Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,6,Mod(67,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("294.67");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.e (of order \(3\), degree \(2\), not 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: | \(47.1528430250\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 6) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.79 |
Dual form | 294.6.e.g.67.1 |
$q$-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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | + | 3.46410i | −0.353553 | + | 0.612372i | ||||
\(3\) | 4.50000 | + | 7.79423i | 0.288675 | + | 0.500000i | ||||
\(4\) | −8.00000 | − | 13.8564i | −0.250000 | − | 0.433013i | ||||
\(5\) | 33.0000 | − | 57.1577i | 0.590322 | − | 1.02247i | −0.403867 | − | 0.914818i | \(-0.632334\pi\) |
0.994189 | − | 0.107650i | \(-0.0343325\pi\) | |||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | 132.000 | + | 228.631i | 0.417421 | + | 0.722994i | ||||
\(11\) | 30.0000 | + | 51.9615i | 0.0747549 | + | 0.129479i | 0.900980 | − | 0.433861i | \(-0.142849\pi\) |
−0.826225 | + | 0.563341i | \(0.809516\pi\) | |||||||
\(12\) | 72.0000 | − | 124.708i | 0.144338 | − | 0.250000i | ||||
\(13\) | −658.000 | −1.07986 | −0.539930 | − | 0.841710i | \(-0.681549\pi\) | ||||
−0.539930 | + | 0.841710i | \(0.681549\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 594.000 | 0.681645 | ||||||||
\(16\) | −128.000 | + | 221.703i | −0.125000 | + | 0.216506i | ||||
\(17\) | 207.000 | + | 358.535i | 0.173719 | + | 0.300891i | 0.939717 | − | 0.341952i | \(-0.111088\pi\) |
−0.765998 | + | 0.642843i | \(0.777755\pi\) | |||||||
\(18\) | −162.000 | − | 280.592i | −0.117851 | − | 0.204124i | ||||
\(19\) | −478.000 | + | 827.920i | −0.303769 | + | 0.526144i | −0.976987 | − | 0.213301i | \(-0.931579\pi\) |
0.673217 | + | 0.739445i | \(0.264912\pi\) | |||||||
\(20\) | −1056.00 | −0.590322 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −240.000 | −0.105719 | ||||||||
\(23\) | −300.000 | + | 519.615i | −0.118250 | + | 0.204815i | −0.919074 | − | 0.394084i | \(-0.871062\pi\) |
0.800824 | + | 0.598900i | \(0.204395\pi\) | |||||||
\(24\) | 288.000 | + | 498.831i | 0.102062 | + | 0.176777i | ||||
\(25\) | −615.500 | − | 1066.08i | −0.196960 | − | 0.341145i | ||||
\(26\) | 1316.00 | − | 2279.38i | 0.381788 | − | 0.661277i | ||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5574.00 | 1.23076 | 0.615378 | − | 0.788232i | \(-0.289003\pi\) | ||||
0.615378 | + | 0.788232i | \(0.289003\pi\) | |||||||
\(30\) | −1188.00 | + | 2057.68i | −0.240998 | + | 0.417421i | ||||
\(31\) | 1796.00 | + | 3110.76i | 0.335662 | + | 0.581384i | 0.983612 | − | 0.180299i | \(-0.0577067\pi\) |
−0.647950 | + | 0.761683i | \(0.724373\pi\) | |||||||
\(32\) | −512.000 | − | 886.810i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −270.000 | + | 467.654i | −0.0431597 | + | 0.0747549i | ||||
\(34\) | −1656.00 | −0.245676 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 4229.00 | − | 7324.84i | 0.507848 | − | 0.879618i | −0.492111 | − | 0.870532i | \(-0.663775\pi\) |
0.999959 | − | 0.00908542i | \(-0.00289202\pi\) | |||||||
\(38\) | −1912.00 | − | 3311.68i | −0.214797 | − | 0.372040i | ||||
\(39\) | −2961.00 | − | 5128.60i | −0.311729 | − | 0.539930i | ||||
\(40\) | 2112.00 | − | 3658.09i | 0.208710 | − | 0.361497i | ||||
\(41\) | 19194.0 | 1.78322 | 0.891612 | − | 0.452800i | \(-0.149575\pi\) | ||||
0.891612 | + | 0.452800i | \(0.149575\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13316.0 | 1.09825 | 0.549127 | − | 0.835739i | \(-0.314960\pi\) | ||||
0.549127 | + | 0.835739i | \(0.314960\pi\) | |||||||
\(44\) | 480.000 | − | 831.384i | 0.0373774 | − | 0.0647396i | ||||
\(45\) | 2673.00 | + | 4629.77i | 0.196774 | + | 0.340823i | ||||
\(46\) | −1200.00 | − | 2078.46i | −0.0836155 | − | 0.144826i | ||||
\(47\) | 9840.00 | − | 17043.4i | 0.649756 | − | 1.12541i | −0.333425 | − | 0.942777i | \(-0.608204\pi\) |
0.983181 | − | 0.182634i | \(-0.0584624\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4924.00 | 0.278544 | ||||||||
\(51\) | −1863.00 | + | 3226.81i | −0.100297 | + | 0.173719i | ||||
\(52\) | 5264.00 | + | 9117.52i | 0.269965 | + | 0.467593i | ||||
\(53\) | 15633.0 | + | 27077.2i | 0.764456 | + | 1.32408i | 0.940534 | + | 0.339701i | \(0.110326\pi\) |
−0.176077 | + | 0.984376i | \(0.556341\pi\) | |||||||
\(54\) | 1458.00 | − | 2525.33i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 3960.00 | 0.176518 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8604.00 | −0.350763 | ||||||||
\(58\) | −11148.0 | + | 19308.9i | −0.435138 | + | 0.753681i | ||||
\(59\) | −13170.0 | − | 22811.1i | −0.492556 | − | 0.853132i | 0.507407 | − | 0.861706i | \(-0.330604\pi\) |
−0.999963 | + | 0.00857419i | \(0.997271\pi\) | |||||||
\(60\) | −4752.00 | − | 8230.71i | −0.170411 | − | 0.295161i | ||||
\(61\) | 15545.0 | − | 26924.7i | 0.534892 | − | 0.926460i | −0.464277 | − | 0.885690i | \(-0.653686\pi\) |
0.999169 | − | 0.0407699i | \(-0.0129811\pi\) | |||||||
\(62\) | −14368.0 | −0.474698 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −21714.0 | + | 37609.8i | −0.637465 | + | 1.10412i | ||||
\(66\) | −1080.00 | − | 1870.61i | −0.0305186 | − | 0.0528597i | ||||
\(67\) | 8402.00 | + | 14552.7i | 0.228663 | + | 0.396056i | 0.957412 | − | 0.288725i | \(-0.0932313\pi\) |
−0.728749 | + | 0.684781i | \(0.759898\pi\) | |||||||
\(68\) | 3312.00 | − | 5736.55i | 0.0868596 | − | 0.150445i | ||||
\(69\) | −5400.00 | −0.136544 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6120.00 | 0.144081 | 0.0720403 | − | 0.997402i | \(-0.477049\pi\) | ||||
0.0720403 | + | 0.997402i | \(0.477049\pi\) | |||||||
\(72\) | −2592.00 | + | 4489.48i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 12779.0 | + | 22133.9i | 0.280666 | + | 0.486128i | 0.971549 | − | 0.236839i | \(-0.0761114\pi\) |
−0.690883 | + | 0.722967i | \(0.742778\pi\) | |||||||
\(74\) | 16916.0 | + | 29299.4i | 0.359102 | + | 0.621984i | ||||
\(75\) | 5539.50 | − | 9594.70i | 0.113715 | − | 0.196960i | ||||
\(76\) | 15296.0 | 0.303769 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 23688.0 | 0.440851 | ||||||||
\(79\) | −37204.0 | + | 64439.2i | −0.670690 | + | 1.16167i | 0.307019 | + | 0.951704i | \(0.400669\pi\) |
−0.977709 | + | 0.209966i | \(0.932665\pi\) | |||||||
\(80\) | 8448.00 | + | 14632.4i | 0.147580 | + | 0.255617i | ||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −38388.0 | + | 66490.0i | −0.630465 | + | 1.09200i | ||||
\(83\) | −6468.00 | −0.103056 | −0.0515282 | − | 0.998672i | \(-0.516409\pi\) | ||||
−0.0515282 | + | 0.998672i | \(0.516409\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 27324.0 | 0.410201 | ||||||||
\(86\) | −26632.0 | + | 46128.0i | −0.388291 | + | 0.672540i | ||||
\(87\) | 25083.0 | + | 43445.0i | 0.355289 | + | 0.615378i | ||||
\(88\) | 1920.00 | + | 3325.54i | 0.0264298 | + | 0.0457778i | ||||
\(89\) | 16371.0 | − | 28355.4i | 0.219079 | − | 0.379455i | −0.735448 | − | 0.677581i | \(-0.763028\pi\) |
0.954527 | + | 0.298126i | \(0.0963615\pi\) | |||||||
\(90\) | −21384.0 | −0.278280 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9600.00 | 0.118250 | ||||||||
\(93\) | −16164.0 | + | 27996.9i | −0.193795 | + | 0.335662i | ||||
\(94\) | 39360.0 | + | 68173.5i | 0.459447 | + | 0.795786i | ||||
\(95\) | 31548.0 | + | 54642.7i | 0.358643 | + | 0.621189i | ||||
\(96\) | 4608.00 | − | 7981.29i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 166082. | 1.79223 | 0.896114 | − | 0.443824i | \(-0.146378\pi\) | ||||
0.896114 | + | 0.443824i | \(0.146378\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4860.00 | −0.0498366 | ||||||||
\(100\) | −9848.00 | + | 17057.2i | −0.0984800 | + | 0.170572i | ||||
\(101\) | 11001.0 | + | 19054.3i | 0.107307 | + | 0.185861i | 0.914678 | − | 0.404182i | \(-0.132444\pi\) |
−0.807371 | + | 0.590044i | \(0.799111\pi\) | |||||||
\(102\) | −7452.00 | − | 12907.2i | −0.0709206 | − | 0.122838i | ||||
\(103\) | 39632.0 | − | 68644.6i | 0.368089 | − | 0.637549i | −0.621178 | − | 0.783670i | \(-0.713345\pi\) |
0.989267 | + | 0.146121i | \(0.0466788\pi\) | |||||||
\(104\) | −42112.0 | −0.381788 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −125064. | −1.08110 | ||||||||
\(107\) | −113994. | + | 197443.i | −0.962548 | + | 1.66718i | −0.246486 | + | 0.969146i | \(0.579276\pi\) |
−0.716062 | + | 0.698036i | \(0.754057\pi\) | |||||||
\(108\) | 5832.00 | + | 10101.3i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 4265.00 | + | 7387.20i | 0.0343837 | + | 0.0595543i | 0.882705 | − | 0.469927i | \(-0.155720\pi\) |
−0.848321 | + | 0.529482i | \(0.822386\pi\) | |||||||
\(110\) | −7920.00 | + | 13717.8i | −0.0624085 | + | 0.108095i | ||||
\(111\) | 76122.0 | 0.586412 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −195438. | −1.43984 | −0.719918 | − | 0.694059i | \(-0.755821\pi\) | ||||
−0.719918 | + | 0.694059i | \(0.755821\pi\) | |||||||
\(114\) | 17208.0 | − | 29805.1i | 0.124013 | − | 0.214797i | ||||
\(115\) | 19800.0 | + | 34294.6i | 0.139611 | + | 0.241814i | ||||
\(116\) | −44592.0 | − | 77235.6i | −0.307689 | − | 0.532933i | ||||
\(117\) | 26649.0 | − | 46157.4i | 0.179977 | − | 0.311729i | ||||
\(118\) | 105360. | 0.696580 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 38016.0 | 0.240998 | ||||||||
\(121\) | 78725.5 | − | 136357.i | 0.488823 | − | 0.846667i | ||||
