Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 372.6 | ||
Character | \(\chi\) | \(=\) | 847.372 |
Dual form | 847.2.f.y.148.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.835334 | − | 2.57089i | 0.590670 | − | 1.81790i | 0.0154732 | − | 0.999880i | \(-0.495075\pi\) |
0.575197 | − | 0.818015i | \(-0.304925\pi\) | |||||||
\(3\) | 2.27106 | − | 1.65003i | 1.31120 | − | 0.952643i | 0.311203 | − | 0.950344i | \(-0.399268\pi\) |
0.999997 | − | 0.00229892i | \(-0.000731771\pi\) | |||||||
\(4\) | −4.29367 | − | 3.11953i | −2.14684 | − | 1.55977i | ||||
\(5\) | −0.137535 | − | 0.423289i | −0.0615075 | − | 0.189301i | 0.915581 | − | 0.402133i | \(-0.131731\pi\) |
−0.977089 | + | 0.212833i | \(0.931731\pi\) | |||||||
\(6\) | −2.34494 | − | 7.21698i | −0.957318 | − | 2.94632i | ||||
\(7\) | −0.809017 | − | 0.587785i | −0.305780 | − | 0.222162i | ||||
\(8\) | −7.23277 | + | 5.25492i | −2.55717 | + | 1.85789i | ||||
\(9\) | 1.50810 | − | 4.64146i | 0.502701 | − | 1.54715i | ||||
\(10\) | −1.20312 | −0.380459 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −14.8985 | −4.30083 | ||||||||
\(13\) | 0.139346 | − | 0.428863i | 0.0386476 | − | 0.118945i | −0.929871 | − | 0.367885i | \(-0.880082\pi\) |
0.968519 | + | 0.248940i | \(0.0800821\pi\) | |||||||
\(14\) | −2.18693 | + | 1.58890i | −0.584482 | + | 0.424651i | ||||
\(15\) | −1.01079 | − | 0.734380i | −0.260984 | − | 0.189616i | ||||
\(16\) | 4.18797 | + | 12.8893i | 1.04699 | + | 3.22231i | ||||
\(17\) | 1.49291 | + | 4.59472i | 0.362085 | + | 1.11438i | 0.951786 | + | 0.306762i | \(0.0992455\pi\) |
−0.589701 | + | 0.807621i | \(0.700755\pi\) | |||||||
\(18\) | −10.6729 | − | 7.75433i | −2.51563 | − | 1.82771i | ||||
\(19\) | 0.878946 | − | 0.638592i | 0.201644 | − | 0.146503i | −0.482381 | − | 0.875962i | \(-0.660228\pi\) |
0.684025 | + | 0.729459i | \(0.260228\pi\) | |||||||
\(20\) | −0.729935 | + | 2.24651i | −0.163218 | + | 0.502334i | ||||
\(21\) | −2.80719 | −0.612579 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.57222 | 0.953373 | 0.476687 | − | 0.879073i | \(-0.341838\pi\) | ||||
0.476687 | + | 0.879073i | \(0.341838\pi\) | |||||||
\(24\) | −7.75535 | + | 23.8685i | −1.58305 | + | 4.87214i | ||||
\(25\) | 3.88483 | − | 2.82249i | 0.776965 | − | 0.564498i | ||||
\(26\) | −0.986160 | − | 0.716487i | −0.193402 | − | 0.140515i | ||||
\(27\) | −1.63112 | − | 5.02007i | −0.313909 | − | 0.966113i | ||||
\(28\) | 1.64004 | + | 5.04751i | 0.309938 | + | 0.953890i | ||||
\(29\) | 1.60534 | + | 1.16635i | 0.298105 | + | 0.216586i | 0.726776 | − | 0.686875i | \(-0.241018\pi\) |
−0.428671 | + | 0.903461i | \(0.641018\pi\) | |||||||
\(30\) | −2.73236 | + | 1.98517i | −0.498858 | + | 0.362442i | ||||
\(31\) | 2.55205 | − | 7.85440i | 0.458362 | − | 1.41069i | −0.408781 | − | 0.912632i | \(-0.634046\pi\) |
0.867143 | − | 0.498060i | \(-0.165954\pi\) | |||||||
\(32\) | 18.7549 | 3.31542 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.0596 | 2.23970 | ||||||||
\(35\) | −0.137535 | + | 0.423289i | −0.0232476 | + | 0.0715489i | ||||
\(36\) | −20.9545 | + | 15.2243i | −3.49241 | + | 2.53739i | ||||
\(37\) | −5.91978 | − | 4.30097i | −0.973206 | − | 0.707076i | −0.0170260 | − | 0.999855i | \(-0.505420\pi\) |
−0.956180 | + | 0.292780i | \(0.905420\pi\) | |||||||
\(38\) | −0.907538 | − | 2.79311i | −0.147222 | − | 0.453103i | ||||
\(39\) | −0.391171 | − | 1.20390i | −0.0626375 | − | 0.192778i | ||||
\(40\) | 3.21911 | + | 2.33882i | 0.508985 | + | 0.369799i | ||||
\(41\) | −1.43255 | + | 1.04081i | −0.223727 | + | 0.162547i | −0.694003 | − | 0.719972i | \(-0.744154\pi\) |
0.470276 | + | 0.882520i | \(0.344154\pi\) | |||||||
\(42\) | −2.34494 | + | 7.21698i | −0.361832 | + | 1.11360i | ||||
\(43\) | −11.4084 | −1.73977 | −0.869884 | − | 0.493257i | \(-0.835806\pi\) | ||||
−0.869884 | + | 0.493257i | \(0.835806\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.17209 | −0.323797 | ||||||||
\(46\) | 3.81933 | − | 11.7547i | 0.563129 | − | 1.73313i | ||||
\(47\) | −0.827289 | + | 0.601061i | −0.120672 | + | 0.0876737i | −0.646485 | − | 0.762927i | \(-0.723762\pi\) |
0.525812 | + | 0.850601i | \(0.323762\pi\) | |||||||
\(48\) | 30.7788 | + | 22.3621i | 4.44253 | + | 3.22769i | ||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | −4.01120 | − | 12.3452i | −0.567269 | − | 1.74587i | ||||
\(51\) | 10.9719 | + | 7.97156i | 1.53637 | + | 1.11624i | ||||
\(52\) | −1.93616 | + | 1.40670i | −0.268497 | + | 0.195074i | ||||
\(53\) | −1.10388 | + | 3.39738i | −0.151629 | + | 0.466666i | −0.997804 | − | 0.0662394i | \(-0.978900\pi\) |
0.846175 | + | 0.532906i | \(0.178900\pi\) | |||||||
\(54\) | −14.2686 | −1.94171 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.94020 | 1.19468 | ||||||||
\(57\) | 0.942452 | − | 2.90057i | 0.124831 | − | 0.384190i | ||||
\(58\) | 4.33956 | − | 3.15287i | 0.569812 | − | 0.413993i | ||||
\(59\) | 11.6495 | + | 8.46386i | 1.51664 | + | 1.10190i | 0.963123 | + | 0.269061i | \(0.0867133\pi\) |
0.553514 | + | 0.832840i | \(0.313287\pi\) | |||||||
\(60\) | 2.04907 | + | 6.30638i | 0.264533 | + | 0.814150i | ||||
\(61\) | 1.52335 | + | 4.68837i | 0.195044 | + | 0.600285i | 0.999976 | + | 0.00691741i | \(0.00220190\pi\) |
−0.804932 | + | 0.593367i | \(0.797798\pi\) | |||||||
\(62\) | −18.0610 | − | 13.1221i | −2.29375 | − | 1.66651i | ||||
\(63\) | −3.94826 | + | 2.86858i | −0.497434 | + | 0.361407i | ||||
\(64\) | 7.29061 | − | 22.4382i | 0.911326 | − | 2.80477i | ||||
\(65\) | −0.200698 | −0.0248935 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.18858 | −0.756055 | −0.378028 | − | 0.925794i | \(-0.623398\pi\) | ||||
−0.378028 | + | 0.925794i | \(0.623398\pi\) | |||||||
\(68\) | 7.92330 | − | 24.3854i | 0.960841 | − | 2.95717i | ||||
\(69\) | 10.3838 | − | 7.54427i | 1.25006 | − | 0.908224i | ||||
\(70\) | 0.973343 | + | 0.707175i | 0.116337 | + | 0.0845236i | ||||
\(71\) | −1.82989 | − | 5.63182i | −0.217168 | − | 0.668375i | −0.998993 | − | 0.0448760i | \(-0.985711\pi\) |
0.781825 | − | 0.623499i | \(-0.214289\pi\) | |||||||
\(72\) | 13.4827 | + | 41.4956i | 1.58895 | + | 4.89030i | ||||
\(73\) | 1.34116 | + | 0.974409i | 0.156971 | + | 0.114046i | 0.663498 | − | 0.748178i | \(-0.269071\pi\) |
−0.506527 | + | 0.862224i | \(0.669071\pi\) | |||||||
\(74\) | −16.0023 | + | 11.6264i | −1.86023 | + | 1.35154i | ||||
\(75\) | 4.16551 | − | 12.8201i | 0.480992 | − | 1.48034i | ||||
\(76\) | −5.76602 | −0.661407 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.42186 | −0.387449 | ||||||||
\(79\) | −1.11504 | + | 3.43173i | −0.125451 | + | 0.386099i | −0.993983 | − | 0.109534i | \(-0.965064\pi\) |
0.868532 | + | 0.495634i | \(0.165064\pi\) | |||||||
\(80\) | 4.87989 | − | 3.54545i | 0.545588 | − | 0.396393i | ||||
\(81\) | −0.142838 | − | 0.103778i | −0.0158709 | − | 0.0115309i | ||||
\(82\) | 1.47915 | + | 4.55236i | 0.163345 | + | 0.502724i | ||||
\(83\) | −3.33888 | − | 10.2760i | −0.366489 | − | 1.12794i | −0.949043 | − | 0.315146i | \(-0.897947\pi\) |
0.582554 | − | 0.812792i | \(-0.302053\pi\) | |||||||
\(84\) | 12.0532 | + | 8.75713i | 1.31511 | + | 0.955481i | ||||
\(85\) | 1.73957 | − | 1.26387i | 0.188682 | − | 0.137086i | ||||
\(86\) | −9.52984 | + | 29.3298i | −1.02763 | + | 3.16272i | ||||
\(87\) | 5.57035 | 0.597204 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.21170 | −0.552439 | −0.276220 | − | 0.961095i | \(-0.589082\pi\) | ||||
−0.276220 | + | 0.961095i | \(0.589082\pi\) | |||||||
\(90\) | −1.81442 | + | 5.58422i | −0.191257 | + | 0.588629i | ||||
\(91\) | −0.364813 | + | 0.265052i | −0.0382428 | + | 0.0277850i | ||||
\(92\) | −19.6316 | − | 14.2632i | −2.04674 | − | 1.48704i | ||||
\(93\) | −7.16409 | − | 22.0488i | −0.742882 | − | 2.28635i | ||||
\(94\) | 0.854200 | + | 2.62896i | 0.0881040 | + | 0.271156i | ||||
\(95\) | −0.391195 | − | 0.284220i | −0.0401357 | − | 0.0291603i | ||||
\(96\) | 42.5935 | − | 30.9460i | 4.34718 | − | 3.15841i | ||||
\(97\) | −1.64083 | + | 5.04996i | −0.166601 | + | 0.512746i | −0.999151 | − | 0.0412047i | \(-0.986880\pi\) |
0.832549 | + | 0.553951i | \(0.186880\pi\) | |||||||
\(98\) | 2.70320 | 0.273064 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −25.4850 | −2.54850 | ||||||||
\(101\) | 4.80842 | − | 14.7988i | 0.478456 | − | 1.47254i | −0.362783 | − | 0.931873i | \(-0.618174\pi\) |
0.841239 | − | 0.540663i | \(-0.181826\pi\) | |||||||
\(102\) | 29.6592 | − | 21.5487i | 2.93670 | − | 2.13364i | ||||
\(103\) | 11.4649 | + | 8.32970i | 1.12967 | + | 0.820750i | 0.985646 | − | 0.168825i | \(-0.0539972\pi\) |
0.144019 | + | 0.989575i | \(0.453997\pi\) | |||||||
\(104\) | 1.24578 | + | 3.83412i | 0.122159 | + | 0.375966i | ||||
\(105\) | 0.386087 | + | 1.18825i | 0.0376782 | + | 0.115962i | ||||
\(106\) | 7.81220 | + | 5.67589i | 0.758787 | + | 0.551291i | ||||
\(107\) | 9.51009 | − | 6.90949i | 0.919375 | − | 0.667965i | −0.0239932 | − | 0.999712i | \(-0.507638\pi\) |
0.943368 | + | 0.331747i | \(0.107638\pi\) | |||||||
\(108\) | −8.65679 | + | 26.6429i | −0.833000 | + | 2.56371i | ||||
\(109\) | 15.7800 | 1.51145 | 0.755723 | − | 0.654891i | \(-0.227286\pi\) | ||||
0.755723 | + | 0.654891i | \(0.227286\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.5409 | −1.94966 | ||||||||
\(112\) | 4.18797 | − | 12.8893i | 0.395726 | − | 1.21792i | ||||
\(113\) | 4.79219 | − | 3.48173i | 0.450811 | − | 0.327534i | −0.339105 | − | 0.940749i | \(-0.610124\pi\) |
0.789916 | + | 0.613215i | \(0.210124\pi\) | |||||||
\(114\) | −6.66979 | − | 4.84588i | −0.624683 | − | 0.453859i | ||||
\(115\) | −0.628839 | − | 1.93537i | −0.0586396 | − | 0.180474i | ||||
