Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,3,Mod(263,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("294.263");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.h (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.01091977219\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12745506816.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 275.2 | ||
Root | \(-1.00781 - 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.275 |
Dual form | 294.3.h.d.263.2 |
$q$-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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.612372 | − | 0.353553i | ||||
\(3\) | 2.54762 | + | 1.58418i | 0.849207 | + | 0.528060i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.250000 | + | 0.433013i | ||||
\(5\) | −5.68986 | − | 3.28504i | −1.13797 | − | 0.657008i | −0.192044 | − | 0.981386i | \(-0.561512\pi\) |
−0.945928 | + | 0.324378i | \(0.894845\pi\) | |||||||
\(6\) | −2.00000 | − | 3.74166i | −0.333333 | − | 0.623610i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 3.98074 | + | 8.07178i | 0.442305 | + | 0.896865i | ||||
\(10\) | 4.64575 | + | 8.04668i | 0.464575 | + | 0.804668i | ||||
\(11\) | 0.357016 | − | 0.206123i | 0.0324560 | − | 0.0187385i | −0.483684 | − | 0.875243i | \(-0.660702\pi\) |
0.516140 | + | 0.856504i | \(0.327368\pi\) | |||||||
\(12\) | −0.196262 | + | 5.99679i | −0.0163551 | + | 0.499732i | ||||
\(13\) | 20.5830 | 1.58331 | 0.791654 | − | 0.610970i | \(-0.209220\pi\) | ||||
0.791654 | + | 0.610970i | \(0.209220\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.29150 | − | 17.3828i | −0.619434 | − | 1.15885i | ||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 13.7524 | − | 7.93993i | 0.808962 | − | 0.467055i | −0.0376330 | − | 0.999292i | \(-0.511982\pi\) |
0.846595 | + | 0.532237i | \(0.178648\pi\) | |||||||
\(18\) | 0.832222 | − | 12.7007i | 0.0462345 | − | 0.705594i | ||||
\(19\) | 8.00000 | − | 13.8564i | 0.421053 | − | 0.729285i | −0.574990 | − | 0.818160i | \(-0.694994\pi\) |
0.996043 | + | 0.0888758i | \(0.0283274\pi\) | |||||||
\(20\) | − | 13.1402i | − | 0.657008i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.583005 | −0.0265002 | ||||||||
\(23\) | 31.1790 | + | 18.0012i | 1.35561 | + | 0.782660i | 0.989028 | − | 0.147727i | \(-0.0471957\pi\) |
0.366579 | + | 0.930387i | \(0.380529\pi\) | |||||||
\(24\) | 4.48074 | − | 7.20576i | 0.186698 | − | 0.300240i | ||||
\(25\) | 9.08301 | + | 15.7322i | 0.363320 | + | 0.629289i | ||||
\(26\) | −25.2089 | − | 14.5544i | −0.969574 | − | 0.559784i | ||||
\(27\) | −2.64575 | + | 26.8701i | −0.0979908 | + | 0.995187i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 20.8010i | 0.717274i | 0.933477 | + | 0.358637i | \(0.116758\pi\) | ||||
−0.933477 | + | 0.358637i | \(0.883242\pi\) | |||||||
\(30\) | −0.911782 | + | 27.8596i | −0.0303927 | + | 0.928653i | ||||
\(31\) | 2.77124 | + | 4.79993i | 0.0893949 | + | 0.154837i | 0.907256 | − | 0.420580i | \(-0.138173\pi\) |
−0.817861 | + | 0.575416i | \(0.804840\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 1.23608 | + | 0.0404541i | 0.0374569 | + | 0.00122588i | ||||
\(34\) | −22.4575 | −0.660515 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10.0000 | + | 14.9666i | −0.277778 | + | 0.415740i | ||||
\(37\) | −10.0000 | + | 17.3205i | −0.270270 | + | 0.468122i | −0.968931 | − | 0.247331i | \(-0.920446\pi\) |
0.698661 | + | 0.715453i | \(0.253780\pi\) | |||||||
\(38\) | −19.5959 | + | 11.3137i | −0.515682 | + | 0.297729i | ||||
\(39\) | 52.4377 | + | 32.6072i | 1.34456 | + | 0.836082i | ||||
\(40\) | −9.29150 | + | 16.0934i | −0.232288 | + | 0.402334i | ||||
\(41\) | − | 76.1013i | − | 1.85613i | −0.372418 | − | 0.928065i | \(-0.621471\pi\) | ||
0.372418 | − | 0.928065i | \(-0.378529\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 51.7490 | 1.20347 | 0.601733 | − | 0.798698i | \(-0.294477\pi\) | ||||
0.601733 | + | 0.798698i | \(0.294477\pi\) | |||||||
\(44\) | 0.714033 | + | 0.412247i | 0.0162280 | + | 0.00936925i | ||||
\(45\) | 3.86630 | − | 59.0042i | 0.0859177 | − | 1.31121i | ||||
\(46\) | −25.4575 | − | 44.0937i | −0.553424 | − | 0.958559i | ||||
\(47\) | 7.34847 | + | 4.24264i | 0.156350 | + | 0.0902690i | 0.576134 | − | 0.817355i | \(-0.304561\pi\) |
−0.419784 | + | 0.907624i | \(0.637894\pi\) | |||||||
\(48\) | −10.5830 | + | 5.65685i | −0.220479 | + | 0.117851i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 25.6906i | − | 0.513812i | ||||||
\(51\) | 47.6141 | + | 1.55830i | 0.933610 | + | 0.0305550i | ||||
\(52\) | 20.5830 | + | 35.6508i | 0.395827 | + | 0.685593i | ||||
\(53\) | −44.0908 | + | 25.4558i | −0.831902 | + | 0.480299i | −0.854504 | − | 0.519446i | \(-0.826138\pi\) |
0.0226013 | + | 0.999745i | \(0.492805\pi\) | |||||||
\(54\) | 22.2404 | − | 31.0381i | 0.411859 | − | 0.574780i | ||||
\(55\) | −2.70850 | −0.0492454 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 42.3320 | − | 22.6274i | 0.742667 | − | 0.396972i | ||||
\(58\) | 14.7085 | − | 25.4759i | 0.253595 | − | 0.439239i | ||||
\(59\) | −1.42807 | + | 0.824494i | −0.0242045 | + | 0.0139745i | −0.512053 | − | 0.858954i | \(-0.671115\pi\) |
0.487849 | + | 0.872928i | \(0.337782\pi\) | |||||||
\(60\) | 20.8164 | − | 33.4762i | 0.346940 | − | 0.557936i | ||||
\(61\) | 33.4575 | − | 57.9501i | 0.548484 | − | 0.950002i | −0.449895 | − | 0.893082i | \(-0.648539\pi\) |
0.998379 | − | 0.0569203i | \(-0.0181281\pi\) | |||||||
\(62\) | − | 7.83826i | − | 0.126424i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −117.114 | − | 67.6160i | −1.80176 | − | 1.04025i | ||||
\(66\) | −1.48528 | − | 0.923586i | −0.0225042 | − | 0.0139937i | ||||
\(67\) | −24.7085 | − | 42.7964i | −0.368784 | − | 0.638752i | 0.620592 | − | 0.784134i | \(-0.286892\pi\) |
−0.989376 | + | 0.145382i | \(0.953559\pi\) | |||||||
\(68\) | 27.5047 | + | 15.8799i | 0.404481 | + | 0.233527i | ||||
\(69\) | 50.9150 | + | 95.2533i | 0.737899 | + | 1.38048i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 87.7385i | 1.23575i | 0.786275 | + | 0.617877i | \(0.212007\pi\) | ||||
−0.786275 | + | 0.617877i | \(0.787993\pi\) | |||||||
\(72\) | 22.8305 | − | 11.2592i | 0.317090 | − | 0.156378i | ||||
\(73\) | 6.16601 | + | 10.6798i | 0.0844659 | + | 0.146299i | 0.905163 | − | 0.425064i | \(-0.139748\pi\) |
−0.820698 | + | 0.571363i | \(0.806415\pi\) | |||||||
\(74\) | 24.4949 | − | 14.1421i | 0.331012 | − | 0.191110i | ||||
\(75\) | −1.78264 | + | 54.4689i | −0.0237686 | + | 0.726252i | ||||
\(76\) | 32.0000 | 0.421053 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −41.1660 | − | 77.0146i | −0.527769 | − | 0.987366i | ||||
\(79\) | 42.4575 | − | 73.5386i | 0.537437 | − | 0.930868i | −0.461604 | − | 0.887086i | \(-0.652726\pi\) |
0.999041 | − | 0.0437820i | \(-0.0139407\pi\) | |||||||
\(80\) | 22.7594 | − | 13.1402i | 0.284493 | − | 0.164252i | ||||
\(81\) | −49.3074 | + | 64.2634i | −0.608733 | + | 0.793375i | ||||
\(82\) | −53.8118 | + | 93.2047i | −0.656241 | + | 1.13664i | ||||
\(83\) | 4.12247i | 0.0496683i | 0.999692 | + | 0.0248342i | \(0.00790577\pi\) | ||||
−0.999692 | + | 0.0248342i | \(0.992094\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −104.332 | −1.22744 | ||||||||