\(122\) | 62180.0 | + | 107699.i | 0.378226 | + | 0.655106i | ||||
\(123\) | 86373.0 | + | 149602.i | 0.514772 | + | 0.891612i | ||||
\(124\) | 28736.0 | − | 49772.2i | 0.167831 | − | 0.290692i | ||||
\(125\) | 125004. | 0.715565 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 173000. | 0.951780 | 0.475890 | − | 0.879505i | \(-0.342126\pi\) | ||||
0.475890 | + | 0.879505i | \(0.342126\pi\) | |||||||
\(128\) | −8192.00 | + | 14189.0i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 59922.0 | + | 103788.i | 0.317039 | + | 0.549127i | ||||
\(130\) | −86856.0 | − | 150439.i | −0.450756 | − | 0.780732i | ||||
\(131\) | −75630.0 | + | 130995.i | −0.385049 | + | 0.666924i | −0.991776 | − | 0.127986i | \(-0.959149\pi\) |
0.606727 | + | 0.794910i | \(0.292482\pi\) | |||||||
\(132\) | 8640.00 | 0.0431597 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −67216.0 | −0.323378 | ||||||||
\(135\) | −24057.0 | + | 41667.9i | −0.113608 | + | 0.196774i | ||||
\(136\) | 13248.0 | + | 22946.2i | 0.0614190 | + | 0.106381i | ||||
\(137\) | 64227.0 | + | 111244.i | 0.292359 | + | 0.506380i | 0.974367 | − | 0.224964i | \(-0.0722265\pi\) |
−0.682008 | + | 0.731345i | \(0.738893\pi\) | |||||||
\(138\) | 10800.0 | − | 18706.1i | 0.0482754 | − | 0.0836155i | ||||
\(139\) | 154196. | 0.676918 | 0.338459 | − | 0.940981i | \(-0.390094\pi\) | ||||
0.338459 | + | 0.940981i | \(0.390094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 177120. | 0.750274 | ||||||||
\(142\) | −12240.0 | + | 21200.3i | −0.0509402 | + | 0.0882310i | ||||
\(143\) | −19740.0 | − | 34190.7i | −0.0807248 | − | 0.139819i | ||||
\(144\) | −10368.0 | − | 17957.9i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 183942. | − | 318597.i | 0.726542 | − | 1.25841i | ||||
\(146\) | −102232. | −0.396922 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −135328. | −0.507848 | ||||||||
\(149\) | −14727.0 | + | 25507.9i | −0.0543436 | + | 0.0941259i | −0.891917 | − | 0.452198i | \(-0.850640\pi\) |
0.837574 | + | 0.546324i | \(0.183973\pi\) | |||||||
\(150\) | 22158.0 | + | 38378.8i | 0.0804086 | + | 0.139272i | ||||
\(151\) | 101936. | + | 176558.i | 0.363819 | + | 0.630153i | 0.988586 | − | 0.150658i | \(-0.0481394\pi\) |
−0.624767 | + | 0.780811i | \(0.714806\pi\) | |||||||
\(152\) | −30592.0 | + | 52986.9i | −0.107399 | + | 0.186020i | ||||
\(153\) | −33534.0 | −0.115813 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 237072. | 0.792594 | ||||||||
\(156\) | −47376.0 | + | 82057.6i | −0.155864 | + | 0.269965i | ||||
\(157\) | −68071.0 | − | 117902.i | −0.220401 | − | 0.381745i | 0.734529 | − | 0.678577i | \(-0.237403\pi\) |
−0.954930 | + | 0.296832i | \(0.904070\pi\) | |||||||
\(158\) | −148816. | − | 257757.i | −0.474250 | − | 0.821424i | ||||
\(159\) | −140697. | + | 243694.i | −0.441359 | + | 0.764456i | ||||
\(160\) | −67584.0 | −0.208710 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | 85562.0 | − | 148198.i | 0.252239 | − | 0.436890i | −0.711903 | − | 0.702278i | \(-0.752166\pi\) |
0.964142 | + | 0.265387i | \(0.0854998\pi\) | |||||||
\(164\) | −153552. | − | 265960.i | −0.445806 | − | 0.772159i | ||||
\(165\) | 17820.0 | + | 30865.1i | 0.0509563 | + | 0.0882589i | ||||
\(166\) | 12936.0 | − | 22405.8i | 0.0364359 | − | 0.0631089i | ||||
\(167\) | −676200. | −1.87622 | −0.938110 | − | 0.346336i | \(-0.887426\pi\) | ||||
−0.938110 | + | 0.346336i | \(0.887426\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 61671.0 | 0.166098 | ||||||||
\(170\) | −54648.0 | + | 94653.1i | −0.145028 | + | 0.251196i | ||||
\(171\) | −38718.0 | − | 67061.5i | −0.101256 | − | 0.175381i | ||||
\(172\) | −106528. | − | 184512.i | −0.274563 | − | 0.475558i | ||||
\(173\) | −66579.0 | + | 115318.i | −0.169131 | + | 0.292943i | −0.938114 | − | 0.346325i | \(-0.887429\pi\) |
0.768984 | + | 0.639268i | \(0.220763\pi\) | |||||||
\(174\) | −200664. | −0.502454 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −15360.0 | −0.0373774 | ||||||||
\(177\) | 118530. | − | 205300.i | 0.284377 | − | 0.492556i | ||||
\(178\) | 65484.0 | + | 113422.i | 0.154912 | + | 0.268316i | ||||
\(179\) | 346698. | + | 600499.i | 0.808758 | + | 1.40081i | 0.913724 | + | 0.406335i | \(0.133193\pi\) |
−0.104966 | + | 0.994476i | \(0.533473\pi\) | |||||||
\(180\) | 42768.0 | − | 74076.3i | 0.0983870 | − | 0.170411i | ||||
\(181\) | 377174. | 0.855747 | 0.427873 | − | 0.903839i | \(-0.359263\pi\) | ||||
0.427873 | + | 0.903839i | \(0.359263\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 279810. | 0.617640 | ||||||||
\(184\) | −19200.0 | + | 33255.4i | −0.0418077 | + | 0.0724131i | ||||
\(185\) | −279114. | − | 483440.i | −0.599587 | − | 1.03852i | ||||
\(186\) | −64656.0 | − | 111987.i | −0.137033 | − | 0.237349i | ||||
\(187\) | −12420.0 | + | 21512.1i | −0.0259727 | + | 0.0449861i | ||||
\(188\) | −314880. | −0.649756 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −252384. | −0.507198 | ||||||||
\(191\) | 132672. | − | 229795.i | 0.263145 | − | 0.455781i | −0.703931 | − | 0.710269i | \(-0.748573\pi\) |
0.967076 | + | 0.254487i | \(0.0819068\pi\) | |||||||
\(192\) | 18432.0 | + | 31925.2i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −147649. | − | 255736.i | −0.285323 | − | 0.494194i | 0.687364 | − | 0.726313i | \(-0.258768\pi\) |
−0.972688 | + | 0.232118i | \(0.925434\pi\) | |||||||
\(194\) | −332164. | + | 575325.i | −0.633648 | + | 1.09751i | ||||
\(195\) | −390852. | −0.736081 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 201294. | 0.369543 | 0.184772 | − | 0.982781i | \(-0.440845\pi\) | ||||
0.184772 | + | 0.982781i | \(0.440845\pi\) | |||||||
\(198\) | 9720.00 | − | 16835.5i | 0.0176199 | − | 0.0305186i | ||||
\(199\) | −326224. | − | 565037.i | −0.583960 | − | 1.01145i | −0.995004 | − | 0.0998332i | \(-0.968169\pi\) |
0.411044 | − | 0.911615i | \(-0.365164\pi\) | |||||||
\(200\) | −39392.0 | − | 68228.9i | −0.0696359 | − | 0.120613i | ||||
\(201\) | −75618.0 | + | 130974.i | −0.132019 | + | 0.228663i | ||||
\(202\) | −88008.0 | −0.151755 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 59616.0 | 0.100297 | ||||||||
\(205\) | 633402. | − | 1.09708e6i | 1.05268 | − | 1.82329i | ||||
\(206\) | 158528. | + | 274579.i | 0.260278 | + | 0.450815i | ||||
\(207\) | −24300.0 | − | 42088.8i | −0.0394167 | − | 0.0682718i | ||||
\(208\) | 84224.0 | − | 145880.i | 0.134983 | − | 0.233797i | ||||
\(209\) | −57360.0 | −0.0908330 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.14706e6 | −1.77370 | −0.886850 | − | 0.462058i | \(-0.847111\pi\) | ||||
−0.886850 | + | 0.462058i | \(0.847111\pi\) | |||||||
\(212\) | 250128. | − | 433234.i | 0.382228 | − | 0.662039i | ||||
\(213\) | 27540.0 | + | 47700.7i | 0.0415925 | + | 0.0720403i | ||||
\(214\) | −455976. | − | 789774.i | −0.680624 | − | 1.17888i | ||||
\(215\) | 439428. | − | 761112.i | 0.648323 | − | 1.12293i | ||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −34120.0 | −0.0486259 | ||||||||
\(219\) | −115011. | + | 199205.i | −0.162043 | + | 0.280666i | ||||
\(220\) | −31680.0 | − | 54871.4i | −0.0441294 | − | 0.0764344i | ||||
\(221\) | −136206. | − | 235916.i | −0.187593 | − | 0.324920i | ||||
\(222\) | −152244. | + | 263694.i | −0.207328 | + | 0.359102i | ||||
\(223\) | 701960. | 0.945258 | 0.472629 | − | 0.881262i | \(-0.343305\pi\) | ||||
0.472629 | + | 0.881262i | \(0.343305\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 99711.0 | 0.131307 | ||||||||
\(226\) | 390876. | − | 677017.i | 0.509059 | − | 0.881716i | ||||
\(227\) | −618054. | − | 1.07050e6i | −0.796089 | − | 1.37887i | −0.922145 | − | 0.386844i | \(-0.873565\pi\) |
0.126056 | − | 0.992023i | \(-0.459768\pi\) | |||||||
\(228\) | 68832.0 | + | 119221.i | 0.0876906 | + | 0.151885i | ||||
\(229\) | −52915.0 | + | 91651.5i | −0.0666792 | + | 0.115492i | −0.897438 | − | 0.441141i | \(-0.854574\pi\) |
0.830758 | + | 0.556633i | \(0.187907\pi\) | |||||||
\(230\) | −158400. | −0.197440 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 356736. | 0.435138 | ||||||||
\(233\) | 219339. | − | 379906.i | 0.264683 | − | 0.458444i | −0.702798 | − | 0.711390i | \(-0.748066\pi\) |
0.967481 | + | 0.252946i | \(0.0813993\pi\) | |||||||
\(234\) | 106596. | + | 184630.i | 0.127263 | + | 0.220426i | ||||
\(235\) | −649440. | − | 1.12486e6i | −0.767131 | − | 1.32871i | ||||
\(236\) | −210720. | + | 364978.i | −0.246278 | + | 0.426566i | ||||
\(237\) | −669672. | −0.774446 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28464.0 | 0.0322330 | 0.0161165 | − | 0.999870i | \(-0.494870\pi\) | ||||
0.0161165 | + | 0.999870i | \(0.494870\pi\) | |||||||
\(240\) | −76032.0 | + | 131691.i | −0.0852056 | + | 0.147580i | ||||
\(241\) | −446281. | − | 772981.i | −0.494955 | − | 0.857287i | 0.505028 | − | 0.863103i | \(-0.331482\pi\) |
−0.999983 | + | 0.00581560i | \(0.998149\pi\) | |||||||
\(242\) | 314902. | + | 545426.i | 0.345650 | + | 0.598684i | ||||
\(243\) | 29524.5 | − | 51137.9i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −497440. | −0.534892 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −690984. | −0.727998 | ||||||||
\(247\) | 314524. | − | 544772.i | 0.328028 | − | 0.568162i | ||||
\(248\) | 114944. | + | 199089.i | 0.118674 | + | 0.205550i | ||||
\(249\) | −29106.0 | − | 50413.1i | −0.0297498 | − | 0.0515282i | ||||
\(250\) | −250008. | + | 433027.i | −0.252990 | + | 0.438192i | ||||
