-0.152978\pi\) | ||||
0.886721 | + | 0.462306i | \(0.152978\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4022.09 | 0.299488 | ||||||||
\(566\) | 543.636 | − | 18430.1i | 0.0403723 | − | 1.36868i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2126.29 | + | 188.597i | 0.157072 | + | 0.0139319i | ||||
\(569\) | 21184.2i | 1.56079i | 0.625289 | + | 0.780393i | \(0.284981\pi\) | ||||
−0.625289 | + | 0.780393i | \(0.715019\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14344.6i | 1.05132i | 0.850695 | + | 0.525660i | \(0.176182\pi\) | ||||
−0.850695 | + | 0.525660i | \(0.823818\pi\) | |||||||
\(572\) | −1309.33 | − | 77.3105i | −0.0957094 | − | 0.00565125i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8922.12 | − | 263.178i | −0.648784 | − | 0.0191373i | ||||
\(575\) | 2084.36 | 0.151172 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4374.69 | −0.315634 | −0.157817 | − | 0.987468i | \(-0.550446\pi\) | ||||
−0.157817 | + | 0.987468i | \(0.550446\pi\) | |||||||
\(578\) | 10262.3 | + | 302.710i | 0.738505 | + | 0.0217839i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −880.412 | − | 51.9847i | −0.0630295 | − | 0.00372163i | ||||
\(581\) | 8174.85i | 0.583735i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 25994.1i | − | 1.84659i | ||||||
\(584\) | −14355.9 | − | 1273.34i | −1.01721 | − | 0.0902243i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 481.689 | − | 16329.9i | 0.0339563 | − | 1.15117i | ||||
\(587\) | 4899.69 | 0.344518 | 0.172259 | − | 0.985052i | \(-0.444893\pi\) | ||||
0.172259 | + | 0.985052i | \(0.444893\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6021.42 | −0.421236 | ||||||||
\(590\) | −283.212 | + | 9601.30i | −0.0197621 | + | 0.669965i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −21593.3 | − | 2558.91i | −1.49912 | − | 0.177653i | ||||
\(593\) | − | 23704.4i | − | 1.64152i | −0.571271 | − | 0.820761i | \(-0.693550\pi\) | ||
0.571271 | − | 0.820761i | \(-0.306450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2163.11i | 0.149040i | ||||||||
\(596\) | 1327.52 | − | 22482.9i | 0.0912374 | − | 1.54519i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −431.607 | − | 12.7312i | −0.0295146 | − | 0.000870600i | ||||
\(599\) | −5334.79 | −0.363896 | −0.181948 | − | 0.983308i | \(-0.558240\pi\) | ||||
−0.181948 | + | 0.983308i | \(0.558240\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 300.297 | 0.0203817 | 0.0101908 | − | 0.999948i | \(-0.496756\pi\) | ||||
0.0101908 | + | 0.999948i | \(0.496756\pi\) | |||||||
\(602\) | −1191.63 | − | 35.1498i | −0.0806763 | − | 0.00237973i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −778.508 | + | 13184.8i | −0.0524454 | + | 0.888215i | ||||
\(605\) | 5413.89i | 0.363812i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 12004.3i | − | 0.802702i | −0.915924 | − | 0.401351i | \(-0.868541\pi\) | ||
0.915924 | − | 0.401351i | \(-0.131459\pi\) | |||||||
\(608\) | −2361.74 | + | 15901.7i | −0.157535 | + | 1.06069i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 640.756 | − | 21722.5i | 0.0425302 | − | 1.44184i | ||||
\(611\) | −901.801 | −0.0597103 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3051.53 | −0.201060 | −0.100530 | − | 0.994934i | \(-0.532054\pi\) | ||||
−0.100530 | + | 0.994934i | \(0.532054\pi\) | |||||||
\(614\) | 595.331 | − | 20182.6i | 0.0391296 | − | 1.32655i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 619.318 | − | 6982.35i | 0.0405082 | − | 0.456700i | ||||
