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 | 71.9 | ||
Character | \(\chi\) | \(=\) | 108.71 |
Dual form | 108.4.h.b.35.9 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.65391 | − | 2.29447i | 0.584746 | − | 0.811216i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.52915 | − | 7.58969i | −0.316144 | − | 0.948711i | ||||
\(5\) | 14.4924 | + | 8.36717i | 1.29624 | + | 0.748383i | 0.979752 | − | 0.200215i | \(-0.0641640\pi\) |
0.316485 | + | 0.948598i | \(0.397497\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.7175 | − | 9.65186i | 0.902661 | − | 0.521152i | 0.0245984 | − | 0.999697i | \(-0.492169\pi\) |
0.878063 | + | 0.478546i | \(0.158836\pi\) | |||||||
\(8\) | −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 | \(-0.145354\pi\) |
−0.830632 | + | 0.556822i | \(0.812021\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.03848 | − | 10.4590i | 0.128829 | − | 0.223138i | −0.794394 | − | 0.607402i | \(-0.792212\pi\) |
0.923223 | + | 0.384264i | \(0.125545\pi\) | |||||||
\(14\) | 5.50343 | − | 54.3211i | 0.105061 | − | 1.03699i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −51.2068 | + | 38.3909i | −0.800106 | + | 0.599858i | ||||
\(17\) | − | 71.2528i | − | 1.01655i | −0.861195 | − | 0.508275i | \(-0.830283\pi\) | ||
0.861195 | − | 0.508275i | \(-0.169717\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 68.3003i | − | 0.824693i | −0.911027 | − | 0.412347i | \(-0.864709\pi\) | ||
0.911027 | − | 0.412347i | \(-0.135291\pi\) | |||||||
\(20\) | 26.8509 | − | 131.154i | 0.300202 | − | 1.46635i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.7376 | + | 1.39180i | 0.133130 | + | 0.0134878i | ||||
\(23\) | −68.0491 | + | 117.865i | −0.616923 | + | 1.06854i | 0.373121 | + | 0.927783i | \(0.378288\pi\) |
−0.990044 | + | 0.140759i | \(0.955046\pi\) | |||||||
\(24\) | 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 | −0.964520 | − | 0.264009i | \(-0.914955\pi\) |
−0.253622 | + | 0.967303i | \(0.581622\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 285.221 | + | 164.672i | 1.65249 | + | 0.954065i | 0.976044 | + | 0.217571i | \(0.0698134\pi\) |
0.676444 | + | 0.736494i | \(0.263520\pi\) | |||||||
\(32\) | 3.39507 | + | 180.987i | 0.0187553 | + | 0.999824i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −163.487 | − | 117.846i | −0.824642 | − | 0.594424i | ||||
\(35\) | 323.035 | 1.56008 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −133.618 | −0.593693 | −0.296847 | − | 0.954925i | \(-0.595935\pi\) | ||||
−0.296847 | + | 0.954925i | \(0.595935\pi\) | |||||||
\(38\) | −156.713 | − | 112.963i | −0.669005 | − | 0.482236i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −256.520 | − | 278.526i | −1.01399 | − | 1.10097i | ||||
\(41\) | 29.5326 | + | 17.0507i | 0.112493 | + | 0.0649480i | 0.555191 | − | 0.831723i | \(-0.312645\pi\) |
−0.442698 | + | 0.896671i | \(0.645979\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.558209 | − | 0.322282i | 0.00197967 | − | 0.00114297i | −0.499010 | − | 0.866596i | \(-0.666303\pi\) |
0.500990 | + | 0.865453i | \(0.332970\pi\) | |||||||
\(44\) | 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 | \(-0.0729775\pi\) |
−0.683732 | + | 0.729733i | \(0.739644\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.8169 | − | 25.6636i | 0.0431979 | − | 0.0748210i | ||||
\(50\) | 436.282 | + | 44.2010i | 1.23399 | + | 0.125019i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −94.6525 | − | 19.3780i | −0.252422 | − | 0.0516777i | ||||
\(53\) | 266.453i | 0.690569i | 0.938498 | + | 0.345284i | \(0.112218\pi\) | ||||
−0.938498 | + | 0.345284i | \(0.887782\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 81.6944i | 0.200285i | ||||||||
\(56\) | −426.199 | + | 95.6168i | −1.01702 | + | 0.228167i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −62.6263 | + | 618.147i | −0.141780 | + | 1.39943i | ||||
\(59\) | −104.347 | + | 180.734i | −0.230251 | + | 0.398806i | −0.957882 | − | 0.287163i | \(-0.907288\pi\) |
0.727631 | + | 0.685969i | \(0.240621\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.801886 | + | 1.38891i | 0.00168313 | + | 0.00291527i | 0.866866 | − | 0.498542i | \(-0.166131\pi\) |
−0.865183 | + | 0.501457i | \(0.832798\pi\) | |||||||
\(62\) | 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 | \(-0.461204\pi\) |
−0.798812 | + | 0.601581i | \(0.794538\pi\) | |||||||
\(68\) | −540.787 | + | 180.209i | −0.964412 | + | 0.321376i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 534.272 | − | 741.193i | 0.912253 | − | 1.26557i | ||||
\(71\) | −386.365 | −0.645817 | −0.322909 | − | 0.946430i | \(-0.604661\pi\) | ||||
−0.322909 | + | 0.946430i | \(0.604661\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −776.832 | −1.24550 | −0.622749 | − | 0.782422i | \(-0.713984\pi\) | ||||
−0.622749 | + | 0.782422i | \(0.713984\pi\) | |||||||
\(74\) | −220.992 | + | 306.582i | −0.347160 | + | 0.481614i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −518.378 | + | 172.742i | −0.782396 | + | 0.260721i | ||||
\(77\) | 81.6122 | + | 47.1188i | 0.120787 | + | 0.0697362i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −68.5000 | + | 39.5485i | −0.0975551 | + | 0.0563235i | −0.547984 | − | 0.836489i | \(-0.684604\pi\) |
0.450429 | + | 0.892812i | \(0.351271\pi\) | |||||||
\(80\) | −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 | −0.990927 | − | 0.134404i | \(-0.957088\pi\) |
0.379066 | − | 0.925370i | \(-0.376245\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 596.185 | − | 1032.62i | 0.760768 | − | 1.31769i | ||||
\(86\) | 0.183763 | − | 1.81382i | 0.000230415 | − | 0.00227429i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −24.1811 | − | 107.784i | −0.0292922 | − | 0.130566i | ||||
\(89\) | − | 1044.26i | − | 1.24372i | −0.783128 | − | 0.621861i | \(-0.786377\pi\) | ||
0.783128 | − | 0.621861i | \(-0.213623\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 233.130i | − | 0.268557i | ||||||
\(92\) | 1066.66 | + | 218.375i | 1.20877 | + | 0.247469i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 526.083 | + | 53.2991i | 0.577248 | + | 0.0584828i | ||||
\(95\) | 571.481 | − | 989.834i | 0.617186 | − | 1.06900i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 733.184 | + | 1269.91i | 0.767460 | + | 1.32928i | 0.938936 | + | 0.344091i | \(0.111813\pi\) |
−0.171477 | + | 0.985188i | \(0.554854\pi\) | |||||||
\(98\) | −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 | −0.337122 | − | 0.941461i | \(-0.609454\pi\) |
0.646768 | + | 0.762687i | \(0.276120\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −466.128 | − | 269.119i | −0.445912 | − | 0.257447i | 0.260190 | − | 0.965557i | \(-0.416215\pi\) |
−0.706102 | + | 0.708110i | \(0.749548\pi\) | |||||||