\(86\) | −63.3793 | − | 36.5921i | −0.736969 | − | 0.425489i | ||||
\(87\) | −32.9525 | + | 52.9929i | −0.378764 | + | 0.609114i | ||||
\(88\) | −0.583005 | − | 1.00979i | −0.00662506 | − | 0.0114749i | ||||
\(89\) | −27.0212 | − | 15.6007i | −0.303609 | − | 0.175289i | 0.340454 | − | 0.940261i | \(-0.389419\pi\) |
−0.644063 | + | 0.764972i | \(0.722753\pi\) | |||||||
\(90\) | −46.4575 | + | 69.5312i | −0.516195 | + | 0.772569i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 72.0047i | 0.782660i | ||||||||
\(93\) | −0.543889 | + | 16.6186i | −0.00584826 | + | 0.178694i | ||||
\(94\) | −6.00000 | − | 10.3923i | −0.0638298 | − | 0.110556i | ||||
\(95\) | −91.0378 | + | 52.5607i | −0.958292 | + | 0.553270i | ||||
\(96\) | 16.9615 | + | 0.555112i | 0.176682 | + | 0.00578241i | ||||
\(97\) | −68.8340 | −0.709629 | −0.354814 | − | 0.934937i | \(-0.615456\pi\) | ||||
−0.354814 | + | 0.934937i | \(0.615456\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.08497 | + | 2.06123i | 0.0311614 | + | 0.0208206i | ||||
\(100\) | −18.1660 | + | 31.4645i | −0.181660 | + | 0.314645i | ||||
\(101\) | −121.376 | + | 70.0766i | −1.20174 | + | 0.693828i | −0.960943 | − | 0.276747i | \(-0.910744\pi\) |
−0.240802 | + | 0.970574i | \(0.577410\pi\) | |||||||
\(102\) | −57.2132 | − | 35.5768i | −0.560914 | − | 0.348792i | ||||
\(103\) | −19.6863 | + | 34.0976i | −0.191129 | + | 0.331045i | −0.945625 | − | 0.325260i | \(-0.894548\pi\) |
0.754496 | + | 0.656305i | \(0.227881\pi\) | |||||||
\(104\) | − | 58.2175i | − | 0.559784i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 72.0000 | 0.679245 | ||||||||
\(107\) | −93.5369 | − | 54.0035i | −0.874176 | − | 0.504706i | −0.00544256 | − | 0.999985i | \(-0.501732\pi\) |
−0.868734 | + | 0.495279i | \(0.835066\pi\) | |||||||
\(108\) | −49.1861 | + | 22.2875i | −0.455426 | + | 0.206366i | ||||
\(109\) | 61.9150 | + | 107.240i | 0.568028 | + | 0.983853i | 0.996761 | + | 0.0804218i | \(0.0256267\pi\) |
−0.428733 | + | 0.903431i | \(0.641040\pi\) | |||||||
\(110\) | 3.31722 | + | 1.91520i | 0.0301565 | + | 0.0174109i | ||||
\(111\) | −52.9150 | + | 28.2843i | −0.476712 | + | 0.254813i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 80.4900i | − | 0.712301i | −0.934429 | − | 0.356150i | \(-0.884089\pi\) | ||
0.934429 | − | 0.356150i | \(-0.115911\pi\) | |||||||
\(114\) | −67.8459 | − | 2.22045i | −0.595140 | − | 0.0194776i | ||||
\(115\) | −118.269 | − | 204.848i | −1.02843 | − | 1.78129i | ||||
\(116\) | −36.0283 | + | 20.8010i | −0.310589 | + | 0.179319i | ||||
\(117\) | 81.9356 | + | 166.142i | 0.700304 | + | 1.42001i | ||||
\(118\) | 2.33202 | 0.0197629 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −49.1660 | + | 26.2803i | −0.409717 | + | 0.219003i | ||||
\(121\) | −60.4150 | + | 104.642i | −0.499298 | + | 0.864809i | ||||
\(122\) | −81.9538 | + | 47.3161i | −0.671753 | + | 0.387837i | ||||
\(123\) | 120.558 | − | 193.877i | 0.980149 | − | 1.57624i | ||||
\(124\) | −5.54249 | + | 9.59987i | −0.0446975 | + | 0.0774183i | ||||
\(125\) | 44.8999i | 0.359199i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −132.915 | −1.04658 | −0.523288 | − | 0.852156i | \(-0.675295\pi\) | ||||
−0.523288 | + | 0.852156i | \(0.675295\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 131.837 | + | 81.9798i | 1.02199 | + | 0.635502i | ||||
\(130\) | 95.6235 | + | 165.625i | 0.735566 | + | 1.27404i | ||||
\(131\) | 3.57016 | + | 2.06123i | 0.0272532 | + | 0.0157346i | 0.513565 | − | 0.858051i | \(-0.328325\pi\) |
−0.486312 | + | 0.873786i | \(0.661658\pi\) | |||||||
\(132\) | 1.16601 | + | 2.18141i | 0.00883341 | + | 0.0165258i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 69.8862i | 0.521539i | ||||||||
\(135\) | 103.323 | − | 144.195i | 0.765357 | − | 1.06811i | ||||
\(136\) | −22.4575 | − | 38.8976i | −0.165129 | − | 0.286011i | ||||
\(137\) | 86.2925 | − | 49.8210i | 0.629872 | − | 0.363657i | −0.150830 | − | 0.988560i | \(-0.548195\pi\) |
0.780703 | + | 0.624903i | \(0.214861\pi\) | |||||||
\(138\) | 4.99633 | − | 152.663i | 0.0362053 | − | 1.10626i | ||||
\(139\) | 93.5425 | 0.672968 | 0.336484 | − | 0.941689i | \(-0.390762\pi\) | ||||
0.336484 | + | 0.941689i | \(0.390762\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | + | 22.4499i | 0.0851064 | + | 0.159219i | ||||
\(142\) | 62.0405 | − | 107.457i | 0.436905 | − | 0.756742i | ||||
\(143\) | 7.34847 | − | 4.24264i | 0.0513879 | − | 0.0296688i | ||||
\(144\) | −35.9230 | − | 2.35388i | −0.249465 | − | 0.0163464i | ||||
\(145\) | 68.3320 | − | 118.355i | 0.471255 | − | 0.816238i | ||||
\(146\) | − | 17.4401i | − | 0.119453i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −40.0000 | −0.270270 | ||||||||
\(149\) | 43.1686 | + | 24.9234i | 0.289722 | + | 0.167271i | 0.637817 | − | 0.770188i | \(-0.279838\pi\) |
−0.348094 | + | 0.937460i | \(0.613171\pi\) | |||||||
\(150\) | 40.6986 | − | 65.4499i | 0.271324 | − | 0.436333i | ||||
\(151\) | −105.830 | − | 183.303i | −0.700861 | − | 1.21393i | −0.968164 | − | 0.250315i | \(-0.919466\pi\) |
0.267303 | − | 0.963612i | \(-0.413867\pi\) | |||||||
\(152\) | −39.1918 | − | 22.6274i | −0.257841 | − | 0.148865i | ||||
\(153\) | 118.834 | + | 79.3993i | 0.776693 | + | 0.518950i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 36.4146i | − | 0.234933i | ||||||
\(156\) | −4.03965 | + | 123.432i | −0.0258952 | + | 0.791230i | ||||
\(157\) | 54.3725 | + | 94.1760i | 0.346322 | + | 0.599847i | 0.985593 | − | 0.169134i | \(-0.0540972\pi\) |
−0.639271 | + | 0.768981i | \(0.720764\pi\) | |||||||
\(158\) | −103.999 | + | 60.0440i | −0.658223 | + | 0.380025i | ||||
\(159\) | −152.653 | − | 4.99600i | −0.960084 | − | 0.0314214i | ||||
\(160\) | −37.1660 | −0.232288 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 105.830 | − | 43.8406i | 0.653272 | − | 0.270621i | ||||
\(163\) | −6.50197 | + | 11.2617i | −0.0398894 | + | 0.0690904i | −0.885281 | − | 0.465057i | \(-0.846034\pi\) |
0.845391 | + | 0.534147i | \(0.179367\pi\) | |||||||
\(164\) | 131.811 | − | 76.1013i | 0.803728 | − | 0.464032i | ||||
\(165\) | −6.90022 | − | 4.29075i | −0.0418195 | − | 0.0260045i | ||||
\(166\) | 2.91503 | − | 5.04897i | 0.0175604 | − | 0.0304155i | ||||
\(167\) | − | 156.858i | − | 0.939267i | −0.882862 | − | 0.469633i | \(-0.844386\pi\) | ||
0.882862 | − | 0.469633i | \(-0.155614\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 254.660 | 1.50686 | ||||||||
\(170\) | 127.780 | + | 73.7739i | 0.751648 | + | 0.433964i | ||||
\(171\) | 143.692 | + | 9.41551i | 0.840303 | + | 0.0550615i | ||||
\(172\) | 51.7490 | + | 89.6319i | 0.300866 | + | 0.521116i | ||||
\(173\) | 4.72288 | + | 2.72676i | 0.0272999 | + | 0.0157616i | 0.513588 | − | 0.858037i | \(-0.328316\pi\) |
−0.486288 | + | 0.873799i | \(0.661649\pi\) | |||||||
\(174\) | 77.8301 | − | 41.6019i | 0.447299 | − | 0.239091i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.64899i | 0.00936925i | ||||||||
\(177\) | −4.94432 | − | 0.161816i | −0.0279340 | − | 0.000914217i | ||||
\(178\) | 22.0627 | + | 38.2138i | 0.123948 | + | 0.214684i | ||||
\(179\) | 1.07105 | − | 0.618370i | 0.00598351 | − | 0.00345458i | −0.497005 | − | 0.867748i | \(-0.665567\pi\) |
