Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,5,Mod(2,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.h (of order \(6\), degree \(2\), 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: | \(2.17076922476\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 103 x^{14} + 7227 x^{12} - 270898 x^{10} + 7374256 x^{8} - 115494792 x^{6} + 1245573504 x^{4} + \cdots + 5639409216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2.7 | ||
Root | \(4.46939 + 2.58040i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.2 |
Dual form | 21.5.h.b.11.7 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.46939 | + | 2.58040i | 1.11735 | + | 0.645101i | 0.940723 | − | 0.339177i | \(-0.110149\pi\) |
0.176625 | + | 0.984278i | \(0.443482\pi\) | |||||||
\(3\) | −6.70973 | + | 5.99830i | −0.745525 | + | 0.666477i | ||||
\(4\) | 5.31698 | + | 9.20927i | 0.332311 | + | 0.575579i | ||||
\(5\) | 31.7353 | + | 18.3224i | 1.26941 | + | 0.732896i | 0.974877 | − | 0.222744i | \(-0.0715015\pi\) |
0.294536 | + | 0.955640i | \(0.404835\pi\) | |||||||
\(6\) | −45.4664 | + | 9.49493i | −1.26296 | + | 0.263748i | ||||
\(7\) | −18.9163 | − | 45.2015i | −0.386047 | − | 0.922479i | ||||
\(8\) | − | 27.6932i | − | 0.432706i | ||||||
\(9\) | 9.04086 | − | 80.4939i | 0.111616 | − | 0.993751i | ||||
\(10\) | 94.5584 | + | 163.780i | 0.945584 | + | 1.63780i | ||||
\(11\) | −32.7370 | + | 18.9007i | −0.270554 | + | 0.156204i | −0.629139 | − | 0.777292i | \(-0.716593\pi\) |
0.358585 | + | 0.933497i | \(0.383259\pi\) | |||||||
\(12\) | −90.9154 | − | 29.8989i | −0.631357 | − | 0.207631i | ||||
\(13\) | 127.139 | 0.752300 | 0.376150 | − | 0.926559i | \(-0.377248\pi\) | ||||
0.376150 | + | 0.926559i | \(0.377248\pi\) | |||||||
\(14\) | 32.0939 | − | 250.835i | 0.163744 | − | 1.27977i | ||||
\(15\) | −322.839 | + | 67.4196i | −1.43484 | + | 0.299643i | ||||
\(16\) | 156.531 | − | 271.120i | 0.611450 | − | 1.05906i | ||||
\(17\) | −248.343 | + | 143.381i | −0.859318 | + | 0.496127i | −0.863784 | − | 0.503863i | \(-0.831912\pi\) |
0.00446598 | + | 0.999990i | \(0.498578\pi\) | |||||||
\(18\) | 248.114 | − | 336.430i | 0.765784 | − | 1.03836i | ||||
\(19\) | −161.952 | + | 280.509i | −0.448620 | + | 0.777032i | −0.998296 | − | 0.0583452i | \(-0.981418\pi\) |
0.549677 | + | 0.835378i | \(0.314751\pi\) | |||||||
\(20\) | 389.679i | 0.974197i | ||||||||
\(21\) | 398.055 | + | 189.824i | 0.902619 | + | 0.430440i | ||||
\(22\) | −195.086 | −0.403071 | ||||||||
\(23\) | −303.425 | − | 175.183i | −0.573583 | − | 0.331158i | 0.184996 | − | 0.982739i | \(-0.440773\pi\) |
−0.758579 | + | 0.651581i | \(0.774106\pi\) | |||||||
\(24\) | 166.112 | + | 185.814i | 0.288389 | + | 0.322593i | ||||
\(25\) | 358.921 | + | 621.669i | 0.574273 | + | 0.994670i | ||||
\(26\) | 568.233 | + | 328.069i | 0.840581 | + | 0.485310i | ||||
\(27\) | 422.164 | + | 594.322i | 0.579101 | + | 0.815256i | ||||
\(28\) | 315.695 | − | 414.540i | 0.402673 | − | 0.528750i | ||||
\(29\) | 210.131i | 0.249858i | 0.992166 | + | 0.124929i | \(0.0398703\pi\) | ||||
−0.992166 | + | 0.124929i | \(0.960130\pi\) | |||||||
\(30\) | −1616.86 | − | 531.729i | −1.79651 | − | 0.590810i | ||||
\(31\) | −658.024 | − | 1139.73i | −0.684728 | − | 1.18598i | −0.973522 | − | 0.228593i | \(-0.926588\pi\) |
0.288794 | − | 0.957391i | \(-0.406746\pi\) | |||||||
\(32\) | 1015.47 | − | 586.282i | 0.991670 | − | 0.572541i | ||||
\(33\) | 106.284 | − | 323.185i | 0.0975981 | − | 0.296773i | ||||
\(34\) | −1479.92 | −1.28021 | ||||||||
\(35\) | 227.885 | − | 1781.08i | 0.186029 | − | 1.45394i | ||||
\(36\) | 789.360 | − | 344.724i | 0.609074 | − | 0.265991i | ||||
\(37\) | −497.558 | + | 861.795i | −0.363446 | + | 0.629507i | −0.988525 | − | 0.151054i | \(-0.951733\pi\) |
0.625079 | + | 0.780561i | \(0.285067\pi\) | |||||||
\(38\) | −1447.65 | + | 835.802i | −1.00253 | + | 0.578810i | ||||
\(39\) | −853.066 | + | 762.616i | −0.560859 | + | 0.501391i | ||||
\(40\) | 507.405 | − | 878.851i | 0.317128 | − | 0.549282i | ||||
\(41\) | 288.879i | 0.171850i | 0.996302 | + | 0.0859249i | \(0.0273845\pi\) | ||||
−0.996302 | + | 0.0859249i | \(0.972615\pi\) | |||||||
\(42\) | 1289.24 | + | 1875.54i | 0.730862 | + | 1.06323i | ||||
\(43\) | 1811.84 | 0.979902 | 0.489951 | − | 0.871750i | \(-0.337015\pi\) | ||||
0.489951 | + | 0.871750i | \(0.337015\pi\) | |||||||
\(44\) | −348.124 | − | 200.990i | −0.179816 | − | 0.103817i | ||||
\(45\) | 1761.76 | − | 2388.85i | 0.870003 | − | 1.17968i | ||||
\(46\) | −904.085 | − | 1565.92i | −0.427261 | − | 0.740038i | ||||
\(47\) | 91.1152 | + | 52.6054i | 0.0412473 | + | 0.0238141i | 0.520482 | − | 0.853873i | \(-0.325752\pi\) |
−0.479235 | + | 0.877687i | \(0.659086\pi\) | |||||||
\(48\) | 575.977 | + | 2758.06i | 0.249990 | + | 1.19708i | ||||
\(49\) | −1685.35 | + | 1710.09i | −0.701936 | + | 0.712240i | ||||
\(50\) | 3704.64i | 1.48186i | ||||||||
\(51\) | 806.272 | − | 2451.68i | 0.309985 | − | 0.942591i | ||||
\(52\) | 675.993 | + | 1170.85i | 0.249998 | + | 0.433008i | ||||
\(53\) | 2851.06 | − | 1646.06i | 1.01497 | − | 0.585996i | 0.102330 | − | 0.994750i | \(-0.467370\pi\) |
0.912644 | + | 0.408755i | \(0.134037\pi\) | |||||||
\(54\) | 353.228 | + | 3745.61i | 0.121135 | + | 1.28450i | ||||
\(55\) | −1385.23 | −0.457926 | ||||||||
\(56\) | −1251.77 | + | 523.852i | −0.399162 | + | 0.167045i | ||||
\(57\) | −595.922 | − | 2853.57i | −0.183417 | − | 0.878292i | ||||
\(58\) | −542.222 | + | 939.156i | −0.161184 | + | 0.279178i | ||||
\(59\) | −4709.64 | + | 2719.11i | −1.35296 | + | 0.781130i | −0.988663 | − | 0.150154i | \(-0.952023\pi\) |
−0.364294 | + | 0.931284i | \(0.618690\pi\) | |||||||
\(60\) | −2337.41 | − | 2614.64i | −0.649281 | − | 0.726289i | ||||
\(61\) | 1907.51 | − | 3303.91i | 0.512635 | − | 0.887909i | −0.487258 | − | 0.873258i | \(-0.662003\pi\) |
0.999893 | − | 0.0146511i | \(-0.00466374\pi\) | |||||||
\(62\) | − | 6791.87i | − | 1.76688i | ||||||
\(63\) | −3809.46 | + | 1113.98i | −0.959804 | + | 0.280671i | ||||
\(64\) | 1042.38 | 0.254488 | ||||||||
\(65\) | 4034.79 | + | 2329.49i | 0.954980 | + | 0.551358i | ||||
\(66\) | 1308.98 | − | 1170.19i | 0.300499 | − | 0.268638i | ||||
\(67\) | 4335.41 | + | 7509.16i | 0.965786 | + | 1.67279i | 0.707488 | + | 0.706726i | \(0.249829\pi\) |
0.258299 | + | 0.966065i | \(0.416838\pi\) | |||||||
\(68\) | −2640.87 | − | 1524.70i | −0.571121 | − | 0.329737i | ||||
\(69\) | 3086.70 | − | 644.608i | 0.648330 | − | 0.135393i | ||||
\(70\) | 5614.40 | − | 7372.29i | 1.14580 | − | 1.50455i | ||||
\(71\) | − | 3288.73i | − | 0.652397i | −0.945301 | − | 0.326198i | \(-0.894232\pi\) | ||
0.945301 | − | 0.326198i | \(-0.105768\pi\) | |||||||
\(72\) | −2229.13 | − | 250.370i | −0.430002 | − | 0.0482967i | ||||
\(73\) | 2766.11 | + | 4791.04i | 0.519067 | + | 0.899051i | 0.999754 | + | 0.0221588i | \(0.00705393\pi\) |
−0.480687 | + | 0.876892i | \(0.659613\pi\) | |||||||
\(74\) | −4447.56 | + | 2567.80i | −0.812191 | + | 0.468919i | ||||
\(75\) | −6137.21 | − | 2018.31i | −1.09106 | − | 0.358811i | ||||
\(76\) | −3444.37 | −0.596325 | ||||||||
\(77\) | 1473.60 | + | 1122.23i | 0.248542 | + | 0.189278i | ||||
\(78\) | −5780.54 | + | 1207.17i | −0.950122 | + | 0.198418i | ||||
\(79\) | 384.200 | − | 665.453i | 0.0615606 | − | 0.106626i | −0.833603 | − | 0.552365i | \(-0.813726\pi\) |
0.895163 | + | 0.445739i | \(0.147059\pi\) | |||||||
\(80\) | 9935.13 | − | 5736.05i | 1.55236 | − | 0.896258i | ||||
\(81\) | −6397.53 | − | 1455.47i | −0.975084 | − | 0.221836i | ||||
\(82\) | −745.426 | + | 1291.12i | −0.110860 | + | 0.192016i | ||||
\(83\) | 3700.12i | 0.537106i | 0.963265 | + | 0.268553i | \(0.0865454\pi\) | ||||
−0.963265 | + | 0.268553i | \(0.913455\pi\) | |||||||
\(84\) | 368.307 | + | 4675.09i | 0.0521977 | + | 0.662569i | ||||
\(85\) | −10508.3 | −1.45444 | ||||||||
\(86\) | 8097.82 | + | 4675.28i | 1.09489 | + | 0.632136i | ||||
\(87\) | −1260.43 | − | 1409.92i | −0.166525 | − | 0.186275i | ||||
\(88\) | 523.421 | + | 906.592i | 0.0675905 | + | 0.117070i | ||||
\(89\) | 4320.33 | + | 2494.34i | 0.545427 | + | 0.314902i | 0.747276 | − | 0.664514i | \(-0.231362\pi\) |
−0.201848 | + | 0.979417i | \(0.564695\pi\) | |||||||
\(90\) | 14038.2 | − | 6130.66i | 1.73311 | − | 0.756872i | ||||
\(91\) | −2404.99 | − | 5746.86i | −0.290423 | − | 0.693981i | ||||
\(92\) | − | 3725.77i | − | 0.440190i | ||||||
\(93\) | 11251.6 | + | 3700.26i | 1.30091 | + | 0.427825i | ||||
\(94\) | 271.486 | + | 470.228i | 0.0307250 | + | 0.0532173i | ||||
\(95\) | −10279.2 | + | 5934.69i | −1.13897 | + | 0.657583i | ||||
\(96\) | −3296.83 | + | 10024.9i | −0.357729 | + | 1.08777i | ||||
\(97\) | 1964.73 | 0.208814 | 0.104407 | − | 0.994535i | \(-0.466706\pi\) | ||||
0.104407 | + | 0.994535i | \(0.466706\pi\) | |||||||
\(98\) | −11945.2 | + | 3294.17i | −1.24377 | + | 0.343000i | ||||
\(99\) | 1225.42 | + | 2806.01i | 0.125030 | + | 0.286298i | ||||
\(100\) | −3816.74 | + | 6610.79i | −0.381674 | + | 0.661079i | ||||
\(101\) | −2685.48 | + | 1550.46i | −0.263256 | + | 0.151991i | −0.625819 | − | 0.779968i | \(-0.715235\pi\) |
0.362563 | + | 0.931959i | \(0.381902\pi\) | |||||||
\(102\) | 9929.87 | − | 8877.01i | 0.954428 | − | 0.853231i | ||||
\(103\) | 2952.98 | − | 5114.72i | 0.278347 | − | 0.482111i | −0.692627 | − | 0.721296i | \(-0.743547\pi\) |
0.970974 | + | 0.239185i | \(0.0768802\pi\) | |||||||
\(104\) | − | 3520.87i | − | 0.325524i | ||||||
\(105\) | 9154.37 | + | 13317.5i | 0.830329 | + | 1.20793i | ||||
\(106\) | 16990.0 | 1.51211 | ||||||||
\(107\) | −5864.51 | − | 3385.88i | −0.512229 | − | 0.295736i | 0.221520 | − | 0.975156i | \(-0.428898\pi\) |
−0.733750 | + | 0.679420i | \(0.762231\pi\) | |||||||
\(108\) | −3228.63 | + | 7047.82i | −0.276803 | + | 0.604237i | ||||
\(109\) | −3174.60 | − | 5498.57i | −0.267200 | − | 0.462803i | 0.700938 | − | 0.713222i | \(-0.252765\pi\) |
−0.968138 | + | 0.250419i | \(0.919432\pi\) | |||||||
\(110\) | −6191.12 | − | 3574.45i | −0.511663 | − | 0.295409i | ||||
\(111\) | −1830.83 | − | 8766.91i | −0.148594 | − | 0.711542i | ||||
\(112\) | −15216.0 | − | 1946.86i | −1.21301 | − | 0.155203i | ||||
