Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(22,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.22");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.f (of order \(3\), 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: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + 599392 x^{8} - 1089732 x^{7} + 4808401 x^{6} - 7939134 x^{5} + \cdots + 21307456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 43.4 | ||
Root | \(0.797492 - 1.38130i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.43 |
Dual form | 63.4.f.b.22.4 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.797492 | + | 1.38130i | −0.281956 | + | 0.488362i | −0.971866 | − | 0.235532i | \(-0.924317\pi\) |
0.689910 | + | 0.723895i | \(0.257650\pi\) | |||||||
\(3\) | 5.17737 | + | 0.441383i | 0.996386 | + | 0.0849442i | ||||
\(4\) | 2.72801 | + | 4.72505i | 0.341001 | + | 0.590632i | ||||
\(5\) | 1.27816 | + | 2.21384i | 0.114322 | + | 0.198012i | 0.917509 | − | 0.397716i | \(-0.130197\pi\) |
−0.803186 | + | 0.595728i | \(0.796864\pi\) | |||||||
\(6\) | −4.73860 | + | 6.79949i | −0.322421 | + | 0.462647i | ||||
\(7\) | 3.50000 | − | 6.06218i | 0.188982 | − | 0.327327i | ||||
\(8\) | −21.4622 | −0.948502 | ||||||||
\(9\) | 26.6104 | + | 4.57041i | 0.985569 | + | 0.169274i | ||||
\(10\) | −4.07730 | −0.128935 | ||||||||
\(11\) | −4.04539 | + | 7.00681i | −0.110885 | + | 0.192058i | −0.916127 | − | 0.400888i | \(-0.868702\pi\) |
0.805243 | + | 0.592945i | \(0.202035\pi\) | |||||||
\(12\) | 12.0384 | + | 25.6675i | 0.289598 | + | 0.617463i | ||||
\(13\) | 13.1187 | + | 22.7222i | 0.279882 | + | 0.484769i | 0.971355 | − | 0.237633i | \(-0.0763714\pi\) |
−0.691473 | + | 0.722402i | \(0.743038\pi\) | |||||||
\(14\) | 5.58245 | + | 9.66908i | 0.106569 | + | 0.184584i | ||||
\(15\) | 5.64037 | + | 12.0260i | 0.0970891 | + | 0.207007i | ||||
\(16\) | −4.70819 | + | 8.15482i | −0.0735654 | + | 0.127419i | ||||
\(17\) | −69.7407 | −0.994977 | −0.497489 | − | 0.867471i | \(-0.665744\pi\) | ||||
−0.497489 | + | 0.867471i | \(0.665744\pi\) | |||||||
\(18\) | −27.5347 | + | 33.1120i | −0.360554 | + | 0.433587i | ||||
\(19\) | 105.751 | 1.27689 | 0.638445 | − | 0.769667i | \(-0.279578\pi\) | ||||
0.638445 | + | 0.769667i | \(0.279578\pi\) | |||||||
\(20\) | −6.97368 | + | 12.0788i | −0.0779681 | + | 0.135045i | ||||
\(21\) | 20.7965 | − | 29.8413i | 0.216104 | − | 0.310091i | ||||
\(22\) | −6.45233 | − | 11.1758i | −0.0625291 | − | 0.108304i | ||||
\(23\) | −77.1585 | − | 133.642i | −0.699507 | − | 1.21158i | −0.968638 | − | 0.248477i | \(-0.920070\pi\) |
0.269131 | − | 0.963104i | \(-0.413263\pi\) | |||||||
\(24\) | −111.118 | − | 9.47303i | −0.945074 | − | 0.0805697i | ||||
\(25\) | 59.2326 | − | 102.594i | 0.473861 | − | 0.820751i | ||||
\(26\) | −41.8481 | −0.315657 | ||||||||
\(27\) | 135.754 | + | 35.4080i | 0.967628 | + | 0.252381i | ||||
\(28\) | 38.1922 | 0.257773 | ||||||||
\(29\) | 36.3274 | − | 62.9209i | 0.232615 | − | 0.402900i | −0.725962 | − | 0.687735i | \(-0.758605\pi\) |
0.958577 | + | 0.284834i | \(0.0919386\pi\) | |||||||
\(30\) | −21.1097 | − | 1.79965i | −0.128469 | − | 0.0109523i | ||||
\(31\) | −141.400 | − | 244.911i | −0.819230 | − | 1.41895i | −0.906251 | − | 0.422741i | \(-0.861068\pi\) |
0.0870211 | − | 0.996206i | \(-0.472265\pi\) | |||||||
\(32\) | −93.3581 | − | 161.701i | −0.515736 | − | 0.893280i | ||||
\(33\) | −24.0372 | + | 34.4913i | −0.126798 | + | 0.181944i | ||||
\(34\) | 55.6177 | − | 96.3327i | 0.280540 | − | 0.485909i | ||||
\(35\) | 17.8943 | 0.0864195 | ||||||||
\(36\) | 50.9980 | + | 138.204i | 0.236102 | + | 0.639831i | ||||
\(37\) | 25.7974 | 0.114623 | 0.0573117 | − | 0.998356i | \(-0.481747\pi\) | ||||
0.0573117 | + | 0.998356i | \(0.481747\pi\) | |||||||
\(38\) | −84.3355 | + | 146.073i | −0.360027 | + | 0.623585i | ||||
\(39\) | 57.8910 | + | 123.432i | 0.237692 | + | 0.506791i | ||||
\(40\) | −27.4321 | − | 47.5138i | −0.108435 | − | 0.187815i | ||||
\(41\) | 43.5544 | + | 75.4385i | 0.165904 | + | 0.287354i | 0.936976 | − | 0.349394i | \(-0.113613\pi\) |
−0.771072 | + | 0.636748i | \(0.780279\pi\) | |||||||
\(42\) | 24.6346 | + | 52.5244i | 0.0905049 | + | 0.192969i | ||||
\(43\) | −44.5553 | + | 77.1721i | −0.158014 | + | 0.273689i | −0.934153 | − | 0.356874i | \(-0.883843\pi\) |
0.776138 | + | 0.630563i | \(0.217176\pi\) | |||||||
\(44\) | −44.1434 | −0.151247 | ||||||||
\(45\) | 23.8942 | + | 64.7528i | 0.0791541 | + | 0.214506i | ||||
\(46\) | 246.133 | 0.788921 | ||||||||
\(47\) | −157.309 | + | 272.467i | −0.488209 | + | 0.845603i | −0.999908 | − | 0.0135621i | \(-0.995683\pi\) |
0.511699 | + | 0.859165i | \(0.329016\pi\) | |||||||
\(48\) | −27.9754 | + | 40.1424i | −0.0841231 | + | 0.120710i | ||||
\(49\) | −24.5000 | − | 42.4352i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 94.4751 | + | 163.636i | 0.267216 | + | 0.462832i | ||||
\(51\) | −361.074 | − | 30.7824i | −0.991381 | − | 0.0845175i | ||||
\(52\) | −71.5757 | + | 123.973i | −0.190880 | + | 0.330614i | ||||
\(53\) | 356.536 | 0.924038 | 0.462019 | − | 0.886870i | \(-0.347125\pi\) | ||||
0.462019 | + | 0.886870i | \(0.347125\pi\) | |||||||
\(54\) | −157.172 | + | 159.280i | −0.396082 | + | 0.401393i | ||||
\(55\) | −20.6826 | −0.0507063 | ||||||||
\(56\) | −75.1175 | + | 130.107i | −0.179250 | + | 0.310470i | ||||
\(57\) | 547.512 | + | 46.6766i | 1.27228 | + | 0.108464i | ||||
\(58\) | 57.9416 | + | 100.358i | 0.131174 | + | 0.227200i | ||||
\(59\) | −206.245 | − | 357.226i | −0.455098 | − | 0.788252i | 0.543596 | − | 0.839347i | \(-0.317062\pi\) |
−0.998694 | + | 0.0510946i | \(0.983729\pi\) | |||||||
\(60\) | −41.4367 | + | 59.4582i | −0.0891576 | + | 0.127934i | ||||
\(61\) | −73.3780 | + | 127.094i | −0.154018 | + | 0.266767i | −0.932701 | − | 0.360651i | \(-0.882555\pi\) |
0.778683 | + | 0.627417i | \(0.215888\pi\) | |||||||
\(62\) | 451.060 | 0.923947 | ||||||||
\(63\) | 120.843 | − | 145.320i | 0.241663 | − | 0.290613i | ||||
\(64\) | 222.479 | 0.434528 | ||||||||
\(65\) | −33.5355 | + | 58.0852i | −0.0639934 | + | 0.110840i | ||||
\(66\) | −28.4733 | − | 60.7090i | −0.0531034 | − | 0.113224i | ||||
\(67\) | 153.201 | + | 265.352i | 0.279350 | + | 0.483849i | 0.971223 | − | 0.238170i | \(-0.0765476\pi\) |
−0.691873 | + | 0.722019i | \(0.743214\pi\) | |||||||
\(68\) | −190.254 | − | 329.529i | −0.339289 | − | 0.587665i | ||||
\(69\) | −340.491 | − | 725.973i | −0.594062 | − | 1.26662i | ||||
\(70\) | −14.2705 | + | 24.7173i | −0.0243665 | + | 0.0422040i | ||||
\(71\) | 1038.77 | 1.73632 | 0.868160 | − | 0.496284i | \(-0.165302\pi\) | ||||
0.868160 | + | 0.496284i | \(0.165302\pi\) | |||||||
\(72\) | −571.116 | − | 98.0908i | −0.934814 | − | 0.160557i | ||||
\(73\) | −1157.10 | −1.85518 | −0.927590 | − | 0.373600i | \(-0.878123\pi\) | ||||
−0.927590 | + | 0.373600i | \(0.878123\pi\) | |||||||
\(74\) | −20.5732 | + | 35.6339i | −0.0323188 | + | 0.0559777i | ||||
\(75\) | 351.952 | − | 505.022i | 0.541866 | − | 0.777533i | ||||
\(76\) | 288.490 | + | 499.679i | 0.435421 | + | 0.754172i | ||||
\(77\) | 28.3177 | + | 49.0477i | 0.0419104 | + | 0.0725910i | ||||
\(78\) | −216.663 | − | 18.4710i | −0.314516 | − | 0.0268133i | ||||
\(79\) | −373.147 | + | 646.309i | −0.531421 | + | 0.920449i | 0.467906 | + | 0.883778i | \(0.345009\pi\) |
−0.999327 | + | 0.0366706i | \(0.988325\pi\) | |||||||
\(80\) | −24.0713 | −0.0336407 | ||||||||
\(81\) | 687.223 | + | 243.240i | 0.942692 | + | 0.333663i | ||||
\(82\) | −138.937 | −0.187111 | ||||||||
\(83\) | −262.712 | + | 455.031i | −0.347427 | + | 0.601761i | −0.985792 | − | 0.167973i | \(-0.946278\pi\) |
0.638365 | + | 0.769734i | \(0.279611\pi\) | |||||||
\(84\) | 197.735 | + | 16.8574i | 0.256841 | + | 0.0218963i | ||||
\(85\) | −89.1399 | − | 154.395i | −0.113748 | − | 0.197017i | ||||
\(86\) | −71.0651 | − | 123.088i | −0.0891063 | − | 0.154337i | ||||
\(87\) | 215.852 | − | 309.730i | 0.265998 | − | 0.381685i | ||||
\(88\) | 86.8227 | − | 150.381i | 0.105174 | − | 0.182167i | ||||
\(89\) | −643.894 | −0.766883 | −0.383441 | − | 0.923565i | \(-0.625261\pi\) | ||||
−0.383441 | + | 0.923565i | \(0.625261\pi\) | |||||||
\(90\) | −108.498 | − | 18.6349i | −0.127075 | − | 0.0218255i | ||||
\(91\) | 183.661 | 0.211571 | ||||||||
\(92\) | 420.978 | − | 729.156i | 0.477066 | − | 0.826302i | ||||
\(93\) | −623.979 | − | 1330.41i | −0.695737 | − | 1.48341i | ||||
\(94\) | −250.905 | − | 434.580i | −0.275307 | − | 0.476846i | ||||
\(95\) | 135.167 | + | 234.116i | 0.145977 | + | 0.252839i | ||||
\(96\) | −411.978 | − | 878.393i | −0.437993 | − | 0.933860i | ||||
\(97\) | −154.581 | + | 267.742i | −0.161808 | + | 0.280259i | −0.935517 | − | 0.353282i | \(-0.885066\pi\) |
0.773709 | + | 0.633541i | \(0.218399\pi\) | |||||||
\(98\) | 78.1543 | 0.0805589 | ||||||||
\(99\) | −139.673 | + | 167.965i | −0.141795 | + | 0.170516i | ||||
\(100\) | 646.349 | 0.646349 | ||||||||
\(101\) | −560.283 | + | 970.439i | −0.551983 | + | 0.956062i | 0.446149 | + | 0.894959i | \(0.352795\pi\) |
−0.998131 | + | 0.0611033i | \(0.980538\pi\) | |||||||
\(102\) | 330.473 | − | 474.201i | 0.320801 | − | 0.460323i | ||||
\(103\) | −282.613 | − | 489.500i | −0.270356 | − | 0.468271i | 0.698597 | − | 0.715516i | \(-0.253808\pi\) |
−0.968953 | + | 0.247245i | \(0.920475\pi\) | |||||||
\(104\) | −281.555 | − | 487.667i | −0.265468 | − | 0.459805i | ||||
\(105\) | 92.6452 | + | 7.89822i | 0.0861071 | + | 0.00734083i | ||||
\(106\) | −284.335 | + | 492.483i | −0.260538 | + | 0.451266i | ||||
\(107\) | 1593.24 | 1.43948 | 0.719738 | − | 0.694246i | \(-0.244262\pi\) | ||||
0.719738 | + | 0.694246i | \(0.244262\pi\) | |||||||
\(108\) | 203.035 | + | 738.041i | 0.180898 | + | 0.657574i | ||||
\(109\) | −1498.64 | −1.31691 | −0.658457 | − | 0.752619i | \(-0.728790\pi\) | ||||
−0.658457 | + | 0.752619i | \(0.728790\pi\) | |||||||
\(110\) | 16.4942 | − | 28.5689i | 0.0142969 | − | 0.0247630i | ||||
