Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(13,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.13");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.i (of order \(9\), degree \(6\), 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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 49.6 | ||
Character | \(\chi\) | \(=\) | 108.49 |
Dual form | 108.4.i.a.97.6 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{7}{9}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.81053 | + | 4.87052i | 0.348437 | + | 0.937332i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −13.0875 | + | 4.76347i | −1.17058 | + | 0.426058i | −0.852867 | − | 0.522128i | \(-0.825138\pi\) |
−0.317717 | + | 0.948186i | \(0.602916\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.689494 | − | 3.91032i | −0.0372292 | − | 0.211137i | 0.960518 | − | 0.278216i | \(-0.0897432\pi\) |
−0.997748 | + | 0.0670790i | \(0.978632\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −20.4440 | + | 17.6365i | −0.757184 | + | 0.653202i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −41.0823 | − | 14.9527i | −1.12607 | − | 0.409856i | −0.289206 | − | 0.957267i | \(-0.593391\pi\) |
−0.836864 | + | 0.547411i | \(0.815613\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.04425 | + | 3.39352i | 0.0862825 | + | 0.0723996i | 0.684909 | − | 0.728629i | \(-0.259842\pi\) |
−0.598626 | + | 0.801028i | \(0.704287\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −46.8959 | − | 55.1187i | −0.807232 | − | 0.948772i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.06285 | + | 5.30501i | −0.0436970 | + | 0.0756855i | −0.887047 | − | 0.461680i | \(-0.847247\pi\) |
0.843350 | + | 0.537365i | \(0.180580\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.42787 | − | 12.8654i | −0.0896879 | − | 0.155344i | 0.817691 | − | 0.575657i | \(-0.195254\pi\) |
−0.907379 | + | 0.420313i | \(0.861920\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17.7969 | − | 10.4379i | 0.184934 | − | 0.108464i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −21.3706 | + | 121.199i | −0.193743 | + | 1.09877i | 0.720455 | + | 0.693502i | \(0.243933\pi\) |
−0.914198 | + | 0.405268i | \(0.867178\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 52.8371 | − | 44.3356i | 0.422697 | − | 0.354685i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −122.913 | − | 67.6414i | −0.876098 | − | 0.482133i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −108.223 | + | 90.8101i | −0.692985 | + | 0.581483i | −0.919768 | − | 0.392462i | \(-0.871623\pi\) |
0.226784 | + | 0.973945i | \(0.427179\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46.8412 | + | 265.650i | −0.271385 | + | 1.53910i | 0.478831 | + | 0.877907i | \(0.341061\pi\) |
−0.750216 | + | 0.661193i | \(0.770050\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.55313 | − | 227.164i | −0.00819291 | − | 1.19831i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 27.6504 | + | 47.8920i | 0.133537 | + | 0.231292i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 100.261 | − | 173.657i | 0.445481 | − | 0.771595i | −0.552605 | − | 0.833443i | \(-0.686366\pi\) |
0.998086 | + | 0.0618483i | \(0.0196995\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.20601 | + | 25.8417i | −0.0377985 | + | 0.106102i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 239.406 | + | 200.886i | 0.911927 | + | 0.765197i | 0.972485 | − | 0.232967i | \(-0.0748435\pi\) |
−0.0605578 | + | 0.998165i | \(0.519288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 462.032 | + | 168.166i | 1.63859 | + | 0.596397i | 0.986791 | − | 0.161998i | \(-0.0517939\pi\) |
0.651795 | + | 0.758395i | \(0.274016\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 183.550 | − | 328.202i | 0.608045 | − | 1.08723i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.6113 | − | 60.1798i | −0.0329323 | − | 0.186769i | 0.963904 | − | 0.266250i | \(-0.0857847\pi\) |
−0.996836 | + | 0.0794815i | \(0.974674\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 307.499 | − | 111.921i | 0.896500 | − | 0.326299i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −31.3835 | − | 5.31279i | −0.0861681 | − | 0.0145870i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −380.159 | −0.985262 | −0.492631 | − | 0.870238i | \(-0.663965\pi\) | ||||
−0.492631 | + | 0.870238i | \(0.663965\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 608.892 | 1.49278 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 49.2130 | − | 59.4709i | 0.114358 | − | 0.138195i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −154.748 | + | 56.3238i | −0.341467 | + | 0.124284i | −0.507061 | − | 0.861910i | \(-0.669268\pi\) |
0.165594 | + | 0.986194i | \(0.447046\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −149.877 | − | 849.997i | −0.314588 | − | 1.78411i | −0.574523 | − | 0.818488i | \(-0.694812\pi\) |
0.259935 | − | 0.965626i | \(-0.416299\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 83.0601 | + | 67.7821i | 0.166105 | + | 0.135551i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −69.0941 | − | 25.1482i | −0.131847 | − | 0.0479885i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 159.359 | + | 133.718i | 0.290579 | + | 0.243825i | 0.776410 | − | 0.630228i | \(-0.217039\pi\) |
−0.485831 | + | 0.874053i | \(0.661483\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −628.994 | + | 115.348i | −1.09742 | + | 0.201250i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −451.411 | + | 781.866i | −0.754543 | + | 1.30691i | 0.191058 | + | 0.981579i | \(0.438808\pi\) |
−0.945601 | + | 0.325329i | \(0.894525\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 353.597 | + | 612.447i | 0.566923 | + | 0.981939i | 0.996868 | + | 0.0790840i | \(0.0251995\pi\) |
−0.429945 | + | 0.902855i | \(0.641467\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 311.601 | + | 177.073i | 0.479741 | + | 0.272622i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −30.1439 | + | 170.954i | −0.0446132 | + | 0.253014i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −847.858 | + | 711.438i | −1.20749 | + | 1.01320i | −0.208104 | + | 0.978107i | \(0.566729\pi\) |
−0.999384 | + | 0.0350955i | \(0.988826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 106.911 | − | 721.118i | 0.146654 | − | 0.989188i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 652.401 | − | 547.430i | 0.862775 | − | 0.723954i | −0.0997890 | − | 0.995009i | \(-0.531817\pi\) |
0.962564 | + | 0.271054i | \(0.0873723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.8148 | − | 84.0192i | 0.0189047 | − | 0.107214i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −638.234 | − | 362.689i | −0.786504 | − | 0.446947i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 214.477 | + | 371.485i | 0.255444 | + | 0.442442i | 0.965016 | − | 0.262191i | \(-0.0844450\pi\) |
−0.709572 | + | 0.704633i | \(0.751112\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4813 | − | 18.1541i | 0.0120740 | − | 0.0209128i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1378.66 | + | 252.826i | −1.53721 | + | 0.281901i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 158.497 | + | 132.994i | 0.171173 | + | 0.143631i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1166.45 | − | 424.552i | −1.22098 | − | 0.444400i | −0.350480 | − | 0.936570i | \(-0.613981\pi\) |
−0.870499 | + | 0.492171i | \(0.836204\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1103.60 | − | 418.853i | 1.12036 | − | 0.425215i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −142.775 | − | 809.715i | −0.140659 | − | 0.797719i | −0.970750 | − | 0.240091i | \(-0.922823\pi\) |
0.830091 | − | 0.557628i | \(-0.188288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1713.66 | + | 623.722i | −1.63934 | + | 0.596672i | −0.986924 | − | 0.161187i | \(-0.948468\pi\) |
−0.652418 | + | 0.757859i | \(0.726245\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −183.197 | + | 221.382i | −0.170268 | + | 0.205759i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2093.70 | −1.89164 | −0.945819 | − | 0.324695i | \(-0.894738\pi\) | ||||
−0.945819 | + | 0.324695i | \(0.894738\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 785.096 | 0.689895 | 0.344947 | − | 0.938622i | \(-0.387897\pi\) | ||||
