Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,3,Mod(37,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 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("315.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.ca (of order \(12\), degree \(4\), 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: | \(8.58312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 163.1 | ||
Character | \(\chi\) | \(=\) | 315.163 |
Dual form | 315.3.ca.b.172.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.955194 | − | 3.56483i | −0.477597 | − | 1.78242i | −0.611304 | − | 0.791396i | \(-0.709355\pi\) |
0.133707 | − | 0.991021i | \(-0.457312\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.33154 | + | 4.81021i | −2.08288 | + | 1.20255i | ||||
\(5\) | 3.70210 | − | 3.36072i | 0.740421 | − | 0.672143i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.07429 | + | 6.28878i | 0.439185 | + | 0.898397i | ||||
\(8\) | 14.6673 | + | 14.6673i | 1.83341 | + | 1.83341i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −15.5166 | − | 9.98725i | −1.55166 | − | 0.998725i | ||||
\(11\) | 4.09367 | + | 7.09045i | 0.372152 | + | 0.644586i | 0.989896 | − | 0.141793i | \(-0.0452866\pi\) |
−0.617744 | + | 0.786379i | \(0.711953\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.0569 | + | 14.0569i | 1.08130 | + | 1.08130i | 0.996389 | + | 0.0849086i | \(0.0270598\pi\) |
0.0849086 | + | 0.996389i | \(0.472940\pi\) | |||||||
\(14\) | 19.4819 | − | 16.9663i | 1.39156 | − | 1.21188i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 19.0355 | − | 32.9704i | 1.18972 | − | 2.06065i | ||||
\(17\) | 6.76150 | + | 1.81174i | 0.397735 | + | 0.106573i | 0.452142 | − | 0.891946i | \(-0.350660\pi\) |
−0.0544067 | + | 0.998519i | \(0.517327\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.2350 | + | 10.5280i | 0.959739 | + | 0.554105i | 0.896093 | − | 0.443867i | \(-0.146394\pi\) |
0.0636460 | + | 0.997973i | \(0.479727\pi\) | |||||||
\(20\) | −14.6784 | + | 45.8079i | −0.733922 | + | 2.29039i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 21.3660 | − | 21.3660i | 0.971183 | − | 0.971183i | ||||
\(23\) | −31.4621 | + | 8.43024i | −1.36792 | + | 0.366532i | −0.866717 | − | 0.498800i | \(-0.833774\pi\) |
−0.501199 | + | 0.865332i | \(0.667108\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.41116 | − | 24.8835i | 0.0964464 | − | 0.995338i | ||||
\(26\) | 36.6833 | − | 63.5374i | 1.41090 | − | 2.44375i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −55.8639 | − | 37.6072i | −1.99514 | − | 1.34311i | ||||
\(29\) | − | 22.1129i | − | 0.762515i | −0.924469 | − | 0.381258i | \(-0.875491\pi\) | ||
0.924469 | − | 0.381258i | \(-0.124509\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 13.7286 | + | 23.7786i | 0.442857 | + | 0.767052i | 0.997900 | − | 0.0647702i | \(-0.0206314\pi\) |
−0.555043 | + | 0.831822i | \(0.687298\pi\) | |||||||
\(32\) | −55.5730 | − | 14.8907i | −1.73666 | − | 0.465335i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 25.8342i | − | 0.759829i | ||||||
\(35\) | 32.5162 | + | 12.9499i | 0.929033 | + | 0.369997i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.01580 | − | 14.9872i | −0.108535 | − | 0.405058i | 0.890187 | − | 0.455595i | \(-0.150573\pi\) |
−0.998722 | + | 0.0505367i | \(0.983907\pi\) | |||||||
\(38\) | 20.1126 | − | 75.0611i | 0.529278 | − | 1.97529i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 103.592 | + | 5.00723i | 2.58981 | + | 0.125181i | ||||
\(41\) | −0.496183 | −0.0121020 | −0.00605101 | − | 0.999982i | \(-0.501926\pi\) | ||||
−0.00605101 | + | 0.999982i | \(0.501926\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −33.4554 | − | 33.4554i | −0.778032 | − | 0.778032i | 0.201464 | − | 0.979496i | \(-0.435430\pi\) |
−0.979496 | + | 0.201464i | \(0.935430\pi\) | |||||||
\(44\) | −68.2132 | − | 39.3829i | −1.55030 | − | 0.895066i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 60.1048 | + | 104.105i | 1.30663 | + | 2.26314i | ||||
\(47\) | 6.46488 | + | 24.1272i | 0.137551 | + | 0.513346i | 0.999974 | + | 0.00715874i | \(0.00227872\pi\) |
−0.862424 | + | 0.506187i | \(0.831055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −30.0975 | + | 38.6671i | −0.614234 | + | 0.789124i | ||||
\(50\) | −91.0085 | + | 15.1731i | −1.82017 | + | 0.303463i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −184.732 | − | 49.4987i | −3.55253 | − | 0.951899i | ||||
\(53\) | −9.20667 | + | 34.3598i | −0.173711 | + | 0.648297i | 0.823057 | + | 0.567959i | \(0.192267\pi\) |
−0.996768 | + | 0.0803384i | \(0.974400\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 38.9842 | + | 12.4919i | 0.708804 | + | 0.227126i | ||||
\(56\) | −47.1478 | + | 137.331i | −0.841925 | + | 2.45234i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −78.8289 | + | 21.1222i | −1.35912 | + | 0.364175i | ||||
\(59\) | −15.5949 | + | 9.00371i | −0.264320 | + | 0.152605i | −0.626304 | − | 0.779579i | \(-0.715433\pi\) |
0.361984 | + | 0.932184i | \(0.382100\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.4849 | − | 23.3565i | 0.221064 | − | 0.382894i | −0.734067 | − | 0.679077i | \(-0.762380\pi\) |
0.955131 | + | 0.296183i | \(0.0957137\pi\) | |||||||
\(62\) | 71.6533 | − | 71.6533i | 1.15570 | − | 1.15570i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 60.0481i | 0.938252i | ||||||||
\(65\) | 99.2811 | + | 4.79884i | 1.52740 | + | 0.0738283i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.37586 | + | 1.44046i | 0.0802367 | + | 0.0214993i | 0.298714 | − | 0.954343i | \(-0.403442\pi\) |
−0.218477 | + | 0.975842i | \(0.570109\pi\) | |||||||
\(68\) | −65.0485 | + | 17.4297i | −0.956596 | + | 0.256319i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 15.1050 | − | 128.284i | 0.215785 | − | 1.83263i | ||||
\(71\) | 105.010 | 1.47902 | 0.739509 | − | 0.673146i | \(-0.235058\pi\) | ||||
0.739509 | + | 0.673146i | \(0.235058\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 21.8814 | − | 81.6625i | 0.299745 | − | 1.11866i | −0.637630 | − | 0.770343i | \(-0.720085\pi\) |
0.937375 | − | 0.348321i | \(-0.113248\pi\) | |||||||
\(74\) | −49.5909 | + | 28.6313i | −0.670147 | + | 0.386909i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −202.568 | −2.66537 | ||||||||
\(77\) | −32.0051 | + | 47.5423i | −0.415651 | + | 0.617433i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 86.5708 | + | 49.9817i | 1.09583 | + | 0.632679i | 0.935123 | − | 0.354322i | \(-0.115288\pi\) |
0.160710 | + | 0.987002i | \(0.448622\pi\) | |||||||
\(80\) | −40.3329 | − | 186.033i | −0.504161 | − | 2.32541i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.473951 | + | 1.76881i | 0.00577989 | + | 0.0215708i | ||||
\(83\) | −95.6303 | − | 95.6303i | −1.15217 | − | 1.15217i | −0.986116 | − | 0.166057i | \(-0.946897\pi\) |
−0.166057 | − | 0.986116i | \(-0.553103\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 31.1205 | − | 16.0162i | 0.366124 | − | 0.188426i | ||||
\(86\) | −87.3064 | + | 151.219i | −1.01519 | + | 1.75836i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −43.9546 | + | 164.041i | −0.499484 | + | 1.86410i | ||||
\(89\) | 54.3480 | + | 31.3778i | 0.610651 | + | 0.352560i | 0.773220 | − | 0.634137i | \(-0.218645\pi\) |
−0.162569 | + | 0.986697i | \(0.551978\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −45.1856 | + | 131.615i | −0.496545 | + | 1.44632i | ||||
\(92\) | 221.576 | − | 221.576i | 2.40844 | − | 2.40844i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 79.8344 | − | 46.0924i | 0.849302 | − | 0.490345i | ||||
\(95\) | 102.890 | − | 22.3070i | 1.08305 | − | 0.234811i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 59.0158 | − | 59.0158i | 0.608410 | − | 0.608410i | −0.334120 | − | 0.942530i | \(-0.608439\pi\) |
0.942530 | + | 0.334120i | \(0.108439\pi\) | |||||||
\(98\) | 166.591 | + | 70.3578i | 1.69990 | + | 0.717937i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 99.6061 | + | 218.916i | 0.996061 | + | 2.18916i | ||||
\(101\) | −19.3636 | − | 33.5388i | −0.191719 | − | 0.332067i | 0.754101 | − | 0.656758i | \(-0.228073\pi\) |
−0.945820 | + | 0.324691i | \(0.894740\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 29.9227 | − | 8.01775i | 0.290511 | − | 0.0778422i | −0.110620 | − | 0.993863i | \(-0.535284\pi\) |
0.401131 | + | 0.916021i | \(0.368617\pi\) | |||||||
\(104\) | 412.352i | 3.96493i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 131.281 | 1.23850 | ||||||||
\(107\) | 5.02357 | + | 18.7482i | 0.0469492 | + | 0.175217i | 0.985419 | − | 0.170144i | \(-0.0544232\pi\) |
−0.938470 | + | 0.345361i | \(0.887757\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 73.5876 | − | 42.4858i | 0.675116 | − | 0.389778i | −0.122896 | − | 0.992419i | \(-0.539218\pi\) |
0.798012 | + | 0.602641i | \(0.205885\pi\) | |||||||
\(110\) | 7.29410 | − | 150.904i | 0.0663100 | − | 1.37186i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 265.864 | + | 18.3492i | 2.37379 | + | 0.163832i | ||||