\(111\) | 133.563 | + | 11.3865i | 0.114209 | + | 0.00973658i | ||||
\(112\) | 32.9573 | + | 57.0838i | 0.0278051 | + | 0.0481599i | ||||
\(113\) | −347.639 | − | 602.129i | −0.289408 | − | 0.501270i | 0.684260 | − | 0.729238i | \(-0.260125\pi\) |
−0.973669 | + | 0.227968i | \(0.926792\pi\) | |||||||
\(114\) | −501.111 | + | 719.052i | −0.411696 | + | 0.590749i | ||||
\(115\) | 197.242 | − | 341.633i | 0.159938 | − | 0.277021i | ||||
\(116\) | 396.406 | 0.317288 | ||||||||
\(117\) | 245.243 | + | 664.603i | 0.193784 | + | 0.525150i | ||||
\(118\) | 657.914 | 0.513270 | ||||||||
\(119\) | −244.093 | + | 422.781i | −0.188033 | + | 0.325683i | ||||
\(120\) | −121.054 | − | 258.105i | −0.0920892 | − | 0.196347i | ||||
\(121\) | 632.770 | + | 1095.99i | 0.475409 | + | 0.823433i | ||||
\(122\) | −117.037 | − | 202.714i | −0.0868526 | − | 0.150433i | ||||
\(123\) | 192.200 | + | 409.797i | 0.140895 | + | 0.300408i | ||||
\(124\) | 771.479 | − | 1336.24i | 0.558717 | − | 0.967726i | ||||
\(125\) | 622.376 | 0.445336 | ||||||||
\(126\) | 104.359 | + | 282.812i | 0.0737862 | + | 0.199959i | ||||
\(127\) | −1377.51 | −0.962475 | −0.481237 | − | 0.876590i | \(-0.659812\pi\) | ||||
−0.481237 | + | 0.876590i | \(0.659812\pi\) | |||||||
\(128\) | 569.440 | − | 986.299i | 0.393218 | − | 0.681073i | ||||
\(129\) | −264.742 | + | 379.883i | −0.180692 | + | 0.259278i | ||||
\(130\) | −53.4887 | − | 92.6451i | −0.0360867 | − | 0.0625039i | ||||
\(131\) | 1361.14 | + | 2357.56i | 0.907809 | + | 1.57237i | 0.817102 | + | 0.576493i | \(0.195579\pi\) |
0.0907071 | + | 0.995878i | \(0.471087\pi\) | |||||||
\(132\) | −228.547 | − | 19.4842i | −0.150700 | − | 0.0128476i | ||||
\(133\) | 370.128 | − | 641.081i | 0.241310 | − | 0.417960i | ||||
\(134\) | −488.706 | −0.315058 | ||||||||
\(135\) | 95.1283 | + | 345.796i | 0.0606470 | + | 0.220455i | ||||
\(136\) | 1496.79 | 0.943738 | ||||||||
\(137\) | −1176.31 | + | 2037.43i | −0.733570 | + | 1.27058i | 0.221777 | + | 0.975097i | \(0.428814\pi\) |
−0.955348 | + | 0.295484i | \(0.904519\pi\) | |||||||
\(138\) | 1274.32 | + | 108.639i | 0.786069 | + | 0.0670142i | ||||
\(139\) | 1024.35 | + | 1774.22i | 0.625065 | + | 1.08264i | 0.988528 | + | 0.151036i | \(0.0482608\pi\) |
−0.363464 | + | 0.931608i | \(0.618406\pi\) | |||||||
\(140\) | 48.8157 | + | 84.5514i | 0.0294692 | + | 0.0510421i | ||||
\(141\) | −934.707 | + | 1341.23i | −0.558273 | + | 0.801076i | ||||
\(142\) | −828.408 | + | 1434.84i | −0.489566 | + | 0.847954i | ||||
\(143\) | −212.280 | −0.124138 | ||||||||
\(144\) | −162.557 | + | 195.484i | −0.0940726 | + | 0.113128i | ||||
\(145\) | 185.729 | 0.106372 | ||||||||
\(146\) | 922.777 | − | 1598.30i | 0.523079 | − | 0.906000i | ||||
\(147\) | −108.115 | − | 230.517i | −0.0606613 | − | 0.129338i | ||||
\(148\) | 70.3756 | + | 121.894i | 0.0390867 | + | 0.0677002i | ||||
\(149\) | −646.993 | − | 1120.63i | −0.355730 | − | 0.616142i | 0.631513 | − | 0.775366i | \(-0.282434\pi\) |
−0.987243 | + | 0.159223i | \(0.949101\pi\) | |||||||
\(150\) | 416.907 | + | 888.903i | 0.226935 | + | 0.483857i | ||||
\(151\) | 1070.84 | − | 1854.76i | 0.577113 | − | 0.999589i | −0.418695 | − | 0.908127i | \(-0.637512\pi\) |
0.995809 | − | 0.0914626i | \(-0.0291542\pi\) | |||||||
\(152\) | −2269.64 | −1.21113 | ||||||||
\(153\) | −1855.83 | − | 318.743i | −0.980619 | − | 0.168424i | ||||
\(154\) | −90.3326 | −0.0472676 | ||||||||
\(155\) | 361.463 | − | 626.072i | 0.187312 | − | 0.324434i | ||||
\(156\) | −425.293 | + | 610.261i | −0.218274 | + | 0.313205i | ||||
\(157\) | −1294.10 | − | 2241.44i | −0.657835 | − | 1.13940i | −0.981175 | − | 0.193121i | \(-0.938139\pi\) |
0.323340 | − | 0.946283i | \(-0.395194\pi\) | |||||||
\(158\) | −595.163 | − | 1030.85i | −0.299675 | − | 0.519052i | ||||
\(159\) | 1845.92 | + | 157.369i | 0.920699 | + | 0.0784917i | ||||
\(160\) | 238.653 | − | 413.360i | 0.117920 | − | 0.204244i | ||||
\(161\) | −1080.22 | −0.528777 | ||||||||
\(162\) | −884.042 | + | 755.277i | −0.428746 | + | 0.366297i | ||||
\(163\) | 842.940 | 0.405056 | 0.202528 | − | 0.979276i | \(-0.435084\pi\) | ||||
0.202528 | + | 0.979276i | \(0.435084\pi\) | |||||||
\(164\) | −237.634 | + | 411.594i | −0.113147 | + | 0.195976i | ||||
\(165\) | −107.082 | − | 9.12895i | −0.0505230 | − | 0.00430720i | ||||
\(166\) | −419.022 | − | 725.767i | −0.195918 | − | 0.339340i | ||||
\(167\) | −828.694 | − | 1435.34i | −0.383990 | − | 0.665089i | 0.607639 | − | 0.794213i | \(-0.292117\pi\) |
−0.991628 | + | 0.129124i | \(0.958783\pi\) | |||||||
\(168\) | −446.339 | + | 640.459i | −0.204975 | + | 0.294122i | ||||
\(169\) | 754.302 | − | 1306.49i | 0.343333 | − | 0.594669i | ||||
\(170\) | 284.354 | 0.128288 | ||||||||
\(171\) | 2814.07 | + | 483.324i | 1.25846 | + | 0.216145i | ||||
\(172\) | −486.190 | −0.215533 | ||||||||
\(173\) | −973.548 | + | 1686.23i | −0.427847 | + | 0.741052i | −0.996682 | − | 0.0813995i | \(-0.974061\pi\) |
0.568835 | + | 0.822452i | \(0.307394\pi\) | |||||||
\(174\) | 255.689 | + | 545.164i | 0.111401 | + | 0.237522i | ||||
\(175\) | −414.628 | − | 718.157i | −0.179103 | − | 0.310215i | ||||
\(176\) | −38.0929 | − | 65.9788i | −0.0163145 | − | 0.0282576i | ||||
\(177\) | −910.132 | − | 1940.53i | −0.386495 | − | 0.824061i | ||||
\(178\) | 513.500 | − | 889.409i | 0.216227 | − | 0.374517i | ||||
\(179\) | −841.904 | −0.351547 | −0.175773 | − | 0.984431i | \(-0.556243\pi\) | ||||
−0.175773 | + | 0.984431i | \(0.556243\pi\) | |||||||
\(180\) | −240.777 | + | 289.548i | −0.0997025 | + | 0.119898i | ||||
\(181\) | 158.260 | 0.0649912 | 0.0324956 | − | 0.999472i | \(-0.489655\pi\) | ||||
0.0324956 | + | 0.999472i | \(0.489655\pi\) | |||||||
\(182\) | −146.468 | + | 253.691i | −0.0596536 | + | 0.103323i | ||||
\(183\) | −436.003 | + | 625.628i | −0.176122 | + | 0.252720i | ||||
\(184\) | 1655.99 | + | 2868.25i | 0.663483 | + | 1.14919i | ||||
\(185\) | 32.9732 | + | 57.1113i | 0.0131040 | + | 0.0226968i | ||||
\(186\) | 2335.31 | + | 199.090i | 0.920608 | + | 0.0784839i | ||||
\(187\) | 282.128 | − | 488.660i | 0.110328 | − | 0.191093i | ||||
\(188\) | −1716.56 | −0.665920 | ||||||||
\(189\) | 689.790 | − | 699.039i | 0.265476 | − | 0.269035i | ||||
\(190\) | −431.178 | −0.164636 | ||||||||
\(191\) | 2309.48 | − | 4000.14i | 0.874912 | − | 1.51539i | 0.0180552 | − | 0.999837i | \(-0.494253\pi\) |
0.856857 | − | 0.515555i | \(-0.172414\pi\) | |||||||
\(192\) | 1151.85 | + | 98.1982i | 0.432958 | + | 0.0369106i | ||||
\(193\) | −2295.48 | − | 3975.89i | −0.856126 | − | 1.48285i | −0.875596 | − | 0.483044i | \(-0.839531\pi\) |
0.0194700 | − | 0.999810i | \(-0.493802\pi\) | |||||||
\(194\) | −246.555 | − | 427.045i | −0.0912453 | − | 0.158041i | ||||
\(195\) | −199.264 | + | 285.927i | −0.0731773 | + | 0.105003i | ||||
\(196\) | 133.673 | − | 231.528i | 0.0487145 | − | 0.0843760i | ||||
\(197\) | −2646.03 | −0.956965 | −0.478482 | − | 0.878097i | \(-0.658813\pi\) | ||||
−0.478482 | + | 0.878097i | \(0.658813\pi\) | |||||||
\(198\) | −120.621 | − | 326.881i | −0.0432938 | − | 0.117325i | ||||
\(199\) | 4741.58 | 1.68905 | 0.844527 | − | 0.535513i | \(-0.179882\pi\) | ||||
0.844527 | + | 0.535513i | \(0.179882\pi\) | |||||||
\(200\) | −1271.26 | + | 2201.89i | −0.449458 | + | 0.778484i | ||||
\(201\) | 676.056 | + | 1441.45i | 0.237241 | + | 0.505829i | ||||
\(202\) | −893.643 | − | 1547.84i | −0.311270 | − | 0.539135i | ||||
\(203\) | −254.292 | − | 440.446i | −0.0879201 | − | 0.152282i | ||||
\(204\) | −839.565 | − | 1790.07i | −0.288144 | − | 0.614362i | ||||
\(205\) | −111.339 | + | 192.845i | −0.0379330 | + | 0.0657019i | ||||
\(206\) | 901.527 | 0.304915 | ||||||||
\(207\) | −1442.41 | − | 3908.92i | −0.484322 | − | 1.31251i | ||||
\(208\) | −247.060 | −0.0823585 | ||||||||
\(209\) | −427.803 | + | 740.977i | −0.141587 | + | 0.245236i | ||||
\(210\) | −84.7937 | + | 121.672i | −0.0278634 | + | 0.0399817i | ||||
\(211\) | 2290.39 | + | 3967.08i | 0.747285 | + | 1.29434i | 0.949119 | + | 0.314916i | \(0.101977\pi\) |
−0.201834 | + | 0.979420i | \(0.564690\pi\) | |||||||
\(212\) | 972.635 | + | 1684.65i | 0.315098 | + | 0.545766i | ||||
\(213\) | 5378.07 | + | 458.493i | 1.73005 | + | 0.147490i | ||||
\(214\) | −1270.59 | + | 2200.73i | −0.405869 | + | 0.702986i | ||||
\(215\) | −227.796 | −0.0722583 | ||||||||
\(216\) | −2913.58 | − | 759.933i | −0.917797 | − | 0.239384i | ||||
\(217\) | −1979.59 | −0.619279 | ||||||||
\(218\) | 1195.15 | − | 2070.07i | 0.371312 | − | 0.643131i | ||||
\(219\) | −5990.73 | − | 510.723i | −1.84847 | − | 0.157587i | ||||
\(220\) | −56.4224 | − | 97.7265i | −0.0172909 | − | 0.0299487i | ||||
\(221\) | −914.905 | − | 1584.66i | −0.278476 | − | 0.482334i | ||||
\(222\) | −122.243 | + | 175.409i | −0.0369569 | + | 0.0530301i | ||||
\(223\) | −2238.14 | + | 3876.57i | −0.672093 | + | 1.16410i | 0.305216 | + | 0.952283i | \(0.401271\pi\) |
−0.977309 | + | 0.211817i | \(0.932062\pi\) | |||||||
\(224\) | −1307.01 | −0.389859 | ||||||||
\(225\) | 2045.10 | − | 2459.34i | 0.605955 | − | 0.728694i | ||||
\(226\) | 1108.96 | 0.326402 | ||||||||
\(227\) | −787.439 | + | 1363.88i | −0.230239 | + | 0.398785i | −0.957878 | − | 0.287175i | \(-0.907284\pi\) |
0.727640 | + | 0.685960i | \(0.240617\pi\) | |||||||
\(228\) | 1273.07 | + | 2714.36i | 0.369785 | + | 0.788433i | ||||
\(229\) | −223.577 | − | 387.247i | −0.0645170 | − | 0.111747i | 0.831963 | − | 0.554832i | \(-0.187217\pi\) |
−0.896480 | + | 0.443085i | \(0.853884\pi\) | |||||||
\(230\) | 314.598 | + | 544.900i | 0.0901912 | + | 0.156216i | ||||
\(231\) | 124.962 | + | 266.437i | 0.0355928 | + | 0.0758886i | ||||
\(232\) | −779.664 | + | 1350.42i | −0.220635 | + | 0.382152i | ||||
\(233\) | 3933.72 | 1.10604 | 0.553018 | − | 0.833169i | \(-0.313476\pi\) | ||||
0.553018 | + | 0.833169i | \(0.313476\pi\) | |||||||
\(234\) | −1113.59 | − | 191.263i | −0.311102 | − | 0.0534327i | ||||
\(235\) | −804.263 | −0.223253 | ||||||||
\(236\) | 1125.28 | − | 1949.03i | 0.310378 | − | 0.537590i | ||||