0.344947 | + | 0.938622i | \(0.387897\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1027.32 | + | 173.912i | 0.878463 | + | 0.148711i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1484.56 | − | 540.337i | 1.23589 | − | 0.449828i | 0.360281 | − | 0.932844i | \(-0.382681\pi\) |
0.875612 | + | 0.483015i | \(0.160458\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −297.638 | − | 1687.99i | −0.241347 | − | 1.36875i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −142.530 | + | 1.94906i | −0.112623 | + | 0.00154009i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 22.8561 | + | 8.31893i | 0.0176068 | + | 0.00640836i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 444.562 | + | 373.032i | 0.334006 | + | 0.280265i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −544.966 | + | 1529.74i | −0.399495 | + | 1.12140i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 390.150 | − | 675.760i | 0.279169 | − | 0.483534i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −197.197 | − | 341.555i | −0.137783 | − | 0.238646i | 0.788874 | − | 0.614554i | \(-0.210664\pi\) |
−0.926657 | + | 0.375908i | \(0.877331\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.4673 | + | 2554.81i | 0.0119218 | + | 1.74371i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 104.311 | − | 591.579i | 0.0695704 | − | 0.394553i | −0.930061 | − | 0.367405i | \(-0.880246\pi\) |
0.999631 | − | 0.0271482i | \(-0.00864260\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −45.1865 | + | 37.9160i | −0.0294599 | + | 0.0247198i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1930.84 | + | 299.766i | 1.23096 | + | 0.191109i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 875.032 | − | 734.239i | 0.545686 | − | 0.457885i | −0.327791 | − | 0.944750i | \(-0.606304\pi\) |
0.873477 | + | 0.486865i | \(0.161860\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −359.669 | + | 2039.78i | −0.219473 | + | 1.24469i | 0.653501 | + | 0.756926i | \(0.273300\pi\) |
−0.872974 | + | 0.487767i | \(0.837812\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 273.895 | − | 160.640i | 0.163589 | − | 0.0959455i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −115.404 | − | 199.886i | −0.0674867 | − | 0.116890i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 983.804 | − | 1704.00i | 0.563451 | − | 0.975926i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1101.85 | + | 1295.05i | 0.618224 | + | 0.726624i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2383.51 | + | 2000.00i | 1.31050 | + | 1.09964i | 0.988227 | + | 0.152997i | \(0.0488924\pi\) |
0.322276 | + | 0.946646i | \(0.395552\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −35.5500 | − | 12.9391i | −0.0191590 | − | 0.00697332i | 0.332423 | − | 0.943130i | \(-0.392134\pi\) |
−0.351582 | + | 0.936157i | \(0.614356\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −30.9448 | − | 162.473i | −0.0163512 | − | 0.0858508i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −652.379 | − | 3699.82i | −0.338067 | − | 1.91727i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2170.17 | + | 789.878i | −1.10318 | + | 0.401523i | −0.828486 | − | 0.560010i | \(-0.810797\pi\) |
−0.274689 | + | 0.961533i | \(0.588575\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −688.290 | − | 1851.57i | −0.343301 | − | 0.923517i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 488.661 | 0.239204 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 232.306 | 0.111630 | 0.0558148 | − | 0.998441i | \(-0.482224\pi\) | ||||
0.0558148 | + | 0.998441i | \(0.482224\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1102.42 | + | 2965.62i | 0.520140 | + | 1.39923i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1530.58 | − | 557.084i | 0.709218 | − | 0.258134i | 0.0378768 | − | 0.999282i | \(-0.487941\pi\) |
0.671342 | + | 0.741148i | \(0.265718\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −376.665 | − | 2136.17i | −0.171445 | − | 0.972314i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 378.756 | + | 132.019i | 0.169381 | + | 0.0590396i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1144.54 | − | 416.577i | −0.502992 | − | 0.183074i | 0.0780474 | − | 0.996950i | \(-0.475131\pi\) |
−0.581039 | + | 0.813876i | \(0.697354\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −209.797 | − | 176.041i | −0.0906238 | − | 0.0760424i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −554.503 | − | 651.730i | −0.235475 | − | 0.276763i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1158.73 | − | 2006.98i | 0.483842 | − | 0.838039i | −0.515986 | − | 0.856597i | \(-0.672574\pi\) |
0.999828 | + | 0.0185580i | \(0.00590754\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −77.3428 | − | 133.962i | −0.0317616 | − | 0.0550127i | 0.849708 | − | 0.527254i | \(-0.176778\pi\) |
−0.881469 | + | 0.472241i | \(0.843445\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3868.57 | − | 2268.93i | 1.56269 | − | 0.916524i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −484.957 | + | 2750.33i | −0.192728 | + | 1.09302i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 205.153 | − | 172.144i | 0.0802260 | − | 0.0673176i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −179.751 | + | 527.268i | −0.0691798 | + | 0.202926i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2149.29 | − | 1803.47i | 0.814227 | − | 0.683217i | −0.137386 | − | 0.990518i | \(-0.543870\pi\) |
0.951613 | + | 0.307300i | \(0.0994256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −475.369 | + | 2695.95i | −0.177294 | + | 1.00549i | 0.758168 | + | 0.652060i | \(0.226095\pi\) |
−0.935462 | + | 0.353427i | \(0.885016\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.61214 | − | 382.056i | −0.000959277 | − | 0.140306i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1571.62 | + | 2722.12i | 0.568391 | + | 0.984482i | 0.996725 | + | 0.0808620i | \(0.0257673\pi\) |
−0.428334 | + | 0.903620i | \(0.640899\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −935.924 | + | 1621.07i | −0.333396 | + | 0.577459i | −0.983175 | − | 0.182664i | \(-0.941528\pi\) |
0.649779 | + | 0.760123i | \(0.274861\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −362.752 | + | 1018.26i | −0.127296 | + | 0.357326i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 429.716 | + | 360.574i | 0.148572 | + | 0.124667i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4090.15 | − | 1488.69i | −1.39350 | − | 0.507194i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1700.62 | − | 2854.69i | −0.571020 | − | 0.958524i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 112.780 | + | 639.608i | 0.0373262 | + | 0.211687i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 238.052 | − | 86.6438i | 0.0776691 | − | 0.0282692i | −0.302893 | − | 0.953024i | \(-0.597953\pi\) |
0.380562 | + | 0.924755i | \(0.375730\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4625.39 | − | 783.013i | −1.48792 | − | 0.251883i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6847.91 | −2.17220 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1071.07 | 0.335065 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2342.74 | + | 2831.05i | −0.722866 | + | 0.873539i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.3896 | + | 11.0609i | −0.00924988 | + | 0.00336668i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 600.687 | + | 3406.66i | 0.180381 | + | 1.02299i | 0.931748 | + | 0.363106i | \(0.118284\pi\) |
−0.751367 | + | 0.659885i | \(0.770605\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −298.277 | + | 1838.25i | −0.0883784 | + | 0.544668i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1925.67 | − | 700.886i | −0.563044 | − | 0.204931i | 0.0447883 | − | 0.998997i | \(-0.485739\pi\) |
−0.607833 | + | 0.794065i | \(0.707961\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −693.662 | − | 582.052i | −0.200168 | − | 0.167961i | 0.537194 | − | 0.843459i | \(-0.319484\pi\) |
−0.737362 | + | 0.675498i | \(0.763929\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −887.213 | + | 162.702i | −0.252703 | + | 0.0463419i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −696.488 | + | 1206.35i | −0.195830 | + | 0.339188i | −0.947172 | − | 0.320725i | \(-0.896073\pi\) |