\(113\) | 94.3686 | + | 94.3686i | 0.835120 | + | 0.835120i | 0.988212 | − | 0.153092i | \(-0.0489231\pi\) |
−0.153092 | + | 0.988212i | \(0.548923\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −88.1443 | + | 136.945i | −0.766472 | + | 1.19082i | ||||
\(116\) | 106.368 | + | 184.235i | 0.916966 | + | 1.58823i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 46.9929 | + | 46.9929i | 0.398245 | + | 0.398245i | ||||
\(119\) | 9.39320 | + | 48.0914i | 0.0789345 | + | 0.404129i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.9837 | − | 46.7371i | 0.223006 | − | 0.386257i | ||||
\(122\) | −96.1428 | − | 25.7614i | −0.788056 | − | 0.211159i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −228.760 | − | 132.075i | −1.84484 | − | 1.06512i | ||||
\(125\) | −74.6999 | − | 100.224i | −0.597599 | − | 0.801795i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −146.532 | + | 146.532i | −1.15380 | + | 1.15380i | −0.168010 | + | 0.985785i | \(0.553734\pi\) |
−0.985785 | + | 0.168010i | \(0.946266\pi\) | |||||||
\(128\) | −8.23036 | + | 2.20532i | −0.0642997 | + | 0.0172290i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −77.7257 | − | 358.504i | −0.597890 | − | 2.75773i | ||||
\(131\) | 57.4723 | − | 99.5449i | 0.438720 | − | 0.759885i | −0.558871 | − | 0.829254i | \(-0.688765\pi\) |
0.997591 | + | 0.0693695i | \(0.0220987\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.1484 | + | 147.042i | −0.0763041 | + | 1.10558i | ||||
\(134\) | − | 20.5399i | − | 0.153283i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 72.5996 | + | 125.746i | 0.533820 | + | 0.924604i | ||||
\(137\) | −105.092 | − | 28.1594i | −0.767096 | − | 0.205543i | −0.146008 | − | 0.989283i | \(-0.546643\pi\) |
−0.621088 | + | 0.783741i | \(0.713309\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 188.782i | 1.35814i | 0.734071 | + | 0.679072i | \(0.237618\pi\) | ||||
−0.734071 | + | 0.679072i | \(0.762382\pi\) | |||||||
\(140\) | −333.201 | + | 48.5172i | −2.38001 | + | 0.346552i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −100.305 | − | 374.344i | −0.706375 | − | 2.63623i | ||||
\(143\) | −42.1253 | + | 157.214i | −0.294582 | + | 1.09940i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −74.3154 | − | 81.8644i | −0.512520 | − | 0.564582i | ||||
\(146\) | −312.014 | −2.13708 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 105.549 | + | 105.549i | 0.713170 | + | 0.713170i | ||||
\(149\) | −102.211 | − | 59.0115i | −0.685979 | − | 0.396050i | 0.116125 | − | 0.993235i | \(-0.462953\pi\) |
−0.802104 | + | 0.597184i | \(0.796286\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −89.3003 | − | 154.673i | −0.591393 | − | 1.02432i | −0.994045 | − | 0.108969i | \(-0.965245\pi\) |
0.402653 | − | 0.915353i | \(-0.368088\pi\) | |||||||
\(152\) | 113.041 | + | 421.876i | 0.743693 | + | 2.77550i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 200.052 | + | 68.6808i | 1.29904 | + | 0.445979i | ||||
\(155\) | 130.738 | + | 41.8930i | 0.843470 | + | 0.270277i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 57.3089 | + | 15.3559i | 0.365025 | + | 0.0978081i | 0.436669 | − | 0.899622i | \(-0.356158\pi\) |
−0.0716444 | + | 0.997430i | \(0.522825\pi\) | |||||||
\(158\) | 95.4844 | − | 356.353i | 0.604332 | − | 2.25540i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −255.780 | + | 131.638i | −1.59863 | + | 0.822737i | ||||
\(161\) | −149.740 | − | 171.941i | −0.930059 | − | 1.06796i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −121.490 | + | 32.5532i | −0.745338 | + | 0.199713i | −0.611449 | − | 0.791284i | \(-0.709413\pi\) |
−0.133889 | + | 0.990996i | \(0.542747\pi\) | |||||||
\(164\) | 4.13396 | − | 2.38674i | 0.0252071 | − | 0.0145533i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −249.561 | + | 432.252i | −1.50338 | + | 2.60393i | ||||
\(167\) | 30.2982 | − | 30.2982i | 0.181427 | − | 0.181427i | −0.610551 | − | 0.791977i | \(-0.709052\pi\) |
0.791977 | + | 0.610551i | \(0.209052\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 226.191i | 1.33841i | ||||||||
\(170\) | −86.8214 | − | 95.6408i | −0.510714 | − | 0.562593i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 439.662 | + | 117.807i | 2.55617 | + | 0.684925i | ||||
\(173\) | −34.7961 | + | 9.32360i | −0.201134 | + | 0.0538936i | −0.357979 | − | 0.933730i | \(-0.616534\pi\) |
0.156846 | + | 0.987623i | \(0.449868\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 163.899 | − | 61.3358i | 0.936566 | − | 0.350490i | ||||
\(176\) | 311.700 | 1.77102 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 59.9438 | − | 223.713i | 0.336763 | − | 1.25682i | ||||
\(179\) | 65.4777 | − | 37.8036i | 0.365797 | − | 0.211193i | −0.305823 | − | 0.952088i | \(-0.598932\pi\) |
0.671621 | + | 0.740895i | \(0.265598\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −182.419 | −1.00784 | −0.503919 | − | 0.863751i | \(-0.668109\pi\) | ||||
−0.503919 | + | 0.863751i | \(0.668109\pi\) | |||||||
\(182\) | 512.348 | + | 35.3608i | 2.81510 | + | 0.194290i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −585.112 | − | 337.815i | −3.17996 | − | 1.83595i | ||||
\(185\) | −65.2345 | − | 41.9881i | −0.352619 | − | 0.226963i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.8333 | + | 55.3587i | 0.0793226 | + | 0.296036i | ||||
\(188\) | −169.920 | − | 169.920i | −0.903827 | − | 0.903827i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −177.800 | − | 345.477i | −0.935792 | − | 1.81830i | ||||
\(191\) | 7.66297 | − | 13.2727i | 0.0401203 | − | 0.0694904i | −0.845268 | − | 0.534343i | \(-0.820559\pi\) |
0.885388 | + | 0.464852i | \(0.153893\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 58.2576 | − | 217.420i | 0.301853 | − | 1.12653i | −0.633768 | − | 0.773523i | \(-0.718493\pi\) |
0.935621 | − | 0.353007i | \(-0.114841\pi\) | |||||||
\(194\) | −266.753 | − | 154.010i | −1.37502 | − | 0.793865i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 64.7611 | − | 466.931i | 0.330414 | − | 2.38230i | ||||
\(197\) | −261.191 | + | 261.191i | −1.32584 | + | 1.32584i | −0.416883 | + | 0.908960i | \(0.636878\pi\) |
−0.908960 | + | 0.416883i | \(0.863122\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −57.1020 | + | 32.9678i | −0.286945 | + | 0.165668i | −0.636563 | − | 0.771225i | \(-0.719645\pi\) |
0.349619 | + | 0.936892i | \(0.386311\pi\) | |||||||
\(200\) | 400.338 | − | 329.608i | 2.00169 | − | 1.64804i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −101.064 | + | 101.064i | −0.500317 | + | 0.500317i | ||||
\(203\) | 139.063 | − | 67.9816i | 0.685041 | − | 0.334885i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.83692 | + | 1.66753i | −0.00896058 | + | 0.00813429i | ||||
\(206\) | −57.1639 | − | 99.0107i | −0.277495 | − | 0.480635i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 731.039 | − | 195.881i | 3.51461 | − | 0.941738i | ||||
\(209\) | 172.393i | 0.824846i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 408.766 | 1.93728 | 0.968639 | − | 0.248472i | \(-0.0799283\pi\) | ||||
0.968639 | + | 0.248472i | \(0.0799283\pi\) | |||||||
\(212\) | −88.5721 | − | 330.556i | −0.417793 | − | 1.55922i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 62.0357 | − | 35.8164i | 0.289887 | − | 0.167366i | ||||
\(215\) | −236.289 | − | 11.4212i | −1.09902 | − | 0.0531221i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −107.333 | + | 159.438i | −0.494621 | + | 0.734739i | ||||
\(218\) | −221.745 | − | 221.745i | −1.01718 | − | 1.01718i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −384.887 | + | 83.4456i | −1.74949 | + | 0.379298i | ||||
\(221\) | 69.5781 | + | 120.513i | 0.314833 | + | 0.545307i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −180.123 | − | 180.123i | −0.807725 | − | 0.807725i | 0.176564 | − | 0.984289i | \(-0.443502\pi\) |
−0.984289 | + | 0.176564i | \(0.943502\pi\) | |||||||
\(224\) | −77.2030 | − | 395.264i | −0.344656 | − | 1.76457i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 246.268 | − | 426.548i | 1.08968 | − | 1.88738i | ||||
\(227\) | −211.989 | − | 56.8024i | −0.933874 | − | 0.250231i | −0.240368 | − | 0.970682i | \(-0.577268\pi\) |
−0.693506 | + | 0.720451i | \(0.743935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −292.008 | − | 168.591i | −1.27515 | − | 0.736206i | −0.299194 | − | 0.954192i | \(-0.596718\pi\) |
−0.975952 | + | 0.217986i | \(0.930051\pi\) | |||||||
\(230\) | 572.380 | + | 183.411i | 2.48861 | + | 0.797438i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 324.337 | − | 324.337i | 1.39800 | − | 1.39800i | ||||
\(233\) | −284.131 | + | 76.1326i | −1.21945 | + | 0.326749i | −0.810461 | − | 0.585792i | \(-0.800783\pi\) |
−0.408984 | + | 0.912542i | \(0.634117\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 105.018 | + | 67.5950i | 0.446887 | + | 0.287638i | ||||