\(237\) | −2217.19 | + | 3181.48i | −0.607687 | + | 0.871981i | ||||
\(238\) | −389.324 | − | 674.329i | −0.106034 | − | 0.183656i | ||||
\(239\) | 1839.53 | + | 3186.15i | 0.497862 | + | 0.862322i | 0.999997 | − | 0.00246688i | \(-0.000785234\pi\) |
−0.502135 | + | 0.864789i | \(0.667452\pi\) | |||||||
\(240\) | −124.626 | − | 10.6247i | −0.0335191 | − | 0.00285758i | ||||
\(241\) | −416.504 | + | 721.407i | −0.111325 | + | 0.192821i | −0.916305 | − | 0.400481i | \(-0.868843\pi\) |
0.804980 | + | 0.593303i | \(0.202176\pi\) | |||||||
\(242\) | −2018.52 | −0.536178 | ||||||||
\(243\) | 3450.65 | + | 1562.67i | 0.910943 | + | 0.412533i | ||||
\(244\) | −800.705 | −0.210081 | ||||||||
\(245\) | 62.6299 | − | 108.478i | 0.0163317 | − | 0.0282874i | ||||
\(246\) | −719.330 | − | 61.3246i | −0.186434 | − | 0.0158939i | ||||
\(247\) | 1387.31 | + | 2402.89i | 0.357378 | + | 0.618997i | ||||
\(248\) | 3034.74 | + | 5256.32i | 0.777041 | + | 1.34587i | ||||
\(249\) | −1561.00 | + | 2239.91i | −0.397287 | + | 0.570074i | ||||
\(250\) | −496.340 | + | 859.686i | −0.125565 | + | 0.217485i | ||||
\(251\) | 7237.27 | 1.81997 | 0.909985 | − | 0.414640i | \(-0.136093\pi\) | ||||
0.909985 | + | 0.414640i | \(0.136093\pi\) | |||||||
\(252\) | 1016.31 | + | 174.554i | 0.254053 | + | 0.0436343i | ||||
\(253\) | 1248.54 | 0.310258 | ||||||||
\(254\) | 1098.55 | − | 1902.75i | 0.271376 | − | 0.470036i | ||||
\(255\) | −393.363 | − | 838.704i | −0.0966014 | − | 0.205967i | ||||
\(256\) | 1798.16 | + | 3114.51i | 0.439004 | + | 0.760378i | ||||
\(257\) | 1539.39 | + | 2666.29i | 0.373635 | + | 0.647155i | 0.990122 | − | 0.140210i | \(-0.0447779\pi\) |
−0.616487 | + | 0.787365i | \(0.711445\pi\) | |||||||
\(258\) | −313.601 | − | 668.641i | −0.0756743 | − | 0.161348i | ||||
\(259\) | 90.2908 | − | 156.388i | 0.0216618 | − | 0.0375193i | ||||
\(260\) | −365.941 | −0.0872873 | ||||||||
\(261\) | 1254.26 | − | 1508.32i | 0.297458 | − | 0.357710i | ||||
\(262\) | −4341.98 | −1.02385 | ||||||||
\(263\) | 1978.57 | − | 3426.99i | 0.463894 | − | 0.803488i | −0.535257 | − | 0.844689i | \(-0.679785\pi\) |
0.999151 | + | 0.0412015i | \(0.0131186\pi\) | |||||||
\(264\) | 515.889 | − | 740.258i | 0.120268 | − | 0.172575i | ||||
\(265\) | 455.711 | + | 789.315i | 0.105638 | + | 0.182971i | ||||
\(266\) | 590.349 | + | 1022.51i | 0.136077 | + | 0.235693i | ||||
\(267\) | −3333.68 | − | 284.204i | −0.764111 | − | 0.0651422i | ||||
\(268\) | −835.868 | + | 1447.77i | −0.190518 | + | 0.329986i | ||||
\(269\) | −2552.30 | −0.578499 | −0.289249 | − | 0.957254i | \(-0.593406\pi\) | ||||
−0.289249 | + | 0.957254i | \(0.593406\pi\) | |||||||
\(270\) | −553.511 | − | 144.369i | −0.124762 | − | 0.0325408i | ||||
\(271\) | −1888.99 | −0.423424 | −0.211712 | − | 0.977332i | \(-0.567904\pi\) | ||||
−0.211712 | + | 0.977332i | \(0.567904\pi\) | |||||||
\(272\) | 328.352 | − | 568.723i | 0.0731959 | − | 0.126779i | ||||
\(273\) | 950.882 | + | 81.0649i | 0.210806 | + | 0.0179717i | ||||
\(274\) | −1876.20 | − | 3249.67i | −0.413669 | − | 0.716496i | ||||
\(275\) | 479.237 | + | 830.064i | 0.105088 | + | 0.182017i | ||||
\(276\) | 2501.40 | − | 3589.30i | 0.545531 | − | 0.782791i | ||||
\(277\) | 1476.48 | − | 2557.34i | 0.320264 | − | 0.554713i | −0.660278 | − | 0.751021i | \(-0.729562\pi\) |
0.980542 | + | 0.196307i | \(0.0628951\pi\) | |||||||
\(278\) | −3267.64 | −0.704963 | ||||||||
\(279\) | −2643.35 | − | 7163.43i | −0.567216 | − | 1.53714i | ||||
\(280\) | −384.049 | −0.0819691 | ||||||||
\(281\) | −603.238 | + | 1044.84i | −0.128065 | + | 0.221814i | −0.922927 | − | 0.384976i | \(-0.874210\pi\) |
0.794862 | + | 0.606790i | \(0.207543\pi\) | |||||||
\(282\) | −1107.21 | − | 2360.73i | −0.233807 | − | 0.498508i | ||||
\(283\) | −1848.75 | − | 3202.14i | −0.388329 | − | 0.672605i | 0.603896 | − | 0.797063i | \(-0.293614\pi\) |
−0.992225 | + | 0.124458i | \(0.960281\pi\) | |||||||
\(284\) | 2833.76 | + | 4908.22i | 0.592088 | + | 1.02553i | ||||
\(285\) | 596.474 | + | 1271.76i | 0.123972 | + | 0.264326i | ||||
\(286\) | 169.292 | − | 293.222i | 0.0350015 | − | 0.0606244i | ||||
\(287\) | 609.762 | 0.125412 | ||||||||
\(288\) | −1745.25 | − | 4729.61i | −0.357084 | − | 0.967690i | ||||
\(289\) | −49.2304 | −0.0100204 | ||||||||
\(290\) | −148.117 | + | 256.547i | −0.0299923 | + | 0.0519481i | ||||
\(291\) | −918.501 | + | 1317.97i | −0.185029 | + | 0.265501i | ||||
\(292\) | −3156.58 | − | 5467.35i | −0.632619 | − | 1.09573i | ||||
\(293\) | −1242.99 | − | 2152.92i | −0.247837 | − | 0.429267i | 0.715088 | − | 0.699034i | \(-0.246386\pi\) |
−0.962925 | + | 0.269768i | \(0.913053\pi\) | |||||||
\(294\) | 404.634 | + | 34.4959i | 0.0802677 | + | 0.00684301i | ||||
\(295\) | 527.228 | − | 913.185i | 0.104056 | − | 0.180230i | ||||
\(296\) | −553.667 | −0.108720 | ||||||||
\(297\) | −797.277 | + | 807.967i | −0.155767 | + | 0.157855i | ||||
\(298\) | 2063.89 | 0.401201 | ||||||||
\(299\) | 2024.43 | − | 3506.42i | 0.391558 | − | 0.678198i | ||||
\(300\) | 3346.39 | + | 285.287i | 0.644013 | + | 0.0549036i | ||||
\(301\) | 311.887 | + | 540.205i | 0.0597239 | + | 0.103445i | ||||
\(302\) | 1707.98 | + | 2958.31i | 0.325441 | + | 0.563681i | ||||
\(303\) | −3329.13 | + | 4777.02i | −0.631200 | + | 0.905719i | ||||
\(304\) | −497.895 | + | 862.379i | −0.0939350 | + | 0.162700i | ||||
\(305\) | −375.156 | −0.0704307 | ||||||||
\(306\) | 1920.29 | − | 2309.25i | 0.358743 | − | 0.431409i | ||||
\(307\) | −2167.98 | −0.403040 | −0.201520 | − | 0.979484i | \(-0.564588\pi\) | ||||
−0.201520 | + | 0.979484i | \(0.564588\pi\) | |||||||
\(308\) | −154.502 | + | 267.605i | −0.0285830 | + | 0.0495072i | ||||
\(309\) | −1247.14 | − | 2659.07i | −0.229602 | − | 0.489544i | ||||
\(310\) | 576.528 | + | 998.576i | 0.105628 | + | 0.182953i | ||||
\(311\) | −2330.99 | − | 4037.39i | −0.425010 | − | 0.736140i | 0.571411 | − | 0.820664i | \(-0.306396\pi\) |
−0.996421 | + | 0.0845244i | \(0.973063\pi\) | |||||||
\(312\) | −1242.47 | − | 2649.11i | −0.225451 | − | 0.480693i | ||||
\(313\) | −249.595 | + | 432.311i | −0.0450733 | + | 0.0780693i | −0.887682 | − | 0.460457i | \(-0.847685\pi\) |
0.842609 | + | 0.538526i | \(0.181019\pi\) | |||||||
\(314\) | 4128.13 | 0.741923 | ||||||||
\(315\) | 476.173 | + | 81.7840i | 0.0851724 | + | 0.0146286i | ||||
\(316\) | −4071.79 | −0.724862 | ||||||||
\(317\) | 4906.82 | − | 8498.87i | 0.869384 | − | 1.50582i | 0.00675620 | − | 0.999977i | \(-0.497849\pi\) |
0.862628 | − | 0.505840i | \(-0.168817\pi\) | |||||||
\(318\) | −1689.48 | + | 2424.27i | −0.297929 | + | 0.427503i | ||||
\(319\) | 293.916 | + | 509.078i | 0.0515867 | + | 0.0893508i | ||||
\(320\) | 284.363 | + | 492.532i | 0.0496762 | + | 0.0860418i | ||||
\(321\) | 8248.78 | + | 703.227i | 1.43427 | + | 0.122275i | ||||
\(322\) | 861.466 | − | 1492.10i | 0.149092 | − | 0.258235i | ||||
\(323\) | −7375.14 | −1.27048 | ||||||||
\(324\) | 725.428 | + | 3910.73i | 0.124387 | + | 0.670564i | ||||
\(325\) | 3108.21 | 0.530500 | ||||||||
\(326\) | −672.238 | + | 1164.35i | −0.114208 | + | 0.197814i | ||||
\(327\) | −7759.01 | − | 661.473i | −1.31215 | − | 0.111864i | ||||
\(328\) | −934.772 | − | 1619.07i | −0.157360 | − | 0.272556i | ||||
\(329\) | 1101.16 | + | 1907.27i | 0.184526 | + | 0.319608i | ||||
\(330\) | 98.0066 | − | 140.631i | 0.0163487 | − | 0.0234591i | ||||
\(331\) | −5015.18 | + | 8686.55i | −0.832807 | + | 1.44246i | 0.0629962 | + | 0.998014i | \(0.479934\pi\) |
−0.895803 | + | 0.444451i | \(0.853399\pi\) | |||||||
\(332\) | −2866.73 | −0.473892 | ||||||||
\(333\) | 686.478 | + | 117.905i | 0.112969 | + | 0.0194028i | ||||
\(334\) | 2643.51 | 0.433073 | ||||||||
\(335\) | −391.631 | + | 678.325i | −0.0638719 | + | 0.110629i | ||||
\(336\) | 145.437 | + | 310.091i | 0.0236137 | + | 0.0503477i | ||||
\(337\) | 4402.86 | + | 7625.97i | 0.711688 | + | 1.23268i | 0.964223 | + | 0.265092i | \(0.0854023\pi\) |
−0.252535 | + | 0.967588i | \(0.581264\pi\) | |||||||
\(338\) | 1203.10 | + | 2083.83i | 0.193609 | + | 0.335341i | ||||
\(339\) | −1534.09 | − | 3270.89i | −0.245782 | − | 0.524042i | ||||
\(340\) | 486.349 | − | 842.382i | 0.0775765 | − | 0.134366i | ||||
\(341\) | 2288.06 | 0.363359 | ||||||||
\(342\) | −2911.81 | + | 3501.62i | −0.460388 | + | 0.553643i | ||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 956.253 | − | 1656.28i | 0.149877 | − | 0.259595i | ||||
\(345\) | 1171.99 | − | 1681.70i | 0.182892 | − | 0.262434i | ||||
\(346\) | −1552.79 | − | 2689.52i | −0.241268 | − | 0.417889i | ||||
\(347\) | −3186.28 | − | 5518.79i | −0.492934 | − | 0.853788i | 0.507032 | − | 0.861927i | \(-0.330742\pi\) |
−0.999967 | + | 0.00813945i | \(0.997409\pi\) | |||||||
\(348\) | 2052.34 | + | 174.967i | 0.316141 | + | 0.0269517i | ||||
\(349\) | 1373.67 | − | 2379.26i | 0.210690 | − | 0.364925i | −0.741241 | − | 0.671239i | \(-0.765762\pi\) |
0.951931 | + | 0.306314i | \(0.0990957\pi\) | |||||||
\(350\) | 1322.65 | 0.201996 | ||||||||
\(351\) | 976.368 | + | 3549.14i | 0.148475 | + | 0.539713i | ||||
\(352\) | 1510.68 | 0.228748 | ||||||||
\(353\) | −5139.65 | + | 8902.14i | −0.774947 | + | 1.34225i | 0.159878 | + | 0.987137i | \(0.448890\pi\) |
−0.934824 | + | 0.355110i | \(0.884443\pi\) | |||||||
\(354\) | 3406.27 | + | 290.392i | 0.511415 | + | 0.0435993i | ||||
\(355\) | 1327.71 | + | 2299.66i | 0.198500 | + | 0.343812i | ||||
\(356\) | −1756.55 | − | 3042.43i | −0.261508 | − | 0.452946i | ||||
\(357\) | −1450.37 | + | 2081.15i | −0.215018 | + | 0.308533i | ||||
\(358\) | 671.412 | − | 1162.92i | 0.0991208 | − | 0.171682i | ||||
\(359\) | −10473.7 | −1.53978 | −0.769891 | − | 0.638176i | \(-0.779689\pi\) | ||||
−0.769891 | + | 0.638176i | \(0.779689\pi\) | |||||||
\(360\) | −512.821 | − | 1389.73i | −0.0750778 | − | 0.203460i | ||||
\(361\) | 4324.25 | 0.630448 | ||||||||
\(362\) | −126.212 | + | 218.605i | −0.0183247 | + | 0.0317393i | ||||