\(116\) | −3.25435 | − | 10.0158i | −0.302158 | − | 0.929948i | ||||
\(117\) | −1.78040 | − | 1.29354i | −0.164598 | − | 0.119588i | ||||
\(118\) | 31.4909 | − | 22.8795i | 2.89897 | − | 2.10623i | ||||
\(119\) | 1.49291 | − | 4.59472i | 0.136855 | − | 0.421197i | ||||
\(120\) | 11.1699 | 1.01967 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 13.3258 | 1.20646 | ||||||||
\(123\) | −1.53606 | + | 4.72749i | −0.138501 | + | 0.426264i | ||||
\(124\) | −35.4597 | + | 25.7630i | −3.18438 | + | 2.31359i | ||||
\(125\) | −3.52938 | − | 2.56425i | −0.315678 | − | 0.229353i | ||||
\(126\) | 4.07669 | + | 12.5468i | 0.363181 | + | 1.11776i | ||||
\(127\) | 3.13149 | + | 9.63774i | 0.277875 | + | 0.855211i | 0.988444 | + | 0.151584i | \(0.0484374\pi\) |
−0.710569 | + | 0.703627i | \(0.751563\pi\) | |||||||
\(128\) | −21.2501 | − | 15.4391i | −1.87826 | − | 1.36464i | ||||
\(129\) | −25.9093 | + | 18.8242i | −2.28118 | + | 1.65738i | ||||
\(130\) | −0.167650 | + | 0.515973i | −0.0147038 | + | 0.0452538i | ||||
\(131\) | −6.83340 | −0.597037 | −0.298519 | − | 0.954404i | \(-0.596492\pi\) | ||||
−0.298519 | + | 0.954404i | \(0.596492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.08644 | −0.0942061 | ||||||||
\(134\) | −5.16953 | + | 15.9102i | −0.446579 | + | 1.37443i | ||||
\(135\) | −1.90060 | + | 1.38087i | −0.163578 | + | 0.118846i | ||||
\(136\) | −34.9428 | − | 25.3874i | −2.99632 | − | 2.17695i | ||||
\(137\) | 4.47064 | + | 13.7592i | 0.381952 | + | 1.17553i | 0.938667 | + | 0.344825i | \(0.112062\pi\) |
−0.556715 | + | 0.830704i | \(0.687938\pi\) | |||||||
\(138\) | −10.7216 | − | 32.9976i | −0.912681 | − | 2.80894i | ||||
\(139\) | 11.8890 | + | 8.63790i | 1.00842 | + | 0.732657i | 0.963876 | − | 0.266351i | \(-0.0858180\pi\) |
0.0445393 | + | 0.999008i | \(0.485818\pi\) | |||||||
\(140\) | 1.91099 | − | 1.38842i | 0.161508 | − | 0.117343i | ||||
\(141\) | −0.887062 | + | 2.73010i | −0.0747041 | + | 0.229915i | ||||
\(142\) | −16.0074 | −1.34331 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 66.1409 | 5.51174 | ||||||||
\(145\) | 0.272912 | − | 0.839938i | 0.0226641 | − | 0.0697531i | ||||
\(146\) | 3.62542 | − | 2.63402i | 0.300042 | − | 0.217993i | ||||
\(147\) | 2.27106 | + | 1.65003i | 0.187314 | + | 0.136092i | ||||
\(148\) | 12.0006 | + | 36.9339i | 0.986440 | + | 3.03595i | ||||
\(149\) | 0.309449 | + | 0.952386i | 0.0253510 | + | 0.0780225i | 0.962932 | − | 0.269746i | \(-0.0869396\pi\) |
−0.937581 | + | 0.347768i | \(0.886940\pi\) | |||||||
\(150\) | −29.4796 | − | 21.4182i | −2.40700 | − | 1.74879i | ||||
\(151\) | −1.11271 | + | 0.808431i | −0.0905511 | + | 0.0657892i | −0.632140 | − | 0.774855i | \(-0.717823\pi\) |
0.541589 | + | 0.840644i | \(0.317823\pi\) | |||||||
\(152\) | −3.00147 | + | 9.23758i | −0.243451 | + | 0.749267i | ||||
\(153\) | 23.5777 | 1.90614 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.67568 | −0.295237 | ||||||||
\(156\) | −2.07605 | + | 6.38942i | −0.166217 | + | 0.511563i | ||||
\(157\) | −4.34983 | + | 3.16034i | −0.347154 | + | 0.252222i | −0.747674 | − | 0.664066i | \(-0.768829\pi\) |
0.400520 | + | 0.916288i | \(0.368829\pi\) | |||||||
\(158\) | 7.89117 | + | 5.73327i | 0.627788 | + | 0.456115i | ||||
\(159\) | 3.09879 | + | 9.53710i | 0.245750 | + | 0.756341i | ||||
\(160\) | −2.57945 | − | 7.93872i | −0.203923 | − | 0.627611i | ||||
\(161\) | −3.69900 | − | 2.68748i | −0.291522 | − | 0.211803i | ||||
\(162\) | −0.386120 | + | 0.280532i | −0.0303364 | + | 0.0220407i | ||||
\(163\) | −2.91252 | + | 8.96383i | −0.228127 | + | 0.702101i | 0.769833 | + | 0.638246i | \(0.220340\pi\) |
−0.997959 | + | 0.0638555i | \(0.979660\pi\) | |||||||
\(164\) | 9.39775 | 0.733841 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −29.2076 | −2.26695 | ||||||||
\(167\) | 6.18400 | − | 19.0324i | 0.478532 | − | 1.47277i | −0.362602 | − | 0.931944i | \(-0.618112\pi\) |
0.841134 | − | 0.540826i | \(-0.181888\pi\) | |||||||
\(168\) | 20.3038 | − | 14.7516i | 1.56647 | − | 1.13811i | ||||
\(169\) | 10.3527 | + | 7.52169i | 0.796363 | + | 0.578591i | ||||
\(170\) | −1.79615 | − | 5.52799i | −0.137759 | − | 0.423977i | ||||
\(171\) | −1.63846 | − | 5.04266i | −0.125296 | − | 0.385622i | ||||
\(172\) | 48.9840 | + | 35.5890i | 3.73499 | + | 2.71363i | ||||
\(173\) | −8.77504 | + | 6.37544i | −0.667154 | + | 0.484716i | −0.869071 | − | 0.494687i | \(-0.835283\pi\) |
0.201917 | + | 0.979403i | \(0.435283\pi\) | |||||||
\(174\) | 4.65310 | − | 14.3208i | 0.352750 | − | 1.08565i | ||||
\(175\) | −4.80191 | −0.362990 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 40.4224 | 3.03833 | ||||||||
\(178\) | −4.35351 | + | 13.3987i | −0.326309 | + | 1.00428i | ||||
\(179\) | −13.6306 | + | 9.90324i | −1.01880 | + | 0.740203i | −0.966037 | − | 0.258404i | \(-0.916803\pi\) |
−0.0527648 | + | 0.998607i | \(0.516803\pi\) | |||||||
\(180\) | 9.32626 | + | 6.77592i | 0.695138 | + | 0.505048i | ||||
\(181\) | −6.27432 | − | 19.3104i | −0.466367 | − | 1.43533i | −0.857256 | − | 0.514891i | \(-0.827832\pi\) |
0.390889 | − | 0.920438i | \(-0.372168\pi\) | |||||||
\(182\) | 0.376680 | + | 1.15930i | 0.0279214 | + | 0.0859331i | ||||
\(183\) | 11.1956 | + | 8.13405i | 0.827599 | + | 0.601286i | ||||
\(184\) | −33.0698 | + | 24.0266i | −2.43794 | + | 1.77127i | ||||
\(185\) | −1.00638 | + | 3.09731i | −0.0739903 | + | 0.227719i | ||||
\(186\) | −62.6695 | −4.59515 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.42714 | 0.395815 | ||||||||
\(189\) | −1.63112 | + | 5.02007i | −0.118647 | + | 0.365156i | ||||
\(190\) | −1.05748 | + | 0.768301i | −0.0767174 | + | 0.0557384i | ||||
\(191\) | −2.05842 | − | 1.49553i | −0.148942 | − | 0.108213i | 0.510819 | − | 0.859689i | \(-0.329342\pi\) |
−0.659761 | + | 0.751476i | \(0.729342\pi\) | |||||||
\(192\) | −20.4661 | − | 62.9883i | −1.47702 | − | 4.54579i | ||||
\(193\) | 5.41045 | + | 16.6517i | 0.389453 | + | 1.19861i | 0.933198 | + | 0.359363i | \(0.117006\pi\) |
−0.543745 | + | 0.839250i | \(0.682994\pi\) | |||||||
\(194\) | 11.6123 | + | 8.43681i | 0.833712 | + | 0.605727i | ||||
\(195\) | −0.455798 | + | 0.331157i | −0.0326404 | + | 0.0237146i | ||||
\(196\) | 1.64004 | − | 5.04751i | 0.117145 | − | 0.360537i | ||||
\(197\) | −2.16558 | −0.154291 | −0.0771457 | − | 0.997020i | \(-0.524581\pi\) | ||||
−0.0771457 | + | 0.997020i | \(0.524581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.5756 | −1.03324 | −0.516620 | − | 0.856215i | \(-0.672810\pi\) | ||||
−0.516620 | + | 0.856215i | \(0.672810\pi\) | |||||||
\(200\) | −13.2661 | + | 40.8289i | −0.938055 | + | 2.88704i | ||||
\(201\) | −14.0547 | + | 10.2113i | −0.991339 | + | 0.720250i | ||||
\(202\) | −34.0295 | − | 24.7239i | −2.39431 | − | 1.73957i | ||||
\(203\) | −0.613187 | − | 1.88719i | −0.0430373 | − | 0.132455i | ||||
\(204\) | −22.2422 | − | 68.4545i | −1.55727 | − | 4.79277i | ||||
\(205\) | 0.637589 | + | 0.463235i | 0.0445311 | + | 0.0323538i | ||||
\(206\) | 30.9917 | − | 22.5168i | 2.15930 | − | 1.56882i | ||||
\(207\) | 6.89537 | − | 21.2218i | 0.479261 | − | 1.47501i | ||||
\(208\) | 6.11130 | 0.423743 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.37738 | 0.233061 | ||||||||
\(211\) | −1.12184 | + | 3.45266i | −0.0772304 | + | 0.237691i | −0.982217 | − | 0.187749i | \(-0.939881\pi\) |
0.904987 | + | 0.425440i | \(0.139881\pi\) | |||||||
\(212\) | 15.3379 | − | 11.1437i | 1.05341 | − | 0.765349i | ||||
\(213\) | −13.4485 | − | 9.77087i | −0.921473 | − | 0.669489i | ||||
\(214\) | −9.81945 | − | 30.2211i | −0.671243 | − | 2.06587i | ||||
\(215\) | 1.56906 | + | 4.82906i | 0.107009 | + | 0.329339i | ||||
\(216\) | 38.1776 | + | 27.7376i | 2.59765 | + | 1.88731i | ||||
\(217\) | −6.68135 | + | 4.85429i | −0.453560 | + | 0.329530i | ||||
\(218\) | 13.1815 | − | 40.5686i | 0.892766 | − | 2.74765i | ||||
\(219\) | 4.65366 | 0.314465 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.17854 | 0.146544 | ||||||||
\(222\) | −17.1585 | + | 52.8085i | −1.15160 | + | 3.54427i | ||||
\(223\) | 3.91614 | − | 2.84524i | 0.262244 | − | 0.190532i | −0.448892 | − | 0.893586i | \(-0.648181\pi\) |
0.711136 | + | 0.703055i | \(0.248181\pi\) | |||||||
\(224\) | −15.1730 | − | 11.0238i | −1.01379 | − | 0.736560i | ||||
\(225\) | −7.24177 | − | 22.2879i | −0.482785 | − | 1.48586i | ||||
\(226\) | −4.94808 | − | 15.2286i | −0.329141 | − | 1.01299i | ||||
\(227\) | −18.3895 | − | 13.3607i | −1.22055 | − | 0.886782i | −0.224405 | − | 0.974496i | \(-0.572044\pi\) |
−0.996146 | + | 0.0877139i | \(0.972044\pi\) | |||||||
\(228\) | −13.0950 | + | 9.51407i | −0.867237 | + | 0.630085i | ||||
\(229\) | −7.00639 | + | 21.5635i | −0.462995 | + | 1.42495i | 0.398491 | + | 0.917172i | \(0.369534\pi\) |
−0.861486 | + | 0.507781i | \(0.830466\pi\) | |||||||
\(230\) | −5.50092 | −0.362720 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.7402 | −1.16470 | ||||||||
\(233\) | −0.181480 | + | 0.558539i | −0.0118892 | + | 0.0365911i | −0.956825 | − | 0.290664i | \(-0.906124\pi\) |
0.944936 | + | 0.327255i | \(0.106124\pi\) | |||||||
\(234\) | −4.81278 | + | 3.49669i | −0.314621 | + | 0.228586i | ||||
\(235\) | 0.368203 | + | 0.267515i | 0.0240189 | + | 0.0174508i | ||||
\(236\) | −23.6158 | − | 72.6821i | −1.53726 | − | 4.73120i | ||||
\(237\) | 3.13012 | + | 9.63351i | 0.203323 | + | 0.625764i | ||||
\(238\) | −10.5654 | − | 7.67625i | −0.684856 | − | 0.497577i | ||||
\(239\) | 12.1127 | − | 8.80039i | 0.783505 | − | 0.569250i | −0.122524 | − | 0.992466i | \(-0.539099\pi\) |
0.906029 | + | 0.423216i | \(0.139099\pi\) | |||||||
\(240\) | 5.23247 | − | 16.1039i | 0.337754 | − | 1.03950i | ||||