\(617\) | 6684.09i | 0.436129i | 0.975934 | + | 0.218064i | \(0.0699743\pi\) | ||||
−0.975934 | + | 0.218064i | \(0.930026\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5493.15i | 0.356686i | 0.983968 | + | 0.178343i | \(0.0570736\pi\) | ||||
−0.983968 | + | 0.178343i | \(0.942926\pi\) | |||||||
\(620\) | −4671.11 | − | 275.810i | −0.302575 | − | 0.0178658i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6942.36 | − | 204.781i | −0.447530 | − | 0.0132009i | ||||
\(623\) | 2297.60 | 0.147755 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6744.00 | −0.431616 | ||||||||
\(626\) | −27822.5 | − | 820.686i | −1.77637 | − | 0.0523981i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14162.8 | + | 836.256i | 0.899933 | + | 0.0531373i | ||||
\(629\) | − | 12170.4i | − | 0.771487i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 20126.1i | − | 1.26974i | −0.772619 | − | 0.634870i | \(-0.781053\pi\) | ||
0.772619 | − | 0.634870i | \(-0.218947\pi\) | |||||||
\(632\) | 2235.31 | − | 25201.4i | 0.140689 | − | 1.58617i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.4250 | + | 624.633i | −0.00115418 | + | 0.0391283i | ||||
\(635\) | 11772.2 | 0.735693 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 181.527 | 0.0112910 | ||||||||
\(638\) | −47.1647 | + | 1598.95i | −0.00292675 | + | 0.0992212i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2560.49 | + | 12227.5i | −0.158144 | + | 0.755212i | ||||
\(641\) | 29220.8i | 1.80055i | 0.435323 | + | 0.900275i | \(0.356634\pi\) | ||||
−0.435323 | + | 0.900275i | \(0.643366\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13497.5i | 0.827821i | 0.910318 | + | 0.413911i | \(0.135837\pi\) | ||||
−0.910318 | + | 0.413911i | \(0.864163\pi\) | |||||||
\(644\) | 136.022 | − | 2303.67i | 0.00832303 | − | 0.140959i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8993.95 | − | 265.297i | −0.547775 | − | 0.0161578i | ||||
\(647\) | −5544.47 | −0.336902 | −0.168451 | − | 0.985710i | \(-0.553877\pi\) | ||||
−0.168451 | + | 0.985710i | \(0.553877\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17422.1 | 1.05374 | ||||||||
\(650\) | −529.768 | − | 15.6267i | −0.0319680 | − | 0.000942968i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1246.20 | − | 21105.7i | 0.0748544 | − | 1.26773i | ||||
\(653\) | − | 9054.79i | − | 0.542636i | −0.962490 | − | 0.271318i | \(-0.912540\pi\) | ||
0.962490 | − | 0.271318i | \(-0.0874595\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10673.8i | 0.636734i | ||||||||
\(656\) | 3395.48 | − | 28652.7i | 0.202091 | − | 1.70533i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 142.103 | − | 4817.49i | 0.00841905 | − | 0.285418i | ||||
\(659\) | 154.743 | 0.00914709 | 0.00457354 | − | 0.999990i | \(-0.498544\pi\) | ||||
0.00457354 | + | 0.999990i | \(0.498544\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19351.7 | 1.13872 | 0.569360 | − | 0.822088i | \(-0.307191\pi\) | ||||
0.569360 | + | 0.822088i | \(0.307191\pi\) | |||||||
\(662\) | −488.057 | + | 16545.8i | −0.0286539 | + | 0.971409i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −26321.8 | − | 2334.68i | −1.53838 | − | 0.136450i | ||||
\(665\) | 5362.87i | 0.312726i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 526.620i | 0.0305709i | ||||||||
\(668\) | −19665.3 | − | 1161.15i | −1.13903 | − | 0.0672550i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12125.0 | − | 357.653i | −0.699146 | − | 0.0206229i | ||||
