Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,7,Mod(53,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.53");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.d (of order \(6\), 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: | \(37.2687615464\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 54) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.107 |
Dual form | 162.7.d.c.53.2 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.89898 | + | 2.82843i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | + | 27.7128i | 0.250000 | + | 0.433013i | ||||
\(5\) | −29.3939 | + | 16.9706i | −0.235151 | + | 0.135765i | −0.612946 | − | 0.790125i | \(-0.710016\pi\) |
0.377795 | + | 0.925889i | \(0.376682\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 102.500 | − | 177.535i | 0.298834 | − | 0.517595i | −0.677036 | − | 0.735950i | \(-0.736736\pi\) |
0.975869 | + | 0.218355i | \(0.0700690\pi\) | |||||||
\(8\) | 181.019i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −192.000 | −0.192000 | ||||||||
\(11\) | −911.210 | − | 526.087i | −0.684606 | − | 0.395257i | 0.116982 | − | 0.993134i | \(-0.462678\pi\) |
−0.801588 | + | 0.597877i | \(0.796011\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1020.50 | + | 1767.56i | 0.464497 | + | 0.804532i | 0.999179 | − | 0.0405211i | \(-0.0129018\pi\) |
−0.534682 | + | 0.845054i | \(0.679568\pi\) | |||||||
\(14\) | 1004.29 | − | 579.828i | 0.365995 | − | 0.211307i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −512.000 | + | 886.810i | −0.125000 | + | 0.216506i | ||||
\(17\) | 8247.69i | 1.67875i | 0.543554 | + | 0.839374i | \(0.317078\pi\) | ||||
−0.543554 | + | 0.839374i | \(0.682922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1501.00 | −0.218837 | −0.109418 | − | 0.993996i | \(-0.534899\pi\) | ||||
−0.109418 | + | 0.993996i | \(0.534899\pi\) | |||||||
\(20\) | −940.604 | − | 543.058i | −0.117576 | − | 0.0678823i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2976.00 | − | 5154.58i | −0.279489 | − | 0.484089i | ||||
\(23\) | 6143.32 | − | 3546.85i | 0.504917 | − | 0.291514i | −0.225825 | − | 0.974168i | \(-0.572508\pi\) |
0.730742 | + | 0.682654i | \(0.239174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7236.50 | + | 12534.0i | −0.463136 | + | 0.802175i | ||||
\(26\) | 11545.6i | 0.656898i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6560.00 | 0.298834 | ||||||||
\(29\) | −24632.1 | − | 14221.3i | −1.00997 | − | 0.583104i | −0.0987845 | − | 0.995109i | \(-0.531495\pi\) |
−0.911182 | + | 0.412005i | \(0.864829\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 17495.0 | + | 30302.2i | 0.587258 | + | 1.01716i | 0.994590 | + | 0.103880i | \(0.0331259\pi\) |
−0.407332 | + | 0.913280i | \(0.633541\pi\) | |||||||
\(32\) | −5016.55 | + | 2896.31i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −23328.0 | + | 40405.3i | −0.593527 | + | 1.02802i | ||||
\(35\) | 6957.93i | 0.162284i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −57625.0 | −1.13764 | −0.568821 | − | 0.822461i | \(-0.692600\pi\) | ||||
−0.568821 | + | 0.822461i | \(0.692600\pi\) | |||||||
\(38\) | −7353.37 | − | 4245.47i | −0.134009 | − | 0.0773704i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3072.00 | − | 5320.86i | −0.0480000 | − | 0.0831384i | ||||
\(41\) | −116341. | + | 67169.5i | −1.68803 | + | 0.974587i | −0.732011 | + | 0.681292i | \(0.761418\pi\) |
−0.956022 | + | 0.293294i | \(0.905248\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 31283.0 | − | 54183.7i | 0.393462 | − | 0.681497i | −0.599441 | − | 0.800419i | \(-0.704611\pi\) |
0.992904 | + | 0.118922i | \(0.0379439\pi\) | |||||||
\(44\) | − | 33669.6i | − | 0.395257i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 40128.0 | 0.412263 | ||||||||
\(47\) | 44943.2 | + | 25948.0i | 0.432883 | + | 0.249925i | 0.700574 | − | 0.713580i | \(-0.252927\pi\) |
−0.267691 | + | 0.963505i | \(0.586261\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 37812.0 | + | 65492.3i | 0.321397 | + | 0.556675i | ||||
\(50\) | −70902.9 | + | 40935.8i | −0.567223 | + | 0.327487i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −32656.0 | + | 56561.9i | −0.232249 | + | 0.402266i | ||||
\(53\) | 77182.1i | 0.518429i | 0.965820 | + | 0.259214i | \(0.0834636\pi\) | ||||
−0.965820 | + | 0.259214i | \(0.916536\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 35712.0 | 0.214648 | ||||||||
\(56\) | 32137.3 | + | 18554.5i | 0.182998 | + | 0.105654i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −80448.0 | − | 139340.i | −0.412317 | − | 0.714154i | ||||
\(59\) | −321540. | + | 185641.i | −1.56559 | + | 0.903895i | −0.568918 | + | 0.822394i | \(0.692638\pi\) |
−0.996673 | + | 0.0815006i | \(0.974029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 30648.5 | − | 53084.8i | 0.135027 | − | 0.233873i | −0.790581 | − | 0.612358i | \(-0.790221\pi\) |
0.925608 | + | 0.378484i | \(0.123555\pi\) | |||||||
\(62\) | 197933.i | 0.830508i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | −59992.9 | − | 34636.9i | −0.218454 | − | 0.126124i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −33845.5 | − | 58622.1i | −0.112532 | − | 0.194911i | 0.804258 | − | 0.594280i | \(-0.202563\pi\) |
−0.916791 | + | 0.399368i | \(0.869229\pi\) | |||||||
\(68\) | −228567. | + | 131963.i | −0.726920 | + | 0.419687i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −19680.0 | + | 34086.8i | −0.0573761 | + | 0.0993783i | ||||
\(71\) | 509524.i | 1.42361i | 0.702379 | + | 0.711803i | \(0.252121\pi\) | ||||
−0.702379 | + | 0.711803i | \(0.747879\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 423983. | 1.08988 | 0.544941 | − | 0.838474i | \(-0.316552\pi\) | ||||
0.544941 | + | 0.838474i | \(0.316552\pi\) | |||||||
\(74\) | −282304. | − | 162988.i | −0.696661 | − | 0.402217i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −24016.0 | − | 41596.9i | −0.0547091 | − | 0.0947590i | ||||
\(77\) | −186798. | + | 107848.i | −0.409167 | + | 0.236232i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 353766. | − | 612742.i | 0.717522 | − | 1.24279i | −0.244456 | − | 0.969660i | \(-0.578609\pi\) |
0.961979 | − | 0.273125i | \(-0.0880572\pi\) | |||||||
\(80\) | − | 34755.7i | − | 0.0678823i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −759936. | −1.37827 | ||||||||
\(83\) | −745605. | − | 430475.i | −1.30399 | − | 0.752860i | −0.322905 | − | 0.946431i | \(-0.604659\pi\) |
−0.981086 | + | 0.193572i | \(0.937993\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −139968. | − | 242432.i | −0.227915 | − | 0.394760i | ||||
\(86\) | 306510. | − | 176963.i | 0.481891 | − | 0.278220i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 95232.0 | − | 164947.i | 0.139745 | − | 0.242045i | ||||
\(89\) | 667656.i | 0.947071i | 0.880775 | + | 0.473536i | \(0.157022\pi\) | ||||
−0.880775 | + | 0.473536i | \(0.842978\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 418405. | 0.555230 | ||||||||
\(92\) | 196586. | + | 113499.i | 0.252458 | + | 0.145757i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 146784. | + | 254237.i | 0.176724 | + | 0.306095i | ||||
\(95\) | 44120.2 | − | 25472.8i | 0.0514596 | − | 0.0297102i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −263076. | + | 455660.i | −0.288247 | + | 0.499259i | −0.973391 | − | 0.229149i | \(-0.926406\pi\) |
0.685144 | + | 0.728407i | \(0.259739\pi\) | |||||||
\(98\) | 427794.i | 0.454524i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −463136. | −0.463136 | ||||||||
\(101\) | 77129.5 | + | 44530.8i | 0.0748612 | + | 0.0432211i | 0.536963 | − | 0.843606i | \(-0.319571\pi\) |
−0.462102 | + | 0.886827i | \(0.652905\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 142626. | + | 247036.i | 0.130523 | + | 0.226073i | 0.923878 | − | 0.382686i | \(-0.125001\pi\) |
−0.793355 | + | 0.608759i | \(0.791668\pi\) | |||||||
\(104\) | −319962. | + | 184730.i | −0.284445 | + | 0.164225i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −218304. | + | 378114.i | −0.183292 | + | 0.317471i | ||||
\(107\) | − | 1.33684e6i | − | 1.09126i | −0.838027 | − | 0.545629i | \(-0.816291\pi\) | ||
0.838027 | − | 0.545629i | \(-0.183709\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.21292e6 | 1.70878 | 0.854391 | − | 0.519631i | \(-0.173931\pi\) | ||||
0.854391 | + | 0.519631i | \(0.173931\pi\) | |||||||
\(110\) | 174952. | + | 101009.i | 0.131444 | + | 0.0758894i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 104960. | + | 181796.i | 0.0747085 | + | 0.129399i | ||||
\(113\) | −384854. | + | 222196.i | −0.266723 | + | 0.153993i | −0.627398 | − | 0.778699i | \(-0.715880\pi\) |