0.751342 | + | 0.659913i | \(0.229407\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 425.540 | + | 737.057i | 0.118124 | + | 0.204597i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5000.15 | − | 2841.43i | −1.37044 | − | 0.778780i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −43.4332 | + | 246.322i | −0.0117551 | + | 0.0666663i | −0.990121 | − | 0.140216i | \(-0.955220\pi\) |
0.978366 | + | 0.206882i | \(0.0663316\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3775.11 | − | 3167.70i | 1.00903 | − | 0.846677i | 0.0208208 | − | 0.999783i | \(-0.493372\pi\) |
0.988210 | + | 0.153106i | \(0.0489276\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3705.79 | − | 784.894i | 0.978297 | − | 0.207206i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3491.28 | + | 2929.53i | −0.910406 | + | 0.763921i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.6191 | − | 77.2377i | 0.00350835 | − | 0.0198968i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3847.46 | + | 2186.40i | 0.979208 | + | 0.556455i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 557.386 | + | 965.420i | 0.140167 | + | 0.242776i | 0.927559 | − | 0.373676i | \(-0.121903\pi\) |
−0.787392 | + | 0.616452i | \(0.788569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2690.21 | − | 4659.57i | 0.668505 | − | 1.15788i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 436.040 | − | 79.9632i | 0.107082 | − | 0.0196372i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2365.04 | − | 1984.51i | −0.574037 | − | 0.481674i | 0.308946 | − | 0.951080i | \(-0.400024\pi\) |
−0.882983 | + | 0.469406i | \(0.844468\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −748.183 | − | 272.316i | −0.179497 | − | 0.0653317i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 610.944 | − | 3765.19i | 0.144891 | − | 0.892949i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 187.667 | + | 1064.32i | 0.0440003 | + | 0.249538i | 0.998872 | − | 0.0474799i | \(-0.0151190\pi\) |
−0.954872 | + | 0.297018i | \(0.904008\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4975.34 | − | 1810.88i | 1.15333 | − | 0.419778i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1421.01 | + | 1717.20i | −0.325709 | + | 0.393599i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5507.29 | −1.24827 | −0.624137 | − | 0.781315i | \(-0.714549\pi\) | ||||
−0.624137 | + | 0.781315i | \(0.714549\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4075.64 | 0.913570 | 0.456785 | − | 0.889577i | \(-0.349001\pi\) | ||||
0.456785 | + | 0.889577i | \(0.349001\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 107.397 | + | 18.1807i | 0.0238093 | + | 0.00403058i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2833.61 | + | 1031.35i | −0.621356 | + | 0.226155i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 615.311 | + | 3489.60i | 0.133467 | + | 0.756931i | 0.975915 | + | 0.218152i | \(0.0700029\pi\) |
−0.842447 | + | 0.538779i | \(0.818886\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3727.50 | − | 6257.04i | −0.799855 | − | 1.34265i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6900.33 | + | 2511.51i | 1.46491 | + | 0.533183i | 0.946713 | − | 0.322080i | \(-0.104382\pi\) |
0.518195 | + | 0.855262i | \(0.326604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −102.360 | − | 85.8899i | −0.0215005 | − | 0.0180411i | 0.631974 | − | 0.774990i | \(-0.282245\pi\) |
−0.653475 | + | 0.756948i | \(0.726689\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −360.789 | + | 1012.75i | −0.0749871 | + | 0.210492i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 620.458 | − | 1074.66i | 0.127611 | − | 0.221029i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2437.74 | + | 4222.29i | 0.496181 | + | 0.859411i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −44.0982 | − | 6449.88i | −0.00888343 | − | 1.29931i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 710.916 | − | 4031.81i | 0.141748 | − | 0.803893i | −0.828173 | − | 0.560473i | \(-0.810619\pi\) |
0.969921 | − | 0.243420i | \(-0.0782694\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1756.98 | − | 1474.28i | 0.346763 | − | 0.290969i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4038.13 | + | 4616.75i | 0.788942 | + | 0.901989i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −497.719 | + | 417.636i | −0.0962671 | + | 0.0807777i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 339.013 | − | 1922.64i | 0.0649183 | − | 0.368170i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3685.23 | − | 2161.40i | 0.698717 | − | 0.409799i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6010.46 | + | 10410.4i | 1.12839 | + | 1.95442i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4191.33 | + | 7259.59i | −0.779191 | + | 1.34960i | 0.153217 | + | 0.988192i | \(0.451037\pi\) |
−0.932409 | + | 0.361406i | \(0.882297\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6140.49 | − | 7217.16i | −1.13049 | − | 1.32871i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1493.12 | + | 1252.88i | 0.272242 | + | 0.228438i | 0.768679 | − | 0.639635i | \(-0.220914\pi\) |
−0.496437 | + | 0.868073i | \(0.665359\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1191.53 | − | 433.681i | −0.215173 | − | 0.0783165i | 0.232185 | − | 0.972672i | \(-0.425413\pi\) |
−0.447358 | + | 0.894355i | \(0.647635\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1409.93 | − | 491.446i | −0.252192 | − | 0.0879042i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1155.38 | + | 6552.49i | 0.204709 | + | 1.16096i | 0.897898 | + | 0.440204i | \(0.145094\pi\) |
−0.693189 | + | 0.720756i | \(0.743795\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5803.91 | − | 2112.45i | 1.01867 | − | 0.370767i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3790.70 | − | 10197.4i | −0.659116 | − | 1.77309i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 91.0017 | 0.0156764 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 364.140 | 0.0621504 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1421.44 | + | 3823.83i | 0.240385 | + | 0.646661i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −228.005 | + | 82.9872i | −0.0382077 | + | 0.0139065i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 988.638 | + | 5606.85i | 0.164171 | + | 0.931058i | 0.949915 | + | 0.312507i | \(0.101169\pi\) |
−0.785745 | + | 0.618551i | \(0.787720\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1012.96 | + | 5318.48i | 0.166697 | + | 0.875228i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2722.58 | − | 990.936i | −0.444030 | − | 0.161614i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4026.87 | + | 3378.95i | 0.650913 | + | 0.546181i | 0.907348 | − | 0.420381i | \(-0.138103\pi\) |
−0.256435 | + | 0.966561i | \(0.582548\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5319.57 | + | 6252.30i | 0.852269 | + | 1.00171i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5896.53 | − | 10213.1i | 0.936407 | − | 1.62190i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1330.63 | − | 2304.72i | −0.209467 | − | 0.362808i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7682.52 | − | 4505.81i | 1.19888 | − | 0.703145i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1204.18 | + | 6829.25i | −0.186293 | + | 1.05652i | 0.737989 | + | 0.674813i | \(0.235776\pi\) |
−0.924282 | + | 0.381710i | \(0.875335\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −362.713 | + | 304.352i | −0.0556320 | + | 0.0466808i | −0.670180 | − | 0.742199i | \(-0.733783\pi\) |
0.614548 | + | 0.788880i | \(0.289339\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −267.548 | − | 690.667i | −0.0406856 | − | 0.105029i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1133.07 | − | 950.758i | 0.170842 | − | 0.143353i | −0.553358 | − | 0.832944i | \(-0.686654\pi\) |
0.724200 | + | 0.689590i | \(0.242209\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2183.45 | − | 12383.0i | 0.326438 | − | 1.85132i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.864085 | + | 126.383i | 0.000128101 | + | 0.0187364i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1718.27 | + | 2976.14i | 0.252610 | + | 0.437534i | 0.964244 | − | 0.265017i | \(-0.0853777\pi\) |