\(104\) | −201.009 | + | 185.127i | −0.189525 | + | 0.174550i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 611.368 | + | 440.690i | 0.560201 | + | 0.403808i | ||||
\(107\) | −430.456 | −0.388914 | −0.194457 | − | 0.980911i | \(-0.562294\pi\) | ||||
−0.194457 | + | 0.980911i | \(0.562294\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 899.324 | 0.790272 | 0.395136 | − | 0.918623i | \(-0.370697\pi\) | ||||
0.395136 | + | 0.918623i | \(0.370697\pi\) | |||||||
\(110\) | 187.445 | + | 135.115i | 0.162474 | + | 0.117116i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −485.507 | + | 1136.04i | −0.409608 | + | 0.958445i | ||||
\(113\) | 330.860 | + | 191.022i | 0.275440 | + | 0.159025i | 0.631357 | − | 0.775492i | \(-0.282498\pi\) |
−0.355917 | + | 0.934517i | \(0.615832\pi\) | |||||||
\(114\) | 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 | ||||
\(122\) | 4.51305 | + | 0.457231i | 0.00334912 | + | 0.000339309i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 528.446 | − | 2581.22i | 0.382708 | − | 1.86936i | ||||
\(125\) | 502.674i | 0.359684i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1677.92i | − | 1.17237i | −0.810177 | − | 0.586186i | \(-0.800629\pi\) | ||
0.810177 | − | 0.586186i | \(-0.199371\pi\) | |||||||
\(128\) | 1365.05 | − | 483.512i | 0.942615 | − | 0.333881i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 57.6181 | − | 568.714i | 0.0388727 | − | 0.383689i | ||||
\(131\) | −712.418 | + | 1233.94i | −0.475147 | + | 0.822979i | −0.999595 | − | 0.0284637i | \(-0.990938\pi\) |
0.524448 | + | 0.851443i | \(0.324272\pi\) | |||||||
\(132\) | 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 | −0.507226 | − | 0.861813i | \(-0.669329\pi\) |
0.492739 | + | 0.870177i | \(0.335996\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1434.57 | + | 828.252i | 0.875388 | + | 0.505406i | 0.869135 | − | 0.494575i | \(-0.164676\pi\) |
0.00625321 | + | 0.999980i | \(0.498010\pi\) | |||||||
\(140\) | −817.004 | − | 2451.74i | −0.493210 | − | 1.48007i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −639.013 | + | 886.500i | −0.377639 | + | 0.523898i | ||||
\(143\) | 58.9578 | 0.0344776 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3675.98 | −2.10533 | ||||||||
\(146\) | −1284.81 | + | 1782.42i | −0.728300 | + | 1.01037i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 337.940 | + | 1014.12i | 0.187692 | + | 0.563244i | ||||
\(149\) | −738.285 | − | 426.249i | −0.405924 | − | 0.234360i | 0.283113 | − | 0.959087i | \(-0.408633\pi\) |
−0.689037 | + | 0.724726i | \(0.741966\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1272.06 | − | 734.422i | 0.685553 | − | 0.395804i | −0.116391 | − | 0.993203i | \(-0.537133\pi\) |
0.801944 | + | 0.597399i | \(0.203799\pi\) | |||||||
\(152\) | −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 | 0.290446 | + | 0.956891i | \(0.406196\pi\) |
−0.973915 | + | 0.226912i | \(0.927137\pi\) | |||||||
\(158\) | −22.5503 | + | 222.581i | −0.0113545 | + | 0.112073i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1465.15 | + | 2651.35i | −0.723940 | + | 1.31005i | ||||
\(161\) | 2627.20i | 1.28604i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2186.50i | 1.05067i | 0.850895 | + | 0.525336i | \(0.176060\pi\) | ||||
−0.850895 | + | 0.525336i | \(0.823940\pi\) | |||||||
\(164\) | 54.7169 | − | 267.267i | 0.0260529 | − | 0.127256i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2603.92 | − | 263.811i | −1.21749 | − | 0.123348i | ||||
\(167\) | 1790.65 | − | 3101.49i | 0.829726 | − | 1.43713i | −0.0685268 | − | 0.997649i | \(-0.521830\pi\) |
0.898253 | − | 0.439479i | \(-0.144837\pi\) | |||||||
\(168\) | 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 | −0.479090 | − | 0.877766i | \(-0.659033\pi\) |
0.520622 | + | 0.853787i | \(0.325700\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2591.86 | + | 1496.41i | 1.11958 | + | 0.646388i | ||||
\(176\) | −287.301 | − | 122.783i | −0.123046 | − | 0.0525858i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2396.02 | − | 1727.11i | −1.00893 | − | 0.727262i | ||||
\(179\) | −268.397 | −0.112072 | −0.0560361 | − | 0.998429i | \(-0.517846\pi\) | ||||
−0.0560361 | + | 0.998429i | \(0.517846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 898.582 | 0.369011 | 0.184506 | − | 0.982831i | \(-0.440932\pi\) | ||||
0.184506 | + | 0.982831i | \(0.440932\pi\) | |||||||
\(182\) | −534.910 | − | 385.577i | −0.217858 | − | 0.157038i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2265.22 | − | 2086.25i | 0.907577 | − | 0.835870i | ||||
\(185\) | −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 | \(-0.135587\pi\) |
−0.813157 | + | 0.582044i | \(0.802253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1229.66 | − | 2129.83i | 0.458616 | − | 0.794346i | −0.540272 | − | 0.841490i | \(-0.681679\pi\) |
0.998888 | + | 0.0471443i | \(0.0150121\pi\) | |||||||
\(194\) | 4126.39 | + | 418.057i | 1.52710 | + | 0.154715i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −232.253 | − | 47.5485i | −0.0846403 | − | 0.0173282i | ||||
\(197\) | 646.506i | 0.233815i | 0.993143 | + | 0.116908i | \(0.0372982\pi\) | ||||
−0.993143 | + | 0.116908i | \(0.962702\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1742.98i | − | 0.620886i | −0.950592 | − | 0.310443i | \(-0.899523\pi\) | ||
0.950592 | − | 0.310443i | \(-0.100477\pi\) | |||||||
\(200\) | −767.949 | − | 3423.03i | −0.271511 | − | 1.21022i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 103.469 | − | 1021.28i | 0.0360398 | − | 0.355727i | ||||
\(203\) | −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 | \(-0.574507\pi\) |
−0.958379 | + | 0.285499i | \(0.907841\pi\) | |||||||
\(212\) | 2022.30 | − | 673.900i | 0.655151 | − | 0.218319i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −711.937 | + | 987.667i | −0.227416 | + | 0.315493i | ||||
\(215\) | 10.7864 | 0.00342150 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6357.58 | 1.98885 | ||||||||
\(218\) | 1487.40 | − | 2063.47i | 0.462109 | − | 0.641081i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 620.035 | − | 206.617i | 0.190013 | − | 0.0633188i | ||||
\(221\) | −745.230 | − | 430.259i | −0.226831 | − | 0.130961i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5558.55 | − | 3209.23i | 1.66918 | − | 0.963703i | 0.701103 | − | 0.713060i | \(-0.252691\pi\) |
0.968080 | − | 0.250643i | \(-0.0806420\pi\) | |||||||
\(224\) | 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 | \(-0.273341\pi\) |
−0.982292 | + | 0.187358i | \(0.940008\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1735.36 | + | 3005.74i | −0.500769 | + | 0.867357i | 0.499231 | + | 0.866469i | \(0.333616\pi\) |
−1.00000 | 0.000888202i | \(0.999717\pi\) | ||||||||
\(230\) | −649.313 | + | 6408.98i | −0.186150 | + | 1.83737i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4849.94 | − | 1088.07i | 1.37247 | − | 0.307911i | ||||