\(113\) | − | 15830.6i | − | 1.23976i | −0.784695 | − | 0.619882i | \(-0.787180\pi\) | ||
0.784695 | − | 0.619882i | \(-0.212820\pi\) | |||||||
\(114\) | 4699.96 | − | 14291.4i | 0.361646 | − | 1.09968i | ||||
\(115\) | −6419.54 | − | 11119.0i | −0.485409 | − | 0.840753i | ||||
\(116\) | −1935.15 | + | 1117.26i | −0.143813 | + | 0.0830306i | ||||
\(117\) | 1149.44 | − | 10233.9i | 0.0839684 | − | 0.747599i | ||||
\(118\) | −28065.6 | −2.01563 | ||||||||
\(119\) | 11178.7 | + | 8513.23i | 0.789404 | + | 0.601175i | ||||
\(120\) | 1867.06 | + | 8940.42i | 0.129657 | + | 0.620862i | ||||
\(121\) | −6606.02 | + | 11442.0i | −0.451200 | + | 0.781502i | ||||
\(122\) | 17050.8 | − | 9844.31i | 1.14558 | − | 0.661402i | ||||
\(123\) | −1732.78 | − | 1938.30i | −0.114534 | − | 0.128118i | ||||
\(124\) | 6997.39 | − | 12119.8i | 0.455085 | − | 0.788231i | ||||
\(125\) | 3402.14i | 0.217737i | ||||||||
\(126\) | −19900.5 | − | 4851.12i | −1.25350 | − | 0.305563i | ||||
\(127\) | 20018.5 | 1.24115 | 0.620574 | − | 0.784148i | \(-0.286899\pi\) | ||||
0.620574 | + | 0.784148i | \(0.286899\pi\) | |||||||
\(128\) | −11588.7 | − | 6690.74i | −0.707319 | − | 0.408371i | ||||
\(129\) | −12156.9 | + | 10868.0i | −0.730542 | + | 0.653083i | ||||
\(130\) | 12022.0 | + | 20822.8i | 0.711363 | + | 1.23212i | ||||
\(131\) | 344.947 | + | 199.155i | 0.0201007 | + | 0.0116051i | 0.510017 | − | 0.860165i | \(-0.329639\pi\) |
−0.489916 | + | 0.871770i | \(0.662973\pi\) | |||||||
\(132\) | 3541.41 | − | 739.567i | 0.203249 | − | 0.0424453i | ||||
\(133\) | 15742.9 | + | 2014.28i | 0.889984 | + | 0.113872i | ||||
\(134\) | 44748.5i | 2.49212i | ||||||||
\(135\) | 2508.13 | + | 26596.1i | 0.137620 | + | 1.45932i | ||||
\(136\) | 3970.67 | + | 6877.40i | 0.214677 | + | 0.371832i | ||||
\(137\) | 21305.6 | − | 12300.8i | 1.13515 | − | 0.655378i | 0.189923 | − | 0.981799i | \(-0.439176\pi\) |
0.945225 | + | 0.326421i | \(0.105843\pi\) | |||||||
\(138\) | 15459.0 | + | 5083.93i | 0.811753 | + | 0.266957i | ||||
\(139\) | −11376.9 | −0.588834 | −0.294417 | − | 0.955677i | \(-0.595125\pi\) | ||||
−0.294417 | + | 0.955677i | \(0.595125\pi\) | |||||||
\(140\) | 17614.1 | − | 7371.28i | 0.898677 | − | 0.376086i | ||||
\(141\) | −926.901 | + | 193.568i | −0.0466225 | + | 0.00973635i | ||||
\(142\) | 8486.26 | − | 14698.6i | 0.420862 | − | 0.728954i | ||||
\(143\) | −4162.15 | + | 2403.02i | −0.203538 | + | 0.117513i | ||||
\(144\) | −20408.3 | − | 15051.0i | −0.984197 | − | 0.725837i | ||||
\(145\) | −3850.10 | + | 6668.56i | −0.183120 | + | 0.317173i | ||||
\(146\) | 28550.7i | 1.33940i | ||||||||
\(147\) | 1050.61 | − | 21583.4i | 0.0486192 | − | 0.998817i | ||||
\(148\) | −10582.0 | −0.483108 | ||||||||
\(149\) | −21348.1 | − | 12325.3i | −0.961581 | − | 0.555169i | −0.0649218 | − | 0.997890i | \(-0.520680\pi\) |
−0.896659 | + | 0.442721i | \(0.854013\pi\) | |||||||
\(150\) | −22221.5 | − | 24857.1i | −0.987624 | − | 1.10476i | ||||
\(151\) | 155.754 | + | 269.773i | 0.00683100 | + | 0.0118316i | 0.869421 | − | 0.494073i | \(-0.164492\pi\) |
−0.862590 | + | 0.505904i | \(0.831159\pi\) | |||||||
\(152\) | 7768.17 | + | 4484.96i | 0.336226 | + | 0.194120i | ||||
\(153\) | 9296.04 | + | 21286.4i | 0.397114 | + | 0.909324i | ||||
\(154\) | 3690.31 | + | 8818.19i | 0.155604 | + | 0.371824i | ||||
\(155\) | − | 48226.3i | − | 2.00734i | ||||||
\(156\) | −11558.9 | − | 3801.31i | −0.474970 | − | 0.156201i | ||||
\(157\) | −4499.01 | − | 7792.52i | −0.182523 | − | 0.316139i | 0.760216 | − | 0.649670i | \(-0.225093\pi\) |
−0.942739 | + | 0.333531i | \(0.891760\pi\) | |||||||
\(158\) | 3434.28 | − | 1982.78i | 0.137569 | − | 0.0794256i | ||||
\(159\) | −9256.29 | + | 28146.2i | −0.366136 | + | 1.11333i | ||||
\(160\) | 42968.4 | 1.67845 | ||||||||
\(161\) | −2178.84 | + | 17029.1i | −0.0840570 | + | 0.656961i | ||||
\(162\) | −24837.4 | − | 23013.3i | −0.946401 | − | 0.876896i | ||||
\(163\) | 4340.53 | − | 7518.02i | 0.163368 | − | 0.282962i | −0.772706 | − | 0.634764i | \(-0.781098\pi\) |
0.936075 | + | 0.351802i | \(0.114431\pi\) | |||||||
\(164\) | −2660.37 | + | 1535.96i | −0.0989132 | + | 0.0571075i | ||||
\(165\) | 9294.50 | − | 8309.01i | 0.341396 | − | 0.305198i | ||||
\(166\) | −9547.81 | + | 16537.3i | −0.346488 | + | 0.600134i | ||||
\(167\) | 12116.9i | 0.434470i | 0.976119 | + | 0.217235i | \(0.0697038\pi\) | ||||
−0.976119 | + | 0.217235i | \(0.930296\pi\) | |||||||
\(168\) | 5256.83 | − | 11023.4i | 0.186254 | − | 0.390568i | ||||
\(169\) | −12396.7 | −0.434045 | ||||||||
\(170\) | −46965.8 | − | 27115.7i | −1.62511 | − | 0.938260i | ||||
\(171\) | 21115.0 | + | 15572.2i | 0.722104 | + | 0.532546i | ||||
\(172\) | 9633.50 | + | 16685.7i | 0.325632 | + | 0.564012i | ||||
\(173\) | −18544.6 | − | 10706.8i | −0.619621 | − | 0.357738i | 0.157100 | − | 0.987583i | \(-0.449785\pi\) |
−0.776722 | + | 0.629844i | \(0.783119\pi\) | |||||||
\(174\) | −1995.18 | − | 9553.89i | −0.0658996 | − | 0.315560i | ||||
\(175\) | 21310.9 | − | 27983.4i | 0.695866 | − | 0.913744i | ||||
\(176\) | 11834.2i | 0.382045i | ||||||||
\(177\) | 15290.4 | − | 46494.3i | 0.488058 | − | 1.48407i | ||||
\(178\) | 12872.8 | + | 22296.4i | 0.406288 | + | 0.703711i | ||||
\(179\) | −870.662 | + | 502.677i | −0.0271734 | + | 0.0156885i | −0.513525 | − | 0.858075i | \(-0.671661\pi\) |
0.486352 | + | 0.873763i | \(0.338327\pi\) | |||||||
\(180\) | 31366.8 | + | 3523.03i | 0.968110 | + | 0.108736i | ||||
\(181\) | −6601.70 | −0.201511 | −0.100755 | − | 0.994911i | \(-0.532126\pi\) | ||||
−0.100755 | + | 0.994911i | \(0.532126\pi\) | |||||||
\(182\) | 4080.37 | − | 31890.8i | 0.123185 | − | 0.962771i | ||||
\(183\) | 7018.94 | + | 33610.2i | 0.209589 | + | 1.00362i | ||||
\(184\) | −4851.36 | + | 8402.81i | −0.143294 | + | 0.248193i | ||||
\(185\) | −31580.3 | + | 18232.9i | −0.922726 | + | 0.532736i | ||||
\(186\) | 40739.7 | + | 45571.6i | 1.17758 | + | 1.31725i | ||||
\(187\) | 5420.01 | − | 9387.73i | 0.154995 | − | 0.268459i | ||||
\(188\) | 1118.81i | 0.0316548i | ||||||||
\(189\) | 18878.4 | − | 30324.8i | 0.528497 | − | 0.848935i | ||||
\(190\) | −61255.6 | −1.69683 | ||||||||
\(191\) | 59094.9 | + | 34118.5i | 1.61988 | + | 0.935239i | 0.986949 | + | 0.161032i | \(0.0514823\pi\) |
0.632933 | + | 0.774207i | \(0.281851\pi\) | |||||||
\(192\) | −6994.11 | + | 6252.52i | −0.189727 | + | 0.169611i | ||||
\(193\) | −24043.5 | − | 41644.6i | −0.645481 | − | 1.11801i | −0.984190 | − | 0.177115i | \(-0.943324\pi\) |
0.338709 | − | 0.940891i | \(-0.390010\pi\) | |||||||
\(194\) | 8781.14 | + | 5069.79i | 0.233318 | + | 0.134706i | ||||
\(195\) | −41045.3 | + | 8571.65i | −1.07943 | + | 0.225421i | ||||
\(196\) | −24709.6 | − | 6428.34i | −0.643212 | − | 0.167335i | ||||
\(197\) | 36590.3i | 0.942830i | 0.881912 | + | 0.471415i | \(0.156257\pi\) | ||||
−0.881912 | + | 0.471415i | \(0.843743\pi\) | |||||||
\(198\) | −1763.75 | + | 15703.2i | −0.0449890 | + | 0.400552i | ||||
\(199\) | 11396.0 | + | 19738.4i | 0.287770 | + | 0.498432i | 0.973277 | − | 0.229634i | \(-0.0737528\pi\) |
−0.685507 | + | 0.728066i | \(0.740419\pi\) | |||||||
\(200\) | 17216.0 | − | 9939.64i | 0.430399 | − | 0.248491i | ||||
\(201\) | −74131.6 | − | 24379.3i | −1.83490 | − | 0.603433i | ||||
\(202\) | −16003.3 | −0.392198 | ||||||||
\(203\) | 9498.22 | − | 3974.89i | 0.230489 | − | 0.0964569i | ||||
\(204\) | 26865.1 | − | 5610.35i | 0.645548 | − | 0.134812i | ||||
\(205\) | −5292.96 | + | 9167.68i | −0.125948 | + | 0.218148i | ||||
\(206\) | 26396.1 | − | 15239.8i | 0.622021 | − | 0.359124i | ||||
\(207\) | −16844.4 | + | 22840.1i | −0.393110 | + | 0.533037i | ||||
\(208\) | 19901.2 | − | 34469.8i | 0.459994 | − | 0.796733i | ||||
\(209\) | − | 12244.0i | − | 0.280306i | ||||||
\(210\) | 6550.06 | + | 83142.9i | 0.148527 | + | 1.88533i | ||||
\(211\) | 38671.0 | 0.868602 | 0.434301 | − | 0.900768i | \(-0.356995\pi\) | ||||
0.434301 | + | 0.900768i | \(0.356995\pi\) | |||||||
\(212\) | 30318.1 | + | 17504.1i | 0.674574 | + | 0.389466i | ||||
\(213\) | 19726.8 | + | 22066.5i | 0.434808 | + | 0.486378i | ||||
\(214\) | −17473.9 | − | 30265.6i | −0.381559 | − | 0.660879i | ||||
\(215\) | 57499.3 | + | 33197.2i | 1.24390 | + | 0.718166i | ||||
\(216\) | 16458.6 | − | 11691.1i | 0.352766 | − | 0.250580i | ||||
\(217\) | −39070.2 | + | 51303.1i | −0.829709 | + | 1.08949i | ||||
\(218\) | − | 32767.0i | − | 0.689483i | ||||||
\(219\) | −47297.9 | − | 15554.6i | −0.986175 | − | 0.324318i | ||||
\(220\) | −7365.22 | − | 12756.9i | −0.152174 | − | 0.263573i | ||||
\(221\) | −31574.0 | + | 18229.3i | −0.646465 | + | 0.373237i | ||||
\(222\) | 14439.5 | − | 43907.0i | 0.292985 | − | 0.890898i | ||||
\(223\) | 12801.0 | 0.257416 | 0.128708 | − | 0.991683i | \(-0.458917\pi\) | ||||
0.128708 | + | 0.991683i | \(0.458917\pi\) | |||||||
\(224\) | −45709.7 | − | 34810.5i | −0.910988 | − | 0.693768i | ||||
\(225\) | 53285.5 | − | 23270.5i | 1.05255 | − | 0.459664i | ||||
\(226\) | 40849.2 | − | 70752.9i | 0.799773 | − | 1.38525i | ||||
\(227\) | −21642.4 | + | 12495.3i | −0.420005 | + | 0.242490i | −0.695079 | − | 0.718933i | \(-0.744631\pi\) |
0.275074 | + | 0.961423i | \(0.411297\pi\) | |||||||
\(228\) | 23110.8 | − | 20660.4i | 0.444575 | − | 0.397437i | ||||
\(229\) | −44349.7 | + | 76816.0i | −0.845707 | + | 1.46481i | 0.0392979 | + | 0.999228i | \(0.487488\pi\) |
−0.885005 | + | 0.465581i | \(0.845845\pi\) | |||||||
\(230\) | − | 66260.0i | − | 1.25255i | ||||||
\(231\) | −16619.0 | + | 1309.25i | −0.311444 | + | 0.0245358i | ||||
\(232\) | 5819.18 | 0.108115 | ||||||||
\(233\) | 20767.3 | + | 11990.0i | 0.382532 | + | 0.220855i | 0.678919 | − | 0.734213i | \(-0.262449\pi\) |
−0.296387 | + | 0.955068i | \(0.595782\pi\) | |||||||
\(234\) | 31544.9 | − | 42773.2i | 0.576099 | − | 0.781160i | ||||
\(235\) | 1927.71 | + | 3338.90i | 0.0349066 | + | 0.0604599i | ||||
\(236\) | −50082.1 | − | 28914.9i | −0.899204 | − | 0.519156i | ||||
\(237\) | 1413.71 | + | 6769.55i | 0.0251689 | + | 0.120521i | ||||
\(238\) | 27994.6 | + | 66894.7i | 0.494220 | + | 1.18097i | ||||
