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 | 11.2 | ||
Root | \(-4.46939 + 2.58040i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.11 |
Dual form | 21.5.h.b.2.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.46939 | + | 2.58040i | −1.11735 | + | 0.645101i | −0.940723 | − | 0.339177i | \(-0.889851\pi\) |
−0.176625 | + | 0.984278i | \(0.556518\pi\) | |||||||
\(3\) | 8.54954 | + | 2.81164i | 0.949949 | + | 0.312405i | ||||
\(4\) | 5.31698 | − | 9.20927i | 0.332311 | − | 0.575579i | ||||
\(5\) | −31.7353 | + | 18.3224i | −1.26941 | + | 0.732896i | −0.974877 | − | 0.222744i | \(-0.928498\pi\) |
−0.294536 | + | 0.955640i | \(0.595165\pi\) | |||||||
\(6\) | −45.4664 | + | 9.49493i | −1.26296 | + | 0.263748i | ||||
\(7\) | −18.9163 | + | 45.2015i | −0.386047 | + | 0.922479i | ||||
\(8\) | − | 27.6932i | − | 0.432706i | ||||||
\(9\) | 65.1893 | + | 48.0765i | 0.804806 | + | 0.593538i | ||||
\(10\) | 94.5584 | − | 163.780i | 0.945584 | − | 1.63780i | ||||
\(11\) | 32.7370 | + | 18.9007i | 0.270554 | + | 0.156204i | 0.629139 | − | 0.777292i | \(-0.283407\pi\) |
−0.358585 | + | 0.933497i | \(0.616741\pi\) | |||||||
\(12\) | 71.3509 | − | 63.7856i | 0.495492 | − | 0.442956i | ||||
\(13\) | 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 | \(-0.168088\pi\) |
−0.00446598 | + | 0.999990i | \(0.501422\pi\) | |||||||
\(18\) | −415.413 | − | 46.6581i | −1.28214 | − | 0.144007i | ||||
\(19\) | −161.952 | − | 280.509i | −0.448620 | − | 0.777032i | 0.549677 | − | 0.835378i | \(-0.314751\pi\) |
−0.998296 | + | 0.0583452i | \(0.981418\pi\) | |||||||
\(20\) | 389.679i | 0.974197i | ||||||||
\(21\) | −288.816 | + | 333.266i | −0.654912 | + | 0.755705i | ||||
\(22\) | −195.086 | −0.403071 | ||||||||
\(23\) | 303.425 | − | 175.183i | 0.573583 | − | 0.331158i | −0.184996 | − | 0.982739i | \(-0.559227\pi\) |
0.758579 | + | 0.651581i | \(0.225894\pi\) | |||||||
\(24\) | 77.8633 | − | 236.764i | 0.135179 | − | 0.411048i | ||||
\(25\) | 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 | \(0.960130\pi\) | |||||||
\(30\) | 1268.92 | − | 1134.38i | 1.40991 | − | 1.26042i | ||||
\(31\) | −658.024 | + | 1139.73i | −0.684728 | + | 1.18598i | 0.288794 | + | 0.957391i | \(0.406746\pi\) |
−0.973522 | + | 0.228593i | \(0.926588\pi\) | |||||||
\(32\) | −1015.47 | − | 586.282i | −0.991670 | − | 0.572541i | ||||
\(33\) | 226.745 | + | 253.638i | 0.208214 | + | 0.232909i | ||||
\(34\) | −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 | 0.625079 | − | 0.780561i | \(-0.285067\pi\) |
−0.988525 | + | 0.151054i | \(0.951733\pi\) | |||||||
\(38\) | 1447.65 | + | 835.802i | 1.00253 | + | 0.578810i | ||||
\(39\) | 1086.98 | + | 357.469i | 0.714647 | + | 0.235022i | ||||
\(40\) | 507.405 | + | 878.851i | 0.317128 | + | 0.549282i | ||||
\(41\) | 288.879i | 0.171850i | 0.996302 | + | 0.0859249i | \(0.0273845\pi\) | ||||
−0.996302 | + | 0.0859249i | \(0.972615\pi\) | |||||||
\(42\) | 430.871 | − | 2234.76i | 0.244258 | − | 1.26687i | ||||
\(43\) | 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 | ||||
\(45\) | −2949.68 | − | 331.300i | −1.45663 | − | 0.163605i | ||||
\(46\) | −904.085 | + | 1565.92i | −0.427261 | + | 0.740038i | ||||
\(47\) | −91.1152 | + | 52.6054i | −0.0412473 | + | 0.0238141i | −0.520482 | − | 0.853873i | \(-0.674248\pi\) |
0.479235 | + | 0.877687i | \(0.340914\pi\) | |||||||
\(48\) | 575.977 | + | 2758.06i | 0.249990 | + | 1.19708i | ||||
\(49\) | −1685.35 | − | 1710.09i | −0.701936 | − | 0.712240i | ||||
\(50\) | 3704.64i | 1.48186i | ||||||||
\(51\) | 1720.08 | + | 1924.09i | 0.661315 | + | 0.739751i | ||||
\(52\) | 675.993 | − | 1170.85i | 0.249998 | − | 0.433008i | ||||
\(53\) | −2851.06 | − | 1646.06i | −1.01497 | − | 0.585996i | −0.102330 | − | 0.994750i | \(-0.532630\pi\) |
−0.912644 | + | 0.408755i | \(0.865963\pi\) | |||||||
\(54\) | −3420.41 | − | 1566.90i | −1.17298 | − | 0.537346i | ||||
\(55\) | −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 | \(-0.0479771\pi\) |
0.364294 | + | 0.931284i | \(0.381310\pi\) | |||||||
\(60\) | −1095.64 | + | 3331.58i | −0.304344 | + | 0.925438i | ||||
\(61\) | 1907.51 | + | 3303.91i | 0.512635 | + | 0.887909i | 0.999893 | + | 0.0146511i | \(0.00466374\pi\) |
−0.487258 | + | 0.873258i | \(0.662003\pi\) | |||||||
\(62\) | − | 6791.87i | − | 1.76688i | ||||||
\(63\) | −3406.27 | + | 2037.22i | −0.858219 | + | 0.513284i | ||||
\(64\) | 1042.38 | 0.254488 | ||||||||
\(65\) | −4034.79 | + | 2329.49i | −0.954980 | + | 0.551358i | ||||
\(66\) | −1667.90 | − | 548.513i | −0.382897 | − | 0.125921i | ||||
\(67\) | 4335.41 | − | 7509.16i | 0.965786 | − | 1.67279i | 0.258299 | − | 0.966065i | \(-0.416838\pi\) |
0.707488 | − | 0.706726i | \(-0.249829\pi\) | |||||||
\(68\) | 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 | \(-0.105768\pi\) | |||||||
\(72\) | 1331.39 | − | 1805.30i | 0.256827 | − | 0.348244i | ||||
\(73\) | 2766.11 | − | 4791.04i | 0.519067 | − | 0.899051i | −0.480687 | − | 0.876892i | \(-0.659613\pi\) |
0.999754 | − | 0.0221588i | \(-0.00705393\pi\) | |||||||
\(74\) | 4447.56 | + | 2567.80i | 0.812191 | + | 0.468919i | ||||
\(75\) | 4816.52 | − | 4305.82i | 0.856270 | − | 0.765480i | ||||
\(76\) | −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 | 0.895163 | − | 0.445739i | \(-0.147059\pi\) |
−0.833603 | + | 0.552365i | \(0.813726\pi\) | |||||||
\(80\) | −9935.13 | − | 5736.05i | −1.55236 | − | 0.896258i | ||||
\(81\) | 1938.29 | + | 6268.15i | 0.295426 | + | 0.955366i | ||||
\(82\) | −745.426 | − | 1291.12i | −0.110860 | − | 0.192016i | ||||
\(83\) | 3700.12i | 0.537106i | 0.963265 | + | 0.268553i | \(0.0865454\pi\) | ||||
−0.963265 | + | 0.268553i | \(0.913455\pi\) | |||||||
\(84\) | 1533.51 | + | 4431.75i | 0.217334 | + | 0.628083i | ||||
\(85\) | −10508.3 | −1.45444 | ||||||||
\(86\) | −8097.82 | + | 4675.28i | −1.09489 | + | 0.632136i | ||||
\(87\) | −590.813 | + | 1796.52i | −0.0780569 | + | 0.237352i | ||||
\(88\) | 523.421 | − | 906.592i | 0.0675905 | − | 0.117070i | ||||
\(89\) | −4320.33 | + | 2494.34i | −0.545427 | + | 0.314902i | −0.747276 | − | 0.664514i | \(-0.768638\pi\) |
0.201848 | + | 0.979417i | \(0.435305\pi\) | |||||||
\(90\) | 14038.2 | − | 6130.66i | 1.73311 | − | 0.756872i | ||||
\(91\) | −2404.99 | + | 5746.86i | −0.290423 | + | 0.693981i | ||||
\(92\) | − | 3725.77i | − | 0.440190i | ||||||
\(93\) | −8830.32 | + | 7894.05i | −1.02096 | + | 0.912712i | ||||
\(94\) | 271.486 | − | 470.228i | 0.0307250 | − | 0.0532173i | ||||
\(95\) | 10279.2 | + | 5934.69i | 1.13897 | + | 0.657583i | ||||
\(96\) | −7033.39 | − | 7867.59i | −0.763172 | − | 0.853688i | ||||
\(97\) | 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 | \(-0.284765\pi\) |
−0.362563 | + | 0.931959i | \(0.618098\pi\) | |||||||
\(102\) | −12652.7 | − | 4161.01i | −1.21613 | − | 0.399944i | ||||
\(103\) | 2952.98 | + | 5114.72i | 0.278347 | + | 0.482111i | 0.970974 | − | 0.239185i | \(-0.0768802\pi\) |
−0.692627 | + | 0.721296i | \(0.743547\pi\) | |||||||
\(104\) | − | 3520.87i | − | 0.325524i | ||||||
\(105\) | 3059.44 | − | 15868.1i | 0.277500 | − | 1.43928i | ||||
\(106\) | 16990.0 | 1.51211 | ||||||||
\(107\) | 5864.51 | − | 3385.88i | 0.512229 | − | 0.295736i | −0.221520 | − | 0.975156i | \(-0.571102\pi\) |
0.733750 | + | 0.679420i | \(0.237769\pi\) | |||||||