\(363\) | 2792.33 | + | 5953.64i | 0.403745 | + | 0.860840i | ||||
\(364\) | 501.030 | + | 867.809i | 0.0721459 | + | 0.124960i | ||||
\(365\) | −1478.96 | − | 2561.63i | −0.212088 | − | 0.367348i | ||||
\(366\) | −516.469 | − | 1101.18i | −0.0737603 | − | 0.157267i | ||||
\(367\) | −991.263 | + | 1716.92i | −0.140990 | + | 0.244203i | −0.927870 | − | 0.372904i | \(-0.878362\pi\) |
0.786879 | + | 0.617107i | \(0.211695\pi\) | |||||||
\(368\) | 1453.11 | 0.205838 | ||||||||
\(369\) | 814.215 | + | 2206.51i | 0.114868 | + | 0.311290i | ||||
\(370\) | −105.184 | −0.0147790 | ||||||||
\(371\) | 1247.88 | − | 2161.39i | 0.174627 | − | 0.302463i | ||||
\(372\) | 4584.03 | − | 6577.70i | 0.638900 | − | 0.916769i | ||||
\(373\) | −4670.83 | − | 8090.12i | −0.648382 | − | 1.12303i | −0.983509 | − | 0.180858i | \(-0.942113\pi\) |
0.335127 | − | 0.942173i | \(-0.391221\pi\) | |||||||
\(374\) | 449.990 | + | 779.406i | 0.0622151 | + | 0.107760i | ||||
\(375\) | 3222.27 | + | 274.706i | 0.443726 | + | 0.0378287i | ||||
\(376\) | 3376.18 | − | 5847.72i | 0.463067 | − | 0.802056i | ||||
\(377\) | 1906.27 | 0.260418 | ||||||||
\(378\) | 415.479 | + | 1510.28i | 0.0565342 | + | 0.205504i | ||||
\(379\) | 8964.44 | 1.21497 | 0.607483 | − | 0.794333i | \(-0.292179\pi\) | ||||
0.607483 | + | 0.794333i | \(0.292179\pi\) | |||||||
\(380\) | −737.473 | + | 1277.34i | −0.0995567 | + | 0.172437i | ||||
\(381\) | −7131.88 | − | 608.009i | −0.958996 | − | 0.0817566i | ||||
\(382\) | 3683.59 | + | 6380.16i | 0.493374 | + | 0.854548i | ||||
\(383\) | −2285.75 | − | 3959.03i | −0.304951 | − | 0.528190i | 0.672300 | − | 0.740279i | \(-0.265307\pi\) |
−0.977250 | + | 0.212089i | \(0.931973\pi\) | |||||||
\(384\) | 3383.54 | − | 4855.10i | 0.449650 | − | 0.645210i | ||||
\(385\) | −72.3892 | + | 125.382i | −0.00958258 | + | 0.0165975i | ||||
\(386\) | 7322.52 | 0.965560 | ||||||||
\(387\) | −1538.34 | + | 1849.94i | −0.202063 | + | 0.242992i | ||||
\(388\) | −1686.80 | −0.220706 | ||||||||
\(389\) | −4418.60 | + | 7653.23i | −0.575917 | + | 0.997517i | 0.420024 | + | 0.907513i | \(0.362021\pi\) |
−0.995941 | + | 0.0900045i | \(0.971312\pi\) | |||||||
\(390\) | −236.039 | − | 503.267i | −0.0306469 | − | 0.0653434i | ||||
\(391\) | 5381.09 | + | 9320.32i | 0.695993 | + | 1.20550i | ||||
\(392\) | 525.823 | + | 910.752i | 0.0677502 | + | 0.117347i | ||||
\(393\) | 6006.52 | + | 12806.7i | 0.770964 | + | 1.64380i | ||||
\(394\) | 2110.19 | − | 3654.96i | 0.269822 | − | 0.467346i | ||||
\(395\) | −1907.77 | −0.243013 | ||||||||
\(396\) | −1174.67 | − | 201.753i | −0.149064 | − | 0.0256023i | ||||
\(397\) | −3649.31 | −0.461344 | −0.230672 | − | 0.973032i | \(-0.574092\pi\) | ||||
−0.230672 | + | 0.973032i | \(0.574092\pi\) | |||||||
\(398\) | −3781.37 | + | 6549.53i | −0.476239 | + | 0.824870i | ||||
\(399\) | 2199.25 | − | 3155.74i | 0.275941 | − | 0.395952i | ||||
\(400\) | 557.757 | + | 966.063i | 0.0697196 | + | 0.120758i | ||||
\(401\) | 509.732 | + | 882.882i | 0.0634784 | + | 0.109948i | 0.896018 | − | 0.444018i | \(-0.146447\pi\) |
−0.832540 | + | 0.553965i | \(0.813114\pi\) | |||||||
\(402\) | −2530.21 | − | 215.707i | −0.313919 | − | 0.0267624i | ||||
\(403\) | 3709.95 | − | 6425.81i | 0.458575 | − | 0.794274i | ||||
\(404\) | −6113.84 | −0.752908 | ||||||||
\(405\) | 339.886 | + | 1832.30i | 0.0417015 | + | 0.224809i | ||||
\(406\) | 811.182 | 0.0991584 | ||||||||
\(407\) | −104.360 | + | 180.757i | −0.0127100 | + | 0.0220143i | ||||
\(408\) | 7749.42 | + | 660.656i | 0.940327 | + | 0.0801650i | ||||
\(409\) | −690.083 | − | 1195.26i | −0.0834289 | − | 0.144503i | 0.821292 | − | 0.570508i | \(-0.193254\pi\) |
−0.904721 | + | 0.426005i | \(0.859920\pi\) | |||||||
\(410\) | −177.584 | − | 307.585i | −0.0213909 | − | 0.0370501i | ||||
\(411\) | −6989.49 | + | 10029.3i | −0.838847 | + | 1.20368i | ||||
\(412\) | 1541.94 | − | 2670.73i | 0.184384 | − | 0.319362i | ||||
\(413\) | −2887.42 | −0.344022 | ||||||||
\(414\) | 6549.69 | + | 1124.93i | 0.777536 | + | 0.133544i | ||||
\(415\) | −1343.15 | −0.158874 | ||||||||
\(416\) | 2449.47 | − | 4242.60i | 0.288690 | − | 0.500025i | ||||
\(417\) | 4520.32 | + | 9637.93i | 0.530841 | + | 1.13183i | ||||
\(418\) | −682.339 | − | 1181.85i | −0.0798428 | − | 0.138292i | ||||
\(419\) | −5644.76 | − | 9777.01i | −0.658149 | − | 1.13995i | −0.981094 | − | 0.193530i | \(-0.938006\pi\) |
0.322945 | − | 0.946418i | \(-0.395327\pi\) | |||||||
\(420\) | 215.418 | + | 459.300i | 0.0250269 | + | 0.0533609i | ||||
\(421\) | 5670.06 | − | 9820.84i | 0.656394 | − | 1.13691i | −0.325148 | − | 0.945663i | \(-0.605414\pi\) |
0.981542 | − | 0.191245i | \(-0.0612525\pi\) | |||||||
\(422\) | −7306.29 | −0.842807 | ||||||||
\(423\) | −5431.32 | + | 6531.47i | −0.624302 | + | 0.750759i | ||||
\(424\) | −7652.04 | −0.876452 | ||||||||
\(425\) | −4130.93 | + | 7154.97i | −0.471481 | + | 0.816629i | ||||
\(426\) | −4922.29 | + | 7063.08i | −0.559826 | + | 0.803303i | ||||
\(427\) | 513.646 | + | 889.661i | 0.0582133 | + | 0.100828i | ||||
\(428\) | 4346.37 | + | 7528.13i | 0.490863 | + | 0.850200i | ||||
\(429\) | −1099.05 | − | 93.6968i | −0.123689 | − | 0.0105448i | ||||
\(430\) | 181.665 | − | 314.653i | 0.0203737 | − | 0.0352882i | ||||
\(431\) | 15264.9 | 1.70600 | 0.853000 | − | 0.521911i | \(-0.174781\pi\) | ||||
0.853000 | + | 0.521911i | \(0.174781\pi\) | |||||||
\(432\) | −927.904 | + | 940.346i | −0.103342 | + | 0.104728i | ||||
\(433\) | −3367.10 | −0.373701 | −0.186851 | − | 0.982388i | \(-0.559828\pi\) | ||||
−0.186851 | + | 0.982388i | \(0.559828\pi\) | |||||||
\(434\) | 1578.71 | − | 2734.41i | 0.174610 | − | 0.302433i | ||||
\(435\) | 961.588 | + | 81.9776i | 0.105988 | + | 0.00903569i | ||||
\(436\) | −4088.30 | − | 7081.15i | −0.449069 | − | 0.777811i | ||||
\(437\) | −8159.57 | − | 14132.8i | −0.893193 | − | 1.54706i | ||||
\(438\) | 5483.02 | − | 7867.68i | 0.598148 | − | 0.858293i | ||||
\(439\) | −5526.68 | + | 9572.50i | −0.600852 | + | 1.04071i | 0.391840 | + | 0.920033i | \(0.371839\pi\) |
−0.992692 | + | 0.120673i | \(0.961495\pi\) | |||||||
\(440\) | 443.894 | 0.0480950 | ||||||||
\(441\) | −458.008 | − | 1241.19i | −0.0494555 | − | 0.134024i | ||||
\(442\) | 2918.52 | 0.314072 | ||||||||
\(443\) | −3869.09 | + | 6701.45i | −0.414957 | + | 0.718726i | −0.995424 | − | 0.0955576i | \(-0.969537\pi\) |
0.580467 | + | 0.814284i | \(0.302870\pi\) | |||||||
\(444\) | 310.559 | + | 662.153i | 0.0331947 | + | 0.0707757i | ||||
\(445\) | −823.000 | − | 1425.48i | −0.0876718 | − | 0.151852i | ||||
\(446\) | −3569.80 | − | 6183.07i | −0.379002 | − | 0.656450i | ||||
\(447\) | −2855.10 | − | 6087.47i | −0.302106 | − | 0.644133i | ||||
\(448\) | 778.675 | − | 1348.70i | 0.0821181 | − | 0.142233i | ||||
\(449\) | 1209.56 | 0.127133 | 0.0635665 | − | 0.997978i | \(-0.479752\pi\) | ||||
0.0635665 | + | 0.997978i | \(0.479752\pi\) | |||||||
\(450\) | 1766.14 | + | 4786.19i | 0.185014 | + | 0.501385i | ||||
\(451\) | −704.778 | −0.0735847 | ||||||||
\(452\) | 1896.73 | − | 3285.23i | 0.197377 | − | 0.341867i | ||||
\(453\) | 6362.82 | − | 9130.12i | 0.659937 | − | 0.946954i | ||||
\(454\) | −1255.95 | − | 2175.38i | −0.129834 | − | 0.224880i | ||||
\(455\) | 234.749 | + | 406.597i | 0.0241872 | + | 0.0418935i | ||||
\(456\) | −11750.8 | − | 1001.78i | −1.20676 | − | 0.102879i | ||||
\(457\) | 7128.81 | − | 12347.5i | 0.729697 | − | 1.26387i | −0.227314 | − | 0.973821i | \(-0.572994\pi\) |
0.957011 | − | 0.290051i | \(-0.0936722\pi\) | |||||||
\(458\) | 713.204 | 0.0727638 | ||||||||
\(459\) | −9467.61 | − | 2469.38i | −0.962768 | − | 0.251113i | ||||
\(460\) | 2152.31 | 0.218157 | ||||||||
\(461\) | −5958.98 | + | 10321.2i | −0.602033 | + | 1.04275i | 0.390480 | + | 0.920611i | \(0.372309\pi\) |
−0.992513 | + | 0.122140i | \(0.961024\pi\) | |||||||
\(462\) | −467.685 | − | 39.8713i | −0.0470967 | − | 0.00401511i | ||||
\(463\) | −3930.43 | − | 6807.71i | −0.394520 | − | 0.683329i | 0.598520 | − | 0.801108i | \(-0.295756\pi\) |
−0.993040 | + | 0.117779i | \(0.962422\pi\) | |||||||
\(464\) | 342.072 | + | 592.486i | 0.0342248 | + | 0.0592791i | ||||
\(465\) | 2147.77 | − | 3081.87i | 0.214194 | − | 0.307351i | ||||
\(466\) | −3137.11 | + | 5433.63i | −0.311854 | + | 0.540146i | ||||
\(467\) | 16152.3 | 1.60051 | 0.800257 | − | 0.599657i | \(-0.204696\pi\) | ||||
0.800257 | + | 0.599657i | \(0.204696\pi\) | |||||||
\(468\) | −2471.26 | + | 2971.83i | −0.244090 | + | 0.293532i | ||||
\(469\) | 2144.81 | 0.211169 | ||||||||
\(470\) | 641.394 | − | 1110.93i | 0.0629474 | − | 0.109028i | ||||
\(471\) | −5710.69 | − | 12176.0i | −0.558672 | − | 1.19117i | ||||
\(472\) | 4426.45 | + | 7666.84i | 0.431661 | + | 0.747659i | ||||
\(473\) | −360.487 | − | 624.382i | −0.0350427 | − | 0.0606958i | ||||
\(474\) | −2626.38 | − | 5599.81i | −0.254501 | − | 0.542632i | ||||
\(475\) | 6263.90 | − | 10849.4i | 0.605068 | − | 1.04801i | ||||
\(476\) | −2663.55 | −0.256478 | ||||||||
\(477\) | 9487.56 | + | 1629.52i | 0.910703 | + | 0.156416i | ||||
\(478\) | −5868.03 | −0.561501 | ||||||||
\(479\) | 5851.93 | − | 10135.8i | 0.558207 | − | 0.966844i | −0.439439 | − | 0.898273i | \(-0.644823\pi\) |
0.997646 | − | 0.0685711i | \(-0.0218440\pi\) | |||||||
\(480\) | 1418.05 | − | 2034.78i | 0.134843 | − | 0.193489i | ||||
\(481\) | 338.427 | + | 586.173i | 0.0320810 | + | 0.0555659i | ||||
\(482\) | −664.318 | − | 1150.63i | −0.0627777 | − | 0.108734i | ||||
\(483\) | −5592.69 | − | 476.790i | −0.526866 | − | 0.0449165i | ||||
\(484\) | −3452.41 | + | 5979.74i | −0.324230 | + | 0.561584i | ||||
\(485\) | −790.318 | −0.0739928 | ||||||||
\(486\) | −4910.38 | + | 3520.15i | −0.458312 | + | 0.328554i | ||||
\(487\) | 41.1258 | 0.00382667 | 0.00191333 | − | 0.999998i | \(-0.499391\pi\) | ||||
0.00191333 | + | 0.999998i | \(0.499391\pi\) | |||||||
\(488\) | 1574.85 | − | 2727.72i | 0.146086 | − | 0.253029i | ||||
\(489\) | 4364.21 | + | 372.059i | 0.403592 | + | 0.0344072i | ||||