\(233\) | − | 3852.67i | − | 1.08325i | −0.840621 | − | 0.541624i | \(-0.817810\pi\) | ||
0.840621 | − | 0.541624i | \(-0.182190\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3128.50i | 0.868428i | ||||||||
\(236\) | 1635.62 | + | 334.857i | 0.451144 | + | 0.0923615i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3870.53 | − | 392.135i | −1.05416 | − | 0.106800i | ||||
\(239\) | 19.9334 | − | 34.5257i | 0.00539491 | − | 0.00934426i | −0.863315 | − | 0.504665i | \(-0.831616\pi\) |
0.868710 | + | 0.495321i | \(0.164949\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1729.18 | − | 2995.03i | −0.462184 | − | 0.800527i | 0.536885 | − | 0.843655i | \(-0.319601\pi\) |
−0.999070 | + | 0.0431286i | \(0.986267\pi\) | |||||||
\(242\) | −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 | ||||
\(248\) | −5048.51 | − | 5481.61i | −1.29267 | − | 1.40356i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1153.37 | + | 831.378i | 0.291781 | + | 0.210324i | ||||
\(251\) | 2977.61 | 0.748786 | 0.374393 | − | 0.927270i | \(-0.377851\pi\) | ||||
0.374393 | + | 0.927270i | \(0.377851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −664.410 | −0.165103 | ||||||||
\(254\) | −3849.93 | − | 2775.13i | −0.951047 | − | 0.685540i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1148.28 | − | 3931.75i | 0.280341 | − | 0.959901i | ||||
\(257\) | 5593.28 | + | 3229.28i | 1.35758 | + | 0.783802i | 0.989298 | − | 0.145910i | \(-0.0466111\pi\) |
0.368287 | + | 0.929712i | \(0.379944\pi\) | |||||||
\(258\) | 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 | −0.971987 | − | 0.235036i | \(-0.924479\pi\) |
0.282447 | − | 0.959283i | \(-0.408854\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2229.46 | + | 3861.54i | −0.516810 | + | 0.895141i | ||||
\(266\) | −3710.15 | − | 375.886i | −0.855203 | − | 0.0866431i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −688.129 | + | 3361.20i | −0.156844 | + | 0.766111i | ||||
\(269\) | − | 2967.07i | − | 0.672510i | −0.941771 | − | 0.336255i | \(-0.890840\pi\) | ||
0.941771 | − | 0.336255i | \(-0.109160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1985.78i | 0.445121i | 0.974919 | + | 0.222561i | \(0.0714415\pi\) | ||||
−0.974919 | + | 0.222561i | \(0.928559\pi\) | |||||||
\(272\) | 2735.46 | + | 3648.63i | 0.609785 | + | 0.813348i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.64719 | + | 75.4808i | −0.00168607 | + | 0.0166422i | ||||
\(275\) | −378.436 | + | 655.471i | −0.0829839 | + | 0.143732i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2171.48 | − | 3761.12i | −0.471017 | − | 0.815825i | 0.528433 | − | 0.848975i | \(-0.322780\pi\) |
−0.999450 | + | 0.0331494i | \(0.989446\pi\) | |||||||
\(278\) | 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 | −0.997381 | − | 0.0723220i | \(-0.976959\pi\) |
−0.436058 | + | 0.899919i | \(0.643626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1771.47 | − | 1022.76i | −0.372094 | − | 0.214829i | 0.302279 | − | 0.953220i | \(-0.402253\pi\) |
−0.674373 | + | 0.738391i | \(0.735586\pi\) | |||||||
\(284\) | 977.173 | + | 2932.39i | 0.204171 | + | 0.612694i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 97.5110 | − | 135.277i | 0.0201607 | − | 0.0279688i | ||||
\(287\) | 658.283 | 0.135391 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −163.963 | −0.0333732 | ||||||||
\(290\) | −6079.75 | + | 8434.41i | −1.23109 | + | 1.70788i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1964.72 | + | 5895.92i | 0.393756 | + | 1.18162i | ||||
\(293\) | 2041.60 | + | 1178.72i | 0.407070 | + | 0.235022i | 0.689530 | − | 0.724257i | \(-0.257817\pi\) |
−0.282460 | + | 0.959279i | \(0.591151\pi\) | |||||||
\(294\) | 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 | ||||
\(302\) | 418.763 | − | 4133.36i | 0.0797917 | − | 0.787576i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2622.11 | + | 3497.44i | 0.494699 | + | 0.659842i | ||||
\(305\) | 26.8381i | 0.00503851i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5521.27i | − | 1.02643i | −0.858259 | − | 0.513217i | \(-0.828454\pi\) | ||
0.858259 | − | 0.513217i | \(-0.171546\pi\) | |||||||
\(308\) | 151.208 | − | 738.582i | 0.0279736 | − | 0.136638i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15509.1 | + | 1571.27i | 2.84148 | + | 0.287879i | ||||
\(311\) | −767.330 | + | 1329.05i | −0.139908 | + | 0.242327i | −0.927461 | − | 0.373919i | \(-0.878014\pi\) |
0.787554 | + | 0.616246i | \(0.211347\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4383.28 | − | 7592.06i | −0.791557 | − | 1.37102i | −0.925003 | − | 0.379961i | \(-0.875937\pi\) |
0.133446 | − | 0.991056i | \(-0.457396\pi\) | |||||||
\(314\) | 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 | 0.146376 | − | 0.989229i | \(-0.453239\pi\) |
0.929886 | + | 0.367849i | \(0.119906\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −928.706 | − | 536.189i | −0.163002 | − | 0.0941091i | ||||
\(320\) | 3660.19 | + | 7746.83i | 0.639409 | + | 1.35332i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6028.03 | + | 4345.16i | 1.04326 | + | 0.752008i | ||||
\(323\) | −4866.59 | −0.838342 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1872.39 | 0.319574 | ||||||||
\(326\) | 5016.84 | + | 3616.27i | 0.852323 | + | 0.614377i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −522.738 | − | 567.582i | −0.0879982 | − | 0.0955473i | ||||
\(329\) | 3125.35 | + | 1804.42i | 0.523727 | + | 0.302374i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8563.21 | + | 4943.97i | −1.42198 | + | 0.820982i | −0.996468 | − | 0.0839692i | \(-0.973240\pi\) |
−0.425515 | + | 0.904951i | \(0.639907\pi\) | |||||||
\(332\) | −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 | −0.589527 | − | 0.807749i | \(-0.700686\pi\) |
0.994294 | + | 0.106670i | \(0.0340190\pi\) | |||||||
\(338\) | 5771.97 | + | 584.776i | 0.928858 | + | 0.0941054i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9345.12 | − | 1913.20i | −1.49062 | − | 0.305170i | ||||
\(341\) | 1607.81i | 0.255330i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6049.14i | 0.952252i | ||||||||
\(344\) | −14.2311 | + | 3.19271i | −0.00223049 | + | 0.000500405i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.1112 | − | 307.080i | 0.00483396 | − | 0.0477131i | ||||
\(347\) | 3897.53 | − | 6750.72i | 0.602969 | − | 1.04437i | −0.389399 | − | 0.921069i | \(-0.627317\pi\) |
0.992369 | − | 0.123305i | \(-0.0393493\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4540.81 | + | 7864.91i | 0.696458 | + | 1.20630i | 0.969687 | + | 0.244352i | \(0.0785753\pi\) |
−0.273228 | + | 0.961949i | \(0.588091\pi\) | |||||||
\(350\) | 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 | −0.766974 | − | 0.641678i | \(-0.778239\pi\) |