0.502989 | + | 0.864293i | \(0.332234\pi\) | |||||||
\(180\) | 106.065 | − | 52.3076i | 0.589248 | − | 0.290598i | ||||
\(181\) | −186.915 | −1.03268 | −0.516340 | − | 0.856384i | \(-0.672706\pi\) | ||||
−0.516340 | + | 0.856384i | \(0.672706\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 177.041 | − | 94.6321i | 0.967435 | − | 0.517116i | ||||
\(184\) | 50.9150 | − | 88.1874i | 0.276712 | − | 0.479279i | ||||
\(185\) | 113.797 | − | 65.7008i | 0.615120 | − | 0.355140i | ||||
\(186\) | 12.4172 | − | 19.9689i | 0.0667593 | − | 0.107360i | ||||
\(187\) | 3.27321 | − | 5.66937i | 0.0175038 | − | 0.0303175i | ||||
\(188\) | 16.9706i | 0.0902690i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 148.664 | 0.782442 | ||||||||
\(191\) | 303.578 | + | 175.271i | 1.58941 | + | 0.917649i | 0.993403 | + | 0.114673i | \(0.0365820\pi\) |
0.596011 | + | 0.802976i | \(0.296751\pi\) | |||||||
\(192\) | −20.3810 | − | 12.6734i | −0.106151 | − | 0.0660075i | ||||
\(193\) | −135.247 | − | 234.255i | −0.700762 | − | 1.21376i | −0.968199 | − | 0.250180i | \(-0.919510\pi\) |
0.267437 | − | 0.963575i | \(-0.413823\pi\) | |||||||
\(194\) | 84.3041 | + | 48.6730i | 0.434557 | + | 0.250892i | ||||
\(195\) | −191.247 | − | 357.790i | −0.980754 | − | 1.83482i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 63.5194i | 0.322434i | 0.986919 | + | 0.161217i | \(0.0515419\pi\) | ||||
−0.986919 | + | 0.161217i | \(0.948458\pi\) | |||||||
\(198\) | −2.32079 | − | 4.70589i | −0.0117212 | − | 0.0237671i | ||||
\(199\) | 44.0000 | + | 76.2102i | 0.221106 | + | 0.382966i | 0.955144 | − | 0.296142i | \(-0.0957001\pi\) |
−0.734038 | + | 0.679108i | \(0.762367\pi\) | |||||||
\(200\) | 44.4975 | − | 25.6906i | 0.222487 | − | 0.128453i | ||||
\(201\) | 4.84933 | − | 148.172i | 0.0241260 | − | 0.737172i | ||||
\(202\) | 198.207 | 0.981220 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 44.9150 | + | 84.0283i | 0.220172 | + | 0.411904i | ||||
\(205\) | −249.996 | + | 433.006i | −1.21949 | + | 2.11222i | ||||
\(206\) | 48.2213 | − | 27.8406i | 0.234084 | − | 0.135148i | ||||
\(207\) | −21.1863 | + | 323.328i | −0.102349 | + | 1.56197i | ||||
\(208\) | −41.1660 | + | 71.3016i | −0.197914 | + | 0.342796i | ||||
\(209\) | − | 6.59595i | − | 0.0315596i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −378.745 | −1.79500 | −0.897500 | − | 0.441014i | \(-0.854619\pi\) | ||||
−0.897500 | + | 0.441014i | \(0.854619\pi\) | |||||||
\(212\) | −88.1816 | − | 50.9117i | −0.415951 | − | 0.240149i | ||||
\(213\) | −138.994 | + | 223.525i | −0.652553 | + | 1.04941i | ||||
\(214\) | 76.3725 | + | 132.281i | 0.356881 | + | 0.618136i | ||||
\(215\) | −294.445 | − | 169.998i | −1.36951 | − | 0.790687i | ||||
\(216\) | 76.0000 | + | 7.48331i | 0.351852 | + | 0.0346450i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 175.122i | − | 0.803313i | ||||||
\(219\) | −1.21015 | + | 36.9763i | −0.00552580 | + | 0.168841i | ||||
\(220\) | −2.70850 | − | 4.69126i | −0.0123114 | − | 0.0213239i | ||||
\(221\) | 283.065 | − | 163.428i | 1.28084 | − | 0.739491i | ||||
\(222\) | 84.8074 | + | 2.77556i | 0.382015 | + | 0.0125025i | ||||
\(223\) | −230.494 | −1.03361 | −0.516803 | − | 0.856104i | \(-0.672878\pi\) | ||||
−0.516803 | + | 0.856104i | \(0.672878\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −90.8301 | + | 135.942i | −0.403689 | + | 0.604187i | ||||
\(226\) | −56.9150 | + | 98.5797i | −0.251836 | + | 0.436193i | ||||
\(227\) | 223.816 | − | 129.220i | 0.985974 | − | 0.569252i | 0.0819056 | − | 0.996640i | \(-0.473899\pi\) |
0.904068 | + | 0.427388i | \(0.140566\pi\) | |||||||
\(228\) | 81.5239 | + | 50.6938i | 0.357561 | + | 0.222341i | ||||
\(229\) | 18.5425 | − | 32.1165i | 0.0809716 | − | 0.140247i | −0.822696 | − | 0.568482i | \(-0.807531\pi\) |
0.903668 | + | 0.428235i | \(0.140864\pi\) | |||||||
\(230\) | 334.516i | 1.45442i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 58.8340 | 0.253595 | ||||||||
\(233\) | 71.5955 | + | 41.3357i | 0.307277 | + | 0.177406i | 0.645707 | − | 0.763585i | \(-0.276563\pi\) |
−0.338430 | + | 0.940991i | \(0.609896\pi\) | |||||||
\(234\) | 17.1296 | − | 261.418i | 0.0732035 | − | 1.11717i | ||||
\(235\) | −27.8745 | − | 48.2801i | −0.118615 | − | 0.205447i | ||||
\(236\) | −2.85613 | − | 1.64899i | −0.0121022 | − | 0.00698724i | ||||
\(237\) | 224.664 | − | 120.088i | 0.947950 | − | 0.506700i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 168.469i | − | 0.704891i | −0.935832 | − | 0.352445i | \(-0.885350\pi\) | ||
0.935832 | − | 0.352445i | \(-0.114650\pi\) | |||||||
\(240\) | 78.7988 | + | 2.57891i | 0.328328 | + | 0.0107455i | ||||
\(241\) | 65.0000 | + | 112.583i | 0.269710 | + | 0.467151i | 0.968787 | − | 0.247896i | \(-0.0797390\pi\) |
−0.699077 | + | 0.715046i | \(0.746406\pi\) | |||||||
\(242\) | 147.986 | − | 85.4397i | 0.611512 | − | 0.353057i | ||||
\(243\) | −227.421 | + | 85.6068i | −0.935890 | + | 0.352291i | ||||
\(244\) | 133.830 | 0.548484 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −284.745 | + | 152.203i | −1.15750 | + | 0.618710i | ||||
\(247\) | 164.664 | − | 285.206i | 0.666656 | − | 1.15468i | ||||
\(248\) | 13.5763 | − | 7.83826i | 0.0547430 | − | 0.0316059i | ||||
\(249\) | −6.53074 | + | 10.5025i | −0.0262279 | + | 0.0421787i | ||||
\(250\) | 31.7490 | − | 54.9909i | 0.126996 | − | 0.219964i | ||||
\(251\) | 119.859i | 0.477525i | 0.971078 | + | 0.238763i | \(0.0767417\pi\) | ||||
−0.971078 | + | 0.238763i | \(0.923258\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.8419 | 0.0586635 | ||||||||
\(254\) | 162.787 | + | 93.9851i | 0.640894 | + | 0.370020i | ||||
\(255\) | −265.798 | − | 165.281i | −1.04235 | − | 0.648160i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 193.894 | + | 111.945i | 0.754451 | + | 0.435583i | 0.827300 | − | 0.561760i | \(-0.189876\pi\) |
−0.0728489 | + | 0.997343i | \(0.523209\pi\) | |||||||
\(258\) | −103.498 | − | 193.627i | −0.401155 | − | 0.750493i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 270.464i | − | 1.04025i | ||||||
\(261\) | −167.901 | + | 82.8032i | −0.643298 | + | 0.317254i | ||||
\(262\) | −2.91503 | − | 5.04897i | −0.0111261 | − | 0.0192709i | ||||
\(263\) | 185.705 | − | 107.217i | 0.706102 | − | 0.407668i | −0.103514 | − | 0.994628i | \(-0.533009\pi\) |
0.809616 | + | 0.586960i | \(0.199675\pi\) | |||||||
\(264\) | 0.114422 | − | 3.49616i | 0.000433415 | − | 0.0132430i | ||||
\(265\) | 334.494 | 1.26224 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −44.1255 | − | 82.5512i | −0.165264 | − | 0.309181i | ||||
\(268\) | 49.4170 | − | 85.5927i | 0.184392 | − | 0.319376i | ||||
\(269\) | −330.956 | + | 191.078i | −1.23032 | + | 0.710326i | −0.967097 | − | 0.254408i | \(-0.918119\pi\) |
−0.263224 | + | 0.964735i | \(0.584786\pi\) | |||||||
\(270\) | −228.506 | + | 103.542i | −0.846319 | + | 0.383489i | ||||
\(271\) | −57.2288 | + | 99.1231i | −0.211176 | + | 0.365768i | −0.952083 | − | 0.305840i | \(-0.901063\pi\) |
0.740907 | + | 0.671608i | \(0.234396\pi\) | |||||||
\(272\) | 63.5194i | 0.233527i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −140.915 | −0.514288 | ||||||||
\(275\) | 6.48556 | + | 3.74444i | 0.0235839 | + | 0.0136162i | ||||