\(671\) | −39416.9 | −2.26777 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8696.70 | 0.498117 | 0.249059 | − | 0.968488i | \(-0.419879\pi\) | ||||
0.249059 | + | 0.968488i | \(0.419879\pi\) | |||||||
\(674\) | −952.511 | − | 28.0964i | −0.0544352 | − | 0.00160569i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17435.8 | − | 1029.51i | −0.992025 | − | 0.0585750i | ||||
\(677\) | 11717.8i | 0.665218i | 0.943065 | + | 0.332609i | \(0.107929\pi\) | ||||
−0.943065 | + | 0.332609i | \(0.892071\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3271.53i | 0.184904i | ||||||||
\(680\) | −6964.89 | − | 617.770i | −0.392782 | − | 0.0348388i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −250.237 | + | 8483.39i | −0.0140499 | + | 0.476313i | ||||
\(683\) | −17566.1 | −0.984112 | −0.492056 | − | 0.870564i | \(-0.663754\pi\) | ||||
−0.492056 | + | 0.870564i | \(0.663754\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3673.32 | 0.204891 | ||||||||
\(686\) | −28.6043 | + | 969.729i | −0.00159201 | + | 0.0539714i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 453.497 | − | 3826.82i | 0.0251300 | − | 0.212058i | ||||
\(689\) | 2175.95i | 0.120315i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 22587.0i | − | 1.24349i | −0.783222 | − | 0.621743i | \(-0.786425\pi\) | ||
0.783222 | − | 0.621743i | \(-0.213575\pi\) | |||||||
\(692\) | −1774.19 | + | 30047.7i | −0.0974633 | + | 1.65064i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4328.88 | + | 127.690i | 0.236775 | + | 0.00698422i | ||||
\(695\) | −12164.0 | −0.663894 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16149.2 | 0.877613 | ||||||||
\(698\) | −20645.2 | − | 608.978i | −1.11953 | − | 0.0330231i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 166.958 | − | 2827.59i | 0.00901488 | − | 0.152676i | ||||
\(701\) | 4908.37i | 0.264460i | 0.991219 | + | 0.132230i | \(0.0422138\pi\) | ||||
−0.991219 | + | 0.132230i | \(0.957786\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 30173.3i | − | 1.61879i | ||||||
\(704\) | 22305.2 | + | 3988.22i | 1.19412 | + | 0.213511i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −187.306 | + | 6349.96i | −0.00998494 | + | 0.338504i | ||||
\(707\) | −1140.27 | −0.0606568 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8955.08 | −0.474351 | −0.237176 | − | 0.971467i | \(-0.576222\pi\) | ||||
−0.237176 | + | 0.971467i | \(0.576222\pi\) | |||||||
\(710\) | −67.8686 | + | 2300.85i | −0.00358741 | + | 0.121619i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −656.178 | + | 7397.92i | −0.0345384 | + | 0.389394i | ||||
\(713\) | 2794.03i | 0.146756i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1414.35i | − | 0.0739773i | ||||||
\(716\) | 3593.42 | + | 212.177i | 0.187559 | + | 0.0110746i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.1619 | + | 0.712711i | 0.00125587 | + | 3.70447e-5i | ||||
\(719\) | 22577.2 | 1.17105 | 0.585527 | − | 0.810653i | \(-0.300888\pi\) | ||||
0.585527 | + | 0.810653i | \(0.300888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6812.39 | −0.351882 | ||||||||
\(722\) | −2906.37 | − | 85.7300i | −0.149812 | − | 0.00441903i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5818.12 | − | 343.536i | −0.298658 | − | 0.0176345i | ||||
\(725\) | 646.389i | 0.0331121i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9030.29i | 0.460681i | 0.973110 | + | 0.230340i | \(0.0739840\pi\) | ||||
−0.973110 | + | 0.230340i | \(0.926016\pi\) | |||||||
