Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,4,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, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("294.67");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
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: | \(17.3465615417\) |
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 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.67 |
Dual form | 294.4.e.e.79.1 |
$q$-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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | −7.50000 | − | 12.9904i | −0.670820 | − | 1.16190i | −0.977672 | − | 0.210138i | \(-0.932609\pi\) |
0.306851 | − | 0.951757i | \(-0.400725\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 15.0000 | − | 25.9808i | 0.474342 | − | 0.821584i | ||||
\(11\) | 4.50000 | − | 7.79423i | 0.123346 | − | 0.213641i | −0.797739 | − | 0.603002i | \(-0.793971\pi\) |
0.921085 | + | 0.389362i | \(0.127304\pi\) | |||||||
\(12\) | −6.00000 | − | 10.3923i | −0.144338 | − | 0.250000i | ||||
\(13\) | 88.0000 | 1.87745 | 0.938723 | − | 0.344671i | \(-0.112010\pi\) | ||||
0.938723 | + | 0.344671i | \(0.112010\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 45.0000 | 0.774597 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −42.0000 | + | 72.7461i | −0.599206 | + | 1.03785i | 0.393733 | + | 0.919225i | \(0.371183\pi\) |
−0.992939 | + | 0.118630i | \(0.962150\pi\) | |||||||
\(18\) | 9.00000 | − | 15.5885i | 0.117851 | − | 0.204124i | ||||
\(19\) | 52.0000 | + | 90.0666i | 0.627875 | + | 1.08751i | 0.987977 | + | 0.154598i | \(0.0494083\pi\) |
−0.360103 | + | 0.932913i | \(0.617258\pi\) | |||||||
\(20\) | 60.0000 | 0.670820 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.0000 | 0.174437 | ||||||||
\(23\) | 42.0000 | + | 72.7461i | 0.380765 | + | 0.659505i | 0.991172 | − | 0.132583i | \(-0.0423272\pi\) |
−0.610406 | + | 0.792088i | \(0.708994\pi\) | |||||||
\(24\) | 12.0000 | − | 20.7846i | 0.102062 | − | 0.176777i | ||||
\(25\) | −50.0000 | + | 86.6025i | −0.400000 | + | 0.692820i | ||||
\(26\) | 88.0000 | + | 152.420i | 0.663778 | + | 1.14970i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 51.0000 | 0.326568 | 0.163284 | − | 0.986579i | \(-0.447791\pi\) | ||||
0.163284 | + | 0.986579i | \(0.447791\pi\) | |||||||
\(30\) | 45.0000 | + | 77.9423i | 0.273861 | + | 0.474342i | ||||
\(31\) | 92.5000 | − | 160.215i | 0.535919 | − | 0.928239i | −0.463199 | − | 0.886254i | \(-0.653299\pi\) |
0.999118 | − | 0.0419848i | \(-0.0133681\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 13.5000 | + | 23.3827i | 0.0712136 | + | 0.123346i | ||||
\(34\) | −168.000 | −0.847405 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −22.0000 | − | 38.1051i | −0.0977507 | − | 0.169309i | 0.813003 | − | 0.582260i | \(-0.197831\pi\) |
−0.910753 | + | 0.412951i | \(0.864498\pi\) | |||||||
\(38\) | −104.000 | + | 180.133i | −0.443974 | + | 0.768986i | ||||
\(39\) | −132.000 | + | 228.631i | −0.541972 | + | 0.938723i | ||||
\(40\) | 60.0000 | + | 103.923i | 0.237171 | + | 0.410792i | ||||
\(41\) | 168.000 | 0.639932 | 0.319966 | − | 0.947429i | \(-0.396329\pi\) | ||||
0.319966 | + | 0.947429i | \(0.396329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 326.000 | 1.15615 | 0.578076 | − | 0.815983i | \(-0.303804\pi\) | ||||
0.578076 | + | 0.815983i | \(0.303804\pi\) | |||||||
\(44\) | 18.0000 | + | 31.1769i | 0.0616728 | + | 0.106820i | ||||
\(45\) | −67.5000 | + | 116.913i | −0.223607 | + | 0.387298i | ||||
\(46\) | −84.0000 | + | 145.492i | −0.269242 | + | 0.466341i | ||||
\(47\) | −69.0000 | − | 119.512i | −0.214142 | − | 0.370905i | 0.738865 | − | 0.673854i | \(-0.235362\pi\) |
−0.953007 | + | 0.302949i | \(0.902029\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −200.000 | −0.565685 | ||||||||
\(51\) | −126.000 | − | 218.238i | −0.345952 | − | 0.599206i | ||||
\(52\) | −176.000 | + | 304.841i | −0.469362 | + | 0.812958i | ||||
\(53\) | −319.500 | + | 553.390i | −0.828051 | + | 1.43423i | 0.0715141 | + | 0.997440i | \(0.477217\pi\) |
−0.899565 | + | 0.436787i | \(0.856116\pi\) | |||||||
\(54\) | 27.0000 | + | 46.7654i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −135.000 | −0.330971 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −312.000 | −0.725007 | ||||||||
\(58\) | 51.0000 | + | 88.3346i | 0.115459 | + | 0.199981i | ||||
\(59\) | 79.5000 | − | 137.698i | 0.175424 | − | 0.303843i | −0.764884 | − | 0.644168i | \(-0.777204\pi\) |
0.940308 | + | 0.340325i | \(0.110537\pi\) | |||||||
\(60\) | −90.0000 | + | 155.885i | −0.193649 | + | 0.335410i | ||||
\(61\) | 361.000 | + | 625.270i | 0.757726 | + | 1.31242i | 0.944007 | + | 0.329924i | \(0.107023\pi\) |
−0.186281 | + | 0.982497i | \(0.559643\pi\) | |||||||
\(62\) | 370.000 | 0.757904 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −660.000 | − | 1143.15i | −1.25943 | − | 2.18140i | ||||
\(66\) | −27.0000 | + | 46.7654i | −0.0503556 | + | 0.0872185i | ||||
\(67\) | 83.0000 | − | 143.760i | 0.151344 | − | 0.262136i | −0.780378 | − | 0.625309i | \(-0.784973\pi\) |
0.931722 | + | 0.363173i | \(0.118306\pi\) | |||||||
\(68\) | −168.000 | − | 290.985i | −0.299603 | − | 0.518927i | ||||
\(69\) | −252.000 | −0.439670 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1086.00 | 1.81527 | 0.907637 | − | 0.419755i | \(-0.137884\pi\) | ||||
0.907637 | + | 0.419755i | \(0.137884\pi\) | |||||||
\(72\) | 36.0000 | + | 62.3538i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 109.000 | − | 188.794i | 0.174760 | − | 0.302693i | −0.765318 | − | 0.643652i | \(-0.777418\pi\) |
0.940078 | + | 0.340959i | \(0.110752\pi\) | |||||||
\(74\) | 44.0000 | − | 76.2102i | 0.0691202 | − | 0.119720i | ||||
\(75\) | −150.000 | − | 259.808i | −0.230940 | − | 0.400000i | ||||
\(76\) | −416.000 | −0.627875 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −528.000 | −0.766464 | ||||||||
\(79\) | 291.500 | + | 504.893i | 0.415143 | + | 0.719049i | 0.995443 | − | 0.0953535i | \(-0.0303981\pi\) |
−0.580300 | + | 0.814403i | \(0.697065\pi\) | |||||||
\(80\) | −120.000 | + | 207.846i | −0.167705 | + | 0.290474i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 168.000 | + | 290.985i | 0.226250 | + | 0.391876i | ||||
\(83\) | 597.000 | 0.789509 | 0.394755 | − | 0.918787i | \(-0.370830\pi\) | ||||
0.394755 | + | 0.918787i | \(0.370830\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1260.00 | 1.60784 | ||||||||
\(86\) | 326.000 | + | 564.649i | 0.408761 | + | 0.707996i | ||||
\(87\) | −76.5000 | + | 132.502i | −0.0942720 | + | 0.163284i | ||||
\(88\) | −36.0000 | + | 62.3538i | −0.0436092 | + | 0.0755334i | ||||
\(89\) | −519.000 | − | 898.934i | −0.618134 | − | 1.07064i | −0.989826 | − | 0.142283i | \(-0.954556\pi\) |
0.371692 | − | 0.928356i | \(-0.378778\pi\) | |||||||
\(90\) | −270.000 | −0.316228 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −336.000 | −0.380765 | ||||||||
\(93\) | 277.500 | + | 480.644i | 0.309413 | + | 0.535919i | ||||
\(94\) | 138.000 | − | 239.023i | 0.151421 | − | 0.262270i | ||||
\(95\) | 780.000 | − | 1351.00i | 0.842382 | − | 1.45905i | ||||
\(96\) | 48.0000 | + | 83.1384i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 169.000 | 0.176901 | 0.0884503 | − | 0.996081i | \(-0.471809\pi\) | ||||
0.0884503 | + | 0.996081i | \(0.471809\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −81.0000 | −0.0822304 | ||||||||
\(100\) | −200.000 | − | 346.410i | −0.200000 | − | 0.346410i | ||||
\(101\) | 321.000 | − | 555.988i | 0.316244 | − | 0.547752i | −0.663457 | − | 0.748215i | \(-0.730911\pi\) |
0.979701 | + | 0.200463i | \(0.0642447\pi\) | |||||||
\(102\) | 252.000 | − | 436.477i | 0.244625 | − | 0.423702i | ||||
\(103\) | 232.000 | + | 401.836i | 0.221938 | + | 0.384408i | 0.955396 | − | 0.295326i | \(-0.0954283\pi\) |
−0.733458 | + | 0.679735i | \(0.762095\pi\) | |||||||
\(104\) | −704.000 | −0.663778 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1278.00 | −1.17104 | ||||||||
\(107\) | −196.500 | − | 340.348i | −0.177536 | − | 0.307502i | 0.763500 | − | 0.645808i | \(-0.223479\pi\) |
−0.941036 | + | 0.338306i | \(0.890146\pi\) | |||||||
\(108\) | −54.0000 | + | 93.5307i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | −7.00000 | + | 12.1244i | −0.00615118 | + | 0.0106542i | −0.869085 | − | 0.494663i | \(-0.835291\pi\) |
0.862933 | + | 0.505318i | \(0.168625\pi\) | |||||||
\(110\) | −135.000 | − | 233.827i | −0.117016 | − | 0.202677i | ||||
\(111\) | 132.000 | 0.112873 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2184.00 | −1.81817 | −0.909086 | − | 0.416608i | \(-0.863219\pi\) | ||||
−0.909086 | + | 0.416608i | \(0.863219\pi\) | |||||||
\(114\) | −312.000 | − | 540.400i | −0.256329 | − | 0.443974i | ||||
\(115\) | 630.000 | − | 1091.19i | 0.510850 | − | 0.884819i | ||||
\(116\) | −102.000 | + | 176.669i | −0.0816419 | + | 0.141408i | ||||
\(117\) | −396.000 | − | 685.892i | −0.312908 | − | 0.541972i | ||||
\(118\) | 318.000 | 0.248087 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −360.000 | −0.273861 | ||||||||