0.360674 | + | 0.932692i | \(0.382547\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −120384. | + | 208511.i | −0.0791544 | + | 0.137100i | ||||
\(116\) | − | 910165.i | − | 0.583104i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.10029e6 | −1.27830 | ||||||||
\(119\) | 1.46426e6 | + | 845389.i | 0.868913 | + | 0.501667i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −332244. | − | 575464.i | −0.187543 | − | 0.324835i | ||||
\(122\) | 300293. | − | 173374.i | 0.165373 | − | 0.0954783i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −559840. | + | 969671.i | −0.293629 | + | 0.508580i | ||||
\(125\) | − | 1.02156e6i | − | 0.523039i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −330478. | −0.161336 | −0.0806680 | − | 0.996741i | \(-0.525705\pi\) | ||||
−0.0806680 | + | 0.996741i | \(0.525705\pi\) | |||||||
\(128\) | −160530. | − | 92681.9i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −195936. | − | 339371.i | −0.0891834 | − | 0.154470i | ||||
\(131\) | 1.07446e6 | − | 620342.i | 0.477945 | − | 0.275942i | −0.241615 | − | 0.970372i | \(-0.577677\pi\) |
0.719560 | + | 0.694431i | \(0.244344\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −153852. | + | 266480.i | −0.0653958 | + | 0.113269i | ||||
\(134\) | − | 382918.i | − | 0.159144i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.49299e6 | −0.593527 | ||||||||
\(137\) | 2.09199e6 | + | 1.20781e6i | 0.813576 | + | 0.469718i | 0.848196 | − | 0.529682i | \(-0.177689\pi\) |
−0.0346200 | + | 0.999401i | \(0.511022\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.55445e6 | + | 4.42443e6i | 0.951157 | + | 1.64745i | 0.742926 | + | 0.669373i | \(0.233437\pi\) |
0.208231 | + | 0.978080i | \(0.433229\pi\) | |||||||
\(140\) | −192824. | + | 111327.i | −0.0702711 | + | 0.0405710i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.44115e6 | + | 2.49615e6i | −0.503321 | + | 0.871777i | ||||
\(143\) | − | 2.14749e6i | − | 0.734383i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 965376. | 0.316659 | ||||||||
\(146\) | 2.07708e6 | + | 1.19921e6i | 0.667414 | + | 0.385332i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −922000. | − | 1.59695e6i | −0.284411 | − | 0.492614i | ||||
\(149\) | 4.60649e6 | − | 2.65956e6i | 1.39255 | − | 0.803990i | 0.398955 | − | 0.916971i | \(-0.369373\pi\) |
0.993597 | + | 0.112980i | \(0.0360397\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.48349e6 | − | 4.30153e6i | 0.721326 | − | 1.24937i | −0.239142 | − | 0.970985i | \(-0.576866\pi\) |
0.960468 | − | 0.278389i | \(-0.0898004\pi\) | |||||||
\(152\) | − | 271710.i | − | 0.0773704i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.22016e6 | −0.334083 | ||||||||
\(155\) | −1.02849e6 | − | 593800.i | −0.276189 | − | 0.159458i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −413101. | − | 715512.i | −0.106747 | − | 0.184892i | 0.807703 | − | 0.589589i | \(-0.200710\pi\) |
−0.914451 | + | 0.404697i | \(0.867377\pi\) | |||||||
\(158\) | 3.46619e6 | − | 2.00121e6i | 0.878782 | − | 0.507365i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 98304.0 | − | 170268.i | 0.0240000 | − | 0.0415692i | ||||
\(161\) | − | 1.45421e6i | − | 0.348457i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.90160e6 | 0.439094 | 0.219547 | − | 0.975602i | \(-0.429542\pi\) | ||||
0.219547 | + | 0.975602i | \(0.429542\pi\) | |||||||
\(164\) | −3.72291e6 | − | 2.14942e6i | −0.844017 | − | 0.487293i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.43514e6 | − | 4.21778e6i | −0.532352 | − | 0.922061i | ||||
\(167\) | 5.05789e6 | − | 2.92018e6i | 1.08598 | − | 0.626988i | 0.153474 | − | 0.988153i | \(-0.450954\pi\) |
0.932502 | + | 0.361164i | \(0.117621\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 330564. | − | 572554.i | 0.0684850 | − | 0.118619i | ||||
\(170\) | − | 1.58356e6i | − | 0.322320i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00211e6 | 0.393462 | ||||||||
\(173\) | −3.35331e6 | − | 1.93604e6i | −0.647643 | − | 0.373917i | 0.139910 | − | 0.990164i | \(-0.455319\pi\) |
−0.787553 | + | 0.616247i | \(0.788652\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.48348e6 | + | 2.56947e6i | 0.276801 | + | 0.479434i | ||||
\(176\) | 933079. | − | 538714.i | 0.171151 | − | 0.0988143i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.88842e6 | + | 3.27083e6i | −0.334840 | + | 0.579960i | ||||
\(179\) | 3.25305e6i | 0.567195i | 0.958943 | + | 0.283597i | \(0.0915279\pi\) | ||||
−0.958943 | + | 0.283597i | \(0.908472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.83110e6 | 0.814724 | 0.407362 | − | 0.913267i | \(-0.366449\pi\) | ||||
0.407362 | + | 0.913267i | \(0.366449\pi\) | |||||||
\(182\) | 2.04976e6 | + | 1.18343e6i | 0.340007 | + | 0.196303i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 642048. | + | 1.11206e6i | 0.103066 | + | 0.178515i | ||||
\(185\) | 1.69382e6 | − | 977929.i | 0.267518 | − | 0.154451i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.33901e6 | − | 7.51538e6i | 0.663538 | − | 1.14928i | ||||
\(188\) | 1.66067e6i | 0.249925i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 288192. | 0.0420166 | ||||||||
\(191\) | 1.72621e6 | + | 996630.i | 0.247739 | + | 0.143032i | 0.618729 | − | 0.785605i | \(-0.287648\pi\) |
−0.370989 | + | 0.928637i | \(0.620981\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.80510e6 | − | 1.00547e7i | −0.807491 | − | 1.39861i | −0.914597 | − | 0.404367i | \(-0.867492\pi\) |
0.107106 | − | 0.994248i | \(-0.465841\pi\) | |||||||
\(194\) | −2.57760e6 | + | 1.48818e6i | −0.353029 | + | 0.203822i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.20998e6 | + | 2.09575e6i | −0.160698 | + | 0.278338i | ||||
\(197\) | − | 4.62309e6i | − | 0.604691i | −0.953198 | − | 0.302345i | \(-0.902230\pi\) | ||
0.953198 | − | 0.302345i | \(-0.0977696\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.03916e6 | −1.14701 | −0.573507 | − | 0.819201i | \(-0.694417\pi\) | ||||
−0.573507 | + | 0.819201i | \(0.694417\pi\) | |||||||
\(200\) | −2.26889e6 | − | 1.30995e6i | −0.283612 | − | 0.163743i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 251904. | + | 436311.i | 0.0305619 | + | 0.0529348i | ||||
\(203\) | −5.04957e6 | + | 2.91537e6i | −0.603624 | + | 0.348503i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.27981e6 | − | 3.94874e6i | 0.264629 | − | 0.458350i | ||||
\(206\) | 1.61363e6i | 0.184588i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.08998e6 | −0.232249 | ||||||||
\(209\) | 1.36773e6 | + | 789657.i | 0.149817 | + | 0.0864967i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.47667e6 | + | 9.48588e6i | 0.583001 | + | 1.00979i | 0.995121 | + | 0.0986584i | \(0.0314551\pi\) |
−0.412120 | + | 0.911130i | \(0.635212\pi\) | |||||||
\(212\) | −2.13893e6 | + | 1.23491e6i | −0.224486 | + | 0.129607i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.78115e6 | − | 6.54915e6i | 0.385818 | − | 0.668257i | ||||
\(215\) | 2.12356e6i | 0.213673i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.17295e6 | 0.701970 | ||||||||
\(218\) | 1.08411e7 | + | 6.25909e6i | 1.04641 | + | 0.604146i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 571392. | + | 989680.i | 0.0536619 | + | 0.0929452i | ||||
\(221\) | −1.45783e7 | + | 8.41677e6i | −1.35061 | + | 0.779774i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.18660e6 | + | 1.07155e7i | −0.557876 | + | 0.966269i | 0.439798 | + | 0.898097i | \(0.355050\pi\) |
−0.997674 | + | 0.0681724i | \(0.978283\pi\) | |||||||
\(224\) | 1.18749e6i | 0.105654i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.51386e6 | −0.217779 | ||||||||
\(227\) | 5.33275e6 | + | 3.07887e6i | 0.455905 | + | 0.263217i | 0.710321 | − | 0.703878i | \(-0.248550\pi\) |
−0.254416 | + | 0.967095i | \(0.581883\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.77895e6 | − | 4.81328e6i | −0.231406 | − | 0.400807i | 0.726816 | − | 0.686832i | \(-0.240999\pi\) |
−0.958222 | + | 0.286025i | \(0.907666\pi\) | |||||||
\(230\) | −1.17952e6 | + | 680995.i | −0.0969440 | + | 0.0559706i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.57434e6 | − | 4.45888e6i | 0.206159 | − | 0.357077i | ||||
\(233\) | 1.17231e7i | 0.926778i | 0.886155 | + | 0.463389i | \(0.153367\pi\) | ||||
−0.886155 | + | 0.463389i | \(0.846633\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.76141e6 | −0.135724 | ||||||||
\(236\) | −1.02893e7 | − | 5.94051e6i | −0.782796 | − | 0.451947i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.78224e6 | + | 8.28308e6i | 0.354732 | + | 0.614414i | ||||
\(239\) | −1.53042e7 | + | 8.83589e6i | −1.12103 | + | 0.647227i | −0.941664 | − | 0.336555i | \(-0.890738\pi\) |
