Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(25,63)]
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([4, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.h (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: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 58.19 | ||
Character | \(\chi\) | \(=\) | 63.58 |
Dual form | 63.4.h.a.25.19 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.86663 | 1.36706 | 0.683531 | − | 0.729922i | \(-0.260443\pi\) | ||||
0.683531 | + | 0.729922i | \(0.260443\pi\) | |||||||
\(3\) | −3.99989 | + | 3.31676i | −0.769779 | + | 0.638311i | ||||
\(4\) | 6.95086 | 0.868858 | ||||||||
\(5\) | 6.67810 | + | 11.5668i | 0.597307 | + | 1.03457i | 0.993217 | + | 0.116277i | \(0.0370959\pi\) |
−0.395910 | + | 0.918289i | \(0.629571\pi\) | |||||||
\(6\) | −15.4661 | + | 12.8247i | −1.05234 | + | 0.872610i | ||||
\(7\) | 15.1080 | + | 10.7120i | 0.815757 | + | 0.578395i | ||||
\(8\) | −4.05663 | −0.179279 | ||||||||
\(9\) | 4.99821 | − | 26.5333i | 0.185119 | − | 0.982716i | ||||
\(10\) | 25.8218 | + | 44.7246i | 0.816556 | + | 1.41432i | ||||
\(11\) | 14.3605 | − | 24.8730i | 0.393622 | − | 0.681773i | −0.599302 | − | 0.800523i | \(-0.704555\pi\) |
0.992924 | + | 0.118750i | \(0.0378886\pi\) | |||||||
\(12\) | −27.8027 | + | 23.0543i | −0.668828 | + | 0.554601i | ||||
\(13\) | 2.75723 | − | 4.77566i | 0.0588244 | − | 0.101887i | −0.835114 | − | 0.550078i | \(-0.814598\pi\) |
0.893938 | + | 0.448191i | \(0.147931\pi\) | |||||||
\(14\) | 58.4172 | + | 41.4195i | 1.11519 | + | 0.790702i | ||||
\(15\) | −65.0759 | − | 24.1163i | −1.12017 | − | 0.415120i | ||||
\(16\) | −71.2924 | −1.11394 | ||||||||
\(17\) | −8.48010 | − | 14.6880i | −0.120984 | − | 0.209550i | 0.799172 | − | 0.601102i | \(-0.205272\pi\) |
−0.920156 | + | 0.391552i | \(0.871938\pi\) | |||||||
\(18\) | 19.3263 | − | 102.595i | 0.253069 | − | 1.34343i | ||||
\(19\) | 31.6694 | − | 54.8530i | 0.382393 | − | 0.662323i | −0.609011 | − | 0.793162i | \(-0.708434\pi\) |
0.991404 | + | 0.130838i | \(0.0417669\pi\) | |||||||
\(20\) | 46.4185 | + | 80.3993i | 0.518975 | + | 0.898891i | ||||
\(21\) | −95.9596 | + | 7.26276i | −0.997148 | + | 0.0754697i | ||||
\(22\) | 55.5266 | − | 96.1750i | 0.538106 | − | 0.932026i | ||||
\(23\) | −67.4183 | − | 116.772i | −0.611204 | − | 1.05864i | −0.991038 | − | 0.133582i | \(-0.957352\pi\) |
0.379834 | − | 0.925055i | \(-0.375981\pi\) | |||||||
\(24\) | 16.2261 | − | 13.4549i | 0.138005 | − | 0.114436i | ||||
\(25\) | −26.6939 | + | 46.2352i | −0.213551 | + | 0.369882i | ||||
\(26\) | 10.6612 | − | 18.4657i | 0.0804166 | − | 0.139286i | ||||
\(27\) | 68.0124 | + | 122.708i | 0.484778 | + | 0.874637i | ||||
\(28\) | 105.014 | + | 74.4579i | 0.708777 | + | 0.502543i | ||||
\(29\) | 118.224 | + | 204.770i | 0.757022 | + | 1.31120i | 0.944363 | + | 0.328905i | \(0.106680\pi\) |
−0.187341 | + | 0.982295i | \(0.559987\pi\) | |||||||
\(30\) | −251.625 | − | 93.2488i | −1.53134 | − | 0.567494i | ||||
\(31\) | 92.9315 | 0.538419 | 0.269210 | − | 0.963082i | \(-0.413238\pi\) | ||||
0.269210 | + | 0.963082i | \(0.413238\pi\) | |||||||
\(32\) | −243.209 | −1.34355 | ||||||||
\(33\) | 25.0577 | + | 147.120i | 0.132181 | + | 0.776068i | ||||
\(34\) | −32.7895 | − | 56.7930i | −0.165393 | − | 0.286468i | ||||
\(35\) | −23.0111 | + | 246.287i | −0.111131 | + | 1.18943i | ||||
\(36\) | 34.7419 | − | 184.430i | 0.160842 | − | 0.853841i | ||||
\(37\) | 202.752 | − | 351.177i | 0.900872 | − | 1.56036i | 0.0745066 | − | 0.997221i | \(-0.476262\pi\) |
0.826365 | − | 0.563135i | \(-0.190405\pi\) | |||||||
\(38\) | 122.454 | − | 212.097i | 0.522754 | − | 0.905437i | ||||
\(39\) | 4.81111 | + | 28.2472i | 0.0197537 | + | 0.115979i | ||||
\(40\) | −27.0905 | − | 46.9222i | −0.107085 | − | 0.185476i | ||||
\(41\) | −166.014 | + | 287.545i | −0.632368 | + | 1.09529i | 0.354698 | + | 0.934981i | \(0.384584\pi\) |
−0.987066 | + | 0.160313i | \(0.948750\pi\) | |||||||
\(42\) | −371.041 | + | 28.0824i | −1.36316 | + | 0.103172i | ||||
\(43\) | −173.016 | − | 299.673i | −0.613599 | − | 1.06279i | −0.990629 | − | 0.136584i | \(-0.956388\pi\) |
0.377029 | − | 0.926201i | \(-0.376946\pi\) | |||||||
\(44\) | 99.8176 | − | 172.889i | 0.342002 | − | 0.592364i | ||||
\(45\) | 340.284 | − | 119.379i | 1.12726 | − | 0.395465i | ||||
\(46\) | −260.682 | − | 451.514i | −0.835554 | − | 1.44722i | ||||
\(47\) | −304.957 | −0.946437 | −0.473218 | − | 0.880945i | \(-0.656908\pi\) | ||||
−0.473218 | + | 0.880945i | \(0.656908\pi\) | |||||||
\(48\) | 285.162 | − | 236.460i | 0.857490 | − | 0.711042i | ||||
\(49\) | 113.505 | + | 323.675i | 0.330918 | + | 0.943660i | ||||
\(50\) | −103.216 | + | 178.775i | −0.291938 | + | 0.505651i | ||||
\(51\) | 82.6359 | + | 30.6238i | 0.226889 | + | 0.0840821i | ||||
\(52\) | 19.1651 | − | 33.1949i | 0.0511100 | − | 0.0885252i | ||||
\(53\) | 332.075 | + | 575.170i | 0.860641 | + | 1.49067i | 0.871311 | + | 0.490730i | \(0.163270\pi\) |
−0.0106707 | + | 0.999943i | \(0.503397\pi\) | |||||||
\(54\) | 262.979 | + | 474.468i | 0.662721 | + | 1.19568i | ||||
\(55\) | 383.602 | 0.940453 | ||||||||
\(56\) | −61.2876 | − | 43.4547i | −0.146248 | − | 0.103694i | ||||
\(57\) | 55.2602 | + | 324.446i | 0.128410 | + | 0.753928i | ||||
\(58\) | 457.129 | + | 791.770i | 1.03490 | + | 1.79249i | ||||
\(59\) | −137.659 | −0.303757 | −0.151878 | − | 0.988399i | \(-0.548532\pi\) | ||||
−0.151878 | + | 0.988399i | \(0.548532\pi\) | |||||||
\(60\) | −452.334 | − | 167.629i | −0.973268 | − | 0.360680i | ||||
\(61\) | −620.516 | −1.30244 | −0.651221 | − | 0.758888i | \(-0.725743\pi\) | ||||
−0.651221 | + | 0.758888i | \(0.725743\pi\) | |||||||
\(62\) | 359.332 | 0.736052 | ||||||||
\(63\) | 359.739 | − | 347.325i | 0.719410 | − | 0.694585i | ||||
\(64\) | −370.060 | −0.722773 | ||||||||
\(65\) | 73.6521 | 0.140545 | ||||||||
\(66\) | 96.8889 | + | 568.858i | 0.180700 | + | 1.06093i | ||||
\(67\) | −587.763 | −1.07174 | −0.535871 | − | 0.844300i | \(-0.680017\pi\) | ||||
−0.535871 | + | 0.844300i | \(0.680017\pi\) | |||||||
\(68\) | −58.9440 | − | 102.094i | −0.105118 | − | 0.182069i | ||||
\(69\) | 656.970 | + | 243.464i | 1.14623 | + | 0.424778i | ||||
\(70\) | −88.9755 | + | 952.304i | −0.151923 | + | 1.62603i | ||||
\(71\) | −121.903 | −0.203764 | −0.101882 | − | 0.994796i | \(-0.532486\pi\) | ||||
−0.101882 | + | 0.994796i | \(0.532486\pi\) | |||||||
\(72\) | −20.2759 | + | 107.636i | −0.0331880 | + | 0.176181i | ||||
\(73\) | 143.624 | + | 248.763i | 0.230272 | + | 0.398843i | 0.957888 | − | 0.287142i | \(-0.0927051\pi\) |
−0.727616 | + | 0.685985i | \(0.759372\pi\) | |||||||
\(74\) | 783.969 | − | 1357.87i | 1.23155 | − | 2.13310i | ||||
\(75\) | −46.5784 | − | 273.473i | −0.0717122 | − | 0.421039i | ||||
\(76\) | 220.130 | − | 381.276i | 0.332245 | − | 0.575465i | ||||
\(77\) | 483.399 | − | 221.953i | 0.715434 | − | 0.328492i | ||||
\(78\) | 18.6028 | + | 109.221i | 0.0270045 | + | 0.158550i | ||||
\(79\) | 977.500 | 1.39212 | 0.696059 | − | 0.717984i | \(-0.254935\pi\) | ||||
0.696059 | + | 0.717984i | \(0.254935\pi\) | |||||||
\(80\) | −476.097 | − | 824.625i | −0.665366 | − | 1.15245i | ||||
\(81\) | −679.036 | − | 265.238i | −0.931462 | − | 0.363839i | ||||
\(82\) | −641.917 | + | 1111.83i | −0.864487 | + | 1.49733i | ||||
\(83\) | −507.709 | − | 879.377i | −0.671425 | − | 1.16294i | −0.977500 | − | 0.210934i | \(-0.932349\pi\) |
0.306075 | − | 0.952007i | \(-0.400984\pi\) | |||||||
\(84\) | −667.002 | + | 50.4824i | −0.866380 | + | 0.0655725i | ||||
\(85\) | 113.262 | − | 196.175i | 0.144529 | − | 0.250332i | ||||
\(86\) | −668.992 | − | 1158.73i | −0.838828 | − | 1.45289i | ||||
\(87\) | −1152.05 | − | 426.936i | −1.41969 | − | 0.526119i | ||||
\(88\) | −58.2550 | + | 100.901i | −0.0705683 | + | 0.122228i | ||||
\(89\) | −258.781 | + | 448.222i | −0.308211 | + | 0.533837i | −0.977971 | − | 0.208741i | \(-0.933063\pi\) |
0.669760 | + | 0.742577i | \(0.266397\pi\) | |||||||
\(90\) | 1315.76 | − | 461.594i | 1.54103 | − | 0.540626i | ||||
\(91\) | 92.8132 | − | 42.6152i | 0.106917 | − | 0.0490911i | ||||
\(92\) | −468.616 | − | 811.666i | −0.531049 | − | 0.919805i | ||||
\(93\) | −371.716 | + | 308.231i | −0.414464 | + | 0.343679i | ||||
\(94\) | −1179.16 | −1.29384 | ||||||||
\(95\) | 845.965 | 0.913623 | ||||||||
\(96\) | 972.807 | − | 806.665i | 1.03424 | − | 0.857603i | ||||
\(97\) | −823.870 | − | 1426.99i | −0.862385 | − | 1.49369i | −0.869620 | − | 0.493721i | \(-0.835636\pi\) |
0.00723506 | − | 0.999974i | \(-0.497697\pi\) | |||||||
\(98\) | 438.882 | + | 1251.53i | 0.452385 | + | 1.29004i | ||||
\(99\) | −588.188 | − | 505.352i | −0.597123 | − | 0.513028i | ||||
\(100\) | −185.546 | + | 321.375i | −0.185546 | + | 0.321375i | ||||
\(101\) | −470.263 | + | 814.519i | −0.463296 | + | 0.802452i | −0.999123 | − | 0.0418759i | \(-0.986667\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(102\) | 319.523 | + | 118.411i | 0.310171 | + | 0.114945i | ||||
\(103\) | −50.1054 | − | 86.7851i | −0.0479323 | − | 0.0830212i | 0.841064 | − | 0.540936i | \(-0.181930\pi\) |
−0.888996 | + | 0.457915i | \(0.848597\pi\) | |||||||
\(104\) | −11.1850 | + | 19.3731i | −0.0105460 | + | 0.0182662i | ||||
\(105\) | −724.835 | − | 1061.44i | −0.673682 | − | 0.986537i | ||||
\(106\) | 1284.01 | + | 2223.97i | 1.17655 | + | 2.03784i | ||||
\(107\) | 232.210 | − | 402.200i | 0.209800 | − | 0.363384i | −0.741851 | − | 0.670564i | \(-0.766052\pi\) |
0.951651 | + | 0.307180i | \(0.0993853\pi\) | |||||||
\(108\) | 472.745 | + | 852.928i | 0.421203 | + | 0.759936i | ||||
\(109\) | −227.492 | − | 394.028i | −0.199906 | − | 0.346248i | 0.748591 | − | 0.663032i | \(-0.230730\pi\) |
−0.948498 | + | 0.316783i | \(0.897397\pi\) | |||||||
\(110\) | 1483.25 | 1.28566 | ||||||||
\(111\) | 353.784 | + | 2077.15i | 0.302520 | + | 1.77616i | ||||
\(112\) | −1077.09 | − | 763.686i | −0.908707 | − | 0.644300i | ||||
\(113\) | −443.068 | + | 767.417i | −0.368853 | + | 0.638872i | −0.989386 | − | 0.145308i | \(-0.953583\pi\) |