\(121\) | 625.000 | + | 1082.53i | 0.469572 | + | 0.813322i | ||||
\(122\) | −722.000 | + | 1250.54i | −0.535794 | + | 0.928022i | ||||
\(123\) | −252.000 | + | 436.477i | −0.184732 | + | 0.319966i | ||||
\(124\) | 370.000 | + | 640.859i | 0.267960 | + | 0.464120i | ||||
\(125\) | −375.000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −373.000 | −0.260617 | −0.130309 | − | 0.991473i | \(-0.541597\pi\) | ||||
−0.130309 | + | 0.991473i | \(0.541597\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −489.000 | + | 846.973i | −0.333752 | + | 0.578076i | ||||
\(130\) | 1320.00 | − | 2286.31i | 0.890551 | − | 1.54248i | ||||
\(131\) | −586.500 | − | 1015.85i | −0.391166 | − | 0.677519i | 0.601438 | − | 0.798920i | \(-0.294595\pi\) |
−0.992604 | + | 0.121400i | \(0.961261\pi\) | |||||||
\(132\) | −108.000 | −0.0712136 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 332.000 | 0.214033 | ||||||||
\(135\) | −202.500 | − | 350.740i | −0.129099 | − | 0.223607i | ||||
\(136\) | 336.000 | − | 581.969i | 0.211851 | − | 0.366937i | ||||
\(137\) | −15.0000 | + | 25.9808i | −0.00935428 | + | 0.0162021i | −0.870665 | − | 0.491877i | \(-0.836311\pi\) |
0.861310 | + | 0.508079i | \(0.169644\pi\) | |||||||
\(138\) | −252.000 | − | 436.477i | −0.155447 | − | 0.269242i | ||||
\(139\) | 82.0000 | 0.0500370 | 0.0250185 | − | 0.999687i | \(-0.492036\pi\) | ||||
0.0250185 | + | 0.999687i | \(0.492036\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 414.000 | 0.247270 | ||||||||
\(142\) | 1086.00 | + | 1881.01i | 0.641796 | + | 1.11162i | ||||
\(143\) | 396.000 | − | 685.892i | 0.231575 | − | 0.401099i | ||||
\(144\) | −72.0000 | + | 124.708i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −382.500 | − | 662.509i | −0.219068 | − | 0.379437i | ||||
\(146\) | 436.000 | 0.247148 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 176.000 | 0.0977507 | ||||||||
\(149\) | 717.000 | + | 1241.88i | 0.394221 | + | 0.682811i | 0.993001 | − | 0.118102i | \(-0.0376811\pi\) |
−0.598780 | + | 0.800913i | \(0.704348\pi\) | |||||||
\(150\) | 300.000 | − | 519.615i | 0.163299 | − | 0.282843i | ||||
\(151\) | 1335.50 | − | 2313.15i | 0.719745 | − | 1.24663i | −0.241356 | − | 0.970437i | \(-0.577592\pi\) |
0.961101 | − | 0.276198i | \(-0.0890745\pi\) | |||||||
\(152\) | −416.000 | − | 720.533i | −0.221987 | − | 0.384493i | ||||
\(153\) | 756.000 | 0.399470 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2775.00 | −1.43802 | ||||||||
\(156\) | −528.000 | − | 914.523i | −0.270986 | − | 0.469362i | ||||
\(157\) | 1126.00 | − | 1950.29i | 0.572386 | − | 0.991401i | −0.423934 | − | 0.905693i | \(-0.639351\pi\) |
0.996320 | − | 0.0857085i | \(-0.0273154\pi\) | |||||||
\(158\) | −583.000 | + | 1009.79i | −0.293551 | + | 0.508444i | ||||
\(159\) | −958.500 | − | 1660.17i | −0.478075 | − | 0.828051i | ||||
\(160\) | −480.000 | −0.237171 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −838.000 | − | 1451.46i | −0.402682 | − | 0.697466i | 0.591366 | − | 0.806403i | \(-0.298589\pi\) |
−0.994049 | + | 0.108937i | \(0.965255\pi\) | |||||||
\(164\) | −336.000 | + | 581.969i | −0.159983 | + | 0.277098i | ||||
\(165\) | 202.500 | − | 350.740i | 0.0955431 | − | 0.165485i | ||||
\(166\) | 597.000 | + | 1034.03i | 0.279134 | + | 0.483474i | ||||
\(167\) | −3030.00 | −1.40400 | −0.702001 | − | 0.712176i | \(-0.747710\pi\) | ||||
−0.702001 | + | 0.712176i | \(0.747710\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5547.00 | 2.52481 | ||||||||
\(170\) | 1260.00 | + | 2182.38i | 0.568456 | + | 0.984595i | ||||
\(171\) | 468.000 | − | 810.600i | 0.209292 | − | 0.362504i | ||||
\(172\) | −652.000 | + | 1129.30i | −0.289038 | + | 0.500628i | ||||
\(173\) | 1719.00 | + | 2977.40i | 0.755452 | + | 1.30848i | 0.945149 | + | 0.326638i | \(0.105916\pi\) |
−0.189698 | + | 0.981843i | \(0.560751\pi\) | |||||||
\(174\) | −306.000 | −0.133321 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −144.000 | −0.0616728 | ||||||||
\(177\) | 238.500 | + | 413.094i | 0.101281 | + | 0.175424i | ||||
\(178\) | 1038.00 | − | 1797.87i | 0.437086 | − | 0.757056i | ||||
\(179\) | 606.000 | − | 1049.62i | 0.253042 | − | 0.438282i | −0.711320 | − | 0.702869i | \(-0.751902\pi\) |
0.964362 | + | 0.264587i | \(0.0852355\pi\) | |||||||
\(180\) | −270.000 | − | 467.654i | −0.111803 | − | 0.193649i | ||||
\(181\) | −3032.00 | −1.24512 | −0.622560 | − | 0.782572i | \(-0.713907\pi\) | ||||
−0.622560 | + | 0.782572i | \(0.713907\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2166.00 | −0.874947 | ||||||||
\(184\) | −336.000 | − | 581.969i | −0.134621 | − | 0.233170i | ||||
\(185\) | −330.000 | + | 571.577i | −0.131146 | + | 0.227152i | ||||
\(186\) | −555.000 | + | 961.288i | −0.218788 | + | 0.378952i | ||||
\(187\) | 378.000 | + | 654.715i | 0.147819 | + | 0.256030i | ||||
\(188\) | 552.000 | 0.214142 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3120.00 | 1.19131 | ||||||||
\(191\) | −1260.00 | − | 2182.38i | −0.477332 | − | 0.826763i | 0.522331 | − | 0.852743i | \(-0.325063\pi\) |
−0.999662 | + | 0.0259799i | \(0.991729\pi\) | |||||||
\(192\) | −96.0000 | + | 166.277i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −182.500 | + | 316.099i | −0.0680655 | + | 0.117893i | −0.898050 | − | 0.439894i | \(-0.855016\pi\) |
0.829984 | + | 0.557787i | \(0.188349\pi\) | |||||||
\(194\) | 169.000 | + | 292.717i | 0.0625438 | + | 0.108329i | ||||
\(195\) | 3960.00 | 1.45426 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1590.00 | −0.575040 | −0.287520 | − | 0.957775i | \(-0.592831\pi\) | ||||
−0.287520 | + | 0.957775i | \(0.592831\pi\) | |||||||
\(198\) | −81.0000 | − | 140.296i | −0.0290728 | − | 0.0503556i | ||||
\(199\) | −2690.00 | + | 4659.22i | −0.958236 | + | 1.65971i | −0.231455 | + | 0.972846i | \(0.574348\pi\) |
−0.726782 | + | 0.686868i | \(0.758985\pi\) | |||||||
\(200\) | 400.000 | − | 692.820i | 0.141421 | − | 0.244949i | ||||
\(201\) | 249.000 | + | 431.281i | 0.0873786 | + | 0.151344i | ||||
\(202\) | 1284.00 | 0.447237 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1008.00 | 0.345952 | ||||||||
\(205\) | −1260.00 | − | 2182.38i | −0.429279 | − | 0.743533i | ||||
\(206\) | −464.000 | + | 803.672i | −0.156934 | + | 0.271818i | ||||
\(207\) | 378.000 | − | 654.715i | 0.126922 | − | 0.219835i | ||||
\(208\) | −704.000 | − | 1219.36i | −0.234681 | − | 0.406479i | ||||
\(209\) | 936.000 | 0.309782 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5362.00 | −1.74946 | −0.874728 | − | 0.484614i | \(-0.838960\pi\) | ||||
−0.874728 | + | 0.484614i | \(0.838960\pi\) | |||||||
\(212\) | −1278.00 | − | 2213.56i | −0.414025 | − | 0.717113i | ||||
\(213\) | −1629.00 | + | 2821.51i | −0.524025 | + | 0.907637i | ||||
\(214\) | 393.000 | − | 680.696i | 0.125537 | − | 0.217437i | ||||
\(215\) | −2445.00 | − | 4234.86i | −0.775570 | − | 1.34333i | ||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −28.0000 | −0.00869908 | ||||||||
\(219\) | 327.000 | + | 566.381i | 0.100898 | + | 0.174760i | ||||
\(220\) | 270.000 | − | 467.654i | 0.0827427 | − | 0.143315i | ||||
\(221\) | −3696.00 | + | 6401.66i | −1.12498 | + | 1.94852i | ||||
\(222\) | 132.000 | + | 228.631i | 0.0399066 | + | 0.0691202i | ||||
\(223\) | 1573.00 | 0.472358 | 0.236179 | − | 0.971710i | \(-0.424105\pi\) | ||||
0.236179 | + | 0.971710i | \(0.424105\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 900.000 | 0.266667 | ||||||||
\(226\) | −2184.00 | − | 3782.80i | −0.642821 | − | 1.11340i | ||||
\(227\) | 460.500 | − | 797.609i | 0.134645 | − | 0.233212i | −0.790817 | − | 0.612053i | \(-0.790344\pi\) |
0.925462 | + | 0.378841i | \(0.123677\pi\) | |||||||
\(228\) | 624.000 | − | 1080.80i | 0.181252 | − | 0.313937i | ||||
\(229\) | 2026.00 | + | 3509.13i | 0.584637 | + | 1.01262i | 0.994921 | + | 0.100663i | \(0.0320963\pi\) |
−0.410284 | + | 0.911958i | \(0.634570\pi\) | |||||||
\(230\) | 2520.00 | 0.722452 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −408.000 | −0.115459 | ||||||||
\(233\) | 234.000 | + | 405.300i | 0.0657933 | + | 0.113957i | 0.897046 | − | 0.441938i | \(-0.145709\pi\) |
−0.831252 | + | 0.555895i | \(0.812376\pi\) | |||||||
\(234\) | 792.000 | − | 1371.78i | 0.221259 | − | 0.383232i | ||||
\(235\) | −1035.00 | + | 1792.67i | −0.287302 | + | 0.497622i | ||||
\(236\) | 318.000 | + | 550.792i | 0.0877120 | + | 0.151922i | ||||
\(237\) | −1749.00 | −0.479366 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4932.00 | 1.33483 | 0.667415 | − | 0.744686i | \(-0.267401\pi\) | ||||
0.667415 | + | 0.744686i | \(0.267401\pi\) | |||||||
\(240\) | −360.000 | − | 623.538i | −0.0968246 | − | 0.167705i | ||||
\(241\) | −768.500 | + | 1331.08i | −0.205408 | + | 0.355778i | −0.950263 | − | 0.311449i | \(-0.899186\pi\) |
0.744854 | + | 0.667227i | \(0.232519\pi\) | |||||||
\(242\) | −1250.00 | + | 2165.06i | −0.332037 | + | 0.575106i | ||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −2888.00 | −0.757726 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1008.00 | −0.261251 | ||||||||
