Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,5,Mod(7,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("22.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.d (of order \(10\), degree \(4\), 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: | \(2.27413918784\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 138 x^{14} - 428 x^{13} + 7783 x^{12} - 18620 x^{11} + 235604 x^{10} + \cdots + 1499670491 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8}\cdot 11^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 13.3 | ||
Root | \(0.809017 + 3.04259i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.13 |
Dual form | 22.5.d.a.17.3 |
$q$-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 \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).
\(n\) | \(13\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.68999 | + | 0.874032i | 0.672499 | + | 0.218508i | ||||
\(3\) | −13.1019 | + | 9.51912i | −1.45577 | + | 1.05768i | −0.471332 | + | 0.881956i | \(0.656227\pi\) |
−0.984439 | + | 0.175724i | \(0.943773\pi\) | |||||||
\(4\) | 6.47214 | + | 4.70228i | 0.404508 | + | 0.293893i | ||||
\(5\) | 8.38512 | + | 25.8068i | 0.335405 | + | 1.03227i | 0.966522 | + | 0.256583i | \(0.0825967\pi\) |
−0.631117 | + | 0.775687i | \(0.717403\pi\) | |||||||
\(6\) | −43.5642 | + | 14.1549i | −1.21012 | + | 0.393190i | ||||
\(7\) | 26.6976 | − | 36.7461i | 0.544849 | − | 0.749921i | −0.444453 | − | 0.895802i | \(-0.646602\pi\) |
0.989302 | + | 0.145881i | \(0.0466018\pi\) | |||||||
\(8\) | 13.3001 | + | 18.3060i | 0.207813 | + | 0.286031i | ||||
\(9\) | 56.0169 | − | 172.402i | 0.691567 | − | 2.12842i | ||||
\(10\) | 76.7489i | 0.767489i | ||||||||
\(11\) | −50.8926 | + | 109.777i | −0.420600 | + | 0.907246i | ||||
\(12\) | −129.559 | −0.899716 | ||||||||
\(13\) | 148.981 | + | 48.4067i | 0.881542 | + | 0.286430i | 0.714597 | − | 0.699536i | \(-0.246610\pi\) |
0.166944 | + | 0.985966i | \(0.446610\pi\) | |||||||
\(14\) | 103.934 | − | 75.5123i | 0.530274 | − | 0.385267i | ||||
\(15\) | −355.519 | − | 258.300i | −1.58008 | − | 1.14800i | ||||
\(16\) | 19.7771 | + | 60.8676i | 0.0772542 | + | 0.237764i | ||||
\(17\) | 310.069 | − | 100.748i | 1.07290 | − | 0.348608i | 0.281286 | − | 0.959624i | \(-0.409239\pi\) |
0.791618 | + | 0.611016i | \(0.209239\pi\) | |||||||
\(18\) | 301.370 | − | 414.801i | 0.930155 | − | 1.28025i | ||||
\(19\) | −62.7848 | − | 86.4159i | −0.173919 | − | 0.239379i | 0.713155 | − | 0.701007i | \(-0.247266\pi\) |
−0.887074 | + | 0.461627i | \(0.847266\pi\) | |||||||
\(20\) | −67.0810 | + | 206.454i | −0.167702 | + | 0.516135i | ||||
\(21\) | 735.583i | 1.66799i | ||||||||
\(22\) | −232.849 | + | 250.817i | −0.481093 | + | 0.518217i | ||||
\(23\) | −467.991 | −0.884671 | −0.442335 | − | 0.896850i | \(-0.645850\pi\) | ||||
−0.442335 | + | 0.896850i | \(0.645850\pi\) | |||||||
\(24\) | −348.513 | − | 113.239i | −0.605058 | − | 0.196595i | ||||
\(25\) | −90.0429 | + | 65.4200i | −0.144069 | + | 0.104672i | ||||
\(26\) | 358.448 | + | 260.428i | 0.530248 | + | 0.385248i | ||||
\(27\) | 501.823 | + | 1544.45i | 0.688372 | + | 2.11859i | ||||
\(28\) | 345.581 | − | 112.286i | 0.440792 | − | 0.143222i | ||||
\(29\) | 104.073 | − | 143.244i | 0.123749 | − | 0.170326i | −0.742648 | − | 0.669682i | \(-0.766430\pi\) |
0.866397 | + | 0.499357i | \(0.166430\pi\) | |||||||
\(30\) | −730.582 | − | 1005.56i | −0.811758 | − | 1.11729i | ||||
\(31\) | 84.3454 | − | 259.588i | 0.0877683 | − | 0.270123i | −0.897533 | − | 0.440947i | \(-0.854643\pi\) |
0.985302 | + | 0.170823i | \(0.0546428\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | −378.187 | − | 1922.74i | −0.347279 | − | 1.76560i | ||||
\(34\) | 922.141 | 0.797700 | ||||||||
\(35\) | 1172.16 | + | 380.858i | 0.956866 | + | 0.310905i | ||||
\(36\) | 1173.23 | − | 852.404i | 0.905273 | − | 0.657719i | ||||
\(37\) | −1730.83 | − | 1257.52i | −1.26430 | − | 0.918571i | −0.265344 | − | 0.964154i | \(-0.585485\pi\) |
−0.998961 | + | 0.0455830i | \(0.985485\pi\) | |||||||
\(38\) | −93.3606 | − | 287.334i | −0.0646541 | − | 0.198985i | ||||
\(39\) | −2412.72 | + | 783.942i | −1.58627 | + | 0.515412i | ||||
\(40\) | −360.895 | + | 496.729i | −0.225559 | + | 0.310456i | ||||
\(41\) | 764.111 | + | 1051.71i | 0.454557 | + | 0.625645i | 0.973369 | − | 0.229244i | \(-0.0736254\pi\) |
−0.518812 | + | 0.854889i | \(0.673625\pi\) | |||||||
\(42\) | −642.924 | + | 1978.72i | −0.364469 | + | 1.12172i | ||||
\(43\) | − | 2337.65i | − | 1.26428i | −0.774855 | − | 0.632139i | \(-0.782177\pi\) | ||
0.774855 | − | 0.632139i | \(-0.217823\pi\) | |||||||
\(44\) | −845.585 | + | 471.179i | −0.436769 | + | 0.243378i | ||||
\(45\) | 4918.85 | 2.42906 | ||||||||
\(46\) | −1258.89 | − | 409.039i | −0.594940 | − | 0.193308i | ||||
\(47\) | 2128.07 | − | 1546.13i | 0.963361 | − | 0.699923i | 0.00943244 | − | 0.999956i | \(-0.496998\pi\) |
0.953929 | + | 0.300032i | \(0.0969975\pi\) | |||||||
\(48\) | −838.524 | − | 609.224i | −0.363943 | − | 0.264420i | ||||
\(49\) | 104.435 | + | 321.418i | 0.0434965 | + | 0.133869i | ||||
\(50\) | −299.394 | + | 97.2791i | −0.119758 | + | 0.0389116i | ||||
\(51\) | −3103.48 | + | 4271.58i | −1.19319 | + | 1.64228i | ||||
\(52\) | 736.600 | + | 1013.84i | 0.272411 | + | 0.374942i | ||||
\(53\) | 503.892 | − | 1550.82i | 0.179385 | − | 0.552090i | −0.820422 | − | 0.571759i | \(-0.806261\pi\) |
0.999807 | + | 0.0196691i | \(0.00626126\pi\) | |||||||
\(54\) | 4593.18i | 1.57517i | ||||||||
\(55\) | −3259.72 | − | 392.880i | −1.07759 | − | 0.129878i | ||||
\(56\) | 1027.75 | 0.327727 | ||||||||
\(57\) | 1645.21 | + | 534.560i | 0.506373 | + | 0.164531i | ||||
\(58\) | 405.156 | − | 294.363i | 0.120439 | − | 0.0875038i | ||||
\(59\) | 3560.56 | + | 2586.90i | 1.02286 | + | 0.743149i | 0.966866 | − | 0.255283i | \(-0.0821685\pi\) |
0.0559900 | + | 0.998431i | \(0.482169\pi\) | |||||||
\(60\) | −1086.37 | − | 3343.50i | −0.301769 | − | 0.928750i | ||||
\(61\) | −4518.12 | + | 1468.03i | −1.21422 | + | 0.394525i | −0.844975 | − | 0.534806i | \(-0.820385\pi\) |
−0.369248 | + | 0.929331i | \(0.620385\pi\) | |||||||
\(62\) | 453.777 | − | 624.571i | 0.118048 | − | 0.162479i | ||||
\(63\) | −4839.60 | − | 6661.14i | −1.21935 | − | 1.67829i | ||||
\(64\) | −158.217 | + | 486.941i | −0.0386271 | + | 0.118882i | ||||
\(65\) | 4250.60i | 1.00606i | ||||||||
\(66\) | 663.217 | − | 5502.71i | 0.152254 | − | 1.26325i | ||||
\(67\) | −1184.26 | −0.263813 | −0.131907 | − | 0.991262i | \(-0.542110\pi\) | ||||
−0.131907 | + | 0.991262i | \(0.542110\pi\) | |||||||
\(68\) | 2480.55 | + | 805.981i | 0.536452 | + | 0.174304i | ||||
\(69\) | 6131.59 | − | 4454.86i | 1.28788 | − | 0.935698i | ||||
\(70\) | 2820.22 | + | 2049.01i | 0.575556 | + | 0.418166i | ||||
\(71\) | 1333.37 | + | 4103.69i | 0.264505 | + | 0.814062i | 0.991807 | + | 0.127745i | \(0.0407739\pi\) |
−0.727302 | + | 0.686317i | \(0.759226\pi\) | |||||||
\(72\) | 3901.02 | − | 1267.52i | 0.752511 | − | 0.244506i | ||||
\(73\) | 1111.87 | − | 1530.35i | 0.208644 | − | 0.287174i | −0.691851 | − | 0.722041i | \(-0.743204\pi\) |
0.900495 | + | 0.434866i | \(0.143204\pi\) | |||||||
\(74\) | −3556.81 | − | 4895.53i | −0.649528 | − | 0.893998i | ||||
\(75\) | 556.996 | − | 1714.26i | 0.0990216 | − | 0.304757i | ||||
\(76\) | − | 854.528i | − | 0.147945i | ||||||
\(77\) | 2675.16 | + | 4800.88i | 0.451199 | + | 0.809729i | ||||
\(78\) | −7175.40 | −1.17939 | ||||||||
\(79\) | −1208.14 | − | 392.547i | −0.193580 | − | 0.0628981i | 0.210622 | − | 0.977568i | \(-0.432451\pi\) |
−0.404203 | + | 0.914669i | \(0.632451\pi\) | |||||||
\(80\) | −1404.96 | + | 1020.77i | −0.219525 | + | 0.159495i | ||||
\(81\) | −9397.71 | − | 6827.84i | −1.43236 | − | 1.04067i | ||||
\(82\) | 1136.23 | + | 3496.95i | 0.168981 | + | 0.520069i | ||||
\(83\) | 2203.70 | − | 716.026i | 0.319887 | − | 0.103938i | −0.144672 | − | 0.989480i | \(-0.546213\pi\) |
0.464559 | + | 0.885542i | \(0.346213\pi\) | |||||||
\(84\) | −3458.92 | + | 4760.80i | −0.490210 | + | 0.674716i | ||||
\(85\) | 5199.94 | + | 7157.10i | 0.719715 | + | 0.990603i | ||||
\(86\) | 2043.18 | − | 6288.27i | 0.276255 | − | 0.850226i | ||||
\(87\) | 2867.46i | 0.378843i | ||||||||
\(88\) | −2686.44 | + | 528.401i | −0.346907 | + | 0.0682336i | ||||
\(89\) | −13826.8 | −1.74558 | −0.872792 | − | 0.488092i | \(-0.837693\pi\) | ||||
−0.872792 | + | 0.488092i | \(0.837693\pi\) | |||||||
\(90\) | 13231.7 | + | 4299.24i | 1.63354 | + | 0.530770i | ||||
\(91\) | 5756.19 | − | 4182.11i | 0.695108 | − | 0.505025i | ||||
\(92\) | −3028.90 | − | 2200.62i | −0.357857 | − | 0.259998i | ||||
\(93\) | 1365.96 | + | 4204.01i | 0.157933 | + | 0.486068i | ||||
\(94\) | 7075.85 | − | 2299.08i | 0.800798 | − | 0.260195i | ||||
\(95\) | 1703.66 | − | 2344.88i | 0.188771 | − | 0.259821i | ||||
\(96\) | −1723.14 | − | 2371.70i | −0.186973 | − | 0.257346i | ||||
\(97\) | 588.049 | − | 1809.83i | 0.0624986 | − | 0.192351i | −0.914932 | − | 0.403608i | \(-0.867756\pi\) |
0.977430 | + | 0.211257i | \(0.0677558\pi\) | |||||||
\(98\) | 955.893i | 0.0995307i | ||||||||
\(99\) | 16074.9 | + | 14923.4i | 1.64013 | + | 1.52264i | ||||
\(100\) | −890.394 | −0.0890394 | ||||||||
\(101\) | −11404.7 | − | 3705.62i | −1.11800 | − | 0.363261i | −0.308997 | − | 0.951063i | \(-0.599993\pi\) |
−0.809005 | + | 0.587802i | \(0.799993\pi\) | |||||||
\(102\) | −12081.8 | + | 8777.97i | −1.16127 | + | 0.843711i | ||||
\(103\) | 1974.12 | + | 1434.28i | 0.186080 | + | 0.135195i | 0.676925 | − | 0.736052i | \(-0.263312\pi\) |
−0.490846 | + | 0.871247i | \(0.663312\pi\) | |||||||
\(104\) | 1095.32 | + | 3371.05i | 0.101268 | + | 0.311672i | ||||
\(105\) | −18983.0 | + | 6167.96i | −1.72182 | + | 0.559452i | ||||
\(106\) | 2710.93 | − | 3731.28i | 0.241272 | − | 0.332083i | ||||
\(107\) | −7701.96 | − | 10600.8i | −0.672719 | − | 0.925919i | 0.327099 | − | 0.944990i | \(-0.393929\pi\) |
−0.999818 | + | 0.0190714i | \(0.993929\pi\) | |||||||
\(108\) | −4014.59 | + | 12355.6i | −0.344186 | + | 1.05930i | ||||
\(109\) | − | 934.389i | − | 0.0786457i | −0.999227 | − | 0.0393228i | \(-0.987480\pi\) | ||