−0.179367 | + | 0.983782i | \(0.557405\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.07844e7 | + | 1.86791e7i | −0.770451 | + | 1.33446i | 0.166866 | + | 0.985980i | \(0.446635\pi\) |
−0.937316 | + | 0.348480i | \(0.886698\pi\) | |||||||
\(242\) | − | 3.75892e6i | − | 0.265226i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.96150e6 | 0.135027 | ||||||||
\(245\) | −2.22288e6 | − | 1.28338e6i | −0.151154 | − | 0.0872685i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.53177e6 | − | 2.65310e6i | −0.101649 | − | 0.176061i | ||||
\(248\) | −5.48529e6 | + | 3.16693e6i | −0.359621 | + | 0.207627i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.88941e6 | − | 5.00460e6i | 0.184922 | − | 0.320294i | ||||
\(251\) | − | 1.51574e6i | − | 0.0958527i | −0.998851 | − | 0.0479263i | \(-0.984739\pi\) | ||
0.998851 | − | 0.0479263i | \(-0.0152613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.46381e6 | −0.460892 | ||||||||
\(254\) | −1.61900e6 | − | 934733.i | −0.0987977 | − | 0.0570409i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −524288. | − | 908093.i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.00354e7 | + | 5.79392e6i | −0.591199 | + | 0.341329i | −0.765571 | − | 0.643351i | \(-0.777544\pi\) |
0.174372 | + | 0.984680i | \(0.444210\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.90656e6 | + | 1.02305e7i | −0.339966 | + | 0.588838i | ||||
\(260\) | − | 2.21676e6i | − | 0.126124i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.01837e6 | 0.390240 | ||||||||
\(263\) | −2.25139e7 | − | 1.29984e7i | −1.23761 | − | 0.714535i | −0.269006 | − | 0.963138i | \(-0.586695\pi\) |
−0.968605 | + | 0.248603i | \(0.920029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.30982e6 | − | 2.26868e6i | −0.0703842 | − | 0.121909i | ||||
\(266\) | −1.50744e6 | + | 870321.i | −0.0800931 | + | 0.0462418i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.08306e6 | − | 1.87591e6i | 0.0562661 | − | 0.0974557i | ||||
\(269\) | 8.77605e6i | 0.450861i | 0.974259 | + | 0.225430i | \(0.0723788\pi\) | ||||
−0.974259 | + | 0.225430i | \(0.927621\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.16794e7 | 0.586831 | 0.293416 | − | 0.955985i | \(-0.405208\pi\) | ||||
0.293416 | + | 0.955985i | \(0.405208\pi\) | |||||||
\(272\) | −7.31414e6 | − | 4.22282e6i | −0.363460 | − | 0.209844i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.83242e6 | + | 1.18341e7i | 0.332141 | + | 0.575285i | ||||
\(275\) | 1.31879e7 | − | 7.61406e6i | 0.634131 | − | 0.366116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.71151e6 | + | 9.89262e6i | −0.268727 | + | 0.465449i | −0.968533 | − | 0.248884i | \(-0.919936\pi\) |
0.699806 | + | 0.714333i | \(0.253270\pi\) | |||||||
\(278\) | 2.89003e7i | 1.34514i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.25952e6 | −0.0573761 | ||||||||
\(281\) | −1.04576e7 | − | 6.03768e6i | −0.471316 | − | 0.272114i | 0.245474 | − | 0.969403i | \(-0.421056\pi\) |
−0.716790 | + | 0.697289i | \(0.754390\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.94454e6 | − | 3.36804e6i | −0.0857942 | − | 0.148600i | 0.819935 | − | 0.572456i | \(-0.194009\pi\) |
−0.905729 | + | 0.423857i | \(0.860676\pi\) | |||||||
\(284\) | −1.41203e7 | + | 8.15239e6i | −0.616439 | + | 0.355901i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.07402e6 | − | 1.05205e7i | 0.259644 | − | 0.449716i | ||||
\(287\) | 2.75395e7i | 1.16496i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.38869e7 | −1.81820 | ||||||||
\(290\) | 4.72936e6 | + | 2.73050e6i | 0.193914 | + | 0.111956i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.78373e6 | + | 1.17498e7i | 0.272471 | + | 0.471933i | ||||
\(293\) | 2.31342e7 | − | 1.33566e7i | 0.919713 | − | 0.530997i | 0.0361697 | − | 0.999346i | \(-0.488484\pi\) |
0.883544 | + | 0.468349i | \(0.155151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.30086e6 | − | 1.09134e7i | 0.245434 | − | 0.425104i | ||||
\(296\) | − | 1.04312e7i | − | 0.402217i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00895e7 | 1.13701 | ||||||||
\(299\) | 1.25385e7 | + | 7.23912e6i | 0.469065 | + | 0.270815i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.41302e6 | − | 1.11077e7i | −0.235160 | − | 0.407308i | ||||
\(302\) | 2.43331e7 | − | 1.40487e7i | 0.883440 | − | 0.510055i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 768512. | − | 1.33110e6i | 0.0273546 | − | 0.0473795i | ||||
\(305\) | 2.08049e6i | 0.0733273i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.79714e7 | −0.621108 | −0.310554 | − | 0.950556i | \(-0.600515\pi\) | ||||
−0.310554 | + | 0.950556i | \(0.600515\pi\) | |||||||
\(308\) | −5.97754e6 | − | 3.45113e6i | −0.204583 | − | 0.118116i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.35904e6 | − | 5.81803e6i | −0.112754 | − | 0.195295i | ||||
\(311\) | −3.59069e7 | + | 2.07308e7i | −1.19370 | + | 0.689185i | −0.959144 | − | 0.282917i | \(-0.908698\pi\) |
−0.234559 | + | 0.972102i | \(0.575365\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.13070e6 | − | 1.95843e6i | 0.0368735 | − | 0.0638668i | −0.847000 | − | 0.531593i | \(-0.821593\pi\) |
0.883873 | + | 0.467727i | \(0.154927\pi\) | |||||||
\(314\) | − | 4.67370e6i | − | 0.150964i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.26411e7 | 0.717522 | ||||||||
\(317\) | 9.86582e6 | + | 5.69603e6i | 0.309710 | + | 0.178811i | 0.646797 | − | 0.762662i | \(-0.276108\pi\) |
−0.337087 | + | 0.941474i | \(0.609442\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.49633e7 | + | 2.59172e7i | 0.460952 | + | 0.798393i | ||||
\(320\) | 963179. | − | 556091.i | 0.0293939 | − | 0.0169706i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.11312e6 | − | 7.12413e6i | 0.123198 | − | 0.213385i | ||||
\(323\) | − | 1.23798e7i | − | 0.367372i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.95394e7 | −0.860501 | ||||||||
\(326\) | 9.31591e6 | + | 5.37855e6i | 0.268889 | + | 0.155243i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.21590e7 | − | 2.10600e7i | −0.344568 | − | 0.596810i | ||||
\(329\) | 9.21336e6 | − | 5.31934e6i | 0.258720 | − | 0.149372i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.03387e6 | + | 1.21830e7i | −0.193959 | + | 0.335947i | −0.946559 | − | 0.322531i | \(-0.895466\pi\) |
0.752600 | + | 0.658478i | \(0.228800\pi\) | |||||||
\(332\) | − | 2.75504e7i | − | 0.752860i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.30380e7 | 0.886696 | ||||||||
\(335\) | 1.98970e6 | + | 1.14875e6i | 0.0529241 | + | 0.0305557i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.39591e7 | − | 4.14983e7i | −0.626008 | − | 1.08428i | −0.988345 | − | 0.152231i | \(-0.951354\pi\) |
0.362336 | − | 0.932047i | \(-0.381979\pi\) | |||||||
\(338\) | 3.23885e6 | − | 1.86995e6i | 0.0838766 | − | 0.0484262i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.47898e6 | − | 7.75781e6i | 0.113957 | − | 0.197380i | ||||
\(341\) | − | 3.68156e7i | − | 0.928472i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.96210e7 | 0.981844 | ||||||||
\(344\) | 9.80831e6 | + | 5.66283e6i | 0.240945 | + | 0.139110i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.09519e7 | − | 1.89692e7i | −0.264399 | − | 0.457953i | ||||
\(347\) | 3.68196e7 | − | 2.12578e7i | 0.881233 | − | 0.508780i | 0.0101680 | − | 0.999948i | \(-0.496763\pi\) |
0.871065 | + | 0.491168i | \(0.163430\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.06997e7 | − | 7.04940e7i | 0.957448 | − | 1.65835i | 0.228785 | − | 0.973477i | \(-0.426525\pi\) |
0.728663 | − | 0.684872i | \(-0.240142\pi\) | |||||||
\(350\) | 1.67837e7i | 0.391456i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.09485e6 | 0.139745 | ||||||||
\(353\) | 3.30207e7 | + | 1.90645e7i | 0.750693 | + | 0.433413i | 0.825944 | − | 0.563752i | \(-0.190642\pi\) |
−0.0752511 | + | 0.997165i | \(0.523976\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.64691e6 | − | 1.49769e7i | −0.193275 | − | 0.334762i | ||||
\(356\) | −1.85026e7 | + | 1.06825e7i | −0.410094 | + | 0.236768i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.20102e6 | + | 1.59366e7i | −0.200534 | + | 0.347334i | ||||
\(359\) | − | 7.04340e7i | − | 1.52230i | −0.648579 | − | 0.761148i | \(-0.724636\pi\) | ||
0.648579 | − | 0.761148i | \(-0.275364\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.47929e7 | −0.952111 | ||||||||
\(362\) | 2.36675e7 | + | 1.36644e7i | 0.498915 | + | 0.288048i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.69448e6 | + | 1.15952e7i | 0.138807 | + | 0.240422i | ||||
\(365\) | −1.24625e7 | + | 7.19523e6i | −0.256287 | + | 0.147967i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.93498e7 | + | 3.35148e7i | −0.391452 | + | 0.678014i | −0.992641 | − | 0.121092i | \(-0.961360\pi\) |