\(247\) | 4576.00 | + | 7925.86i | 1.17880 | + | 2.04174i | ||||
\(248\) | −740.000 | + | 1281.72i | −0.189476 | + | 0.328182i | ||||
\(249\) | −895.500 | + | 1551.05i | −0.227912 | + | 0.394755i | ||||
\(250\) | −375.000 | − | 649.519i | −0.0948683 | − | 0.164317i | ||||
\(251\) | −5319.00 | −1.33758 | −0.668789 | − | 0.743452i | \(-0.733187\pi\) | ||||
−0.668789 | + | 0.743452i | \(0.733187\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 756.000 | 0.187863 | ||||||||
\(254\) | −373.000 | − | 646.055i | −0.0921421 | − | 0.159595i | ||||
\(255\) | −1890.00 | + | 3273.58i | −0.464143 | + | 0.803919i | ||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2673.00 | + | 4629.77i | 0.648783 | + | 1.12372i | 0.983414 | + | 0.181375i | \(0.0580549\pi\) |
−0.334631 | + | 0.942349i | \(0.608612\pi\) | |||||||
\(258\) | −1956.00 | −0.471997 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5280.00 | 1.25943 | ||||||||
\(261\) | −229.500 | − | 397.506i | −0.0544279 | − | 0.0942720i | ||||
\(262\) | 1173.00 | − | 2031.70i | 0.276596 | − | 0.479079i | ||||
\(263\) | −387.000 | + | 670.304i | −0.0907355 | + | 0.157159i | −0.907821 | − | 0.419358i | \(-0.862255\pi\) |
0.817085 | + | 0.576517i | \(0.195588\pi\) | |||||||
\(264\) | −108.000 | − | 187.061i | −0.0251778 | − | 0.0436092i | ||||
\(265\) | 9585.00 | 2.22189 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3114.00 | 0.713759 | ||||||||
\(268\) | 332.000 | + | 575.041i | 0.0756721 | + | 0.131068i | ||||
\(269\) | 1207.50 | − | 2091.45i | 0.273690 | − | 0.474045i | −0.696114 | − | 0.717931i | \(-0.745089\pi\) |
0.969804 | + | 0.243887i | \(0.0784225\pi\) | |||||||
\(270\) | 405.000 | − | 701.481i | 0.0912871 | − | 0.158114i | ||||
\(271\) | −237.500 | − | 411.362i | −0.0532365 | − | 0.0922084i | 0.838179 | − | 0.545395i | \(-0.183620\pi\) |
−0.891416 | + | 0.453187i | \(0.850287\pi\) | |||||||
\(272\) | 1344.00 | 0.299603 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −60.0000 | −0.0132290 | ||||||||
\(275\) | 450.000 | + | 779.423i | 0.0986764 | + | 0.170913i | ||||
\(276\) | 504.000 | − | 872.954i | 0.109918 | − | 0.190383i | ||||
\(277\) | −1864.00 | + | 3228.54i | −0.404321 | + | 0.700304i | −0.994242 | − | 0.107156i | \(-0.965825\pi\) |
0.589921 | + | 0.807461i | \(0.299159\pi\) | |||||||
\(278\) | 82.0000 | + | 142.028i | 0.0176908 | + | 0.0306413i | ||||
\(279\) | −1665.00 | −0.357279 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1602.00 | 0.340097 | 0.170049 | − | 0.985436i | \(-0.445608\pi\) | ||||
0.170049 | + | 0.985436i | \(0.445608\pi\) | |||||||
\(282\) | 414.000 | + | 717.069i | 0.0874232 | + | 0.151421i | ||||
\(283\) | 343.000 | − | 594.093i | 0.0720468 | − | 0.124789i | −0.827751 | − | 0.561095i | \(-0.810380\pi\) |
0.899798 | + | 0.436306i | \(0.143714\pi\) | |||||||
\(284\) | −2172.00 | + | 3762.01i | −0.453819 | + | 0.786037i | ||||
\(285\) | 2340.00 | + | 4053.00i | 0.486350 | + | 0.842382i | ||||
\(286\) | 1584.00 | 0.327496 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −1071.50 | − | 1855.89i | −0.218095 | − | 0.377751i | ||||
\(290\) | 765.000 | − | 1325.02i | 0.154905 | − | 0.268303i | ||||
\(291\) | −253.500 | + | 439.075i | −0.0510668 | + | 0.0884503i | ||||
\(292\) | 436.000 | + | 755.174i | 0.0873800 | + | 0.151347i | ||||
\(293\) | 1101.00 | 0.219526 | 0.109763 | − | 0.993958i | \(-0.464991\pi\) | ||||
0.109763 | + | 0.993958i | \(0.464991\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2385.00 | −0.470712 | ||||||||
\(296\) | 176.000 | + | 304.841i | 0.0345601 | + | 0.0598599i | ||||
\(297\) | 121.500 | − | 210.444i | 0.0237379 | − | 0.0411152i | ||||
\(298\) | −1434.00 | + | 2483.76i | −0.278756 | + | 0.482820i | ||||
\(299\) | 3696.00 | + | 6401.66i | 0.714867 | + | 1.23819i | ||||
\(300\) | 1200.00 | 0.230940 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5342.00 | 1.01787 | ||||||||
\(303\) | 963.000 | + | 1667.96i | 0.182584 | + | 0.316244i | ||||
\(304\) | 832.000 | − | 1441.07i | 0.156969 | − | 0.271878i | ||||
\(305\) | 5415.00 | − | 9379.06i | 1.01660 | − | 1.76080i | ||||
\(306\) | 756.000 | + | 1309.43i | 0.141234 | + | 0.244625i | ||||
\(307\) | −2780.00 | −0.516818 | −0.258409 | − | 0.966036i | \(-0.583198\pi\) | ||||
−0.258409 | + | 0.966036i | \(0.583198\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1392.00 | −0.256272 | ||||||||
\(310\) | −2775.00 | − | 4806.44i | −0.508417 | − | 0.880605i | ||||
\(311\) | 2148.00 | − | 3720.45i | 0.391646 | − | 0.678351i | −0.601021 | − | 0.799233i | \(-0.705239\pi\) |
0.992667 | + | 0.120883i | \(0.0385725\pi\) | |||||||
\(312\) | 1056.00 | − | 1829.05i | 0.191616 | − | 0.331889i | ||||
\(313\) | 2744.50 | + | 4753.61i | 0.495618 | + | 0.858435i | 0.999987 | − | 0.00505298i | \(-0.00160842\pi\) |
−0.504370 | + | 0.863488i | \(0.668275\pi\) | |||||||
\(314\) | 4504.00 | 0.809476 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2332.00 | −0.415143 | ||||||||
\(317\) | −2245.50 | − | 3889.32i | −0.397854 | − | 0.689104i | 0.595607 | − | 0.803276i | \(-0.296912\pi\) |
−0.993461 | + | 0.114172i | \(0.963578\pi\) | |||||||
\(318\) | 1917.00 | − | 3320.34i | 0.338050 | − | 0.585520i | ||||
\(319\) | 229.500 | − | 397.506i | 0.0402807 | − | 0.0697682i | ||||
\(320\) | −480.000 | − | 831.384i | −0.0838525 | − | 0.145237i | ||||
\(321\) | 1179.00 | 0.205001 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8736.00 | −1.50490 | ||||||||
\(324\) | −162.000 | − | 280.592i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −4400.00 | + | 7621.02i | −0.750979 | + | 1.30073i | ||||
\(326\) | 1676.00 | − | 2902.92i | 0.284739 | − | 0.493183i | ||||
\(327\) | −21.0000 | − | 36.3731i | −0.00355138 | − | 0.00615118i | ||||
\(328\) | −1344.00 | −0.226250 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 810.000 | 0.135118 | ||||||||
\(331\) | 1982.00 | + | 3432.92i | 0.329126 | + | 0.570062i | 0.982339 | − | 0.187112i | \(-0.0599127\pi\) |
−0.653213 | + | 0.757174i | \(0.726579\pi\) | |||||||
\(332\) | −1194.00 | + | 2068.07i | −0.197377 | + | 0.341868i | ||||
\(333\) | −198.000 | + | 342.946i | −0.0325836 | + | 0.0564364i | ||||
\(334\) | −3030.00 | − | 5248.11i | −0.496390 | − | 0.859773i | ||||
\(335\) | −2490.00 | −0.406099 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 161.000 | 0.0260244 | 0.0130122 | − | 0.999915i | \(-0.495858\pi\) | ||||
0.0130122 | + | 0.999915i | \(0.495858\pi\) | |||||||
\(338\) | 5547.00 | + | 9607.69i | 0.892654 | + | 1.54612i | ||||
\(339\) | 3276.00 | − | 5674.20i | 0.524861 | − | 0.909086i | ||||
\(340\) | −2520.00 | + | 4364.77i | −0.401959 | + | 0.696214i | ||||
\(341\) | −832.500 | − | 1441.93i | −0.132206 | − | 0.228988i | ||||
\(342\) | 1872.00 | 0.295983 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2608.00 | −0.408761 | ||||||||
\(345\) | 1890.00 | + | 3273.58i | 0.294940 | + | 0.510850i | ||||
\(346\) | −3438.00 | + | 5954.79i | −0.534185 | + | 0.925236i | ||||
\(347\) | 2958.00 | − | 5123.41i | 0.457619 | − | 0.792619i | −0.541216 | − | 0.840884i | \(-0.682036\pi\) |
0.998835 | + | 0.0482646i | \(0.0153691\pi\) | |||||||
\(348\) | −306.000 | − | 530.008i | −0.0471360 | − | 0.0816419i | ||||
\(349\) | 142.000 | 0.0217796 | 0.0108898 | − | 0.999941i | \(-0.496534\pi\) | ||||
0.0108898 | + | 0.999941i | \(0.496534\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2376.00 | 0.361315 | ||||||||
\(352\) | −144.000 | − | 249.415i | −0.0218046 | − | 0.0377667i | ||||
\(353\) | −2220.00 | + | 3845.15i | −0.334727 | + | 0.579764i | −0.983432 | − | 0.181275i | \(-0.941977\pi\) |
0.648705 | + | 0.761040i | \(0.275311\pi\) | |||||||
\(354\) | −477.000 | + | 826.188i | −0.0716166 | + | 0.124044i | ||||
\(355\) | −8145.00 | − | 14107.6i | −1.21772 | − | 2.10916i | ||||
\(356\) | 4152.00 | 0.618134 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2424.00 | 0.357856 | ||||||||
\(359\) | −1143.00 | − | 1979.73i | −0.168037 | − | 0.291048i | 0.769693 | − | 0.638415i | \(-0.220409\pi\) |
−0.937730 | + | 0.347366i | \(0.887076\pi\) | |||||||
\(360\) | 540.000 | − | 935.307i | 0.0790569 | − | 0.136931i | ||||
\(361\) | −1978.50 | + | 3426.86i | −0.288453 | + | 0.499615i | ||||
\(362\) | −3032.00 | − | 5251.58i | −0.440217 | − | 0.762477i | ||||
\(363\) | −3750.00 | −0.542215 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3270.00 | −0.468930 | ||||||||
\(366\) | −2166.00 | − | 3751.62i | −0.309341 | − | 0.535794i | ||||
\(367\) | −1434.50 | + | 2484.63i | −0.204033 | + | 0.353396i | −0.949824 | − | 0.312784i | \(-0.898738\pi\) |
0.745791 | + | 0.666180i | \(0.232072\pi\) | |||||||
\(368\) | 672.000 | − | 1163.94i | 0.0951914 | − | 0.164876i | ||||
\(369\) | −756.000 | − | 1309.43i | −0.106655 | − | 0.184732i | ||||
\(370\) | −1320.00 | −0.185469 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2220.00 | −0.309413 | ||||||||
\(373\) | 1532.00 | + | 2653.50i | 0.212665 | + | 0.368346i | 0.952548 | − | 0.304390i | \(-0.0984524\pi\) |