\(236\) | 86.6195 | − | 150.029i | 0.367032 | − | 0.635718i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 162.465 | − | 79.4218i | 0.682628 | − | 0.333705i | ||||
\(239\) | 191.663i | 0.801937i | 0.916092 | + | 0.400968i | \(0.131326\pi\) | ||||
−0.916092 | + | 0.400968i | \(0.868674\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −61.5720 | − | 106.646i | −0.255486 | − | 0.442514i | 0.709542 | − | 0.704663i | \(-0.248902\pi\) |
−0.965027 | + | 0.262149i | \(0.915569\pi\) | |||||||
\(242\) | −192.385 | − | 51.5493i | −0.794978 | − | 0.213014i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 259.461i | 1.06337i | ||||||||
\(245\) | 18.5252 | + | 244.299i | 0.0756130 | + | 0.997137i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 108.337 | + | 404.318i | 0.438610 | + | 1.63692i | ||||
\(248\) | −147.407 | + | 550.129i | −0.594381 | + | 2.21826i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −285.930 | + | 362.026i | −1.14372 | + | 1.44811i | ||||
\(251\) | 21.1349 | 0.0842027 | 0.0421014 | − | 0.999113i | \(-0.486595\pi\) | ||||
0.0421014 | + | 0.999113i | \(0.486595\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −188.570 | − | 188.570i | −0.745335 | − | 0.745335i | ||||
\(254\) | 662.329 | + | 382.396i | 2.60759 | + | 1.50549i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 135.819 | + | 235.246i | 0.530545 | + | 0.918930i | ||||
\(257\) | 48.9113 | + | 182.539i | 0.190316 | + | 0.710270i | 0.993430 | + | 0.114444i | \(0.0365086\pi\) |
−0.803114 | + | 0.595826i | \(0.796825\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 81.9052 | − | 71.3294i | 0.316236 | − | 0.275403i | ||||
\(260\) | −850.248 | + | 437.582i | −3.27018 | + | 1.68301i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −409.758 | − | 109.794i | −1.56396 | − | 0.419063i | ||||
\(263\) | 36.1131 | − | 134.776i | 0.137312 | − | 0.512457i | −0.862665 | − | 0.505775i | \(-0.831207\pi\) |
0.999978 | − | 0.00668144i | \(-0.00212678\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 81.3894 | + | 158.144i | 0.307130 | + | 0.596771i | ||||
\(266\) | 533.875 | − | 104.276i | 2.00705 | − | 0.392016i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −51.7180 | + | 13.8578i | −0.192978 | + | 0.0517082i | ||||
\(269\) | 169.522 | − | 97.8736i | 0.630194 | − | 0.363842i | −0.150634 | − | 0.988590i | \(-0.548131\pi\) |
0.780827 | + | 0.624747i | \(0.214798\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 123.964 | − | 214.711i | 0.457430 | − | 0.792292i | −0.541394 | − | 0.840769i | \(-0.682103\pi\) |
0.998824 | + | 0.0484766i | \(0.0154366\pi\) | |||||||
\(272\) | 188.442 | − | 188.442i | 0.692802 | − | 0.692802i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 401.534i | 1.46545i | ||||||||
\(275\) | 186.305 | − | 84.7685i | 0.677474 | − | 0.308249i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −263.603 | − | 70.6321i | −0.951634 | − | 0.254989i | −0.250578 | − | 0.968096i | \(-0.580621\pi\) |
−0.701055 | + | 0.713107i | \(0.747287\pi\) | |||||||
\(278\) | 672.977 | − | 180.324i | 2.42078 | − | 0.648646i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 286.984 | + | 666.864i | 1.02494 | + | 2.38166i | ||||
\(281\) | 426.012 | 1.51606 | 0.758028 | − | 0.652222i | \(-0.226163\pi\) | ||||
0.758028 | + | 0.652222i | \(0.226163\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.5453 | + | 106.533i | −0.100867 | + | 0.376440i | −0.997844 | − | 0.0656376i | \(-0.979092\pi\) |
0.896977 | + | 0.442078i | \(0.145759\pi\) | |||||||
\(284\) | −874.897 | + | 505.122i | −3.08062 | + | 1.77860i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 600.679 | 2.10027 | ||||||||
\(287\) | −1.52541 | − | 3.12038i | −0.00531502 | − | 0.0108724i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −207.846 | − | 120.000i | −0.719190 | − | 0.415224i | ||||
\(290\) | −220.847 | + | 343.118i | −0.761543 | + | 1.18317i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 210.508 | + | 785.628i | 0.720919 | + | 2.69051i | ||||
\(293\) | −224.196 | − | 224.196i | −0.765175 | − | 0.765175i | 0.212078 | − | 0.977253i | \(-0.431977\pi\) |
−0.977253 | + | 0.212078i | \(0.931977\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.4750 | + | 85.7427i | −0.0931355 | + | 0.290653i | ||||
\(296\) | 160.920 | − | 278.722i | 0.543649 | − | 0.941628i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −112.735 | + | 420.732i | −0.378305 | + | 1.41185i | ||||
\(299\) | −560.761 | − | 323.755i | −1.87545 | − | 1.08279i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 107.542 | − | 313.245i | 0.357282 | − | 1.04068i | ||||
\(302\) | −466.083 | + | 466.083i | −1.54332 | + | 1.54332i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 694.225 | − | 400.811i | 2.28363 | − | 1.31846i | ||||
\(305\) | −28.5722 | − | 131.787i | −0.0936793 | − | 0.432089i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 348.544 | − | 348.544i | 1.13532 | − | 1.13532i | 0.146043 | − | 0.989278i | \(-0.453346\pi\) |
0.989278 | − | 0.146043i | \(-0.0466539\pi\) | |||||||
\(308\) | 37.9631 | − | 550.052i | 0.123257 | − | 1.78588i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 24.4615 | − | 506.074i | 0.0789082 | − | 1.63250i | ||||
\(311\) | 7.38338 | + | 12.7884i | 0.0237408 | + | 0.0411202i | 0.877652 | − | 0.479299i | \(-0.159109\pi\) |
−0.853911 | + | 0.520419i | \(0.825776\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −116.758 | + | 31.2853i | −0.373030 | + | 0.0999530i | −0.440463 | − | 0.897771i | \(-0.645186\pi\) |
0.0674334 | + | 0.997724i | \(0.478519\pi\) | |||||||
\(314\) | − | 218.964i | − | 0.697339i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −961.690 | −3.04332 | ||||||||
\(317\) | −80.4604 | − | 300.282i | −0.253818 | − | 0.947262i | −0.968744 | − | 0.248062i | \(-0.920206\pi\) |
0.714926 | − | 0.699200i | \(-0.246460\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 156.791 | − | 90.5232i | 0.491507 | − | 0.283772i | ||||
\(320\) | 201.805 | + | 222.304i | 0.630640 | + | 0.694701i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −469.911 | + | 698.033i | −1.45935 | + | 2.16781i | ||||
\(323\) | 104.222 | + | 104.222i | 0.322669 | + | 0.322669i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 383.677 | − | 315.890i | 1.18054 | − | 0.971969i | ||||
\(326\) | 232.093 | + | 401.998i | 0.711943 | + | 1.23312i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.27765 | − | 7.27765i | −0.0221880 | − | 0.0221880i | ||||
\(329\) | −131.856 | + | 114.830i | −0.400778 | + | 0.349028i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 64.5929 | − | 111.878i | 0.195145 | − | 0.338001i | −0.751803 | − | 0.659388i | \(-0.770816\pi\) |
0.946948 | + | 0.321387i | \(0.104149\pi\) | |||||||
\(332\) | 1256.75 | + | 336.745i | 3.78539 | + | 1.01429i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −136.949 | − | 79.0675i | −0.410027 | − | 0.236729i | ||||
\(335\) | 24.7429 | − | 12.7340i | 0.0738595 | − | 0.0380120i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −51.0347 | + | 51.0347i | −0.151438 | + | 0.151438i | −0.778760 | − | 0.627322i | \(-0.784151\pi\) |
0.627322 | + | 0.778760i | \(0.284151\pi\) | |||||||
\(338\) | 806.333 | − | 216.056i | 2.38560 | − | 0.639220i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −182.240 | + | 283.136i | −0.536000 | + | 0.832754i | ||||
\(341\) | −112.401 | + | 194.684i | −0.329621 | + | 0.570920i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −335.697 | − | 70.4023i | −0.978709 | − | 0.205255i | ||||
\(344\) | − | 981.399i | − | 2.85290i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 66.4741 | + | 115.137i | 0.192122 | + | 0.332765i | ||||
\(347\) | 585.959 | + | 157.007i | 1.68864 | + | 0.452470i | 0.970039 | − | 0.242950i | \(-0.0781151\pi\) |
0.718603 | + | 0.695420i | \(0.244782\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 82.1983i | 0.235525i | 0.993042 | + | 0.117763i | \(0.0375722\pi\) | ||||
−0.993042 | + | 0.117763i | \(0.962428\pi\) | |||||||
\(350\) | −375.207 | − | 525.685i | −1.07202 | − | 1.50196i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −121.916 | − | 454.995i | −0.346351 | − | 1.29260i | ||||
\(353\) | −38.0031 | + | 141.830i | −0.107658 | + | 0.401783i | −0.998633 | − | 0.0522678i | \(-0.983355\pi\) |
0.890976 | + | 0.454051i | \(0.150022\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 388.759 | − | 352.910i | 1.09510 | − | 0.994112i | ||||
\(356\) | −603.736 | −1.69589 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −197.307 | − | 197.307i | −0.551138 | − | 0.551138i | ||||
\(359\) | 175.063 | + | 101.073i | 0.487641 | + | 0.281539i | 0.723595 | − | 0.690225i | \(-0.242488\pi\) |
−0.235955 | + | 0.971764i | \(0.575822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.1776 | + | 71.3218i | 0.114065 | + | 0.197567i | ||||
\(362\) | 174.245 | + | 650.292i | 0.481340 | + | 1.79639i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −256.633 | − | 1313.91i | −0.705036 | − | 3.60965i | ||||