\(251\) | −110124. | −0.110331 | −0.0551655 | − | 0.998477i | \(-0.517569\pi\) | ||||
−0.0551655 | + | 0.998477i | \(0.517569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −36000.0 | −0.0353591 | ||||||||
\(254\) | −346000. | + | 599290.i | −0.336505 | + | 0.582844i | ||||
\(255\) | 122958. | + | 212970.i | 0.118415 | + | 0.205101i | ||||
\(256\) | −32768.0 | − | 56755.8i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −70401.0 | + | 121938.i | −0.0664884 | + | 0.115161i | −0.897353 | − | 0.441313i | \(-0.854513\pi\) |
0.830865 | + | 0.556474i | \(0.187846\pi\) | |||||||
\(258\) | −479376. | −0.448360 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 694848. | 0.637465 | ||||||||
\(261\) | −225747. | + | 391005.i | −0.205126 | + | 0.355289i | ||||
\(262\) | −302520. | − | 523980.i | −0.272271 | − | 0.471587i | ||||
\(263\) | 469380. | + | 812990.i | 0.418442 | + | 0.724763i | 0.995783 | − | 0.0917404i | \(-0.0292430\pi\) |
−0.577341 | + | 0.816503i | \(0.695910\pi\) | |||||||
\(264\) | −17280.0 | + | 29929.8i | −0.0152593 | + | 0.0264298i | ||||
\(265\) | 2.06356e6 | 1.80510 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 294678. | 0.252970 | ||||||||
\(268\) | 134432. | − | 232843.i | 0.114331 | − | 0.198028i | ||||
\(269\) | 557253. | + | 965191.i | 0.469539 | + | 0.813265i | 0.999393 | − | 0.0348231i | \(-0.0110868\pi\) |
−0.529854 | + | 0.848089i | \(0.677753\pi\) | |||||||
\(270\) | −96228.0 | − | 166672.i | −0.0803326 | − | 0.139140i | ||||
\(271\) | −283852. | + | 491646.i | −0.234784 | + | 0.406658i | −0.959210 | − | 0.282695i | \(-0.908772\pi\) |
0.724426 | + | 0.689353i | \(0.242105\pi\) | |||||||
\(272\) | −105984. | −0.0868596 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −513816. | −0.413458 | ||||||||
\(275\) | 36930.0 | − | 63964.6i | 0.0294474 | − | 0.0510045i | ||||
\(276\) | 43200.0 | + | 74824.6i | 0.0341359 | + | 0.0591251i | ||||
\(277\) | 606629. | + | 1.05071e6i | 0.475033 | + | 0.822781i | 0.999591 | − | 0.0285934i | \(-0.00910280\pi\) |
−0.524558 | + | 0.851375i | \(0.675769\pi\) | |||||||
\(278\) | −308392. | + | 534151.i | −0.239327 | + | 0.414526i | ||||
\(279\) | −290952. | −0.223775 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 687738. | 0.519586 | 0.259793 | − | 0.965664i | \(-0.416346\pi\) | ||||
0.259793 | + | 0.965664i | \(0.416346\pi\) | |||||||
\(282\) | −354240. | + | 613562.i | −0.265262 | + | 0.459447i | ||||
\(283\) | 415454. | + | 719587.i | 0.308359 | + | 0.534094i | 0.978004 | − | 0.208588i | \(-0.0668868\pi\) |
−0.669644 | + | 0.742682i | \(0.733553\pi\) | |||||||
\(284\) | −48960.0 | − | 84801.2i | −0.0360202 | − | 0.0623887i | ||||
\(285\) | −283932. | + | 491785.i | −0.207063 | + | 0.358643i | ||||
\(286\) | 157920. | 0.114162 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | 624230. | − | 1.08120e6i | 0.439643 | − | 0.761484i | ||||
\(290\) | 735768. | + | 1.27439e6i | 0.513743 | + | 0.889829i | ||||
\(291\) | 747369. | + | 1.29448e6i | 0.517372 | + | 0.896114i | ||||
\(292\) | 204464. | − | 354142.i | 0.140333 | − | 0.243064i | ||||
\(293\) | −1.31263e6 | −0.893248 | −0.446624 | − | 0.894722i | \(-0.647374\pi\) | ||||
−0.446624 | + | 0.894722i | \(0.647374\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.73844e6 | −1.16307 | ||||||||
\(296\) | 270656. | − | 468790.i | 0.179551 | − | 0.310992i | ||||
\(297\) | −21870.0 | − | 37880.0i | −0.0143866 | − | 0.0249183i | ||||
\(298\) | −58908.0 | − | 102032.i | −0.0384267 | − | 0.0665571i | ||||
\(299\) | 197400. | − | 341907.i | 0.127694 | − | 0.221172i | ||||
\(300\) | −177264. | −0.113715 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −815488. | −0.514518 | ||||||||
\(303\) | −99009.0 | + | 171489.i | −0.0619538 | + | 0.107307i | ||||
\(304\) | −122368. | − | 211948.i | −0.0759423 | − | 0.131536i | ||||
\(305\) | −1.02597e6 | − | 1.77703e6i | −0.631517 | − | 1.09382i | ||||
\(306\) | 67068.0 | − | 116165.i | 0.0409460 | − | 0.0709206i | ||||
\(307\) | 1.69022e6 | 1.02352 | 0.511761 | − | 0.859128i | \(-0.328993\pi\) | ||||
0.511761 | + | 0.859128i | \(0.328993\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 713376. | 0.425033 | ||||||||
\(310\) | −474144. | + | 821241.i | −0.280224 | + | 0.485363i | ||||
\(311\) | 751020. | + | 1.30080e6i | 0.440302 | + | 0.762625i | 0.997712 | − | 0.0676123i | \(-0.0215381\pi\) |
−0.557410 | + | 0.830238i | \(0.688205\pi\) | |||||||
\(312\) | −189504. | − | 328231.i | −0.110213 | − | 0.190894i | ||||
\(313\) | −405421. | + | 702210.i | −0.233908 | + | 0.405141i | −0.958955 | − | 0.283559i | \(-0.908485\pi\) |
0.725047 | + | 0.688700i | \(0.241818\pi\) | |||||||
\(314\) | 544568. | 0.311694 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.19053e6 | 0.670690 | ||||||||
\(317\) | −451779. | + | 782504.i | −0.252510 | + | 0.437359i | −0.964216 | − | 0.265117i | \(-0.914589\pi\) |
0.711707 | + | 0.702477i | \(0.247923\pi\) | |||||||
\(318\) | −562788. | − | 974777.i | −0.312088 | − | 0.540552i | ||||
\(319\) | 167220. | + | 289634.i | 0.0920050 | + | 0.159357i | ||||
\(320\) | 135168. | − | 234118.i | 0.0737902 | − | 0.127808i | ||||
\(321\) | −2.05189e6 | −1.11146 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −395784. | −0.211082 | ||||||||
\(324\) | −52488.0 | + | 90911.9i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 404999. | + | 701479.i | 0.212689 | + | 0.368389i | ||||
\(326\) | 342248. | + | 592791.i | 0.178360 | + | 0.308928i | ||||
\(327\) | −38385.0 | + | 66484.8i | −0.0198514 | + | 0.0343837i | ||||
\(328\) | 1.22842e6 | 0.630465 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −142560. | −0.0720631 | ||||||||
\(331\) | −560986. | + | 971656.i | −0.281438 | + | 0.487464i | −0.971739 | − | 0.236058i | \(-0.924145\pi\) |
0.690301 | + | 0.723522i | \(0.257478\pi\) | |||||||
\(332\) | 51744.0 | + | 89623.2i | 0.0257641 | + | 0.0446247i | ||||
\(333\) | 342549. | + | 593312.i | 0.169283 | + | 0.293206i | ||||
\(334\) | 1.35240e6 | − | 2.34243e6i | 0.663344 | − | 1.14895i | ||||
\(335\) | 1.10906e6 | 0.539939 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.75217e6 | −1.32008 | −0.660041 | − | 0.751229i | \(-0.729461\pi\) | ||||
−0.660041 | + | 0.751229i | \(0.729461\pi\) | |||||||
\(338\) | −123342. | + | 213635.i | −0.0587245 | + | 0.101714i | ||||
\(339\) | −879471. | − | 1.52329e6i | −0.415645 | − | 0.719918i | ||||
\(340\) | −218592. | − | 378612.i | −0.102550 | − | 0.177622i | ||||
\(341\) | −107760. | + | 186646.i | −0.0501847 | + | 0.0869225i | ||||
\(342\) | 309744. | 0.143198 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 852224. | 0.388291 | ||||||||
\(345\) | −178200. | + | 308651.i | −0.0806046 | + | 0.139611i | ||||
\(346\) | −266316. | − | 461273.i | −0.119593 | − | 0.207142i | ||||
\(347\) | −958746. | − | 1.66060e6i | −0.427445 | − | 0.740356i | 0.569201 | − | 0.822199i | \(-0.307253\pi\) |
−0.996645 | + | 0.0818428i | \(0.973919\pi\) | |||||||
\(348\) | 401328. | − | 695120.i | 0.177644 | − | 0.307689i | ||||
\(349\) | 1.83659e6 | 0.807140 | 0.403570 | − | 0.914949i | \(-0.367769\pi\) | ||||
0.403570 | + | 0.914949i | \(0.367769\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 479682. | 0.207819 | ||||||||
\(352\) | 30720.0 | − | 53208.6i | 0.0132149 | − | 0.0228889i | ||||
\(353\) | 311007. | + | 538680.i | 0.132841 | + | 0.230088i | 0.924771 | − | 0.380525i | \(-0.124257\pi\) |
−0.791929 | + | 0.610613i | \(0.790923\pi\) | |||||||
\(354\) | 474120. | + | 821200.i | 0.201085 | + | 0.348290i | ||||
\(355\) | 201960. | − | 349805.i | 0.0850539 | − | 0.147318i | ||||
\(356\) | −523872. | −0.219079 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.77358e6 | −1.14376 | ||||||||
\(359\) | −1.87031e6 | + | 3.23947e6i | −0.765909 | + | 1.32659i | 0.173856 | + | 0.984771i | \(0.444377\pi\) |
−0.939765 | + | 0.341822i | \(0.888956\pi\) | |||||||
\(360\) | 171072. | + | 296305.i | 0.0695701 | + | 0.120499i | ||||
\(361\) | 781082. | + | 1.35287e6i | 0.315448 | + | 0.546373i | ||||
\(362\) | −754348. | + | 1.30657e6i | −0.302552 | + | 0.524036i | ||||
\(363\) | 1.41706e6 | 0.564445 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.68683e6 | 0.662733 | ||||||||
\(366\) | −559620. | + | 969290.i | −0.218369 | + | 0.378226i | ||||
\(367\) | −8116.00 | − | 14057.3i | −0.00314541 | − | 0.00544801i | 0.864448 | − | 0.502722i | \(-0.167668\pi\) |
−0.867594 | + | 0.497274i | \(0.834335\pi\) | |||||||
\(368\) | −76800.0 | − | 133022.i | −0.0295625 | − | 0.0512038i | ||||
\(369\) | −777357. | + | 1.34642e6i | −0.297204 | + | 0.514772i | ||||
\(370\) | 2.23291e6 | 0.847944 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 517248. | 0.193795 | ||||||||
\(373\) | −146803. | + | 254270.i | −0.0546340 | + | 0.0946288i | −0.892049 | − | 0.451939i | \(-0.850733\pi\) |
0.837415 | + | 0.546568i | \(0.184066\pi\) | |||||||
\(374\) | −49680.0 | − | 86048.3i | −0.0183655 | − | 0.0318100i | ||||
\(375\) | 562518. | + | 974310.i | 0.206566 | + | 0.357782i | ||||
\(376\) | 629760. | − | 1.09078e6i | 0.229724 | − | 0.397893i | ||||
\(377\) | −3.66769e6 | −1.32904 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.18012e6 | 1.13722 | 0.568611 | − | 0.822607i | \(-0.307481\pi\) | ||||
0.568611 | + | 0.822607i | \(0.307481\pi\) | |||||||
\(380\) | 504768. | − | 874284.i | 0.179322 | − | 0.310594i | ||||
\(381\) | 778500. | + | 1.34840e6i | 0.274755 | + | 0.475890i | ||||