−0.739883 | + | 0.672736i | \(0.765119\pi\) | |||||||
\(374\) | −756.000 | + | 1309.43i | −0.104524 | + | 0.181040i | ||||
\(375\) | 562.500 | − | 974.279i | 0.0774597 | − | 0.134164i | ||||
\(376\) | 552.000 | + | 956.092i | 0.0757107 | + | 0.131135i | ||||
\(377\) | 4488.00 | 0.613113 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6040.00 | −0.818612 | −0.409306 | − | 0.912397i | \(-0.634229\pi\) | ||||
−0.409306 | + | 0.912397i | \(0.634229\pi\) | |||||||
\(380\) | 3120.00 | + | 5404.00i | 0.421191 | + | 0.729524i | ||||
\(381\) | 559.500 | − | 969.082i | 0.0752337 | − | 0.130309i | ||||
\(382\) | 2520.00 | − | 4364.77i | 0.337525 | − | 0.584610i | ||||
\(383\) | 921.000 | + | 1595.22i | 0.122874 | + | 0.212825i | 0.920900 | − | 0.389799i | \(-0.127455\pi\) |
−0.798026 | + | 0.602623i | \(0.794122\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −730.000 | −0.0962591 | ||||||||
\(387\) | −1467.00 | − | 2540.92i | −0.192692 | − | 0.333752i | ||||
\(388\) | −338.000 | + | 585.433i | −0.0442251 | + | 0.0766002i | ||||
\(389\) | −3915.00 | + | 6780.98i | −0.510279 | + | 0.883828i | 0.489650 | + | 0.871919i | \(0.337124\pi\) |
−0.999929 | + | 0.0119097i | \(0.996209\pi\) | |||||||
\(390\) | 3960.00 | + | 6858.92i | 0.514160 | + | 0.890551i | ||||
\(391\) | −7056.00 | −0.912627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3519.00 | 0.451680 | ||||||||
\(394\) | −1590.00 | − | 2753.96i | −0.203307 | − | 0.352138i | ||||
\(395\) | 4372.50 | − | 7573.39i | 0.556973 | − | 0.964706i | ||||
\(396\) | 162.000 | − | 280.592i | 0.0205576 | − | 0.0356068i | ||||
\(397\) | −7382.00 | − | 12786.0i | −0.933229 | − | 1.61640i | −0.777762 | − | 0.628559i | \(-0.783645\pi\) |
−0.155467 | − | 0.987841i | \(-0.549688\pi\) | |||||||
\(398\) | −10760.0 | −1.35515 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1600.00 | 0.200000 | ||||||||
\(401\) | −3132.00 | − | 5424.78i | −0.390036 | − | 0.675563i | 0.602417 | − | 0.798181i | \(-0.294204\pi\) |
−0.992454 | + | 0.122618i | \(0.960871\pi\) | |||||||
\(402\) | −498.000 | + | 862.561i | −0.0617860 | + | 0.107017i | ||||
\(403\) | 8140.00 | − | 14098.9i | 1.00616 | − | 1.74272i | ||||
\(404\) | 1284.00 | + | 2223.95i | 0.158122 | + | 0.273876i | ||||
\(405\) | 1215.00 | 0.149071 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −396.000 | −0.0482285 | ||||||||
\(408\) | 1008.00 | + | 1745.91i | 0.122312 | + | 0.211851i | ||||
\(409\) | 2375.50 | − | 4114.49i | 0.287191 | − | 0.497429i | −0.685948 | − | 0.727651i | \(-0.740612\pi\) |
0.973138 | + | 0.230222i | \(0.0739454\pi\) | |||||||
\(410\) | 2520.00 | − | 4364.77i | 0.303546 | − | 0.525757i | ||||
\(411\) | −45.0000 | − | 77.9423i | −0.00540070 | − | 0.00935428i | ||||
\(412\) | −1856.00 | −0.221938 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1512.00 | 0.179495 | ||||||||
\(415\) | −4477.50 | − | 7755.26i | −0.529619 | − | 0.917327i | ||||
\(416\) | 1408.00 | − | 2438.73i | 0.165944 | − | 0.287424i | ||||
\(417\) | −123.000 | + | 213.042i | −0.0144445 | + | 0.0250185i | ||||
\(418\) | 936.000 | + | 1621.20i | 0.109525 | + | 0.189702i | ||||
\(419\) | 4704.00 | 0.548462 | 0.274231 | − | 0.961664i | \(-0.411577\pi\) | ||||
0.274231 | + | 0.961664i | \(0.411577\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4474.00 | −0.517932 | −0.258966 | − | 0.965886i | \(-0.583382\pi\) | ||||
−0.258966 | + | 0.965886i | \(0.583382\pi\) | |||||||
\(422\) | −5362.00 | − | 9287.26i | −0.618526 | − | 1.07132i | ||||
\(423\) | −621.000 | + | 1075.60i | −0.0713807 | + | 0.123635i | ||||
\(424\) | 2556.00 | − | 4427.12i | 0.292760 | − | 0.507076i | ||||
\(425\) | −4200.00 | − | 7274.61i | −0.479365 | − | 0.830284i | ||||
\(426\) | −6516.00 | −0.741083 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1572.00 | 0.177536 | ||||||||
\(429\) | 1188.00 | + | 2057.68i | 0.133700 | + | 0.231575i | ||||
\(430\) | 4890.00 | − | 8469.73i | 0.548411 | − | 0.949876i | ||||
\(431\) | 6402.00 | − | 11088.6i | 0.715484 | − | 1.23925i | −0.247289 | − | 0.968942i | \(-0.579540\pi\) |
0.962773 | − | 0.270312i | \(-0.0871270\pi\) | |||||||
\(432\) | −216.000 | − | 374.123i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 5074.00 | 0.563143 | 0.281571 | − | 0.959540i | \(-0.409144\pi\) | ||||
0.281571 | + | 0.959540i | \(0.409144\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2295.00 | 0.252958 | ||||||||
\(436\) | −28.0000 | − | 48.4974i | −0.00307559 | − | 0.00532708i | ||||
\(437\) | −4368.00 | + | 7565.60i | −0.478146 | + | 0.828173i | ||||
\(438\) | −654.000 | + | 1132.76i | −0.0713455 | + | 0.123574i | ||||
\(439\) | −633.500 | − | 1097.25i | −0.0688731 | − | 0.119292i | 0.829532 | − | 0.558459i | \(-0.188607\pi\) |
−0.898406 | + | 0.439167i | \(0.855274\pi\) | |||||||
\(440\) | 1080.00 | 0.117016 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14784.0 | −1.59096 | ||||||||
\(443\) | 3466.50 | + | 6004.15i | 0.371780 | + | 0.643941i | 0.989839 | − | 0.142190i | \(-0.0454144\pi\) |
−0.618060 | + | 0.786131i | \(0.712081\pi\) | |||||||
\(444\) | −264.000 | + | 457.261i | −0.0282182 | + | 0.0488754i | ||||
\(445\) | −7785.00 | + | 13484.0i | −0.829313 | + | 1.43641i | ||||
\(446\) | 1573.00 | + | 2724.52i | 0.167004 | + | 0.289259i | ||||
\(447\) | −4302.00 | −0.455207 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11688.0 | 1.22849 | 0.614244 | − | 0.789116i | \(-0.289461\pi\) | ||||
0.614244 | + | 0.789116i | \(0.289461\pi\) | |||||||
\(450\) | 900.000 | + | 1558.85i | 0.0942809 | + | 0.163299i | ||||
\(451\) | 756.000 | − | 1309.43i | 0.0789327 | − | 0.136715i | ||||
\(452\) | 4368.00 | − | 7565.60i | 0.454543 | − | 0.787292i | ||||
\(453\) | 4006.50 | + | 6939.46i | 0.415545 | + | 0.719745i | ||||
\(454\) | 1842.00 | 0.190417 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2496.00 | 0.256329 | ||||||||
\(457\) | −275.500 | − | 477.180i | −0.0281999 | − | 0.0488436i | 0.851581 | − | 0.524223i | \(-0.175644\pi\) |
−0.879781 | + | 0.475379i | \(0.842311\pi\) | |||||||
\(458\) | −4052.00 | + | 7018.27i | −0.413401 | + | 0.716031i | ||||
\(459\) | −1134.00 | + | 1964.15i | −0.115317 | + | 0.199735i | ||||
\(460\) | 2520.00 | + | 4364.77i | 0.255425 | + | 0.442409i | ||||
\(461\) | −13386.0 | −1.35238 | −0.676191 | − | 0.736726i | \(-0.736371\pi\) | ||||
−0.676191 | + | 0.736726i | \(0.736371\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6376.00 | −0.639995 | −0.319998 | − | 0.947418i | \(-0.603682\pi\) | ||||
−0.319998 | + | 0.947418i | \(0.603682\pi\) | |||||||
\(464\) | −408.000 | − | 706.677i | −0.0408210 | − | 0.0707040i | ||||
\(465\) | 4162.50 | − | 7209.66i | 0.415121 | − | 0.719011i | ||||
\(466\) | −468.000 | + | 810.600i | −0.0465229 | + | 0.0805801i | ||||
\(467\) | 2850.00 | + | 4936.34i | 0.282403 | + | 0.489137i | 0.971976 | − | 0.235080i | \(-0.0755351\pi\) |
−0.689573 | + | 0.724216i | \(0.742202\pi\) | |||||||
\(468\) | 3168.00 | 0.312908 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4140.00 | −0.406306 | ||||||||
\(471\) | 3378.00 | + | 5850.87i | 0.330467 | + | 0.572386i | ||||
\(472\) | −636.000 | + | 1101.58i | −0.0620218 | + | 0.107425i | ||||
\(473\) | 1467.00 | − | 2540.92i | 0.142606 | − | 0.247001i | ||||
\(474\) | −1749.00 | − | 3029.36i | −0.169481 | − | 0.293551i | ||||
\(475\) | −10400.0 | −1.00460 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5751.00 | 0.552034 | ||||||||
\(478\) | 4932.00 | + | 8542.47i | 0.471934 | + | 0.817414i | ||||
\(479\) | 9897.00 | − | 17142.1i | 0.944062 | − | 1.63516i | 0.186442 | − | 0.982466i | \(-0.440304\pi\) |
0.757619 | − | 0.652697i | \(-0.226362\pi\) | |||||||
\(480\) | 720.000 | − | 1247.08i | 0.0684653 | − | 0.118585i | ||||
\(481\) | −1936.00 | − | 3353.25i | −0.183522 | − | 0.317869i | ||||
\(482\) | −3074.00 | −0.290491 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5000.00 | −0.469572 | ||||||||
\(485\) | −1267.50 | − | 2195.37i | −0.118668 | − | 0.205540i | ||||
\(486\) | 243.000 | − | 420.888i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | −7967.50 | + | 13800.1i | −0.741359 | + | 1.28407i | 0.210517 | + | 0.977590i | \(0.432485\pi\) |
−0.951877 | + | 0.306482i | \(0.900848\pi\) | |||||||
\(488\) | −2888.00 | − | 5002.16i | −0.267897 | − | 0.464011i | ||||
\(489\) | 5028.00 | 0.464978 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9963.00 | 0.915731 | 0.457865 | − | 0.889021i | \(-0.348614\pi\) | ||||
0.457865 | + | 0.889021i | \(0.348614\pi\) | |||||||
\(492\) | −1008.00 | − | 1745.91i | −0.0923662 | − | 0.159983i | ||||
\(493\) | −2142.00 | + | 3710.05i | −0.195681 | + | 0.338930i | ||||
\(494\) | −9152.00 | + | 15851.7i | −0.833538 | + | 1.44373i | ||||
\(495\) | 607.500 | + | 1052.22i | 0.0551618 | + | 0.0955431i | ||||
\(496\) | −2960.00 | −0.267960 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3582.00 | −0.322316 | ||||||||
\(499\) | −9571.00 | − | 16577.5i | −0.858631 | − | 1.48719i | −0.873235 | − | 0.487299i | \(-0.837982\pi\) |
0.0146043 | − | 0.999893i | \(-0.495351\pi\) | |||||||