0.601190 | + | 0.799106i | \(0.294694\pi\) | |||||||
\(368\) | 7.26394e6i | 0.145757i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.10640e7 | 0.218427 | ||||||||
\(371\) | 1.37025e7 | + | 7.91117e6i | 0.268336 | + | 0.154924i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.88381e7 | + | 4.99491e7i | 0.555700 | + | 0.962500i | 0.997849 | + | 0.0655585i | \(0.0208829\pi\) |
−0.442149 | + | 0.896942i | \(0.645784\pi\) | |||||||
\(374\) | 4.25134e7 | − | 2.45451e7i | 0.812664 | − | 0.469192i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.69709e6 | + | 8.13560e6i | −0.0883619 | + | 0.153047i | ||||
\(377\) | − | 5.80515e7i | − | 1.08340i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.45022e7 | 0.817455 | 0.408728 | − | 0.912656i | \(-0.365973\pi\) | ||||
0.408728 | + | 0.912656i | \(0.365973\pi\) | |||||||
\(380\) | 1.41185e6 | + | 815130.i | 0.0257298 | + | 0.0148551i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.63779e6 | + | 9.76494e6i | 0.101139 | + | 0.175178i | ||||
\(383\) | 9.36936e7 | − | 5.40940e7i | 1.66768 | − | 0.962837i | 0.698800 | − | 0.715317i | \(-0.253718\pi\) |
0.968883 | − | 0.247520i | \(-0.0796157\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.66048e6 | − | 6.34014e6i | 0.0641440 | − | 0.111101i | ||||
\(386\) | − | 6.56772e7i | − | 1.14196i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.68368e7 | −0.288247 | ||||||||
\(389\) | −7.41575e6 | − | 4.28149e6i | −0.125981 | − | 0.0727354i | 0.435685 | − | 0.900099i | \(-0.356506\pi\) |
−0.561666 | + | 0.827364i | \(0.689840\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.92533e7 | + | 5.06682e7i | 0.489378 | + | 0.847628i | ||||
\(392\) | −1.18554e7 | + | 6.84470e6i | −0.196814 | + | 0.113631i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.30761e7 | − | 2.26484e7i | 0.213790 | − | 0.370296i | ||||
\(395\) | 2.40145e7i | 0.389656i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.09229e7 | −1.29330 | −0.646651 | − | 0.762786i | \(-0.723831\pi\) | ||||
−0.646651 | + | 0.762786i | \(0.723831\pi\) | |||||||
\(398\) | −4.42826e7 | − | 2.55666e7i | −0.702400 | − | 0.405531i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.41018e6 | − | 1.28348e7i | −0.115784 | − | 0.200544i | ||||
\(401\) | 4.36170e7 | − | 2.51823e7i | 0.676429 | − | 0.390537i | −0.122079 | − | 0.992520i | \(-0.538956\pi\) |
0.798508 | + | 0.601984i | \(0.205623\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.57073e7 | + | 6.18468e7i | −0.545559 | + | 0.944936i | ||||
\(404\) | 2.84997e6i | 0.0432211i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.29837e7 | −0.492857 | ||||||||
\(407\) | 5.25085e7 | + | 3.03158e7i | 0.778836 | + | 0.449661i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.11297e7 | − | 5.39183e7i | −0.454994 | − | 0.788072i | 0.543694 | − | 0.839283i | \(-0.317025\pi\) |
−0.998688 | + | 0.0512112i | \(0.983692\pi\) | |||||||
\(410\) | 2.23375e7 | − | 1.28965e7i | 0.324102 | − | 0.187121i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.56405e6 | + | 7.90516e6i | −0.0652617 | + | 0.113037i | ||||
\(413\) | 7.61128e7i | 1.08046i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.92216e7 | 0.408846 | ||||||||
\(416\) | −1.02388e7 | − | 5.91137e6i | −0.142223 | − | 0.0821123i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.46698e6 | + | 7.73703e6i | 0.0611624 | + | 0.105936i | ||||
\(419\) | −1.03266e7 | + | 5.96208e6i | −0.140384 | + | 0.0810505i | −0.568547 | − | 0.822651i | \(-0.692494\pi\) |
0.428163 | + | 0.903701i | \(0.359161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.80026e7 | − | 4.85019e7i | 0.375277 | − | 0.649999i | −0.615091 | − | 0.788456i | \(-0.710881\pi\) |
0.990368 | + | 0.138457i | \(0.0442142\pi\) | |||||||
\(422\) | 6.19615e7i | 0.824488i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.39715e7 | −0.183292 | ||||||||
\(425\) | −1.03376e8 | − | 5.96844e7i | −1.34665 | − | 0.777489i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.28294e6 | − | 1.08824e7i | −0.0807011 | − | 0.139778i | ||||
\(428\) | 3.70476e7 | − | 2.13894e7i | 0.472529 | − | 0.272815i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.00634e6 | + | 1.04033e7i | −0.0755447 | + | 0.130847i | ||||
\(431\) | 2.91184e6i | 0.0363694i | 0.999835 | + | 0.0181847i | \(0.00578869\pi\) | ||||
−0.999835 | + | 0.0181847i | \(0.994211\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.23835e7 | 0.645254 | 0.322627 | − | 0.946526i | \(-0.395434\pi\) | ||||
0.322627 | + | 0.946526i | \(0.395434\pi\) | |||||||
\(434\) | 3.51401e7 | + | 2.02882e7i | 0.429867 | + | 0.248184i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.54068e7 | + | 6.13263e7i | 0.427195 | + | 0.739924i | ||||
\(437\) | −9.22112e6 | + | 5.32382e6i | −0.110494 | + | 0.0637939i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.23044e7 | + | 1.25235e8i | −0.854616 | + | 1.48024i | 0.0223839 | + | 0.999749i | \(0.492874\pi\) |
−0.877000 | + | 0.480490i | \(0.840459\pi\) | |||||||
\(440\) | 6.46456e6i | 0.0758894i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.52249e7 | −1.10277 | ||||||||
\(443\) | −7.69878e7 | − | 4.44489e7i | −0.885545 | − | 0.511270i | −0.0130624 | − | 0.999915i | \(-0.504158\pi\) |
−0.872483 | + | 0.488645i | \(0.837491\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.13305e7 | − | 1.96250e7i | −0.128579 | − | 0.222705i | ||||
\(446\) | −6.06161e7 | + | 3.49967e7i | −0.683256 | + | 0.394478i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.35872e6 | + | 5.81747e6i | −0.0373542 | + | 0.0646994i | ||||
\(449\) | 9.48526e7i | 1.04788i | 0.851756 | + | 0.523939i | \(0.175538\pi\) | ||||
−0.851756 | + | 0.523939i | \(0.824462\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.41348e8 | 1.54085 | ||||||||
\(452\) | −1.23153e7 | − | 7.11026e6i | −0.133362 | − | 0.0769963i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.74167e7 | + | 3.01666e7i | 0.186122 | + | 0.322373i | ||||
\(455\) | −1.22985e7 | + | 7.10057e6i | −0.130563 | + | 0.0753805i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.90119e6 | − | 1.02212e7i | 0.0618288 | − | 0.107091i | −0.833454 | − | 0.552589i | \(-0.813640\pi\) |
0.895283 | + | 0.445498i | \(0.146973\pi\) | |||||||
\(458\) | − | 3.14402e7i | − | 0.327257i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.70458e6 | −0.0791544 | ||||||||
\(461\) | 1.28196e8 | + | 7.40142e7i | 1.30850 | + | 0.755461i | 0.981845 | − | 0.189684i | \(-0.0607462\pi\) |
0.326652 | + | 0.945145i | \(0.394080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.06114e7 | + | 5.30205e7i | 0.308418 | + | 0.534196i | 0.978017 | − | 0.208527i | \(-0.0668670\pi\) |
−0.669598 | + | 0.742724i | \(0.733534\pi\) | |||||||
\(464\) | 2.52232e7 | − | 1.45626e7i | 0.252492 | − | 0.145776i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.31580e7 | + | 5.74314e7i | −0.327666 | + | 0.567533i | ||||
\(467\) | − | 5.91925e7i | − | 0.581187i | −0.956847 | − | 0.290593i | \(-0.906147\pi\) | ||
0.956847 | − | 0.290593i | \(-0.0938527\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.38767e7 | −0.134514 | ||||||||
\(470\) | −8.62910e6 | − | 4.98201e6i | −0.0831136 | − | 0.0479857i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.36046e7 | − | 5.82049e7i | −0.319575 | − | 0.553520i | ||||
\(473\) | −5.70108e7 | + | 3.29152e7i | −0.538733 | + | 0.311038i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.08620e7 | − | 1.88135e7i | 0.101351 | − | 0.175545i | ||||
\(476\) | 5.41049e7i | 0.501667i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.99667e7 | −0.915317 | ||||||||
\(479\) | −5.31167e7 | − | 3.06669e7i | −0.483308 | − | 0.279038i | 0.238486 | − | 0.971146i | \(-0.423349\pi\) |
−0.721794 | + | 0.692108i | \(0.756682\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.88063e7 | − | 1.01856e8i | −0.528432 | − | 0.915270i | ||||
\(482\) | −1.05665e8 | + | 6.10058e7i | −0.943606 | + | 0.544791i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.06318e7 | − | 1.84149e7i | 0.0937717 | − | 0.162417i | ||||
\(485\) | − | 1.78582e7i | − | 0.156535i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.20027e8 | 1.03918 | 0.519592 | − | 0.854415i | \(-0.326084\pi\) | ||||
0.519592 | + | 0.854415i | \(0.326084\pi\) | |||||||
\(488\) | 9.60937e6 | + | 5.54797e6i | 0.0826866 | + | 0.0477392i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.25990e6 | − | 1.25745e7i | −0.0617082 | − | 0.106882i | ||||
\(491\) | −1.89139e8 | + | 1.09200e8i | −1.59786 | + | 0.922522i | −0.605956 | + | 0.795498i | \(0.707209\pi\) |
