Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,5,Mod(163,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.163");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.d (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: | \(33.4918680392\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 163.19 | ||
Character | \(\chi\) | \(=\) | 324.163 |
Dual form | 324.5.d.e.163.20 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.49753 | − | 1.94095i | 0.874382 | − | 0.485238i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 8.46540 | − | 13.5771i | 0.529087 | − | 0.848567i | ||||
\(5\) | 33.2277 | 1.32911 | 0.664554 | − | 0.747240i | \(-0.268621\pi\) | ||||
0.664554 | + | 0.747240i | \(0.268621\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 46.1602i | − | 0.942045i | −0.882121 | − | 0.471023i | \(-0.843885\pi\) | ||
0.882121 | − | 0.471023i | \(-0.156115\pi\) | |||||||
\(8\) | 3.25547 | − | 63.9171i | 0.0508667 | − | 0.998705i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 116.215 | − | 64.4935i | 1.16215 | − | 0.644935i | ||||
\(11\) | − | 73.4515i | − | 0.607037i | −0.952825 | − | 0.303519i | \(-0.901839\pi\) | ||
0.952825 | − | 0.303519i | \(-0.0981615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −303.039 | −1.79313 | −0.896566 | − | 0.442911i | \(-0.853946\pi\) | ||||
−0.896566 | + | 0.442911i | \(0.853946\pi\) | |||||||
\(14\) | −89.5949 | − | 161.447i | −0.457117 | − | 0.823707i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −112.674 | − | 229.871i | −0.440133 | − | 0.897932i | ||||
\(17\) | 182.019 | 0.629823 | 0.314912 | − | 0.949121i | \(-0.398025\pi\) | ||||
0.314912 | + | 0.949121i | \(0.398025\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 314.215i | − | 0.870402i | −0.900333 | − | 0.435201i | \(-0.856677\pi\) | ||
0.900333 | − | 0.435201i | \(-0.143323\pi\) | |||||||
\(20\) | 281.286 | − | 451.135i | 0.703214 | − | 1.12784i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −142.566 | − | 256.899i | −0.294558 | − | 0.530782i | ||||
\(23\) | 335.924i | 0.635018i | 0.948255 | + | 0.317509i | \(0.102846\pi\) | ||||
−0.948255 | + | 0.317509i | \(0.897154\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 479.081 | 0.766529 | ||||||||
\(26\) | −1059.89 | + | 588.185i | −1.56788 | + | 0.870096i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −626.721 | − | 390.765i | −0.799389 | − | 0.498424i | ||||
\(29\) | 714.740 | 0.849869 | 0.424935 | − | 0.905224i | \(-0.360297\pi\) | ||||
0.424935 | + | 0.905224i | \(0.360297\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1137.60i | 1.18376i | 0.806025 | + | 0.591881i | \(0.201614\pi\) | ||||
−0.806025 | + | 0.591881i | \(0.798386\pi\) | |||||||
\(32\) | −840.249 | − | 585.284i | −0.820556 | − | 0.571566i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 636.616 | − | 353.290i | 0.550706 | − | 0.305614i | ||||
\(35\) | − | 1533.80i | − | 1.25208i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1008.45 | 0.736632 | 0.368316 | − | 0.929701i | \(-0.379934\pi\) | ||||
0.368316 | + | 0.929701i | \(0.379934\pi\) | |||||||
\(38\) | −609.877 | − | 1098.98i | −0.422353 | − | 0.761064i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 108.172 | − | 2123.82i | 0.0676074 | − | 1.32739i | ||||
\(41\) | −1115.11 | −0.663358 | −0.331679 | − | 0.943392i | \(-0.607615\pi\) | ||||
−0.331679 | + | 0.943392i | \(0.607615\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2519.63i | − | 1.36270i | −0.731958 | − | 0.681349i | \(-0.761393\pi\) | ||
0.731958 | − | 0.681349i | \(-0.238607\pi\) | |||||||
\(44\) | −997.257 | − | 621.796i | −0.515112 | − | 0.321176i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 652.014 | + | 1174.90i | 0.308135 | + | 0.555248i | ||||
\(47\) | 1132.16i | 0.512520i | 0.966608 | + | 0.256260i | \(0.0824903\pi\) | ||||
−0.966608 | + | 0.256260i | \(0.917510\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 270.233 | 0.112550 | ||||||||
\(50\) | 1675.60 | − | 929.873i | 0.670239 | − | 0.371949i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2565.35 | + | 4114.39i | −0.948723 | + | 1.52159i | ||||
\(53\) | 1057.77 | 0.376566 | 0.188283 | − | 0.982115i | \(-0.439708\pi\) | ||||
0.188283 | + | 0.982115i | \(0.439708\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2440.63i | − | 0.806818i | ||||||
\(56\) | −2950.43 | − | 150.273i | −0.940826 | − | 0.0479188i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2499.82 | − | 1387.28i | 0.743110 | − | 0.412389i | ||||
\(59\) | − | 1014.38i | − | 0.291404i | −0.989329 | − | 0.145702i | \(-0.953456\pi\) | ||
0.989329 | − | 0.145702i | \(-0.0465440\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 860.608 | 0.231284 | 0.115642 | − | 0.993291i | \(-0.463107\pi\) | ||||
0.115642 | + | 0.993291i | \(0.463107\pi\) | |||||||
\(62\) | 2208.02 | + | 3978.77i | 0.574407 | + | 1.03506i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4074.80 | − | 416.161i | −0.994825 | − | 0.101602i | ||||
\(65\) | −10069.3 | −2.38327 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 645.525i | 0.143802i | 0.997412 | + | 0.0719008i | \(0.0229065\pi\) | ||||
−0.997412 | + | 0.0719008i | \(0.977094\pi\) | |||||||
\(68\) | 1540.86 | − | 2471.29i | 0.333231 | − | 0.534448i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2977.03 | − | 5364.50i | −0.607558 | − | 1.09480i | ||||
\(71\) | − | 9567.89i | − | 1.89801i | −0.315254 | − | 0.949007i | \(-0.602090\pi\) | ||
0.315254 | − | 0.949007i | \(-0.397910\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1899.10 | 0.356372 | 0.178186 | − | 0.983997i | \(-0.442977\pi\) | ||||
0.178186 | + | 0.983997i | \(0.442977\pi\) | |||||||
\(74\) | 3527.08 | − | 1957.35i | 0.644098 | − | 0.357442i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4266.13 | − | 2659.96i | −0.738595 | − | 0.460519i | ||||
\(77\) | −3390.54 | −0.571857 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7815.14i | 1.25223i | 0.779733 | + | 0.626113i | \(0.215355\pi\) | ||||
−0.779733 | + | 0.626113i | \(0.784645\pi\) | |||||||
\(80\) | −3743.90 | − | 7638.08i | −0.584985 | − | 1.19345i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3900.11 | + | 2164.37i | −0.580028 | + | 0.321887i | ||||
\(83\) | − | 8143.59i | − | 1.18212i | −0.806629 | − | 0.591058i | \(-0.798711\pi\) | ||
0.806629 | − | 0.591058i | \(-0.201289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6048.07 | 0.837103 | ||||||||
\(86\) | −4890.49 | − | 8812.48i | −0.661234 | − | 1.19152i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4694.81 | − | 239.119i | −0.606251 | − | 0.0308780i | ||||
\(89\) | −7653.39 | −0.966215 | −0.483107 | − | 0.875561i | \(-0.660492\pi\) | ||||
−0.483107 | + | 0.875561i | \(0.660492\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13988.4i | 1.68921i | ||||||||
\(92\) | 4560.87 | + | 2843.73i | 0.538855 | + | 0.335980i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2197.46 | + | 3959.75i | 0.248694 | + | 0.448138i | ||||
\(95\) | − | 10440.7i | − | 1.15686i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12733.5 | 1.35333 | 0.676666 | − | 0.736290i | \(-0.263424\pi\) | ||||
0.676666 | + | 0.736290i | \(0.263424\pi\) | |||||||
\(98\) | 945.149 | − | 524.510i | 0.0984120 | − | 0.0546137i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4055.61 | − | 6504.52i | 0.405561 | − | 0.650452i | ||||
\(101\) | 13746.4 | 1.34755 | 0.673777 | − | 0.738935i | \(-0.264671\pi\) | ||||
0.673777 | + | 0.738935i | \(0.264671\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12992.1i | 1.22463i | 0.790615 | + | 0.612313i | \(0.209761\pi\) | ||||
−0.790615 | + | 0.612313i | \(0.790239\pi\) | |||||||
\(104\) | −986.536 | + | 19369.4i | −0.0912108 | + | 1.79081i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3699.59 | − | 2053.09i | 0.329262 | − | 0.182724i | ||||
\(107\) | 14891.8i | 1.30071i | 0.759631 | + | 0.650354i | \(0.225379\pi\) | ||||
−0.759631 | + | 0.650354i | \(0.774621\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7539.02 | 0.634544 | 0.317272 | − | 0.948335i | \(-0.397233\pi\) | ||||
0.317272 | + | 0.948335i | \(0.397233\pi\) | |||||||