\(241\) | −18.2746 | −1.17717 | −0.588586 | − | 0.808435i | \(-0.700315\pi\) | ||||
−0.588586 | + | 0.808435i | \(0.700315\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3396 | 0.984037 | ||||||||
\(244\) | 8.08480 | − | 24.8825i | 0.517577 | − | 1.59294i | ||||
\(245\) | 0.360071 | − | 0.261607i | 0.0230041 | − | 0.0167135i | ||||
\(246\) | 10.8708 | + | 7.89807i | 0.693094 | + | 0.503562i | ||||
\(247\) | −0.151391 | − | 0.465933i | −0.00963276 | − | 0.0296466i | ||||
\(248\) | 22.8158 | + | 70.2199i | 1.44881 | + | 4.45897i | ||||
\(249\) | −24.5385 | − | 17.8282i | −1.55506 | − | 1.12982i | ||||
\(250\) | −9.54062 | + | 6.93166i | −0.603402 | + | 0.438397i | ||||
\(251\) | 3.26473 | − | 10.0478i | 0.206068 | − | 0.634212i | −0.793600 | − | 0.608440i | \(-0.791796\pi\) |
0.999668 | − | 0.0257719i | \(-0.00820435\pi\) | |||||||
\(252\) | 25.9012 | 1.63162 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 27.3934 | 1.71882 | ||||||||
\(255\) | 1.86525 | − | 5.74065i | 0.116807 | − | 0.359494i | ||||
\(256\) | −19.2690 | + | 13.9998i | −1.20431 | + | 0.874986i | ||||
\(257\) | 15.7499 | + | 11.4430i | 0.982453 | + | 0.713794i | 0.958255 | − | 0.285913i | \(-0.0922969\pi\) |
0.0241975 | + | 0.999707i | \(0.492297\pi\) | |||||||
\(258\) | 26.7521 | + | 82.3344i | 1.66551 | + | 5.12592i | ||||
\(259\) | 2.26116 | + | 6.95912i | 0.140501 | + | 0.432419i | ||||
\(260\) | 0.861731 | + | 0.626084i | 0.0534423 | + | 0.0388281i | ||||
\(261\) | 7.83459 | − | 5.69216i | 0.484949 | − | 0.352336i | ||||
\(262\) | −5.70817 | + | 17.5679i | −0.352652 | + | 1.08535i | ||||
\(263\) | 21.1885 | 1.30654 | 0.653269 | − | 0.757126i | \(-0.273397\pi\) | ||||
0.653269 | + | 0.757126i | \(0.273397\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.58989 | 0.0976665 | ||||||||
\(266\) | −0.907538 | + | 2.79311i | −0.0556447 | + | 0.171257i | ||||
\(267\) | −11.8361 | + | 8.59944i | −0.724358 | + | 0.526277i | ||||
\(268\) | 26.5717 | + | 19.3055i | 1.62313 | + | 1.17927i | ||||
\(269\) | 7.15572 | + | 22.0230i | 0.436292 | + | 1.34277i | 0.891757 | + | 0.452515i | \(0.149473\pi\) |
−0.455465 | + | 0.890254i | \(0.650527\pi\) | |||||||
\(270\) | 1.96243 | + | 6.03974i | 0.119430 | + | 0.367567i | ||||
\(271\) | −21.7004 | − | 15.7663i | −1.31821 | − | 0.957733i | −0.999953 | − | 0.00972711i | \(-0.996904\pi\) |
−0.318253 | − | 0.948006i | \(-0.603096\pi\) | |||||||
\(272\) | −52.9702 | + | 38.4851i | −3.21179 | + | 2.33350i | ||||
\(273\) | −0.391171 | + | 1.20390i | −0.0236747 | + | 0.0728633i | ||||
\(274\) | 39.1079 | 2.36260 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −68.1193 | −4.10030 | ||||||||
\(277\) | −4.34193 | + | 13.3631i | −0.260881 | + | 0.802910i | 0.731732 | + | 0.681592i | \(0.238712\pi\) |
−0.992614 | + | 0.121318i | \(0.961288\pi\) | |||||||
\(278\) | 32.1384 | − | 23.3499i | 1.92753 | − | 1.40044i | ||||
\(279\) | −32.6071 | − | 23.6905i | −1.95214 | − | 1.41831i | ||||
\(280\) | −1.22959 | − | 3.78429i | −0.0734820 | − | 0.226154i | ||||
\(281\) | −0.539351 | − | 1.65995i | −0.0321750 | − | 0.0990244i | 0.933679 | − | 0.358110i | \(-0.116579\pi\) |
−0.965854 | + | 0.259086i | \(0.916579\pi\) | |||||||
\(282\) | 6.27779 | + | 4.56108i | 0.373837 | + | 0.271608i | ||||
\(283\) | 3.77431 | − | 2.74220i | 0.224360 | − | 0.163007i | −0.469927 | − | 0.882705i | \(-0.655720\pi\) |
0.694287 | + | 0.719698i | \(0.255720\pi\) | |||||||
\(284\) | −9.71172 | + | 29.8896i | −0.576285 | + | 1.77362i | ||||
\(285\) | −1.35740 | −0.0804053 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.77073 | 0.104523 | ||||||||
\(288\) | 28.2842 | − | 87.0499i | 1.66666 | − | 5.12946i | ||||
\(289\) | −5.12936 | + | 3.72670i | −0.301727 | + | 0.219218i | ||||
\(290\) | −1.93142 | − | 1.40326i | −0.113417 | − | 0.0824021i | ||||
\(291\) | 4.60613 | + | 14.1762i | 0.270016 | + | 0.831024i | ||||
\(292\) | −2.71879 | − | 8.36758i | −0.159105 | − | 0.489676i | ||||
\(293\) | −11.7382 | − | 8.52830i | −0.685753 | − | 0.498229i | 0.189508 | − | 0.981879i | \(-0.439311\pi\) |
−0.875261 | + | 0.483650i | \(0.839311\pi\) | |||||||
\(294\) | 6.13913 | − | 4.46034i | 0.358042 | − | 0.260132i | ||||
\(295\) | 1.98045 | − | 6.09518i | 0.115306 | − | 0.354875i | ||||
\(296\) | 65.4177 | 3.80232 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.70698 | 0.156811 | ||||||||
\(299\) | 0.637120 | − | 1.96085i | 0.0368456 | − | 0.113399i | ||||
\(300\) | −57.8782 | + | 42.0509i | −3.34160 | + | 2.42781i | ||||
\(301\) | 9.22961 | + | 6.70570i | 0.531986 | + | 0.386510i | ||||
\(302\) | 1.14891 | + | 3.53597i | 0.0661121 | + | 0.203472i | ||||
\(303\) | −13.4982 | − | 41.5431i | −0.775449 | − | 2.38659i | ||||
\(304\) | 11.9120 | + | 8.65456i | 0.683199 | + | 0.496373i | ||||
\(305\) | 1.77502 | − | 1.28963i | 0.101638 | − | 0.0738440i | ||||
\(306\) | 19.6952 | − | 60.6157i | 1.12590 | − | 3.46517i | ||||
\(307\) | 2.35679 | 0.134509 | 0.0672547 | − | 0.997736i | \(-0.478576\pi\) | ||||
0.0672547 | + | 0.997736i | \(0.478576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 39.7816 | 2.26310 | ||||||||
\(310\) | −3.07042 | + | 9.44977i | −0.174388 | + | 0.536711i | ||||
\(311\) | 16.1844 | − | 11.7586i | 0.917732 | − | 0.666772i | −0.0252262 | − | 0.999682i | \(-0.508031\pi\) |
0.942959 | + | 0.332910i | \(0.108031\pi\) | |||||||
\(312\) | 9.15564 | + | 6.65196i | 0.518336 | + | 0.376593i | ||||
\(313\) | 5.79501 | + | 17.8352i | 0.327553 | + | 1.00811i | 0.970275 | + | 0.242005i | \(0.0778052\pi\) |
−0.642722 | + | 0.766100i | \(0.722195\pi\) | |||||||
\(314\) | 4.49133 | + | 13.8229i | 0.253460 | + | 0.780070i | ||||
\(315\) | 1.75726 | + | 1.27673i | 0.0990105 | + | 0.0719353i | ||||
\(316\) | 15.4930 | − | 11.2563i | 0.871549 | − | 0.633217i | ||||
\(317\) | 1.29850 | − | 3.99637i | 0.0729309 | − | 0.224458i | −0.907946 | − | 0.419087i | \(-0.862350\pi\) |
0.980877 | + | 0.194629i | \(0.0623502\pi\) | |||||||
\(318\) | 27.1074 | 1.52011 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −10.5005 | −0.586999 | ||||||||
\(321\) | 10.1972 | − | 31.3838i | 0.569153 | − | 1.75167i | ||||
\(322\) | −9.99913 | + | 7.26479i | −0.557230 | + | 0.404851i | ||||
\(323\) | 4.24634 | + | 3.08515i | 0.236273 | + | 0.171662i | ||||
\(324\) | 0.289561 | + | 0.891177i | 0.0160867 | + | 0.0495098i | ||||
\(325\) | −0.669127 | − | 2.05936i | −0.0371165 | − | 0.114233i | ||||
\(326\) | 20.6121 | + | 14.9756i | 1.14160 | + | 0.829420i | ||||
\(327\) | 35.8373 | − | 26.0373i | 1.98181 | − | 1.43987i | ||||
\(328\) | 4.89195 | − | 15.0559i | 0.270113 | − | 0.831322i | ||||
\(329\) | 1.02259 | 0.0563770 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.0682694 | −0.00375242 | −0.00187621 | − | 0.999998i | \(-0.500597\pi\) | ||||
−0.00187621 | + | 0.999998i | \(0.500597\pi\) | |||||||
\(332\) | −17.7203 | + | 54.5375i | −0.972529 | + | 2.99314i | ||||
\(333\) | −28.8904 | + | 20.9901i | −1.58319 | + | 1.15025i | ||||
\(334\) | −43.7645 | − | 31.7968i | −2.39469 | − | 1.73984i | ||||
\(335\) | 0.851145 | + | 2.61956i | 0.0465030 | + | 0.143122i | ||||
\(336\) | −11.7564 | − | 36.1826i | −0.641366 | − | 1.97392i | ||||
\(337\) | −17.5930 | − | 12.7821i | −0.958351 | − | 0.696283i | −0.00558394 | − | 0.999984i | \(-0.501777\pi\) |
−0.952767 | + | 0.303702i | \(0.901777\pi\) | |||||||
\(338\) | 27.9854 | − | 20.3326i | 1.52221 | − | 1.10595i | ||||
\(339\) | 5.13843 | − | 15.8145i | 0.279081 | − | 0.858924i | ||||
\(340\) | −11.4118 | −0.618892 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −14.3328 | −0.775028 | ||||||||
\(343\) | 0.309017 | − | 0.951057i | 0.0166853 | − | 0.0513522i | ||||
\(344\) | 82.5145 | − | 59.9503i | 4.44888 | − | 3.23230i | ||||
\(345\) | −4.62154 | − | 3.35775i | −0.248815 | − | 0.180775i | ||||
\(346\) | 9.06048 | + | 27.8853i | 0.487094 | + | 1.49912i | ||||
\(347\) | 7.39635 | + | 22.7636i | 0.397057 | + | 1.22202i | 0.927348 | + | 0.374200i | \(0.122083\pi\) |
−0.530291 | + | 0.847816i | \(0.677917\pi\) | |||||||
\(348\) | −23.9172 | − | 17.3769i | −1.28210 | − | 0.931499i | ||||
\(349\) | 21.3702 | − | 15.5264i | 1.14392 | − | 0.831108i | 0.156262 | − | 0.987716i | \(-0.450056\pi\) |
0.987661 | + | 0.156607i | \(0.0500557\pi\) | |||||||
\(350\) | −4.01120 | + | 12.3452i | −0.214407 | + | 0.659878i | ||||
\(351\) | −2.38021 | −0.127046 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.44182 | −0.236414 | −0.118207 | − | 0.992989i | \(-0.537715\pi\) | ||||
−0.118207 | + | 0.992989i | \(0.537715\pi\) | |||||||
\(354\) | 33.7662 | − | 103.922i | 1.79465 | − | 5.52337i | ||||
\(355\) | −2.13221 | + | 1.54914i | −0.113166 | + | 0.0822201i | ||||
\(356\) | 22.3773 | + | 16.2581i | 1.18600 | + | 0.861677i | ||||
\(357\) | −4.19090 | − | 12.8983i | −0.221806 | − | 0.682648i | ||||
\(358\) | 14.0740 | + | 43.3154i | 0.743836 | + | 2.28929i | ||||
\(359\) | 11.7571 | + | 8.54200i | 0.620514 | + | 0.450830i | 0.853101 | − | 0.521746i | \(-0.174719\pi\) |
−0.232587 | + | 0.972576i | \(0.574719\pi\) | |||||||
\(360\) | 15.7103 | − | 11.4142i | 0.828004 | − | 0.601580i | ||||
\(361\) | −5.50658 | + | 16.9475i | −0.289820 | + | 0.891974i | ||||
\(362\) | −54.8860 | −2.88475 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.39322 | 0.125439 | ||||||||
\(365\) | 0.228000 | − | 0.701713i | 0.0119341 | − | 0.0367293i | ||||
\(366\) | 30.2638 | − | 21.9879i | 1.58191 | − | 1.14933i | ||||
\(367\) | −4.03019 | − | 2.92810i | −0.210374 | − | 0.152846i | 0.477609 | − | 0.878573i | \(-0.341504\pi\) |
−0.687983 | + | 0.725727i | \(0.741504\pi\) | |||||||
\(368\) | 19.1483 | + | 58.9325i | 0.998175 | + | 3.07207i | ||||
\(369\) | 2.67044 | + | 8.21878i | 0.139018 | + | 0.427852i | ||||