−0.991900 | + | 0.127024i | \(0.959457\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.17293e8 | − | 2.03158e8i | 0.978886 | − | 1.69548i | ||||
\(494\) | − | 1.73300e7i | − | 0.143753i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.58298e7 | −0.293629 | ||||||||
\(497\) | 9.04585e7 | + | 5.22262e7i | 0.736852 | + | 0.425422i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.59663e7 | + | 1.66219e8i | 0.772355 | + | 1.33776i | 0.936269 | + | 0.351284i | \(0.114255\pi\) |
−0.163914 | + | 0.986475i | \(0.552412\pi\) | |||||||
\(500\) | 2.83103e7 | − | 1.63450e7i | 0.226482 | − | 0.130760i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.28717e6 | − | 7.42559e6i | 0.0338890 | − | 0.0586976i | ||||
\(503\) | 2.12153e8i | 1.66704i | 0.552491 | + | 0.833519i | \(0.313678\pi\) | ||||
−0.552491 | + | 0.833519i | \(0.686322\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.02285e6 | −0.0234716 | ||||||||
\(506\) | −3.65650e7 | − | 2.11108e7i | −0.282237 | − | 0.162950i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.28765e6 | − | 9.15847e6i | −0.0403340 | − | 0.0698606i | ||||
\(509\) | −6.15952e6 | + | 3.55620e6i | −0.0467082 | + | 0.0269670i | −0.523172 | − | 0.852227i | \(-0.675252\pi\) |
0.476464 | + | 0.879194i | \(0.341918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.34583e7 | − | 7.52719e7i | 0.325694 | − | 0.564118i | ||||
\(512\) | − | 5.93164e6i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.55507e7 | −0.482712 | ||||||||
\(515\) | −8.38469e6 | − | 4.84090e6i | −0.0613854 | − | 0.0354409i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.73018e7 | − | 4.72881e7i | −0.197570 | − | 0.342201i | ||||
\(518\) | −5.78723e7 | + | 3.34126e7i | −0.416372 | + | 0.240392i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.26995e6 | − | 1.08599e7i | 0.0445917 | − | 0.0772351i | ||||
\(521\) | − | 2.39355e8i | − | 1.69251i | −0.532781 | − | 0.846253i | \(-0.678853\pi\) | ||
0.532781 | − | 0.846253i | \(-0.321147\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.44195e8 | 1.00796 | 0.503982 | − | 0.863714i | \(-0.331868\pi\) | ||||
0.503982 | + | 0.863714i | \(0.331868\pi\) | |||||||
\(524\) | 3.43828e7 | + | 1.98509e7i | 0.238972 | + | 0.137971i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.35302e7 | − | 1.27358e8i | −0.505253 | − | 0.875124i | ||||
\(527\) | −2.49923e8 | + | 1.44293e8i | −1.70756 | + | 0.985859i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.88577e7 | + | 8.46240e7i | −0.330039 | + | 0.571645i | ||||
\(530\) | − | 1.48190e7i | − | 0.0995383i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.84656e6 | −0.0653958 | ||||||||
\(533\) | −2.37452e8 | − | 1.37093e8i | −1.56817 | − | 0.905385i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.26869e7 | + | 3.92949e7i | 0.148154 | + | 0.256611i | ||||
\(536\) | 1.06117e7 | − | 6.12669e6i | 0.0689116 | − | 0.0397861i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.48224e7 | + | 4.29937e7i | −0.159403 | + | 0.276095i | ||||
\(539\) | − | 7.95697e7i | − | 0.508138i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.23812e8 | −1.41348 | −0.706742 | − | 0.707472i | \(-0.749836\pi\) | ||||
−0.706742 | + | 0.707472i | \(0.749836\pi\) | |||||||
\(542\) | 5.72172e7 | + | 3.30344e7i | 0.359359 | + | 0.207476i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.38879e7 | − | 4.13750e7i | −0.148382 | − | 0.257005i | ||||
\(545\) | −6.50464e7 | + | 3.75545e7i | −0.401822 | + | 0.231992i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.08691e8 | − | 1.88258e8i | 0.664097 | − | 1.15025i | −0.315432 | − | 0.948948i | \(-0.602149\pi\) |
0.979529 | − | 0.201302i | \(-0.0645172\pi\) | |||||||
\(548\) | 7.73000e7i | 0.469718i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.61433e7 | 0.517766 | ||||||||
\(551\) | 3.69727e7 | + | 2.13462e7i | 0.221018 | + | 0.127605i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.25221e7 | − | 1.25612e8i | −0.428840 | − | 0.742772i | ||||
\(554\) | −5.59611e7 | + | 3.23092e7i | −0.329122 | + | 0.190019i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.17423e7 | + | 1.41582e8i | −0.475579 | + | 0.823727i | ||||
\(557\) | 3.00003e8i | 1.73604i | 0.496528 | + | 0.868021i | \(0.334608\pi\) | ||||
−0.496528 | + | 0.868021i | \(0.665392\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.27697e8 | 0.731048 | ||||||||
\(560\) | −6.17036e6 | − | 3.56246e6i | −0.0351355 | − | 0.0202855i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.41543e7 | − | 5.91570e7i | −0.192414 | − | 0.333271i | ||||
\(563\) | 2.66439e8 | − | 1.53828e8i | 1.49304 | − | 0.862009i | 0.493074 | − | 0.869987i | \(-0.335873\pi\) |
0.999968 | + | 0.00797863i | \(0.00253971\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.54157e6 | − | 1.30624e7i | 0.0418135 | − | 0.0724231i | ||||
\(566\) | − | 2.20000e7i | − | 0.121331i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.22337e7 | −0.503321 | ||||||||
\(569\) | 2.44559e7 | + | 1.41196e7i | 0.132754 | + | 0.0766455i | 0.564906 | − | 0.825155i | \(-0.308912\pi\) |
−0.432152 | + | 0.901801i | \(0.642246\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.89628e7 | + | 1.71409e8i | 0.531574 | + | 0.920713i | 0.999321 | + | 0.0368506i | \(0.0117326\pi\) |
−0.467747 | + | 0.883862i | \(0.654934\pi\) | |||||||
\(572\) | 5.95130e7 | − | 3.43598e7i | 0.317997 | − | 0.183596i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.78934e7 | + | 1.34915e8i | −0.411875 | + | 0.713388i | ||||
\(575\) | 1.02667e8i | 0.540042i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.56557e8 | 0.814978 | 0.407489 | − | 0.913210i | \(-0.366405\pi\) | ||||
0.407489 | + | 0.913210i | \(0.366405\pi\) | |||||||
\(578\) | −2.15001e8 | − | 1.24131e8i | −1.11341 | − | 0.642830i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.54460e7 | + | 2.67533e7i | 0.0791649 | + | 0.137118i | ||||
\(581\) | −1.52849e8 | + | 8.82474e7i | −0.779353 | + | 0.449960i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.06045e7 | − | 7.03291e7i | 0.204913 | − | 0.354919i | ||||
\(584\) | 7.67491e7i | 0.385332i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.51112e8 | 0.750943 | ||||||||
\(587\) | −6.68861e6 | − | 3.86167e6i | −0.0330690 | − | 0.0190924i | 0.483374 | − | 0.875414i | \(-0.339411\pi\) |
−0.516443 | + | 0.856321i | \(0.672744\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.62600e7 | − | 4.54836e7i | −0.128514 | − | 0.222592i | ||||
\(590\) | 6.17356e7 | − | 3.56431e7i | 0.300594 | − | 0.173548i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.95040e7 | − | 5.11024e7i | 0.142205 | − | 0.246307i | ||||
\(593\) | 2.02243e8i | 0.969861i | 0.874553 | + | 0.484930i | \(0.161155\pi\) | ||||
−0.874553 | + | 0.484930i | \(0.838845\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.73869e7 | −0.272434 | ||||||||
\(596\) | 1.47408e8 | + | 8.51059e7i | 0.696276 | + | 0.401995i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.09506e7 | + | 7.09286e7i | 0.191495 | + | 0.331679i | ||||
\(599\) | 2.87407e8 | − | 1.65935e8i | 1.33726 | − | 0.772070i | 0.350863 | − | 0.936427i | \(-0.385888\pi\) |
0.986401 | + | 0.164357i | \(0.0525548\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.82333e7 | − | 8.35425e7i | 0.222190 | − | 0.384844i | −0.733283 | − | 0.679924i | \(-0.762013\pi\) |
0.955473 | + | 0.295080i | \(0.0953463\pi\) | |||||||
\(602\) | − | 7.25550e7i | − | 0.332566i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.58943e8 | 0.721326 | ||||||||
\(605\) | 1.95319e7 | + | 1.12768e7i | 0.0882020 | + | 0.0509235i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.42770e7 | + | 1.45972e8i | 0.376828 | + | 0.652685i | 0.990599 | − | 0.136799i | \(-0.0436815\pi\) |
−0.613771 | + | 0.789484i | \(0.710348\pi\) | |||||||
\(608\) | 7.52985e6 | − | 4.34736e6i | 0.0335024 | − | 0.0193426i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.88451e6 | + | 1.01923e7i | −0.0259251 | + | 0.0449036i | ||||
\(611\) | 1.05920e8i | 0.464358i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.19543e8 | −1.38723 | −0.693614 | − | 0.720347i | \(-0.743983\pi\) | ||||
−0.693614 | + | 0.720347i | \(0.743983\pi\) | |||||||
\(614\) | −8.80416e7 | − | 5.08308e7i | −0.380349 | − | 0.219595i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.95226e7 | − | 3.38141e7i | −0.0835208 | − | 0.144662i | ||||
\(617\) | 1.87744e8 | − | 1.08394e8i | 0.799301 | − | 0.461477i | −0.0439255 | − | 0.999035i | \(-0.513986\pi\) |
0.843227 | + | 0.537558i | \(0.180653\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.37724e8 | + | 2.38546e8i | −0.580683 | + | 1.00577i | 0.414716 | + | 0.909951i | \(0.363881\pi\) |
−0.995399 | + | 0.0958210i | \(0.969452\pi\) | |||||||