0.172222 | + | 0.985058i | \(0.444905\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5599.34 | − | 3232.78i | −0.837133 | − | 0.483319i | ||||
\(356\) | −7925.61 | + | 2641.09i | −1.17993 | + | 0.393195i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −443.905 | + | 615.828i | −0.0655338 | + | 0.0909148i | ||||
\(359\) | 5415.10 | 0.796095 | 0.398047 | − | 0.917365i | \(-0.369688\pi\) | ||||
0.398047 | + | 0.917365i | \(0.369688\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2194.06 | 0.319881 | ||||||||
\(362\) | 1486.18 | − | 2061.77i | 0.215778 | − | 0.299348i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1769.39 | + | 589.621i | −0.254783 | + | 0.0849026i | ||||
\(365\) | −11258.1 | − | 6499.89i | −1.61446 | − | 0.932109i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9228.51 | − | 5328.08i | 1.31260 | − | 0.757830i | 0.330074 | − | 0.943955i | \(-0.392926\pi\) |
0.982526 | + | 0.186125i | \(0.0595928\pi\) | |||||||
\(368\) | −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 | −0.944614 | − | 0.328183i | \(-0.893564\pi\) |
0.756522 | + | 0.653969i | \(0.226897\pi\) | |||||||
\(374\) | 99.1695 | − | 978.843i | 0.0137111 | − | 0.135334i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −926.019 | − | 4127.61i | −0.127010 | − | 0.566131i | ||||
\(377\) | 2652.91i | 0.362418i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6395.35i | 0.866774i | 0.901208 | + | 0.433387i | \(0.142682\pi\) | ||||
−0.901208 | + | 0.433387i | \(0.857318\pi\) | |||||||
\(380\) | −8957.89 | − | 1833.93i | −1.20929 | − | 0.247575i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1448.27 | + | 146.729i | 0.193979 | + | 0.0196526i | ||||
\(383\) | −682.579 | + | 1182.26i | −0.0910656 | + | 0.157730i | −0.907960 | − | 0.419057i | \(-0.862361\pi\) |
0.816894 | + | 0.576788i | \(0.195694\pi\) | |||||||
\(384\) | 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 | −0.106510 | − | 0.994312i | \(-0.533968\pi\) |
0.807844 | + | 0.589397i | \(0.200634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8398.18 | + | 4848.69i | 1.08623 | + | 0.627133i | ||||
\(392\) | −493.224 | + | 454.255i | −0.0635500 | + | 0.0585290i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1483.39 | + | 1069.26i | 0.189675 | + | 0.136723i | ||||
\(395\) | −1323.64 | −0.168606 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3291.69 | 0.416134 | 0.208067 | − | 0.978115i | \(-0.433283\pi\) | ||||
0.208067 | + | 0.978115i | \(0.433283\pi\) | |||||||
\(398\) | −3999.20 | − | 2882.73i | −0.503672 | − | 0.363061i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9124.15 | − | 3899.36i | −1.14052 | − | 0.487420i | ||||
\(401\) | −3529.51 | − | 2037.76i | −0.439539 | − | 0.253768i | 0.263863 | − | 0.964560i | \(-0.415003\pi\) |
−0.703402 | + | 0.710792i | \(0.748337\pi\) | |||||||
\(402\) | 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 | 0.0256787 | + | 0.999670i | \(0.491825\pi\) |
−0.878579 | + | 0.477597i | \(0.841508\pi\) | |||||||
\(410\) | 1605.86 | + | 162.694i | 0.193434 | + | 0.0195973i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −863.624 | + | 4218.41i | −0.103271 | + | 0.504432i | ||||
\(413\) | 4028.56i | 0.479982i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15484.9i | − | 1.83162i | ||||||
\(416\) | 1913.44 | + | 1057.38i | 0.225515 | + | 0.124621i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 95.0603 | − | 938.283i | 0.0111233 | − | 0.109792i | ||||
\(419\) | −3184.20 | + | 5515.19i | −0.371261 | + | 0.643042i | −0.989760 | − | 0.142743i | \(-0.954408\pi\) |
0.618499 | + | 0.785786i | \(0.287741\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5406.24 | − | 9363.89i | −0.625853 | − | 1.08401i | −0.988375 | − | 0.152034i | \(-0.951418\pi\) |
0.362522 | − | 0.931975i | \(-0.381916\pi\) | |||||||
\(422\) | −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 | ||||
\(428\) | 1088.69 | + | 3267.03i | 0.122953 | + | 0.368967i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.8397 | − | 24.7489i | 0.00200071 | − | 0.00277558i | ||||
\(431\) | −10968.4 | −1.22583 | −0.612913 | − | 0.790150i | \(-0.710002\pi\) | ||||
−0.612913 | + | 0.790150i | \(0.710002\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1491.10 | −0.165491 | −0.0827457 | − | 0.996571i | \(-0.526369\pi\) | ||||
−0.0827457 | + | 0.996571i | \(0.526369\pi\) | |||||||
\(434\) | 10514.9 | − | 14587.2i | 1.16297 | − | 1.61339i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2274.52 | − | 6825.59i | −0.249839 | − | 0.749740i | ||||
\(437\) | 8050.19 | + | 4647.78i | 0.881219 | + | 0.508772i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1927.62 | − | 1112.91i | 0.209567 | − | 0.120994i | −0.391543 | − | 0.920160i | \(-0.628059\pi\) |
0.601110 | + | 0.799166i | \(0.294725\pi\) | |||||||
\(440\) | 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 | 0.879923 | + | 0.475117i | \(0.157594\pi\) |
−0.0284982 | + | 0.999594i | \(0.509073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8737.50 | − | 15133.8i | 0.930780 | − | 1.61216i | ||||
\(446\) | 1829.88 | − | 18061.7i | 0.194277 | − | 1.91759i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9850.13 | + | 811.629i | 1.03878 | + | 0.0855934i | ||||
\(449\) | − | 11558.7i | − | 1.21490i | −0.794358 | − | 0.607450i | \(-0.792193\pi\) | ||
0.794358 | − | 0.607450i | \(-0.207807\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 166.477i | 0.0173816i | ||||||||
\(452\) | 613.004 | − | 2994.25i | 0.0637905 | − | 0.311588i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6330.61 | − | 641.373i | −0.654428 | − | 0.0663021i | ||||
\(455\) | 1950.64 | − | 3378.61i | 0.200984 | − | 0.348114i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5444.85 | + | 9430.75i | 0.557329 | + | 0.965322i | 0.997718 | + | 0.0675148i | \(0.0215070\pi\) |
−0.440390 | + | 0.897807i | \(0.645160\pi\) | |||||||
\(458\) | 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 | −0.917057 | − | 0.398757i | \(-0.869442\pi\) |
−0.113195 | + | 0.993573i | \(0.536108\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2303.58 | − | 1329.97i | −0.231223 | − | 0.133497i | 0.379913 | − | 0.925022i | \(-0.375954\pi\) |
−0.611136 | + | 0.791525i | \(0.709287\pi\) | |||||||
\(464\) | 5524.83 | − | 12927.6i | 0.552766 | − | 1.29342i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8839.82 | − | 6371.98i | −0.878749 | − | 0.633426i | ||||
\(467\) | 32.9750 | 0.00326746 | 0.00163373 | − | 0.999999i | \(-0.499480\pi\) | ||||
0.00163373 | + | 0.999999i | \(0.499480\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8278.68 | −0.815083 | ||||||||
\(470\) | 7178.23 | + | 5174.26i | 0.704483 | + | 0.507810i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3473.49 | − | 3199.06i | 0.338730 | − | 0.311967i | ||||
\(473\) | 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 | \(-0.0397831\pi\) |