0.620534 | + | 0.784180i | \(0.286916\pi\) | |||||||
\(114\) | 213.671 | + | 1254.51i | 0.175545 | + | 1.03067i | ||||
\(115\) | 900.452 | − | 1559.63i | 0.730153 | − | 1.26466i | ||||
\(116\) | 821.758 | + | 1423.33i | 0.657744 | + | 1.13925i | ||||
\(117\) | −112.933 | − | 97.0282i | −0.0892363 | − | 0.0766689i | ||||
\(118\) | −532.276 | −0.415254 | ||||||||
\(119\) | 29.2204 | − | 312.745i | 0.0225095 | − | 0.240919i | ||||
\(120\) | 263.989 | + | 97.8307i | 0.200823 | + | 0.0744224i | ||||
\(121\) | 253.054 | + | 438.303i | 0.190124 | + | 0.329304i | ||||
\(122\) | −2399.31 | −1.78052 | ||||||||
\(123\) | −289.680 | − | 1700.78i | −0.212354 | − | 1.24678i | ||||
\(124\) | 645.954 | 0.467810 | ||||||||
\(125\) | 956.466 | 0.684391 | ||||||||
\(126\) | 1390.98 | − | 1342.98i | 0.983478 | − | 0.949541i | ||||
\(127\) | −225.747 | −0.157731 | −0.0788655 | − | 0.996885i | \(-0.525130\pi\) | ||||
−0.0788655 | + | 0.996885i | \(0.525130\pi\) | |||||||
\(128\) | 514.783 | 0.355475 | ||||||||
\(129\) | 1685.99 | + | 624.806i | 1.15072 | + | 0.426443i | ||||
\(130\) | 284.786 | 0.192134 | ||||||||
\(131\) | −258.667 | − | 448.024i | −0.172518 | − | 0.298809i | 0.766782 | − | 0.641908i | \(-0.221857\pi\) |
−0.939299 | + | 0.343098i | \(0.888524\pi\) | |||||||
\(132\) | 174.173 | + | 1022.61i | 0.114847 | + | 0.674293i | ||||
\(133\) | 1066.05 | − | 489.477i | 0.695024 | − | 0.319121i | ||||
\(134\) | −2272.66 | −1.46514 | ||||||||
\(135\) | −965.148 | + | 1606.14i | −0.615309 | + | 1.02396i | ||||
\(136\) | 34.4006 | + | 59.5836i | 0.0216899 | + | 0.0375680i | ||||
\(137\) | −627.205 | + | 1086.35i | −0.391137 | + | 0.677469i | −0.992600 | − | 0.121432i | \(-0.961251\pi\) |
0.601463 | + | 0.798901i | \(0.294585\pi\) | |||||||
\(138\) | 2540.26 | + | 941.388i | 1.56697 | + | 0.580698i | ||||
\(139\) | −380.390 | + | 658.855i | −0.232117 | + | 0.402039i | −0.958431 | − | 0.285325i | \(-0.907899\pi\) |
0.726314 | + | 0.687363i | \(0.241232\pi\) | |||||||
\(140\) | −159.947 | + | 1711.91i | −0.0965571 | + | 1.03345i | ||||
\(141\) | 1219.79 | − | 1011.47i | 0.728547 | − | 0.604121i | ||||
\(142\) | −471.355 | −0.278558 | ||||||||
\(143\) | −79.1901 | − | 137.161i | −0.0463091 | − | 0.0802098i | ||||
\(144\) | −356.335 | + | 1891.63i | −0.206212 | + | 1.09469i | ||||
\(145\) | −1579.02 | + | 2734.94i | −0.904349 | + | 1.56638i | ||||
\(146\) | 555.340 | + | 961.876i | 0.314796 | + | 0.545243i | ||||
\(147\) | −1527.56 | − | 918.197i | −0.857081 | − | 0.515181i | ||||
\(148\) | 1409.30 | − | 2440.98i | 0.782729 | − | 1.35573i | ||||
\(149\) | −1281.40 | − | 2219.46i | −0.704541 | − | 1.22030i | −0.966857 | − | 0.255319i | \(-0.917820\pi\) |
0.262316 | − | 0.964982i | \(-0.415514\pi\) | |||||||
\(150\) | −180.102 | − | 1057.42i | −0.0980350 | − | 0.575587i | ||||
\(151\) | 46.7419 | − | 80.9593i | 0.0251907 | − | 0.0436316i | −0.853155 | − | 0.521657i | \(-0.825314\pi\) |
0.878346 | + | 0.478026i | \(0.158647\pi\) | |||||||
\(152\) | −128.471 | + | 222.518i | −0.0685551 | + | 0.118741i | ||||
\(153\) | −432.106 | + | 151.592i | −0.228325 | + | 0.0801011i | ||||
\(154\) | 1869.13 | − | 858.211i | 0.978043 | − | 0.449069i | ||||
\(155\) | 620.606 | + | 1074.92i | 0.321602 | + | 0.557030i | ||||
\(156\) | 33.4413 | + | 196.342i | 0.0171631 | + | 0.100769i | ||||
\(157\) | 2822.48 | 1.43477 | 0.717384 | − | 0.696678i | \(-0.245339\pi\) | ||||
0.717384 | + | 0.696678i | \(0.245339\pi\) | |||||||
\(158\) | 3779.64 | 1.90311 | ||||||||
\(159\) | −3235.96 | − | 1199.20i | −1.61402 | − | 0.598133i | ||||
\(160\) | −1624.17 | − | 2813.15i | −0.802512 | − | 1.38999i | ||||
\(161\) | 232.307 | − | 2486.38i | 0.113717 | − | 1.21711i | ||||
\(162\) | −2625.58 | − | 1025.58i | −1.27337 | − | 0.497390i | ||||
\(163\) | 998.302 | − | 1729.11i | 0.479712 | − | 0.830886i | −0.520017 | − | 0.854156i | \(-0.674074\pi\) |
0.999729 | + | 0.0232701i | \(0.00740778\pi\) | |||||||
\(164\) | −1153.94 | + | 1998.69i | −0.549438 | + | 0.951655i | ||||
\(165\) | −1534.37 | + | 1272.32i | −0.723941 | + | 0.600301i | ||||
\(166\) | −1963.12 | − | 3400.23i | −0.917879 | − | 1.58981i | ||||
\(167\) | −1551.97 | + | 2688.08i | −0.719130 | + | 1.24557i | 0.242215 | + | 0.970223i | \(0.422126\pi\) |
−0.961345 | + | 0.275347i | \(0.911207\pi\) | |||||||
\(168\) | 389.273 | − | 29.4623i | 0.178768 | − | 0.0135302i | ||||
\(169\) | 1083.30 | + | 1876.32i | 0.493079 | + | 0.854039i | ||||
\(170\) | 437.942 | − | 758.538i | 0.197580 | − | 0.342219i | ||||
\(171\) | −1297.14 | − | 1114.46i | −0.580088 | − | 0.498392i | ||||
\(172\) | −1202.61 | − | 2082.99i | −0.533131 | − | 0.923409i | ||||
\(173\) | 320.396 | 0.140805 | 0.0704024 | − | 0.997519i | \(-0.477572\pi\) | ||||
0.0704024 | + | 0.997519i | \(0.477572\pi\) | |||||||
\(174\) | −4454.57 | − | 1650.81i | −1.94081 | − | 0.719237i | ||||
\(175\) | −898.566 | + | 412.577i | −0.388144 | + | 0.178216i | ||||
\(176\) | −1023.79 | + | 1773.26i | −0.438473 | + | 0.759457i | ||||
\(177\) | 550.619 | − | 456.581i | 0.233825 | − | 0.193891i | ||||
\(178\) | −1000.61 | + | 1733.11i | −0.421343 | + | 0.729788i | ||||
\(179\) | 1051.64 | + | 1821.50i | 0.439125 | + | 0.760587i | 0.997622 | − | 0.0689193i | \(-0.0219551\pi\) |
−0.558497 | + | 0.829507i | \(0.688622\pi\) | |||||||
\(180\) | 2365.27 | − | 829.786i | 0.979427 | − | 0.343603i | ||||
\(181\) | 2247.71 | 0.923045 | 0.461522 | − | 0.887129i | \(-0.347303\pi\) | ||||
0.461522 | + | 0.887129i | \(0.347303\pi\) | |||||||
\(182\) | 358.875 | − | 164.778i | 0.146162 | − | 0.0671106i | ||||
\(183\) | 2482.00 | − | 2058.10i | 1.00259 | − | 0.831363i | ||||
\(184\) | 273.491 | + | 473.700i | 0.109576 | + | 0.189792i | ||||
\(185\) | 5415.99 | 2.15239 | ||||||||
\(186\) | −1437.29 | + | 1191.82i | −0.566597 | + | 0.469830i | ||||
\(187\) | −487.113 | −0.190488 | ||||||||
\(188\) | −2119.71 | −0.822319 | ||||||||
\(189\) | −286.921 | + | 2582.43i | −0.110426 | + | 0.993884i | ||||
\(190\) | 3271.04 | 1.24898 | ||||||||
\(191\) | 141.725 | 0.0536904 | 0.0268452 | − | 0.999640i | \(-0.491454\pi\) | ||||
0.0268452 | + | 0.999640i | \(0.491454\pi\) | |||||||
\(192\) | 1480.20 | − | 1227.40i | 0.556375 | − | 0.461354i | ||||
\(193\) | 609.033 | 0.227146 | 0.113573 | − | 0.993530i | \(-0.463770\pi\) | ||||
0.113573 | + | 0.993530i | \(0.463770\pi\) | |||||||
\(194\) | −3185.61 | − | 5517.63i | −1.17893 | − | 2.04197i | ||||
\(195\) | −294.600 | + | 244.286i | −0.108188 | + | 0.0897113i | ||||
\(196\) | 788.956 | + | 2249.82i | 0.287521 | + | 0.819906i | ||||
\(197\) | 2446.99 | 0.884978 | 0.442489 | − | 0.896774i | \(-0.354096\pi\) | ||||
0.442489 | + | 0.896774i | \(0.354096\pi\) | |||||||
\(198\) | −2274.31 | − | 1954.01i | −0.816304 | − | 0.701341i | ||||
\(199\) | 1295.56 | + | 2243.98i | 0.461507 | + | 0.799354i | 0.999036 | − | 0.0438910i | \(-0.0139754\pi\) |
−0.537529 | + | 0.843245i | \(0.680642\pi\) | |||||||
\(200\) | 108.287 | − | 187.559i | 0.0382853 | − | 0.0663122i | ||||
\(201\) | 2350.99 | − | 1949.47i | 0.825004 | − | 0.684104i | ||||
\(202\) | −1818.33 | + | 3149.45i | −0.633354 | + | 1.09700i | ||||
\(203\) | −407.371 | + | 4360.08i | −0.140846 | + | 1.50748i | ||||
\(204\) | 574.391 | + | 212.862i | 0.197134 | + | 0.0730554i | ||||
\(205\) | −4434.64 | −1.51087 | ||||||||
\(206\) | −193.739 | − | 335.566i | −0.0655265 | − | 0.113495i | ||||
\(207\) | −3435.32 | + | 1205.18i | −1.15348 | + | 0.404666i | ||||
\(208\) | −196.569 | + | 340.468i | −0.0655271 | + | 0.113496i | ||||
\(209\) | −909.574 | − | 1575.43i | −0.301036 | − | 0.521410i | ||||
\(210\) | −2802.67 | − | 4104.22i | −0.920965 | − | 1.34866i | ||||
\(211\) | 140.960 | − | 244.150i | 0.0459910 | − | 0.0796588i | −0.842114 | − | 0.539300i | \(-0.818689\pi\) |
0.888105 | + | 0.459642i | \(0.152022\pi\) | |||||||
\(212\) | 2308.21 | + | 3997.93i | 0.747775 | + | 1.29518i | ||||
\(213\) | 487.599 | − | 404.324i | 0.156853 | − | 0.130065i | ||||
\(214\) | 897.872 | − | 1555.16i | 0.286810 | − | 0.496769i | ||||
\(215\) | 2310.84 | − | 4002.49i | 0.733014 | − | 1.26962i | ||||
\(216\) | −275.901 | − | 497.782i | −0.0869106 | − | 0.156804i | ||||
\(217\) | 1404.01 | + | 995.485i | 0.439219 | + | 0.311419i | ||||
\(218\) | −879.629 | − | 1523.56i | −0.273284 | − | 0.473342i | ||||
\(219\) | −1399.57 | − | 518.660i | −0.431844 | − | 0.160036i | ||||
\(220\) | 2666.37 | 0.817120 | ||||||||
\(221\) | −93.5263 | −0.0284672 | ||||||||
\(222\) | 1367.95 | + | 8031.58i | 0.413563 | + | 2.42813i | ||||
\(223\) | −803.773 | − | 1392.18i | −0.241366 | − | 0.418058i | 0.719738 | − | 0.694246i | \(-0.244262\pi\) |
−0.961104 | + | 0.276188i | \(0.910929\pi\) | |||||||
\(224\) | −3674.40 | − | 2605.26i | −1.09601 | − | 0.777103i | ||||
\(225\) | 1093.35 | + | 939.372i | 0.323956 | + | 0.278333i | ||||
\(226\) | −1713.18 | + | 2967.32i | −0.504245 | + | 0.873377i | ||||
\(227\) | 2094.27 | − | 3627.38i | 0.612342 | − | 1.06061i | −0.378503 | − | 0.925600i | \(-0.623561\pi\) |
0.990845 | − | 0.135007i | \(-0.0431057\pi\) | |||||||
\(228\) | 384.106 | + | 2255.18i | 0.111570 | + | 0.655056i | ||||
\(229\) | 1355.15 | + | 2347.19i | 0.391052 | + | 0.677322i | 0.992589 | − | 0.121523i | \(-0.0387778\pi\) |
−0.601536 | + | 0.798845i | \(0.705444\pi\) | |||||||
\(230\) | 3481.72 | − | 6030.51i | 0.998164 | − | 1.72887i | ||||
\(231\) | −1197.38 | + | 2491.10i | −0.341046 | + | 0.709535i | ||||
\(232\) | −479.590 | − | 830.675i | −0.135718 | − | 0.235071i | ||||
\(233\) | −1520.98 | + | 2634.42i | −0.427652 | + | 0.740715i | −0.996664 | − | 0.0816144i | \(-0.973992\pi\) |
0.569012 | + | 0.822329i | \(0.307326\pi\) | |||||||
\(234\) | −436.670 | − | 375.172i | −0.121992 | − | 0.104811i | ||||
\(235\) | −2036.53 | − | 3527.37i | −0.565313 | − | 0.979151i | ||||
\(236\) | −956.847 | −0.263921 | ||||||||
\(237\) | −3909.89 | + | 3242.13i | −1.07162 | + | 0.888604i | ||||
\(238\) | 112.985 | − | 1209.27i | 0.0307718 | − | 0.329351i | ||||