\(500\) | 750.000 | − | 1299.04i | 0.0670820 | − | 0.116190i | ||||
\(501\) | 4545.00 | − | 7872.17i | 0.405301 | − | 0.702001i | ||||
\(502\) | −5319.00 | − | 9212.78i | −0.472906 | − | 0.819096i | ||||
\(503\) | 12192.0 | 1.08074 | 0.540372 | − | 0.841426i | \(-0.318283\pi\) | ||||
0.540372 | + | 0.841426i | \(0.318283\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9630.00 | −0.848573 | ||||||||
\(506\) | 756.000 | + | 1309.43i | 0.0664196 | + | 0.115042i | ||||
\(507\) | −8320.50 | + | 14411.5i | −0.728849 | + | 1.26240i | ||||
\(508\) | 746.000 | − | 1292.11i | 0.0651543 | − | 0.112851i | ||||
\(509\) | −9904.50 | − | 17155.1i | −0.862494 | − | 1.49388i | −0.869515 | − | 0.493907i | \(-0.835568\pi\) |
0.00702091 | − | 0.999975i | \(-0.497765\pi\) | |||||||
\(510\) | −7560.00 | −0.656397 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 1404.00 | + | 2431.80i | 0.120835 | + | 0.209292i | ||||
\(514\) | −5346.00 | + | 9259.54i | −0.458759 | + | 0.794593i | ||||
\(515\) | 3480.00 | − | 6027.54i | 0.297761 | − | 0.515738i | ||||
\(516\) | −1956.00 | − | 3387.89i | −0.166876 | − | 0.289038i | ||||
\(517\) | −1242.00 | −0.105654 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10314.0 | −0.872321 | ||||||||
\(520\) | 5280.00 | + | 9145.23i | 0.445276 | + | 0.771240i | ||||
\(521\) | −897.000 | + | 1553.65i | −0.0754286 | + | 0.130646i | −0.901273 | − | 0.433253i | \(-0.857366\pi\) |
0.825844 | + | 0.563899i | \(0.190699\pi\) | |||||||
\(522\) | 459.000 | − | 795.011i | 0.0384864 | − | 0.0666603i | ||||
\(523\) | −3224.00 | − | 5584.13i | −0.269552 | − | 0.466878i | 0.699194 | − | 0.714932i | \(-0.253542\pi\) |
−0.968746 | + | 0.248054i | \(0.920209\pi\) | |||||||
\(524\) | 4692.00 | 0.391166 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1548.00 | −0.128319 | ||||||||
\(527\) | 7770.00 | + | 13458.0i | 0.642251 | + | 1.11241i | ||||
\(528\) | 216.000 | − | 374.123i | 0.0178034 | − | 0.0308364i | ||||
\(529\) | 2555.50 | − | 4426.26i | 0.210035 | − | 0.363792i | ||||
\(530\) | 9585.00 | + | 16601.7i | 0.785558 | + | 1.36063i | ||||
\(531\) | −1431.00 | −0.116949 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14784.0 | 1.20144 | ||||||||
\(534\) | 3114.00 | + | 5393.61i | 0.252352 | + | 0.437086i | ||||
\(535\) | −2947.50 | + | 5105.22i | −0.238190 | + | 0.412557i | ||||
\(536\) | −664.000 | + | 1150.08i | −0.0535083 | + | 0.0926790i | ||||
\(537\) | 1818.00 | + | 3148.87i | 0.146094 | + | 0.253042i | ||||
\(538\) | 4830.00 | 0.387056 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1620.00 | 0.129099 | ||||||||
\(541\) | −3631.00 | − | 6289.08i | −0.288556 | − | 0.499794i | 0.684909 | − | 0.728628i | \(-0.259842\pi\) |
−0.973465 | + | 0.228835i | \(0.926509\pi\) | |||||||
\(542\) | 475.000 | − | 822.724i | 0.0376439 | − | 0.0652012i | ||||
\(543\) | 4548.00 | − | 7877.37i | 0.359435 | − | 0.622560i | ||||
\(544\) | 1344.00 | + | 2327.88i | 0.105926 | + | 0.183469i | ||||
\(545\) | 210.000 | 0.0165053 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14204.0 | 1.11027 | 0.555136 | − | 0.831759i | \(-0.312666\pi\) | ||||
0.555136 | + | 0.831759i | \(0.312666\pi\) | |||||||
\(548\) | −60.0000 | − | 103.923i | −0.00467714 | − | 0.00810104i | ||||
\(549\) | 3249.00 | − | 5627.43i | 0.252575 | − | 0.437474i | ||||
\(550\) | −900.000 | + | 1558.85i | −0.0697748 | + | 0.120853i | ||||
\(551\) | 2652.00 | + | 4593.40i | 0.205044 | + | 0.355146i | ||||
\(552\) | 2016.00 | 0.155447 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −7456.00 | −0.571796 | ||||||||
\(555\) | −990.000 | − | 1714.73i | −0.0757174 | − | 0.131146i | ||||
\(556\) | −164.000 | + | 284.056i | −0.0125093 | + | 0.0216667i | ||||
\(557\) | −7912.50 | + | 13704.9i | −0.601909 | + | 1.04254i | 0.390623 | + | 0.920551i | \(0.372260\pi\) |
−0.992532 | + | 0.121986i | \(0.961074\pi\) | |||||||
\(558\) | −1665.00 | − | 2883.86i | −0.126317 | − | 0.218788i | ||||
\(559\) | 28688.0 | 2.17061 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2268.00 | −0.170686 | ||||||||
\(562\) | 1602.00 | + | 2774.75i | 0.120243 | + | 0.208266i | ||||
\(563\) | 529.500 | − | 917.121i | 0.0396372 | − | 0.0686537i | −0.845526 | − | 0.533934i | \(-0.820713\pi\) |
0.885163 | + | 0.465280i | \(0.154046\pi\) | |||||||
\(564\) | −828.000 | + | 1434.14i | −0.0618175 | + | 0.107071i | ||||
\(565\) | 16380.0 | + | 28371.0i | 1.21967 | + | 2.11252i | ||||
\(566\) | 1372.00 | 0.101890 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8688.00 | −0.641796 | ||||||||
\(569\) | −1980.00 | − | 3429.46i | −0.145880 | − | 0.252672i | 0.783821 | − | 0.620987i | \(-0.213268\pi\) |
−0.929701 | + | 0.368315i | \(0.879935\pi\) | |||||||
\(570\) | −4680.00 | + | 8106.00i | −0.343901 | + | 0.595654i | ||||
\(571\) | 1265.00 | − | 2191.04i | 0.0927121 | − | 0.160582i | −0.815939 | − | 0.578138i | \(-0.803780\pi\) |
0.908651 | + | 0.417555i | \(0.137113\pi\) | |||||||
\(572\) | 1584.00 | + | 2743.57i | 0.115787 | + | 0.200550i | ||||
\(573\) | 7560.00 | 0.551175 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8400.00 | −0.609225 | ||||||||
\(576\) | −288.000 | − | 498.831i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 5915.50 | − | 10245.9i | 0.426803 | − | 0.739245i | −0.569784 | − | 0.821795i | \(-0.692973\pi\) |
0.996587 | + | 0.0825498i | \(0.0263063\pi\) | |||||||
\(578\) | 2143.00 | − | 3711.78i | 0.154216 | − | 0.267111i | ||||
\(579\) | −547.500 | − | 948.298i | −0.0392976 | − | 0.0680655i | ||||
\(580\) | 3060.00 | 0.219068 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1014.00 | −0.0722193 | ||||||||
\(583\) | 2875.50 | + | 4980.51i | 0.204273 | + | 0.353811i | ||||
\(584\) | −872.000 | + | 1510.35i | −0.0617870 | + | 0.107018i | ||||
\(585\) | −5940.00 | + | 10288.4i | −0.419810 | + | 0.727132i | ||||
\(586\) | 1101.00 | + | 1906.99i | 0.0776141 | + | 0.134432i | ||||
\(587\) | −4809.00 | −0.338141 | −0.169070 | − | 0.985604i | \(-0.554077\pi\) | ||||
−0.169070 | + | 0.985604i | \(0.554077\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19240.0 | 1.34596 | ||||||||
\(590\) | −2385.00 | − | 4130.94i | −0.166422 | − | 0.288251i | ||||
\(591\) | 2385.00 | − | 4130.94i | 0.166000 | − | 0.287520i | ||||
\(592\) | −352.000 | + | 609.682i | −0.0244377 | + | 0.0423273i | ||||
\(593\) | 10902.0 | + | 18882.8i | 0.754960 | + | 1.30763i | 0.945394 | + | 0.325930i | \(0.105677\pi\) |
−0.190434 | + | 0.981700i | \(0.560989\pi\) | |||||||
\(594\) | 486.000 | 0.0335704 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5736.00 | −0.394221 | ||||||||
\(597\) | −8070.00 | − | 13977.7i | −0.553238 | − | 0.958236i | ||||
\(598\) | −7392.00 | + | 12803.3i | −0.505487 | + | 0.875530i | ||||
\(599\) | −7083.00 | + | 12268.1i | −0.483144 | + | 0.836831i | −0.999813 | − | 0.0193549i | \(-0.993839\pi\) |
0.516668 | + | 0.856186i | \(0.327172\pi\) | |||||||
\(600\) | 1200.00 | + | 2078.46i | 0.0816497 | + | 0.141421i | ||||
\(601\) | −5891.00 | −0.399832 | −0.199916 | − | 0.979813i | \(-0.564067\pi\) | ||||
−0.199916 | + | 0.979813i | \(0.564067\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1494.00 | −0.100896 | ||||||||
\(604\) | 5342.00 | + | 9252.62i | 0.359872 | + | 0.623317i | ||||
\(605\) | 9375.00 | − | 16238.0i | 0.629997 | − | 1.09119i | ||||
\(606\) | −1926.00 | + | 3335.93i | −0.129106 | + | 0.223619i | ||||
\(607\) | −1368.50 | − | 2370.31i | −0.0915086 | − | 0.158497i | 0.816638 | − | 0.577151i | \(-0.195836\pi\) |
−0.908146 | + | 0.418653i | \(0.862502\pi\) | |||||||
\(608\) | 3328.00 | 0.221987 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21660.0 | 1.43768 | ||||||||
\(611\) | −6072.00 | − | 10517.0i | −0.402041 | − | 0.696355i | ||||
\(612\) | −1512.00 | + | 2618.86i | −0.0998676 | + | 0.172976i | ||||
\(613\) | 13094.0 | − | 22679.5i | 0.862743 | − | 1.49432i | −0.00652719 | − | 0.999979i | \(-0.502078\pi\) |
0.869271 | − | 0.494337i | \(-0.164589\pi\) | |||||||
\(614\) | −2780.00 | − | 4815.10i | −0.182723 | − | 0.316485i | ||||
\(615\) | 7560.00 | 0.495689 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2358.00 | −0.153857 | −0.0769283 | − | 0.997037i | \(-0.524511\pi\) | ||||
−0.0769283 | + | 0.997037i | \(0.524511\pi\) | |||||||
\(618\) | −1392.00 | − | 2411.01i | −0.0906059 | − | 0.156934i | ||||
\(619\) | 6883.00 | − | 11921.7i | 0.446932 | − | 0.774110i | −0.551252 | − | 0.834339i | \(-0.685850\pi\) |
0.998185 | + | 0.0602291i | \(0.0191831\pi\) | |||||||
\(620\) | 5550.00 | − | 9612.88i | 0.359505 | − | 0.622682i | ||||
\(621\) | 1134.00 | + | 1964.15i | 0.0732783 | + | 0.126922i | ||||
\(622\) | 8592.00 | 0.553871 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4224.00 | 0.270986 | ||||||||
\(625\) | 9062.50 | + | 15696.7i | 0.580000 | + | 1.00459i | ||||
\(626\) | −5489.00 | + | 9507.23i | −0.350455 | + | 0.607005i | ||||
\(627\) | −1404.00 | + | 2431.80i | −0.0894264 | + | 0.154891i | ||||
\(628\) | 4504.00 | + | 7801.16i | 0.286193 | + | 0.495701i | ||||