\(382\) | 530688. | + | 919179.i | 0.186072 | + | 0.322286i | ||||
\(383\) | 1.48992e6 | − | 2.58062e6i | 0.518998 | − | 0.898932i | −0.480758 | − | 0.876853i | \(-0.659638\pi\) |
0.999756 | − | 0.0220782i | \(-0.00702828\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.18119e6 | 0.403508 | ||||||||
\(387\) | −539298. | + | 934092.i | −0.183042 | + | 0.317039i | ||||
\(388\) | −1.32866e6 | − | 2.30130e6i | −0.448057 | − | 0.776057i | ||||
\(389\) | −1.72989e6 | − | 2.99625e6i | −0.579620 | − | 1.00393i | −0.995523 | − | 0.0945228i | \(-0.969867\pi\) |
0.415902 | − | 0.909409i | \(-0.363466\pi\) | |||||||
\(390\) | 781704. | − | 1.35395e6i | 0.260244 | − | 0.450756i | ||||
\(391\) | −248400. | −0.0821693 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.36134e6 | −0.444616 | ||||||||
\(394\) | −402588. | + | 697303.i | −0.130653 | + | 0.226298i | ||||
\(395\) | 2.45546e6 | + | 4.25299e6i | 0.791846 | + | 1.37152i | ||||
\(396\) | 38880.0 | + | 67342.1i | 0.0124591 | + | 0.0215799i | ||||
\(397\) | 1.95208e6 | − | 3.38110e6i | 0.621615 | − | 1.07667i | −0.367570 | − | 0.929996i | \(-0.619810\pi\) |
0.989185 | − | 0.146673i | \(-0.0468565\pi\) | |||||||
\(398\) | 2.60979e6 | 0.825844 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 315136. | 0.0984800 | ||||||||
\(401\) | −2.72058e6 | + | 4.71218e6i | −0.844890 | + | 1.46339i | 0.0408270 | + | 0.999166i | \(0.487001\pi\) |
−0.885717 | + | 0.464226i | \(0.846333\pi\) | |||||||
\(402\) | −302472. | − | 523897.i | −0.0933512 | − | 0.161689i | ||||
\(403\) | −1.18177e6 | − | 2.04688e6i | −0.362468 | − | 0.627813i | ||||
\(404\) | 176016. | − | 304869.i | 0.0536536 | − | 0.0929307i | ||||
\(405\) | −433026. | −0.131183 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 507480. | 0.151856 | ||||||||
\(408\) | −119232. | + | 206516.i | −0.0354603 | + | 0.0614190i | ||||
\(409\) | −984973. | − | 1.70602e6i | −0.291150 | − | 0.504286i | 0.682932 | − | 0.730482i | \(-0.260704\pi\) |
−0.974082 | + | 0.226196i | \(0.927371\pi\) | |||||||
\(410\) | 2.53361e6 | + | 4.38834e6i | 0.744354 | + | 1.28926i | ||||
\(411\) | −578043. | + | 1.00120e6i | −0.168793 | + | 0.292359i | ||||
\(412\) | −1.26822e6 | −0.368089 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 194400. | 0.0557437 | ||||||||
\(415\) | −213444. | + | 369696.i | −0.0608364 | + | 0.105372i | ||||
\(416\) | 336896. | + | 583521.i | 0.0954471 | + | 0.165319i | ||||
\(417\) | 693882. | + | 1.20184e6i | 0.195409 | + | 0.338459i | ||||
\(418\) | 114720. | − | 198701.i | 0.0321143 | − | 0.0556236i | ||||
\(419\) | 139020. | 0.0386850 | 0.0193425 | − | 0.999813i | \(-0.493843\pi\) | ||||
0.0193425 | + | 0.999813i | \(0.493843\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.32743e6 | 1.18994 | 0.594970 | − | 0.803748i | \(-0.297164\pi\) | ||||
0.594970 | + | 0.803748i | \(0.297164\pi\) | |||||||
\(422\) | 2.29412e6 | − | 3.97353e6i | 0.627097 | − | 1.08616i | ||||
\(423\) | 797040. | + | 1.38051e6i | 0.216585 | + | 0.375137i | ||||
\(424\) | 1.00051e6 | + | 1.73294e6i | 0.270276 | + | 0.468132i | ||||
\(425\) | 254817. | − | 441356.i | 0.0684315 | − | 0.118527i | ||||
\(426\) | −220320. | −0.0588207 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.64781e6 | 0.962548 | ||||||||
\(429\) | 177660. | − | 307716.i | 0.0466065 | − | 0.0807248i | ||||
\(430\) | 1.75771e6 | + | 3.04445e6i | 0.458434 | + | 0.794031i | ||||
\(431\) | 1.39968e6 | + | 2.42432e6i | 0.362941 | + | 0.628632i | 0.988443 | − | 0.151590i | \(-0.0484394\pi\) |
−0.625503 | + | 0.780222i | \(0.715106\pi\) | |||||||
\(432\) | 93312.0 | − | 161621.i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −5.90241e6 | −1.51290 | −0.756449 | − | 0.654052i | \(-0.773068\pi\) | ||||
−0.756449 | + | 0.654052i | \(0.773068\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.31096e6 | 0.838939 | ||||||||
\(436\) | 68240.0 | − | 118195.i | 0.0171919 | − | 0.0297772i | ||||
\(437\) | −286800. | − | 496752.i | −0.0718415 | − | 0.124433i | ||||
\(438\) | −460044. | − | 796820.i | −0.114581 | − | 0.198461i | ||||
\(439\) | 223256. | − | 386691.i | 0.0552894 | − | 0.0957640i | −0.837056 | − | 0.547117i | \(-0.815725\pi\) |
0.892345 | + | 0.451353i | \(0.149059\pi\) | |||||||
\(440\) | 253440. | 0.0624085 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.08965e6 | 0.265296 | ||||||||
\(443\) | −1.74763e6 | + | 3.02698e6i | −0.423096 | + | 0.732824i | −0.996241 | − | 0.0866303i | \(-0.972390\pi\) |
0.573144 | + | 0.819454i | \(0.305723\pi\) | |||||||
\(444\) | −608976. | − | 1.05478e6i | −0.146603 | − | 0.253924i | ||||
\(445\) | −1.08049e6 | − | 1.87146e6i | −0.258654 | − | 0.448002i | ||||
\(446\) | −1.40392e6 | + | 2.43166e6i | −0.334199 | + | 0.578850i | ||||
\(447\) | −265086. | −0.0627506 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.20613e6 | −0.282343 | −0.141171 | − | 0.989985i | \(-0.545087\pi\) | ||||
−0.141171 | + | 0.989985i | \(0.545087\pi\) | |||||||
\(450\) | −199422. | + | 345409.i | −0.0464239 | + | 0.0804086i | ||||
\(451\) | 575820. | + | 997349.i | 0.133305 | + | 0.230890i | ||||
\(452\) | 1.56350e6 | + | 2.70807e6i | 0.359959 | + | 0.623467i | ||||
\(453\) | −917424. | + | 1.58902e6i | −0.210051 | + | 0.363819i | ||||
\(454\) | 4.94443e6 | 1.12584 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −550656. | −0.124013 | ||||||||
\(457\) | −116773. | + | 202257.i | −0.0261548 | + | 0.0453015i | −0.878807 | − | 0.477178i | \(-0.841660\pi\) |
0.852652 | + | 0.522480i | \(0.174993\pi\) | |||||||
\(458\) | −211660. | − | 366606.i | −0.0471493 | − | 0.0816650i | ||||
\(459\) | −150903. | − | 261372.i | −0.0334323 | − | 0.0579064i | ||||
\(460\) | 316800. | − | 548714.i | 0.0698057 | − | 0.120907i | ||||
\(461\) | −1.74489e6 | −0.382398 | −0.191199 | − | 0.981551i | \(-0.561238\pi\) | ||||
−0.191199 | + | 0.981551i | \(0.561238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.91786e6 | −0.632576 | −0.316288 | − | 0.948663i | \(-0.602437\pi\) | ||||
−0.316288 | + | 0.948663i | \(0.602437\pi\) | |||||||
\(464\) | −713472. | + | 1.23577e6i | −0.153845 | + | 0.266466i | ||||
\(465\) | 1.06682e6 | + | 1.84779e6i | 0.228802 | + | 0.396297i | ||||
\(466\) | 877356. | + | 1.51963e6i | 0.187159 | + | 0.324169i | ||||
\(467\) | 2.65538e6 | − | 4.59925e6i | 0.563422 | − | 0.975876i | −0.433772 | − | 0.901023i | \(-0.642818\pi\) |
0.997195 | − | 0.0748537i | \(-0.0238490\pi\) | |||||||
\(468\) | −852768. | −0.179977 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.19552e6 | 1.08489 | ||||||||
\(471\) | 612639. | − | 1.06112e6i | 0.127248 | − | 0.220401i | ||||
\(472\) | −842880. | − | 1.45991e6i | −0.174145 | − | 0.301628i | ||||
\(473\) | 399480. | + | 691920.i | 0.0820998 | + | 0.142201i | ||||
\(474\) | 1.33934e6 | − | 2.31981e6i | 0.273808 | − | 0.474250i | ||||
\(475\) | 1.17684e6 | 0.239322 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.53255e6 | −0.509638 | ||||||||
\(478\) | −56928.0 | + | 98602.2i | −0.0113961 | + | 0.0197386i | ||||
\(479\) | −1.17233e6 | − | 2.03053e6i | −0.233459 | − | 0.404363i | 0.725365 | − | 0.688365i | \(-0.241671\pi\) |
−0.958824 | + | 0.284002i | \(0.908338\pi\) | |||||||
\(480\) | −304128. | − | 526765.i | −0.0602495 | − | 0.104355i | ||||
\(481\) | −2.78268e6 | + | 4.81975e6i | −0.548404 | + | 0.949864i | ||||
\(482\) | 3.57025e6 | 0.699972 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.51922e6 | −0.488823 | ||||||||
\(485\) | 5.48071e6 | − | 9.49286e6i | 1.05799 | − | 1.83249i | ||||
\(486\) | 118098. | + | 204552.i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | −4.90766e6 | − | 8.50031e6i | −0.937674 | − | 1.62410i | −0.769795 | − | 0.638291i | \(-0.779642\pi\) |
−0.167878 | − | 0.985808i | \(-0.553692\pi\) | |||||||
\(488\) | 994880. | − | 1.72318e6i | 0.189113 | − | 0.327553i | ||||
\(489\) | 1.54012e6 | 0.291260 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.94520e6 | −1.11292 | −0.556458 | − | 0.830876i | \(-0.687840\pi\) | ||||
−0.556458 | + | 0.830876i | \(0.687840\pi\) | |||||||
\(492\) | 1.38197e6 | − | 2.39364e6i | 0.257386 | − | 0.445806i | ||||
\(493\) | 1.15382e6 | + | 1.99847e6i | 0.213806 | + | 0.370323i | ||||
\(494\) | 1.25810e6 | + | 2.17909e6i | 0.231951 | + | 0.401751i | ||||
\(495\) | −160380. | + | 277786.i | −0.0294196 | + | 0.0509563i | ||||
\(496\) | −919552. | −0.167831 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 232848. | 0.0420726 | ||||||||
\(499\) | −3.23916e6 | + | 5.61039e6i | −0.582346 | + | 1.00865i | 0.412855 | + | 0.910797i | \(0.364532\pi\) |
−0.995201 | + | 0.0978554i | \(0.968802\pi\) | |||||||
\(500\) | −1.00003e6 | − | 1.73211e6i | −0.178891 | − | 0.309849i | ||||
\(501\) | −3.04290e6 | − | 5.27046e6i | −0.541618 | − | 0.938110i | ||||
\(502\) | 220248. | − | 381481.i | 0.0390079 | − | 0.0675637i | ||||
\(503\) | 4.71794e6 | 0.831444 | 0.415722 | − | 0.909492i | \(-0.363529\pi\) | ||||
0.415722 | + | 0.909492i | \(0.363529\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.45213e6 | 0.253383 | ||||||||
\(506\) | 72000.0 | − | 124708.i | 0.0125013 | − | 0.0216529i | ||||
\(507\) | 277520. | + | 480678.i | 0.0479483 | + | 0.0830490i | ||||
\(508\) | −1.38400e6 | − | 2.39716e6i | −0.237945 | − | 0.412133i | ||||
\(509\) | 953853. | − | 1.65212e6i | 0.163188 | − | 0.282649i | −0.772823 | − | 0.634622i | \(-0.781156\pi\) |
0.936010 | + | 0.351973i | \(0.114489\pi\) | |||||||