0.999227 | − | 0.0393228i | \(-0.0125201\pi\) | |||||||
\(110\) | −8425.25 | − | 3905.95i | −0.696302 | − | 0.322806i | ||||
\(111\) | 34647.8 | 2.81209 | ||||||||
\(112\) | 2764.65 | + | 898.289i | 0.220396 | + | 0.0716111i | ||||
\(113\) | −5601.04 | + | 4069.39i | −0.438643 | + | 0.318693i | −0.785096 | − | 0.619375i | \(-0.787386\pi\) |
0.346452 | + | 0.938068i | \(0.387386\pi\) | |||||||
\(114\) | 3958.37 | + | 2875.93i | 0.304584 | + | 0.221293i | ||||
\(115\) | −3924.16 | − | 12077.3i | −0.296723 | − | 0.913219i | ||||
\(116\) | 1347.15 | − | 437.715i | 0.100115 | − | 0.0325294i | ||||
\(117\) | 16690.9 | − | 22973.0i | 1.21929 | − | 1.67821i | ||||
\(118\) | 7316.86 | + | 10070.8i | 0.525486 | + | 0.723269i | ||||
\(119\) | 4576.03 | − | 14083.6i | 0.323143 | − | 0.994532i | ||||
\(120\) | − | 9943.52i | − | 0.690522i | ||||||
\(121\) | −9460.89 | − | 11173.6i | −0.646192 | − | 0.763175i | ||||
\(122\) | −13436.8 | −0.902770 | ||||||||
\(123\) | −20022.7 | − | 6505.76i | −1.32346 | − | 0.430019i | ||||
\(124\) | 1766.55 | − | 1283.48i | 0.114890 | − | 0.0834727i | ||||
\(125\) | 11277.0 | + | 8193.25i | 0.721730 | + | 0.524368i | ||||
\(126\) | −7196.44 | − | 22148.4i | −0.453291 | − | 1.39509i | ||||
\(127\) | 13172.5 | − | 4280.02i | 0.816699 | − | 0.265362i | 0.129267 | − | 0.991610i | \(-0.458738\pi\) |
0.687433 | + | 0.726248i | \(0.258738\pi\) | |||||||
\(128\) | −851.204 | + | 1171.58i | −0.0519534 | + | 0.0715077i | ||||
\(129\) | 22252.4 | + | 30627.8i | 1.33720 | + | 1.84050i | ||||
\(130\) | −3715.16 | + | 11434.1i | −0.219832 | + | 0.676574i | ||||
\(131\) | − | 23230.6i | − | 1.35368i | −0.736128 | − | 0.676842i | \(-0.763348\pi\) | ||
0.736128 | − | 0.676842i | \(-0.236652\pi\) | |||||||
\(132\) | 6593.60 | − | 14222.6i | 0.378420 | − | 0.816264i | ||||
\(133\) | −4851.66 | −0.274275 | ||||||||
\(134\) | −3185.64 | − | 1035.08i | −0.177414 | − | 0.0576453i | ||||
\(135\) | −35649.5 | + | 25900.9i | −1.95608 | + | 1.42117i | ||||
\(136\) | 5968.22 | + | 4336.17i | 0.322676 | + | 0.234438i | ||||
\(137\) | 285.958 | + | 880.087i | 0.0152356 | + | 0.0468905i | 0.958385 | − | 0.285478i | \(-0.0921523\pi\) |
−0.943150 | + | 0.332368i | \(0.892152\pi\) | |||||||
\(138\) | 20387.6 | − | 6624.34i | 1.07055 | − | 0.347844i | ||||
\(139\) | −20601.7 | + | 28355.8i | −1.06629 | + | 1.46762i | −0.192506 | + | 0.981296i | \(0.561661\pi\) |
−0.873780 | + | 0.486321i | \(0.838339\pi\) | |||||||
\(140\) | 5795.48 | + | 7976.80i | 0.295688 | + | 0.406980i | ||||
\(141\) | −13164.0 | + | 40514.6i | −0.662140 | + | 2.03786i | ||||
\(142\) | 12204.3i | 0.605252i | ||||||||
\(143\) | −12895.9 | + | 13891.1i | −0.630639 | + | 0.679303i | ||||
\(144\) | 11601.6 | 0.559489 | ||||||||
\(145\) | 4569.33 | + | 1484.67i | 0.217328 | + | 0.0706143i | ||||
\(146\) | 4328.49 | − | 3144.83i | 0.203063 | − | 0.147534i | ||||
\(147\) | −4427.92 | − | 3217.07i | −0.204911 | − | 0.148877i | ||||
\(148\) | −5288.95 | − | 16277.7i | −0.241461 | − | 0.743139i | ||||
\(149\) | 9990.22 | − | 3246.02i | 0.449990 | − | 0.146210i | −0.0752503 | − | 0.997165i | \(-0.523976\pi\) |
0.525240 | + | 0.850954i | \(0.323976\pi\) | |||||||
\(150\) | 2996.63 | − | 4124.51i | 0.133184 | − | 0.183312i | ||||
\(151\) | 13070.9 | + | 17990.5i | 0.573258 | + | 0.789023i | 0.992936 | − | 0.118651i | \(-0.0378569\pi\) |
−0.419678 | + | 0.907673i | \(0.637857\pi\) | |||||||
\(152\) | 746.885 | − | 2298.67i | 0.0323271 | − | 0.0994925i | ||||
\(153\) | − | 59100.2i | − | 2.52468i | ||||||
\(154\) | 3000.04 | + | 15252.5i | 0.126499 | + | 0.643132i | ||||
\(155\) | 7406.38 | 0.308278 | ||||||||
\(156\) | −19301.8 | − | 6271.53i | −0.793137 | − | 0.257706i | ||||
\(157\) | 5926.18 | − | 4305.62i | 0.240423 | − | 0.174677i | −0.461049 | − | 0.887375i | \(-0.652527\pi\) |
0.701472 | + | 0.712697i | \(0.252527\pi\) | |||||||
\(158\) | −2906.78 | − | 2111.90i | −0.116439 | − | 0.0845978i | ||||
\(159\) | 8160.48 | + | 25115.4i | 0.322791 | + | 0.993448i | ||||
\(160\) | −4671.52 | + | 1517.87i | −0.182481 | + | 0.0592918i | ||||
\(161\) | −12494.2 | + | 17196.8i | −0.482012 | + | 0.663433i | ||||
\(162\) | −19312.0 | − | 26580.7i | −0.735865 | − | 1.01283i | ||||
\(163\) | 13118.6 | − | 40375.0i | 0.493758 | − | 1.51963i | −0.325126 | − | 0.945671i | \(-0.605407\pi\) |
0.818884 | − | 0.573959i | \(-0.194593\pi\) | |||||||
\(164\) | 10399.9i | 0.386670i | ||||||||
\(165\) | 46448.6 | − | 25882.2i | 1.70610 | − | 0.950678i | ||||
\(166\) | 6553.77 | 0.237835 | ||||||||
\(167\) | −13590.5 | − | 4415.82i | −0.487306 | − | 0.158335i | 0.0550508 | − | 0.998484i | \(-0.482468\pi\) |
−0.542357 | + | 0.840148i | \(0.682468\pi\) | |||||||
\(168\) | −13465.6 | + | 9783.31i | −0.477096 | + | 0.346631i | ||||
\(169\) | −3254.34 | − | 2364.41i | −0.113943 | − | 0.0827847i | ||||
\(170\) | 7732.27 | + | 23797.5i | 0.267553 | + | 0.823442i | ||||
\(171\) | −18415.3 | + | 5983.50i | −0.629777 | + | 0.204627i | ||||
\(172\) | 10992.3 | − | 15129.6i | 0.371562 | − | 0.511412i | ||||
\(173\) | 16635.9 | + | 22897.3i | 0.555845 | + | 0.765055i | 0.990791 | − | 0.135402i | \(-0.0432325\pi\) |
−0.434946 | + | 0.900457i | \(0.643233\pi\) | |||||||
\(174\) | −2506.25 | + | 7713.45i | −0.0827801 | + | 0.254771i | ||||
\(175\) | 5055.29i | 0.165071i | ||||||||
\(176\) | −7688.36 | − | 926.644i | −0.248204 | − | 0.0299149i | ||||
\(177\) | −71275.3 | −2.27506 | ||||||||
\(178\) | −37193.9 | − | 12085.0i | −1.17390 | − | 0.381424i | ||||
\(179\) | −9919.07 | + | 7206.63i | −0.309574 | + | 0.224919i | −0.731714 | − | 0.681612i | \(-0.761279\pi\) |
0.422139 | + | 0.906531i | \(0.361279\pi\) | |||||||
\(180\) | 31835.5 | + | 23129.8i | 0.982577 | + | 0.713884i | ||||
\(181\) | −8052.11 | − | 24781.8i | −0.245783 | − | 0.756443i | −0.995507 | − | 0.0946919i | \(-0.969813\pi\) |
0.749723 | − | 0.661752i | \(-0.230187\pi\) | |||||||
\(182\) | 19139.4 | − | 6218.77i | 0.577811 | − | 0.187742i | ||||
\(183\) | 45221.8 | − | 62242.5i | 1.35035 | − | 1.85860i | ||||
\(184\) | −6224.31 | − | 8567.02i | −0.183846 | − | 0.253043i | ||||
\(185\) | 17939.4 | − | 55211.7i | 0.524160 | − | 1.61320i | ||||
\(186\) | 12502.6i | 0.361390i | ||||||||
\(187\) | −4720.47 | + | 39165.7i | −0.134990 | + | 1.12001i | ||||
\(188\) | 21043.5 | 0.595390 | ||||||||
\(189\) | 70150.2 | + | 22793.2i | 1.96384 | + | 0.638089i | ||||
\(190\) | 6632.33 | − | 4818.67i | 0.183721 | − | 0.133481i | ||||
\(191\) | 9625.10 | + | 6993.05i | 0.263839 | + | 0.191690i | 0.711838 | − | 0.702344i | \(-0.247863\pi\) |
−0.447999 | + | 0.894034i | \(0.647863\pi\) | |||||||
\(192\) | −2562.30 | − | 7885.96i | −0.0695069 | − | 0.213920i | ||||
\(193\) | −17700.3 | + | 5751.17i | −0.475188 | + | 0.154398i | −0.536813 | − | 0.843701i | \(-0.680372\pi\) |
0.0616245 | + | 0.998099i | \(0.480372\pi\) | |||||||
\(194\) | 3163.70 | − | 4354.46i | 0.0840604 | − | 0.115699i | ||||
\(195\) | −40462.0 | − | 55691.1i | −1.06409 | − | 1.46459i | ||||
\(196\) | −835.481 | + | 2571.35i | −0.0217483 | + | 0.0669343i | ||||
\(197\) | 51063.1i | 1.31575i | 0.753125 | + | 0.657877i | \(0.228545\pi\) | ||||
−0.753125 | + | 0.657877i | \(0.771455\pi\) | |||||||
\(198\) | 30198.0 | + | 54193.7i | 0.770278 | + | 1.38235i | ||||
\(199\) | −32814.0 | −0.828616 | −0.414308 | − | 0.910137i | \(-0.635976\pi\) | ||||
−0.414308 | + | 0.910137i | \(0.635976\pi\) | |||||||
\(200\) | −2395.15 | − | 778.233i | −0.0598788 | − | 0.0194558i | ||||
\(201\) | 15516.1 | − | 11273.1i | 0.384051 | − | 0.279030i | ||||
\(202\) | −27439.9 | − | 19936.2i | −0.672479 | − | 0.488585i | ||||
\(203\) | −2485.17 | − | 7648.56i | −0.0603064 | − | 0.185604i | ||||
\(204\) | −40172.3 | + | 13052.8i | −0.965309 | + | 0.313648i | ||||
\(205\) | −20734.0 | + | 28537.9i | −0.493374 | + | 0.679070i | ||||
\(206\) | 4056.76 | + | 5583.65i | 0.0955971 | + | 0.131578i | ||||
\(207\) | −26215.4 | + | 80682.7i | −0.611809 | + | 1.88295i | ||||
\(208\) | 10025.4i | 0.231727i | ||||||||
\(209\) | 12681.7 | − | 2494.39i | 0.290326 | − | 0.0571047i | ||||
\(210\) | −56455.2 | −1.28016 | ||||||||
\(211\) | 61926.5 | + | 20121.1i | 1.39095 | + | 0.451947i | 0.906254 | − | 0.422734i | \(-0.138930\pi\) |
0.484697 | + | 0.874682i | \(0.338930\pi\) | |||||||
\(212\) | 10553.7 | − | 7667.68i | 0.234818 | − | 0.170605i | ||||
\(213\) | −56533.2 | − | 41073.8i | −1.24608 | − | 0.905327i | ||||
\(214\) | −11452.8 | − | 35248.0i | −0.250082 | − | 0.769674i | ||||
\(215\) | 60327.2 | − | 19601.5i | 1.30508 | − | 0.424045i | ||||
\(216\) | −21598.4 | + | 29727.7i | −0.462929 | + | 0.637168i | ||||
\(217\) | −7287.05 | − | 10029.8i | −0.154751 | − | 0.212996i | ||||
\(218\) | 816.686 | − | 2513.50i | 0.0171847 | − | 0.0528891i | ||||
\(219\) | 30634.6i | 0.638739i | ||||||||
\(220\) | −19249.9 | − | 17870.9i | −0.397726 | − | 0.369234i | ||||
\(221\) | 51071.2 | 1.04566 | ||||||||
\(222\) | 93202.3 | + | 30283.3i | 1.89113 | + | 0.614465i | ||||
\(223\) | −15247.4 | + | 11077.9i | −0.306610 | + | 0.222765i | −0.730440 | − | 0.682977i | \(-0.760685\pi\) |
0.423831 | + | 0.905741i | \(0.360685\pi\) | |||||||
\(224\) | 6651.76 | + | 4832.79i | 0.132569 | + | 0.0963167i | ||||
\(225\) | 6234.64 | + | 19188.2i | 0.123153 | + | 0.379027i | ||||
\(226\) | −18623.5 | + | 6051.15i | −0.364624 | + | 0.118473i | ||||
\(227\) | −35440.6 | + | 48779.8i | −0.687780 | + | 0.946648i | −0.999994 | − | 0.00336373i | \(-0.998929\pi\) |
0.312214 | + | 0.950012i | \(0.398929\pi\) | |||||||
\(228\) | 8134.35 | + | 11196.0i | 0.156478 | + | 0.215373i | ||||
\(229\) | 25553.4 | − | 78645.3i | 0.487279 | − | 1.49969i | −0.341373 | − | 0.939928i | \(-0.610892\pi\) |
0.828652 | − | 0.559764i | \(-0.189108\pi\) | |||||||
\(230\) | − | 35917.8i | − | 0.678975i | ||||||
\(231\) | −80750.0 | − | 37435.7i | −1.51328 | − | 0.701556i | ||||
\(232\) | 4006.40 | 0.0744352 | ||||||||
\(233\) | −38593.9 | − | 12539.9i | −0.710897 | − | 0.230984i | −0.0688249 | − | 0.997629i | \(-0.521925\pi\) |
−0.642072 | + | 0.766644i | \(0.721925\pi\) | |||||||
\(234\) | 64977.5 | − | 47208.9i | 1.18667 | − | 0.862168i | ||||
\(235\) | 57744.7 | + | 41954.0i | 1.04563 | + | 0.759692i | ||||