\(629\) | 3696.00 | 0.234291 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21287.0 | 1.34298 | 0.671491 | − | 0.741012i | \(-0.265654\pi\) | ||||
0.671491 | + | 0.741012i | \(0.265654\pi\) | |||||||
\(632\) | −2332.00 | − | 4039.14i | −0.146775 | − | 0.254222i | ||||
\(633\) | 8043.00 | − | 13930.9i | 0.505025 | − | 0.874728i | ||||
\(634\) | 4491.00 | − | 7778.64i | 0.281326 | − | 0.487270i | ||||
\(635\) | 2797.50 | + | 4845.41i | 0.174827 | + | 0.302810i | ||||
\(636\) | 7668.00 | 0.478075 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 918.000 | 0.0569655 | ||||||||
\(639\) | −4887.00 | − | 8464.53i | −0.302546 | − | 0.524025i | ||||
\(640\) | 960.000 | − | 1662.77i | 0.0592927 | − | 0.102698i | ||||
\(641\) | −10713.0 | + | 18555.5i | −0.660122 | + | 1.14336i | 0.320462 | + | 0.947262i | \(0.396162\pi\) |
−0.980583 | + | 0.196103i | \(0.937171\pi\) | |||||||
\(642\) | 1179.00 | + | 2042.09i | 0.0724788 | + | 0.125537i | ||||
\(643\) | −9962.00 | −0.610984 | −0.305492 | − | 0.952195i | \(-0.598821\pi\) | ||||
−0.305492 | + | 0.952195i | \(0.598821\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14670.0 | 0.895551 | ||||||||
\(646\) | −8736.00 | − | 15131.2i | −0.532064 | − | 0.921562i | ||||
\(647\) | −9087.00 | + | 15739.1i | −0.552159 | + | 0.956367i | 0.445960 | + | 0.895053i | \(0.352863\pi\) |
−0.998119 | + | 0.0613142i | \(0.980471\pi\) | |||||||
\(648\) | 324.000 | − | 561.184i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −715.500 | − | 1239.28i | −0.0432755 | − | 0.0749555i | ||||
\(650\) | −17600.0 | −1.06204 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6704.00 | 0.402682 | ||||||||
\(653\) | 9583.50 | + | 16599.1i | 0.574321 | + | 0.994752i | 0.996115 | + | 0.0880610i | \(0.0280670\pi\) |
−0.421795 | + | 0.906691i | \(0.638600\pi\) | |||||||
\(654\) | 42.0000 | − | 72.7461i | 0.00251121 | − | 0.00434954i | ||||
\(655\) | −8797.50 | + | 15237.7i | −0.524804 | + | 0.908988i | ||||
\(656\) | −1344.00 | − | 2327.88i | −0.0799914 | − | 0.138549i | ||||
\(657\) | −1962.00 | −0.116507 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13080.0 | 0.773178 | 0.386589 | − | 0.922252i | \(-0.373653\pi\) | ||||
0.386589 | + | 0.922252i | \(0.373653\pi\) | |||||||
\(660\) | 810.000 | + | 1402.96i | 0.0477715 | + | 0.0827427i | ||||
\(661\) | −7595.00 | + | 13154.9i | −0.446916 | + | 0.774081i | −0.998183 | − | 0.0602477i | \(-0.980811\pi\) |
0.551268 | + | 0.834328i | \(0.314144\pi\) | |||||||
\(662\) | −3964.00 | + | 6865.85i | −0.232727 | + | 0.403095i | ||||
\(663\) | −11088.0 | − | 19205.0i | −0.649506 | − | 1.12498i | ||||
\(664\) | −4776.00 | −0.279134 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −792.000 | −0.0460801 | ||||||||
\(667\) | 2142.00 | + | 3710.05i | 0.124346 | + | 0.215373i | ||||
\(668\) | 6060.00 | − | 10496.2i | 0.351001 | − | 0.607951i | ||||
\(669\) | −2359.50 | + | 4086.77i | −0.136358 | + | 0.236179i | ||||
\(670\) | −2490.00 | − | 4312.81i | −0.143578 | − | 0.248684i | ||||
\(671\) | 6498.00 | 0.373849 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4397.00 | 0.251845 | 0.125923 | − | 0.992040i | \(-0.459811\pi\) | ||||
0.125923 | + | 0.992040i | \(0.459811\pi\) | |||||||
\(674\) | 161.000 | + | 278.860i | 0.00920102 | + | 0.0159366i | ||||
\(675\) | −1350.00 | + | 2338.27i | −0.0769800 | + | 0.133333i | ||||
\(676\) | −11094.0 | + | 19215.4i | −0.631202 | + | 1.09327i | ||||
\(677\) | 2014.50 | + | 3489.22i | 0.114363 | + | 0.198082i | 0.917525 | − | 0.397679i | \(-0.130184\pi\) |
−0.803162 | + | 0.595761i | \(0.796851\pi\) | |||||||
\(678\) | 13104.0 | 0.742266 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −10080.0 | −0.568456 | ||||||||
\(681\) | 1381.50 | + | 2392.83i | 0.0777374 | + | 0.134645i | ||||
\(682\) | 1665.00 | − | 2883.86i | 0.0934841 | − | 0.161919i | ||||
\(683\) | −7510.50 | + | 13008.6i | −0.420763 | + | 0.728783i | −0.996014 | − | 0.0891936i | \(-0.971571\pi\) |
0.575251 | + | 0.817977i | \(0.304904\pi\) | |||||||
\(684\) | 1872.00 | + | 3242.40i | 0.104646 | + | 0.181252i | ||||
\(685\) | 450.000 | 0.0251002 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12156.0 | −0.675081 | ||||||||
\(688\) | −2608.00 | − | 4517.19i | −0.144519 | − | 0.250314i | ||||
\(689\) | −28116.0 | + | 48698.3i | −1.55462 | + | 2.69268i | ||||
\(690\) | −3780.00 | + | 6547.15i | −0.208554 | + | 0.361226i | ||||
\(691\) | −6992.00 | − | 12110.5i | −0.384932 | − | 0.666722i | 0.606828 | − | 0.794834i | \(-0.292442\pi\) |
−0.991760 | + | 0.128111i | \(0.959109\pi\) | |||||||
\(692\) | −13752.0 | −0.755452 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11832.0 | 0.647171 | ||||||||
\(695\) | −615.000 | − | 1065.21i | −0.0335659 | − | 0.0581378i | ||||
\(696\) | 612.000 | − | 1060.02i | 0.0333302 | − | 0.0577296i | ||||
\(697\) | −7056.00 | + | 12221.4i | −0.383451 | + | 0.664156i | ||||
\(698\) | 142.000 | + | 245.951i | 0.00770026 | + | 0.0133372i | ||||
\(699\) | −1404.00 | −0.0759716 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31053.0 | −1.67312 | −0.836559 | − | 0.547877i | \(-0.815436\pi\) | ||||
−0.836559 | + | 0.547877i | \(0.815436\pi\) | |||||||
\(702\) | 2376.00 | + | 4115.35i | 0.127744 | + | 0.221259i | ||||
\(703\) | 2288.00 | − | 3962.93i | 0.122750 | − | 0.212610i | ||||
\(704\) | 288.000 | − | 498.831i | 0.0154182 | − | 0.0267051i | ||||
\(705\) | −3105.00 | − | 5378.02i | −0.165874 | − | 0.287302i | ||||
\(706\) | −8880.00 | −0.473376 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1908.00 | −0.101281 | ||||||||
\(709\) | −7543.00 | − | 13064.9i | −0.399553 | − | 0.692047i | 0.594117 | − | 0.804378i | \(-0.297501\pi\) |
−0.993671 | + | 0.112332i | \(0.964168\pi\) | |||||||
\(710\) | 16290.0 | − | 28215.1i | 0.861060 | − | 1.49140i | ||||
\(711\) | 2623.50 | − | 4544.04i | 0.138381 | − | 0.239683i | ||||
\(712\) | 4152.00 | + | 7191.47i | 0.218543 | + | 0.378528i | ||||
\(713\) | 15540.0 | 0.816238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11880.0 | −0.621380 | ||||||||
\(716\) | 2424.00 | + | 4198.49i | 0.126521 | + | 0.219141i | ||||
\(717\) | −7398.00 | + | 12813.7i | −0.385332 | + | 0.667415i | ||||
\(718\) | 2286.00 | − | 3959.47i | 0.118820 | − | 0.205802i | ||||
\(719\) | −3189.00 | − | 5523.51i | −0.165410 | − | 0.286498i | 0.771391 | − | 0.636362i | \(-0.219561\pi\) |
−0.936801 | + | 0.349863i | \(0.886228\pi\) | |||||||
\(720\) | 2160.00 | 0.111803 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7914.00 | −0.407934 | ||||||||
\(723\) | −2305.50 | − | 3993.24i | −0.118593 | − | 0.205408i | ||||
\(724\) | 6064.00 | − | 10503.2i | 0.311280 | − | 0.539153i | ||||
\(725\) | −2550.00 | + | 4416.73i | −0.130627 | + | 0.226253i | ||||
\(726\) | −3750.00 | − | 6495.19i | −0.191702 | − | 0.332037i | ||||
\(727\) | 7363.00 | 0.375624 | 0.187812 | − | 0.982205i | \(-0.439860\pi\) | ||||
0.187812 | + | 0.982205i | \(0.439860\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −3270.00 | − | 5663.81i | −0.165792 | − | 0.287160i | ||||
\(731\) | −13692.0 | + | 23715.2i | −0.692773 | + | 1.19992i | ||||
\(732\) | 4332.00 | − | 7503.24i | 0.218737 | − | 0.378863i | ||||
\(733\) | 16405.0 | + | 28414.3i | 0.826647 | + | 1.43180i | 0.900654 | + | 0.434537i | \(0.143088\pi\) |
−0.0740064 | + | 0.997258i | \(0.523579\pi\) | |||||||
\(734\) | −5738.00 | −0.288547 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2688.00 | 0.134621 | ||||||||
\(737\) | −747.000 | − | 1293.84i | −0.0373353 | − | 0.0646666i | ||||
\(738\) | 1512.00 | − | 2618.86i | 0.0754167 | − | 0.130625i | ||||
\(739\) | 12017.0 | − | 20814.1i | 0.598177 | − | 1.03607i | −0.394914 | − | 0.918718i | \(-0.629225\pi\) |
0.993090 | − | 0.117354i | \(-0.0374412\pi\) | |||||||
\(740\) | −1320.00 | − | 2286.31i | −0.0655732 | − | 0.113576i | ||||
\(741\) | −27456.0 | −1.36116 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8022.00 | −0.396095 | −0.198048 | − | 0.980192i | \(-0.563460\pi\) | ||||
−0.198048 | + | 0.980192i | \(0.563460\pi\) | |||||||
\(744\) | −2220.00 | − | 3845.15i | −0.109394 | − | 0.189476i | ||||
\(745\) | 10755.0 | − | 18628.2i | 0.528903 | − | 0.916087i | ||||
\(746\) | −3064.00 | + | 5307.00i | −0.150377 | + | 0.260460i | ||||
\(747\) | −2686.50 | − | 4653.15i | −0.131585 | − | 0.227912i | ||||
\(748\) | −3024.00 | −0.147819 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2250.00 | 0.109545 | ||||||||
\(751\) | −14759.5 | − | 25564.2i | −0.717153 | − | 1.24215i | −0.962123 | − | 0.272615i | \(-0.912112\pi\) |
0.244970 | − | 0.969531i | \(-0.421222\pi\) | |||||||
\(752\) | −1104.00 | + | 1912.18i | −0.0535356 | + | 0.0927263i | ||||
\(753\) | 7978.50 | − | 13819.2i | 0.386126 | − | 0.668789i | ||||
\(754\) | 4488.00 | + | 7773.44i | 0.216768 | + | 0.375454i | ||||
\(755\) | −40065.0 | −1.93128 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3742.00 | −0.179664 | −0.0898318 | − | 0.995957i | \(-0.528633\pi\) | ||||
−0.0898318 | + | 0.995957i | \(0.528633\pi\) | |||||||
\(758\) | −6040.00 | − | 10461.6i | −0.289423 | − | 0.501295i | ||||