−0.604056 | + | 0.796942i | \(0.706450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −806.850 | + | 1397.50i | −0.0764848 | + | 0.132476i | ||||
\(482\) | −9731.91 | − | 985.969i | −0.919661 | − | 0.0931736i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10244.8 | − | 2097.40i | −0.962138 | − | 0.196976i | ||||
\(485\) | 24538.7i | 2.29741i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1992.29i | 0.185378i | 0.995695 | + | 0.0926891i | \(0.0295463\pi\) | ||||
−0.995695 | + | 0.0926891i | \(0.970454\pi\) | |||||||
\(488\) | −7.94394 | − | 35.4091i | −0.000736896 | − | 0.00328462i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 141.380 | − | 1395.48i | 0.0130345 | − | 0.128656i | ||||
\(491\) | −4407.34 | + | 7633.75i | −0.405093 | + | 0.701642i | −0.994332 | − | 0.106317i | \(-0.966094\pi\) |
0.589239 | + | 0.807959i | \(0.299428\pi\) | |||||||
\(492\) | 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 | 0.981691 | + | 0.190479i | \(0.0610042\pi\) |
0.655806 | + | 0.754930i | \(0.272329\pi\) | |||||||
\(500\) | 3815.14 | − | 1271.34i | 0.341236 | − | 0.113712i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4924.71 | − | 6832.04i | 0.437850 | − | 0.607428i | ||||
\(503\) | 19011.6 | 1.68526 | 0.842629 | − | 0.538494i | \(-0.181006\pi\) | ||||
0.842629 | + | 0.538494i | \(0.181006\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6073.31 | 0.535166 | ||||||||
\(506\) | −1098.88 | + | 1524.47i | −0.0965434 | + | 0.133934i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12734.9 | + | 4243.70i | −1.11224 | + | 0.370638i | ||||
\(509\) | −11096.0 | − | 6406.27i | −0.966250 | − | 0.557865i | −0.0681588 | − | 0.997674i | \(-0.521712\pi\) |
−0.898091 | + | 0.439810i | \(0.855046\pi\) | |||||||
\(510\) | 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 | ||||
\(518\) | −735.357 | + | 7258.27i | −0.0623740 | + | 0.615657i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4462.09 | + | 1001.06i | −0.376299 | + | 0.0844218i | ||||
\(521\) | − | 14455.7i | − | 1.21558i | −0.794100 | − | 0.607788i | \(-0.792057\pi\) | ||
0.794100 | − | 0.607788i | \(-0.207943\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15232.9i | 1.27359i | 0.771032 | + | 0.636796i | \(0.219741\pi\) | ||||
−0.771032 | + | 0.636796i | \(0.780259\pi\) | |||||||
\(524\) | 11167.1 | + | 2286.20i | 0.930984 | + | 0.190598i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16552.0 | − | 1676.93i | −1.37206 | − | 0.139007i | ||||
\(527\) | 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 | ||||
\(536\) | 6574.05 | + | 7138.01i | 0.529768 | + | 0.575215i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6807.83 | − | 4907.27i | −0.545551 | − | 0.393248i | ||||
\(539\) | 144.667 | 0.0115608 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23075.7 | −1.83383 | −0.916915 | − | 0.399083i | \(-0.869328\pi\) | ||||
−0.916915 | + | 0.399083i | \(0.869328\pi\) | |||||||
\(542\) | 4556.31 | + | 3284.31i | 0.361089 | + | 0.260283i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12895.9 | − | 241.908i | 1.01637 | − | 0.0190657i | ||||
\(545\) | 13033.3 | + | 7524.80i | 1.02438 | + | 0.591426i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 317.151 | − | 183.107i | 0.0247905 | − | 0.0143128i | −0.487554 | − | 0.873093i | \(-0.662111\pi\) |
0.512344 | + | 0.858780i | \(0.328777\pi\) | |||||||
\(548\) | 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 | ||||
\(554\) | −12221.2 | − | 1238.17i | −0.937236 | − | 0.0949542i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2657.92 | − | 12982.7i | 0.202736 | − | 0.990272i | ||||
\(557\) | − | 3402.66i | − | 0.258842i | −0.991590 | − | 0.129421i | \(-0.958688\pi\) | ||
0.991590 | − | 0.129421i | \(-0.0413119\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.78437i | − | 0.000588987i | ||||||
\(560\) | −16541.6 | + | 12401.6i | −1.24823 | + | 0.935829i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2222.80 | + | 21940.0i | −0.166839 | + | 1.64676i | ||||
\(563\) | −2461.45 | + | 4263.36i | −0.184259 | + | 0.319146i | −0.943327 | − | 0.331866i | \(-0.892322\pi\) |
0.759068 | + | 0.651012i | \(0.225655\pi\) | |||||||
\(564\) | 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 | −0.832157 | − | 0.554540i | \(-0.812894\pi\) |
0.0641669 | + | 0.997939i | \(0.479561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −522.706 | − | 301.784i | −0.0383092 | − | 0.0221178i | 0.480723 | − | 0.876872i | \(-0.340374\pi\) |
−0.519032 | + | 0.854755i | \(0.673708\pi\) | |||||||
\(572\) | −149.113 | − | 447.472i | −0.0108999 | − | 0.0327093i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1088.74 | − | 1510.41i | 0.0791694 | − | 0.109831i | ||||
\(575\) | −21100.5 | −1.53035 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6971.52 | −0.502995 | −0.251497 | − | 0.967858i | \(-0.580923\pi\) | ||||
−0.251497 | + | 0.967858i | \(0.580923\pi\) | |||||||
\(578\) | −271.180 | + | 376.207i | −0.0195149 | + | 0.0270729i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9297.10 | + | 27899.5i | 0.665588 | + | 1.99735i | ||||
\(581\) | −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 | −0.958274 | − | 0.285851i | \(-0.907724\pi\) |
0.231583 | − | 0.972815i | \(-0.425610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11247.2 | − | 19480.7i | 0.786811 | − | 1.36280i | ||||
\(590\) | −995.659 | + | 9827.55i | −0.0694756 | + | 0.685752i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6842.15 | − | 5129.71i | 0.475018 | − | 0.356132i | ||||
\(593\) | 2417.22i | 0.167392i | 0.996491 | + | 0.0836958i | \(0.0266724\pi\) | ||||
−0.996491 | + | 0.0836958i | \(0.973328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 23017.2i | − | 1.58590i | ||||||
\(596\) | −1367.87 | + | 6681.40i | −0.0940100 | + | 0.459196i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4625.28 | + | 468.601i | 0.316290 | + | 0.0320443i | ||||
\(599\) | −14467.5 | + | 25058.4i | −0.986852 | + | 1.70928i | −0.353452 | + | 0.935453i | \(0.614992\pi\) |
−0.633400 | + | 0.773825i | \(0.718341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −318.246 | − | 551.219i | −0.0215999 | − | 0.0374121i | 0.855023 | − | 0.518589i | \(-0.173543\pi\) |
−0.876623 | + | 0.481177i | \(0.840209\pi\) | |||||||
\(602\) | −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 | \(-0.555017\pi\) |
−0.939112 | + | 0.343610i | \(0.888350\pi\) | |||||||
\(608\) | 12361.5 | − | 231.885i | 0.824548 | − | 0.0154674i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 61.5791 | + | 44.3878i | 0.00408732 | + | 0.00294625i | ||||
\(611\) | 2257.80 | 0.149494 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6429.22 | 0.423612 | 0.211806 | − | 0.977312i | \(-0.432066\pi\) | ||||
0.211806 | + | 0.977312i | \(0.432066\pi\) | |||||||
