Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(35,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.35");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\), degree \(2\), not 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: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 35.12 | ||
Character | \(\chi\) | \(=\) | 108.35 |
Dual form | 108.4.h.b.71.12 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.81402 | + | 0.285097i | 0.994907 | + | 0.100797i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.83744 | + | 1.60454i | 0.979680 | + | 0.200567i | ||||
\(5\) | 14.4924 | − | 8.36717i | 1.29624 | − | 0.748383i | 0.316485 | − | 0.948598i | \(-0.397497\pi\) |
0.979752 | + | 0.200215i | \(0.0641640\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.7175 | − | 9.65186i | −0.902661 | − | 0.521152i | −0.0245984 | − | 0.999697i | \(-0.507831\pi\) |
−0.878063 | + | 0.478546i | \(0.841164\pi\) | |||||||
\(8\) | 21.5973 | + | 6.74964i | 0.954474 | + | 0.298295i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 43.1673 | − | 19.4137i | 1.36507 | − | 0.613915i | ||||
\(11\) | −2.44092 | + | 4.22780i | −0.0669059 | + | 0.115884i | −0.897538 | − | 0.440937i | \(-0.854646\pi\) |
0.830632 | + | 0.556822i | \(0.187979\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.03848 | + | 10.4590i | 0.128829 | + | 0.223138i | 0.923223 | − | 0.384264i | \(-0.125545\pi\) |
−0.794394 | + | 0.607402i | \(0.792212\pi\) | |||||||
\(14\) | −44.2917 | − | 31.9267i | −0.845533 | − | 0.609483i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 58.8509 | + | 25.1509i | 0.919546 | + | 0.392984i | ||||
\(17\) | 71.2528i | 1.01655i | 0.861195 | + | 0.508275i | \(0.169717\pi\) | ||||
−0.861195 | + | 0.508275i | \(0.830283\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 68.3003i | − | 0.824693i | −0.911027 | − | 0.412347i | \(-0.864709\pi\) | ||
0.911027 | − | 0.412347i | \(-0.135291\pi\) | |||||||
\(20\) | 127.009 | − | 42.3237i | 1.42000 | − | 0.473193i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.07414 | + | 11.2012i | −0.0782460 | + | 0.108550i | ||||
\(23\) | 68.0491 | + | 117.865i | 0.616923 | + | 1.06854i | 0.990044 | + | 0.140759i | \(0.0449543\pi\) |
−0.373121 | + | 0.927783i | \(0.621712\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 77.5192 | − | 134.267i | 0.620154 | − | 1.07414i | ||||
\(26\) | 14.0106 | + | 31.1533i | 0.105681 | + | 0.234987i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −115.536 | − | 102.470i | −0.779793 | − | 0.691606i | ||||
\(29\) | −190.237 | − | 109.833i | −1.21814 | − | 0.703295i | −0.253622 | − | 0.967303i | \(-0.581622\pi\) |
−0.964520 | + | 0.264009i | \(0.914955\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −285.221 | + | 164.672i | −1.65249 | + | 0.954065i | −0.676444 | + | 0.736494i | \(0.736480\pi\) |
−0.976044 | + | 0.217571i | \(0.930187\pi\) | |||||||
\(32\) | 158.437 | + | 87.5535i | 0.875251 | + | 0.483669i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −20.3140 | + | 200.507i | −0.102465 | + | 1.01137i | ||||
\(35\) | −323.035 | −1.56008 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −133.618 | −0.593693 | −0.296847 | − | 0.954925i | \(-0.595935\pi\) | ||||
−0.296847 | + | 0.954925i | \(0.595935\pi\) | |||||||
\(38\) | 19.4722 | − | 192.199i | 0.0831266 | − | 0.820493i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 369.471 | − | 82.8899i | 1.46046 | − | 0.327651i | ||||
\(41\) | 29.5326 | − | 17.0507i | 0.112493 | − | 0.0649480i | −0.442698 | − | 0.896671i | \(-0.645979\pi\) |
0.555191 | + | 0.831723i | \(0.312645\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.558209 | − | 0.322282i | −0.00197967 | − | 0.00114297i | 0.499010 | − | 0.866596i | \(-0.333697\pi\) |
−0.500990 | + | 0.865453i | \(0.667030\pi\) | |||||||
\(44\) | −25.9142 | + | 29.2186i | −0.0887890 | + | 0.100111i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 157.889 | + | 351.074i | 0.506075 | + | 1.12528i | ||||
\(47\) | −93.4753 | + | 161.904i | −0.290102 | + | 0.502471i | −0.973834 | − | 0.227263i | \(-0.927022\pi\) |
0.683732 | + | 0.729733i | \(0.260356\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.8169 | + | 25.6636i | 0.0431979 | + | 0.0748210i | ||||
\(50\) | 256.420 | − | 355.730i | 0.725265 | − | 1.00616i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 30.5444 | + | 91.6604i | 0.0814568 | + | 0.244443i | ||||
\(53\) | − | 266.453i | − | 0.690569i | −0.938498 | − | 0.345284i | \(-0.887782\pi\) | ||
0.938498 | − | 0.345284i | \(-0.112218\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 81.6944i | 0.200285i | ||||||||
\(56\) | −295.906 | − | 321.291i | −0.706110 | − | 0.766684i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −504.018 | − | 363.309i | −1.14105 | − | 0.822498i | ||||
\(59\) | 104.347 | + | 180.734i | 0.230251 | + | 0.398806i | 0.957882 | − | 0.287163i | \(-0.0927120\pi\) |
−0.727631 | + | 0.685969i | \(0.759379\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.801886 | − | 1.38891i | 0.00168313 | − | 0.00291527i | −0.865183 | − | 0.501457i | \(-0.832798\pi\) |
0.866866 | + | 0.498542i | \(0.166131\pi\) | |||||||
\(62\) | −849.565 | + | 382.076i | −1.74024 | + | 0.782640i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 420.885 | + | 291.548i | 0.822041 | + | 0.569429i | ||||
\(65\) | 175.024 | + | 101.050i | 0.333985 | + | 0.192826i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 371.407 | − | 214.432i | 0.677233 | − | 0.391001i | −0.121579 | − | 0.992582i | \(-0.538796\pi\) |
0.798812 | + | 0.601581i | \(0.205462\pi\) | |||||||
\(68\) | −114.328 | + | 558.440i | −0.203887 | + | 0.995893i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −909.028 | − | 92.0964i | −1.55214 | − | 0.157252i | ||||
\(71\) | 386.365 | 0.645817 | 0.322909 | − | 0.946430i | \(-0.395339\pi\) | ||||
0.322909 | + | 0.946430i | \(0.395339\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −776.832 | −1.24550 | −0.622749 | − | 0.782422i | \(-0.713984\pi\) | ||||
−0.622749 | + | 0.782422i | \(0.713984\pi\) | |||||||
\(74\) | −376.004 | − | 38.0941i | −0.590670 | − | 0.0598425i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 109.591 | − | 535.300i | 0.165407 | − | 0.807935i | ||||
\(77\) | 81.6122 | − | 47.1188i | 0.120787 | − | 0.0697362i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 68.5000 | + | 39.5485i | 0.0975551 | + | 0.0563235i | 0.547984 | − | 0.836489i | \(-0.315396\pi\) |
−0.450429 | + | 0.892812i | \(0.648729\pi\) | |||||||
\(80\) | 1063.33 | − | 127.919i | 1.48605 | − | 0.178772i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 87.9665 | − | 39.5613i | 0.118467 | − | 0.0532782i | ||||
\(83\) | 462.668 | − | 801.365i | 0.611861 | − | 1.05977i | −0.379066 | − | 0.925370i | \(-0.623755\pi\) |
0.990927 | − | 0.134404i | \(-0.0429121\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 596.185 | + | 1032.62i | 0.760768 | + | 1.31769i | ||||
\(86\) | −1.47893 | − | 1.06605i | −0.00185438 | − | 0.00133669i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −81.2533 | + | 74.8336i | −0.0984277 | + | 0.0906510i | ||||
\(89\) | 1044.26i | 1.24372i | 0.783128 | + | 0.621861i | \(0.213623\pi\) | ||||
−0.783128 | + | 0.621861i | \(0.786377\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 233.130i | − | 0.268557i | ||||||
\(92\) | 344.213 | + | 1032.94i | 0.390072 | + | 1.17056i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −309.200 | + | 428.952i | −0.339272 | + | 0.470670i | ||||
\(95\) | −571.481 | − | 989.834i | −0.617186 | − | 1.06900i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 733.184 | − | 1269.91i | 0.767460 | − | 1.32928i | −0.171477 | − | 0.985188i | \(-0.554854\pi\) |
0.938936 | − | 0.344091i | \(-0.111813\pi\) | |||||||
\(98\) | 34.3784 | + | 76.4422i | 0.0354362 | + | 0.0787941i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 822.989 | − | 927.929i | 0.822989 | − | 0.927929i | ||||
\(101\) | 314.302 | + | 181.462i | 0.309646 | + | 0.178774i | 0.646768 | − | 0.762687i | \(-0.276120\pi\) |
−0.337122 | + | 0.941461i | \(0.609454\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 466.128 | − | 269.119i | 0.445912 | − | 0.257447i | −0.260190 | − | 0.965557i | \(-0.583785\pi\) |
0.706102 | + | 0.708110i | \(0.250452\pi\) | |||||||
\(104\) | 59.8206 | + | 266.643i | 0.0564028 | + | 0.251408i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 75.9650 | − | 749.805i | 0.0696073 | − | 0.687052i | ||||
\(107\) | 430.456 | 0.388914 | 0.194457 | − | 0.980911i | \(-0.437706\pi\) | ||||
0.194457 | + | 0.980911i | \(0.437706\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 899.324 | 0.790272 | 0.395136 | − | 0.918623i | \(-0.370697\pi\) | ||||
0.395136 | + | 0.918623i | \(0.370697\pi\) | |||||||
\(110\) | −23.2908 | + | 229.890i | −0.0201881 | + | 0.199265i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −741.088 | − | 988.482i | −0.625234 | − | 0.833953i | ||||