\(239\) | − | 20859.2i | − | 0.365176i | −0.983190 | − | 0.182588i | \(-0.941553\pi\) | ||
0.983190 | − | 0.182588i | \(-0.0584475\pi\) | |||||||
\(240\) | −32255.5 | + | 98081.2i | −0.559991 | + | 1.70280i | ||||
\(241\) | −52741.0 | − | 91350.2i | −0.908060 | − | 1.57281i | −0.816756 | − | 0.576983i | \(-0.804230\pi\) |
−0.0913040 | − | 0.995823i | \(-0.529103\pi\) | |||||||
\(242\) | −59049.8 | + | 34092.4i | −1.00830 | + | 0.582140i | ||||
\(243\) | 51656.0 | − | 28608.5i | 0.874798 | − | 0.484487i | ||||
\(244\) | 40568.8 | 0.681416 | ||||||||
\(245\) | −84818.0 | + | 23390.6i | −1.41304 | + | 0.389680i | ||||
\(246\) | −2742.89 | − | 13134.3i | −0.0453250 | − | 0.217039i | ||||
\(247\) | −20590.3 | + | 35663.5i | −0.337497 | + | 0.584562i | ||||
\(248\) | −31562.7 | + | 18222.8i | −0.513182 | + | 0.296286i | ||||
\(249\) | −22194.4 | − | 24826.8i | −0.357969 | − | 0.400426i | ||||
\(250\) | −8778.91 | + | 15205.5i | −0.140463 | + | 0.243288i | ||||
\(251\) | − | 98405.1i | − | 1.56196i | −0.624555 | − | 0.780980i | \(-0.714720\pi\) | ||
0.624555 | − | 0.780980i | \(-0.285280\pi\) | |||||||
\(252\) | −30513.8 | − | 29159.3i | −0.480502 | − | 0.459173i | ||||
\(253\) | 13244.3 | 0.206914 | ||||||||
\(254\) | 89470.5 | + | 51655.8i | 1.38680 | + | 0.800667i | ||||
\(255\) | 70508.0 | − | 63032.0i | 1.08432 | − | 0.969351i | ||||
\(256\) | −42868.7 | − | 74250.8i | −0.654125 | − | 1.13298i | ||||
\(257\) | 16976.3 | + | 9801.28i | 0.257026 | + | 0.148394i | 0.622977 | − | 0.782240i | \(-0.285923\pi\) |
−0.365951 | + | 0.930634i | \(0.619256\pi\) | |||||||
\(258\) | −82377.9 | + | 17203.3i | −1.23757 | + | 0.258447i | ||||
\(259\) | 48366.4 | + | 6188.39i | 0.721014 | + | 0.0922524i | ||||
\(260\) | 49543.3i | 0.732889i | ||||||||
\(261\) | 16914.2 | + | 1899.76i | 0.248297 | + | 0.0278880i | ||||
\(262\) | 1027.80 | + | 1780.21i | 0.0149730 | + | 0.0259339i | ||||
\(263\) | 15118.6 | − | 8728.74i | 0.218575 | − | 0.126194i | −0.386715 | − | 0.922199i | \(-0.626390\pi\) |
0.605290 | + | 0.796005i | \(0.293057\pi\) | |||||||
\(264\) | −8950.02 | − | 2943.35i | −0.128415 | − | 0.0422312i | ||||
\(265\) | 120639. | 1.71790 | ||||||||
\(266\) | 65163.7 | + | 49625.7i | 0.920963 | + | 0.701364i | ||||
\(267\) | −43950.0 | + | 9178.26i | −0.616505 | + | 0.128747i | ||||
\(268\) | −46102.6 | + | 79852.0i | −0.641883 | + | 1.11177i | ||||
\(269\) | 51554.7 | − | 29765.1i | 0.712465 | − | 0.411342i | −0.0995082 | − | 0.995037i | \(-0.531727\pi\) |
0.811973 | + | 0.583695i | \(0.198394\pi\) | |||||||
\(270\) | −57418.8 | + | 125340.i | −0.787637 | + | 1.71934i | ||||
\(271\) | 22679.5 | − | 39282.0i | 0.308812 | − | 0.534879i | −0.669291 | − | 0.743001i | \(-0.733402\pi\) |
0.978103 | + | 0.208122i | \(0.0667352\pi\) | |||||||
\(272\) | 89774.3i | 1.21343i | ||||||||
\(273\) | 50608.2 | + | 24134.0i | 0.679040 | + | 0.323820i | ||||
\(274\) | 126964. | 1.69114 | ||||||||
\(275\) | −23500.0 | − | 13567.7i | −0.310744 | − | 0.179408i | ||||
\(276\) | 22348.3 | + | 24998.9i | 0.293377 | + | 0.328173i | ||||
\(277\) | 69907.3 | + | 121083.i | 0.911094 | + | 1.57806i | 0.812522 | + | 0.582931i | \(0.198094\pi\) |
0.0985717 | + | 0.995130i | \(0.468573\pi\) | |||||||
\(278\) | −50847.7 | − | 29356.9i | −0.657933 | − | 0.379858i | ||||
\(279\) | −97690.5 | + | 42662.7i | −1.25500 | + | 0.548076i | ||||
\(280\) | −49323.6 | − | 6310.86i | −0.629128 | − | 0.0804957i | ||||
\(281\) | 47041.5i | 0.595756i | 0.954604 | + | 0.297878i | \(0.0962789\pi\) | ||||
−0.954604 | + | 0.297878i | \(0.903721\pi\) | |||||||
\(282\) | −4642.17 | − | 1526.65i | −0.0583744 | − | 0.0191973i | ||||
\(283\) | 6861.88 | + | 11885.1i | 0.0856781 | + | 0.148399i | 0.905680 | − | 0.423962i | \(-0.139361\pi\) |
−0.820002 | + | 0.572361i | \(0.806028\pi\) | |||||||
\(284\) | 30286.8 | − | 17486.1i | 0.375506 | − | 0.216799i | ||||
\(285\) | 33372.5 | − | 101478.i | 0.410865 | − | 1.24934i | ||||
\(286\) | −24803.0 | −0.303230 | ||||||||
\(287\) | 13057.8 | − | 5464.52i | 0.158528 | − | 0.0663420i | ||||
\(288\) | −38011.4 | − | 87039.6i | −0.458278 | − | 1.04938i | ||||
\(289\) | −644.389 | + | 1116.11i | −0.00771529 | + | 0.0133633i | ||||
\(290\) | −34415.2 | + | 19869.6i | −0.409217 | + | 0.236262i | ||||
\(291\) | −13182.8 | + | 11785.0i | −0.155676 | + | 0.139170i | ||||
\(292\) | −29414.7 | + | 50947.7i | −0.344983 | + | 0.597529i | ||||
\(293\) | − | 100474.i | − | 1.17036i | −0.810902 | − | 0.585181i | \(-0.801023\pi\) | ||
0.810902 | − | 0.585181i | \(-0.198977\pi\) | |||||||
\(294\) | 60389.6 | − | 93753.9i | 0.698663 | − | 1.08466i | ||||
\(295\) | −199283. | −2.28995 | ||||||||
\(296\) | 23865.8 | + | 13778.9i | 0.272391 | + | 0.157265i | ||||
\(297\) | −25053.5 | − | 11477.1i | −0.284025 | − | 0.130113i | ||||
\(298\) | −63608.6 | − | 110173.i | −0.716280 | − | 1.24063i | ||||
\(299\) | −38577.1 | − | 22272.5i | −0.431507 | − | 0.249130i | ||||
\(300\) | −14044.2 | − | 67250.6i | −0.156047 | − | 0.747229i | ||||
\(301\) | −34273.3 | − | 81897.8i | −0.378288 | − | 0.903940i | ||||
\(302\) | 1607.63i | 0.0176267i | ||||||||
\(303\) | 8718.69 | − | 26511.5i | 0.0949655 | − | 0.288768i | ||||
\(304\) | 50701.0 | + | 87816.7i | 0.548617 | + | 0.950233i | ||||
\(305\) | 121071. | − | 69900.4i | 1.30149 | − | 0.751416i | ||||
\(306\) | −13379.8 | + | 119125.i | −0.142891 | + | 1.27221i | ||||
\(307\) | 106043. | 1.12514 | 0.562571 | − | 0.826749i | \(-0.309812\pi\) | ||||
0.562571 | + | 0.826749i | \(0.309812\pi\) | |||||||
\(308\) | −2499.81 | + | 19537.7i | −0.0263515 | + | 0.205955i | ||||
\(309\) | 10865.9 | + | 52031.2i | 0.113802 | + | 0.544938i | ||||
\(310\) | 124443. | − | 215542.i | 1.29494 | − | 2.24290i | ||||
\(311\) | −32648.3 | + | 18849.5i | −0.337552 | + | 0.194886i | −0.659189 | − | 0.751977i | \(-0.729100\pi\) |
0.321637 | + | 0.946863i | \(0.395767\pi\) | |||||||
\(312\) | 21119.2 | + | 23624.1i | 0.216955 | + | 0.242687i | ||||
\(313\) | −37574.7 | + | 65081.3i | −0.383536 | + | 0.664305i | −0.991565 | − | 0.129611i | \(-0.958627\pi\) |
0.608029 | + | 0.793915i | \(0.291961\pi\) | |||||||
\(314\) | − | 46437.1i | − | 0.470983i | ||||||
\(315\) | −141305. | − | 34445.8i | −1.42409 | − | 0.347149i | ||||
\(316\) | 8171.12 | 0.0818290 | ||||||||
\(317\) | −74293.1 | − | 42893.1i | −0.739315 | − | 0.426844i | 0.0825050 | − | 0.996591i | \(-0.473708\pi\) |
−0.821820 | + | 0.569747i | \(0.807041\pi\) | |||||||
\(318\) | −113998. | + | 101911.i | −1.12731 | + | 1.00778i | ||||
\(319\) | −3971.62 | − | 6879.06i | −0.0390289 | − | 0.0676001i | ||||
\(320\) | 33080.4 | + | 19099.0i | 0.323051 | + | 0.186513i | ||||
\(321\) | 59658.8 | − | 12458.8i | 0.578981 | − | 0.120911i | ||||
\(322\) | −53680.0 | + | 70487.4i | −0.517727 | + | 0.679829i | ||||
\(323\) | − | 92883.1i | − | 0.890290i | ||||||
\(324\) | −20611.7 | − | 66655.2i | −0.196347 | − | 0.634957i | ||||
\(325\) | 45632.7 | + | 79038.2i | 0.432026 | + | 0.748290i | ||||
\(326\) | 38799.0 | − | 22400.6i | 0.365078 | − | 0.210778i | ||||
\(327\) | 54282.7 | + | 17851.7i | 0.507652 | + | 0.166949i | ||||
\(328\) | 7999.98 | 0.0743603 | ||||||||
\(329\) | 654.281 | − | 5113.64i | 0.00604467 | − | 0.0472431i | ||||
\(330\) | 62981.4 | − | 13152.6i | 0.578341 | − | 0.120777i | ||||
\(331\) | 14556.8 | − | 25213.2i | 0.132865 | − | 0.230129i | −0.791915 | − | 0.610632i | \(-0.790916\pi\) |
0.924780 | + | 0.380503i | \(0.124249\pi\) | |||||||
\(332\) | −34075.4 | + | 19673.5i | −0.309147 | + | 0.178486i | ||||
\(333\) | 64870.9 | + | 47841.7i | 0.585007 | + | 0.431438i | ||||
\(334\) | −31266.6 | + | 54155.3i | −0.280277 | + | 0.485454i | ||||
\(335\) | 317741.i | 2.83128i | ||||||||
\(336\) | 113773. | − | 78207.3i | 1.00777 | − | 0.692737i | ||||
\(337\) | −152796. | −1.34540 | −0.672702 | − | 0.739913i | \(-0.734867\pi\) | ||||
−0.672702 | + | 0.739913i | \(0.734867\pi\) | |||||||
\(338\) | −55405.9 | − | 31988.6i | −0.484979 | − | 0.280003i | ||||
\(339\) | 94956.4 | + | 106219.i | 0.826275 | + | 0.924276i | ||||
\(340\) | −55872.5 | − | 96774.0i | −0.483326 | − | 0.837145i | ||||
\(341\) | 43083.5 | + | 24874.3i | 0.370512 | + | 0.213915i | ||||
\(342\) | 54188.9 | + | 124083.i | 0.463296 | + | 1.06087i | ||||
\(343\) | 109179. | + | 43831.8i | 0.928007 | + | 0.372564i | ||||
\(344\) | − | 50175.5i | − | 0.424009i | ||||||
\(345\) | 109768. | + | 36098.9i | 0.922228 | + | 0.303289i | ||||
\(346\) | −55255.5 | − | 95705.4i | −0.461555 | − | 0.799437i | ||||
\(347\) | −200198. | + | 115584.i | −1.66265 | + | 0.959929i | −0.691202 | + | 0.722661i | \(0.742919\pi\) |
−0.971444 | + | 0.237268i | \(0.923748\pi\) | |||||||
\(348\) | 6282.67 | − | 19104.1i | 0.0518783 | − | 0.157750i | ||||
\(349\) | −168428. | −1.38281 | −0.691407 | − | 0.722466i | \(-0.743009\pi\) | ||||
−0.691407 | + | 0.722466i | \(0.743009\pi\) | |||||||
\(350\) | 167455. | − | 70078.0i | 1.36698 | − | 0.572066i | ||||
\(351\) | 53673.4 | + | 75561.3i | 0.435658 | + | 0.613317i | ||||
\(352\) | −22162.3 | + | 38386.3i | −0.178867 | + | 0.309807i | ||||
\(353\) | 116942. | − | 67516.5i | 0.938471 | − | 0.541827i | 0.0489906 | − | 0.998799i | \(-0.484400\pi\) |
0.889481 | + | 0.456973i | \(0.151066\pi\) | |||||||
\(354\) | 188313. | − | 168346.i | 1.50270 | − | 1.34337i | ||||
\(355\) | 60257.4 | − | 104369.i | 0.478139 | − | 0.828161i | ||||
\(356\) | 53049.4i | 0.418582i | ||||||||
\(357\) | −126071. | + | 9931.99i | −0.989190 | + | 0.0779291i | ||||
\(358\) | −5188.44 | −0.0404828 | ||||||||
\(359\) | −142620. | − | 82342.0i | −1.10661 | − | 0.638899i | −0.168658 | − | 0.985675i | \(-0.553943\pi\) |
−0.937948 | + | 0.346775i | \(0.887277\pi\) | |||||||
\(360\) | −66154.8 | − | 48788.6i | −0.510453 | − | 0.376455i | ||||
\(361\) | 12703.8 | + | 22003.5i | 0.0974805 | + | 0.168841i | ||||
\(362\) | −29505.6 | − | 17035.1i | −0.225158 | − | 0.129995i | ||||
\(363\) | −24307.7 | − | 116397.i | −0.184472 | − | 0.883344i | ||||
\(364\) | 40137.1 | − | 52704.1i | 0.302931 | − | 0.397779i | ||||
\(365\) | 202727.i | 1.52169i | ||||||||
\(366\) | −55357.4 | + | 168329.i | −0.413251 | + | 1.25660i | ||||