\(490\) | 99.8938 | + | 173.021i | 0.00920967 | + | 0.0159516i | ||||
\(491\) | −4217.83 | − | 7305.49i | −0.387674 | − | 0.671471i | 0.604462 | − | 0.796634i | \(-0.293388\pi\) |
−0.992136 | + | 0.125163i | \(0.960055\pi\) | |||||||
\(492\) | −1411.99 | + | 2026.09i | −0.129385 | + | 0.185657i | ||||
\(493\) | −2533.50 | + | 4388.15i | −0.231446 | + | 0.400877i | ||||
\(494\) | −4425.48 | −0.403060 | ||||||||
\(495\) | −550.372 | − | 94.5280i | −0.0499745 | − | 0.00858327i | ||||
\(496\) | 2662.94 | 0.241068 | ||||||||
\(497\) | 3635.68 | − | 6297.18i | 0.328134 | − | 0.568344i | ||||
\(498\) | −1849.09 | − | 3942.52i | −0.166385 | − | 0.354756i | ||||
\(499\) | −1093.08 | − | 1893.27i | −0.0980618 | − | 0.169848i | 0.812821 | − | 0.582514i | \(-0.197931\pi\) |
−0.910882 | + | 0.412666i | \(0.864598\pi\) | |||||||
\(500\) | 1697.85 | + | 2940.76i | 0.151860 | + | 0.263029i | ||||
\(501\) | −3656.92 | − | 7797.06i | −0.326106 | − | 0.695303i | ||||
\(502\) | −5771.67 | + | 9996.83i | −0.513152 | + | 0.888805i | ||||
\(503\) | 14676.6 | 1.30098 | 0.650492 | − | 0.759513i | \(-0.274563\pi\) | ||||
0.650492 | + | 0.759513i | \(0.274563\pi\) | |||||||
\(504\) | −2593.55 | + | 3118.89i | −0.229218 | + | 0.275647i | ||||
\(505\) | −2864.53 | −0.252416 | ||||||||
\(506\) | −995.703 | + | 1724.61i | −0.0874791 | + | 0.151518i | ||||
\(507\) | 4481.96 | − | 6431.24i | 0.392605 | − | 0.563356i | ||||
\(508\) | −3757.86 | − | 6508.81i | −0.328205 | − | 0.568468i | ||||
\(509\) | 6449.79 | + | 11171.4i | 0.561654 | + | 0.972814i | 0.997352 | + | 0.0727208i | \(0.0231682\pi\) |
−0.435698 | + | 0.900093i | \(0.643498\pi\) | |||||||
\(510\) | 1472.20 | + | 125.509i | 0.127824 | + | 0.0108973i | ||||
\(511\) | −4049.84 | + | 7014.54i | −0.350596 | + | 0.607250i | ||||
\(512\) | 3374.96 | 0.291315 | ||||||||
\(513\) | 14356.2 | + | 3744.43i | 1.23555 | + | 0.322263i | ||||
\(514\) | −4910.59 | −0.421395 | ||||||||
\(515\) | 722.451 | − | 1251.32i | 0.0618155 | − | 0.107068i | ||||
\(516\) | −2517.19 | − | 214.596i | −0.214754 | − | 0.0183082i | ||||
\(517\) | −1272.75 | − | 2204.46i | −0.108270 | − | 0.187528i | ||||
\(518\) | 144.013 | + | 249.437i | 0.0122153 | + | 0.0211576i | ||||
\(519\) | −5784.70 | + | 8300.56i | −0.489248 | + | 0.702031i | ||||
\(520\) | 719.745 | − | 1246.63i | 0.0606979 | − | 0.105132i | ||||
\(521\) | 11771.7 | 0.989880 | 0.494940 | − | 0.868927i | \(-0.335190\pi\) | ||||
0.494940 | + | 0.868927i | \(0.335190\pi\) | |||||||
\(522\) | 1083.17 | + | 2935.37i | 0.0908221 | + | 0.246126i | ||||
\(523\) | 5339.23 | 0.446402 | 0.223201 | − | 0.974772i | \(-0.428349\pi\) | ||||
0.223201 | + | 0.974772i | \(0.428349\pi\) | |||||||
\(524\) | −7426.39 | + | 12862.9i | −0.619128 | + | 1.07236i | ||||
\(525\) | −1829.70 | − | 3901.18i | −0.152104 | − | 0.324307i | ||||
\(526\) | 3155.80 | + | 5466.00i | 0.261595 | + | 0.453097i | ||||
\(527\) | 9861.31 | + | 17080.3i | 0.815115 | + | 1.41182i | ||||
\(528\) | −168.099 | − | 358.410i | −0.0138553 | − | 0.0295413i | ||||
\(529\) | −5823.36 | + | 10086.3i | −0.478619 | + | 0.828992i | ||||
\(530\) | −1453.70 | −0.119141 | ||||||||
\(531\) | −3855.58 | − | 10448.5i | −0.315099 | − | 0.853913i | ||||
\(532\) | 4038.85 | 0.329148 | ||||||||
\(533\) | −1142.75 | + | 1979.30i | −0.0928669 | + | 0.160850i | ||||
\(534\) | 3051.15 | − | 4378.15i | 0.247259 | − | 0.354796i | ||||
\(535\) | 2036.41 | + | 3527.17i | 0.164564 | + | 0.285033i | ||||
\(536\) | −3288.02 | − | 5695.02i | −0.264964 | − | 0.458932i | ||||
\(537\) | −4358.85 | − | 371.602i | −0.350276 | − | 0.0298618i | ||||
\(538\) | 2035.44 | − | 3525.48i | 0.163111 | − | 0.282517i | ||||
\(539\) | 396.448 | 0.0316813 | ||||||||
\(540\) | −1374.39 | + | 1392.82i | −0.109527 | + | 0.110995i | ||||
\(541\) | 828.599 | 0.0658489 | 0.0329244 | − | 0.999458i | \(-0.489518\pi\) | ||||
0.0329244 | + | 0.999458i | \(0.489518\pi\) | |||||||
\(542\) | 1506.46 | − | 2609.26i | 0.119387 | − | 0.206784i | ||||
\(543\) | 819.373 | + | 69.8534i | 0.0647563 | + | 0.00552062i | ||||
\(544\) | 6510.86 | + | 11277.1i | 0.513145 | + | 0.888793i | ||||
\(545\) | −1915.50 | − | 3317.75i | −0.150552 | − | 0.260765i | ||||
\(546\) | −870.296 | + | 1248.80i | −0.0682147 | + | 0.0978825i | ||||
\(547\) | −6948.69 | + | 12035.5i | −0.543153 | + | 0.940768i | 0.455568 | + | 0.890201i | \(0.349436\pi\) |
−0.998721 | + | 0.0505673i | \(0.983897\pi\) | |||||||
\(548\) | −12836.0 | −1.00059 | ||||||||
\(549\) | −2533.49 | + | 3046.66i | −0.196952 | + | 0.236846i | ||||
\(550\) | −1528.75 | −0.118520 | ||||||||
\(551\) | 3841.65 | − | 6653.93i | 0.297023 | − | 0.514459i | ||||
\(552\) | 7307.66 | + | 15580.9i | 0.563469 | + | 1.20139i | ||||
\(553\) | 2612.03 | + | 4524.16i | 0.200858 | + | 0.347897i | ||||
\(554\) | 2354.96 | + | 4078.92i | 0.180601 | + | 0.312810i | ||||
\(555\) | 145.507 | + | 310.240i | 0.0111287 | + | 0.0237279i | ||||
\(556\) | −5588.86 | + | 9680.19i | −0.426296 | + | 0.738366i | ||||
\(557\) | 11168.5 | 0.849595 | 0.424798 | − | 0.905288i | \(-0.360345\pi\) | ||||
0.424798 | + | 0.905288i | \(0.360345\pi\) | |||||||
\(558\) | 12002.9 | + | 2061.53i | 0.910614 | + | 0.156401i | ||||
\(559\) | −2338.02 | −0.176901 | ||||||||
\(560\) | −84.2495 | + | 145.924i | −0.00635749 | + | 0.0110115i | ||||
\(561\) | 1676.37 | − | 2405.45i | 0.126161 | − | 0.181031i | ||||
\(562\) | −962.156 | − | 1666.50i | −0.0722172 | − | 0.125084i | ||||
\(563\) | 322.865 | + | 559.218i | 0.0241689 | + | 0.0418618i | 0.877857 | − | 0.478923i | \(-0.158973\pi\) |
−0.853688 | + | 0.520785i | \(0.825639\pi\) | |||||||
\(564\) | −8887.26 | − | 757.660i | −0.663513 | − | 0.0565660i | ||||
\(565\) | 888.678 | − | 1539.23i | 0.0661716 | − | 0.114613i | ||||
\(566\) | 5897.47 | 0.437967 | ||||||||
\(567\) | 3879.85 | − | 3314.73i | 0.287369 | − | 0.245512i | ||||
\(568\) | −22294.1 | −1.64690 | ||||||||
\(569\) | −9542.50 | + | 16528.1i | −0.703062 | + | 1.21774i | 0.264324 | + | 0.964434i | \(0.414851\pi\) |
−0.967386 | + | 0.253306i | \(0.918482\pi\) | |||||||
\(570\) | −2232.37 | − | 190.314i | −0.164041 | − | 0.0139849i | ||||
\(571\) | 1409.15 | + | 2440.71i | 0.103277 | + | 0.178880i | 0.913033 | − | 0.407886i | \(-0.133734\pi\) |
−0.809756 | + | 0.586766i | \(0.800401\pi\) | |||||||
\(572\) | −579.103 | − | 1003.04i | −0.0423313 | − | 0.0733199i | ||||
\(573\) | 13722.6 | − | 19690.8i | 1.00047 | − | 1.43560i | ||||
\(574\) | −486.281 | + | 842.263i | −0.0353606 | + | 0.0612463i | ||||
\(575\) | −18281.2 | −1.32588 | ||||||||
\(576\) | 5920.23 | + | 1016.82i | 0.428258 | + | 0.0735545i | ||||
\(577\) | 16153.2 | 1.16546 | 0.582728 | − | 0.812667i | \(-0.301985\pi\) | ||||
0.582728 | + | 0.812667i | \(0.301985\pi\) | |||||||
\(578\) | 39.2609 | − | 68.0019i | 0.00282533 | − | 0.00489361i | ||||
\(579\) | −10129.7 | − | 21597.8i | −0.727072 | − | 1.55022i | ||||
\(580\) | 506.671 | + | 877.580i | 0.0362730 | + | 0.0628267i | ||||
\(581\) | 1838.99 | + | 3185.22i | 0.131315 | + | 0.227444i | ||||
\(582\) | −1088.01 | − | 2319.80i | −0.0774908 | − | 0.165221i | ||||
\(583\) | −1442.33 | + | 2498.18i | −0.102462 | + | 0.177469i | ||||
\(584\) | 24833.8 | 1.75964 | ||||||||
\(585\) | −1157.87 | + | 1392.40i | −0.0818322 | + | 0.0984078i | ||||
\(586\) | 3965.10 | 0.279517 | ||||||||
\(587\) | −6970.50 | + | 12073.3i | −0.490125 | + | 0.848921i | −0.999935 | − | 0.0113658i | \(-0.996382\pi\) |
0.509811 | + | 0.860287i | \(0.329715\pi\) | |||||||
\(588\) | 794.265 | − | 1139.70i | 0.0557057 | − | 0.0799330i | ||||
\(589\) | −14953.1 | − | 25899.6i | −1.04607 | − | 1.81184i | ||||
\(590\) | 840.920 | + | 1456.52i | 0.0586782 | + | 0.101634i | ||||
\(591\) | −13699.5 | − | 1167.91i | −0.953506 | − | 0.0812886i | ||||
\(592\) | −121.459 | + | 210.373i | −0.00843232 | + | 0.0146052i | ||||
\(593\) | 203.913 | 0.0141209 | 0.00706046 | − | 0.999975i | \(-0.497753\pi\) | ||||
0.00706046 | + | 0.999975i | \(0.497753\pi\) | |||||||
\(594\) | −480.220 | − | 1745.62i | −0.0331712 | − | 0.120579i | ||||
\(595\) | −1247.96 | −0.0859854 | ||||||||
\(596\) | 3530.01 | − | 6114.16i | 0.242609 | − | 0.420211i | ||||
\(597\) | 24548.9 | + | 2092.85i | 1.68295 | + | 0.143475i | ||||
\(598\) | 3228.94 | + | 5592.68i | 0.220804 | + | 0.382444i | ||||
\(599\) | 1154.51 | + | 1999.67i | 0.0787514 | + | 0.136401i | 0.902711 | − | 0.430246i | \(-0.141573\pi\) |
−0.823960 | + | 0.566648i | \(0.808240\pi\) | |||||||
\(600\) | −7553.66 | + | 10838.9i | −0.513961 | + | 0.737492i | ||||
\(601\) | −11175.2 | + | 19356.0i | −0.758477 | + | 1.31372i | 0.185150 | + | 0.982710i | \(0.440723\pi\) |
−0.943627 | + | 0.331010i | \(0.892611\pi\) | |||||||
\(602\) | −994.911 | −0.0673580 | ||||||||
\(603\) | 2863.97 | + | 7761.30i | 0.193416 | + | 0.524153i | ||||
\(604\) | 11685.1 | 0.787186 | ||||||||
\(605\) | −1617.56 | + | 2801.70i | −0.108700 | + | 0.188273i | ||||
\(606\) | −3943.54 | − | 8408.16i | −0.264348 | − | 0.563627i | ||||
\(607\) | 8552.63 | + | 14813.6i | 0.571895 | + | 0.990552i | 0.996371 | + | 0.0851126i | \(0.0271250\pi\) |
−0.424476 | + | 0.905439i | \(0.639542\pi\) | |||||||
\(608\) | −9872.70 | − | 17100.0i | −0.658538 | − | 1.14062i | ||||
\(609\) | −1122.16 | − | 2392.59i | −0.0746668 | − | 0.159200i | ||||
\(610\) | 299.184 | − | 518.202i | 0.0198584 | − | 0.0343957i | ||||
\(611\) | −8254.71 | −0.546563 | ||||||||
\(612\) | −3556.63 | − | 9638.42i | −0.234916 | − | 0.636617i | ||||
\(613\) | −7474.70 | −0.492496 | −0.246248 | − | 0.969207i | \(-0.579198\pi\) | ||||
−0.246248 | + | 0.969207i | \(0.579198\pi\) | |||||||
\(614\) | 1728.95 | − | 2994.63i | 0.113639 | − | 0.196829i | ||||
\(615\) | −661.563 | + | 949.288i | −0.0433769 | + | 0.0622423i | ||||
\(616\) | −607.759 | − | 1052.67i | −0.0397521 | − | 0.0688527i | ||||
\(617\) | −1802.12 | − | 3121.37i | −0.117586 | − | 0.203665i | 0.801224 | − | 0.598364i | \(-0.204182\pi\) |
−0.918811 | + | 0.394699i | \(0.870849\pi\) | |||||||
