Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(67,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.67");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.k (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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} - 116 x^{3} + 60 x^{2} - 20 x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 67.4 | ||
Root | \(-2.29733 + 1.90372i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.67 |
Dual form | 392.3.k.l.275.4 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.371518 | + | 1.96519i | 0.185759 | + | 0.982595i | ||||
\(3\) | 0.824388 | − | 1.42788i | 0.274796 | − | 0.475961i | −0.695288 | − | 0.718732i | \(-0.744723\pi\) |
0.970084 | + | 0.242771i | \(0.0780563\pi\) | |||||||
\(4\) | −3.72395 | + | 1.46021i | −0.930987 | + | 0.365052i | ||||
\(5\) | 3.95004 | − | 2.28056i | 0.790008 | − | 0.456111i | −0.0499573 | − | 0.998751i | \(-0.515909\pi\) |
0.839965 | + | 0.542640i | \(0.182575\pi\) | |||||||
\(6\) | 3.11234 | + | 1.08960i | 0.518723 | + | 0.181599i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.25310 | − | 6.77577i | −0.531638 | − | 0.846972i | ||||
\(9\) | 3.14077 | + | 5.43997i | 0.348974 | + | 0.604441i | ||||
\(10\) | 5.94924 | + | 6.91531i | 0.594924 | + | 0.691531i | ||||
\(11\) | 6.18983 | − | 10.7211i | 0.562712 | − | 0.974645i | −0.434547 | − | 0.900649i | \(-0.643091\pi\) |
0.997259 | − | 0.0739960i | \(-0.0235752\pi\) | |||||||
\(12\) | −0.984972 | + | 6.52114i | −0.0820810 | + | 0.543428i | ||||
\(13\) | − | 18.3741i | − | 1.41340i | −0.707516 | − | 0.706698i | \(-0.750184\pi\) | ||
0.707516 | − | 0.706698i | \(-0.249816\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 7.52026i | − | 0.501350i | ||||||
\(16\) | 11.7356 | − | 10.8755i | 0.733474 | − | 0.679718i | ||||
\(17\) | −6.51422 | + | 11.2830i | −0.383189 | + | 0.663703i | −0.991516 | − | 0.129983i | \(-0.958508\pi\) |
0.608327 | + | 0.793687i | \(0.291841\pi\) | |||||||
\(18\) | −9.52373 | + | 8.19326i | −0.529096 | + | 0.455181i | ||||
\(19\) | −1.51262 | − | 2.61993i | −0.0796115 | − | 0.137891i | 0.823471 | − | 0.567359i | \(-0.192035\pi\) |
−0.903082 | + | 0.429467i | \(0.858701\pi\) | |||||||
\(20\) | −11.3797 | + | 14.2606i | −0.568983 | + | 0.713028i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 23.3686 | + | 8.18111i | 1.06221 | + | 0.371869i | ||||
\(23\) | 26.2611 | − | 15.1619i | 1.14179 | − | 0.659211i | 0.194915 | − | 0.980820i | \(-0.437557\pi\) |
0.946873 | + | 0.321609i | \(0.104224\pi\) | |||||||
\(24\) | −13.1812 | + | 0.487065i | −0.549217 | + | 0.0202944i | ||||
\(25\) | −2.09812 | + | 3.63405i | −0.0839248 | + | 0.145362i | ||||
\(26\) | 36.1087 | − | 6.82633i | 1.38880 | − | 0.262551i | ||||
\(27\) | 25.1958 | 0.933179 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 22.7701i | − | 0.785176i | −0.919714 | − | 0.392588i | \(-0.871580\pi\) | ||
0.919714 | − | 0.392588i | \(-0.128420\pi\) | |||||||
\(30\) | 14.7787 | − | 2.79391i | 0.492625 | − | 0.0931305i | ||||
\(31\) | 19.5382 | + | 11.2804i | 0.630264 | + | 0.363883i | 0.780855 | − | 0.624713i | \(-0.214784\pi\) |
−0.150590 | + | 0.988596i | \(0.548117\pi\) | |||||||
\(32\) | 25.7324 | + | 19.0222i | 0.804137 | + | 0.594444i | ||||
\(33\) | −10.2056 | − | 17.6767i | −0.309262 | − | 0.535657i | ||||
\(34\) | −24.5933 | − | 8.60985i | −0.723333 | − | 0.253231i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −19.6396 | − | 15.6720i | −0.545543 | − | 0.435333i | ||||
\(37\) | −11.9335 | + | 6.88983i | −0.322528 | + | 0.186212i | −0.652519 | − | 0.757772i | \(-0.726288\pi\) |
0.329991 | + | 0.943984i | \(0.392954\pi\) | |||||||
\(38\) | 4.58670 | − | 3.94594i | 0.120703 | − | 0.103840i | ||||
\(39\) | −26.2361 | − | 15.1474i | −0.672721 | − | 0.388395i | ||||
\(40\) | −32.2525 | − | 17.0651i | −0.806312 | − | 0.426628i | ||||
\(41\) | 60.5026 | 1.47567 | 0.737837 | − | 0.674979i | \(-0.235847\pi\) | ||||
0.737837 | + | 0.674979i | \(0.235847\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 39.0188 | 0.907414 | 0.453707 | − | 0.891151i | \(-0.350101\pi\) | ||||
0.453707 | + | 0.891151i | \(0.350101\pi\) | |||||||
\(44\) | −7.39556 | + | 48.9633i | −0.168081 | + | 1.11280i | ||||
\(45\) | 24.8123 | + | 14.3254i | 0.551385 | + | 0.318342i | ||||
\(46\) | 39.5524 | + | 45.9752i | 0.859835 | + | 0.999460i | ||||
\(47\) | −17.6115 | + | 10.1680i | −0.374713 | + | 0.216341i | −0.675516 | − | 0.737346i | \(-0.736079\pi\) |
0.300802 | + | 0.953686i | \(0.402746\pi\) | |||||||
\(48\) | −5.85424 | − | 25.7226i | −0.121963 | − | 0.535888i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.92109 | − | 2.77309i | −0.158422 | − | 0.0554618i | ||||
\(51\) | 10.7405 | + | 18.6031i | 0.210598 | + | 0.364766i | ||||
\(52\) | 26.8301 | + | 68.4243i | 0.515963 | + | 1.31585i | ||||
\(53\) | −4.12744 | − | 2.38298i | −0.0778762 | − | 0.0449619i | 0.460556 | − | 0.887631i | \(-0.347650\pi\) |
−0.538432 | + | 0.842669i | \(0.680983\pi\) | |||||||
\(54\) | 9.36072 | + | 49.5146i | 0.173347 | + | 0.916937i | ||||
\(55\) | − | 56.4650i | − | 1.02664i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.98794 | −0.0875077 | ||||||||
\(58\) | 44.7476 | − | 8.45951i | 0.771510 | − | 0.145854i | ||||
\(59\) | 5.86884 | − | 10.1651i | 0.0994718 | − | 0.172290i | −0.811994 | − | 0.583665i | \(-0.801618\pi\) |
0.911466 | + | 0.411375i | \(0.134951\pi\) | |||||||
\(60\) | 10.9811 | + | 28.0050i | 0.183019 | + | 0.466751i | ||||
\(61\) | −94.3137 | + | 54.4520i | −1.54613 | + | 0.892656i | −0.547694 | + | 0.836679i | \(0.684494\pi\) |
−0.998432 | + | 0.0559779i | \(0.982172\pi\) | |||||||
\(62\) | −14.9093 | + | 42.5872i | −0.240473 | + | 0.686890i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −27.8222 | + | 57.6361i | −0.434722 | + | 0.900565i | ||||
\(65\) | −41.9033 | − | 72.5786i | −0.644666 | − | 1.11659i | ||||
\(66\) | 30.9465 | − | 26.6232i | 0.468886 | − | 0.403383i | ||||
\(67\) | 39.5997 | − | 68.5887i | 0.591041 | − | 1.02371i | −0.403052 | − | 0.915177i | \(-0.632051\pi\) |
0.994093 | − | 0.108535i | \(-0.0346160\pi\) | |||||||
\(68\) | 7.78313 | − | 51.5293i | 0.114458 | − | 0.757783i | ||||
\(69\) | − | 49.9970i | − | 0.724595i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.9952i | 0.183031i | 0.995804 | + | 0.0915157i | \(0.0291712\pi\) | ||||
−0.995804 | + | 0.0915157i | \(0.970829\pi\) | |||||||
\(72\) | 23.5020 | − | 44.4179i | 0.326417 | − | 0.616915i | ||||
\(73\) | −49.2909 | + | 85.3744i | −0.675218 | + | 1.16951i | 0.301187 | + | 0.953565i | \(0.402617\pi\) |
−0.976405 | + | 0.215947i | \(0.930716\pi\) | |||||||
\(74\) | −17.9734 | − | 20.8920i | −0.242883 | − | 0.282324i | ||||
\(75\) | 3.45933 | + | 5.99173i | 0.0461244 | + | 0.0798898i | ||||
\(76\) | 9.45857 | + | 7.54776i | 0.124455 | + | 0.0993126i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 20.0204 | − | 57.1865i | 0.256671 | − | 0.733160i | ||||
\(79\) | −113.644 | + | 65.6123i | −1.43853 | + | 0.830535i | −0.997748 | − | 0.0670794i | \(-0.978632\pi\) |
−0.440781 | + | 0.897615i | \(0.645299\pi\) | |||||||
\(80\) | 21.5539 | − | 69.7223i | 0.269423 | − | 0.871528i | ||||
\(81\) | −7.49577 | + | 12.9831i | −0.0925404 | + | 0.160285i | ||||
\(82\) | 22.4778 | + | 118.899i | 0.274120 | + | 1.44999i | ||||
\(83\) | −28.3732 | −0.341846 | −0.170923 | − | 0.985284i | \(-0.554675\pi\) | ||||
−0.170923 | + | 0.985284i | \(0.554675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 59.4242i | 0.699108i | ||||||||
\(86\) | 14.4962 | + | 76.6794i | 0.168561 | + | 0.891621i | ||||
\(87\) | −32.5130 | − | 18.7714i | −0.373713 | − | 0.215763i | ||||
\(88\) | −98.9697 | + | 3.65707i | −1.12466 | + | 0.0415576i | ||||
\(89\) | −78.7090 | − | 136.328i | −0.884371 | − | 1.53178i | −0.846433 | − | 0.532495i | \(-0.821254\pi\) |
−0.0379380 | − | 0.999280i | \(-0.512079\pi\) | |||||||
\(90\) | −18.9339 | + | 54.0831i | −0.210377 | + | 0.600923i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −75.6555 | + | 94.8087i | −0.822343 | + | 1.03053i | ||||
\(93\) | 32.2141 | − | 18.5988i | 0.346388 | − | 0.199987i | ||||
\(94\) | −26.5251 | − | 30.8324i | −0.282182 | − | 0.328004i | ||||
\(95\) | −11.9498 | − | 6.89923i | −0.125788 | − | 0.0726235i | ||||
\(96\) | 48.3749 | − | 21.0611i | 0.503906 | − | 0.219387i | ||||
\(97\) | 39.6175 | 0.408428 | 0.204214 | − | 0.978926i | \(-0.434536\pi\) | ||||
0.204214 | + | 0.978926i | \(0.434536\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 77.7633 | 0.785488 | ||||||||
\(100\) | 2.50682 | − | 16.5967i | 0.0250682 | − | 0.165967i | ||||
\(101\) | 37.7745 | + | 21.8091i | 0.374005 | + | 0.215932i | 0.675207 | − | 0.737628i | \(-0.264054\pi\) |
−0.301202 | + | 0.953560i | \(0.597388\pi\) | |||||||
\(102\) | −32.5683 | + | 28.0185i | −0.319297 | + | 0.274691i | ||||
\(103\) | 54.4748 | − | 31.4510i | 0.528881 | − | 0.305350i | −0.211679 | − | 0.977339i | \(-0.567893\pi\) |
0.740561 | + | 0.671989i | \(0.234560\pi\) | |||||||
\(104\) | −124.499 | + | 78.1471i | −1.19711 | + | 0.751415i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.14959 | − | 8.99653i | 0.0297131 | − | 0.0848729i | ||||
\(107\) | −22.1133 | − | 38.3014i | −0.206667 | − | 0.357957i | 0.743996 | − | 0.668184i | \(-0.232928\pi\) |
−0.950663 | + | 0.310227i | \(0.899595\pi\) | |||||||
\(108\) | −93.8280 | + | 36.7912i | −0.868778 | + | 0.340659i | ||||
\(109\) | −7.63419 | − | 4.40760i | −0.0700384 | − | 0.0404367i | 0.464572 | − | 0.885535i | \(-0.346208\pi\) |
−0.534610 | + | 0.845099i | \(0.679542\pi\) | |||||||
\(110\) | 110.965 | − | 20.9778i | 1.00877 | − | 0.190707i | ||||
\(111\) | 22.7196i | 0.204681i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −121.408 | −1.07440 | −0.537202 | − | 0.843454i | \(-0.680519\pi\) | ||||