\(108\) | 7717.91 | − | 727.834i | 0.661686 | − | 0.0624000i | ||||
\(109\) | −3174.60 | + | 5498.57i | −0.267200 | + | 0.462803i | −0.968138 | − | 0.250419i | \(-0.919432\pi\) |
0.700938 | + | 0.713222i | \(0.252765\pi\) | |||||||
\(110\) | 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 | \(-0.212820\pi\) | |||||||
\(114\) | 10026.8 | + | 11216.0i | 0.771528 | + | 0.863035i | ||||
\(115\) | −6419.54 | + | 11119.0i | −0.485409 | + | 0.840753i | ||||
\(116\) | 1935.15 | + | 1117.26i | 0.143813 | + | 0.0830306i | ||||
\(117\) | 8288.08 | + | 6112.39i | 0.605456 | + | 0.446518i | ||||
\(118\) | −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 | ||||
\(123\) | −812.226 | + | 2469.79i | −0.0536867 | + | 0.163248i | ||||
\(124\) | 6997.39 | + | 12119.8i | 0.455085 | + | 0.788231i | ||||
\(125\) | 3402.14i | 0.217737i | ||||||||
\(126\) | 9967.10 | − | 17894.7i | 0.627809 | − | 1.12715i | ||||
\(127\) | 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 | ||||
\(129\) | 15490.4 | + | 5094.25i | 0.930857 | + | 0.306126i | ||||
\(130\) | 12022.0 | − | 20822.8i | 0.711363 | − | 1.23212i | ||||
\(131\) | −344.947 | + | 199.155i | −0.0201007 | + | 0.0116051i | −0.510017 | − | 0.860165i | \(-0.670361\pi\) |
0.489916 | + | 0.871770i | \(0.337027\pi\) | |||||||
\(132\) | 3541.41 | − | 739.567i | 0.203249 | − | 0.0424453i | ||||
\(133\) | 15742.9 | − | 2014.28i | 0.889984 | − | 0.113872i | ||||
\(134\) | 44748.5i | 2.49212i | ||||||||
\(135\) | −24286.9 | − | 11125.9i | −1.33262 | − | 0.610476i | ||||
\(136\) | 3970.67 | − | 6877.40i | 0.214677 | − | 0.371832i | ||||
\(137\) | −21305.6 | − | 12300.8i | −1.13515 | − | 0.655378i | −0.189923 | − | 0.981799i | \(-0.560824\pi\) |
−0.945225 | + | 0.326421i | \(0.894157\pi\) | |||||||
\(138\) | −12132.3 | + | 10845.9i | −0.637068 | + | 0.569520i | ||||
\(139\) | −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 | ||||
\(144\) | −2830.35 | + | 25199.6i | −0.136495 | + | 1.21526i | ||||
\(145\) | −3850.10 | − | 6668.56i | −0.183120 | − | 0.317173i | ||||
\(146\) | 28550.7i | 1.33940i | ||||||||
\(147\) | −9600.80 | − | 19359.1i | −0.444296 | − | 0.895880i | ||||
\(148\) | −10582.0 | −0.483108 | ||||||||
\(149\) | 21348.1 | − | 12325.3i | 0.961581 | − | 0.555169i | 0.0649218 | − | 0.997890i | \(-0.479320\pi\) |
0.896659 | + | 0.442721i | \(0.145987\pi\) | |||||||
\(150\) | −10416.1 | + | 31673.0i | −0.462939 | + | 1.40769i | ||||
\(151\) | 155.754 | − | 269.773i | 0.00683100 | − | 0.0118316i | −0.862590 | − | 0.505904i | \(-0.831159\pi\) |
0.869421 | + | 0.494073i | \(0.164492\pi\) | |||||||
\(152\) | −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 | ||||||
\(156\) | 9071.46 | − | 8109.62i | 0.372759 | − | 0.333235i | ||||
\(157\) | −4499.01 | + | 7792.52i | −0.182523 | + | 0.316139i | −0.942739 | − | 0.333531i | \(-0.891760\pi\) |
0.760216 | + | 0.649670i | \(0.225093\pi\) | |||||||
\(158\) | −3434.28 | − | 1982.78i | −0.137569 | − | 0.0794256i | ||||
\(159\) | −19747.1 | − | 22089.3i | −0.781106 | − | 0.873749i | ||||
\(160\) | 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 | 0.936075 | − | 0.351802i | \(-0.114431\pi\) |
−0.772706 | + | 0.634764i | \(0.781098\pi\) | |||||||
\(164\) | 2660.37 | + | 1535.96i | 0.0989132 | + | 0.0571075i | ||||
\(165\) | −11843.1 | − | 3894.77i | −0.435007 | − | 0.143059i | ||||
\(166\) | −9547.81 | − | 16537.3i | −0.346488 | − | 0.600134i | ||||
\(167\) | 12116.9i | 0.434470i | 0.976119 | + | 0.217235i | \(0.0697038\pi\) | ||||
−0.976119 | + | 0.217235i | \(0.930296\pi\) | |||||||
\(168\) | 9229.19 | + | 7998.23i | 0.326998 | + | 0.283384i | ||||
\(169\) | −12396.7 | −0.434045 | ||||||||
\(170\) | 46965.8 | − | 27115.7i | 1.62511 | − | 0.938260i | ||||
\(171\) | 2928.37 | − | 26072.2i | 0.100146 | − | 0.891633i | ||||
\(172\) | 9633.50 | − | 16685.7i | 0.325632 | − | 0.564012i | ||||
\(173\) | 18544.6 | − | 10706.8i | 0.619621 | − | 0.357738i | −0.157100 | − | 0.987583i | \(-0.550215\pi\) |
0.776722 | + | 0.629844i | \(0.216881\pi\) | |||||||
\(174\) | −1995.18 | − | 9553.89i | −0.0658996 | − | 0.315560i | ||||
\(175\) | 21310.9 | + | 27983.4i | 0.695866 | + | 0.913744i | ||||
\(176\) | 11834.2i | 0.382045i | ||||||||
\(177\) | 32620.1 | + | 36489.0i | 1.04121 | + | 1.16470i | ||||
\(178\) | 12872.8 | − | 22296.4i | 0.406288 | − | 0.703711i | ||||
\(179\) | 870.662 | + | 502.677i | 0.0271734 | + | 0.0156885i | 0.513525 | − | 0.858075i | \(-0.328339\pi\) |
−0.486352 | + | 0.873763i | \(0.661673\pi\) | |||||||
\(180\) | −18734.4 | + | 25402.9i | −0.578223 | + | 0.784040i | ||||
\(181\) | −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 | ||||
\(186\) | 19096.3 | − | 58067.4i | 0.551981 | − | 1.67844i | ||||
\(187\) | 5420.01 | + | 9387.73i | 0.154995 | + | 0.268459i | ||||
\(188\) | 1118.81i | 0.0316548i | ||||||||
\(189\) | −34850.0 | + | 7840.11i | −0.975617 | + | 0.219482i | ||||
\(190\) | −61255.6 | −1.69683 | ||||||||
\(191\) | −59094.9 | + | 34118.5i | −1.61988 | + | 0.935239i | −0.632933 | + | 0.774207i | \(0.718149\pi\) |
−0.986949 | + | 0.161032i | \(0.948518\pi\) | |||||||
\(192\) | 8911.90 | + | 2930.81i | 0.241751 | + | 0.0795034i | ||||
\(193\) | −24043.5 | + | 41644.6i | −0.645481 | + | 1.11801i | 0.338709 | + | 0.940891i | \(0.390010\pi\) |
−0.984190 | + | 0.177115i | \(0.943324\pi\) | |||||||
\(194\) | −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 | \(0.843743\pi\) | |||||||
\(198\) | −12717.5 | − | 9379.07i | −0.324394 | − | 0.239238i | ||||
\(199\) | 11396.0 | − | 19738.4i | 0.287770 | − | 0.498432i | −0.685507 | − | 0.728066i | \(-0.740419\pi\) |
0.973277 | + | 0.229634i | \(0.0737528\pi\) | |||||||
\(200\) | −17216.0 | − | 9939.64i | −0.430399 | − | 0.248491i | ||||
\(201\) | 58178.9 | − | 52010.2i | 1.44004 | − | 1.28735i | ||||
\(202\) | −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 | ||||
\(207\) | 28202.3 | + | 3167.60i | 0.658178 | + | 0.0739248i | ||||
\(208\) | 19901.2 | + | 34469.8i | 0.459994 | + | 0.796733i | ||||
\(209\) | − | 12244.0i | − | 0.280306i | ||||||
\(210\) | 27272.3 | + | 78815.4i | 0.618420 | + | 1.78720i | ||||
\(211\) | 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 | ||||
\(213\) | 9246.74 | − | 28117.1i | 0.203812 | − | 0.619743i | ||||
\(214\) | −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 | ||||||
\(219\) | 37119.7 | − | 33183.9i | 0.773955 | − | 0.691893i | ||||
\(220\) | −7365.22 | + | 12756.9i | −0.152174 | + | 0.263573i | ||||
\(221\) | 31574.0 | + | 18229.3i | 0.646465 | + | 0.373237i | ||||
\(222\) | 30804.9 | + | 34458.5i | 0.625048 | + | 0.699182i | ||||
\(223\) | 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 | \(-0.255369\pi\) |
−0.275074 | + | 0.961423i | \(0.588703\pi\) | |||||||
\(228\) | −29447.8 | − | 9684.36i | −0.566478 | − | 0.186295i | ||||
\(229\) | −44349.7 | − | 76816.0i | −0.845707 | − | 1.46481i | −0.885005 | − | 0.465581i | \(-0.845845\pi\) |
0.0392979 | − | 0.999228i | \(-0.487488\pi\) | |||||||
\(230\) | − | 66260.0i | − | 1.25255i | ||||||
\(231\) | −15754.0 | + | 5451.31i | −0.295234 | + | 0.102159i | ||||
\(232\) | 5819.18 | 0.108115 | ||||||||
\(233\) | −20767.3 | + | 11990.0i | −0.382532 | + | 0.220855i | −0.678919 | − | 0.734213i | \(-0.737551\pi\) |
0.296387 | + | 0.955068i | \(0.404218\pi\) | |||||||