\(276\) | −114.069 | + | 183.441i | −0.413292 | + | 0.664640i | ||||
\(277\) | 115.247 | + | 199.614i | 0.416054 | + | 0.720627i | 0.995538 | − | 0.0943563i | \(-0.0300793\pi\) |
−0.579484 | + | 0.814983i | \(0.696746\pi\) | |||||||
\(278\) | −114.566 | − | 66.1445i | −0.412107 | − | 0.237930i | ||||
\(279\) | −27.7124 | + | 41.4762i | −0.0993277 | + | 0.148660i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 73.9458i | 0.263152i | 0.991306 | + | 0.131576i | \(0.0420038\pi\) | ||||
−0.991306 | + | 0.131576i | \(0.957996\pi\) | |||||||
\(282\) | 1.17757 | − | 35.9807i | 0.00417578 | − | 0.127591i | ||||
\(283\) | −70.5830 | − | 122.253i | −0.249410 | − | 0.431991i | 0.713952 | − | 0.700194i | \(-0.246903\pi\) |
−0.963362 | + | 0.268204i | \(0.913570\pi\) | |||||||
\(284\) | −151.968 | + | 87.7385i | −0.535097 | + | 0.308939i | ||||
\(285\) | −315.195 | − | 10.3156i | −1.10595 | − | 0.0361952i | ||||
\(286\) | −12.0000 | −0.0419580 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 42.3320 | + | 28.2843i | 0.146986 | + | 0.0982093i | ||||
\(289\) | −18.4150 | + | 31.8958i | −0.0637198 | + | 0.110366i | ||||
\(290\) | −167.379 | + | 96.6361i | −0.577168 | + | 0.333228i | ||||
\(291\) | −175.363 | − | 109.046i | −0.602622 | − | 0.374727i | ||||
\(292\) | −12.3320 | + | 21.3597i | −0.0422329 | + | 0.0731496i | ||||
\(293\) | 329.595i | 1.12490i | 0.826832 | + | 0.562449i | \(0.190141\pi\) | ||||
−0.826832 | + | 0.562449i | \(0.809859\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.8340 | 0.0367254 | ||||||||
\(296\) | 48.9898 | + | 28.2843i | 0.165506 | + | 0.0955550i | ||||
\(297\) | 4.59397 | + | 10.1384i | 0.0154679 | + | 0.0341360i | ||||
\(298\) | −35.2470 | − | 61.0497i | −0.118279 | − | 0.204865i | ||||
\(299\) | 641.757 | + | 370.518i | 2.14634 | + | 1.23919i | ||||
\(300\) | −96.1255 | + | 51.3812i | −0.320418 | + | 0.171271i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 299.333i | 0.991168i | ||||||||
\(303\) | −420.235 | − | 13.7533i | −1.38691 | − | 0.0453906i | ||||
\(304\) | 32.0000 | + | 55.4256i | 0.105263 | + | 0.182321i | ||||
\(305\) | −380.737 | + | 219.819i | −1.24832 | + | 0.720717i | ||||
\(306\) | −89.3975 | − | 181.272i | −0.292149 | − | 0.592393i | ||||
\(307\) | −105.830 | −0.344723 | −0.172362 | − | 0.985034i | \(-0.555140\pi\) | ||||
−0.172362 | + | 0.985034i | \(0.555140\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −104.170 | + | 55.6812i | −0.337120 | + | 0.180198i | ||||
\(310\) | −25.7490 | + | 44.5986i | −0.0830613 | + | 0.143866i | ||||
\(311\) | 333.537 | − | 192.568i | 1.07247 | − | 0.619189i | 0.143613 | − | 0.989634i | \(-0.454128\pi\) |
0.928854 | + | 0.370445i | \(0.120795\pi\) | |||||||
\(312\) | 92.2271 | − | 148.316i | 0.295600 | − | 0.475372i | ||||
\(313\) | 39.6640 | − | 68.7001i | 0.126722 | − | 0.219489i | −0.795683 | − | 0.605714i | \(-0.792888\pi\) |
0.922405 | + | 0.386224i | \(0.126221\pi\) | |||||||
\(314\) | − | 153.789i | − | 0.489773i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 169.830 | 0.537437 | ||||||||
\(317\) | −356.089 | − | 205.588i | −1.12331 | − | 0.648542i | −0.181064 | − | 0.983471i | \(-0.557954\pi\) |
−0.942243 | + | 0.334929i | \(0.891288\pi\) | |||||||
\(318\) | 183.429 | + | 114.061i | 0.576820 | + | 0.358683i | ||||
\(319\) | 4.28757 | + | 7.42628i | 0.0134406 | + | 0.0232799i | ||||
\(320\) | 45.5189 | + | 26.2803i | 0.142247 | + | 0.0821261i | ||||
\(321\) | −152.745 | − | 285.760i | −0.475841 | − | 0.890218i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 254.078i | − | 0.786618i | ||||||
\(324\) | −160.615 | − | 21.1396i | −0.495725 | − | 0.0652456i | ||||
\(325\) | 186.956 | + | 323.817i | 0.575248 | + | 0.996358i | ||||
\(326\) | 15.9265 | − | 9.19517i | 0.0488543 | − | 0.0282060i | ||||
\(327\) | −12.1515 | + | 371.291i | −0.0371607 | + | 1.13545i | ||||
\(328\) | −215.247 | −0.656241 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.41699 | + | 10.1343i | 0.0164151 | + | 0.0307099i | ||||
\(331\) | 244.745 | − | 423.911i | 0.739411 | − | 1.28070i | −0.213350 | − | 0.976976i | \(-0.568437\pi\) |
0.952761 | − | 0.303722i | \(-0.0982293\pi\) | |||||||
\(332\) | −7.14033 | + | 4.12247i | −0.0215070 | + | 0.0124171i | ||||
\(333\) | −179.615 | − | 11.7694i | −0.539384 | − | 0.0353435i | ||||
\(334\) | −110.915 | + | 192.110i | −0.332081 | + | 0.575181i | ||||
\(335\) | 324.674i | 0.969176i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 500.316 | 1.48462 | 0.742309 | − | 0.670058i | \(-0.233731\pi\) | ||||
0.742309 | + | 0.670058i | \(0.233731\pi\) | |||||||
\(338\) | −311.894 | − | 180.072i | −0.922762 | − | 0.532757i | ||||
\(339\) | 127.511 | − | 205.058i | 0.376138 | − | 0.604891i | ||||
\(340\) | −104.332 | − | 180.708i | −0.306859 | − | 0.531495i | ||||
\(341\) | 1.97876 | + | 1.14244i | 0.00580281 | + | 0.00335025i | ||||
\(342\) | −169.328 | − | 113.137i | −0.495111 | − | 0.330810i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 146.368i | − | 0.425489i | ||||||
\(345\) | 23.2117 | − | 709.236i | 0.0672803 | − | 2.05576i | ||||
\(346\) | −3.85622 | − | 6.67916i | −0.0111451 | − | 0.0193039i | ||||
\(347\) | 167.022 | − | 96.4299i | 0.481330 | − | 0.277896i | −0.239640 | − | 0.970862i | \(-0.577030\pi\) |
0.720971 | + | 0.692966i | \(0.243696\pi\) | |||||||
\(348\) | −124.739 | − | 4.08243i | −0.358445 | − | 0.0117311i | ||||
\(349\) | 148.405 | 0.425230 | 0.212615 | − | 0.977136i | \(-0.431802\pi\) | ||||
0.212615 | + | 0.977136i | \(0.431802\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −54.4575 | + | 553.067i | −0.155150 | + | 1.57569i | ||||
\(352\) | 1.16601 | − | 2.01959i | 0.00331253 | − | 0.00573747i | ||||
\(353\) | −141.830 | + | 81.8857i | −0.401785 | + | 0.231971i | −0.687254 | − | 0.726417i | \(-0.741184\pi\) |
0.285469 | + | 0.958388i | \(0.407851\pi\) | |||||||
\(354\) | 5.94110 | + | 3.69434i | 0.0167828 | + | 0.0104360i | ||||
\(355\) | 288.225 | − | 499.220i | 0.811901 | − | 1.40625i | ||||
\(356\) | − | 62.4029i | − | 0.175289i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.74902 | −0.00488552 | ||||||||
\(359\) | 290.012 | + | 167.438i | 0.807832 | + | 0.466402i | 0.846202 | − | 0.532862i | \(-0.178883\pi\) |
−0.0383706 | + | 0.999264i | \(0.512217\pi\) | |||||||
\(360\) | −166.889 | − | 10.9355i | −0.463581 | − | 0.0303765i | ||||
\(361\) | 52.5000 | + | 90.9327i | 0.145429 | + | 0.251891i | ||||
\(362\) | 228.923 | + | 132.169i | 0.632385 | + | 0.365107i | ||||
\(363\) | −319.686 | + | 170.879i | −0.880678 | + | 0.470742i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 81.0224i | − | 0.221979i | ||||||
\(366\) | −283.744 | − | 9.28633i | −0.775258 | − | 0.0253725i | ||||
\(367\) | −163.498 | − | 283.187i | −0.445499 | − | 0.771626i | 0.552588 | − | 0.833454i | \(-0.313640\pi\) |
−0.998087 | + | 0.0618281i | \(0.980307\pi\) | |||||||
\(368\) | −124.716 | + | 72.0047i | −0.338902 | + | 0.195665i | ||||
\(369\) | 614.273 | − | 302.940i | 1.66470 | − | 0.820975i | ||||
\(370\) | −185.830 | −0.502243 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −29.3281 | + | 15.6765i | −0.0788389 | + | 0.0421412i | ||||