\(510\) | −983664. | −0.167464 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 348462. | − | 603554.i | 0.0584604 | − | 0.101256i | ||||
\(514\) | −281604. | − | 487752.i | −0.0470144 | − | 0.0814314i | ||||
\(515\) | −2.61571e6 | − | 4.53055e6i | −0.434582 | − | 0.752718i | ||||
\(516\) | 958752. | − | 1.66061e6i | 0.158519 | − | 0.274563i | ||||
\(517\) | 1.18080e6 | 0.194290 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.19842e6 | −0.195295 | ||||||||
\(520\) | −1.38970e6 | + | 2.40702e6i | −0.225378 | + | 0.390366i | ||||
\(521\) | −4.00987e6 | − | 6.94530e6i | −0.647196 | − | 1.12098i | −0.983790 | − | 0.179326i | \(-0.942608\pi\) |
0.336594 | − | 0.941650i | \(-0.390725\pi\) | |||||||
\(522\) | −902988. | − | 1.56402e6i | −0.145046 | − | 0.251227i | ||||
\(523\) | −955810. | + | 1.65551e6i | −0.152798 | + | 0.264654i | −0.932255 | − | 0.361802i | \(-0.882162\pi\) |
0.779457 | + | 0.626456i | \(0.215495\pi\) | |||||||
\(524\) | 2.42016e6 | 0.385049 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.75504e6 | −0.591766 | ||||||||
\(527\) | −743544. | + | 1.28786e6i | −0.116622 | + | 0.201995i | ||||
\(528\) | −69120.0 | − | 119719.i | −0.0107899 | − | 0.0186887i | ||||
\(529\) | 3.03817e6 | + | 5.26227e6i | 0.472034 | + | 0.817587i | ||||
\(530\) | −4.12711e6 | + | 7.14837e6i | −0.638200 | + | 1.10539i | ||||
\(531\) | 2.13354e6 | 0.328371 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.26297e7 | −1.92563 | ||||||||
\(534\) | −589356. | + | 1.02079e6i | −0.0894385 | + | 0.154912i | ||||
\(535\) | 7.52360e6 | + | 1.30313e7i | 1.13643 | + | 1.96835i | ||||
\(536\) | 537728. | + | 931372.i | 0.0808445 | + | 0.140027i | ||||
\(537\) | −3.12028e6 | + | 5.40449e6i | −0.466937 | + | 0.808758i | ||||
\(538\) | −4.45802e6 | −0.664028 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 769824. | 0.113608 | ||||||||
\(541\) | 5.99502e6 | − | 1.03837e7i | 0.880639 | − | 1.52531i | 0.0300068 | − | 0.999550i | \(-0.490447\pi\) |
0.850632 | − | 0.525762i | \(-0.176220\pi\) | |||||||
\(542\) | −1.13541e6 | − | 1.96658e6i | −0.166017 | − | 0.287551i | ||||
\(543\) | 1.69728e6 | + | 2.93978e6i | 0.247033 | + | 0.427873i | ||||
\(544\) | 211968. | − | 367139.i | 0.0307095 | − | 0.0531905i | ||||
\(545\) | 562980. | 0.0811898 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.45809e6 | 0.637061 | 0.318530 | − | 0.947913i | \(-0.396811\pi\) | ||||
0.318530 | + | 0.947913i | \(0.396811\pi\) | |||||||
\(548\) | 1.02763e6 | − | 1.77991e6i | 0.146179 | − | 0.253190i | ||||
\(549\) | 1.25914e6 | + | 2.18090e6i | 0.178297 | + | 0.308820i | ||||
\(550\) | 147720. | + | 255859.i | 0.0208225 | + | 0.0360656i | ||||
\(551\) | −2.66437e6 | + | 4.61483e6i | −0.373866 | + | 0.647555i | ||||
\(552\) | −345600. | −0.0482754 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.85303e6 | −0.671798 | ||||||||
\(555\) | 2.51203e6 | − | 4.35096e6i | 0.346172 | − | 0.599587i | ||||
\(556\) | −1.23357e6 | − | 2.13660e6i | −0.169230 | − | 0.293114i | ||||
\(557\) | −4.51306e6 | − | 7.81685e6i | −0.616358 | − | 1.06756i | −0.990145 | − | 0.140049i | \(-0.955274\pi\) |
0.373787 | − | 0.927515i | \(-0.378059\pi\) | |||||||
\(558\) | 581904. | − | 1.00789e6i | 0.0791163 | − | 0.137033i | ||||
\(559\) | −8.76193e6 | −1.18596 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −223560. | −0.0299907 | ||||||||
\(562\) | −1.37548e6 | + | 2.38239e6i | −0.183701 | + | 0.318180i | ||||
\(563\) | −3.42449e6 | − | 5.93140e6i | −0.455329 | − | 0.788653i | 0.543378 | − | 0.839488i | \(-0.317145\pi\) |
−0.998707 | + | 0.0508350i | \(0.983812\pi\) | |||||||
\(564\) | −1.41696e6 | − | 2.45425e6i | −0.187568 | − | 0.324878i | ||||
\(565\) | −6.44945e6 | + | 1.11708e7i | −0.849967 | + | 1.47219i | ||||
\(566\) | −3.32363e6 | −0.436086 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 391680. | 0.0509402 | ||||||||
\(569\) | 2.73161e6 | − | 4.73129e6i | 0.353703 | − | 0.612631i | −0.633192 | − | 0.773994i | \(-0.718256\pi\) |
0.986895 | + | 0.161364i | \(0.0515892\pi\) | |||||||
\(570\) | −1.13573e6 | − | 1.96714e6i | −0.146416 | − | 0.253599i | ||||
\(571\) | 5.11619e6 | + | 8.86150e6i | 0.656684 | + | 1.13741i | 0.981469 | + | 0.191622i | \(0.0613748\pi\) |
−0.324785 | + | 0.945788i | \(0.605292\pi\) | |||||||
\(572\) | −315840. | + | 547051.i | −0.0403624 | + | 0.0699097i | ||||
\(573\) | 2.38810e6 | 0.303854 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 738600. | 0.0931622 | ||||||||
\(576\) | −165888. | + | 287326.i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −7.97184e6 | − | 1.38076e7i | −0.996825 | − | 1.72655i | −0.567364 | − | 0.823467i | \(-0.692037\pi\) |
−0.429461 | − | 0.903085i | \(-0.641296\pi\) | |||||||
\(578\) | 2.49692e6 | + | 4.32480e6i | 0.310875 | + | 0.538451i | ||||
\(579\) | 1.32884e6 | − | 2.30162e6i | 0.164731 | − | 0.285323i | ||||
\(580\) | −5.88614e6 | −0.726542 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.97895e6 | −0.731674 | ||||||||
\(583\) | −937980. | + | 1.62463e6i | −0.114294 | + | 0.197962i | ||||
\(584\) | 817856. | + | 1.41657e6i | 0.0992304 | + | 0.171872i | ||||
\(585\) | −1.75883e6 | − | 3.04639e6i | −0.212488 | − | 0.368041i | ||||
\(586\) | 2.62525e6 | − | 4.54707e6i | 0.315811 | − | 0.547000i | ||||
\(587\) | −9.47713e6 | −1.13522 | −0.567612 | − | 0.823296i | \(-0.692133\pi\) | ||||
−0.567612 | + | 0.823296i | \(0.692133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.43395e6 | −0.407855 | ||||||||
\(590\) | 3.47688e6 | − | 6.02213e6i | 0.411206 | − | 0.712230i | ||||
\(591\) | 905823. | + | 1.56893e6i | 0.106678 | + | 0.184772i | ||||
\(592\) | 1.08262e6 | + | 1.87516e6i | 0.126962 | + | 0.219904i | ||||
\(593\) | −1.22674e6 | + | 2.12478e6i | −0.143258 | + | 0.248129i | −0.928722 | − | 0.370778i | \(-0.879091\pi\) |
0.785464 | + | 0.618907i | \(0.212424\pi\) | |||||||
\(594\) | 174960. | 0.0203457 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 471264. | 0.0543436 | ||||||||
\(597\) | 2.93602e6 | − | 5.08533e6i | 0.337150 | − | 0.583960i | ||||
\(598\) | 789600. | + | 1.36763e6i | 0.0902930 | + | 0.156392i | ||||
\(599\) | 4.64989e6 | + | 8.05385e6i | 0.529512 | + | 0.917142i | 0.999407 | + | 0.0344196i | \(0.0109583\pi\) |
−0.469895 | + | 0.882722i | \(0.655708\pi\) | |||||||
\(600\) | 354528. | − | 614061.i | 0.0402043 | − | 0.0696359i | ||||
\(601\) | −1.14617e7 | −1.29438 | −0.647192 | − | 0.762327i | \(-0.724057\pi\) | ||||
−0.647192 | + | 0.762327i | \(0.724057\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.36112e6 | −0.152442 | ||||||||
\(604\) | 1.63098e6 | − | 2.82493e6i | 0.181909 | − | 0.315076i | ||||
\(605\) | −5.19588e6 | − | 8.99953e6i | −0.577126 | − | 0.999612i | ||||
\(606\) | −396036. | − | 685954.i | −0.0438080 | − | 0.0758776i | ||||
\(607\) | −5.63919e6 | + | 9.76736e6i | −0.621219 | + | 1.07598i | 0.368040 | + | 0.929810i | \(0.380029\pi\) |
−0.989259 | + | 0.146173i | \(0.953304\pi\) | |||||||
\(608\) | 978944. | 0.107399 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.20776e6 | 0.893100 | ||||||||
\(611\) | −6.47472e6 | + | 1.12145e7i | −0.701646 | + | 1.21529i | ||||
\(612\) | 268272. | + | 464661.i | 0.0289532 | + | 0.0501484i | ||||
\(613\) | −46891.0 | − | 81217.6i | −0.00504009 | − | 0.00872969i | 0.863494 | − | 0.504358i | \(-0.168271\pi\) |
−0.868534 | + | 0.495629i | \(0.834938\pi\) | |||||||
\(614\) | −3.38044e6 | + | 5.85509e6i | −0.361870 | + | 0.626777i | ||||
\(615\) | 1.14012e7 | 1.21553 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.49642e7 | −1.58248 | −0.791242 | − | 0.611504i | \(-0.790565\pi\) | ||||
−0.791242 | + | 0.611504i | \(0.790565\pi\) | |||||||
\(618\) | −1.42675e6 | + | 2.47121e6i | −0.150272 | + | 0.260278i | ||||
\(619\) | 2.53444e6 | + | 4.38978e6i | 0.265861 | + | 0.460485i | 0.967789 | − | 0.251763i | \(-0.0810104\pi\) |
−0.701928 | + | 0.712248i | \(0.747677\pi\) | |||||||
\(620\) | −1.89658e6 | − | 3.28497e6i | −0.198149 | − | 0.343203i | ||||
\(621\) | 218700. | − | 378800.i | 0.0227573 | − | 0.0394167i | ||||
\(622\) | −6.00816e6 | −0.622681 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.51603e6 | 0.155864 | ||||||||
\(625\) | 6.04857e6 | − | 1.04764e7i | 0.619374 | − | 1.07279i | ||||
\(626\) | −1.62168e6 | − | 2.80884e6i | −0.165398 | − | 0.286478i | ||||
\(627\) | −258120. | − | 447077.i | −0.0262212 | − | 0.0454165i | ||||
\(628\) | −1.08914e6 | + | 1.88644e6i | −0.110200 | + | 0.190873i | ||||
\(629\) | 3.50161e6 | 0.352892 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.55919e7 | 1.55892 | 0.779462 | − | 0.626450i | \(-0.215493\pi\) | ||||
0.779462 | + | 0.626450i | \(0.215493\pi\) | |||||||
\(632\) | −2.38106e6 | + | 4.12411e6i | −0.237125 | + | 0.410712i | ||||
\(633\) | −5.16177e6 | − | 8.94045e6i | −0.512023 | − | 0.886850i | ||||
\(634\) | −1.80712e6 | − | 3.13002e6i | −0.178551 | − | 0.309260i | ||||
\(635\) | 5.70900e6 | − | 9.88828e6i | 0.561857 | − | 0.973165i | ||||
\(636\) | 4.50230e6 | 0.441359 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.33776e6 | −0.130115 | ||||||||
\(639\) | −247860. | + | 429306.i | −0.0240134 | + | 0.0415925i | ||||
\(640\) | 540672. | + | 936471.i | 0.0521776 | + | 0.0903742i | ||||
\(641\) | −5.48506e6 | − | 9.50041e6i | −0.527274 | − | 0.913266i | −0.999495 | − | 0.0317855i | \(-0.989881\pi\) |
0.472220 | − | 0.881481i | \(-0.343453\pi\) | |||||||
\(642\) | 4.10378e6 | − | 7.10796e6i | 0.392959 | − | 0.680624i | ||||