\(370\) | 7.12219 | + | 5.17458i | 0.370265 | + | 0.269013i | ||||
\(371\) | 2.88998 | − | 2.09970i | 0.150041 | − | 0.109011i | ||||
\(372\) | −38.0218 | + | 117.019i | −1.97134 | + | 6.06715i | ||||
\(373\) | −13.6638 | −0.707485 | −0.353743 | − | 0.935343i | \(-0.615091\pi\) | ||||
−0.353743 | + | 0.935343i | \(0.615091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.2465 | −0.632408 | ||||||||
\(376\) | 2.82507 | − | 8.69467i | 0.145692 | − | 0.448393i | ||||
\(377\) | 0.723903 | − | 0.525946i | 0.0372829 | − | 0.0270876i | ||||
\(378\) | 11.5435 | + | 8.38687i | 0.593735 | + | 0.431374i | ||||
\(379\) | −2.58410 | − | 7.95304i | −0.132736 | − | 0.408520i | 0.862495 | − | 0.506066i | \(-0.168901\pi\) |
−0.995231 | + | 0.0975457i | \(0.968901\pi\) | |||||||
\(380\) | 0.793028 | + | 2.44069i | 0.0406815 | + | 0.125205i | ||||
\(381\) | 23.0143 | + | 16.7209i | 1.17906 | + | 0.856637i | ||||
\(382\) | −5.56431 | + | 4.04271i | −0.284695 | + | 0.206843i | ||||
\(383\) | −0.613952 | + | 1.88955i | −0.0313715 | + | 0.0965514i | −0.965516 | − | 0.260343i | \(-0.916164\pi\) |
0.934145 | + | 0.356894i | \(0.116164\pi\) | |||||||
\(384\) | −73.7352 | −3.76278 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 47.3292 | 2.40899 | ||||||||
\(387\) | −17.2051 | + | 52.9517i | −0.874582 | + | 2.69169i | ||||
\(388\) | 22.7987 | − | 16.5642i | 1.15743 | − | 0.840922i | ||||
\(389\) | −11.9998 | − | 8.71834i | −0.608412 | − | 0.442037i | 0.240443 | − | 0.970663i | \(-0.422707\pi\) |
−0.848855 | + | 0.528626i | \(0.822707\pi\) | |||||||
\(390\) | 0.470625 | + | 1.44843i | 0.0238310 | + | 0.0733443i | ||||
\(391\) | 6.82593 | + | 21.0081i | 0.345202 | + | 1.06242i | ||||
\(392\) | −7.23277 | − | 5.25492i | −0.365310 | − | 0.265413i | ||||
\(393\) | −15.5191 | + | 11.2753i | −0.782835 | + | 0.568763i | ||||
\(394\) | −1.80898 | + | 5.56748i | −0.0911353 | + | 0.280486i | ||||
\(395\) | 1.60597 | 0.0808050 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.4630 | 0.575314 | 0.287657 | − | 0.957734i | \(-0.407124\pi\) | ||||
0.287657 | + | 0.957734i | \(0.407124\pi\) | |||||||
\(398\) | −12.1755 | + | 37.4724i | −0.610304 | + | 1.87832i | ||||
\(399\) | −2.46737 | + | 1.79265i | −0.123523 | + | 0.0897447i | ||||
\(400\) | 52.6494 | + | 38.2520i | 2.63247 | + | 1.91260i | ||||
\(401\) | 1.33195 | + | 4.09934i | 0.0665146 | + | 0.204711i | 0.978790 | − | 0.204867i | \(-0.0656761\pi\) |
−0.912275 | + | 0.409578i | \(0.865676\pi\) | |||||||
\(402\) | 14.5118 | + | 44.6629i | 0.723785 | + | 2.22758i | ||||
\(403\) | −3.01284 | − | 2.18896i | −0.150080 | − | 0.109040i | ||||
\(404\) | −66.8112 | + | 48.5412i | −3.32398 | + | 2.41501i | ||||
\(405\) | −0.0242828 | + | 0.0747349i | −0.00120662 | + | 0.00371361i | ||||
\(406\) | −5.36399 | −0.266210 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −121.247 | −6.00263 | ||||||||
\(409\) | −2.87757 | + | 8.85626i | −0.142287 | + | 0.437914i | −0.996652 | − | 0.0817591i | \(-0.973946\pi\) |
0.854365 | + | 0.519673i | \(0.173946\pi\) | |||||||
\(410\) | 1.72353 | − | 1.25222i | 0.0851190 | − | 0.0618426i | ||||
\(411\) | 32.8562 | + | 23.8714i | 1.62067 | + | 1.17749i | ||||
\(412\) | −23.2415 | − | 71.5300i | −1.14503 | − | 3.52403i | ||||
\(413\) | −4.44972 | − | 13.6948i | −0.218956 | − | 0.673878i | ||||
\(414\) | −48.7989 | − | 35.4545i | −2.39834 | − | 1.74249i | ||||
\(415\) | −3.89051 | + | 2.82662i | −0.190977 | + | 0.138753i | ||||
\(416\) | 2.61341 | − | 8.04326i | 0.128133 | − | 0.394353i | ||||
\(417\) | 41.2535 | 2.02019 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.3424 | −1.28691 | −0.643454 | − | 0.765485i | \(-0.722499\pi\) | ||||
−0.643454 | + | 0.765485i | \(0.722499\pi\) | |||||||
\(420\) | 2.04907 | − | 6.30638i | 0.0999842 | − | 0.307720i | ||||
\(421\) | −11.4712 | + | 8.33434i | −0.559074 | + | 0.406191i | −0.831120 | − | 0.556093i | \(-0.812300\pi\) |
0.272046 | + | 0.962284i | \(0.412300\pi\) | |||||||
\(422\) | 7.93930 | + | 5.76824i | 0.386479 | + | 0.280794i | ||||
\(423\) | 1.54216 | + | 4.74629i | 0.0749825 | + | 0.230772i | ||||
\(424\) | −9.86887 | − | 30.3733i | −0.479275 | − | 1.47506i | ||||
\(425\) | 18.7683 | + | 13.6360i | 0.910395 | + | 0.661441i | ||||
\(426\) | −36.3538 | + | 26.4126i | −1.76135 | + | 1.27969i | ||||
\(427\) | 1.52335 | − | 4.68837i | 0.0737198 | − | 0.226886i | ||||
\(428\) | −62.3876 | −3.01562 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.7257 | 0.661911 | ||||||||
\(431\) | 2.34708 | − | 7.22357i | 0.113055 | − | 0.347947i | −0.878482 | − | 0.477776i | \(-0.841443\pi\) |
0.991536 | + | 0.129829i | \(0.0414429\pi\) | |||||||
\(432\) | 57.8739 | − | 42.0478i | 2.78446 | − | 2.02303i | ||||
\(433\) | −18.1227 | − | 13.1669i | −0.870920 | − | 0.632760i | 0.0599138 | − | 0.998204i | \(-0.480917\pi\) |
−0.930834 | + | 0.365443i | \(0.880917\pi\) | |||||||
\(434\) | 6.89869 | + | 21.2320i | 0.331148 | + | 1.01917i | ||||
\(435\) | −0.766117 | − | 2.35787i | −0.0367325 | − | 0.113051i | ||||
\(436\) | −67.7540 | − | 49.2261i | −3.24483 | − | 2.35750i | ||||
\(437\) | 4.01873 | − | 2.91978i | 0.192242 | − | 0.139672i | ||||
\(438\) | 3.88736 | − | 11.9641i | 0.185745 | − | 0.571665i | ||||
\(439\) | 15.4051 | 0.735244 | 0.367622 | − | 0.929975i | \(-0.380172\pi\) | ||||
0.367622 | + | 0.929975i | \(0.380172\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.88032 | 0.232396 | ||||||||
\(442\) | 1.81980 | − | 5.60078i | 0.0865593 | − | 0.266402i | ||||
\(443\) | −17.1592 | + | 12.4669i | −0.815258 | + | 0.592319i | −0.915350 | − | 0.402659i | \(-0.868086\pi\) |
0.100092 | + | 0.994978i | \(0.468086\pi\) | |||||||
\(444\) | 88.1959 | + | 64.0781i | 4.18559 | + | 3.04101i | ||||
\(445\) | 0.716791 | + | 2.20606i | 0.0339791 | + | 0.104577i | ||||
\(446\) | −4.04353 | − | 12.4447i | −0.191467 | − | 0.589274i | ||||
\(447\) | 2.27424 | + | 1.65233i | 0.107568 | + | 0.0781526i | ||||
\(448\) | −19.0871 | + | 13.8676i | −0.901779 | + | 0.655181i | ||||
\(449\) | −3.59438 | + | 11.0623i | −0.169629 | + | 0.522065i | −0.999348 | − | 0.0361175i | \(-0.988501\pi\) |
0.829718 | + | 0.558182i | \(0.188501\pi\) | |||||||
\(450\) | −63.3490 | −2.98630 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −31.4375 | −1.47869 | ||||||||
\(453\) | −1.19311 | + | 3.67200i | −0.0560570 | + | 0.172526i | ||||
\(454\) | −49.7103 | + | 36.1166i | −2.33302 | + | 1.69504i | ||||
\(455\) | 0.162368 | + | 0.117967i | 0.00761193 | + | 0.00553039i | ||||
\(456\) | 8.42570 | + | 25.9316i | 0.394570 | + | 1.21436i | ||||
\(457\) | 9.76419 | + | 30.0511i | 0.456750 | + | 1.40573i | 0.869069 | + | 0.494692i | \(0.164719\pi\) |
−0.412319 | + | 0.911040i | \(0.635281\pi\) | |||||||
\(458\) | 49.5846 | + | 36.0253i | 2.31694 | + | 1.68335i | ||||
\(459\) | 20.6307 | − | 14.9891i | 0.962958 | − | 0.699630i | ||||
\(460\) | −3.33742 | + | 10.2715i | −0.155608 | + | 0.478912i | ||||
\(461\) | −8.86324 | −0.412802 | −0.206401 | − | 0.978467i | \(-0.566175\pi\) | ||||
−0.206401 | + | 0.978467i | \(0.566175\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.6132 | −1.19035 | −0.595173 | − | 0.803597i | \(-0.702917\pi\) | ||||
−0.595173 | + | 0.803597i | \(0.702917\pi\) | |||||||
\(464\) | −8.31025 | + | 25.5763i | −0.385794 | + | 1.18735i | ||||
\(465\) | −8.34770 | + | 6.06496i | −0.387115 | + | 0.281256i | ||||
\(466\) | 1.28435 | + | 0.933132i | 0.0594962 | + | 0.0432265i | ||||
\(467\) | 6.34726 | + | 19.5349i | 0.293716 | + | 0.903966i | 0.983650 | + | 0.180093i | \(0.0576399\pi\) |
−0.689933 | + | 0.723873i | \(0.742360\pi\) | |||||||
\(468\) | 3.60922 | + | 11.1081i | 0.166836 | + | 0.513470i | ||||
\(469\) | 5.00666 | + | 3.63755i | 0.231186 | + | 0.167967i | ||||
\(470\) | 0.995326 | − | 0.723147i | 0.0459110 | − | 0.0333563i | ||||
\(471\) | −4.66411 | + | 14.3547i | −0.214911 | + | 0.661428i | ||||
\(472\) | −128.735 | −5.92551 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 27.3814 | 1.25767 | ||||||||
\(475\) | 1.61213 | − | 4.96164i | 0.0739698 | − | 0.227656i | ||||
\(476\) | −20.7435 | + | 15.0710i | −0.950775 | + | 0.690779i | ||||
\(477\) | 14.1040 | + | 10.2472i | 0.645780 | + | 0.469187i | ||||
\(478\) | −12.5067 | − | 38.4917i | −0.572043 | − | 1.76057i | ||||
\(479\) | −8.51303 | − | 26.2004i | −0.388970 | − | 1.19713i | −0.933559 | − | 0.358424i | \(-0.883314\pi\) |
0.544588 | − | 0.838703i | \(-0.316686\pi\) | |||||||
\(480\) | −18.9572 | − | 13.7732i | −0.865273 | − | 0.628658i | ||||
\(481\) | −2.66943 | + | 1.93945i | −0.121715 | + | 0.0884314i | ||||
\(482\) | −15.2654 | + | 46.9821i | −0.695320 | + | 2.13998i | ||||
\(483\) | −12.8351 | −0.584017 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.36327 | 0.107310 | ||||||||
\(486\) | 12.8137 | − | 39.4365i | 0.581241 | − | 1.78888i | ||||
\(487\) | 9.79018 | − | 7.11299i | 0.443636 | − | 0.322320i | −0.343442 | − | 0.939174i | \(-0.611593\pi\) |
0.787078 | + | 0.616854i | \(0.211593\pi\) | |||||||
\(488\) | −35.6550 | − | 25.9049i | −1.61403 | − | 1.17266i | ||||
\(489\) | 8.17601 | + | 25.1632i | 0.369732 | + | 1.13792i | ||||
\(490\) | −0.371784 | − | 1.14423i | −0.0167955 | − | 0.0516912i | ||||
\(491\) | 31.8645 | + | 23.1509i | 1.43803 | + | 1.04479i | 0.988450 | + | 0.151546i | \(0.0484250\pi\) |
0.449576 | + | 0.893242i | \(0.351575\pi\) | |||||||
\(492\) | 21.3429 | − | 15.5065i | 0.962212 | − | 0.699088i | ||||
\(493\) | −2.96241 | + | 9.11736i | −0.133420 | + | 0.410625i | ||||
\(494\) | −1.32432 | −0.0595842 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 111.925 | 5.02560 | ||||||||
\(497\) | −1.82989 | + | 5.63182i | −0.0820818 | + | 0.252622i | ||||