\(367\) | −63154.9 | − | 109387.i | −0.468894 | − | 0.812148i | 0.530474 | − | 0.847701i | \(-0.322014\pi\) |
−0.999368 | + | 0.0355532i | \(0.988681\pi\) | |||||||
\(368\) | −94991.1 | + | 54843.1i | −0.701435 | + | 0.404973i | ||||
\(369\) | 23253.0 | + | 2611.72i | 0.170776 | + | 0.0191811i | ||||
\(370\) | −188193. | −1.37468 | ||||||||
\(371\) | −128336. | − | 97734.9i | −0.932397 | − | 0.710071i | ||||
\(372\) | 25747.8 | + | 123293.i | 0.186061 | + | 0.890950i | ||||
\(373\) | −30930.6 | + | 53573.3i | −0.222316 | + | 0.385062i | −0.955511 | − | 0.294956i | \(-0.904695\pi\) |
0.733195 | + | 0.680018i | \(0.238028\pi\) | |||||||
\(374\) | 48448.3 | − | 27971.6i | 0.346366 | − | 0.199974i | ||||
\(375\) | −20407.1 | − | 22827.5i | −0.145117 | − | 0.162329i | ||||
\(376\) | 1456.81 | − | 2523.27i | 0.0103045 | − | 0.0178479i | ||||
\(377\) | 26715.7i | 0.187968i | ||||||||
\(378\) | 162625. | − | 86819.5i | 1.13816 | − | 0.607622i | ||||
\(379\) | 119910. | 0.834786 | 0.417393 | − | 0.908726i | \(-0.362944\pi\) | ||||
0.417393 | + | 0.908726i | \(0.362944\pi\) | |||||||
\(380\) | −109308. | − | 63109.2i | −0.756983 | − | 0.437044i | ||||
\(381\) | −134319. | + | 120077.i | −0.925308 | + | 0.827198i | ||||
\(382\) | 176079. | + | 304978.i | 1.20665 | + | 2.08998i | ||||
\(383\) | 209920. | + | 121198.i | 1.43106 | + | 0.826221i | 0.997201 | − | 0.0747618i | \(-0.0238197\pi\) |
0.433855 | + | 0.900983i | \(0.357153\pi\) | |||||||
\(384\) | 117890. | − | 24619.5i | 0.799494 | − | 0.166961i | ||||
\(385\) | 26203.4 | + | 62614.3i | 0.176781 | + | 0.422428i | ||||
\(386\) | − | 248168.i | − | 1.66560i | ||||||
\(387\) | 16380.6 | − | 145842.i | 0.109372 | − | 0.973779i | ||||
\(388\) | 10446.4 | + | 18093.7i | 0.0693911 | + | 0.120189i | ||||
\(389\) | 256161. | − | 147895.i | 1.69283 | − | 0.977357i | 0.740616 | − | 0.671928i | \(-0.234534\pi\) |
0.952215 | − | 0.305428i | \(-0.0987996\pi\) | |||||||
\(390\) | −205566. | − | 67603.4i | −1.35152 | − | 0.444467i | ||||
\(391\) | 100471. | 0.657187 | ||||||||
\(392\) | 47357.7 | + | 46672.6i | 0.308190 | + | 0.303732i | ||||
\(393\) | −3509.10 | + | 732.818i | −0.0227201 | + | 0.00474473i | ||||
\(394\) | −94417.7 | + | 163536.i | −0.608221 | + | 1.05347i | ||||
\(395\) | 24385.4 | − | 14078.9i | 0.156292 | − | 0.0902350i | ||||
\(396\) | −19325.8 | + | 26204.7i | −0.123238 | + | 0.167105i | ||||
\(397\) | 117340. | − | 203238.i | 0.744498 | − | 1.28951i | −0.205930 | − | 0.978567i | \(-0.566022\pi\) |
0.950429 | − | 0.310942i | \(-0.100645\pi\) | |||||||
\(398\) | 117625.i | 0.742563i | ||||||||
\(399\) | −117713. | + | 80915.5i | −0.739399 | + | 0.508260i | ||||
\(400\) | 224729. | 1.40456 | ||||||||
\(401\) | −198091. | − | 114368.i | −1.23190 | − | 0.711239i | −0.264476 | − | 0.964392i | \(-0.585199\pi\) |
−0.967426 | + | 0.253153i | \(0.918532\pi\) | |||||||
\(402\) | −268415. | − | 300250.i | −1.66094 | − | 1.85794i | ||||
\(403\) | −83660.3 | − | 144904.i | −0.515121 | − | 0.892216i | ||||
\(404\) | −28557.2 | − | 16487.5i | −0.174966 | − | 0.101017i | ||||
\(405\) | −176360. | − | 163408.i | −1.07520 | − | 0.996237i | ||||
\(406\) | 52708.1 | + | 6743.90i | 0.319761 | + | 0.0409128i | ||||
\(407\) | − | 37616.8i | − | 0.227088i | ||||||
\(408\) | −67894.8 | − | 22328.2i | −0.407865 | − | 0.134132i | ||||
\(409\) | −89133.0 | − | 154383.i | −0.532834 | − | 0.922895i | −0.999265 | − | 0.0383377i | \(-0.987794\pi\) |
0.466431 | − | 0.884558i | \(-0.345540\pi\) | |||||||
\(410\) | −47312.7 | + | 27316.0i | −0.281455 | + | 0.162498i | ||||
\(411\) | −69170.9 | + | 210332.i | −0.409487 | + | 1.24515i | ||||
\(412\) | 62803.7 | 0.369991 | ||||||||
\(413\) | 211997. | + | 161447.i | 1.24288 | + | 0.946522i | ||||
\(414\) | −134221. | + | 58616.0i | −0.783103 | + | 0.341992i | ||||
\(415\) | −67795.1 | + | 117425.i | −0.393643 | + | 0.681809i | ||||
\(416\) | 129106. | − | 74539.2i | 0.746034 | − | 0.430723i | ||||
\(417\) | 76335.6 | − | 68241.8i | 0.438991 | − | 0.392445i | ||||
\(418\) | 31594.6 | − | 54723.4i | 0.180826 | − | 0.313199i | ||||
\(419\) | − | 90551.7i | − | 0.515785i | −0.966174 | − | 0.257892i | \(-0.916972\pi\) | ||
0.966174 | − | 0.257892i | \(-0.0830280\pi\) | |||||||
\(420\) | −73970.5 | + | 155114.i | −0.419334 | + | 0.879329i | ||||
\(421\) | 152897. | 0.862651 | 0.431325 | − | 0.902196i | \(-0.358046\pi\) | ||||
0.431325 | + | 0.902196i | \(0.358046\pi\) | |||||||
\(422\) | 172836. | + | 99786.9i | 0.970530 | + | 0.560336i | ||||
\(423\) | 5058.17 | − | 6858.62i | 0.0282692 | − | 0.0383315i | ||||
\(424\) | −45584.7 | − | 78955.0i | −0.253564 | − | 0.439185i | ||||
\(425\) | −178271. | − | 102925.i | −0.986966 | − | 0.569825i | ||||
\(426\) | 31226.3 | + | 149527.i | 0.172068 | + | 0.823948i | ||||
\(427\) | −185425. | − | 23724.7i | −1.01698 | − | 0.130121i | ||||
\(428\) | − | 72010.5i | − | 0.393105i | ||||||
\(429\) | 13512.9 | − | 41089.4i | 0.0734231 | − | 0.223262i | ||||
\(430\) | 171325. | + | 296743.i | 0.926580 | + | 1.60488i | ||||
\(431\) | −181702. | + | 104905.i | −0.978147 | + | 0.564733i | −0.901710 | − | 0.432341i | \(-0.857688\pi\) |
−0.0764366 | + | 0.997074i | \(0.524354\pi\) | |||||||
\(432\) | 227214. | − | 21427.4i | 1.21750 | − | 0.114816i | ||||
\(433\) | 82648.1 | 0.440816 | 0.220408 | − | 0.975408i | \(-0.429261\pi\) | ||||
0.220408 | + | 0.975408i | \(0.429261\pi\) | |||||||
\(434\) | −307003. | + | 128477.i | −1.62991 | + | 0.682096i | ||||
\(435\) | −14166.9 | − | 67838.3i | −0.0748682 | − | 0.358506i | ||||
\(436\) | 33758.5 | − | 58471.5i | 0.177587 | − | 0.307589i | ||||
\(437\) | 98280.6 | − | 56742.3i | 0.514642 | − | 0.297128i | ||||
\(438\) | −171256. | − | 191568.i | −0.892682 | − | 0.998559i | ||||
\(439\) | −129364. | + | 224065.i | −0.671249 | + | 1.16264i | 0.306301 | + | 0.951935i | \(0.400909\pi\) |
−0.977550 | + | 0.210703i | \(0.932425\pi\) | |||||||
\(440\) | 38361.3i | 0.198147i | ||||||||
\(441\) | 122415. | + | 151121.i | 0.629442 | + | 0.777047i | ||||
\(442\) | −188155. | −0.963102 | ||||||||
\(443\) | 271422. | + | 156706.i | 1.38305 | + | 0.798504i | 0.992520 | − | 0.122086i | \(-0.0389583\pi\) |
0.390530 | + | 0.920590i | \(0.372292\pi\) | |||||||
\(444\) | 71002.4 | − | 63474.0i | 0.360169 | − | 0.321981i | ||||
\(445\) | 91404.7 | + | 158318.i | 0.461581 | + | 0.799483i | ||||
\(446\) | 57212.8 | + | 33031.8i | 0.287623 | + | 0.166059i | ||||
\(447\) | 217171. | − | 45352.6i | 1.08689 | − | 0.226980i | ||||
\(448\) | −19718.0 | − | 47117.3i | −0.0982443 | − | 0.234760i | ||||
\(449\) | 332034.i | 1.64699i | 0.567325 | + | 0.823494i | \(0.307978\pi\) | ||||
−0.567325 | + | 0.823494i | \(0.692022\pi\) | |||||||
\(450\) | 298201. | + | 33493.1i | 1.47260 | + | 0.165398i | ||||
\(451\) | −5460.03 | − | 9457.06i | −0.0268437 | − | 0.0464946i | ||||
\(452\) | 145788. | − | 84170.6i | 0.713583 | − | 0.411987i | ||||
\(453\) | −2663.24 | − | 875.848i | −0.0129782 | − | 0.00426808i | ||||
\(454\) | −128971. | −0.625722 | ||||||||
\(455\) | 28973.0 | − | 226444.i | 0.139950 | − | 1.09380i | ||||
\(456\) | −79024.4 | + | 16503.0i | −0.380042 | + | 0.0793656i | ||||
\(457\) | 47747.9 | − | 82701.8i | 0.228624 | − | 0.395988i | −0.728777 | − | 0.684752i | \(-0.759911\pi\) |
0.957401 | + | 0.288763i | \(0.0932440\pi\) | |||||||
\(458\) | −396433. | + | 228881.i | −1.88990 | + | 1.09113i | ||||
\(459\) | −190056. | − | 87065.2i | −0.902102 | − | 0.413256i | ||||
\(460\) | 68265.0 | − | 118239.i | 0.322614 | − | 0.558783i | ||||
\(461\) | − | 116352.i | − | 0.547484i | −0.961803 | − | 0.273742i | \(-0.911738\pi\) | ||
0.961803 | − | 0.273742i | \(-0.0882615\pi\) | |||||||
\(462\) | −77655.1 | − | 37032.1i | −0.363819 | − | 0.173498i | ||||
\(463\) | 89139.4 | 0.415822 | 0.207911 | − | 0.978148i | \(-0.433334\pi\) | ||||
0.207911 | + | 0.978148i | \(0.433334\pi\) | |||||||
\(464\) | 56970.6 | + | 32892.0i | 0.264615 | + | 0.152776i | ||||
\(465\) | 289276. | + | 323585.i | 1.33785 | + | 1.49652i | ||||
\(466\) | 61878.1 | + | 107176.i | 0.284948 | + | 0.493544i | ||||
\(467\) | −201039. | − | 116070.i | −0.921823 | − | 0.532215i | −0.0376069 | − | 0.999293i | \(-0.511973\pi\) |
−0.884216 | + | 0.467078i | \(0.845307\pi\) | |||||||
\(468\) | 100358. | − | 43827.8i | 0.458206 | − | 0.200105i | ||||
\(469\) | 257415. | − | 338013.i | 1.17028 | − | 1.53669i | ||||
\(470\) | 19897.1i | 0.0900730i | ||||||||
\(471\) | 76929.0 | + | 25299.2i | 0.346775 | + | 0.114042i | ||||
\(472\) | 75300.8 | + | 130425.i | 0.337999 | + | 0.585432i | ||||
\(473\) | −59314.3 | + | 34245.1i | −0.265117 | + | 0.153065i | ||||
\(474\) | −11149.8 | + | 33903.7i | −0.0496259 | + | 0.150901i | ||||
\(475\) | −232511. | −1.03052 | ||||||||
\(476\) | −18963.6 | + | 148213.i | −0.0836962 | + | 0.654142i | ||||
\(477\) | −106722. | − | 244375.i | −0.469047 | − | 1.07404i | ||||
\(478\) | 53825.2 | − | 93228.0i | 0.235576 | − | 0.408029i | ||||
\(479\) | 201273. | − | 116205.i | 0.877232 | − | 0.506470i | 0.00748747 | − | 0.999972i | \(-0.497617\pi\) |
0.869745 | + | 0.493502i | \(0.164283\pi\) | |||||||
\(480\) | −288306. | + | 257737.i | −1.25133 | + | 1.11865i | ||||
\(481\) | −63258.8 | + | 109568.i | −0.273420 | + | 0.473578i | ||||
\(482\) | − | 544373.i | − | 2.34316i | ||||||
\(483\) | −87526.1 | − | 127330.i | −0.375183 | − | 0.545803i | ||||
\(484\) | −140496. | −0.599755 | ||||||||
\(485\) | 62351.3 | + | 35998.5i | 0.265071 | + | 0.153039i | ||||
\(486\) | 304692. | + | 5430.83i | 1.29000 | + | 0.0229929i | ||||
\(487\) | 49939.0 | + | 86496.8i | 0.210563 | + | 0.364705i | 0.951891 | − | 0.306437i | \(-0.0991370\pi\) |
−0.741328 | + | 0.671143i | \(0.765804\pi\) | |||||||
\(488\) | −91495.7 | − | 52825.1i | −0.384203 | − | 0.221820i | ||||
\(489\) | 15971.5 | + | 76479.6i | 0.0667927 | + | 0.319836i | ||||
\(490\) | −439442. | − | 114323.i | −1.83025 | − | 0.476148i | ||||
\(491\) | − | 121641.i | − | 0.504566i | −0.967654 | − | 0.252283i | \(-0.918819\pi\) | ||
0.967654 | − | 0.252283i | \(-0.0811813\pi\) | |||||||
\(492\) | 8637.17 | − | 26263.6i | 0.0356814 | − | 0.108499i | ||||
\(493\) | −30128.7 | − | 52184.4i | −0.123961 | − | 0.214707i | ||||