\(110\) | −4737.14 | − | 8536.16i | −0.391499 | − | 0.705467i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10610.9 | + | 5201.06i | −0.845893 | + | 0.414626i | ||||
\(113\) | 992.279 | 0.0777100 | 0.0388550 | − | 0.999245i | \(-0.487629\pi\) | ||||
0.0388550 | + | 0.999245i | \(0.487629\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11162.0i | 0.844007i | ||||||||
\(116\) | 6050.56 | − | 9704.08i | 0.449655 | − | 0.721171i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1968.86 | − | 3547.81i | −0.141400 | − | 0.254798i | ||||
\(119\) | − | 8402.04i | − | 0.593322i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9245.87 | 0.631506 | ||||||||
\(122\) | 3010.00 | − | 1670.40i | 0.202231 | − | 0.112228i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15445.2 | + | 9630.20i | 1.00450 | + | 0.626313i | ||||
\(125\) | −4848.57 | −0.310308 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7123.52i | 0.441659i | 0.975312 | + | 0.220829i | \(0.0708764\pi\) | ||||
−0.975312 | + | 0.220829i | \(0.929124\pi\) | |||||||
\(128\) | −15059.5 | + | 6453.47i | −0.919158 | + | 0.393889i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −35217.7 | + | 19544.0i | −2.08388 | + | 1.15645i | ||||
\(131\) | 6959.56i | 0.405545i | 0.979226 | + | 0.202773i | \(0.0649952\pi\) | ||||
−0.979226 | + | 0.202773i | \(0.935005\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14504.2 | −0.819959 | ||||||||
\(134\) | 1252.93 | + | 2257.74i | 0.0697780 | + | 0.125737i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 592.557 | − | 11634.1i | 0.0320371 | − | 0.629008i | ||||
\(137\) | 8488.85 | 0.452280 | 0.226140 | − | 0.974095i | \(-0.427389\pi\) | ||||
0.226140 | + | 0.974095i | \(0.427389\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 21343.3i | − | 1.10467i | −0.833622 | − | 0.552335i | \(-0.813737\pi\) | ||
0.833622 | − | 0.552335i | \(-0.186263\pi\) | |||||||
\(140\) | −20824.5 | − | 12984.2i | −1.06247 | − | 0.662460i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −18570.8 | − | 33464.0i | −0.920990 | − | 1.65959i | ||||
\(143\) | 22258.7i | 1.08850i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23749.2 | 1.12957 | ||||||||
\(146\) | 6642.17 | − | 3686.07i | 0.311605 | − | 0.172925i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8536.92 | − | 13691.8i | 0.389743 | − | 0.625082i | ||||
\(149\) | 12733.6 | 0.573558 | 0.286779 | − | 0.957997i | \(-0.407415\pi\) | ||||
0.286779 | + | 0.957997i | \(0.407415\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3535.51i | 0.155059i | 0.996990 | + | 0.0775296i | \(0.0247032\pi\) | ||||
−0.996990 | + | 0.0775296i | \(0.975297\pi\) | |||||||
\(152\) | −20083.7 | − | 1022.92i | −0.869276 | − | 0.0442745i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11858.5 | + | 6580.88i | −0.500021 | + | 0.277487i | ||||
\(155\) | 37799.7i | 1.57335i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 29741.1 | 1.20658 | 0.603292 | − | 0.797520i | \(-0.293855\pi\) | ||||
0.603292 | + | 0.797520i | \(0.293855\pi\) | |||||||
\(158\) | 15168.8 | + | 27333.7i | 0.607628 | + | 1.09492i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −27919.6 | − | 19447.6i | −1.09061 | − | 0.759673i | ||||
\(161\) | 15506.3 | 0.598216 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5903.96i | − | 0.222213i | −0.993809 | − | 0.111106i | \(-0.964561\pi\) | ||
0.993809 | − | 0.111106i | \(-0.0354394\pi\) | |||||||
\(164\) | −9439.81 | + | 15139.9i | −0.350974 | + | 0.562904i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15806.3 | − | 28482.4i | −0.573608 | − | 1.03362i | ||||
\(167\) | 20566.0i | 0.737425i | 0.929544 | + | 0.368712i | \(0.120201\pi\) | ||||
−0.929544 | + | 0.368712i | \(0.879799\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 63271.8 | 2.21532 | ||||||||
\(170\) | 21153.3 | − | 11739.0i | 0.731948 | − | 0.406195i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −34209.2 | − | 21329.7i | −1.15634 | − | 0.720987i | ||||
\(173\) | −6109.97 | −0.204149 | −0.102074 | − | 0.994777i | \(-0.532548\pi\) | ||||
−0.102074 | + | 0.994777i | \(0.532548\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 22114.5i | − | 0.722105i | ||||||
\(176\) | −16884.4 | + | 8276.09i | −0.545079 | + | 0.267177i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −26767.9 | + | 14854.9i | −0.844840 | + | 0.468844i | ||||
\(179\) | 11534.8i | 0.360001i | 0.983667 | + | 0.180001i | \(0.0576099\pi\) | ||||
−0.983667 | + | 0.180001i | \(0.942390\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25544.2 | −0.779713 | −0.389857 | − | 0.920876i | \(-0.627475\pi\) | ||||
−0.389857 | + | 0.920876i | \(0.627475\pi\) | |||||||
\(182\) | 27150.8 | + | 48924.7i | 0.819670 | + | 1.47702i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 21471.3 | + | 1093.59i | 0.634196 | + | 0.0323013i | ||||
\(185\) | 33508.5 | 0.979064 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 13369.6i | − | 0.382326i | ||||||
\(188\) | 15371.4 | + | 9584.15i | 0.434908 | + | 0.271168i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20264.8 | − | 36516.5i | −0.561353 | − | 1.01154i | ||||
\(191\) | − | 39067.8i | − | 1.07091i | −0.844564 | − | 0.535454i | \(-0.820141\pi\) | ||
0.844564 | − | 0.535454i | \(-0.179859\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27830.3 | 0.747143 | 0.373572 | − | 0.927601i | \(-0.378133\pi\) | ||||
0.373572 | + | 0.927601i | \(0.378133\pi\) | |||||||
\(194\) | 44535.8 | − | 24715.1i | 1.18333 | − | 0.656689i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2287.63 | − | 3668.98i | 0.0595489 | − | 0.0955065i | ||||
\(197\) | 21103.0 | 0.543765 | 0.271883 | − | 0.962330i | \(-0.412354\pi\) | ||||
0.271883 | + | 0.962330i | \(0.412354\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5447.97i | − | 0.137572i | −0.997631 | − | 0.0687858i | \(-0.978087\pi\) | ||
0.997631 | − | 0.0687858i | \(-0.0219125\pi\) | |||||||
\(200\) | 1559.63 | − | 30621.5i | 0.0389908 | − | 0.765537i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 48078.4 | − | 26681.1i | 1.17828 | − | 0.653885i | ||||
\(203\) | − | 32992.6i | − | 0.800615i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −37052.4 | −0.881675 | ||||||||
\(206\) | 25217.0 | + | 45440.1i | 0.594236 | + | 1.07079i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 34144.7 | + | 69659.8i | 0.789217 | + | 1.61011i | ||||
\(209\) | −23079.6 | −0.528367 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 69207.1i | 1.55448i | 0.629203 | + | 0.777241i | \(0.283381\pi\) | ||||
−0.629203 | + | 0.777241i | \(0.716619\pi\) | |||||||
\(212\) | 8954.47 | − | 14361.5i | 0.199236 | − | 0.319542i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 28904.3 | + | 52084.5i | 0.631154 | + | 1.13732i | ||||
\(215\) | − | 83721.5i | − | 1.81117i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 52511.7 | 1.11516 | ||||||||
\(218\) | 26367.9 | − | 14632.9i | 0.554834 | − | 0.307905i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −33136.6 | − | 20660.9i | −0.684640 | − | 0.426877i | ||||
\(221\) | −55158.9 | −1.12936 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25327.7i | 0.509315i | 0.967031 | + | 0.254658i | \(0.0819628\pi\) | ||||
−0.967031 | + | 0.254658i | \(0.918037\pi\) | |||||||
\(224\) | −27016.8 | + | 38786.1i | −0.538441 | + | 0.773001i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3470.52 | − | 1925.97i | 0.0679482 | − | 0.0377079i | ||||
\(227\) | 97207.4i | 1.88646i | 0.332139 | + | 0.943230i | \(0.392230\pi\) | ||||
−0.332139 | + | 0.943230i | \(0.607770\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −85892.8 | −1.63789 | −0.818947 | − | 0.573869i | \(-0.805442\pi\) | ||||
−0.818947 | + | 0.573869i | \(0.805442\pi\) | |||||||
\(230\) | 21664.9 | + | 39039.4i | 0.409545 | + | 0.737985i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2326.82 | − | 45684.1i | 0.0432301 | − | 0.848769i | ||||
\(233\) | 12774.0 | 0.235297 | 0.117649 | − | 0.993055i | \(-0.462464\pi\) | ||||
0.117649 | + | 0.993055i | \(0.462464\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 37619.0i | 0.681194i | ||||||||
\(236\) | −13772.3 | − | 8587.10i | −0.247276 | − | 0.154178i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −16308.0 | − | 29386.3i | −0.287903 | − | 0.518790i | ||||