\(365\) | −193.437 | − | 375.860i | −0.529965 | − | 1.02975i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 486.132 | + | 130.259i | 1.32461 | + | 0.354928i | 0.850703 | − | 0.525647i | \(-0.176177\pi\) |
0.473907 | + | 0.880575i | \(0.342843\pi\) | |||||||
\(368\) | −320.947 | + | 1197.79i | −0.872139 | + | 3.25487i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −87.3689 | + | 272.657i | −0.236132 | + | 0.736911i | ||||
\(371\) | −244.385 | + | 47.7332i | −0.658719 | + | 0.128661i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 178.568 | − | 47.8471i | 0.478735 | − | 0.128277i | −0.0113788 | − | 0.999935i | \(-0.503622\pi\) |
0.490113 | + | 0.871659i | \(0.336955\pi\) | |||||||
\(374\) | 183.176 | − | 105.757i | 0.489775 | − | 0.282772i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −259.059 | + | 448.703i | −0.688987 | + | 1.19336i | ||||
\(377\) | 310.839 | − | 310.839i | 0.824506 | − | 0.824506i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 348.414i | 0.919299i | 0.888100 | + | 0.459649i | \(0.152025\pi\) | ||||
−0.888100 | + | 0.459649i | \(0.847975\pi\) | |||||||
\(380\) | −749.927 | + | 680.773i | −1.97349 | + | 1.79151i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −54.6344 | − | 14.6393i | −0.143022 | − | 0.0383226i | ||||
\(383\) | −436.725 | + | 117.020i | −1.14028 | + | 0.305536i | −0.779062 | − | 0.626947i | \(-0.784304\pi\) |
−0.361214 | + | 0.932483i | \(0.617638\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 41.2900 | + | 283.567i | 0.107247 | + | 0.736537i | ||||
\(386\) | −830.714 | −2.15211 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −207.814 | + | 775.571i | −0.535602 | + | 1.99889i | ||||
\(389\) | 565.646 | − | 326.576i | 1.45410 | − | 0.839527i | 0.455393 | − | 0.890290i | \(-0.349499\pi\) |
0.998711 | + | 0.0507630i | \(0.0161653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −228.004 | −0.583131 | ||||||||
\(392\) | −1008.59 | + | 125.693i | −2.57293 | + | 0.320646i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1180.59 | + | 681.614i | 2.99642 | + | 1.72999i | ||||
\(395\) | 488.468 | − | 105.903i | 1.23663 | − | 0.268108i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.0735 | + | 63.7193i | 0.0430064 | + | 0.160502i | 0.984090 | − | 0.177673i | \(-0.0568570\pi\) |
−0.941083 | + | 0.338175i | \(0.890190\pi\) | |||||||
\(398\) | 172.068 | + | 172.068i | 0.432333 | + | 0.432333i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −774.520 | − | 553.165i | −1.93630 | − | 1.38291i | ||||
\(401\) | −54.6685 | + | 94.6886i | −0.136330 | + | 0.236131i | −0.926105 | − | 0.377266i | \(-0.876864\pi\) |
0.789775 | + | 0.613397i | \(0.210198\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −141.272 | + | 527.233i | −0.350550 | + | 1.30827i | ||||
\(404\) | 322.657 | + | 186.286i | 0.798657 | + | 0.461105i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −375.176 | − | 430.802i | −0.924078 | − | 1.06109i | ||||
\(407\) | 89.8264 | − | 89.8264i | 0.220704 | − | 0.220704i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −254.528 | + | 146.952i | −0.622318 | + | 0.359295i | −0.777771 | − | 0.628548i | \(-0.783650\pi\) |
0.155453 | + | 0.987843i | \(0.450316\pi\) | |||||||
\(410\) | 7.69908 | + | 4.95550i | 0.0187782 | + | 0.0120866i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −210.735 | + | 210.735i | −0.511492 | + | 0.511492i | ||||
\(413\) | −104.566 | − | 70.3927i | −0.253185 | − | 0.170442i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −675.420 | − | 32.6470i | −1.62752 | − | 0.0786675i | ||||
\(416\) | −571.865 | − | 990.499i | −1.37467 | − | 2.38101i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 614.552 | − | 164.669i | 1.47022 | − | 0.393944i | ||||
\(419\) | − | 234.794i | − | 0.560368i | −0.959946 | − | 0.280184i | \(-0.909605\pi\) | ||
0.959946 | − | 0.280184i | \(-0.0903955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −124.297 | −0.295242 | −0.147621 | − | 0.989044i | \(-0.547162\pi\) | ||||
−0.147621 | + | 0.989044i | \(0.547162\pi\) | |||||||
\(422\) | −390.451 | − | 1457.18i | −0.925238 | − | 3.45304i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −639.001 | + | 368.928i | −1.50708 | + | 0.870112i | ||||
\(425\) | 61.3854 | − | 163.881i | 0.144436 | − | 0.385602i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 188.341 | + | 12.9987i | 0.441079 | + | 0.0304420i | ||||
\(428\) | −132.037 | − | 132.037i | −0.308498 | − | 0.308498i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 184.987 | + | 853.241i | 0.430203 | + | 1.98428i | ||||
\(431\) | −105.297 | − | 182.380i | −0.244309 | − | 0.423155i | 0.717628 | − | 0.696426i | \(-0.245228\pi\) |
−0.961937 | + | 0.273271i | \(0.911894\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −549.109 | − | 549.109i | −1.26815 | − | 1.26815i | −0.947042 | − | 0.321109i | \(-0.895944\pi\) |
−0.321109 | − | 0.947042i | \(-0.604056\pi\) | |||||||
\(434\) | 670.895 | + | 230.328i | 1.54584 | + | 0.530711i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −408.732 | + | 707.944i | −0.937459 | + | 1.62373i | ||||
\(437\) | −662.466 | − | 177.507i | −1.51594 | − | 0.406195i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 83.0573 | + | 47.9532i | 0.189197 | + | 0.109233i | 0.591606 | − | 0.806227i | \(-0.298494\pi\) |
−0.402410 | + | 0.915460i | \(0.631827\pi\) | |||||||
\(440\) | 388.570 | + | 755.015i | 0.883114 | + | 1.71594i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 363.148 | − | 363.148i | 0.821601 | − | 0.821601i | ||||
\(443\) | 96.6633 | − | 25.9009i | 0.218202 | − | 0.0584670i | −0.148062 | − | 0.988978i | \(-0.547304\pi\) |
0.366264 | + | 0.930511i | \(0.380637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 306.654 | − | 66.4842i | 0.689110 | − | 0.149403i | ||||
\(446\) | −470.055 | + | 814.159i | −1.05394 | + | 1.82547i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −377.629 | + | 184.605i | −0.842922 | + | 0.412066i | ||||
\(449\) | 344.308i | 0.766832i | 0.923576 | + | 0.383416i | \(0.125252\pi\) | ||||
−0.923576 | + | 0.383416i | \(0.874748\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.03121 | − | 3.51816i | −0.00450379 | − | 0.00780079i | ||||
\(452\) | −1240.17 | − | 332.302i | −2.74373 | − | 0.735181i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 809.964i | 1.78406i | ||||||||
\(455\) | 275.040 | + | 639.110i | 0.604484 | + | 1.40464i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.3113 | − | 83.2667i | −0.0488211 | − | 0.182203i | 0.937210 | − | 0.348767i | \(-0.113399\pi\) |
−0.986031 | + | 0.166564i | \(0.946733\pi\) | |||||||
\(458\) | −322.074 | + | 1202.00i | −0.703219 | + | 2.62445i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 75.6434 | − | 1564.95i | 0.164442 | − | 3.40207i | ||||
\(461\) | 618.594 | 1.34185 | 0.670926 | − | 0.741524i | \(-0.265897\pi\) | ||||
0.670926 | + | 0.741524i | \(0.265897\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 113.717 | + | 113.717i | 0.245610 | + | 0.245610i | 0.819166 | − | 0.573556i | \(-0.194437\pi\) |
−0.573556 | + | 0.819166i | \(0.694437\pi\) | |||||||
\(464\) | −729.073 | − | 420.930i | −1.57128 | − | 0.907177i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 542.800 | + | 940.157i | 1.16481 | + | 2.01750i | ||||
\(467\) | −13.0497 | − | 48.7023i | −0.0279438 | − | 0.104288i | 0.950545 | − | 0.310585i | \(-0.100525\pi\) |
−0.978489 | + | 0.206298i | \(0.933858\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.46824 | + | 38.2359i | 0.0159238 | + | 0.0815265i | ||||
\(470\) | 140.652 | − | 438.940i | 0.299259 | − | 0.933914i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −360.795 | − | 96.6746i | −0.764395 | − | 0.204819i | ||||
\(473\) | 100.258 | − | 374.169i | 0.211963 | − | 0.791055i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 305.941 | − | 428.366i | 0.644086 | − | 0.901823i | ||||
\(476\) | −309.590 | − | 355.492i | −0.650398 | − | 0.746831i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 683.246 | − | 183.075i | 1.42938 | − | 0.383003i | ||||
\(479\) | −152.207 | + | 87.8766i | −0.317760 | + | 0.183459i | −0.650393 | − | 0.759597i | \(-0.725396\pi\) |
0.332634 | + | 0.943056i | \(0.392063\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 154.223 | − | 267.122i | 0.320630 | − | 0.555347i | ||||
\(482\) | −321.361 | + | 321.361i | −0.666725 | + | 0.666725i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 519.189i | 1.07270i | ||||||||
\(485\) | 20.1473 | − | 416.818i | 0.0415408 | − | 0.859419i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −245.352 | − | 65.7419i | −0.503803 | − | 0.134994i | −0.00203876 | − | 0.999998i | \(-0.500649\pi\) |
−0.501765 | + | 0.865004i | \(0.667316\pi\) | |||||||
\(488\) | 540.364 | − | 144.790i | 1.10730 | − | 0.296701i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 853.189 | − | 299.392i | 1.74120 | − | 0.611004i | ||||