\(236\) | 10880.1 | + | 33485.5i | 0.195348 | + | 0.601220i | ||||
\(237\) | 19565.6 | − | 6357.26i | 0.348335 | − | 0.113181i | ||||
\(238\) | 24619.0 | − | 33885.1i | 0.434626 | − | 0.598212i | ||||
\(239\) | −45431.0 | − | 62530.4i | −0.795347 | − | 1.09470i | −0.993422 | − | 0.114514i | \(-0.963469\pi\) |
0.198075 | − | 0.980187i | \(-0.436531\pi\) | |||||||
\(240\) | 8690.96 | − | 26748.0i | 0.150885 | − | 0.464375i | ||||
\(241\) | 81225.5i | 1.39849i | 0.714884 | + | 0.699243i | \(0.246479\pi\) | ||||
−0.714884 | + | 0.699243i | \(0.753521\pi\) | |||||||
\(242\) | −15683.6 | − | 38326.2i | −0.267803 | − | 0.654432i | ||||
\(243\) | 56584.6 | 0.958265 | ||||||||
\(244\) | −36145.0 | − | 11744.2i | −0.607111 | − | 0.197262i | ||||
\(245\) | −7419.06 | + | 5390.26i | −0.123600 | + | 0.0898003i | ||||
\(246\) | −48174.6 | − | 35000.9i | −0.796064 | − | 0.578375i | ||||
\(247\) | −5170.61 | − | 15913.5i | −0.0847516 | − | 0.260839i | ||||
\(248\) | 5873.81 | − | 1908.52i | 0.0955030 | − | 0.0310308i | ||||
\(249\) | −22056.8 | + | 30358.6i | −0.355750 | + | 0.489647i | ||||
\(250\) | 23174.0 | + | 31896.3i | 0.370784 | + | 0.510340i | ||||
\(251\) | −21528.8 | + | 66258.7i | −0.341721 | + | 1.05171i | 0.621595 | + | 0.783339i | \(0.286485\pi\) |
−0.963316 | + | 0.268370i | \(0.913515\pi\) | |||||||
\(252\) | − | 65868.9i | − | 1.03724i | ||||||
\(253\) | 23817.3 | − | 51374.5i | 0.372092 | − | 0.802614i | ||||
\(254\) | 39174.9 | 0.607213 | ||||||||
\(255\) | −136259. | − | 44273.1i | −2.09548 | − | 0.680863i | ||||
\(256\) | −3313.73 | + | 2407.57i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 55501.3 | + | 40324.1i | 0.840305 | + | 0.610517i | 0.922456 | − | 0.386103i | \(-0.126179\pi\) |
−0.0821509 | + | 0.996620i | \(0.526179\pi\) | |||||||
\(258\) | 33089.1 | + | 101838.i | 0.497102 | + | 1.52992i | ||||
\(259\) | −92418.2 | + | 30028.5i | −1.37771 | + | 0.447645i | ||||
\(260\) | −19987.5 | + | 27510.5i | −0.295674 | + | 0.406960i | ||||
\(261\) | −18865.8 | − | 25966.5i | −0.276945 | − | 0.381182i | ||||
\(262\) | 20304.3 | − | 62490.1i | 0.295791 | − | 0.910350i | ||||
\(263\) | − | 29173.5i | − | 0.421772i | −0.977511 | − | 0.210886i | \(-0.932365\pi\) | ||
0.977511 | − | 0.210886i | \(-0.0676349\pi\) | |||||||
\(264\) | 30167.7 | − | 32495.7i | 0.432847 | − | 0.466249i | ||||
\(265\) | 44246.9 | 0.630073 | ||||||||
\(266\) | −13050.9 | − | 4240.50i | −0.184450 | − | 0.0599314i | ||||
\(267\) | 181158. | − | 131619.i | 2.54117 | − | 1.84627i | ||||
\(268\) | −7664.67 | − | 5568.71i | −0.106715 | − | 0.0775327i | ||||
\(269\) | −2622.05 | − | 8069.84i | −0.0362357 | − | 0.111522i | 0.931303 | − | 0.364246i | \(-0.118673\pi\) |
−0.967538 | + | 0.252724i | \(0.918673\pi\) | |||||||
\(270\) | −118535. | + | 38514.4i | −1.62600 | + | 0.528318i | ||||
\(271\) | 46946.4 | − | 64616.2i | 0.639240 | − | 0.879838i | −0.359335 | − | 0.933209i | \(-0.616997\pi\) |
0.998575 | + | 0.0533708i | \(0.0169965\pi\) | |||||||
\(272\) | 12264.5 | + | 16880.7i | 0.165773 | + | 0.228167i | ||||
\(273\) | −35607.2 | + | 109588.i | −0.477763 | + | 1.47040i | ||||
\(274\) | 2617.36i | 0.0348629i | ||||||||
\(275\) | −2599.08 | − | 13214.0i | −0.0343681 | − | 0.174731i | ||||
\(276\) | 60632.5 | 0.795953 | ||||||||
\(277\) | 46263.9 | + | 15032.0i | 0.602952 | + | 0.195911i | 0.594556 | − | 0.804054i | \(-0.297328\pi\) |
0.00839523 | + | 0.999965i | \(0.497328\pi\) | |||||||
\(278\) | −80202.4 | + | 58270.4i | −1.03776 | + | 0.753978i | ||||
\(279\) | −40028.9 | − | 29082.7i | −0.514239 | − | 0.373616i | ||||
\(280\) | 8617.84 | + | 26523.0i | 0.109921 | + | 0.338303i | ||||
\(281\) | 6074.58 | − | 1973.75i | 0.0769314 | − | 0.0249965i | −0.270298 | − | 0.962777i | \(-0.587122\pi\) |
0.347230 | + | 0.937780i | \(0.387122\pi\) | |||||||
\(282\) | −70822.1 | + | 97478.3i | −0.890576 | + | 1.22577i | ||||
\(283\) | 74679.6 | + | 102788.i | 0.932458 | + | 1.28342i | 0.958893 | + | 0.283768i | \(0.0915844\pi\) |
−0.0264353 | + | 0.999651i | \(0.508416\pi\) | |||||||
\(284\) | −10667.0 | + | 32829.5i | −0.132252 | + | 0.407031i | ||||
\(285\) | 46939.8i | 0.577899i | ||||||||
\(286\) | −46831.2 | + | 26095.4i | −0.572537 | + | 0.319031i | ||||
\(287\) | 59046.2 | 0.716849 | ||||||||
\(288\) | 31208.2 | + | 10140.1i | 0.376256 | + | 0.122253i | ||||
\(289\) | 18423.0 | − | 13385.1i | 0.220579 | − | 0.160260i | ||||
\(290\) | 10993.8 | + | 7987.48i | 0.130723 | + | 0.0949760i | ||||
\(291\) | 9523.39 | + | 29310.0i | 0.112462 | + | 0.346122i | ||||
\(292\) | 14392.3 | − | 4676.34i | 0.168797 | − | 0.0548454i | ||||
\(293\) | −52337.8 | + | 72036.8i | −0.609649 | + | 0.839110i | −0.996549 | − | 0.0830119i | \(-0.973546\pi\) |
0.386899 | + | 0.922122i | \(0.373546\pi\) | |||||||
\(294\) | −9099.26 | − | 12524.1i | −0.105272 | − | 0.144894i | ||||
\(295\) | −36903.8 | + | 113578.i | −0.424059 | + | 1.30512i | ||||
\(296\) | − | 48409.7i | − | 0.552521i | ||||||
\(297\) | −195084. | − | 23512.6i | −2.21161 | − | 0.266556i | ||||
\(298\) | 29710.8 | 0.334566 | ||||||||
\(299\) | −69721.5 | − | 22653.9i | −0.779874 | − | 0.253396i | ||||
\(300\) | 11665.9 | − | 8475.76i | 0.129621 | − | 0.0941751i | ||||
\(301\) | −85899.6 | − | 62409.7i | −0.948109 | − | 0.688842i | ||||
\(302\) | 19436.3 | + | 59818.7i | 0.213108 | + | 0.655878i | ||||
\(303\) | 184699. | − | 60012.2i | 2.01177 | − | 0.653664i | ||||
\(304\) | 4018.23 | − | 5530.62i | 0.0434798 | − | 0.0598448i | ||||
\(305\) | −75770.0 | − | 104288.i | −0.814512 | − | 1.12108i | ||||
\(306\) | 51655.5 | − | 158979.i | 0.551663 | − | 1.69784i | ||||
\(307\) | 88760.8i | 0.941769i | 0.882195 | + | 0.470885i | \(0.156065\pi\) | ||||
−0.882195 | + | 0.470885i | \(0.843935\pi\) | |||||||
\(308\) | −5261.10 | + | 43651.3i | −0.0554594 | + | 0.460147i | ||||
\(309\) | −39517.9 | −0.413882 | ||||||||
\(310\) | 19923.1 | + | 6473.42i | 0.207317 | + | 0.0673612i | ||||
\(311\) | 104314. | − | 75788.4i | 1.07850 | − | 0.783577i | 0.101081 | − | 0.994878i | \(-0.467770\pi\) |
0.977421 | + | 0.211301i | \(0.0677700\pi\) | |||||||
\(312\) | −46440.2 | − | 33740.8i | −0.477073 | − | 0.346614i | ||||
\(313\) | −29030.5 | − | 89346.6i | −0.296323 | − | 0.911989i | −0.982774 | − | 0.184813i | \(-0.940832\pi\) |
0.686451 | − | 0.727176i | \(-0.259168\pi\) | |||||||
\(314\) | 19704.6 | − | 6402.43i | 0.199852 | − | 0.0649360i | ||||
\(315\) | 131322. | − | 180749.i | 1.32347 | − | 1.82161i | ||||
\(316\) | −5973.35 | − | 8221.61i | −0.0598197 | − | 0.0823347i | ||||
\(317\) | 1162.02 | − | 3576.32i | 0.0115636 | − | 0.0355892i | −0.945108 | − | 0.326758i | \(-0.894044\pi\) |
0.956672 | + | 0.291168i | \(0.0940440\pi\) | |||||||
\(318\) | 74692.7i | 0.738625i | ||||||||
\(319\) | 10428.3 | + | 18714.9i | 0.102479 | + | 0.183910i | ||||
\(320\) | −13893.0 | −0.135674 | ||||||||
\(321\) | 201821. | + | 65575.7i | 1.95865 | + | 0.636404i | ||||
\(322\) | −48640.0 | + | 35339.1i | −0.469118 | + | 0.340834i | ||||
\(323\) | −28173.9 | − | 20469.5i | −0.270048 | − | 0.196201i | ||||
\(324\) | −28716.9 | − | 88381.4i | −0.273556 | − | 0.841920i | ||||
\(325\) | −16581.4 | + | 5387.63i | −0.156984 | + | 0.0510071i | ||||
\(326\) | 70578.2 | − | 97142.5i | 0.664102 | − | 0.914059i | ||||
\(327\) | 8894.56 | + | 12242.3i | 0.0831819 | + | 0.114490i | ||||
\(328\) | −9089.82 | + | 27975.6i | −0.0844904 | + | 0.260035i | ||||
\(329\) | − | 119476.i | − | 1.10380i | ||||||
\(330\) | 147568. | − | 29025.4i | 1.35508 | − | 0.266533i | ||||
\(331\) | −98750.2 | −0.901326 | −0.450663 | − | 0.892694i | \(-0.648812\pi\) | ||||
−0.450663 | + | 0.892694i | \(0.648812\pi\) | |||||||
\(332\) | 17629.6 | + | 5728.21i | 0.159943 | + | 0.0519688i | ||||
\(333\) | −313756. | + | 227957.i | −2.82946 | + | 2.05572i | ||||
\(334\) | −32698.7 | − | 23757.0i | −0.293115 | − | 0.212961i | ||||
\(335\) | −9930.14 | − | 30561.8i | −0.0884842 | − | 0.272326i | ||||
\(336\) | −44773.2 | + | 14547.7i | −0.396588 | + | 0.128859i | ||||
\(337\) | 71066.4 | − | 97814.5i | 0.625755 | − | 0.861278i | −0.372001 | − | 0.928232i | \(-0.621328\pi\) |
0.997756 | + | 0.0669543i | \(0.0213282\pi\) | |||||||
\(338\) | −6687.57 | − | 9204.65i | −0.0585376 | − | 0.0805701i | ||||
\(339\) | 34647.4 | − | 106634.i | 0.301489 | − | 0.927888i | ||||
\(340\) | 70773.3i | 0.612226i | ||||||||
\(341\) | 24204.2 | + | 22470.3i | 0.208153 | + | 0.193241i | ||||
\(342\) | −54766.9 | −0.468237 | ||||||||
\(343\) | 118317. | + | 38443.4i | 1.00567 | + | 0.326764i | ||||
\(344\) | 42793.0 | − | 31090.9i | 0.361623 | − | 0.262734i | ||||
\(345\) | 166380. | + | 120882.i | 1.39785 | + | 1.01560i | ||||
\(346\) | 24737.4 | + | 76134.0i | 0.206634 | + | 0.635955i | ||||
\(347\) | −90973.1 | + | 29559.0i | −0.755534 | + | 0.245488i | −0.661361 | − | 0.750068i | \(-0.730021\pi\) |
−0.0941733 | + | 0.995556i | \(0.530021\pi\) | |||||||
\(348\) | −13483.6 | + | 18558.6i | −0.111339 | + | 0.153245i | ||||
\(349\) | −71159.3 | − | 97942.4i | −0.584226 | − | 0.804118i | 0.409925 | − | 0.912119i | \(-0.365555\pi\) |
−0.994151 | + | 0.108001i | \(0.965555\pi\) | |||||||
\(350\) | −4418.48 | + | 13598.7i | −0.0360693 | + | 0.111010i | ||||
\(351\) | 254385.i | 2.06480i | ||||||||
\(352\) | −19871.7 | − | 9212.54i | −0.160380 | − | 0.0743522i | ||||
\(353\) | −170898. | −1.37148 | −0.685739 | − | 0.727848i | \(-0.740521\pi\) | ||||
−0.685739 | + | 0.727848i | \(0.740521\pi\) | |||||||
\(354\) | −191730. | − | 62296.9i | −1.52997 | − | 0.497119i | ||||
\(355\) | −94722.4 | + | 68819.9i | −0.751616 | + | 0.546081i | ||||
\(356\) | −89488.8 | − | 65017.4i | −0.706104 | − | 0.513014i | ||||
\(357\) | 74108.3 | + | 228082.i | 0.581474 | + | 1.78959i | ||||
\(358\) | −32981.1 | + | 10716.2i | −0.257335 | + | 0.0836132i | ||||
\(359\) | −86522.0 | + | 119087.i | −0.671333 | + | 0.924010i | −0.999790 | − | 0.0205088i | \(-0.993471\pi\) |
0.328457 | + | 0.944519i | \(0.393471\pi\) | |||||||
\(360\) | 65421.1 | + | 90044.4i | 0.504792 | + | 0.694787i | ||||
\(361\) | 36745.6 | − | 113091.i | 0.281962 | − | 0.867791i | ||||
\(362\) | − | 73700.8i | − | 0.562413i | ||||||
\(363\) | 230319. | + | 56337.1i | 1.74790 | + | 0.427545i | ||||