\(643\) | −2.83704e6 | −0.270607 | −0.135303 | − | 0.990804i | \(-0.543201\pi\) | ||||
−0.135303 | + | 0.990804i | \(0.543201\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.90970e6 | 0.748619 | ||||||||
\(646\) | 791568. | − | 1.37104e6i | 0.0746289 | − | 0.129261i | ||||
\(647\) | 3.02843e6 | + | 5.24539e6i | 0.284418 | + | 0.492626i | 0.972468 | − | 0.233037i | \(-0.0748664\pi\) |
−0.688050 | + | 0.725663i | \(0.741533\pi\) | |||||||
\(648\) | −209952. | − | 363648.i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 790200. | − | 1.36867e6i | 0.0736420 | − | 0.127552i | ||||
\(650\) | −3.23999e6 | −0.300788 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.73798e6 | −0.252239 | ||||||||
\(653\) | 544461. | − | 943034.i | 0.0499671 | − | 0.0865455i | −0.839960 | − | 0.542648i | \(-0.817422\pi\) |
0.889927 | + | 0.456103i | \(0.150755\pi\) | |||||||
\(654\) | −153540. | − | 265939.i | −0.0140371 | − | 0.0243130i | ||||
\(655\) | 4.99158e6 | + | 8.64567e6i | 0.454606 | + | 0.787400i | ||||
\(656\) | −2.45683e6 | + | 4.25536e6i | −0.222903 | + | 0.386079i | ||||
\(657\) | −2.07020e6 | −0.187111 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.41803e6 | 0.665388 | 0.332694 | − | 0.943035i | \(-0.392042\pi\) | ||||
0.332694 | + | 0.943035i | \(0.392042\pi\) | |||||||
\(660\) | 285120. | − | 493842.i | 0.0254781 | − | 0.0441294i | ||||
\(661\) | −383827. | − | 664808.i | −0.0341690 | − | 0.0591824i | 0.848435 | − | 0.529299i | \(-0.177545\pi\) |
−0.882604 | + | 0.470117i | \(0.844212\pi\) | |||||||
\(662\) | −2.24394e6 | − | 3.88663e6i | −0.199006 | − | 0.344689i | ||||
\(663\) | 1.22585e6 | − | 2.12324e6i | 0.108307 | − | 0.187593i | ||||
\(664\) | −413952. | −0.0364359 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.74039e6 | −0.239402 | ||||||||
\(667\) | −1.67220e6 | + | 2.89634e6i | −0.145537 | + | 0.252078i | ||||
\(668\) | 5.40960e6 | + | 9.36970e6i | 0.469055 | + | 0.812428i | ||||
\(669\) | 3.15882e6 | + | 5.47124e6i | 0.272872 | + | 0.472629i | ||||
\(670\) | −2.21813e6 | + | 3.84191e6i | −0.190897 | + | 0.330644i | ||||
\(671\) | 1.86540e6 | 0.159943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.42263e6 | 0.121075 | 0.0605373 | − | 0.998166i | \(-0.480719\pi\) | ||||
0.0605373 | + | 0.998166i | \(0.480719\pi\) | |||||||
\(674\) | 5.50435e6 | − | 9.53381e6i | 0.466720 | − | 0.808382i | ||||
\(675\) | 448700. | + | 777170.i | 0.0379050 | + | 0.0656533i | ||||
\(676\) | −493368. | − | 854538.i | −0.0415245 | − | 0.0719225i | ||||
\(677\) | 3.08115e6 | − | 5.33671e6i | 0.258370 | − | 0.447509i | −0.707436 | − | 0.706778i | \(-0.750148\pi\) |
0.965805 | + | 0.259268i | \(0.0834814\pi\) | |||||||
\(678\) | 7.03577e6 | 0.587810 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.74874e6 | 0.145028 | ||||||||
\(681\) | 5.56249e6 | − | 9.63451e6i | 0.459622 | − | 0.796089i | ||||
\(682\) | −431040. | − | 746583.i | −0.0354860 | − | 0.0614635i | ||||
\(683\) | −7.53107e6 | − | 1.30442e7i | −0.617739 | − | 1.06996i | −0.989897 | − | 0.141786i | \(-0.954715\pi\) |
0.372158 | − | 0.928169i | \(-0.378618\pi\) | |||||||
\(684\) | −619488. | + | 1.07298e6i | −0.0506282 | + | 0.0876906i | ||||
\(685\) | 8.47796e6 | 0.690343 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −952470. | −0.0769945 | ||||||||
\(688\) | −1.70445e6 | + | 2.95219e6i | −0.137282 | + | 0.237779i | ||||
\(689\) | −1.02865e7 | − | 1.78168e7i | −0.825506 | − | 1.42982i | ||||
\(690\) | −712800. | − | 1.23461e6i | −0.0569961 | − | 0.0987201i | ||||
\(691\) | 2.93818e6 | − | 5.08907e6i | 0.234090 | − | 0.405456i | −0.724918 | − | 0.688835i | \(-0.758122\pi\) |
0.959008 | + | 0.283380i | \(0.0914556\pi\) | |||||||
\(692\) | 2.13053e6 | 0.169131 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.66997e6 | 0.604498 | ||||||||
\(695\) | 5.08847e6 | − | 8.81349e6i | 0.399600 | − | 0.692127i | ||||
\(696\) | 1.60531e6 | + | 2.78048e6i | 0.125614 | + | 0.217569i | ||||
\(697\) | 3.97316e6 | + | 6.88171e6i | 0.309780 | + | 0.536555i | ||||
\(698\) | −3.67318e6 | + | 6.36213e6i | −0.285367 | + | 0.494270i | ||||
\(699\) | 3.94810e6 | 0.305630 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.60077e6 | 0.276758 | 0.138379 | − | 0.990379i | \(-0.455811\pi\) | ||||
0.138379 | + | 0.990379i | \(0.455811\pi\) | |||||||
\(702\) | −959364. | + | 1.66167e6i | −0.0734752 | + | 0.127263i | ||||
\(703\) | 4.04292e6 | + | 7.00255e6i | 0.308537 | + | 0.534402i | ||||
\(704\) | 122880. | + | 212834.i | 0.00934436 | + | 0.0161849i | ||||
\(705\) | 5.84496e6 | − | 1.01238e7i | 0.442903 | − | 0.767131i | ||||
\(706\) | −2.48806e6 | −0.187866 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.79296e6 | −0.284377 | ||||||||
\(709\) | −4.61258e6 | + | 7.98922e6i | −0.344610 | + | 0.596883i | −0.985283 | − | 0.170932i | \(-0.945322\pi\) |
0.640673 | + | 0.767814i | \(0.278656\pi\) | |||||||
\(710\) | 807840. | + | 1.39922e6i | 0.0601422 | + | 0.104169i | ||||
\(711\) | −3.01352e6 | − | 5.21958e6i | −0.223563 | − | 0.387223i | ||||
\(712\) | 1.04774e6 | − | 1.81475e6i | 0.0774560 | − | 0.134158i | ||||
\(713\) | −2.15520e6 | −0.158768 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.60568e6 | −0.190615 | ||||||||
\(716\) | 5.54717e6 | − | 9.60798e6i | 0.404379 | − | 0.700405i | ||||
\(717\) | 128088. | + | 221855.i | 0.00930488 | + | 0.0161165i | ||||
\(718\) | −7.48123e6 | − | 1.29579e7i | −0.541579 | − | 0.938043i | ||||
\(719\) | 1.31962e7 | − | 2.28564e7i | 0.951975 | − | 1.64887i | 0.210830 | − | 0.977523i | \(-0.432383\pi\) |
0.741144 | − | 0.671346i | \(-0.234283\pi\) | |||||||
\(720\) | −1.36858e6 | −0.0983870 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.24865e6 | −0.446111 | ||||||||
\(723\) | 4.01653e6 | − | 6.95683e6i | 0.285762 | − | 0.494955i | ||||
\(724\) | −3.01739e6 | − | 5.22628e6i | −0.213937 | − | 0.370549i | ||||
\(725\) | −3.43080e6 | − | 5.94231e6i | −0.242410 | − | 0.419866i | ||||
\(726\) | −2.83412e6 | + | 4.90884e6i | −0.199561 | + | 0.345650i | ||||
\(727\) | −9.79485e6 | −0.687324 | −0.343662 | − | 0.939093i | \(-0.611667\pi\) | ||||
−0.343662 | + | 0.939093i | \(0.611667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −3.37366e6 | + | 5.84334e6i | −0.234312 | + | 0.405839i | ||||
\(731\) | 2.75641e6 | + | 4.77425e6i | 0.190788 | + | 0.330454i | ||||
\(732\) | −2.23848e6 | − | 3.87716e6i | −0.154410 | − | 0.267446i | ||||
\(733\) | −2.03792e6 | + | 3.52978e6i | −0.140096 | + | 0.242654i | −0.927533 | − | 0.373742i | \(-0.878075\pi\) |
0.787436 | + | 0.616396i | \(0.211408\pi\) | |||||||
\(734\) | 64928.0 | 0.00444828 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 614400. | 0.0418077 | ||||||||
\(737\) | −504120. | + | 873161.i | −0.0341873 | + | 0.0592142i | ||||
\(738\) | −3.10943e6 | − | 5.38569e6i | −0.210155 | − | 0.363999i | ||||
\(739\) | 8.28543e6 | + | 1.43508e7i | 0.558089 | + | 0.966639i | 0.997656 | + | 0.0684291i | \(0.0217987\pi\) |
−0.439567 | + | 0.898210i | \(0.644868\pi\) | |||||||
\(740\) | −4.46582e6 | + | 7.73503e6i | −0.299794 | + | 0.519258i | ||||
\(741\) | 5.66143e6 | 0.378775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.44141e7 | 0.957892 | 0.478946 | − | 0.877844i | \(-0.341019\pi\) | ||||
0.478946 | + | 0.877844i | \(0.341019\pi\) | |||||||
\(744\) | −1.03450e6 | + | 1.79180e6i | −0.0685167 | + | 0.118674i | ||||
\(745\) | 971982. | + | 1.68352e6i | 0.0641605 | + | 0.111129i | ||||
\(746\) | −587212. | − | 1.01708e6i | −0.0386321 | − | 0.0669127i | ||||
\(747\) | 261954. | − | 453718.i | 0.0171761 | − | 0.0297498i | ||||
\(748\) | 397440. | 0.0259727 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −4.50014e6 | −0.292128 | ||||||||
\(751\) | −8.39722e6 | + | 1.45444e7i | −0.543295 | + | 0.941015i | 0.455417 | + | 0.890278i | \(0.349490\pi\) |
−0.998712 | + | 0.0507363i | \(0.983843\pi\) | |||||||
\(752\) | 2.51904e6 | + | 4.36311e6i | 0.162439 | + | 0.281353i | ||||
\(753\) | −495558. | − | 858332.i | −0.0318498 | − | 0.0551655i | ||||
\(754\) | 7.33538e6 | − | 1.27053e7i | 0.469888 | − | 0.813870i | ||||
\(755\) | 1.34556e7 | 0.859081 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.32943e7 | 0.843188 | 0.421594 | − | 0.906785i | \(-0.361471\pi\) | ||||
0.421594 | + | 0.906785i | \(0.361471\pi\) | |||||||
\(758\) | −6.36023e6 | + | 1.10162e7i | −0.402068 | + | 0.696403i | ||||
\(759\) | −162000. | − | 280592.i | −0.0102073 | − | 0.0176795i | ||||
\(760\) | 2.01907e6 | + | 3.49714e6i | 0.126800 | + | 0.219623i | ||||
\(761\) | 1.07393e6 | − | 1.86010e6i | 0.0672225 | − | 0.116433i | −0.830455 | − | 0.557085i | \(-0.811920\pi\) |
0.897678 | + | 0.440653i | \(0.145253\pi\) | |||||||
\(762\) | −6.22800e6 | −0.388563 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.24550e6 | −0.263145 | ||||||||
\(765\) | −1.10662e6 | + | 1.91673e6i | −0.0683669 | + | 0.118415i | ||||
\(766\) | 5.95968e6 | + | 1.03225e7i | 0.366987 | + | 0.635641i | ||||
\(767\) | 8.66586e6 | + | 1.50097e7i | 0.531892 | + | 0.921264i | ||||
\(768\) | 294912. | − | 510803.i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | −1.31059e7 | −0.799193 | −0.399596 | − | 0.916691i | \(-0.630850\pi\) | ||||
−0.399596 | + | 0.916691i | \(0.630850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.26722e6 | −0.0767742 | ||||||||
\(772\) | −2.36238e6 | + | 4.09177e6i | −0.142662 | + | 0.247097i | ||||
\(773\) | 1.18577e7 | + | 2.05381e7i | 0.713759 | + | 1.23627i | 0.963436 | + | 0.267937i | \(0.0863419\pi\) |