\(491\) | −275.796 | −0.561704 | −0.280852 | − | 0.959751i | \(-0.590617\pi\) | ||||
−0.280852 | + | 0.959751i | \(0.590617\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 40.0629 | − | 149.517i | 0.0812634 | − | 0.303279i | ||||
\(494\) | 1337.84 | − | 772.405i | 2.70819 | − | 1.56357i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1045.32 | 2.10750 | ||||||||
\(497\) | 322.832 | + | 660.386i | 0.649562 | + | 1.32875i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −520.379 | − | 300.441i | −1.04284 | − | 0.602086i | −0.122206 | − | 0.992505i | \(-0.538997\pi\) |
−0.920637 | + | 0.390419i | \(0.872330\pi\) | |||||||
\(500\) | 1104.47 | + | 475.701i | 2.20893 | + | 0.951401i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −20.1879 | − | 75.3423i | −0.0402150 | − | 0.150084i | ||||
\(503\) | 513.924 | + | 513.924i | 1.02172 | + | 1.02172i | 0.999759 | + | 0.0219593i | \(0.00699042\pi\) |
0.0219593 | + | 0.999759i | \(0.493010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −184.401 | − | 59.0884i | −0.365150 | − | 0.117007i | ||||
\(506\) | −492.099 | + | 852.340i | −0.972527 | + | 1.68447i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 515.986 | − | 1925.69i | 1.01572 | − | 3.79072i | ||||
\(509\) | 406.687 | + | 234.801i | 0.798993 | + | 0.461299i | 0.843119 | − | 0.537727i | \(-0.180717\pi\) |
−0.0441259 | + | 0.999026i | \(0.514050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 580.827 | − | 113.447i | 1.13665 | − | 0.222010i | ||||
\(512\) | 684.779 | − | 684.779i | 1.33746 | − | 1.33746i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 604.002 | − | 348.721i | 1.17510 | − | 0.678446i | ||||
\(515\) | 83.8314 | − | 130.244i | 0.162779 | − | 0.252901i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −144.608 | + | 144.608i | −0.279706 | + | 0.279706i | ||||
\(518\) | −332.513 | − | 223.845i | −0.641916 | − | 0.432133i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1385.80 | + | 1526.57i | 2.66500 | + | 2.93571i | ||||
\(521\) | −72.5876 | − | 125.725i | −0.139324 | − | 0.241316i | 0.787917 | − | 0.615781i | \(-0.211160\pi\) |
−0.927241 | + | 0.374466i | \(0.877826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −809.900 | + | 217.012i | −1.54857 | + | 0.414937i | −0.929022 | − | 0.370026i | \(-0.879349\pi\) |
−0.619543 | + | 0.784962i | \(0.712682\pi\) | |||||||
\(524\) | 1105.82i | 2.11034i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −514.949 | −0.978991 | ||||||||
\(527\) | 49.7452 | + | 185.652i | 0.0943932 | + | 0.352280i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 460.666 | − | 265.966i | 0.870824 | − | 0.502770i | ||||
\(530\) | 486.016 | − | 441.198i | 0.917011 | − | 0.832449i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −622.753 | − | 1273.90i | −1.17059 | − | 2.39456i | ||||
\(533\) | −6.97477 | − | 6.97477i | −0.0130859 | − | 0.0130859i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 81.6052 | + | 52.5250i | 0.152533 | + | 0.0981777i | ||||
\(536\) | 57.7216 | + | 99.9768i | 0.107690 | + | 0.186524i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −510.829 | − | 510.829i | −0.949497 | − | 0.949497i | ||||
\(539\) | −397.376 | − | 55.1141i | −0.737247 | − | 0.102253i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −225.980 | + | 391.408i | −0.417708 | + | 0.723491i | −0.995708 | − | 0.0925455i | \(-0.970500\pi\) |
0.578001 | + | 0.816036i | \(0.303833\pi\) | |||||||
\(542\) | −883.819 | − | 236.819i | −1.63066 | − | 0.436935i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −348.778 | − | 201.367i | −0.641137 | − | 0.370160i | ||||
\(545\) | 129.646 | − | 404.594i | 0.237883 | − | 0.742375i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 389.492 | − | 389.492i | 0.712051 | − | 0.712051i | −0.254913 | − | 0.966964i | \(-0.582047\pi\) |
0.966964 | + | 0.254913i | \(0.0820469\pi\) | |||||||
\(548\) | 1011.03 | − | 270.905i | 1.84495 | − | 0.494353i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −480.143 | − | 583.177i | −0.872988 | − | 1.06032i | ||||
\(551\) | 232.805 | − | 403.230i | 0.422514 | − | 0.731815i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −48.1797 | + | 698.083i | −0.0871243 | + | 1.26236i | ||||
\(554\) | 1007.17i | 1.81799i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −908.083 | − | 1572.85i | −1.63324 | − | 2.82886i | ||||
\(557\) | 950.780 | + | 254.761i | 1.70697 | + | 0.457380i | 0.974678 | − | 0.223615i | \(-0.0717859\pi\) |
0.732288 | + | 0.680995i | \(0.238453\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 940.555i | − | 1.68257i | ||||||
\(560\) | 1045.92 | − | 825.563i | 1.86772 | − | 1.47422i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −406.924 | − | 1518.66i | −0.724064 | − | 2.70224i | ||||
\(563\) | 222.762 | − | 831.358i | 0.395669 | − | 1.47666i | −0.424968 | − | 0.905208i | \(-0.639715\pi\) |
0.820637 | − | 0.571450i | \(-0.193619\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 666.508 | + | 32.2163i | 1.17966 | + | 0.0570199i | ||||
\(566\) | 407.037 | 0.719147 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1540.22 | + | 1540.22i | 2.71165 | + | 2.71165i | ||||
\(569\) | −343.723 | − | 198.449i | −0.604083 | − | 0.348768i | 0.166563 | − | 0.986031i | \(-0.446733\pi\) |
−0.770646 | + | 0.637263i | \(0.780066\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 402.947 | + | 697.924i | 0.705686 | + | 1.22228i | 0.966443 | + | 0.256880i | \(0.0826944\pi\) |
−0.260757 | + | 0.965404i | \(0.583972\pi\) | |||||||
\(572\) | −405.263 | − | 1512.46i | −0.708502 | − | 2.64417i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.66658 | + | 8.41840i | −0.0168407 | + | 0.0146662i | ||||
\(575\) | 133.913 | + | 803.212i | 0.232893 | + | 1.39689i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1000.77 | − | 268.157i | −1.73445 | − | 0.464743i | −0.753246 | − | 0.657739i | \(-0.771513\pi\) |
−0.981200 | + | 0.192996i | \(0.938180\pi\) | |||||||
\(578\) | −229.246 | + | 855.559i | −0.396620 | + | 1.48021i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1012.95 | + | 324.584i | 1.74646 | + | 0.559627i | ||||
\(581\) | 307.402 | − | 895.394i | 0.529092 | − | 1.54113i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −281.315 | + | 75.3782i | −0.482530 | + | 0.129294i | ||||
\(584\) | 1518.71 | − | 876.826i | 2.60053 | − | 1.50141i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −585.071 | + | 1013.37i | −0.998415 | + | 1.72930i | ||||
\(587\) | −541.901 | + | 541.901i | −0.923170 | + | 0.923170i | −0.997252 | − | 0.0740817i | \(-0.976397\pi\) |
0.0740817 | + | 0.997252i | \(0.476397\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 578.138i | 0.981559i | ||||||||
\(590\) | 331.902 | + | 16.0428i | 0.562546 | + | 0.0271912i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −570.575 | − | 152.885i | −0.963810 | − | 0.258252i | ||||
\(593\) | −767.912 | + | 205.761i | −1.29496 | + | 0.346984i | −0.839543 | − | 0.543293i | \(-0.817177\pi\) |
−0.455419 | + | 0.890277i | \(0.650510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 196.396 | + | 146.471i | 0.330078 | + | 0.246170i | ||||
\(596\) | 1135.43 | 1.90509 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −618.499 | + | 2308.27i | −1.03428 | + | 3.85998i | ||||
\(599\) | −357.782 | + | 206.565i | −0.597299 | + | 0.344850i | −0.767978 | − | 0.640476i | \(-0.778737\pi\) |
0.170680 | + | 0.985327i | \(0.445404\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −439.370 | −0.731066 | −0.365533 | − | 0.930798i | \(-0.619113\pi\) | ||||
−0.365533 | + | 0.930798i | \(0.619113\pi\) | |||||||
\(602\) | −1219.39 | − | 84.1588i | −2.02556 | − | 0.139799i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1488.02 | + | 859.107i | 2.46360 | + | 1.42236i | ||||
\(605\) | −57.1738 | − | 263.710i | −0.0945021 | − | 0.435884i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 56.8754 | + | 212.262i | 0.0936991 | + | 0.349690i | 0.996819 | − | 0.0796986i | \(-0.0253958\pi\) |
−0.903120 | + | 0.429388i | \(0.858729\pi\) | |||||||
\(608\) | −856.605 | − | 856.605i | −1.40889 | − | 1.40889i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −442.508 | + | 227.738i | −0.725422 | + | 0.373340i | ||||
\(611\) | −248.278 | + | 430.029i | −0.406346 | + | 0.703812i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 253.466 | − | 945.946i | 0.413484 | − | 1.54314i | −0.374370 | − | 0.927280i | \(-0.622141\pi\) |
0.787853 | − | 0.615863i | \(-0.211192\pi\) | |||||||
\(614\) | −1575.43 | − | 909.573i | −2.56584 | − | 1.48139i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1166.75 | + | 227.889i | −1.89407 | + | 0.369949i | ||||
\(617\) | 56.3252 | − | 56.3252i | 0.0912887 | − | 0.0912887i | −0.659988 | − | 0.751276i | \(-0.729439\pi\) |
0.751276 | + | 0.659988i | \(0.229439\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 451.442 | − | 260.640i | 0.729309 | − | 0.421067i | −0.0888604 | − | 0.996044i | \(-0.528323\pi\) |