\(364\) | 56920.3 | 0.429600 | ||||||||
\(365\) | 48816.6 | + | 15861.5i | 0.366422 | + | 0.119058i | ||||
\(366\) | 176048. | − | 127907.i | 1.31423 | − | 0.954841i | ||||
\(367\) | 73050.5 | + | 53074.3i | 0.542364 | + | 0.394051i | 0.824962 | − | 0.565188i | \(-0.191196\pi\) |
−0.282598 | + | 0.959238i | \(0.591196\pi\) | |||||||
\(368\) | −9255.49 | − | 28485.5i | −0.0683446 | − | 0.210343i | ||||
\(369\) | 224120. | − | 72821.0i | 1.64599 | − | 0.534816i | ||||
\(370\) | 96513.5 | − | 132839.i | 0.704993 | − | 0.970340i | ||||
\(371\) | −43533.9 | − | 59919.3i | −0.316286 | − | 0.435330i | ||||
\(372\) | −10927.7 | + | 33632.0i | −0.0789666 | + | 0.243034i | ||||
\(373\) | − | 225814.i | − | 1.62305i | −0.584316 | − | 0.811526i | \(-0.698637\pi\) | ||
0.584316 | − | 0.811526i | \(-0.301363\pi\) | |||||||
\(374\) | −46930.1 | + | 101230.i | −0.335512 | + | 0.723710i | ||||
\(375\) | −225744. | −1.60529 | ||||||||
\(376\) | 56606.8 | + | 18392.7i | 0.400399 | + | 0.130098i | ||||
\(377\) | 22438.8 | − | 16302.8i | 0.157876 | − | 0.114704i | ||||
\(378\) | 168782. | + | 122627.i | 1.18125 | + | 0.858228i | ||||
\(379\) | −68671.2 | − | 211348.i | −0.478075 | − | 1.47137i | −0.841765 | − | 0.539845i | \(-0.818483\pi\) |
0.363689 | − | 0.931520i | \(-0.381517\pi\) | |||||||
\(380\) | 22052.6 | − | 7165.32i | 0.152719 | − | 0.0496213i | ||||
\(381\) | −131844. | + | 181468.i | −0.908260 | + | 1.25011i | ||||
\(382\) | 19779.3 | + | 27223.9i | 0.135545 | + | 0.186562i | ||||
\(383\) | −25147.5 | + | 77396.0i | −0.171434 | + | 0.527620i | −0.999453 | − | 0.0330810i | \(-0.989468\pi\) |
0.828019 | + | 0.560700i | \(0.189468\pi\) | |||||||
\(384\) | − | 23452.7i | − | 0.159049i | ||||||
\(385\) | −101464. | + | 109293.i | −0.684525 | + | 0.737347i | ||||
\(386\) | −52640.4 | −0.353301 | ||||||||
\(387\) | −403017. | − | 130948.i | −2.69092 | − | 0.874333i | ||||
\(388\) | 12316.3 | − | 8948.29i | 0.0818117 | − | 0.0594397i | ||||
\(389\) | −147847. | − | 107417.i | −0.977039 | − | 0.709860i | −0.0199941 | − | 0.999800i | \(-0.506365\pi\) |
−0.957045 | + | 0.289940i | \(0.906365\pi\) | |||||||
\(390\) | −60166.7 | − | 185174.i | −0.395573 | − | 1.21745i | ||||
\(391\) | −145110. | + | 47149.0i | −0.949167 | + | 0.308403i | ||||
\(392\) | −4494.88 | + | 6186.67i | −0.0292513 | + | 0.0402610i | ||||
\(393\) | 221135. | + | 304366.i | 1.43176 | + | 1.97065i | ||||
\(394\) | −44630.8 | + | 137359.i | −0.287503 | + | 0.884843i | ||||
\(395\) | − | 34469.6i | − | 0.220924i | ||||||
\(396\) | 33865.3 | + | 172175.i | 0.215956 | + | 1.09794i | ||||
\(397\) | 272916. | 1.73160 | 0.865799 | − | 0.500391i | \(-0.166811\pi\) | ||||
0.865799 | + | 0.500391i | \(0.166811\pi\) | |||||||
\(398\) | −88269.6 | − | 28680.5i | −0.557243 | − | 0.181059i | ||||
\(399\) | 63566.1 | − | 46183.5i | 0.399282 | − | 0.290096i | ||||
\(400\) | −5762.75 | − | 4186.88i | −0.0360172 | − | 0.0261680i | ||||
\(401\) | 80904.1 | + | 248997.i | 0.503132 | + | 1.54848i | 0.803888 | + | 0.594780i | \(0.202761\pi\) |
−0.300757 | + | 0.953701i | \(0.597239\pi\) | |||||||
\(402\) | 51591.1 | − | 16763.0i | 0.319244 | − | 0.103729i | ||||
\(403\) | 25131.6 | − | 34590.7i | 0.154743 | − | 0.212985i | ||||
\(404\) | −56388.1 | − | 77611.6i | −0.345482 | − | 0.475515i | ||||
\(405\) | 97403.4 | − | 299777.i | 0.593833 | − | 1.82763i | ||||
\(406\) | − | 22746.7i | − | 0.137996i | ||||||
\(407\) | 226133. | − | 126007.i | 1.36514 | − | 0.760685i | ||||
\(408\) | −119472. | −0.717704 | ||||||||
\(409\) | 204557. | + | 66464.5i | 1.22283 | + | 0.397322i | 0.848113 | − | 0.529816i | \(-0.177739\pi\) |
0.374720 | + | 0.927138i | \(0.377739\pi\) | |||||||
\(410\) | −80717.5 | + | 58644.7i | −0.480175 | + | 0.348868i | ||||
\(411\) | −12124.3 | − | 8808.78i | −0.0717747 | − | 0.0521474i | ||||
\(412\) | 6032.37 | + | 18565.7i | 0.0355380 | + | 0.109375i | ||||
\(413\) | 190117. | − | 61772.8i | 1.11461 | − | 0.362157i | ||||
\(414\) | −141039. | + | 194123.i | −0.822881 | + | 1.13260i | ||||
\(415\) | 36956.6 | + | 50866.4i | 0.214583 | + | 0.295349i | ||||
\(416\) | −8762.55 | + | 26968.4i | −0.0506342 | + | 0.155836i | ||||
\(417\) | − | 567627.i | − | 3.26430i | ||||||
\(418\) | 36294.0 | + | 4374.36i | 0.207722 | + | 0.0250358i | ||||
\(419\) | 6203.42 | 0.0353348 | 0.0176674 | − | 0.999844i | \(-0.494376\pi\) | ||||
0.0176674 | + | 0.999844i | \(0.494376\pi\) | |||||||
\(420\) | −151864. | − | 49343.7i | −0.860908 | − | 0.279726i | ||||
\(421\) | −194115. | + | 141033.i | −1.09521 | + | 0.795713i | −0.980271 | − | 0.197660i | \(-0.936666\pi\) |
−0.114935 | + | 0.993373i | \(0.536666\pi\) | |||||||
\(422\) | 148995. | + | 108252.i | 0.836658 | + | 0.607868i | ||||
\(423\) | −147349. | − | 453493.i | −0.823504 | − | 2.53448i | ||||
\(424\) | 35091.1 | − | 11401.8i | 0.195193 | − | 0.0634221i | ||||
\(425\) | −21328.6 | + | 29356.4i | −0.118082 | + | 0.162527i | ||||
\(426\) | −116174. | − | 159900.i | −0.640163 | − | 0.881109i | ||||
\(427\) | −66678.8 | + | 205216.i | −0.365706 | + | 1.12553i | ||||
\(428\) | − | 104827.i | − | 0.572249i | ||||||
\(429\) | 36731.1 | − | 304758.i | 0.199581 | − | 1.65592i | ||||
\(430\) | 179412. | 0.970320 | ||||||||
\(431\) | 161263. | + | 52397.5i | 0.868120 | + | 0.282069i | 0.709016 | − | 0.705193i | \(-0.249139\pi\) |
0.159104 | + | 0.987262i | \(0.449139\pi\) | |||||||
\(432\) | −84082.6 | + | 61089.6i | −0.450546 | + | 0.327341i | ||||
\(433\) | 166162. | + | 120724.i | 0.886249 | + | 0.643898i | 0.934897 | − | 0.354918i | \(-0.115491\pi\) |
−0.0486480 | + | 0.998816i | \(0.515491\pi\) | |||||||
\(434\) | −10835.8 | − | 33349.1i | −0.0575282 | − | 0.177054i | ||||
\(435\) | −73999.8 | + | 24044.0i | −0.391068 | + | 0.127066i | ||||
\(436\) | 4393.76 | − | 6047.49i | 0.0231134 | − | 0.0318128i | ||||
\(437\) | 29382.7 | + | 40441.9i | 0.153861 | + | 0.211772i | ||||
\(438\) | −26775.6 | + | 82406.8i | −0.139570 | + | 0.429551i | ||||
\(439\) | 155401.i | 0.806350i | 0.915123 | + | 0.403175i | \(0.132093\pi\) | ||||
−0.915123 | + | 0.403175i | \(0.867907\pi\) | |||||||
\(440\) | −36162.5 | − | 64897.7i | −0.186790 | − | 0.335216i | ||||
\(441\) | 61263.4 | 0.315010 | ||||||||
\(442\) | 137381. | + | 44637.8i | 0.703206 | + | 0.228485i | ||||
\(443\) | −118242. | + | 85907.9i | −0.602511 | + | 0.437750i | −0.846769 | − | 0.531961i | \(-0.821455\pi\) |
0.244259 | + | 0.969710i | \(0.421455\pi\) | |||||||
\(444\) | 224245. | + | 162924.i | 1.13752 | + | 0.826453i | ||||
\(445\) | −115939. | − | 356824.i | −0.585478 | − | 1.80192i | ||||
\(446\) | −50697.8 | + | 16472.7i | −0.254870 | + | 0.0828124i | ||||
\(447\) | −99992.0 | + | 137627.i | −0.500438 | + | 0.688794i | ||||
\(448\) | 13669.2 | + | 18814.0i | 0.0681062 | + | 0.0937401i | ||||
\(449\) | −1879.14 | + | 5783.41i | −0.00932110 | + | 0.0286874i | −0.955609 | − | 0.294638i | \(-0.904801\pi\) |
0.946288 | + | 0.323326i | \(0.104801\pi\) | |||||||
\(450\) | 57065.5i | 0.281805i | ||||||||
\(451\) | −154341. | + | 30357.5i | −0.758800 | + | 0.149250i | ||||
\(452\) | −55386.1 | −0.271096 | ||||||||
\(453\) | −342507. | − | 111287.i | −1.66907 | − | 0.542313i | ||||
\(454\) | −137970. | + | 100241.i | −0.669381 | + | 0.486334i | ||||
\(455\) | 156193. | + | 113481.i | 0.754465 | + | 0.548151i | ||||
\(456\) | 12095.7 | + | 37226.8i | 0.0581704 | + | 0.179030i | ||||
\(457\) | −325507. | + | 105763.i | −1.55857 | + | 0.506411i | −0.956426 | − | 0.291974i | \(-0.905688\pi\) |
−0.602147 | + | 0.798385i | \(0.705688\pi\) | |||||||
\(458\) | 137477. | − | 189221.i | 0.655389 | − | 0.902066i | ||||
\(459\) | 311200. | + | 428330.i | 1.47712 | + | 2.03307i | ||||
\(460\) | 31393.3 | − | 96618.6i | 0.148361 | − | 0.456610i | ||||
\(461\) | 394901.i | 1.85818i | 0.369860 | + | 0.929088i | \(0.379406\pi\) | ||||
−0.369860 | + | 0.929088i | \(0.620594\pi\) | |||||||
\(462\) | −184497. | − | 171280.i | −0.864381 | − | 0.802459i | ||||
\(463\) | 87290.1 | 0.407196 | 0.203598 | − | 0.979055i | \(-0.434736\pi\) | ||||
0.203598 | + | 0.979055i | \(0.434736\pi\) | |||||||
\(464\) | 10777.2 | + | 3501.72i | 0.0500575 | + | 0.0162647i | ||||
\(465\) | −97038.0 | + | 70502.2i | −0.448782 | + | 0.326060i | ||||
\(466\) | −92857.0 | − | 67464.6i | −0.427605 | − | 0.310673i | ||||
\(467\) | 32278.7 | + | 99343.5i | 0.148007 | + | 0.455518i | 0.997385 | − | 0.0722660i | \(-0.0230230\pi\) |
−0.849379 | + | 0.527784i | \(0.823023\pi\) | |||||||
\(468\) | 216051. | − | 70199.2i | 0.986426 | − | 0.320509i | ||||
\(469\) | −31616.8 | + | 43516.8i | −0.143738 | + | 0.197839i | ||||
\(470\) | 118664. | + | 163327.i | 0.537183 | + | 0.739369i | ||||
\(471\) | −36658.8 | + | 112824.i | −0.165248 | + | 0.508581i | ||||
\(472\) | 99585.5i | 0.447005i | ||||||||
\(473\) | 256620. | + | 118969.i | 1.14701 | + | 0.531755i | ||||
\(474\) | 58187.9 | 0.258986 | ||||||||
\(475\) | 11306.7 | + | 3673.76i | 0.0501126 | + | 0.0162826i | ||||
\(476\) | 95841.6 | − | 69633.0i | 0.423000 | − | 0.307327i | ||||
\(477\) | −239139. | − | 173744.i | −1.05102 | − | 0.763614i | ||||
\(478\) | −67555.6 | − | 207915.i | −0.295669 | − | 0.909975i | ||||
\(479\) | −26588.0 | + | 8638.97i | −0.115882 | + | 0.0376522i | −0.366384 | − | 0.930464i | \(-0.619404\pi\) |
0.250502 | + | 0.968116i | \(0.419404\pi\) | |||||||
\(480\) | 46757.2 | − | 64355.8i | 0.202939 | − | 0.279322i | ||||
\(481\) | −196988. | − | 271130.i | −0.851431 | − | 1.17189i | ||||
\(482\) | −70993.6 | + | 218496.i | −0.305580 | + | 0.940480i | ||||
\(483\) | − | 344246.i | − | 1.47562i | ||||||
\(484\) | −8690.55 | − | 116805.i | −0.0370985 | − | 0.498622i | ||||
\(485\) | 51636.7 | 0.219520 | ||||||||
\(486\) | 152212. | + | 49456.7i | 0.644432 | + | 0.209389i | ||||
\(487\) | 227490. | − | 165281.i | 0.959188 | − | 0.696891i | 0.00622636 | − | 0.999981i | \(-0.498018\pi\) |
0.952962 | + | 0.303089i | \(0.0980181\pi\) | |||||||
\(488\) | −86964.9 | − | 63183.7i | −0.365178 | − | 0.265317i | ||||
\(489\) | 212455. | + | 653869.i | 0.888483 | + | 2.73447i | ||||
\(490\) | −24668.5 | + | 8015.28i | −0.102743 | + | 0.0333831i | ||||