\(728\) | −51.8427 | + | 584.488i | −0.00263931 | + | 0.0297563i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 458.224 | − | 15534.5i | 0.0232324 | − | 0.787612i | ||||
\(731\) | 2156.88 | 0.109131 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19124.7 | 0.963694 | 0.481847 | − | 0.876255i | \(-0.339966\pi\) | ||||
0.481847 | + | 0.876255i | \(0.339966\pi\) | |||||||
\(734\) | 1074.94 | − | 36442.1i | 0.0540556 | − | 1.83256i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7378.63 | + | 1095.88i | 0.369538 | + | 0.0548842i | ||||
\(737\) | 22001.5i | 1.09964i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35083.3i | 1.74636i | 0.487398 | + | 0.873180i | \(0.337946\pi\) | ||||
−0.487398 | + | 0.873180i | \(0.662054\pi\) | |||||||
\(740\) | 1382.08 | − | 23406.9i | 0.0686571 | − | 1.16278i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11624.1 | − | 342.878i | −0.575112 | − | 0.0169642i | ||||
\(743\) | −30463.7 | −1.50418 | −0.752090 | − | 0.659060i | \(-0.770954\pi\) | ||||
−0.752090 | + | 0.659060i | \(0.770954\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24286.3 | 1.19434 | ||||||||
\(746\) | −35564.3 | − | 1049.05i | −1.74544 | − | 0.0514858i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −747.537 | + | 12660.3i | −0.0365410 | + | 0.618857i | ||||
\(749\) | 6583.81i | 0.321184i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 36497.4i | − | 1.77338i | −0.462365 | − | 0.886690i | \(-0.652999\pi\) | ||
0.462365 | − | 0.886690i | \(-0.347001\pi\) | |||||||
\(752\) | 15471.0 | + | 1833.39i | 0.750225 | + | 0.0889053i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.94813 | − | 133.847i | 0.000190693 | − | 0.00646476i | ||||
\(755\) | −14242.4 | −0.686533 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27788.7 | 1.33421 | 0.667105 | − | 0.744964i | \(-0.267533\pi\) | ||||
0.667105 | + | 0.744964i | \(0.267533\pi\) | |||||||
\(758\) | −802.904 | + | 27219.6i | −0.0384733 | + | 1.30430i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17267.6 | − | 1531.60i | −0.824160 | − | 0.0731011i | ||||
\(761\) | − | 30159.1i | − | 1.43662i | −0.695724 | − | 0.718310i | \(-0.744916\pi\) | ||
0.695724 | − | 0.718310i | \(-0.255084\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 250.389i | − | 0.0118803i | ||||||
\(764\) | 28844.1 | + | 1703.13i | 1.36590 | + | 0.0806505i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17455.3 | − | 514.885i | −0.823352 | − | 0.0242866i | ||||
\(767\) | −1458.40 | −0.0686566 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35782.2 | 1.67794 | 0.838972 | − | 0.544175i | \(-0.183157\pi\) | ||||
0.838972 | + | 0.544175i | \(0.183157\pi\) | |||||||
\(770\) | 7555.57 | + | 222.869i | 0.353615 | + | 0.0104307i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14942.2 | + | 882.277i | 0.696610 | + | 0.0411319i | ||||
\(773\) | 21533.3i | 1.00194i | 0.865465 | + | 0.500969i | \(0.167023\pi\) | ||||
−0.865465 | + | 0.500969i | \(0.832977\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3429.48i | 0.158955i | ||||||||
\(776\) | −10533.8 | − | 934.324i | −0.487296 | − | 0.0432220i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 180.505 | − | 6119.38i | 0.00831802 | − | 0.281993i | ||||
\(779\) | 40037.8 | 1.84147 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4175.02 | 0.191286 | ||||||||
\(782\) | −123.102 | + | 4173.33i | −0.00562930 | + | 0.190842i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3114.21 | − | 369.049i | −0.141864 | − | 0.0168116i | ||||