−0.711634 | + | 0.702551i | \(0.752044\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3319.15 | − | 5748.94i | 0.483912 | − | 0.838160i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1011.97 | + | 2840.64i | −0.146321 | + | 0.410729i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7545.08 | − | 6331.07i | −1.08199 | − | 0.907900i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8040.63 | + | 2926.55i | 1.14364 | + | 0.416253i | 0.843228 | − | 0.537556i | \(-0.180652\pi\) |
0.300416 | + | 0.953808i | \(0.402874\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8437.33 | + | 115.378i | −1.19032 | + | 0.0162774i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 262.117 | + | 1486.54i | 0.0366805 | + | 0.208025i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8918.15 | + | 3245.94i | −1.23797 | + | 0.450586i | −0.876321 | − | 0.481727i | \(-0.840010\pi\) |
−0.361653 | + | 0.932313i | \(0.617787\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3997.68 | + | 676.751i | 0.550505 | + | 0.0931927i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −745.848 | −0.101892 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11784.3 | −1.59714 | −0.798572 | − | 0.601899i | \(-0.794411\pi\) | ||||
−0.798572 | + | 0.601899i | \(0.794411\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1306.52 | − | 1578.85i | 0.175682 | − | 0.212301i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8550.92 | + | 3112.28i | −1.14081 | + | 0.415222i | −0.842207 | − | 0.539155i | \(-0.818744\pi\) |
−0.298606 | + | 0.954376i | \(0.596522\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −419.827 | − | 2380.96i | −0.0555750 | − | 0.315182i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12411.6 | + | 4710.63i | −1.63028 | + | 0.618746i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8567.80 | − | 3118.43i | −1.11672 | − | 0.406454i | −0.283267 | − | 0.959041i | \(-0.591418\pi\) |
−0.833455 | + | 0.552587i | \(0.813641\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −577.506 | − | 484.585i | −0.0746949 | − | 0.0626765i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3070.16 | − | 563.021i | 0.394068 | − | 0.0722663i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7707.46 | − | 13349.7i | 0.981783 | − | 1.70050i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4029.27 | − | 6978.90i | −0.509378 | − | 0.882269i | −0.999941 | − | 0.0108631i | \(-0.996542\pi\) |
0.490563 | − | 0.871406i | \(-0.336791\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −266.482 | − | 151.434i | −0.0334356 | − | 0.0190004i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2031.54 | − | 11521.4i | 0.252993 | − | 1.43479i | −0.548180 | − | 0.836361i | \(-0.684679\pi\) |
0.801173 | − | 0.598433i | \(-0.204210\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1090.93 | + | 915.396i | −0.134846 | + | 0.113149i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2035.82 | + | 9946.92i | 0.249780 | + | 1.22041i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6715.58 | + | 5635.04i | −0.817885 | + | 0.686287i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −489.847 | + | 2778.06i | −0.0592210 | + | 0.335859i | −0.999995 | − | 0.00317545i | \(-0.998989\pi\) |
0.940774 | + | 0.339034i | \(0.110100\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5160.40 | + | 2932.50i | 0.619328 | + | 0.351945i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 326.942 | + | 566.281i | 0.0389535 | + | 0.0674694i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5930.65 | + | 10272.2i | −0.701504 | + | 1.21504i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10586.0 | + | 1941.32i | −1.24316 | + | 0.227978i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7349.28 | + | 6166.78i | 0.856887 | + | 0.719014i | 0.961295 | − | 0.275521i | \(-0.0888503\pi\) |
−0.104408 | + | 0.994535i | \(0.533295\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11950.5 | + | 4349.63i | 1.38345 | + | 0.503535i | 0.923222 | − | 0.384266i | \(-0.125545\pi\) |
0.460228 | + | 0.887801i | \(0.347768\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1278.29 | + | 1043.17i | 0.146933 | + | 0.119907i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 73.3687 | + | 416.094i | 0.00837389 | + | 0.0474907i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3220.42 | + | 1172.14i | −0.364981 | + | 0.132842i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 764.607 | − | 923.979i | 0.0860502 | − | 0.103986i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7867.05 | −0.879216 | −0.439608 | − | 0.898190i | \(-0.644883\pi\) | ||||
−0.439608 | + | 0.898190i | \(0.644883\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17294.1 | −1.91940 | −0.959702 | − | 0.281018i | \(-0.909328\pi\) | ||||
−0.959702 | + | 0.281018i | \(0.909328\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10080.6 | + | 1706.50i | 1.11109 | + | 0.188093i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1718.02 | − | 625.306i | 0.188064 | − | 0.0684496i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 578.944 | + | 3283.35i | 0.0629418 | + | 0.356961i | 0.999970 | + | 0.00770790i | \(0.00245352\pi\) |
−0.937028 | + | 0.349253i | \(0.886435\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4312.62 | + | 7711.30i | −0.465676 | + | 0.832664i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12292.3 | + | 4474.02i | 1.31834 | + | 0.479836i | 0.902925 | − | 0.429797i | \(-0.141415\pi\) |
0.415413 | + | 0.909633i | \(0.363637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4576.53 | − | 3840.17i | −0.487525 | − | 0.409082i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5425.64 | + | 15230.0i | −0.574103 | + | 1.61153i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9483.66 | − | 16426.2i | 0.996796 | − | 1.72650i | 0.429132 | − | 0.903242i | \(-0.358820\pi\) |
0.567665 | − | 0.823260i | \(-0.307847\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6831.56 | − | 11832.6i | −0.713272 | − | 1.23542i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.34398 | − | 196.574i | −0.000139395 | − | 0.0203881i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −50.6974 | + | 287.519i | −0.00522359 | + | 0.0296244i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10486.3 | + | 8799.07i | −1.07337 | + | 0.900664i | −0.995353 | − | 0.0962885i | \(-0.969303\pi\) |
−0.0780156 | + | 0.996952i | \(0.524858\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 735.302 | − | 444.880i | 0.0747733 | − | 0.0452401i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7991.70 | + | 6705.83i | −0.807398 | + | 0.677488i | −0.949985 | − | 0.312295i | \(-0.898902\pi\) |
0.142587 | + | 0.989782i | \(0.454458\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 848.557 | − | 4812.41i | 0.0851745 | − | 0.483048i | −0.912144 | − | 0.409869i | \(-0.865574\pi\) |
0.997319 | − | 0.0731793i | \(-0.0233145\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16838.9 | − | 9876.07i | 1.67933 | − | 0.984928i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3003.39 | + | 5202.03i | 0.297602 | + | 0.515463i | 0.975587 | − | 0.219614i | \(-0.0704797\pi\) |
−0.677984 | + | 0.735076i | \(0.737146\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 413.003 | − | 715.341i | 0.0406624 | − | 0.0704294i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7776.28 | − | 9139.77i | −0.760747 | − | 0.894136i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16466.8 | − | 13817.3i | −1.60073 | − | 1.34317i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −962.864 | − | 350.454i | −0.0930089 | − | 0.0338525i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7771.96 | − | 6704.66i | 0.746024 | − | 0.643575i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 529.337 | + | 3002.02i | 0.0504928 | + | 0.286359i | 0.999590 | − | 0.0286237i | \(-0.00911246\pi\) |
−0.949097 | + | 0.314982i | \(0.898001\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 994.788 | − | 362.073i | 0.0943003 | − | 0.0343225i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 884.735 | + | 2380.03i | 0.0833475 | + | 0.224214i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17288.3 | 1.61860 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1795.38 | −0.167056 | −0.0835281 | − | 0.996505i | \(-0.526619\pi\) | ||||