\(491\) | 216203. | − | 297578.i | 0.896808 | − | 1.23435i | −0.0746676 | − | 0.997208i | \(-0.523790\pi\) |
0.971475 | − | 0.237141i | \(-0.0762104\pi\) | |||||||
\(492\) | −98997.6 | − | 136258.i | −0.408973 | − | 0.562903i | ||||
\(493\) | 17838.3 | − | 54900.7i | 0.0733939 | − | 0.225883i | ||||
\(494\) | − | 47326.5i | − | 0.193932i | ||||||
\(495\) | −250333. | + | 539976.i | −1.02166 | + | 2.20376i | ||||
\(496\) | 17468.6 | 0.0710061 | ||||||||
\(497\) | 186392. | + | 60562.6i | 0.754598 | + | 0.245184i | ||||
\(498\) | −85867.2 | + | 62386.1i | −0.346233 | + | 0.251553i | ||||
\(499\) | −119340. | − | 86705.4i | −0.479274 | − | 0.348213i | 0.321770 | − | 0.946818i | \(-0.395722\pi\) |
−0.801045 | + | 0.598605i | \(0.795722\pi\) | |||||||
\(500\) | 34459.6 | + | 106056.i | 0.137838 | + | 0.424223i | ||||
\(501\) | 220096. | − | 71513.6i | 0.876874 | − | 0.284914i | ||||
\(502\) | −115825. | + | 159419.i | −0.459614 | + | 0.632604i | ||||
\(503\) | −199460. | − | 274533.i | −0.788352 | − | 1.08507i | −0.994311 | − | 0.106513i | \(-0.966032\pi\) |
0.205959 | − | 0.978561i | \(-0.433968\pi\) | |||||||
\(504\) | 57571.6 | − | 177187.i | 0.226645 | − | 0.697543i | ||||
\(505\) | − | 325392.i | − | 1.27592i | ||||||
\(506\) | 108971. | − | 117380.i | 0.425609 | − | 0.458452i | ||||
\(507\) | 65145.2 | 0.253435 | ||||||||
\(508\) | 105380. | + | 34240.1i | 0.408350 | + | 0.132681i | ||||
\(509\) | −57307.6 | + | 41636.4i | −0.221196 | + | 0.160708i | −0.692865 | − | 0.721068i | \(-0.743652\pi\) |
0.471669 | + | 0.881776i | \(0.343652\pi\) | |||||||
\(510\) | −327839. | − | 238189.i | −1.26043 | − | 0.915759i | ||||
\(511\) | −26550.3 | − | 81713.5i | −0.101678 | − | 0.312934i | ||||
\(512\) | −11018.2 | + | 3580.04i | −0.0420312 | + | 0.0136568i | ||||
\(513\) | 101958. | − | 140334.i | 0.387426 | − | 0.533246i | ||||
\(514\) | 114054. | + | 156981.i | 0.431701 | + | 0.594185i | ||||
\(515\) | −20460.9 | + | 62972.2i | −0.0771455 | + | 0.237429i | ||||
\(516\) | 302864.i | 1.13749i | ||||||||
\(517\) | 61426.5 | + | 312299.i | 0.229813 | + | 1.16839i | ||||
\(518\) | −274850. | −1.02432 | ||||||||
\(519\) | −435925. | − | 141641.i | −1.61837 | − | 0.525839i | ||||
\(520\) | −77811.4 | + | 56533.3i | −0.287764 | + | 0.209073i | ||||
\(521\) | −252967. | − | 183791.i | −0.931942 | − | 0.677095i | 0.0145256 | − | 0.999894i | \(-0.495376\pi\) |
−0.946468 | + | 0.322799i | \(0.895376\pi\) | |||||||
\(522\) | −28053.3 | − | 86339.0i | −0.102954 | − | 0.316859i | ||||
\(523\) | −243282. | + | 79047.2i | −0.889421 | + | 0.288990i | −0.717863 | − | 0.696184i | \(-0.754880\pi\) |
−0.171557 | + | 0.985174i | \(0.554880\pi\) | |||||||
\(524\) | 109237. | − | 150351.i | 0.397838 | − | 0.547577i | ||||
\(525\) | −48121.9 | − | 66234.1i | −0.174592 | − | 0.240305i | ||||
\(526\) | 25498.6 | − | 78476.7i | 0.0921605 | − | 0.283641i | ||||
\(527\) | − | 88988.0i | − | 0.320413i | ||||||
\(528\) | 109553. | − | 61045.6i | 0.392968 | − | 0.218971i | ||||
\(529\) | −60825.6 | −0.217358 | ||||||||
\(530\) | 119024. | + | 38673.2i | 0.423723 | + | 0.137676i | ||||
\(531\) | 645439. | − | 468939.i | 2.28911 | − | 1.66313i | ||||
\(532\) | −31400.6 | − | 22813.9i | −0.110947 | − | 0.0806075i | ||||
\(533\) | 62927.9 | + | 193672.i | 0.221508 | + | 0.681731i | ||||
\(534\) | 602352. | − | 195716.i | 2.11236 | − | 0.686347i | ||||
\(535\) | 208992. | − | 287652.i | 0.730165 | − | 1.00499i | ||||
\(536\) | −15750.7 | − | 21679.0i | −0.0548239 | − | 0.0754586i | ||||
\(537\) | 61358.4 | − | 188842.i | 0.212777 | − | 0.654861i | ||||
\(538\) | − | 23999.6i | − | 0.0829161i | ||||||
\(539\) | −40599.2 | − | 4893.25i | −0.139746 | − | 0.0168430i | ||||
\(540\) | −352522. | −1.20892 | ||||||||
\(541\) | −182923. | − | 59435.3i | −0.624991 | − | 0.203072i | −0.0206361 | − | 0.999787i | \(-0.506569\pi\) |
−0.604355 | + | 0.796715i | \(0.706569\pi\) | |||||||
\(542\) | 182762. | − | 132784.i | 0.622139 | − | 0.452011i | ||||
\(543\) | 341400. | + | 248041.i | 1.15788 | + | 0.841249i | ||||
\(544\) | 18237.3 | + | 56128.5i | 0.0616257 | + | 0.189664i | ||||
\(545\) | 24113.6 | − | 7834.97i | 0.0811836 | − | 0.0263781i | ||||
\(546\) | −191566. | + | 263668.i | −0.642590 | + | 0.884449i | ||||
\(547\) | −65954.5 | − | 90778.6i | −0.220429 | − | 0.303395i | 0.684453 | − | 0.729057i | \(-0.260041\pi\) |
−0.904882 | + | 0.425662i | \(0.860041\pi\) | |||||||
\(548\) | −2287.66 | + | 7040.69i | −0.00761782 | + | 0.0234452i | ||||
\(549\) | 861169.i | 2.85722i | ||||||||
\(550\) | 4557.95 | − | 37817.3i | 0.0150676 | − | 0.125016i | ||||
\(551\) | −18912.8 | −0.0622948 | ||||||||
\(552\) | 163101. | + | 52994.7i | 0.535277 | + | 0.173922i | ||||
\(553\) | −46678.9 | + | 33914.2i | −0.152641 | + | 0.110900i | ||||
\(554\) | 111311. | + | 80872.2i | 0.362676 | + | 0.263500i | ||||
\(555\) | 290526. | + | 894147.i | 0.943190 | + | 2.90284i | ||||
\(556\) | −266674. | + | 86647.7i | −0.862644 | + | 0.280290i | ||||
\(557\) | 17182.2 | − | 23649.2i | 0.0553819 | − | 0.0762267i | −0.780428 | − | 0.625246i | \(-0.784999\pi\) |
0.835810 | + | 0.549019i | \(0.184999\pi\) | |||||||
\(558\) | −82258.2 | − | 113219.i | −0.264187 | − | 0.363622i | ||||
\(559\) | 113158. | − | 348265.i | 0.362128 | − | 1.11451i | ||||
\(560\) | 78878.9i | 0.251527i | ||||||||
\(561\) | −310976. | − | 558082.i | −0.988100 | − | 1.77326i | ||||
\(562\) | 18065.7 | 0.0571982 | ||||||||
\(563\) | −254276. | − | 82619.2i | −0.802210 | − | 0.260654i | −0.120915 | − | 0.992663i | \(-0.538583\pi\) |
−0.681295 | + | 0.732009i | \(0.738583\pi\) | |||||||
\(564\) | −275710. | + | 200315.i | −0.866752 | + | 0.629732i | ||||
\(565\) | −151983. | − | 110422.i | −0.476100 | − | 0.345907i | ||||
\(566\) | 111048. | + | 341771.i | 0.346639 | + | 1.06685i | ||||
\(567\) | −501793. | + | 163042.i | −1.56084 | + | 0.507148i | ||||
\(568\) | −57388.1 | + | 78987.9i | −0.177879 | + | 0.244830i | ||||
\(569\) | 184215. | + | 253550.i | 0.568984 | + | 0.783139i | 0.992434 | − | 0.122781i | \(-0.0391812\pi\) |
−0.423450 | + | 0.905919i | \(0.639181\pi\) | |||||||
\(570\) | −41026.9 | + | 126268.i | −0.126275 | + | 0.388636i | ||||
\(571\) | 467241.i | 1.43308i | 0.697549 | + | 0.716538i | \(0.254274\pi\) | ||||
−0.697549 | + | 0.716538i | \(0.745726\pi\) | |||||||
\(572\) | −148784. | + | 29264.5i | −0.454741 | + | 0.0894437i | ||||
\(573\) | −192675. | −0.586836 | ||||||||
\(574\) | 158834. | + | 51608.2i | 0.482080 | + | 0.156637i | ||||
\(575\) | 42139.3 | − | 30616.0i | 0.127453 | − | 0.0926003i | ||||
\(576\) | 75086.9 | + | 54553.8i | 0.226318 | + | 0.164430i | ||||
\(577\) | −55363.0 | − | 170390.i | −0.166291 | − | 0.511790i | 0.832838 | − | 0.553516i | \(-0.186714\pi\) |
−0.999129 | + | 0.0417260i | \(0.986714\pi\) | |||||||
\(578\) | 61256.7 | − | 19903.5i | 0.183357 | − | 0.0595764i | ||||
\(579\) | 177162. | − | 243843.i | 0.528462 | − | 0.727365i | ||||
\(580\) | 22592.0 | + | 31095.2i | 0.0671582 | + | 0.0924353i | ||||
\(581\) | 32522.4 | − | 100094.i | 0.0963453 | − | 0.296520i | ||||
\(582\) | 87167.5i | 0.257341i | ||||||||
\(583\) | 144600. | + | 134241.i | 0.425432 | + | 0.394955i | ||||
\(584\) | 42802.5 | 0.125500 | ||||||||
\(585\) | 732814. | + | 238106.i | 2.14132 | + | 0.695757i | ||||
\(586\) | −203751. | + | 148034.i | −0.593340 | + | 0.431087i | ||||
\(587\) | −220845. | − | 160454.i | −0.640932 | − | 0.465665i | 0.219238 | − | 0.975671i | \(-0.429643\pi\) |
−0.860170 | + | 0.510007i | \(0.829643\pi\) | |||||||
\(588\) | −13530.5 | − | 41642.7i | −0.0391345 | − | 0.120444i | ||||
\(589\) | −27728.2 | + | 9009.43i | −0.0799265 | + | 0.0259697i | ||||
\(590\) | −198542. | + | 273269.i | −0.570358 | + | 0.785031i | ||||
\(591\) | −486076. | − | 669026.i | −1.39165 | − | 1.91544i | ||||
\(592\) | 42311.6 | − | 130222.i | 0.120730 | − | 0.371570i | ||||
\(593\) | − | 11945.3i | − | 0.0339694i | −0.999856 | − | 0.0169847i | \(-0.994593\pi\) | ||
0.999856 | − | 0.0169847i | \(-0.00540665\pi\) | |||||||
\(594\) | −504225. | − | 233759.i | −1.42906 | − | 0.662514i | ||||
\(595\) | 401822. | 1.13501 | ||||||||
\(596\) | 79921.8 | + | 25968.2i | 0.224995 | + | 0.0731052i | ||||
\(597\) | 429928. | − | 312361.i | 1.20628 | − | 0.876411i | ||||
\(598\) | −167750. | − | 121878.i | −0.469095 | − | 0.340818i | ||||
\(599\) | −88096.2 | − | 271132.i | −0.245529 | − | 0.755662i | −0.995549 | − | 0.0942462i | \(-0.969956\pi\) |
0.750019 | − | 0.661416i | \(-0.230044\pi\) | |||||||
\(600\) | 38789.2 | − | 12603.4i | 0.107748 | − | 0.0350094i | ||||
\(601\) | −258160. | + | 355327.i | −0.714728 | + | 0.983738i | 0.284955 | + | 0.958541i | \(0.408021\pi\) |
−0.999682 | + | 0.0251973i | \(0.991979\pi\) | |||||||
\(602\) | −176521. | − | 242961.i | −0.487085 | − | 0.670414i | ||||
\(603\) | −66338.4 | + | 204169.i | −0.182444 | + | 0.561506i | ||||
\(604\) | 177900.i | 0.487643i | ||||||||
\(605\) | 209025. | − | 337847.i | 0.571067 | − | 0.923017i | ||||
\(606\) | 549291. | 1.49574 | ||||||||
\(607\) | 386802. | + | 125680.i | 1.04981 | + | 0.341105i | 0.782595 | − | 0.622532i | \(-0.213896\pi\) |
0.267218 | + | 0.963636i | \(0.413896\pi\) | |||||||
\(608\) | 15643.0 | − | 11365.3i | 0.0423167 | − | 0.0307449i | ||||
\(609\) | 105368. | + | 76554.3i | 0.284102 | + | 0.206412i | ||||
\(610\) | −112669. | − | 346761.i | −0.302793 | − | 0.931902i | ||||
\(611\) | 391883. | − | 127331.i | 1.04972 | − | 0.341076i | ||||
\(612\) | 277906. | − | 382505.i | 0.741985 | − | 1.02125i | ||||
\(613\) | 329984. | + | 454184.i | 0.878156 | + | 1.20868i | 0.976928 | + | 0.213568i | \(0.0685085\pi\) |
−0.0987722 | + | 0.995110i | \(0.531492\pi\) | |||||||
\(614\) | −77579.8 | + | 238766.i | −0.205784 | + | 0.633338i | ||||
\(615\) | − | 571272.i | − | 1.51040i | ||||||
\(616\) | −52305.0 | + | 112823.i | −0.137842 | + | 0.297330i | ||||
\(617\) | −361868. | −0.950559 | −0.475280 | − | 0.879835i | \(-0.657653\pi\) | ||||
−0.475280 | + | 0.879835i | \(0.657653\pi\) | |||||||
\(618\) | −106303. | − | 34539.9i | −0.278335 | − | 0.0904365i | ||||
\(619\) | 80076.6 | − | 58179.1i | 0.208989 | − | 0.151840i | −0.478367 | − | 0.878160i | \(-0.658771\pi\) |