\(234\) | −52815.1 | − | 5932.06i | −0.964554 | − | 0.108336i | ||||
\(235\) | 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 | \(-0.0584475\pi\) | |||||||
\(240\) | −68813.1 | − | 76974.7i | −1.19467 | − | 1.33637i | ||||
\(241\) | −52741.0 | + | 91350.2i | −0.908060 | + | 1.57281i | −0.0913040 | + | 0.995823i | \(0.529103\pi\) |
−0.816756 | + | 0.576983i | \(0.804230\pi\) | |||||||
\(242\) | 59049.8 | + | 34092.4i | 1.00830 | + | 0.582140i | ||||
\(243\) | −1052.32 | + | 59039.6i | −0.0178211 | + | 0.999841i | ||||
\(244\) | 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 | ||||
\(249\) | −10403.4 | + | 31634.4i | −0.167795 | + | 0.510223i | ||||
\(250\) | −8778.91 | − | 15205.5i | −0.140463 | − | 0.243288i | ||||
\(251\) | − | 98405.1i | − | 1.56196i | −0.624555 | − | 0.780980i | \(-0.714720\pi\) | ||
0.624555 | − | 0.780980i | \(-0.285280\pi\) | |||||||
\(252\) | 650.293 | + | 42201.1i | 0.0102402 | + | 0.664543i | ||||
\(253\) | 13244.3 | 0.206914 | ||||||||
\(254\) | −89470.5 | + | 51655.8i | −1.38680 | + | 0.800667i | ||||
\(255\) | −89841.3 | − | 29545.7i | −1.38164 | − | 0.454374i | ||||
\(256\) | −42868.7 | + | 74250.8i | −0.654125 | + | 1.13298i | ||||
\(257\) | −16976.3 | + | 9801.28i | −0.257026 | + | 0.148394i | −0.622977 | − | 0.782240i | \(-0.714077\pi\) |
0.365951 | + | 0.930634i | \(0.380744\pi\) | |||||||
\(258\) | −82377.9 | + | 17203.3i | −1.23757 | + | 0.258447i | ||||
\(259\) | 48366.4 | − | 6188.39i | 0.721014 | − | 0.0922524i | ||||
\(260\) | 49543.3i | 0.732889i | ||||||||
\(261\) | −10102.4 | + | 13698.3i | −0.148300 | + | 0.201087i | ||||
\(262\) | 1027.80 | − | 1780.21i | 0.0149730 | − | 0.0259339i | ||||
\(263\) | −15118.6 | − | 8728.74i | −0.218575 | − | 0.126194i | 0.386715 | − | 0.922199i | \(-0.373610\pi\) |
−0.605290 | + | 0.796005i | \(0.706943\pi\) | |||||||
\(264\) | 7024.03 | − | 6279.27i | 0.100781 | − | 0.0900952i | ||||
\(265\) | 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 | \(-0.468273\pi\) |
−0.811973 | + | 0.583695i | \(0.801606\pi\) | |||||||
\(270\) | 137257. | − | 12944.0i | 1.88281 | − | 0.177558i | ||||
\(271\) | 22679.5 | + | 39282.0i | 0.308812 | + | 0.534879i | 0.978103 | − | 0.208122i | \(-0.0667352\pi\) |
−0.669291 | + | 0.743001i | \(0.733402\pi\) | |||||||
\(272\) | 89774.3i | 1.21343i | ||||||||
\(273\) | −36719.7 | + | 42371.0i | −0.492690 | + | 0.568517i | ||||
\(274\) | 126964. | 1.69114 | ||||||||
\(275\) | 23500.0 | − | 13567.7i | 0.310744 | − | 0.179408i | ||||
\(276\) | 10475.5 | − | 31853.6i | 0.137518 | − | 0.418158i | ||||
\(277\) | 69907.3 | − | 121083.i | 0.911094 | − | 1.57806i | 0.0985717 | − | 0.995130i | \(-0.468573\pi\) |
0.812522 | − | 0.582931i | \(-0.198094\pi\) | |||||||
\(278\) | 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 | \(0.903721\pi\) | |||||||
\(282\) | 3643.20 | − | 3256.91i | 0.0458126 | − | 0.0409551i | ||||
\(283\) | 6861.88 | − | 11885.1i | 0.0856781 | − | 0.148399i | −0.820002 | − | 0.572361i | \(-0.806028\pi\) |
0.905680 | + | 0.423962i | \(0.139361\pi\) | |||||||
\(284\) | −30286.8 | − | 17486.1i | −0.375506 | − | 0.216799i | ||||
\(285\) | 71196.1 | + | 79640.3i | 0.876529 | + | 0.980490i | ||||
\(286\) | −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 | ||||
\(291\) | 16797.5 | + | 5524.12i | 0.198362 | + | 0.0652344i | ||||
\(292\) | −29414.7 | − | 50947.7i | −0.344983 | − | 0.597529i | ||||
\(293\) | − | 100474.i | − | 1.17036i | −0.810902 | − | 0.585181i | \(-0.801023\pi\) | ||
0.810902 | − | 0.585181i | \(-0.198977\pi\) | |||||||
\(294\) | 92864.0 | + | 61749.3i | 1.07437 | + | 0.714394i | ||||
\(295\) | −199283. | −2.28995 | ||||||||
\(296\) | −23865.8 | + | 13778.9i | −0.272391 | + | 0.157265i | ||||
\(297\) | 2587.30 | + | 27435.6i | 0.0293315 | + | 0.311029i | ||||
\(298\) | −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 | ||||||||
\(303\) | 18600.3 | + | 20806.3i | 0.202597 | + | 0.226626i | ||||
\(304\) | 50701.0 | − | 87816.7i | 0.548617 | − | 0.950233i | ||||
\(305\) | −121071. | − | 69900.4i | −1.30149 | − | 0.751416i | ||||
\(306\) | −96475.1 | − | 71149.5i | −1.03032 | − | 0.759852i | ||||
\(307\) | 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 | \(-0.270900\pi\) |
−0.321637 | + | 0.946863i | \(0.604233\pi\) | |||||||
\(312\) | 9899.44 | − | 30101.8i | 0.101695 | − | 0.309232i | ||||
\(313\) | −37574.7 | − | 65081.3i | −0.383536 | − | 0.664305i | 0.608029 | − | 0.793915i | \(-0.291961\pi\) |
−0.991565 | + | 0.129611i | \(0.958627\pi\) | |||||||
\(314\) | − | 46437.1i | − | 0.470983i | ||||||
\(315\) | 70772.3 | − | 127063.i | 0.713250 | − | 1.28055i | ||||
\(316\) | 8171.12 | 0.0818290 | ||||||||
\(317\) | 74293.1 | − | 42893.1i | 0.739315 | − | 0.426844i | −0.0825050 | − | 0.996591i | \(-0.526292\pi\) |
0.821820 | + | 0.569747i | \(0.192959\pi\) | |||||||
\(318\) | 145257. | + | 47769.9i | 1.43642 | + | 0.472390i | ||||
\(319\) | −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 | ||||||
\(324\) | 68031.0 | + | 15477.4i | 0.648062 | + | 0.147437i | ||||
\(325\) | 45632.7 | − | 79038.2i | 0.432026 | − | 0.748290i | ||||
\(326\) | −38799.0 | − | 22400.6i | −0.365078 | − | 0.210778i | ||||
\(327\) | −42601.4 | + | 38084.4i | −0.398408 | + | 0.356165i | ||||
\(328\) | 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 | 0.924780 | − | 0.380503i | \(-0.124249\pi\) |
−0.791915 | + | 0.610632i | \(0.790916\pi\) | |||||||
\(332\) | 34075.4 | + | 19673.5i | 0.309147 | + | 0.178486i | ||||
\(333\) | 8996.70 | − | 80100.7i | 0.0811324 | − | 0.722350i | ||||
\(334\) | −31266.6 | − | 54155.3i | −0.280277 | − | 0.485454i | ||||
\(335\) | 317741.i | 2.83128i | ||||||||
\(336\) | −135564. | − | 26137.3i | −1.20078 | − | 0.231516i | ||||
\(337\) | −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 | ||||
\(339\) | 44509.9 | − | 135344.i | 0.387309 | − | 1.17771i | ||||
\(340\) | −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 | ||||||
\(345\) | −86146.7 | + | 77012.6i | −0.723770 | + | 0.647029i | ||||
\(346\) | −55255.5 | + | 95705.4i | −0.461555 | + | 0.799437i | ||||
\(347\) | 200198. | + | 115584.i | 1.66265 | + | 0.959929i | 0.971444 | + | 0.237268i | \(0.0762520\pi\) |
0.691202 | + | 0.722661i | \(0.257081\pi\) | |||||||
\(348\) | 13403.3 | + | 14993.0i | 0.110676 | + | 0.123803i | ||||
\(349\) | −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 | \(-0.515600\pi\) |
−0.889481 | + | 0.456973i | \(0.848934\pi\) | |||||||
\(354\) | −239948. | − | 78910.6i | −1.91475 | − | 0.629693i | ||||
\(355\) | 60257.4 | + | 104369.i | 0.478139 | + | 0.828161i | ||||
\(356\) | 53049.4i | 0.418582i | ||||||||
\(357\) | −119509. | + | 41353.6i | −0.937703 | + | 0.324472i | ||||
\(358\) | −5188.44 | −0.0404828 | ||||||||
\(359\) | 142620. | − | 82342.0i | 1.10661 | − | 0.638899i | 0.168658 | − | 0.985675i | \(-0.446057\pi\) |
0.937948 | + | 0.346775i | \(0.112723\pi\) | |||||||
\(360\) | −9174.75 | + | 81686.0i | −0.0707929 | + | 0.630293i | ||||
\(361\) | 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 | ||||||||
\(366\) | −118098. | − | 132105.i | −0.881619 | − | 0.986184i | ||||
\(367\) | −63154.9 | + | 109387.i | −0.468894 | + | 0.812148i | −0.999368 | − | 0.0355532i | \(-0.988681\pi\) |
0.530474 | + | 0.847701i | \(0.322014\pi\) | |||||||