−0.537202 | + | 0.843454i | \(0.680519\pi\) | |||||||
\(114\) | −1.85311 | − | 9.80226i | −0.0162554 | − | 0.0859847i | ||||
\(115\) | 69.1550 | − | 119.780i | 0.601347 | − | 1.04156i | ||||
\(116\) | 33.2491 | + | 84.7947i | 0.286630 | + | 0.730989i | ||||
\(117\) | 99.9548 | − | 57.7089i | 0.854314 | − | 0.493239i | ||||
\(118\) | 22.1568 | + | 7.75685i | 0.187769 | + | 0.0657360i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −50.9556 | + | 31.9844i | −0.424630 | + | 0.266537i | ||||
\(121\) | −16.1279 | − | 27.9344i | −0.133289 | − | 0.230863i | ||||
\(122\) | −142.048 | − | 165.114i | −1.16433 | − | 1.35340i | ||||
\(123\) | 49.8776 | − | 86.3906i | 0.405509 | − | 0.702363i | ||||
\(124\) | −89.2310 | − | 13.4777i | −0.719605 | − | 0.108691i | ||||
\(125\) | 133.167i | 1.06534i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 222.845i | − | 1.75468i | −0.479868 | − | 0.877341i | \(-0.659315\pi\) | ||
0.479868 | − | 0.877341i | \(-0.340685\pi\) | |||||||
\(128\) | −123.602 | − | 33.2631i | −0.965644 | − | 0.259868i | ||||
\(129\) | 32.1666 | − | 55.7143i | 0.249354 | − | 0.431893i | ||||
\(130\) | 127.063 | − | 109.312i | 0.977407 | − | 0.840863i | ||||
\(131\) | 118.527 | + | 205.294i | 0.904785 | + | 1.56713i | 0.821206 | + | 0.570632i | \(0.193302\pi\) |
0.0835786 | + | 0.996501i | \(0.473365\pi\) | |||||||
\(132\) | 63.8169 | + | 50.9247i | 0.483462 | + | 0.385793i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 149.502 | + | 52.3390i | 1.11569 | + | 0.390590i | ||||
\(135\) | 99.5246 | − | 57.4605i | 0.737219 | − | 0.425634i | ||||
\(136\) | 104.156 | − | 3.84873i | 0.765856 | − | 0.0282995i | ||||
\(137\) | 4.83138 | − | 8.36820i | 0.0352656 | − | 0.0610818i | −0.847854 | − | 0.530230i | \(-0.822106\pi\) |
0.883119 | + | 0.469148i | \(0.155439\pi\) | |||||||
\(138\) | 98.2537 | − | 18.5748i | 0.711983 | − | 0.134600i | ||||
\(139\) | 63.0621 | 0.453684 | 0.226842 | − | 0.973932i | \(-0.427160\pi\) | ||||
0.226842 | + | 0.973932i | \(0.427160\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.5296i | 0.237798i | ||||||||
\(142\) | −25.5381 | + | 4.82797i | −0.179846 | + | 0.0339998i | ||||
\(143\) | −196.991 | − | 113.733i | −1.37756 | − | 0.795334i | ||||
\(144\) | 96.0211 | + | 29.6838i | 0.666813 | + | 0.206138i | ||||
\(145\) | −51.9285 | − | 89.9428i | −0.358128 | − | 0.620295i | ||||
\(146\) | −186.089 | − | 65.1479i | −1.27459 | − | 0.446219i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 34.3793 | − | 43.0829i | 0.232293 | − | 0.291100i | ||||
\(149\) | −233.751 | + | 134.956i | −1.56880 | + | 0.905746i | −0.572489 | + | 0.819912i | \(0.694022\pi\) |
−0.996309 | + | 0.0858343i | \(0.972644\pi\) | |||||||
\(150\) | −10.4897 | + | 9.02428i | −0.0699313 | + | 0.0601619i | ||||
\(151\) | −93.6846 | − | 54.0888i | −0.620428 | − | 0.358204i | 0.156608 | − | 0.987661i | \(-0.449944\pi\) |
−0.777036 | + | 0.629457i | \(0.783277\pi\) | |||||||
\(152\) | −11.3187 | + | 21.3920i | −0.0744654 | + | 0.140737i | ||||
\(153\) | −81.8386 | −0.534893 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 102.902 | 0.663885 | ||||||||
\(156\) | 119.820 | + | 18.0980i | 0.768079 | + | 0.116013i | ||||
\(157\) | −102.565 | − | 59.2159i | −0.653280 | − | 0.377171i | 0.136432 | − | 0.990649i | \(-0.456437\pi\) |
−0.789712 | + | 0.613478i | \(0.789770\pi\) | |||||||
\(158\) | −171.161 | − | 198.956i | −1.08330 | − | 1.25921i | ||||
\(159\) | −6.80523 | + | 3.92900i | −0.0428002 | + | 0.0247107i | ||||
\(160\) | 145.025 | + | 16.4543i | 0.906407 | + | 0.102839i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −28.2990 | − | 9.90717i | −0.174685 | − | 0.0611554i | ||||
\(163\) | 41.0142 | + | 71.0387i | 0.251621 | + | 0.435820i | 0.963972 | − | 0.266003i | \(-0.0857031\pi\) |
−0.712351 | + | 0.701823i | \(0.752370\pi\) | |||||||
\(164\) | −225.309 | + | 88.3465i | −1.37383 | + | 0.538698i | ||||
\(165\) | −80.6254 | − | 46.5491i | −0.488639 | − | 0.282116i | ||||
\(166\) | −10.5412 | − | 55.7588i | −0.0635011 | − | 0.335896i | ||||
\(167\) | 131.596i | 0.788002i | 0.919110 | + | 0.394001i | \(0.128909\pi\) | ||||
−0.919110 | + | 0.394001i | \(0.871091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −168.609 | −0.997687 | ||||||||
\(170\) | −116.780 | + | 22.0772i | −0.686940 | + | 0.129866i | ||||
\(171\) | 9.50157 | − | 16.4572i | 0.0555648 | − | 0.0962410i | ||||
\(172\) | −145.304 | + | 56.9756i | −0.844791 | + | 0.331254i | ||||
\(173\) | −95.3611 | + | 55.0568i | −0.551220 | + | 0.318247i | −0.749614 | − | 0.661875i | \(-0.769761\pi\) |
0.198394 | + | 0.980122i | \(0.436428\pi\) | |||||||
\(174\) | 24.8102 | − | 70.8682i | 0.142587 | − | 0.407289i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −43.9559 | − | 193.136i | −0.249749 | − | 1.09736i | ||||
\(177\) | −9.67640 | − | 16.7600i | −0.0546689 | − | 0.0946893i | ||||
\(178\) | 238.669 | − | 205.327i | 1.34084 | − | 1.15352i | ||||
\(179\) | −76.9263 | + | 133.240i | −0.429756 | + | 0.744359i | −0.996851 | − | 0.0792929i | \(-0.974734\pi\) |
0.567095 | + | 0.823652i | \(0.308067\pi\) | |||||||
\(180\) | −113.318 | − | 17.1159i | −0.629544 | − | 0.0950882i | ||||
\(181\) | − | 227.511i | − | 1.25697i | −0.777823 | − | 0.628484i | \(-0.783676\pi\) | ||
0.777823 | − | 0.628484i | \(-0.216324\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 179.558i | 0.981194i | ||||||||
\(184\) | −214.425 | − | 113.454i | −1.16535 | − | 0.616600i | ||||
\(185\) | −31.4253 | + | 54.4303i | −0.169867 | + | 0.294218i | ||||
\(186\) | 48.5184 | + | 56.3971i | 0.260852 | + | 0.303210i | ||||
\(187\) | 80.6438 | + | 139.679i | 0.431250 | + | 0.746947i | ||||
\(188\) | 50.7370 | − | 63.5817i | 0.269877 | − | 0.338200i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.11872 | − | 26.0469i | 0.0479933 | − | 0.137089i | ||||
\(191\) | 105.262 | − | 60.7728i | 0.551107 | − | 0.318182i | −0.198461 | − | 0.980109i | \(-0.563594\pi\) |
0.749569 | + | 0.661927i | \(0.230261\pi\) | |||||||
\(192\) | 59.3613 | + | 87.2414i | 0.309174 | + | 0.454382i | ||||
\(193\) | −42.7276 | + | 74.0064i | −0.221386 | + | 0.383453i | −0.955229 | − | 0.295867i | \(-0.904392\pi\) |
0.733843 | + | 0.679319i | \(0.237725\pi\) | |||||||
\(194\) | 14.7186 | + | 77.8560i | 0.0758692 | + | 0.401319i | ||||
\(195\) | −138.178 | −0.708606 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 214.100i | 1.08680i | 0.839474 | + | 0.543400i | \(0.182863\pi\) | ||||
−0.839474 | + | 0.543400i | \(0.817137\pi\) | |||||||
\(198\) | 28.8905 | + | 152.820i | 0.145912 | + | 0.771816i | ||||
\(199\) | 214.968 | + | 124.112i | 1.08024 | + | 0.623677i | 0.930961 | − | 0.365118i | \(-0.118971\pi\) |
0.149279 | + | 0.988795i | \(0.452305\pi\) | |||||||
\(200\) | 33.5470 | − | 1.23961i | 0.167735 | − | 0.00619805i | ||||
\(201\) | −65.2911 | − | 113.087i | −0.324831 | − | 0.562624i | ||||
\(202\) | −28.8252 | + | 82.3366i | −0.142699 | + | 0.407607i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −67.1614 | − | 53.5935i | −0.329222 | − | 0.262713i | ||||
\(205\) | 238.988 | − | 137.980i | 1.16579 | − | 0.673071i | ||||
\(206\) | 82.0456 | + | 95.3687i | 0.398280 | + | 0.462955i | ||||
\(207\) | 164.960 | + | 95.2398i | 0.796909 | + | 0.460096i | ||||
\(208\) | −199.828 | − | 215.631i | −0.960710 | − | 1.03669i | ||||
\(209\) | −37.4514 | −0.179193 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 191.753 | 0.908783 | 0.454392 | − | 0.890802i | \(-0.349857\pi\) | ||||
0.454392 | + | 0.890802i | \(0.349857\pi\) | |||||||
\(212\) | 18.8500 | + | 2.84716i | 0.0889152 | + | 0.0134300i | ||||
\(213\) | 18.5557 | + | 10.7131i | 0.0871157 | + | 0.0502963i | ||||
\(214\) | 67.0541 | − | 57.6866i | 0.313337 | − | 0.269564i | ||||
\(215\) | 154.126 | − | 88.9846i | 0.716864 | − | 0.413882i | ||||
\(216\) | −107.161 | − | 170.721i | −0.496113 | − | 0.790376i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.82553 | − | 16.6401i | 0.0267226 | − | 0.0763309i | ||||
\(219\) | 81.2697 | + | 140.763i | 0.371095 | + | 0.642755i | ||||
\(220\) | 82.4507 | + | 210.273i | 0.374776 | + | 0.955786i | ||||
\(221\) | 207.315 | + | 119.693i | 0.938075 | + | 0.541598i | ||||
\(222\) | −44.6483 | + | 8.44075i | −0.201119 | + | 0.0380214i | ||||
\(223\) | − | 41.2269i | − | 0.184874i | −0.995719 | − | 0.0924370i | \(-0.970534\pi\) | ||
0.995719 | − | 0.0924370i | \(-0.0294657\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −26.3588 | −0.117150 | ||||||||
\(226\) | −45.1052 | − | 238.589i | −0.199580 | − | 1.05570i | ||||
\(227\) | 35.2219 | − | 61.0060i | 0.155162 | − | 0.268749i | −0.777956 | − | 0.628319i | \(-0.783743\pi\) |
0.933118 | + | 0.359570i | \(0.117077\pi\) | |||||||
\(228\) | 18.5748 | − | 7.28344i | 0.0814686 | − | 0.0319449i | ||||
\(229\) | −81.8558 | + | 47.2595i | −0.357449 | + | 0.206373i | −0.667961 | − | 0.744196i | \(-0.732833\pi\) |
0.310512 | + | 0.950569i | \(0.399499\pi\) | |||||||
\(230\) | 261.083 | + | 91.4022i | 1.13514 | + | 0.397401i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −154.285 | + | 96.8436i | −0.665022 | + | 0.417429i | ||||
\(233\) | 68.1434 | + | 118.028i | 0.292461 | + | 0.506557i | 0.974391 | − | 0.224860i | \(-0.0721925\pi\) |
−0.681930 | + | 0.731417i | \(0.738859\pi\) | |||||||
\(234\) | 150.544 | + | 174.990i | 0.643351 | + | 0.747822i | ||||
\(235\) | −46.3775 | + | 80.3281i | −0.197351 | + | 0.341822i | ||||
\(236\) | −7.01204 | + | 46.4241i | −0.0297120 | + | 0.196712i | ||||
\(237\) | 216.360i | 0.912911i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 173.230i | 0.724813i | 0.932020 | + | 0.362406i | \(0.118045\pi\) | ||||
−0.932020 | + | 0.362406i | \(0.881955\pi\) | |||||||
\(240\) | −81.7864 | − | 88.2546i | −0.340777 | − | 0.367727i | ||||