0.818169 | + | 0.574977i | \(0.194989\pi\) | |||||||
\(620\) | −1290.76 | + | 279.844i | −2.08187 | + | 0.451361i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 38.5359 | − | 38.5359i | 0.0619548 | − | 0.0619548i | ||||
\(623\) | −30.2466 | + | 438.247i | −0.0485499 | + | 0.703446i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −613.373 | − | 119.996i | −0.981396 | − | 0.191994i | ||||
\(626\) | 223.054 | + | 386.340i | 0.356316 | + | 0.617157i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −551.336 | + | 147.730i | −0.877924 | + | 0.235239i | ||||
\(629\) | − | 108.611i | − | 0.172673i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 606.021 | 0.960413 | 0.480207 | − | 0.877155i | \(-0.340562\pi\) | ||||
0.480207 | + | 0.877155i | \(0.340562\pi\) | |||||||
\(632\) | 536.663 | + | 2002.85i | 0.849151 | + | 3.16907i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −993.601 | + | 573.656i | −1.56719 | + | 0.904819i | ||||
\(635\) | −50.0242 | + | 1034.93i | −0.0787783 | + | 1.62981i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −966.614 | + | 120.462i | −1.51745 | + | 0.189108i | ||||
\(638\) | −472.466 | − | 472.466i | −0.740542 | − | 0.740542i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −23.0582 | + | 35.8242i | −0.0360284 | + | 0.0559753i | ||||
\(641\) | −552.914 | − | 957.675i | −0.862580 | − | 1.49403i | −0.869430 | − | 0.494056i | \(-0.835514\pi\) |
0.00685032 | − | 0.999977i | \(-0.497819\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 495.423 | + | 495.423i | 0.770487 | + | 0.770487i | 0.978192 | − | 0.207704i | \(-0.0665992\pi\) |
−0.207704 | + | 0.978192i | \(0.566599\pi\) | |||||||
\(644\) | 2074.63 | + | 712.253i | 3.22148 | + | 1.10598i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 271.982 | − | 471.087i | 0.421025 | − | 0.729237i | ||||
\(647\) | 747.117 | + | 200.190i | 1.15474 | + | 0.309412i | 0.784864 | − | 0.619669i | \(-0.212733\pi\) |
0.369877 | + | 0.929081i | \(0.379400\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −127.681 | − | 73.7165i | −0.196735 | − | 0.113585i | ||||
\(650\) | −1492.58 | − | 1066.01i | −2.29628 | − | 1.64001i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 855.612 | − | 855.612i | 1.31229 | − | 1.31229i | ||||
\(653\) | −1045.38 | + | 280.108i | −1.60089 | + | 0.428956i | −0.945310 | − | 0.326172i | \(-0.894241\pi\) |
−0.655576 | + | 0.755129i | \(0.727574\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −121.774 | − | 561.674i | −0.185914 | − | 0.857517i | ||||
\(656\) | −9.44507 | + | 16.3593i | −0.0143980 | + | 0.0249380i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 535.299 | + | 360.359i | 0.813524 | + | 0.547658i | ||||
\(659\) | − | 388.022i | − | 0.588805i | −0.955682 | − | 0.294402i | \(-0.904879\pi\) | ||
0.955682 | − | 0.294402i | \(-0.0951206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −309.552 | − | 536.160i | −0.468308 | − | 0.811134i | 0.531036 | − | 0.847350i | \(-0.321803\pi\) |
−0.999344 | + | 0.0362155i | \(0.988470\pi\) | |||||||
\(662\) | −460.526 | − | 123.398i | −0.695658 | − | 0.186401i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 2805.28i | − | 4.22481i | ||||||
\(665\) | 456.597 | + | 578.472i | 0.686612 | + | 0.869882i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 186.417 | + | 695.719i | 0.279486 | + | 1.04306i | ||||
\(668\) | −106.690 | + | 398.172i | −0.159715 | + | 0.596066i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −69.0289 | − | 76.0410i | −0.103028 | − | 0.113494i | ||||
\(671\) | 220.811 | 0.329078 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 185.772 | + | 185.772i | 0.276036 | + | 0.276036i | 0.831524 | − | 0.555488i | \(-0.187469\pi\) |
−0.555488 | + | 0.831524i | \(0.687469\pi\) | |||||||
\(674\) | 230.678 | + | 133.182i | 0.342253 | + | 0.197600i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1088.03 | − | 1884.52i | −1.60951 | − | 2.78775i | ||||
\(677\) | −191.084 | − | 713.136i | −0.282252 | − | 1.05338i | −0.950824 | − | 0.309731i | \(-0.899761\pi\) |
0.668573 | − | 0.743647i | \(-0.266906\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 552.569 | + | 189.705i | 0.813798 | + | 0.279389i | ||||
\(680\) | 691.368 | + | 221.539i | 1.01672 | + | 0.325792i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 801.379 | + | 214.729i | 1.17504 | + | 0.314852i | ||||
\(683\) | 135.236 | − | 504.707i | 0.198003 | − | 0.738957i | −0.793466 | − | 0.608614i | \(-0.791726\pi\) |
0.991469 | − | 0.130342i | \(-0.0416077\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −483.698 | + | 248.936i | −0.706129 | + | 0.363411i | ||||
\(686\) | 69.6833 | + | 1263.95i | 0.101579 | + | 1.84250i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1739.88 | + | 466.198i | −2.52889 | + | 0.677614i | ||||
\(689\) | −612.407 | + | 353.574i | −0.888835 | + | 0.513169i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −301.546 | + | 522.293i | −0.436391 | + | 0.755851i | −0.997408 | − | 0.0719534i | \(-0.977077\pi\) |
0.561017 | + | 0.827804i | \(0.310410\pi\) | |||||||
\(692\) | 245.057 | − | 245.057i | 0.354128 | − | 0.354128i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 2238.82i | − | 3.22596i | ||||||
\(695\) | 634.443 | + | 698.891i | 0.912868 | + | 1.00560i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.35494 | − | 0.898953i | −0.00481340 | − | 0.00128975i | ||||
\(698\) | 293.023 | − | 78.5153i | 0.419804 | − | 0.112486i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1070.49 | + | 1299.41i | −1.52928 | + | 1.85630i | ||||
\(701\) | −100.279 | −0.143052 | −0.0715259 | − | 0.997439i | \(-0.522787\pi\) | ||||
−0.0715259 | + | 0.997439i | \(0.522787\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 84.5567 | − | 315.570i | 0.120280 | − | 0.448890i | ||||
\(704\) | −425.768 | + | 245.817i | −0.604784 | + | 0.349172i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 541.899 | 0.767562 | ||||||||
\(707\) | 151.389 | − | 224.882i | 0.214128 | − | 0.318079i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 339.531 | + | 196.029i | 0.478888 | + | 0.276486i | 0.719953 | − | 0.694023i | \(-0.244163\pi\) |
−0.241065 | + | 0.970509i | \(0.577497\pi\) | |||||||
\(710\) | −1629.41 | − | 1048.76i | −2.29494 | − | 1.47713i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 336.910 | + | 1257.36i | 0.473188 | + | 1.76596i | ||||
\(713\) | −632.389 | − | 632.389i | −0.886941 | − | 0.886941i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 372.399 | + | 723.593i | 0.520837 | + | 1.01202i | ||||
\(716\) | −363.687 | + | 629.924i | −0.507942 | + | 0.879782i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 193.088 | − | 720.614i | 0.268925 | − | 1.00364i | ||||
\(719\) | −1001.31 | − | 578.104i | −1.39264 | − | 0.804039i | −0.399031 | − | 0.916938i | \(-0.630653\pi\) |
−0.993607 | + | 0.112898i | \(0.963987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 142.413 | + | 163.528i | 0.197521 | + | 0.226807i | ||||
\(722\) | 214.918 | − | 214.918i | 0.297670 | − | 0.297670i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1519.83 | − | 877.472i | 2.09921 | − | 1.21198i | ||||
\(725\) | −550.246 | − | 53.3179i | −0.758961 | − | 0.0735419i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.8958 | + | 27.8958i | −0.0383712 | + | 0.0383712i | −0.726032 | − | 0.687661i | \(-0.758638\pi\) |
0.687661 | + | 0.726032i | \(0.258638\pi\) | |||||||
\(728\) | −2593.19 | + | 1267.69i | −3.56208 | + | 1.74133i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1155.11 | + | 1048.59i | −1.58234 | + | 1.43643i | ||||
\(731\) | −165.596 | − | 286.821i | −0.226534 | − | 0.392368i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 780.690 | − | 209.185i | 1.06506 | − | 0.285382i | 0.316599 | − | 0.948559i | \(-0.397459\pi\) |
0.748463 | + | 0.663177i | \(0.230792\pi\) | |||||||
\(734\) | − | 1857.40i | − | 2.53052i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1873.97 | 2.54616 | ||||||||
\(737\) | 11.7935 | + | 44.0140i | 0.0160021 | + | 0.0597205i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −452.698 | + | 261.365i | −0.612582 | + | 0.353674i | −0.773975 | − | 0.633216i | \(-0.781735\pi\) |
0.161393 | + | 0.986890i | \(0.448401\pi\) | |||||||
\(740\) | 745.475 | + | 36.0332i | 1.00740 | + | 0.0486935i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 403.596 | + | 825.597i | 0.543930 | + | 1.11266i | ||||
\(743\) | 34.1788 | + | 34.1788i | 0.0460011 | + | 0.0460011i | 0.729733 | − | 0.683732i | \(-0.239644\pi\) |
−0.683732 | + | 0.729733i | \(0.739644\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −576.717 | + | 125.035i | −0.774116 | + | 0.167833i | ||||
\(746\) | −341.134 | − | 590.862i | −0.457284 | − | 0.792040i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −389.872 | − | 389.872i | −0.521219 | − | 0.521219i | ||||