\(239\) | 105942.i | 1.85469i | 0.374202 | + | 0.927347i | \(0.377917\pi\) | ||||
−0.374202 | + | 0.927347i | \(0.622083\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10179.5 | −0.175263 | −0.0876316 | − | 0.996153i | \(-0.527930\pi\) | ||||
−0.0876316 | + | 0.996153i | \(0.527930\pi\) | |||||||
\(242\) | 32337.7 | − | 17945.8i | 0.552177 | − | 0.306431i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7285.38 | − | 11684.5i | 0.122369 | − | 0.196260i | ||||
\(245\) | 8979.23 | 0.149592 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 95219.6i | 1.56075i | ||||||||
\(248\) | 72711.9 | + | 3703.41i | 1.18223 | + | 0.0602141i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −16958.0 | + | 9410.84i | −0.271328 | + | 0.150573i | ||||
\(251\) | 21848.1i | 0.346790i | 0.984852 | + | 0.173395i | \(0.0554738\pi\) | ||||
−0.984852 | + | 0.173395i | \(0.944526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24674.2 | 0.385479 | ||||||||
\(254\) | 13826.4 | + | 24914.7i | 0.214310 | + | 0.386178i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −40145.1 | + | 51801.0i | −0.612565 | + | 0.790420i | ||||
\(257\) | −55561.4 | −0.841216 | −0.420608 | − | 0.907243i | \(-0.638183\pi\) | ||||
−0.420608 | + | 0.907243i | \(0.638183\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 46550.3i | − | 0.693941i | ||||||
\(260\) | −85240.6 | + | 136712.i | −1.26096 | + | 2.02236i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13508.2 | + | 24341.3i | 0.196786 | + | 0.354601i | ||||
\(263\) | − | 25163.3i | − | 0.363794i | −0.983318 | − | 0.181897i | \(-0.941776\pi\) | ||
0.983318 | − | 0.181897i | \(-0.0582238\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35147.4 | 0.500497 | ||||||||
\(266\) | −50729.0 | + | 28152.1i | −0.716957 | + | 0.397875i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8764.34 | + | 5464.62i | 0.122025 | + | 0.0760835i | ||||
\(269\) | −54154.0 | −0.748386 | −0.374193 | − | 0.927351i | \(-0.622080\pi\) | ||||
−0.374193 | + | 0.927351i | \(0.622080\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 94942.5i | − | 1.29277i | −0.763011 | − | 0.646386i | \(-0.776280\pi\) | ||
0.763011 | − | 0.646386i | \(-0.223720\pi\) | |||||||
\(272\) | −20508.8 | − | 41840.8i | −0.277206 | − | 0.565539i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 29690.0 | − | 16476.5i | 0.395466 | − | 0.219464i | ||||
\(275\) | − | 35189.2i | − | 0.465312i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 108039. | 1.40807 | 0.704033 | − | 0.710167i | \(-0.251381\pi\) | ||||
0.704033 | + | 0.710167i | \(0.251381\pi\) | |||||||
\(278\) | −41426.4 | − | 74648.9i | −0.536029 | − | 0.965904i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −98036.0 | − | 4993.24i | −1.25046 | − | 0.0636893i | ||||
\(281\) | 68926.1 | 0.872913 | 0.436456 | − | 0.899725i | \(-0.356233\pi\) | ||||
0.436456 | + | 0.899725i | \(0.356233\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 45211.4i | − | 0.564514i | −0.959339 | − | 0.282257i | \(-0.908917\pi\) | ||
0.959339 | − | 0.282257i | \(-0.0910831\pi\) | |||||||
\(284\) | −129904. | − | 80996.0i | −1.61059 | − | 1.00422i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 43203.1 | + | 77850.4i | 0.528181 | + | 0.951763i | ||||
\(287\) | 51473.5i | 0.624914i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −50390.1 | −0.603323 | ||||||||
\(290\) | 83063.4 | − | 46096.0i | 0.987674 | − | 0.548110i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16076.7 | − | 25784.3i | 0.188552 | − | 0.302405i | ||||
\(293\) | 71707.2 | 0.835271 | 0.417636 | − | 0.908615i | \(-0.362859\pi\) | ||||
0.417636 | + | 0.908615i | \(0.362859\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 33705.4i | − | 0.387307i | ||||||
\(296\) | 3282.98 | − | 64457.2i | 0.0374701 | − | 0.735679i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 44536.0 | − | 24715.3i | 0.501509 | − | 0.278313i | ||||
\(299\) | − | 101798.i | − | 1.13867i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −116307. | −1.28372 | ||||||||
\(302\) | 6862.25 | + | 12365.5i | 0.0752407 | + | 0.135581i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −72228.9 | + | 35403.9i | −0.781563 | + | 0.383093i | ||||
\(305\) | 28596.0 | 0.307401 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 95866.9i | 1.01717i | 0.861013 | + | 0.508583i | \(0.169830\pi\) | ||||
−0.861013 | + | 0.508583i | \(0.830170\pi\) | |||||||
\(308\) | −28702.3 | + | 46033.6i | −0.302562 | + | 0.485259i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 73367.4 | + | 132205.i | 0.763449 | + | 1.37571i | ||||
\(311\) | − | 24068.5i | − | 0.248845i | −0.992229 | − | 0.124423i | \(-0.960292\pi\) | ||
0.992229 | − | 0.124423i | \(-0.0397078\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −99309.0 | −1.01368 | −0.506839 | − | 0.862041i | \(-0.669186\pi\) | ||||
−0.506839 | + | 0.862041i | \(0.669186\pi\) | |||||||
\(314\) | 104020. | − | 57726.1i | 1.05502 | − | 0.585481i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 106107. | + | 66158.2i | 1.06260 | + | 0.662536i | ||||
\(317\) | −59441.0 | −0.591517 | −0.295759 | − | 0.955263i | \(-0.595572\pi\) | ||||
−0.295759 | + | 0.955263i | \(0.595572\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 52498.7i | − | 0.515902i | ||||||
\(320\) | −135396. | − | 13828.1i | −1.32223 | − | 0.135040i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 54233.9 | − | 30097.1i | 0.523069 | − | 0.290277i | ||||
\(323\) | − | 57193.1i | − | 0.548200i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −145180. | −1.37449 | ||||||||
\(326\) | −11459.3 | − | 20649.3i | −0.107826 | − | 0.194299i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3630.19 | + | 71274.3i | −0.0337429 | + | 0.662499i | ||||
\(329\) | 52260.6 | 0.482817 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 92205.2i | 0.841588i | 0.907156 | + | 0.420794i | \(0.138248\pi\) | ||||
−0.907156 | + | 0.420794i | \(0.861752\pi\) | |||||||
\(332\) | −110566. | − | 68938.8i | −1.00310 | − | 0.625442i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 39917.7 | + | 71930.3i | 0.357827 | + | 0.644791i | ||||
\(335\) | 21449.3i | 0.191128i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 45908.3 | 0.404233 | 0.202117 | − | 0.979361i | \(-0.435218\pi\) | ||||
0.202117 | + | 0.979361i | \(0.435218\pi\) | |||||||
\(338\) | 221295. | − | 122808.i | 1.93704 | − | 1.07496i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 51199.3 | − | 82115.2i | 0.442901 | − | 0.710339i | ||||
\(341\) | 83558.1 | 0.718588 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 123305.i | − | 1.04807i | ||||||
\(344\) | −161048. | − | 8202.58i | −1.36093 | − | 0.0693161i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21369.8 | + | 11859.2i | −0.178504 | + | 0.0990609i | ||||
\(347\) | − | 151976.i | − | 1.26216i | −0.775717 | − | 0.631081i | \(-0.782611\pi\) | ||
0.775717 | − | 0.631081i | \(-0.217389\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −187291. | −1.53768 | −0.768841 | − | 0.639440i | \(-0.779166\pi\) | ||||
−0.768841 | + | 0.639440i | \(0.779166\pi\) | |||||||
\(350\) | −42923.2 | − | 77346.0i | −0.350393 | − | 0.631396i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −42990.0 | + | 61717.6i | −0.346962 | + | 0.498108i | ||||
\(353\) | −45415.6 | −0.364465 | −0.182232 | − | 0.983255i | \(-0.558332\pi\) | ||||
−0.182232 | + | 0.983255i | \(0.558332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 317919.i | − | 2.52267i | ||||||
\(356\) | −64788.9 | + | 103911.i | −0.511212 | + | 0.819898i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22388.5 | + | 40343.3i | 0.174686 | + | 0.314778i | ||||
\(359\) | − | 71504.2i | − | 0.554808i | −0.960753 | − | 0.277404i | \(-0.910526\pi\) | ||
0.960753 | − | 0.277404i | \(-0.0894740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31589.8 | 0.242400 | ||||||||
\(362\) | −89341.5 | + | 49580.1i | −0.681767 | + | 0.378347i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 189921. | + | 118417.i | 1.43341 | + | 0.893740i | ||||