\(241\) | −164.461 | + | 284.856i | −0.682413 | + | 1.18197i | 0.291830 | + | 0.956470i | \(0.405736\pi\) |
−0.974242 | + | 0.225503i | \(0.927597\pi\) | |||||||
\(242\) | 48.9046 | − | 42.0726i | 0.202085 | − | 0.173854i | ||||
\(243\) | 125.740 | + | 217.788i | 0.517449 | + | 0.896248i | ||||
\(244\) | 271.708 | − | 340.494i | 1.11356 | − | 1.39547i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 188.304 | + | 65.9234i | 0.765465 | + | 0.267981i | ||||
\(247\) | −48.1390 | + | 27.7931i | −0.194895 | + | 0.112523i | ||||
\(248\) | −6.66467 | − | 180.363i | −0.0268737 | − | 0.727270i | ||||
\(249\) | −23.3905 | + | 40.5136i | −0.0939379 | + | 0.162705i | ||||
\(250\) | −261.699 | + | 49.4741i | −1.04680 | + | 0.197897i | ||||
\(251\) | −160.255 | −0.638466 | −0.319233 | − | 0.947676i | \(-0.603425\pi\) | ||||
−0.319233 | + | 0.947676i | \(0.603425\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 375.397i | − | 1.48378i | ||||||
\(254\) | 437.932 | − | 82.7909i | 1.72414 | − | 0.325948i | ||||
\(255\) | 84.8507 | + | 48.9886i | 0.332748 | + | 0.192112i | ||||
\(256\) | 19.4476 | − | 255.260i | 0.0759674 | − | 0.997110i | ||||
\(257\) | 72.7208 | + | 125.956i | 0.282960 | + | 0.490102i | 0.972113 | − | 0.234515i | \(-0.0753502\pi\) |
−0.689152 | + | 0.724617i | \(0.742017\pi\) | |||||||
\(258\) | 121.440 | + | 42.5147i | 0.470696 | + | 0.164786i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 262.026 | + | 209.091i | 1.00779 | + | 0.804198i | ||||
\(261\) | 123.869 | − | 71.5156i | 0.474593 | − | 0.274006i | ||||
\(262\) | −359.408 | + | 309.198i | −1.37179 | + | 1.18015i | ||||
\(263\) | 175.617 | + | 101.392i | 0.667745 | + | 0.385523i | 0.795222 | − | 0.606319i | \(-0.207355\pi\) |
−0.127477 | + | 0.991842i | \(0.540688\pi\) | |||||||
\(264\) | −76.3676 | + | 144.332i | −0.289271 | + | 0.546712i | ||||
\(265\) | −21.7381 | −0.0820305 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −259.547 | −0.972087 | ||||||||
\(268\) | −47.3134 | + | 313.245i | −0.176543 | + | 1.16882i | ||||
\(269\) | 191.662 | + | 110.656i | 0.712497 | + | 0.411360i | 0.811985 | − | 0.583679i | \(-0.198387\pi\) |
−0.0994882 | + | 0.995039i | \(0.531721\pi\) | |||||||
\(270\) | 149.896 | + | 174.237i | 0.555171 | + | 0.645323i | ||||
\(271\) | 101.651 | − | 58.6880i | 0.375095 | − | 0.216561i | −0.300587 | − | 0.953754i | \(-0.597183\pi\) |
0.675682 | + | 0.737193i | \(0.263849\pi\) | |||||||
\(272\) | 46.2595 | + | 203.257i | 0.170072 | + | 0.747269i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.2401 | + | 6.38565i | 0.0665695 | + | 0.0233053i | ||||
\(275\) | 25.9740 | + | 44.9883i | 0.0944509 | + | 0.163594i | ||||
\(276\) | 73.0061 | + | 186.186i | 0.264515 | + | 0.674588i | ||||
\(277\) | 221.277 | + | 127.755i | 0.798835 | + | 0.461208i | 0.843064 | − | 0.537814i | \(-0.180750\pi\) |
−0.0442283 | + | 0.999021i | \(0.514083\pi\) | |||||||
\(278\) | 23.4287 | + | 123.929i | 0.0842760 | + | 0.445788i | ||||
\(279\) | 141.716i | 0.507944i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −278.004 | −0.989336 | −0.494668 | − | 0.869082i | \(-0.664710\pi\) | ||||
−0.494668 | + | 0.869082i | \(0.664710\pi\) | |||||||
\(282\) | −65.8920 | + | 12.4569i | −0.233660 | + | 0.0441732i | ||||
\(283\) | 28.3448 | − | 49.0947i | 0.100158 | − | 0.173479i | −0.811591 | − | 0.584225i | \(-0.801398\pi\) |
0.911750 | + | 0.410746i | \(0.134732\pi\) | |||||||
\(284\) | −18.9757 | − | 48.3936i | −0.0668160 | − | 0.170400i | ||||
\(285\) | −19.7026 | + | 11.3753i | −0.0691318 | + | 0.0399133i | ||||
\(286\) | 150.321 | − | 429.379i | 0.525597 | − | 1.50132i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −22.6608 | + | 199.728i | −0.0786833 | + | 0.693499i | ||||
\(289\) | 59.6300 | + | 103.282i | 0.206332 | + | 0.357378i | ||||
\(290\) | 157.462 | − | 135.465i | 0.542974 | − | 0.467120i | ||||
\(291\) | 32.6602 | − | 56.5691i | 0.112234 | − | 0.194396i | ||||
\(292\) | 58.8924 | − | 389.905i | 0.201686 | − | 1.33529i | ||||
\(293\) | 287.871i | 0.982493i | 0.871020 | + | 0.491247i | \(0.163459\pi\) | ||||
−0.871020 | + | 0.491247i | \(0.836541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 53.5369i | − | 0.181481i | ||||||
\(296\) | 97.4386 | + | 51.5558i | 0.329184 | + | 0.174175i | ||||
\(297\) | 155.958 | − | 270.127i | 0.525111 | − | 0.909518i | ||||
\(298\) | −352.058 | − | 409.227i | −1.18140 | − | 1.37324i | ||||
\(299\) | −278.586 | − | 482.525i | −0.931726 | − | 1.61380i | ||||
\(300\) | −21.6315 | − | 17.2616i | −0.0721052 | − | 0.0575385i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 71.4893 | − | 204.203i | 0.236720 | − | 0.676169i | ||||
\(303\) | 62.2817 | − | 35.9584i | 0.205550 | − | 0.118675i | ||||
\(304\) | −46.2445 | − | 14.2960i | −0.152120 | − | 0.0470262i | ||||
\(305\) | −248.362 | + | 430.176i | −0.814302 | + | 1.41041i | ||||
\(306\) | −30.4045 | − | 160.828i | −0.0993612 | − | 0.525583i | ||||
\(307\) | −53.6483 | −0.174750 | −0.0873750 | − | 0.996175i | \(-0.527848\pi\) | ||||
−0.0873750 | + | 0.996175i | \(0.527848\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 103.711i | − | 0.335636i | ||||||
\(310\) | 38.2301 | + | 202.223i | 0.123323 | + | 0.652331i | ||||
\(311\) | 91.0263 | + | 52.5541i | 0.292689 | + | 0.168984i | 0.639154 | − | 0.769079i | \(-0.279285\pi\) |
−0.346465 | + | 0.938063i | \(0.612618\pi\) | |||||||
\(312\) | 8.94939 | + | 242.193i | 0.0286839 | + | 0.776261i | ||||
\(313\) | 105.245 | + | 182.290i | 0.336246 | + | 0.582395i | 0.983723 | − | 0.179690i | \(-0.0575093\pi\) |
−0.647477 | + | 0.762085i | \(0.724176\pi\) | |||||||
\(314\) | 78.2657 | − | 223.559i | 0.249254 | − | 0.711973i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 327.396 | − | 410.280i | 1.03606 | − | 1.29836i | ||||
\(317\) | −54.4626 | + | 31.4440i | −0.171806 | + | 0.0991925i | −0.583437 | − | 0.812158i | \(-0.698293\pi\) |
0.411631 | + | 0.911351i | \(0.364959\pi\) | |||||||
\(318\) | −10.2495 | − | 11.9139i | −0.0322311 | − | 0.0374650i | ||||
\(319\) | −244.120 | − | 140.943i | −0.765268 | − | 0.441828i | ||||
\(320\) | 21.5437 | + | 291.115i | 0.0673239 | + | 0.909735i | ||||
\(321\) | −72.9199 | −0.227165 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.4141 | 0.122025 | ||||||||
\(324\) | 8.95589 | − | 59.2936i | 0.0276416 | − | 0.183005i | ||||
\(325\) | 66.7725 | + | 38.5511i | 0.205454 | + | 0.118619i | ||||
\(326\) | −124.367 | + | 106.993i | −0.381494 | + | 0.328199i | ||||
\(327\) | −12.5871 | + | 7.26715i | −0.0384926 | + | 0.0222237i | ||||
\(328\) | −257.324 | − | 409.952i | −0.784524 | − | 1.24985i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 61.5240 | − | 175.738i | 0.186436 | − | 0.532540i | ||||
\(331\) | −98.2893 | − | 170.242i | −0.296947 | − | 0.514327i | 0.678489 | − | 0.734610i | \(-0.262635\pi\) |
−0.975436 | + | 0.220284i | \(0.929302\pi\) | |||||||
\(332\) | 105.660 | − | 41.4308i | 0.318254 | − | 0.124792i | ||||
\(333\) | −74.9610 | − | 43.2787i | −0.225108 | − | 0.129966i | ||||
\(334\) | −258.612 | + | 48.8905i | −0.774287 | + | 0.146379i | ||||
\(335\) | − | 361.238i | − | 1.07832i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 591.516 | 1.75524 | 0.877620 | − | 0.479358i | \(-0.159130\pi\) | ||||
0.877620 | + | 0.479358i | \(0.159130\pi\) | |||||||
\(338\) | −62.6414 | − | 331.349i | −0.185329 | − | 0.980322i | ||||
\(339\) | −100.087 | + | 173.356i | −0.295242 | + | 0.511374i | ||||
\(340\) | −86.7717 | − | 221.293i | −0.255211 | − | 0.650860i | ||||
\(341\) | 241.876 | − | 139.647i | 0.709314 | − | 0.409523i | ||||
\(342\) | 35.8716 | + | 12.5582i | 0.104888 | + | 0.0367200i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −165.951 | − | 264.383i | −0.482416 | − | 0.768554i | ||||
\(345\) | −114.021 | − | 197.490i | −0.330496 | − | 0.572436i | ||||
\(346\) | −143.625 | − | 166.948i | −0.415102 | − | 0.482509i | ||||
\(347\) | −123.770 | + | 214.376i | −0.356685 | + | 0.617797i | −0.987405 | − | 0.158214i | \(-0.949427\pi\) |
0.630719 | + | 0.776011i | \(0.282760\pi\) | |||||||
\(348\) | 148.487 | + | 22.4279i | 0.426687 | + | 0.0644480i | ||||
\(349\) | − | 288.749i | − | 0.827362i | −0.910422 | − | 0.413681i | \(-0.864243\pi\) | ||
0.910422 | − | 0.413681i | \(-0.135757\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 462.952i | − | 1.31895i | ||||||
\(352\) | 363.218 | − | 158.135i | 1.03187 | − | 0.449248i | ||||
\(353\) | −0.634830 | + | 1.09956i | −0.00179839 | + | 0.00311490i | −0.866923 | − | 0.498442i | \(-0.833906\pi\) |
0.865125 | + | 0.501557i | \(0.167239\pi\) | |||||||
\(354\) | 29.3417 | − | 25.2426i | 0.0828860 | − | 0.0713068i | ||||
\(355\) | 29.6364 | + | 51.3317i | 0.0834827 | + | 0.144596i | ||||
\(356\) | 492.176 | + | 392.747i | 1.38252 | + | 1.10322i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −290.422 | − | 101.674i | −0.811235 | − | 0.284005i | ||||
\(359\) | 15.0707 | − | 8.70105i | 0.0419796 | − | 0.0242369i | −0.478863 | − | 0.877889i | \(-0.658951\pi\) |
0.520843 | + | 0.853653i | \(0.325618\pi\) | |||||||
\(360\) | −8.46373 | − | 229.050i | −0.0235104 | − | 0.636250i | ||||
\(361\) | 175.924 | − | 304.709i | 0.487324 | − | 0.844070i | ||||
\(362\) | 447.103 | − | 84.5246i | 1.23509 | − | 0.233493i | ||||
\(363\) | −53.1828 | −0.146509 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 449.643i | 1.23190i | ||||||||
\(366\) | −352.867 | + | 66.7093i | −0.964116 | + | 0.182266i | ||||
\(367\) | −459.021 | − | 265.016i | −1.25074 | − | 0.722115i | −0.279483 | − | 0.960151i | \(-0.590163\pi\) |
−0.971256 | + | 0.238036i | \(0.923496\pi\) | |||||||
\(368\) | 143.297 | − | 463.535i | 0.389393 | − | 1.25961i | ||||
\(369\) | 190.025 | + | 329.132i | 0.514972 | + | 0.891958i | ||||