\(373\) | 152.668 | − | 264.429i | 0.409298 | − | 0.708924i | −0.585514 | − | 0.810663i | \(-0.699107\pi\) |
0.994811 | + | 0.101738i | \(0.0324405\pi\) | |||||||
\(374\) | −8.01770 | + | 4.62902i | −0.0214377 | + | 0.0123771i | ||||
\(375\) | −71.1296 | + | 114.388i | −0.189679 | + | 0.305034i | ||||
\(376\) | 12.0000 | − | 20.7846i | 0.0319149 | − | 0.0552782i | ||||
\(377\) | 428.146i | 1.13567i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 199.660 | 0.526808 | 0.263404 | − | 0.964686i | \(-0.415155\pi\) | ||||
0.263404 | + | 0.964686i | \(0.415155\pi\) | |||||||
\(380\) | −182.076 | − | 105.121i | −0.479146 | − | 0.276635i | ||||
\(381\) | −338.617 | − | 210.561i | −0.888759 | − | 0.552655i | ||||
\(382\) | −247.871 | − | 429.324i | −0.648876 | − | 1.12389i | ||||
\(383\) | −458.551 | − | 264.744i | −1.19726 | − | 0.691239i | −0.237317 | − | 0.971432i | \(-0.576268\pi\) |
−0.959944 | + | 0.280193i | \(0.909601\pi\) | |||||||
\(384\) | 16.0000 | + | 29.9333i | 0.0416667 | + | 0.0779512i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 382.536i | 0.991027i | ||||||||
\(387\) | 205.999 | + | 417.707i | 0.532298 | + | 1.07935i | ||||
\(388\) | −68.8340 | − | 119.224i | −0.177407 | − | 0.307278i | ||||
\(389\) | −206.724 | + | 119.352i | −0.531424 | + | 0.306818i | −0.741596 | − | 0.670846i | \(-0.765931\pi\) |
0.210172 | + | 0.977664i | \(0.432598\pi\) | |||||||
\(390\) | −18.7672 | + | 573.434i | −0.0481211 | + | 1.47034i | ||||
\(391\) | 571.712 | 1.46218 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.83005 | + | 10.9070i | 0.0148347 | + | 0.0277533i | ||||
\(394\) | 44.9150 | − | 77.7951i | 0.113998 | − | 0.197450i | ||||
\(395\) | −483.155 | + | 278.949i | −1.22318 | + | 0.706201i | ||||
\(396\) | −0.485190 | + | 7.40457i | −0.00122523 | + | 0.0186984i | ||||
\(397\) | −160.292 | + | 277.633i | −0.403757 | + | 0.699328i | −0.994176 | − | 0.107769i | \(-0.965629\pi\) |
0.590419 | + | 0.807097i | \(0.298963\pi\) | |||||||
\(398\) | − | 124.451i | − | 0.312690i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −72.6640 | −0.181660 | ||||||||
\(401\) | 201.012 | + | 116.054i | 0.501276 | + | 0.289412i | 0.729241 | − | 0.684257i | \(-0.239874\pi\) |
−0.227964 | + | 0.973670i | \(0.573207\pi\) | |||||||
\(402\) | −110.712 | + | 178.043i | −0.275404 | + | 0.442894i | ||||
\(403\) | 57.0405 | + | 98.7971i | 0.141540 | + | 0.245154i | ||||
\(404\) | −242.752 | − | 140.153i | −0.600872 | − | 0.346914i | ||||
\(405\) | 491.660 | − | 203.673i | 1.21398 | − | 0.502895i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.24494i | 0.0202578i | ||||||||
\(408\) | 4.40755 | − | 134.673i | 0.0108028 | − | 0.330081i | ||||
\(409\) | −264.490 | − | 458.110i | −0.646675 | − | 1.12007i | −0.983912 | − | 0.178654i | \(-0.942826\pi\) |
0.337237 | − | 0.941420i | \(-0.390508\pi\) | |||||||
\(410\) | 612.363 | − | 353.548i | 1.49357 | − | 0.862312i | ||||
\(411\) | 298.766 | + | 9.77794i | 0.726924 | + | 0.0237906i | ||||
\(412\) | −78.7451 | −0.191129 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 254.575 | − | 381.013i | 0.614916 | − | 0.920322i | ||||
\(415\) | 13.5425 | − | 23.4563i | 0.0326325 | − | 0.0565211i | ||||
\(416\) | 100.836 | − | 58.2175i | 0.242394 | − | 0.139946i | ||||
\(417\) | 238.311 | + | 148.188i | 0.571489 | + | 0.355367i | ||||
\(418\) | −4.66404 | + | 8.07836i | −0.0111580 | + | 0.0193262i | ||||
\(419\) | 89.7998i | 0.214319i | 0.994242 | + | 0.107160i | \(0.0341756\pi\) | ||||
−0.994242 | + | 0.107160i | \(0.965824\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −777.150 | −1.84596 | −0.922981 | − | 0.384845i | \(-0.874255\pi\) | ||||
−0.922981 | + | 0.384845i | \(0.874255\pi\) | |||||||
\(422\) | 463.866 | + | 267.813i | 1.09921 | + | 0.634628i | ||||
\(423\) | −4.99333 | + | 76.2041i | −0.0118046 | + | 0.180152i | ||||
\(424\) | 72.0000 | + | 124.708i | 0.169811 | + | 0.294122i | ||||
\(425\) | 249.826 | + | 144.237i | 0.587825 | + | 0.339381i | ||||
\(426\) | 328.288 | − | 175.477i | 0.770628 | − | 0.411918i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 216.014i | − | 0.504706i | ||||||
\(429\) | 25.4422 | + | 0.832667i | 0.0593059 | + | 0.00194095i | ||||
\(430\) | 240.413 | + | 416.408i | 0.559100 | + | 0.968390i | ||||
\(431\) | −212.957 | + | 122.951i | −0.494099 | + | 0.285268i | −0.726273 | − | 0.687406i | \(-0.758749\pi\) |
0.232174 | + | 0.972674i | \(0.425416\pi\) | |||||||
\(432\) | −87.7891 | − | 62.9053i | −0.203216 | − | 0.145614i | ||||
\(433\) | −796.996 | −1.84064 | −0.920319 | − | 0.391169i | \(-0.872071\pi\) | ||||
−0.920319 | + | 0.391169i | \(0.872071\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 361.579 | − | 193.272i | 0.831216 | − | 0.444304i | ||||
\(436\) | −123.830 | + | 214.480i | −0.284014 | + | 0.491926i | ||||
\(437\) | 498.863 | − | 288.019i | 1.14156 | − | 0.659082i | ||||
\(438\) | 27.6283 | − | 44.4308i | 0.0630783 | − | 0.101440i | ||||
\(439\) | −276.915 | + | 479.631i | −0.630786 | + | 1.09255i | 0.356605 | + | 0.934255i | \(0.383934\pi\) |
−0.987391 | + | 0.158298i | \(0.949399\pi\) | |||||||
\(440\) | 7.66079i | 0.0174109i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −462.243 | −1.04580 | ||||||||
\(443\) | −670.288 | − | 386.991i | −1.51306 | − | 0.873568i | −0.999883 | − | 0.0152882i | \(-0.995133\pi\) |
−0.513182 | − | 0.858280i | \(-0.671533\pi\) | |||||||
\(444\) | −101.905 | − | 63.3672i | −0.229515 | − | 0.142719i | ||||
\(445\) | 102.498 | + | 177.532i | 0.230333 | + | 0.398948i | ||||
\(446\) | 282.296 | + | 162.984i | 0.632952 | + | 0.365435i | ||||
\(447\) | 70.4941 | + | 131.882i | 0.157705 | + | 0.295039i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 677.174i | 1.50818i | 0.656770 | + | 0.754091i | \(0.271922\pi\) | ||||
−0.656770 | + | 0.754091i | \(0.728078\pi\) | |||||||
\(450\) | 207.369 | − | 102.268i | 0.460820 | − | 0.227262i | ||||
\(451\) | −15.6863 | − | 27.1694i | −0.0347811 | − | 0.0602426i | ||||
\(452\) | 139.413 | − | 80.4900i | 0.308435 | − | 0.178075i | ||||
\(453\) | 20.7704 | − | 634.641i | 0.0458507 | − | 1.40097i | ||||
\(454\) | −365.490 | −0.805044 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −64.0000 | − | 119.733i | −0.140351 | − | 0.262572i | ||||
\(457\) | −417.332 | + | 722.840i | −0.913199 | + | 1.58171i | −0.103683 | + | 0.994610i | \(0.533063\pi\) |
−0.809517 | + | 0.587097i | \(0.800271\pi\) | |||||||
\(458\) | −45.4196 | + | 26.2230i | −0.0991695 | + | 0.0572555i | ||||
\(459\) | 176.961 | + | 390.534i | 0.385536 | + | 0.850836i | ||||
\(460\) | 236.539 | − | 409.697i | 0.514214 | − | 0.890645i | ||||
\(461\) | − | 347.150i | − | 0.753036i | −0.926409 | − | 0.376518i | \(-0.877121\pi\) | ||
0.926409 | − | 0.376518i | \(-0.122879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 317.668 | 0.686108 | 0.343054 | − | 0.939316i | \(-0.388539\pi\) | ||||
0.343054 | + | 0.939316i | \(0.388539\pi\) | |||||||
\(464\) | −72.0566 | − | 41.6019i | −0.155294 | − | 0.0896593i | ||||
\(465\) | 57.6873 | − | 92.7706i | 0.124059 | − | 0.199507i | ||||
\(466\) | −58.4575 | − | 101.251i | −0.125445 | − | 0.217278i | ||||
\(467\) | −474.080 | − | 273.710i | −1.01516 | − | 0.586104i | −0.102463 | − | 0.994737i | \(-0.532672\pi\) |