\(365\) | 63102.9 | 0.473656 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 66286.7i | 0.492146i | 0.969251 | + | 0.246073i | \(0.0791404\pi\) | ||||
−0.969251 | + | 0.246073i | \(0.920860\pi\) | |||||||
\(368\) | 77219.2 | − | 37850.0i | 0.570203 | − | 0.279492i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 117197. | − | 65038.4i | 0.856076 | − | 0.475080i | ||||
\(371\) | − | 48827.1i | − | 0.354742i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 143569. | 1.03191 | 0.515955 | − | 0.856616i | \(-0.327437\pi\) | ||||
0.515955 | + | 0.856616i | \(0.327437\pi\) | |||||||
\(374\) | −25949.7 | − | 46760.4i | −0.185519 | − | 0.334299i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 72364.2 | + | 3685.70i | 0.511856 | + | 0.0260702i | ||||
\(377\) | −216594. | −1.52393 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 183178.i | 1.27525i | 0.770348 | + | 0.637624i | \(0.220083\pi\) | ||||
−0.770348 | + | 0.637624i | \(0.779917\pi\) | |||||||
\(380\) | −141754. | − | 88384.3i | −0.981673 | − | 0.612079i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −75828.8 | − | 136641.i | −0.519646 | − | 0.936382i | ||||
\(383\) | − | 17523.6i | − | 0.119461i | −0.998215 | − | 0.0597303i | \(-0.980976\pi\) | ||
0.998215 | − | 0.0597303i | \(-0.0190241\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −112660. | −0.760060 | ||||||||
\(386\) | 97337.4 | − | 54017.4i | 0.653288 | − | 0.362543i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 107794. | − | 172884.i | 0.716031 | − | 1.14839i | ||||
\(389\) | −76861.5 | −0.507937 | −0.253968 | − | 0.967212i | \(-0.581736\pi\) | ||||
−0.253968 | + | 0.967212i | \(0.581736\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 61144.6i | 0.399949i | ||||||||
\(392\) | 879.737 | − | 17272.5i | 0.00572507 | − | 0.112405i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 73808.3 | − | 40959.9i | 0.475459 | − | 0.263856i | ||||
\(395\) | 259679.i | 1.66434i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −73295.7 | −0.465047 | −0.232524 | − | 0.972591i | \(-0.574698\pi\) | ||||
−0.232524 | + | 0.972591i | \(0.574698\pi\) | |||||||
\(398\) | −10574.3 | − | 19054.4i | −0.0667550 | − | 0.120290i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −53980.0 | − | 110127.i | −0.337375 | − | 0.688291i | ||||
\(401\) | −284548. | −1.76957 | −0.884784 | − | 0.466002i | \(-0.845694\pi\) | ||||
−0.884784 | + | 0.466002i | \(0.845694\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 344736.i | − | 2.12264i | ||||||
\(404\) | 116369. | − | 186636.i | 0.712973 | − | 1.14349i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −64037.0 | − | 115392.i | −0.388489 | − | 0.700044i | ||||
\(407\) | − | 74072.1i | − | 0.447163i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −113154. | −0.676430 | −0.338215 | − | 0.941069i | \(-0.609823\pi\) | ||||
−0.338215 | + | 0.941069i | \(0.609823\pi\) | |||||||
\(410\) | −129592. | + | 71917.0i | −0.770921 | + | 0.427823i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 176394. | + | 109983.i | 1.03918 | + | 0.647934i | ||||
\(413\) | −46823.9 | −0.274516 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 270593.i | − | 1.57116i | ||||||
\(416\) | 254628. | + | 177364.i | 1.47136 | + | 1.02489i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −80721.5 | + | 44796.4i | −0.461994 | + | 0.256384i | ||||
\(419\) | − | 274026.i | − | 1.56086i | −0.625242 | − | 0.780431i | \(-0.715000\pi\) | ||
0.625242 | − | 0.780431i | \(-0.285000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12483.8 | 0.0704339 | 0.0352170 | − | 0.999380i | \(-0.488788\pi\) | ||||
0.0352170 | + | 0.999380i | \(0.488788\pi\) | |||||||
\(422\) | 134328. | + | 242054.i | 0.754294 | + | 1.35921i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3443.55 | − | 67609.9i | 0.0191547 | − | 0.376078i | ||||
\(425\) | 87201.7 | 0.482778 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 39725.8i | − | 0.217880i | ||||||
\(428\) | 202187. | + | 126065.i | 1.10374 | + | 0.688188i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −162500. | − | 292818.i | −0.878852 | − | 1.58366i | ||||
\(431\) | − | 119855.i | − | 0.645211i | −0.946533 | − | 0.322606i | \(-0.895441\pi\) | ||
0.946533 | − | 0.322606i | \(-0.104559\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −282465. | −1.50657 | −0.753284 | − | 0.657696i | \(-0.771531\pi\) | ||||
−0.753284 | + | 0.657696i | \(0.771531\pi\) | |||||||
\(434\) | 183661. | − | 101923.i | 0.975074 | − | 0.541117i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 63820.8 | − | 102358.i | 0.335729 | − | 0.538454i | ||||
\(437\) | 105553. | 0.552721 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 171426.i | 0.889501i | 0.895654 | + | 0.444751i | \(0.146708\pi\) | ||||
−0.895654 | + | 0.444751i | \(0.853292\pi\) | |||||||
\(440\) | −155998. | − | 7945.39i | −0.805774 | − | 0.0410402i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −192920. | + | 107061.i | −0.987488 | + | 0.548007i | ||||
\(443\) | − | 83009.3i | − | 0.422980i | −0.977380 | − | 0.211490i | \(-0.932168\pi\) | ||
0.977380 | − | 0.211490i | \(-0.0678315\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −254304. | −1.28420 | ||||||||
\(446\) | 49160.0 | + | 88584.5i | 0.247139 | + | 0.445336i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19210.1 | + | 188094.i | −0.0957135 | + | 0.937171i | ||||
\(449\) | −252767. | −1.25380 | −0.626898 | − | 0.779101i | \(-0.715676\pi\) | ||||
−0.626898 | + | 0.779101i | \(0.715676\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 81906.2i | 0.402683i | ||||||||
\(452\) | 8400.04 | − | 13472.3i | 0.0411154 | − | 0.0659422i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 188675. | + | 339986.i | 0.915383 | + | 1.64949i | ||||
\(455\) | 464801.i | 2.24515i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18979.6 | −0.0908771 | −0.0454386 | − | 0.998967i | \(-0.514469\pi\) | ||||
−0.0454386 | + | 0.998967i | \(0.514469\pi\) | |||||||
\(458\) | −300412. | + | 166714.i | −1.43214 | + | 0.794769i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 151547. | + | 94490.7i | 0.716197 | + | 0.446554i | ||||
\(461\) | 194152. | 0.913565 | 0.456783 | − | 0.889578i | \(-0.349002\pi\) | ||||
0.456783 | + | 0.889578i | \(0.349002\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 99567.3i | − | 0.464467i | −0.972660 | − | 0.232234i | \(-0.925397\pi\) | ||
0.972660 | − | 0.232234i | \(-0.0746034\pi\) | |||||||
\(464\) | −80532.7 | − | 164298.i | −0.374056 | − | 0.763125i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 44677.6 | − | 24793.8i | 0.205740 | − | 0.114175i | ||||
\(467\) | − | 126990.i | − | 0.582287i | −0.956679 | − | 0.291144i | \(-0.905964\pi\) | ||
0.956679 | − | 0.291144i | \(-0.0940358\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29797.6 | 0.135468 | ||||||||
\(470\) | 73016.7 | + | 131573.i | 0.330542 | + | 0.595624i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −64836.1 | − | 3302.27i | −0.291027 | − | 0.0148228i | ||||
\(473\) | −185071. | −0.827209 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 150534.i | − | 0.667189i | ||||||
\(476\) | −114075. | − | 71126.6i | −0.503474 | − | 0.313919i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 205628. | + | 370535.i | 0.899969 | + | 1.62171i | ||||
\(479\) | 55931.1i | 0.243771i | 0.992544 | + | 0.121886i | \(0.0388941\pi\) | ||||
−0.992544 | + | 0.121886i | \(0.961106\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −305600. | −1.32088 | ||||||||
\(482\) | −35602.9 | + | 19757.9i | −0.153247 | + | 0.0850445i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 78270.0 | − | 125532.i | 0.334122 | − | 0.535875i | ||||
\(485\) | 423105. | 1.79872 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 274913.i | − | 1.15914i | −0.814921 | − | 0.579572i | \(-0.803220\pi\) | ||
0.814921 | − | 0.579572i | \(-0.196780\pi\) | |||||||
\(488\) | 2801.68 | − | 55007.6i | 0.0117647 | − | 0.230985i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 31405.1 | − | 17428.3i | 0.130800 | − | 0.0725876i | ||||
\(491\) | 32375.0i | 0.134291i | 0.997743 | + | 0.0671455i | \(0.0213892\pi\) | ||||