0.687356 | + | 0.726320i | \(0.258771\pi\) | |||||||
\(620\) | 47935.1 | + | 34826.9i | 0.124701 | + | 0.0906007i | ||||
\(621\) | −234849. | − | 722790.i | −0.608983 | − | 1.87426i | ||||
\(622\) | 346845. | − | 112697.i | 0.896509 | − | 0.291293i | ||||
\(623\) | −369142. | + | 508080.i | −0.951081 | + | 1.30905i | ||||
\(624\) | −95433.3 | − | 131353.i | −0.245093 | − | 0.337342i | ||||
\(625\) | −138378. | + | 425883.i | −0.354247 | + | 1.09026i | ||||
\(626\) | − | 265716.i | − | 0.678060i | ||||||
\(627\) | −142411. | + | 153400.i | −0.362250 | + | 0.390204i | ||||
\(628\) | 58601.3 | 0.148589 | ||||||||
\(629\) | −663371. | − | 215542.i | −1.67670 | − | 0.544792i | ||||
\(630\) | 511235. | − | 371434.i | 1.28807 | − | 0.935837i | ||||
\(631\) | −3482.93 | − | 2530.50i | −0.00874755 | − | 0.00635547i | 0.583403 | − | 0.812183i | \(-0.301721\pi\) |
−0.592150 | + | 0.805827i | \(0.701721\pi\) | |||||||
\(632\) | −8882.33 | − | 27337.0i | −0.0222378 | − | 0.0684410i | ||||
\(633\) | −1.00289e6 | + | 325860.i | −2.50292 | + | 0.813249i | ||||
\(634\) | 6251.64 | − | 8604.65i | 0.0155531 | − | 0.0214069i | ||||
\(635\) | 220907. | + | 304052.i | 0.547850 | + | 0.754051i | ||||
\(636\) | −65283.8 | + | 200923.i | −0.161395 | + | 0.496724i | ||||
\(637\) | 52940.4i | 0.130469i | ||||||||
\(638\) | 11694.8 | + | 59457.6i | 0.0287310 | + | 0.146072i | ||||
\(639\) | 782176. | 1.91559 | ||||||||
\(640\) | −37372.2 | − | 12143.0i | −0.0912407 | − | 0.0296459i | ||||
\(641\) | 306286. | − | 222530.i | 0.745438 | − | 0.541592i | −0.148972 | − | 0.988841i | \(-0.547596\pi\) |
0.894409 | + | 0.447249i | \(0.147596\pi\) | |||||||
\(642\) | 485583. | + | 352797.i | 1.17813 | + | 0.855962i | ||||
\(643\) | −75113.6 | − | 231176.i | −0.181676 | − | 0.559140i | 0.818200 | − | 0.574934i | \(-0.194972\pi\) |
−0.999875 | + | 0.0157940i | \(0.994972\pi\) | |||||||
\(644\) | −161729. | + | 52548.9i | −0.389956 | + | 0.126704i | ||||
\(645\) | −603815. | + | 831080.i | −1.45139 | + | 1.99767i | ||||
\(646\) | −57896.5 | − | 79687.7i | −0.138735 | − | 0.190953i | ||||
\(647\) | 65343.8 | − | 201107.i | 0.156097 | − | 0.480418i | −0.842173 | − | 0.539207i | \(-0.818724\pi\) |
0.998270 | + | 0.0587889i | \(0.0187239\pi\) | |||||||
\(648\) | − | 262845.i | − | 0.625964i | ||||||
\(649\) | −465188. | + | 259213.i | −1.10443 | + | 0.615415i | ||||
\(650\) | −49312.9 | −0.116717 | ||||||||
\(651\) | 190949. | + | 62043.1i | 0.450563 | + | 0.146397i | ||||
\(652\) | 274760. | − | 199625.i | 0.646337 | − | 0.469591i | ||||
\(653\) | −194030. | − | 140971.i | −0.455032 | − | 0.330600i | 0.336547 | − | 0.941667i | \(-0.390741\pi\) |
−0.791579 | + | 0.611066i | \(0.790741\pi\) | |||||||
\(654\) | 13226.1 | + | 40705.9i | 0.0309227 | + | 0.0951703i | ||||
\(655\) | 599506. | − | 194791.i | 1.39737 | − | 0.454032i | ||||
\(656\) | −48903.1 | + | 67309.3i | −0.113639 | + | 0.156411i | ||||
\(657\) | −201553. | − | 277414.i | −0.466937 | − | 0.642684i | ||||
\(658\) | 104426. | − | 321390.i | 0.241189 | − | 0.742302i | ||||
\(659\) | 474194.i | 1.09191i | 0.837816 | + | 0.545953i | \(0.183832\pi\) | ||||
−0.837816 | + | 0.545953i | \(0.816168\pi\) | |||||||
\(660\) | 422327. | + | 50901.2i | 0.969529 | + | 0.116853i | ||||
\(661\) | 808699. | 1.85090 | 0.925452 | − | 0.378865i | \(-0.123686\pi\) | ||||
0.925452 | + | 0.378865i | \(0.123686\pi\) | |||||||
\(662\) | −265637. | − | 86310.8i | −0.606140 | − | 0.196947i | ||||
\(663\) | −669131. | + | 486152.i | −1.52224 | + | 1.10598i | ||||
\(664\) | 42416.9 | + | 30817.7i | 0.0962062 | + | 0.0698979i | ||||
\(665\) | −40681.7 | − | 125206.i | −0.0919933 | − | 0.283126i | ||||
\(666\) | −1.04324e6 | + | 338970.i | −2.35200 | + | 0.764211i | ||||
\(667\) | −48705.2 | + | 67036.9i | −0.109477 | + | 0.150682i | ||||
\(668\) | −67195.0 | − | 92486.0i | −0.150586 | − | 0.207264i | ||||
\(669\) | 94318.8 | − | 290283.i | 0.210739 | − | 0.648589i | ||||
\(670\) | − | 90890.4i | − | 0.202474i | ||||||
\(671\) | 68783.5 | − | 570697.i | 0.152770 | − | 1.26754i | ||||
\(672\) | −133155. | −0.294862 | ||||||||
\(673\) | 648968. | + | 210863.i | 1.43283 | + | 0.465553i | 0.919653 | − | 0.392732i | \(-0.128470\pi\) |
0.513173 | + | 0.858285i | \(0.328470\pi\) | |||||||
\(674\) | 276661. | − | 201006.i | 0.609016 | − | 0.442476i | ||||
\(675\) | −146224. | − | 106238.i | −0.320930 | − | 0.233170i | ||||
\(676\) | −9944.37 | − | 30605.6i | −0.0217612 | − | 0.0669742i | ||||
\(677\) | −775084. | + | 251840.i | −1.69111 | + | 0.549474i | −0.987014 | − | 0.160633i | \(-0.948646\pi\) |
−0.704093 | + | 0.710107i | \(0.748646\pi\) | |||||||
\(678\) | 186403. | − | 256561.i | 0.405502 | − | 0.558126i | ||||
\(679\) | −50804.7 | − | 69926.7i | −0.110196 | − | 0.151671i | ||||
\(680\) | −61858.2 | + | 190380.i | −0.133776 | + | 0.411721i | ||||
\(681\) | − | 976474.i | − | 2.10555i | ||||||
\(682\) | 45469.5 | + | 81600.2i | 0.0977578 | + | 0.175438i | ||||
\(683\) | 303153. | 0.649861 | 0.324930 | − | 0.945738i | \(-0.394659\pi\) | ||||
0.324930 | + | 0.945738i | \(0.394659\pi\) | |||||||
\(684\) | −147323. | − | 47868.0i | −0.314889 | − | 0.102314i | ||||
\(685\) | −20314.4 | + | 14759.3i | −0.0432935 | + | 0.0314546i | ||||
\(686\) | 284670. | + | 206825.i | 0.604914 | + | 0.439496i | ||||
\(687\) | 413835. | + | 1.27365e6i | 0.876826 | + | 2.69859i | ||||
\(688\) | 142287. | − | 46231.9i | 0.300600 | − | 0.0976709i | ||||
\(689\) | 150140. | − | 206650.i | 0.316271 | − | 0.435309i | ||||
\(690\) | 341906. | + | 470593.i | 0.718138 | + | 0.988432i | ||||
\(691\) | −37702.7 | + | 116037.i | −0.0789617 | + | 0.243019i | −0.982743 | − | 0.184975i | \(-0.940780\pi\) |
0.903782 | + | 0.427994i | \(0.140780\pi\) | |||||||
\(692\) | 226421.i | 0.472830i | ||||||||
\(693\) | 977538. | − | 192273.i | 2.03548 | − | 0.400362i | ||||
\(694\) | −270553. | −0.561737 | ||||||||
\(695\) | −904520. | − | 293896.i | −1.87262 | − | 0.608450i | ||||
\(696\) | −52491.6 | + | 38137.4i | −0.108361 | + | 0.0787286i | ||||
\(697\) | 342884. | + | 249120.i | 0.705801 | + | 0.512794i | ||||
\(698\) | −105813. | − | 325660.i | −0.217185 | − | 0.668426i | ||||
\(699\) | 625024. | − | 203083.i | 1.27921 | − | 0.415641i | ||||
\(700\) | −23771.4 | + | 32718.5i | −0.0485130 | + | 0.0667725i | ||||
\(701\) | 298000. | + | 410162.i | 0.606429 | + | 0.834679i | 0.996278 | − | 0.0862005i | \(-0.0274726\pi\) |
−0.389848 | + | 0.920879i | \(0.627473\pi\) | |||||||
\(702\) | −222341. | + | 684295.i | −0.451175 | + | 1.38857i | ||||
\(703\) | 228525.i | 0.462405i | ||||||||
\(704\) | −45402.8 | − | 42150.2i | −0.0916088 | − | 0.0850461i | ||||
\(705\) | −1.15593e6 | −2.32570 | ||||||||
\(706\) | −459716. | − | 149371.i | −0.922317 | − | 0.299679i | ||||
\(707\) | −440647. | + | 320149.i | −0.881560 | + | 0.640491i | ||||
\(708\) | −461304. | − | 335157.i | −0.920281 | − | 0.668623i | ||||
\(709\) | 197648. | + | 608297.i | 0.393187 | + | 1.21010i | 0.930365 | + | 0.366636i | \(0.119490\pi\) |
−0.537178 | + | 0.843469i | \(0.680510\pi\) | |||||||
\(710\) | −314954. | + | 102335.i | −0.624784 | + | 0.203005i | ||||
\(711\) | −135352. | + | 186296.i | −0.267748 | + | 0.368523i | ||||
\(712\) | −183897. | − | 253112.i | −0.362756 | − | 0.499291i | ||||
\(713\) | −39472.9 | + | 121485.i | −0.0776461 | + | 0.238970i | ||||
\(714\) | 678312.i | 1.33056i | ||||||||
\(715\) | −466618. | − | 216324.i | −0.912744 | − | 0.423148i | ||||
\(716\) | −98085.2 | −0.191328 | ||||||||
\(717\) | 1.19047e6 | + | 386807.i | 2.31569 | + | 0.752412i | ||||
\(718\) | −336830. | + | 244721.i | −0.653374 | + | 0.474704i | ||||
\(719\) | −44104.7 | − | 32043.9i | −0.0853153 | − | 0.0619852i | 0.544310 | − | 0.838884i | \(-0.316792\pi\) |
−0.629625 | + | 0.776899i | \(0.716792\pi\) | |||||||
\(720\) | 97280.6 | + | 299399.i | 0.187655 | + | 0.577544i | ||||
\(721\) | 105409. | − | 34249.3i | 0.202771 | − | 0.0658842i | ||||
\(722\) | 197691. | − | 272098.i | 0.379239 | − | 0.521977i | ||||
\(723\) | −773195. | − | 1.06421e6i | −1.47915 | − | 2.03588i | ||||
\(724\) | 64416.9 | − | 198255.i | 0.122892 | − | 0.378222i | ||||
\(725\) | 19706.6i | 0.0374917i | ||||||||
\(726\) | 570317. | + | 352853.i | 1.08204 | + | 0.669454i | ||||
\(727\) | −671062. | −1.26968 | −0.634839 | − | 0.772644i | \(-0.718934\pi\) | ||||
−0.634839 | + | 0.772644i | \(0.718934\pi\) | |||||||
\(728\) | 153115. | + | 49750.2i | 0.288905 | + | 0.0938711i | ||||
\(729\) | 19846.8 | − | 14419.6i | 0.0373453 | − | 0.0271330i | ||||
\(730\) | 117453. | + | 85334.5i | 0.220403 | + | 0.160132i | ||||
\(731\) | −235513. | − | 724834.i | −0.440737 | − | 1.35645i | ||||
\(732\) | 585364. | − | 190196.i | 1.09246 | − | 0.354960i | ||||
\(733\) | 518514. | − | 713673.i | 0.965056 | − | 1.32829i | 0.0205511 | − | 0.999789i | \(-0.493458\pi\) |
0.944505 | − | 0.328497i | \(-0.106542\pi\) | |||||||
\(734\) | 150117. | + | 206618.i | 0.278636 | + | 0.383509i | ||||
\(735\) | 45893.6 | − | 141246.i | 0.0849527 | − | 0.261457i | ||||
\(736\) | − | 84715.4i | − | 0.156389i | ||||||
\(737\) | 60269.9 | − | 130004.i | 0.110960 | − | 0.239343i | ||||
\(738\) | 666530. | 1.22379 | ||||||||
\(739\) | −83308.5 | − | 27068.6i | −0.152546 | − | 0.0495652i | 0.231749 | − | 0.972776i | \(-0.425555\pi\) |
−0.384295 | + | 0.923211i | \(0.625555\pi\) | |||||||
\(740\) | 375727. | − | 272982.i | 0.686134 | − | 0.498505i | ||||
\(741\) | 219228. | + | 159278.i | 0.399263 | + | 0.290081i | ||||
\(742\) | −64734.6 | − | 199233.i | −0.117579 | − | 0.361870i | ||||
\(743\) | 981482. | − | 318903.i | 1.77789 | − | 0.577671i | 0.779102 | − | 0.626898i | \(-0.215676\pi\) |
0.998788 | + | 0.0492263i | \(0.0156756\pi\) | |||||||
\(744\) | −58791.0 | + | 80918.8i | −0.106210 | + | 0.146185i | ||||
\(745\) | 167538. | + | 230597.i | 0.301858 | + | 0.415471i | ||||
\(746\) | 197368. | − | 607437.i | 0.354650 | − | 1.09150i | ||||
\(747\) | − | 420033.i | − | 0.752735i | ||||||
\(748\) | −214720. | + | 231289.i | −0.383768 | + | 0.413382i | ||||
\(749\) | −595164. | −1.06090 | ||||||||
\(750\) | −607249. | − | 197307.i | −1.07955 | − | 0.350768i | ||||