−0.0835281 | + | 0.996505i | \(0.526619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 420.597 | + | 1131.45i | 0.0388959 | + | 0.104634i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11759.8 | − | 4280.20i | 1.08088 | − | 0.393407i | 0.260643 | − | 0.965435i | \(-0.416065\pi\) |
0.820234 | + | 0.572028i | \(0.193843\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −150.277 | − | 852.262i | −0.0137285 | − | 0.0778580i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12448.2 | + | 10738.7i | −1.13031 | + | 0.975088i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3368.59 | + | 1226.07i | 0.304028 | + | 0.110657i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10407.7 | − | 8733.06i | −0.933688 | − | 0.783458i | 0.0427875 | − | 0.999084i | \(-0.486376\pi\) |
−0.976476 | + | 0.215627i | \(0.930821\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5484.44 | + | 6446.08i | 0.489075 | + | 0.574830i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6402.30 | − | 11089.1i | 0.567523 | − | 0.982979i | −0.429287 | − | 0.903168i | \(-0.641235\pi\) |
0.996810 | − | 0.0798111i | \(-0.0254317\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5725.62 | + | 9917.06i | 0.504528 | + | 0.873868i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9722.32 | − | 5702.16i | 0.851644 | − | 0.499491i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.7863 | − | 83.8573i | 0.00128761 | − | 0.00730237i | −0.984157 | − | 0.177298i | \(-0.943264\pi\) |
0.985445 | + | 0.169996i | \(0.0543754\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2151.06 | − | 1804.95i | 0.186218 | − | 0.156255i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 42.7457 | + | 2083.76i | 0.00367889 | + | 0.179338i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19456.5 | − | 16326.0i | 1.66477 | − | 1.39691i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −463.914 | + | 2630.99i | −0.0394641 | + | 0.223812i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −43.2698 | − | 6328.72i | −0.00365960 | − | 0.535260i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8164.42 | + | 14141.2i | 0.686545 | + | 1.18913i | 0.972949 | + | 0.231021i | \(0.0742068\pi\) |
−0.286404 | + | 0.958109i | \(0.592460\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5508.00 | + | 9540.13i | −0.460512 | + | 0.797630i | −0.998986 | − | 0.0450116i | \(-0.985668\pi\) |
0.538474 | + | 0.842642i | \(0.319001\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 477.566 | − | 1340.55i | 0.0397004 | − | 0.111441i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1265.81 | − | 1062.14i | −0.104629 | − | 0.0877940i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2799.22 | − | 1018.83i | −0.230067 | − | 0.0837374i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2170.32 | − | 3880.70i | 0.177371 | − | 0.317152i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 286.507 | + | 1624.86i | 0.0232833 | + | 0.132046i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27401.3 | − | 9973.26i | 2.21432 | − | 0.805947i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11873.0 | + | 2009.93i | 0.954110 | + | 0.161517i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14306.3 | −1.14326 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8618.57 | 0.684919 | 0.342460 | − | 0.939533i | \(-0.388740\pi\) | ||||
0.342460 | + | 0.939533i | \(0.388740\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 512.432 | − | 619.242i | 0.0404983 | − | 0.0489396i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10275.0 | + | 3739.78i | −0.807580 | + | 0.293935i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −118.470 | − | 671.876i | −0.00926034 | − | 0.0525180i | 0.979827 | − | 0.199845i | \(-0.0640440\pi\) |
−0.989088 | + | 0.147327i | \(0.952933\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18055.0 | + | 14734.0i | 1.40359 | + | 1.14541i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1972.18 | + | 717.815i | 0.152482 | + | 0.0554990i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3366.54 | + | 2824.86i | 0.258878 | + | 0.217225i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14273.6 | + | 2617.56i | −1.09167 | + | 0.200197i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −706.450 | + | 1223.61i | −0.0537401 | + | 0.0930806i | −0.891644 | − | 0.452737i | \(-0.850448\pi\) |
0.837904 | + | 0.545818i | \(0.183781\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1297.90 | + | 2248.02i | 0.0982024 | + | 0.170092i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1209.87 | + | 687.530i | 0.0910527 | + | 0.0517425i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3353.19 | − | 19016.9i | 0.251013 | − | 1.42356i | −0.555092 | − | 0.831789i | \(-0.687317\pi\) |
0.806104 | − | 0.591774i | \(-0.201572\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16855.4 | + | 14143.3i | −1.25506 | + | 1.05312i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2893.51 | + | 79.1509i | −0.214314 | + | 0.00586248i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10023.8 | + | 8410.99i | −0.738525 | + | 0.619696i | −0.932441 | − | 0.361322i | \(-0.882325\pi\) |
0.193916 | + | 0.981018i | \(0.437881\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3569.22 | − | 20242.1i | 0.261589 | − | 1.48354i | −0.516987 | − | 0.855993i | \(-0.672946\pi\) |
0.778576 | − | 0.627551i | \(-0.215943\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12675.2 | + | 7202.93i | 0.924108 | + | 0.525143i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4244.26 | + | 7351.28i | 0.307823 | + | 0.533164i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1699.26 | − | 2943.21i | 0.122602 | − | 0.212352i | −0.798191 | − | 0.602404i | \(-0.794210\pi\) |
0.920793 | + | 0.390052i | \(0.127543\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13991.4 | + | 2565.81i | −1.00425 | + | 0.184165i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2590.45 | − | 2173.65i | −0.184974 | − | 0.155212i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15617.8 | + | 5684.41i | 1.10947 | + | 0.403815i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1856.08 | − | 704.446i | 0.131179 | − | 0.0497868i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2010.20 | + | 11400.4i | 0.141346 | + | 0.801612i | 0.970229 | + | 0.242190i | \(0.0778657\pi\) |
−0.828883 | + | 0.559422i | \(0.811023\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3765.63 | − | 1370.58i | 0.263430 | − | 0.0958806i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10412.7 | + | 12583.1i | −0.724739 | + | 0.875801i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20424.8 | −1.41441 | −0.707205 | − | 0.707008i | \(-0.750044\pi\) | ||||
−0.707205 | + | 0.707008i | \(0.750044\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −338.756 | −0.0233406 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9589.96 | − | 1623.44i | −0.657439 | − | 0.111295i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15491.8 | + | 5638.56i | −1.05672 | + | 0.384616i | −0.811197 | − | 0.584773i | \(-0.801184\pi\) |
−0.245528 | + | 0.969389i | \(0.578961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3430.04 | − | 19452.7i | −0.232803 | − | 1.32029i | −0.847192 | − | 0.531286i | \(-0.821709\pi\) |
0.614390 | − | 0.789003i | \(-0.289402\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5616.24 | + | 76.8006i | −0.379288 | + | 0.00518667i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7595.15 | − | 2764.41i | −0.510391 | − | 0.185767i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3232.28 | − | 2712.21i | −0.216136 | − | 0.181359i | 0.528291 | − | 0.849063i | \(-0.322833\pi\) |
−0.744427 | + | 0.667704i | \(0.767277\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −978.171 | + | 2745.77i | −0.0650862 | + | 0.182700i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 161.307 | − | 279.391i | 0.0106805 | − | 0.0184991i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5986.71 | + | 10369.3i | 0.394455 | + | 0.683216i | 0.993031 | − | 0.117850i | \(-0.0376001\pi\) |
−0.598577 | + | 0.801066i | \(0.704267\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −154.630 | − | 22616.5i | −0.0101387 | − | 1.48290i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −766.653 | + | 4347.91i | −0.0500232 | + | 0.283695i | −0.999550 | − | 0.0299897i | \(-0.990453\pi\) |