−0.997743 | + | 0.0671455i | \(0.978611\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 130096. | 0.535267 | ||||||||
\(494\) | 184817. | + | 333033.i | 0.757334 | + | 1.36469i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 261500. | − | 128178.i | 1.06294 | − | 0.521013i | ||||
\(497\) | −441656. | −1.78802 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 290345.i | 1.16604i | 0.812458 | + | 0.583019i | \(0.198129\pi\) | ||||
−0.812458 | + | 0.583019i | \(0.801871\pi\) | |||||||
\(500\) | −41045.0 | + | 65829.4i | −0.164180 | + | 0.263317i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 42406.2 | + | 76414.4i | 0.168276 | + | 0.303227i | ||||
\(503\) | 9486.90i | 0.0374963i | 0.999824 | + | 0.0187481i | \(0.00596807\pi\) | ||||
−0.999824 | + | 0.0187481i | \(0.994032\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 456761. | 1.79104 | ||||||||
\(506\) | 86298.5 | − | 47891.4i | 0.337056 | − | 0.187049i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 96716.5 | + | 60303.4i | 0.374777 | + | 0.233676i | ||||
\(509\) | 292751. | 1.12996 | 0.564980 | − | 0.825104i | \(-0.308884\pi\) | ||||
0.564980 | + | 0.825104i | \(0.308884\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 87663.1i | − | 0.335718i | ||||||
\(512\) | −39865.2 | + | 259095.i | −0.152074 | + | 0.988369i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −194328. | + | 107842.i | −0.735544 | + | 0.408190i | ||||
\(515\) | 431697.i | 1.62766i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 83158.6 | 0.311119 | ||||||||
\(518\) | −90351.9 | − | 162811.i | −0.336727 | − | 0.606769i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −32780.3 | + | 643601.i | −0.121229 | + | 2.38018i | ||||
\(521\) | 344253. | 1.26824 | 0.634120 | − | 0.773234i | \(-0.281362\pi\) | ||||
0.634120 | + | 0.773234i | \(0.281362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 79326.1i | − | 0.290010i | −0.989431 | − | 0.145005i | \(-0.953680\pi\) | ||
0.989431 | − | 0.145005i | \(-0.0463198\pi\) | |||||||
\(524\) | 94490.5 | + | 58915.4i | 0.344132 | + | 0.214569i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −48840.8 | − | 88009.3i | −0.176527 | − | 0.318095i | ||||
\(527\) | 207064.i | 0.745561i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 166996. | 0.596753 | ||||||||
\(530\) | 122929. | − | 68219.5i | 0.437625 | − | 0.242860i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −122784. | + | 196925.i | −0.433830 | + | 0.695790i | ||||
\(533\) | 337921. | 1.18949 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 494821.i | 1.72878i | ||||||||
\(536\) | 41260.1 | + | 2101.49i | 0.143615 | + | 0.00731471i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −189405. | + | 105110.i | −0.654375 | + | 0.363146i | ||||
\(539\) | − | 19849.0i | − | 0.0683223i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 167330. | 0.571715 | 0.285857 | − | 0.958272i | \(-0.407722\pi\) | ||||
0.285857 | + | 0.958272i | \(0.407722\pi\) | |||||||
\(542\) | −184279. | − | 332064.i | −0.627303 | − | 1.13038i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −152941. | − | 106533.i | −0.516805 | − | 0.359986i | ||||
\(545\) | 250504. | 0.843378 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 285069.i | 0.952743i | 0.879244 | + | 0.476372i | \(0.158048\pi\) | ||||
−0.879244 | + | 0.476372i | \(0.841952\pi\) | |||||||
\(548\) | 71861.5 | − | 115254.i | 0.239296 | − | 0.383790i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −68300.6 | − | 123075.i | −0.225787 | − | 0.406860i | ||||
\(551\) | − | 224582.i | − | 0.739728i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 360749. | 1.17965 | ||||||||
\(554\) | 377871. | − | 209700.i | 1.23119 | − | 0.683248i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −289780. | − | 180680.i | −0.937387 | − | 0.584467i | ||||
\(557\) | −51271.9 | −0.165260 | −0.0826302 | − | 0.996580i | \(-0.526332\pi\) | ||||
−0.0826302 | + | 0.996580i | \(0.526332\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 763547.i | 2.44350i | ||||||||
\(560\) | −352575. | + | 172819.i | −1.12428 | + | 0.551082i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 241071. | − | 133782.i | 0.763259 | − | 0.423571i | ||||
\(563\) | 2873.82i | 0.00906656i | 0.999990 | + | 0.00453328i | \(0.00144299\pi\) | ||||
−0.999990 | + | 0.00453328i | \(0.998557\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32971.2 | 0.103285 | ||||||||
\(566\) | −87753.2 | − | 158128.i | −0.273924 | − | 0.493601i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −611552. | − | 31148.0i | −1.89556 | − | 0.0965458i | ||||
\(569\) | 113753. | 0.351350 | 0.175675 | − | 0.984448i | \(-0.443789\pi\) | ||||
0.175675 | + | 0.984448i | \(0.443789\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 31475.3i | − | 0.0965379i | −0.998834 | − | 0.0482689i | \(-0.984630\pi\) | ||
0.998834 | − | 0.0482689i | \(-0.0153705\pi\) | |||||||
\(572\) | 302208. | + | 188429.i | 0.923664 | + | 0.575910i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 99907.7 | + | 180030.i | 0.303232 | + | 0.546413i | ||||
\(575\) | 160935.i | 0.486760i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −654654. | −1.96635 | −0.983174 | − | 0.182671i | \(-0.941526\pi\) | ||||
−0.983174 | + | 0.182671i | \(0.941526\pi\) | |||||||
\(578\) | −176241. | + | 97804.9i | −0.527534 | + | 0.292755i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 201046. | − | 322444.i | 0.597640 | − | 0.958515i | ||||
\(581\) | −375910. | −1.11361 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 77695.1i | − | 0.228590i | ||||||
\(584\) | 6182.48 | − | 121385.i | 0.0181275 | − | 0.355910i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 250798. | − | 139180.i | 0.730346 | − | 0.405306i | ||||
\(587\) | 643491.i | 1.86753i | 0.357893 | + | 0.933763i | \(0.383495\pi\) | ||||
−0.357893 | + | 0.933763i | \(0.616505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 357450. | 1.03035 | ||||||||
\(590\) | −65420.6 | − | 117886.i | −0.187936 | − | 0.338654i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −113626. | − | 231813.i | −0.324216 | − | 0.661446i | ||||
\(593\) | 183090. | 0.520661 | 0.260330 | − | 0.965520i | \(-0.416169\pi\) | ||||
0.260330 | + | 0.965520i | \(0.416169\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 279180.i | − | 0.788589i | ||||||
\(596\) | 107795. | − | 172885.i | 0.303462 | − | 0.486703i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −197586. | − | 356042.i | −0.552527 | − | 0.995633i | ||||
\(599\) | − | 27833.2i | − | 0.0775728i | −0.999248 | − | 0.0387864i | \(-0.987651\pi\) | ||
0.999248 | − | 0.0387864i | \(-0.0123492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −271528. | −0.751736 | −0.375868 | − | 0.926673i | \(-0.622655\pi\) | ||||
−0.375868 | + | 0.926673i | \(0.622655\pi\) | |||||||
\(602\) | −406786. | + | 225746.i | −1.12247 | + | 0.622912i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 48001.8 | + | 29929.5i | 0.131578 | + | 0.0820399i | ||||
\(605\) | 307219. | 0.839339 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 100450.i | 0.272628i | 0.990666 | + | 0.136314i | \(0.0435256\pi\) | ||||
−0.990666 | + | 0.136314i | \(0.956474\pi\) | |||||||
\(608\) | −183905. | + | 264019.i | −0.497493 | + | 0.714214i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 100015. | − | 55503.6i | 0.268786 | − | 0.149163i | ||||
\(611\) | − | 343088.i | − | 0.919015i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 458408. | 1.21992 | 0.609960 | − | 0.792432i | \(-0.291185\pi\) | ||||
0.609960 | + | 0.792432i | \(0.291185\pi\) | |||||||
\(614\) | 186073. | + | 335297.i | 0.493568 | + | 0.889391i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11037.8 | + | 216714.i | −0.0290885 | + | 0.571116i | ||||
\(617\) | 474635. | 1.24678 | 0.623389 | − | 0.781912i | \(-0.285755\pi\) | ||||
0.623389 | + | 0.781912i | \(0.285755\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6598.31i | 0.0172207i | 0.999963 | + | 0.00861036i | \(0.00274080\pi\) | ||||
−0.999963 | + | 0.00861036i | \(0.997259\pi\) | |||||||
\(620\) | 513209. | + | 319989.i | 1.33509 | + | 0.832438i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −46715.9 | − | 84180.4i | −0.120749 | − | 0.217586i | ||||