\(113\) | 330.860 | − | 191.022i | 0.275440 | − | 0.159025i | −0.355917 | − | 0.934517i | \(-0.615832\pi\) |
0.631357 | + | 0.775492i | \(0.282498\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1972.39 | + | 1138.76i | 1.59936 | + | 0.923389i | ||||
\(116\) | −1314.74 | − | 1166.05i | −1.05233 | − | 0.933323i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 242.107 | + | 538.338i | 0.188880 | + | 0.419983i | ||||
\(119\) | 687.722 | − | 1191.17i | 0.529776 | − | 0.917600i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 653.584 | + | 1132.04i | 0.491047 | + | 0.850519i | ||||
\(122\) | 2.65250 | − | 3.67980i | 0.00196841 | − | 0.00273077i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2499.62 | + | 832.961i | −1.81026 | + | 0.603243i | ||||
\(125\) | − | 502.674i | − | 0.359684i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1677.92i | − | 1.17237i | −0.810177 | − | 0.586186i | \(-0.800629\pi\) | ||
0.810177 | − | 0.586186i | \(-0.199371\pi\) | |||||||
\(128\) | 1101.26 | + | 940.414i | 0.760457 | + | 0.649388i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 463.712 | + | 334.256i | 0.312848 | + | 0.225509i | ||||
\(131\) | 712.418 | + | 1233.94i | 0.475147 | + | 0.822979i | 0.999595 | − | 0.0284637i | \(-0.00906150\pi\) |
−0.524448 | + | 0.851443i | \(0.675728\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −659.225 | + | 1141.81i | −0.429790 | + | 0.744418i | ||||
\(134\) | 1106.28 | − | 497.529i | 0.713196 | − | 0.320746i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −480.931 | + | 1538.87i | −0.303231 | + | 0.970270i | ||||
\(137\) | −23.2295 | − | 13.4116i | −0.0144864 | − | 0.00836370i | 0.492739 | − | 0.870177i | \(-0.335996\pi\) |
−0.507226 | + | 0.861813i | \(0.669329\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1434.57 | + | 828.252i | −0.875388 | + | 0.505406i | −0.869135 | − | 0.494575i | \(-0.835324\pi\) |
−0.00625321 | + | 0.999980i | \(0.501990\pi\) | |||||||
\(140\) | −2531.77 | − | 518.322i | −1.52838 | − | 0.312902i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1087.24 | + | 110.151i | 0.642528 | + | 0.0650965i | ||||
\(143\) | −58.9578 | −0.0344776 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3675.98 | −2.10533 | ||||||||
\(146\) | −2186.02 | − | 221.473i | −1.23915 | − | 0.125542i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1047.22 | − | 214.395i | −0.581629 | − | 0.119075i | ||||
\(149\) | −738.285 | + | 426.249i | −0.405924 | + | 0.234360i | −0.689037 | − | 0.724726i | \(-0.741966\pi\) |
0.283113 | + | 0.959087i | \(0.408633\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1272.06 | − | 734.422i | −0.685553 | − | 0.395804i | 0.116391 | − | 0.993203i | \(-0.462867\pi\) |
−0.801944 | + | 0.597399i | \(0.796201\pi\) | |||||||
\(152\) | 461.002 | − | 1475.10i | 0.246002 | − | 0.787148i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 243.092 | − | 109.326i | 0.127201 | − | 0.0572061i | ||||
\(155\) | −2755.68 | + | 4772.98i | −1.42801 | + | 2.47339i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1344.52 | − | 2328.78i | −0.683469 | − | 1.18380i | −0.973915 | − | 0.226912i | \(-0.927137\pi\) |
0.290446 | − | 0.956891i | \(-0.406196\pi\) | |||||||
\(158\) | 181.485 | + | 130.820i | 0.0913811 | + | 0.0658699i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3028.71 | − | 56.8143i | 1.49650 | − | 0.0280723i | ||||
\(161\) | − | 2627.20i | − | 1.28604i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2186.50i | 1.05067i | 0.850895 | + | 0.525336i | \(0.176060\pi\) | ||||
−0.850895 | + | 0.525336i | \(0.823940\pi\) | |||||||
\(164\) | 258.819 | − | 86.2473i | 0.123234 | − | 0.0410658i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1530.43 | − | 2123.15i | 0.715567 | − | 0.992703i | ||||
\(167\) | −1790.65 | − | 3101.49i | −0.829726 | − | 1.43713i | −0.898253 | − | 0.439479i | \(-0.855163\pi\) |
0.0685268 | − | 0.997649i | \(-0.478170\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1025.57 | − | 1776.35i | 0.466806 | − | 0.808532i | ||||
\(170\) | 1383.28 | + | 3075.79i | 0.624075 | + | 1.38766i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.85781 | − | 3.42153i | −0.00171021 | − | 0.00151680i | ||||
\(173\) | 94.5051 | + | 54.5625i | 0.0415323 | + | 0.0239787i | 0.520622 | − | 0.853787i | \(-0.325700\pi\) |
−0.479090 | + | 0.877766i | \(0.659033\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2591.86 | + | 1496.41i | −1.11958 | + | 0.646388i | ||||
\(176\) | −249.983 | + | 187.418i | −0.107064 | + | 0.0802681i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −297.715 | + | 2938.57i | −0.125363 | + | 1.23739i | ||||
\(179\) | 268.397 | 0.112072 | 0.0560361 | − | 0.998429i | \(-0.482154\pi\) | ||||
0.0560361 | + | 0.998429i | \(0.482154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 898.582 | 0.369011 | 0.184506 | − | 0.982831i | \(-0.440932\pi\) | ||||
0.184506 | + | 0.982831i | \(0.440932\pi\) | |||||||
\(182\) | 66.4648 | − | 656.034i | 0.0270698 | − | 0.267189i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 674.133 | + | 3004.86i | 0.270096 | + | 1.20392i | ||||
\(185\) | −1936.44 | + | 1118.00i | −0.769567 | + | 0.444310i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −301.242 | − | 173.922i | −0.117802 | − | 0.0680132i | ||||
\(188\) | −992.388 | + | 1118.93i | −0.384986 | + | 0.434076i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1325.96 | − | 2948.34i | −0.506291 | − | 1.12576i | ||||
\(191\) | −257.331 | + | 445.711i | −0.0974860 | + | 0.168851i | −0.910643 | − | 0.413193i | \(-0.864413\pi\) |
0.813157 | + | 0.582044i | \(0.197747\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1229.66 | + | 2129.83i | 0.458616 | + | 0.794346i | 0.998888 | − | 0.0471443i | \(-0.0150121\pi\) |
−0.540272 | + | 0.841490i | \(0.681679\pi\) | |||||||
\(194\) | 2425.24 | − | 3364.53i | 0.897538 | − | 1.24515i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 74.9482 | + | 224.911i | 0.0273135 | + | 0.0819647i | ||||
\(197\) | − | 646.506i | − | 0.233815i | −0.993143 | − | 0.116908i | \(-0.962702\pi\) | ||
0.993143 | − | 0.116908i | \(-0.0372982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1742.98i | − | 0.620886i | −0.950592 | − | 0.310443i | \(-0.899523\pi\) | ||
0.950592 | − | 0.310443i | \(-0.100477\pi\) | |||||||
\(200\) | 2580.46 | − | 2376.58i | 0.912330 | − | 0.840248i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 832.719 | + | 600.246i | 0.290049 | + | 0.209075i | ||||
\(203\) | 2120.19 | + | 3672.28i | 0.733046 | + | 1.26967i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 285.332 | − | 494.209i | 0.0972119 | − | 0.168376i | ||||
\(206\) | 1388.42 | − | 624.415i | 0.469591 | − | 0.211190i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 92.3175 | + | 767.393i | 0.0307744 | + | 0.255813i | ||||
\(209\) | 288.760 | + | 166.716i | 0.0955691 | + | 0.0551769i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3648.27 | − | 2106.33i | 1.19032 | − | 0.687231i | 0.231940 | − | 0.972730i | \(-0.425493\pi\) |
0.958379 | + | 0.285499i | \(0.0921593\pi\) | |||||||
\(212\) | 427.534 | − | 2088.31i | 0.138506 | − | 0.676537i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1211.31 | + | 122.722i | 0.386933 | + | 0.0392013i | ||||
\(215\) | −10.7864 | −0.00342150 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6357.58 | 1.98885 | ||||||||
\(218\) | 2530.72 | + | 256.395i | 0.786247 | + | 0.0796570i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −131.082 | + | 640.275i | −0.0401706 | + | 0.196215i | ||||
\(221\) | −745.230 | + | 430.259i | −0.226831 | + | 0.130961i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5558.55 | − | 3209.23i | −1.66918 | − | 0.963703i | −0.968080 | − | 0.250643i | \(-0.919358\pi\) |
−0.701103 | − | 0.713060i | \(-0.747309\pi\) | |||||||
\(224\) | −1803.62 | − | 2992.89i | −0.537990 | − | 0.892728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 985.507 | − | 443.213i | 0.290066 | − | 0.130452i | ||||
\(227\) | 1124.83 | − | 1948.27i | 0.328889 | − | 0.569653i | −0.653403 | − | 0.757011i | \(-0.726659\pi\) |
0.982292 | + | 0.187358i | \(0.0599924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1735.36 | − | 3005.74i | −0.500769 | − | 0.867357i | −1.00000 | 0.000888202i | \(-0.999717\pi\) | |
0.499231 | − | 0.866469i | \(-0.333616\pi\) | |||||||
\(230\) | 5225.68 | + | 3766.81i | 1.49814 | + | 1.07990i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3367.27 | − | 3656.13i | −0.952896 | − | 1.03464i | ||||
\(233\) | 3852.67i | 1.08325i | 0.840621 | + | 0.541624i | \(0.182190\pi\) | ||||
−0.840621 | + | 0.541624i | \(0.817810\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3128.50i | 0.868428i | ||||||||
\(236\) | 527.817 | + | 1583.92i | 0.145585 | + | 0.436883i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2274.86 | − | 3155.91i | 0.619570 | − | 0.859527i | ||||