\(239\) | −697.856 | + | 1208.72i | −0.188873 | + | 0.327137i | −0.944875 | − | 0.327432i | \(-0.893817\pi\) |
0.756002 | + | 0.654569i | \(0.227150\pi\) | |||||||
\(240\) | 4639.42 | + | 1719.31i | 1.24781 | + | 0.462420i | ||||
\(241\) | −1973.58 | + | 3418.33i | −0.527507 | + | 0.913669i | 0.471979 | + | 0.881610i | \(0.343540\pi\) |
−0.999486 | + | 0.0320590i | \(0.989794\pi\) | |||||||
\(242\) | 978.469 | + | 1694.76i | 0.259911 | + | 0.450178i | ||||
\(243\) | 3595.80 | − | 1191.27i | 0.949262 | − | 0.314487i | ||||
\(244\) | −4313.12 | −1.13164 | ||||||||
\(245\) | −2985.89 | + | 3474.42i | −0.778619 | + | 0.906011i | ||||
\(246\) | −1120.09 | − | 6576.29i | −0.290301 | − | 1.70443i | ||||
\(247\) | −174.639 | − | 302.484i | −0.0449880 | − | 0.0779215i | ||||
\(248\) | −376.989 | −0.0965274 | ||||||||
\(249\) | 4947.46 | + | 1833.46i | 1.25917 | + | 0.466630i | ||||
\(250\) | 3698.30 | 0.935605 | ||||||||
\(251\) | 50.3155 | 0.0126529 | 0.00632646 | − | 0.999980i | \(-0.497986\pi\) | ||||
0.00632646 | + | 0.999980i | \(0.497986\pi\) | |||||||
\(252\) | 2500.50 | − | 2414.21i | 0.625065 | − | 0.603496i | ||||
\(253\) | −3872.63 | −0.962333 | ||||||||
\(254\) | −872.882 | −0.215628 | ||||||||
\(255\) | 197.632 | + | 1160.34i | 0.0485340 | + | 0.284955i | ||||
\(256\) | 4950.96 | 1.20873 | ||||||||
\(257\) | −1160.46 | − | 2009.98i | −0.281664 | − | 0.487857i | 0.690130 | − | 0.723685i | \(-0.257553\pi\) |
−0.971795 | + | 0.235828i | \(0.924220\pi\) | |||||||
\(258\) | 6519.11 | + | 2415.90i | 1.57311 | + | 0.582973i | ||||
\(259\) | 6825.00 | − | 3133.70i | 1.63739 | − | 0.751810i | ||||
\(260\) | 511.946 | 0.122114 | ||||||||
\(261\) | 6024.13 | − | 2113.39i | 1.42868 | − | 0.501209i | ||||
\(262\) | −1000.17 | − | 1732.35i | −0.235842 | − | 0.408491i | ||||
\(263\) | −1702.16 | + | 2948.22i | −0.399086 | + | 0.691237i | −0.993613 | − | 0.112838i | \(-0.964006\pi\) |
0.594528 | + | 0.804075i | \(0.297339\pi\) | |||||||
\(264\) | −101.650 | − | 596.809i | −0.0236974 | − | 0.139133i | ||||
\(265\) | −4435.25 | + | 7682.08i | −1.02813 | + | 1.78078i | ||||
\(266\) | 4122.02 | − | 1892.63i | 0.950141 | − | 0.436258i | ||||
\(267\) | −451.549 | − | 2651.15i | −0.103500 | − | 0.607670i | ||||
\(268\) | −4085.46 | −0.931191 | ||||||||
\(269\) | −3140.95 | − | 5440.28i | −0.711922 | − | 1.23308i | −0.964135 | − | 0.265413i | \(-0.914492\pi\) |
0.252213 | − | 0.967672i | \(-0.418842\pi\) | |||||||
\(270\) | −3731.88 | + | 6210.37i | −0.841166 | + | 1.39982i | ||||
\(271\) | 1804.21 | − | 3124.98i | 0.404419 | − | 0.700475i | −0.589834 | − | 0.807524i | \(-0.700807\pi\) |
0.994254 | + | 0.107049i | \(0.0341403\pi\) | |||||||
\(272\) | 604.567 | + | 1047.14i | 0.134769 | + | 0.233427i | ||||
\(273\) | −229.898 | + | 478.295i | −0.0509673 | + | 0.106036i | ||||
\(274\) | −2425.17 | + | 4200.52i | −0.534708 | + | 0.926142i | ||||
\(275\) | 766.674 | + | 1327.92i | 0.168117 | + | 0.291187i | ||||
\(276\) | 4566.51 | + | 1692.29i | 0.995912 | + | 0.369072i | ||||
\(277\) | −1053.04 | + | 1823.92i | −0.228415 | + | 0.395627i | −0.957339 | − | 0.288969i | \(-0.906688\pi\) |
0.728923 | + | 0.684595i | \(0.240021\pi\) | |||||||
\(278\) | −1470.83 | + | 2547.55i | −0.317318 | + | 0.549612i | ||||
\(279\) | 464.491 | − | 2465.78i | 0.0996716 | − | 0.529113i | ||||
\(280\) | 93.3475 | − | 999.097i | 0.0199235 | − | 0.213241i | ||||
\(281\) | 972.004 | + | 1683.56i | 0.206352 | + | 0.357412i | 0.950563 | − | 0.310533i | \(-0.100507\pi\) |
−0.744211 | + | 0.667945i | \(0.767174\pi\) | |||||||
\(282\) | 4716.49 | − | 3910.98i | 0.995969 | − | 0.825870i | ||||
\(283\) | −9241.49 | −1.94116 | −0.970582 | − | 0.240771i | \(-0.922600\pi\) | ||||
−0.970582 | + | 0.240771i | \(0.922600\pi\) | |||||||
\(284\) | −847.332 | −0.177042 | ||||||||
\(285\) | −3383.77 | + | 2805.86i | −0.703288 | + | 0.583175i | ||||
\(286\) | −306.199 | − | 530.352i | −0.0633075 | − | 0.109652i | ||||
\(287\) | −5588.35 | + | 2565.89i | −1.14937 | + | 0.527735i | ||||
\(288\) | −1215.61 | + | 6453.14i | −0.248717 | + | 1.32033i | ||||
\(289\) | 2312.68 | − | 4005.67i | 0.470726 | − | 0.815321i | ||||
\(290\) | −6105.50 | + | 10575.0i | −1.23630 | + | 2.14134i | ||||
\(291\) | 8028.36 | + | 2975.20i | 1.61729 | + | 0.599345i | ||||
\(292\) | 998.307 | + | 1729.12i | 0.200074 | + | 0.346538i | ||||
\(293\) | 3079.42 | − | 5333.71i | 0.613998 | − | 1.06348i | −0.376561 | − | 0.926392i | \(-0.622894\pi\) |
0.990559 | − | 0.137084i | \(-0.0437731\pi\) | |||||||
\(294\) | −5906.51 | − | 3550.33i | −1.17168 | − | 0.704284i | ||||
\(295\) | −919.298 | − | 1592.27i | −0.181436 | − | 0.314256i | ||||
\(296\) | −822.490 | + | 1424.59i | −0.161508 | + | 0.279739i | ||||
\(297\) | 4028.82 | + | 70.4710i | 0.787123 | + | 0.0137682i | ||||
\(298\) | −4954.72 | − | 8581.82i | −0.963151 | − | 1.66823i | ||||
\(299\) | −743.550 | −0.143815 | ||||||||
\(300\) | −323.760 | − | 1900.87i | −0.0623077 | − | 0.365823i | ||||
\(301\) | 596.173 | − | 6380.83i | 0.114162 | − | 1.22188i | ||||
\(302\) | 180.734 | − | 313.040i | 0.0344373 | − | 0.0596471i | ||||
\(303\) | −820.565 | − | 4817.73i | −0.155578 | − | 0.913437i | ||||
\(304\) | −2257.79 | + | 3910.60i | −0.425964 | + | 0.737791i | ||||
\(305\) | −4143.87 | − | 7177.39i | −0.777958 | − | 1.34746i | ||||
\(306\) | −1670.80 | + | 586.150i | −0.312134 | + | 0.109503i | ||||
\(307\) | 3956.54 | 0.735544 | 0.367772 | − | 0.929916i | \(-0.380121\pi\) | ||||
0.367772 | + | 0.929916i | \(0.380121\pi\) | |||||||
\(308\) | 3360.04 | − | 1542.76i | 0.621611 | − | 0.285413i | ||||
\(309\) | 488.261 | + | 180.943i | 0.0898907 | + | 0.0333123i | ||||
\(310\) | 2399.65 | + | 4156.32i | 0.439649 | + | 0.761495i | ||||
\(311\) | 5557.43 | 1.01329 | 0.506644 | − | 0.862155i | \(-0.330886\pi\) | ||||
0.506644 | + | 0.862155i | \(0.330886\pi\) | |||||||
\(312\) | −19.5169 | − | 114.588i | −0.00354143 | − | 0.0207926i | ||||
\(313\) | −5348.55 | −0.965873 | −0.482936 | − | 0.875655i | \(-0.660430\pi\) | ||||
−0.482936 | + | 0.875655i | \(0.660430\pi\) | |||||||
\(314\) | 10913.5 | 1.96142 | ||||||||
\(315\) | 6419.81 | + | 1841.56i | 1.14830 | + | 0.329397i | ||||
\(316\) | 6794.47 | 1.20955 | ||||||||
\(317\) | −6418.11 | −1.13715 | −0.568576 | − | 0.822631i | \(-0.692505\pi\) | ||||
−0.568576 | + | 0.822631i | \(0.692505\pi\) | |||||||
\(318\) | −12512.3 | − | 4636.89i | −2.20646 | − | 0.817684i | ||||
\(319\) | 6791.00 | 1.19192 | ||||||||
\(320\) | −2471.29 | − | 4280.41i | −0.431717 | − | 0.747756i | ||||
\(321\) | 405.186 | + | 2378.94i | 0.0704525 | + | 0.413643i | ||||
\(322\) | 898.247 | − | 9613.93i | 0.155458 | − | 1.66386i | ||||
\(323\) | −1074.24 | −0.185053 | ||||||||
\(324\) | −4719.88 | − | 1843.64i | −0.809308 | − | 0.316124i | ||||
\(325\) | 147.202 | + | 254.962i | 0.0251241 | + | 0.0435161i | ||||
\(326\) | 3860.07 | − | 6685.84i | 0.655796 | − | 1.13587i | ||||
\(327\) | 2216.84 | + | 821.531i | 0.374898 | + | 0.138932i | ||||
\(328\) | 673.459 | − | 1166.46i | 0.113371 | − | 0.196364i | ||||
\(329\) | −4607.29 | − | 3266.71i | −0.772062 | − | 0.547415i | ||||
\(330\) | −5932.83 | + | 4919.58i | −0.989671 | + | 0.820648i | ||||
\(331\) | −3261.47 | −0.541590 | −0.270795 | − | 0.962637i | \(-0.587287\pi\) | ||||
−0.270795 | + | 0.962637i | \(0.587287\pi\) | |||||||
\(332\) | −3529.01 | − | 6112.43i | −0.583373 | − | 1.01043i | ||||
\(333\) | −8304.50 | − | 7134.95i | −1.36662 | − | 1.17415i | ||||
\(334\) | −6000.89 | + | 10393.8i | −0.983096 | + | 1.70277i | ||||
\(335\) | −3925.14 | − | 6798.54i | −0.640159 | − | 1.10879i | ||||
\(336\) | 6841.19 | − | 517.779i | 1.11077 | − | 0.0840690i | ||||
\(337\) | 897.370 | − | 1554.29i | 0.145053 | − | 0.251239i | −0.784340 | − | 0.620332i | \(-0.786998\pi\) |
0.929393 | + | 0.369092i | \(0.120331\pi\) | |||||||
\(338\) | 4188.71 | + | 7255.05i | 0.674070 | + | 1.16752i | ||||
\(339\) | −773.114 | − | 4539.13i | −0.123864 | − | 0.727233i | ||||
\(340\) | 787.268 | − | 1363.59i | 0.125575 | − | 0.217503i | ||||
\(341\) | 1334.54 | − | 2311.49i | 0.211934 | − | 0.367080i | ||||
\(342\) | −5015.58 | − | 4309.22i | −0.793016 | − | 0.681333i | ||||
\(343\) | −1752.39 | + | 6105.96i | −0.275860 | + | 0.961198i | ||||
\(344\) | 701.863 | + | 1215.66i | 0.110006 | + | 0.190535i | ||||
\(345\) | 1571.21 | + | 9224.92i | 0.245191 | + | 1.43957i | ||||
\(346\) | 1238.85 | 0.192489 | ||||||||
\(347\) | 1866.26 | 0.288721 | 0.144360 | − | 0.989525i | \(-0.453888\pi\) | ||||
0.144360 | + | 0.989525i | \(0.453888\pi\) | |||||||
\(348\) | −8007.77 | − | 2967.57i | −1.23351 | − | 0.457123i | ||||
\(349\) | 2296.96 | + | 3978.45i | 0.352302 | + | 0.610205i | 0.986652 | − | 0.162841i | \(-0.0520657\pi\) |
−0.634350 | + | 0.773046i | \(0.718732\pi\) | |||||||
\(350\) | −3474.42 | + | 1595.28i | −0.530617 | + | 0.243633i | ||||
\(351\) | 773.538 | + | 13.5305i | 0.117631 | + | 0.00205757i | ||||
\(352\) | −3492.59 | + | 6049.34i | −0.528851 | + | 0.915997i | ||||
\(353\) | 3078.87 | − | 5332.76i | 0.464226 | − | 0.804062i | −0.534941 | − | 0.844890i | \(-0.679666\pi\) |
0.999166 | + | 0.0408273i | \(0.0129993\pi\) | |||||||
\(354\) | 2129.04 | − | 1765.43i | 0.319654 | − | 0.265061i | ||||
\(355\) | −814.081 | − | 1410.03i | −0.121710 | − | 0.210807i | ||||
\(356\) | −1798.75 | + | 3115.53i | −0.267791 | + | 0.463828i | ||||
\(357\) | 920.423 | + | 1347.86i | 0.136454 | + | 0.199822i | ||||
\(358\) | 4066.32 | + | 7043.07i | 0.600311 | + | 1.03977i | ||||
\(359\) | 1828.80 | − | 3167.58i | 0.268859 | − | 0.465678i | −0.699708 | − | 0.714429i | \(-0.746687\pi\) |
0.968568 | + | 0.248751i | \(0.0800200\pi\) | |||||||
\(360\) | −1380.41 | + | 484.275i | −0.202094 | + | 0.0708988i | ||||
\(361\) | 1423.60 | + | 2465.74i | 0.207552 | + | 0.359490i | ||||
\(362\) | 8691.08 | 1.26186 | ||||||||
\(363\) | −2465.94 | − | 913.843i | −0.356551 | − | 0.132133i | ||||
\(364\) | 645.132 | − | 296.213i | 0.0928959 | − | 0.0426532i | ||||
\(365\) | −1918.26 | + | 3322.53i | −0.275086 | + | 0.476463i | ||||