\(614\) | −12668.4 | − | 9131.69i | −0.832660 | − | 0.600204i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1444.57 | − | 1568.49i | −0.0944858 | − | 0.102591i | ||||
\(617\) | 6024.79 | + | 3478.41i | 0.393110 | + | 0.226962i | 0.683507 | − | 0.729944i | \(-0.260454\pi\) |
−0.290397 | + | 0.956906i | \(0.593787\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19227.5 | + | 11101.0i | −1.24850 | + | 0.720819i | −0.970809 | − | 0.239853i | \(-0.922901\pi\) |
−0.277686 | + | 0.960672i | \(0.589567\pi\) | |||||||
\(620\) | 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 | ||||
\(626\) | −24669.3 | − | 2499.32i | −1.57505 | − | 0.159573i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21075.2 | + | 4314.68i | 1.33916 | + | 0.274163i | ||||
\(629\) | 9520.65i | 0.603519i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 529.250i | 0.0333901i | 0.999861 | + | 0.0166950i | \(0.00531444\pi\) | ||||
−0.999861 | + | 0.0166950i | \(0.994686\pi\) | |||||||
\(632\) | 1746.35 | − | 391.790i | 0.109915 | − | 0.0246591i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1999.72 | − | 19738.0i | 0.125266 | − | 1.23643i | ||||
\(635\) | 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 | 0.258339 | − | 0.966054i | \(-0.416825\pi\) |
0.965797 | + | 0.259299i | \(0.0834915\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2182.17 | − | 1259.88i | −0.133836 | − | 0.0772702i | 0.431587 | − | 0.902071i | \(-0.357954\pi\) |
−0.565423 | + | 0.824801i | \(0.691287\pi\) | |||||||
\(644\) | 19939.7 | − | 6644.59i | 1.22008 | − | 0.406574i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8048.91 | + | 11166.2i | −0.490217 | + | 0.680076i | ||||
\(647\) | 5938.61 | 0.360851 | 0.180426 | − | 0.983589i | \(-0.442252\pi\) | ||||
0.180426 | + | 0.983589i | \(0.442252\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1018.81 | −0.0616205 | ||||||||
\(650\) | 3096.77 | − | 4296.14i | 0.186870 | − | 0.259244i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16594.8 | − | 5529.97i | 0.996785 | − | 0.332163i | ||||
\(653\) | 22562.1 | + | 13026.3i | 1.35210 | + | 0.780638i | 0.988544 | − | 0.150933i | \(-0.0482277\pi\) |
0.363561 | + | 0.931571i | \(0.381561\pi\) | |||||||
\(654\) | 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 | −0.891558 | − | 0.452907i | \(-0.850387\pi\) |
0.0535504 | − | 0.998565i | \(-0.482946\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5168.04 | − | 8951.31i | 0.304105 | − | 0.526725i | −0.672957 | − | 0.739682i | \(-0.734976\pi\) |
0.977062 | + | 0.212957i | \(0.0683093\pi\) | |||||||
\(662\) | −2819.02 | + | 27824.9i | −0.165505 | + | 1.63360i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4583.45 | + | 20430.2i | 0.267880 | + | 1.19404i | ||||
\(665\) | − | 22063.4i | − | 1.28659i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 29896.3i | − | 1.73551i | ||||||
\(668\) | −28068.1 | − | 5746.32i | −1.62573 | − | 0.332832i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −20195.6 | − | 2046.07i | −1.16451 | − | 0.117980i | ||||
\(671\) | −3.91468 | + | 6.78042i | −0.000225223 | + | 0.000390097i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7541.97 | + | 13063.1i | 0.431979 | + | 0.748209i | 0.997044 | − | 0.0768374i | \(-0.0244822\pi\) |
−0.565065 | + | 0.825046i | \(0.691149\pi\) | |||||||
\(674\) | −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 | −0.123550 | − | 0.992338i | \(-0.539428\pi\) |
0.797615 | + | 0.603167i | \(0.206095\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24514.0 | + | 14153.2i | 1.38551 | + | 0.799925i | ||||
\(680\) | −19845.8 | + | 18277.8i | −1.11919 | + | 1.03077i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3689.06 | + | 2659.17i | 0.207128 | + | 0.149303i | ||||
\(683\) | −807.274 | −0.0452262 | −0.0226131 | − | 0.999744i | \(-0.507199\pi\) | ||||
−0.0226131 | + | 0.999744i | \(0.507199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −448.867 | −0.0250370 | ||||||||
\(686\) | 13879.5 | + | 10004.7i | 0.772483 | + | 0.556826i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −16.2114 | + | 37.9332i | −0.000898333 | + | 0.00210202i | ||||
\(689\) | 2786.82 | + | 1608.97i | 0.154092 | + | 0.0889651i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19006.4 | − | 10973.4i | 1.04636 | − | 0.604119i | 0.124735 | − | 0.992190i | \(-0.460192\pi\) |
0.921629 | + | 0.388072i | \(0.126859\pi\) | |||||||
\(692\) | −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 | ||||
\(698\) | 25555.9 | + | 2589.14i | 1.38582 | + | 0.140402i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4802.09 | − | 23456.0i | 0.259289 | − | 1.26651i | ||||
\(701\) | 3170.45i | 0.170822i | 0.996346 | + | 0.0854110i | \(0.0272203\pi\) | ||||
−0.996346 | + | 0.0854110i | \(0.972780\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9126.15i | 0.489615i | ||||||||
\(704\) | −205.258 | + | 2491.06i | −0.0109886 | + | 0.133360i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1298.55 | + | 12817.2i | −0.0692234 | + | 0.683263i | ||||
\(707\) | 3502.90 | − | 6067.20i | 0.186337 | − | 0.322745i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1413.03 | − | 2447.45i | −0.0748485 | − | 0.129641i | 0.826172 | − | 0.563418i | \(-0.190514\pi\) |
−0.901020 | + | 0.433777i | \(0.857181\pi\) | |||||||
\(710\) | −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 | ||||
\(716\) | 678.816 | + | 2037.05i | 0.0354309 | + | 0.106324i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8956.10 | − | 12424.8i | 0.465514 | − | 0.645805i | ||||
\(719\) | −15469.9 | −0.802408 | −0.401204 | − | 0.915989i | \(-0.631408\pi\) | ||||
−0.401204 | + | 0.915989i | \(0.631408\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10390.0 | −0.536677 | ||||||||
\(722\) | 3628.79 | − | 5034.20i | 0.187049 | − | 0.259493i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2272.65 | − | 6819.96i | −0.116661 | − | 0.350085i | ||||
\(725\) | −29494.0 | − | 17028.4i | −1.51087 | − | 0.872301i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6900.11 | + | 3983.78i | −0.352009 | + | 0.203233i | −0.665570 | − | 0.746336i | \(-0.731811\pi\) |
0.313561 | + | 0.949568i | \(0.398478\pi\) | |||||||
\(728\) | −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 | 0.367656 | + | 0.929962i | \(0.380160\pi\) |
−0.989199 | + | 0.146581i | \(0.953173\pi\) | |||||||
\(734\) | 3038.04 | − | 29986.7i | 0.152774 | − | 1.50794i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21563.0 | − | 11915.9i | −1.07992 | − | 0.596773i | ||||
\(737\) | − | 2093.65i | − | 0.104641i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1182.09i | 0.0588414i | 0.999567 | + | 0.0294207i | \(0.00936624\pi\) | ||||
−0.999567 | + | 0.0294207i | \(0.990634\pi\) | |||||||
\(740\) | −3587.76 | + | 17524.6i | −0.178228 | + | 0.870563i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14474.0 | + | 1466.41i | 0.716116 | + | 0.0725519i | ||||