\(620\) | − | 3.80032e7i | − | 0.159458i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.34543e8 | −0.974655 | ||||||||
\(623\) | 1.18532e8 | + | 6.84347e7i | 0.490200 | + | 0.283017i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.57339e7 | − | 1.65816e8i | −0.392126 | − | 0.679182i | ||||
\(626\) | 1.10786e7 | − | 6.39621e6i | 0.0451607 | − | 0.0260735i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.32192e7 | − | 2.28964e7i | 0.0533737 | − | 0.0924460i | ||||
\(629\) | − | 4.75273e8i | − | 1.90982i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.56044e8 | −1.01912 | −0.509562 | − | 0.860434i | \(-0.670192\pi\) | ||||
−0.509562 | + | 0.860434i | \(0.670192\pi\) | |||||||
\(632\) | 1.10918e8 | + | 6.40386e7i | 0.439391 | + | 0.253682i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.22216e7 | + | 5.58095e7i | 0.126439 | + | 0.218998i | ||||
\(635\) | 9.71403e6 | − | 5.60840e6i | 0.0379383 | − | 0.0219037i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.71743e7 | + | 1.33670e8i | −0.298576 | + | 0.517148i | ||||
\(638\) | 1.69291e8i | 0.651885i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.29146e6 | 0.0240000 | ||||||||
\(641\) | −1.37601e8 | − | 7.94439e7i | −0.522453 | − | 0.301638i | 0.215485 | − | 0.976507i | \(-0.430867\pi\) |
−0.737938 | + | 0.674869i | \(0.764200\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.57338e8 | + | 2.72517e8i | 0.591833 | + | 1.02509i | 0.993985 | + | 0.109513i | \(0.0349290\pi\) |
−0.402152 | + | 0.915573i | \(0.631738\pi\) | |||||||
\(644\) | 4.03002e7 | − | 2.32673e7i | 0.150886 | − | 0.0871142i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.50153e7 | − | 6.06483e7i | 0.129885 | − | 0.224968i | ||||
\(647\) | − | 5.06718e8i | − | 1.87091i | −0.353442 | − | 0.935457i | \(-0.614989\pi\) | ||
0.353442 | − | 0.935457i | \(-0.385011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.90654e8 | 1.42908 | ||||||||
\(650\) | −1.44713e8 | − | 8.35500e7i | −0.526947 | − | 0.304233i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.04256e7 | + | 5.26988e7i | 0.109773 | + | 0.190133i | ||||
\(653\) | 2.86560e8 | − | 1.65445e8i | 1.02914 | − | 0.594176i | 0.112404 | − | 0.993663i | \(-0.464145\pi\) |
0.916739 | + | 0.399487i | \(0.130812\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.10551e7 | + | 3.64685e7i | −0.0749262 | + | 0.129776i | ||||
\(656\) | − | 1.37563e8i | − | 0.487293i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.01814e7 | 0.211244 | ||||||||
\(659\) | 1.25671e8 | + | 7.25563e7i | 0.439116 | + | 0.253524i | 0.703223 | − | 0.710970i | \(-0.251744\pi\) |
−0.264106 | + | 0.964494i | \(0.585077\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.58816e7 | + | 6.21488e7i | 0.124242 | + | 0.215193i | 0.921436 | − | 0.388529i | \(-0.127017\pi\) |
−0.797195 | + | 0.603722i | \(0.793684\pi\) | |||||||
\(662\) | −6.89175e7 | + | 3.97896e7i | −0.237550 | + | 0.137150i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.79244e7 | − | 1.34969e8i | 0.266176 | − | 0.461030i | ||||
\(665\) | − | 1.04439e7i | − | 0.0355137i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.01764e8 | −0.679932 | ||||||||
\(668\) | 1.61853e8 | + | 9.34456e7i | 0.542988 | + | 0.313494i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.49834e6 | + | 1.12554e7i | 0.0216062 | + | 0.0374230i | ||||
\(671\) | −5.58545e7 | + | 3.22476e7i | −0.184880 | + | 0.106741i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.76558e8 | + | 4.79013e8i | −0.907281 | + | 1.57146i | −0.0894545 | + | 0.995991i | \(0.528512\pi\) |
−0.817826 | + | 0.575465i | \(0.804821\pi\) | |||||||
\(674\) | − | 2.71066e8i | − | 0.885310i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.11561e7 | 0.0684850 | ||||||||
\(677\) | 2.69501e8 | + | 1.55596e8i | 0.868548 | + | 0.501456i | 0.866865 | − | 0.498542i | \(-0.166131\pi\) |
0.00168257 | + | 0.999999i | \(0.499464\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.39305e7 | + | 9.34103e7i | 0.172276 | + | 0.298391i | ||||
\(680\) | 4.38848e7 | − | 2.53369e7i | 0.139569 | − | 0.0805799i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.04130e8 | − | 1.80359e8i | 0.328264 | − | 0.568571i | ||||
\(683\) | 6.40636e7i | 0.201071i | 0.994933 | + | 0.100535i | \(0.0320556\pi\) | ||||
−0.994933 | + | 0.100535i | \(0.967944\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.19890e7 | −0.255084 | ||||||||
\(686\) | 1.94102e8 | + | 1.12065e8i | 0.601254 | + | 0.347134i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.20338e7 | + | 5.54842e7i | 0.0983656 | + | 0.170374i | ||||
\(689\) | −1.36424e8 | + | 7.87644e7i | −0.417093 | + | 0.240809i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.16895e7 | + | 2.02469e7i | −0.0354293 | + | 0.0613654i | −0.883196 | − | 0.469003i | \(-0.844613\pi\) |
0.847767 | + | 0.530369i | \(0.177947\pi\) | |||||||
\(692\) | − | 1.23906e8i | − | 0.373917i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.40505e8 | 0.719523 | ||||||||
\(695\) | −1.50170e8 | − | 8.67008e7i | −0.447331 | − | 0.258267i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.53993e8 | − | 9.59545e8i | −1.63609 | − | 2.83378i | ||||
\(698\) | 3.98774e8 | − | 2.30233e8i | 1.17263 | − | 0.677018i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.74714e7 | + | 8.22229e7i | −0.138401 | + | 0.239717i | ||||
\(701\) | − | 4.68576e8i | − | 1.36027i | −0.733086 | − | 0.680136i | \(-0.761921\pi\) | ||
0.733086 | − | 0.680136i | \(-0.238079\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.64951e7 | 0.248958 | ||||||||
\(704\) | 2.98585e7 | + | 1.72388e7i | 0.0855757 | + | 0.0494072i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.07845e8 | + | 1.86793e8i | 0.306469 | + | 0.530820i | ||||
\(707\) | 1.58116e7 | − | 9.12881e6i | 0.0447421 | − | 0.0258319i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.00513e7 | − | 1.38653e8i | 0.224610 | − | 0.389037i | −0.731592 | − | 0.681743i | \(-0.761222\pi\) |
0.956202 | + | 0.292706i | \(0.0945557\pi\) | |||||||
\(710\) | − | 9.78286e7i | − | 0.273332i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.20859e8 | −0.334840 | ||||||||
\(713\) | 2.14955e8 | + | 1.24104e8i | 0.593033 | + | 0.342387i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.64441e7 | + | 6.31230e7i | 0.0997032 | + | 0.172691i | ||||
\(716\) | −9.01513e7 | + | 5.20489e7i | −0.245602 | + | 0.141799i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.99217e8 | − | 3.45055e8i | 0.538213 | − | 0.932212i | ||||
\(719\) | − | 5.03559e7i | − | 0.135477i | −0.997703 | − | 0.0677383i | \(-0.978422\pi\) | ||
0.997703 | − | 0.0677383i | \(-0.0215783\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.84769e7 | 0.156019 | ||||||||
\(722\) | −2.19439e8 | − | 1.26693e8i | −0.583046 | − | 0.336622i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.72976e7 | + | 1.33883e8i | 0.203681 | + | 0.352786i | ||||
\(725\) | 3.56500e8 | − | 2.05825e8i | 0.935504 | − | 0.540113i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.20132e7 | + | 1.42051e8i | −0.213442 | + | 0.369693i | −0.952790 | − | 0.303631i | \(-0.901801\pi\) |
0.739347 | + | 0.673324i | \(0.235134\pi\) | |||||||
\(728\) | 7.57394e7i | 0.196303i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.14047e7 | −0.209258 | ||||||||
\(731\) | 4.46891e8 | + | 2.58013e8i | 1.14406 | + | 0.660524i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.30100e7 | − | 7.44956e7i | −0.109209 | − | 0.189155i | 0.806241 | − | 0.591587i | \(-0.201498\pi\) |
−0.915450 | + | 0.402432i | \(0.868165\pi\) | |||||||
\(734\) | −1.89588e8 | + | 1.09459e8i | −0.479428 | + | 0.276798i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.05455e7 | + | 3.55859e7i | −0.0515328 | + | 0.0892575i | ||||
\(737\) | 7.12228e7i | 0.177917i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.22107e8 | 0.550338 | 0.275169 | − | 0.961396i | \(-0.411266\pi\) | ||||
0.275169 | + | 0.961396i | \(0.411266\pi\) | |||||||
\(740\) | 5.42023e7 | + | 3.12937e7i | 0.133759 | + | 0.0772257i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.47523e7 | + | 7.75133e7i | 0.109548 | + | 0.189742i | ||||
\(743\) | −1.59614e8 | + | 9.21532e7i | −0.389139 | + | 0.224669i | −0.681787 | − | 0.731551i | \(-0.738797\pi\) |
0.292648 | + | 0.956220i | \(0.405464\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.02684e7 | + | 1.56349e8i | −0.218307 | + | 0.378118i | ||||
\(746\) | 3.26266e8i | 0.785878i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.77697e8 | 0.663538 | ||||||||
\(749\) | −2.37336e8 | − | 1.37026e8i | −0.564831 | − | 0.326105i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.30919e8 | + | 2.26758e8i | 0.309088 | + | 0.535357i | 0.978163 | − | 0.207838i | \(-0.0666428\pi\) |