\(759\) | −1134.00 | + | 1964.15i | −0.0542313 | + | 0.0939314i | ||||
\(760\) | −6240.00 | + | 10808.0i | −0.297827 | + | 0.515852i | ||||
\(761\) | −5448.00 | − | 9436.21i | −0.259514 | − | 0.449491i | 0.706598 | − | 0.707615i | \(-0.250229\pi\) |
−0.966112 | + | 0.258124i | \(0.916896\pi\) | |||||||
\(762\) | 2238.00 | 0.106397 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10080.0 | 0.477332 | ||||||||
\(765\) | −5670.00 | − | 9820.73i | −0.267973 | − | 0.464143i | ||||
\(766\) | −1842.00 | + | 3190.44i | −0.0868853 | + | 0.150490i | ||||
\(767\) | 6996.00 | − | 12117.4i | 0.329349 | − | 0.570450i | ||||
\(768\) | −384.000 | − | 665.108i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | −17285.0 | −0.810550 | −0.405275 | − | 0.914195i | \(-0.632824\pi\) | ||||
−0.405275 | + | 0.914195i | \(0.632824\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16038.0 | −0.749150 | ||||||||
\(772\) | −730.000 | − | 1264.40i | −0.0340327 | − | 0.0589464i | ||||
\(773\) | 5913.00 | − | 10241.6i | 0.275130 | − | 0.476540i | −0.695038 | − | 0.718973i | \(-0.744612\pi\) |
0.970168 | + | 0.242434i | \(0.0779456\pi\) | |||||||
\(774\) | 2934.00 | − | 5081.84i | 0.136254 | − | 0.235999i | ||||
\(775\) | 9250.00 | + | 16021.5i | 0.428735 | + | 0.742591i | ||||
\(776\) | −1352.00 | −0.0625438 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15660.0 | −0.721643 | ||||||||
\(779\) | 8736.00 | + | 15131.2i | 0.401797 | + | 0.695932i | ||||
\(780\) | −7920.00 | + | 13717.8i | −0.363566 | + | 0.629715i | ||||
\(781\) | 4887.00 | − | 8464.53i | 0.223906 | − | 0.387817i | ||||
\(782\) | −7056.00 | − | 12221.4i | −0.322662 | − | 0.558868i | ||||
\(783\) | 1377.00 | 0.0628480 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33780.0 | −1.53587 | ||||||||
\(786\) | 3519.00 | + | 6095.09i | 0.159693 | + | 0.276596i | ||||
\(787\) | 8857.00 | − | 15340.8i | 0.401166 | − | 0.694841i | −0.592701 | − | 0.805423i | \(-0.701938\pi\) |
0.993867 | + | 0.110582i | \(0.0352716\pi\) | |||||||
\(788\) | 3180.00 | − | 5507.92i | 0.143760 | − | 0.248999i | ||||
\(789\) | −1161.00 | − | 2010.91i | −0.0523862 | − | 0.0907355i | ||||
\(790\) | 17490.0 | 0.787679 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 648.000 | 0.0290728 | ||||||||
\(793\) | 31768.0 | + | 55023.8i | 1.42259 | + | 2.46400i | ||||
\(794\) | 14764.0 | − | 25572.0i | 0.659893 | − | 1.14297i | ||||
\(795\) | −14377.5 | + | 24902.6i | −0.641406 | + | 1.11095i | ||||
\(796\) | −10760.0 | − | 18636.9i | −0.479118 | − | 0.829857i | ||||
\(797\) | 24939.0 | 1.10839 | 0.554194 | − | 0.832388i | \(-0.313027\pi\) | ||||
0.554194 | + | 0.832388i | \(0.313027\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11592.0 | 0.513261 | ||||||||
\(800\) | 1600.00 | + | 2771.28i | 0.0707107 | + | 0.122474i | ||||
\(801\) | −4671.00 | + | 8090.41i | −0.206045 | + | 0.356880i | ||||
\(802\) | 6264.00 | − | 10849.6i | 0.275797 | − | 0.477695i | ||||
\(803\) | −981.000 | − | 1699.14i | −0.0431118 | − | 0.0746717i | ||||
\(804\) | −1992.00 | −0.0873786 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32560.0 | 1.42292 | ||||||||
\(807\) | 3622.50 | + | 6274.35i | 0.158015 | + | 0.273690i | ||||
\(808\) | −2568.00 | + | 4447.91i | −0.111809 | + | 0.193659i | ||||
\(809\) | 14532.0 | − | 25170.2i | 0.631543 | − | 1.09386i | −0.355694 | − | 0.934602i | \(-0.615755\pi\) |
0.987236 | − | 0.159261i | \(-0.0509112\pi\) | |||||||
\(810\) | 1215.00 | + | 2104.44i | 0.0527046 | + | 0.0912871i | ||||
\(811\) | 15370.0 | 0.665492 | 0.332746 | − | 0.943017i | \(-0.392025\pi\) | ||||
0.332746 | + | 0.943017i | \(0.392025\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1425.00 | 0.0614722 | ||||||||
\(814\) | −396.000 | − | 685.892i | −0.0170513 | − | 0.0295338i | ||||
\(815\) | −12570.0 | + | 21771.9i | −0.540255 | + | 0.935749i | ||||
\(816\) | −2016.00 | + | 3491.81i | −0.0864879 | + | 0.149801i | ||||
\(817\) | 16952.0 | + | 29361.7i | 0.725918 | + | 1.25733i | ||||
\(818\) | 9502.00 | 0.406149 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10080.0 | 0.429279 | ||||||||
\(821\) | −22015.5 | − | 38132.0i | −0.935866 | − | 1.62097i | −0.773082 | − | 0.634306i | \(-0.781286\pi\) |
−0.162785 | − | 0.986662i | \(-0.552048\pi\) | |||||||
\(822\) | 90.0000 | − | 155.885i | 0.00381887 | − | 0.00661448i | ||||
\(823\) | 2096.00 | − | 3630.38i | 0.0887752 | − | 0.153763i | −0.818218 | − | 0.574907i | \(-0.805038\pi\) |
0.906994 | + | 0.421144i | \(0.138371\pi\) | |||||||
\(824\) | −1856.00 | − | 3214.69i | −0.0784670 | − | 0.135909i | ||||
\(825\) | −2700.00 | −0.113942 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33195.0 | 1.39577 | 0.697886 | − | 0.716209i | \(-0.254124\pi\) | ||||
0.697886 | + | 0.716209i | \(0.254124\pi\) | |||||||
\(828\) | 1512.00 | + | 2618.86i | 0.0634609 | + | 0.109918i | ||||
\(829\) | 8224.00 | − | 14244.4i | 0.344549 | − | 0.596777i | −0.640723 | − | 0.767773i | \(-0.721365\pi\) |
0.985272 | + | 0.170996i | \(0.0546984\pi\) | |||||||
\(830\) | 8955.00 | − | 15510.5i | 0.374497 | − | 0.648648i | ||||
\(831\) | −5592.00 | − | 9685.63i | −0.233435 | − | 0.404321i | ||||
\(832\) | 5632.00 | 0.234681 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −492.000 | −0.0204275 | ||||||||
\(835\) | 22725.0 | + | 39360.9i | 0.941834 | + | 1.63130i | ||||
\(836\) | −1872.00 | + | 3242.40i | −0.0774455 | + | 0.134140i | ||||
\(837\) | 2497.50 | − | 4325.80i | 0.103138 | − | 0.178640i | ||||
\(838\) | 4704.00 | + | 8147.57i | 0.193910 | + | 0.335863i | ||||
\(839\) | −16860.0 | −0.693769 | −0.346884 | − | 0.937908i | \(-0.612760\pi\) | ||||
−0.346884 | + | 0.937908i | \(0.612760\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21788.0 | −0.893354 | ||||||||
\(842\) | −4474.00 | − | 7749.20i | −0.183117 | − | 0.317167i | ||||
\(843\) | −2403.00 | + | 4162.12i | −0.0981776 | + | 0.170049i | ||||
\(844\) | 10724.0 | − | 18574.5i | 0.437364 | − | 0.757537i | ||||
\(845\) | −41602.5 | − | 72057.6i | −1.69369 | − | 2.93356i | ||||
\(846\) | −2484.00 | −0.100948 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10224.0 | 0.414025 | ||||||||
\(849\) | 1029.00 | + | 1782.28i | 0.0415962 | + | 0.0720468i | ||||
\(850\) | 8400.00 | − | 14549.2i | 0.338962 | − | 0.587099i | ||||
\(851\) | 1848.00 | − | 3200.83i | 0.0744402 | − | 0.128934i | ||||
\(852\) | −6516.00 | − | 11286.0i | −0.262012 | − | 0.453819i | ||||
\(853\) | −29054.0 | −1.16623 | −0.583113 | − | 0.812391i | \(-0.698165\pi\) | ||||
−0.583113 | + | 0.812391i | \(0.698165\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14040.0 | −0.561588 | ||||||||
\(856\) | 1572.00 | + | 2722.78i | 0.0627685 | + | 0.108718i | ||||
\(857\) | 20979.0 | − | 36336.7i | 0.836207 | − | 1.44835i | −0.0568378 | − | 0.998383i | \(-0.518102\pi\) |
0.893044 | − | 0.449969i | \(-0.148565\pi\) | |||||||
\(858\) | −2376.00 | + | 4115.35i | −0.0945400 | + | 0.163748i | ||||
\(859\) | 2773.00 | + | 4802.98i | 0.110144 | + | 0.190775i | 0.915828 | − | 0.401570i | \(-0.131536\pi\) |
−0.805684 | + | 0.592345i | \(0.798202\pi\) | |||||||
\(860\) | 19560.0 | 0.775570 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25608.0 | 1.01185 | ||||||||
\(863\) | 16269.0 | + | 28178.7i | 0.641719 | + | 1.11149i | 0.985049 | + | 0.172275i | \(0.0551116\pi\) |
−0.343330 | + | 0.939215i | \(0.611555\pi\) | |||||||
\(864\) | 432.000 | − | 748.246i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 25785.0 | − | 44660.9i | 1.01354 | − | 1.75551i | ||||
\(866\) | 5074.00 | + | 8788.43i | 0.199101 | + | 0.344853i | ||||
\(867\) | 6429.00 | 0.251834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5247.00 | 0.204824 | ||||||||
\(870\) | 2295.00 | + | 3975.06i | 0.0894342 | + | 0.154905i | ||||
\(871\) | 7304.00 | − | 12650.9i | 0.284141 | − | 0.492146i | ||||
\(872\) | 56.0000 | − | 96.9948i | 0.00217477 | − | 0.00376681i | ||||
\(873\) | −760.500 | − | 1317.22i | −0.0294834 | − | 0.0510668i | ||||
\(874\) | −17472.0 | −0.676200 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2616.00 | −0.100898 | ||||||||
\(877\) | −16048.0 | − | 27796.0i | −0.617905 | − | 1.07024i | −0.989867 | − | 0.141995i | \(-0.954648\pi\) |
0.371963 | − | 0.928248i | \(-0.378685\pi\) | |||||||
\(878\) | 1267.00 | − | 2194.51i | 0.0487007 | − | 0.0843520i | ||||
\(879\) | −1651.50 | + | 2860.48i | −0.0633717 | + | 0.109763i | ||||
\(880\) | 1080.00 | + | 1870.61i | 0.0413714 | + | 0.0716573i | ||||
\(881\) | 8490.00 | 0.324671 | 0.162336 | − | 0.986736i | \(-0.448097\pi\) | ||||
0.162336 | + | 0.986736i | \(0.448097\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48352.0 | −1.84278 | −0.921390 | − | 0.388640i | \(-0.872945\pi\) | ||||
−0.921390 | + | 0.388640i | \(0.872945\pi\) | |||||||
\(884\) | −14784.0 | − | 25606.6i | −0.562488 | − | 0.974258i | ||||
\(885\) | 3577.50 | − | 6196.41i | 0.135883 | − | 0.235356i | ||||
\(886\) | −6933.00 | + | 12008.3i | −0.262888 | + | 0.455335i | ||||
\(887\) | 7746.00 | + | 13416.5i | 0.293219 | + | 0.507870i | 0.974569 | − | 0.224088i | \(-0.0719402\pi\) |