\(368\) | 94991.1 | + | 54843.1i | 0.701435 | + | 0.404973i | ||||
\(369\) | −13888.3 | + | 18831.8i | −0.101999 | + | 0.138306i | ||||
\(370\) | −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 | 0.733195 | − | 0.680018i | \(-0.238028\pi\) |
−0.955511 | + | 0.294956i | \(0.904695\pi\) | |||||||
\(374\) | −48448.3 | − | 27971.6i | −0.346366 | − | 0.199974i | ||||
\(375\) | −9565.62 | + | 29086.8i | −0.0680222 | + | 0.206839i | ||||
\(376\) | 1456.81 | + | 2523.27i | 0.0103045 | + | 0.0178479i | ||||
\(377\) | 26715.7i | 0.187968i | ||||||||
\(378\) | 135528. | − | 124968.i | 0.948515 | − | 0.874609i | ||||
\(379\) | 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 | ||||
\(381\) | 171149. | + | 56284.9i | 1.17903 | + | 0.387741i | ||||
\(382\) | 176079. | − | 304978.i | 1.20665 | − | 2.08998i | ||||
\(383\) | −209920. | + | 121198.i | −1.43106 | + | 0.826221i | −0.997201 | − | 0.0747618i | \(-0.976180\pi\) |
−0.433855 | + | 0.900983i | \(0.642847\pi\) | |||||||
\(384\) | 117890. | − | 24619.5i | 0.799494 | − | 0.166961i | ||||
\(385\) | 26203.4 | − | 62614.3i | 0.176781 | − | 0.422428i | ||||
\(386\) | − | 248168.i | − | 1.66560i | ||||||
\(387\) | 118113. | + | 87107.0i | 0.788631 | + | 0.581609i | ||||
\(388\) | 10446.4 | − | 18093.7i | 0.0693911 | − | 0.120189i | ||||
\(389\) | −256161. | − | 147895.i | −1.69283 | − | 0.977357i | −0.952215 | − | 0.305428i | \(-0.901200\pi\) |
−0.740616 | − | 0.671928i | \(-0.765466\pi\) | |||||||
\(390\) | 161329. | − | 144223.i | 1.06068 | − | 0.948215i | ||||
\(391\) | 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 | ||||
\(396\) | 32356.9 | + | 3634.24i | 0.206336 | + | 0.0231752i | ||||
\(397\) | 117340. | + | 203238.i | 0.744498 | + | 1.28951i | 0.950429 | + | 0.310942i | \(0.100645\pi\) |
−0.205930 | + | 0.978567i | \(0.566022\pi\) | |||||||
\(398\) | 117625.i | 0.742563i | ||||||||
\(399\) | 140258. | + | 27042.4i | 0.881014 | + | 0.169863i | ||||
\(400\) | 224729. | 1.40456 | ||||||||
\(401\) | 198091. | − | 114368.i | 1.23190 | − | 0.711239i | 0.264476 | − | 0.964392i | \(-0.414801\pi\) |
0.967426 | + | 0.253153i | \(0.0814677\pi\) | |||||||
\(402\) | −125817. | + | 382579.i | −0.778550 | + | 2.36739i | ||||
\(403\) | −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 | ||||||
\(408\) | 53284.2 | − | 47634.5i | 0.320094 | − | 0.286155i | ||||
\(409\) | −89133.0 | + | 154383.i | −0.532834 | + | 0.922895i | 0.466431 | + | 0.884558i | \(0.345540\pi\) |
−0.999265 | + | 0.0383377i | \(0.987794\pi\) | |||||||
\(410\) | 47312.7 | + | 27316.0i | 0.281455 | + | 0.162498i | ||||
\(411\) | −147568. | − | 165070.i | −0.873589 | − | 0.977202i | ||||
\(412\) | 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 | ||||
\(417\) | −97267.0 | − | 31987.7i | −0.559362 | − | 0.183955i | ||||
\(418\) | 31594.6 | + | 54723.4i | 0.180826 | + | 0.313199i | ||||
\(419\) | − | 90551.7i | − | 0.515785i | −0.966174 | − | 0.257892i | \(-0.916972\pi\) | ||
0.966174 | − | 0.257892i | \(-0.0830280\pi\) | |||||||
\(420\) | −129867. | − | 112546.i | −0.736206 | − | 0.638013i | ||||
\(421\) | 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 | ||||
\(423\) | −8468.82 | − | 951.196i | −0.0473306 | − | 0.00531605i | ||||
\(424\) | −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 | ||||||
\(429\) | 28828.0 | + | 32247.2i | 0.156639 | + | 0.175217i | ||||
\(430\) | 171325. | − | 296743.i | 0.926580 | − | 1.60488i | ||||
\(431\) | 181702. | + | 104905.i | 0.978147 | + | 0.564733i | 0.901710 | − | 0.432341i | \(-0.142312\pi\) |
0.0764366 | + | 0.997074i | \(0.475646\pi\) | |||||||
\(432\) | −95050.5 | + | 207487.i | −0.509316 | + | 1.11179i | ||||
\(433\) | 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 | ||||
\(438\) | −80274.5 | + | 244096.i | −0.418436 | + | 1.27237i | ||||
\(439\) | −129364. | − | 224065.i | −0.671249 | − | 1.16264i | −0.977550 | − | 0.210703i | \(-0.932425\pi\) |
0.306301 | − | 0.951935i | \(-0.400909\pi\) | |||||||
\(440\) | 38361.3i | 0.198147i | ||||||||
\(441\) | −27651.6 | − | 192505.i | −0.142181 | − | 0.989841i | ||||
\(442\) | −188155. | −0.963102 | ||||||||
\(443\) | −271422. | + | 156706.i | −1.38305 | + | 0.798504i | −0.992520 | − | 0.122086i | \(-0.961042\pi\) |
−0.390530 | + | 0.920590i | \(0.627708\pi\) | |||||||
\(444\) | −90471.3 | − | 29752.8i | −0.458928 | − | 0.150925i | ||||
\(445\) | 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 | \(0.692022\pi\) | |||||||
\(450\) | −178106. | + | 241503.i | −0.879538 | + | 1.19261i | ||||
\(451\) | −5460.03 | + | 9457.06i | −0.0268437 | + | 0.0464946i | ||||
\(452\) | −145788. | − | 84170.6i | −0.713583 | − | 0.411987i | ||||
\(453\) | 2090.13 | − | 1868.51i | 0.0101854 | − | 0.00910542i | ||||
\(454\) | −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 | 0.957401 | − | 0.288763i | \(-0.0932440\pi\) |
−0.728777 | + | 0.684752i | \(0.759911\pi\) | |||||||
\(458\) | 396433. | + | 228881.i | 1.88990 | + | 1.09113i | ||||
\(459\) | 19627.2 | + | 208126.i | 0.0931608 | + | 0.987872i | ||||
\(460\) | 68265.0 | + | 118239.i | 0.322614 | + | 0.558783i | ||||
\(461\) | − | 116352.i | − | 0.547484i | −0.961803 | − | 0.273742i | \(-0.911738\pi\) | ||
0.961803 | − | 0.273742i | \(-0.0882615\pi\) | |||||||
\(462\) | 56344.0 | − | 65015.6i | 0.263976 | − | 0.304603i | ||||
\(463\) | 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 | ||||
\(465\) | 135595. | − | 412313.i | 0.627103 | − | 1.90687i | ||||
\(466\) | 61878.1 | − | 107176.i | 0.284948 | − | 0.493544i | ||||
\(467\) | 201039. | − | 116070.i | 0.921823 | − | 0.532215i | 0.0376069 | − | 0.999293i | \(-0.488027\pi\) |
0.884216 | + | 0.467078i | \(0.154693\pi\) | |||||||
\(468\) | 100358. | − | 43827.8i | 0.458206 | − | 0.200105i | ||||
\(469\) | 257415. | + | 338013.i | 1.17028 | + | 1.53669i | ||||
\(470\) | 19897.1i | 0.0900730i | ||||||||
\(471\) | −60374.3 | + | 53972.8i | −0.272151 | + | 0.243295i | ||||
\(472\) | 75300.8 | − | 130425.i | 0.337999 | − | 0.585432i | ||||
\(473\) | 59314.3 | + | 34245.1i | 0.265117 | + | 0.153065i | ||||
\(474\) | −23786.6 | − | 26607.8i | −0.105871 | − | 0.118428i | ||||
\(475\) | −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 | \(-0.502383\pi\) |
−0.869745 | + | 0.493502i | \(0.835717\pi\) | |||||||
\(480\) | 367360. | + | 120812.i | 1.59444 | + | 0.524357i | ||||
\(481\) | −63258.8 | − | 109568.i | −0.273420 | − | 0.473578i | ||||
\(482\) | − | 544373.i | − | 2.34316i | ||||||
\(483\) | −29251.7 | + | 151717.i | −0.125388 | + | 0.650339i | ||||
\(484\) | −140496. | −0.599755 | ||||||||
\(485\) | −62351.3 | + | 35998.5i | −0.265071 | + | 0.153039i | ||||
\(486\) | −147643. | − | 266587.i | −0.625086 | − | 1.12867i | ||||
\(487\) | 49939.0 | − | 86496.8i | 0.210563 | − | 0.364705i | −0.741328 | − | 0.671143i | \(-0.765804\pi\) |
0.951891 | + | 0.306437i | \(0.0991370\pi\) | |||||||
\(488\) | 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 | \(-0.0811813\pi\) | |||||||
\(492\) | 18426.3 | + | 20611.8i | 0.0761218 | + | 0.0851502i | ||||
\(493\) | −30128.7 | + | 52184.4i | −0.123961 | + | 0.214707i | ||||
\(494\) | 184053. | + | 106263.i | 0.754203 | + | 0.435439i | ||||
\(495\) | −90302.0 | − | 66597.0i | −0.368542 | − | 0.271797i | ||||
\(496\) | −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 | 0.857481 | − | 0.514516i | \(-0.172029\pi\) |