\(743\) | −13616.4 | + | 23584.4i | −0.672327 | + | 1.16450i | 0.304916 | + | 0.952379i | \(0.401372\pi\) |
−0.977243 | + | 0.212125i | \(0.931962\pi\) | |||||||
\(744\) | 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 | \(-0.445350\pi\) |
−0.767870 | + | 0.640606i | \(0.778683\pi\) | |||||||
\(752\) | −11002.2 | − | 4701.99i | −0.533523 | − | 0.228010i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6087.01 | + | 4387.68i | 0.294000 | + | 0.211923i | ||||
\(755\) | 24580.1 | 1.18485 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30482.1 | 1.46353 | 0.731764 | − | 0.681559i | \(-0.238698\pi\) | ||||
0.731764 | + | 0.681559i | \(0.238698\pi\) | |||||||
\(758\) | 14673.9 | + | 10577.4i | 0.703141 | + | 0.506843i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19023.4 | + | 17520.4i | −0.907965 | + | 0.836227i | ||||
\(761\) | 19985.7 | + | 11538.8i | 0.952013 | + | 0.549645i | 0.893706 | − | 0.448654i | \(-0.148096\pi\) |
0.0583074 | + | 0.998299i | \(0.481430\pi\) | |||||||
\(762\) | 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 | −0.889279 | − | 0.457366i | \(-0.848793\pi\) |
0.840730 | + | 0.541455i | \(0.182126\pi\) | |||||||
\(770\) | 4437.73 | + | 449.600i | 0.207694 | + | 0.0210421i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19274.8 | − | 3946.07i | −0.898594 | − | 0.183967i | ||||
\(773\) | − | 35103.0i | − | 1.63333i | −0.577110 | − | 0.816666i | \(-0.695820\pi\) | ||
0.577110 | − | 0.816666i | \(-0.304180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 51061.1i | 2.36667i | ||||||||
\(776\) | −7263.34 | − | 32375.4i | −0.336003 | − | 1.49769i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1771.38 | − | 17484.2i | 0.0816285 | − | 0.805706i | ||||
\(779\) | 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 | \(-0.514624\pi\) |
−0.888074 | + | 0.459700i | \(0.847957\pi\) | |||||||
\(788\) | 4906.78 | − | 1635.11i | 0.221823 | − | 0.0739192i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2189.18 | + | 3037.04i | −0.0985918 | + | 0.136776i | ||||
\(791\) | 7374.87 | 0.331505 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.3687 | 0.000867343 | ||||||||
\(794\) | 5444.17 | − | 7552.68i | 0.243333 | − | 0.337575i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13228.6 | + | 4408.24i | −0.589041 | + | 0.196289i | ||||
\(797\) | 2079.48 | + | 1200.59i | 0.0924202 | + | 0.0533588i | 0.545498 | − | 0.838112i | \(-0.316341\pi\) |
−0.453078 | + | 0.891471i | \(0.649674\pi\) | |||||||
\(798\) | 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 | ||||
\(806\) | 1133.97 | − | 11192.7i | 0.0495562 | − | 0.489140i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8012.88 | + | 1797.67i | −0.348876 | + | 0.0782695i | ||||
\(809\) | 29338.0i | 1.27499i | 0.770453 | + | 0.637497i | \(0.220030\pi\) | ||||
−0.770453 | + | 0.637497i | \(0.779970\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30884.9i | 1.33726i | 0.743597 | + | 0.668629i | \(0.233118\pi\) | ||||
−0.743597 | + | 0.668629i | \(0.766882\pi\) | |||||||
\(812\) | 33233.8 | + | 6803.86i | 1.43630 | + | 0.294050i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1835.59 | − | 185.969i | −0.0790386 | − | 0.00800764i | ||||
\(815\) | −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 | −0.0834539 | − | 0.996512i | \(-0.526595\pi\) |
0.821277 | + | 0.570529i | \(0.193262\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5398.43 | + | 3116.78i | 0.228648 | + | 0.132010i | 0.609948 | − | 0.792441i | \(-0.291190\pi\) |
−0.381300 | + | 0.924451i | \(0.624524\pi\) | |||||||
\(824\) | 8250.64 | + | 8958.43i | 0.348816 | + | 0.378740i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9243.40 | + | 6662.89i | 0.389369 | + | 0.280668i | ||||
\(827\) | 43288.8 | 1.82019 | 0.910096 | − | 0.414397i | \(-0.136007\pi\) | ||||
0.910096 | + | 0.414397i | \(0.136007\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15655.6 | −0.655902 | −0.327951 | − | 0.944695i | \(-0.606358\pi\) | ||||
−0.327951 | + | 0.944695i | \(0.606358\pi\) | |||||||
\(830\) | −35529.6 | − | 25610.7i | −1.48584 | − | 1.07104i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5590.79 | − | 2641.51i | 0.232964 | − | 0.110070i | ||||
\(833\) | −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 | 0.769336 | + | 0.638845i | \(0.220587\pi\) |
0.168588 | + | 0.985687i | \(0.446079\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11932.2 | − | 20667.2i | 0.489247 | − | 0.847400i | ||||
\(842\) | −30426.6 | − | 3082.61i | −1.24533 | − | 0.126168i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6759.38 | + | 33016.5i | −0.275672 | + | 1.34653i | ||||
\(845\) | 34324.6i | 1.39740i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 25233.2i | − | 1.02364i | ||||||
\(848\) | −10229.4 | − | 13644.2i | −0.414243 | − | 0.552529i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3149.44 | − | 31086.3i | 0.127088 | − | 1.25441i | ||||
\(851\) | 9092.58 | − | 15748.8i | 0.366263 | − | 0.634386i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1318.98 | − | 2284.55i | −0.0529439 | − | 0.0917016i | 0.838339 | − | 0.545150i | \(-0.183527\pi\) |
−0.891283 | + | 0.453448i | \(0.850194\pi\) | |||||||
\(854\) | 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 | −0.0174233 | − | 0.999848i | \(-0.505546\pi\) |
0.857182 | + | 0.515013i | \(0.172213\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38889.0 | + | 22452.6i | 1.54468 | + | 0.891819i | 0.998534 | + | 0.0541273i | \(0.0172377\pi\) |
0.546143 | + | 0.837692i | \(0.316096\pi\) | |||||||
\(860\) | −27.2803 | − | 81.8651i | −0.00108169 | − | 0.00324602i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18140.8 | + | 25166.7i | −0.716797 | + | 0.994410i | ||||
\(863\) | 3830.25 | 0.151081 | 0.0755406 | − | 0.997143i | \(-0.475932\pi\) | ||||
0.0755406 | + | 0.997143i | \(0.475932\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1826.14 | 0.0717809 | ||||||||
\(866\) | −2466.15 | + | 3421.28i | −0.0967705 | + | 0.134249i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −16079.3 | − | 48252.0i | −0.628762 | − | 1.88684i | ||||
\(869\) | −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 | −0.999814 | − | 0.0192844i | \(-0.993861\pi\) |
0.516608 | + | 0.856222i | \(0.327195\pi\) | |||||||
\(878\) | 634.574 | − | 6263.50i | 0.0243916 | − | 0.240755i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3136.32 | − | 4183.31i | −0.120143 | − | 0.160249i | ||||
\(881\) | − | 3336.88i | − | 0.127608i | −0.997962 | − | 0.0638038i | \(-0.979677\pi\) | ||
0.997962 | − | 0.0638038i | \(-0.0203232\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 26792.8i | − | 1.02112i | −0.859841 | − | 0.510561i | \(-0.829438\pi\) | ||
0.859841 | − | 0.510561i | \(-0.170562\pi\) | |||||||