−0.249678 | + | 0.968329i | \(0.580325\pi\) | |||||||
\(774\) | −2.15719e6 | − | 3.73637e6i | −0.129430 | − | 0.224180i | ||||
\(775\) | 2.21088e6 | − | 3.82935e6i | 0.132224 | − | 0.229019i | ||||
\(776\) | 1.06292e7 | 0.633648 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.38391e7 | 0.819707 | ||||||||
\(779\) | −9.17473e6 | + | 1.58911e7i | −0.541689 | + | 0.938232i | ||||
\(780\) | 3.12682e6 | + | 5.41580e6i | 0.184020 | + | 0.318733i | ||||
\(781\) | 183600. | + | 318005.i | 0.0107707 | + | 0.0186554i | ||||
\(782\) | 496800. | − | 860483.i | 0.0290512 | − | 0.0503182i | ||||
\(783\) | −4.06345e6 | −0.236859 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.98537e6 | −0.520430 | ||||||||
\(786\) | 2.72268e6 | − | 4.71582e6i | 0.157196 | − | 0.272271i | ||||
\(787\) | 4.20024e6 | + | 7.27503e6i | 0.241734 | + | 0.418695i | 0.961208 | − | 0.275824i | \(-0.0889506\pi\) |
−0.719474 | + | 0.694519i | \(0.755617\pi\) | |||||||
\(788\) | −1.61035e6 | − | 2.78921e6i | −0.0923858 | − | 0.160017i | ||||
\(789\) | −4.22442e6 | + | 7.31691e6i | −0.241588 | + | 0.418442i | ||||
\(790\) | −1.96437e7 | −1.11984 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −311040. | −0.0176199 | ||||||||
\(793\) | −1.02286e7 | + | 1.77165e7i | −0.577609 | + | 1.00045i | ||||
\(794\) | 7.80832e6 | + | 1.35244e7i | 0.439548 | + | 0.761320i | ||||
\(795\) | 9.28600e6 | + | 1.60838e7i | 0.521088 | + | 0.902551i | ||||
\(796\) | −5.21958e6 | + | 9.04058e6i | −0.291980 | + | 0.505724i | ||||
\(797\) | 5.41023e6 | 0.301696 | 0.150848 | − | 0.988557i | \(-0.451800\pi\) | ||||
0.150848 | + | 0.988557i | \(0.451800\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.14752e6 | 0.451501 | ||||||||
\(800\) | −630272. | + | 1.09166e6i | −0.0348179 | + | 0.0603064i | ||||
\(801\) | 1.32605e6 | + | 2.29679e6i | 0.0730262 | + | 0.126485i | ||||
\(802\) | −1.08823e7 | − | 1.88487e7i | −0.597427 | − | 1.03477i | ||||
\(803\) | −766740. | + | 1.32803e6i | −0.0419623 | + | 0.0726808i | ||||
\(804\) | 2.41978e6 | 0.132019 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.45414e6 | 0.512607 | ||||||||
\(807\) | −5.01528e6 | + | 8.68671e6i | −0.271088 | + | 0.469539i | ||||
\(808\) | 704064. | + | 1.21947e6i | 0.0379388 | + | 0.0657120i | ||||
\(809\) | 1.30389e7 | + | 2.25840e7i | 0.700436 | + | 1.21319i | 0.968313 | + | 0.249738i | \(0.0803445\pi\) |
−0.267877 | + | 0.963453i | \(0.586322\pi\) | |||||||
\(810\) | 866052. | − | 1.50005e6i | 0.0463801 | − | 0.0803326i | ||||
\(811\) | 1.90021e7 | 1.01449 | 0.507247 | − | 0.861800i | \(-0.330663\pi\) | ||||
0.507247 | + | 0.861800i | \(0.330663\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.10934e6 | −0.271105 | ||||||||
\(814\) | −1.01496e6 | + | 1.75796e6i | −0.0536893 | + | 0.0929926i | ||||
\(815\) | −5.64709e6 | − | 9.78105e6i | −0.297804 | − | 0.515812i | ||||
\(816\) | −476928. | − | 826064.i | −0.0250742 | − | 0.0434298i | ||||
\(817\) | −6.36505e6 | + | 1.10246e7i | −0.333616 | + | 0.577839i | ||||
\(818\) | 7.87978e6 | 0.411748 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.02689e7 | −1.05268 | ||||||||
\(821\) | 1.55086e7 | − | 2.68618e7i | 0.803001 | − | 1.39084i | −0.114632 | − | 0.993408i | \(-0.536569\pi\) |
0.917633 | − | 0.397430i | \(-0.130098\pi\) | |||||||
\(822\) | −2.31217e6 | − | 4.00480e6i | −0.119355 | − | 0.206729i | ||||
\(823\) | 7.81448e6 | + | 1.35351e7i | 0.402162 | + | 0.696564i | 0.993987 | − | 0.109502i | \(-0.0349257\pi\) |
−0.591825 | + | 0.806066i | \(0.701592\pi\) | |||||||
\(824\) | 2.53645e6 | − | 4.39326e6i | 0.130139 | − | 0.225408i | ||||
\(825\) | 664740. | 0.0340030 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.58421e7 | 0.805467 | 0.402733 | − | 0.915317i | \(-0.368060\pi\) | ||||
0.402733 | + | 0.915317i | \(0.368060\pi\) | |||||||
\(828\) | −388800. | + | 673421.i | −0.0197084 | + | 0.0341359i | ||||
\(829\) | −1.03088e6 | − | 1.78553e6i | −0.0520980 | − | 0.0902364i | 0.838800 | − | 0.544439i | \(-0.183257\pi\) |
−0.890898 | + | 0.454203i | \(0.849924\pi\) | |||||||
\(830\) | −853776. | − | 1.47878e6i | −0.0430179 | − | 0.0745091i | ||||
\(831\) | −5.45966e6 | + | 9.45641e6i | −0.274260 | + | 0.475033i | ||||
\(832\) | −2.69517e6 | −0.134983 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.55106e6 | −0.276351 | ||||||||
\(835\) | −2.23146e7 | + | 3.86500e7i | −1.10757 | + | 1.91838i | ||||
\(836\) | 458880. | + | 794803.i | 0.0227082 | + | 0.0393318i | ||||
\(837\) | −1.30928e6 | − | 2.26775e6i | −0.0645982 | − | 0.111887i | ||||
\(838\) | −278040. | + | 481579.i | −0.0136772 | + | 0.0236896i | ||||
\(839\) | 3.03900e7 | 1.49048 | 0.745240 | − | 0.666796i | \(-0.232335\pi\) | ||||
0.745240 | + | 0.666796i | \(0.232335\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.05583e7 | 0.514760 | ||||||||
\(842\) | −8.65486e6 | + | 1.49907e7i | −0.420707 | + | 0.728686i | ||||
\(843\) | 3.09482e6 | + | 5.36039e6i | 0.149991 | + | 0.259793i | ||||
\(844\) | 9.17648e6 | + | 1.58941e7i | 0.443425 | + | 0.768034i | ||||
\(845\) | 2.03514e6 | − | 3.52497e6i | 0.0980513 | − | 0.169830i | ||||
\(846\) | −6.37632e6 | −0.306298 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.00410e6 | −0.382228 | ||||||||
\(849\) | −3.73909e6 | + | 6.47629e6i | −0.178031 | + | 0.308359i | ||||
\(850\) | 1.01927e6 | + | 1.76542e6i | 0.0483884 | + | 0.0838111i | ||||
\(851\) | 2.53740e6 | + | 4.39491e6i | 0.120106 | + | 0.208030i | ||||
\(852\) | 440640. | − | 763211.i | 0.0207962 | − | 0.0360202i | ||||
\(853\) | −2.97738e7 | −1.40108 | −0.700538 | − | 0.713615i | \(-0.747056\pi\) | ||||
−0.700538 | + | 0.713615i | \(0.747056\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.11078e6 | −0.239096 | ||||||||
\(856\) | −7.29562e6 | + | 1.26364e7i | −0.340312 | + | 0.589438i | ||||
\(857\) | −4.32050e6 | − | 7.48333e6i | −0.200947 | − | 0.348051i | 0.747887 | − | 0.663826i | \(-0.231069\pi\) |
−0.948834 | + | 0.315776i | \(0.897735\pi\) | |||||||
\(858\) | 710640. | + | 1.23086e6i | 0.0329558 | + | 0.0570811i | ||||
\(859\) | 1.67831e7 | − | 2.90693e7i | 0.776051 | − | 1.34416i | −0.158151 | − | 0.987415i | \(-0.550553\pi\) |
0.934202 | − | 0.356745i | \(-0.116114\pi\) | |||||||
\(860\) | −1.40617e7 | −0.648323 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.11974e7 | −0.513276 | ||||||||
\(863\) | −1.95096e7 | + | 3.37915e7i | −0.891703 | + | 1.54448i | −0.0538706 | + | 0.998548i | \(0.517156\pi\) |
−0.837833 | + | 0.545927i | \(0.816177\pi\) | |||||||
\(864\) | 373248. | + | 646484.i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 4.39421e6 | + | 7.61100e6i | 0.199683 | + | 0.345861i | ||||
\(866\) | 1.18048e7 | − | 2.04466e7i | 0.534891 | − | 0.926458i | ||||
\(867\) | 1.12361e7 | 0.507656 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.46448e6 | −0.200549 | ||||||||
\(870\) | −6.62191e6 | + | 1.14695e7i | −0.296610 | + | 0.513743i | ||||
\(871\) | −5.52852e6 | − | 9.57567e6i | −0.246924 | − | 0.427685i | ||||
\(872\) | 272960. | + | 472781.i | 0.0121565 | + | 0.0210556i | ||||
\(873\) | −6.72632e6 | + | 1.16503e7i | −0.298705 | + | 0.517372i | ||||
\(874\) | 2.29440e6 | 0.101599 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.68035e6 | 0.162043 | ||||||||
\(877\) | 9.06909e6 | − | 1.57081e7i | 0.398166 | − | 0.689645i | −0.595333 | − | 0.803479i | \(-0.702980\pi\) |
0.993500 | + | 0.113834i | \(0.0363133\pi\) | |||||||
\(878\) | 893024. | + | 1.54676e6i | 0.0390955 | + | 0.0677154i | ||||
\(879\) | −5.90682e6 | − | 1.02309e7i | −0.257858 | − | 0.446624i | ||||
\(880\) | −506880. | + | 877942.i | −0.0220647 | + | 0.0382172i | ||||
\(881\) | 3.05312e7 | 1.32527 | 0.662634 | − | 0.748943i | \(-0.269438\pi\) | ||||
0.662634 | + | 0.748943i | \(0.269438\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.35533e7 | −1.87983 | −0.939916 | − | 0.341405i | \(-0.889097\pi\) | ||||
−0.939916 | + | 0.341405i | \(0.889097\pi\) | |||||||
\(884\) | −2.17930e6 | + | 3.77465e6i | −0.0937963 | + | 0.162460i | ||||
\(885\) | −7.82298e6 | − | 1.35498e7i | −0.335748 | − | 0.581533i | ||||
\(886\) | −6.99050e6 | − | 1.21079e7i | −0.299174 | − | 0.518185i | ||||
\(887\) | 6.70758e6 | − | 1.16179e7i | 0.286257 | − | 0.495812i | −0.686656 | − | 0.726983i | \(-0.740922\pi\) |
0.972913 | + | 0.231170i | \(0.0742554\pi\) | |||||||
\(888\) | 4.87181e6 | 0.207328 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.64389e6 | 0.365792 | ||||||||
\(891\) | 196830. | − | 340920.i | 0.00830610 | − | 0.0143866i | ||||
\(892\) | −5.61568e6 | − | 9.72664e6i | −0.236314 | − | 0.409309i | ||||
\(893\) | 9.40704e6 | + | 1.62935e7i | 0.394752 | + | 0.683731i | ||||
\(894\) | 530172. | − | 918285.i | 0.0221857 | − | 0.0384267i | ||||
\(895\) | 4.57641e7 | 1.90971 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.55320e6 | 0.147448 | ||||||||
\(898\) | 2.41225e6 | − | 4.17814e6i | 0.0998233 | − | 0.172899i | ||||
\(899\) | 1.00109e7 | + | 1.73394e7i | 0.413118 | + | 0.715541i | ||||
\(900\) | −797688. | − | 1.38164e6i | −0.0328267 | − | 0.0568575i | ||||
\(901\) | −6.47206e6 | + | 1.12099e7i | −0.265602 | + | 0.460035i | ||||
\(902\) | −4.60656e6 | −0.188521 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.25080e7 | −0.509059 | ||||||||
\(905\) | 1.24467e7 | − | 2.15584e7i | 0.505166 | − | 0.874973i | ||||
\(906\) | −3.66970e6 | − | 6.35610e6i | −0.148528 | − | 0.257259i | ||||