−0.912699 | + | 0.408633i | \(0.866006\pi\) | |||||||
\(468\) | −205.830 | + | 308.058i | −0.439808 | + | 0.658244i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 78.8410i | 0.167747i | ||||||||
\(471\) | −10.6712 | + | 326.061i | −0.0226566 | + | 0.692273i | ||||
\(472\) | 2.33202 | + | 4.03918i | 0.00494072 | + | 0.00855758i | ||||
\(473\) | 18.4752 | − | 10.6667i | 0.0390597 | − | 0.0225511i | ||||
\(474\) | −360.071 | − | 11.7843i | −0.759644 | − | 0.0248615i | ||||
\(475\) | 290.656 | 0.611908 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −380.988 | − | 254.558i | −0.798717 | − | 0.533665i | ||||
\(478\) | −119.125 | + | 206.331i | −0.249217 | + | 0.431656i | ||||
\(479\) | −117.367 | + | 67.7621i | −0.245026 | + | 0.141466i | −0.617484 | − | 0.786583i | \(-0.711848\pi\) |
0.372459 | + | 0.928049i | \(0.378515\pi\) | |||||||
\(480\) | −94.6849 | − | 58.8777i | −0.197260 | − | 0.122662i | ||||
\(481\) | −205.830 | + | 356.508i | −0.427921 | + | 0.741181i | ||||
\(482\) | − | 183.848i | − | 0.381427i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −241.660 | −0.499298 | ||||||||
\(485\) | 391.656 | + | 226.123i | 0.807538 | + | 0.466232i | ||||
\(486\) | 339.066 | + | 55.9647i | 0.697667 | + | 0.115154i | ||||
\(487\) | −11.7490 | − | 20.3499i | −0.0241253 | − | 0.0417862i | 0.853711 | − | 0.520748i | \(-0.174347\pi\) |
−0.877836 | + | 0.478961i | \(0.841013\pi\) | |||||||
\(488\) | −163.908 | − | 94.6321i | −0.335876 | − | 0.193918i | ||||
\(489\) | −34.4052 | + | 18.3903i | −0.0703582 | + | 0.0376081i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 103.404i | 0.210599i | 0.994441 | + | 0.105299i | \(0.0335801\pi\) | ||||
−0.994441 | + | 0.105299i | \(0.966420\pi\) | |||||||
\(492\) | 456.364 | + | 14.9358i | 0.927568 | + | 0.0303572i | ||||
\(493\) | 165.158 | + | 286.062i | 0.335006 | + | 0.580248i | ||||
\(494\) | −403.343 | + | 232.870i | −0.816484 | + | 0.471397i | ||||
\(495\) | −10.7818 | − | 21.8624i | −0.0217815 | − | 0.0441665i | ||||
\(496\) | −22.1699 | −0.0446975 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 15.4249 | − | 8.24494i | 0.0309736 | − | 0.0165561i | ||||
\(499\) | 32.1699 | − | 55.7200i | 0.0644688 | − | 0.111663i | −0.831989 | − | 0.554792i | \(-0.812798\pi\) |
0.896458 | + | 0.443128i | \(0.146131\pi\) | |||||||
\(500\) | −77.7689 | + | 44.8999i | −0.155538 | + | 0.0897998i | ||||
\(501\) | 248.491 | − | 399.613i | 0.495989 | − | 0.797632i | ||||
\(502\) | 84.7530 | − | 146.796i | 0.168831 | − | 0.292423i | ||||
\(503\) | − | 546.940i | − | 1.08736i | −0.839294 | − | 0.543678i | \(-0.817031\pi\) | ||
0.839294 | − | 0.543678i | \(-0.182969\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 920.818 | 1.82340 | ||||||||
\(506\) | −18.1775 | − | 10.4948i | −0.0359239 | − | 0.0207407i | ||||
\(507\) | 648.777 | + | 403.428i | 1.27964 | + | 0.795715i | ||||
\(508\) | −132.915 | − | 230.216i | −0.261644 | − | 0.453180i | ||||
\(509\) | −55.0318 | − | 31.7727i | −0.108118 | − | 0.0624217i | 0.444966 | − | 0.895547i | \(-0.353216\pi\) |
−0.553084 | + | 0.833126i | \(0.686549\pi\) | |||||||
\(510\) | 208.664 | + | 390.375i | 0.409145 | + | 0.765441i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 351.156 | + | 251.621i | 0.684515 | + | 0.490489i | ||||
\(514\) | −158.314 | − | 274.207i | −0.308003 | − | 0.533477i | ||||
\(515\) | 224.024 | − | 129.340i | 0.434999 | − | 0.251147i | ||||
\(516\) | −10.1563 | + | 310.328i | −0.0196828 | + | 0.601411i | ||||
\(517\) | 3.49803 | 0.00676602 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.71243 | + | 14.4286i | 0.0148602 | + | 0.0278009i | ||||
\(520\) | −191.247 | + | 331.250i | −0.367783 | + | 0.637018i | ||||
\(521\) | 556.245 | − | 321.148i | 1.06765 | − | 0.616408i | 0.140111 | − | 0.990136i | \(-0.455254\pi\) |
0.927538 | + | 0.373728i | \(0.121921\pi\) | |||||||
\(522\) | 264.186 | + | 17.3110i | 0.506104 | + | 0.0331629i | ||||
\(523\) | 56.1882 | − | 97.3209i | 0.107434 | − | 0.186082i | −0.807296 | − | 0.590147i | \(-0.799070\pi\) |
0.914730 | + | 0.404065i | \(0.132403\pi\) | |||||||
\(524\) | 8.24494i | 0.0157346i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −303.255 | −0.576530 | ||||||||
\(527\) | 76.2223 | + | 44.0070i | 0.144634 | + | 0.0835047i | ||||
\(528\) | −2.61230 | + | 4.20100i | −0.00494753 | + | 0.00795643i | ||||
\(529\) | 383.585 | + | 664.389i | 0.725113 | + | 1.25593i | ||||
\(530\) | −409.670 | − | 236.523i | −0.772962 | − | 0.446270i | ||||
\(531\) | −12.3399 | − | 8.24494i | −0.0232390 | − | 0.0155272i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1566.39i | − | 2.93883i | ||||||
\(534\) | −4.33007 | + | 132.306i | −0.00810874 | + | 0.247763i | ||||
\(535\) | 354.808 | + | 614.545i | 0.663192 | + | 1.14868i | ||||
\(536\) | −121.046 | + | 69.8862i | −0.225833 | + | 0.130385i | ||||
\(537\) | 3.70824 | + | 0.121362i | 0.00690547 | + | 0.000226001i | ||||
\(538\) | 540.450 | 1.00455 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 353.077 | + | 34.7656i | 0.653846 | + | 0.0643808i | ||||
\(541\) | 16.5751 | − | 28.7090i | 0.0306380 | − | 0.0530665i | −0.850300 | − | 0.526299i | \(-0.823579\pi\) |
0.880938 | + | 0.473232i | \(0.156913\pi\) | |||||||
\(542\) | 140.181 | − | 80.9337i | 0.258637 | − | 0.149324i | ||||
\(543\) | −476.189 | − | 296.107i | −0.876959 | − | 0.545317i | ||||
\(544\) | 44.9150 | − | 77.7951i | 0.0825644 | − | 0.143006i | ||||
\(545\) | − | 813.574i | − | 1.49280i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −919.911 | −1.68174 | −0.840869 | − | 0.541238i | \(-0.817956\pi\) | ||||
−0.840869 | + | 0.541238i | \(0.817956\pi\) | |||||||
\(548\) | 172.585 | + | 99.6420i | 0.314936 | + | 0.181828i | ||||
\(549\) | 600.946 | + | 39.3775i | 1.09462 | + | 0.0717258i | ||||
\(550\) | −5.29544 | − | 9.17197i | −0.00962807 | − | 0.0166763i | ||||
\(551\) | 288.227 | + | 166.408i | 0.523097 | + | 0.302010i | ||||
\(552\) | 269.417 | − | 144.009i | 0.488074 | − | 0.260887i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 325.968i | − | 0.588390i | ||||||
\(555\) | 393.994 | + | 12.8946i | 0.709899 | + | 0.0232334i | ||||
\(556\) | 93.5425 | + | 162.020i | 0.168242 | + | 0.291403i | ||||
\(557\) | −628.190 | + | 362.686i | −1.12781 | + | 0.651141i | −0.943383 | − | 0.331705i | \(-0.892376\pi\) |
−0.184427 | + | 0.982846i | \(0.559043\pi\) | |||||||
\(558\) | 63.2687 | − | 31.2021i | 0.113385 | − | 0.0559177i | ||||
\(559\) | 1065.15 | 1.90546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.3202 | − | 9.25804i | 0.0308738 | − | 0.0165027i | ||||
\(562\) | 52.2876 | − | 90.5647i | 0.0930384 | − | 0.161147i | ||||
\(563\) | −631.136 | + | 364.386i | −1.12102 | + | 0.647223i | −0.941662 | − | 0.336561i | \(-0.890736\pi\) |
−0.179361 | + | 0.983783i | \(0.557403\pi\) | |||||||
\(564\) | −26.8844 | + | 43.2346i | −0.0476675 | + | 0.0766570i | ||||
\(565\) | −264.413 | + | 457.977i | −0.467988 | + | 0.810578i | ||||
\(566\) | 199.639i | 0.352719i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 248.162 | 0.436905 | ||||||||
\(569\) | 144.664 | + | 83.5218i | 0.254242 | + | 0.146787i | 0.621705 | − | 0.783251i | \(-0.286440\pi\) |
−0.367463 | + | 0.930038i | \(0.619773\pi\) | |||||||