\(498\) | −66.3323 | + | 48.1932i | −2.97242 | + | 2.15959i | ||||
\(499\) | 28.1402 | + | 20.4451i | 1.25973 | + | 0.915246i | 0.998744 | − | 0.0500968i | \(-0.0159530\pi\) |
0.260984 | + | 0.965343i | \(0.415953\pi\) | |||||||
\(500\) | 7.15475 | + | 22.0201i | 0.319970 | + | 0.984768i | ||||
\(501\) | −17.3597 | − | 53.4275i | −0.775573 | − | 2.38697i | ||||
\(502\) | −23.1047 | − | 16.7865i | −1.03121 | − | 0.749220i | ||||
\(503\) | −2.61494 | + | 1.89986i | −0.116594 | + | 0.0847107i | −0.644554 | − | 0.764558i | \(-0.722957\pi\) |
0.527960 | + | 0.849269i | \(0.322957\pi\) | |||||||
\(504\) | 13.4827 | − | 41.4956i | 0.600568 | − | 1.84836i | ||||
\(505\) | −6.92550 | −0.308181 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 35.9227 | 1.59538 | ||||||||
\(508\) | 16.6197 | − | 51.1501i | 0.737378 | − | 2.26942i | ||||
\(509\) | 10.6966 | − | 7.77152i | 0.474118 | − | 0.344467i | −0.324926 | − | 0.945739i | \(-0.605339\pi\) |
0.799044 | + | 0.601273i | \(0.205339\pi\) | |||||||
\(510\) | −13.2005 | − | 9.59072i | −0.584528 | − | 0.424684i | ||||
\(511\) | −0.512277 | − | 1.57663i | −0.0226618 | − | 0.0697459i | ||||
\(512\) | 3.66221 | + | 11.2711i | 0.161848 | + | 0.498118i | ||||
\(513\) | −4.63944 | − | 3.37075i | −0.204836 | − | 0.148822i | ||||
\(514\) | 42.5751 | − | 30.9326i | 1.87791 | − | 1.36438i | ||||
\(515\) | 1.94905 | − | 5.99857i | 0.0858856 | − | 0.264329i | ||||
\(516\) | 169.969 | 7.48245 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 19.7800 | 0.869082 | ||||||||
\(519\) | −9.40905 | + | 28.9581i | −0.413011 | + | 1.27112i | ||||
\(520\) | 1.45160 | − | 1.05465i | 0.0636569 | − | 0.0462495i | ||||
\(521\) | −5.90776 | − | 4.29224i | −0.258824 | − | 0.188046i | 0.450805 | − | 0.892623i | \(-0.351137\pi\) |
−0.709628 | + | 0.704576i | \(0.751137\pi\) | |||||||
\(522\) | −8.08944 | − | 24.8967i | −0.354065 | − | 1.08970i | ||||
\(523\) | 2.58958 | + | 7.96992i | 0.113235 | + | 0.348500i | 0.991575 | − | 0.129536i | \(-0.0413488\pi\) |
−0.878340 | + | 0.478036i | \(0.841349\pi\) | |||||||
\(524\) | 29.3404 | + | 21.3170i | 1.28174 | + | 0.931239i | ||||
\(525\) | −10.9055 | + | 7.92327i | −0.475953 | + | 0.345800i | ||||
\(526\) | 17.6995 | − | 54.4733i | 0.771733 | − | 2.37515i | ||||
\(527\) | 39.8988 | 1.73802 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.09483 | −0.0910794 | ||||||||
\(530\) | 1.32809 | − | 4.08745i | 0.0576887 | − | 0.177547i | ||||
\(531\) | 56.8533 | − | 41.3064i | 2.46722 | − | 1.79254i | ||||
\(532\) | 4.66481 | + | 3.38918i | 0.202245 | + | 0.146940i | ||||
\(533\) | 0.246744 | + | 0.759401i | 0.0106877 | + | 0.0328933i | ||||
\(534\) | 12.2211 | + | 37.6128i | 0.528860 | + | 1.62766i | ||||
\(535\) | −4.23268 | − | 3.07522i | −0.182995 | − | 0.132953i | ||||
\(536\) | 44.7606 | − | 32.5205i | 1.93336 | − | 1.40467i | ||||
\(537\) | −14.6155 | + | 44.9818i | −0.630704 | + | 1.94111i | ||||
\(538\) | 62.5963 | 2.69872 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 12.4682 | 0.536548 | ||||||||
\(541\) | −1.17355 | + | 3.61181i | −0.0504547 | + | 0.155284i | −0.973109 | − | 0.230344i | \(-0.926015\pi\) |
0.922655 | + | 0.385627i | \(0.126015\pi\) | |||||||
\(542\) | −58.6605 | + | 42.6193i | −2.51968 | + | 1.83066i | ||||
\(543\) | −46.1120 | − | 33.5023i | −1.97886 | − | 1.43772i | ||||
\(544\) | 27.9994 | + | 86.1733i | 1.20046 | + | 3.69465i | ||||
\(545\) | −2.17030 | − | 6.67948i | −0.0929653 | − | 0.286118i | ||||
\(546\) | 2.76834 | + | 2.01132i | 0.118474 | + | 0.0860764i | ||||
\(547\) | −7.35384 | + | 5.34288i | −0.314428 | + | 0.228445i | −0.733794 | − | 0.679372i | \(-0.762252\pi\) |
0.419366 | + | 0.907817i | \(0.362252\pi\) | |||||||
\(548\) | 23.7269 | − | 73.0238i | 1.01356 | − | 3.11942i | ||||
\(549\) | 24.0583 | 1.02678 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.15583 | 0.0918416 | ||||||||
\(552\) | −35.4591 | + | 109.132i | −1.50924 | + | 4.64497i | ||||
\(553\) | 2.91920 | − | 2.12092i | 0.124137 | − | 0.0901909i | ||||
\(554\) | 30.7281 | + | 22.3253i | 1.30551 | + | 0.948510i | ||||
\(555\) | 2.82509 | + | 8.69474i | 0.119919 | + | 0.369071i | ||||
\(556\) | −24.1014 | − | 74.1766i | −1.02213 | − | 3.14579i | ||||
\(557\) | −14.7542 | − | 10.7196i | −0.625156 | − | 0.454203i | 0.229563 | − | 0.973294i | \(-0.426270\pi\) |
−0.854719 | + | 0.519091i | \(0.826270\pi\) | |||||||
\(558\) | −88.1435 | + | 64.0400i | −3.73141 | + | 2.71103i | ||||
\(559\) | −1.58972 | + | 4.89265i | −0.0672379 | + | 0.206937i | ||||
\(560\) | −6.03187 | −0.254893 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.71809 | −0.199021 | ||||||||
\(563\) | −4.81276 | + | 14.8122i | −0.202834 | + | 0.624258i | 0.796962 | + | 0.604030i | \(0.206439\pi\) |
−0.999795 | + | 0.0202283i | \(0.993561\pi\) | |||||||
\(564\) | 12.3254 | − | 8.95491i | 0.518992 | − | 0.377070i | ||||
\(565\) | −2.13287 | − | 1.54962i | −0.0897306 | − | 0.0651931i | ||||
\(566\) | −3.89709 | − | 11.9940i | −0.163807 | − | 0.504145i | ||||
\(567\) | 0.0545593 | + | 0.167916i | 0.00229128 | + | 0.00705182i | ||||
\(568\) | 42.8299 | + | 31.1178i | 1.79710 | + | 1.30567i | ||||
\(569\) | −19.7606 | + | 14.3569i | −0.828407 | + | 0.601873i | −0.919108 | − | 0.394005i | \(-0.871089\pi\) |
0.0907010 | + | 0.995878i | \(0.471089\pi\) | |||||||
\(570\) | −1.13388 | + | 3.48972i | −0.0474930 | + | 0.146168i | ||||
\(571\) | −14.9541 | −0.625808 | −0.312904 | − | 0.949785i | \(-0.601302\pi\) | ||||
−0.312904 | + | 0.949785i | \(0.601302\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.14247 | −0.298381 | ||||||||
\(574\) | 1.47915 | − | 4.55236i | 0.0617386 | − | 0.190012i | ||||
\(575\) | 17.7623 | − | 12.9050i | 0.740738 | − | 0.538178i | ||||
\(576\) | −93.1510 | − | 67.6781i | −3.88129 | − | 2.81992i | ||||
\(577\) | −6.63405 | − | 20.4175i | −0.276179 | − | 0.849991i | −0.988905 | − | 0.148549i | \(-0.952540\pi\) |
0.712726 | − | 0.701442i | \(-0.247460\pi\) | |||||||
\(578\) | 5.29622 | + | 16.3001i | 0.220294 | + | 0.677994i | ||||
\(579\) | 39.7632 | + | 28.8896i | 1.65250 | + | 1.20061i | ||||
\(580\) | −3.79201 | + | 2.75506i | −0.157455 | + | 0.114398i | ||||
\(581\) | −3.33888 | + | 10.2760i | −0.138520 | + | 0.426320i | ||||
\(582\) | 40.2932 | 1.67021 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −14.8207 | −0.613286 | ||||||||
\(585\) | −0.302673 | + | 0.931531i | −0.0125140 | + | 0.0385141i | ||||
\(586\) | −31.7307 | + | 23.0537i | −1.31078 | + | 0.952338i | ||||
\(587\) | 16.7273 | + | 12.1531i | 0.690408 | + | 0.501611i | 0.876794 | − | 0.480866i | \(-0.159678\pi\) |
−0.186386 | + | 0.982477i | \(0.559678\pi\) | |||||||
\(588\) | −4.60389 | − | 14.1693i | −0.189861 | − | 0.584333i | ||||
\(589\) | −2.77264 | − | 8.53332i | −0.114245 | − | 0.351609i | ||||
\(590\) | −14.0157 | − | 10.1830i | −0.577018 | − | 0.419228i | ||||
\(591\) | −4.91818 | + | 3.57327i | −0.202307 | + | 0.146985i | ||||
\(592\) | 30.6445 | − | 94.3139i | 1.25948 | − | 3.87628i | ||||
\(593\) | 3.30237 | 0.135612 | 0.0678060 | − | 0.997699i | \(-0.478400\pi\) | ||||
0.0678060 | + | 0.997699i | \(0.478400\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.15022 | −0.0881505 | ||||||||
\(596\) | 1.64233 | − | 5.05457i | 0.0672724 | − | 0.207043i | ||||
\(597\) | −33.1022 | + | 24.0502i | −1.35478 | + | 0.984308i | ||||
\(598\) | −4.50894 | − | 3.27594i | −0.184384 | − | 0.133963i | ||||
\(599\) | 12.0273 | + | 37.0163i | 0.491423 | + | 1.51245i | 0.822457 | + | 0.568827i | \(0.192602\pi\) |
−0.331034 | + | 0.943619i | \(0.607398\pi\) | |||||||
\(600\) | 37.2405 | + | 114.614i | 1.52034 | + | 4.67912i | ||||
\(601\) | −35.9028 | − | 26.0849i | −1.46451 | − | 1.06403i | −0.982160 | − | 0.188045i | \(-0.939785\pi\) |
−0.482346 | − | 0.875981i | \(-0.660215\pi\) | |||||||
\(602\) | 24.9494 | − | 18.1268i | 1.01686 | − | 0.738794i | ||||
\(603\) | −9.33300 | + | 28.7240i | −0.380069 | + | 1.16973i | ||||
\(604\) | 7.29954 | 0.297014 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −118.078 | −4.79660 | ||||||||
\(607\) | −5.84223 | + | 17.9805i | −0.237129 | + | 0.729808i | 0.759703 | + | 0.650270i | \(0.225344\pi\) |
−0.996832 | + | 0.0795376i | \(0.974656\pi\) | |||||||
\(608\) | 16.4845 | − | 11.9767i | 0.668535 | − | 0.485719i | ||||
\(609\) | −4.50651 | − | 3.27417i | −0.182613 | − | 0.132676i | ||||
\(610\) | −1.83276 | − | 5.64067i | −0.0742064 | − | 0.228384i | ||||
\(611\) | 0.142493 | + | 0.438549i | 0.00576466 | + | 0.0177418i | ||||
\(612\) | −101.235 | − | 73.5514i | −4.09217 | − | 2.97314i | ||||
\(613\) | 7.83222 | − | 5.69044i | 0.316341 | − | 0.229835i | −0.418272 | − | 0.908322i | \(-0.637364\pi\) |
0.734612 | + | 0.678487i | \(0.237364\pi\) | |||||||
\(614\) | 1.96871 | − | 6.05906i | 0.0794506 | − | 0.244524i | ||||
\(615\) | 2.21236 | 0.0892108 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.2775 | −1.05789 | −0.528947 | − | 0.848655i | \(-0.677413\pi\) | ||||
−0.528947 | + | 0.848655i | \(0.677413\pi\) | |||||||
\(618\) | 33.2309 | − | 102.274i | 1.33674 | − | 4.11408i | ||||
\(619\) | 20.0599 | − | 14.5744i | 0.806275 | − | 0.585793i | −0.106474 | − | 0.994316i | \(-0.533956\pi\) |
0.912748 | + | 0.408523i | \(0.133956\pi\) | |||||||
\(620\) | 15.7821 | + | 11.4664i | 0.633826 | + | 0.460502i | ||||
\(621\) | −7.45783 | − | 22.9529i | −0.299273 | − | 0.921066i | ||||
\(622\) | −16.7108 | − | 51.4307i | −0.670044 | − | 2.06218i | ||||
\(623\) | 4.21636 | + | 3.06336i | 0.168925 | + | 0.122731i | ||||
\(624\) | 13.8792 | − | 10.0838i | 0.555611 | − | 0.403675i | ||||
\(625\) | 6.81936 | − | 20.9878i | 0.272774 | − | 0.839513i | ||||