\(239\) | −19.9334 | − | 34.5257i | −0.00539491 | − | 0.00934426i | 0.863315 | − | 0.504665i | \(-0.168384\pi\) |
−0.868710 | + | 0.495321i | \(0.835051\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1729.18 | + | 2995.03i | −0.462184 | + | 0.800527i | −0.999070 | − | 0.0431286i | \(-0.986267\pi\) |
0.536885 | + | 0.843655i | \(0.319601\pi\) | |||||||
\(242\) | 1516.46 | + | 3371.92i | 0.402817 | + | 0.895683i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.51329 | − | 9.59882i | 0.00223364 | − | 0.00251845i | ||||
\(245\) | 429.464 | + | 247.951i | 0.111989 | + | 0.0646572i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 714.350 | − | 412.430i | 0.184020 | − | 0.106244i | ||||
\(248\) | −7271.47 | + | 1631.34i | −1.86185 | + | 0.417701i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 143.311 | − | 1414.53i | 0.0362551 | − | 0.357852i | ||||
\(251\) | −2977.61 | −0.748786 | −0.374393 | − | 0.927270i | \(-0.622149\pi\) | ||||
−0.374393 | + | 0.927270i | \(0.622149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −664.410 | −0.165103 | ||||||||
\(254\) | 478.369 | − | 4721.70i | 0.118172 | − | 1.16640i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2830.86 | + | 2960.31i | 0.691128 | + | 0.722732i | ||||
\(257\) | 5593.28 | − | 3229.28i | 1.35758 | − | 0.783802i | 0.368287 | − | 0.929712i | \(-0.379944\pi\) |
0.989298 | + | 0.145910i | \(0.0466111\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2233.76 | + | 1289.66i | 0.535904 | + | 0.309404i | ||||
\(260\) | 1209.60 | + | 1072.81i | 0.288524 | + | 0.255895i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1652.97 | + | 3675.46i | 0.389773 | + | 0.866681i | ||||
\(263\) | 2940.99 | − | 5093.94i | 0.689540 | − | 1.19432i | −0.282447 | − | 0.959283i | \(-0.591146\pi\) |
0.971987 | − | 0.235036i | \(-0.0755207\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2229.46 | − | 3861.54i | −0.516810 | − | 0.895141i | ||||
\(266\) | −2180.60 | + | 3025.14i | −0.502636 | + | 0.697306i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3254.95 | − | 1084.66i | 0.741894 | − | 0.247225i | ||||
\(269\) | 2967.07i | 0.672510i | 0.941771 | + | 0.336255i | \(0.109160\pi\) | ||||
−0.941771 | + | 0.336255i | \(0.890840\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1985.78i | 0.445121i | 0.974919 | + | 0.222561i | \(0.0714415\pi\) | ||||
−0.974919 | + | 0.222561i | \(0.928559\pi\) | |||||||
\(272\) | −1792.08 | + | 4193.29i | −0.399487 | + | 0.934764i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −61.5447 | − | 44.3631i | −0.0135695 | − | 0.00978128i | ||||
\(275\) | 378.436 | + | 655.471i | 0.0829839 | + | 0.143732i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2171.48 | + | 3761.12i | −0.471017 | + | 0.815825i | −0.999450 | − | 0.0331494i | \(-0.989446\pi\) |
0.528433 | + | 0.848975i | \(0.322780\pi\) | |||||||
\(278\) | −4273.05 | + | 1921.73i | −0.921873 | + | 0.414595i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6976.68 | − | 2180.37i | −1.48906 | − | 0.465365i | ||||
\(281\) | −6752.10 | − | 3898.33i | −1.43344 | − | 0.827597i | −0.436058 | − | 0.899919i | \(-0.643626\pi\) |
−0.997381 | + | 0.0723220i | \(0.976959\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1771.47 | − | 1022.76i | 0.372094 | − | 0.214829i | −0.302279 | − | 0.953220i | \(-0.597747\pi\) |
0.674373 | + | 0.738391i | \(0.264414\pi\) | |||||||
\(284\) | 3028.11 | + | 619.937i | 0.632694 | + | 0.129530i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −165.909 | − | 16.8087i | −0.0343020 | − | 0.00347524i | ||||
\(287\) | −658.283 | −0.135391 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −163.963 | −0.0333732 | ||||||||
\(290\) | −10344.3 | − | 1048.01i | −2.09461 | − | 0.212211i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6088.38 | − | 1246.46i | −1.22019 | − | 0.249806i | ||||
\(293\) | 2041.60 | − | 1178.72i | 0.407070 | − | 0.235022i | −0.282460 | − | 0.959279i | \(-0.591151\pi\) |
0.689530 | + | 0.724257i | \(0.257817\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3024.46 | + | 1746.18i | 0.596919 | + | 0.344631i | ||||
\(296\) | −2885.78 | − | 901.873i | −0.566665 | − | 0.177096i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2199.07 | + | 988.991i | −0.427479 | + | 0.192251i | ||||
\(299\) | −821.827 | + | 1423.45i | −0.158955 | + | 0.275318i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.22124 | + | 10.7755i | 0.00119132 | + | 0.00206342i | ||||
\(302\) | −3370.21 | − | 2429.34i | −0.642165 | − | 0.462890i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1717.82 | − | 4019.54i | 0.324091 | − | 0.758343i | ||||
\(305\) | − | 26.8381i | − | 0.00503851i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5521.27i | − | 1.02643i | −0.858259 | − | 0.513217i | \(-0.828454\pi\) | ||
0.858259 | − | 0.513217i | \(-0.171546\pi\) | |||||||
\(308\) | 715.235 | − | 238.341i | 0.132319 | − | 0.0440933i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9115.32 | + | 12645.6i | −1.67005 | + | 2.31685i | ||||
\(311\) | 767.330 | + | 1329.05i | 0.139908 | + | 0.242327i | 0.927461 | − | 0.373919i | \(-0.121986\pi\) |
−0.787554 | + | 0.616246i | \(0.788653\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4383.28 | + | 7592.06i | −0.791557 | + | 1.37102i | 0.133446 | + | 0.991056i | \(0.457396\pi\) |
−0.925003 | + | 0.379961i | \(0.875937\pi\) | |||||||
\(314\) | −3119.59 | − | 6936.57i | −0.560664 | − | 1.24667i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 473.408 | + | 419.870i | 0.0842762 | + | 0.0747454i | ||||
\(317\) | 6074.45 | + | 3507.08i | 1.07626 | + | 0.621380i | 0.929886 | − | 0.367849i | \(-0.119906\pi\) |
0.146376 | + | 0.989229i | \(0.453239\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 928.706 | − | 536.189i | 0.163002 | − | 0.0941091i | ||||
\(320\) | 8539.05 | + | 703.599i | 1.49171 | + | 0.122914i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 749.008 | − | 7393.01i | 0.129629 | − | 1.27949i | ||||
\(323\) | 4866.59 | 0.838342 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1872.39 | 0.319574 | ||||||||
\(326\) | −623.363 | + | 6152.85i | −0.105905 | + | 1.04532i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 752.910 | − | 168.914i | 0.126745 | − | 0.0284350i | ||||
\(329\) | 3125.35 | − | 1804.42i | 0.523727 | − | 0.302374i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8563.21 | + | 4943.97i | 1.42198 | + | 0.820982i | 0.996468 | − | 0.0839692i | \(-0.0267597\pi\) |
0.425515 | + | 0.904951i | \(0.360093\pi\) | |||||||
\(332\) | 4911.96 | − | 5538.28i | 0.811984 | − | 0.915520i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4154.69 | − | 9238.16i | −0.680642 | − | 1.51344i | ||||
\(335\) | 3588.38 | − | 6215.26i | 0.585236 | − | 1.01366i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2504.10 | + | 4337.22i | 0.404768 | + | 0.701079i | 0.994294 | − | 0.106670i | \(-0.0340190\pi\) |
−0.589527 | + | 0.807749i | \(0.700686\pi\) | |||||||
\(338\) | 3392.42 | − | 4706.29i | 0.545927 | − | 0.757362i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3015.68 | + | 9049.71i | 0.481024 | + | 1.44350i | ||||
\(341\) | − | 1607.81i | − | 0.255330i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6049.14i | 0.952252i | ||||||||
\(344\) | −9.88050 | − | 10.7281i | −0.00154861 | − | 0.00168146i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 250.384 | + | 180.483i | 0.0389038 | + | 0.0280429i | ||||
\(347\) | −3897.53 | − | 6750.72i | −0.602969 | − | 1.04437i | −0.992369 | − | 0.123305i | \(-0.960651\pi\) |
0.389399 | − | 0.921069i | \(-0.372683\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4540.81 | − | 7864.91i | 0.696458 | − | 1.20630i | −0.273228 | − | 0.961949i | \(-0.588091\pi\) |
0.969687 | − | 0.244352i | \(-0.0785753\pi\) | |||||||
\(350\) | −7720.17 | + | 3472.00i | −1.17903 | + | 0.530246i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −756.891 | + | 456.130i | −0.114609 | + | 0.0690676i | ||||
\(353\) | −3944.55 | − | 2277.39i | −0.594752 | − | 0.343380i | 0.172222 | − | 0.985058i | \(-0.444905\pi\) |
−0.766974 | + | 0.641678i | \(0.778239\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5599.34 | − | 3232.78i | 0.837133 | − | 0.483319i | ||||
\(356\) | −1675.55 | + | 8184.32i | −0.249450 | + | 1.21845i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 755.275 | + | 76.5192i | 0.111501 | + | 0.0112965i | ||||
\(359\) | −5415.10 | −0.796095 | −0.398047 | − | 0.917365i | \(-0.630312\pi\) | ||||
−0.398047 | + | 0.917365i | \(0.630312\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2194.06 | 0.319881 | ||||||||
\(362\) | 2528.63 | + | 256.183i | 0.367132 | + | 0.0371953i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 374.067 | − | 1827.15i | 0.0538638 | − | 0.263100i | ||||