\(494\) | −184053. | + | 106263.i | −0.754203 | + | 0.435439i | ||||
\(495\) | −12523.6 | + | 111502.i | −0.0511117 | + | 0.455065i | ||||
\(496\) | −412005. | −1.67471 | ||||||||
\(497\) | −148656. | + | 62210.6i | −0.601822 | + | 0.251855i | ||||
\(498\) | −35132.4 | − | 168231.i | −0.141661 | − | 0.678341i | ||||
\(499\) | −4194.16 | + | 7264.50i | −0.0168439 | + | 0.0291746i | −0.874325 | − | 0.485342i | \(-0.838695\pi\) |
0.857481 | + | 0.514516i | \(0.172029\pi\) | |||||||
\(500\) | −31331.3 | + | 18089.1i | −0.125325 | + | 0.0723565i | ||||
\(501\) | −72680.9 | − | 81301.3i | −0.289564 | − | 0.323908i | ||||
\(502\) | 253925. | − | 439811.i | 1.00762 | − | 1.74525i | ||||
\(503\) | 17797.2i | 0.0703422i | 0.999381 | + | 0.0351711i | \(0.0111976\pi\) | ||||
−0.999381 | + | 0.0351711i | \(0.988802\pi\) | |||||||
\(504\) | 30849.7 | + | 105496.i | 0.121448 | + | 0.415313i | ||||
\(505\) | −113633. | −0.445575 | ||||||||
\(506\) | 59194.1 | + | 34175.7i | 0.231195 | + | 0.133480i | ||||
\(507\) | 83178.8 | − | 74359.4i | 0.323591 | − | 0.289281i | ||||
\(508\) | 106438. | + | 184356.i | 0.412447 | + | 0.714380i | ||||
\(509\) | −128586. | − | 74239.4i | −0.496317 | − | 0.286549i | 0.230874 | − | 0.972984i | \(-0.425841\pi\) |
−0.727191 | + | 0.686435i | \(0.759175\pi\) | |||||||
\(510\) | 477776. | − | 99775.8i | 1.83689 | − | 0.383606i | ||||
\(511\) | 164238. | − | 215661.i | 0.628972 | − | 0.825904i | ||||
\(512\) | − | 228371.i | − | 0.871165i | ||||||
\(513\) | −235083. | + | 22169.4i | −0.893276 | + | 0.0842401i | ||||
\(514\) | 50582.5 | + | 87611.5i | 0.191458 | + | 0.331616i | ||||
\(515\) | 187428. | − | 108211.i | 0.706674 | − | 0.407999i | ||||
\(516\) | −164724. | − | 54172.0i | −0.618668 | − | 0.203458i | ||||
\(517\) | −3977.12 | −0.0148795 | ||||||||
\(518\) | 200200. | + | 152463.i | 0.746112 | + | 0.568205i | ||||
\(519\) | 188652. | − | 39396.9i | 0.700368 | − | 0.146261i | ||||
\(520\) | 64510.8 | − | 111736.i | 0.238576 | − | 0.413225i | ||||
\(521\) | −408369. | + | 235772.i | −1.50445 | + | 0.868594i | −0.504463 | + | 0.863433i | \(0.668310\pi\) |
−0.999987 | + | 0.00516125i | \(0.998357\pi\) | |||||||
\(522\) | 70694.2 | + | 52136.3i | 0.259443 | + | 0.191337i | ||||
\(523\) | −190874. | + | 330604.i | −0.697820 | + | 1.20866i | 0.271400 | + | 0.962467i | \(0.412513\pi\) |
−0.969221 | + | 0.246194i | \(0.920820\pi\) | |||||||
\(524\) | 4235.62i | 0.0154260i | ||||||||
\(525\) | 24862.4 | + | 315590.i | 0.0902038 | + | 1.14500i | ||||
\(526\) | 90094.7 | 0.325632 | ||||||||
\(527\) | 326831. | + | 188696.i | 1.17680 | + | 0.679425i | ||||
\(528\) | −70985.2 | − | 79404.4i | −0.254624 | − | 0.284824i | ||||
\(529\) | −78542.5 | − | 136040.i | −0.280668 | − | 0.486132i | ||||
\(530\) | 539184. | + | 311298.i | 1.91949 | + | 1.10822i | ||||
\(531\) | 176293. | + | 403680.i | 0.625238 | + | 1.43169i | ||||
\(532\) | 65154.7 | + | 155691.i | 0.230209 | + | 0.550098i | ||||
\(533\) | 36727.8i | 0.129283i | ||||||||
\(534\) | −220113. | − | 72387.6i | −0.771906 | − | 0.253853i | ||||
\(535\) | −124075. | − | 214904.i | −0.433487 | − | 0.750822i | ||||
\(536\) | 207952. | − | 120061.i | 0.723826 | − | 0.417901i | ||||
\(537\) | 2826.70 | − | 8595.31i | 0.00980236 | − | 0.0298066i | ||||
\(538\) | 307224. | 1.06143 | ||||||||
\(539\) | 22851.4 | − | 87837.6i | 0.0786566 | − | 0.302345i | ||||
\(540\) | −231595. | + | 164509.i | −0.794220 | + | 0.564158i | ||||
\(541\) | −227168. | + | 393467.i | −0.776163 | + | 1.34435i | 0.157975 | + | 0.987443i | \(0.449503\pi\) |
−0.934138 | + | 0.356911i | \(0.883830\pi\) | |||||||
\(542\) | 202727. | − | 117044.i | 0.690102 | − | 0.398430i | ||||
\(543\) | 44295.6 | − | 39599.0i | 0.150231 | − | 0.134303i | ||||
\(544\) | −168123. | + | 291198.i | −0.568107 | + | 0.983990i | ||||
\(545\) | − | 232665.i | − | 0.783318i | ||||||
\(546\) | 163912. | + | 238454.i | 0.549828 | + | 0.799870i | ||||
\(547\) | −48588.0 | −0.162388 | −0.0811941 | − | 0.996698i | \(-0.525873\pi\) | ||||
−0.0811941 | + | 0.996698i | \(0.525873\pi\) | |||||||
\(548\) | 226563. | + | 130806.i | 0.754444 | + | 0.435579i | ||||
\(549\) | −248699. | − | 183413.i | −0.825143 | − | 0.608536i | ||||
\(550\) | −70020.5 | − | 121279.i | −0.231473 | − | 0.400922i | ||||
\(551\) | −58943.5 | − | 34031.0i | −0.194148 | − | 0.112091i | ||||
\(552\) | −17851.2 | − | 85480.5i | −0.0585855 | − | 0.280536i | ||||
\(553\) | −37347.1 | − | 4778.49i | −0.122126 | − | 0.0156257i | ||||
\(554\) | 721557.i | 2.35099i | ||||||||
\(555\) | 102529. | − | 311766.i | 0.332859 | − | 1.01214i | ||||
\(556\) | −60490.5 | − | 104773.i | −0.195676 | − | 0.338921i | ||||
\(557\) | −138785. | + | 80127.7i | −0.447335 | + | 0.258269i | −0.706704 | − | 0.707509i | \(-0.749819\pi\) |
0.259369 | + | 0.965778i | \(0.416485\pi\) | |||||||
\(558\) | −546704. | − | 61404.3i | −1.75584 | − | 0.197211i | ||||
\(559\) | 230355. | 0.737181 | ||||||||
\(560\) | −447214. | − | 340578.i | −1.42606 | − | 1.08603i | ||||
\(561\) | 19943.6 | + | 95499.9i | 0.0633692 | + | 0.303443i | ||||
\(562\) | −121386. | + | 210247.i | −0.384323 | + | 0.665667i | ||||
\(563\) | 15705.8 | − | 9067.75i | 0.0495499 | − | 0.0286077i | −0.475020 | − | 0.879975i | \(-0.657559\pi\) |
0.524570 | + | 0.851367i | \(0.324226\pi\) | |||||||
\(564\) | −6710.93 | − | 7506.89i | −0.0210972 | − | 0.0235994i | ||||
\(565\) | 290054. | − | 502388.i | 0.908618 | − | 1.57377i | ||||
\(566\) | 70825.7i | 0.221084i | ||||||||
\(567\) | 55228.1 | + | 316710.i | 0.171788 | + | 0.985134i | ||||
\(568\) | −91075.3 | −0.282296 | ||||||||
\(569\) | 21997.3 | + | 12700.2i | 0.0679431 | + | 0.0392270i | 0.533587 | − | 0.845745i | \(-0.320844\pi\) |
−0.465644 | + | 0.884972i | \(0.654177\pi\) | |||||||
\(570\) | 411008. | − | 367429.i | 1.26503 | − | 1.13090i | ||||
\(571\) | −78397.4 | − | 135788.i | −0.240453 | − | 0.416476i | 0.720391 | − | 0.693568i | \(-0.243963\pi\) |
−0.960843 | + | 0.277092i | \(0.910629\pi\) | |||||||
\(572\) | −44260.0 | − | 25553.6i | −0.135276 | − | 0.0781015i | ||||
\(573\) | −601163. | + | 125543.i | −1.83098 | + | 0.382370i | ||||
\(574\) | 72461.0 | + | 9271.25i | 0.219928 | + | 0.0281394i | ||||
\(575\) | − | 251507.i | − | 0.760701i | ||||||
\(576\) | 9424.04 | − | 83905.5i | 0.0284048 | − | 0.252898i | ||||
\(577\) | 69603.7 | + | 120557.i | 0.209065 | + | 0.362111i | 0.951420 | − | 0.307896i | \(-0.0996248\pi\) |
−0.742356 | + | 0.670006i | \(0.766291\pi\) | |||||||
\(578\) | −5760.05 | + | 3325.57i | −0.0172413 | + | 0.00995428i | ||||
\(579\) | 411122. | + | 135204.i | 1.22635 | + | 0.403303i | ||||
\(580\) | −81883.5 | −0.243411 | ||||||||
\(581\) | 167251. | − | 69992.6i | 0.495469 | − | 0.207348i | ||||
\(582\) | −89329.2 | + | 18655.0i | −0.263723 | + | 0.0550742i | ||||
\(583\) | −62223.6 | + | 107774.i | −0.183070 | + | 0.317087i | ||||
\(584\) | 132679. | − | 76602.3i | 0.389024 | − | 0.224603i | ||||
\(585\) | 223987. | − | 303715.i | 0.654503 | − | 0.887472i | ||||
\(586\) | 259265. | − | 449060.i | 0.755002 | − | 1.30770i | ||||
\(587\) | 381239.i | 1.10642i | 0.833041 | + | 0.553212i | \(0.186598\pi\) | ||||
−0.833041 | + | 0.553212i | \(0.813402\pi\) | |||||||
\(588\) | 204354. | − | 105083.i | 0.591055 | − | 0.303934i | ||||
\(589\) | 426273. | 1.22873 | ||||||||
\(590\) | −890672. | − | 514230.i | −2.55867 | − | 1.47725i | ||||
\(591\) | −219479. | − | 245511.i | −0.628375 | − | 0.702903i | ||||
\(592\) | 155767. | + | 269796.i | 0.444458 | + | 0.769824i | ||||
\(593\) | −359500. | − | 207558.i | −1.02233 | − | 0.590241i | −0.107550 | − | 0.994200i | \(-0.534301\pi\) |
−0.914777 | + | 0.403959i | \(0.867634\pi\) | |||||||
\(594\) | −82358.5 | − | 115944.i | −0.233419 | − | 0.328606i | ||||
\(595\) | 198778. | + | 474992.i | 0.561481 | + | 1.34169i | ||||
\(596\) | − | 262133.i | − | 0.737955i | ||||||
\(597\) | −194861. | − | 64082.9i | −0.546734 | − | 0.179802i | ||||
\(598\) | −114944. | − | 199089.i | −0.321429 | − | 0.556731i | ||||
\(599\) | −512564. | + | 295929.i | −1.42855 | + | 0.824772i | −0.997006 | − | 0.0773215i | \(-0.975363\pi\) |
−0.431541 | + | 0.902093i | \(0.642030\pi\) | |||||||
\(600\) | −55893.5 | + | 169959.i | −0.155260 | + | 0.472108i | ||||
\(601\) | −131825. | −0.364964 | −0.182482 | − | 0.983209i | \(-0.558413\pi\) | ||||
−0.182482 | + | 0.983209i | \(0.558413\pi\) | |||||||
\(602\) | 58148.9 | − | 454472.i | 0.160453 | − | 1.25405i | ||||
\(603\) | 643637. | − | 281085.i | 1.77014 | − | 0.773042i | ||||
\(604\) | −1656.28 | + | 2868.75i | −0.00454003 | + | 0.00786357i | ||||
\(605\) | −419289. | + | 242076.i | −1.14552 | + | 0.661366i | ||||
\(606\) | 107378. | − | 95992.4i | 0.292394 | − | 0.261391i | ||||
\(607\) | −150944. | + | 261443.i | −0.409675 | + | 0.709578i | −0.994853 | − | 0.101327i | \(-0.967691\pi\) |
0.585178 | + | 0.810905i | \(0.301025\pi\) | |||||||
\(608\) | 379798.i | 1.02741i | ||||||||
\(609\) | −39887.9 | + | 83643.6i | −0.107549 | + | 0.225527i | ||||
\(610\) | 721486. | 1.93896 | ||||||||
\(611\) | 11584.3 | + | 6688.18i | 0.0310303 | + | 0.0179154i | ||||
\(612\) | −146605. | + | 198789.i | −0.391423 | + | 0.530749i | ||||
\(613\) | 156611. | + | 271258.i | 0.416775 | + | 0.721875i | 0.995613 | − | 0.0935673i | \(-0.0298270\pi\) |
−0.578838 | + | 0.815442i | \(0.696494\pi\) | |||||||
\(614\) | 473950. | + | 273635.i | 1.25717 | + | 0.725830i | ||||
\(615\) | −19476.1 | − | 93261.4i | −0.0514935 | − | 0.246577i | ||||
\(616\) | 31078.1 | − | 40808.8i | 0.0819018 | − | 0.107545i | ||||
\(617\) | − | 70405.3i | − | 0.184942i | −0.995715 | − | 0.0924709i | \(-0.970523\pi\) | ||
0.995715 | − | 0.0924709i | \(-0.0294765\pi\) | |||||||
\(618\) | −85697.7 | + | 260586.i | −0.224384 | + | 0.682299i | ||||
\(619\) | 337786. | + | 585063.i | 0.881578 | + | 1.52694i | 0.849587 | + | 0.527449i | \(0.176851\pi\) |
0.0319909 | + | 0.999488i | \(0.489815\pi\) | |||||||
\(620\) | 444129. | − | 256418.i | 1.15538 | − | 0.667061i | ||||
\(621\) | −23980.5 | − | 254288.i | −0.0621836 | − | 0.659391i | ||||
\(622\) | −194558. | −0.502884 | ||||||||