0.949527 | + | 0.313685i | \(0.101564\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4277.74 | − | 3589.45i | 0.277766 | − | 0.233073i | −0.493252 | − | 0.869886i | \(-0.664192\pi\) |
0.771018 | + | 0.636813i | \(0.219748\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10824.8 | − | 13451.4i | 0.699491 | − | 0.869220i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1304.74 | − | 1094.81i | 0.0839061 | − | 0.0704055i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3384.29 | + | 19193.3i | −0.216594 | + | 1.22837i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2911.03 | + | 1707.33i | −0.185415 | + | 0.108747i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 614.167 | + | 1063.77i | 0.0389324 | + | 0.0674328i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6743.30 | − | 11679.7i | 0.425431 | − | 0.736867i | −0.571030 | − | 0.820929i | \(-0.693456\pi\) |
0.996461 | + | 0.0840619i | \(0.0267893\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 853.001 | + | 1002.57i | 0.0535604 | + | 0.0629517i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4207.80 | + | 3530.77i | 0.262963 | + | 0.220652i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1623.41 | + | 590.872i | 0.100976 | + | 0.0367523i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4560.72 | − | 23945.7i | −0.282347 | − | 1.48244i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1301.91 | + | 7383.47i | 0.0802218 | + | 0.454960i | 0.998286 | + | 0.0585281i | \(0.0186407\pi\) |
−0.918064 | + | 0.396432i | \(0.870248\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18909.9 | + | 6882.64i | −1.15977 | + | 0.422122i | −0.849016 | − | 0.528367i | \(-0.822804\pi\) |
−0.310756 | + | 0.950490i | \(0.600582\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12398.3 | − | 33352.9i | −0.756875 | − | 2.03608i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13603.1 | −0.826575 | −0.413288 | − | 0.910601i | \(-0.635620\pi\) | ||||
−0.413288 | + | 0.910601i | \(0.635620\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7199.61 | 0.435454 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1939.21 | + | 5216.67i | 0.116749 | + | 0.314067i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21556.3 | − | 7845.87i | 1.29183 | − | 0.470188i | 0.397503 | − | 0.917601i | \(-0.369877\pi\) |
0.894327 | + | 0.447413i | \(0.147655\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1452.79 | + | 8239.19i | 0.0866645 | + | 0.491499i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18030.3 | − | 6284.66i | −1.07067 | − | 0.373193i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15226.4 | + | 5541.95i | 0.900054 | + | 0.327593i | 0.750274 | − | 0.661127i | \(-0.229921\pi\) |
0.149779 | + | 0.988719i | \(0.452144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8534.64 | + | 7161.41i | 0.502207 | + | 0.421402i | 0.858377 | − | 0.513019i | \(-0.171473\pi\) |
−0.356170 | + | 0.934421i | \(0.615918\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −108.894 | − | 127.987i | −0.00637870 | − | 0.00749714i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 410.768 | − | 711.470i | 0.0239532 | − | 0.0414882i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8693.28 | − | 15057.2i | −0.504655 | − | 0.874089i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15504.7 | + | 9093.52i | −0.896031 | + | 0.525525i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6552.46 | + | 37160.9i | −0.376982 | + | 2.13797i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 972.493 | − | 816.019i | 0.0557011 | − | 0.0467388i | −0.614512 | − | 0.788907i | \(-0.710647\pi\) |
0.670213 | + | 0.742169i | \(0.266203\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9493.30 | + | 1875.45i | −0.541329 | + | 0.106942i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15101.6 | + | 12671.8i | −0.857315 | + | 0.719372i | −0.961388 | − | 0.275197i | \(-0.911257\pi\) |
0.104073 | + | 0.994570i | \(0.466812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −855.875 | + | 4853.91i | −0.0483733 | + | 0.274339i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −72.8008 | − | 10648.0i | −0.00409653 | − | 0.599165i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4391.39 | + | 7606.11i | 0.246020 | + | 0.426120i | 0.962418 | − | 0.271572i | \(-0.0875436\pi\) |
−0.716398 | + | 0.697692i | \(0.754210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7954.48 | + | 13777.6i | −0.443686 | + | 0.768487i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1579.00 | − | 4432.32i | 0.0876893 | − | 0.246148i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1537.46 | − | 1290.08i | −0.0850108 | − | 0.0713325i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9374.91 | + | 3412.19i | 0.516119 | + | 0.187852i | 0.586930 | − | 0.809638i | \(-0.300336\pi\) |
−0.0708107 | + | 0.997490i | \(0.522559\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2398.77 | − | 4026.62i | −0.131489 | − | 0.220719i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5009.27 | − | 28409.0i | −0.273399 | − | 1.55053i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1798.97 | + | 654.770i | −0.0977628 | + | 0.0355828i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7136.58 | − | 1208.12i | −0.386166 | − | 0.0653725i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4822.63 | −0.259841 | −0.129920 | − | 0.991524i | \(-0.541472\pi\) | ||||
−0.129920 | + | 0.991524i | \(0.541472\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2978.90 | −0.159817 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2819.40 | + | 3407.07i | −0.150617 | + | 0.182011i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3067.80 | + | 1116.59i | −0.163192 | + | 0.0593969i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2404.44 | + | 13636.3i | 0.127363 | + | 0.722314i | 0.979876 | + | 0.199607i | \(0.0639666\pi\) |
−0.852513 | + | 0.522707i | \(0.824922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4786.34 | − | 29497.8i | 0.252464 | − | 1.55591i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31195.4 | − | 11354.2i | −1.63854 | − | 0.596379i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2462.51 | + | 2066.29i | 0.128801 | + | 0.108077i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1278.35 | + | 234.431i | −0.0665843 | + | 0.0122106i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17247.7 | + | 29874.0i | −0.894621 | + | 1.54953i | −0.0603471 | + | 0.998177i | \(0.519221\pi\) |
−0.834273 | + | 0.551351i | \(0.814113\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3620.51 | + | 6270.91i | 0.187011 | + | 0.323913i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22263.3 | + | 12651.6i | 1.14520 | + | 0.650784i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1692.08 | + | 9596.29i | −0.0866792 | + | 0.491582i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28116.6 | − | 23592.6i | 1.43437 | − | 1.20358i | 0.491295 | − | 0.870993i | \(-0.336524\pi\) |
0.943073 | − | 0.332585i | \(-0.107921\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10532.3 | + | 16628.0i | 0.535095 | + | 0.844792i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2307.25 | + | 1936.02i | −0.116740 | + | 0.0979564i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2455.96 | + | 13928.4i | −0.123756 | + | 0.701854i | 0.858283 | + | 0.513176i | \(0.171531\pi\) |
−0.982039 | + | 0.188678i | \(0.939580\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20589.4 | − | 11700.3i | −1.03327 | − | 0.587175i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4547.38 | − | 7876.28i | −0.227279 | − | 0.393659i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17248.4 | − | 29875.1i | 0.858583 | − | 1.48711i | −0.0146980 | − | 0.999892i | \(-0.504679\pi\) |
0.873281 | − | 0.487217i | \(-0.161988\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 400.845 | − | 73.5091i | 0.0198724 | − | 0.00364430i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29161.7 | + | 24469.5i | 1.43989 | + | 1.20821i | 0.939564 | + | 0.342373i | \(0.111231\pi\) |