\(626\) | 50.6931 | 2.02611 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 28.5355 | 1.13869 | ||||||||
\(629\) | 10.9240 | − | 33.6207i | 0.435570 | − | 1.34055i | ||||
\(630\) | 4.75022 | − | 3.45124i | 0.189253 | − | 0.137501i | ||||
\(631\) | 9.55509 | + | 6.94218i | 0.380382 | + | 0.276364i | 0.761503 | − | 0.648161i | \(-0.224462\pi\) |
−0.381121 | + | 0.924525i | \(0.624462\pi\) | |||||||
\(632\) | −9.96864 | − | 30.6803i | −0.396531 | − | 1.22040i | ||||
\(633\) | 3.14921 | + | 9.69227i | 0.125170 | + | 0.385233i | ||||
\(634\) | −9.18955 | − | 6.67660i | −0.364964 | − | 0.265162i | ||||
\(635\) | 3.64886 | − | 2.65105i | 0.144801 | − | 0.105204i | ||||
\(636\) | 16.4461 | − | 50.6159i | 0.652131 | − | 2.00705i | ||||
\(637\) | 0.450933 | 0.0178666 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.8995 | −1.14325 | ||||||||
\(640\) | −3.61257 | + | 11.1183i | −0.142799 | + | 0.439491i | ||||
\(641\) | 18.2176 | − | 13.2359i | 0.719553 | − | 0.522786i | −0.166688 | − | 0.986010i | \(-0.553307\pi\) |
0.886241 | + | 0.463224i | \(0.153307\pi\) | |||||||
\(642\) | −72.1662 | − | 52.4318i | −2.84817 | − | 2.06932i | ||||
\(643\) | 4.29229 | + | 13.2103i | 0.169271 | + | 0.520964i | 0.999326 | − | 0.0367187i | \(-0.0116906\pi\) |
−0.830054 | + | 0.557683i | \(0.811691\pi\) | |||||||
\(644\) | 7.49860 | + | 23.0783i | 0.295486 | + | 0.909413i | ||||
\(645\) | 11.5315 | + | 8.37812i | 0.454052 | + | 0.329888i | ||||
\(646\) | 11.4787 | − | 8.33976i | 0.451623 | − | 0.328124i | ||||
\(647\) | 15.7016 | − | 48.3247i | 0.617295 | − | 1.89984i | 0.262161 | − | 0.965024i | \(-0.415565\pi\) |
0.355134 | − | 0.934815i | \(-0.384435\pi\) | |||||||
\(648\) | 1.57846 | 0.0620078 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.85334 | −0.229587 | ||||||||
\(651\) | −7.16409 | + | 22.0488i | −0.280783 | + | 0.864161i | ||||
\(652\) | 40.4684 | − | 29.4020i | 1.58486 | − | 1.15147i | ||||
\(653\) | 3.89470 | + | 2.82966i | 0.152411 | + | 0.110733i | 0.661377 | − | 0.750053i | \(-0.269972\pi\) |
−0.508966 | + | 0.860787i | \(0.669972\pi\) | |||||||
\(654\) | −37.0031 | − | 113.884i | −1.44693 | − | 4.45321i | ||||
\(655\) | 0.939831 | + | 2.89250i | 0.0367222 | + | 0.113019i | ||||
\(656\) | −19.4147 | − | 14.1056i | −0.758019 | − | 0.550733i | ||||
\(657\) | 6.54528 | − | 4.75543i | 0.255356 | − | 0.185527i | ||||
\(658\) | 0.854200 | − | 2.62896i | 0.0333002 | − | 0.102487i | ||||
\(659\) | −28.0409 | −1.09232 | −0.546159 | − | 0.837681i | \(-0.683911\pi\) | ||||
−0.546159 | + | 0.837681i | \(0.683911\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.7390 | −1.62346 | −0.811730 | − | 0.584033i | \(-0.801474\pi\) | ||||
−0.811730 | + | 0.584033i | \(0.801474\pi\) | |||||||
\(662\) | −0.0570277 | + | 0.175513i | −0.00221644 | + | 0.00682151i | ||||
\(663\) | 4.94760 | − | 3.59464i | 0.192149 | − | 0.139604i | ||||
\(664\) | 78.1489 | + | 56.7785i | 3.03276 | + | 2.20343i | ||||
\(665\) | 0.149423 | + | 0.459877i | 0.00579438 | + | 0.0178333i | ||||
\(666\) | 29.8302 | + | 91.8079i | 1.15590 | + | 3.55748i | ||||
\(667\) | 7.33998 | + | 5.33281i | 0.284205 | + | 0.206487i | ||||
\(668\) | −85.9243 | + | 62.4276i | −3.32451 | + | 2.41540i | ||||
\(669\) | 4.19909 | − | 12.9235i | 0.162346 | − | 0.499650i | ||||
\(670\) | 7.44559 | 0.287648 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −52.6484 | −2.03096 | ||||||||
\(673\) | −8.89187 | + | 27.3664i | −0.342757 | + | 1.05490i | 0.620017 | + | 0.784588i | \(0.287126\pi\) |
−0.962774 | + | 0.270308i | \(0.912874\pi\) | |||||||
\(674\) | −47.5573 | + | 34.5524i | −1.83184 | + | 1.33091i | ||||
\(675\) | −20.5057 | − | 14.8983i | −0.789266 | − | 0.573435i | ||||
\(676\) | −20.9870 | − | 64.5913i | −0.807192 | − | 2.48428i | ||||
\(677\) | −3.79663 | − | 11.6848i | −0.145916 | − | 0.449085i | 0.851211 | − | 0.524823i | \(-0.175869\pi\) |
−0.997128 | + | 0.0757386i | \(0.975869\pi\) | |||||||
\(678\) | −36.3650 | − | 26.4207i | −1.39659 | − | 1.01468i | ||||
\(679\) | 4.29576 | − | 3.12105i | 0.164856 | − | 0.119775i | ||||
\(680\) | −5.94036 | + | 18.2825i | −0.227802 | + | 0.701104i | ||||
\(681\) | −63.8092 | −2.44517 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.5940 | 1.17065 | 0.585323 | − | 0.810800i | \(-0.300968\pi\) | ||||
0.585323 | + | 0.810800i | \(0.300968\pi\) | |||||||
\(684\) | −8.69574 | + | 26.7627i | −0.332490 | + | 1.02330i | ||||
\(685\) | 5.20925 | − | 3.78474i | 0.199035 | − | 0.144608i | ||||
\(686\) | −2.18693 | − | 1.58890i | −0.0834974 | − | 0.0606644i | ||||
\(687\) | 19.6683 | + | 60.5327i | 0.750391 | + | 2.30947i | ||||
\(688\) | −47.7782 | − | 147.046i | −1.82153 | − | 5.60608i | ||||
\(689\) | 1.30319 | + | 0.946823i | 0.0496476 | + | 0.0360711i | ||||
\(690\) | −12.4929 | + | 9.07665i | −0.475598 | + | 0.345542i | ||||
\(691\) | −5.28794 | + | 16.2746i | −0.201163 | + | 0.619115i | 0.798687 | + | 0.601747i | \(0.205529\pi\) |
−0.999849 | + | 0.0173677i | \(0.994471\pi\) | |||||||
\(692\) | 57.5655 | 2.18831 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 64.7013 | 2.45603 | ||||||||
\(695\) | 2.02117 | − | 6.22051i | 0.0766672 | − | 0.235957i | ||||
\(696\) | −40.2890 | + | 29.2717i | −1.52715 | + | 1.10954i | ||||
\(697\) | −6.92090 | − | 5.02833i | −0.262148 | − | 0.190462i | ||||
\(698\) | −22.0654 | − | 67.9103i | −0.835187 | − | 2.57044i | ||||
\(699\) | 0.509450 | + | 1.56792i | 0.0192692 | + | 0.0593044i | ||||
\(700\) | 20.6178 | + | 14.9797i | 0.779280 | + | 0.566180i | ||||
\(701\) | −10.9975 | + | 7.99012i | −0.415368 | + | 0.301783i | −0.775771 | − | 0.631014i | \(-0.782639\pi\) |
0.360403 | + | 0.932797i | \(0.382639\pi\) | |||||||
\(702\) | −1.98827 | + | 6.11927i | −0.0750425 | + | 0.230957i | ||||
\(703\) | −7.94974 | −0.299830 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.27762 | 0.0481180 | ||||||||
\(706\) | −3.71040 | + | 11.4194i | −0.139643 | + | 0.429776i | ||||
\(707\) | −12.5886 | + | 9.14616i | −0.473444 | + | 0.343977i | ||||
\(708\) | −173.560 | − | 126.099i | −6.52280 | − | 4.73909i | ||||
\(709\) | 9.14675 | + | 28.1508i | 0.343513 | + | 1.05723i | 0.962375 | + | 0.271725i | \(0.0875942\pi\) |
−0.618861 | + | 0.785500i | \(0.712406\pi\) | |||||||
\(710\) | 2.20157 | + | 6.77575i | 0.0826236 | + | 0.254289i | ||||
\(711\) | 14.2466 | + | 10.3508i | 0.534291 | + | 0.388185i | ||||
\(712\) | 37.6950 | − | 27.3871i | 1.41268 | − | 1.02637i | ||||
\(713\) | 11.6685 | − | 35.9120i | 0.436990 | − | 1.34492i | ||||
\(714\) | −36.6608 | −1.37200 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 89.4190 | 3.34174 | ||||||||
\(717\) | 12.9879 | − | 39.9725i | 0.485040 | − | 1.49280i | ||||
\(718\) | 31.7816 | − | 23.0907i | 1.18608 | − | 0.861737i | ||||
\(719\) | −36.8432 | − | 26.7681i | −1.37402 | − | 0.998283i | −0.997411 | − | 0.0719100i | \(-0.977091\pi\) |
−0.376608 | − | 0.926373i | \(-0.622909\pi\) | |||||||
\(720\) | −9.09668 | − | 27.9967i | −0.339013 | − | 1.04337i | ||||
\(721\) | −4.37918 | − | 13.4777i | −0.163089 | − | 0.501937i | ||||
\(722\) | 38.9704 | + | 28.3136i | 1.45033 | + | 1.05372i | ||||
\(723\) | −41.5029 | + | 30.1536i | −1.54351 | + | 1.12142i | ||||
\(724\) | −33.2995 | + | 102.485i | −1.23757 | + | 3.80884i | ||||
\(725\) | 9.52850 | 0.353880 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.8796 | −1.62740 | −0.813702 | − | 0.581283i | \(-0.802551\pi\) | ||||
−0.813702 | + | 0.581283i | \(0.802551\pi\) | |||||||
\(728\) | 1.24578 | − | 3.83412i | 0.0461717 | − | 0.142102i | ||||
\(729\) | 35.2658 | − | 25.6221i | 1.30614 | − | 0.948966i | ||||
\(730\) | −1.61357 | − | 1.17233i | −0.0597210 | − | 0.0433898i | ||||
\(731\) | −17.0318 | − | 52.4185i | −0.629944 | − | 1.93877i | ||||
\(732\) | −22.6956 | − | 69.8498i | −0.838853 | − | 2.58172i | ||||
\(733\) | −11.3973 | − | 8.28060i | −0.420968 | − | 0.305851i | 0.357059 | − | 0.934082i | \(-0.383779\pi\) |
−0.778027 | + | 0.628231i | \(0.783779\pi\) | |||||||
\(734\) | −10.8944 | + | 7.91523i | −0.402119 | + | 0.292157i | ||||
\(735\) | 0.386087 | − | 1.18825i | 0.0142410 | − | 0.0438294i | ||||
\(736\) | 85.7513 | 3.16083 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 23.3603 | 0.859904 | ||||||||
\(739\) | −12.2054 | + | 37.5644i | −0.448983 | + | 1.38183i | 0.429073 | + | 0.903270i | \(0.358840\pi\) |
−0.878056 | + | 0.478558i | \(0.841160\pi\) | |||||||
\(740\) | 13.9832 | − | 10.1594i | 0.514033 | − | 0.373467i | ||||
\(741\) | −1.11262 | − | 0.808365i | −0.0408731 | − | 0.0296960i | ||||
\(742\) | −2.98399 | − | 9.18379i | −0.109546 | − | 0.337147i | ||||
\(743\) | 5.75272 | + | 17.7051i | 0.211047 | + | 0.649535i | 0.999411 | + | 0.0343261i | \(0.0109285\pi\) |
−0.788364 | + | 0.615209i | \(0.789072\pi\) | |||||||
\(744\) | 167.681 | + | 121.827i | 6.14748 | + | 4.46640i | ||||
\(745\) | 0.360574 | − | 0.261973i | 0.0132104 | − | 0.00959794i | ||||
\(746\) | −11.4138 | + | 35.1282i | −0.417890 | + | 1.28613i | ||||
\(747\) | −52.7310 | −1.92933 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.7551 | −0.429523 | ||||||||
\(750\) | −10.2299 | + | 31.4845i | −0.373545 | + | 1.14965i | ||||
\(751\) | 12.7873 | − | 9.29052i | 0.466615 | − | 0.339016i | −0.329505 | − | 0.944154i | \(-0.606882\pi\) |
0.796121 | + | 0.605138i | \(0.206882\pi\) | |||||||
\(752\) | −11.2119 | − | 8.14591i | −0.408855 | − | 0.297051i | ||||
\(753\) | −9.16472 | − | 28.2061i | −0.333981 | − | 1.02789i | ||||
\(754\) | −0.747451 | − | 2.30042i | −0.0272205 | − | 0.0837762i | ||||
\(755\) | 0.495237 | + | 0.359810i | 0.0180235 | + | 0.0130948i | ||||
\(756\) | 22.6638 | − | 16.4662i | 0.824273 | − | 0.598870i | ||||