\(785\) | 15298.8i | 0.695591i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 15807.3i | − | 0.715970i | −0.933727 | − | 0.357985i | \(-0.883464\pi\) | ||
0.933727 | − | 0.357985i | \(-0.116536\pi\) | |||||||
\(788\) | −1725.85 | + | 29228.9i | −0.0780213 | + | 1.32137i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 27270.4 | + | 804.401i | 1.22815 | + | 0.0362270i | ||||
\(791\) | −3263.68 | −0.146704 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3299.56 | 0.147756 | ||||||||
\(794\) | −2090.47 | − | 61.6630i | −0.0934356 | − | 0.00275609i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1860.89 | − | 31516.1i | 0.0828614 | − | 1.40334i | ||||
\(797\) | − | 12689.5i | − | 0.563972i | −0.959419 | − | 0.281986i | \(-0.909007\pi\) | ||
0.959419 | − | 0.281986i | \(-0.0909931\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8719.77i | 0.386087i | ||||||||
\(800\) | 9056.74 | + | 1345.12i | 0.400255 | + | 0.0594464i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 774.453 | − | 26255.1i | 0.0340984 | − | 1.15598i | ||||
\(803\) | −28188.2 | −1.23878 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2488.45 | 0.108952 | ||||||||
\(806\) | 20.9471 | − | 710.139i | 0.000915424 | − | 0.0310342i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 325.654 | − | 3671.50i | 0.0141788 | − | 0.159855i | ||||
\(809\) | 17538.6i | 0.762206i | 0.924533 | + | 0.381103i | \(0.124456\pi\) | ||||
−0.924533 | + | 0.381103i | \(0.875544\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36604.2i | 1.58489i | 0.609943 | + | 0.792445i | \(0.291192\pi\) | ||||
−0.609943 | + | 0.792445i | \(0.708808\pi\) | |||||||
\(812\) | 714.400 | + | 42.1824i | 0.0308750 | + | 0.00182304i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −42510.2 | − | 1253.93i | −1.83044 | − | 0.0539930i | ||||
\(815\) | 22798.6 | 0.979877 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5347.40 | 0.228986 | ||||||||
\(818\) | −32710.4 | − | 964.867i | −1.39816 | − | 0.0412418i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 31059.2 | + | 1833.92i | 1.32273 | + | 0.0781015i | ||||
\(821\) | 22161.7i | 0.942079i | 0.882112 | + | 0.471040i | \(0.156121\pi\) | ||||
−0.882112 | + | 0.471040i | \(0.843879\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 25053.2i | − | 1.06112i | −0.847648 | − | 0.530560i | \(-0.821982\pi\) | ||
0.847648 | − | 0.530560i | \(-0.178018\pi\) | |||||||
\(824\) | 1945.57 | − | 21934.9i | 0.0822538 | − | 0.927351i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 229.809 | − | 7790.86i | 0.00968048 | − | 0.328182i | ||||
\(827\) | 16191.1 | 0.680800 | 0.340400 | − | 0.940281i | \(-0.389438\pi\) | ||||
0.340400 | + | 0.940281i | \(0.389438\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28983.6 | −1.21428 | −0.607142 | − | 0.794593i | \(-0.707684\pi\) | ||||
−0.607142 | + | 0.794593i | \(0.707684\pi\) | |||||||
\(830\) | 840.161 | − | 28482.7i | 0.0351354 | − | 1.19114i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1867.16 | − | 333.851i | −0.0778029 | − | 0.0139113i | ||||
\(833\) | − | 1755.23i | − | 0.0730074i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 21242.6i | − | 0.880397i | ||||||
\(836\) | −1853.32 | + | 31387.8i | −0.0766727 | + | 1.29853i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24276.9 | + | 716.102i | 1.00075 | + | 0.0295195i | ||||