\(366\) | 9596.97 | − | 7957.93i | 1.37061 | − | 1.13652i | ||||
\(367\) | −3541.93 | + | 6134.81i | −0.503780 | + | 0.872573i | 0.496210 | + | 0.868203i | \(0.334725\pi\) |
−0.999990 | + | 0.00437080i | \(0.998609\pi\) | |||||||
\(368\) | 4806.41 | + | 8324.95i | 0.680847 | + | 1.17926i | ||||
\(369\) | 6799.76 | + | 5842.13i | 0.959300 | + | 0.824198i | ||||
\(370\) | 20941.7 | 2.94245 | ||||||||
\(371\) | −1144.25 | + | 12246.9i | −0.160125 | + | 1.71382i | ||||
\(372\) | −2583.74 | + | 2142.47i | −0.360110 | + | 0.298608i | ||||
\(373\) | −6621.10 | − | 11468.1i | −0.919109 | − | 1.59194i | −0.800771 | − | 0.598970i | \(-0.795577\pi\) |
−0.118338 | − | 0.992973i | \(-0.537757\pi\) | |||||||
\(374\) | −1883.49 | −0.260409 | ||||||||
\(375\) | −3825.76 | + | 3172.37i | −0.526830 | + | 0.436854i | ||||
\(376\) | 1237.10 | 0.169677 | ||||||||
\(377\) | 1303.88 | 0.178125 | ||||||||
\(378\) | −1109.42 | + | 9985.31i | −0.150959 | + | 1.35870i | ||||
\(379\) | −1915.73 | −0.259643 | −0.129821 | − | 0.991537i | \(-0.541440\pi\) | ||||
−0.129821 | + | 0.991537i | \(0.541440\pi\) | |||||||
\(380\) | 5880.19 | 0.793809 | ||||||||
\(381\) | 902.964 | − | 748.750i | 0.121418 | − | 0.100681i | ||||
\(382\) | 547.999 | 0.0733981 | ||||||||
\(383\) | 5821.11 | + | 10082.5i | 0.776618 | + | 1.34514i | 0.933881 | + | 0.357585i | \(0.116400\pi\) |
−0.157262 | + | 0.987557i | \(0.550267\pi\) | |||||||
\(384\) | −2059.08 | + | 1707.41i | −0.273637 | + | 0.226904i | ||||
\(385\) | 5795.47 | + | 4109.16i | 0.767180 | + | 0.543953i | ||||
\(386\) | 2354.91 | 0.310522 | ||||||||
\(387\) | −8816.11 | + | 3092.87i | −1.15800 | + | 0.406252i | ||||
\(388\) | −5726.61 | − | 9918.78i | −0.749290 | − | 1.29781i | ||||
\(389\) | 2991.28 | − | 5181.06i | 0.389882 | − | 0.675296i | −0.602551 | − | 0.798080i | \(-0.705849\pi\) |
0.992433 | + | 0.122785i | \(0.0391824\pi\) | |||||||
\(390\) | −1139.11 | + | 944.566i | −0.147900 | + | 0.122641i | ||||
\(391\) | −1143.43 | + | 1980.48i | −0.147892 | + | 0.256156i | ||||
\(392\) | −460.447 | − | 1313.03i | −0.0593267 | − | 0.169179i | ||||
\(393\) | 2520.63 | + | 934.110i | 0.323534 | + | 0.119897i | ||||
\(394\) | 9461.61 | 1.20982 | ||||||||
\(395\) | 6527.84 | + | 11306.5i | 0.831522 | + | 1.44024i | ||||
\(396\) | −4088.42 | − | 3512.63i | −0.518815 | − | 0.445748i | ||||
\(397\) | −4543.74 | + | 7869.98i | −0.574417 | + | 0.994920i | 0.421687 | + | 0.906741i | \(0.361438\pi\) |
−0.996105 | + | 0.0881786i | \(0.971895\pi\) | |||||||
\(398\) | 5009.47 | + | 8676.65i | 0.630909 | + | 1.09277i | ||||
\(399\) | −2640.60 | + | 5493.68i | −0.331317 | + | 0.689294i | ||||
\(400\) | 1903.07 | − | 3296.22i | 0.237884 | − | 0.412028i | ||||
\(401\) | 4173.68 | + | 7229.03i | 0.519760 | + | 0.900250i | 0.999736 | + | 0.0229689i | \(0.00731186\pi\) |
−0.479976 | + | 0.877281i | \(0.659355\pi\) | |||||||
\(402\) | 9090.41 | − | 7537.88i | 1.12783 | − | 0.935213i | ||||
\(403\) | 256.233 | − | 443.809i | 0.0316722 | − | 0.0548578i | ||||
\(404\) | −3268.73 | + | 5661.61i | −0.402538 | + | 0.697217i | ||||
\(405\) | −1466.71 | − | 9625.56i | −0.179954 | − | 1.18098i | ||||
\(406\) | −1575.15 | + | 16858.9i | −0.192546 | + | 2.06082i | ||||
\(407\) | −5823.23 | − | 10086.1i | −0.709206 | − | 1.22838i | ||||
\(408\) | −335.223 | − | 124.229i | −0.0406765 | − | 0.0150742i | ||||
\(409\) | 11706.6 | 1.41530 | 0.707648 | − | 0.706565i | \(-0.249756\pi\) | ||||
0.707648 | + | 0.706565i | \(0.249756\pi\) | |||||||
\(410\) | −17147.1 | −2.06546 | ||||||||
\(411\) | −1094.42 | − | 6425.57i | −0.131347 | − | 0.771168i | ||||
\(412\) | −348.276 | − | 603.231i | −0.0416464 | − | 0.0721337i | ||||
\(413\) | −2079.75 | − | 1474.60i | −0.247791 | − | 0.175691i | ||||
\(414\) | −13283.1 | + | 4660.00i | −1.57688 | + | 0.553204i | ||||
\(415\) | 6781.05 | − | 11745.1i | 0.802093 | − | 1.38927i | ||||
\(416\) | −670.581 | + | 1161.48i | −0.0790336 | + | 0.136890i | ||||
\(417\) | −663.746 | − | 3897.01i | −0.0779467 | − | 0.457644i | ||||
\(418\) | −3516.99 | − | 6091.61i | −0.411535 | − | 0.712800i | ||||
\(419\) | −52.3192 | + | 90.6195i | −0.00610015 | + | 0.0105658i | −0.869059 | − | 0.494708i | \(-0.835275\pi\) |
0.862959 | + | 0.505274i | \(0.168608\pi\) | |||||||
\(420\) | −5038.23 | − | 7377.96i | −0.585334 | − | 0.857161i | ||||
\(421\) | −5909.85 | − | 10236.2i | −0.684153 | − | 1.18499i | −0.973702 | − | 0.227824i | \(-0.926839\pi\) |
0.289550 | − | 0.957163i | \(-0.406494\pi\) | |||||||
\(422\) | 545.042 | − | 944.040i | 0.0628726 | − | 0.108898i | ||||
\(423\) | −1524.24 | + | 8091.52i | −0.175203 | + | 0.930079i | ||||
\(424\) | −1347.10 | − | 2333.25i | −0.154295 | − | 0.267247i | ||||
\(425\) | 905.469 | 0.103345 | ||||||||
\(426\) | 1885.37 | − | 1563.37i | 0.214428 | − | 0.177807i | ||||
\(427\) | −9374.78 | − | 6646.99i | −1.06248 | − | 0.753327i | ||||
\(428\) | 1614.06 | − | 2795.64i | 0.182287 | − | 0.315729i | ||||
\(429\) | 771.682 | + | 285.975i | 0.0868466 | + | 0.0321842i | ||||
\(430\) | 8935.18 | − | 15476.2i | 1.00208 | − | 1.73565i | ||||
\(431\) | −3058.30 | − | 5297.12i | −0.341793 | − | 0.592003i | 0.642972 | − | 0.765889i | \(-0.277701\pi\) |
−0.984766 | + | 0.173886i | \(0.944368\pi\) | |||||||
\(432\) | −4848.77 | − | 8748.17i | −0.540015 | − | 0.974297i | ||||
\(433\) | −8659.36 | −0.961068 | −0.480534 | − | 0.876976i | \(-0.659557\pi\) | ||||
−0.480534 | + | 0.876976i | \(0.659557\pi\) | |||||||
\(434\) | 5428.80 | + | 3849.18i | 0.600439 | + | 0.425729i | ||||
\(435\) | −2755.25 | − | 16176.7i | −0.303687 | − | 1.78302i | ||||
\(436\) | −1581.27 | − | 2738.83i | −0.173690 | − | 0.300840i | ||||
\(437\) | −8540.39 | −0.934879 | ||||||||
\(438\) | −5411.61 | − | 2005.47i | −0.590358 | − | 0.218779i | ||||
\(439\) | 14430.5 | 1.56886 | 0.784429 | − | 0.620219i | \(-0.212956\pi\) | ||||
0.784429 | + | 0.620219i | \(0.212956\pi\) | |||||||
\(440\) | −1556.13 | −0.168604 | ||||||||
\(441\) | 9155.50 | − | 1393.86i | 0.988609 | − | 0.150509i | ||||
\(442\) | −361.632 | −0.0389165 | ||||||||
\(443\) | −1747.73 | −0.187443 | −0.0937216 | − | 0.995598i | \(-0.529876\pi\) | ||||
−0.0937216 | + | 0.995598i | \(0.529876\pi\) | |||||||
\(444\) | 2459.10 | + | 14438.0i | 0.262847 | + | 1.54323i | ||||
\(445\) | −6912.66 | −0.736386 | ||||||||
\(446\) | −3107.90 | − | 5383.03i | −0.329962 | − | 0.571511i | ||||
\(447\) | 12486.9 | + | 4627.47i | 1.32127 | + | 0.489646i | ||||
\(448\) | −5590.87 | − | 3964.09i | −0.589607 | − | 0.418049i | ||||
\(449\) | 6876.18 | 0.722733 | 0.361367 | − | 0.932424i | \(-0.382310\pi\) | ||||
0.361367 | + | 0.932424i | \(0.382310\pi\) | |||||||
\(450\) | 4227.60 | + | 3632.21i | 0.442868 | + | 0.380498i | ||||
\(451\) | 4768.09 | + | 8258.57i | 0.497828 | + | 0.862264i | ||||
\(452\) | −3079.71 | + | 5334.21i | −0.320481 | + | 0.555089i | ||||
\(453\) | 81.5603 | + | 478.860i | 0.00845924 | + | 0.0496662i | ||||
\(454\) | 8097.78 | − | 14025.8i | 0.837109 | − | 1.44992i | ||||
\(455\) | 1112.74 | + | 788.964i | 0.114650 | + | 0.0812905i | ||||
\(456\) | −224.170 | − | 1316.16i | −0.0230213 | − | 0.135164i | ||||
\(457\) | −2719.49 | −0.278365 | −0.139182 | − | 0.990267i | \(-0.544447\pi\) | ||||
−0.139182 | + | 0.990267i | \(0.544447\pi\) | |||||||
\(458\) | 5239.88 | + | 9075.74i | 0.534593 | + | 0.925942i | ||||
\(459\) | 1225.58 | − | 2039.54i | 0.124630 | − | 0.207402i | ||||
\(460\) | 6258.92 | − | 10840.8i | 0.634399 | − | 1.09881i | ||||
\(461\) | 1231.59 | + | 2133.18i | 0.124427 | + | 0.215514i | 0.921509 | − | 0.388357i | \(-0.126957\pi\) |
−0.797082 | + | 0.603871i | \(0.793624\pi\) | |||||||
\(462\) | −4629.82 | + | 9632.19i | −0.466231 | + | 0.969979i | ||||
\(463\) | −488.238 | + | 845.653i | −0.0490072 | + | 0.0848830i | −0.889488 | − | 0.456958i | \(-0.848939\pi\) |
0.840481 | + | 0.541841i | \(0.182272\pi\) | |||||||
\(464\) | −8428.47 | − | 14598.5i | −0.843280 | − | 1.46060i | ||||
\(465\) | −6047.60 | − | 2241.16i | −0.603120 | − | 0.223508i | ||||
\(466\) | −5881.08 | + | 10186.3i | −0.584626 | + | 1.01260i | ||||
\(467\) | −5486.73 | + | 9503.29i | −0.543673 | + | 0.941670i | 0.455016 | + | 0.890483i | \(0.349634\pi\) |
−0.998689 | + | 0.0511862i | \(0.983700\pi\) | |||||||
\(468\) | −784.981 | − | 674.430i | −0.0775337 | − | 0.0666143i | ||||
\(469\) | −8879.94 | − | 6296.14i | −0.874280 | − | 0.619890i | ||||
\(470\) | −7874.52 | − | 13639.1i | −0.772818 | − | 1.33856i | ||||
\(471\) | −11289.6 | + | 9361.50i | −1.10445 | + | 0.915828i | ||||
\(472\) | 558.430 | 0.0544573 | ||||||||
\(473\) | −9938.38 | −0.966104 | ||||||||
\(474\) | −15118.1 | + | 12536.1i | −1.46498 | + | 1.21478i | ||||
\(475\) | 1690.76 | + | 2928.48i | 0.163321 | + | 0.282880i | ||||
\(476\) | 203.107 | − | 2173.85i | 0.0195575 | − | 0.209324i | ||||
\(477\) | 16921.0 | − | 5936.23i | 1.62423 | − | 0.569814i | ||||
\(478\) | −2698.35 | + | 4673.68i | −0.258200 | + | 0.447216i | ||||
\(479\) | 489.544 | − | 847.916i | 0.0466970 | − | 0.0808815i | −0.841732 | − | 0.539895i | \(-0.818464\pi\) |
0.888429 | + | 0.459014i | \(0.151797\pi\) | |||||||
\(480\) | 15827.0 | + | 5865.29i | 1.50500 | + | 0.557734i | ||||
\(481\) | −1118.07 | − | 1936.55i | −0.105986 | − | 0.183574i | ||||
\(482\) | −7631.10 | + | 13217.4i | −0.721135 | + | 1.24904i | ||||
\(483\) | 7317.52 | + | 10715.8i | 0.689356 | + | 1.00949i | ||||
\(484\) | 1758.95 | + | 3046.59i | 0.165190 | + | 0.286118i | ||||
\(485\) | 11003.8 | − | 19059.1i | 1.03022 | − | 1.78439i | ||||
\(486\) | 13903.6 | − | 4606.22i | 1.29770 | − | 0.429923i | ||||
\(487\) | 4370.44 | + | 7569.83i | 0.406660 | + | 0.704357i | 0.994513 | − | 0.104611i | \(-0.0333599\pi\) |
−0.587853 | + | 0.808968i | \(0.700027\pi\) | |||||||
\(488\) | 2517.20 | 0.233501 | ||||||||
\(489\) | 1741.95 | + | 10227.4i | 0.161091 | + | 0.945804i | ||||
\(490\) | −11545.4 | + | 13434.3i | −1.06442 | + | 1.23857i | ||||
\(491\) | −6965.56 | + | 12064.7i | −0.640226 | + | 1.10890i | 0.345156 | + | 0.938545i | \(0.387826\pi\) |