−0.669075 | + | 0.743195i | \(0.733309\pi\) | |||||||
\(752\) | −4.60219e7 | + | 2.65707e7i | −0.108221 | + | 0.0624813i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.64194e8 | − | 2.84393e8i | 0.383040 | − | 0.663445i | ||||
\(755\) | 1.68585e8i | 0.391722i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.61933e8 | −1.52590 | −0.762951 | − | 0.646456i | \(-0.776250\pi\) | ||||
−0.762951 | + | 0.646456i | \(0.776250\pi\) | |||||||
\(758\) | 2.18015e8 | + | 1.25871e8i | 0.500587 | + | 0.289014i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.61107e6 | + | 7.98661e6i | 0.0105042 | + | 0.0181937i | ||||
\(761\) | 1.70270e8 | − | 9.83054e7i | 0.386353 | − | 0.223061i | −0.294226 | − | 0.955736i | \(-0.595062\pi\) |
0.680579 | + | 0.732675i | \(0.261728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.26825e8 | − | 3.92872e8i | 0.510642 | − | 0.884458i | ||||
\(764\) | 6.37843e7i | 0.143032i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.12004e8 | 1.36166 | ||||||||
\(767\) | −6.56262e8 | − | 3.78893e8i | −1.45443 | − | 0.839713i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.15557e7 | − | 8.92971e7i | −0.113370 | − | 0.196362i | 0.803757 | − | 0.594958i | \(-0.202831\pi\) |
−0.917127 | + | 0.398595i | \(0.869498\pi\) | |||||||
\(770\) | 3.58652e7 | − | 2.07068e7i | 0.0785600 | − | 0.0453566i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.85763e8 | − | 3.21751e8i | 0.403745 | − | 0.699307i | ||||
\(773\) | 6.91840e8i | 1.49785i | 0.662657 | + | 0.748923i | \(0.269429\pi\) | ||||
−0.662657 | + | 0.748923i | \(0.730571\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.06410e8 | −1.08792 | ||||||||
\(776\) | −8.24833e7 | − | 4.76218e7i | −0.176515 | − | 0.101911i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.42197e7 | − | 4.19498e7i | −0.0514317 | − | 0.0890823i | ||||
\(779\) | 1.74628e8 | − | 1.00821e8i | 0.369403 | − | 0.213275i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.68054e8 | − | 4.64284e8i | 0.562691 | − | 0.974609i | ||||
\(782\) | 3.30963e8i | 0.692086i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.74390e7 | −0.160698 | ||||||||
\(785\) | 2.42853e7 | + | 1.40211e7i | 0.0502035 | + | 0.0289850i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.98954e8 | − | 5.17803e8i | −0.613310 | − | 1.06228i | −0.990678 | − | 0.136221i | \(-0.956504\pi\) |
0.377368 | − | 0.926063i | \(-0.376829\pi\) | |||||||
\(788\) | 1.28119e8 | − | 7.39694e7i | 0.261839 | − | 0.151173i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.79232e7 | + | 1.17646e8i | −0.137764 | + | 0.238615i | ||||
\(791\) | 9.11002e7i | 0.184073i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.25107e8 | 0.250878 | ||||||||
\(794\) | −3.96440e8 | − | 2.28884e8i | −0.791982 | − | 0.457251i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.44627e8 | − | 2.50500e8i | −0.286753 | − | 0.496672i | ||||
\(797\) | −4.56600e8 | + | 2.63618e8i | −0.901906 | + | 0.520716i | −0.877818 | − | 0.478994i | \(-0.841002\pi\) |
−0.0240879 | + | 0.999710i | \(0.507668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.14011e8 | + | 3.70678e8i | −0.419562 | + | 0.726702i | ||||
\(800\) | − | 8.38366e7i | − | 0.163743i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.84905e8 | 0.552302 | ||||||||
\(803\) | −3.86338e8 | − | 2.23052e8i | −0.746140 | − | 0.430784i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.46787e7 | + | 4.27448e7i | 0.0473080 | + | 0.0819399i | ||||
\(806\) | −3.49859e8 | + | 2.01991e8i | −0.668171 | + | 0.385769i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.06093e6 | + | 1.39619e7i | −0.0152810 | + | 0.0264674i | ||||
\(809\) | 4.15867e8i | 0.785433i | 0.919660 | + | 0.392717i | \(0.128465\pi\) | ||||
−0.919660 | + | 0.392717i | \(0.871535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.91737e7 | 0.167176 | 0.0835880 | − | 0.996500i | \(-0.473362\pi\) | ||||
0.0835880 | + | 0.996500i | \(0.473362\pi\) | |||||||
\(812\) | −1.61586e8 | − | 9.32919e7i | −0.301812 | − | 0.174251i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.71492e8 | + | 2.97033e8i | 0.317959 | + | 0.550721i | ||||
\(815\) | −5.58955e7 | + | 3.22713e7i | −0.103253 | + | 0.0596133i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.69558e7 | + | 8.13298e7i | −0.0861039 | + | 0.149136i | ||||
\(818\) | − | 3.52193e8i | − | 0.643458i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.45908e8 | 0.264629 | ||||||||
\(821\) | −1.37118e8 | − | 7.91654e7i | −0.247780 | − | 0.143056i | 0.370967 | − | 0.928646i | \(-0.379026\pi\) |
−0.618747 | + | 0.785590i | \(0.712360\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.02933e8 | + | 5.24695e8i | 0.543434 | + | 0.941255i | 0.998704 | + | 0.0509014i | \(0.0162094\pi\) |
−0.455270 | + | 0.890353i | \(0.650457\pi\) | |||||||
\(824\) | −4.47184e7 | + | 2.58182e7i | −0.0799290 | + | 0.0461470i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.15280e8 | + | 3.72875e8i | −0.381999 | + | 0.661642i | ||||
\(827\) | 4.44267e7i | 0.0785466i | 0.999229 | + | 0.0392733i | \(0.0125043\pi\) | ||||
−0.999229 | + | 0.0392733i | \(0.987496\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.98743e8 | −0.524365 | −0.262183 | − | 0.965018i | \(-0.584442\pi\) | ||||
−0.262183 | + | 0.965018i | \(0.584442\pi\) | |||||||
\(830\) | 1.43156e8 | + | 8.26513e7i | 0.250366 | + | 0.144549i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.34397e7 | − | 5.79193e7i | −0.0580621 | − | 0.100567i | ||||
\(833\) | −5.40160e8 | + | 3.11862e8i | −0.934518 | + | 0.539544i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.91140e7 | + | 1.71671e8i | −0.170246 | + | 0.294874i | ||||
\(836\) | 5.05381e7i | 0.0864967i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.74532e7 | −0.114623 | ||||||||
\(839\) | 2.41704e8 | + | 1.39548e8i | 0.409260 | + | 0.236286i | 0.690472 | − | 0.723360i | \(-0.257403\pi\) |
−0.281212 | + | 0.959646i | \(0.590736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.07081e8 | + | 1.85470e8i | 0.180021 | + | 0.311806i | ||||
\(842\) | 2.74368e8 | − | 1.58407e8i | 0.459619 | − | 0.265361i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.75254e8 | + | 3.03548e8i | −0.291501 | + | 0.504894i | ||||
\(845\) | 2.24394e7i | 0.0371913i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.36220e8 | −0.224177 | ||||||||
\(848\) | −6.84459e7 | − | 3.95172e7i | −0.112243 | − | 0.0648036i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.37626e8 | − | 5.84786e8i | −0.549768 | − | 0.952226i | ||||
\(851\) | −3.54009e8 | + | 2.04387e8i | −0.574415 | + | 0.331638i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.22254e8 | + | 2.11750e8i | −0.196977 | + | 0.341174i | −0.947547 | − | 0.319617i | \(-0.896446\pi\) |
0.750570 | + | 0.660791i | \(0.229779\pi\) | |||||||
\(854\) | − | 7.10834e7i | − | 0.114129i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.41994e8 | 0.385818 | ||||||||
\(857\) | 2.33813e8 | + | 1.34992e8i | 0.371473 | + | 0.214470i | 0.674102 | − | 0.738639i | \(-0.264531\pi\) |
−0.302629 | + | 0.953108i | \(0.597864\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.88616e6 | − | 1.19272e7i | −0.0108642 | − | 0.0188173i | 0.860542 | − | 0.509379i | \(-0.170125\pi\) |
−0.871406 | + | 0.490562i | \(0.836792\pi\) | |||||||
\(860\) | −5.88498e7 | + | 3.39770e7i | −0.0925230 | + | 0.0534182i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.23594e6 | + | 1.42651e7i | −0.0128585 | + | 0.0222716i | ||||
\(863\) | 4.03111e8i | 0.627180i | 0.949559 | + | 0.313590i | \(0.101532\pi\) | ||||
−0.949559 | + | 0.313590i | \(0.898468\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.31422e8 | 0.203059 | ||||||||
\(866\) | 2.56625e8 | + | 1.48163e8i | 0.395136 | + | 0.228132i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.14767e8 | + | 1.98783e8i | 0.175493 | + | 0.303962i | ||||
\(869\) | −6.44711e8 | + | 3.72224e8i | −0.982440 | + | 0.567212i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.90787e7 | − | 1.19648e8i | 0.104542 | − | 0.181072i | ||||
\(872\) | 4.00582e8i | 0.604146i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.02321e7 | −0.0902181 | ||||||||
\(875\) | −1.81363e8 | − | 1.04710e8i | −0.270722 | − | 0.156302i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.24825e8 | + | 3.89408e8i | 0.333308 | + | 0.577306i | 0.983158 | − | 0.182756i | \(-0.0585019\pi\) |
−0.649851 | + | 0.760062i | \(0.725169\pi\) | |||||||
\(878\) | −7.08436e8 | + | 4.09016e8i | −1.04669 | + | 0.604305i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.82845e7 | + | 3.16698e7i | −0.0268310 | + | 0.0464726i | ||||