−0.681350 | + | 0.731958i | \(0.738607\pi\) | |||||||
\(888\) | −1056.00 | −0.0399066 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −31140.0 | −1.17283 | ||||||||
\(891\) | 364.500 | + | 631.333i | 0.0137051 | + | 0.0237379i | ||||
\(892\) | −3146.00 | + | 5449.03i | −0.118090 | + | 0.204537i | ||||
\(893\) | 7176.00 | − | 12429.2i | 0.268909 | − | 0.465764i | ||||
\(894\) | −4302.00 | − | 7451.28i | −0.160940 | − | 0.278756i | ||||
\(895\) | −18180.0 | −0.678984 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22176.0 | −0.825457 | ||||||||
\(898\) | 11688.0 | + | 20244.2i | 0.434336 | + | 0.752292i | ||||
\(899\) | 4717.50 | − | 8170.95i | 0.175014 | − | 0.303133i | ||||
\(900\) | −1800.00 | + | 3117.69i | −0.0666667 | + | 0.115470i | ||||
\(901\) | −26838.0 | − | 46484.8i | −0.992346 | − | 1.71879i | ||||
\(902\) | 3024.00 | 0.111628 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17472.0 | 0.642821 | ||||||||
\(905\) | 22740.0 | + | 39386.8i | 0.835252 | + | 1.44670i | ||||
\(906\) | −8013.00 | + | 13878.9i | −0.293835 | + | 0.508936i | ||||
\(907\) | 4058.00 | − | 7028.66i | 0.148560 | − | 0.257313i | −0.782136 | − | 0.623108i | \(-0.785870\pi\) |
0.930695 | + | 0.365795i | \(0.119203\pi\) | |||||||
\(908\) | 1842.00 | + | 3190.44i | 0.0673226 | + | 0.116606i | ||||
\(909\) | −5778.00 | −0.210830 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4446.00 | −0.161693 | −0.0808466 | − | 0.996727i | \(-0.525762\pi\) | ||||
−0.0808466 | + | 0.996727i | \(0.525762\pi\) | |||||||
\(912\) | 2496.00 | + | 4323.20i | 0.0906259 | + | 0.156969i | ||||
\(913\) | 2686.50 | − | 4653.15i | 0.0973824 | − | 0.168671i | ||||
\(914\) | 551.000 | − | 954.360i | 0.0199403 | − | 0.0345377i | ||||
\(915\) | 16245.0 | + | 28137.2i | 0.586932 | + | 1.01660i | ||||
\(916\) | −16208.0 | −0.584637 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4536.00 | −0.163083 | ||||||||
\(919\) | −13252.0 | − | 22953.1i | −0.475673 | − | 0.823889i | 0.523939 | − | 0.851756i | \(-0.324462\pi\) |
−0.999612 | + | 0.0278666i | \(0.991129\pi\) | |||||||
\(920\) | −5040.00 | + | 8729.54i | −0.180613 | + | 0.312831i | ||||
\(921\) | 4170.00 | − | 7222.65i | 0.149192 | − | 0.258409i | ||||
\(922\) | −13386.0 | − | 23185.2i | −0.478139 | − | 0.828162i | ||||
\(923\) | 95568.0 | 3.40808 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4400.00 | 0.156401 | ||||||||
\(926\) | −6376.00 | − | 11043.6i | −0.226273 | − | 0.391916i | ||||
\(927\) | 2088.00 | − | 3616.52i | 0.0739794 | − | 0.128136i | ||||
\(928\) | 816.000 | − | 1413.35i | 0.0288648 | − | 0.0499953i | ||||
\(929\) | −2715.00 | − | 4702.52i | −0.0958840 | − | 0.166076i | 0.814093 | − | 0.580734i | \(-0.197234\pi\) |
−0.909977 | + | 0.414658i | \(0.863901\pi\) | |||||||
\(930\) | 16650.0 | 0.587070 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1872.00 | −0.0657933 | ||||||||
\(933\) | 6444.00 | + | 11161.3i | 0.226117 | + | 0.391646i | ||||
\(934\) | −5700.00 | + | 9872.69i | −0.199689 | + | 0.345872i | ||||
\(935\) | 5670.00 | − | 9820.73i | 0.198320 | − | 0.343500i | ||||
\(936\) | 3168.00 | + | 5487.14i | 0.110630 | + | 0.191616i | ||||
\(937\) | −33803.0 | −1.17854 | −0.589272 | − | 0.807935i | \(-0.700585\pi\) | ||||
−0.589272 | + | 0.807935i | \(0.700585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16467.0 | −0.572290 | ||||||||
\(940\) | −4140.00 | − | 7170.69i | −0.143651 | − | 0.248811i | ||||
\(941\) | −24241.5 | + | 41987.5i | −0.839798 | + | 1.45457i | 0.0502645 | + | 0.998736i | \(0.483994\pi\) |
−0.890063 | + | 0.455838i | \(0.849340\pi\) | |||||||
\(942\) | −6756.00 | + | 11701.7i | −0.233676 | + | 0.404738i | ||||
\(943\) | 7056.00 | + | 12221.4i | 0.243664 | + | 0.422038i | ||||
\(944\) | −2544.00 | −0.0877120 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5868.00 | 0.201676 | ||||||||
\(947\) | −18648.0 | − | 32299.3i | −0.639893 | − | 1.10833i | −0.985456 | − | 0.169931i | \(-0.945645\pi\) |
0.345563 | − | 0.938396i | \(-0.387688\pi\) | |||||||
\(948\) | 3498.00 | − | 6058.71i | 0.119842 | − | 0.207572i | ||||
\(949\) | 9592.00 | − | 16613.8i | 0.328103 | − | 0.568291i | ||||
\(950\) | −10400.0 | − | 18013.3i | −0.355180 | − | 0.615189i | ||||
\(951\) | 13473.0 | 0.459403 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38478.0 | −1.30790 | −0.653948 | − | 0.756540i | \(-0.726888\pi\) | ||||
−0.653948 | + | 0.756540i | \(0.726888\pi\) | |||||||
\(954\) | 5751.00 | + | 9961.02i | 0.195173 | + | 0.338050i | ||||
\(955\) | −18900.0 | + | 32735.8i | −0.640408 | + | 1.10922i | ||||
\(956\) | −9864.00 | + | 17084.9i | −0.333708 | + | 0.577999i | ||||
\(957\) | 688.500 | + | 1192.52i | 0.0232561 | + | 0.0402807i | ||||
\(958\) | 39588.0 | 1.33510 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2880.00 | 0.0968246 | ||||||||
\(961\) | −2217.00 | − | 3839.96i | −0.0744184 | − | 0.128897i | ||||
\(962\) | 3872.00 | − | 6706.50i | 0.129770 | − | 0.224767i | ||||
\(963\) | −1768.50 | + | 3063.13i | −0.0591787 | + | 0.102501i | ||||
\(964\) | −3074.00 | − | 5324.32i | −0.102704 | − | 0.177889i | ||||
\(965\) | 5475.00 | 0.182639 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27257.0 | 0.906438 | 0.453219 | − | 0.891399i | \(-0.350275\pi\) | ||||
0.453219 | + | 0.891399i | \(0.350275\pi\) | |||||||
\(968\) | −5000.00 | − | 8660.25i | −0.166019 | − | 0.287553i | ||||
\(969\) | 13104.0 | − | 22696.8i | 0.434428 | − | 0.752452i | ||||
\(970\) | 2535.00 | − | 4390.75i | 0.0839113 | − | 0.145339i | ||||
\(971\) | 17170.5 | + | 29740.2i | 0.567485 | + | 0.982912i | 0.996814 | + | 0.0797641i | \(0.0254167\pi\) |
−0.429329 | + | 0.903148i | \(0.641250\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −31870.0 | −1.04844 | ||||||||
\(975\) | −13200.0 | − | 22863.1i | −0.433578 | − | 0.750979i | ||||
\(976\) | 5776.00 | − | 10004.3i | 0.189432 | − | 0.328105i | ||||
\(977\) | −13713.0 | + | 23751.6i | −0.449046 | + | 0.777770i | −0.998324 | − | 0.0578693i | \(-0.981569\pi\) |
0.549278 | + | 0.835639i | \(0.314903\pi\) | |||||||
\(978\) | 5028.00 | + | 8708.75i | 0.164394 | + | 0.284739i | ||||
\(979\) | −9342.00 | −0.304976 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 126.000 | 0.00410079 | ||||||||
\(982\) | 9963.00 | + | 17256.4i | 0.323760 | + | 0.560768i | ||||
\(983\) | 6162.00 | − | 10672.9i | 0.199936 | − | 0.346300i | −0.748571 | − | 0.663054i | \(-0.769260\pi\) |
0.948508 | + | 0.316755i | \(0.102593\pi\) | |||||||
\(984\) | 2016.00 | − | 3491.81i | 0.0653127 | − | 0.113125i | ||||
\(985\) | 11925.0 | + | 20654.7i | 0.385748 | + | 0.668136i | ||||
\(986\) | −8568.00 | −0.276735 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −36608.0 | −1.17880 | ||||||||
\(989\) | 13692.0 | + | 23715.2i | 0.440223 | + | 0.762488i | ||||
\(990\) | −1215.00 | + | 2104.44i | −0.0390053 | + | 0.0675591i | ||||
\(991\) | −23798.5 | + | 41220.2i | −0.762850 | + | 1.32129i | 0.178526 | + | 0.983935i | \(0.442867\pi\) |
−0.941376 | + | 0.337360i | \(0.890466\pi\) | |||||||
\(992\) | −2960.00 | − | 5126.87i | −0.0947380 | − | 0.164091i | ||||
\(993\) | −11892.0 | −0.380042 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 80700.0 | 2.57122 | ||||||||
\(996\) | −3582.00 | − | 6204.21i | −0.113956 | − | 0.197377i | ||||
\(997\) | −5621.00 | + | 9735.86i | −0.178555 | + | 0.309266i | −0.941386 | − | 0.337332i | \(-0.890475\pi\) |
0.762831 | + | 0.646598i | \(0.223809\pi\) | |||||||
\(998\) | 19142.0 | − | 33154.9i | 0.607144 | − | 1.05160i | ||||
\(999\) | −594.000 | − | 1028.84i | −0.0188121 | − | 0.0325836i |
(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 | 294.4.e.e.67.1 | 2 | ||
3.2 | odd | 2 | 882.4.g.l.361.1 | 2 | |||
7.2 | even | 3 | inner | 294.4.e.e.79.1 | 2 | ||
7.3 | odd | 6 | 294.4.a.a.1.1 | 1 | |||
7.4 | even | 3 | 294.4.a.g.1.1 | 1 | |||
7.5 | odd | 6 | 42.4.e.b.37.1 | yes | 2 | ||
7.6 | odd | 2 | 42.4.e.b.25.1 | ✓ | 2 | ||
21.2 | odd | 6 | 882.4.g.l.667.1 | 2 | |||
21.5 | even | 6 | 126.4.g.a.37.1 | 2 | |||
21.11 | odd | 6 | 882.4.a.h.1.1 | 1 | |||
21.17 | even | 6 | 882.4.a.r.1.1 | 1 | |||
21.20 | even | 2 | 126.4.g.a.109.1 | 2 | |||
28.3 | even | 6 | 2352.4.a.u.1.1 | 1 | |||
28.11 | odd | 6 | 2352.4.a.q.1.1 | 1 | |||
28.19 | even | 6 | 336.4.q.d.289.1 | 2 | |||
28.27 | even | 2 | 336.4.q.d.193.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.b.25.1 | ✓ | 2 | 7.6 | odd | 2 | ||
42.4.e.b.37.1 | yes | 2 | 7.5 | odd | 6 | ||
126.4.g.a.37.1 | 2 | 21.5 | even | 6 | |||
126.4.g.a.109.1 | 2 | 21.20 | even | 2 | |||
294.4.a.a.1.1 | 1 | 7.3 | odd | 6 | |||
294.4.a.g.1.1 | 1 | 7.4 | even | 3 | |||
294.4.e.e.67.1 | 2 | 1.1 | even | 1 | trivial | ||
294.4.e.e.79.1 | 2 | 7.2 | even | 3 | inner | ||
336.4.q.d.193.1 | 2 | 28.27 | even | 2 | |||
336.4.q.d.289.1 | 2 | 28.19 | even | 6 | |||
882.4.a.h.1.1 | 1 | 21.11 | odd | 6 | |||
882.4.a.r.1.1 | 1 | 21.17 | even | 6 | |||
882.4.g.l.361.1 | 2 | 3.2 | odd | 2 | |||
882.4.g.l.667.1 | 2 | 21.2 | odd | 6 | |||
2352.4.a.q.1.1 | 1 | 28.11 | odd | 6 | |||
2352.4.a.u.1.1 | 1 | 28.3 | even | 6 |