\(623\) | 31023.5 | − | 242469.i | 0.0799308 | − | 0.624712i | ||||
\(624\) | 73228.9 | + | 350656.i | 0.188067 | + | 0.900560i | ||||
\(625\) | 161990. | − | 280575.i | 0.414694 | − | 0.718271i | ||||
\(626\) | −335872. | + | 193916.i | −0.857087 | + | 0.494840i | ||||
\(627\) | 73443.4 | + | 82154.1i | 0.186817 | + | 0.208975i | ||||
\(628\) | 47842.3 | − | 82865.2i | 0.121309 | − | 0.210113i | ||||
\(629\) | − | 285361.i | − | 0.721262i | ||||||
\(630\) | −542665. | − | 518577.i | −1.36726 | − | 1.30657i | ||||
\(631\) | −563119. | −1.41430 | −0.707150 | − | 0.707063i | \(-0.750020\pi\) | ||||
−0.707150 | + | 0.707063i | \(0.750020\pi\) | |||||||
\(632\) | −18428.5 | − | 10639.7i | −0.0461377 | − | 0.0266376i | ||||
\(633\) | −259472. | + | 231960.i | −0.647564 | + | 0.578904i | ||||
\(634\) | −221363. | − | 383412.i | −0.550715 | − | 0.953866i | ||||
\(635\) | 635293. | + | 366787.i | 1.57553 | + | 0.909633i | ||||
\(636\) | −308421. | + | 64408.8i | −0.762482 | + | 0.159232i | ||||
\(637\) | −214273. | + | 217418.i | −0.528067 | + | 0.535818i | ||||
\(638\) | − | 40993.6i | − | 0.100710i | ||||||
\(639\) | −264723. | − | 29732.9i | −0.648320 | − | 0.0728176i | ||||
\(640\) | −245181. | − | 424666.i | −0.598586 | − | 1.03678i | ||||
\(641\) | 426375. | − | 246168.i | 1.03771 | − | 0.599122i | 0.118526 | − | 0.992951i | \(-0.462183\pi\) |
0.919184 | + | 0.393829i | \(0.128850\pi\) | |||||||
\(642\) | 298787. | + | 98260.6i | 0.724923 | + | 0.238402i | ||||
\(643\) | −488602. | −1.18177 | −0.590886 | − | 0.806755i | \(-0.701222\pi\) | ||||
−0.590886 | + | 0.806755i | \(0.701222\pi\) | |||||||
\(644\) | −168410. | + | 70477.7i | −0.406066 | + | 0.169934i | ||||
\(645\) | −584932. | + | 122154.i | −1.40600 | + | 0.293621i | ||||
\(646\) | 239676. | − | 415131.i | 0.574327 | − | 0.994764i | ||||
\(647\) | 375629. | − | 216869.i | 0.897326 | − | 0.518072i | 0.0209946 | − | 0.999780i | \(-0.493317\pi\) |
0.876332 | + | 0.481708i | \(0.159983\pi\) | |||||||
\(648\) | −40306.5 | + | 177168.i | −0.0959898 | + | 0.421924i | ||||
\(649\) | 102786. | − | 178031.i | 0.244032 | − | 0.422676i | ||||
\(650\) | 471003.i | 1.11480i | ||||||||
\(651\) | −45581.3 | − | 578584.i | −0.107554 | − | 1.36523i | ||||
\(652\) | 92313.9 | 0.217156 | ||||||||
\(653\) | 447959. | + | 258629.i | 1.05054 | + | 0.606529i | 0.922800 | − | 0.385279i | \(-0.125895\pi\) |
0.127739 | + | 0.991808i | \(0.459228\pi\) | |||||||
\(654\) | 196546. | + | 219858.i | 0.459525 | + | 0.514027i | ||||
\(655\) | 7298.01 | + | 12640.5i | 0.0170107 | + | 0.0294634i | ||||
\(656\) | 78321.0 | + | 45218.6i | 0.182000 | + | 0.105077i | ||||
\(657\) | 410658. | − | 179340.i | 0.951369 | − | 0.415476i | ||||
\(658\) | 16119.5 | − | 21166.6i | 0.0372306 | − | 0.0488876i | ||||
\(659\) | 310016.i | 0.713860i | 0.934131 | + | 0.356930i | \(0.116176\pi\) | ||||
−0.934131 | + | 0.356930i | \(0.883824\pi\) | |||||||
\(660\) | 125939. | + | 41416.8i | 0.289115 | + | 0.0950798i | ||||
\(661\) | 30271.8 | + | 52432.4i | 0.0692845 | + | 0.120004i | 0.898587 | − | 0.438796i | \(-0.144595\pi\) |
−0.829302 | + | 0.558801i | \(0.811262\pi\) | |||||||
\(662\) | 130120. | − | 75125.0i | 0.296913 | − | 0.171423i | ||||
\(663\) | 102508. | − | 311703.i | 0.233202 | − | 0.709112i | ||||
\(664\) | 102468. | 0.232409 | ||||||||
\(665\) | 462701. | + | 352372.i | 1.04630 | + | 0.796816i | ||||
\(666\) | 166482. | + | 381216.i | 0.375336 | + | 0.859455i | ||||
\(667\) | 36811.3 | − | 63759.0i | 0.0827426 | − | 0.143314i | ||||
\(668\) | −111588. | + | 64425.4i | −0.250072 | + | 0.144379i | ||||
\(669\) | −85891.4 | + | 76784.4i | −0.191910 | + | 0.171562i | ||||
\(670\) | −819900. | + | 1.42011e6i | −1.82646 | + | 3.16353i | ||||
\(671\) | 144214.i | 0.320303i | ||||||||
\(672\) | 515504. | − | 40611.8i | 1.14155 | − | 0.0899318i | ||||
\(673\) | −329348. | −0.727151 | −0.363575 | − | 0.931565i | \(-0.618444\pi\) | ||||
−0.363575 | + | 0.931565i | \(0.618444\pi\) | |||||||
\(674\) | −682906. | − | 394276.i | −1.50329 | − | 0.867922i | ||||
\(675\) | −217948. | + | 475761.i | −0.478349 | + | 1.04419i | ||||
\(676\) | −65913.2 | − | 114165.i | −0.144238 | − | 0.249827i | ||||
\(677\) | −588045. | − | 339508.i | −1.28302 | − | 0.740752i | −0.305620 | − | 0.952154i | \(-0.598864\pi\) |
−0.977399 | + | 0.211402i | \(0.932197\pi\) | |||||||
\(678\) | 150310. | + | 719759.i | 0.326986 | + | 1.56577i | ||||
\(679\) | −37165.3 | − | 88808.6i | −0.0806118 | − | 0.192626i | ||||
\(680\) | 291009.i | 0.629344i | ||||||||
\(681\) | 70264.5 | − | 213658.i | 0.151510 | − | 0.460706i | ||||
\(682\) | 128371. | + | 222346.i | 0.275994 | + | 0.478036i | ||||
\(683\) | 31998.1 | − | 18474.1i | 0.0685935 | − | 0.0396025i | −0.465311 | − | 0.885147i | \(-0.654058\pi\) |
0.533905 | + | 0.845545i | \(0.320724\pi\) | |||||||
\(684\) | −31140.1 | + | 277251.i | −0.0665591 | + | 0.592599i | ||||
\(685\) | 901520. | 1.92130 | ||||||||
\(686\) | 374860. | + | 477627.i | 0.796565 | + | 1.01494i | ||||
\(687\) | −163191. | − | 781437.i | −0.345766 | − | 1.65570i | ||||
\(688\) | 283609. | − | 491226.i | 0.599161 | − | 1.03778i | ||||
\(689\) | 362481. | − | 209278.i | 0.763566 | − | 0.440845i | ||||
\(690\) | 397447. | + | 444587.i | 0.834798 | + | 0.933809i | ||||
\(691\) | 268443. | − | 464957.i | 0.562206 | − | 0.973770i | −0.435097 | − | 0.900383i | \(-0.643286\pi\) |
0.997304 | − | 0.0733863i | \(-0.0233806\pi\) | |||||||
\(692\) | − | 227710.i | − | 0.475522i | ||||||
\(693\) | 103655. | − | 108470.i | 0.215837 | − | 0.225862i | ||||
\(694\) | −1.19302e6 | −2.47701 | ||||||||
\(695\) | −361048. | − | 208451.i | −0.747474 | − | 0.431554i | ||||
\(696\) | −39045.1 | + | 34905.2i | −0.0806024 | + | 0.0720562i | ||||
\(697\) | −41419.8 | − | 71741.1i | −0.0852594 | − | 0.147674i | ||||
\(698\) | −752771. | − | 434613.i | −1.54508 | − | 0.892055i | ||||
\(699\) | −211262. | + | 44118.7i | −0.432382 | + | 0.0902960i | ||||
\(700\) | 371016. | + | 47470.8i | 0.757176 | + | 0.0968793i | ||||
\(701\) | − | 441235.i | − | 0.897911i | −0.893554 | − | 0.448956i | \(-0.851796\pi\) | ||
0.893554 | − | 0.448956i | \(-0.148204\pi\) | |||||||
\(702\) | 44909.0 | + | 476212.i | 0.0911295 | + | 0.966332i | ||||
\(703\) | −161161. | − | 279138.i | −0.326098 | − | 0.564819i | ||||
\(704\) | −34124.5 | + | 19701.8i | −0.0688528 | + | 0.0397522i | ||||
\(705\) | −32962.1 | − | 10840.1i | −0.0663189 | − | 0.0218100i | ||||
\(706\) | 696879. | 1.39813 | ||||||||
\(707\) | 120882. | + | 92058.6i | 0.241838 | + | 0.184173i | ||||
\(708\) | 509477. | − | 106396.i | 1.01639 | − | 0.212256i | ||||
\(709\) | 155888. | − | 270006.i | 0.310113 | − | 0.537132i | −0.668273 | − | 0.743916i | \(-0.732966\pi\) |
0.978387 | + | 0.206784i | \(0.0662997\pi\) | |||||||
\(710\) | 538628. | − | 310977.i | 1.06849 | − | 0.616896i | ||||
\(711\) | −50091.4 | − | 36942.0i | −0.0990887 | − | 0.0730770i | ||||
\(712\) | 69076.2 | − | 119644.i | 0.136260 | − | 0.236009i | ||||
\(713\) | 461098.i | 0.907014i | ||||||||
\(714\) | −589090. | − | 280925.i | −1.15554 | − | 0.551054i | ||||
\(715\) | −176116. | −0.344498 | ||||||||
\(716\) | −9258.57 | − | 5345.44i | −0.0180600 | − | 0.0104270i | ||||
\(717\) | 125120. | + | 139960.i | 0.243382 | + | 0.272248i | ||||
\(718\) | −424951. | − | 736037.i | −0.824309 | − | 1.42775i | ||||
\(719\) | −12063.8 | − | 6965.06i | −0.0233361 | − | 0.0134731i | 0.488287 | − | 0.872683i | \(-0.337622\pi\) |
−0.511623 | + | 0.859210i | \(0.670955\pi\) | |||||||
\(720\) | −371895. | − | 851576.i | −0.717390 | − | 1.64270i | ||||
\(721\) | −287052. | − | 36727.8i | −0.552192 | − | 0.0706520i | ||||
\(722\) | 131123.i | 0.251539i | ||||||||
\(723\) | 901823. | + | 296578.i | 1.72522 | + | 0.567365i | ||||
\(724\) | −35101.1 | − | 60796.8i | −0.0669643 | − | 0.115986i | ||||
\(725\) | −130632. | + | 75420.2i | −0.248526 | + | 0.143487i | ||||
\(726\) | 191712. | − | 582949.i | 0.363727 | − | 1.10601i | ||||
\(727\) | 206220. | 0.390176 | 0.195088 | − | 0.980786i | \(-0.437501\pi\) | ||||
0.195088 | + | 0.980786i | \(0.437501\pi\) | |||||||
\(728\) | −159149. | + | 66601.8i | −0.300290 | + | 0.125668i | ||||
\(729\) | −174995. | + | 501803.i | −0.329285 | + | 0.944231i | ||||
\(730\) | −523118. | + | 906067.i | −0.981643 | + | 1.70026i | ||||
\(731\) | −449957. | + | 259783.i | −0.842047 | + | 0.486156i | ||||
\(732\) | −272206. | + | 243344.i | −0.508013 | + | 0.454149i | ||||
\(733\) | −480538. | + | 832316.i | −0.894375 | + | 1.54910i | −0.0597989 | + | 0.998210i | \(0.519046\pi\) |
−0.834576 | + | 0.550893i | \(0.814287\pi\) | |||||||
\(734\) | − | 651860.i | − | 1.20994i | ||||||
\(735\) | 428802. | − | 665708.i | 0.793747 | − | 1.23228i | ||||
\(736\) | −410826. | −0.758407 | ||||||||
\(737\) | −283857. | − | 163885.i | −0.522595 | − | 0.301720i | ||||
\(738\) | 97187.6 | + | 71675.0i | 0.178442 | + | 0.131600i | ||||
\(739\) | 122834. | + | 212754.i | 0.224920 | + | 0.389573i | 0.956295 | − | 0.292402i | \(-0.0944546\pi\) |
−0.731375 | + | 0.681975i | \(0.761121\pi\) | |||||||
\(740\) | −335823. | − | 193888.i | −0.613264 | − | 0.354068i | ||||
\(741\) | −75764.8 | − | 362799.i | −0.137985 | − | 0.660739i | ||||
\(742\) | −321388. | − | 767974.i | −0.583743 | − | 1.39489i | ||||
\(743\) | − | 863206.i | − | 1.56364i | −0.623504 | − | 0.781820i | \(-0.714291\pi\) | ||
0.623504 | − | 0.781820i | \(-0.285709\pi\) | |||||||
\(744\) | 102472. | − | 311592.i | 0.185122 | − | 0.562913i | ||||
\(745\) | −451658. | − | 782295.i | −0.813762 | − | 1.40948i | ||||
\(746\) | −276482. | + | 159627.i | −0.496808 | + | 0.286832i | ||||
\(747\) | 297837. | + | 33452.3i | 0.533750 | + | 0.0599494i | ||||
\(748\) | 115272. | 0.206026 | ||||||||
\(749\) | −42112.0 | + | 329133.i | −0.0750657 | + | 0.586689i | ||||
\(750\) | −32303.1 | − | 154683.i | −0.0574278 | − | 0.274993i | ||||
\(751\) | −255389. | + | 442348.i | −0.452817 | + | 0.784303i | −0.998560 | − | 0.0536502i | \(-0.982914\pi\) |
0.545742 | + | 0.837953i | \(0.316248\pi\) | |||||||
\(752\) | 28524.7 | − | 16468.8i | 0.0504413 | − | 0.0291223i | ||||
\(753\) | 590263. | + | 660271.i | 1.04101 | + | 1.16448i | ||||