\(839\) | 4683.71 | 0.192729 | 0.0963644 | − | 0.995346i | \(-0.469279\pi\) | ||||
0.0963644 | + | 0.995346i | \(0.469279\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24225.7 | 0.993304 | ||||||||
\(842\) | −15186.4 | − | 447.958i | −0.621566 | − | 0.0183345i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2118.19 | + | 35873.6i | −0.0863876 | + | 1.46306i | ||||
\(845\) | − | 18834.4i | − | 0.766772i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4393.04i | − | 0.178213i | ||||||
\(848\) | 4423.77 | − | 37329.8i | 0.179142 | − | 1.51169i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −151.099 | + | 5122.47i | −0.00609723 | + | 0.206705i | ||||
\(851\) | −14000.9 | −0.563976 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21447.0 | −0.860880 | −0.430440 | − | 0.902619i | \(-0.641642\pi\) | ||||
−0.430440 | + | 0.902619i | \(0.641642\pi\) | |||||||
\(854\) | −519.933 | + | 17626.5i | −0.0208334 | + | 0.706284i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21198.9 | − | 1880.29i | −0.846451 | − | 0.0750782i | ||||
\(857\) | 24566.0i | 0.979182i | 0.871952 | + | 0.489591i | \(0.162854\pi\) | ||||
−0.871952 | + | 0.489591i | \(0.837146\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9680.45i | 0.384509i | 0.981345 | + | 0.192254i | \(0.0615798\pi\) | ||||
−0.981345 | + | 0.192254i | \(0.938420\pi\) | |||||||
\(860\) | 4148.24 | + | 244.936i | 0.164481 | + | 0.00971193i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −31367.4 | − | 925.252i | −1.23942 | − | 0.0365594i | ||||
\(863\) | −2384.05 | −0.0940372 | −0.0470186 | − | 0.998894i | \(-0.514972\pi\) | ||||
−0.0470186 | + | 0.998894i | \(0.514972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32457.8 | −1.27584 | ||||||||
\(866\) | −26733.8 | − | 788.574i | −1.04902 | − | 0.0309432i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3790.31 | + | 223.802i | 0.148216 | + | 0.00875155i | ||||
\(869\) | − | 49483.7i | − | 1.93167i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1841.73i | − | 0.0716470i | ||||||
\(872\) | 806.215 | + | 71.5093i | 0.0313095 | + | 0.00277708i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −305.198 | + | 10346.7i | −0.0118118 | + | 0.400436i | ||||
\(875\) | 10602.7 | 0.409643 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23220.5 | −0.894073 | −0.447037 | − | 0.894516i | \(-0.647521\pi\) | ||||
−0.447037 | + | 0.894516i | \(0.647521\pi\) | |||||||
\(878\) | 106.532 | − | 3611.58i | 0.00409484 | − | 0.138821i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2875.42 | + | 24264.1i | −0.110148 | + | 0.929481i | ||||
\(881\) | 8670.93i | 0.331590i | 0.986160 | + | 0.165795i | \(0.0530191\pi\) | ||||
−0.986160 | + | 0.165795i | \(0.946981\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9683.52i | 0.369056i | 0.982827 | + | 0.184528i | \(0.0590756\pi\) | ||||
−0.982827 | + | 0.184528i | \(0.940924\pi\) | |||||||
\(884\) | 62.5758 | − | 1059.78i | 0.00238083 | − | 0.0403217i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22472.5 | + | 662.876i | 0.852118 | + | 0.0251352i | ||||
\(887\) | −17369.1 | −0.657494 | −0.328747 | − | 0.944418i | \(-0.606626\pi\) | ||||
−0.328747 | + | 0.944418i | \(0.606626\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9552.41 | −0.360380 | ||||||||
\(890\) | −8005.26 | − | 236.133i | −0.301502 | − | 0.00889348i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2545.53 | + | 43111.0i | −0.0955499 | + | 1.61823i | ||||