\(365\) | −11258.1 | + | 6499.89i | −1.61446 | + | 0.932109i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9228.51 | − | 5328.08i | −1.31260 | − | 0.757830i | −0.330074 | − | 0.943955i | \(-0.607074\pi\) |
−0.982526 | + | 0.186125i | \(0.940407\pi\) | |||||||
\(368\) | 1040.35 | + | 8647.94i | 0.147369 | + | 1.22501i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5767.93 | + | 2594.02i | −0.810433 | + | 0.364477i | ||||
\(371\) | −2571.77 | + | 4454.43i | −0.359891 | + | 0.623350i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1354.99 | − | 2346.91i | −0.188093 | − | 0.325786i | 0.756522 | − | 0.653969i | \(-0.226897\pi\) |
−0.944614 | + | 0.328183i | \(0.893564\pi\) | |||||||
\(374\) | −798.118 | − | 575.305i | −0.110347 | − | 0.0795409i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3111.61 | + | 2865.76i | −0.426779 | + | 0.393059i | ||||
\(377\) | − | 2652.91i | − | 0.362418i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6395.35i | 0.866774i | 0.901208 | + | 0.433387i | \(0.142682\pi\) | ||||
−0.901208 | + | 0.433387i | \(0.857318\pi\) | |||||||
\(380\) | −2890.72 | − | 8674.73i | −0.390239 | − | 1.17106i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −851.206 | + | 1180.88i | −0.114009 | + | 0.158164i | ||||
\(383\) | 682.579 | + | 1182.26i | 0.0910656 | + | 0.157730i | 0.907960 | − | 0.419057i | \(-0.137639\pi\) |
−0.816894 | + | 0.576788i | \(0.804306\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 788.503 | − | 1365.73i | 0.104379 | − | 0.180789i | ||||
\(386\) | 2853.08 | + | 6343.97i | 0.376212 | + | 0.836528i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7783.91 | − | 8776.44i | 1.01847 | − | 1.14834i | ||||
\(389\) | 5380.83 | + | 3106.62i | 0.701333 | + | 0.404915i | 0.807844 | − | 0.589397i | \(-0.200634\pi\) |
−0.106510 | + | 0.994312i | \(0.533968\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8398.18 | + | 4848.69i | −1.08623 | + | 0.627133i | ||||
\(392\) | 146.784 | + | 654.272i | 0.0189126 | + | 0.0843004i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 184.317 | − | 1819.28i | 0.0235679 | − | 0.232625i | ||||
\(395\) | 1323.64 | 0.168606 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3291.69 | 0.416134 | 0.208067 | − | 0.978115i | \(-0.433283\pi\) | ||||
0.208067 | + | 0.978115i | \(0.433283\pi\) | |||||||
\(398\) | 496.917 | − | 4904.77i | 0.0625834 | − | 0.617723i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7939.02 | − | 5952.07i | 0.992378 | − | 0.744008i | ||||
\(401\) | −3529.51 | + | 2037.76i | −0.439539 | + | 0.253768i | −0.703402 | − | 0.710792i | \(-0.748337\pi\) |
0.263863 | + | 0.964560i | \(0.415003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3444.60 | − | 1988.74i | −0.425776 | − | 0.245822i | ||||
\(404\) | 2172.16 | + | 1926.51i | 0.267498 | + | 0.237246i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4919.31 | + | 10938.3i | 0.601333 | + | 1.33710i | ||||
\(407\) | 326.151 | − | 564.910i | 0.0397216 | − | 0.0687998i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7054.78 | − | 12219.2i | −0.852900 | − | 1.47727i | −0.878579 | − | 0.477597i | \(-0.841508\pi\) |
0.0256787 | − | 0.999670i | \(-0.491825\pi\) | |||||||
\(410\) | 943.828 | − | 1309.37i | 0.113689 | − | 0.157720i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4085.06 | − | 1361.28i | 0.488487 | − | 0.162781i | ||||
\(413\) | − | 4028.56i | − | 0.479982i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15484.9i | − | 1.83162i | ||||||
\(416\) | 41.0022 | + | 2185.78i | 0.00483244 | + | 0.257612i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 765.047 | + | 551.466i | 0.0895207 | + | 0.0645289i | ||||
\(419\) | 3184.20 | + | 5515.19i | 0.371261 | + | 0.643042i | 0.989760 | − | 0.142743i | \(-0.0455923\pi\) |
−0.618499 | + | 0.785786i | \(0.712259\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5406.24 | + | 9363.89i | −0.625853 | + | 1.08401i | 0.362522 | + | 0.931975i | \(0.381916\pi\) |
−0.988375 | + | 0.152034i | \(0.951418\pi\) | |||||||
\(422\) | 10866.8 | − | 4887.15i | 1.25353 | − | 0.563750i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1798.46 | − | 5754.66i | 0.205993 | − | 0.659130i | ||||
\(425\) | 9566.92 | + | 5523.46i | 1.09191 | + | 0.630417i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.8111 | + | 15.4794i | −0.00303859 | + | 0.00175433i | ||||
\(428\) | 3373.67 | + | 690.683i | 0.381011 | + | 0.0780034i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −30.3530 | − | 3.07516i | −0.00340408 | − | 0.000344877i | ||||
\(431\) | 10968.4 | 1.22583 | 0.612913 | − | 0.790150i | \(-0.289998\pi\) | ||||
0.612913 | + | 0.790150i | \(0.289998\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1491.10 | −0.165491 | −0.0827457 | − | 0.996571i | \(-0.526369\pi\) | ||||
−0.0827457 | + | 0.996571i | \(0.526369\pi\) | |||||||
\(434\) | 17890.4 | + | 1812.53i | 1.97872 | + | 0.200470i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7048.40 | + | 1443.00i | 0.774213 | + | 0.158503i | ||||
\(437\) | 8050.19 | − | 4647.78i | 0.881219 | − | 0.508772i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1927.62 | − | 1112.91i | −0.209567 | − | 0.120994i | 0.391543 | − | 0.920160i | \(-0.371941\pi\) |
−0.601110 | + | 0.799166i | \(0.705275\pi\) | |||||||
\(440\) | −551.408 | + | 1764.38i | −0.0597439 | + | 0.191167i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2219.76 | + | 998.295i | −0.238876 | + | 0.107430i | ||||
\(443\) | −7938.74 | + | 13750.3i | −0.851425 | + | 1.47471i | 0.0284982 | + | 0.999594i | \(0.490927\pi\) |
−0.879923 | + | 0.475117i | \(0.842406\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8737.50 | + | 15133.8i | 0.930780 | + | 1.61216i | ||||
\(446\) | −14726.9 | − | 10615.6i | −1.56354 | − | 1.12704i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4222.17 | − | 8936.27i | −0.445265 | − | 0.942409i | ||||
\(449\) | 11558.7i | 1.21490i | 0.794358 | + | 0.607450i | \(0.207807\pi\) | ||||
−0.794358 | + | 0.607450i | \(0.792193\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 166.477i | 0.0173816i | ||||||||
\(452\) | 2899.60 | − | 966.246i | 0.301738 | − | 0.100550i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3720.75 | − | 5161.78i | 0.384633 | − | 0.533600i | ||||
\(455\) | −1950.64 | − | 3378.61i | −0.200984 | − | 0.348114i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5444.85 | − | 9430.75i | 0.557329 | − | 0.965322i | −0.440390 | − | 0.897807i | \(-0.645160\pi\) |
0.997718 | − | 0.0675148i | \(-0.0215070\pi\) | |||||||
\(458\) | −4026.43 | − | 8952.96i | −0.410792 | − | 0.913416i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13631.3 | + | 12089.7i | 1.38166 | + | 1.22540i | ||||
\(461\) | −10197.5 | − | 5887.54i | −1.03025 | − | 0.594816i | −0.113195 | − | 0.993573i | \(-0.536108\pi\) |
−0.917057 | + | 0.398757i | \(0.869442\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2303.58 | − | 1329.97i | 0.231223 | − | 0.133497i | −0.379913 | − | 0.925022i | \(-0.624046\pi\) |
0.611136 | + | 0.791525i | \(0.290713\pi\) | |||||||
\(464\) | −8433.21 | − | 11248.4i | −0.843754 | − | 1.12542i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1098.39 | + | 10841.5i | −0.109188 | + | 1.07773i | ||||
\(467\) | −32.9750 | −0.00326746 | −0.00163373 | − | 0.999999i | \(-0.500520\pi\) | ||||
−0.00163373 | + | 0.999999i | \(0.500520\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8278.68 | −0.815083 | ||||||||
\(470\) | −891.925 | + | 8803.66i | −0.0875350 | + | 0.864006i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1033.72 | + | 4607.66i | 0.100807 | + | 0.449332i | ||||
\(473\) | 2.72509 | − | 1.57333i | 0.000264904 | − | 0.000152942i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9170.50 | − | 5294.59i | −0.885834 | − | 0.511437i | ||||
\(476\) | 7301.26 | − | 8232.25i | 0.703052 | − | 0.792698i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −46.2499 | − | 102.839i | −0.00442556 | − | 0.00984046i | ||||
\(479\) | −4069.08 | + | 7047.85i | −0.388144 | + | 0.672284i | −0.992200 | − | 0.124657i | \(-0.960217\pi\) |
0.604056 | + | 0.796942i | \(0.293550\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −806.850 | − | 1397.50i | −0.0764848 | − | 0.132476i | ||||
\(482\) | −5719.83 | + | 7935.10i | −0.540521 | + | 0.749863i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3306.02 | + | 9921.00i | 0.310483 | + | 0.931724i | ||||
\(485\) | − | 24538.7i | − | 2.29741i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1992.29i | 0.185378i | 0.995695 | + | 0.0926891i | \(0.0295463\pi\) | ||||
−0.995695 | + | 0.0926891i | \(0.970454\pi\) | |||||||
\(488\) | 26.6932 | − | 24.5842i | 0.00247611 | − | 0.00228048i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1137.83 | + | 820.178i | 0.104902 | + | 0.0756161i | ||||
\(491\) | 4407.34 | + | 7633.75i | 0.405093 | + | 0.701642i | 0.994332 | − | 0.106317i | \(-0.0339058\pi\) |
−0.589239 | + | 0.807959i | \(0.700572\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7825.94 | − | 13554.9i | 0.714934 | − | 1.23830i | ||||