\(754\) | −68937.4 | + | 119403.i | −0.121259 | + | 0.210026i | ||||
\(755\) | 11415.1i | 0.0200256i | ||||||||
\(756\) | 379646. | + | 12620.4i | 0.664255 | + | 0.0220815i | ||||
\(757\) | 670170. | 1.16948 | 0.584741 | − | 0.811220i | \(-0.301196\pi\) | ||||
0.584741 | + | 0.811220i | \(0.301196\pi\) | |||||||
\(758\) | 535923. | + | 309415.i | 0.932747 | + | 0.538521i | ||||
\(759\) | −88865.9 | + | 79443.5i | −0.154259 | + | 0.137903i | ||||
\(760\) | 164350. | + | 284663.i | 0.284540 | + | 0.492838i | ||||
\(761\) | 509302. | + | 294046.i | 0.879441 | + | 0.507745i | 0.870474 | − | 0.492215i | \(-0.163812\pi\) |
0.00896665 | + | 0.999960i | \(0.497146\pi\) | |||||||
\(762\) | −910169. | + | 190074.i | −1.56752 | + | 0.327351i | ||||
\(763\) | −188492. | + | 247509.i | −0.323775 | + | 0.425150i | ||||
\(764\) | 725628.i | 1.24316i | ||||||||
\(765\) | −95004.2 | + | 845855.i | −0.162338 | + | 1.44535i | ||||
\(766\) | 625477. | + | 1.08336e6i | 1.06599 | + | 1.84635i | ||||
\(767\) | −598778. | + | 345704.i | −1.01783 | + | 0.587644i | ||||
\(768\) | 733016. | + | 241063.i | 1.24277 | + | 0.408704i | ||||
\(769\) | 90977.2 | 0.153844 | 0.0769218 | − | 0.997037i | \(-0.475491\pi\) | ||||
0.0769218 | + | 0.997037i | \(0.475491\pi\) | |||||||
\(770\) | −44457.3 | + | 347463.i | −0.0749828 | + | 0.586040i | ||||
\(771\) | −172697. | + | 36065.1i | −0.290521 | + | 0.0606706i | ||||
\(772\) | 255678. | − | 442846.i | 0.429001 | − | 0.743051i | ||||
\(773\) | 220575. | − | 127349.i | 0.369146 | − | 0.213127i | −0.303939 | − | 0.952691i | \(-0.598302\pi\) |
0.673085 | + | 0.739565i | \(0.264969\pi\) | |||||||
\(774\) | 449542. | − | 609556.i | 0.750393 | − | 1.01749i | ||||
\(775\) | 472357. | − | 818146.i | 0.786442 | − | 1.36216i | ||||
\(776\) | − | 54409.5i | − | 0.0903548i | ||||||
\(777\) | −361645. | + | 248593.i | −0.599018 | + | 0.411763i | ||||
\(778\) | 1.52651e6 | 2.52198 | ||||||||
\(779\) | −81033.2 | − | 46784.5i | −0.133533 | − | 0.0770952i | ||||
\(780\) | −297175. | − | 332422.i | −0.488454 | − | 0.546387i | ||||
\(781\) | 62159.4 | + | 107663.i | 0.101907 | + | 0.176509i | ||||
\(782\) | 449046. | + | 259257.i | 0.734306 | + | 0.423952i | ||||
\(783\) | −124885. | + | 88709.7i | −0.203698 | + | 0.144693i | ||||
\(784\) | 199829. | + | 724614.i | 0.325108 | + | 1.17889i | ||||
\(785\) | − | 329731.i | − | 0.535082i | ||||||
\(786\) | −17574.5 | − | 5779.64i | −0.0284471 | − | 0.00935525i | ||||
\(787\) | −172264. | − | 298370.i | −0.278128 | − | 0.481732i | 0.692791 | − | 0.721138i | \(-0.256381\pi\) |
−0.970920 | + | 0.239406i | \(0.923047\pi\) | |||||||
\(788\) | −336970. | + | 194550.i | −0.542673 | + | 0.313313i | ||||
\(789\) | −49084.2 | + | 149253.i | −0.0788475 | + | 0.239756i | ||||
\(790\) | 145317. | 0.232843 | ||||||||
\(791\) | −715564. | + | 299455.i | −1.14366 | + | 0.478607i | ||||
\(792\) | 77707.3 | − | 33935.8i | 0.123883 | − | 0.0541013i | ||||
\(793\) | 242519. | − | 420055.i | 0.385655 | − | 0.667974i | ||||
\(794\) | 1.04887e6 | − | 605567.i | 1.66373 | − | 0.960553i | ||||
\(795\) | −809456. | + | 723630.i | −1.28073 | + | 1.14494i | ||||
\(796\) | −121184. | + | 209897.i | −0.191258 | + | 0.331269i | ||||
\(797\) | 693067.i | 1.09108i | 0.838083 | + | 0.545542i | \(0.183676\pi\) | ||||
−0.838083 | + | 0.545542i | \(0.816324\pi\) | |||||||
\(798\) | −734900. | + | 57896.0i | −1.15404 | + | 0.0909165i | ||||
\(799\) | −30170.4 | −0.0472594 | ||||||||
\(800\) | 728946. | + | 420857.i | 1.13898 | + | 0.657590i | ||||
\(801\) | 239839. | − | 325209.i | 0.373813 | − | 0.506871i | ||||
\(802\) | −590231. | − | 1.02231e6i | −0.917642 | − | 1.58940i | ||||
\(803\) | −181108. | − | 104563.i | −0.280872 | − | 0.162161i | ||||
\(804\) | −169640. | − | 812322.i | −0.262432 | − | 1.25666i | ||||
\(805\) | −381160. | + | 500502.i | −0.588187 | + | 0.772350i | ||||
\(806\) | − | 863510.i | − | 1.32922i | ||||||
\(807\) | −167378. | + | 508956.i | −0.257010 | + | 0.781507i | ||||
\(808\) | 42937.2 | + | 74369.4i | 0.0657674 | + | 0.113912i | ||||
\(809\) | 414933. | − | 239562.i | 0.633988 | − | 0.366033i | −0.148307 | − | 0.988941i | \(-0.547382\pi\) |
0.782295 | + | 0.622908i | \(0.214049\pi\) | |||||||
\(810\) | −366563. | − | 1.18541e6i | −0.558701 | − | 1.80676i | ||||
\(811\) | −591420. | −0.899196 | −0.449598 | − | 0.893231i | \(-0.648433\pi\) | ||||
−0.449598 | + | 0.893231i | \(0.648433\pi\) | |||||||
\(812\) | 87107.6 | + | 66337.3i | 0.132113 | + | 0.100611i | ||||
\(813\) | 83452.1 | + | 399610.i | 0.126257 | + | 0.604582i | ||||
\(814\) | 97066.6 | − | 168124.i | 0.146494 | − | 0.253736i | ||||
\(815\) | 275496. | − | 159058.i | 0.414763 | − | 0.239464i | ||||
\(816\) | −538493. | − | 602361.i | −0.808722 | − | 0.904641i | ||||
\(817\) | −293431. | + | 508237.i | −0.439604 | + | 0.761416i | ||||
\(818\) | − | 919997.i | − | 1.37493i | ||||||
\(819\) | −484330. | + | 141631.i | −0.722061 | + | 0.211149i | ||||
\(820\) | −112570. | −0.167416 | ||||||||
\(821\) | 599417. | + | 346074.i | 0.889289 | + | 0.513431i | 0.873710 | − | 0.486448i | \(-0.161708\pi\) |
0.0155788 | + | 0.999879i | \(0.495041\pi\) | |||||||
\(822\) | −851894. | + | 761568.i | −1.26079 | + | 1.12711i | ||||
\(823\) | −20631.5 | − | 35734.7i | −0.0304600 | − | 0.0527583i | 0.850394 | − | 0.526147i | \(-0.176364\pi\) |
−0.880854 | + | 0.473389i | \(0.843031\pi\) | |||||||
\(824\) | −141643. | − | 81777.4i | −0.208612 | − | 0.120442i | ||||
\(825\) | 239062. | − | 49924.2i | 0.351239 | − | 0.0733505i | ||||
\(826\) | 530898. | + | 1.26861e6i | 0.778127 | + | 1.85938i | ||||
\(827\) | 1.30209e6i | 1.90383i | 0.306357 | + | 0.951917i | \(0.400890\pi\) | ||||
−0.306357 | + | 0.951917i | \(0.599110\pi\) | |||||||
\(828\) | −299902. | − | 33684.2i | −0.437440 | − | 0.0491321i | ||||
\(829\) | −58201.1 | − | 100807.i | −0.0846880 | − | 0.146684i | 0.820570 | − | 0.571546i | \(-0.193656\pi\) |
−0.905258 | + | 0.424862i | \(0.860323\pi\) | |||||||
\(830\) | −606006. | + | 349878.i | −0.879672 | + | 0.507879i | ||||
\(831\) | −1.19535e6 | − | 393109.i | −1.73099 | − | 0.569260i | ||||
\(832\) | 132527. | 0.191451 | ||||||||
\(833\) | 173350. | − | 666335.i | 0.249825 | − | 0.960290i | ||||
\(834\) | 517265. | − | 108023.i | 0.743672 | − | 0.155304i | ||||
\(835\) | −222011. | + | 384535.i | −0.318421 | + | 0.551522i | ||||
\(836\) | 112759. | − | 65101.2i | 0.161338 | − | 0.0931486i | ||||
\(837\) | 399572. | − | 872232.i | 0.570354 | − | 1.24503i | ||||
\(838\) | 233660. | − | 404711.i | 0.332733 | − | 0.576311i | ||||
\(839\) | − | 1.08159e6i | − | 1.53652i | −0.640137 | − | 0.768261i | \(-0.721123\pi\) | ||
0.640137 | − | 0.768261i | \(-0.278877\pi\) | |||||||
\(840\) | 368802. | − | 253513.i | 0.522679 | − | 0.359288i | ||||
\(841\) | 663126. | 0.937571 | ||||||||
\(842\) | 683357. | + | 394536.i | 0.963881 | + | 0.556497i | ||||
\(843\) | −282169. | − | 315635.i | −0.397058 | − | 0.444151i | ||||
\(844\) | 205613. | + | 356132.i | 0.288646 | + | 0.499949i | ||||
\(845\) | −393415. | − | 227138.i | −0.550982 | − | 0.318110i | ||||
\(846\) | 40305.0 | − | 17601.7i | 0.0563142 | − | 0.0245932i | ||||
\(847\) | 642155. | + | 82162.6i | 0.895104 | + | 0.114527i | ||||
\(848\) | − | 1.03064e6i | − | 1.43323i | ||||||
\(849\) | −117332. | − | 38586.3i | −0.162780 | − | 0.0535325i | ||||
\(850\) | −531174. | − | 920021.i | −0.735190 | − | 1.27339i | ||||
\(851\) | 301943. | − | 174327.i | 0.416933 | − | 0.240716i | ||||
\(852\) | −98329.4 | + | 298996.i | −0.135458 | + | 0.411895i | ||||
\(853\) | 558935. | 0.768180 | 0.384090 | − | 0.923296i | \(-0.374515\pi\) | ||||
0.384090 | + | 0.923296i | \(0.374515\pi\) | |||||||
\(854\) | −767516. | − | 584506.i | −1.05238 | − | 0.801444i | ||||
\(855\) | 384773. | + | 881066.i | 0.526348 | + | 1.20525i | ||||
\(856\) | −93765.7 | + | 162407.i | −0.127967 | + | 0.221645i | ||||
\(857\) | −557244. | + | 321725.i | −0.758724 | + | 0.438049i | −0.828837 | − | 0.559490i | \(-0.810997\pi\) |
0.0701135 | + | 0.997539i | \(0.477664\pi\) | |||||||
\(858\) | 166421. | − | 148776.i | 0.226066 | − | 0.202096i | ||||
\(859\) | 449263. | − | 778146.i | 0.608855 | − | 1.05457i | −0.382574 | − | 0.923925i | \(-0.624962\pi\) |
0.991429 | − | 0.130644i | \(-0.0417044\pi\) | |||||||
\(860\) | 706036.i | 0.954618i | ||||||||
\(861\) | −54836.3 | + | 114990.i | −0.0739710 | + | 0.155115i | ||||
\(862\) | −1.08279e6 | −1.45724 | ||||||||
\(863\) | −848397. | − | 489822.i | −1.13914 | − | 0.657684i | −0.192924 | − | 0.981214i | \(-0.561797\pi\) |
−0.946218 | + | 0.323530i | \(0.895130\pi\) | |||||||
\(864\) | 777136. | + | 356009.i | 1.04104 | + | 0.476906i | ||||
\(865\) | −392347. | − | 679565.i | −0.524370 | − | 0.908236i | ||||
\(866\) | 369387. | + | 213266.i | 0.492545 | + | 0.284371i | ||||
\(867\) | −2371.11 | − | 11354.1i | −0.00315438 | − | 0.0151047i | ||||
\(868\) | −680200. | − | 87030.3i | −0.902811 | − | 0.115513i | ||||
\(869\) | 29046.6i | 0.0384641i | ||||||||
\(870\) | 111733. | − | 339752.i | 0.147619 | − | 0.448873i | ||||
\(871\) | 551199. | + | 954705.i | 0.726561 | + | 1.25844i | ||||
\(872\) | −152273. | + | 87914.7i | −0.200258 | + | 0.115619i | ||||
\(873\) | 17762.8 | − | 158149.i | 0.0233068 | − | 0.207509i | ||||
\(874\) | 585673. | 0.766711 | ||||||||
\(875\) | 153782. | − | 64355.9i | 0.200858 | − | 0.0840567i | ||||
\(876\) | −108235. | − | 518283.i | −0.141046 | − | 0.675397i | ||||
\(877\) | 577236. | − | 999802.i | 0.750506 | − | 1.29991i | −0.197072 | − | 0.980389i | \(-0.563143\pi\) |
0.947578 | − | 0.319525i | \(-0.103523\pi\) | |||||||
\(878\) | −1.15636e6 | + | 667622.i | −1.50004 | + | 0.866047i | ||||
\(879\) | 602676. | + | 674156.i | 0.780021 | + | 0.872535i | ||||
\(880\) | −216831. | + | 375563.i | −0.279999 | + | 0.484973i | ||||
\(881\) | 316201.i | 0.407391i | 0.979034 | + | 0.203695i | \(0.0652952\pi\) | ||||
−0.979034 | + | 0.203695i | \(0.934705\pi\) | |||||||
\(882\) | 157166. | + | 991298.i | 0.202032 | + | 1.27429i | ||||
\(883\) | −300056. | −0.384841 | −0.192420 | − | 0.981313i | \(-0.561634\pi\) | ||||