\(370\) | −118.641 | − | 41.5349i | −0.320651 | − | 0.112256i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −92.8055 | + | 116.300i | −0.249477 | + | 0.312636i | ||||
\(373\) | 102.722 | − | 59.3066i | 0.275394 | − | 0.158999i | −0.355942 | − | 0.934508i | \(-0.615840\pi\) |
0.631337 | + | 0.775509i | \(0.282507\pi\) | |||||||
\(374\) | −244.535 | + | 210.374i | −0.653838 | + | 0.562497i | ||||
\(375\) | 190.147 | + | 109.782i | 0.507059 | + | 0.292751i | ||||
\(376\) | 143.800 | + | 76.0860i | 0.382446 | + | 0.202356i | ||||
\(377\) | −418.381 | −1.10976 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −345.947 | −0.912790 | −0.456395 | − | 0.889777i | \(-0.650860\pi\) | ||||
−0.456395 | + | 0.889777i | \(0.650860\pi\) | |||||||
\(380\) | 54.5748 | + | 8.24314i | 0.143618 | + | 0.0216925i | ||||
\(381\) | −318.196 | − | 183.710i | −0.835160 | − | 0.482180i | ||||
\(382\) | 158.537 | + | 184.281i | 0.415017 | + | 0.482410i | ||||
\(383\) | −350.630 | + | 202.436i | −0.915483 | + | 0.528555i | −0.882191 | − | 0.470891i | \(-0.843932\pi\) |
−0.0332920 | + | 0.999446i | \(0.510599\pi\) | |||||||
\(384\) | −149.392 | + | 149.068i | −0.389042 | + | 0.388198i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −161.311 | − | 56.4731i | −0.417903 | − | 0.146303i | ||||
\(387\) | 122.549 | + | 212.261i | 0.316664 | + | 0.548478i | ||||
\(388\) | −147.534 | + | 57.8498i | −0.380241 | + | 0.149098i | ||||
\(389\) | −116.391 | − | 67.1985i | −0.299206 | − | 0.172747i | 0.342880 | − | 0.939379i | \(-0.388598\pi\) |
−0.642086 | + | 0.766632i | \(0.721931\pi\) | |||||||
\(390\) | −51.3358 | − | 271.547i | −0.131630 | − | 0.696273i | ||||
\(391\) | 395.070i | 1.01041i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 390.848 | 0.994525 | ||||||||
\(394\) | −420.747 | + | 79.5420i | −1.06789 | + | 0.201883i | ||||
\(395\) | −299.265 | + | 518.342i | −0.757633 | + | 1.31226i | ||||
\(396\) | −289.586 | + | 113.551i | −0.731279 | + | 0.286744i | ||||
\(397\) | 530.424 | − | 306.240i | 1.33608 | − | 0.771386i | 0.349857 | − | 0.936803i | \(-0.386230\pi\) |
0.986224 | + | 0.165417i | \(0.0528969\pi\) | |||||||
\(398\) | −164.039 | + | 468.563i | −0.412158 | + | 1.17729i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.8994 | + | 65.4657i | 0.0372485 | + | 0.163664i | ||||
\(401\) | 63.1234 | + | 109.333i | 0.157415 | + | 0.272651i | 0.933936 | − | 0.357441i | \(-0.116351\pi\) |
−0.776521 | + | 0.630092i | \(0.783017\pi\) | |||||||
\(402\) | 197.982 | − | 170.323i | 0.492491 | − | 0.423690i | ||||
\(403\) | 207.267 | − | 358.998i | 0.514311 | − | 0.890813i | ||||
\(404\) | −172.516 | − | 26.0574i | −0.427021 | − | 0.0644985i | ||||
\(405\) | 68.3781i | 0.168835i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 170.588i | 0.419134i | ||||||||
\(408\) | 80.3698 | − | 151.896i | 0.196985 | − | 0.372294i | ||||
\(409\) | 171.259 | − | 296.630i | 0.418727 | − | 0.725257i | −0.577084 | − | 0.816685i | \(-0.695810\pi\) |
0.995812 | + | 0.0914275i | \(0.0291430\pi\) | |||||||
\(410\) | 359.945 | + | 418.395i | 0.877914 | + | 1.02047i | ||||
\(411\) | −7.96587 | − | 13.7973i | −0.0193817 | − | 0.0335700i | ||||
\(412\) | −156.936 | + | 196.667i | −0.380913 | + | 0.477346i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −125.879 | + | 359.561i | −0.304055 | + | 0.868506i | ||||
\(415\) | −112.075 | + | 64.7068i | −0.270061 | + | 0.155920i | ||||
\(416\) | 349.517 | − | 472.810i | 0.840184 | − | 1.13656i | ||||
\(417\) | 51.9876 | − | 90.0452i | 0.124671 | − | 0.215936i | ||||
\(418\) | −13.9139 | − | 73.5992i | −0.0332868 | − | 0.176075i | ||||
\(419\) | 376.392 | 0.898311 | 0.449155 | − | 0.893454i | \(-0.351725\pi\) | ||||
0.449155 | + | 0.893454i | \(0.351725\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 111.135i | 0.263978i | 0.991251 | + | 0.131989i | \(0.0421363\pi\) | ||||
−0.991251 | + | 0.131989i | \(0.957864\pi\) | |||||||
\(422\) | 71.2399 | + | 376.832i | 0.168815 | + | 0.892966i | ||||
\(423\) | −110.627 | − | 63.8708i | −0.261531 | − | 0.150995i | ||||
\(424\) | 1.40791 | + | 38.1017i | 0.00332054 | + | 0.0898624i | ||||
\(425\) | −27.3352 | − | 47.3460i | −0.0643181 | − | 0.111402i | ||||
\(426\) | −14.1595 | + | 40.4455i | −0.0332384 | + | 0.0949425i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 138.277 | + | 110.342i | 0.323077 | + | 0.257810i | ||||
\(429\) | −324.794 | + | 187.520i | −0.757096 | + | 0.437109i | ||||
\(430\) | 232.132 | + | 269.827i | 0.539843 | + | 0.627505i | ||||
\(431\) | 35.7481 | + | 20.6392i | 0.0829422 | + | 0.0478867i | 0.540898 | − | 0.841089i | \(-0.318085\pi\) |
−0.457955 | + | 0.888975i | \(0.651418\pi\) | |||||||
\(432\) | 295.688 | − | 274.017i | 0.684462 | − | 0.634298i | ||||
\(433\) | 675.176 | 1.55930 | 0.779649 | − | 0.626217i | \(-0.215397\pi\) | ||||
0.779649 | + | 0.626217i | \(0.215397\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −171.237 | −0.393648 | ||||||||
\(436\) | 34.8653 | + | 5.26616i | 0.0799664 | + | 0.0120784i | ||||
\(437\) | −79.4461 | − | 45.8682i | −0.181799 | − | 0.104962i | ||||
\(438\) | −246.434 | + | 212.007i | −0.562634 | + | 0.484033i | ||||
\(439\) | −459.215 | + | 265.128i | −1.04605 | + | 0.603936i | −0.921541 | − | 0.388282i | \(-0.873069\pi\) |
−0.124508 | + | 0.992219i | \(0.539735\pi\) | |||||||
\(440\) | −382.594 | + | 240.152i | −0.869532 | + | 0.545799i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −158.199 | + | 451.881i | −0.357915 | + | 1.02235i | ||||
\(443\) | −166.016 | − | 287.549i | −0.374755 | − | 0.649094i | 0.615535 | − | 0.788109i | \(-0.288940\pi\) |
−0.990290 | + | 0.139015i | \(0.955606\pi\) | |||||||
\(444\) | −33.1753 | − | 84.6066i | −0.0747193 | − | 0.190555i | ||||
\(445\) | −621.808 | − | 359.001i | −1.39732 | − | 0.806743i | ||||
\(446\) | 81.0187 | − | 15.3166i | 0.181656 | − | 0.0343420i | ||||
\(447\) | 445.025i | 0.995582i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.4200 | −0.0432517 | −0.0216259 | − | 0.999766i | \(-0.506884\pi\) | ||||
−0.0216259 | + | 0.999766i | \(0.506884\pi\) | |||||||
\(450\) | −9.79279 | − | 51.8001i | −0.0217618 | − | 0.115111i | ||||
\(451\) | 374.501 | − | 648.654i | 0.830379 | − | 1.43826i | ||||
\(452\) | 452.116 | − | 177.281i | 1.00026 | − | 0.392214i | ||||
\(453\) | −154.465 | + | 89.1804i | −0.340982 | + | 0.196866i | ||||
\(454\) | 132.974 | + | 46.5528i | 0.292894 | + | 0.102539i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 21.2142 | + | 33.7972i | 0.0465224 | + | 0.0741166i | ||||
\(457\) | 88.9796 | + | 154.117i | 0.194704 | + | 0.337237i | 0.946803 | − | 0.321813i | \(-0.104292\pi\) |
−0.752100 | + | 0.659049i | \(0.770959\pi\) | |||||||
\(458\) | −123.285 | − | 143.305i | −0.269181 | − | 0.312892i | ||||
\(459\) | −164.131 | + | 284.283i | −0.357584 | + | 0.619354i | ||||
\(460\) | −82.6258 | + | 547.035i | −0.179621 | + | 1.18921i | ||||
\(461\) | − | 299.341i | − | 0.649329i | −0.945829 | − | 0.324664i | \(-0.894749\pi\) | ||
0.945829 | − | 0.324664i | \(-0.105251\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 505.213i | 1.09117i | 0.838055 | + | 0.545586i | \(0.183693\pi\) | ||||
−0.838055 | + | 0.545586i | \(0.816307\pi\) | |||||||
\(464\) | −247.636 | − | 267.220i | −0.533698 | − | 0.575906i | ||||
\(465\) | 84.8314 | − | 146.932i | 0.182433 | − | 0.315983i | ||||
\(466\) | −206.631 | + | 177.764i | −0.443413 | + | 0.381468i | ||||
\(467\) | −325.162 | − | 563.197i | −0.696278 | − | 1.20599i | −0.969748 | − | 0.244108i | \(-0.921505\pi\) |
0.273470 | − | 0.961881i | \(-0.411829\pi\) | |||||||
\(468\) | −287.959 | + | 360.860i | −0.615298 | + | 0.771068i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −175.090 | − | 61.2972i | −0.372532 | − | 0.130420i | ||||
\(471\) | −169.107 | + | 97.6338i | −0.359037 | + | 0.207290i | ||||
\(472\) | −93.8373 | + | 3.46742i | −0.198808 | + | 0.00734623i | ||||
\(473\) | 241.520 | − | 418.324i | 0.510612 | − | 0.884407i | ||||
\(474\) | −425.188 | + | 80.3817i | −0.897022 | + | 0.169582i | ||||
\(475\) | 12.6946 | 0.0267255 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 29.9375i | − | 0.0627621i | ||||||
\(478\) | −340.430 | + | 64.3582i | −0.712198 | + | 0.134641i | ||||
\(479\) | 572.400 | + | 330.475i | 1.19499 | + | 0.689928i | 0.959434 | − | 0.281933i | \(-0.0909755\pi\) |
0.235556 | + | 0.971861i | \(0.424309\pi\) | |||||||
\(480\) | 143.052 | − | 193.514i | 0.298025 | − | 0.403154i | ||||
\(481\) | 126.595 | + | 219.269i | 0.263191 | + | 0.455860i | ||||
\(482\) | −620.896 | − | 217.369i | −1.28817 | − | 0.450973i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 100.850 | + | 80.4762i | 0.208367 | + | 0.166273i | ||||
\(485\) | 156.491 | − | 90.3500i | 0.322661 | − | 0.186289i | ||||
\(486\) | −381.281 | + | 328.016i | −0.784528 | + | 0.674929i | ||||
\(487\) | −334.373 | − | 193.050i | −0.686597 | − | 0.396407i | 0.115739 | − | 0.993280i | \(-0.463076\pi\) |
−0.802336 | + | 0.596873i | \(0.796410\pi\) | |||||||
\(488\) | 770.081 | + | 407.458i | 1.57803 | + | 0.834955i | ||||
\(489\) | 135.246 | 0.276578 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −898.359 | −1.82965 | −0.914826 | − | 0.403848i | \(-0.867672\pi\) | ||||
−0.914826 | + | 0.403848i | \(0.867672\pi\) | |||||||
\(492\) | −59.5934 | + | 394.546i | −0.121125 | + | 0.801922i | ||||
\(493\) | 256.914 | + | 148.329i | 0.521124 | + | 0.300871i | ||||
\(494\) | −72.5032 | − | 84.2767i | −0.146768 | − | 0.170601i | ||||
\(495\) | 307.168 | − | 177.344i | 0.620542 | − | 0.358270i | ||||
\(496\) | 351.972 | − | 80.1055i | 0.709620 | − | 0.161503i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −88.3070 | − | 30.9153i | −0.177323 | − | 0.0620790i | ||||