\(494\) | 2127.78 | − | 956.929i | 0.193792 | − | 0.0871544i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20927.2 | + | 2517.54i | −1.89447 | + | 0.227905i | ||||
\(497\) | −6459.06 | − | 3729.14i | −0.582954 | − | 0.336569i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18252.9 | + | 10538.3i | −1.63750 | + | 0.945409i | −0.655806 | + | 0.754930i | \(0.727671\pi\) |
−0.981691 | + | 0.190479i | \(0.938996\pi\) | |||||||
\(500\) | 806.559 | − | 3939.67i | 0.0721408 | − | 0.352375i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8379.07 | − | 848.909i | −0.744973 | − | 0.0754754i | ||||
\(503\) | −19011.6 | −1.68526 | −0.842629 | − | 0.538494i | \(-0.818994\pi\) | ||||
−0.842629 | + | 0.538494i | \(0.818994\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6073.31 | 0.535166 | ||||||||
\(506\) | −1869.66 | − | 189.421i | −0.164262 | − | 0.0166419i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2692.28 | − | 13150.6i | 0.235139 | − | 1.14855i | ||||
\(509\) | −11096.0 | + | 6406.27i | −0.966250 | + | 0.557865i | −0.898091 | − | 0.439810i | \(-0.855046\pi\) |
−0.0681588 | + | 0.997674i | \(0.521712\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12986.7 | + | 7497.88i | 1.12426 | + | 0.649093i | ||||
\(512\) | 7122.13 | + | 9137.45i | 0.614759 | + | 0.788715i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16660.3 | − | 7492.64i | 1.42968 | − | 0.642970i | ||||
\(515\) | 4503.53 | − | 7800.35i | 0.385339 | − | 0.667426i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −456.332 | − | 790.390i | −0.0388190 | − | 0.0672365i | ||||
\(518\) | 5918.17 | + | 4265.98i | 0.501987 | + | 0.361846i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3097.99 | + | 3363.75i | 0.261261 | + | 0.283674i | ||||
\(521\) | 14455.7i | 1.21558i | 0.794100 | + | 0.607788i | \(0.207943\pi\) | ||||
−0.794100 | + | 0.607788i | \(0.792057\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15232.9i | 1.27359i | 0.771032 | + | 0.636796i | \(0.219741\pi\) | ||||
−0.771032 | + | 0.636796i | \(0.780259\pi\) | |||||||
\(524\) | 3603.62 | + | 10814.1i | 0.300429 | + | 0.901555i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9728.27 | − | 13496.0i | 0.806412 | − | 1.11873i | ||||
\(527\) | −11733.4 | − | 20322.8i | −0.969854 | − | 1.67984i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3177.87 | + | 5504.23i | −0.261187 | + | 0.452390i | ||||
\(530\) | −5172.84 | − | 11502.1i | −0.423950 | − | 0.942675i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6998.72 | + | 7891.13i | −0.570363 | + | 0.643090i | ||||
\(533\) | 356.664 | + | 205.920i | 0.0289847 | + | 0.0167343i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6238.33 | − | 3601.70i | 0.504124 | − | 0.291056i | ||||
\(536\) | 9468.72 | − | 2124.29i | 0.763035 | − | 0.171185i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −845.902 | + | 8349.39i | −0.0677870 | + | 0.669085i | ||||
\(539\) | −144.667 | −0.0115608 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23075.7 | −1.83383 | −0.916915 | − | 0.399083i | \(-0.869328\pi\) | ||||
−0.916915 | + | 0.399083i | \(0.869328\pi\) | |||||||
\(542\) | −566.141 | + | 5588.04i | −0.0448669 | + | 0.442854i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6238.43 | + | 11289.1i | −0.491674 | + | 0.889736i | ||||
\(545\) | 13033.3 | − | 7524.80i | 1.02438 | − | 0.591426i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −317.151 | − | 183.107i | −0.0247905 | − | 0.0143128i | 0.487554 | − | 0.873093i | \(-0.337889\pi\) |
−0.512344 | + | 0.858780i | \(0.671223\pi\) | |||||||
\(548\) | −160.540 | − | 142.385i | −0.0125145 | − | 0.0110992i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 878.056 | + | 1952.40i | 0.0680735 | + | 0.151365i | ||||
\(551\) | −7501.66 | + | 12993.2i | −0.580002 | + | 1.00459i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −763.434 | − | 1322.31i | −0.0587061 | − | 0.101682i | ||||
\(554\) | −7182.88 | + | 9964.78i | −0.550851 | + | 0.764193i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12572.3 | + | 4189.54i | −0.958968 | + | 0.319562i | ||||
\(557\) | 3402.66i | 0.258842i | 0.991590 | + | 0.129421i | \(0.0413119\pi\) | ||||
−0.991590 | + | 0.129421i | \(0.958688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.78437i | − | 0.000588987i | ||||||
\(560\) | −19010.9 | − | 8124.64i | −1.43457 | − | 0.613087i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17889.2 | − | 12895.0i | −1.34272 | − | 0.967868i | ||||
\(563\) | 2461.45 | + | 4263.36i | 0.184259 | + | 0.319146i | 0.943327 | − | 0.331866i | \(-0.107678\pi\) |
−0.759068 | + | 0.651012i | \(0.774345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3196.63 | − | 5536.73i | 0.238023 | − | 0.412269i | ||||
\(566\) | 5276.53 | − | 2373.02i | 0.391854 | − | 0.176229i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8344.42 | + | 2607.82i | 0.616416 | + | 0.192644i | ||||
\(569\) | −10423.8 | − | 6018.16i | −0.767990 | − | 0.443399i | 0.0641669 | − | 0.997939i | \(-0.479561\pi\) |
−0.832157 | + | 0.554540i | \(0.812894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 522.706 | − | 301.784i | 0.0383092 | − | 0.0221178i | −0.480723 | − | 0.876872i | \(-0.659626\pi\) |
0.519032 | + | 0.854755i | \(0.326292\pi\) | |||||||
\(572\) | −462.078 | − | 94.6001i | −0.0337770 | − | 0.00691508i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1852.42 | − | 187.674i | −0.134701 | − | 0.0136470i | ||||
\(575\) | 21100.5 | 1.53035 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6971.52 | −0.502995 | −0.251497 | − | 0.967858i | \(-0.580923\pi\) | ||||
−0.251497 | + | 0.967858i | \(0.580923\pi\) | |||||||
\(578\) | −461.395 | − | 46.7453i | −0.0332033 | − | 0.00336392i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −28810.3 | − | 5898.25i | −2.06255 | − | 0.422261i | ||||
\(581\) | −15469.3 | + | 8931.22i | −1.10461 | + | 0.637745i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1126.51 | + | 650.391i | 0.0800262 | + | 0.0462032i | ||||
\(584\) | −16777.5 | − | 5243.34i | −1.18880 | − | 0.371525i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6081.15 | − | 2734.88i | 0.428686 | − | 0.192793i | ||||
\(587\) | 10334.9 | − | 17900.6i | 0.726691 | − | 1.25867i | −0.231583 | − | 0.972815i | \(-0.574390\pi\) |
0.958274 | − | 0.285851i | \(-0.0922762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11247.2 | + | 19480.7i | 0.786811 | + | 1.36280i | ||||
\(590\) | 8013.08 | + | 5776.04i | 0.559141 | + | 0.403044i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7863.54 | − | 3360.62i | −0.545928 | − | 0.233312i | ||||
\(593\) | − | 2417.22i | − | 0.167392i | −0.996491 | − | 0.0836958i | \(-0.973328\pi\) | ||
0.996491 | − | 0.0836958i | \(-0.0266724\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 23017.2i | − | 1.58590i | ||||||
\(596\) | −6470.19 | + | 2156.09i | −0.444680 | + | 0.148183i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2718.46 | + | 3771.31i | −0.185896 | + | 0.257893i | ||||
\(599\) | 14467.5 | + | 25058.4i | 0.986852 | + | 1.70928i | 0.633400 | + | 0.773825i | \(0.281659\pi\) |
0.353452 | + | 0.935453i | \(0.385008\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −318.246 | + | 551.219i | −0.0215999 | + | 0.0374121i | −0.876623 | − | 0.481177i | \(-0.840209\pi\) |
0.855023 | + | 0.518589i | \(0.173543\pi\) | |||||||
\(602\) | 14.4346 | + | 32.0962i | 0.000977263 | + | 0.00217299i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8791.25 | − | 7797.05i | −0.592237 | − | 0.525261i | ||||
\(605\) | 18944.0 | + | 10937.3i | 1.27303 | + | 0.734983i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16616.3 | − | 9593.41i | 1.11109 | − | 0.641490i | 0.171981 | − | 0.985100i | \(-0.444983\pi\) |
0.939112 | + | 0.343610i | \(0.111650\pi\) | |||||||
\(608\) | 5979.94 | − | 10821.3i | 0.398879 | − | 0.721813i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.65146 | − | 75.5230i | 0.000507866 | − | 0.00501284i | ||||
\(611\) | −2257.80 | −0.149494 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6429.22 | 0.423612 | 0.211806 | − | 0.977312i | \(-0.432066\pi\) | ||||
0.211806 | + | 0.977312i | \(0.432066\pi\) | |||||||
\(614\) | 1574.10 | − | 15537.0i | 0.103462 | − | 1.02121i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2080.64 | − | 466.786i | 0.136090 | − | 0.0305314i | ||||
\(617\) | 6024.79 | − | 3478.41i | 0.393110 | − | 0.226962i | −0.290397 | − | 0.956906i | \(-0.593787\pi\) |
0.683507 | + | 0.729944i | \(0.260454\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19227.5 | + | 11101.0i | 1.24850 | + | 0.720819i | 0.970809 | − | 0.239853i | \(-0.0770992\pi\) |
0.277686 | + | 0.960672i | \(0.410433\pi\) | |||||||
\(620\) | −29255.9 | + | 32986.4i | −1.89508 | + | 2.13672i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1780.37 | + | 3958.75i | 0.114769 | + | 0.255195i | ||||