\(618\) | 4667.54 | + | 397.919i | 0.303813 | + | 0.0259007i | ||||
\(619\) | 2271.30 | − | 3934.01i | 0.147482 | − | 0.255446i | −0.782814 | − | 0.622256i | \(-0.786216\pi\) |
0.930296 | + | 0.366809i | \(0.119550\pi\) | |||||||
\(620\) | 3944.30 | 0.255495 | ||||||||
\(621\) | −5742.59 | − | 20874.6i | −0.371082 | − | 1.34890i | ||||
\(622\) | 7435.78 | 0.479337 | ||||||||
\(623\) | −2253.63 | + | 3903.40i | −0.144927 | + | 0.251021i | ||||
\(624\) | −1279.12 | − | 109.048i | −0.0820608 | − | 0.00699587i | ||||
\(625\) | −6608.58 | − | 11446.4i | −0.422949 | − | 0.732569i | ||||
\(626\) | −398.100 | − | 689.530i | −0.0254174 | − | 0.0440242i | ||||
\(627\) | −2541.95 | + | 3647.49i | −0.161907 | + | 0.232323i | ||||
\(628\) | 7060.62 | − | 12229.4i | 0.448646 | − | 0.777077i | ||||
\(629\) | −1799.13 | −0.114048 | ||||||||
\(630\) | −492.712 | + | 592.514i | −0.0311589 | + | 0.0374704i | ||||
\(631\) | −11564.2 | −0.729578 | −0.364789 | − | 0.931090i | \(-0.618859\pi\) | ||||
−0.364789 | + | 0.931090i | \(0.618859\pi\) | |||||||
\(632\) | 8008.53 | − | 13871.2i | 0.504054 | − | 0.873048i | ||||
\(633\) | 10107.2 | + | 21550.0i | 0.634638 | + | 1.35314i | ||||
\(634\) | 7826.31 | + | 13555.6i | 0.490256 | + | 0.849149i | ||||
\(635\) | −1760.68 | − | 3049.59i | −0.110032 | − | 0.190581i | ||||
\(636\) | 4292.12 | + | 9151.38i | 0.267600 | + | 0.570560i | ||||
\(637\) | 642.814 | − | 1113.39i | 0.0399831 | − | 0.0692527i | ||||
\(638\) | −937.585 | −0.0581808 | ||||||||
\(639\) | 27641.9 | + | 4747.58i | 1.71126 | + | 0.293914i | ||||
\(640\) | 2911.34 | 0.179814 | ||||||||
\(641\) | −849.583 | + | 1471.52i | −0.0523503 | + | 0.0906733i | −0.891013 | − | 0.453978i | \(-0.850005\pi\) |
0.838663 | + | 0.544651i | \(0.183338\pi\) | |||||||
\(642\) | −7549.70 | + | 10833.2i | −0.464117 | + | 0.665969i | ||||
\(643\) | −14633.7 | − | 25346.3i | −0.897506 | − | 1.55453i | −0.830672 | − | 0.556762i | \(-0.812044\pi\) |
−0.0668341 | − | 0.997764i | \(-0.521290\pi\) | |||||||
\(644\) | −2946.85 | − | 5104.09i | −0.180314 | − | 0.312313i | ||||
\(645\) | −1179.38 | − | 100.545i | −0.0719971 | − | 0.00613792i | ||||
\(646\) | 5881.62 | − | 10187.3i | 0.358219 | − | 0.620453i | ||||
\(647\) | 19018.7 | 1.15564 | 0.577822 | − | 0.816163i | \(-0.303903\pi\) | ||||
0.577822 | + | 0.816163i | \(0.303903\pi\) | |||||||
\(648\) | −14749.3 | − | 5220.46i | −0.894146 | − | 0.316480i | ||||
\(649\) | 3337.36 | 0.201853 | ||||||||
\(650\) | −2478.77 | + | 4293.36i | −0.149578 | + | 0.259076i | ||||
\(651\) | −10249.1 | − | 873.759i | −0.617041 | − | 0.0526042i | ||||
\(652\) | 2299.55 | + | 3982.94i | 0.138125 | + | 0.239239i | ||||
\(653\) | 4734.89 | + | 8201.06i | 0.283753 | + | 0.491474i | 0.972306 | − | 0.233712i | \(-0.0750872\pi\) |
−0.688553 | + | 0.725186i | \(0.741754\pi\) | |||||||
\(654\) | 7101.44 | − | 10190.0i | 0.424600 | − | 0.609266i | ||||
\(655\) | −3479.50 | + | 6026.67i | −0.207565 | + | 0.359514i | ||||
\(656\) | −820.250 | −0.0488192 | ||||||||
\(657\) | −30790.8 | − | 5288.41i | −1.82841 | − | 0.314034i | ||||
\(658\) | −3512.67 | −0.208113 | ||||||||
\(659\) | 8612.54 | − | 14917.4i | 0.509100 | − | 0.881787i | −0.490844 | − | 0.871247i | \(-0.663312\pi\) |
0.999944 | − | 0.0105401i | \(-0.00335508\pi\) | |||||||
\(660\) | −248.985 | − | 530.870i | −0.0146844 | − | 0.0313092i | ||||
\(661\) | 4939.90 | + | 8556.16i | 0.290681 | + | 0.503474i | 0.973971 | − | 0.226673i | \(-0.0727849\pi\) |
−0.683290 | + | 0.730147i | \(0.739452\pi\) | |||||||
\(662\) | −7999.13 | − | 13854.9i | −0.469630 | − | 0.813423i | ||||
\(663\) | −4037.36 | − | 8608.21i | −0.236498 | − | 0.504246i | ||||
\(664\) | 5638.37 | − | 9765.94i | 0.329535 | − | 0.570771i | ||||
\(665\) | 1892.33 | 0.110348 | ||||||||
\(666\) | −710.322 | + | 854.202i | −0.0413280 | + | 0.0496992i | ||||
\(667\) | −11211.9 | −0.650862 | ||||||||
\(668\) | 4521.37 | − | 7831.25i | 0.261882 | − | 0.453593i | ||||
\(669\) | −13298.7 | + | 19082.6i | −0.768548 | + | 1.10280i | ||||
\(670\) | −624.645 | − | 1081.92i | −0.0360181 | − | 0.0623853i | ||||
\(671\) | −593.685 | − | 1028.29i | −0.0341564 | − | 0.0591606i | ||||
\(672\) | −6766.89 | − | 576.893i | −0.388450 | − | 0.0331163i | ||||
\(673\) | 15090.5 | − | 26137.5i | 0.864334 | − | 1.49707i | −0.00337288 | − | 0.999994i | \(-0.501074\pi\) |
0.867707 | − | 0.497076i | \(-0.165593\pi\) | |||||||
\(674\) | −14045.0 | −0.802659 | ||||||||
\(675\) | 11673.7 | − | 11830.3i | 0.665663 | − | 0.674588i | ||||
\(676\) | 8230.97 | 0.468308 | ||||||||
\(677\) | 11225.4 | − | 19443.0i | 0.637265 | − | 1.10378i | −0.348765 | − | 0.937210i | \(-0.613399\pi\) |
0.986030 | − | 0.166566i | \(-0.0532679\pi\) | |||||||
\(678\) | 5741.49 | + | 489.475i | 0.325222 | + | 0.0277259i | ||||
\(679\) | 1082.07 | + | 1874.20i | 0.0611575 | + | 0.105928i | ||||
\(680\) | 1913.13 | + | 3313.65i | 0.107890 | + | 0.186871i | ||||
\(681\) | −4678.86 | + | 6713.78i | −0.263281 | + | 0.377786i | ||||
\(682\) | −1824.71 | + | 3160.50i | −0.102451 | + | 0.177451i | ||||
\(683\) | −12957.7 | −0.725933 | −0.362966 | − | 0.931802i | \(-0.618236\pi\) | ||||
−0.362966 | + | 0.931802i | \(0.618236\pi\) | |||||||
\(684\) | 5393.08 | + | 14615.1i | 0.301476 | + | 0.816994i | ||||
\(685\) | −6014.07 | −0.335454 | ||||||||
\(686\) | 273.540 | − | 473.785i | 0.0152242 | − | 0.0263691i | ||||
\(687\) | −986.617 | − | 2103.60i | −0.0547916 | − | 0.116823i | ||||
\(688\) | −419.550 | − | 726.681i | −0.0232488 | − | 0.0402681i | ||||
\(689\) | 4677.28 | + | 8101.28i | 0.258621 | + | 0.447945i | ||||
\(690\) | 1388.28 | + | 2960.01i | 0.0765956 | + | 0.163312i | ||||
\(691\) | −285.528 | + | 494.549i | −0.0157192 | + | 0.0272265i | −0.873778 | − | 0.486325i | \(-0.838337\pi\) |
0.858059 | + | 0.513551i | \(0.171670\pi\) | |||||||
\(692\) | −10623.4 | −0.583586 | ||||||||
\(693\) | 529.376 | + | 1434.60i | 0.0290178 | + | 0.0786377i | ||||
\(694\) | 10164.1 | 0.555944 | ||||||||
\(695\) | −2618.56 | + | 4535.48i | −0.142918 | + | 0.247541i | ||||
\(696\) | −4632.66 | + | 6647.48i | −0.252300 | + | 0.362029i | ||||
\(697\) | −3037.52 | − | 5261.14i | −0.165071 | − | 0.285911i | ||||
\(698\) | 2190.98 | + | 3794.89i | 0.118811 | + | 0.205786i | ||||
\(699\) | 20366.3 | + | 1736.27i | 1.10204 | + | 0.0939513i | ||||
\(700\) | 2262.22 | − | 3918.28i | 0.122148 | − | 0.211567i | ||||
\(701\) | −26258.8 | −1.41481 | −0.707404 | − | 0.706810i | \(-0.750134\pi\) | ||||
−0.707404 | + | 0.706810i | \(0.750134\pi\) | |||||||
\(702\) | −5681.07 | − | 1481.76i | −0.305439 | − | 0.0796659i | ||||
\(703\) | 2728.10 | 0.146361 | ||||||||
\(704\) | −900.011 | + | 1558.87i | −0.0481825 | + | 0.0834545i | ||||
\(705\) | −4163.97 | − | 354.988i | −0.222446 | − | 0.0189640i | ||||
\(706\) | −8197.67 | − | 14198.8i | −0.437002 | − | 0.756910i | ||||
\(707\) | 3921.98 | + | 6793.07i | 0.208630 | + | 0.361358i | ||||
\(708\) | 6686.24 | − | 9594.20i | 0.354921 | − | 0.509283i | ||||
\(709\) | 5120.65 | − | 8869.22i | 0.271241 | − | 0.469803i | −0.697939 | − | 0.716157i | \(-0.745899\pi\) |
0.969180 | + | 0.246354i | \(0.0792326\pi\) | |||||||
\(710\) | −4235.35 | −0.223873 | ||||||||
\(711\) | −12883.5 | + | 15493.1i | −0.679561 | + | 0.817210i | ||||
\(712\) | 13819.3 | 0.727390 | ||||||||
\(713\) | −21820.3 | + | 37794.0i | −1.14611 | + | 1.98513i | ||||
\(714\) | −1718.04 | − | 3663.09i | −0.0900503 | − | 0.192000i | ||||
\(715\) | −271.328 | − | 469.954i | −0.0141917 | − | 0.0245808i | ||||
\(716\) | −2296.72 | − | 3978.04i | −0.119878 | − | 0.207635i | ||||
\(717\) | 8117.60 | + | 17307.8i | 0.422813 | + | 0.901496i | ||||
\(718\) | 8352.71 | − | 14467.3i | 0.434151 | − | 0.751971i | ||||
\(719\) | −9398.00 | −0.487464 | −0.243732 | − | 0.969843i | \(-0.578372\pi\) | ||||
−0.243732 | + | 0.969843i | \(0.578372\pi\) | |||||||
\(720\) | −640.546 | − | 110.016i | −0.0331552 | − | 0.00569450i | ||||
\(721\) | −3956.58 | −0.204370 | ||||||||
\(722\) | −3448.55 | + | 5973.07i | −0.177759 | + | 0.307887i | ||||
\(723\) | −2474.81 | + | 3551.15i | −0.127302 | + | 0.182668i | ||||
\(724\) | 431.736 | + | 747.789i | 0.0221621 | + | 0.0383859i | ||||
\(725\) | −4303.53 | − | 7453.93i | −0.220454 | − | 0.381837i | ||||
\(726\) | −10450.6 | − | 890.938i | −0.534240 | − | 0.0455452i | ||||
\(727\) | −3140.35 | + | 5439.24i | −0.160205 | + | 0.277483i | −0.934942 | − | 0.354800i | \(-0.884549\pi\) |
0.774737 | + | 0.632283i | \(0.217882\pi\) | |||||||
\(728\) | −3941.77 | −0.200675 | ||||||||
\(729\) | 17175.5 | + | 9613.60i | 0.872608 | + | 0.488422i | ||||
\(730\) | 4717.83 | 0.239198 | ||||||||
\(731\) | 3107.32 | − | 5382.04i | 0.157221 | − | 0.272314i | ||||
\(732\) | −4145.55 | − | 353.417i | −0.209322 | − | 0.0178452i | ||||
\(733\) | −5268.97 | − | 9126.13i | −0.265503 | − | 0.459865i | 0.702192 | − | 0.711988i | \(-0.252205\pi\) |
−0.967695 | + | 0.252122i | \(0.918872\pi\) | |||||||
\(734\) | −1581.05 | − | 2738.46i | −0.0795063 | − | 0.137709i | ||||
\(735\) | 372.139 | − | 533.988i | 0.0186756 | − | 0.0267979i | ||||
\(736\) | −14406.7 | + | 24953.2i | −0.721521 | + | 1.24971i | ||||
\(737\) | −2479.03 | −0.123902 | ||||||||
\(738\) | −3697.17 | − | 635.000i | −0.184410 | − | 0.0316730i | ||||
\(739\) | 20509.6 | 1.02092 | 0.510459 | − | 0.859902i | \(-0.329475\pi\) | ||||
0.510459 | + | 0.859902i | \(0.329475\pi\) | |||||||
\(740\) | −179.903 | + | 311.601i | −0.00893696 | + | 0.0154793i | ||||
\(741\) | 6122.02 | + | 13053.0i | 0.303506 | + | 0.647117i | ||||
\(742\) | 1990.35 | + | 3447.38i | 0.0984742 | + | 0.170562i | ||||
\(743\) | 13139.5 | + | 22758.2i | 0.648776 | + | 1.12371i | 0.983416 | + | 0.181367i | \(0.0580520\pi\) |
−0.334640 | + | 0.942346i | \(0.608615\pi\) | |||||||
\(744\) | 13391.9 | + | 28553.4i | 0.659908 | + | 1.40702i | ||||
\(745\) | 1653.92 | − | 2864.68i | 0.0813357 | − | 0.140878i | ||||
\(746\) | 14899.8 | 0.731261 | ||||||||