\(623\) | 353282.i | 0.910218i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −460532. | −1.17896 | ||||||||
\(626\) | −347336. | + | 192754.i | −0.886342 | + | 0.491876i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 251770. | − | 403797.i | 0.638389 | − | 1.02387i | ||||
\(629\) | 183557. | 0.463948 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 102946.i | − | 0.258553i | −0.991609 | − | 0.129277i | \(-0.958734\pi\) | ||
0.991609 | − | 0.129277i | \(-0.0412655\pi\) | |||||||
\(632\) | 499521. | + | 25442.0i | 1.25060 | + | 0.0636966i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −207897. | + | 115372.i | −0.517212 | + | 0.287027i | ||||
\(635\) | 236698.i | 0.587012i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −81891.3 | −0.201818 | ||||||||
\(638\) | −101898. | − | 183616.i | −0.250336 | − | 0.451096i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −500392. | + | 214434.i | −1.22166 | + | 0.523521i | ||||
\(641\) | −404806. | −0.985215 | −0.492607 | − | 0.870252i | \(-0.663956\pi\) | ||||
−0.492607 | + | 0.870252i | \(0.663956\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 492031.i | − | 1.19006i | −0.803702 | − | 0.595032i | \(-0.797139\pi\) | ||
0.803702 | − | 0.595032i | \(-0.202861\pi\) | |||||||
\(644\) | 131267. | − | 210531.i | 0.316508 | − | 0.507626i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −111009. | − | 200035.i | −0.266008 | − | 0.479336i | ||||
\(647\) | 306912.i | 0.733171i | 0.930384 | + | 0.366586i | \(0.119473\pi\) | ||||
−0.930384 | + | 0.366586i | \(0.880527\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −74507.5 | −0.176893 | ||||||||
\(650\) | −507772. | + | 281788.i | −1.20183 | + | 0.666954i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −80158.6 | − | 49979.4i | −0.188562 | − | 0.117570i | ||||
\(653\) | −195324. | −0.458066 | −0.229033 | − | 0.973419i | \(-0.573556\pi\) | ||||
−0.229033 | + | 0.973419i | \(0.573556\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 231250.i | 0.539013i | ||||||||
\(656\) | 125644. | + | 256330.i | 0.291966 | + | 0.595651i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 182783. | − | 101435.i | 0.422166 | − | 0.234281i | ||||
\(659\) | − | 783894.i | − | 1.80504i | −0.430650 | − | 0.902519i | \(-0.641716\pi\) | ||
0.430650 | − | 0.902519i | \(-0.358284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 742150. | 1.69859 | 0.849295 | − | 0.527918i | \(-0.177027\pi\) | ||||
0.849295 | + | 0.527918i | \(0.177027\pi\) | |||||||
\(662\) | 178966. | + | 322490.i | 0.408371 | + | 0.735869i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −520515. | − | 26511.2i | −1.18059 | − | 0.0601304i | ||||
\(665\) | −481943. | −1.08981 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 240099.i | 0.539682i | ||||||||
\(668\) | 279227. | + | 174100.i | 0.625754 | + | 0.390162i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 41632.1 | + | 75019.6i | 0.0927426 | + | 0.167119i | ||||
\(671\) | − | 63212.9i | − | 0.140398i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 423202. | 0.934366 | 0.467183 | − | 0.884161i | \(-0.345269\pi\) | ||||
0.467183 | + | 0.884161i | \(0.345269\pi\) | |||||||
\(674\) | 160566. | − | 89106.0i | 0.353454 | − | 0.196149i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 535621. | − | 859046.i | 1.17210 | − | 1.87985i | ||||
\(677\) | −308244. | −0.672538 | −0.336269 | − | 0.941766i | \(-0.609165\pi\) | ||||
−0.336269 | + | 0.941766i | \(0.609165\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 587781.i | − | 1.27490i | ||||||
\(680\) | 19689.3 | − | 386576.i | 0.0425807 | − | 0.836020i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 292247. | − | 162182.i | 0.628320 | − | 0.348686i | ||||
\(683\) | 760287.i | 1.62981i | 0.579597 | + | 0.814903i | \(0.303210\pi\) | ||||
−0.579597 | + | 0.814903i | \(0.696790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 282065. | 0.601130 | ||||||||
\(686\) | −239329. | − | 431262.i | −0.508565 | − | 0.916416i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −579189. | + | 283897.i | −1.22361 | + | 0.599769i | ||||
\(689\) | −320547. | −0.675232 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 361693.i | 0.757501i | 0.925499 | + | 0.378751i | \(0.123646\pi\) | ||||
−0.925499 | + | 0.378751i | \(0.876354\pi\) | |||||||
\(692\) | −51723.4 | + | 82955.6i | −0.108013 | + | 0.173234i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −294978. | − | 531539.i | −0.612450 | − | 1.10361i | ||||
\(695\) | − | 709190.i | − | 1.46823i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −202970. | −0.417798 | ||||||||
\(698\) | −655056. | + | 363524.i | −1.34452 | + | 0.746143i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −300250. | − | 187208.i | −0.612755 | − | 0.382057i | ||||
\(701\) | −878492. | −1.78773 | −0.893864 | − | 0.448337i | \(-0.852016\pi\) | ||||
−0.893864 | + | 0.448337i | \(0.852016\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 316870.i | − | 0.641167i | ||||||
\(704\) | −30567.7 | + | 299301.i | −0.0616761 | + | 0.603896i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −158842. | + | 88149.6i | −0.318681 | + | 0.176852i | ||||
\(707\) | − | 634537.i | − | 1.26946i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 862381. | 1.71556 | 0.857781 | − | 0.514015i | \(-0.171842\pi\) | ||||
0.857781 | + | 0.514015i | \(0.171842\pi\) | |||||||
\(710\) | −617066. | − | 1.11193e6i | −1.22409 | − | 2.20577i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −24915.4 | + | 489183.i | −0.0491482 | + | 0.964964i | ||||
\(713\) | −382146. | −0.751710 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 739605.i | 1.44673i | ||||||||
\(716\) | 156609. | + | 97646.6i | 0.305485 | + | 0.190472i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −138786. | − | 250088.i | −0.269214 | − | 0.485114i | ||||
\(719\) | − | 424008.i | − | 0.820193i | −0.912042 | − | 0.410097i | \(-0.865495\pi\) | ||
0.912042 | − | 0.410097i | \(-0.134505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 599717. | 1.15365 | ||||||||
\(722\) | 110486. | − | 61314.3i | 0.211950 | − | 0.117622i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −216242. | + | 346816.i | −0.412536 | + | 0.661639i | ||||
\(725\) | 342418. | 0.651449 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 91032.9i | − | 0.172238i | −0.996285 | − | 0.0861191i | \(-0.972553\pi\) | ||
0.996285 | − | 0.0861191i | \(-0.0274466\pi\) | |||||||
\(728\) | 894096. | + | 45538.7i | 1.68702 | + | 0.0859247i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 220704. | − | 122480.i | 0.414157 | − | 0.229836i | ||||
\(731\) | − | 458620.i | − | 0.858259i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13278.0 | −0.0247129 | −0.0123565 | − | 0.999924i | \(-0.503933\pi\) | ||||
−0.0123565 | + | 0.999924i | \(0.503933\pi\) | |||||||
\(734\) | 128659. | + | 231840.i | 0.238808 | + | 0.430324i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 196611. | − | 282260.i | 0.362955 | − | 0.521068i | ||||
\(737\) | 47414.8 | 0.0872929 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 622195.i | 1.13930i | 0.821888 | + | 0.569650i | \(0.192921\pi\) | ||||
−0.821888 | + | 0.569650i | \(0.807079\pi\) | |||||||
\(740\) | 283662. | − | 454947.i | 0.518010 | − | 0.830802i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −94771.1 | − | 170774.i | −0.172135 | − | 0.310180i | ||||
\(743\) | − | 700428.i | − | 1.26878i | −0.773014 | − | 0.634389i | \(-0.781252\pi\) | ||
0.773014 | − | 0.634389i | \(-0.218748\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 423107. | 0.762321 | ||||||||
\(746\) | 502135. | − | 278660.i | 0.902283 | − | 0.500722i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −181520. | − | 113179.i | −0.324430 | − | 0.202284i | ||||
\(749\) | 687409. | 1.22533 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 85133.1i | − | 0.150945i | −0.997148 | − | 0.0754725i | \(-0.975953\pi\) | ||
0.997148 | − | 0.0754725i | \(-0.0240465\pi\) | |||||||
\(752\) | 260250. | − | 127565.i | 0.460208 | − | 0.225577i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −757544. | + | 420399.i | −1.33249 | + | 0.739468i | ||||