\(570\) | 378.740 | + | 235.511i | 0.664455 | + | 0.413177i | ||||
\(571\) | 36.4575 | + | 63.1463i | 0.0638485 | + | 0.110589i | 0.896183 | − | 0.443685i | \(-0.146329\pi\) |
−0.832334 | + | 0.554274i | \(0.812996\pi\) | |||||||
\(572\) | 14.6969 | + | 8.48528i | 0.0256939 | + | 0.0148344i | ||||
\(573\) | 495.741 | + | 927.447i | 0.865168 | + | 1.61858i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 654.019i | 1.13742i | ||||||||
\(576\) | −31.8459 | − | 64.5743i | −0.0552881 | − | 0.112108i | ||||
\(577\) | −276.077 | − | 478.180i | −0.478470 | − | 0.828734i | 0.521225 | − | 0.853419i | \(-0.325475\pi\) |
−0.999695 | + | 0.0246850i | \(0.992142\pi\) | |||||||
\(578\) | 45.1074 | − | 26.0428i | 0.0780405 | − | 0.0450567i | ||||
\(579\) | 26.5438 | − | 811.048i | 0.0458442 | − | 1.40077i | ||||
\(580\) | 273.328 | 0.471255 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 137.668 | + | 257.553i | 0.236543 | + | 0.442531i | ||||
\(583\) | −10.4941 | + | 18.1763i | −0.0180002 | + | 0.0311772i | ||||
\(584\) | 30.2072 | − | 17.4401i | 0.0517246 | − | 0.0298632i | ||||
\(585\) | 79.5800 | − | 1214.48i | 0.136034 | − | 2.07604i | ||||
\(586\) | 233.059 | − | 403.670i | 0.397711 | − | 0.688856i | ||||
\(587\) | − | 1115.21i | − | 1.89985i | −0.312474 | − | 0.949926i | \(-0.601158\pi\) | ||
0.312474 | − | 0.949926i | \(-0.398842\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 88.6798 | 0.150560 | ||||||||
\(590\) | −13.2689 | − | 7.66079i | −0.0224896 | − | 0.0129844i | ||||
\(591\) | −100.626 | + | 161.823i | −0.170264 | + | 0.273813i | ||||
\(592\) | −40.0000 | − | 69.2820i | −0.0675676 | − | 0.117030i | ||||
\(593\) | −829.224 | − | 478.753i | −1.39835 | − | 0.807340i | −0.404134 | − | 0.914700i | \(-0.632427\pi\) |
−0.994220 | + | 0.107359i | \(0.965761\pi\) | |||||||
\(594\) | 1.54249 | − | 15.6654i | 0.00259678 | − | 0.0263727i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 99.6937i | 0.167271i | ||||||||
\(597\) | −8.63551 | + | 263.859i | −0.0144648 | + | 0.441974i | ||||
\(598\) | −523.992 | − | 907.581i | −0.876241 | − | 1.51769i | ||||
\(599\) | 528.316 | − | 305.024i | 0.881997 | − | 0.509221i | 0.0106810 | − | 0.999943i | \(-0.496600\pi\) |
0.871316 | + | 0.490721i | \(0.163267\pi\) | |||||||
\(600\) | 154.061 | + | 5.04208i | 0.256769 | + | 0.00840347i | ||||
\(601\) | −974.470 | −1.62142 | −0.810708 | − | 0.585451i | \(-0.800917\pi\) | ||||
−0.810708 | + | 0.585451i | \(0.800917\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 247.085 | − | 369.803i | 0.409759 | − | 0.613272i | ||||
\(604\) | 211.660 | − | 366.606i | 0.350431 | − | 0.606964i | ||||
\(605\) | 687.506 | − | 396.932i | 1.13637 | − | 0.656086i | ||||
\(606\) | 504.955 | + | 313.995i | 0.833259 | + | 0.518144i | ||||
\(607\) | 548.073 | − | 949.291i | 0.902921 | − | 1.56391i | 0.0792376 | − | 0.996856i | \(-0.474751\pi\) |
0.823684 | − | 0.567050i | \(-0.191915\pi\) | |||||||
\(608\) | − | 90.5097i | − | 0.148865i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 621.741 | 1.01925 | ||||||||
\(611\) | 151.254 | + | 87.3263i | 0.247551 | + | 0.142924i | ||||
\(612\) | −18.6896 | + | 285.226i | −0.0305386 | + | 0.466055i | ||||
\(613\) | 155.583 | + | 269.478i | 0.253806 | + | 0.439605i | 0.964570 | − | 0.263825i | \(-0.0849842\pi\) |
−0.710765 | + | 0.703430i | \(0.751651\pi\) | |||||||
\(614\) | 129.615 | + | 74.8331i | 0.211099 | + | 0.121878i | ||||
\(615\) | −1322.85 | + | 707.096i | −2.15098 | + | 1.14975i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 905.503i | 1.46759i | 0.679371 | + | 0.733795i | \(0.262253\pi\) | ||||
−0.679371 | + | 0.733795i | \(0.737747\pi\) | |||||||
\(618\) | 166.954 | + | 5.46404i | 0.270152 | + | 0.00884149i | ||||
\(619\) | −27.3987 | − | 47.4559i | −0.0442628 | − | 0.0766655i | 0.843045 | − | 0.537843i | \(-0.180761\pi\) |
−0.887308 | + | 0.461177i | \(0.847427\pi\) | |||||||
\(620\) | 63.0719 | − | 36.4146i | 0.101729 | − | 0.0587332i | ||||
\(621\) | −566.185 | + | 790.154i | −0.911730 | + | 1.27239i | ||||
\(622\) | −544.664 | −0.875666 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −217.830 | + | 116.435i | −0.349087 | + | 0.186595i | ||||
\(625\) | 374.573 | − | 648.780i | 0.599317 | − | 1.03805i | ||||
\(626\) | −97.1567 | + | 56.0934i | −0.155202 | + | 0.0896061i | ||||
\(627\) | 10.4492 | − | 16.8040i | 0.0166654 | − | 0.0268006i | ||||
\(628\) | −108.745 | + | 188.352i | −0.173161 | + | 0.299924i | ||||
\(629\) | 317.597i | 0.504924i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 181.490 | 0.287623 | 0.143812 | − | 0.989605i | \(-0.454064\pi\) | ||||
0.143812 | + | 0.989605i | \(0.454064\pi\) | |||||||
\(632\) | −207.998 | − | 120.088i | −0.329112 | − | 0.190013i | ||||
\(633\) | −964.899 | − | 600.001i | −1.52433 | − | 0.947869i | ||||
\(634\) | 290.745 | + | 503.585i | 0.458588 | + | 0.794298i | ||||
\(635\) | 756.268 | + | 436.631i | 1.19097 | + | 0.687609i | ||||
\(636\) | −144.000 | − | 269.399i | −0.226415 | − | 0.423584i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 12.1271i | − | 0.0190079i | ||||||
\(639\) | −708.207 | + | 349.264i | −1.10830 | + | 0.546580i | ||||
\(640\) | −37.1660 | − | 64.3734i | −0.0580719 | − | 0.100583i | ||||
\(641\) | 725.401 | − | 418.811i | 1.13167 | − | 0.653371i | 0.187316 | − | 0.982300i | \(-0.440021\pi\) |
0.944355 | + | 0.328929i | \(0.106688\pi\) | |||||||
\(642\) | −14.9890 | + | 457.990i | −0.0233473 | + | 0.713380i | ||||
\(643\) | 59.0118 | 0.0917758 | 0.0458879 | − | 0.998947i | \(-0.485388\pi\) | ||||
0.0458879 | + | 0.998947i | \(0.485388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −480.826 | − | 899.543i | −0.745467 | − | 1.39464i | ||||
\(646\) | −179.660 | + | 311.180i | −0.278112 | + | 0.481703i | ||||
\(647\) | −474.288 | + | 273.831i | −0.733058 | + | 0.423231i | −0.819540 | − | 0.573022i | \(-0.805771\pi\) |
0.0864819 | + | 0.996253i | \(0.472438\pi\) | |||||||
\(648\) | 181.764 | + | 139.462i | 0.280500 | + | 0.215220i | ||||
\(649\) | −0.339895 | + | 0.588716i | −0.000523721 | + | 0.000907112i | ||||
\(650\) | − | 528.790i | − | 0.813523i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −26.0079 | −0.0398894 | ||||||||
\(653\) | −662.419 | − | 382.448i | −1.01442 | − | 0.585678i | −0.101940 | − | 0.994791i | \(-0.532505\pi\) |
−0.912484 | + | 0.409113i | \(0.865838\pi\) | |||||||
\(654\) | 277.425 | − | 446.145i | 0.424198 | − | 0.682179i | ||||
\(655\) | −13.5425 | − | 23.4563i | −0.0206756 | − | 0.0358111i | ||||
\(656\) | 263.623 | + | 152.203i | 0.401864 | + | 0.232016i | ||||
\(657\) | −61.6601 | + | 92.2844i | −0.0938510 | + | 0.140463i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1050.80i | 1.59454i | 0.603623 | + | 0.797270i | \(0.293723\pi\) | ||||
−0.603623 | + | 0.797270i | \(0.706277\pi\) | |||||||
\(660\) | 0.531574 | − | 16.2423i | 0.000805415 | − | 0.0246095i | ||||
\(661\) | 72.5425 | + | 125.647i | 0.109747 | + | 0.190087i | 0.915668 | − | 0.401936i | \(-0.131663\pi\) |
−0.805921 | + | 0.592023i | \(0.798329\pi\) | |||||||
\(662\) | −599.501 | + | 346.122i | −0.905590 | + | 0.522843i | ||||
\(663\) | 980.041 | + | 32.0746i | 1.47819 | + | 0.0483779i | ||||