0.500326 | + | 0.865837i | \(0.333214\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40721.2 | − | 14821.3i | −2.00256 | − | 0.728874i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3682.95 | + | 22697.7i | −0.180391 | + | 1.11173i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1443.59 | + | 8187.01i | 0.0704241 | + | 0.399395i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4734.32 | + | 1723.15i | −0.230037 | + | 0.0837266i | −0.454467 | − | 0.890764i | \(-0.650170\pi\) |
0.224430 | + | 0.974490i | \(0.427948\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3692.94 | + | 4462.68i | −0.178723 | + | 0.215975i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 526.896 | 0.0253983 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39695.9 | 1.90591 | 0.952954 | − | 0.303115i | \(-0.0980266\pi\) | ||||
0.952954 | + | 0.303115i | \(0.0980266\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27565.3 | + | 4666.41i | 1.31825 | + | 0.223162i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6617.71 | + | 2408.65i | −0.315233 | + | 0.114735i | −0.494791 | − | 0.869012i | \(-0.664755\pi\) |
0.179558 | + | 0.983747i | \(0.442533\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −541.319 | − | 3069.97i | −0.0256842 | − | 0.145662i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1178.93 | + | 1978.97i | 0.0557179 | + | 0.0935290i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −816.977 | − | 297.355i | −0.0384607 | − | 0.0139985i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30249.5 | + | 25382.4i | 1.41850 | + | 1.19026i | 0.952138 | + | 0.305669i | \(0.0988802\pi\) |
0.466362 | + | 0.884594i | \(0.345564\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5383.60 | − | 15112.0i | 0.251473 | − | 0.705896i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15979.4 | − | 27677.1i | 0.743516 | − | 1.28781i | −0.207369 | − | 0.978263i | \(-0.566490\pi\) |
0.950885 | − | 0.309545i | \(-0.100177\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9302.79 | + | 16112.9i | 0.431182 | + | 0.746829i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −28.2854 | − | 4137.08i | −0.00130596 | − | 0.191013i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 806.206 | − | 4572.22i | 0.0370800 | − | 0.210291i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30236.0 | − | 25371.0i | 1.38531 | − | 1.16241i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19444.6 | − | 3841.38i | 0.887475 | − | 0.175325i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24639.6 | − | 20675.1i | 1.12029 | − | 0.940033i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 787.039 | − | 4463.52i | 0.0356479 | − | 0.202169i | −0.961782 | − | 0.273816i | \(-0.911714\pi\) |
0.997430 | + | 0.0716463i | \(0.0228253\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4843.99 | + | 2841.01i | −0.218569 | + | 0.128191i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3136.48 | − | 5432.55i | −0.140987 | − | 0.244196i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2278.35 | − | 3946.21i | 0.102026 | − | 0.176714i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17827.9 | + | 20953.9i | 0.795335 | + | 0.934788i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3143.57 | + | 2637.77i | 0.139713 | + | 0.117233i | 0.709966 | − | 0.704236i | \(-0.248710\pi\) |
−0.570253 | + | 0.821469i | \(0.693155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 351.755 | + | 128.028i | 0.0155747 | + | 0.00566873i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10936.4 | − | 3812.01i | −0.482422 | − | 0.168153i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5368.79 | − | 30447.9i | −0.235941 | − | 1.33809i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6395.36 | + | 2327.72i | −0.280008 | + | 0.101915i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9971.12 | − | 26823.4i | −0.434944 | − | 1.17005i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3418.34 | 0.148557 | 0.0742783 | − | 0.997238i | \(-0.476335\pi\) | ||||
0.0742783 | + | 0.997238i | \(0.476335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3687.72 | −0.159671 | −0.0798357 | − | 0.996808i | \(-0.525440\pi\) | ||||
−0.0798357 | + | 0.996808i | \(0.525440\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7379.07 | + | 19850.5i | 0.318322 | + | 0.856319i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3040.31 | + | 1106.58i | −0.130672 | + | 0.0475606i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1268.38 | − | 7193.36i | −0.0543147 | − | 0.308034i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 105.895 | + | 555.994i | 0.00451804 | + | 0.0237216i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3319.42 | − | 1208.17i | −0.141107 | − | 0.0513586i | 0.270501 | − | 0.962720i | \(-0.412811\pi\) |
−0.411608 | + | 0.911361i | \(0.635033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3449.91 | − | 2894.82i | −0.146119 | − | 0.122609i | 0.566798 | − | 0.823857i | \(-0.308182\pi\) |
−0.712917 | + | 0.701248i | \(0.752626\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10153.5 | − | 11933.8i | −0.428486 | − | 0.503616i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7788.45 | + | 13490.0i | −0.327486 | + | 0.567223i | −0.982012 | − | 0.188817i | \(-0.939535\pi\) |
0.654526 | + | 0.756039i | \(0.272868\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9335.06 | − | 16168.8i | −0.391098 | − | 0.677401i | 0.601497 | − | 0.798875i | \(-0.294571\pi\) |
−0.992595 | + | 0.121474i | \(0.961238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15882.1 | + | 9314.91i | −0.662991 | + | 0.388846i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −348.084 | + | 1974.08i | −0.0144783 | + | 0.0821103i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17377.8 | + | 14581.7i | −0.720219 | + | 0.604336i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23726.3 | − | 29483.4i | 0.979811 | − | 1.21756i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13863.9 | − | 11633.2i | 0.570482 | − | 0.478691i | −0.311324 | − | 0.950304i | \(-0.600772\pi\) |
0.881806 | + | 0.471613i | \(0.156328\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −769.305 | + | 4362.95i | −0.0315431 | + | 0.178890i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 260.870 | + | 38155.4i | 0.0106582 | + | 1.55889i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15105.2 | + | 26163.0i | 0.614953 | + | 1.06513i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1152.15 | − | 1995.58i | 0.0467395 | − | 0.0809552i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 233.003 | − | 654.051i | 0.00941891 | − | 0.0264393i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18904.4 | + | 15862.7i | 0.761497 | + | 0.638972i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35220.9 | − | 12819.4i | −1.41377 | − | 0.514569i | −0.481533 | − | 0.876428i | \(-0.659920\pi\) |
−0.932233 | + | 0.361860i | \(0.882142\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5585.85 | + | 76.3850i | −0.223429 | + | 0.00305534i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3991.51 | − | 22637.0i | −0.159098 | − | 0.902291i | −0.954943 | − | 0.296790i | \(-0.904084\pi\) |
0.795844 | − | 0.605501i | \(-0.207027\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29016.9 | + | 10561.3i | −1.15256 | + | 0.419496i | −0.846432 | − | 0.532496i | \(-0.821254\pi\) |
−0.306123 | + | 0.951992i | \(0.599032\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6357.53 | + | 1076.24i | 0.251642 | + | 0.0425995i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19121.6 | −0.754236 | −0.377118 | − | 0.926165i | \(-0.623085\pi\) | ||||
−0.377118 | + | 0.926165i | \(0.623085\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16963.5 | 0.666794 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16151.1 | + | 19517.6i | −0.632666 | + | 0.764537i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45469.9 | − | 16549.7i | 1.77498 | − | 0.646040i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 190.711 | + | 1081.58i | 0.00741906 | + | 0.0420756i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31334.4 | − | 11892.5i | 1.21479 | − | 0.461053i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2911.44 | − | 1059.68i | −0.112485 | − | 0.0409413i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12696.7 | − | 10653.8i | −0.488867 | − | 0.410208i | 0.364753 | − | 0.931104i | \(-0.381153\pi\) |