−0.874325 | + | 0.485342i | \(0.838695\pi\) | |||||||
\(500\) | 31331.3 | + | 18089.1i | 0.125325 | + | 0.0723565i | ||||
\(501\) | −34068.5 | + | 103594.i | −0.135731 | + | 0.412724i | ||||
\(502\) | 253925. | + | 439811.i | 1.00762 | + | 1.74525i | ||||
\(503\) | 17797.2i | 0.0703422i | 0.999381 | + | 0.0351711i | \(0.0111976\pi\) | ||||
−0.999381 | + | 0.0351711i | \(0.988802\pi\) | |||||||
\(504\) | 56417.2 | + | 94330.4i | 0.222101 | + | 0.371356i | ||||
\(505\) | −113633. | −0.445575 | ||||||||
\(506\) | −59194.1 | + | 34175.7i | −0.231195 | + | 0.133480i | ||||
\(507\) | −105987. | − | 34855.3i | −0.412320 | − | 0.135598i | ||||
\(508\) | 106438. | − | 184356.i | 0.412447 | − | 0.714380i | ||||
\(509\) | 128586. | − | 74239.4i | 0.496317 | − | 0.286549i | −0.230874 | − | 0.972984i | \(-0.574159\pi\) |
0.727191 | + | 0.686435i | \(0.240825\pi\) | |||||||
\(510\) | 477776. | − | 99775.8i | 1.83689 | − | 0.383606i | ||||
\(511\) | 164238. | + | 215661.i | 0.628972 | + | 0.825904i | ||||
\(512\) | − | 228371.i | − | 0.871165i | ||||||
\(513\) | 98342.1 | − | 214672.i | 0.373684 | − | 0.815720i | ||||
\(514\) | 50582.5 | − | 87611.5i | 0.191458 | − | 0.331616i | ||||
\(515\) | −187428. | − | 108211.i | −0.706674 | − | 0.407999i | ||||
\(516\) | 129276. | − | 115569.i | 0.485534 | − | 0.434053i | ||||
\(517\) | −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 | 0.999987 | + | 0.00516125i | \(0.00164288\pi\) |
0.504463 | + | 0.863433i | \(0.331690\pi\) | |||||||
\(522\) | 9804.31 | − | 87291.1i | 0.0359812 | − | 0.320353i | ||||
\(523\) | −190874. | − | 330604.i | −0.697820 | − | 1.20866i | −0.969221 | − | 0.246194i | \(-0.920820\pi\) |
0.271400 | − | 0.962467i | \(-0.412513\pi\) | |||||||
\(524\) | 4235.62i | 0.0154260i | ||||||||
\(525\) | 103519. | + | 299164.i | 0.375579 | + | 1.08540i | ||||
\(526\) | 90094.7 | 0.325632 | ||||||||
\(527\) | −326831. | + | 188696.i | −1.17680 | + | 0.679425i | ||||
\(528\) | −33273.6 | + | 101177.i | −0.119353 | + | 0.362923i | ||||
\(529\) | −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 | ||||||||
\(534\) | 172746. | − | 154430.i | 0.605796 | − | 0.541563i | ||||
\(535\) | −124075. | + | 214904.i | −0.433487 | + | 0.750822i | ||||
\(536\) | −207952. | − | 120061.i | −0.723826 | − | 0.417901i | ||||
\(537\) | 6030.41 | + | 6745.65i | 0.0209121 | + | 0.0233924i | ||||
\(538\) | 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 | −0.934138 | − | 0.356911i | \(-0.883830\pi\) |
0.157975 | − | 0.987443i | \(-0.449503\pi\) | |||||||
\(542\) | −202727. | − | 117044.i | −0.690102 | − | 0.398430i | ||||
\(543\) | −56441.5 | − | 18561.6i | −0.191425 | − | 0.0629530i | ||||
\(544\) | −168123. | − | 291198.i | −0.568107 | − | 0.983990i | ||||
\(545\) | − | 232665.i | − | 0.783318i | ||||||
\(546\) | 54780.3 | − | 284124.i | 0.183755 | − | 0.953067i | ||||
\(547\) | −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 | ||||
\(549\) | −34491.1 | + | 307086.i | −0.114436 | + | 1.01886i | ||||
\(550\) | −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 | ||||||||
\(555\) | 218733. | + | 244676.i | 0.710113 | + | 0.794337i | ||||
\(556\) | −60490.5 | + | 104773.i | −0.195676 | + | 0.338921i | ||||
\(557\) | 138785. | + | 80127.7i | 0.447335 | + | 0.258269i | 0.706704 | − | 0.707509i | \(-0.250181\pi\) |
−0.259369 | + | 0.965778i | \(0.583515\pi\) | |||||||
\(558\) | 326530. | − | 442757.i | 1.04871 | − | 1.42199i | ||||
\(559\) | 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 | \(-0.342441\pi\) |
−0.524570 | + | 0.851367i | \(0.675774\pi\) | |||||||
\(564\) | −3145.69 | + | 9565.28i | −0.00988911 | + | 0.0300704i | ||||
\(565\) | 290054. | + | 502388.i | 0.908618 | + | 1.57377i | ||||
\(566\) | 70825.7i | 0.221084i | ||||||||
\(567\) | −319995. | − | 30956.5i | −0.995353 | − | 0.0962910i | ||||
\(568\) | −91075.3 | −0.282296 | ||||||||
\(569\) | −21997.3 | + | 12700.2i | −0.0679431 | + | 0.0392270i | −0.533587 | − | 0.845745i | \(-0.679156\pi\) |
0.465644 | + | 0.884972i | \(0.345823\pi\) | |||||||
\(570\) | −523707. | − | 172229.i | −1.61190 | − | 0.530098i | ||||
\(571\) | −78397.4 | + | 135788.i | −0.240453 | + | 0.416476i | −0.960843 | − | 0.277092i | \(-0.910629\pi\) |
0.720391 | + | 0.693568i | \(0.243963\pi\) | |||||||
\(572\) | 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 | ||||||
\(576\) | 67952.2 | + | 50114.2i | 0.204814 | + | 0.151048i | ||||
\(577\) | 69603.7 | − | 120557.i | 0.209065 | − | 0.362111i | −0.742356 | − | 0.670006i | \(-0.766291\pi\) |
0.951420 | + | 0.307896i | \(0.0996248\pi\) | |||||||
\(578\) | 5760.05 | + | 3325.57i | 0.0172413 | + | 0.00995428i | ||||
\(579\) | −322651. | + | 288440.i | −0.962444 | + | 0.860397i | ||||
\(580\) | −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 | ||||
\(585\) | −375019. | − | 42121.1i | −1.09583 | − | 0.123080i | ||||
\(586\) | 259265. | + | 449060.i | 0.755002 | + | 1.30770i | ||||
\(587\) | 381239.i | 1.10642i | 0.833041 | + | 0.553212i | \(0.186598\pi\) | ||||
−0.833041 | + | 0.553212i | \(0.813402\pi\) | |||||||
\(588\) | −229330. | − | 14515.3i | −0.663295 | − | 0.0419829i | ||||
\(589\) | 426273. | 1.22873 | ||||||||
\(590\) | 890672. | − | 514230.i | 2.55867 | − | 1.47725i | ||||
\(591\) | −102879. | + | 312830.i | −0.294545 | + | 0.895640i | ||||
\(592\) | 155767. | − | 269796.i | 0.444458 | − | 0.769824i | ||||
\(593\) | 359500. | − | 207558.i | 1.02233 | − | 0.590241i | 0.107550 | − | 0.994200i | \(-0.465699\pi\) |
0.914777 | + | 0.403959i | \(0.132366\pi\) | |||||||
\(594\) | −82358.5 | − | 115944.i | −0.233419 | − | 0.328606i | ||||
\(595\) | 198778. | − | 474992.i | 0.561481 | − | 1.34169i | ||||
\(596\) | − | 262133.i | − | 0.737955i | ||||||
\(597\) | 152928. | − | 136713.i | 0.429080 | − | 0.383584i | ||||
\(598\) | −114944. | + | 199089.i | −0.321429 | + | 0.556731i | ||||
\(599\) | 512564. | + | 295929.i | 1.42855 | + | 0.824772i | 0.997006 | − | 0.0773215i | \(-0.0246368\pi\) |
0.431541 | + | 0.902093i | \(0.357970\pi\) | |||||||
\(600\) | −119242. | − | 133385.i | −0.331227 | − | 0.370513i | ||||
\(601\) | −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 | ||||
\(606\) | −136821. | − | 44995.5i | −0.372569 | − | 0.122525i | ||||
\(607\) | −150944. | − | 261443.i | −0.409675 | − | 0.709578i | 0.585178 | − | 0.810905i | \(-0.301025\pi\) |
−0.994853 | + | 0.101327i | \(0.967691\pi\) | |||||||
\(608\) | 379798.i | 1.02741i | ||||||||
\(609\) | −70029.4 | − | 60689.1i | −0.188819 | − | 0.163635i | ||||
\(610\) | 721486. | 1.93896 | ||||||||
\(611\) | −11584.3 | + | 6688.18i | −0.0310303 | + | 0.0179154i | ||||
\(612\) | 245459. | + | 27569.3i | 0.655353 | + | 0.0736076i | ||||
\(613\) | 156611. | − | 271258.i | 0.416775 | − | 0.721875i | −0.578838 | − | 0.815442i | \(-0.696494\pi\) |
0.995613 | + | 0.0935673i | \(0.0298270\pi\) | |||||||
\(614\) | −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 | \(-0.0294765\pi\) | |||||||
\(618\) | −182825. | − | 204510.i | −0.478696 | − | 0.535472i | ||||
\(619\) | 337786. | − | 585063.i | 0.881578 | − | 1.52694i | 0.0319909 | − | 0.999488i | \(-0.489815\pi\) |
0.849587 | − | 0.527449i | \(-0.176851\pi\) | |||||||
\(620\) | −444129. | − | 256418.i | −1.15538 | − | 0.667061i | ||||