\(499\) | −395.588 | − | 685.178i | −0.792761 | − | 1.37310i | −0.924251 | − | 0.381785i | \(-0.875309\pi\) |
0.131490 | − | 0.991318i | \(-0.458024\pi\) | |||||||
\(500\) | −194.452 | − | 495.908i | −0.388904 | − | 0.991817i | ||||
\(501\) | 187.904 | + | 108.486i | 0.375058 | + | 0.216540i | ||||
\(502\) | −59.5377 | − | 314.932i | −0.118601 | − | 0.627354i | ||||
\(503\) | − | 798.990i | − | 1.58845i | −0.607624 | − | 0.794225i | \(-0.707877\pi\) | ||
0.607624 | − | 0.794225i | \(-0.292123\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 198.948 | 0.393956 | ||||||||
\(506\) | 737.727 | − | 139.467i | 1.45796 | − | 0.275626i | ||||
\(507\) | −138.999 | + | 240.754i | −0.274160 | + | 0.474860i | ||||
\(508\) | 325.400 | + | 829.862i | 0.640551 | + | 1.63359i | ||||
\(509\) | −477.272 | + | 275.553i | −0.937666 | + | 0.541362i | −0.889228 | − | 0.457465i | \(-0.848758\pi\) |
−0.0484379 | + | 0.998826i | \(0.515424\pi\) | |||||||
\(510\) | −64.7483 | + | 184.948i | −0.126957 | + | 0.362643i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 508.860 | − | 56.6155i | 0.993868 | − | 0.110577i | ||||
\(513\) | −38.1117 | − | 66.0114i | −0.0742918 | − | 0.128677i | ||||
\(514\) | −220.511 | + | 189.705i | −0.429009 | + | 0.369076i | ||||
\(515\) | 143.452 | − | 248.466i | 0.278547 | − | 0.482458i | ||||
\(516\) | −38.4324 | + | 254.447i | −0.0744815 | + | 0.493114i | ||||
\(517\) | 251.753i | 0.486950i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 181.553i | 0.349812i | ||||||||
\(520\) | −313.557 | + | 592.611i | −0.602995 | + | 1.13964i | ||||
\(521\) | 71.3914 | − | 123.654i | 0.137028 | − | 0.237339i | −0.789343 | − | 0.613953i | \(-0.789578\pi\) |
0.926370 | + | 0.376614i | \(0.122912\pi\) | |||||||
\(522\) | 186.561 | + | 216.856i | 0.357397 | + | 0.415433i | ||||
\(523\) | −416.255 | − | 720.976i | −0.795900 | − | 1.37854i | −0.922266 | − | 0.386555i | \(-0.873665\pi\) |
0.126367 | − | 0.991984i | \(-0.459668\pi\) | |||||||
\(524\) | −741.160 | − | 591.432i | −1.41443 | − | 1.12869i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −134.011 | + | 382.790i | −0.254773 | + | 0.727737i | ||||
\(527\) | −254.552 | + | 146.966i | −0.483021 | + | 0.278872i | ||||
\(528\) | −312.012 | − | 96.4549i | −0.590931 | − | 0.182680i | ||||
\(529\) | 195.264 | − | 338.207i | 0.369119 | − | 0.639333i | ||||
\(530\) | −8.07610 | − | 42.7195i | −0.0152379 | − | 0.0806028i | ||||
\(531\) | 73.7306 | 0.138852 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1111.68i | − | 2.08571i | ||||||
\(534\) | −96.4265 | − | 510.060i | −0.180574 | − | 0.955168i | ||||
\(535\) | −174.697 | − | 100.862i | −0.326537 | − | 0.188526i | ||||
\(536\) | −633.163 | + | 23.3963i | −1.18127 | + | 0.0436498i | ||||
\(537\) | 126.834 | + | 219.683i | 0.236191 | + | 0.409094i | ||||
\(538\) | −146.254 | + | 417.762i | −0.271848 | + | 0.776510i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −286.720 | + | 359.307i | −0.530963 | + | 0.665383i | ||||
\(541\) | −533.874 | + | 308.232i | −0.986829 | + | 0.569746i | −0.904325 | − | 0.426845i | \(-0.859625\pi\) |
−0.0825038 | + | 0.996591i | \(0.526292\pi\) | |||||||
\(542\) | 153.098 | + | 177.959i | 0.282469 | + | 0.328338i | ||||
\(543\) | −324.859 | − | 187.557i | −0.598267 | − | 0.345410i | ||||
\(544\) | −382.253 | + | 166.423i | −0.702671 | + | 0.305924i | ||||
\(545\) | −40.2071 | −0.0737746 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 577.704 | 1.05613 | 0.528065 | − | 0.849204i | \(-0.322918\pi\) | ||||
0.528065 | + | 0.849204i | \(0.322918\pi\) | |||||||
\(548\) | −5.77250 | + | 38.2176i | −0.0105338 | + | 0.0697401i | ||||
\(549\) | −592.435 | − | 342.043i | −1.07912 | − | 0.623028i | ||||
\(550\) | −78.7607 | + | 67.7578i | −0.143201 | + | 0.123196i | ||||
\(551\) | −59.6562 | + | 34.4425i | −0.108269 | + | 0.0625091i | ||||
\(552\) | −338.768 | + | 212.643i | −0.613711 | + | 0.385222i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −168.853 | + | 482.316i | −0.304790 | + | 0.870606i | ||||
\(555\) | 51.8133 | + | 89.7433i | 0.0933573 | + | 0.161700i | ||||
\(556\) | −234.840 | + | 92.0838i | −0.422374 | + | 0.165618i | ||||
\(557\) | 445.752 | + | 257.355i | 0.800273 | + | 0.462038i | 0.843566 | − | 0.537025i | \(-0.180452\pi\) |
−0.0432939 | + | 0.999062i | \(0.513785\pi\) | |||||||
\(558\) | −278.500 | + | 52.6502i | −0.499103 | + | 0.0943552i | ||||
\(559\) | − | 716.937i | − | 1.28253i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 265.927 | 0.474023 | ||||||||
\(562\) | −103.283 | − | 546.330i | −0.183778 | − | 0.972117i | ||||
\(563\) | −304.360 | + | 527.166i | −0.540603 | + | 0.936352i | 0.458266 | + | 0.888815i | \(0.348471\pi\) |
−0.998869 | + | 0.0475374i | \(0.984863\pi\) | |||||||
\(564\) | −48.9602 | − | 124.862i | −0.0868088 | − | 0.221387i | ||||
\(565\) | −479.565 | + | 276.877i | −0.848788 | + | 0.490048i | ||||
\(566\) | 107.011 | + | 37.4634i | 0.189065 | + | 0.0661897i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 88.0527 | − | 55.2701i | 0.155022 | − | 0.0973064i | ||||
\(569\) | −93.1872 | − | 161.405i | −0.163774 | − | 0.283664i | 0.772445 | − | 0.635081i | \(-0.219033\pi\) |
−0.936219 | + | 0.351417i | \(0.885700\pi\) | |||||||
\(570\) | −29.6745 | − | 34.4932i | −0.0520605 | − | 0.0605144i | ||||
\(571\) | −91.8878 | + | 159.154i | −0.160924 | + | 0.278729i | −0.935200 | − | 0.354119i | \(-0.884781\pi\) |
0.774276 | + | 0.632848i | \(0.218114\pi\) | |||||||
\(572\) | 899.658 | + | 135.887i | 1.57283 | + | 0.237565i | ||||
\(573\) | − | 200.401i | − | 0.349741i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 127.246i | 0.221297i | ||||||||
\(576\) | −400.922 | + | 29.6698i | −0.696045 | + | 0.0515100i | ||||
\(577\) | 67.2281 | − | 116.442i | 0.116513 | − | 0.201807i | −0.801870 | − | 0.597498i | \(-0.796162\pi\) |
0.918384 | + | 0.395691i | \(0.129495\pi\) | |||||||
\(578\) | −180.815 | + | 155.555i | −0.312830 | + | 0.269127i | ||||
\(579\) | 70.4482 | + | 122.020i | 0.121672 | + | 0.210743i | ||||
\(580\) | 324.714 | + | 259.116i | 0.559852 | + | 0.446752i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 123.303 | + | 43.1670i | 0.211861 | + | 0.0741702i | ||||
\(583\) | −51.0963 | + | 29.5005i | −0.0876437 | + | 0.0506011i | ||||
\(584\) | 788.117 | − | 29.1220i | 1.34952 | − | 0.0498665i | ||||
\(585\) | 263.217 | − | 455.905i | 0.449944 | − | 0.779325i | ||||
\(586\) | −565.721 | + | 106.949i | −0.965393 | + | 0.182507i | ||||
\(587\) | 921.405 | 1.56968 | 0.784842 | − | 0.619696i | \(-0.212744\pi\) | ||||
0.784842 | + | 0.619696i | \(0.212744\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 68.2517i | − | 0.115877i | ||||||
\(590\) | 105.210 | − | 19.8899i | 0.178322 | − | 0.0337117i | ||||
\(591\) | 305.709 | + | 176.501i | 0.517274 | + | 0.298648i | ||||
\(592\) | −65.1168 | + | 210.639i | −0.109995 | + | 0.355810i | ||||
\(593\) | 48.1873 | + | 83.4628i | 0.0812602 | + | 0.140747i | 0.903791 | − | 0.427973i | \(-0.140772\pi\) |
−0.822531 | + | 0.568720i | \(0.807439\pi\) | |||||||
\(594\) | 588.792 | + | 206.130i | 0.991233 | + | 0.347020i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 673.412 | − | 843.895i | 1.12989 | − | 1.41593i | ||||
\(597\) | 354.434 | − | 204.632i | 0.593692 | − | 0.342768i | ||||
\(598\) | 844.754 | − | 726.742i | 1.41263 | − | 1.21529i | ||||
\(599\) | 144.711 | + | 83.5489i | 0.241587 | + | 0.139481i | 0.615906 | − | 0.787820i | \(-0.288790\pi\) |
−0.374319 | + | 0.927300i | \(0.622123\pi\) | |||||||
\(600\) | 25.8857 | − | 48.9231i | 0.0431429 | − | 0.0815385i | ||||
\(601\) | −88.4635 | −0.147194 | −0.0735969 | − | 0.997288i | \(-0.523448\pi\) | ||||
−0.0735969 | + | 0.997288i | \(0.523448\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 497.494 | 0.825032 | ||||||||
\(604\) | 427.858 | + | 64.6249i | 0.708373 | + | 0.106995i | ||||
\(605\) | −127.412 | − | 73.5614i | −0.210598 | − | 0.121589i | ||||
\(606\) | 93.8039 | + | 109.036i | 0.154792 | + | 0.179928i | ||||
\(607\) | 48.1243 | − | 27.7846i | 0.0792822 | − | 0.0457736i | −0.459835 | − | 0.888004i | \(-0.652091\pi\) |
0.539117 | + | 0.842231i | \(0.318758\pi\) | |||||||
\(608\) | 10.9136 | − | 96.1905i | 0.0179500 | − | 0.158208i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −937.648 | − | 328.260i | −1.53713 | − | 0.538132i | ||||
\(611\) | 186.829 | + | 323.597i | 0.305775 | + | 0.529618i | ||||
\(612\) | 304.763 | − | 119.501i | 0.497978 | − | 0.195264i | ||||
\(613\) | −752.678 | − | 434.559i | −1.22786 | − | 0.708905i | −0.261278 | − | 0.965264i | \(-0.584144\pi\) |
−0.966582 | + | 0.256359i | \(0.917477\pi\) | |||||||
\(614\) | −19.9313 | − | 105.429i | −0.0324614 | − | 0.171709i | ||||
\(615\) | − | 454.995i | − | 0.739829i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −249.359 | −0.404147 | −0.202074 | − | 0.979370i | \(-0.564768\pi\) | ||||
−0.202074 | + | 0.979370i | \(0.564768\pi\) | |||||||
\(618\) | 203.813 | − | 38.5307i | 0.329794 | − | 0.0623474i | ||||
\(619\) | −248.837 | + | 430.998i | −0.401998 | + | 0.696280i | −0.993967 | − | 0.109680i | \(-0.965017\pi\) |
0.591969 | + | 0.805961i | \(0.298351\pi\) | |||||||
\(620\) | −383.203 | + | 150.259i | −0.618069 | + | 0.242353i | ||||
\(621\) | 661.671 | − | 382.016i | 1.06549 | − | 0.615162i | ||||
\(622\) | −69.4608 | + | 198.409i | −0.111673 | + | 0.318985i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −472.631 | + | 107.567i | −0.757422 | + | 0.172382i | ||||
\(625\) | 251.243 | + | 435.165i | 0.401988 | + | 0.696264i | ||||
\(626\) | −319.133 | + | 274.550i | −0.509798 | + | 0.438579i | ||||
\(627\) | −30.8745 | + | 53.4762i | −0.0492416 | + | 0.0852890i | ||||
\(628\) | 468.414 | + | 70.7507i | 0.745882 | + | 0.112660i | ||||