−0.985382 | + | 0.170359i | \(0.945507\pi\) | |||||||
\(492\) | −2013.53 | − | 11821.9i | −0.184506 | − | 1.08328i | ||||
\(493\) | 2005.10 | − | 3472.94i | 0.183175 | − | 0.317268i | ||||
\(494\) | −675.267 | − | 1169.60i | −0.0615014 | − | 0.106524i | ||||
\(495\) | 1917.32 | − | 10178.2i | 0.174096 | − | 0.924198i | ||||
\(496\) | −6625.31 | −0.599769 | ||||||||
\(497\) | −1841.72 | − | 1305.83i | −0.166222 | − | 0.117856i | ||||
\(498\) | 19130.0 | + | 7089.33i | 1.72136 | + | 0.637913i | ||||
\(499\) | 4214.20 | + | 7299.21i | 0.378063 | + | 0.654825i | 0.990780 | − | 0.135477i | \(-0.0432568\pi\) |
−0.612717 | + | 0.790302i | \(0.709923\pi\) | |||||||
\(500\) | 6648.26 | 0.594639 | ||||||||
\(501\) | −2708.04 | − | 15899.5i | −0.241489 | − | 1.41784i | ||||
\(502\) | 194.552 | 0.0172973 | ||||||||
\(503\) | 2009.66 | 0.178144 | 0.0890719 | − | 0.996025i | \(-0.471610\pi\) | ||||
0.0890719 | + | 0.996025i | \(0.471610\pi\) | |||||||
\(504\) | −1459.33 | + | 1408.97i | −0.128975 | + | 0.124525i | ||||
\(505\) | −12561.8 | −1.10692 | ||||||||
\(506\) | −14974.1 | −1.31557 | ||||||||
\(507\) | −10556.4 | − | 3912.05i | −0.924704 | − | 0.342683i | ||||
\(508\) | −1569.14 | −0.137046 | ||||||||
\(509\) | −5865.50 | − | 10159.3i | −0.510773 | − | 0.884685i | −0.999922 | − | 0.0124847i | \(-0.996026\pi\) |
0.489149 | − | 0.872200i | \(-0.337307\pi\) | |||||||
\(510\) | 764.169 | + | 4486.62i | 0.0663490 | + | 0.389551i | ||||
\(511\) | −494.892 | + | 5296.82i | −0.0428429 | + | 0.458547i | ||||
\(512\) | 15025.3 | 1.29693 | ||||||||
\(513\) | 8884.83 | + | 155.411i | 0.764668 | + | 0.0133754i | ||||
\(514\) | −4487.09 | − | 7771.87i | −0.385053 | − | 0.666931i | ||||
\(515\) | 669.217 | − | 1159.12i | 0.0572606 | − | 0.0991784i | ||||
\(516\) | 11719.1 | + | 4342.94i | 0.999815 | + | 0.370518i | ||||
\(517\) | −4379.32 | + | 7585.20i | −0.372538 | + | 0.645255i | ||||
\(518\) | 26389.8 | − | 12116.9i | 2.23842 | − | 1.02777i | ||||
\(519\) | −1281.55 | + | 1062.68i | −0.108389 | + | 0.0898772i | ||||
\(520\) | −298.779 | −0.0251968 | ||||||||
\(521\) | −4418.73 | − | 7653.46i | −0.371570 | − | 0.643578i | 0.618237 | − | 0.785992i | \(-0.287847\pi\) |
−0.989807 | + | 0.142413i | \(0.954514\pi\) | |||||||
\(522\) | 23293.1 | − | 8171.71i | 1.95309 | − | 0.685184i | ||||
\(523\) | 5711.81 | − | 9893.14i | 0.477552 | − | 0.827145i | −0.522117 | − | 0.852874i | \(-0.674857\pi\) |
0.999669 | + | 0.0257292i | \(0.00819077\pi\) | |||||||
\(524\) | −1797.96 | − | 3114.15i | −0.149893 | − | 0.259623i | ||||
\(525\) | 2225.74 | − | 4630.59i | 0.185027 | − | 0.384944i | ||||
\(526\) | −6581.62 | + | 11399.7i | −0.545575 | + | 0.944963i | ||||
\(527\) | −788.069 | − | 1364.98i | −0.0651401 | − | 0.112826i | ||||
\(528\) | −1786.42 | − | 10488.5i | −0.147243 | − | 0.864496i | ||||
\(529\) | −3006.96 | + | 5208.21i | −0.247141 | + | 0.428060i | ||||
\(530\) | −17149.5 | + | 29703.8i | −1.40552 | + | 2.43444i | ||||
\(531\) | −688.047 | + | 3652.54i | −0.0562311 | + | 0.298506i | ||||
\(532\) | 7409.96 | − | 3402.29i | 0.603877 | − | 0.277270i | ||||
\(533\) | 915.479 | + | 1585.66i | 0.0743974 | + | 0.128860i | ||||
\(534\) | −1745.98 | − | 10251.0i | −0.141490 | − | 0.830723i | ||||
\(535\) | 6202.89 | 0.501260 | ||||||||
\(536\) | 2384.34 | 0.192141 | ||||||||
\(537\) | −10247.9 | − | 3797.74i | −0.823520 | − | 0.305186i | ||||
\(538\) | −12144.9 | − | 21035.6i | −0.973241 | − | 1.68570i | ||||
\(539\) | 9680.77 | + | 1824.92i | 0.773618 | + | 0.145834i | ||||
\(540\) | −6708.61 | + | 11164.1i | −0.534616 | + | 0.889677i | ||||
\(541\) | −3532.39 | + | 6118.28i | −0.280719 | + | 0.486220i | −0.971562 | − | 0.236785i | \(-0.923906\pi\) |
0.690843 | + | 0.723005i | \(0.257240\pi\) | |||||||
\(542\) | 6976.20 | − | 12083.1i | 0.552866 | − | 0.957593i | ||||
\(543\) | −8990.59 | + | 7455.12i | −0.710540 | + | 0.589189i | ||||
\(544\) | 2062.43 | + | 3572.24i | 0.162548 | + | 0.281542i | ||||
\(545\) | 3038.43 | − | 5262.71i | 0.238811 | − | 0.413633i | ||||
\(546\) | −888.932 | + | 1849.39i | −0.0696754 | + | 0.144957i | ||||
\(547\) | 5320.04 | + | 9214.58i | 0.415847 | + | 0.720269i | 0.995517 | − | 0.0945828i | \(-0.0301517\pi\) |
−0.579670 | + | 0.814852i | \(0.696818\pi\) | |||||||
\(548\) | −4359.62 | + | 7551.08i | −0.339842 | + | 0.588624i | ||||
\(549\) | −3101.47 | + | 16464.4i | −0.241107 | + | 1.27993i | ||||
\(550\) | 2964.45 | + | 5134.57i | 0.229826 | + | 0.398071i | ||||
\(551\) | 14976.3 | 1.15792 | ||||||||
\(552\) | −2665.08 | − | 987.644i | −0.205495 | − | 0.0761539i | ||||
\(553\) | 14768.1 | + | 10471.0i | 1.13563 | + | 0.805195i | ||||
\(554\) | −4071.72 | + | 7052.42i | −0.312258 | + | 0.540846i | ||||
\(555\) | −21663.4 | + | 17963.5i | −1.65686 | + | 1.37389i | ||||
\(556\) | −2644.04 | + | 4579.61i | −0.201677 | + | 0.349314i | ||||
\(557\) | 3260.15 | + | 5646.75i | 0.248002 | + | 0.429552i | 0.962971 | − | 0.269604i | \(-0.0868927\pi\) |
−0.714969 | + | 0.699156i | \(0.753559\pi\) | |||||||
\(558\) | 1796.02 | − | 9534.28i | 0.136257 | − | 0.723330i | ||||
\(559\) | −1908.18 | −0.144378 | ||||||||
\(560\) | 1640.52 | − | 17558.4i | 0.123794 | − | 1.32496i | ||||
\(561\) | 1948.40 | − | 1615.64i | 0.146633 | − | 0.121590i | ||||
\(562\) | 3758.38 | + | 6509.71i | 0.282096 | + | 0.488604i | ||||
\(563\) | 15770.2 | 1.18052 | 0.590262 | − | 0.807212i | \(-0.299024\pi\) | ||||
0.590262 | + | 0.807212i | \(0.299024\pi\) | |||||||
\(564\) | 8478.62 | − | 7030.58i | 0.633004 | − | 0.524895i | ||||
\(565\) | −11835.4 | −0.881274 | ||||||||
\(566\) | −35733.5 | −2.65369 | ||||||||
\(567\) | −7417.65 | − | 11281.1i | −0.549404 | − | 0.835557i | ||||
\(568\) | 494.516 | 0.0365307 | ||||||||
\(569\) | 12175.2 | 0.897029 | 0.448514 | − | 0.893776i | \(-0.351953\pi\) | ||||
0.448514 | + | 0.893776i | \(0.351953\pi\) | |||||||
\(570\) | −13083.8 | + | 10849.2i | −0.961438 | + | 0.797237i | ||||
\(571\) | 16568.3 | 1.21429 | 0.607147 | − | 0.794590i | \(-0.292314\pi\) | ||||
0.607147 | + | 0.794590i | \(0.292314\pi\) | |||||||
\(572\) | −550.439 | − | 953.389i | −0.0402361 | − | 0.0696909i | ||||
\(573\) | −566.885 | + | 470.068i | −0.0413298 | + | 0.0342712i | ||||
\(574\) | −21608.1 | + | 9921.37i | −1.57126 | + | 0.721446i | ||||
\(575\) | 7198.64 | 0.522094 | ||||||||
\(576\) | −1849.64 | + | 9818.92i | −0.133799 | + | 0.710281i | ||||
\(577\) | −351.578 | − | 608.951i | −0.0253664 | − | 0.0439358i | 0.853064 | − | 0.521807i | \(-0.174742\pi\) |
−0.878430 | + | 0.477871i | \(0.841409\pi\) | |||||||
\(578\) | 8942.27 | − | 15488.5i | 0.643511 | − | 1.11459i | ||||
\(579\) | −2436.06 | + | 2020.02i | −0.174852 | + | 0.144990i | ||||
\(580\) | −10975.6 | + | 19010.2i | −0.785750 | + | 1.36096i | ||||
\(581\) | 1749.44 | − | 18724.2i | 0.124921 | − | 1.33703i | ||||
\(582\) | 31042.7 | + | 11504.0i | 2.21093 | + | 0.819342i | ||||
\(583\) | 19075.0 | 1.35507 | ||||||||
\(584\) | −582.627 | − | 1009.14i | −0.0412830 | − | 0.0715043i | ||||
\(585\) | 368.129 | − | 1954.24i | 0.0260175 | − | 0.138116i | ||||
\(586\) | 11907.0 | − | 20623.5i | 0.839374 | − | 1.45384i | ||||
\(587\) | −548.955 | − | 950.819i | −0.0385993 | − | 0.0668560i | 0.846080 | − | 0.533055i | \(-0.178956\pi\) |
−0.884680 | + | 0.466199i | \(0.845623\pi\) | |||||||
\(588\) | −10617.9 | − | 6382.26i | −0.744682 | − | 0.447619i | ||||
\(589\) | 2943.09 | − | 5097.57i | 0.205887 | − | 0.356608i | ||||
\(590\) | −3554.59 | − | 6156.73i | −0.248034 | − | 0.429608i | ||||
\(591\) | −9787.68 | + | 8116.07i | −0.681237 | + | 0.564891i | ||||
\(592\) | −14454.7 | + | 25036.3i | −1.00352 | + | 1.73815i | ||||
\(593\) | −5626.37 | + | 9745.16i | −0.389625 | + | 0.674850i | −0.992399 | − | 0.123062i | \(-0.960729\pi\) |
0.602774 | + | 0.797912i | \(0.294062\pi\) | |||||||
\(594\) | 15578.0 | + | 272.486i | 1.07605 | + | 0.0188219i | ||||
\(595\) | 3812.60 | − | 1750.56i | 0.262691 | − | 0.120615i | ||||
\(596\) | −8906.86 | − | 15427.1i | −0.612146 | − | 1.06027i | ||||
\(597\) | −12624.8 | − | 4678.60i | −0.865495 | − | 0.320741i | ||||
\(598\) | −2875.04 | −0.196604 | ||||||||
\(599\) | 11640.5 | 0.794023 | 0.397012 | − | 0.917814i | \(-0.370047\pi\) | ||||
0.397012 | + | 0.917814i | \(0.370047\pi\) | |||||||
\(600\) | 188.951 | + | 1109.38i | 0.0128565 | + | 0.0754836i | ||||
\(601\) | 970.960 | + | 1681.75i | 0.0659007 | + | 0.114143i | 0.897093 | − | 0.441841i | \(-0.145675\pi\) |
−0.831192 | + | 0.555985i | \(0.812341\pi\) | |||||||
\(602\) | 2305.18 | − | 24672.3i | 0.156067 | − | 1.67038i | ||||
\(603\) | −2937.76 | + | 15595.3i | −0.198400 | + | 1.05322i | ||||
\(604\) | 324.896 | − | 562.737i | 0.0218872 | − | 0.0379097i | ||||
\(605\) | −3379.84 | + | 5854.06i | −0.227124 | + | 0.393391i | ||||
\(606\) | −3172.82 | − | 18628.4i | −0.212685 | − | 1.24872i | ||||
\(607\) | 6455.68 | + | 11181.6i | 0.431677 | + | 0.747687i | 0.997018 | − | 0.0771708i | \(-0.0245887\pi\) |
−0.565341 | + | 0.824857i | \(0.691255\pi\) | |||||||
\(608\) | −7702.27 | + | 13340.7i | −0.513764 | + | 0.889865i | ||||
\(609\) | −12831.9 | − | 18791.0i | −0.853818 | − | 1.25033i | ||||
\(610\) | −16022.8 | − | 27752.3i | −1.06352 | − | 1.84206i | ||||
\(611\) | −840.835 | + | 1456.37i | −0.0556736 | + | 0.0964294i | ||||
\(612\) | −3003.51 | + | 1053.69i | −0.198382 | + | 0.0695965i | ||||
\(613\) | 9637.25 | + | 16692.2i | 0.634984 | + | 1.09982i | 0.986519 | + | 0.163649i | \(0.0523265\pi\) |
−0.351535 | + | 0.936175i | \(0.614340\pi\) | |||||||
\(614\) | 15298.5 | 1.00553 | ||||||||
\(615\) | 17738.1 | − | 14708.6i | 1.16304 | − | 0.964406i | ||||
\(616\) | −1960.97 | + | 900.380i | −0.128263 | + | 0.0588918i | ||||
\(617\) | −779.062 | + | 1349.38i | −0.0508329 | + | 0.0880451i | −0.890322 | − | 0.455331i | \(-0.849521\pi\) |
0.839489 | + | 0.543376i | \(0.182854\pi\) | |||||||
\(618\) | 1887.93 | + | 699.641i | 0.122886 | + | 0.0455399i | ||||
\(619\) | −3522.77 | + | 6101.62i | −0.228743 | + | 0.396195i | −0.957436 | − | 0.288646i | \(-0.906795\pi\) |