\(621\) | 232210. | + | 106376.i | 0.602141 | + | 0.275843i | ||||
\(622\) | −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 | ||||
\(627\) | 34425.9 | − | 104681.i | 0.0875689 | − | 0.266276i | ||||
\(628\) | 47842.3 | + | 82865.2i | 0.121309 | + | 0.210113i | ||||
\(629\) | − | 285361.i | − | 0.721262i | ||||||
\(630\) | 11565.0 | + | 750515.i | 0.0291382 | + | 1.89094i | ||||
\(631\) | −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 | ||||
\(633\) | 330619. | + | 108729.i | 0.825127 | + | 0.271356i | ||||
\(634\) | −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 | ||||||
\(639\) | 158111. | − | 214390.i | 0.387222 | − | 0.525053i | ||||
\(640\) | −245181. | + | 424666.i | −0.598586 | + | 1.03678i | ||||
\(641\) | −426375. | − | 246168.i | −1.03771 | − | 0.599122i | −0.118526 | − | 0.992951i | \(-0.537817\pi\) |
−0.919184 | + | 0.393829i | \(0.871150\pi\) | |||||||
\(642\) | −234490. | + | 209627.i | −0.568924 | + | 0.508601i | ||||
\(643\) | −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 | \(-0.506683\pi\) |
−0.876332 | + | 0.481708i | \(0.840017\pi\) | |||||||
\(648\) | 173585. | − | 53677.4i | 0.413392 | − | 0.127833i | ||||
\(649\) | 102786. | + | 178031.i | 0.244032 | + | 0.422676i | ||||
\(650\) | 471003.i | 1.11480i | ||||||||
\(651\) | −189786. | − | 548470.i | −0.447818 | − | 1.29417i | ||||
\(652\) | 92313.9 | 0.217156 | ||||||||
\(653\) | −447959. | + | 258629.i | −1.05054 | + | 0.606529i | −0.922800 | − | 0.385279i | \(-0.874105\pi\) |
−0.127739 | + | 0.991808i | \(0.540772\pi\) | |||||||
\(654\) | 92129.2 | − | 280143.i | 0.215398 | − | 0.654974i | ||||
\(655\) | 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 | \(0.883824\pi\) | |||||||
\(660\) | −98837.2 | + | 88357.6i | −0.226899 | + | 0.202841i | ||||
\(661\) | 30271.8 | − | 52432.4i | 0.0692845 | − | 0.120004i | −0.829302 | − | 0.558801i | \(-0.811262\pi\) |
0.898587 | + | 0.438796i | \(0.144595\pi\) | |||||||
\(662\) | −130120. | − | 75125.0i | −0.296913 | − | 0.171423i | ||||
\(663\) | 218689. | + | 244627.i | 0.497508 | + | 0.556515i | ||||
\(664\) | 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 | ||||
\(669\) | 109443. | + | 35992.0i | 0.244532 | + | 0.0804180i | ||||
\(670\) | −819900. | − | 1.42011e6i | −1.82646 | − | 3.16353i | ||||
\(671\) | 144214.i | 0.320303i | ||||||||
\(672\) | 488672. | − | 169094.i | 1.08213 | − | 0.374447i | ||||
\(673\) | −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 | ||||
\(675\) | 520995. | − | 49132.2i | 1.14347 | − | 0.107835i | ||||
\(676\) | −65913.2 | + | 114165.i | −0.144238 | + | 0.249827i | ||||
\(677\) | 588045. | − | 339508.i | 1.28302 | − | 0.740752i | 0.305620 | − | 0.952154i | \(-0.401136\pi\) |
0.977399 | + | 0.211402i | \(0.0678029\pi\) | |||||||
\(678\) | 150310. | + | 719759.i | 0.326986 | + | 1.56577i | ||||
\(679\) | −37165.3 | + | 88808.6i | −0.0806118 | + | 0.192626i | ||||
\(680\) | 291009.i | 0.629344i | ||||||||
\(681\) | 149901. | + | 167680.i | 0.323228 | + | 0.361565i | ||||
\(682\) | 128371. | − | 222346.i | 0.275994 | − | 0.478036i | ||||
\(683\) | −31998.1 | − | 18474.1i | −0.0685935 | − | 0.0396025i | 0.465311 | − | 0.885147i | \(-0.345942\pi\) |
−0.533905 | + | 0.845545i | \(0.679276\pi\) | |||||||
\(684\) | −224536. | − | 165594.i | −0.479926 | − | 0.353941i | ||||
\(685\) | 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 | ||||
\(690\) | 186300. | − | 566493.i | 0.391304 | − | 1.18986i | ||||
\(691\) | 268443. | + | 464957.i | 0.562206 | + | 0.973770i | 0.997304 | + | 0.0733863i | \(0.0233806\pi\) |
−0.435097 | + | 0.900383i | \(0.643286\pi\) | |||||||
\(692\) | − | 227710.i | − | 0.475522i | ||||||
\(693\) | −150016. | + | 2311.65i | −0.312372 | + | 0.00481345i | ||||
\(694\) | −1.19302e6 | −2.47701 | ||||||||
\(695\) | 361048. | − | 208451.i | 0.747474 | − | 0.431554i | ||||
\(696\) | 49751.3 | + | 16361.5i | 0.102704 | + | 0.0337757i | ||||
\(697\) | −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 | \(-0.148204\pi\) | |||||||
\(702\) | −434866. | − | 199214.i | −0.882433 | − | 0.404245i | ||||
\(703\) | −161161. | + | 279138.i | −0.326098 | + | 0.564819i | ||||
\(704\) | 34124.5 | + | 19701.8i | 0.0688528 | + | 0.0397522i | ||||
\(705\) | 25868.9 | − | 23126.0i | 0.0520474 | − | 0.0465289i | ||||
\(706\) | 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 | 0.978387 | − | 0.206784i | \(-0.0662997\pi\) |
−0.668273 | + | 0.743916i | \(0.732966\pi\) | |||||||
\(710\) | −538628. | − | 310977.i | −1.06849 | − | 0.616896i | ||||
\(711\) | −6946.99 | + | 61851.4i | −0.0137422 | + | 0.122352i | ||||
\(712\) | 69076.2 | + | 119644.i | 0.136260 | + | 0.236009i | ||||
\(713\) | 461098.i | 0.907014i | ||||||||
\(714\) | 427425. | − | 493208.i | 0.838424 | − | 0.967461i | ||||
\(715\) | −176116. | −0.344498 | ||||||||
\(716\) | 9258.57 | − | 5345.44i | 0.0180600 | − | 0.0104270i | ||||
\(717\) | 58648.7 | − | 178337.i | 0.114083 | − | 0.346899i | ||||
\(718\) | −424951. | + | 736037.i | −0.824309 | + | 1.42775i | ||||
\(719\) | 12063.8 | − | 6965.06i | 0.0233361 | − | 0.0134731i | −0.488287 | − | 0.872683i | \(-0.662378\pi\) |
0.511623 | + | 0.859210i | \(0.329045\pi\) | |||||||
\(720\) | −371895. | − | 851576.i | −0.717390 | − | 1.64270i | ||||
\(721\) | −287052. | + | 36727.8i | −0.552192 | + | 0.0706520i | ||||
\(722\) | 131123.i | 0.251539i | ||||||||
\(723\) | −707756. | + | 632713.i | −1.35396 | + | 1.21040i | ||||
\(724\) | −35101.1 | + | 60796.8i | −0.0669643 | + | 0.115986i | ||||
\(725\) | 130632. | + | 75420.2i | 0.248526 | + | 0.143487i | ||||
\(726\) | 408993. | + | 457502.i | 0.775966 | + | 0.868000i | ||||
\(727\) | 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 | ||||
\(732\) | 346845. | + | 114065.i | 0.647311 | + | 0.212878i | ||||
\(733\) | −480538. | − | 832316.i | −0.894375 | − | 1.54910i | −0.834576 | − | 0.550893i | \(-0.814287\pi\) |
−0.0597989 | − | 0.998210i | \(-0.519046\pi\) | |||||||
\(734\) | − | 651860.i | − | 1.20994i | ||||||
\(735\) | 659389. | + | 438457.i | 1.22058 | + | 0.811619i | ||||
\(736\) | −410826. | −0.758407 | ||||||||
\(737\) | 283857. | − | 163885.i | 0.522595 | − | 0.301720i | ||||
\(738\) | 13478.6 | − | 120004.i | 0.0247475 | − | 0.220335i | ||||
\(739\) | 122834. | − | 212754.i | 0.224920 | − | 0.389573i | −0.731375 | − | 0.681975i | \(-0.761121\pi\) |
0.956295 | + | 0.292402i | \(0.0944546\pi\) | |||||||
\(740\) | 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 | \(-0.285709\pi\) | |||||||
\(744\) | 218611. | + | 244539.i | 0.394936 | + | 0.441777i | ||||
\(745\) | −451658. | + | 782295.i | −0.813762 | + | 1.40948i | ||||
\(746\) | 276482. | + | 159627.i | 0.496808 | + | 0.286832i | ||||
\(747\) | −177889. | + | 241208.i | −0.318793 | + | 0.432266i | ||||
\(748\) | 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 | 0.545742 | − | 0.837953i | \(-0.316248\pi\) |
−0.998560 | + | 0.0536502i | \(0.982914\pi\) | |||||||
\(752\) | −28524.7 | − | 16468.8i | −0.0504413 | − | 0.0291223i | ||||
\(753\) | 276680. | − | 841318.i | 0.487964 | − | 1.48378i | ||||
\(754\) | −68937.4 | − | 119403.i | −0.121259 | − | 0.210026i | ||||
\(755\) | 11415.1i | 0.0200256i | ||||||||
\(756\) | −113095. | + | 362629.i | −0.197879 | + | 0.634481i | ||||