\(893\) | 21618.3i | 0.810112i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3881.65i | 0.144971i | ||||||||
\(896\) | 2077.68 | − | 9921.88i | 0.0774669 | − | 0.369941i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 891.557 | − | 30225.1i | 0.0331310 | − | 1.12319i | ||||
\(899\) | −866.467 | −0.0321449 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21039.8 | 0.777957 | ||||||||
\(902\) | 1663.88 | − | 56407.9i | 0.0614203 | − | 2.08224i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 932.083 | − | 10508.5i | 0.0342927 | − | 0.386625i | ||||
\(905\) | − | 6284.79i | − | 0.230844i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 16471.6i | − | 0.603011i | −0.953464 | − | 0.301505i | \(-0.902511\pi\) | ||
0.953464 | − | 0.301505i | \(-0.0974891\pi\) | |||||||
\(908\) | 44889.5 | + | 2650.54i | 1.64065 | + | 0.0968736i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −632.472 | − | 18.6562i | −0.0230398 | − | 0.000679612i | ||||
\(911\) | 2224.30 | 0.0808939 | 0.0404469 | − | 0.999182i | \(-0.487122\pi\) | ||||
0.0404469 | + | 0.999182i | \(0.487122\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −51683.5 | −1.87347 | ||||||||
\(914\) | 32454.1 | + | 957.308i | 1.17449 | + | 0.0346443i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11825.7 | − | 698.256i | −0.426562 | − | 0.0251867i | ||||
\(917\) | − | 8661.14i | − | 0.311904i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47222.7i | 1.69503i | 0.530770 | + | 0.847516i | \(0.321903\pi\) | ||||
−0.530770 | + | 0.847516i | \(0.678097\pi\) | |||||||
\(920\) | −710.684 | + | 8012.43i | −0.0254680 | + | 0.287133i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −610.787 | + | 20706.6i | −0.0218169 | + | 0.739625i | ||||
\(923\) | −349.488 | −0.0124632 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17185.1 | −0.610856 | ||||||||
\(926\) | −918.856 | + | 31150.6i | −0.0326085 | + | 1.10548i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −339.848 | + | 2288.21i | −0.0120216 | + | 0.0809420i | ||||
\(929\) | − | 14515.2i | − | 0.512625i | −0.966594 | − | 0.256313i | \(-0.917492\pi\) | ||
0.966594 | − | 0.256313i | \(-0.0825077\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4351.63i | − | 0.153189i | ||||||
\(932\) | 20.2292 | − | 342.601i | 0.000710975 | − | 0.0120411i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31212.2 | + | 920.673i | 1.09346 | + | 0.0322541i | ||||
\(935\) | −13675.8 | −0.478337 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11232.1 | −0.391608 | −0.195804 | − | 0.980643i | \(-0.562732\pi\) | ||||
−0.195804 | + | 0.980643i | \(0.562732\pi\) | |||||||
\(938\) | 9838.65 | + | 290.213i | 0.342477 | + | 0.0101021i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −990.223 | + | 16770.4i | −0.0343591 | + | 0.581904i | ||||
\(941\) | 7300.76i | 0.252920i | 0.991972 | + | 0.126460i | \(0.0403616\pi\) | ||||
−0.991972 | + | 0.126460i | \(0.959638\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 18578.1i | − | 0.641556i | ||||||
\(944\) | 25019.7 | + | 2964.96i | 0.862631 | + | 0.102226i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 222.226 | − | 7533.78i | 0.00763762 | − | 0.258926i | ||||
\(947\) | 32290.7 | 1.10803 | 0.554016 | − | 0.832506i | \(-0.313095\pi\) | ||||
0.554016 | + | 0.832506i | \(0.313095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2359.62 | 0.0807128 | ||||||||
\(950\) | −374.609 | + | 12699.8i | −0.0127936 | + | 0.433722i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5651.58 | + | 501.282i | 0.192404 | + | 0.0170658i | ||||