0.728693 | + | 0.684841i | \(0.240128\pi\) | |||||||
\(620\) | 4313.74 | + | 7471.62i | 0.279426 | + | 0.483980i | ||||
\(621\) | 9743.60 | − | 16214.7i | 0.629625 | − | 1.04779i | ||||
\(622\) | 21488.5 | 1.38523 | ||||||||
\(623\) | −8711.04 | + | 3999.68i | −0.560193 | + | 0.257213i | ||||
\(624\) | −342.995 | − | 2013.81i | −0.0220045 | − | 0.129194i | ||||
\(625\) | 9724.11 | + | 16842.7i | 0.622343 | + | 1.07793i | ||||
\(626\) | −20680.9 | −1.32041 | ||||||||
\(627\) | 8863.51 | + | 3284.70i | 0.564553 | + | 0.209216i | ||||
\(628\) | 19618.7 | 1.24661 | ||||||||
\(629\) | −6877.44 | −0.435964 | ||||||||
\(630\) | 24823.1 | + | 7120.63i | 1.56980 | + | 0.450306i | ||||
\(631\) | −29049.6 | −1.83272 | −0.916361 | − | 0.400354i | \(-0.868887\pi\) | ||||
−0.916361 | + | 0.400354i | \(0.868887\pi\) | |||||||
\(632\) | −3965.35 | −0.249578 | ||||||||
\(633\) | 245.963 | + | 1444.11i | 0.0154441 | + | 0.0906762i | ||||
\(634\) | −24816.5 | −1.55456 | ||||||||
\(635\) | −1507.56 | − | 2611.17i | −0.0942138 | − | 0.163183i | ||||
\(636\) | −22492.7 | − | 8335.51i | −1.40235 | − | 0.519692i | ||||
\(637\) | 1858.72 | + | 350.386i | 0.115613 | + | 0.0217940i | ||||
\(638\) | 26258.3 | 1.62943 | ||||||||
\(639\) | −609.298 | + | 3234.50i | −0.0377206 | + | 0.200242i | ||||
\(640\) | 3437.77 | + | 5954.40i | 0.212328 | + | 0.367763i | ||||
\(641\) | −10141.5 | + | 17565.6i | −0.624908 | + | 1.08237i | 0.363651 | + | 0.931535i | \(0.381530\pi\) |
−0.988559 | + | 0.150836i | \(0.951803\pi\) | |||||||
\(642\) | 1566.70 | + | 9198.49i | 0.0963129 | + | 0.565476i | ||||
\(643\) | 12393.5 | − | 21466.2i | 0.760111 | − | 1.31655i | −0.182682 | − | 0.983172i | \(-0.558478\pi\) |
0.942793 | − | 0.333379i | \(-0.108189\pi\) | |||||||
\(644\) | 1614.74 | − | 17282.5i | 0.0988036 | − | 1.05749i | ||||
\(645\) | 4032.21 | + | 23674.0i | 0.246152 | + | 1.44522i | ||||
\(646\) | −4153.69 | −0.252980 | ||||||||
\(647\) | −5412.76 | − | 9375.17i | −0.328899 | − | 0.569669i | 0.653395 | − | 0.757017i | \(-0.273344\pi\) |
−0.982294 | + | 0.187348i | \(0.940011\pi\) | |||||||
\(648\) | 2754.60 | + | 1075.97i | 0.166992 | + | 0.0652288i | ||||
\(649\) | −1976.84 | + | 3423.99i | −0.119565 | + | 0.207093i | ||||
\(650\) | 569.178 | + | 985.845i | 0.0343461 | + | 0.0594893i | ||||
\(651\) | −8917.67 | + | 674.939i | −0.536884 | + | 0.0406343i | ||||
\(652\) | 6939.06 | − | 12018.8i | 0.416802 | − | 0.721922i | ||||
\(653\) | 5666.71 | + | 9815.03i | 0.339595 | + | 0.588196i | 0.984357 | − | 0.176188i | \(-0.0563766\pi\) |
−0.644761 | + | 0.764384i | \(0.723043\pi\) | |||||||
\(654\) | 8571.71 | + | 3176.56i | 0.512508 | + | 0.189929i | ||||
\(655\) | 3454.80 | − | 5983.89i | 0.206092 | − | 0.356962i | ||||
\(656\) | 11835.6 | − | 20499.8i | 0.704423 | − | 1.22010i | ||||
\(657\) | 7318.38 | − | 2567.44i | 0.434577 | − | 0.152459i | ||||
\(658\) | −17814.7 | − | 12631.2i | −1.05546 | − | 0.748349i | ||||
\(659\) | 1455.83 | + | 2521.57i | 0.0860563 | + | 0.149054i | 0.905841 | − | 0.423618i | \(-0.139240\pi\) |
−0.819785 | + | 0.572672i | \(0.805907\pi\) | |||||||
\(660\) | −10665.2 | + | 8843.69i | −0.629001 | + | 0.521576i | ||||
\(661\) | −26754.1 | −1.57430 | −0.787152 | − | 0.616759i | \(-0.788445\pi\) | ||||
−0.787152 | + | 0.616759i | \(0.788445\pi\) | |||||||
\(662\) | −12610.9 | −0.740387 | ||||||||
\(663\) | 374.095 | − | 310.204i | 0.0219135 | − | 0.0181709i | ||||
\(664\) | 2059.58 | + | 3567.31i | 0.120373 | + | 0.208491i | ||||
\(665\) | 12780.9 | + | 9062.01i | 0.745294 | + | 0.528435i | ||||
\(666\) | −32110.5 | − | 27588.2i | −1.86825 | − | 1.60514i | ||||
\(667\) | 15940.9 | − | 27610.5i | 0.925389 | − | 1.60282i | ||||
\(668\) | −10787.5 | + | 18684.5i | −0.624822 | + | 1.08222i | ||||
\(669\) | 7832.51 | + | 2902.63i | 0.452649 | + | 0.167746i | ||||
\(670\) | −15177.1 | − | 26287.5i | −0.875137 | − | 1.51578i | ||||
\(671\) | −8910.90 | + | 15434.1i | −0.512670 | + | 0.887970i | ||||
\(672\) | 23338.2 | − | 1766.37i | 1.33972 | − | 0.101397i | ||||
\(673\) | −6830.55 | − | 11830.9i | −0.391231 | − | 0.677631i | 0.601382 | − | 0.798962i | \(-0.294617\pi\) |
−0.992612 | + | 0.121331i | \(0.961284\pi\) | |||||||
\(674\) | 3469.80 | − | 6009.88i | 0.198296 | − | 0.343460i | ||||
\(675\) | −7488.96 | − | 130.995i | −0.427037 | − | 0.00746963i | ||||
\(676\) | 7529.84 | + | 13042.1i | 0.428416 | + | 0.742038i | ||||
\(677\) | −8825.29 | −0.501009 | −0.250505 | − | 0.968115i | \(-0.580597\pi\) | ||||
−0.250505 | + | 0.968115i | \(0.580597\pi\) | |||||||
\(678\) | −2989.35 | − | 17551.2i | −0.169329 | − | 0.994172i | ||||
\(679\) | 2838.86 | − | 30384.3i | 0.160450 | − | 1.71729i | ||||
\(680\) | −459.461 | + | 795.810i | −0.0259111 | + | 0.0448793i | ||||
\(681\) | 3654.31 | + | 21455.3i | 0.205629 | + | 1.20730i | ||||
\(682\) | 5160.18 | − | 8937.69i | 0.289726 | − | 0.501821i | ||||
\(683\) | 7312.23 | + | 12665.2i | 0.409655 | + | 0.709544i | 0.994851 | − | 0.101348i | \(-0.0323156\pi\) |
−0.585196 | + | 0.810892i | \(0.698982\pi\) | |||||||
\(684\) | −9016.26 | − | 7746.47i | −0.504014 | − | 0.433032i | ||||
\(685\) | −16754.1 | −0.934515 | ||||||||
\(686\) | −6775.84 | + | 23609.5i | −0.377118 | + | 1.31402i | ||||
\(687\) | −13205.5 | − | 4893.79i | −0.733366 | − | 0.271776i | ||||
\(688\) | 12334.8 | + | 21364.4i | 0.683515 | + | 1.18388i | ||||
\(689\) | 3662.42 | 0.202507 | ||||||||
\(690\) | 6075.28 | + | 35669.4i | 0.335191 | + | 1.96799i | ||||
\(691\) | −4571.67 | −0.251685 | −0.125843 | − | 0.992050i | \(-0.540163\pi\) | ||||
−0.125843 | + | 0.992050i | \(0.540163\pi\) | |||||||
\(692\) | 2227.03 | 0.122339 | ||||||||
\(693\) | −3473.02 | − | 13935.6i | −0.190374 | − | 0.763879i | ||||
\(694\) | 7216.15 | 0.394699 | ||||||||
\(695\) | −10161.1 | −0.554581 | ||||||||
\(696\) | 4673.46 | + | 1731.92i | 0.254521 | + | 0.0943222i | ||||
\(697\) | 5631.28 | 0.306026 | ||||||||
\(698\) | 8881.50 | + | 15383.2i | 0.481618 | + | 0.834188i | ||||
\(699\) | −2653.97 | − | 15582.1i | −0.143609 | − | 0.843161i | ||||
\(700\) | −6245.81 | + | 2867.77i | −0.337242 | + | 0.154845i | ||||
\(701\) | −1521.50 | −0.0819773 | −0.0409886 | − | 0.999160i | \(-0.513051\pi\) | ||||
−0.0409886 | + | 0.999160i | \(0.513051\pi\) | |||||||
\(702\) | 2990.99 | + | 52.3176i | 0.160809 | + | 0.00281282i | ||||
\(703\) | −12842.1 | − | 22243.1i | −0.688973 | − | 1.19334i | ||||
\(704\) | −5314.23 | + | 9204.51i | −0.284499 | + | 0.492767i | ||||
\(705\) | 19845.3 | + | 7354.42i | 1.06017 | + | 0.392884i | ||||
\(706\) | 11904.9 | − | 20619.8i | 0.634625 | − | 1.09920i | ||||
\(707\) | −15829.9 | + | 7268.30i | −0.842071 | + | 0.386637i | ||||
\(708\) | 3827.28 | − | 3173.63i | 0.203161 | − | 0.168464i | ||||
\(709\) | 11662.4 | 0.617758 | 0.308879 | − | 0.951101i | \(-0.400046\pi\) | ||||
0.308879 | + | 0.951101i | \(0.400046\pi\) | |||||||
\(710\) | −3147.75 | − | 5452.07i | −0.166385 | − | 0.288187i | ||||
\(711\) | 4885.75 | − | 25936.3i | 0.257707 | − | 1.36806i | ||||
\(712\) | 1049.78 | − | 1818.27i | 0.0552558 | − | 0.0957058i | ||||
\(713\) | −6265.29 | − | 10851.8i | −0.329084 | − | 0.569990i | ||||
\(714\) | 3558.94 | + | 5211.69i | 0.186541 | + | 0.273169i | ||||
\(715\) | 1057.68 | − | 1831.95i | 0.0553216 | − | 0.0958197i | ||||
\(716\) | 7309.82 | + | 12661.0i | 0.381537 | + | 0.660842i | ||||
\(717\) | −1217.69 | − | 7149.37i | −0.0634248 | − | 0.372382i | ||||
\(718\) | 7071.31 | − | 12247.9i | 0.367547 | − | 0.636611i | ||||
\(719\) | −6176.82 | + | 10698.6i | −0.320384 | + | 0.554922i | −0.980567 | − | 0.196183i | \(-0.937145\pi\) |
0.660183 | + | 0.751105i | \(0.270479\pi\) | |||||||
\(720\) | −24259.7 | + | 8510.80i | −1.25570 | + | 0.440526i | ||||
\(721\) | 172.651 | − | 1847.88i | 0.00891798 | − | 0.0954490i | ||||
\(722\) | 5504.53 | + | 9534.13i | 0.283736 | + | 0.491445i | ||||
\(723\) | −3443.71 | − | 20218.8i | −0.177141 | − | 1.04004i | ||||
\(724\) | 15623.5 | 0.801995 | ||||||||
\(725\) | −12623.4 | −0.646652 | ||||||||
\(726\) | −9534.87 | − | 3533.50i | −0.487427 | − | 0.180634i | ||||
\(727\) | −5157.33 | − | 8932.76i | −0.263102 | − | 0.455705i | 0.703963 | − | 0.710237i | \(-0.251412\pi\) |
−0.967064 | + | 0.254531i | \(0.918079\pi\) | |||||||
\(728\) | −376.509 | + | 172.874i | −0.0191681 | + | 0.00880102i | ||||
\(729\) | −10431.6 | + | 16691.4i | −0.529981 | + | 0.848009i | ||||
\(730\) | −7417.22 | + | 12847.0i | −0.376060 | + | 0.651355i | ||||
\(731\) | −2934.40 | + | 5082.52i | −0.148471 | + | 0.257160i | ||||
\(732\) | 17252.0 | − | 14305.6i | 0.871110 | − | 0.722336i | ||||
\(733\) | −5418.34 | − | 9384.84i | −0.273030 | − | 0.472902i | 0.696606 | − | 0.717454i | \(-0.254692\pi\) |
−0.969636 | + | 0.244552i | \(0.921359\pi\) | |||||||
\(734\) | −13695.4 | + | 23721.1i | −0.688699 | + | 1.19286i | ||||
\(735\) | 419.410 | − | 23800.8i | 0.0210479 | − | 1.19443i | ||||
\(736\) | 16396.7 | + | 28399.9i | 0.821184 | + | 1.42233i | ||||
\(737\) | −8440.55 | + | 14619.5i | −0.421861 | + | 0.730685i | ||||
\(738\) | 26292.2 | + | 22589.4i | 1.31142 | + | 1.12673i | ||||
\(739\) | 6152.50 | + | 10656.4i | 0.306256 | + | 0.530451i | 0.977540 | − | 0.210749i | \(-0.0675902\pi\) |
−0.671284 | + | 0.741200i | \(0.734257\pi\) | |||||||
\(740\) | 37645.8 | 1.87012 | ||||||||
\(741\) | 1701.81 | + | 630.667i | 0.0843690 | + | 0.0312660i | ||||
\(742\) | −4424.39 | + | 47354.2i | −0.218901 | + | 2.34289i | ||||
\(743\) | 10676.9 | − | 18492.9i | 0.527182 | − | 0.913105i | −0.472316 | − | 0.881429i | \(-0.656582\pi\) |
0.999498 | − | 0.0316764i | \(-0.0100846\pi\) | |||||||
\(744\) | 1507.91 | − | 1250.38i | 0.0743048 | − | 0.0616145i | ||||
\(745\) | 17114.7 | − | 29643.5i | 0.841655 | − | 1.45779i | ||||
\(746\) | −25601.4 | − | 44342.9i | −1.25648 | − | 2.17629i | ||||
\(747\) | −25870.4 | + | 9075.89i | −1.26714 | + | 0.444537i | ||||
\(748\) | −3385.85 | −0.165507 | ||||||||
\(749\) | 7816.62 | − | 3589.00i | 0.381326 | − | 0.175086i | ||||
\(750\) | −14792.8 | + | 12266.4i | −0.720209 | + | 0.597207i | ||||