\(751\) | −523567. | + | 380394.i | −0.928309 | + | 0.674456i | −0.945578 | − | 0.325395i | \(-0.894503\pi\) |
0.0172688 | + | 0.999851i | \(0.494503\pi\) | |||||||
\(752\) | 136196. | + | 98952.3i | 0.240840 | + | 0.174981i | ||||
\(753\) | −348656. | − | 1.07305e6i | −0.614904 | − | 1.89248i | ||||
\(754\) | 74609.4 | − | 24242.1i | 0.131235 | − | 0.0426410i | ||||
\(755\) | −354676. | + | 488169.i | −0.622211 | + | 0.856400i | ||||
\(756\) | 346842. | + | 477386.i | 0.606859 | + | 0.835269i | ||||
\(757\) | 333021. | − | 1.02493e6i | 0.581140 | − | 1.78856i | −0.0331096 | − | 0.999452i | \(-0.510541\pi\) |
0.614249 | − | 0.789112i | \(-0.289459\pi\) | |||||||
\(758\) | − | 628547.i | − | 1.09395i | ||||||
\(759\) | 176988. | + | 899825.i | 0.307228 | + | 1.56198i | ||||
\(760\) | 65584.1 | 0.113546 | ||||||||
\(761\) | 129907. | + | 42209.4i | 0.224318 | + | 0.0728854i | 0.419020 | − | 0.907977i | \(-0.362374\pi\) |
−0.194702 | + | 0.980863i | \(0.562374\pi\) | |||||||
\(762\) | −513268. | + | 372911.i | −0.883963 | + | 0.642237i | ||||
\(763\) | −34335.2 | − | 24946.0i | −0.0589780 | − | 0.0428500i | ||||
\(764\) | 29411.7 | + | 90519.9i | 0.0503887 | + | 0.155081i | ||||
\(765\) | 1.52519e6 | − | 495563.i | 2.60615 | − | 0.846790i | ||||
\(766\) | −135293. | + | 186215.i | −0.230578 | + | 0.317364i | ||||
\(767\) | 405231. | + | 557753.i | 0.688830 | + | 0.948094i | ||||
\(768\) | 20498.4 | − | 63087.6i | 0.0347534 | − | 0.106960i | ||||
\(769\) | − | 24012.2i | − | 0.0406050i | −0.999794 | − | 0.0203025i | \(-0.993537\pi\) | ||
0.999794 | − | 0.0203025i | \(-0.00646292\pi\) | |||||||
\(770\) | −368463. | + | 205316.i | −0.621458 | + | 0.346291i | ||||
\(771\) | −1.11102e6 | −1.86902 | ||||||||
\(772\) | −141602. | − | 46009.4i | −0.237594 | − | 0.0771990i | ||||
\(773\) | 61225.6 | − | 44483.0i | 0.102465 | − | 0.0744449i | −0.535373 | − | 0.844616i | \(-0.679829\pi\) |
0.637838 | + | 0.770171i | \(0.279829\pi\) | |||||||
\(774\) | −969659. | − | 704499.i | −1.61859 | − | 1.17598i | ||||
\(775\) | 9387.57 | + | 28892.0i | 0.0156297 | + | 0.0481032i | ||||
\(776\) | 40951.8 | − | 13306.0i | 0.0680063 | − | 0.0220966i | ||||
\(777\) | 925013. | − | 1.27317e6i | 1.53217 | − | 2.10885i | ||||
\(778\) | −303821. | − | 418173.i | −0.501947 | − | 0.690871i | ||||
\(779\) | 42909.8 | − | 132063.i | 0.0707101 | − | 0.217623i | ||||
\(780\) | − | 550704.i | − | 0.905168i | ||||||
\(781\) | −518348. | − | 62474.2i | −0.849806 | − | 0.102423i | ||||
\(782\) | −431554. | −0.705702 | ||||||||
\(783\) | 273460. | + | 88852.6i | 0.446037 | + | 0.144926i | ||||
\(784\) | −17498.5 | + | 12713.4i | −0.0284688 | + | 0.0206838i | ||||
\(785\) | 160806. | + | 116832.i | 0.260953 | + | 0.189594i | ||||
\(786\) | 328825. | + | 1.01202e6i | 0.532256 | + | 1.63811i | ||||
\(787\) | −469650. | + | 152599.i | −0.758272 | + | 0.246378i | −0.662537 | − | 0.749029i | \(-0.730520\pi\) |
−0.0957352 | + | 0.995407i | \(0.530520\pi\) | |||||||
\(788\) | −240113. | + | 330487.i | −0.386691 | + | 0.532234i | ||||
\(789\) | 277706. | + | 382230.i | 0.446100 | + | 0.614004i | ||||
\(790\) | 30127.6 | − | 92723.1i | 0.0482736 | − | 0.148571i | ||||
\(791\) | 314459.i | 0.502587i | ||||||||
\(792\) | −59388.8 | + | 492749.i | −0.0946791 | + | 0.785552i | ||||
\(793\) | −744175. | −1.18339 | ||||||||
\(794\) | 734141. | + | 238537.i | 1.16450 | + | 0.378368i | ||||
\(795\) | −579720. | + | 421191.i | −0.917242 | + | 0.666415i | ||||
\(796\) | −212377. | − | 154301.i | −0.335182 | − | 0.243524i | ||||
\(797\) | 46535.4 | + | 143221.i | 0.0732599 | + | 0.225471i | 0.980981 | − | 0.194103i | \(-0.0621796\pi\) |
−0.907721 | + | 0.419574i | \(0.862180\pi\) | |||||||
\(798\) | 211358. | − | 68674.5i | 0.331905 | − | 0.107842i | ||||
\(799\) | 504079. | − | 693805.i | 0.789596 | − | 1.08679i | ||||
\(800\) | −11842.3 | − | 16299.5i | −0.0185036 | − | 0.0254680i | ||||
\(801\) | −774533. | + | 2.38377e6i | −1.20719 | + | 3.71534i | ||||
\(802\) | 740514.i | 1.15129i | ||||||||
\(803\) | 111411. | + | 199941.i | 0.172782 | + | 0.310077i | ||||
\(804\) | 153431. | 0.237357 | ||||||||
\(805\) | −548561. | − | 178238.i | −0.846512 | − | 0.275048i | ||||
\(806\) | 97837.4 | − | 71083.0i | 0.150603 | − | 0.109420i | ||||
\(807\) | 111172. | + | 80770.9i | 0.170705 | + | 0.124025i | ||||
\(808\) | −83848.7 | − | 258060.i | −0.128432 | − | 0.395273i | ||||
\(809\) | −423444. | + | 137585.i | −0.646992 | + | 0.210220i | −0.614087 | − | 0.789238i | \(-0.710476\pi\) |
−0.0329044 | + | 0.999459i | \(0.510476\pi\) | |||||||
\(810\) | 524029. | − | 721264.i | 0.798703 | − | 1.09932i | ||||
\(811\) | 398266. | + | 548166.i | 0.605524 | + | 0.833432i | 0.996200 | − | 0.0870964i | \(-0.0277588\pi\) |
−0.390676 | + | 0.920528i | \(0.627759\pi\) | |||||||
\(812\) | 19881.3 | − | 61188.4i | 0.0301532 | − | 0.0928020i | ||||
\(813\) | 1.29349e6i | 1.95695i | ||||||||
\(814\) | 718431. | − | 141309.i | 1.08427 | − | 0.213266i | ||||
\(815\) | 1.15195e6 | 1.73428 | ||||||||
\(816\) | −321378. | − | 104422.i | −0.482655 | − | 0.156824i | ||||
\(817\) | −202010. | + | 146769.i | −0.302642 | + | 0.219882i | ||||
\(818\) | 492164. | + | 357578.i | 0.735535 | + | 0.534398i | ||||
\(819\) | −398562. | − | 1.22665e6i | −0.594194 | − | 1.82874i | ||||
\(820\) | −268387. | + | 87204.2i | −0.399148 | + | 0.129691i | ||||
\(821\) | 513481. | − | 706746.i | 0.761795 | − | 1.04852i | −0.235268 | − | 0.971931i | \(-0.575597\pi\) |
0.997063 | − | 0.0765900i | \(-0.0244033\pi\) | |||||||
\(822\) | −24915.0 | − | 34292.6i | −0.0368737 | − | 0.0507524i | ||||
\(823\) | −38380.5 | + | 118123.i | −0.0566645 | + | 0.174395i | −0.975383 | − | 0.220518i | \(-0.929225\pi\) |
0.918718 | + | 0.394913i | \(0.129225\pi\) | |||||||
\(824\) | 55214.2i | 0.0813198i | ||||||||
\(825\) | 159839. | + | 148388.i | 0.234841 | + | 0.218018i | ||||
\(826\) | 565405. | 0.828705 | ||||||||
\(827\) | −69119.1 | − | 22458.1i | −0.101062 | − | 0.0328370i | 0.258050 | − | 0.966132i | \(-0.416920\pi\) |
−0.359111 | + | 0.933295i | \(0.616920\pi\) | |||||||
\(828\) | −549062. | + | 398917.i | −0.800868 | + | 0.581865i | ||||
\(829\) | 295399. | + | 214620.i | 0.429834 | + | 0.312292i | 0.781582 | − | 0.623802i | \(-0.214413\pi\) |
−0.351749 | + | 0.936094i | \(0.614413\pi\) | |||||||
\(830\) | 54954.2 | + | 169132.i | 0.0797709 | + | 0.245510i | ||||
\(831\) | −749238. | + | 243442.i | −1.08497 | + | 0.352528i | ||||
\(832\) | −47142.4 | + | 64886.0i | −0.0681029 | + | 0.0937355i | ||||
\(833\) | 64764.3 | + | 89140.4i | 0.0933352 | + | 0.128465i | ||||
\(834\) | 496124. | − | 1.52691e6i | 0.713277 | − | 2.19524i | ||||
\(835\) | − | 387753.i | − | 0.556138i | ||||||
\(836\) | 93807.3 | + | 43489.1i | 0.134222 | + | 0.0622254i | ||||
\(837\) | 443249. | 0.632698 | ||||||||
\(838\) | 16687.2 | + | 5421.98i | 0.0237626 | + | 0.00772094i | ||||
\(839\) | 43362.3 | − | 31504.6i | 0.0616011 | − | 0.0447558i | −0.556559 | − | 0.830808i | \(-0.687879\pi\) |
0.618160 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(840\) | −365386. | − | 265468.i | −0.517837 | − | 0.376231i | ||||
\(841\) | 208874. | + | 642849.i | 0.295320 | + | 0.908901i | ||||
\(842\) | −645437. | + | 209715.i | −0.910394 | + | 0.295805i | ||||
\(843\) | −60800.5 | + | 83684.7i | −0.0855562 | + | 0.117758i | ||||
\(844\) | 306182. | + | 421423.i | 0.429828 | + | 0.591607i | ||||
\(845\) | 33729.8 | − | 103810.i | 0.0472390 | − | 0.145387i | ||||
\(846\) | − | 1.34868e6i | − | 1.88438i | ||||||
\(847\) | −663172. | + | 49341.4i | −0.924398 | + | 0.0687772i | ||||
\(848\) | 104360. | 0.145125 | ||||||||
\(849\) | −1.95690e6 | − | 635834.i | −2.71489 | − | 0.882121i | ||||
\(850\) | −83032.3 | + | 60326.5i | −0.114924 | + | 0.0834969i | ||||
\(851\) | 810014. | + | 588509.i | 1.11849 | + | 0.812633i | ||||
\(852\) | −172750. | − | 531670.i | −0.237979 | − | 0.732425i | ||||
\(853\) | 290734. | − | 94465.3i | 0.399575 | − | 0.129830i | −0.102334 | − | 0.994750i | \(-0.532631\pi\) |
0.501909 | + | 0.864920i | \(0.332631\pi\) | |||||||
\(854\) | −358731. | + | 493751.i | −0.491874 | + | 0.677006i | ||||
\(855\) | −308829. | − | 425067.i | −0.422461 | − | 0.581468i | ||||
\(856\) | 91622.1 | − | 281984.i | 0.125041 | − | 0.384837i | ||||
\(857\) | − | 344594.i | − | 0.469187i | −0.972094 | − | 0.234594i | \(-0.924624\pi\) | ||
0.972094 | − | 0.234594i | \(-0.0753759\pi\) | |||||||
\(858\) | 365175. | − | 787693.i | 0.496051 | − | 1.07000i | ||||
\(859\) | −267027. | −0.361884 | −0.180942 | − | 0.983494i | \(-0.557915\pi\) | ||||
−0.180942 | + | 0.983494i | \(0.557915\pi\) | |||||||
\(860\) | 482618. | + | 156812.i | 0.652539 | + | 0.212023i | ||||
\(861\) | −773619. | + | 562067.i | −1.04357 | + | 0.758197i | ||||
\(862\) | 387999. | + | 281898.i | 0.522175 | + | 0.379382i | ||||
\(863\) | 395026. | + | 1.21577e6i | 0.530401 | + | 1.63241i | 0.753382 | + | 0.657583i | \(0.228421\pi\) |
−0.222981 | + | 0.974823i | \(0.571579\pi\) | |||||||
\(864\) | −279576. | + | 90839.7i | −0.374518 | + | 0.121688i | ||||
\(865\) | −451412. | + | 621315.i | −0.603310 | + | 0.830385i | ||||
\(866\) | 341458. | + | 469977.i | 0.455305 | + | 0.626673i | ||||
\(867\) | −113963. | + | 350741.i | −0.151609 | + | 0.466604i | ||||
\(868\) | − | 99179.7i | − | 0.131639i | ||||||
\(869\) | 104578. | − | 112648.i | 0.138484 | − | 0.149170i | ||||
\(870\) | −220074. | −0.290757 | ||||||||
\(871\) | −176431. | − | 57326.0i | −0.232562 | − | 0.0755640i | ||||
\(872\) | 17104.9 | − | 12427.4i | 0.0224951 | − | 0.0163436i | ||||
\(873\) | −279078. | − | 202762.i | −0.366182 | − | 0.266047i | ||||
\(874\) | 43691.9 | + | 134470.i | 0.0571976 | + | 0.176036i | ||||
\(875\) | 602140. | − | 195647.i | 0.786469 | − | 0.255539i | ||||
\(876\) | −144052. | + | 198271.i | −0.187721 | + | 0.258375i | ||||
\(877\) | −72068.5 | − | 99193.8i | −0.0937014 | − | 0.128969i | 0.759592 | − | 0.650400i | \(-0.225399\pi\) |
−0.853294 | + | 0.521431i | \(0.825399\pi\) | |||||||
\(878\) | −135825. | + | 418026.i | −0.176194 | + | 0.542269i | ||||
\(879\) | − | 1.44203e6i | − | 1.86637i | ||||||