\(623\) | 10079.0 | − | 17457.4i | 0.648168 | − | 1.12266i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5483.94 | + | 9498.47i | 0.350972 | + | 0.607902i | ||||
\(626\) | −14499.1 | + | 20114.6i | −0.925720 | + | 1.28425i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6801.00 | − | 20409.0i | −0.432149 | − | 1.29683i | ||||
\(629\) | − | 9520.65i | − | 0.603519i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 529.250i | 0.0333901i | 0.999861 | + | 0.0166950i | \(0.00531444\pi\) | ||||
−0.999861 | + | 0.0166950i | \(0.994686\pi\) | |||||||
\(632\) | 1212.48 | + | 1316.49i | 0.0763128 | + | 0.0828595i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16093.8 | + | 11600.8i | 1.00815 | + | 0.726699i | ||||
\(635\) | −14039.4 | − | 24317.0i | −0.877383 | − | 1.51967i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −178.943 | + | 309.938i | −0.0111303 | + | 0.0192782i | ||||
\(638\) | 2766.27 | − | 1244.08i | 0.171658 | − | 0.0771997i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 23828.5 | + | 4414.40i | 1.47172 | + | 0.272648i | ||||
\(641\) | 19866.3 | + | 11469.8i | 1.22414 | + | 0.706755i | 0.965797 | − | 0.259299i | \(-0.0834915\pi\) |
0.258339 | + | 0.966054i | \(0.416825\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2182.17 | − | 1259.88i | 0.133836 | − | 0.0772702i | −0.431587 | − | 0.902071i | \(-0.642046\pi\) |
0.565423 | + | 0.824801i | \(0.308713\pi\) | |||||||
\(644\) | 4215.45 | − | 20590.5i | 0.257938 | − | 1.25991i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13694.7 | + | 1387.45i | 0.834072 | + | 0.0845023i | ||||
\(647\) | −5938.61 | −0.360851 | −0.180426 | − | 0.983589i | \(-0.557748\pi\) | ||||
−0.180426 | + | 0.983589i | \(0.557748\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1018.81 | −0.0616205 | ||||||||
\(650\) | 5268.96 | + | 533.814i | 0.317947 | + | 0.0322122i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3508.32 | + | 17136.5i | −0.210731 | + | 1.02932i | ||||
\(653\) | 22562.1 | − | 13026.3i | 1.35210 | − | 0.780638i | 0.363561 | − | 0.931571i | \(-0.381561\pi\) |
0.988544 | + | 0.150933i | \(0.0482277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20649.3 | + | 11921.9i | 1.23181 | + | 0.711184i | ||||
\(656\) | 2166.86 | − | 260.674i | 0.128966 | − | 0.0155146i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9309.24 | − | 4186.66i | 0.551538 | − | 0.248044i | ||||
\(659\) | 14176.7 | − | 24554.8i | 0.838008 | − | 1.45147i | −0.0535504 | − | 0.998565i | \(-0.517054\pi\) |
0.891558 | − | 0.452907i | \(-0.149613\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5168.04 | + | 8951.31i | 0.304105 | + | 0.526725i | 0.977062 | − | 0.212957i | \(-0.0683093\pi\) |
−0.672957 | + | 0.739682i | \(0.734976\pi\) | |||||||
\(662\) | 22687.5 | + | 16353.8i | 1.33199 | + | 0.960133i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15401.3 | − | 14184.5i | 0.900130 | − | 0.829012i | ||||
\(665\) | 22063.4i | 1.28659i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 29896.3i | − | 1.73551i | ||||||
\(668\) | −9057.62 | − | 27180.9i | −0.524625 | − | 1.57434i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11869.7 | − | 16466.8i | 0.684430 | − | 0.949507i | ||||
\(671\) | 3.91468 | + | 6.78042i | 0.000225223 | + | 0.000390097i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7541.97 | − | 13063.1i | 0.431979 | − | 0.748209i | −0.565065 | − | 0.825046i | \(-0.691149\pi\) |
0.997044 | + | 0.0768374i | \(0.0244822\pi\) | |||||||
\(674\) | 5810.05 | + | 12918.9i | 0.332040 | + | 0.738307i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10888.1 | − | 12276.4i | 0.619486 | − | 0.698477i | ||||
\(677\) | 11873.7 | + | 6855.26i | 0.674065 | + | 0.389172i | 0.797615 | − | 0.603167i | \(-0.206095\pi\) |
−0.123550 | + | 0.992338i | \(0.539428\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24514.0 | + | 14153.2i | −1.38551 | + | 0.799925i | ||||
\(680\) | 5906.14 | + | 26325.9i | 0.333074 | + | 1.48463i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 458.381 | − | 4524.41i | 0.0257365 | − | 0.254030i | ||||
\(683\) | 807.274 | 0.0452262 | 0.0226131 | − | 0.999744i | \(-0.492801\pi\) | ||||
0.0226131 | + | 0.999744i | \(0.492801\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −448.867 | −0.0250370 | ||||||||
\(686\) | −1724.59 | + | 17022.4i | −0.0959842 | + | 0.947403i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24.7454 | − | 33.0061i | −0.00137123 | − | 0.00182899i | ||||
\(689\) | 2786.82 | − | 1608.97i | 0.154092 | − | 0.0889651i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19006.4 | − | 10973.4i | −1.04636 | − | 0.604119i | −0.124735 | − | 0.992190i | \(-0.539808\pi\) |
−0.921629 | + | 0.388072i | \(0.873141\pi\) | |||||||
\(692\) | 653.130 | + | 579.268i | 0.0358790 | + | 0.0318215i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9043.13 | − | 20107.9i | −0.494629 | − | 1.09983i | ||||
\(695\) | −13860.3 | + | 24006.7i | −0.756474 | + | 1.31025i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1214.91 | + | 2104.28i | 0.0660228 | + | 0.114355i | ||||
\(698\) | 15020.2 | − | 20837.5i | 0.814503 | − | 1.12996i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −22714.6 | + | 7569.28i | −1.22647 | + | 0.408703i | ||||
\(701\) | − | 3170.45i | − | 0.170822i | −0.996346 | − | 0.0854110i | \(-0.972780\pi\) | ||
0.996346 | − | 0.0854110i | \(-0.0272203\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9126.15i | 0.489615i | ||||||||
\(704\) | −2259.95 | + | 1067.77i | −0.120987 | + | 0.0571636i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10450.8 | − | 7533.20i | −0.557111 | − | 0.401580i | ||||
\(707\) | −3502.90 | − | 6067.20i | −0.186337 | − | 0.322745i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1413.03 | + | 2447.45i | −0.0748485 | + | 0.129641i | −0.901020 | − | 0.433777i | \(-0.857181\pi\) |
0.826172 | + | 0.563418i | \(0.190514\pi\) | |||||||
\(710\) | 16678.3 | − | 7500.76i | 0.881586 | − | 0.396477i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7048.37 | + | 22553.2i | −0.370996 | + | 1.18710i | ||||
\(713\) | −38818.0 | − | 22411.6i | −2.03892 | − | 1.17717i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −854.438 | + | 493.310i | −0.0446912 | + | 0.0258025i | ||||
\(716\) | 2103.54 | + | 430.653i | 0.109795 | + | 0.0224780i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15238.2 | − | 1543.83i | −0.792040 | − | 0.0802440i | ||||
\(719\) | 15469.9 | 0.802408 | 0.401204 | − | 0.915989i | \(-0.368592\pi\) | ||||
0.401204 | + | 0.915989i | \(0.368592\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10390.0 | −0.536677 | ||||||||
\(722\) | 6174.14 | + | 625.521i | 0.318252 | + | 0.0322430i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7042.58 | + | 1441.81i | 0.361513 | + | 0.0740116i | ||||
\(725\) | −29494.0 | + | 17028.4i | −1.51087 | + | 0.872301i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6900.11 | + | 3983.78i | 0.352009 | + | 0.203233i | 0.665570 | − | 0.746336i | \(-0.268189\pi\) |
−0.313561 | + | 0.949568i | \(0.601522\pi\) | |||||||
\(728\) | 1573.55 | − | 5034.98i | 0.0801092 | − | 0.256331i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −33533.8 | + | 15081.2i | −1.70019 | + | 0.764629i | ||||
\(731\) | 22.9635 | − | 39.7739i | 0.00116188 | − | 0.00201244i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12334.6 | − | 21364.2i | −0.621542 | − | 1.07654i | −0.989199 | − | 0.146581i | \(-0.953173\pi\) |
0.367656 | − | 0.929962i | \(-0.380160\pi\) | |||||||
\(734\) | −24450.2 | − | 17624.4i | −1.22953 | − | 0.886277i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 462.063 | + | 24632.1i | 0.0231411 | + | 1.23363i | ||||
\(737\) | 2093.65i | 0.104641i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1182.09i | 0.0588414i | 0.999567 | + | 0.0294207i | \(0.00936624\pi\) | ||||
−0.999567 | + | 0.0294207i | \(0.990634\pi\) | |||||||
\(740\) | −16970.6 | + | 5655.20i | −0.843044 | + | 0.280931i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8506.96 | + | 11801.7i | −0.420890 | + | 0.583899i | ||||
\(743\) | 13616.4 | + | 23584.4i | 0.672327 | + | 1.16450i | 0.977243 | + | 0.212125i | \(0.0680383\pi\) |
−0.304916 | + | 0.952379i | \(0.598628\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7133.00 | + | 12354.7i | −0.350782 | + | 0.607573i | ||||
\(746\) | −3143.87 | − | 6990.55i | −0.154296 | − | 0.343086i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2081.90 | − | 1846.46i | −0.101767 | − | 0.0902584i | ||||
\(749\) | −7196.16 | − | 4154.70i | −0.351057 | − | 0.202683i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12287.2 | − | 7093.99i | 0.597024 | − | 0.344692i | −0.170846 | − | 0.985298i | \(-0.554650\pi\) |
0.767870 | + | 0.640606i | \(0.221317\pi\) | |||||||
\(752\) | −9573.15 | + | 7177.21i | −0.464224 | + | 0.348040i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 756.336 | − | 7465.34i | 0.0365307 | − | 0.360572i | ||||