\(757\) | 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 | ||||
\(759\) | 113233. | + | 37238.4i | 0.196557 | + | 0.0646409i | ||||
\(760\) | 164350. | − | 284663.i | 0.284540 | − | 0.492838i | ||||
\(761\) | −509302. | + | 294046.i | −0.879441 | + | 0.507745i | −0.870474 | − | 0.492215i | \(-0.836188\pi\) |
−0.00896665 | + | 0.999960i | \(0.502854\pi\) | |||||||
\(762\) | −910169. | + | 190074.i | −1.56752 | + | 0.327351i | ||||
\(763\) | −188492. | − | 247509.i | −0.323775 | − | 0.425150i | ||||
\(764\) | 725628.i | 1.24316i | ||||||||
\(765\) | −685030. | − | 505204.i | −1.17054 | − | 0.863264i | ||||
\(766\) | 625477. | − | 1.08336e6i | 1.06599 | − | 1.84635i | ||||
\(767\) | 598778. | + | 345704.i | 1.01783 | + | 0.587644i | ||||
\(768\) | −575275. | + | 514279.i | −0.975333 | + | 0.871919i | ||||
\(769\) | 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 | \(-0.401698\pi\) |
−0.673085 | + | 0.739565i | \(0.735031\pi\) | |||||||
\(774\) | −752662. | − | 84537.0i | −1.25637 | − | 0.141112i | ||||
\(775\) | 472357. | + | 818146.i | 0.786442 | + | 1.36216i | ||||
\(776\) | − | 54409.5i | − | 0.0903548i | ||||||
\(777\) | 430910. | + | 83081.2i | 0.713747 | + | 0.137613i | ||||
\(778\) | 1.52651e6 | 2.52198 | ||||||||
\(779\) | 81033.2 | − | 46784.5i | 0.133533 | − | 0.0770952i | ||||
\(780\) | −139298. | + | 423572.i | −0.228958 | + | 0.696207i | ||||
\(781\) | 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 | ||||||
\(786\) | 13792.6 | − | 12330.1i | 0.0223254 | − | 0.0199583i | ||||
\(787\) | −172264. | + | 298370.i | −0.278128 | + | 0.481732i | −0.970920 | − | 0.239406i | \(-0.923047\pi\) |
0.692791 | + | 0.721138i | \(0.256381\pi\) | |||||||
\(788\) | 336970. | + | 194550.i | 0.542673 | + | 0.313313i | ||||
\(789\) | −104715. | − | 117135.i | −0.168211 | − | 0.188162i | ||||
\(790\) | 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 | ||||
\(795\) | 1.03141e6 | + | 339195.i | 1.63191 | + | 0.536679i | ||||
\(796\) | −121184. | − | 209897.i | −0.191258 | − | 0.331269i | ||||
\(797\) | 693067.i | 1.09108i | 0.838083 | + | 0.545542i | \(0.183676\pi\) | ||||
−0.838083 | + | 0.545542i | \(0.816324\pi\) | |||||||
\(798\) | −696650. | + | 241060.i | −1.09398 | + | 0.378547i | ||||
\(799\) | −30170.4 | −0.0472594 | ||||||||
\(800\) | −728946. | + | 420857.i | −1.13898 | + | 0.657590i | ||||
\(801\) | −401559. | − | 45102.0i | −0.625870 | − | 0.0702960i | ||||
\(802\) | −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 | ||||||
\(807\) | −357080. | − | 399431.i | −0.548300 | − | 0.613331i | ||||
\(808\) | 42937.2 | − | 74369.4i | 0.0657674 | − | 0.113912i | ||||
\(809\) | −414933. | − | 239562.i | −0.633988 | − | 0.366033i | 0.148307 | − | 0.988941i | \(-0.452618\pi\) |
−0.782295 | + | 0.622908i | \(0.785951\pi\) | |||||||
\(810\) | 1.20988e6 | + | 275253.i | 1.84405 | + | 0.419530i | ||||
\(811\) | −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 | ||||
\(816\) | −252413. | + | 767529.i | −0.379081 | + | 1.15269i | ||||
\(817\) | −293431. | − | 508237.i | −0.439604 | − | 0.761416i | ||||
\(818\) | − | 919997.i | − | 1.37493i | ||||||
\(819\) | −433069. | + | 259010.i | −0.645638 | + | 0.386144i | ||||
\(820\) | −112570. | −0.167416 | ||||||||
\(821\) | −599417. | + | 346074.i | −0.889289 | + | 0.513431i | −0.873710 | − | 0.486448i | \(-0.838292\pi\) |
−0.0155788 | + | 0.999879i | \(0.504959\pi\) | |||||||
\(822\) | 1.08548e6 | + | 356978.i | 1.60650 | + | 0.528321i | ||||
\(823\) | −20631.5 | + | 35734.7i | −0.0304600 | + | 0.0527583i | −0.880854 | − | 0.473389i | \(-0.843031\pi\) |
0.850394 | + | 0.526147i | \(0.176364\pi\) | |||||||
\(824\) | 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 | \(0.599110\pi\) | |||||||
\(828\) | 179122. | − | 242880.i | 0.261269 | − | 0.354268i | ||||
\(829\) | −58201.1 | + | 100807.i | −0.0846880 | + | 0.146684i | −0.905258 | − | 0.424862i | \(-0.860323\pi\) |
0.820570 | + | 0.571546i | \(0.193656\pi\) | |||||||
\(830\) | 606006. | + | 349878.i | 0.879672 | + | 0.507879i | ||||
\(831\) | 938118. | − | 838650.i | 1.35849 | − | 1.21445i | ||||
\(832\) | 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 | ||||
\(837\) | −955161. | + | 90076.1i | −1.36341 | + | 0.128576i | ||||
\(838\) | 233660. | + | 404711.i | 0.332733 | + | 0.576311i | ||||
\(839\) | − | 1.08159e6i | − | 1.53652i | −0.640137 | − | 0.768261i | \(-0.721123\pi\) | ||
0.640137 | − | 0.768261i | \(-0.278877\pi\) | |||||||
\(840\) | −439438. | − | 84725.5i | −0.622786 | − | 0.120076i | ||||
\(841\) | 663126. | 0.937571 | ||||||||
\(842\) | −683357. | + | 394536.i | −0.963881 | + | 0.556497i | ||||
\(843\) | −132264. | + | 402183.i | −0.186117 | + | 0.565938i | ||||
\(844\) | 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 | ||||||
\(849\) | 92082.6 | − | 82319.1i | 0.127750 | − | 0.114205i | ||||
\(850\) | −531174. | + | 920021.i | −0.735190 | + | 1.27339i | ||||
\(851\) | −301943. | − | 174327.i | −0.416933 | − | 0.240716i | ||||
\(852\) | −209774. | − | 234654.i | −0.288983 | − | 0.323257i | ||||
\(853\) | 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 | \(-0.189003\pi\) |
−0.0701135 | + | 0.997539i | \(0.522336\pi\) | |||||||
\(858\) | −212054. | − | 69737.3i | −0.288053 | − | 0.0947306i | ||||
\(859\) | 449263. | + | 778146.i | 0.608855 | + | 1.05457i | 0.991429 | + | 0.130644i | \(0.0417044\pi\) |
−0.382574 | + | 0.923925i | \(0.624962\pi\) | |||||||
\(860\) | 706036.i | 0.954618i | ||||||||
\(861\) | −96273.7 | − | 83433.0i | −0.129868 | − | 0.112546i | ||||
\(862\) | −1.08279e6 | −1.45724 | ||||||||
\(863\) | 848397. | − | 489822.i | 1.13914 | − | 0.657684i | 0.192924 | − | 0.981214i | \(-0.438203\pi\) |
0.946218 | + | 0.323530i | \(0.104870\pi\) | |||||||
\(864\) | −80255.4 | − | 851023.i | −0.107510 | − | 1.14002i | ||||
\(865\) | −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 | ||||||||
\(870\) | 238368. | + | 266639.i | 0.314926 | + | 0.352278i | ||||
\(871\) | 551199. | − | 954705.i | 0.726561 | − | 1.25844i | ||||
\(872\) | 152273. | + | 87914.7i | 0.200258 | + | 0.115619i | ||||
\(873\) | 128079. | + | 94457.3i | 0.168055 | + | 0.123939i | ||||
\(874\) | 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 | 0.947578 | + | 0.319525i | \(0.103523\pi\) |
−0.197072 | + | 0.980389i | \(0.563143\pi\) | |||||||
\(878\) | 1.15636e6 | + | 667622.i | 1.50004 | + | 0.866047i | ||||
\(879\) | 282499. | − | 859011.i | 0.365627 | − | 1.11179i | ||||
\(880\) | −216831. | − | 375563.i | −0.279999 | − | 0.484973i | ||||
\(881\) | 316201.i | 0.407391i | 0.979034 | + | 0.203695i | \(0.0652952\pi\) | ||||
−0.979034 | + | 0.203695i | \(0.934705\pi\) | |||||||
\(882\) | 620327. | + | 789029.i | 0.797413 | + | 1.01427i | ||||
\(883\) | −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 | ||||
\(885\) | −1.70378e6 | − | 560312.i | −2.17533 | − | 0.715391i | ||||
\(886\) | 808728. | − | 1.40076e6i | 1.03023 | − | 1.78441i | ||||
\(887\) | −269736. | + | 155732.i | −0.342840 | + | 0.197939i | −0.661527 | − | 0.749921i | \(-0.730091\pi\) |
0.318687 | + | 0.947860i | \(0.396758\pi\) | |||||||
\(888\) | −242783. | + | 50701.4i | −0.307888 | + | 0.0642975i | ||||
\(889\) | −378675. | + | 904865.i | −0.479141 | + | 1.14493i | ||||
\(890\) | 943444.i | 1.19107i | ||||||||