\(881\) | − | 1.62295e7i | − | 0.0237344i | −0.999930 | − | 0.0118672i | \(-0.996222\pi\) | ||
0.999930 | − | 0.0118672i | \(-0.00377753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.08844e8 | −0.303347 | −0.151673 | − | 0.988431i | \(-0.548466\pi\) | ||||
−0.151673 | + | 0.988431i | \(0.548466\pi\) | |||||||
\(884\) | −4.66505e8 | − | 2.69337e8i | −0.675304 | − | 0.389887i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.51441e8 | − | 4.35509e8i | −0.361522 | − | 0.626175i | ||||
\(887\) | 4.93999e6 | − | 2.85211e6i | 0.00707873 | − | 0.00408691i | −0.496456 | − | 0.868062i | \(-0.665366\pi\) |
0.503535 | + | 0.863975i | \(0.332032\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.38740e7 | + | 5.86715e7i | −0.0482127 | + | 0.0835068i | ||||
\(890\) | − | 1.28190e8i | − | 0.181838i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.95942e8 | −0.557876 | ||||||||
\(893\) | −6.74598e7 | − | 3.89479e7i | −0.0947307 | − | 0.0546928i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.52061e7 | − | 9.56198e7i | −0.0770049 | − | 0.133376i | ||||
\(896\) | −3.29086e7 | + | 1.89998e7i | −0.0457494 | + | 0.0264134i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.68284e8 | + | 4.64681e8i | −0.370481 | + | 0.641691i | ||||
\(899\) | − | 9.95209e8i | − | 1.36973i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.36574e8 | −0.870312 | ||||||||
\(902\) | 6.92461e8 | + | 3.99793e8i | 0.943574 | + | 0.544773i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.02217e7 | − | 6.96660e7i | −0.0544446 | − | 0.0943009i | ||||
\(905\) | −1.42005e8 | + | 8.19865e7i | −0.191583 | + | 0.110611i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.61190e7 | − | 1.14521e8i | 0.0886144 | − | 0.153485i | −0.818311 | − | 0.574775i | \(-0.805089\pi\) |
0.906926 | + | 0.421291i | \(0.138423\pi\) | |||||||
\(908\) | 1.97048e8i | 0.263217i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.03338e7 | −0.106604 | ||||||||
\(911\) | 7.94695e8 | + | 4.58817e8i | 1.05110 | + | 0.606854i | 0.922958 | − | 0.384901i | \(-0.125764\pi\) |
0.128145 | + | 0.991755i | \(0.459098\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.52935e8 | + | 7.84507e8i | 0.595146 | + | 1.03082i | ||||
\(914\) | 5.78196e7 | − | 3.33822e7i | 0.0757245 | − | 0.0437196i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.89264e7 | − | 1.54025e8i | 0.115703 | − | 0.200403i | ||||
\(917\) | − | 2.54340e8i | − | 0.329843i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.69732e8 | 0.734047 | 0.367024 | − | 0.930212i | \(-0.380377\pi\) | ||||
0.367024 | + | 0.930212i | \(0.380377\pi\) | |||||||
\(920\) | −3.77446e7 | − | 2.17918e7i | −0.0484720 | − | 0.0279853i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.18687e8 | + | 7.25188e8i | 0.534192 | + | 0.925247i | ||||
\(923\) | −9.00613e8 | + | 5.19969e8i | −1.14534 | + | 0.661261i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.17003e8 | − | 7.22271e8i | 0.526883 | − | 0.912588i | ||||
\(926\) | 3.46329e8i | 0.436170i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.64758e8 | 0.206159 | ||||||||
\(929\) | −7.11434e8 | − | 4.10746e8i | −0.887334 | − | 0.512303i | −0.0142647 | − | 0.999898i | \(-0.504541\pi\) |
−0.873070 | + | 0.487596i | \(0.837874\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.67558e7 | − | 9.83040e7i | −0.0703333 | − | 0.121821i | ||||
\(932\) | −3.24881e8 | + | 1.87570e8i | −0.401307 | + | 0.231695i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.67422e8 | − | 2.89983e8i | 0.205481 | − | 0.355903i | ||||
\(935\) | 2.94542e8i | 0.360339i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.62725e8 | 0.805591 | 0.402796 | − | 0.915290i | \(-0.368039\pi\) | ||||
0.402796 | + | 0.915290i | \(0.368039\pi\) | |||||||
\(938\) | −6.79814e7 | − | 3.92491e7i | −0.0823724 | − | 0.0475577i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.81825e7 | − | 4.88136e7i | −0.0339310 | − | 0.0587702i | ||||
\(941\) | 1.11503e8 | − | 6.43765e7i | 0.133819 | − | 0.0772607i | −0.431596 | − | 0.902067i | \(-0.642049\pi\) |
0.565415 | + | 0.824806i | \(0.308716\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.76480e8 | + | 8.25287e8i | −0.568211 | + | 0.984170i | ||||
\(944\) | − | 3.80193e8i | − | 0.451947i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.72393e8 | −0.439874 | ||||||||
\(947\) | −2.13619e8 | − | 1.23333e8i | −0.251530 | − | 0.145221i | 0.368934 | − | 0.929455i | \(-0.379723\pi\) |
−0.620465 | + | 0.784234i | \(0.713056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.32675e8 | + | 7.49414e8i | 0.506247 | + | 0.876846i | ||||
\(950\) | 1.06425e8 | − | 6.14447e7i | 0.124129 | − | 0.0716660i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.53032e8 | + | 2.65059e8i | −0.177366 | + | 0.307207i | ||||
\(953\) | 2.79388e8i | 0.322797i | 0.986889 | + | 0.161398i | \(0.0516004\pi\) | ||||
−0.986889 | + | 0.161398i | \(0.948400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.76535e7 | −0.0776748 | ||||||||
\(956\) | −4.89735e8 | − | 2.82749e8i | −0.560515 | − | 0.323614i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.73478e8 | − | 3.00473e8i | −0.197310 | − | 0.341751i | ||||
\(959\) | 4.28858e8 | − | 2.47601e8i | 0.486248 | − | 0.280736i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.68398e8 | + | 2.91674e8i | −0.189744 | + | 0.328646i | ||||
\(962\) | − | 6.65317e8i | − | 0.747315i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.90202e8 | −0.770451 | ||||||||
\(965\) | 3.41269e8 | + | 1.97031e8i | 0.379764 | + | 0.219257i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.25321e8 | − | 1.25629e9i | −0.802142 | − | 1.38935i | −0.918204 | − | 0.396108i | \(-0.870361\pi\) |
0.116062 | − | 0.993242i | \(-0.462973\pi\) | |||||||
\(968\) | 1.04170e8 | − | 6.01427e7i | 0.114846 | − | 0.0663066i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.05105e7 | − | 8.74867e7i | 0.0553435 | − | 0.0958577i | ||||
\(971\) | 1.50823e9i | 1.64744i | 0.566999 | + | 0.823719i | \(0.308104\pi\) | ||||
−0.566999 | + | 0.823719i | \(0.691896\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.04732e9 | 1.13695 | ||||||||
\(974\) | 5.88010e8 | + | 3.39488e8i | 0.636368 | + | 0.367407i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.13841e7 | + | 5.43588e7i | 0.0337567 | + | 0.0584683i | ||||
\(977\) | 1.05626e9 | − | 6.09831e8i | 1.13263 | − | 0.653922i | 0.188032 | − | 0.982163i | \(-0.439789\pi\) |
0.944594 | + | 0.328241i | \(0.106456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.51245e8 | − | 6.08375e8i | 0.374337 | − | 0.648370i | ||||
\(980\) | − | 8.21364e7i | − | 0.0872685i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.23545e9 | −1.30464 | ||||||||
\(983\) | 8.80047e8 | + | 5.08095e8i | 0.926499 | + | 0.534915i | 0.885703 | − | 0.464253i | \(-0.153677\pi\) |
0.0407967 | + | 0.999167i | \(0.487010\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.84564e7 | + | 1.35890e8i | 0.0820955 | + | 0.142194i | ||||
\(986\) | 1.14923e9 | − | 6.63510e8i | 1.19889 | − | 0.692177i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.90167e7 | − | 8.48993e7i | 0.0508245 | − | 0.0880306i | ||||
\(989\) | − | 4.43824e8i | − | 0.458799i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.53703e8 | 0.774425 | 0.387213 | − | 0.921990i | \(-0.373438\pi\) | ||||
0.387213 | + | 0.921990i | \(0.373438\pi\) | |||||||
\(992\) | −1.75529e8 | − | 1.01342e8i | −0.179810 | − | 0.103814i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.95436e8 | + | 5.11710e8i | 0.300818 | + | 0.521033i | ||||
\(995\) | 2.65696e8 | − | 1.53400e8i | 0.269721 | − | 0.155724i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.09571e8 | − | 7.09398e8i | 0.413280 | − | 0.715822i | −0.581966 | − | 0.813213i | \(-0.697716\pi\) |
0.995246 | + | 0.0973913i | \(0.0310498\pi\) | |||||||
\(998\) | 1.08573e9i | 1.09228i | ||||||||
\(999\) | 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 | 162.7.d.c.107.2 | 4 | ||
3.2 | odd | 2 | inner | 162.7.d.c.107.1 | 4 | ||
9.2 | odd | 6 | 54.7.b.a.53.2 | yes | 2 | ||
9.4 | even | 3 | inner | 162.7.d.c.53.1 | 4 | ||
9.5 | odd | 6 | inner | 162.7.d.c.53.2 | 4 | ||
9.7 | even | 3 | 54.7.b.a.53.1 | ✓ | 2 | ||
36.7 | odd | 6 | 432.7.e.f.161.1 | 2 | |||
36.11 | even | 6 | 432.7.e.f.161.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.7.b.a.53.1 | ✓ | 2 | 9.7 | even | 3 | ||
54.7.b.a.53.2 | yes | 2 | 9.2 | odd | 6 | ||
162.7.d.c.53.1 | 4 | 9.4 | even | 3 | inner | ||
162.7.d.c.53.2 | 4 | 9.5 | odd | 6 | inner | ||
162.7.d.c.107.1 | 4 | 3.2 | odd | 2 | inner | ||
162.7.d.c.107.2 | 4 | 1.1 | even | 1 | trivial | ||
432.7.e.f.161.1 | 2 | 36.7 | odd | 6 | |||
432.7.e.f.161.2 | 2 | 36.11 | even | 6 |