\(751\) | −5214.18 | − | 9031.22i | −0.253353 | − | 0.438820i | 0.711094 | − | 0.703097i | \(-0.248200\pi\) |
−0.964447 | + | 0.264277i | \(0.914867\pi\) | |||||||
\(752\) | 21741.1 | 1.05428 | ||||||||
\(753\) | −201.256 | + | 166.884i | −0.00973996 | + | 0.00807650i | ||||
\(754\) | 5041.63 | 0.243508 | ||||||||
\(755\) | 1248.59 | 0.0601864 | ||||||||
\(756\) | −1994.35 | + | 17950.1i | −0.0959443 | + | 0.863544i | ||||
\(757\) | 38937.7 | 1.86950 | 0.934751 | − | 0.355303i | \(-0.115622\pi\) | ||||
0.934751 | + | 0.355303i | \(0.115622\pi\) | |||||||
\(758\) | −7407.43 | −0.354947 | ||||||||
\(759\) | 15490.1 | − | 12844.6i | 0.740784 | − | 0.614268i | ||||
\(760\) | −3431.77 | −0.163794 | ||||||||
\(761\) | −711.985 | − | 1233.19i | −0.0339152 | − | 0.0587428i | 0.848570 | − | 0.529084i | \(-0.177464\pi\) |
−0.882485 | + | 0.470341i | \(0.844131\pi\) | |||||||
\(762\) | 3491.43 | − | 2895.14i | 0.165986 | − | 0.137638i | ||||
\(763\) | 783.883 | − | 8389.89i | 0.0371933 | − | 0.398079i | ||||
\(764\) | 985.112 | 0.0466494 | ||||||||
\(765\) | −4639.08 | − | 3985.74i | −0.219250 | − | 0.188372i | ||||
\(766\) | 22508.1 | + | 38985.2i | 1.06168 | + | 1.83889i | ||||
\(767\) | −379.556 | + | 657.411i | −0.0178683 | + | 0.0309488i | ||||
\(768\) | −19803.3 | + | 16421.1i | −0.930455 | + | 0.771545i | ||||
\(769\) | 7436.72 | − | 12880.8i | 0.348732 | − | 0.604022i | −0.637292 | − | 0.770622i | \(-0.719946\pi\) |
0.986025 | + | 0.166600i | \(0.0532790\pi\) | |||||||
\(770\) | 22409.0 | + | 15888.6i | 1.04878 | + | 0.743618i | ||||
\(771\) | 11308.4 | + | 4190.73i | 0.528224 | + | 0.195753i | ||||
\(772\) | 4233.30 | 0.197357 | ||||||||
\(773\) | −13639.2 | − | 23623.8i | −0.634630 | − | 1.09921i | −0.986593 | − | 0.163197i | \(-0.947819\pi\) |
0.351964 | − | 0.936014i | \(-0.385514\pi\) | |||||||
\(774\) | −34088.7 | + | 11959.0i | −1.58306 | + | 0.555372i | ||||
\(775\) | −2480.71 | + | 4296.71i | −0.114980 | + | 0.199151i | ||||
\(776\) | 3342.14 | + | 5788.75i | 0.154608 | + | 0.267789i | ||||
\(777\) | −16905.5 | + | 35171.4i | −0.780543 | + | 1.62389i | ||||
\(778\) | 11566.2 | − | 20033.3i | 0.532993 | − | 0.923171i | ||||
\(779\) | 10515.2 | + | 18212.8i | 0.483626 | + | 0.837665i | ||||
\(780\) | −2047.73 | + | 1698.00i | −0.0940004 | + | 0.0779464i | ||||
\(781\) | −1750.59 | + | 3032.10i | −0.0802060 | + | 0.138921i | ||||
\(782\) | −4421.22 | + | 7657.78i | −0.202177 | + | 0.350181i | ||||
\(783\) | −17086.2 | + | 28433.9i | −0.779837 | + | 1.29776i | ||||
\(784\) | −8092.03 | − | 23075.6i | −0.368624 | − | 1.05118i | ||||
\(785\) | 18848.8 | + | 32647.1i | 0.856997 | + | 1.48436i | ||||
\(786\) | 9746.34 | + | 3611.86i | 0.442291 | + | 0.163907i | ||||
\(787\) | −22518.8 | −1.01996 | −0.509981 | − | 0.860186i | \(-0.670348\pi\) | ||||
−0.509981 | + | 0.860186i | \(0.670348\pi\) | |||||||
\(788\) | 17008.7 | 0.768920 | ||||||||
\(789\) | −2970.11 | − | 17438.2i | −0.134016 | − | 0.786840i | ||||
\(790\) | 25240.8 | + | 43718.3i | 1.13674 | + | 1.96890i | ||||
\(791\) | −14914.5 | + | 6847.99i | −0.670415 | + | 0.307821i | ||||
\(792\) | 2386.06 | + | 2050.02i | 0.107052 | + | 0.0919753i | ||||
\(793\) | −1710.90 | + | 2963.37i | −0.0766154 | + | 0.132702i | ||||
\(794\) | −17569.0 | + | 30430.4i | −0.785264 | + | 1.36012i | ||||
\(795\) | −7739.11 | − | 45438.1i | −0.345255 | − | 2.02707i | ||||
\(796\) | 9005.28 | + | 15597.6i | 0.400984 | + | 0.694525i | ||||
\(797\) | 14101.5 | − | 24424.5i | 0.626727 | − | 1.08552i | −0.361478 | − | 0.932381i | \(-0.617728\pi\) |
0.988204 | − | 0.153142i | \(-0.0489391\pi\) | |||||||
\(798\) | −10210.2 | + | 21242.1i | −0.452930 | + | 0.942307i | ||||
\(799\) | 2586.07 | + | 4479.20i | 0.114504 | + | 0.198326i | ||||
\(800\) | 6492.19 | − | 11244.8i | 0.286917 | − | 0.496955i | ||||
\(801\) | 10599.4 | + | 9106.64i | 0.467554 | + | 0.401707i | ||||
\(802\) | 16138.1 | + | 27952.0i | 0.710544 | + | 1.23070i | ||||
\(803\) | 8250.00 | 0.362561 | ||||||||
\(804\) | 16341.4 | − | 13550.5i | 0.716811 | − | 0.594389i | ||||
\(805\) | 30310.8 | − | 13917.2i | 1.32710 | − | 0.609339i | ||||
\(806\) | 990.760 | − | 1716.05i | 0.0432978 | − | 0.0749940i | ||||
\(807\) | 30607.5 | + | 11342.7i | 1.33511 | + | 0.494775i | ||||
\(808\) | 1907.68 | − | 3304.20i | 0.0830593 | − | 0.143863i | ||||
\(809\) | 7209.83 | + | 12487.8i | 0.313330 | + | 0.542704i | 0.979081 | − | 0.203470i | \(-0.0652220\pi\) |
−0.665751 | + | 0.746174i | \(0.731889\pi\) | |||||||
\(810\) | −5671.21 | − | 37218.5i | −0.246008 | − | 1.61448i | ||||
\(811\) | −22959.6 | −0.994106 | −0.497053 | − | 0.867720i | \(-0.665585\pi\) | ||||
−0.497053 | + | 0.867720i | \(0.665585\pi\) | |||||||
\(812\) | −2831.58 | + | 30306.4i | −0.122376 | + | 1.30978i | ||||
\(813\) | 3148.17 | + | 18483.7i | 0.135807 | + | 0.797356i | ||||
\(814\) | −22516.3 | − | 38999.4i | −0.969528 | − | 1.67927i | ||||
\(815\) | 26667.0 | 1.14614 | ||||||||
\(816\) | −5891.31 | − | 2183.24i | −0.252742 | − | 0.0936627i | ||||
\(817\) | −21917.3 | −0.938543 | ||||||||
\(818\) | 45265.3 | 1.93480 | ||||||||
\(819\) | −666.824 | − | 2675.64i | −0.0284502 | − | 0.114157i | ||||
\(820\) | −30824.6 | −1.31273 | ||||||||
\(821\) | −3439.91 | −0.146229 | −0.0731143 | − | 0.997324i | \(-0.523294\pi\) | ||||
−0.0731143 | + | 0.997324i | \(0.523294\pi\) | |||||||
\(822\) | −4231.70 | − | 24845.3i | −0.179559 | − | 1.05423i | ||||
\(823\) | −19562.2 | −0.828547 | −0.414273 | − | 0.910153i | \(-0.635964\pi\) | ||||
−0.414273 | + | 0.910153i | \(0.635964\pi\) | |||||||
\(824\) | 203.259 | + | 352.055i | 0.00859328 | + | 0.0148840i | ||||
\(825\) | −7471.00 | − | 2768.65i | −0.315281 | − | 0.116839i | ||||
\(826\) | −8041.64 | − | 5701.76i | −0.338746 | − | 0.240181i | ||||
\(827\) | −10120.5 | −0.425544 | −0.212772 | − | 0.977102i | \(-0.568249\pi\) | ||||
−0.212772 | + | 0.977102i | \(0.568249\pi\) | |||||||
\(828\) | −23878.4 | + | 8377.05i | −1.00221 | + | 0.351598i | ||||
\(829\) | 6005.06 | + | 10401.1i | 0.251586 | + | 0.435759i | 0.963963 | − | 0.266038i | \(-0.0857147\pi\) |
−0.712377 | + | 0.701797i | \(0.752381\pi\) | |||||||
\(830\) | 26219.9 | − | 45414.1i | 1.09651 | − | 1.89921i | ||||
\(831\) | −1837.46 | − | 10788.1i | −0.0767036 | − | 0.450345i | ||||
\(832\) | −1020.34 | + | 1767.28i | −0.0425167 | + | 0.0736411i | ||||
\(833\) | 3791.60 | − | 4411.95i | 0.157708 | − | 0.183512i | ||||
\(834\) | −2566.46 | − | 15068.3i | −0.106558 | − | 0.625627i | ||||
\(835\) | −41456.7 | −1.71817 | ||||||||
\(836\) | −6322.33 | − | 10950.6i | −0.261558 | − | 0.453031i | ||||
\(837\) | 6320.50 | + | 11403.5i | 0.261013 | + | 0.470922i | ||||
\(838\) | −202.299 | + | 350.393i | −0.00833928 | + | 0.0144440i | ||||
\(839\) | −15824.0 | − | 27407.9i | −0.651136 | − | 1.12780i | −0.982847 | − | 0.184420i | \(-0.940959\pi\) |
0.331711 | − | 0.943381i | \(-0.392374\pi\) | |||||||
\(840\) | 2940.38 | + | 4305.89i | 0.120777 | + | 0.176866i | ||||
\(841\) | −15759.3 | + | 27295.9i | −0.646163 | + | 1.11919i | ||||
\(842\) | −22851.2 | − | 39579.5i | −0.935279 | − | 1.61995i | ||||
\(843\) | −9471.87 | − | 3510.15i | −0.386985 | − | 0.143412i | ||||
\(844\) | 979.796 | − | 1697.06i | 0.0399597 | − | 0.0692122i | ||||
\(845\) | −14468.7 | + | 25060.5i | −0.589040 | + | 1.02025i | ||||
\(846\) | −5893.67 | + | 31287.0i | −0.239514 | + | 1.27147i | ||||
\(847\) | −871.964 | + | 9332.62i | −0.0353731 | + | 0.378598i | ||||
\(848\) | −23674.4 | − | 41005.3i | −0.958705 | − | 1.66053i | ||||
\(849\) | 36964.9 | − | 30651.8i | 1.49427 | − | 1.23907i | ||||
\(850\) | 3501.12 | 0.141279 | ||||||||
\(851\) | −54676.8 | −2.20247 | ||||||||
\(852\) | 3389.24 | − | 2810.40i | 0.136283 | − | 0.113008i | ||||
\(853\) | 20475.4 | + | 35464.4i | 0.821880 | + | 1.42354i | 0.904281 | + | 0.426939i | \(0.140408\pi\) |
−0.0824005 | + | 0.996599i | \(0.526259\pi\) | |||||||
\(854\) | −36248.8 | − | 25701.5i | −1.45247 | − | 1.02984i | ||||
\(855\) | 4228.31 | − | 22446.3i | 0.169129 | − | 0.897832i | ||||
\(856\) | −941.991 | + | 1631.58i | −0.0376128 | + | 0.0651473i | ||||
\(857\) | 9585.51 | − | 16602.6i | 0.382071 | − | 0.661766i | −0.609287 | − | 0.792950i | \(-0.708544\pi\) |
0.991358 | + | 0.131183i | \(0.0418777\pi\) | |||||||
\(858\) | 2983.81 | + | 1105.76i | 0.118725 | + | 0.0439978i | ||||
\(859\) | 15262.4 | + | 26435.2i | 0.606222 | + | 1.05001i | 0.991857 | + | 0.127356i | \(0.0406491\pi\) |
−0.385635 | + | 0.922651i | \(0.626018\pi\) | |||||||
\(860\) | 16062.3 | − | 27820.8i | 0.636885 | − | 1.10312i | ||||
\(861\) | 13842.3 | − | 28798.5i | 0.547903 | − | 1.13990i | ||||
\(862\) | −11825.3 | − | 20482.0i | −0.467253 | − | 0.809305i | ||||
\(863\) | 7085.52 | − | 12272.5i | 0.279483 | − | 0.484079i | −0.691773 | − | 0.722115i | \(-0.743170\pi\) |
0.971256 | + | 0.238036i | \(0.0765036\pi\) | |||||||
\(864\) | −16541.2 | − | 29843.7i | −0.651323 | − | 1.17512i | ||||
\(865\) | 2139.63 | + | 3705.95i | 0.0841037 | + | 0.145672i | ||||
\(866\) | −33482.6 | −1.31384 | ||||||||
\(867\) | 4035.41 | + | 23692.8i | 0.158073 | + | 0.928086i | ||||
\(868\) | 9759.09 | + | 6919.48i | 0.381619 | + | 0.270579i | ||||
\(869\) | 14037.4 | − | 24313.4i | 0.547968 | − | 0.949109i | ||||
\(870\) | −10653.5 | − | 62549.4i | −0.415159 | − | 2.43750i | ||||
\(871\) | −1620.60 | + | 2806.95i | −0.0630445 | + | 0.109196i | ||||
\(872\) | 922.851 | + | 1598.42i | 0.0358391 | + | 0.0620751i | ||||
\(873\) | −41980.6 | + | 14727.7i | −1.62752 | + | 0.570969i | ||||
\(874\) | −33022.6 | −1.27804 | ||||||||
\(875\) | 14450.3 | + | 10245.7i | 0.558297 | + | 0.395849i | ||||
\(876\) | −9728.19 | − | 3605.14i | −0.375211 | − | 0.139048i | ||||
\(877\) | −18131.3 | − | 31404.4i | −0.698121 | − | 1.20918i | −0.969117 | − | 0.246600i | \(-0.920687\pi\) |
0.270997 | − | 0.962580i | \(-0.412647\pi\) | |||||||
\(878\) | 55797.3 | 2.14473 | ||||||||
\(879\) | 5373.30 | + | 31547.9i | 0.206185 | + | 1.21056i | ||||
\(880\) | −27347.9 | −1.04761 | ||||||||