\(891\) | −55018.8 | + | 241836.i | −0.0693036 | + | 0.304625i | ||||
\(892\) | 68062.8 | − | 117888.i | 0.0855421 | − | 0.148163i | ||||
\(893\) | 29512.5 | + | 17039.1i | 0.0370087 | + | 0.0213670i | ||||
\(894\) | −853592. | + | 763086.i | −1.06801 | + | 0.954770i | ||||
\(895\) | −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 | ||||
\(900\) | 69013.3 | − | 614449.i | 0.0852016 | − | 0.758579i | ||||
\(901\) | −472028. | − | 817576.i | −0.581457 | − | 1.00711i | ||||
\(902\) | − | 56356.4i | − | 0.0692676i | ||||||
\(903\) | −523288. | + | 603825.i | −0.641749 | + | 0.740517i | ||||
\(904\) | −438398. | −0.536453 | ||||||||
\(905\) | 209507. | − | 120959.i | 0.255801 | − | 0.147687i | ||||
\(906\) | −4520.08 | + | 13744.5i | −0.00550668 | + | 0.0167445i | ||||
\(907\) | −699399. | + | 1.21139e6i | −0.850179 | + | 1.47255i | 0.0308669 | + | 0.999524i | \(0.490173\pi\) |
−0.881046 | + | 0.473030i | \(0.843160\pi\) | |||||||
\(908\) | 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 | \(-0.0687518\pi\) | |||||||
\(912\) | 680380. | − | 608239.i | 0.818016 | − | 0.731282i | ||||
\(913\) | −69935.1 | + | 121131.i | −0.0838984 | + | 0.145316i | ||||
\(914\) | −426808. | − | 246418.i | −0.510905 | − | 0.294971i | ||||
\(915\) | −838567. | − | 938025.i | −1.00160 | − | 1.12040i | ||||
\(916\) | −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 | 0.981193 | − | 0.193030i | \(-0.0618313\pi\) |
−0.657765 | + | 0.753223i | \(0.728498\pi\) | |||||||
\(920\) | 307919. | + | 177777.i | 0.363799 | + | 0.210039i | ||||
\(921\) | 906623. | + | 298157.i | 1.06883 | + | 0.351500i | ||||
\(922\) | 300235. | + | 520022.i | 0.353183 | + | 0.611731i | ||||
\(923\) | − | 418125.i | − | 0.490798i | ||||||
\(924\) | −33560.8 | + | 174067.i | −0.0393087 | + | 0.203879i | ||||
\(925\) | −714335. | −0.834869 | ||||||||
\(926\) | −398399. | + | 230016.i | −0.464618 | + | 0.268247i | ||||
\(927\) | −53395.0 | + | 475394.i | −0.0621357 | + | 0.553215i | ||||
\(928\) | 123196. | − | 213381.i | 0.143054 | − | 0.247777i | ||||
\(929\) | −1.17155e6 | + | 676395.i | −1.35747 | + | 0.783734i | −0.989282 | − | 0.146018i | \(-0.953354\pi\) |
−0.368186 | + | 0.929752i | \(0.620021\pi\) | |||||||
\(930\) | 457906. | + | 2.19268e6i | 0.529432 | + | 2.53518i | ||||
\(931\) | −206749. | + | 749707.i | −0.238531 | + | 0.864952i | ||||
\(932\) | 255002.i | 0.293570i | ||||||||
\(933\) | 226130. | + | 252950.i | 0.259774 | + | 0.290584i | ||||
\(934\) | −599016. | + | 1.03753e6i | −0.686665 | + | 1.18934i | ||||
\(935\) | −344011. | − | 198615.i | −0.393504 | − | 0.227190i | ||||
\(936\) | 169271. | − | 229523.i | 0.193211 | − | 0.261984i | ||||
\(937\) | −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 | \(-0.154911\pi\) |
0.0369222 | + | 0.999318i | \(0.488245\pi\) | |||||||
\(942\) | 130565. | − | 397016.i | 0.147138 | − | 0.447410i | ||||
\(943\) | 50606.7 | + | 87653.4i | 0.0569095 | + | 0.0985701i | ||||
\(944\) | 1.70250e6i | 1.91049i | ||||||||
\(945\) | 962327. | − | 887344.i | 1.07760 | − | 0.993638i | ||||
\(946\) | −353465. | −0.394970 | ||||||||
\(947\) | 220936. | − | 127558.i | 0.246358 | − | 0.142235i | −0.371737 | − | 0.928338i | \(-0.621238\pi\) |
0.618096 | + | 0.786103i | \(0.287904\pi\) | |||||||
\(948\) | 69859.3 | + | 22974.3i | 0.0777334 | + | 0.0255638i | ||||
\(949\) | 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 | \(0.987334\pi\) | |||||||
\(954\) | 1.10757e6 | + | 816822.i | 1.21695 | + | 0.897492i | ||||
\(955\) | 1.25026e6 | − | 2.16552e6i | 1.37087 | − | 2.37441i | ||||
\(956\) | −192098. | − | 110908.i | −0.210188 | − | 0.121352i | ||||
\(957\) | −53297.0 | + | 47646.0i | −0.0581941 | + | 0.0520238i | ||||
\(958\) | 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 | ||||
\(963\) | 545085. | + | 61222.5i | 0.587776 | + | 0.0660174i | ||||
\(964\) | 560846. | + | 971413.i | 0.603517 | + | 1.04532i | ||||
\(965\) | − | 1.76214e6i | − | 1.89228i | ||||||
\(966\) | −260754. | − | 753564.i | −0.279433 | − | 0.807543i | ||||
\(967\) | 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 | ||||
\(969\) | 261154. | − | 794108.i | 0.278131 | − | 0.845730i | ||||
\(970\) | 185782. | − | 321783.i | 0.197451 | − | 0.341995i | ||||
\(971\) | −1.05107e6 | + | 606836.i | −1.11479 | + | 0.643625i | −0.940066 | − | 0.340992i | \(-0.889237\pi\) |
−0.174725 | + | 0.984617i | \(0.555904\pi\) | |||||||
\(972\) | 538117. | + | 323603.i | 0.569566 | + | 0.342516i | ||||
\(973\) | 215208. | − | 514251.i | 0.227317 | − | 0.543187i | ||||
\(974\) | 515451.i | 0.543337i | ||||||||
\(975\) | 612366. | − | 547437.i | 0.644172 | − | 0.575871i | ||||
\(976\) | −597170. | + | 1.03433e6i | −0.626901 | + | 1.08582i | ||||
\(977\) | −1.13374e6 | − | 654566.i | −1.18775 | − | 0.685748i | −0.229955 | − | 0.973201i | \(-0.573858\pi\) |
−0.957795 | + | 0.287454i | \(0.907191\pi\) | |||||||
\(978\) | −268731. | − | 300604.i | −0.280958 | − | 0.314281i | ||||
\(979\) | −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 | \(-0.262063\pi\) |
−0.295230 | + | 0.955426i | \(0.595396\pi\) | |||||||
\(984\) | 68396.2 | + | 22493.1i | 0.0706385 | + | 0.0232305i | ||||
\(985\) | −670422. | − | 1.16120e6i | −0.690996 | − | 1.19684i | ||||
\(986\) | − | 310977.i | − | 0.319871i | ||||||
\(987\) | 8783.94 | − | 45558.9i | 0.00901686 | − | 0.0467669i | ||||
\(988\) | −437913. | −0.448615 | ||||||||
\(989\) | 549758. | − | 317403.i | 0.562055 | − | 0.324503i | ||||
\(990\) | 575442. | + | 64632.1i | 0.587126 | + | 0.0659444i | ||||
\(991\) | −271321. | + | 469942.i | −0.276272 | + | 0.478517i | −0.970455 | − | 0.241281i | \(-0.922432\pi\) |
0.694183 | + | 0.719798i | \(0.255766\pi\) | |||||||
\(992\) | 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 | ||||||||
\(996\) | 236015. | + | 264007.i | 0.237914 | + | 0.266132i | ||||
\(997\) | 566787. | − | 981704.i | 0.570203 | − | 0.987621i | −0.426341 | − | 0.904562i | \(-0.640198\pi\) |
0.996545 | − | 0.0830587i | \(-0.0264689\pi\) | |||||||
\(998\) | 37490.7 | + | 21645.3i | 0.0376411 | + | 0.0217321i | ||||
\(999\) | 302132. | − | 659529.i | 0.302737 | − | 0.660850i |
(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.11.2 | yes | 16 | |
3.2 | odd | 2 | inner | 21.5.h.b.11.7 | yes | 16 | |
7.2 | even | 3 | inner | 21.5.h.b.2.7 | yes | 16 | |
7.3 | odd | 6 | 147.5.b.f.50.2 | 8 | |||
7.4 | even | 3 | 147.5.b.c.50.2 | 8 | |||
7.5 | odd | 6 | 147.5.h.b.128.7 | 16 | |||
7.6 | odd | 2 | 147.5.h.b.116.2 | 16 | |||
21.2 | odd | 6 | inner | 21.5.h.b.2.2 | ✓ | 16 | |
21.5 | even | 6 | 147.5.h.b.128.2 | 16 | |||
21.11 | odd | 6 | 147.5.b.c.50.7 | 8 | |||
21.17 | even | 6 | 147.5.b.f.50.7 | 8 | |||
21.20 | even | 2 | 147.5.h.b.116.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.5.h.b.2.2 | ✓ | 16 | 21.2 | odd | 6 | inner | |
21.5.h.b.2.7 | yes | 16 | 7.2 | even | 3 | inner | |
21.5.h.b.11.2 | yes | 16 | 1.1 | even | 1 | trivial | |
21.5.h.b.11.7 | yes | 16 | 3.2 | odd | 2 | inner | |
147.5.b.c.50.2 | 8 | 7.4 | even | 3 | |||
147.5.b.c.50.7 | 8 | 21.11 | odd | 6 | |||
147.5.b.f.50.2 | 8 | 7.3 | odd | 6 | |||
147.5.b.f.50.7 | 8 | 21.17 | even | 6 | |||
147.5.h.b.116.2 | 16 | 7.6 | odd | 2 | |||
147.5.h.b.116.7 | 16 | 21.20 | even | 2 | |||
147.5.h.b.128.2 | 16 | 21.5 | even | 6 | |||
147.5.h.b.128.7 | 16 | 7.5 | odd | 6 |