−0.853620 | + | 0.520896i | \(0.825598\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20924.1 | − | 3837.18i | 0.802905 | − | 0.147241i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15481.4 | + | 26814.5i | −0.592032 | + | 1.02543i | 0.401926 | + | 0.915672i | \(0.368341\pi\) |
−0.993958 | + | 0.109758i | \(0.964993\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12180.7 | + | 21097.6i | 0.464229 | + | 0.804068i | 0.999166 | − | 0.0408239i | \(-0.0129983\pi\) |
−0.534938 | + | 0.844891i | \(0.679665\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10361.6 | + | 5888.17i | 0.393560 | + | 0.223648i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4420.12 | − | 25067.7i | 0.167320 | − | 0.948920i | −0.779320 | − | 0.626627i | \(-0.784435\pi\) |
0.946640 | − | 0.322293i | \(-0.104454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1199.62 | + | 1006.60i | −0.0452576 | + | 0.0379756i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15174.8 | + | 28026.5i | −0.570567 | + | 1.05379i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −695.420 | + | 583.527i | −0.0260597 | + | 0.0218667i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5604.74 | + | 31786.0i | −0.209325 | + | 1.18714i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2935.24 | − | 1668.01i | −0.109259 | − | 0.0620883i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19054.4 | − | 33003.1i | −0.706895 | − | 1.22438i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1164.37 | − | 2016.75i | 0.0430530 | − | 0.0745700i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9978.05 | − | 1829.83i | 0.367717 | − | 0.0674339i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1650.35 | + | 1384.81i | 0.0606182 | + | 0.0508647i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25805.9 | − | 9392.59i | −0.944731 | − | 0.343854i | −0.176699 | − | 0.984265i | \(-0.556542\pi\) |
−0.768033 | + | 0.640411i | \(0.778764\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17199.4 | + | 14035.7i | 0.627577 | + | 0.512141i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5849.43 | + | 33173.7i | 0.212733 | + | 1.20647i | 0.884797 | + | 0.465977i | \(0.154297\pi\) |
−0.672063 | + | 0.740494i | \(0.734592\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34987.7 | + | 12734.5i | −1.26826 | + | 0.461609i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −39822.1 | + | 48122.5i | −1.43877 | + | 1.73867i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2385.18 | −0.0858949 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16064.8 | −0.576635 | −0.288318 | − | 0.957535i | \(-0.593096\pi\) | ||||
−0.288318 | + | 0.957535i | \(0.593096\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −42946.5 | − | 7270.24i | −1.53652 | − | 0.260111i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4478.90 | + | 1630.19i | −0.159723 | + | 0.0581346i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2401.69 | − | 13620.7i | −0.0853698 | − | 0.484156i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24033.8 | − | 42974.3i | 0.851536 | − | 1.52261i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34871.8 | + | 12692.3i | 1.23155 | + | 0.448247i | 0.874127 | − | 0.485697i | \(-0.161434\pi\) |
0.357420 | + | 0.933944i | \(0.383656\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3723.97 | − | 3124.78i | −0.131094 | − | 0.110001i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3398.83 | + | 9540.66i | −0.119263 | + | 0.334777i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1864.94 | + | 3230.17i | −0.0652301 | + | 0.112982i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11227.4 | − | 19446.5i | −0.391445 | − | 0.678003i | 0.601195 | − | 0.799102i | \(-0.294691\pi\) |
−0.992640 | + | 0.121099i | \(0.961358\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −45.0463 | − | 6588.55i | −0.00156553 | − | 0.228977i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1443.08 | − | 8184.09i | 0.0499925 | − | 0.283521i | −0.949555 | − | 0.313600i | \(-0.898465\pi\) |
0.999548 | + | 0.0300789i | \(0.00957587\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29463.4 | + | 24722.7i | −1.01746 | + | 0.853746i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −159.122 | − | 7756.87i | −0.00547751 | − | 0.267017i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23700.6 | − | 19887.2i | 0.813270 | − | 0.682415i | −0.138116 | − | 0.990416i | \(-0.544105\pi\) |
0.951386 | + | 0.308001i | \(0.0996601\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −648.324 | + | 3676.83i | −0.0221765 | + | 0.125769i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29822.2 | + | 17490.8i | −1.01688 | + | 0.596401i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26600.7 | − | 46073.8i | −0.904178 | − | 1.56608i | −0.822017 | − | 0.569463i | \(-0.807151\pi\) |
−0.0821613 | − | 0.996619i | \(-0.526182\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19538.1 | + | 33841.0i | −0.662031 | + | 1.14667i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20796.9 | + | 24443.4i | 0.702475 | + | 0.825647i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3474.44 | − | 2915.40i | −0.116992 | − | 0.0981680i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −40381.3 | − | 14697.6i | −1.35549 | − | 0.493357i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42803.4 | − | 36925.4i | 1.43232 | − | 1.23562i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6620.68 | − | 37547.8i | −0.220857 | − | 1.25254i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20742.7 | − | 7549.73i | 0.689804 | − | 0.251068i | 0.0267528 | − | 0.999642i | \(-0.491483\pi\) |
0.663051 | + | 0.748574i | \(0.269261\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 164.761 | + | 443.226i | 0.00546222 | + | 0.0146940i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2497.51 | 0.0825425 | 0.0412712 | − | 0.999148i | \(-0.486859\pi\) | ||||
0.0412712 | + | 0.999148i | \(0.486859\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8224.19 | 0.270972 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 659.287 | + | 1773.55i | 0.0216555 | + | 0.0582555i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18538.1 | − | 6747.30i | 0.607047 | − | 0.220947i | −0.0201636 | − | 0.999797i | \(-0.506419\pi\) |
0.627211 | + | 0.778850i | \(0.284196\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3256.49 | − | 18468.5i | −0.106310 | − | 0.602916i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16050.5 | + | 13846.3i | −0.522377 | + | 0.450641i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9110.97 | − | 3316.12i | −0.295620 | − | 0.107597i | 0.189952 | − | 0.981793i | \(-0.439167\pi\) |
−0.485573 | + | 0.874196i | \(0.661389\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33535.3 | − | 28139.5i | −1.08480 | − | 0.910252i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −817.002 | − | 960.255i | −0.0263480 | − | 0.0309678i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30255.4 | + | 52403.9i | −0.972767 | + | 1.68488i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16318.5 | + | 28264.5i | 0.523083 | + | 0.906006i | 0.999639 | + | 0.0268620i | \(0.00855148\pi\) |
−0.476556 | + | 0.879144i | \(0.658115\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25518.3 | + | 14966.5i | −0.815507 | + | 0.478297i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4527.02 | − | 25674.0i | 0.144237 | − | 0.818011i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5862.89 | − | 4919.55i | 0.186238 | − | 0.156273i | −0.544902 | − | 0.838500i | \(-0.683433\pi\) |
0.731140 | + | 0.682227i | \(0.238989\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24069.8 | + | 14562.9i | −0.762296 | + | 0.461212i |
(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 | 108.4.i.a.49.6 | ✓ | 54 | |
3.2 | odd | 2 | 324.4.i.a.37.9 | 54 | |||
27.11 | odd | 18 | 324.4.i.a.289.9 | 54 | |||
27.16 | even | 9 | inner | 108.4.i.a.97.6 | yes | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.i.a.49.6 | ✓ | 54 | 1.1 | even | 1 | trivial | |
108.4.i.a.97.6 | yes | 54 | 27.16 | even | 9 | inner | |
324.4.i.a.37.9 | 54 | 3.2 | odd | 2 | |||
324.4.i.a.289.9 | 54 | 27.11 | odd | 18 |