\(880\) | −40554.2 | − | 206182.i | −0.0523685 | − | 0.266247i | ||||
\(881\) | 870902. | 1.12206 | 0.561032 | − | 0.827794i | \(-0.310405\pi\) | ||||
0.561032 | + | 0.827794i | \(0.310405\pi\) | |||||||
\(882\) | 164798. | + | 53546.2i | 0.211843 | + | 0.0688321i | ||||
\(883\) | 625562. | − | 454497.i | 0.802322 | − | 0.582921i | −0.109272 | − | 0.994012i | \(-0.534852\pi\) |
0.911594 | + | 0.411091i | \(0.134852\pi\) | |||||||
\(884\) | 330540. | + | 240151.i | 0.422979 | + | 0.307312i | ||||
\(885\) | −597652. | − | 1.83938e6i | −0.763066 | − | 2.34848i | ||||
\(886\) | −393157. | + | 127744.i | −0.500839 | + | 0.162733i | ||||
\(887\) | −213314. | + | 293601.i | −0.271127 | + | 0.373174i | −0.922770 | − | 0.385352i | \(-0.874080\pi\) |
0.651643 | + | 0.758526i | \(0.274080\pi\) | |||||||
\(888\) | 460818. | + | 634261.i | 0.584391 | + | 0.804345i | ||||
\(889\) | 194401. | − | 598306.i | 0.245978 | − | 0.757042i | ||||
\(890\) | − | 1.06119e6i | − | 1.33972i | ||||||
\(891\) | 1.22781e6 | − | 684165.i | 1.54659 | − | 0.861798i | ||||
\(892\) | −150774. | −0.189495 | ||||||||
\(893\) | −267221. | − | 86825.2i | −0.335094 | − | 0.108879i | ||||
\(894\) | −389269. | + | 282820.i | −0.487051 | + | 0.353863i | ||||
\(895\) | −269152. | − | 195551.i | −0.336010 | − | 0.244126i | ||||
\(896\) | 20326.0 | + | 62556.9i | 0.0253183 | + | 0.0779218i | ||||
\(897\) | 1.12913e6 | − | 366877.i | 1.40333 | − | 0.455970i | ||||
\(898\) | −10109.8 | + | 13914.9i | −0.0125369 | + | 0.0172555i | ||||
\(899\) | −28406.4 | − | 39098.1i | −0.0351477 | − | 0.0483767i | ||||
\(900\) | −49877.1 | + | 153506.i | −0.0615767 | + | 0.189513i | ||||
\(901\) | − | 531628.i | − | 0.654875i | ||||||
\(902\) | −441709. | − | 53237.3i | −0.542904 | − | 0.0654339i | ||||
\(903\) | 1.71954e6 | 2.10880 | ||||||||
\(904\) | −148988. | − | 48409.2i | −0.182312 | − | 0.0592367i | ||||
\(905\) | 572021. | − | 415598.i | 0.698417 | − | 0.507430i | ||||
\(906\) | −824074. | − | 598725.i | −1.00395 | − | 0.729409i | ||||
\(907\) | −333162. | − | 1.02537e6i | −0.404986 | − | 1.24642i | −0.920907 | − | 0.389783i | \(-0.872550\pi\) |
0.515920 | − | 0.856637i | \(-0.327450\pi\) | |||||||
\(908\) | −458753. | + | 149058.i | −0.556426 | + | 0.180794i | ||||
\(909\) | −1.27772e6 | + | 1.75863e6i | −1.54635 | + | 2.12836i | ||||
\(910\) | 320973. | + | 441781.i | 0.387601 | + | 0.533487i | ||||
\(911\) | −173639. | + | 534405.i | −0.209223 | + | 0.643922i | 0.790290 | + | 0.612732i | \(0.209930\pi\) |
−0.999513 | + | 0.0311899i | \(0.990070\pi\) | |||||||
\(912\) | 110712.i | 0.133108i | ||||||||
\(913\) | −33549.0 | + | 278356.i | −0.0402474 | + | 0.333932i | ||||
\(914\) | −968051. | −1.15879 | ||||||||
\(915\) | 1.98547e6 | + | 645118.i | 2.37149 | + | 0.770543i | ||||
\(916\) | 535198. | − | 388844.i | 0.637857 | − | 0.463430i | ||||
\(917\) | −853633. | − | 620201.i | −1.01516 | − | 0.737554i | ||||
\(918\) | 462752. | + | 1.42420e6i | 0.549115 | + | 1.69000i | ||||
\(919\) | 293285. | − | 95294.1i | 0.347263 | − | 0.112833i | −0.130192 | − | 0.991489i | \(-0.541559\pi\) |
0.477455 | + | 0.878656i | \(0.341559\pi\) | |||||||
\(920\) | 168896. | − | 232465.i | 0.199546 | − | 0.274651i | ||||
\(921\) | −844924. | − | 1.16294e6i | −0.996090 | − | 1.37100i | ||||
\(922\) | −345156. | + | 1.06228e6i | −0.406026 | + | 1.24962i | ||||
\(923\) | 675914.i | 0.793392i | ||||||||
\(924\) | −346592. | − | 621998.i | −0.405951 | − | 0.728526i | ||||
\(925\) | 238116. | 0.278295 | ||||||||
\(926\) | 234810. | + | 76294.4i | 0.273838 | + | 0.0889755i | ||||
\(927\) | 357857. | − | 259999.i | 0.416438 | − | 0.302560i | ||||
\(928\) | 25930.0 | + | 18839.2i | 0.0301097 | + | 0.0218759i | ||||
\(929\) | −126116. | − | 388145.i | −0.146130 | − | 0.449742i | 0.851025 | − | 0.525126i | \(-0.175982\pi\) |
−0.997155 | + | 0.0753841i | \(0.975982\pi\) | |||||||
\(930\) | −322653. | + | 104836.i | −0.373052 | + | 0.121212i | ||||
\(931\) | 21218.7 | − | 29205.1i | 0.0244805 | − | 0.0336945i | ||||
\(932\) | −190819. | − | 262639.i | −0.219679 | − | 0.302363i | ||||
\(933\) | −645274. | + | 1.98595e6i | −0.741278 | + | 2.28142i | ||||
\(934\) | 295446.i | 0.338676i | ||||||||
\(935\) | −1.05032e6 | + | 206589.i | −1.20143 | + | 0.236311i | ||||
\(936\) | 642532. | 0.733404 | ||||||||
\(937\) | −1.04830e6 | − | 340614.i | −1.19401 | − | 0.387957i | −0.356455 | − | 0.934313i | \(-0.616015\pi\) |
−0.837553 | + | 0.546356i | \(0.816015\pi\) | |||||||
\(938\) | −123084. | + | 89425.9i | −0.139893 | + | 0.101638i | ||||
\(939\) | 1.23086e6 | + | 894270.i | 1.39597 | + | 1.01423i | ||||
\(940\) | 176452. | + | 543064.i | 0.199697 | + | 0.614604i | ||||
\(941\) | 1.46503e6 | − | 476017.i | 1.65450 | − | 0.537580i | 0.674793 | − | 0.738007i | \(-0.264233\pi\) |
0.979709 | + | 0.200426i | \(0.0642327\pi\) | |||||||
\(942\) | −197224. | + | 271455.i | −0.222258 | + | 0.305912i | ||||
\(943\) | −357597. | − | 492190.i | −0.402134 | − | 0.553489i | ||||
\(944\) | −87040.9 | + | 267884.i | −0.0976741 | + | 0.300610i | ||||
\(945\) | 2.00147e6i | 2.24123i | ||||||||
\(946\) | 586323. | + | 544320.i | 0.655171 | + | 0.608236i | ||||
\(947\) | −1.56708e6 | −1.74739 | −0.873697 | − | 0.486470i | \(-0.838284\pi\) | ||||
−0.873697 | + | 0.486470i | \(0.838284\pi\) | |||||||
\(948\) | 156525. | + | 50858.1i | 0.174168 | + | 0.0565905i | ||||
\(949\) | 239726. | − | 174171.i | 0.266184 | − | 0.193394i | ||||
\(950\) | 27203.9 | + | 19764.8i | 0.0301428 | + | 0.0219000i | ||||
\(951\) | 18818.8 | + | 57918.2i | 0.0208080 | + | 0.0640404i | ||||
\(952\) | 318675. | − | 103544.i | 0.351620 | − | 0.114248i | ||||
\(953\) | 25772.9 | − | 35473.3i | 0.0283777 | − | 0.0390585i | −0.794592 | − | 0.607143i | \(-0.792315\pi\) |
0.822970 | + | 0.568085i | \(0.192315\pi\) | |||||||
\(954\) | −491423. | − | 676386.i | −0.539957 | − | 0.743187i | ||||
\(955\) | −99760.2 | + | 307030.i | −0.109383 | + | 0.336647i | ||||
\(956\) | − | 618335.i | − | 0.676563i | ||||||
\(957\) | −314780. | − | 145932.i | −0.343703 | − | 0.159341i | ||||
\(958\) | −79072.3 | −0.0861576 | ||||||||
\(959\) | 39974.2 | + | 12988.4i | 0.0434653 | + | 0.0141227i | ||||
\(960\) | 182026. | − | 132249.i | 0.197511 | − | 0.143500i | ||||
\(961\) | 686872. | + | 499042.i | 0.743754 | + | 0.540369i | ||||
\(962\) | −292919. | − | 901513.i | −0.316518 | − | 0.974141i | ||||
\(963\) | −2.25905e6 | + | 734010.i | −2.43598 | + | 0.791497i | ||||
\(964\) | −381945. | + | 525702.i | −0.411005 | + | 0.565699i | ||||
\(965\) | −296838. | − | 408563.i | −0.318761 | − | 0.438737i | ||||
\(966\) | 300882. | − | 926020.i | 0.322435 | − | 0.992353i | ||||
\(967\) | − | 1.00897e6i | − | 1.07901i | −0.841982 | − | 0.539506i | \(-0.818611\pi\) | ||
0.841982 | − | 0.539506i | \(-0.181389\pi\) | |||||||
\(968\) | 78713.9 | − | 321801.i | 0.0840042 | − | 0.343429i | ||||
\(969\) | 563984. | 0.600647 | ||||||||
\(970\) | 138902. | + | 45132.1i | 0.147627 | + | 0.0479670i | ||||
\(971\) | −265599. | + | 192969.i | −0.281700 | + | 0.204667i | −0.719659 | − | 0.694328i | \(-0.755702\pi\) |
0.437958 | + | 0.898995i | \(0.355702\pi\) | |||||||
\(972\) | 366223. | + | 266077.i | 0.387626 | + | 0.281627i | ||||
\(973\) | 491950. | + | 1.51407e6i | 0.519631 | + | 1.59926i | ||||
\(974\) | 756407. | − | 245772.i | 0.797329 | − | 0.259068i | ||||
\(975\) | 165963. | − | 228429.i | 0.174583 | − | 0.240293i | ||||
\(976\) | −178711. | − | 245974.i | −0.187608 | − | 0.258220i | ||||
\(977\) | 312850. | − | 962853.i | 0.327753 | − | 1.00872i | −0.642429 | − | 0.766345i | \(-0.722073\pi\) |
0.970182 | − | 0.242376i | \(-0.0779266\pi\) | |||||||
\(978\) | 1.94460e6i | 2.03307i | ||||||||
\(979\) | 703680. | − | 1.51786e6i | 0.734192 | − | 1.58368i | ||||
\(980\) | −73363.7 | −0.0763887 | ||||||||
\(981\) | −161091. | − | 52341.6i | −0.167391 | − | 0.0543887i | ||||
\(982\) | 841678. | − | 611515.i | 0.872817 | − | 0.634139i | ||||
\(983\) | −842719. | − | 612271.i | −0.872119 | − | 0.633632i | 0.0590354 | − | 0.998256i | \(-0.481198\pi\) |
−0.931155 | + | 0.364624i | \(0.881198\pi\) | |||||||
\(984\) | −147209. | − | 453061.i | −0.152035 | − | 0.467915i | ||||
\(985\) | −1.31777e6 | + | 428171.i | −1.35821 | + | 0.441311i | ||||
\(986\) | 95970.0 | − | 132091.i | 0.0987146 | − | 0.135869i | ||||
\(987\) | 1.13731e6 | + | 1.56537e6i | 1.16746 | + | 1.60688i | ||||
\(988\) | 41364.9 | − | 127308.i | 0.0423758 | − | 0.130419i | ||||
\(989\) | 1.09400e6i | 1.11847i | ||||||||
\(990\) | −1.14535e6 | + | 1.23373e6i | −1.16861 | + | 1.25878i | ||||
\(991\) | −1.89936e6 | −1.93401 | −0.967006 | − | 0.254755i | \(-0.918005\pi\) | ||||
−0.967006 | + | 0.254755i | \(0.918005\pi\) | |||||||
\(992\) | 46990.5 | + | 15268.1i | 0.0477515 | + | 0.0155154i | ||||
\(993\) | 1.29382e6 | − | 940014.i | 1.31212 | − | 0.953314i | ||||
\(994\) | 448461. | + | 325826.i | 0.453891 | + | 0.329771i | ||||
\(995\) | −275150. | − | 846824.i | −0.277922 | − | 0.855356i | ||||
\(996\) | −285510. | + | 92767.7i | −0.287807 | + | 0.0935143i | ||||
\(997\) | 353820. | − | 486992.i | 0.355953 | − | 0.489927i | −0.593063 | − | 0.805156i | \(-0.702081\pi\) |
0.949016 | + | 0.315229i | \(0.102081\pi\) | |||||||
\(998\) | −245240. | − | 337544.i | −0.246224 | − | 0.338898i | ||||
\(999\) | 1.07361e6 | − | 3.30425e6i | 1.07576 | − | 3.31086i |
(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 | 22.5.d.a.13.3 | ✓ | 16 | |
3.2 | odd | 2 | 198.5.j.a.145.1 | 16 | |||
4.3 | odd | 2 | 176.5.n.c.145.4 | 16 | |||
11.4 | even | 5 | 242.5.b.e.241.16 | 16 | |||
11.6 | odd | 10 | inner | 22.5.d.a.17.3 | yes | 16 | |
11.7 | odd | 10 | 242.5.b.e.241.8 | 16 | |||
33.17 | even | 10 | 198.5.j.a.127.1 | 16 | |||
44.39 | even | 10 | 176.5.n.c.17.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.5.d.a.13.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
22.5.d.a.17.3 | yes | 16 | 11.6 | odd | 10 | inner | |
176.5.n.c.17.4 | 16 | 44.39 | even | 10 | |||
176.5.n.c.145.4 | 16 | 4.3 | odd | 2 | |||
198.5.j.a.127.1 | 16 | 33.17 | even | 10 | |||
198.5.j.a.145.1 | 16 | 3.2 | odd | 2 | |||
242.5.b.e.241.8 | 16 | 11.7 | odd | 10 | |||
242.5.b.e.241.16 | 16 | 11.4 | even | 5 |