\(757\) | −1.11590 | + | 3.43438i | −0.0405579 | + | 0.124825i | −0.969285 | − | 0.245939i | \(-0.920904\pi\) |
0.928727 | + | 0.370763i | \(0.120904\pi\) | |||||||
\(758\) | −22.6050 | −0.821051 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.32297 | 0.156811 | ||||||||
\(761\) | 12.2315 | − | 37.6446i | 0.443391 | − | 1.36462i | −0.440848 | − | 0.897582i | \(-0.645322\pi\) |
0.884239 | − | 0.467035i | \(-0.154678\pi\) | |||||||
\(762\) | 62.2123 | − | 45.1998i | 2.25371 | − | 1.63742i | ||||
\(763\) | −12.7663 | − | 9.27523i | −0.462170 | − | 0.335786i | ||||
\(764\) | 4.17282 | + | 12.8426i | 0.150967 | + | 0.464630i | ||||
\(765\) | −3.24275 | − | 9.98017i | −0.117242 | − | 0.360834i | ||||
\(766\) | 4.34497 | + | 3.15681i | 0.156990 | + | 0.114060i | ||||
\(767\) | 5.25315 | − | 3.81664i | 0.189680 | − | 0.137811i | ||||
\(768\) | −20.6612 | + | 63.5888i | −0.745548 | + | 2.29456i | ||||
\(769\) | −10.5472 | −0.380341 | −0.190171 | − | 0.981751i | \(-0.560904\pi\) | ||||
−0.190171 | + | 0.981751i | \(0.560904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54.6503 | 1.96818 | ||||||||
\(772\) | 28.7147 | − | 88.3749i | 1.03347 | − | 3.18068i | ||||
\(773\) | −33.6253 | + | 24.4302i | −1.20942 | + | 0.878694i | −0.995178 | − | 0.0980867i | \(-0.968728\pi\) |
−0.214241 | + | 0.976781i | \(0.568728\pi\) | |||||||
\(774\) | 121.761 | + | 88.4647i | 4.37662 | + | 3.17980i | ||||
\(775\) | −12.2547 | − | 37.7161i | −0.440202 | − | 1.35480i | ||||
\(776\) | −14.6694 | − | 45.1477i | −0.526600 | − | 1.62071i | ||||
\(777\) | 16.6180 | + | 12.0736i | 0.596166 | + | 0.433140i | ||||
\(778\) | −32.4377 | + | 23.5674i | −1.16295 | + | 0.844932i | ||||
\(779\) | −0.594483 | + | 1.82963i | −0.0212996 | + | 0.0655534i | ||||
\(780\) | 2.99010 | 0.107063 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 59.7114 | 2.13527 | ||||||||
\(783\) | 3.23665 | − | 9.96139i | 0.115669 | − | 0.355991i | ||||
\(784\) | −10.9643 | + | 7.96600i | −0.391581 | + | 0.284500i | ||||
\(785\) | 1.93599 | + | 1.40658i | 0.0690984 | + | 0.0502029i | ||||
\(786\) | 16.0239 | + | 49.3165i | 0.571554 | + | 1.75906i | ||||
\(787\) | 3.56834 | + | 10.9822i | 0.127198 | + | 0.391474i | 0.994295 | − | 0.106665i | \(-0.0340171\pi\) |
−0.867097 | + | 0.498139i | \(0.834017\pi\) | |||||||
\(788\) | 9.29830 | + | 6.75561i | 0.331238 | + | 0.240659i | ||||
\(789\) | 48.1204 | − | 34.9616i | 1.71313 | − | 1.24466i | ||||
\(790\) | 1.34152 | − | 4.12877i | 0.0477291 | − | 0.146895i | ||||
\(791\) | −5.92347 | −0.210614 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.22294 | 0.0789390 | ||||||||
\(794\) | 9.57547 | − | 29.4703i | 0.339821 | − | 1.04586i | ||||
\(795\) | 3.61075 | − | 2.62337i | 0.128060 | − | 0.0930412i | ||||
\(796\) | 62.5830 | + | 45.4692i | 2.21820 | + | 1.61161i | ||||
\(797\) | 13.0762 | + | 40.2445i | 0.463183 | + | 1.42553i | 0.861253 | + | 0.508177i | \(0.169680\pi\) |
−0.398069 | + | 0.917355i | \(0.630320\pi\) | |||||||
\(798\) | 2.54763 | + | 7.84080i | 0.0901852 | + | 0.277561i | ||||
\(799\) | −3.99678 | − | 2.90383i | −0.141396 | − | 0.102730i | ||||
\(800\) | 72.8594 | − | 52.9354i | 2.57597 | − | 1.87155i | ||||
\(801\) | −7.85978 | + | 24.1899i | −0.277712 | + | 0.854708i | ||||
\(802\) | 11.6516 | 0.411431 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 92.2006 | 3.25167 | ||||||||
\(805\) | −0.628839 | + | 1.93537i | −0.0221637 | + | 0.0682128i | ||||
\(806\) | −8.14431 | + | 5.91719i | −0.286871 | + | 0.208424i | ||||
\(807\) | 52.5897 | + | 38.2086i | 1.85124 | + | 1.34501i | ||||
\(808\) | 42.9883 | + | 132.304i | 1.51232 | + | 4.65445i | ||||
\(809\) | −5.55657 | − | 17.1014i | −0.195359 | − | 0.601252i | −0.999972 | − | 0.00745333i | \(-0.997628\pi\) |
0.804614 | − | 0.593799i | \(-0.202372\pi\) | |||||||
\(810\) | 0.171851 | + | 0.124857i | 0.00603823 | + | 0.00438703i | ||||
\(811\) | −25.1766 | + | 18.2919i | −0.884071 | + | 0.642315i | −0.934325 | − | 0.356421i | \(-0.883997\pi\) |
0.0502542 | + | 0.998736i | \(0.483997\pi\) | |||||||
\(812\) | −3.25435 | + | 10.0158i | −0.114205 | + | 0.351487i | ||||
\(813\) | −75.2978 | −2.64081 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.19486 | 0.146940 | ||||||||
\(816\) | −56.7974 | + | 174.804i | −1.98831 | + | 6.11938i | ||||
\(817\) | −10.0274 | + | 7.28533i | −0.350814 | + | 0.254881i | ||||
\(818\) | 20.3648 | + | 14.7959i | 0.712037 | + | 0.517325i | ||||
\(819\) | 0.680053 | + | 2.09299i | 0.0237630 | + | 0.0731349i | ||||
\(820\) | −1.29252 | − | 3.97796i | −0.0451367 | − | 0.138916i | ||||
\(821\) | −39.5346 | − | 28.7236i | −1.37977 | − | 1.00246i | −0.996902 | − | 0.0786568i | \(-0.974937\pi\) |
−0.382867 | − | 0.923804i | \(-0.625063\pi\) | |||||||
\(822\) | 88.8166 | − | 64.5291i | 3.09784 | − | 2.25071i | ||||
\(823\) | 9.14138 | − | 28.1343i | 0.318649 | − | 0.980700i | −0.655578 | − | 0.755128i | \(-0.727575\pi\) |
0.974226 | − | 0.225572i | \(-0.0724251\pi\) | |||||||
\(824\) | −126.695 | −4.41361 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −38.9249 | −1.35437 | ||||||||
\(827\) | 7.84669 | − | 24.1496i | 0.272856 | − | 0.839764i | −0.716923 | − | 0.697153i | \(-0.754450\pi\) |
0.989779 | − | 0.142612i | \(-0.0455500\pi\) | |||||||
\(828\) | −95.8085 | + | 69.6089i | −3.32957 | + | 2.41908i | ||||
\(829\) | −5.74063 | − | 4.17081i | −0.199380 | − | 0.144858i | 0.483616 | − | 0.875281i | \(-0.339323\pi\) |
−0.682996 | + | 0.730422i | \(0.739323\pi\) | |||||||
\(830\) | 4.01706 | + | 12.3632i | 0.139434 | + | 0.429134i | ||||
\(831\) | 12.1886 | + | 37.5127i | 0.422819 | + | 1.30130i | ||||
\(832\) | −8.60699 | − | 6.25334i | −0.298394 | − | 0.216796i | ||||
\(833\) | −3.90850 | + | 2.83969i | −0.135422 | + | 0.0983895i | ||||
\(834\) | 34.4605 | − | 106.058i | 1.19327 | − | 3.67250i | ||||
\(835\) | −8.90671 | −0.308230 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −43.5923 | −1.50677 | ||||||||
\(838\) | −22.0047 | + | 67.7234i | −0.760138 | + | 2.33946i | ||||
\(839\) | 19.1967 | − | 13.9472i | 0.662745 | − | 0.481512i | −0.204844 | − | 0.978795i | \(-0.565669\pi\) |
0.867589 | + | 0.497283i | \(0.165669\pi\) | |||||||
\(840\) | −9.03664 | − | 6.56551i | −0.311794 | − | 0.226531i | ||||
\(841\) | −7.74474 | − | 23.8359i | −0.267060 | − | 0.821926i | ||||
\(842\) | 11.8444 | + | 36.4532i | 0.408184 | + | 1.25626i | ||||
\(843\) | −3.96386 | − | 2.87991i | −0.136523 | − | 0.0991895i | ||||
\(844\) | 15.5875 | − | 11.3250i | 0.536543 | − | 0.389821i | ||||
\(845\) | 1.75999 | − | 5.41668i | 0.0605454 | − | 0.186340i | ||||
\(846\) | 13.4904 | 0.463810 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −48.4127 | −1.66250 | ||||||||
\(849\) | 4.04701 | − | 12.4554i | 0.138893 | − | 0.427469i | ||||
\(850\) | 50.7343 | − | 36.8606i | 1.74017 | − | 1.26431i | ||||
\(851\) | −27.0665 | − | 19.6650i | −0.927829 | − | 0.674107i | ||||
\(852\) | 27.2627 | + | 83.9058i | 0.934003 | + | 2.87457i | ||||
\(853\) | −11.9448 | − | 36.7624i | −0.408983 | − | 1.25872i | −0.917524 | − | 0.397681i | \(-0.869815\pi\) |
0.508541 | − | 0.861038i | \(-0.330185\pi\) | |||||||
\(854\) | −10.7808 | − | 7.83271i | −0.368912 | − | 0.268030i | ||||
\(855\) | −1.90915 | + | 1.38708i | −0.0652917 | + | 0.0474372i | ||||
\(856\) | −32.4755 | + | 99.9495i | −1.10999 | + | 3.41620i | ||||
\(857\) | 34.0838 | 1.16428 | 0.582139 | − | 0.813089i | \(-0.302216\pi\) | ||||
0.582139 | + | 0.813089i | \(0.302216\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.7283 | 1.93555 | 0.967773 | − | 0.251825i | \(-0.0810308\pi\) | ||||
0.967773 | + | 0.251825i | \(0.0810308\pi\) | |||||||
\(860\) | 8.32740 | − | 25.6291i | 0.283962 | − | 0.873945i | ||||
\(861\) | 4.02144 | − | 2.92175i | 0.137050 | − | 0.0995730i | ||||
\(862\) | −16.6104 | − | 12.0682i | −0.565753 | − | 0.411044i | ||||
\(863\) | 7.53784 | + | 23.1991i | 0.256591 | + | 0.789706i | 0.993512 | + | 0.113727i | \(0.0362790\pi\) |
−0.736921 | + | 0.675979i | \(0.763721\pi\) | |||||||
\(864\) | −30.5914 | − | 94.1507i | −1.04074 | − | 3.20307i | ||||
\(865\) | 3.90553 | + | 2.83753i | 0.132792 | + | 0.0964789i | ||||
\(866\) | −48.9891 | + | 35.5927i | −1.66472 | + | 1.20949i | ||||
\(867\) | −5.49997 | + | 16.9272i | −0.186789 | + | 0.574876i | ||||
\(868\) | 43.8306 | 1.48771 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −6.70178 | −0.227212 | ||||||||
\(871\) | −0.862354 | + | 2.65405i | −0.0292197 | + | 0.0899291i | ||||
\(872\) | −114.133 | + | 82.9224i | −3.86503 | + | 2.80811i | ||||
\(873\) | 20.9647 | + | 15.2317i | 0.709546 | + | 0.515515i | ||||
\(874\) | −4.14946 | − | 12.7707i | −0.140358 | − | 0.431976i | ||||
\(875\) | 1.34810 | + | 4.14904i | 0.0455743 | + | 0.140263i | ||||
\(876\) | −19.9813 | − | 14.5172i | −0.675105 | − | 0.490492i | ||||
\(877\) | −24.6710 | + | 17.9245i | −0.833080 | + | 0.605268i | −0.920429 | − | 0.390910i | \(-0.872160\pi\) |
0.0873493 | + | 0.996178i | \(0.472160\pi\) | |||||||
\(878\) | 12.8684 | − | 39.6048i | 0.434286 | − | 1.33660i | ||||
\(879\) | −40.7301 | −1.37379 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.10056 | 0.0707697 | 0.0353848 | − | 0.999374i | \(-0.488734\pi\) | ||||
0.0353848 | + | 0.999374i | \(0.488734\pi\) | |||||||
\(882\) | 4.07669 | − | 12.5468i | 0.137269 | − | 0.422472i | ||||
\(883\) | −36.5639 | + | 26.5653i | −1.23047 | + | 0.893992i | −0.996926 | − | 0.0783529i | \(-0.975034\pi\) |
−0.233549 | + | 0.972345i | \(0.575034\pi\) | |||||||
\(884\) | −9.35392 | − | 6.79602i | −0.314606 | − | 0.228575i | ||||
\(885\) | −5.55949 | − | 17.1103i | −0.186880 | − | 0.575158i | ||||