\(881\) | −2958.35 | −0.113132 | −0.0565660 | − | 0.998399i | \(-0.518015\pi\) | ||||
−0.0565660 | + | 0.998399i | \(0.518015\pi\) | |||||||
\(882\) | 35401.0 | − | 5389.56i | 1.35149 | − | 0.205755i | ||||
\(883\) | 23107.6 | 0.880671 | 0.440335 | − | 0.897833i | \(-0.354860\pi\) | ||||
0.440335 | + | 0.897833i | \(0.354860\pi\) | |||||||
\(884\) | −650.088 | −0.0247340 | ||||||||
\(885\) | 8958.27 | + | 3319.81i | 0.340259 | + | 0.126095i | ||||
\(886\) | −6757.85 | −0.256246 | ||||||||
\(887\) | −12367.0 | − | 21420.2i | −0.468143 | − | 0.810847i | 0.531195 | − | 0.847250i | \(-0.321743\pi\) |
−0.999337 | + | 0.0364031i | \(0.988410\pi\) | |||||||
\(888\) | −1435.17 | − | 8426.22i | −0.0542355 | − | 0.318430i | ||||
\(889\) | −3410.60 | − | 2418.21i | −0.128670 | − | 0.0912309i | ||||
\(890\) | −26728.7 | −1.00668 | ||||||||
\(891\) | −16348.6 | + | 13080.7i | −0.614699 | + | 0.491831i | ||||
\(892\) | −5586.92 | − | 9676.82i | −0.209713 | − | 0.363233i | ||||
\(893\) | −9657.80 | + | 16727.8i | −0.361910 | + | 0.626847i | ||||
\(894\) | 48282.2 | + | 17892.7i | 1.80626 | + | 0.669376i | ||||
\(895\) | −14045.9 | + | 24328.3i | −0.524585 | + | 0.908608i | ||||
\(896\) | 7777.36 | + | 5514.37i | 0.289981 | + | 0.205605i | ||||
\(897\) | 2974.12 | − | 2466.18i | 0.110706 | − | 0.0917985i | ||||
\(898\) | 26587.7 | 0.988021 | ||||||||
\(899\) | 10986.7 | + | 19029.6i | 0.407595 | + | 0.705975i | ||||
\(900\) | 7599.75 | + | 6529.45i | 0.281472 | + | 0.241831i | ||||
\(901\) | 5632.05 | − | 9755.00i | 0.208247 | − | 0.360695i | ||||
\(902\) | 18436.5 | + | 31932.9i | 0.680562 | + | 1.17877i | ||||
\(903\) | 18779.1 | + | 27500.0i | 0.692057 | + | 1.01345i | ||||
\(904\) | 1797.36 | − | 3113.12i | 0.0661277 | − | 0.114536i | ||||
\(905\) | 15010.4 | + | 25998.8i | 0.551341 | + | 0.954951i | ||||
\(906\) | 315.364 | + | 1851.58i | 0.0115643 | + | 0.0678968i | ||||
\(907\) | 25287.5 | − | 43799.2i | 0.925751 | − | 1.60345i | 0.135403 | − | 0.990791i | \(-0.456767\pi\) |
0.790348 | − | 0.612658i | \(-0.209900\pi\) | |||||||
\(908\) | 14557.0 | − | 25213.4i | 0.532038 | − | 0.921517i | ||||
\(909\) | 19261.4 | + | 16548.8i | 0.702818 | + | 0.603837i | ||||
\(910\) | 4302.55 | + | 3050.63i | 0.156734 | + | 0.111129i | ||||
\(911\) | −18448.5 | − | 31953.7i | −0.670939 | − | 1.16210i | −0.977638 | − | 0.210295i | \(-0.932558\pi\) |
0.306699 | − | 0.951807i | \(-0.400776\pi\) | |||||||
\(912\) | −3939.63 | − | 23130.5i | −0.143042 | − | 0.839833i | ||||
\(913\) | −29163.7 | −1.05715 | ||||||||
\(914\) | −10515.3 | −0.380542 | ||||||||
\(915\) | 40380.7 | + | 14964.5i | 1.45896 | + | 0.540669i | ||||
\(916\) | 9419.48 | + | 16315.0i | 0.339769 | + | 0.588497i | ||||
\(917\) | 891.303 | − | 9539.60i | 0.0320975 | − | 0.343539i | ||||
\(918\) | 4738.88 | − | 7886.17i | 0.170377 | − | 0.283532i | ||||
\(919\) | −5914.26 | + | 10243.8i | −0.212289 | + | 0.367695i | −0.952431 | − | 0.304756i | \(-0.901425\pi\) |
0.740142 | + | 0.672451i | \(0.234758\pi\) | |||||||
\(920\) | −3652.80 | + | 6326.83i | −0.130901 | + | 0.226728i | ||||
\(921\) | −15825.7 | + | 13122.9i | −0.566206 | + | 0.469505i | ||||
\(922\) | 4762.11 | + | 8248.22i | 0.170100 | + | 0.294621i | ||||
\(923\) | −336.115 | + | 582.168i | −0.0119863 | + | 0.0207609i | ||||
\(924\) | −8322.81 | + | 17315.3i | −0.296321 | + | 0.616485i | ||||
\(925\) | 10824.5 | + | 18748.6i | 0.384765 | + | 0.666432i | ||||
\(926\) | −1887.84 | + | 3269.83i | −0.0669959 | + | 0.116040i | ||||
\(927\) | −2553.14 | + | 895.693i | −0.0904595 | + | 0.0317351i | ||||
\(928\) | −28753.1 | − | 49801.8i | −1.01710 | − | 1.76166i | ||||
\(929\) | −15503.0 | −0.547510 | −0.273755 | − | 0.961800i | \(-0.588266\pi\) | ||||
−0.273755 | + | 0.961800i | \(0.588266\pi\) | |||||||
\(930\) | −23383.9 | − | 8665.75i | −0.824503 | − | 0.305550i | ||||
\(931\) | 21349.2 | + | 4024.52i | 0.751548 | + | 0.141674i | ||||
\(932\) | −10572.1 | + | 18311.5i | −0.371569 | + | 0.643576i | ||||
\(933\) | −22229.1 | + | 18432.6i | −0.780008 | + | 0.646793i | ||||
\(934\) | −21215.2 | + | 36745.7i | −0.743235 | + | 1.28732i | ||||
\(935\) | −3252.99 | − | 5634.34i | −0.113780 | − | 0.197072i | ||||
\(936\) | 458.127 | + | 393.607i | 0.0159982 | + | 0.0137451i | ||||
\(937\) | 45491.1 | 1.58605 | 0.793026 | − | 0.609188i | \(-0.208505\pi\) | ||||
0.793026 | + | 0.609188i | \(0.208505\pi\) | |||||||
\(938\) | −34335.5 | − | 24344.9i | −1.19520 | − | 0.847428i | ||||
\(939\) | 21393.6 | − | 17739.9i | 0.743508 | − | 0.616527i | ||||
\(940\) | −14155.6 | − | 24518.3i | −0.491177 | − | 0.850743i | ||||
\(941\) | −3493.66 | −0.121031 | −0.0605154 | − | 0.998167i | \(-0.519274\pi\) | ||||
−0.0605154 | + | 0.998167i | \(0.519274\pi\) | |||||||
\(942\) | −43652.8 | + | 36197.5i | −1.50986 | + | 1.25199i | ||||
\(943\) | 44769.7 | 1.54602 | ||||||||
\(944\) | 9814.02 | 0.338368 | ||||||||
\(945\) | −31786.5 | + | 13927.0i | −1.09420 | + | 0.479411i | ||||
\(946\) | −38428.1 | −1.32072 | ||||||||
\(947\) | 41769.8 | 1.43330 | 0.716651 | − | 0.697432i | \(-0.245674\pi\) | ||||
0.716651 | + | 0.697432i | \(0.245674\pi\) | |||||||
\(948\) | −27177.1 | + | 22535.6i | −0.931088 | + | 0.772071i | ||||
\(949\) | 1584.01 | 0.0541825 | ||||||||
\(950\) | 6537.56 | + | 11323.4i | 0.223270 | + | 0.386715i | ||||
\(951\) | 25671.7 | − | 21287.3i | 0.875355 | − | 0.725856i | ||||
\(952\) | −118.536 | + | 1268.69i | −0.00403548 | + | 0.0431917i | ||||
\(953\) | −7119.73 | −0.242005 | −0.121002 | − | 0.992652i | \(-0.538611\pi\) | ||||
−0.121002 | + | 0.992652i | \(0.538611\pi\) | |||||||
\(954\) | 65427.2 | − | 22953.2i | 2.22042 | − | 0.778970i | ||||
\(955\) | 946.454 | + | 1639.31i | 0.0320697 | + | 0.0555463i | ||||
\(956\) | −4850.70 | + | 8401.66i | −0.164103 | + | 0.284235i | ||||
\(957\) | −27163.2 | + | 22524.1i | −0.917516 | + | 0.760816i | ||||
\(958\) | 1892.89 | − | 3278.58i | 0.0638377 | − | 0.110570i | ||||
\(959\) | −21112.9 | + | 9693.98i | −0.710917 | + | 0.326418i | ||||
\(960\) | 24082.0 | + | 8924.46i | 0.809628 | + | 0.300037i | ||||
\(961\) | −21154.7 | −0.710105 | ||||||||
\(962\) | −4323.16 | − | 7487.93i | −0.144890 | − | 0.250957i | ||||
\(963\) | −9511.07 | − | 8171.59i | −0.318266 | − | 0.273443i | ||||
\(964\) | −13718.1 | + | 23760.4i | −0.458329 | + | 0.793848i | ||||
\(965\) | 4067.18 | + | 7044.56i | 0.135676 | + | 0.234997i | ||||
\(966\) | 28294.2 | + | 41433.9i | 0.942392 | + | 1.38003i | ||||
\(967\) | −27441.1 | + | 47529.4i | −0.912562 | + | 1.58060i | −0.102129 | + | 0.994771i | \(0.532565\pi\) |
−0.810433 | + | 0.585832i | \(0.800768\pi\) | |||||||
\(968\) | −1026.55 | − | 1778.03i | −0.0340852 | − | 0.0590373i | ||||
\(969\) | 4296.84 | − | 3562.99i | 0.142450 | − | 0.118122i | ||||
\(970\) | 42547.6 | − | 73694.5i | 1.40837 | − | 2.43937i | ||||
\(971\) | 19341.9 | − | 33501.1i | 0.639248 | − | 1.10721i | −0.346350 | − | 0.938105i | \(-0.612579\pi\) |
0.985598 | − | 0.169105i | \(-0.0540877\pi\) | |||||||
\(972\) | 24993.9 | − | 8280.38i | 0.824774 | − | 0.273244i | ||||
\(973\) | −12804.6 | + | 5879.25i | −0.421888 | + | 0.193710i | ||||
\(974\) | 16898.9 | + | 29269.8i | 0.555930 | + | 0.962899i | ||||
\(975\) | −1434.44 | − | 531.585i | −0.0471168 | − | 0.0174609i | ||||
\(976\) | 44238.1 | 1.45085 | ||||||||
\(977\) | 38104.9 | 1.24778 | 0.623892 | − | 0.781511i | \(-0.285551\pi\) | ||||
0.623892 | + | 0.781511i | \(0.285551\pi\) | |||||||
\(978\) | 6735.47 | + | 39545.5i | 0.220221 | + | 1.29297i | ||||
\(979\) | 7432.43 | + | 12873.4i | 0.242637 | + | 0.420260i | ||||
\(980\) | −20754.5 | + | 24150.2i | −0.676509 | + | 0.787195i | ||||
\(981\) | −11591.9 | + | 4066.69i | −0.377270 | + | 0.132354i | ||||
\(982\) | −26933.3 | + | 46649.8i | −0.875229 | + | 1.51594i | ||||
\(983\) | −27677.0 | + | 47938.0i | −0.898026 | + | 1.55543i | −0.0680127 | + | 0.997684i | \(0.521666\pi\) |
−0.830014 | + | 0.557743i | \(0.811668\pi\) | |||||||
\(984\) | 1175.12 | + | 6899.43i | 0.0380707 | + | 0.223522i | ||||
\(985\) | 16341.2 | + | 28303.8i | 0.528604 | + | 0.915568i | ||||
\(986\) | 7753.00 | − | 13428.6i | 0.250411 | − | 0.433725i | ||||
\(987\) | 29263.5 | − | 2214.83i | 0.943737 | − | 0.0714273i | ||||
\(988\) | −1213.89 | − | 2102.53i | −0.0390882 | − | 0.0677028i | ||||
\(989\) | −23329.0 | + | 40406.9i | −0.750069 | + | 1.29916i | ||||
\(990\) | 7413.59 | − | 39355.5i | 0.237999 | − | 1.26344i | ||||
\(991\) | −21782.9 | − | 37729.0i | −0.698239 | − | 1.20939i | −0.969076 | − | 0.246761i | \(-0.920634\pi\) |
0.270837 | − | 0.962625i | \(-0.412700\pi\) | |||||||
\(992\) | −22601.7 | −0.723393 | ||||||||
\(993\) | 13045.5 | − | 10817.5i | 0.416905 | − | 0.345703i | ||||
\(994\) | −7121.24 | − | 5049.17i | −0.227236 | − | 0.161117i | ||||
\(995\) | −17303.8 | + | 29971.0i | −0.551323 | + | 0.954920i | ||||
\(996\) | 34389.1 | + | 12744.1i | 1.09404 | + | 0.405436i | ||||
\(997\) | 18601.3 | − | 32218.3i | 0.590881 | − | 1.02344i | −0.403233 | − | 0.915097i | \(-0.632114\pi\) |
0.994114 | − | 0.108338i | \(-0.0345529\pi\) | |||||||
\(998\) | 16294.8 | + | 28223.4i | 0.516836 | + | 0.895186i | ||||
\(999\) | 56882.0 | + | 994.965i | 1.80147 | + | 0.0315108i |
(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.h.a.58.19 | yes | 44 | |
3.2 | odd | 2 | 189.4.h.a.37.4 | 44 | |||
7.4 | even | 3 | 63.4.g.a.4.4 | ✓ | 44 | ||
9.2 | odd | 6 | 189.4.g.a.100.19 | 44 | |||
9.7 | even | 3 | 63.4.g.a.16.4 | yes | 44 | ||
21.11 | odd | 6 | 189.4.g.a.172.19 | 44 | |||
63.11 | odd | 6 | 189.4.h.a.46.4 | 44 | |||
63.25 | even | 3 | inner | 63.4.h.a.25.19 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.g.a.4.4 | ✓ | 44 | 7.4 | even | 3 | ||
63.4.g.a.16.4 | yes | 44 | 9.7 | even | 3 | ||
63.4.h.a.25.19 | yes | 44 | 63.25 | even | 3 | inner | |
63.4.h.a.58.19 | yes | 44 | 1.1 | even | 1 | trivial | |
189.4.g.a.100.19 | 44 | 9.2 | odd | 6 | |||
189.4.g.a.172.19 | 44 | 21.11 | odd | 6 | |||
189.4.h.a.37.4 | 44 | 3.2 | odd | 2 | |||
189.4.h.a.46.4 | 44 | 63.11 | odd | 6 |