\(953\) | − | 36928.6i | − | 1.25523i | −0.778524 | − | 0.627615i | \(-0.784031\pi\) | ||
0.778524 | − | 0.627615i | \(-0.215969\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31157.7i | 1.05575i | ||||||||
\(956\) | 1299.41 | + | 76.7248i | 0.0439602 | + | 0.00259567i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 47854.4 | + | 1411.57i | 1.61389 | + | 0.0476053i | ||||
\(959\) | −2980.67 | −0.100366 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25193.9 | 0.845688 | ||||||||
\(962\) | 3558.50 | + | 104.966i | 0.119263 | + | 0.00351792i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 37003.8 | + | 2184.92i | 1.23632 | + | 0.0729995i | ||||
\(965\) | 16140.8i | 0.538435i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 6532.84i | − | 0.217251i | −0.994083 | − | 0.108626i | \(-0.965355\pi\) | ||
0.994083 | − | 0.108626i | \(-0.0346450\pi\) | |||||||
\(968\) | 14144.9 | + | 1254.62i | 0.469664 | + | 0.0416581i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 336.227 | − | 11398.6i | 0.0111295 | − | 0.377306i | ||||
\(971\) | 48395.7 | 1.59948 | 0.799739 | − | 0.600348i | \(-0.204971\pi\) | ||||
0.799739 | + | 0.600348i | \(0.204971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9870.32 | 0.325209 | ||||||||
\(974\) | −803.876 | + | 27252.6i | −0.0264454 | + | 0.896539i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −56606.1 | − | 6708.11i | −1.85647 | − | 0.220001i | ||||
\(977\) | − | 37053.8i | − | 1.21336i | −0.794944 | − | 0.606682i | \(-0.792500\pi\) | ||
0.794944 | − | 0.606682i | \(-0.207500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14526.0i | 0.474212i | ||||||||
\(980\) | 199.325 | − | 3375.77i | 0.00649716 | − | 0.110036i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13547.2 | − | 399.605i | −0.440232 | − | 0.0129856i | ||||
\(983\) | −27818.2 | −0.902608 | −0.451304 | − | 0.892370i | \(-0.649041\pi\) | ||||
−0.451304 | + | 0.892370i | \(0.649041\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31573.4 | −1.02133 | ||||||||
\(986\) | −1294.21 | − | 38.1755i | −0.0418011 | − | 0.00123302i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 155.140 | − | 2627.45i | 0.00499561 | − | 0.0846056i | ||||
\(989\) | − | 2481.28i | − | 0.0797775i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42743.2i | 1.37011i | 0.728490 | + | 0.685057i | \(0.240223\pi\) | ||||
−0.728490 | + | 0.685057i | \(0.759777\pi\) | |||||||
\(992\) | −1803.10 | + | 12140.3i | −0.0577100 | + | 0.388564i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 55.0712 | − | 1866.99i | 0.00175730 | − | 0.0595749i | ||||
\(995\) | 34044.0 | 1.08469 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10810.6 | −0.343407 | −0.171703 | − | 0.985149i | \(-0.554927\pi\) | ||||
−0.171703 | + | 0.985149i | \(0.554927\pi\) | |||||||
\(998\) | −185.482 | + | 6288.13i | −0.00588311 | + | 0.199446i | ||||
\(999\) | 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 | 252.4.e.a.71.36 | yes | 36 | |
3.2 | odd | 2 | inner | 252.4.e.a.71.1 | ✓ | 36 | |
4.3 | odd | 2 | inner | 252.4.e.a.71.2 | yes | 36 | |
12.11 | even | 2 | inner | 252.4.e.a.71.35 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.e.a.71.1 | ✓ | 36 | 3.2 | odd | 2 | inner | |
252.4.e.a.71.2 | yes | 36 | 4.3 | odd | 2 | inner | |
252.4.e.a.71.35 | yes | 36 | 12.11 | even | 2 | inner | |
252.4.e.a.71.36 | yes | 36 | 1.1 | even | 1 | trivial |