\(907\) | −1.55408e6 | − | 2.69175e6i | −0.0627272 | − | 0.108647i | 0.832956 | − | 0.553339i | \(-0.186646\pi\) |
−0.895684 | + | 0.444692i | \(0.853313\pi\) | |||||||
\(908\) | −9.88886e6 | + | 1.71280e7i | −0.398045 | + | 0.689434i | ||||
\(909\) | −1.78216e6 | −0.0715381 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.19035e6 | 0.0475203 | 0.0237602 | − | 0.999718i | \(-0.492436\pi\) | ||||
0.0237602 | + | 0.999718i | \(0.492436\pi\) | |||||||
\(912\) | 1.10131e6 | − | 1.90753e6i | 0.0438453 | − | 0.0759423i | ||||
\(913\) | −194040. | − | 336087.i | −0.00770397 | − | 0.0133437i | ||||
\(914\) | −467092. | − | 809027.i | −0.0184943 | − | 0.0320330i | ||||
\(915\) | 9.23373e6 | − | 1.59933e7i | 0.364607 | − | 0.631517i | ||||
\(916\) | 1.69328e6 | 0.0666792 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.20722e6 | 0.0472804 | ||||||||
\(919\) | 2.35998e7 | − | 4.08761e7i | 0.921764 | − | 1.59654i | 0.125079 | − | 0.992147i | \(-0.460082\pi\) |
0.796685 | − | 0.604395i | \(-0.206585\pi\) | |||||||
\(920\) | 1.26720e6 | + | 2.19485e6i | 0.0493601 | + | 0.0854941i | ||||
\(921\) | 7.60599e6 | + | 1.31740e7i | 0.295465 | + | 0.511761i | ||||
\(922\) | 3.48978e6 | − | 6.04448e6i | 0.135198 | − | 0.234170i | ||||
\(923\) | −4.02696e6 | −0.155587 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.04118e7 | −0.400103 | ||||||||
\(926\) | 5.83573e6 | − | 1.01078e7i | 0.223649 | − | 0.387372i | ||||
\(927\) | 3.21019e6 | + | 5.56022e6i | 0.122696 | + | 0.212516i | ||||
\(928\) | −2.85389e6 | − | 4.94308e6i | −0.108784 | − | 0.188420i | ||||
\(929\) | −667977. | + | 1.15697e6i | −0.0253935 | + | 0.0439828i | −0.878443 | − | 0.477847i | \(-0.841417\pi\) |
0.853049 | + | 0.521830i | \(0.174751\pi\) | |||||||
\(930\) | −8.53459e6 | −0.323575 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.01885e6 | −0.264683 | ||||||||
\(933\) | −6.75918e6 | + | 1.17072e7i | −0.254208 | + | 0.440302i | ||||
\(934\) | 1.06215e7 | + | 1.83970e7i | 0.398400 | + | 0.690049i | ||||
\(935\) | 819720. | + | 1.41980e6i | 0.0306645 | + | 0.0531125i | ||||
\(936\) | 1.70554e6 | − | 2.95408e6i | 0.0636314 | − | 0.110213i | ||||
\(937\) | 1.47238e7 | 0.547861 | 0.273931 | − | 0.961749i | \(-0.411676\pi\) | ||||
0.273931 | + | 0.961749i | \(0.411676\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.29758e6 | −0.270094 | ||||||||
\(940\) | −1.03910e7 | + | 1.79978e7i | −0.383565 | + | 0.664355i | ||||
\(941\) | 1.34598e7 | + | 2.33131e7i | 0.495525 | + | 0.858274i | 0.999987 | − | 0.00516005i | \(-0.00164250\pi\) |
−0.504462 | + | 0.863434i | \(0.668309\pi\) | |||||||
\(942\) | 2.45056e6 | + | 4.24449e6i | 0.0899782 | + | 0.155847i | ||||
\(943\) | −5.75820e6 | + | 9.97349e6i | −0.210866 | + | 0.365231i | ||||
\(944\) | 6.74304e6 | 0.246278 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.19584e6 | −0.116107 | ||||||||
\(947\) | 1.86580e6 | − | 3.23166e6i | 0.0676068 | − | 0.117098i | −0.830241 | − | 0.557405i | \(-0.811797\pi\) |
0.897847 | + | 0.440307i | \(0.145130\pi\) | |||||||
\(948\) | 5.35738e6 | + | 9.27925e6i | 0.193612 | + | 0.335345i | ||||
\(949\) | −8.40858e6 | − | 1.45641e7i | −0.303080 | − | 0.524950i | ||||
\(950\) | −2.35367e6 | + | 4.07668e6i | −0.0846130 | + | 0.146554i | ||||
\(951\) | −8.13202e6 | −0.291573 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.18735e7 | 0.780166 | 0.390083 | − | 0.920780i | \(-0.372446\pi\) | ||||
0.390083 | + | 0.920780i | \(0.372446\pi\) | |||||||
\(954\) | 5.06509e6 | − | 8.77300e6i | 0.180184 | − | 0.312088i | ||||
\(955\) | −8.75635e6 | − | 1.51664e7i | −0.310681 | − | 0.538115i | ||||
\(956\) | −227712. | − | 394409.i | −0.00805826 | − | 0.0139573i | ||||
\(957\) | −1.50498e6 | + | 2.60670e6i | −0.0531191 | + | 0.0920050i | ||||
\(958\) | 9.37862e6 | 0.330161 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.43302e6 | 0.0852056 | ||||||||
\(961\) | 7.86334e6 | − | 1.36197e7i | 0.274662 | − | 0.475729i | ||||
\(962\) | −1.11307e7 | − | 1.92790e7i | −0.387780 | − | 0.671655i | ||||
\(963\) | −9.23351e6 | − | 1.59929e7i | −0.320849 | − | 0.555728i | ||||
\(964\) | −7.14050e6 | + | 1.23677e7i | −0.247478 | + | 0.428644i | ||||
\(965\) | −1.94897e7 | −0.673730 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.76025e7 | 0.605352 | 0.302676 | − | 0.953093i | \(-0.402120\pi\) | ||||
0.302676 | + | 0.953093i | \(0.402120\pi\) | |||||||
\(968\) | 5.03843e6 | − | 8.72682e6i | 0.172825 | − | 0.299342i | ||||
\(969\) | −1.78103e6 | − | 3.08483e6i | −0.0609342 | − | 0.105541i | ||||
\(970\) | 2.19228e7 | + | 3.79714e7i | 0.748113 | + | 1.29577i | ||||
\(971\) | −8.36584e6 | + | 1.44901e7i | −0.284749 | + | 0.493199i | −0.972548 | − | 0.232702i | \(-0.925243\pi\) |
0.687800 | + | 0.725901i | \(0.258577\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.92612e7 | 1.32607 | ||||||||
\(975\) | −3.64499e6 | + | 6.31331e6i | −0.122796 | + | 0.212689i | ||||
\(976\) | 3.97952e6 | + | 6.89273e6i | 0.133723 | + | 0.231615i | ||||
\(977\) | −2.77691e7 | − | 4.80975e7i | −0.930733 | − | 1.61208i | −0.782071 | − | 0.623189i | \(-0.785837\pi\) |
−0.148662 | − | 0.988888i | \(-0.547497\pi\) | |||||||
\(978\) | −3.08023e6 | + | 5.33512e6i | −0.102976 | + | 0.178360i | ||||
\(979\) | 1.96452e6 | 0.0655088 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −690930. | −0.0229225 | ||||||||
\(982\) | 1.18904e7 | − | 2.05948e7i | 0.393475 | − | 0.681519i | ||||
\(983\) | 1.93392e7 | + | 3.34965e7i | 0.638344 | + | 1.10564i | 0.985796 | + | 0.167947i | \(0.0537137\pi\) |
−0.347452 | + | 0.937698i | \(0.612953\pi\) | |||||||
\(984\) | 5.52787e6 | + | 9.57456e6i | 0.182000 | + | 0.315232i | ||||
\(985\) | 6.64270e6 | − | 1.15055e7i | 0.218149 | − | 0.377846i | ||||
\(986\) | −9.23054e6 | −0.302367 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.00648e7 | −0.328028 | ||||||||
\(989\) | −3.99480e6 | + | 6.91920e6i | −0.129869 | + | 0.224939i | ||||
\(990\) | −641520. | − | 1.11115e6i | −0.0208028 | − | 0.0360315i | ||||
\(991\) | −4.79249e6 | − | 8.30084e6i | −0.155016 | − | 0.268496i | 0.778049 | − | 0.628204i | \(-0.216210\pi\) |
−0.933065 | + | 0.359708i | \(0.882876\pi\) | |||||||
\(992\) | 1.83910e6 | − | 3.18542e6i | 0.0593372 | − | 0.102775i | ||||
\(993\) | −1.00977e7 | −0.324976 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.30616e7 | −1.37890 | ||||||||
\(996\) | −465696. | + | 806609.i | −0.0148749 | + | 0.0257641i | ||||
\(997\) | 5.18252e6 | + | 8.97638e6i | 0.165121 | + | 0.285998i | 0.936698 | − | 0.350137i | \(-0.113865\pi\) |
−0.771577 | + | 0.636136i | \(0.780532\pi\) | |||||||
\(998\) | −1.29566e7 | − | 2.24415e7i | −0.411780 | − | 0.713225i | ||||
\(999\) | −3.08294e6 | + | 5.33981e6i | −0.0977353 | + | 0.169283i |
(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 | 294.6.e.g.79.1 | 2 | ||
7.2 | even | 3 | 6.6.a.a.1.1 | ✓ | 1 | ||
7.3 | odd | 6 | 294.6.e.a.67.1 | 2 | |||
7.4 | even | 3 | inner | 294.6.e.g.67.1 | 2 | ||
7.5 | odd | 6 | 294.6.a.m.1.1 | 1 | |||
7.6 | odd | 2 | 294.6.e.a.79.1 | 2 | |||
21.2 | odd | 6 | 18.6.a.b.1.1 | 1 | |||
21.5 | even | 6 | 882.6.a.a.1.1 | 1 | |||
28.23 | odd | 6 | 48.6.a.c.1.1 | 1 | |||
35.2 | odd | 12 | 150.6.c.b.49.2 | 2 | |||
35.9 | even | 6 | 150.6.a.d.1.1 | 1 | |||
35.23 | odd | 12 | 150.6.c.b.49.1 | 2 | |||
56.37 | even | 6 | 192.6.a.o.1.1 | 1 | |||
56.51 | odd | 6 | 192.6.a.g.1.1 | 1 | |||
63.2 | odd | 6 | 162.6.c.h.109.1 | 2 | |||
63.16 | even | 3 | 162.6.c.e.109.1 | 2 | |||
63.23 | odd | 6 | 162.6.c.h.55.1 | 2 | |||
63.58 | even | 3 | 162.6.c.e.55.1 | 2 | |||
77.65 | odd | 6 | 726.6.a.a.1.1 | 1 | |||
84.23 | even | 6 | 144.6.a.j.1.1 | 1 | |||
91.51 | even | 6 | 1014.6.a.c.1.1 | 1 | |||
105.2 | even | 12 | 450.6.c.j.199.1 | 2 | |||
105.23 | even | 12 | 450.6.c.j.199.2 | 2 | |||
105.44 | odd | 6 | 450.6.a.m.1.1 | 1 | |||
112.37 | even | 12 | 768.6.d.c.385.2 | 2 | |||
112.51 | odd | 12 | 768.6.d.p.385.2 | 2 | |||
112.93 | even | 12 | 768.6.d.c.385.1 | 2 | |||
112.107 | odd | 12 | 768.6.d.p.385.1 | 2 | |||
168.107 | even | 6 | 576.6.a.i.1.1 | 1 | |||
168.149 | odd | 6 | 576.6.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.6.a.a.1.1 | ✓ | 1 | 7.2 | even | 3 | ||
18.6.a.b.1.1 | 1 | 21.2 | odd | 6 | |||
48.6.a.c.1.1 | 1 | 28.23 | odd | 6 | |||
144.6.a.j.1.1 | 1 | 84.23 | even | 6 | |||
150.6.a.d.1.1 | 1 | 35.9 | even | 6 | |||
150.6.c.b.49.1 | 2 | 35.23 | odd | 12 | |||
150.6.c.b.49.2 | 2 | 35.2 | odd | 12 | |||
162.6.c.e.55.1 | 2 | 63.58 | even | 3 | |||
162.6.c.e.109.1 | 2 | 63.16 | even | 3 | |||
162.6.c.h.55.1 | 2 | 63.23 | odd | 6 | |||
162.6.c.h.109.1 | 2 | 63.2 | odd | 6 | |||
192.6.a.g.1.1 | 1 | 56.51 | odd | 6 | |||
192.6.a.o.1.1 | 1 | 56.37 | even | 6 | |||
294.6.a.m.1.1 | 1 | 7.5 | odd | 6 | |||
294.6.e.a.67.1 | 2 | 7.3 | odd | 6 | |||
294.6.e.a.79.1 | 2 | 7.6 | odd | 2 | |||
294.6.e.g.67.1 | 2 | 7.4 | even | 3 | inner | ||
294.6.e.g.79.1 | 2 | 1.1 | even | 1 | trivial | ||
450.6.a.m.1.1 | 1 | 105.44 | odd | 6 | |||
450.6.c.j.199.1 | 2 | 105.2 | even | 12 | |||
450.6.c.j.199.2 | 2 | 105.23 | even | 12 | |||
576.6.a.i.1.1 | 1 | 168.107 | even | 6 | |||
576.6.a.j.1.1 | 1 | 168.149 | odd | 6 | |||
726.6.a.a.1.1 | 1 | 77.65 | odd | 6 | |||
768.6.d.c.385.1 | 2 | 112.93 | even | 12 | |||
768.6.d.c.385.2 | 2 | 112.37 | even | 12 | |||
768.6.d.p.385.1 | 2 | 112.107 | odd | 12 | |||
768.6.d.p.385.2 | 2 | 112.51 | odd | 12 | |||
882.6.a.a.1.1 | 1 | 21.5 | even | 6 | |||
1014.6.a.c.1.1 | 1 | 91.51 | even | 6 |