\(755\) | −24580.1 | −1.18485 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30482.1 | 1.46353 | 0.731764 | − | 0.681559i | \(-0.238698\pi\) | ||||
0.731764 | + | 0.681559i | \(0.238698\pi\) | |||||||
\(758\) | −1823.30 | + | 17996.7i | −0.0873682 | + | 0.862359i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5661.41 | − | 25235.0i | −0.270212 | − | 1.20443i | ||||
\(761\) | 19985.7 | − | 11538.8i | 0.952013 | − | 0.549645i | 0.0583074 | − | 0.998299i | \(-0.481430\pi\) |
0.893706 | + | 0.448654i | \(0.148096\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15034.5 | − | 8680.15i | −0.713348 | − | 0.411851i | ||||
\(764\) | −2731.98 | + | 3080.33i | −0.129371 | + | 0.145867i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1583.73 | + | 3521.51i | 0.0747031 | + | 0.166106i | ||||
\(767\) | −1260.19 | + | 2182.72i | −0.0593258 | + | 0.102755i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1035.31 | − | 1793.21i | −0.0485491 | − | 0.0840895i | 0.840730 | − | 0.541455i | \(-0.182126\pi\) |
−0.889279 | + | 0.457366i | \(0.848793\pi\) | |||||||
\(770\) | 2608.23 | − | 3618.39i | 0.122070 | − | 0.169348i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6219.99 | + | 18665.5i | 0.289977 | + | 0.870188i | ||||
\(773\) | 35103.0i | 1.63333i | 0.577110 | + | 0.816666i | \(0.304180\pi\) | ||||
−0.577110 | + | 0.816666i | \(0.695820\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 51061.1i | 2.36667i | ||||||||
\(776\) | 24406.2 | − | 22477.9i | 1.12904 | − | 1.03983i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14256.1 | + | 10276.2i | 0.656947 | + | 0.473545i | ||||
\(779\) | −1164.57 | − | 2017.09i | −0.0535622 | − | 0.0927724i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −943.085 | + | 1633.47i | −0.0432090 | + | 0.0748402i | ||||
\(782\) | −25015.0 | + | 11250.0i | −1.14391 | + | 0.514450i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 226.523 | + | 1882.98i | 0.0103190 | + | 0.0857774i | ||||
\(785\) | −38970.7 | − | 22499.7i | −1.77188 | − | 1.02299i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20621.0 | − | 11905.5i | 0.934000 | − | 0.539245i | 0.0459253 | − | 0.998945i | \(-0.485376\pi\) |
0.888074 | + | 0.459700i | \(0.152043\pi\) | |||||||
\(788\) | 1037.34 | − | 5066.95i | 0.0468957 | − | 0.229064i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3724.74 | + | 377.365i | 0.167747 | + | 0.0169950i | ||||
\(791\) | −7374.87 | −0.331505 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.3687 | 0.000867343 | ||||||||
\(794\) | 9262.90 | + | 938.452i | 0.414015 | + | 0.0419451i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2796.67 | − | 13660.5i | 0.124529 | − | 0.608269i | ||||
\(797\) | 2079.48 | − | 1200.59i | 0.0924202 | − | 0.0533588i | −0.453078 | − | 0.891471i | \(-0.649674\pi\) |
0.545498 | + | 0.838112i | \(0.316341\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11536.1 | − | 6660.38i | −0.510787 | − | 0.294903i | ||||
\(800\) | 24037.5 | − | 14485.9i | 1.06232 | − | 0.640190i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10513.1 | + | 4728.06i | −0.462880 | + | 0.208171i | ||||
\(803\) | 1896.19 | − | 3284.29i | 0.0833312 | − | 0.144334i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21982.3 | − | 38074.4i | −0.962451 | − | 1.66701i | ||||
\(806\) | −9126.20 | − | 6578.41i | −0.398830 | − | 0.287487i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5563.27 | + | 6040.52i | 0.242222 | + | 0.263001i | ||||
\(809\) | − | 29338.0i | − | 1.27499i | −0.770453 | − | 0.637497i | \(-0.779970\pi\) | ||
0.770453 | − | 0.637497i | \(-0.220030\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30884.9i | 1.33726i | 0.743597 | + | 0.668629i | \(0.233118\pi\) | ||||
−0.743597 | + | 0.668629i | \(0.766882\pi\) | |||||||
\(812\) | 10724.6 | + | 32183.2i | 0.463496 | + | 1.39090i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1078.85 | − | 1496.68i | 0.0464541 | − | 0.0644456i | ||||
\(815\) | 18294.8 | + | 31687.5i | 0.786305 | + | 1.36192i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.0120 | + | 38.1258i | −0.000942596 | + | 0.00163262i | ||||
\(818\) | −16368.6 | − | 36396.5i | −0.699653 | − | 1.55571i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3029.25 | − | 3415.51i | 0.129007 | − | 0.145457i | ||||
\(821\) | 17356.7 | + | 10020.9i | 0.737824 | + | 0.425983i | 0.821277 | − | 0.570529i | \(-0.193262\pi\) |
−0.0834539 | + | 0.996512i | \(0.526595\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5398.43 | + | 3116.78i | −0.228648 | + | 0.132010i | −0.609948 | − | 0.792441i | \(-0.708810\pi\) |
0.381300 | + | 0.924451i | \(0.375476\pi\) | |||||||
\(824\) | 11883.5 | − | 2666.05i | 0.502407 | − | 0.112714i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1148.53 | − | 11336.5i | 0.0483808 | − | 0.477538i | ||||
\(827\) | −43288.8 | −1.82019 | −0.910096 | − | 0.414397i | \(-0.863993\pi\) | ||||
−0.910096 | + | 0.414397i | \(0.863993\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15655.6 | −0.655902 | −0.327951 | − | 0.944695i | \(-0.606358\pi\) | ||||
−0.327951 | + | 0.944695i | \(0.606358\pi\) | |||||||
\(830\) | 4414.70 | − | 43574.9i | 0.184622 | − | 1.82230i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −507.778 | + | 6162.52i | −0.0211587 | + | 0.256787i | ||||
\(833\) | −1828.60 | + | 1055.74i | −0.0760592 | + | 0.0439128i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −51901.4 | − | 29965.3i | −2.15104 | − | 1.24191i | ||||
\(836\) | 1995.64 | + | 1769.95i | 0.0825605 | + | 0.0732237i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7388.04 | + | 16427.7i | 0.304553 | + | 0.677189i | ||||
\(839\) | −22793.5 | + | 39479.4i | −0.937924 | + | 1.62453i | −0.168588 | + | 0.985687i | \(0.553921\pi\) |
−0.769336 | + | 0.638845i | \(0.779413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11932.2 | + | 20667.2i | 0.489247 | + | 0.847400i | ||||
\(842\) | −17882.9 | + | 24808.9i | −0.731931 | + | 1.01540i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 31972.8 | − | 10654.4i | 1.30397 | − | 0.434527i | ||||
\(845\) | − | 34324.6i | − | 1.39740i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 25233.2i | − | 1.02364i | ||||||
\(848\) | 6701.55 | − | 15681.0i | 0.271382 | − | 0.635010i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 25346.8 | + | 18270.6i | 1.02281 | + | 0.737268i | ||||
\(851\) | −9092.58 | − | 15748.8i | −0.366263 | − | 0.634386i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1318.98 | + | 2284.55i | −0.0529439 | + | 0.0917016i | −0.891283 | − | 0.453448i | \(-0.850194\pi\) |
0.838339 | + | 0.545150i | \(0.183527\pi\) | |||||||
\(854\) | −79.8601 | + | 35.9156i | −0.00319995 | + | 0.00143912i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9296.68 | + | 2905.42i | 0.371208 | + | 0.116011i | ||||
\(857\) | 21068.1 | + | 12163.7i | 0.839759 | + | 0.484835i | 0.857182 | − | 0.515013i | \(-0.172213\pi\) |
−0.0174233 | + | 0.999848i | \(0.505546\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38889.0 | + | 22452.6i | −1.54468 | + | 0.891819i | −0.546143 | + | 0.837692i | \(0.683904\pi\) |
−0.998534 | + | 0.0541273i | \(0.982762\pi\) | |||||||
\(860\) | −84.5374 | − | 17.3071i | −0.00335198 | − | 0.000686242i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30865.4 | + | 3127.07i | 1.21958 | + | 0.123560i | ||||
\(863\) | −3830.25 | −0.151081 | −0.0755406 | − | 0.997143i | \(-0.524068\pi\) | ||||
−0.0755406 | + | 0.997143i | \(0.524068\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1826.14 | 0.0717809 | ||||||||
\(866\) | −4195.99 | − | 425.109i | −0.164649 | − | 0.0166810i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 49827.1 | + | 10201.0i | 1.94844 | + | 0.398898i | ||||
\(869\) | −334.406 | + | 193.070i | −0.0130540 | + | 0.00753675i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4485.47 | + | 2589.69i | 0.174494 | + | 0.100744i | ||||
\(872\) | 19423.0 | + | 6070.11i | 0.754294 | + | 0.235734i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23978.5 | − | 10783.9i | 0.928014 | − | 0.417357i | ||||
\(875\) | −4851.74 | + | 8403.45i | −0.187450 | + | 0.324673i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12549.7 | − | 21736.6i | −0.483206 | − | 0.836938i | 0.516608 | − | 0.856222i | \(-0.327195\pi\) |
−0.999814 | + | 0.0192844i | \(0.993861\pi\) | |||||||
\(878\) | −5107.07 | − | 3681.31i | −0.196304 | − | 0.141501i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2054.69 | + | 4807.79i | −0.0787087 | + | 0.184171i | ||||
\(881\) | 3336.88i | 0.127608i | 0.997962 | + | 0.0638038i | \(0.0203232\pi\) | ||||
−0.997962 | + | 0.0638038i | \(0.979677\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 26792.8i | − | 1.02112i | −0.859841 | − | 0.510561i | \(-0.829438\pi\) | ||
0.859841 | − | 0.510561i | \(-0.170562\pi\) | |||||||