\(749\) | −102.459 | + | 89.2296i | −0.136795 | + | 0.119132i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 352.812 | − | 611.088i | 0.469790 | − | 0.813700i | −0.529614 | − | 0.848239i | \(-0.677663\pi\) |
0.999403 | + | 0.0345394i | \(0.0109964\pi\) | |||||||
\(752\) | 918.547 | + | 246.124i | 1.22147 | + | 0.327292i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1405.00 | − | 811.177i | −1.86339 | − | 1.07583i | ||||
\(755\) | −850.410 | − | 272.501i | −1.12637 | − | 0.360929i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 395.694 | − | 395.694i | 0.522713 | − | 0.522713i | −0.395677 | − | 0.918390i | \(-0.629490\pi\) |
0.918390 | + | 0.395677i | \(0.129490\pi\) | |||||||
\(758\) | 1242.04 | − | 332.803i | 1.63857 | − | 0.439054i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1836.30 | + | 1181.93i | 2.41618 | + | 1.55517i | ||||
\(761\) | 692.529 | − | 1199.50i | 0.910025 | − | 1.57621i | 0.0959984 | − | 0.995381i | \(-0.469396\pi\) |
0.814026 | − | 0.580828i | \(-0.197271\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 493.414 | + | 332.162i | 0.646676 | + | 0.435337i | ||||
\(764\) | 147.442i | 0.192987i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 834.315 | + | 1445.08i | 1.08918 | + | 1.88652i | ||||
\(767\) | −345.779 | − | 92.6512i | −0.450820 | − | 0.120797i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 907.238i | 1.17976i | 0.807490 | + | 0.589882i | \(0.200826\pi\) | ||||
−0.807490 | + | 0.589882i | \(0.799174\pi\) | |||||||
\(770\) | 971.428 | − | 418.053i | 1.26160 | − | 0.542926i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 560.463 | + | 2091.68i | 0.725988 | + | 2.70942i | ||||
\(773\) | −161.404 | + | 602.366i | −0.208802 | + | 0.779258i | 0.779456 | + | 0.626458i | \(0.215496\pi\) |
−0.988257 | + | 0.152800i | \(0.951171\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 624.796 | − | 284.281i | 0.806188 | − | 0.366814i | ||||
\(776\) | 1731.20 | 2.23093 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1704.49 | − | 1704.49i | −2.19086 | − | 2.19086i | ||||
\(779\) | −9.04791 | − | 5.22381i | −0.0116148 | − | 0.00670579i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 429.878 | + | 744.570i | 0.550420 | + | 0.953355i | ||||
\(782\) | 217.788 | + | 812.797i | 0.278502 | + | 1.03938i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 701.950 | + | 1728.37i | 0.895344 | + | 2.20455i | ||||
\(785\) | 263.770 | − | 135.750i | 0.336013 | − | 0.172930i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −647.269 | − | 173.435i | −0.822451 | − | 0.220375i | −0.177033 | − | 0.984205i | \(-0.556650\pi\) |
−0.645418 | + | 0.763830i | \(0.723317\pi\) | |||||||
\(788\) | 919.738 | − | 3432.51i | 1.16718 | − | 4.35598i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −844.107 | − | 1640.15i | −1.06849 | − | 2.07614i | ||||
\(791\) | −303.346 | + | 883.579i | −0.383497 | + | 1.11704i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 517.875 | − | 138.764i | 0.653058 | − | 0.174986i | ||||
\(794\) | 210.840 | − | 121.729i | 0.265542 | − | 0.153311i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 317.165 | − | 549.346i | 0.398448 | − | 0.690133i | ||||
\(797\) | −499.339 | + | 499.339i | −0.626524 | + | 0.626524i | −0.947192 | − | 0.320668i | \(-0.896093\pi\) |
0.320668 | + | 0.947192i | \(0.396093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 174.849i | 0.218835i | ||||||||
\(800\) | −504.528 | + | 1346.94i | −0.630660 | + | 1.68368i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 389.768 | + | 104.438i | 0.485995 | + | 0.130222i | ||||
\(803\) | 668.599 | − | 179.151i | 0.832626 | − | 0.223102i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1132.20 | − | 133.311i | −1.40646 | − | 0.165604i | ||||
\(806\) | 2014.44 | 2.49931 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 207.911 | − | 775.935i | 0.257316 | − | 0.960315i | ||||
\(809\) | −1117.27 | + | 645.054i | −1.38105 | + | 0.797347i | −0.992283 | − | 0.123990i | \(-0.960431\pi\) |
−0.388763 | + | 0.921338i | \(0.627097\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1511.76 | −1.86407 | −0.932036 | − | 0.362364i | \(-0.881970\pi\) | ||||
−0.932036 | + | 0.362364i | \(0.881970\pi\) | |||||||
\(812\) | −831.605 | + | 1235.32i | −1.02414 | + | 1.52133i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −406.018 | − | 234.414i | −0.498793 | − | 0.287978i | ||||
\(815\) | −340.367 | + | 528.809i | −0.417629 | + | 0.648846i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −257.842 | − | 962.278i | −0.315596 | − | 1.17782i | ||||
\(818\) | 766.982 | + | 766.982i | 0.937631 | + | 0.937631i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.28319 | − | 22.7291i | 0.00888194 | − | 0.0277184i | ||||
\(821\) | 480.446 | − | 832.156i | 0.585196 | − | 1.01359i | −0.409656 | − | 0.912240i | \(-0.634351\pi\) |
0.994851 | − | 0.101348i | \(-0.0323156\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.71404 | + | 25.0572i | −0.00815801 | + | 0.0304461i | −0.969885 | − | 0.243564i | \(-0.921683\pi\) |
0.961727 | + | 0.274010i | \(0.0883501\pi\) | |||||||
\(824\) | 556.483 | + | 321.286i | 0.675343 | + | 0.389910i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −151.058 | + | 439.997i | −0.182879 | + | 0.532684i | ||||
\(827\) | −471.697 | + | 471.697i | −0.570371 | + | 0.570371i | −0.932232 | − | 0.361861i | \(-0.882141\pi\) |
0.361861 | + | 0.932232i | \(0.382141\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.2384 | − | 19.1902i | 0.0400945 | − | 0.0231486i | −0.479819 | − | 0.877368i | \(-0.659298\pi\) |
0.519913 | + | 0.854219i | \(0.325964\pi\) | |||||||
\(830\) | 528.776 | + | 2438.94i | 0.637080 | + | 2.93849i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −844.088 | + | 844.088i | −1.01453 | + | 1.01453i | ||||
\(833\) | −273.559 | + | 206.919i | −0.328402 | + | 0.248402i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.3434 | − | 213.991i | 0.0123874 | − | 0.256277i | ||||
\(836\) | −829.246 | − | 1436.30i | −0.991922 | − | 1.71806i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −837.002 | + | 224.274i | −0.998809 | + | 0.267630i | ||||
\(839\) | 641.866i | 0.765037i | 0.923948 | + | 0.382519i | \(0.124943\pi\) | ||||
−0.923948 | + | 0.382519i | \(0.875057\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 352.018 | 0.418570 | ||||||||
\(842\) | 118.728 | + | 443.097i | 0.141007 | + | 0.526244i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3405.65 | + | 1966.25i | −4.03513 | + | 2.32968i | ||||
\(845\) | 760.164 | + | 837.383i | 0.899602 | + | 0.990985i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 376.875 | + | 26.0109i | 0.444953 | + | 0.0307094i | ||||
\(848\) | 957.602 | + | 957.602i | 1.12925 | + | 1.12925i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −642.844 | − | 62.2903i | −0.756286 | − | 0.0732828i | ||||
\(851\) | 252.691 | + | 437.673i | 0.296934 | + | 0.514304i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 873.730 | + | 873.730i | 1.02430 | + | 1.02430i | 0.999697 | + | 0.0246050i | \(0.00783282\pi\) |
0.0246050 | + | 0.999697i | \(0.492167\pi\) | |||||||
\(854\) | −133.563 | − | 683.819i | −0.156398 | − | 0.800725i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −201.303 | + | 348.668i | −0.235167 | + | 0.407322i | ||||
\(857\) | −218.566 | − | 58.5645i | −0.255036 | − | 0.0683367i | 0.129036 | − | 0.991640i | \(-0.458812\pi\) |
−0.384072 | + | 0.923303i | \(0.625478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −54.8471 | − | 31.6660i | −0.0638499 | − | 0.0368638i | 0.467735 | − | 0.883869i | \(-0.345070\pi\) |
−0.531585 | + | 0.847005i | \(0.678403\pi\) | |||||||
\(860\) | 2023.59 | − | 1041.45i | 2.35301 | − | 1.21098i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −549.575 | + | 549.575i | −0.637558 | + | 0.637558i | ||||
\(863\) | −705.658 | + | 189.081i | −0.817680 | + | 0.219097i | −0.643332 | − | 0.765587i | \(-0.722449\pi\) |
−0.174348 | + | 0.984684i | \(0.555782\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −97.4850 | + | 151.457i | −0.112699 | + | 0.175095i | ||||
\(866\) | −1432.98 | + | 2481.99i | −1.65471 | + | 2.86604i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 127.313 | − | 1844.66i | 0.146674 | − | 2.12518i | ||||
\(869\) | 818.435i | 0.941812i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.3194 | + | 95.8160i | 0.0635125 | + | 0.110007i | ||||
\(872\) | 1702.48 | + | 456.179i | 1.95239 | + | 0.523141i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2531.13i | 2.89603i | ||||||||
\(875\) | 400.640 | − | 777.890i | 0.457874 | − | 0.889017i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 136.821 | + | 510.621i | 0.156010 | + | 0.582236i | 0.999017 | + | 0.0443338i | \(0.0141165\pi\) |
−0.843007 | + | 0.537903i | \(0.819217\pi\) | |||||||
\(878\) | 91.6092 | − | 341.890i | 0.104338 | − | 0.389396i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1153.95 | − | 1047.54i | 1.31130 | − | 1.19038i | ||||