\(747\) | −9070.54 | + | 10907.8i | −0.444276 | + | 0.534266i | ||||
\(748\) | 3078.60 | 0.150487 | ||||||||
\(749\) | 5576.33 | − | 9658.48i | 0.272035 | − | 0.471179i | ||||
\(750\) | −2949.19 | + | 4231.84i | −0.143585 | + | 0.206033i | ||||
\(751\) | 688.771 | + | 1192.99i | 0.0334668 | + | 0.0579663i | 0.882274 | − | 0.470737i | \(-0.156012\pi\) |
−0.848807 | + | 0.528703i | \(0.822679\pi\) | |||||||
\(752\) | −1481.28 | − | 2565.65i | −0.0718306 | − | 0.124414i | ||||
\(753\) | 37470.1 | + | 3194.41i | 1.81339 | + | 0.154596i | ||||
\(754\) | −1520.23 | + | 2633.12i | −0.0734265 | + | 0.127178i | ||||
\(755\) | 5474.85 | 0.263907 | ||||||||
\(756\) | 5184.76 | + | 1352.31i | 0.249428 | + | 0.0650569i | ||||
\(757\) | 13632.8 | 0.654549 | 0.327275 | − | 0.944929i | \(-0.393870\pi\) | ||||
0.327275 | + | 0.944929i | \(0.393870\pi\) | |||||||
\(758\) | −7149.07 | + | 12382.6i | −0.342567 | + | 0.593344i | ||||
\(759\) | 6464.17 | + | 551.085i | 0.309136 | + | 0.0263546i | ||||
\(760\) | −2900.97 | − | 5024.62i | −0.138459 | − | 0.239819i | ||||
\(761\) | −776.057 | − | 1344.17i | −0.0369672 | − | 0.0640291i | 0.846950 | − | 0.531673i | \(-0.178436\pi\) |
−0.883917 | + | 0.467644i | \(0.845103\pi\) | |||||||
\(762\) | 6527.47 | − | 9366.37i | 0.310322 | − | 0.445286i | ||||
\(763\) | −5245.24 | + | 9085.01i | −0.248873 | + | 0.431061i | ||||
\(764\) | 25201.2 | 1.19338 | ||||||||
\(765\) | −1666.40 | − | 4515.91i | −0.0787565 | − | 0.213429i | ||||
\(766\) | 7291.46 | 0.343931 | ||||||||
\(767\) | 5411.31 | − | 9372.66i | 0.254747 | − | 0.441235i | ||||
\(768\) | 7935.06 | + | 16918.6i | 0.372828 | + | 0.794921i | ||||
\(769\) | 5314.20 | + | 9204.46i | 0.249200 | + | 0.431627i | 0.963304 | − | 0.268412i | \(-0.0864990\pi\) |
−0.714104 | + | 0.700040i | \(0.753166\pi\) | |||||||
\(770\) | −115.460 | − | 199.982i | −0.00540374 | − | 0.00935955i | ||||
\(771\) | 6793.11 | + | 14483.8i | 0.317313 | + | 0.676554i | ||||
\(772\) | 12524.2 | − | 21692.6i | 0.583881 | − | 1.01131i | ||||
\(773\) | −20748.7 | −0.965432 | −0.482716 | − | 0.875777i | \(-0.660350\pi\) | ||||
−0.482716 | + | 0.875777i | \(0.660350\pi\) | |||||||
\(774\) | −1328.50 | − | 3600.22i | −0.0616952 | − | 0.167193i | ||||
\(775\) | −33501.9 | −1.55280 | ||||||||
\(776\) | 3317.64 | − | 5746.33i | 0.153475 | − | 0.265826i | ||||
\(777\) | 536.496 | − | 769.828i | 0.0247705 | − | 0.0355436i | ||||
\(778\) | −7047.59 | − | 12206.8i | −0.324767 | − | 0.562512i | ||||
\(779\) | 4605.92 | + | 7977.69i | 0.211841 | + | 0.366920i | ||||
\(780\) | −1894.61 | − | 161.520i | −0.0869719 | − | 0.00741455i | ||||
\(781\) | −4202.21 | + | 7278.44i | −0.192531 | + | 0.333474i | ||||
\(782\) | −17165.5 | −0.784958 | ||||||||
\(783\) | 7159.51 | − | 7255.50i | 0.326769 | − | 0.331150i | ||||
\(784\) | 461.402 | 0.0210187 | ||||||||
\(785\) | 3308.13 | − | 5729.85i | 0.150410 | − | 0.260518i | ||||
\(786\) | −22480.1 | − | 1916.48i | −1.02015 | − | 0.0869700i | ||||
\(787\) | 11193.0 | + | 19386.9i | 0.506973 | + | 0.878103i | 0.999967 | + | 0.00807037i | \(0.00256891\pi\) |
−0.492995 | + | 0.870032i | \(0.664098\pi\) | |||||||
\(788\) | −7218.41 | − | 12502.7i | −0.326326 | − | 0.565214i | ||||
\(789\) | 11756.4 | − | 16869.5i | 0.530469 | − | 0.761179i | ||||
\(790\) | 1521.43 | − | 2635.19i | 0.0685190 | − | 0.118678i | ||||
\(791\) | −4866.95 | −0.218772 | ||||||||
\(792\) | 2997.69 | − | 3604.89i | 0.134493 | − | 0.161735i | ||||
\(793\) | −3850.49 | −0.172427 | ||||||||
\(794\) | 2910.30 | − | 5040.78i | 0.130079 | − | 0.225303i | ||||
\(795\) | 2011.00 | + | 4287.72i | 0.0897140 | + | 0.191283i | ||||
\(796\) | 12935.1 | + | 22404.2i | 0.575970 | + | 0.997609i | ||||
\(797\) | 518.525 | + | 898.112i | 0.0230453 | + | 0.0399156i | 0.877318 | − | 0.479909i | \(-0.159330\pi\) |
−0.854273 | + | 0.519825i | \(0.825997\pi\) | |||||||
\(798\) | 2605.13 | + | 5554.50i | 0.115565 | + | 0.246400i | ||||
\(799\) | 10970.8 | − | 19002.0i | 0.485757 | − | 0.841355i | ||||
\(800\) | −22119.4 | −0.977548 | ||||||||
\(801\) | −17134.2 | − | 2942.86i | −0.755816 | − | 0.129814i | ||||
\(802\) | −1626.03 | −0.0715925 | ||||||||
\(803\) | 4680.91 | − | 8107.57i | 0.205711 | − | 0.356301i | ||||
\(804\) | −4966.62 | + | 7126.68i | −0.217860 | + | 0.312610i | ||||
\(805\) | −1380.69 | − | 2391.43i | −0.0604510 | − | 0.104704i | ||||
\(806\) | 5917.31 | + | 10249.1i | 0.258596 | + | 0.447901i | ||||
\(807\) | −13214.2 | − | 1126.54i | −0.576408 | − | 0.0491401i | ||||
\(808\) | 12024.9 | − | 20827.7i | 0.523557 | − | 0.906827i | ||||
\(809\) | −10345.1 | −0.449586 | −0.224793 | − | 0.974407i | \(-0.572171\pi\) | ||||
−0.224793 | + | 0.974407i | \(0.572171\pi\) | |||||||
\(810\) | −2802.01 | − | 991.763i | −0.121546 | − | 0.0430210i | ||||
\(811\) | 8037.38 | 0.348003 | 0.174002 | − | 0.984745i | \(-0.444330\pi\) | ||||
0.174002 | + | 0.984745i | \(0.444330\pi\) | |||||||
\(812\) | 1387.42 | − | 2403.08i | 0.0599617 | − | 0.103857i | ||||
\(813\) | −9780.00 | − | 833.768i | −0.421894 | − | 0.0359674i | ||||
\(814\) | −166.453 | − | 288.305i | −0.00716730 | − | 0.0124141i | ||||
\(815\) | 1077.41 | + | 1866.13i | 0.0463069 | + | 0.0802059i | ||||
\(816\) | 1951.03 | − | 2799.56i | 0.0837005 | − | 0.120103i | ||||
\(817\) | −4711.76 | + | 8161.02i | −0.201767 | + | 0.349471i | ||||
\(818\) | 2201.34 | 0.0940931 | ||||||||
\(819\) | 4887.29 | + | 839.406i | 0.208517 | + | 0.0358135i | ||||
\(820\) | −1214.94 | −0.0517408 | ||||||||
\(821\) | 6094.85 | − | 10556.6i | 0.259089 | − | 0.448755i | −0.706909 | − | 0.707304i | \(-0.749911\pi\) |
0.965998 | + | 0.258549i | \(0.0832445\pi\) | |||||||
\(822\) | −8279.44 | − | 17652.9i | −0.351312 | − | 0.749045i | ||||
\(823\) | 8913.36 | + | 15438.4i | 0.377521 | + | 0.653886i | 0.990701 | − | 0.136057i | \(-0.0434431\pi\) |
−0.613180 | + | 0.789944i | \(0.710110\pi\) | |||||||
\(824\) | 6065.49 | + | 10505.7i | 0.256434 | + | 0.444156i | ||||
\(825\) | 2114.81 | + | 4509.08i | 0.0892465 | + | 0.190286i | ||||
\(826\) | 2302.70 | − | 3988.39i | 0.0969990 | − | 0.168007i | ||||
\(827\) | −41268.6 | −1.73525 | −0.867624 | − | 0.497220i | \(-0.834354\pi\) | ||||
−0.867624 | + | 0.497220i | \(0.834354\pi\) | |||||||
\(828\) | 14534.9 | − | 17479.1i | 0.610053 | − | 0.733622i | ||||
\(829\) | −42762.2 | −1.79155 | −0.895774 | − | 0.444509i | \(-0.853378\pi\) | ||||
−0.895774 | + | 0.444509i | \(0.853378\pi\) | |||||||
\(830\) | 1071.16 | − | 1855.30i | 0.0447956 | − | 0.0775883i | ||||
\(831\) | 8773.06 | − | 12588.6i | 0.366226 | − | 0.525504i | ||||
\(832\) | 2918.62 | + | 5055.20i | 0.121616 | + | 0.210646i | ||||
\(833\) | 1708.65 | + | 2959.46i | 0.0710698 | + | 0.123097i | ||||
\(834\) | −16917.8 | − | 1442.28i | −0.702416 | − | 0.0598825i | ||||
\(835\) | 2118.41 | − | 3669.19i | 0.0877971 | − | 0.152069i | ||||
\(836\) | −4668.21 | −0.193126 | ||||||||
\(837\) | −10523.8 | − | 38254.5i | −0.434594 | − | 1.57977i | ||||
\(838\) | 18006.6 | 0.742277 | ||||||||
\(839\) | 22207.9 | − | 38465.2i | 0.913828 | − | 1.58280i | 0.105220 | − | 0.994449i | \(-0.466445\pi\) |
0.808608 | − | 0.588348i | \(-0.200221\pi\) | |||||||
\(840\) | −1988.37 | − | 169.513i | −0.0816728 | − | 0.00696279i | ||||
\(841\) | 9555.14 | + | 16550.0i | 0.391781 | + | 0.678584i | ||||
\(842\) | 9043.67 | + | 15664.1i | 0.370149 | + | 0.641117i | ||||
\(843\) | −3584.36 | + | 5143.26i | −0.146444 | + | 0.210134i | ||||
\(844\) | −12496.4 | + | 21644.5i | −0.509651 | + | 0.882741i | ||||
\(845\) | 3856.48 | 0.157002 | ||||||||
\(846\) | −4690.46 | − | 12711.1i | −0.190616 | − | 0.516567i | ||||
\(847\) | 8858.78 | 0.359376 | ||||||||
\(848\) | −1678.64 | + | 2907.49i | −0.0679773 | + | 0.117740i | ||||
\(849\) | −8158.32 | − | 17394.7i | −0.329791 | − | 0.703161i | ||||
\(850\) | −6588.76 | − | 11412.1i | −0.265874 | − | 0.460507i | ||||
\(851\) | −1990.49 | − | 3447.62i | −0.0801798 | − | 0.138875i | ||||
\(852\) | 12505.0 | + | 26662.5i | 0.502835 | + | 1.07211i | ||||
\(853\) | −4585.60 | + | 7942.50i | −0.184066 | + | 0.318811i | −0.943261 | − | 0.332051i | \(-0.892259\pi\) |
0.759196 | + | 0.650863i | \(0.225593\pi\) | |||||||
\(854\) | −1638.52 | −0.0656544 | ||||||||
\(855\) | 2526.83 | + | 6847.67i | 0.101071 | + | 0.273901i | ||||
\(856\) | −34194.3 | −1.36535 | ||||||||
\(857\) | −5911.62 | + | 10239.2i | −0.235633 | + | 0.408128i | −0.959456 | − | 0.281857i | \(-0.909050\pi\) |
0.723824 | + | 0.689985i | \(0.242383\pi\) | |||||||
\(858\) | 1005.91 | − | 1443.40i | 0.0400247 | − | 0.0574321i | ||||
\(859\) | −1386.20 | − | 2400.97i | −0.0550600 | − | 0.0953667i | 0.837182 | − | 0.546925i | \(-0.184202\pi\) |
−0.892242 | + | 0.451558i | \(0.850868\pi\) | |||||||
\(860\) | −621.429 | − | 1076.35i | −0.0246402 | − | 0.0426780i | ||||
\(861\) | 3156.97 | + | 269.139i | 0.124958 | + | 0.0106530i | ||||
\(862\) | −12173.7 | + | 21085.4i | −0.481017 | + | 0.833146i | ||||
\(863\) | 7669.34 | 0.302512 | 0.151256 | − | 0.988495i | \(-0.451668\pi\) | ||||
0.151256 | + | 0.988495i | \(0.451668\pi\) | |||||||
\(864\) | −6948.26 | − | 25257.3i | −0.273593 | − | 0.994525i | ||||
\(865\) | −4977.41 | −0.195650 | ||||||||
\(866\) | 2685.24 | − | 4650.97i | 0.105367 | − | 0.182502i | ||||
\(867\) | −254.884 | − | 21.7295i | −0.00998422 | − | 0.000851178i | ||||
\(868\) | −5400.36 | − | 9353.69i | −0.211175 | − | 0.365766i | ||||
\(869\) | −3019.04 | − | 5229.14i | −0.117853 | − | 0.204127i | ||||
\(870\) | −880.095 | + | 1262.86i | −0.0342966 | + | 0.0492127i | ||||
\(871\) | −4019.58 | + | 6962.12i | −0.156370 | + | 0.270841i | ||||
\(872\) | 32164.0 | 1.24910 | ||||||||
\(873\) | −5337.15 | + | 6418.22i | −0.206913 | + | 0.248825i | ||||
\(874\) | 26028.8 | 1.00737 | ||||||||
\(875\) | 2178.31 | − | 3772.95i | 0.0841606 | − | 0.145770i | ||||
\(876\) | −13929.6 | − | 29699.8i | −0.537257 | − | 1.14551i | ||||
\(877\) | 6933.86 | + | 12009.8i | 0.266978 | + | 0.462420i | 0.968080 | − | 0.250642i | \(-0.0806415\pi\) |