\(629\) | − | 179.527i | − | 0.285417i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 172.763i | − | 0.273792i | −0.990585 | − | 0.136896i | \(-0.956287\pi\) | ||
0.990585 | − | 0.136896i | \(-0.0437126\pi\) | |||||||
\(632\) | 927.913 | + | 490.969i | 1.46822 | + | 0.776849i | ||||
\(633\) | 158.079 | − | 273.801i | 0.249730 | − | 0.432545i | ||||
\(634\) | −82.0273 | − | 95.3474i | −0.129381 | − | 0.150390i | ||||
\(635\) | −508.210 | − | 880.245i | −0.800330 | − | 1.38621i | ||||
\(636\) | 19.6051 | − | 24.5684i | 0.0308257 | − | 0.0386296i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 186.285 | − | 532.106i | 0.291982 | − | 0.834022i | ||||
\(639\) | −70.6937 | + | 40.8150i | −0.110632 | + | 0.0638732i | ||||
\(640\) | −564.093 | + | 150.492i | −0.881395 | + | 0.235144i | ||||
\(641\) | 213.949 | − | 370.570i | 0.333774 | − | 0.578113i | −0.649475 | − | 0.760383i | \(-0.725011\pi\) |
0.983248 | + | 0.182270i | \(0.0583446\pi\) | |||||||
\(642\) | −27.0911 | − | 143.302i | −0.0421980 | − | 0.223211i | ||||
\(643\) | 15.9463 | 0.0247998 | 0.0123999 | − | 0.999923i | \(-0.496053\pi\) | ||||
0.0123999 | + | 0.999923i | \(0.496053\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 293.431i | − | 0.454932i | ||||||
\(646\) | 14.6431 | + | 77.4563i | 0.0226673 | + | 0.119901i | ||||
\(647\) | 450.510 | + | 260.102i | 0.696306 | + | 0.402012i | 0.805970 | − | 0.591956i | \(-0.201644\pi\) |
−0.109664 | + | 0.993969i | \(0.534978\pi\) | |||||||
\(648\) | 119.851 | − | 4.42865i | 0.184955 | − | 0.00683433i | ||||
\(649\) | −72.6542 | − | 125.841i | −0.111948 | − | 0.193899i | ||||
\(650\) | −50.9531 | + | 145.543i | −0.0783894 | + | 0.223913i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −256.466 | − | 204.655i | −0.393353 | − | 0.313888i | ||||
\(653\) | 367.687 | − | 212.284i | 0.563074 | − | 0.325091i | −0.191305 | − | 0.981531i | \(-0.561272\pi\) |
0.754378 | + | 0.656440i | \(0.227939\pi\) | |||||||
\(654\) | −18.9577 | − | 22.0361i | −0.0289872 | − | 0.0336943i | ||||
\(655\) | 936.371 | + | 540.614i | 1.42957 | + | 0.825365i | ||||
\(656\) | 710.033 | − | 657.995i | 1.08237 | − | 1.00304i | ||||
\(657\) | −619.246 | −0.942535 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 304.044 | 0.461372 | 0.230686 | − | 0.973028i | \(-0.425903\pi\) | ||||
0.230686 | + | 0.973028i | \(0.425903\pi\) | |||||||
\(660\) | 368.216 | + | 55.6165i | 0.557903 | + | 0.0842674i | ||||
\(661\) | 155.112 | + | 89.5542i | 0.234663 | + | 0.135483i | 0.612722 | − | 0.790299i | \(-0.290075\pi\) |
−0.378058 | + | 0.925782i | \(0.623408\pi\) | |||||||
\(662\) | 298.042 | − | 256.405i | 0.450214 | − | 0.387319i | ||||
\(663\) | 341.815 | − | 197.347i | 0.515559 | − | 0.297658i | ||||
\(664\) | 120.674 | + | 192.251i | 0.181738 | + | 0.289534i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 57.2016 | − | 163.391i | 0.0858883 | − | 0.245333i | ||||
\(667\) | −345.237 | − | 597.968i | −0.517597 | − | 0.896504i | ||||
\(668\) | −192.158 | − | 490.058i | −0.287662 | − | 0.733620i | ||||
\(669\) | −58.8671 | − | 33.9870i | −0.0879927 | − | 0.0508026i | ||||
\(670\) | 709.901 | − | 134.206i | 1.05955 | − | 0.200308i | ||||
\(671\) | 1348.20i | 2.00923i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 544.352 | 0.808844 | 0.404422 | − | 0.914573i | \(-0.367473\pi\) | ||||
0.404422 | + | 0.914573i | \(0.367473\pi\) | |||||||
\(674\) | 219.759 | + | 1162.44i | 0.326052 | + | 1.72469i | ||||
\(675\) | −52.8639 | + | 91.5629i | −0.0783168 | + | 0.135649i | ||||
\(676\) | 627.891 | − | 246.204i | 0.928833 | − | 0.364208i | ||||
\(677\) | −471.416 | + | 272.172i | −0.696330 | + | 0.402027i | −0.805979 | − | 0.591944i | \(-0.798361\pi\) |
0.109649 | + | 0.993970i | \(0.465027\pi\) | |||||||
\(678\) | −377.861 | − | 132.285i | −0.557318 | − | 0.195111i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 402.645 | − | 252.737i | 0.592125 | − | 0.371672i | ||||
\(681\) | −58.0730 | − | 100.585i | −0.0852760 | − | 0.147702i | ||||
\(682\) | 364.295 | + | 423.451i | 0.534157 | + | 0.620896i | ||||
\(683\) | −443.494 | + | 768.154i | −0.649332 | + | 1.12468i | 0.333951 | + | 0.942591i | \(0.391618\pi\) |
−0.983283 | + | 0.182086i | \(0.941715\pi\) | |||||||
\(684\) | −11.3524 | + | 75.1601i | −0.0165971 | + | 0.109883i | ||||
\(685\) | − | 44.0730i | − | 0.0643401i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 155.841i | 0.226842i | ||||||||
\(688\) | 457.908 | − | 424.348i | 0.665564 | − | 0.616786i | ||||
\(689\) | −43.7852 | + | 75.8382i | −0.0635489 | + | 0.110070i | ||||
\(690\) | 345.745 | − | 297.444i | 0.501080 | − | 0.431079i | ||||
\(691\) | 589.242 | + | 1020.60i | 0.852738 | + | 1.47698i | 0.878728 | + | 0.477323i | \(0.158393\pi\) |
−0.0259906 | + | 0.999662i | \(0.508274\pi\) | |||||||
\(692\) | 274.725 | − | 344.276i | 0.397002 | − | 0.497508i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −467.272 | − | 163.587i | −0.673302 | − | 0.235716i | ||||
\(695\) | 249.098 | − | 143.817i | 0.358414 | − | 0.206930i | ||||
\(696\) | 11.0905 | + | 300.138i | 0.0159346 | + | 0.431232i | ||||
\(697\) | −394.127 | + | 682.648i | −0.565462 | + | 0.979409i | ||||
\(698\) | 567.447 | − | 107.276i | 0.812962 | − | 0.153690i | ||||
\(699\) | 224.706 | 0.321468 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 901.601i | 1.28616i | 0.765797 | + | 0.643082i | \(0.222345\pi\) | ||||
−0.765797 | + | 0.643082i | \(0.777655\pi\) | |||||||
\(702\) | 909.789 | − | 171.995i | 1.29600 | − | 0.245007i | ||||
\(703\) | 36.1018 | + | 20.8434i | 0.0513539 | + | 0.0296492i | ||||
\(704\) | 445.708 | + | 655.042i | 0.633108 | + | 0.930458i | ||||
\(705\) | 76.4661 | + | 132.443i | 0.108463 | + | 0.187863i | ||||
\(706\) | −2.39669 | − | 0.839056i | −0.00339475 | − | 0.00118846i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 60.5075 | + | 48.2839i | 0.0854626 | + | 0.0681975i | ||||
\(709\) | 288.215 | − | 166.401i | 0.406510 | − | 0.234698i | −0.282779 | − | 0.959185i | \(-0.591256\pi\) |
0.689289 | + | 0.724487i | \(0.257923\pi\) | |||||||
\(710\) | −89.8661 | + | 77.3118i | −0.126572 | + | 0.108890i | ||||
\(711\) | −713.858 | − | 412.146i | −1.00402 | − | 0.579671i | ||||
\(712\) | −588.970 | + | 1113.13i | −0.827205 | + | 1.56339i | ||||
\(713\) | 684.126 | 0.959504 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1037.50 | −1.45104 | ||||||||
\(716\) | 91.9110 | − | 608.509i | 0.128367 | − | 0.849872i | ||||
\(717\) | 247.352 | + | 142.809i | 0.344982 | + | 0.199176i | ||||
\(718\) | 22.6983 | + | 26.3841i | 0.0316132 | + | 0.0367467i | ||||
\(719\) | −1026.20 | + | 592.475i | −1.42726 | + | 0.824027i | −0.996904 | − | 0.0786341i | \(-0.974944\pi\) |
−0.430353 | + | 0.902661i | \(0.641611\pi\) | |||||||
\(720\) | 446.983 | − | 101.729i | 0.620809 | − | 0.141291i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 664.171 | + | 232.519i | 0.919904 | + | 0.322049i | ||||
\(723\) | 271.160 | + | 469.663i | 0.375049 | + | 0.649603i | ||||
\(724\) | 332.214 | + | 847.240i | 0.458859 | + | 1.17022i | ||||
\(725\) | 82.7477 | + | 47.7744i | 0.114135 | + | 0.0658957i | ||||
\(726\) | −19.7584 | − | 104.514i | −0.0272154 | − | 0.143959i | ||||
\(727\) | − | 19.9398i | − | 0.0274275i | −0.999906 | − | 0.0137138i | \(-0.995635\pi\) | ||
0.999906 | − | 0.0137138i | \(-0.00436536\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 279.711 | 0.383691 | ||||||||
\(730\) | −883.635 | + | 167.051i | −1.21046 | + | 0.228837i | ||||
\(731\) | −254.177 | + | 440.247i | −0.347711 | + | 0.602254i | ||||
\(732\) | −262.193 | − | 668.666i | −0.358187 | − | 0.913479i | ||||
\(733\) | 898.325 | − | 518.648i | 1.22555 | − | 0.707569i | 0.259450 | − | 0.965756i | \(-0.416459\pi\) |
0.966095 | + | 0.258188i | \(0.0831252\pi\) | |||||||
\(734\) | 350.272 | − | 1000.52i | 0.477210 | − | 1.36311i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 964.173 | + | 109.393i | 1.31002 | + | 0.148632i | ||||
\(737\) | −490.231 | − | 849.105i | −0.665171 | − | 1.15211i | ||||
\(738\) | −576.210 | + | 495.713i | −0.780773 | + | 0.671699i | ||||
\(739\) | 209.986 | − | 363.706i | 0.284148 | − | 0.492160i | −0.688254 | − | 0.725470i | \(-0.741622\pi\) |
0.972402 | + | 0.233310i | \(0.0749558\pi\) | |||||||
\(740\) | 37.5467 | − | 248.583i | 0.0507388 | − | 0.335923i | ||||
\(741\) | 91.6491i | 0.123683i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1241.67i | − | 1.67116i | −0.549370 | − | 0.835579i | \(-0.685132\pi\) | ||
0.549370 | − | 0.835579i | \(-0.314868\pi\) | |||||||
\(744\) | −263.031 | − | 139.173i | −0.353537 | − | 0.187060i | ||||
\(745\) | −615.551 | + | 1066.17i | −0.826243 | + | 1.43109i | ||||
\(746\) | 154.712 | + | 179.835i | 0.207389 | + | 0.241066i | ||||
\(747\) | −89.1137 | − | 154.349i | −0.119295 | − | 0.206626i | ||||
\(748\) | −504.274 | − | 402.401i | −0.674163 | − | 0.537969i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −145.099 | + | 414.462i | −0.193465 | + | 0.552615i | ||||
\(751\) | 561.008 | − | 323.898i | 0.747015 | − | 0.431289i | −0.0775992 | − | 0.996985i | \(-0.524725\pi\) |
0.824614 | + | 0.565695i | \(0.191392\pi\) | |||||||
\(752\) | −96.0993 | + | 310.861i | −0.127792 | + | 0.413379i | ||||
\(753\) | −132.112 | + | 228.825i | −0.175448 | + | 0.303885i | ||||
\(754\) | −155.436 | − | 822.198i | −0.206149 | − | 1.09045i | ||||
\(755\) | −493.411 | −0.653524 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 105.310i | − | 0.139116i | −0.997578 | − | 0.0695578i | \(-0.977841\pi\) | ||
0.997578 | − | 0.0695578i | \(-0.0221588\pi\) | |||||||
\(758\) | −128.526 | − | 679.852i | −0.169559 | − | 0.896903i | ||||
\(759\) | −536.023 | − | 309.473i | −0.706223 | − | 0.407738i | ||||
\(760\) | 4.07620 | + | 110.312i | 0.00536342 | + | 0.145148i | ||||