−0.192420 | + | 0.981313i | \(0.561634\pi\) | |||||||
\(884\) | −335756. | − | 193849.i | −0.429655 | − | 0.248061i | ||||
\(885\) | 1.33713e6 | − | 1.19536e6i | 1.70721 | − | 1.52620i | ||||
\(886\) | 808728. | + | 1.40076e6i | 1.03023 | + | 1.78441i | ||||
\(887\) | 269736. | + | 155732.i | 0.342840 | + | 0.197939i | 0.661527 | − | 0.749921i | \(-0.269909\pi\) |
−0.318687 | + | 0.947860i | \(0.603242\pi\) | |||||||
\(888\) | −242783. | + | 50701.4i | −0.307888 | + | 0.0642975i | ||||
\(889\) | −378675. | − | 904865.i | −0.479141 | − | 1.14493i | ||||
\(890\) | 943444.i | 1.19107i | ||||||||
\(891\) | 236945. | − | 73270.3i | 0.298465 | − | 0.0922938i | ||||
\(892\) | 68062.8 | + | 117888.i | 0.0855421 | + | 0.148163i | ||||
\(893\) | −29512.5 | + | 17039.1i | −0.0370087 | + | 0.0213670i | ||||
\(894\) | 1.08765e6 | + | 357689.i | 1.36086 | + | 0.447539i | ||||
\(895\) | −36841.0 | −0.0459923 | ||||||||
\(896\) | −83216.3 | + | 650391.i | −0.103656 | + | 0.810137i | ||||
\(897\) | 392439. | − | 81954.6i | 0.487739 | − | 0.101856i | ||||
\(898\) | −856783. | + | 1.48399e6i | −1.06247 | + | 1.84026i | ||||
\(899\) | 239492. | − | 138271.i | 0.296328 | − | 0.171085i | ||||
\(900\) | 497622. | + | 366992.i | 0.614348 | + | 0.453076i | ||||
\(901\) | −472028. | + | 817576.i | −0.581457 | + | 1.00711i | ||||
\(902\) | − | 56356.4i | − | 0.0692676i | ||||||
\(903\) | 721212. | + | 343931.i | 0.884478 | + | 0.421789i | ||||
\(904\) | −438398. | −0.536453 | ||||||||
\(905\) | −209507. | − | 120959.i | −0.255801 | − | 0.147687i | ||||
\(906\) | −9643.04 | − | 10786.8i | −0.0117478 | − | 0.0131412i | ||||
\(907\) | −699399. | − | 1.21139e6i | −0.850179 | − | 1.47255i | −0.881046 | − | 0.473030i | \(-0.843160\pi\) |
0.0308669 | − | 0.999524i | \(-0.490173\pi\) | |||||||
\(908\) | −230145. | − | 132874.i | −0.279145 | − | 0.161164i | ||||
\(909\) | 100524. | + | 230182.i | 0.121658 | + | 0.278576i | ||||
\(910\) | 713808. | − | 937303.i | 0.861983 | − | 1.13187i | ||||
\(911\) | − | 355728.i | − | 0.428629i | −0.976765 | − | 0.214315i | \(-0.931248\pi\) | ||
0.976765 | − | 0.214315i | \(-0.0687518\pi\) | |||||||
\(912\) | −866940. | − | 285106.i | −1.04232 | − | 0.342781i | ||||
\(913\) | −69935.1 | − | 121131.i | −0.0838984 | − | 0.145316i | ||||
\(914\) | 426808. | − | 246418.i | 0.510905 | − | 0.294971i | ||||
\(915\) | −393070. | + | 1.19523e6i | −0.469492 | + | 1.42761i | ||||
\(916\) | −943226. | −1.12415 | ||||||||
\(917\) | 2477.00 | − | 19359.4i | 0.00294569 | − | 0.0230226i | ||||
\(918\) | −624770. | − | 879550.i | −0.741370 | − | 1.04370i | ||||
\(919\) | 273155. | − | 473118.i | 0.323428 | − | 0.560194i | −0.657765 | − | 0.753223i | \(-0.728498\pi\) |
0.981193 | + | 0.193030i | \(0.0618313\pi\) | |||||||
\(920\) | −307919. | + | 177777.i | −0.363799 | + | 0.210039i | ||||
\(921\) | −711523. | + | 636080.i | −0.838821 | + | 0.749881i | ||||
\(922\) | 300235. | − | 520022.i | 0.353183 | − | 0.611731i | ||||
\(923\) | − | 418125.i | − | 0.490798i | ||||||
\(924\) | −100420. | − | 146087.i | −0.117619 | − | 0.171107i | ||||
\(925\) | −714335. | −0.834869 | ||||||||
\(926\) | 398399. | + | 230016.i | 0.464618 | + | 0.268247i | ||||
\(927\) | −385006. | − | 283938.i | −0.448031 | − | 0.330419i | ||||
\(928\) | 123196. | + | 213381.i | 0.143054 | + | 0.247777i | ||||
\(929\) | 1.17155e6 | + | 676395.i | 1.35747 | + | 0.783734i | 0.989282 | − | 0.146018i | \(-0.0466457\pi\) |
0.368186 | + | 0.929752i | \(0.379979\pi\) | |||||||
\(930\) | 457906. | + | 2.19268e6i | 0.529432 | + | 2.53518i | ||||
\(931\) | −206749. | − | 749707.i | −0.238531 | − | 0.864952i | ||||
\(932\) | 255002.i | 0.293570i | ||||||||
\(933\) | 105996. | − | 322310.i | 0.121766 | − | 0.370263i | ||||
\(934\) | −599016. | − | 1.03753e6i | −0.686665 | − | 1.18934i | ||||
\(935\) | 344011. | − | 198615.i | 0.393504 | − | 0.227190i | ||||
\(936\) | −283409. | − | 31831.7i | −0.323490 | − | 0.0363336i | ||||
\(937\) | −1.57072e6 | −1.78903 | −0.894517 | − | 0.447033i | \(-0.852480\pi\) | ||||
−0.894517 | + | 0.447033i | \(0.852480\pi\) | |||||||
\(938\) | 2.02270e6 | − | 846475.i | 2.29893 | − | 0.962074i | ||||
\(939\) | −138261. | − | 662061.i | −0.156808 | − | 0.750874i | ||||
\(940\) | −20499.2 | + | 35505.7i | −0.0231997 | + | 0.0401830i | ||||
\(941\) | −815367. | + | 470752.i | −0.920818 | + | 0.531635i | −0.883896 | − | 0.467684i | \(-0.845089\pi\) |
−0.0369222 | + | 0.999318i | \(0.511755\pi\) | |||||||
\(942\) | 278543. | + | 311580.i | 0.313900 | + | 0.351130i | ||||
\(943\) | 50606.7 | − | 87653.4i | 0.0569095 | − | 0.0985701i | ||||
\(944\) | 1.70250e6i | 1.91049i | ||||||||
\(945\) | 1.15474e6 | − | 616470.i | 1.29306 | − | 0.690316i | ||||
\(946\) | −353465. | −0.394970 | ||||||||
\(947\) | −220936. | − | 127558.i | −0.246358 | − | 0.142235i | 0.371737 | − | 0.928338i | \(-0.378762\pi\) |
−0.618096 | + | 0.786103i | \(0.712096\pi\) | |||||||
\(948\) | −54826.0 | + | 49012.8i | −0.0610056 | + | 0.0545372i | ||||
\(949\) | 351680. | + | 609127.i | 0.390494 | + | 0.676356i | ||||
\(950\) | −1.03918e6 | − | 599973.i | −1.15145 | − | 0.664790i | ||||
\(951\) | 755772. | − | 157831.i | 0.835660 | − | 0.174514i | ||||
\(952\) | 235758. | − | 309575.i | 0.260132 | − | 0.341579i | ||||
\(953\) | 72256.0i | 0.0795588i | 0.999208 | + | 0.0397794i | \(0.0126655\pi\) | ||||
−0.999208 | + | 0.0397794i | \(0.987334\pi\) | |||||||
\(954\) | 153604. | − | 1.36759e6i | 0.168775 | − | 1.50266i | ||||
\(955\) | 1.25026e6 | + | 2.16552e6i | 1.37087 | + | 2.37441i | ||||
\(956\) | 192098. | − | 110908.i | 0.210188 | − | 0.121352i | ||||
\(957\) | 67911.1 | + | 22333.6i | 0.0741510 | + | 0.0243857i | ||||
\(958\) | 1.19942e6 | 1.30690 | ||||||||
\(959\) | −959037. | − | 730359.i | −1.04279 | − | 0.794144i | ||||
\(960\) | −336522. | + | 70277.1i | −0.365149 | + | 0.0762555i | ||||
\(961\) | −404231. | + | 700148.i | −0.437706 | + | 0.758129i | ||||
\(962\) | −565457. | + | 326467.i | −0.611012 | + | 0.352768i | ||||
\(963\) | −325563. | + | 441446.i | −0.351061 | + | 0.476020i | ||||
\(964\) | 560846. | − | 971413.i | 0.603517 | − | 1.04532i | ||||
\(965\) | − | 1.76214e6i | − | 1.89228i | ||||||
\(966\) | −62625.9 | − | 794940.i | −0.0671120 | − | 0.851883i | ||||
\(967\) | 631353. | 0.675180 | 0.337590 | − | 0.941293i | \(-0.390388\pi\) | ||||
0.337590 | + | 0.941293i | \(0.390388\pi\) | |||||||
\(968\) | 316864. | + | 182942.i | 0.338160 | + | 0.195237i | ||||
\(969\) | 557140. | + | 623220.i | 0.593358 | + | 0.663734i | ||||
\(970\) | 185782. | + | 321783.i | 0.197451 | + | 0.341995i | ||||
\(971\) | 1.05107e6 | + | 606836.i | 1.11479 | + | 0.643625i | 0.940066 | − | 0.340992i | \(-0.110763\pi\) |
0.174725 | + | 0.984617i | \(0.444096\pi\) | |||||||
\(972\) | 538117. | + | 323603.i | 0.569566 | + | 0.342516i | ||||
\(973\) | 215208. | + | 514251.i | 0.227317 | + | 0.543187i | ||||
\(974\) | 515451.i | 0.543337i | ||||||||
\(975\) | −780277. | − | 256606.i | −0.820805 | − | 0.269934i | ||||
\(976\) | −597170. | − | 1.03433e6i | −0.626901 | − | 1.08582i | ||||
\(977\) | 1.13374e6 | − | 654566.i | 1.18775 | − | 0.685748i | 0.229955 | − | 0.973201i | \(-0.426142\pi\) |
0.957795 | + | 0.287454i | \(0.0928087\pi\) | |||||||
\(978\) | −125965. | + | 383030.i | −0.131696 | + | 0.400457i | ||||
\(979\) | −188580. | −0.196757 | ||||||||
\(980\) | −666385. | − | 656745.i | −0.693862 | − | 0.683824i | ||||
\(981\) | −471302. | + | 205824.i | −0.489735 | + | 0.213874i | ||||
\(982\) | 313883. | − | 543662.i | 0.325496 | − | 0.563775i | ||||
\(983\) | −371615. | + | 214552.i | −0.384579 | + | 0.222037i | −0.679809 | − | 0.733389i | \(-0.737937\pi\) |
0.295230 | + | 0.955426i | \(0.404604\pi\) | |||||||
\(984\) | −53677.7 | + | 47986.3i | −0.0554375 | + | 0.0495595i | ||||
\(985\) | −670422. | + | 1.16120e6i | −0.690996 | + | 1.19684i | ||||
\(986\) | − | 310977.i | − | 0.319871i | ||||||
\(987\) | 26283.1 | + | 38235.7i | 0.0269800 | + | 0.0392496i | ||||
\(988\) | −437913. | −0.448615 | ||||||||
\(989\) | −549758. | − | 317403.i | −0.562055 | − | 0.324503i | ||||
\(990\) | −343694. | + | 466032.i | −0.350673 | + | 0.475494i | ||||
\(991\) | −271321. | − | 469942.i | −0.276272 | − | 0.478517i | 0.694183 | − | 0.719798i | \(-0.255766\pi\) |
−0.970455 | + | 0.241281i | \(0.922432\pi\) | |||||||
\(992\) | −1.33641e6 | − | 771575.i | −1.35805 | − | 0.784070i | ||||
\(993\) | 53563.7 | + | 256490.i | 0.0543216 | + | 0.260118i | ||||
\(994\) | −824928. | − | 105548.i | −0.834917 | − | 0.106826i | ||||
\(995\) | 835207.i | 0.843622i | ||||||||
\(996\) | 110630. | − | 336398.i | 0.111520 | − | 0.339106i | ||||
\(997\) | 566787. | + | 981704.i | 0.570203 | + | 0.987621i | 0.996545 | + | 0.0830587i | \(0.0264689\pi\) |
−0.426341 | + | 0.904562i | \(0.640198\pi\) | |||||||
\(998\) | −37490.7 | + | 21645.3i | −0.0376411 | + | 0.0217321i | ||||
\(999\) | −722235. | + | 68110.0i | −0.723681 | + | 0.0682465i |
(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 | 21.5.h.b.2.7 | yes | 16 | |
3.2 | odd | 2 | inner | 21.5.h.b.2.2 | ✓ | 16 | |
7.2 | even | 3 | 147.5.b.c.50.2 | 8 | |||
7.3 | odd | 6 | 147.5.h.b.116.2 | 16 | |||
7.4 | even | 3 | inner | 21.5.h.b.11.2 | yes | 16 | |
7.5 | odd | 6 | 147.5.b.f.50.2 | 8 | |||
7.6 | odd | 2 | 147.5.h.b.128.7 | 16 | |||
21.2 | odd | 6 | 147.5.b.c.50.7 | 8 | |||
21.5 | even | 6 | 147.5.b.f.50.7 | 8 | |||
21.11 | odd | 6 | inner | 21.5.h.b.11.7 | yes | 16 | |
21.17 | even | 6 | 147.5.h.b.116.7 | 16 | |||
21.20 | even | 2 | 147.5.h.b.128.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.5.h.b.2.2 | ✓ | 16 | 3.2 | odd | 2 | inner | |
21.5.h.b.2.7 | yes | 16 | 1.1 | even | 1 | trivial | |
21.5.h.b.11.2 | yes | 16 | 7.4 | even | 3 | inner | |
21.5.h.b.11.7 | yes | 16 | 21.11 | odd | 6 | inner | |
147.5.b.c.50.2 | 8 | 7.2 | even | 3 | |||
147.5.b.c.50.7 | 8 | 21.2 | odd | 6 | |||
147.5.b.f.50.2 | 8 | 7.5 | odd | 6 | |||
147.5.b.f.50.7 | 8 | 21.5 | even | 6 | |||
147.5.h.b.116.2 | 16 | 7.3 | odd | 6 | |||
147.5.h.b.116.7 | 16 | 21.17 | even | 6 | |||
147.5.h.b.128.2 | 16 | 21.20 | even | 2 | |||
147.5.h.b.128.7 | 16 | 7.6 | odd | 2 |