\(886\) | 17.7174 | + | 54.5284i | 0.595226 | + | 1.83192i | ||||
\(887\) | −4.19684 | − | 3.04919i | −0.140916 | − | 0.102382i | 0.515094 | − | 0.857134i | \(-0.327757\pi\) |
−0.656010 | + | 0.754752i | \(0.727757\pi\) | |||||||
\(888\) | 148.568 | − | 107.941i | 4.98561 | − | 3.62226i | ||||
\(889\) | 3.13149 | − | 9.63774i | 0.105027 | − | 0.323239i | ||||
\(890\) | 6.27029 | 0.210181 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.6905 | −0.860181 | ||||||||
\(893\) | −0.343310 | + | 1.05660i | −0.0114884 | + | 0.0353578i | ||||
\(894\) | 6.14772 | − | 4.46658i | 0.205610 | − | 0.149385i | ||||
\(895\) | 6.06662 | + | 4.40766i | 0.202785 | + | 0.147332i | ||||
\(896\) | 8.11681 | + | 24.9810i | 0.271164 | + | 0.834556i | ||||
\(897\) | −1.78852 | − | 5.50449i | −0.0597169 | − | 0.183790i | ||||
\(898\) | 25.4376 | + | 18.4815i | 0.848864 | + | 0.616736i | ||||
\(899\) | 13.2579 | − | 9.63243i | 0.442176 | − | 0.321259i | ||||
\(900\) | −38.4340 | + | 118.288i | −1.28113 | + | 3.94292i | ||||
\(901\) | −17.2580 | −0.574947 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 32.0256 | 1.06575 | ||||||||
\(904\) | −16.3646 | + | 50.3651i | −0.544279 | + | 1.67512i | ||||
\(905\) | −7.31093 | + | 5.31170i | −0.243024 | + | 0.176567i | ||||
\(906\) | 8.44368 | + | 6.13469i | 0.280522 | + | 0.203811i | ||||
\(907\) | −11.9427 | − | 36.7558i | −0.396550 | − | 1.22045i | −0.927748 | − | 0.373207i | \(-0.878258\pi\) |
0.531198 | − | 0.847248i | \(-0.321742\pi\) | |||||||
\(908\) | 37.2790 | + | 114.733i | 1.23715 | + | 3.80755i | ||||
\(909\) | −61.4365 | − | 44.6362i | −2.03772 | − | 1.48049i | ||||
\(910\) | 0.438912 | − | 0.318889i | 0.0145498 | − | 0.0105711i | ||||
\(911\) | −5.68560 | + | 17.4985i | −0.188372 | + | 0.579750i | −0.999990 | − | 0.00443848i | \(-0.998587\pi\) |
0.811618 | + | 0.584189i | \(0.198587\pi\) | |||||||
\(912\) | 41.3331 | 1.36868 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 85.4145 | 2.82526 | ||||||||
\(915\) | 1.90327 | − | 5.85767i | 0.0629202 | − | 0.193649i | ||||
\(916\) | 97.3511 | − | 70.7297i | 3.21657 | − | 2.33697i | ||||
\(917\) | 5.52834 | + | 4.01657i | 0.182562 | + | 0.132639i | ||||
\(918\) | −21.3018 | − | 65.5602i | −0.703064 | − | 2.16381i | ||||
\(919\) | 5.45518 | + | 16.7893i | 0.179950 | + | 0.553829i | 0.999825 | − | 0.0187137i | \(-0.00595709\pi\) |
−0.819875 | + | 0.572543i | \(0.805957\pi\) | |||||||
\(920\) | 14.7185 | + | 10.6936i | 0.485253 | + | 0.352557i | ||||
\(921\) | 5.35243 | − | 3.88877i | 0.176369 | − | 0.128139i | ||||
\(922\) | −7.40376 | + | 22.7864i | −0.243830 | + | 0.750431i | ||||
\(923\) | −2.67027 | −0.0878930 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.1368 | −1.15529 | ||||||||
\(926\) | −21.3956 | + | 65.8488i | −0.703102 | + | 2.16393i | ||||
\(927\) | 55.9521 | − | 40.6516i | 1.83771 | − | 1.33517i | ||||
\(928\) | 30.1080 | + | 21.8747i | 0.988343 | + | 0.718073i | ||||
\(929\) | −4.15577 | − | 12.7901i | −0.136346 | − | 0.419631i | 0.859451 | − | 0.511219i | \(-0.170806\pi\) |
−0.995797 | + | 0.0915876i | \(0.970806\pi\) | |||||||
\(930\) | 8.61924 | + | 26.5273i | 0.282636 | + | 0.869865i | ||||
\(931\) | 0.878946 | + | 0.638592i | 0.0288063 | + | 0.0209290i | ||||
\(932\) | 2.52160 | − | 1.83205i | 0.0825977 | − | 0.0600107i | ||||
\(933\) | 17.3537 | − | 53.4093i | 0.568136 | − | 1.74854i | ||||
\(934\) | 55.5241 | 1.81680 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 19.6747 | 0.643087 | ||||||||
\(937\) | −2.65625 | + | 8.17510i | −0.0867759 | + | 0.267069i | −0.985023 | − | 0.172421i | \(-0.944841\pi\) |
0.898247 | + | 0.439490i | \(0.144841\pi\) | |||||||
\(938\) | 13.5340 | − | 9.83302i | 0.441901 | − | 0.321060i | ||||
\(939\) | 42.5894 | + | 30.9430i | 1.38985 | + | 1.00979i | ||||
\(940\) | −0.746421 | − | 2.29725i | −0.0243456 | − | 0.0749279i | ||||
\(941\) | −10.4131 | − | 32.0483i | −0.339458 | − | 1.04474i | −0.964484 | − | 0.264140i | \(-0.914912\pi\) |
0.625027 | − | 0.780603i | \(-0.285088\pi\) | |||||||
\(942\) | 33.0082 | + | 23.9819i | 1.07546 | + | 0.781371i | ||||
\(943\) | −6.54994 | + | 4.75881i | −0.213295 | + | 0.154968i | ||||
\(944\) | −60.3051 | + | 185.600i | −1.96276 | + | 6.04076i | ||||
\(945\) | 2.34928 | 0.0764220 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.3289 | −0.498121 | −0.249061 | − | 0.968488i | \(-0.580122\pi\) | ||||
−0.249061 | + | 0.968488i | \(0.580122\pi\) | |||||||
\(948\) | 16.6124 | − | 51.1276i | 0.539545 | − | 1.66055i | ||||
\(949\) | 0.604773 | − | 0.439393i | 0.0196318 | − | 0.0142633i | ||||
\(950\) | −11.4092 | − | 8.28925i | −0.370162 | − | 0.268939i | ||||
\(951\) | −3.64513 | − | 11.2186i | −0.118202 | − | 0.363787i | ||||
\(952\) | 13.3470 | + | 41.0777i | 0.432577 | + | 1.33134i | ||||
\(953\) | −36.3553 | − | 26.4136i | −1.17766 | − | 0.855622i | −0.185756 | − | 0.982596i | \(-0.559473\pi\) |
−0.991906 | + | 0.126974i | \(0.959473\pi\) | |||||||
\(954\) | 38.1260 | − | 27.7002i | 1.23438 | − | 0.896826i | ||||
\(955\) | −0.349937 | + | 1.07699i | −0.0113237 | + | 0.0348507i | ||||
\(956\) | −79.4610 | −2.56995 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −74.4697 | −2.40601 | ||||||||
\(959\) | 4.47064 | − | 13.7592i | 0.144364 | − | 0.444308i | ||||
\(960\) | −23.8474 | + | 17.3262i | −0.769672 | + | 0.559200i | ||||
\(961\) | −30.0991 | − | 21.8683i | −0.970940 | − | 0.705429i | ||||
\(962\) | 2.75626 | + | 8.48289i | 0.0888654 | + | 0.273499i | ||||
\(963\) | −17.7279 | − | 54.5609i | −0.571274 | − | 1.75820i | ||||
\(964\) | 78.4652 | + | 57.0083i | 2.52719 | + | 1.83611i | ||||
\(965\) | 6.30434 | − | 4.58037i | 0.202944 | − | 0.147447i | ||||
\(966\) | −10.7216 | + | 32.9976i | −0.344961 | + | 1.06168i | ||||
\(967\) | 33.9453 | 1.09161 | 0.545804 | − | 0.837913i | \(-0.316224\pi\) | ||||
0.545804 | + | 0.837913i | \(0.316224\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.7343 | 0.473334 | ||||||||
\(970\) | 1.97411 | − | 6.07570i | 0.0633850 | − | 0.195079i | ||||
\(971\) | 44.8681 | − | 32.5986i | 1.43989 | − | 1.04614i | 0.451820 | − | 0.892109i | \(-0.350775\pi\) |
0.988066 | − | 0.154029i | \(-0.0492250\pi\) | |||||||
\(972\) | −65.8632 | − | 47.8524i | −2.11256 | − | 1.53487i | ||||
\(973\) | −4.54121 | − | 13.9764i | −0.145585 | − | 0.448063i | ||||
\(974\) | −10.1086 | − | 31.1112i | −0.323902 | − | 0.996868i | ||||
\(975\) | −4.91763 | − | 3.57287i | −0.157490 | − | 0.114423i | ||||
\(976\) | −54.0499 | + | 39.2696i | −1.73010 | + | 1.25699i | ||||
\(977\) | −11.7200 | + | 36.0706i | −0.374957 | + | 1.15400i | 0.568550 | + | 0.822649i | \(0.307505\pi\) |
−0.943507 | + | 0.331351i | \(0.892495\pi\) | |||||||
\(978\) | 71.5215 | 2.28701 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.36212 | −0.0754551 | ||||||||
\(981\) | 23.7978 | − | 73.2421i | 0.759805 | − | 2.33844i | ||||
\(982\) | 86.1361 | − | 62.5815i | 2.74871 | − | 1.99706i | ||||
\(983\) | −25.5113 | − | 18.5350i | −0.813683 | − | 0.591176i | 0.101213 | − | 0.994865i | \(-0.467728\pi\) |
−0.914896 | + | 0.403689i | \(0.867728\pi\) | |||||||
\(984\) | −13.7326 | − | 42.2647i | −0.437780 | − | 1.34735i | ||||
\(985\) | 0.297843 | + | 0.916668i | 0.00949008 | + | 0.0292075i | ||||
\(986\) | 20.9652 | + | 15.2321i | 0.667667 | + | 0.485088i | ||||
\(987\) | 2.32236 | − | 1.68729i | 0.0739215 | − | 0.0537071i | ||||
\(988\) | −0.803471 | + | 2.47283i | −0.0255618 | + | 0.0786712i | ||||
\(989\) | −52.1618 | −1.65865 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.8173 | 1.26484 | 0.632419 | − | 0.774627i | \(-0.282062\pi\) | ||||
0.632419 | + | 0.774627i | \(0.282062\pi\) | |||||||
\(992\) | 47.8633 | − | 147.308i | 1.51966 | − | 4.67704i | ||||
\(993\) | −0.155044 | + | 0.112646i | −0.00492018 | + | 0.00357472i | ||||
\(994\) | 12.9502 | + | 9.40890i | 0.410757 | + | 0.298432i | ||||
\(995\) | 2.00466 | + | 6.16971i | 0.0635520 | + | 0.195593i | ||||
\(996\) | 49.7443 | + | 153.097i | 1.57621 | + | 4.85107i | ||||
\(997\) | 15.1440 | + | 11.0027i | 0.479614 | + | 0.348460i | 0.801176 | − | 0.598428i | \(-0.204208\pi\) |
−0.321562 | + | 0.946889i | \(0.604208\pi\) | |||||||
\(998\) | 76.0685 | − | 55.2670i | 2.40791 | − | 1.74945i | ||||
\(999\) | −11.9353 | + | 36.7331i | −0.377617 | + | 1.16218i |
(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 | 847.2.f.y.372.6 | 24 | ||
11.2 | odd | 10 | 847.2.f.z.729.6 | 24 | |||
11.3 | even | 5 | inner | 847.2.f.y.323.1 | 24 | ||
11.4 | even | 5 | 847.2.a.n.1.6 | yes | 6 | ||
11.5 | even | 5 | inner | 847.2.f.y.148.6 | 24 | ||
11.6 | odd | 10 | 847.2.f.z.148.1 | 24 | |||
11.7 | odd | 10 | 847.2.a.m.1.1 | ✓ | 6 | ||
11.8 | odd | 10 | 847.2.f.z.323.6 | 24 | |||
11.9 | even | 5 | inner | 847.2.f.y.729.1 | 24 | ||
11.10 | odd | 2 | 847.2.f.z.372.1 | 24 | |||
33.26 | odd | 10 | 7623.2.a.cp.1.1 | 6 | |||
33.29 | even | 10 | 7623.2.a.cs.1.6 | 6 | |||
77.48 | odd | 10 | 5929.2.a.bm.1.6 | 6 | |||
77.62 | even | 10 | 5929.2.a.bj.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.m.1.1 | ✓ | 6 | 11.7 | odd | 10 | ||
847.2.a.n.1.6 | yes | 6 | 11.4 | even | 5 | ||
847.2.f.y.148.6 | 24 | 11.5 | even | 5 | inner | ||
847.2.f.y.323.1 | 24 | 11.3 | even | 5 | inner | ||
847.2.f.y.372.6 | 24 | 1.1 | even | 1 | trivial | ||
847.2.f.y.729.1 | 24 | 11.9 | even | 5 | inner | ||
847.2.f.z.148.1 | 24 | 11.6 | odd | 10 | |||
847.2.f.z.323.6 | 24 | 11.8 | odd | 10 | |||
847.2.f.z.372.1 | 24 | 11.10 | odd | 2 | |||
847.2.f.z.729.6 | 24 | 11.2 | odd | 10 | |||
5929.2.a.bj.1.1 | 6 | 77.62 | even | 10 | |||
5929.2.a.bm.1.6 | 6 | 77.48 | odd | 10 | |||
7623.2.a.cp.1.1 | 6 | 33.26 | odd | 10 | |||
7623.2.a.cs.1.6 | 6 | 33.29 | even | 10 |