\(761\) | −210.942 | − | 365.362i | −0.277190 | − | 0.480108i | 0.693495 | − | 0.720461i | \(-0.256070\pi\) |
−0.970685 | + | 0.240354i | \(0.922737\pi\) | |||||||
\(762\) | 242.810 | − | 693.567i | 0.318649 | − | 0.910193i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −303.247 | + | 380.018i | −0.396921 | + | 0.497406i | ||||
\(765\) | −323.266 | + | 186.638i | −0.422570 | + | 0.243971i | ||||
\(766\) | −528.092 | − | 613.846i | −0.689415 | − | 0.801366i | ||||
\(767\) | −186.775 | − | 107.835i | −0.243514 | − | 0.140593i | ||||
\(768\) | −348.449 | − | 238.202i | −0.453710 | − | 0.310159i | ||||
\(769\) | 189.767 | 0.246772 | 0.123386 | − | 0.992359i | \(-0.460625\pi\) | ||||
0.123386 | + | 0.992359i | \(0.460625\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 239.801 | 0.311025 | ||||||||
\(772\) | 51.0506 | − | 337.987i | 0.0661277 | − | 0.437807i | ||||
\(773\) | 729.875 | + | 421.394i | 0.944211 | + | 0.545141i | 0.891278 | − | 0.453457i | \(-0.149810\pi\) |
0.0529334 | + | 0.998598i | \(0.483143\pi\) | |||||||
\(774\) | −371.604 | + | 319.691i | −0.480109 | + | 0.413038i | ||||
\(775\) | −81.9870 | + | 47.3352i | −0.105790 | + | 0.0610777i | ||||
\(776\) | −168.497 | − | 268.439i | −0.217136 | − | 0.345927i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 88.8164 | − | 253.696i | 0.114160 | − | 0.326088i | ||||
\(779\) | −91.5174 | − | 158.513i | −0.117481 | − | 0.203482i | ||||
\(780\) | 514.569 | − | 201.769i | 0.659703 | − | 0.258678i | ||||
\(781\) | 139.323 | + | 80.4382i | 0.178391 | + | 0.102994i | ||||
\(782\) | −776.389 | + | 146.776i | −0.992825 | + | 0.187693i | ||||
\(783\) | − | 573.712i | − | 0.732710i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −540.181 | −0.688128 | ||||||||
\(786\) | 145.207 | + | 768.091i | 0.184742 | + | 0.977216i | ||||
\(787\) | 747.098 | − | 1294.01i | 0.949298 | − | 1.64423i | 0.202391 | − | 0.979305i | \(-0.435129\pi\) |
0.746907 | − | 0.664928i | \(-0.231538\pi\) | |||||||
\(788\) | −312.630 | − | 797.296i | −0.396739 | − | 1.01180i | ||||
\(789\) | 289.553 | − | 167.173i | 0.366987 | − | 0.211880i | ||||
\(790\) | −1129.82 | − | 395.539i | −1.43016 | − | 0.500682i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −330.735 | − | 526.906i | −0.417595 | − | 0.665286i | ||||
\(793\) | 1000.51 | + | 1732.93i | 1.26168 | + | 2.18529i | ||||
\(794\) | 798.883 | + | 928.610i | 1.00615 | + | 1.16953i | ||||
\(795\) | −17.9206 | + | 31.0394i | −0.0225417 | + | 0.0390433i | ||||
\(796\) | −981.758 | − | 148.288i | −1.23336 | − | 0.186291i | ||||
\(797\) | − | 292.040i | − | 0.366424i | −0.983073 | − | 0.183212i | \(-0.941351\pi\) | ||
0.983073 | − | 0.183212i | \(-0.0586494\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 264.947i | − | 0.331598i | ||||||
\(800\) | −123.117 | + | 53.6019i | −0.153897 | + | 0.0670024i | ||||
\(801\) | 494.414 | − | 856.349i | 0.617245 | − | 1.06910i | ||||
\(802\) | −191.408 | + | 164.669i | −0.238664 | + | 0.205322i | ||||
\(803\) | 610.205 | + | 1056.91i | 0.759906 | + | 1.31620i | ||||
\(804\) | 408.272 | + | 325.793i | 0.507801 | + | 0.405215i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 782.502 | + | 273.946i | 0.970847 | + | 0.339883i | ||||
\(807\) | 316.007 | − | 182.447i | 0.391582 | − | 0.226080i | ||||
\(808\) | −12.8853 | − | 348.708i | −0.0159471 | − | 0.431570i | ||||
\(809\) | −78.4531 | + | 135.885i | −0.0969754 | + | 0.167966i | −0.910431 | − | 0.413660i | \(-0.864250\pi\) |
0.813456 | + | 0.581627i | \(0.197583\pi\) | |||||||
\(810\) | −134.376 | + | 25.4037i | −0.165896 | + | 0.0313626i | ||||
\(811\) | −1183.00 | −1.45869 | −0.729347 | − | 0.684144i | \(-0.760176\pi\) | ||||
−0.729347 | + | 0.684144i | \(0.760176\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 193.527i | − | 0.238040i | ||||||
\(814\) | −335.237 | + | 63.3764i | −0.411839 | + | 0.0778580i | ||||
\(815\) | 324.015 | + | 187.070i | 0.397565 | + | 0.229534i | ||||
\(816\) | 328.363 | + | 101.510i | 0.402406 | + | 0.124399i | ||||
\(817\) | −59.0206 | − | 102.227i | −0.0722406 | − | 0.125124i | ||||
\(818\) | 646.561 | + | 226.354i | 0.790417 | + | 0.276716i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −688.499 | + | 862.801i | −0.839633 | + | 1.05220i | ||||
\(821\) | −160.574 | + | 92.7074i | −0.195583 | + | 0.112920i | −0.594594 | − | 0.804026i | \(-0.702687\pi\) |
0.399010 | + | 0.916946i | \(0.369354\pi\) | |||||||
\(822\) | 24.1548 | − | 20.7804i | 0.0293854 | − | 0.0252803i | ||||
\(823\) | 564.922 | + | 326.158i | 0.686418 | + | 0.396304i | 0.802269 | − | 0.596963i | \(-0.203626\pi\) |
−0.115850 | + | 0.993267i | \(0.536959\pi\) | |||||||
\(824\) | −444.792 | − | 235.344i | −0.539796 | − | 0.285612i | ||||
\(825\) | 85.6506 | 0.103819 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −829.430 | −1.00294 | −0.501469 | − | 0.865176i | \(-0.667207\pi\) | ||||
−0.501469 | + | 0.865176i | \(0.667207\pi\) | |||||||
\(828\) | −753.373 | − | 113.792i | −0.909871 | − | 0.137430i | ||||
\(829\) | 653.961 | + | 377.565i | 0.788856 | + | 0.455446i | 0.839560 | − | 0.543268i | \(-0.182813\pi\) |
−0.0507039 | + | 0.998714i | \(0.516146\pi\) | |||||||
\(830\) | −168.799 | − | 196.210i | −0.203372 | − | 0.236397i | ||||
\(831\) | 364.837 | − | 210.639i | 0.439034 | − | 0.253476i | ||||
\(832\) | 1059.01 | + | 511.209i | 1.27285 | + | 0.614434i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 196.270 | + | 68.7122i | 0.235336 | + | 0.0823887i | ||||
\(835\) | 300.113 | + | 519.811i | 0.359417 | + | 0.622528i | ||||
\(836\) | 139.467 | − | 54.6869i | 0.166827 | − | 0.0654149i | ||||
\(837\) | 492.281 | + | 284.219i | 0.588150 | + | 0.339568i | ||||
\(838\) | 139.837 | + | 739.682i | 0.166869 | + | 0.882676i | ||||
\(839\) | 88.6147i | 0.105619i | 0.998605 | + | 0.0528097i | \(0.0168177\pi\) | ||||
−0.998605 | + | 0.0528097i | \(0.983182\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 322.522 | 0.383499 | ||||||||
\(842\) | −218.401 | + | 41.2886i | −0.259383 | + | 0.0490363i | ||||
\(843\) | −229.183 | + | 396.956i | −0.271866 | + | 0.470885i | ||||
\(844\) | −714.079 | + | 280.000i | −0.846066 | + | 0.331753i | ||||
\(845\) | −666.013 | + | 384.523i | −0.788181 | + | 0.455056i | ||||
\(846\) | 84.4181 | − | 241.133i | 0.0997850 | − | 0.285027i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −74.3540 | + | 16.9223i | −0.0876816 | + | 0.0199555i | ||||
\(849\) | −46.7343 | − | 80.9461i | −0.0550462 | − | 0.0953429i | ||||
\(850\) | 82.8883 | − | 71.3088i | 0.0975157 | − | 0.0838927i | ||||
\(851\) | −208.925 | + | 361.869i | −0.245506 | + | 0.425228i | ||||
\(852\) | −84.7437 | − | 12.7999i | −0.0994644 | − | 0.0150234i | ||||
\(853\) | 367.466i | 0.430792i | 0.976527 | + | 0.215396i | \(0.0691042\pi\) | ||||
−0.976527 | + | 0.215396i | \(0.930896\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 86.6755i | − | 0.101375i | ||||||
\(856\) | −165.472 | + | 312.735i | −0.193308 | + | 0.365345i | ||||
\(857\) | −82.6698 | + | 143.188i | −0.0964642 | + | 0.167081i | −0.910219 | − | 0.414128i | \(-0.864087\pi\) |
0.813755 | + | 0.581209i | \(0.197420\pi\) | |||||||
\(858\) | −489.179 | − | 568.615i | −0.570139 | − | 0.662721i | ||||
\(859\) | −325.486 | − | 563.758i | −0.378913 | − | 0.656296i | 0.611992 | − | 0.790864i | \(-0.290369\pi\) |
−0.990904 | + | 0.134568i | \(0.957035\pi\) | |||||||
\(860\) | −444.021 | + | 556.430i | −0.516303 | + | 0.647012i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.2788 | + | 77.9197i | −0.0316460 | + | 0.0903941i | ||||
\(863\) | −118.417 | + | 68.3679i | −0.137215 | + | 0.0792212i | −0.567036 | − | 0.823693i | \(-0.691910\pi\) |
0.429821 | + | 0.902914i | \(0.358577\pi\) | |||||||
\(864\) | 648.349 | + | 479.280i | 0.750404 | + | 0.554723i | ||||
\(865\) | −251.120 | + | 434.953i | −0.290312 | + | 0.502836i | ||||
\(866\) | 250.840 | + | 1326.85i | 0.289654 | + | 1.53216i | ||||
\(867\) | 196.633 | 0.226797 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1624.51i | 1.86941i | ||||||||
\(870\) | −63.6177 | − | 336.513i | −0.0731238 | − | 0.386797i | ||||
\(871\) | −1260.26 | − | 727.611i | −1.44691 | − | 0.835374i | ||||
\(872\) | 2.60410 | + | 70.4735i | 0.00298635 | + | 0.0808182i | ||||
\(873\) | 124.429 | + | 215.518i | 0.142531 | + | 0.246871i | ||||
\(874\) | 60.6241 | − | 173.168i | 0.0693640 | − | 0.198132i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −508.188 | − | 405.524i | −0.580123 | − | 0.462927i | ||||
\(877\) | −152.855 | + | 88.2509i | −0.174293 | + | 0.100628i | −0.584609 | − | 0.811315i | \(-0.698752\pi\) |
0.410316 | + | 0.911944i | \(0.365419\pi\) | |||||||
\(878\) | −691.634 | − | 803.946i | −0.787738 | − | 0.915656i | ||||
\(879\) | 411.045 | + | 237.317i | 0.467628 | + | 0.269985i | ||||
\(880\) | −614.085 | − | 662.650i | −0.697823 | − | 0.753011i | ||||
\(881\) | −734.879 | −0.834142 | −0.417071 | − | 0.908874i | \(-0.636943\pi\) | ||||
−0.417071 | + | 0.908874i | \(0.636943\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 872.637 | 0.988264 | 0.494132 | − | 0.869387i | \(-0.335486\pi\) | ||||
0.494132 | + | 0.869387i | \(0.335486\pi\) | |||||||
\(884\) | −946.806 | − | 143.008i | −1.07105 | − | 0.161774i | ||||
\(885\) | −76.4443 | − | 44.1352i | −0.0863778 | − | 0.0498702i | ||||
\(886\) | 503.410 | − | 433.084i | 0.568183 | − | 0.488808i | ||||
\(887\) | 20.8696 | − | 12.0490i | 0.0235282 | − | 0.0135840i | −0.488190 | − | 0.872738i | \(-0.662343\pi\) |
0.511718 | + | 0.859153i | \(0.329009\pi\) | |||||||
\(888\) | 153.943 | − | 96.6288i | 0.173359 | − | 0.108816i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 474.492 | − | 1355.35i | 0.533137 | − | 1.52286i | ||||