\(881\) | −956.484 | −1.08568 | −0.542840 | − | 0.839836i | \(-0.682651\pi\) | ||||
−0.542840 | + | 0.839836i | \(0.682651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 883.412 | + | 883.412i | 1.00047 | + | 1.00047i | 1.00000 | 0.000466858i | \(0.000148605\pi\) | |
0.000466858 | 1.00000i | \(0.499851\pi\) | ||||||||
\(884\) | −1159.39 | − | 669.371i | −1.31152 | − | 0.757207i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −184.664 | − | 319.848i | −0.208425 | − | 0.361003i | ||||
\(887\) | 5.96195 | + | 22.2503i | 0.00672148 | + | 0.0250849i | 0.969205 | − | 0.246255i | \(-0.0792000\pi\) |
−0.962484 | + | 0.271340i | \(0.912533\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1371.99 | − | 471.025i | −1.54330 | − | 0.529837i | ||||
\(890\) | −529.919 | − | 1029.66i | −0.595415 | − | 1.15693i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2367.13 | + | 634.270i | 2.65373 | + | 0.711065i | ||||
\(893\) | −136.124 | + | 508.023i | −0.152435 | + | 0.568895i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 115.358 | − | 360.005i | 0.128892 | − | 0.402240i | ||||
\(896\) | −39.1713 | − | 44.9791i | −0.0437179 | − | 0.0501999i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1227.40 | − | 328.881i | 1.36681 | − | 0.366237i | ||||
\(899\) | 525.815 | − | 303.579i | 0.584889 | − | 0.337686i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −124.502 | + | 215.643i | −0.138182 | + | 0.239338i | ||||
\(902\) | −10.6014 | + | 10.6014i | −0.0117533 | + | 0.0117533i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2768.26i | 3.06224i | ||||||||
\(905\) | −675.333 | + | 613.057i | −0.746224 | + | 0.677411i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −783.082 | − | 209.826i | −0.863376 | − | 0.231341i | −0.200155 | − | 0.979764i | \(-0.564144\pi\) |
−0.663221 | + | 0.748424i | \(0.730811\pi\) | |||||||
\(908\) | 2039.43 | − | 546.463i | 2.24607 | − | 0.601832i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2015.60 | − | 1590.95i | 2.21495 | − | 1.74829i | ||||
\(911\) | 302.928 | 0.332523 | 0.166261 | − | 0.986082i | \(-0.446830\pi\) | ||||
0.166261 | + | 0.986082i | \(0.446830\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 286.583 | − | 1069.54i | 0.313891 | − | 1.17146i | ||||
\(914\) | −275.520 | + | 159.072i | −0.301445 | + | 0.174039i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3243.84 | 3.54131 | ||||||||
\(917\) | 802.703 | + | 55.4003i | 0.875357 | + | 0.0604147i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −838.092 | − | 483.873i | −0.911961 | − | 0.526521i | −0.0308992 | − | 0.999523i | \(-0.509837\pi\) |
−0.881061 | + | 0.473002i | \(0.843170\pi\) | |||||||
\(920\) | −3301.45 | + | 715.771i | −3.58853 | + | 0.778012i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −590.877 | − | 2205.18i | −0.640864 | − | 2.39174i | ||||
\(923\) | 1476.12 | + | 1476.12i | 1.59926 | + | 1.59926i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −382.615 | + | 63.7905i | −0.413638 | + | 0.0689627i | ||||
\(926\) | 296.762 | − | 514.006i | 0.320477 | − | 0.555082i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −329.278 | + | 1228.88i | −0.354825 | + | 1.32423i | ||||
\(929\) | 985.363 | + | 568.900i | 1.06067 | + | 0.612379i | 0.925618 | − | 0.378460i | \(-0.123546\pi\) |
0.135053 | + | 0.990838i | \(0.456879\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −955.915 | + | 388.229i | −1.02676 | + | 0.417003i | ||||
\(932\) | 2001.03 | − | 2001.03i | 2.14703 | − | 2.14703i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −161.150 | + | 93.0402i | −0.172538 | + | 0.0996148i | ||||
\(935\) | 240.960 | + | 155.093i | 0.257711 | + | 0.165875i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 695.689 | − | 695.689i | 0.742465 | − | 0.742465i | −0.230587 | − | 0.973052i | \(-0.574065\pi\) |
0.973052 | + | 0.230587i | \(0.0740646\pi\) | |||||||
\(938\) | 129.171 | − | 63.1458i | 0.137709 | − | 0.0673196i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1200.11 | − | 58.0084i | −1.27671 | − | 0.0617111i | ||||
\(941\) | −175.936 | − | 304.730i | −0.186967 | − | 0.323836i | 0.757271 | − | 0.653101i | \(-0.226532\pi\) |
−0.944238 | + | 0.329265i | \(0.893199\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.6109 | − | 4.18294i | 0.0165545 | − | 0.00443578i | ||||
\(944\) | 685.559i | 0.726228i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1429.62 | −1.51122 | ||||||||
\(947\) | −411.444 | − | 1535.53i | −0.434471 | − | 1.62147i | −0.742330 | − | 0.670034i | \(-0.766279\pi\) |
0.307859 | − | 0.951432i | \(-0.400387\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1455.50 | − | 840.334i | 1.53372 | − | 0.885495i | ||||
\(950\) | −1819.29 | − | 681.455i | −1.91504 | − | 0.717321i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −567.597 | + | 843.143i | −0.596216 | + | 0.885654i | ||||
\(953\) | 808.505 | + | 808.505i | 0.848379 | + | 0.848379i | 0.989931 | − | 0.141552i | \(-0.0452093\pi\) |
−0.141552 | + | 0.989931i | \(0.545209\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.2365 | − | 74.8899i | −0.0170016 | − | 0.0784187i | ||||
\(956\) | −921.939 | − | 1596.85i | −0.964372 | − | 1.67034i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 458.653 | + | 458.653i | 0.478761 | + | 0.478761i | ||||
\(959\) | −145.996 | − | 747.472i | −0.152238 | − | 0.779428i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 103.552 | − | 179.357i | 0.107755 | − | 0.186636i | ||||
\(962\) | −1099.56 | − | 294.626i | −1.14299 | − | 0.306264i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1025.98 | + | 592.349i | 1.06429 | + | 0.614470i | ||||
\(965\) | −515.012 | − | 1000.70i | −0.533691 | − | 1.03699i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −412.298 | + | 412.298i | −0.426369 | + | 0.426369i | −0.887389 | − | 0.461021i | \(-0.847483\pi\) |
0.461021 | + | 0.887389i | \(0.347483\pi\) | |||||||
\(968\) | 1081.28 | − | 289.729i | 1.11703 | − | 0.299307i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1505.13 | + | 326.321i | −1.55168 | + | 0.336413i | ||||
\(971\) | 281.316 | − | 487.254i | 0.289718 | − | 0.501806i | −0.684024 | − | 0.729459i | \(-0.739772\pi\) |
0.973742 | + | 0.227653i | \(0.0731052\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1187.21 | + | 580.371i | −1.22015 | + | 0.596476i | ||||
\(974\) | 937.436i | 0.962460i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −513.383 | − | 889.205i | −0.526007 | − | 0.911071i | ||||
\(977\) | 1661.12 | + | 445.096i | 1.70023 | + | 0.455575i | 0.972997 | − | 0.230818i | \(-0.0741403\pi\) |
0.727231 | + | 0.686393i | \(0.240807\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 513.802i | 0.524823i | ||||||||
\(980\) | −1329.47 | − | 1946.27i | −1.35660 | − | 1.98599i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 263.439 | + | 983.168i | 0.268268 | + | 1.00119i | ||||
\(983\) | 91.6612 | − | 342.084i | 0.0932463 | − | 0.348000i | −0.903501 | − | 0.428585i | \(-0.859012\pi\) |
0.996748 | + | 0.0805851i | \(0.0256789\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −89.1674 | + | 1844.75i | −0.0905253 | + | 1.87284i | ||||
\(986\) | −571.270 | −0.579381 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2847.47 | − | 2847.47i | −2.88205 | − | 2.88205i | ||||
\(989\) | 1334.61 | + | 770.539i | 1.34946 | + | 0.779109i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −433.964 | − | 751.647i | −0.437905 | − | 0.758473i | 0.559623 | − | 0.828747i | \(-0.310946\pi\) |
−0.997528 | + | 0.0702740i | \(0.977613\pi\) | |||||||
\(992\) | −408.857 | − | 1525.88i | −0.412154 | − | 1.53818i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2045.80 | − | 1781.64i | 2.05815 | − | 1.79239i | ||||
\(995\) | −100.602 | + | 313.954i | −0.101107 | + | 0.315532i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1418.75 | + | 380.153i | 1.42302 | + | 0.381297i | 0.886554 | − | 0.462625i | \(-0.153092\pi\) |
0.536466 | + | 0.843922i | \(0.319759\pi\) | |||||||
\(998\) | −573.959 | + | 2142.04i | −0.575109 | + | 2.14634i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 315.3.ca.b.163.1 | 64 | ||
3.2 | odd | 2 | 105.3.v.a.58.16 | yes | 64 | ||
5.2 | odd | 4 | inner | 315.3.ca.b.37.16 | 64 | ||
7.4 | even | 3 | inner | 315.3.ca.b.298.16 | 64 | ||
15.2 | even | 4 | 105.3.v.a.37.1 | ✓ | 64 | ||
21.11 | odd | 6 | 105.3.v.a.88.1 | yes | 64 | ||
35.32 | odd | 12 | inner | 315.3.ca.b.172.1 | 64 | ||
105.32 | even | 12 | 105.3.v.a.67.16 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.v.a.37.1 | ✓ | 64 | 15.2 | even | 4 | ||
105.3.v.a.58.16 | yes | 64 | 3.2 | odd | 2 | ||
105.3.v.a.67.16 | yes | 64 | 105.32 | even | 12 | ||
105.3.v.a.88.1 | yes | 64 | 21.11 | odd | 6 | ||
315.3.ca.b.37.16 | 64 | 5.2 | odd | 4 | inner | ||
315.3.ca.b.163.1 | 64 | 1.1 | even | 1 | trivial | ||
315.3.ca.b.172.1 | 64 | 35.32 | odd | 12 | inner | ||
315.3.ca.b.298.16 | 64 | 7.4 | even | 3 | inner |