−0.701102 | + | 0.713061i | \(0.747308\pi\) | |||||||
\(878\) | −8814.98 | − | 15268.0i | −0.338828 | − | 0.586867i | ||||
\(879\) | −5485.16 | − | 11695.1i | −0.210478 | − | 0.448767i | ||||
\(880\) | 97.3777 | − | 168.663i | 0.00373023 | − | 0.00646095i | ||||
\(881\) | 19974.2 | 0.763846 | 0.381923 | − | 0.924194i | \(-0.375262\pi\) | ||||
0.381923 | + | 0.924194i | \(0.375262\pi\) | |||||||
\(882\) | 2079.71 | + | 357.197i | 0.0793964 | + | 0.0136366i | ||||
\(883\) | 22197.0 | 0.845969 | 0.422984 | − | 0.906137i | \(-0.360983\pi\) | ||||
0.422984 | + | 0.906137i | \(0.360983\pi\) | |||||||
\(884\) | 4991.74 | − | 8645.95i | 0.189921 | − | 0.328953i | ||||
\(885\) | 3132.72 | − | 4495.19i | 0.118989 | − | 0.170739i | ||||
\(886\) | −6171.13 | − | 10688.7i | −0.233999 | − | 0.405298i | ||||
\(887\) | 16850.9 | + | 29186.6i | 0.637877 | + | 1.10484i | 0.985898 | + | 0.167349i | \(0.0535206\pi\) |
−0.348021 | + | 0.937487i | \(0.613146\pi\) | |||||||
\(888\) | −2866.54 | − | 244.379i | −0.108328 | − | 0.00923517i | ||||
\(889\) | −4821.29 | + | 8350.71i | −0.181891 | + | 0.315044i | ||||
\(890\) | 2625.34 | 0.0988784 | ||||||||
\(891\) | −4484.42 | + | 3831.24i | −0.168613 | + | 0.144053i | ||||
\(892\) | −24422.7 | −0.916739 | ||||||||
\(893\) | −16635.5 | + | 28813.6i | −0.623389 | + | 1.07974i | ||||
\(894\) | 10685.5 | + | 910.965i | 0.399751 | + | 0.0340797i | ||||
\(895\) | −1076.09 | − | 1863.84i | −0.0401896 | − | 0.0696104i | ||||
\(896\) | −3986.08 | − | 6904.09i | −0.148622 | − | 0.257421i | ||||
\(897\) | 12028.9 | − | 17260.5i | 0.447752 | − | 0.642487i | ||||
\(898\) | −964.616 | + | 1670.76i | −0.0358459 | + | 0.0620870i | ||||
\(899\) | −20546.7 | −0.762259 | ||||||||
\(900\) | 17199.6 | + | 2954.08i | 0.637021 | + | 0.109410i | ||||
\(901\) | −24865.1 | −0.919397 | ||||||||
\(902\) | 562.055 | − | 973.508i | 0.0207477 | − | 0.0359360i | ||||
\(903\) | 1376.32 | + | 2934.50i | 0.0507210 | + | 0.108144i | ||||
\(904\) | 7461.08 | + | 12923.0i | 0.274504 | + | 0.475456i | ||||
\(905\) | 202.282 | + | 350.363i | 0.00742994 | + | 0.0128690i | ||||
\(906\) | 7537.11 | + | 16070.1i | 0.276384 | + | 0.589288i | ||||
\(907\) | 11950.2 | − | 20698.3i | 0.437485 | − | 0.757746i | −0.560010 | − | 0.828486i | \(-0.689203\pi\) |
0.997495 | + | 0.0707396i | \(0.0225359\pi\) | |||||||
\(908\) | −8592.58 | −0.314047 | ||||||||
\(909\) | −19344.6 | + | 23263.0i | −0.705854 | + | 0.848829i | ||||
\(910\) | −748.841 | −0.0272789 | ||||||||
\(911\) | 6376.80 | − | 11044.9i | 0.231913 | − | 0.401685i | −0.726458 | − | 0.687211i | \(-0.758835\pi\) |
0.958371 | + | 0.285526i | \(0.0921682\pi\) | |||||||
\(912\) | −2958.43 | + | 4245.10i | −0.107416 | + | 0.154133i | ||||
\(913\) | −2125.54 | − | 3681.55i | −0.0770485 | − | 0.133452i | ||||
\(914\) | 11370.3 | + | 19694.0i | 0.411485 | + | 0.712713i | ||||
\(915\) | −1942.32 | − | 165.587i | −0.0701761 | − | 0.00598268i | ||||
\(916\) | 1219.84 | − | 2112.83i | 0.0440008 | − | 0.0762115i | ||||
\(917\) | 19055.9 | 0.686239 | ||||||||
\(918\) | 10961.3 | − | 11108.3i | 0.394093 | − | 0.399377i | ||||
\(919\) | −10491.5 | −0.376585 | −0.188293 | − | 0.982113i | \(-0.560295\pi\) | ||||
−0.188293 | + | 0.982113i | \(0.560295\pi\) | |||||||
\(920\) | −4233.24 | + | 7332.18i | −0.151702 | + | 0.262755i | ||||
\(921\) | −11224.4 | − | 956.909i | −0.401583 | − | 0.0342359i | ||||
\(922\) | −9504.48 | − | 16462.2i | −0.339494 | − | 0.588020i | ||||
\(923\) | 13627.2 | + | 23603.0i | 0.485964 | + | 0.841715i | ||||
\(924\) | −918.031 | + | 1317.30i | −0.0326851 | + | 0.0469003i | ||||
\(925\) | 1528.05 | − | 2646.65i | 0.0543155 | − | 0.0940772i | ||||
\(926\) | 12538.0 | 0.444949 | ||||||||
\(927\) | −5283.22 | − | 14317.4i | −0.187189 | − | 0.507278i | ||||
\(928\) | −13565.8 | −0.479870 | ||||||||
\(929\) | 25022.9 | − | 43341.0i | 0.883720 | − | 1.53065i | 0.0365465 | − | 0.999332i | \(-0.488364\pi\) |
0.847174 | − | 0.531316i | \(-0.178302\pi\) | |||||||
\(930\) | 2544.15 | + | 5424.47i | 0.0897052 | + | 0.191264i | ||||
\(931\) | −2590.90 | − | 4487.56i | −0.0912064 | − | 0.157974i | ||||
\(932\) | 10731.2 | + | 18587.0i | 0.377160 | + | 0.653260i | ||||
\(933\) | −10286.4 | − | 21931.9i | −0.360944 | − | 0.769581i | ||||
\(934\) | −12881.4 | + | 22311.2i | −0.451275 | + | 0.781631i | ||||
\(935\) | 1442.42 | 0.0504516 | ||||||||
\(936\) | −5263.44 | − | 14263.8i | −0.183804 | − | 0.498106i | ||||
\(937\) | −35500.0 | −1.23771 | −0.618855 | − | 0.785505i | \(-0.712403\pi\) | ||||
−0.618855 | + | 0.785505i | \(0.712403\pi\) | |||||||
\(938\) | −1710.47 | + | 2962.62i | −0.0595404 | + | 0.103127i | ||||
\(939\) | −1483.06 | + | 2128.07i | −0.0515419 | + | 0.0739584i | ||||
\(940\) | −2194.04 | − | 3800.19i | −0.0761294 | − | 0.131860i | ||||
\(941\) | −21132.1 | − | 36601.8i | −0.732078 | − | 1.26800i | −0.955994 | − | 0.293387i | \(-0.905217\pi\) |
0.223916 | − | 0.974608i | \(-0.428116\pi\) | |||||||
\(942\) | 21372.9 | + | 1822.09i | 0.739241 | + | 0.0630220i | ||||
\(943\) | 6721.19 | − | 11641.4i | 0.232102 | − | 0.402012i | ||||
\(944\) | 3884.15 | 0.133918 | ||||||||
\(945\) | 2429.23 | + | 633.601i | 0.0836219 | + | 0.0218106i | ||||
\(946\) | 1149.94 | 0.0395220 | ||||||||
\(947\) | 24497.8 | − | 42431.4i | 0.840624 | − | 1.45600i | −0.0487434 | − | 0.998811i | \(-0.515522\pi\) |
0.889368 | − | 0.457193i | \(-0.151145\pi\) | |||||||
\(948\) | −21081.2 | − | 1797.22i | −0.722242 | − | 0.0615728i | ||||
\(949\) | −15179.6 | − | 26291.8i | −0.519231 | − | 0.899334i | ||||
\(950\) | 9990.82 | + | 17304.6i | 0.341205 | + | 0.590985i | ||||
\(951\) | 29155.7 | − | 41836.0i | 0.994152 | − | 1.42653i | ||||
\(952\) | 5238.75 | − | 9073.78i | 0.178350 | − | 0.308911i | ||||
\(953\) | 5041.88 | 0.171377 | 0.0856886 | − | 0.996322i | \(-0.472691\pi\) | ||||
0.0856886 | + | 0.996322i | \(0.472691\pi\) | |||||||
\(954\) | −9817.10 | + | 11805.6i | −0.333166 | + | 0.400651i | ||||
\(955\) | 11807.6 | 0.400087 | ||||||||
\(956\) | −10036.5 | + | 17383.7i | −0.339543 | + | 0.588106i | ||||
\(957\) | 1297.02 | + | 2765.42i | 0.0438104 | + | 0.0934099i | ||||
\(958\) | 9333.73 | + | 16166.5i | 0.314780 | + | 0.545215i | ||||
\(959\) | 8234.19 | + | 14262.0i | 0.277264 | + | 0.480234i | ||||
\(960\) | 1254.86 | + | 2675.53i | 0.0421880 | + | 0.0899505i | ||||
\(961\) | −25092.2 | + | 43460.9i | −0.842274 | + | 1.45886i | ||||
\(962\) | −1079.57 | −0.0361817 | ||||||||
\(963\) | 42396.6 | + | 7281.74i | 1.41870 | + | 0.243666i | ||||
\(964\) | −4544.91 | −0.151848 | ||||||||
\(965\) | 5867.99 | − | 10163.7i | 0.195749 | − | 0.339046i | ||||
\(966\) | 5118.72 | − | 7344.94i | 0.170489 | − | 0.244637i | ||||
\(967\) | 3479.68 | + | 6026.99i | 0.115718 | + | 0.200429i | 0.918066 | − | 0.396427i | \(-0.129750\pi\) |
−0.802349 | + | 0.596856i | \(0.796417\pi\) | |||||||
\(968\) | −13580.6 | − | 23522.3i | −0.450927 | − | 0.781028i | ||||
\(969\) | −38183.9 | − | 3255.26i | −1.26588 | − | 0.107920i | ||||
\(970\) | 630.273 | − | 1091.66i | 0.0208627 | − | 0.0361353i | ||||
\(971\) | −12979.8 | −0.428983 | −0.214492 | − | 0.976726i | \(-0.568809\pi\) | ||||
−0.214492 | + | 0.976726i | \(0.568809\pi\) | |||||||
\(972\) | 2029.68 | + | 20567.5i | 0.0669774 | + | 0.678706i | ||||
\(973\) | 14340.9 | 0.472505 | ||||||||
\(974\) | −32.7975 | + | 56.8070i | −0.00107895 | + | 0.00186880i | ||||
\(975\) | 16092.4 | + | 1371.91i | 0.528582 | + | 0.0450629i | ||||
\(976\) | −690.955 | − | 1196.77i | −0.0226608 | − | 0.0392497i | ||||
\(977\) | 21131.1 | + | 36600.1i | 0.691958 | + | 1.19851i | 0.971195 | + | 0.238284i | \(0.0765850\pi\) |
−0.279238 | + | 0.960222i | \(0.590082\pi\) | |||||||
\(978\) | −3994.35 | + | 5731.56i | −0.130598 | + | 0.187398i | ||||
\(979\) | 2604.80 | − | 4511.64i | 0.0850354 | − | 0.147286i | ||||
\(980\) | 683.420 | 0.0222766 | ||||||||
\(981\) | −39879.3 | − | 6849.39i | −1.29791 | − | 0.222920i | ||||
\(982\) | 13454.7 | 0.437228 | ||||||||
\(983\) | −27093.9 | + | 46927.9i | −0.879105 | + | 1.52265i | −0.0267799 | + | 0.999641i | \(0.508525\pi\) |
−0.852325 | + | 0.523013i | \(0.824808\pi\) | |||||||
\(984\) | −4125.03 | − | 8795.13i | −0.133639 | − | 0.284938i | ||||
\(985\) | −3382.06 | − | 5857.90i | −0.109402 | − | 0.189490i | ||||
\(986\) | −4040.89 | − | 6999.03i | −0.130515 | − | 0.226059i | ||||
\(987\) | 4859.28 | + | 10360.7i | 0.156710 | + | 0.334127i | ||||
\(988\) | −7569.19 | + | 13110.2i | −0.243733 | + | 0.422158i | ||||
\(989\) | 13751.3 | 0.442129 | ||||||||
\(990\) | 569.489 | − | 684.842i | 0.0182824 | − | 0.0219856i | ||||
\(991\) | 37682.0 | 1.20788 | 0.603940 | − | 0.797030i | \(-0.293597\pi\) | ||||
0.603940 | + | 0.797030i | \(0.293597\pi\) | |||||||
\(992\) | −26401.6 | + | 45728.9i | −0.845012 | + | 1.46360i | ||||
\(993\) | −29799.5 | + | 42759.9i | −0.952326 | + | 1.36651i | ||||
\(994\) | 5798.85 | + | 10043.9i | 0.185039 | + | 0.320496i | ||||
\(995\) | 6060.51 | + | 10497.1i | 0.193096 | + | 0.334453i | ||||
\(996\) | −14842.1 | − | 1265.32i | −0.472179 | − | 0.0402544i | ||||
\(997\) | 24932.3 | − | 43184.1i | 0.791991 | − | 1.37177i | −0.132741 | − | 0.991151i | \(-0.542378\pi\) |
0.924732 | − | 0.380618i | \(-0.124289\pi\) | |||||||
\(998\) | 3486.88 | 0.110597 | ||||||||
\(999\) | 3502.11 | + | 913.435i | 0.110913 | + | 0.0289287i |
(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 | 63.4.f.b.43.4 | yes | 16 | |
3.2 | odd | 2 | 189.4.f.b.127.5 | 16 | |||
9.2 | odd | 6 | 567.4.a.g.1.4 | 8 | |||
9.4 | even | 3 | inner | 63.4.f.b.22.4 | ✓ | 16 | |
9.5 | odd | 6 | 189.4.f.b.64.5 | 16 | |||
9.7 | even | 3 | 567.4.a.i.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.f.b.22.4 | ✓ | 16 | 9.4 | even | 3 | inner | |
63.4.f.b.43.4 | yes | 16 | 1.1 | even | 1 | trivial | |
189.4.f.b.64.5 | 16 | 9.5 | odd | 6 | |||
189.4.f.b.127.5 | 16 | 3.2 | odd | 2 | |||
567.4.a.g.1.4 | 8 | 9.2 | odd | 6 | |||
567.4.a.i.1.5 | 8 | 9.7 | even | 3 |