\(891\) | 92.7951 | + | 160.726i | 0.104147 | + | 0.180388i | ||||
\(892\) | 60.1999 | + | 153.527i | 0.0674887 | + | 0.172115i | ||||
\(893\) | 53.2790 | + | 30.7607i | 0.0596630 | + | 0.0344464i | ||||
\(894\) | −874.559 | + | 165.335i | −0.978254 | + | 0.184939i | ||||
\(895\) | 701.740i | 0.784067i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −918.652 | −1.02414 | ||||||||
\(898\) | −7.21490 | − | 38.1641i | −0.00803441 | − | 0.0424989i | ||||
\(899\) | 256.855 | − | 444.887i | 0.285712 | − | 0.494868i | ||||
\(900\) | 98.1589 | − | 38.4894i | 0.109065 | − | 0.0427660i | ||||
\(901\) | 53.7741 | − | 31.0465i | 0.0596827 | − | 0.0344578i | ||||
\(902\) | 1413.86 | + | 494.978i | 1.56748 | + | 0.548756i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 516.360 | + | 822.631i | 0.571194 | + | 0.909990i | ||||
\(905\) | −518.852 | − | 898.678i | −0.573317 | − | 0.993014i | ||||
\(906\) | −232.643 | − | 270.421i | −0.256780 | − | 0.298478i | ||||
\(907\) | 706.653 | − | 1223.96i | 0.779110 | − | 1.34946i | −0.153345 | − | 0.988173i | \(-0.549005\pi\) |
0.932455 | − | 0.361285i | \(-0.117662\pi\) | |||||||
\(908\) | −42.0828 | + | 278.615i | −0.0463467 | + | 0.306844i | ||||
\(909\) | 273.990i | 0.301419i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1778.28i | 1.95201i | 0.217746 | + | 0.976005i | \(0.430129\pi\) | ||||
−0.217746 | + | 0.976005i | \(0.569871\pi\) | |||||||
\(912\) | −58.5364 | + | 54.2463i | −0.0641846 | + | 0.0594806i | ||||
\(913\) | −175.625 | + | 304.192i | −0.192361 | + | 0.333179i | ||||
\(914\) | −269.812 | + | 232.119i | −0.295199 | + | 0.253960i | ||||
\(915\) | 409.493 | + | 709.263i | 0.447534 | + | 0.775151i | ||||
\(916\) | 235.818 | − | 295.518i | 0.257443 | − | 0.322618i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −619.649 | − | 216.932i | −0.674999 | − | 0.236310i | ||||
\(919\) | −774.089 | + | 446.921i | −0.842317 | + | 0.486312i | −0.858051 | − | 0.513564i | \(-0.828325\pi\) |
0.0157340 | + | 0.999876i | \(0.494991\pi\) | |||||||
\(920\) | −1105.72 | + | 40.8581i | −1.20187 | + | 0.0444110i | ||||
\(921\) | −44.2270 | + | 76.6034i | −0.0480206 | + | 0.0831742i | ||||
\(922\) | 588.261 | − | 111.211i | 0.638028 | − | 0.120619i | ||||
\(923\) | 238.776 | 0.258696 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 57.8228i | − | 0.0625111i | ||||||
\(926\) | −992.840 | + | 187.696i | −1.07218 | + | 0.202695i | ||||
\(927\) | 342.185 | + | 197.561i | 0.369132 | + | 0.213118i | ||||
\(928\) | 433.138 | − | 585.929i | 0.466743 | − | 0.631389i | ||||
\(929\) | −364.730 | − | 631.731i | −0.392605 | − | 0.680012i | 0.600187 | − | 0.799859i | \(-0.295093\pi\) |
−0.992792 | + | 0.119848i | \(0.961759\pi\) | |||||||
\(930\) | 320.266 | + | 112.122i | 0.344372 | + | 0.120561i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −426.108 | − | 340.026i | −0.457197 | − | 0.364835i | ||||
\(933\) | 150.082 | − | 86.6499i | 0.160860 | − | 0.0928724i | ||||
\(934\) | 985.986 | − | 848.243i | 1.05566 | − | 0.908183i | ||||
\(935\) | 637.092 | + | 367.825i | 0.681382 | + | 0.393396i | ||||
\(936\) | −816.141 | − | 431.829i | −0.871945 | − | 0.461356i | ||||
\(937\) | −637.240 | −0.680085 | −0.340042 | − | 0.940410i | \(-0.610441\pi\) | ||||
−0.340042 | + | 0.940410i | \(0.610441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 347.051 | 0.369596 | ||||||||
\(940\) | 55.4114 | − | 366.859i | 0.0589483 | − | 0.390275i | ||||
\(941\) | −1518.64 | − | 876.787i | −1.61386 | − | 0.931761i | −0.988465 | − | 0.151451i | \(-0.951605\pi\) |
−0.625393 | − | 0.780310i | \(-0.715061\pi\) | |||||||
\(942\) | −254.695 | − | 296.054i | −0.270377 | − | 0.314282i | ||||
\(943\) | 1588.87 | − | 917.332i | 1.68491 | − | 0.972780i | ||||
\(944\) | −41.6764 | − | 183.120i | −0.0441488 | − | 0.193983i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 911.816 | + | 319.217i | 0.963865 | + | 0.337439i | ||||
\(947\) | 436.996 | + | 756.900i | 0.461453 | + | 0.799261i | 0.999034 | − | 0.0439519i | \(-0.0139948\pi\) |
−0.537580 | + | 0.843213i | \(0.680661\pi\) | |||||||
\(948\) | −315.931 | − | 805.713i | −0.333260 | − | 0.849908i | ||||
\(949\) | 1568.68 | + | 905.679i | 1.65298 | + | 0.954351i | ||||
\(950\) | 4.71629 | + | 24.9474i | 0.00496451 | + | 0.0262604i | ||||
\(951\) | 103.688i | 0.109031i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −880.208 | −0.923618 | −0.461809 | − | 0.886979i | \(-0.652800\pi\) | ||||
−0.461809 | + | 0.886979i | \(0.652800\pi\) | |||||||
\(954\) | 58.8330 | − | 11.1223i | 0.0616698 | − | 0.0116586i | ||||
\(955\) | 277.191 | − | 480.110i | 0.290253 | − | 0.502733i | ||||
\(956\) | −252.952 | − | 645.100i | −0.264594 | − | 0.674791i | ||||
\(957\) | −402.500 | + | 232.383i | −0.420585 | + | 0.242825i | ||||
\(958\) | −436.790 | + | 1247.65i | −0.455939 | + | 1.30235i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 433.439 | + | 209.230i | 0.451498 | + | 0.217948i | ||||
\(961\) | −226.006 | − | 391.454i | −0.235178 | − | 0.407340i | ||||
\(962\) | −383.872 | + | 330.245i | −0.399036 | + | 0.343290i | ||||
\(963\) | 138.906 | − | 240.592i | 0.144243 | − | 0.249836i | ||||
\(964\) | 196.497 | − | 1300.94i | 0.203835 | − | 1.34952i | ||||
\(965\) | 389.771i | 0.403908i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 259.016i | 0.267855i | 0.990991 | + | 0.133928i | \(0.0427590\pi\) | ||||
−0.990991 | + | 0.133928i | \(0.957241\pi\) | |||||||
\(968\) | −120.683 | + | 228.087i | −0.124673 | + | 0.235627i | ||||
\(969\) | 32.4925 | − | 56.2787i | 0.0335320 | − | 0.0580792i | ||||
\(970\) | 235.694 | + | 273.967i | 0.242984 | + | 0.282441i | ||||
\(971\) | −216.325 | − | 374.686i | −0.222786 | − | 0.385877i | 0.732867 | − | 0.680372i | \(-0.238182\pi\) |
−0.955653 | + | 0.294495i | \(0.904848\pi\) | |||||||
\(972\) | −786.266 | − | 627.425i | −0.808916 | − | 0.645499i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 255.155 | − | 728.827i | 0.261966 | − | 0.748283i | ||||
\(975\) | 110.093 | − | 63.5622i | 0.112916 | − | 0.0651920i | ||||
\(976\) | −514.634 | + | 1664.73i | −0.527289 | + | 1.70567i | ||||
\(977\) | −407.755 | + | 706.252i | −0.417354 | + | 0.722878i | −0.995672 | − | 0.0929330i | \(-0.970376\pi\) |
0.578319 | + | 0.815811i | \(0.303709\pi\) | |||||||
\(978\) | 50.2465 | + | 265.785i | 0.0513768 | + | 0.271764i | ||||
\(979\) | −1948.78 | −1.99058 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 55.3730i | − | 0.0564455i | ||||||
\(982\) | −333.757 | − | 1765.45i | −0.339875 | − | 1.79781i | ||||
\(983\) | 120.735 | + | 69.7061i | 0.122822 | + | 0.0709116i | 0.560153 | − | 0.828389i | \(-0.310743\pi\) |
−0.437330 | + | 0.899301i | \(0.644076\pi\) | |||||||
\(984\) | −797.498 | + | 29.4687i | −0.810465 | + | 0.0299478i | ||||
\(985\) | 488.267 | + | 845.702i | 0.495702 | + | 0.858581i | ||||
\(986\) | −196.047 | + | 559.992i | −0.198831 | + | 0.567943i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 138.684 | − | 173.793i | 0.140368 | − | 0.175904i | ||||
\(989\) | 1024.68 | − | 591.598i | 1.03607 | − | 0.598178i | ||||
\(990\) | 462.633 | + | 537.757i | 0.467306 | + | 0.543189i | ||||
\(991\) | −1341.28 | − | 774.390i | −1.35346 | − | 0.781423i | −0.364731 | − | 0.931113i | \(-0.618839\pi\) |
−0.988733 | + | 0.149690i | \(0.952172\pi\) | |||||||
\(992\) | 288.187 | + | 661.931i | 0.290511 | + | 0.667269i | ||||
\(993\) | −324.114 | −0.326399 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1132.18 | 1.13786 | ||||||||
\(996\) | 27.9468 | − | 185.026i | 0.0280591 | − | 0.185769i | ||||
\(997\) | −1110.67 | − | 641.248i | −1.11402 | − | 0.643178i | −0.174150 | − | 0.984719i | \(-0.555718\pi\) |
−0.939867 | + | 0.341541i | \(0.889051\pi\) | |||||||
\(998\) | 1199.54 | − | 1031.96i | 1.20194 | − | 1.03403i | ||||
\(999\) | −300.676 | + | 173.595i | −0.300977 | + | 0.173769i |
(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 | 392.3.k.l.67.4 | 12 | ||
7.2 | even | 3 | inner | 392.3.k.l.275.5 | 12 | ||
7.3 | odd | 6 | 392.3.g.j.99.1 | 6 | |||
7.4 | even | 3 | 392.3.g.i.99.1 | 6 | |||
7.5 | odd | 6 | 56.3.k.d.51.5 | yes | 12 | ||
7.6 | odd | 2 | 56.3.k.d.11.4 | ✓ | 12 | ||
8.3 | odd | 2 | inner | 392.3.k.l.67.5 | 12 | ||
28.3 | even | 6 | 1568.3.g.j.687.3 | 6 | |||
28.11 | odd | 6 | 1568.3.g.l.687.4 | 6 | |||
28.19 | even | 6 | 224.3.o.d.79.4 | 12 | |||
28.27 | even | 2 | 224.3.o.d.207.3 | 12 | |||
56.3 | even | 6 | 392.3.g.j.99.2 | 6 | |||
56.5 | odd | 6 | 224.3.o.d.79.3 | 12 | |||
56.11 | odd | 6 | 392.3.g.i.99.2 | 6 | |||
56.13 | odd | 2 | 224.3.o.d.207.4 | 12 | |||
56.19 | even | 6 | 56.3.k.d.51.4 | yes | 12 | ||
56.27 | even | 2 | 56.3.k.d.11.5 | yes | 12 | ||
56.45 | odd | 6 | 1568.3.g.j.687.4 | 6 | |||
56.51 | odd | 6 | inner | 392.3.k.l.275.4 | 12 | ||
56.53 | even | 6 | 1568.3.g.l.687.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.k.d.11.4 | ✓ | 12 | 7.6 | odd | 2 | ||
56.3.k.d.11.5 | yes | 12 | 56.27 | even | 2 | ||
56.3.k.d.51.4 | yes | 12 | 56.19 | even | 6 | ||
56.3.k.d.51.5 | yes | 12 | 7.5 | odd | 6 | ||
224.3.o.d.79.3 | 12 | 56.5 | odd | 6 | |||
224.3.o.d.79.4 | 12 | 28.19 | even | 6 | |||
224.3.o.d.207.3 | 12 | 28.27 | even | 2 | |||
224.3.o.d.207.4 | 12 | 56.13 | odd | 2 | |||
392.3.g.i.99.1 | 6 | 7.4 | even | 3 | |||
392.3.g.i.99.2 | 6 | 56.11 | odd | 6 | |||
392.3.g.j.99.1 | 6 | 7.3 | odd | 6 | |||
392.3.g.j.99.2 | 6 | 56.3 | even | 6 | |||
392.3.k.l.67.4 | 12 | 1.1 | even | 1 | trivial | ||
392.3.k.l.67.5 | 12 | 8.3 | odd | 2 | inner | ||
392.3.k.l.275.4 | 12 | 56.51 | odd | 6 | inner | ||
392.3.k.l.275.5 | 12 | 7.2 | even | 3 | inner | ||
1568.3.g.j.687.3 | 6 | 28.3 | even | 6 | |||
1568.3.g.j.687.4 | 6 | 56.45 | odd | 6 | |||
1568.3.g.l.687.3 | 6 | 56.53 | even | 6 | |||
1568.3.g.l.687.4 | 6 | 28.11 | odd | 6 |