\(884\) | −6531.06 | + | 2176.38i | −0.248488 | + | 0.0828048i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26260.0 | + | 36430.4i | −0.995735 | + | 1.38138i | ||||
\(887\) | −13004.9 | − | 22525.1i | −0.492290 | − | 0.852672i | 0.507670 | − | 0.861551i | \(-0.330507\pi\) |
−0.999961 | + | 0.00887981i | \(0.997173\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16195.0 | + | 28050.6i | −0.610983 | + | 1.05825i | ||||
\(890\) | 20272.9 | + | 45077.9i | 0.763539 | + | 1.69777i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −38415.4 | − | 34071.0i | −1.44198 | − | 1.27890i | ||||
\(893\) | 11058.1 | + | 6384.40i | 0.414384 | + | 0.239245i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3889.71 | − | 2245.72i | 0.145272 | − | 0.0838729i | ||||
\(896\) | −9333.58 | − | 26350.6i | −0.348006 | − | 0.982491i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3295.36 | + | 32526.5i | −0.122458 | + | 1.20871i | ||||
\(899\) | 72346.0 | 2.68395 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18985.5 | 0.701998 | ||||||||
\(902\) | −47.4622 | + | 468.471i | −0.00175201 | + | 0.0172931i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8435.00 | − | 1892.37i | 0.310336 | − | 0.0696232i | ||||
\(905\) | 13022.6 | − | 7518.59i | 0.478326 | − | 0.276162i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23690.0 | + | 13677.4i | 0.867269 | + | 0.500718i | 0.866440 | − | 0.499282i | \(-0.166403\pi\) |
0.000829418 | 1.00000i | \(0.499736\pi\) | ||||||||
\(908\) | 11941.9 | − | 13464.6i | 0.436460 | − | 0.492113i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4525.92 | − | 10063.6i | −0.164871 | − | 0.366599i | ||||
\(911\) | −2661.94 | + | 4610.61i | −0.0968100 | + | 0.167680i | −0.910363 | − | 0.413812i | \(-0.864197\pi\) |
0.813553 | + | 0.581491i | \(0.197531\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2258.67 | + | 3912.14i | 0.0818742 | + | 0.141810i | ||||
\(914\) | 18010.6 | − | 24986.0i | 0.651792 | − | 0.904228i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8777.99 | − | 26341.8i | −0.316630 | − | 0.950170i | ||||
\(917\) | − | 27504.7i | − | 0.990495i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3951.52i | − | 0.141837i | −0.997482 | − | 0.0709187i | \(-0.977407\pi\) | ||
0.997482 | − | 0.0709187i | \(-0.0225931\pi\) | |||||||
\(920\) | 34912.0 | + | 37907.0i | 1.25110 | + | 1.35843i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27017.5 | − | 19475.0i | −0.965049 | − | 0.695633i | ||||
\(923\) | 2333.06 | + | 4040.97i | 0.0831999 | + | 0.144106i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10358.0 | + | 17940.5i | −0.368181 | + | 0.637708i | ||||
\(926\) | 6861.49 | − | 3085.82i | 0.243502 | − | 0.109510i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20524.3 | − | 34057.6i | −0.726017 | − | 1.20474i | ||||
\(929\) | −2705.24 | − | 1561.87i | −0.0955394 | − | 0.0551597i | 0.451469 | − | 0.892287i | \(-0.350900\pi\) |
−0.547008 | + | 0.837127i | \(0.684233\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1752.83 | − | 1012.00i | 0.0617044 | − | 0.0356250i | ||||
\(932\) | −6181.76 | + | 30195.1i | −0.217264 | + | 1.06124i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −92.7925 | − | 9.40108i | −0.00325082 | − | 0.000329350i | ||||
\(935\) | −5820.96 | −0.203600 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24002.2 | 0.836838 | 0.418419 | − | 0.908254i | \(-0.362584\pi\) | ||||
0.418419 | + | 0.908254i | \(0.362584\pi\) | |||||||
\(938\) | −23296.4 | − | 2360.23i | −0.810931 | − | 0.0821579i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5019.79 | + | 24519.4i | −0.174178 | + | 0.850782i | ||||
\(941\) | −42104.3 | + | 24308.9i | −1.45862 | + | 0.842135i | −0.998944 | − | 0.0459518i | \(-0.985368\pi\) |
−0.459676 | + | 0.888086i | \(0.652035\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4019.34 | + | 2320.57i | 0.138799 | + | 0.0801358i | ||||
\(944\) | 1595.27 | + | 13260.8i | 0.0550019 | + | 0.457205i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.11700 | − | 3.65047i | 0.000278971 | − | 0.000125462i | ||||
\(947\) | 9870.34 | − | 17095.9i | 0.338694 | − | 0.586635i | −0.645493 | − | 0.763766i | \(-0.723348\pi\) |
0.984187 | + | 0.177131i | \(0.0566816\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4690.89 | − | 8124.86i | −0.160456 | − | 0.277918i | ||||
\(950\) | −24296.5 | − | 17513.6i | −0.829771 | − | 0.598121i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 22892.9 | − | 21084.2i | 0.779373 | − | 0.717795i | ||||
\(953\) | 47895.5i | 1.62800i | 0.580863 | + | 0.814002i | \(0.302715\pi\) | ||||
−0.580863 | + | 0.814002i | \(0.697285\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8612.54i | 0.291827i | ||||||||
\(956\) | −100.829 | − | 302.577i | −0.00341113 | − | 0.0102364i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13459.8 | + | 18672.7i | −0.453931 | + | 0.629737i | ||||
\(959\) | 258.893 | + | 448.416i | 0.00871751 | + | 0.0150992i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39338.4 | − | 68136.1i | 1.32048 | − | 2.28714i | ||||
\(962\) | −1872.07 | − | 4162.64i | −0.0627421 | − | 0.139510i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18358.0 | + | 20698.8i | −0.613352 | + | 0.691561i | ||||
\(965\) | 35641.4 | + | 20577.6i | 1.18895 | + | 0.686441i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39942.4 | − | 23060.8i | 1.32830 | − | 0.766892i | 0.343259 | − | 0.939241i | \(-0.388469\pi\) |
0.985036 | + | 0.172349i | \(0.0551356\pi\) | |||||||
\(968\) | 6474.77 | + | 28860.4i | 0.214987 | + | 0.958275i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6995.91 | − | 69052.5i | 0.231572 | − | 2.28571i | ||||
\(971\) | 51058.5 | 1.68748 | 0.843741 | − | 0.536751i | \(-0.180349\pi\) | ||||
0.843741 | + | 0.536751i | \(0.180349\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31976.7 | 1.05357 | ||||||||
\(974\) | −567.995 | + | 5606.34i | −0.0186856 | + | 0.184434i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 82.1241 | − | 61.5703i | 0.00269337 | − | 0.00201928i | ||||
\(977\) | −19394.5 | + | 11197.4i | −0.635093 | + | 0.366671i | −0.782722 | − | 0.622372i | \(-0.786169\pi\) |
0.147629 | + | 0.989043i | \(0.452836\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4414.92 | − | 2548.95i | −0.144128 | − | 0.0832124i | ||||
\(980\) | 2968.05 | + | 2632.39i | 0.0967457 | + | 0.0858047i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10226.0 | + | 22738.0i | 0.332307 | + | 0.738900i | ||||
\(983\) | 6698.78 | − | 11602.6i | 0.217353 | − | 0.376466i | −0.736645 | − | 0.676280i | \(-0.763591\pi\) |
0.953998 | + | 0.299813i | \(0.0969244\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5409.43 | − | 9369.40i | −0.174983 | − | 0.303080i | ||||
\(986\) | 25886.8 | − | 35912.7i | 0.836110 | − | 1.15993i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6260.44 | − | 2086.20i | 0.201590 | − | 0.0671768i | ||||
\(989\) | − | 87.7240i | − | 0.00282049i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24672.3i | − | 0.790858i | −0.918496 | − | 0.395429i | \(-0.870596\pi\) | ||
0.918496 | − | 0.395429i | \(-0.129404\pi\) | |||||||
\(992\) | −59607.2 | + | 1118.15i | −1.90779 | + | 0.0357875i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17112.8 | − | 12335.3i | −0.546060 | − | 0.393615i | ||||
\(995\) | −14583.8 | − | 25259.8i | −0.464660 | − | 0.804815i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29032.1 | + | 50285.1i | −0.922223 | + | 1.59734i | −0.126255 | + | 0.991998i | \(0.540296\pi\) |
−0.795968 | + | 0.605339i | \(0.793038\pi\) | |||||||
\(998\) | −54368.4 | + | 24451.2i | −1.72445 | + | 0.775539i | ||||
\(999\) | 0 | 0 |
(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.h.b.35.12 | 24 | ||
3.2 | odd | 2 | 36.4.h.b.11.1 | ✓ | 24 | ||
4.3 | odd | 2 | inner | 108.4.h.b.35.9 | 24 | ||
9.2 | odd | 6 | 324.4.b.c.323.16 | 24 | |||
9.4 | even | 3 | 36.4.h.b.23.4 | yes | 24 | ||
9.5 | odd | 6 | inner | 108.4.h.b.71.9 | 24 | ||
9.7 | even | 3 | 324.4.b.c.323.9 | 24 | |||
12.11 | even | 2 | 36.4.h.b.11.4 | yes | 24 | ||
36.7 | odd | 6 | 324.4.b.c.323.15 | 24 | |||
36.11 | even | 6 | 324.4.b.c.323.10 | 24 | |||
36.23 | even | 6 | inner | 108.4.h.b.71.12 | 24 | ||
36.31 | odd | 6 | 36.4.h.b.23.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.4.h.b.11.1 | ✓ | 24 | 3.2 | odd | 2 | ||
36.4.h.b.11.4 | yes | 24 | 12.11 | even | 2 | ||
36.4.h.b.23.1 | yes | 24 | 36.31 | odd | 6 | ||
36.4.h.b.23.4 | yes | 24 | 9.4 | even | 3 | ||
108.4.h.b.35.9 | 24 | 4.3 | odd | 2 | inner | ||
108.4.h.b.35.12 | 24 | 1.1 | even | 1 | trivial | ||
108.4.h.b.71.9 | 24 | 9.5 | odd | 6 | inner | ||
108.4.h.b.71.12 | 24 | 36.23 | even | 6 | inner | ||
324.4.b.c.323.9 | 24 | 9.7 | even | 3 | |||
324.4.b.c.323.10 | 24 | 36.11 | even | 6 | |||
324.4.b.c.323.15 | 24 | 36.7 | odd | 6 | |||
324.4.b.c.323.16 | 24 | 9.2 | odd | 6 |