\(884\) | −1380.73 | + | 6744.25i | −0.0525329 | + | 0.256599i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 44679.6 | + | 4526.62i | 1.69418 | + | 0.171642i | ||||
\(887\) | 13004.9 | − | 22525.1i | 0.492290 | − | 0.852672i | −0.507670 | − | 0.861551i | \(-0.669493\pi\) |
0.999961 | + | 0.00887981i | \(0.00282657\pi\) | |||||||
\(888\) | 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 | ||||
\(896\) | 18153.5 | − | 21258.4i | 0.676859 | − | 0.792627i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26521.1 | − | 19117.1i | −0.985547 | − | 0.710408i | ||||
\(899\) | −72346.0 | −2.68395 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18985.5 | 0.701998 | ||||||||
\(902\) | 381.976 | + | 275.339i | 0.0141002 | + | 0.0101638i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5856.34 | − | 6358.74i | −0.215464 | − | 0.233948i | ||||
\(905\) | 13022.6 | + | 7518.59i | 0.478326 | + | 0.276162i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23690.0 | + | 13677.4i | −0.867269 | + | 0.500718i | −0.866440 | − | 0.499282i | \(-0.833597\pi\) |
−0.000829418 | 1.00000i | \(0.500264\pi\) | ||||||||
\(908\) | −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 | \(-0.135803\pi\) |
−0.813553 | + | 0.581491i | \(0.802469\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2258.67 | − | 3912.14i | 0.0818742 | − | 0.141810i | ||||
\(914\) | 30643.8 | + | 3104.62i | 1.10898 | + | 0.112354i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27201.6 | + | 5568.92i | 0.981187 | + | 0.200876i | ||||
\(917\) | 27504.7i | 0.990495i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3951.52i | − | 0.141837i | −0.997482 | − | 0.0709187i | \(-0.977407\pi\) | ||
0.997482 | − | 0.0709187i | \(-0.0225931\pi\) | |||||||
\(920\) | 50284.4 | − | 11281.2i | 1.80199 | − | 0.404271i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3357.04 | + | 33135.3i | −0.119911 | + | 1.18357i | ||||
\(923\) | −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 | −0.547008 | − | 0.837127i | \(-0.684233\pi\) |
0.451469 | + | 0.892287i | \(0.350900\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1752.83 | − | 1012.00i | −0.0617044 | − | 0.0356250i | ||||
\(932\) | −29240.6 | + | 9743.98i | −1.02769 | + | 0.342462i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 54.5378 | − | 75.6601i | 0.00191063 | − | 0.00265061i | ||||
\(935\) | 5820.96 | 0.203600 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24002.2 | 0.836838 | 0.418419 | − | 0.908254i | \(-0.362584\pi\) | ||||
0.418419 | + | 0.908254i | \(0.362584\pi\) | |||||||
\(938\) | −13692.2 | + | 18995.1i | −0.476616 | + | 0.661208i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 23744.3 | − | 7912.44i | 0.823888 | − | 0.274548i | ||||
\(941\) | −42104.3 | − | 24308.9i | −1.45862 | − | 0.842135i | −0.459676 | − | 0.888086i | \(-0.652035\pi\) |
−0.998944 | + | 0.0459518i | \(0.985368\pi\) | |||||||
\(942\) | 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 | \(-0.276652\pi\) |
−0.984187 | + | 0.177131i | \(0.943318\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4690.89 | + | 8124.86i | −0.160456 | + | 0.277918i | ||||
\(950\) | 3018.94 | − | 29798.2i | 0.103103 | − | 1.01766i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6812.96 | + | 30367.9i | 0.231943 | + | 1.03385i | ||||
\(953\) | − | 47895.5i | − | 1.62800i | −0.580863 | − | 0.814002i | \(-0.697285\pi\) | ||
0.580863 | − | 0.814002i | \(-0.302715\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8612.54i | 0.291827i | ||||||||
\(956\) | −312.454 | − | 63.9678i | −0.0105706 | − | 0.00216409i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22900.9 | + | 2320.16i | 0.772334 | + | 0.0782474i | ||||
\(959\) | −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 | \(-0.611531\pi\) |
−0.985036 | + | 0.172349i | \(0.944864\pi\) | |||||||
\(968\) | −21756.5 | + | 20037.5i | −0.722397 | + | 0.665321i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 56303.3 | + | 40584.9i | 1.86370 | + | 1.34340i | ||||
\(971\) | −51058.5 | −1.68748 | −0.843741 | − | 0.536751i | \(-0.819651\pi\) | ||||
−0.843741 | + | 0.536751i | \(0.819651\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31976.7 | 1.05357 | ||||||||
\(974\) | 4571.24 | + | 3295.07i | 0.150382 | + | 0.108399i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −94.3835 | − | 40.3364i | −0.00309543 | − | 0.00132289i | ||||
\(977\) | −19394.5 | − | 11197.4i | −0.635093 | − | 0.366671i | 0.147629 | − | 0.989043i | \(-0.452836\pi\) |
−0.782722 | + | 0.622372i | \(0.786169\pi\) | |||||||
\(978\) | 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 | \(-0.236409\pi\) |
−0.953998 | + | 0.299813i | \(0.903076\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5409.43 | + | 9369.40i | −0.174983 | + | 0.303080i | ||||
\(986\) | 44044.7 | + | 4462.30i | 1.42259 | + | 0.144126i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1323.52 | + | 6464.80i | −0.0426182 | + | 0.208171i | ||||
\(989\) | 87.7240i | 0.00282049i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24672.3i | − | 0.790858i | −0.918496 | − | 0.395429i | \(-0.870596\pi\) | ||
0.918496 | − | 0.395429i | \(-0.129404\pi\) | |||||||
\(992\) | −28835.3 | + | 52180.5i | −0.922904 | + | 1.67009i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2126.33 | + | 20987.8i | −0.0678503 | + | 0.669709i | ||||
\(995\) | 14583.8 | − | 25259.8i | 0.464660 | − | 0.804815i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29032.1 | − | 50285.1i | −0.922223 | − | 1.59734i | −0.795968 | − | 0.605339i | \(-0.793038\pi\) |
−0.126255 | − | 0.991998i | \(-0.540296\pi\) | |||||||
\(998\) | 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.71.9 | 24 | ||
3.2 | odd | 2 | 36.4.h.b.23.4 | yes | 24 | ||
4.3 | odd | 2 | inner | 108.4.h.b.71.12 | 24 | ||
9.2 | odd | 6 | inner | 108.4.h.b.35.12 | 24 | ||
9.4 | even | 3 | 324.4.b.c.323.16 | 24 | |||
9.5 | odd | 6 | 324.4.b.c.323.9 | 24 | |||
9.7 | even | 3 | 36.4.h.b.11.1 | ✓ | 24 | ||
12.11 | even | 2 | 36.4.h.b.23.1 | yes | 24 | ||
36.7 | odd | 6 | 36.4.h.b.11.4 | yes | 24 | ||
36.11 | even | 6 | inner | 108.4.h.b.35.9 | 24 | ||
36.23 | even | 6 | 324.4.b.c.323.15 | 24 | |||
36.31 | odd | 6 | 324.4.b.c.323.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.4.h.b.11.1 | ✓ | 24 | 9.7 | even | 3 | ||
36.4.h.b.11.4 | yes | 24 | 36.7 | odd | 6 | ||
36.4.h.b.23.1 | yes | 24 | 12.11 | even | 2 | ||
36.4.h.b.23.4 | yes | 24 | 3.2 | odd | 2 | ||
108.4.h.b.35.9 | 24 | 36.11 | even | 6 | inner | ||
108.4.h.b.35.12 | 24 | 9.2 | odd | 6 | inner | ||
108.4.h.b.71.9 | 24 | 1.1 | even | 1 | trivial | ||
108.4.h.b.71.12 | 24 | 4.3 | odd | 2 | inner | ||
324.4.b.c.323.9 | 24 | 9.5 | odd | 6 | |||
324.4.b.c.323.10 | 24 | 36.31 | odd | 6 | |||
324.4.b.c.323.15 | 24 | 36.23 | even | 6 | |||
324.4.b.c.323.16 | 24 | 9.4 | even | 3 |