\(755\) | 117477.i | 0.206091i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 319528. | 0.557592 | 0.278796 | − | 0.960350i | \(-0.410065\pi\) | ||||
0.278796 | + | 0.960350i | \(0.410065\pi\) | |||||||
\(758\) | 355540. | + | 640669.i | 0.618799 | + | 1.11505i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −667337. | − | 33989.3i | −1.15536 | − | 0.0588457i | ||||
\(761\) | −753777. | −1.30159 | −0.650794 | − | 0.759255i | \(-0.725564\pi\) | ||||
−0.650794 | + | 0.759255i | \(0.725564\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 348003.i | − | 0.597770i | ||||||
\(764\) | −530426. | − | 330724.i | −0.908737 | − | 0.566604i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34012.4 | − | 61289.2i | −0.0579669 | − | 0.104454i | ||||
\(767\) | 307396.i | 0.522525i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 850312. | 1.43789 | 0.718945 | − | 0.695067i | \(-0.244625\pi\) | ||||
0.718945 | + | 0.695067i | \(0.244625\pi\) | |||||||
\(770\) | −394031. | + | 218668.i | −0.664582 | + | 0.368810i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 235595. | − | 377855.i | 0.395304 | − | 0.634001i | ||||
\(773\) | −13034.7 | −0.0218143 | −0.0109071 | − | 0.999941i | \(-0.503472\pi\) | ||||
−0.0109071 | + | 0.999941i | \(0.503472\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 545000.i | 0.907388i | ||||||||
\(776\) | 41453.6 | − | 813889.i | 0.0688396 | − | 1.35158i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −268825. | + | 149185.i | −0.444131 | + | 0.246471i | ||||
\(779\) | 350383.i | 0.577389i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −702776. | −1.15217 | ||||||||
\(782\) | 118679. | + | 213855.i | 0.194071 | + | 0.349708i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −30448.3 | − | 62118.7i | −0.0495372 | − | 0.101063i | ||||
\(785\) | 988229. | 1.60368 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 547203.i | − | 0.883484i | −0.897142 | − | 0.441742i | \(-0.854361\pi\) | ||
0.897142 | − | 0.441742i | \(-0.145639\pi\) | |||||||
\(788\) | 178645. | − | 286517.i | 0.287699 | − | 0.461422i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 504025. | + | 908235.i | 0.807603 | + | 1.45527i | ||||
\(791\) | − | 45803.8i | − | 0.0732064i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −260798. | −0.414723 | ||||||||
\(794\) | −256354. | + | 142264.i | −0.406629 | + | 0.225659i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −73967.5 | − | 46119.2i | −0.116739 | − | 0.0727874i | ||||
\(797\) | 208455. | 0.328167 | 0.164083 | − | 0.986446i | \(-0.447533\pi\) | ||||
0.164083 | + | 0.986446i | \(0.447533\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 206074.i | 0.322797i | ||||||||
\(800\) | −402547. | − | 280398.i | −0.628980 | − | 0.438122i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −995215. | + | 552295.i | −1.54728 | + | 0.858662i | ||||
\(803\) | − | 139492.i | − | 0.216331i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 515240. | 0.795093 | ||||||||
\(806\) | −669117. | − | 1.20572e6i | −1.02999 | − | 1.85600i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 44751.0 | − | 878630.i | 0.0685457 | − | 1.34581i | ||||
\(809\) | −844500. | −1.29034 | −0.645168 | − | 0.764041i | \(-0.723213\pi\) | ||||
−0.645168 | + | 0.764041i | \(0.723213\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 769174.i | − | 1.16945i | −0.811230 | − | 0.584727i | \(-0.801202\pi\) | ||
0.811230 | − | 0.584727i | \(-0.198798\pi\) | |||||||
\(812\) | −447943. | − | 279295.i | −0.679376 | − | 0.423595i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −143771. | − | 259069.i | −0.216981 | − | 0.390991i | ||||
\(815\) | − | 196175.i | − | 0.295345i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −791706. | −1.18610 | ||||||||
\(818\) | −395759. | + | 219627.i | −0.591458 | + | 0.328230i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −313663. | + | 503063.i | −0.466483 | + | 0.748161i | ||||
\(821\) | −645734. | −0.958004 | −0.479002 | − | 0.877814i | \(-0.659001\pi\) | ||||
−0.479002 | + | 0.877814i | \(0.659001\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 234055.i | − | 0.345555i | −0.984961 | − | 0.172778i | \(-0.944726\pi\) | ||
0.984961 | − | 0.172778i | \(-0.0552742\pi\) | |||||||
\(824\) | 830416. | + | 42295.3i | 1.22304 | + | 0.0622928i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −163768. | + | 90882.9i | −0.240031 | + | 0.133206i | ||||
\(827\) | − | 1.14409e6i | − | 1.67282i | −0.548108 | − | 0.836408i | \(-0.684652\pi\) | ||
0.548108 | − | 0.836408i | \(-0.315348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −563769. | −0.820336 | −0.410168 | − | 0.912010i | \(-0.634530\pi\) | ||||
−0.410168 | + | 0.912010i | \(0.634530\pi\) | |||||||
\(830\) | −525209. | − | 946406.i | −0.762387 | − | 1.37379i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.23483e6 | + | 126113.i | 1.78385 | + | 0.182185i | ||||
\(833\) | 49187.6 | 0.0708868 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 683362.i | 0.980117i | ||||||||
\(836\) | −195378. | + | 313353.i | −0.279552 | + | 0.448355i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −531873. | − | 958415.i | −0.757390 | − | 1.36479i | ||||
\(839\) | 267428.i | 0.379912i | 0.981793 | + | 0.189956i | \(0.0608345\pi\) | ||||
−0.981793 | + | 0.189956i | \(0.939165\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −196428. | −0.277722 | ||||||||
\(842\) | 43662.4 | − | 24230.4i | 0.0615862 | − | 0.0341773i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 939630. | + | 585865.i | 1.31908 | + | 0.822456i | ||||
\(845\) | 2.10238e6 | 2.94440 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 426792.i | − | 0.594907i | ||||||
\(848\) | −119184. | − | 243151.i | −0.165739 | − | 0.338131i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 304991. | − | 169255.i | 0.422132 | − | 0.234262i | ||||
\(851\) | 338763.i | 0.467775i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 366834. | 0.504164 | 0.252082 | − | 0.967706i | \(-0.418885\pi\) | ||||
0.252082 | + | 0.967706i | \(0.418885\pi\) | |||||||
\(854\) | −77106.0 | − | 138942.i | −0.105724 | − | 0.190510i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 951842. | + | 48479.9i | 1.29902 | + | 0.0661628i | ||||
\(857\) | −1.15213e6 | −1.56870 | −0.784348 | − | 0.620321i | \(-0.787002\pi\) | ||||
−0.784348 | + | 0.620321i | \(0.787002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.45765e6i | 1.97546i | 0.156173 | + | 0.987730i | \(0.450084\pi\) | ||||
−0.156173 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(860\) | −1.13669e6 | − | 708736.i | −1.53690 | − | 0.958269i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −232633. | − | 419196.i | −0.313081 | − | 0.564161i | ||||
\(863\) | − | 237901.i | − | 0.319430i | −0.987163 | − | 0.159715i | \(-0.948943\pi\) | ||
0.987163 | − | 0.159715i | \(-0.0510575\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −203020. | −0.271336 | ||||||||
\(866\) | −987928. | + | 548251.i | −1.31732 | + | 0.731044i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 444532. | − | 712955.i | 0.590016 | − | 0.946286i | ||||
\(869\) | 574034. | 0.760147 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 195619.i | − | 0.257855i | ||||||
\(872\) | 24543.1 | − | 481873.i | 0.0322772 | − | 0.633723i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 369173. | − | 204873.i | 0.483289 | − | 0.268201i | ||||
\(875\) | 223811.i | 0.292324i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −662067. | −0.860801 | −0.430400 | − | 0.902638i | \(-0.641628\pi\) | ||||
−0.430400 | + | 0.902638i | \(0.641628\pi\) | |||||||
\(878\) | 332729. | + | 599566.i | 0.431620 | + | 0.777764i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −561028. | + | 274995.i | −0.724468 | + | 0.355108i | ||||
\(881\) | −245234. | −0.315957 | −0.157979 | − | 0.987443i | \(-0.550498\pi\) | ||||
−0.157979 | + | 0.987443i | \(0.550498\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 924835.i | 1.18616i | 0.805144 | + | 0.593079i | \(0.202088\pi\) | ||||
−0.805144 | + | 0.593079i | \(0.797912\pi\) | |||||||
\(884\) | −466942. | + | 748896.i | −0.597528 | + | 0.958335i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −161117. | − | 290327.i | −0.205246 | − | 0.369846i | ||||
\(887\) | − | 1.26949e6i | − | 1.61355i | −0.590857 | − | 0.806776i | \(-0.701210\pi\) | ||
0.590857 | − | 0.806776i | \(-0.298790\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 328823. | 0.416063 | ||||||||
\(890\) | −889437. | + | 493593.i | −1.12288 | + | 0.623145i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 343877. | + | 214409.i | 0.432188 | + | 0.269472i | ||||
\(893\) | 355741. | 0.446098 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 383275.i | 0.478480i | ||||||||
\(896\) | 297894. | + | 695149.i | 0.371061 | + | 0.865889i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −884058. | + | 490608.i | −1.09630 | + | 0.608390i | ||||
\(899\) | 813085.i | 1.00604i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 192535. | 0.237170 | ||||||||
\(902\) | 158976. | + | 286469.i | 0.195397 | + | 0.352099i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3230.34 | − | 63423.6i | 0.00395285 | − | 0.0776094i | ||||
\(905\) | −848775. | −1.03632 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 47511.7i | − | 0.0577545i | −0.999583 | − | 0.0288772i | \(-0.990807\pi\) | ||
0.999583 | − | 0.0288772i | \(-0.00919319\pi\) | |||||||
\(908\) | 1.31979e6 | + | 822900.i | 1.60079 | + | 0.998102i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 902158. | + | 1.62565e6i | 1.08943 | + | 1.96311i | ||||
\(911\) | 486970.i | 0.586767i | 0.955995 | + | 0.293383i | \(0.0947813\pi\) | ||||
−0.955995 | + | 0.293383i | \(0.905219\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −598159. | −0.717588 | ||||||||
\(914\) | −66381.6 | + | 36838.5i | −0.0794613 | + | 0.0440971i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −727116. | + | 1.16617e6i | −0.866589 | + | 1.38986i | ||||
\(917\) | 321255. | 0.382042 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.08957e6i | 1.29010i | 0.764141 | + | 0.645049i | \(0.223163\pi\) | ||||
−0.764141 | + | 0.645049i | \(0.776837\pi\) | |||||||
\(920\) | 713443. | + | 36337.6i | 0.842915 | + | 0.0429319i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 679051. | − | 376840.i | 0.798805 | − | 0.443297i | ||||
\(923\) | 2.89945e6i | 3.40339i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 483129. | 0.564650 | ||||||||
\(926\) | −193256. | − | 348240.i | −0.225377 | − | 0.406122i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −600560. | − | 418326.i | −0.697365 | − | 0.485757i | ||||
\(929\) | −1.34285e6 | −1.55596 | −0.777978 | − | 0.628292i | \(-0.783754\pi\) | ||||
−0.777978 | + | 0.628292i | \(0.783754\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 84911.4i | − | 0.0979641i | ||||||
\(932\) | 108137. | − | 173434.i | 0.124493 | − | 0.199666i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −246483. | − | 444153.i | −0.282548 | − | 0.509142i | ||||
\(935\) | − | 444240.i | − | 0.508153i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.37506e6 | 1.56618 | 0.783089 | − | 0.621909i | \(-0.213643\pi\) | ||||
0.783089 | + | 0.621909i | \(0.213643\pi\) | |||||||
\(938\) | 104218. | − | 57835.7i | 0.118450 | − | 0.0657341i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 510755. | + | 318459.i | 0.578039 | + | 0.360411i | ||||
\(941\) | 1.57373e6 | 1.77726 | 0.888628 | − | 0.458628i | \(-0.151659\pi\) | ||||
0.888628 | + | 0.458628i | \(0.151659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 374591.i | − | 0.421244i | ||||||
\(944\) | −233175. | + | 114294.i | −0.261661 | + | 0.128257i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −647290. | + | 359214.i | −0.723297 | + | 0.401394i | ||||
\(947\) | 1.08422e6i | 1.20898i | 0.796613 | + | 0.604489i | \(0.206623\pi\) | ||||
−0.796613 | + | 0.604489i | \(0.793377\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −575503. | −0.639021 | ||||||||
\(950\) | −292180. | − | 526498.i | −0.323746 | − | 0.583378i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −537034. | − | 27352.6i | −0.592554 | − | 0.0301804i | ||||
\(953\) | −461469. | −0.508108 | −0.254054 | − | 0.967190i | \(-0.581764\pi\) | ||||
−0.254054 | + | 0.967190i | \(0.581764\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.29813e6i | − | 1.42335i | ||||||
\(956\) | 1.43838e6 | + | 896841.i | 1.57383 | + | 0.981295i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 108560. | + | 195621.i | 0.118287 | + | 0.213149i | ||||
\(959\) | − | 391847.i | − | 0.426069i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −370602. | −0.401293 | ||||||||
\(962\) | −1.06884e6 | + | 593155.i | −1.15495 | + | 0.640941i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −86173.2 | + | 138207.i | −0.0927295 | + | 0.148723i | ||||
\(965\) | 924738. | 0.993034 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.15329e6i | 1.23335i | 0.787218 | + | 0.616675i | \(0.211521\pi\) | ||||
−0.787218 | + | 0.616675i | \(0.788479\pi\) | |||||||
\(968\) | 30099.7 | − | 590970.i | 0.0321226 | − | 0.630688i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.47982e6 | − | 821227.i | 1.57277 | − | 0.872811i | ||||
\(971\) | − | 438562.i | − | 0.465149i | −0.972579 | − | 0.232575i | \(-0.925285\pi\) | ||
0.972579 | − | 0.232575i | \(-0.0747150\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −985213. | −1.04065 | ||||||||
\(974\) | −533594. | − | 961516.i | −0.562461 | − | 1.01353i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −96968.2 | − | 197828.i | −0.101796 | − | 0.207677i | ||||
\(977\) | −777229. | −0.814254 | −0.407127 | − | 0.913371i | \(-0.633469\pi\) | ||||
−0.407127 | + | 0.913371i | \(0.633469\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 562153.i | 0.586528i | ||||||||
\(980\) | 76012.8 | − | 121912.i | 0.0791470 | − | 0.126939i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 62838.4 | + | 113233.i | 0.0651632 | + | 0.117422i | ||||
\(983\) | − | 803420.i | − | 0.831449i | −0.909491 | − | 0.415724i | \(-0.863528\pi\) | ||
0.909491 | − | 0.415724i | \(-0.136472\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 701204. | 0.722723 | ||||||||
\(986\) | 455015. | − | 252511.i | 0.468028 | − | 0.259732i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.29280e6 | + | 806071.i | 1.32440 | + | 0.825771i | ||||
\(989\) | 846405. | 0.865338 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 206876.i | − | 0.210651i | −0.994438 | − | 0.105325i | \(-0.966412\pi\) | ||
0.994438 | − | 0.105325i | \(-0.0335884\pi\) | |||||||
\(992\) | 665816. | − | 955864.i | 0.676598 | − | 0.971343i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.54470e6 | + | 857234.i | −1.56341 | + | 0.867614i | ||||
\(995\) | − | 181024.i | − | 0.182848i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29662.7 | −0.0298414 | −0.0149207 | − | 0.999889i | \(-0.504750\pi\) | ||||
−0.0149207 | + | 0.999889i | \(0.504750\pi\) | |||||||
\(998\) | 563546. | + | 1.01549e6i | 0.565807 | + | 1.01956i | ||||
\(999\) | 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 | 324.5.d.e.163.19 | 22 | ||
3.2 | odd | 2 | 324.5.d.f.163.4 | 22 | |||
4.3 | odd | 2 | inner | 324.5.d.e.163.20 | 22 | ||
9.2 | odd | 6 | 36.5.f.a.31.18 | yes | 44 | ||
9.4 | even | 3 | 108.5.f.a.19.11 | 44 | |||
9.5 | odd | 6 | 36.5.f.a.7.12 | ✓ | 44 | ||
9.7 | even | 3 | 108.5.f.a.91.5 | 44 | |||
12.11 | even | 2 | 324.5.d.f.163.3 | 22 | |||
36.7 | odd | 6 | 108.5.f.a.91.11 | 44 | |||
36.11 | even | 6 | 36.5.f.a.31.12 | yes | 44 | ||
36.23 | even | 6 | 36.5.f.a.7.18 | yes | 44 | ||
36.31 | odd | 6 | 108.5.f.a.19.5 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.12 | ✓ | 44 | 9.5 | odd | 6 | ||
36.5.f.a.7.18 | yes | 44 | 36.23 | even | 6 | ||
36.5.f.a.31.12 | yes | 44 | 36.11 | even | 6 | ||
36.5.f.a.31.18 | yes | 44 | 9.2 | odd | 6 | ||
108.5.f.a.19.5 | 44 | 36.31 | odd | 6 | |||
108.5.f.a.19.11 | 44 | 9.4 | even | 3 | |||
108.5.f.a.91.5 | 44 | 9.7 | even | 3 | |||
108.5.f.a.91.11 | 44 | 36.7 | odd | 6 | |||
324.5.d.e.163.19 | 22 | 1.1 | even | 1 | trivial | ||
324.5.d.e.163.20 | 22 | 4.3 | odd | 2 | inner | ||
324.5.d.f.163.3 | 22 | 12.11 | even | 2 | |||
324.5.d.f.163.4 | 22 | 3.2 | odd | 2 |