\(664\) | 11.6601 | 0.0175604 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 211.660 | + | 141.421i | 0.317808 | + | 0.212344i | ||||
\(667\) | −374.442 | + | 648.552i | −0.561382 | + | 0.972342i | ||||
\(668\) | 271.685 | − | 156.858i | 0.406714 | − | 0.234817i | ||||
\(669\) | −587.211 | − | 365.144i | −0.877745 | − | 0.545806i | ||||
\(670\) | 229.579 | − | 397.643i | 0.342655 | − | 0.593496i | ||||
\(671\) | − | 27.5855i | − | 0.0411111i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 323.498 | 0.480681 | 0.240340 | − | 0.970689i | \(-0.422741\pi\) | ||||
0.240340 | + | 0.970689i | \(0.422741\pi\) | |||||||
\(674\) | −612.760 | − | 353.777i | −0.909139 | − | 0.524892i | ||||
\(675\) | −446.757 | + | 202.437i | −0.661863 | + | 0.299907i | ||||
\(676\) | 254.660 | + | 441.084i | 0.376716 | + | 0.652491i | ||||
\(677\) | −144.136 | − | 83.2168i | −0.212903 | − | 0.122920i | 0.389757 | − | 0.920918i | \(-0.372559\pi\) |
−0.602660 | + | 0.797998i | \(0.705892\pi\) | |||||||
\(678\) | −301.166 | + | 160.980i | −0.444198 | + | 0.237434i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 295.096i | 0.433964i | ||||||||
\(681\) | 774.907 | + | 25.3610i | 1.13790 | + | 0.0372408i | ||||
\(682\) | −1.61565 | − | 2.79839i | −0.00236899 | − | 0.00410321i | ||||
\(683\) | −843.081 | + | 486.753i | −1.23438 | + | 0.712669i | −0.967940 | − | 0.251183i | \(-0.919180\pi\) |
−0.266439 | + | 0.963852i | \(0.585847\pi\) | |||||||
\(684\) | 127.384 | + | 258.297i | 0.186233 | + | 0.377627i | ||||
\(685\) | −654.656 | −0.955702 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 98.1176 | − | 52.4461i | 0.142820 | − | 0.0763407i | ||||
\(688\) | −103.498 | + | 179.264i | −0.150433 | + | 0.260558i | ||||
\(689\) | −907.521 | + | 523.958i | −1.31716 | + | 0.760461i | ||||
\(690\) | −529.934 | + | 852.220i | −0.768020 | + | 1.23510i | ||||
\(691\) | −634.431 | + | 1098.87i | −0.918135 | + | 1.59026i | −0.115890 | + | 0.993262i | \(0.536972\pi\) |
−0.802245 | + | 0.596995i | \(0.796361\pi\) | |||||||
\(692\) | 10.9070i | 0.0157616i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −272.745 | −0.393004 | ||||||||
\(695\) | −532.244 | − | 307.291i | −0.765818 | − | 0.442145i | ||||
\(696\) | 149.887 | + | 93.2037i | 0.215354 | + | 0.133913i | ||||
\(697\) | −604.239 | − | 1046.57i | −0.866914 | − | 1.50154i | ||||
\(698\) | −181.758 | − | 104.938i | −0.260399 | − | 0.150341i | ||||
\(699\) | 116.915 | + | 218.728i | 0.167260 | + | 0.312916i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 798.940i | 1.13971i | 0.821744 | + | 0.569857i | \(0.193002\pi\) | ||||
−0.821744 | + | 0.569857i | \(0.806998\pi\) | |||||||
\(702\) | 457.774 | − | 638.858i | 0.652099 | − | 0.910054i | ||||
\(703\) | 160.000 | + | 277.128i | 0.227596 | + | 0.394208i | ||||
\(704\) | −2.85613 | + | 1.64899i | −0.00405700 | + | 0.00234231i | ||||
\(705\) | 5.47069 | − | 167.158i | 0.00775985 | − | 0.237103i | ||||
\(706\) | 231.608 | 0.328056 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.66404 | − | 8.72562i | −0.00658763 | − | 0.0123243i | ||||
\(709\) | 325.745 | − | 564.207i | 0.459443 | − | 0.795779i | −0.539489 | − | 0.841993i | \(-0.681382\pi\) |
0.998932 | + | 0.0462143i | \(0.0147157\pi\) | |||||||
\(710\) | −706.004 | + | 407.611i | −0.994371 | + | 0.574101i | ||||
\(711\) | 762.600 | + | 49.9699i | 1.07257 | + | 0.0702812i | ||||
\(712\) | −44.1255 | + | 76.4276i | −0.0619740 | + | 0.107342i | ||||
\(713\) | 199.543i | 0.279863i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −55.7490 | −0.0779707 | ||||||||
\(716\) | 2.14210 | + | 1.23674i | 0.00299176 | + | 0.00172729i | ||||
\(717\) | 266.885 | − | 429.195i | 0.372225 | − | 0.598598i | ||||
\(718\) | −236.793 | − | 410.138i | −0.329796 | − | 0.571223i | ||||
\(719\) | −760.879 | − | 439.294i | −1.05825 | − | 0.610979i | −0.133299 | − | 0.991076i | \(-0.542557\pi\) |
−0.924947 | + | 0.380097i | \(0.875891\pi\) | |||||||
\(720\) | 196.664 | + | 131.402i | 0.273145 | + | 0.182502i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 148.492i | − | 0.205668i | ||||||
\(723\) | −12.7570 | + | 389.791i | −0.0176445 | + | 0.539130i | ||||
\(724\) | −186.915 | − | 323.746i | −0.258170 | − | 0.447163i | ||||
\(725\) | −327.245 | + | 188.935i | −0.451373 | + | 0.260600i | ||||
\(726\) | 512.364 | + | 16.7685i | 0.705736 | + | 0.0230972i | ||||
\(727\) | 442.782 | 0.609053 | 0.304527 | − | 0.952504i | \(-0.401502\pi\) | ||||
0.304527 | + | 0.952504i | \(0.401502\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −715.000 | − | 142.183i | −0.980796 | − | 0.195038i | ||||
\(730\) | −57.2915 | + | 99.2318i | −0.0784815 | + | 0.135934i | ||||
\(731\) | 711.671 | − | 410.884i | 0.973558 | − | 0.562084i | ||||
\(732\) | 340.948 | + | 212.011i | 0.465776 | + | 0.289633i | ||||
\(733\) | −481.280 | + | 833.601i | −0.656589 | + | 1.13725i | 0.324904 | + | 0.945747i | \(0.394668\pi\) |
−0.981493 | + | 0.191498i | \(0.938665\pi\) | |||||||
\(734\) | 462.442i | 0.630030i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 203.660 | 0.276712 | ||||||||
\(737\) | −17.6427 | − | 10.1860i | −0.0239385 | − | 0.0138209i | ||||
\(738\) | −966.539 | − | 63.3332i | −1.30967 | − | 0.0858173i | ||||
\(739\) | −612.405 | − | 1060.72i | −0.828694 | − | 1.43534i | −0.899063 | − | 0.437820i | \(-0.855751\pi\) |
0.0703683 | − | 0.997521i | \(-0.477583\pi\) | |||||||
\(740\) | 227.594 | + | 131.402i | 0.307560 | + | 0.177570i | ||||
\(741\) | 871.320 | − | 465.740i | 1.17587 | − | 0.628529i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1447.24i | − | 1.94783i | −0.226908 | − | 0.973916i | \(-0.572862\pi\) | ||
0.226908 | − | 0.973916i | \(-0.427138\pi\) | |||||||
\(744\) | 47.0044 | + | 1.53835i | 0.0631779 | + | 0.00206767i | ||||
\(745\) | −163.749 | − | 283.622i | −0.219797 | − | 0.380700i | ||||
\(746\) | −373.959 | + | 215.905i | −0.501285 | + | 0.289417i | ||||
\(747\) | −33.2757 | + | 16.4105i | −0.0445458 | + | 0.0219685i | ||||
\(748\) | 13.0928 | 0.0175038 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 168.000 | − | 89.7998i | 0.224000 | − | 0.119733i | ||||
\(751\) | 342.458 | − | 593.154i | 0.456002 | − | 0.789819i | −0.542743 | − | 0.839899i | \(-0.682614\pi\) |
0.998745 | + | 0.0500800i | \(0.0159476\pi\) | |||||||
\(752\) | −29.3939 | + | 16.9706i | −0.0390876 | + | 0.0225672i | ||||
\(753\) | −189.878 | + | 305.355i | −0.252162 | + | 0.405517i | ||||
\(754\) | 302.745 | − | 524.370i | 0.401519 | − | 0.695451i | ||||
\(755\) | 1390.62i | 1.84189i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −907.135 | −1.19833 | −0.599164 | − | 0.800626i | \(-0.704500\pi\) | ||||
−0.599164 | + | 0.800626i | \(0.704500\pi\) | |||||||
\(758\) | −244.533 | − | 141.181i | −0.322602 | − | 0.186255i | ||||
\(759\) | 37.8114 | + | 23.5122i | 0.0498174 | + | 0.0309779i | ||||
\(760\) | 148.664 | + | 257.494i | 0.195611 | + | 0.338807i | ||||
\(761\) | 1257.04 | + | 725.754i | 1.65183 | + | 0.953685i | 0.976319 | + | 0.216335i | \(0.0694102\pi\) |
0.675511 | + | 0.737350i | \(0.263923\pi\) | |||||||
\(762\) | 265.830 | + | 497.322i | 0.348858 | + | 0.652654i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 701.084i | 0.917649i | ||||||||
\(765\) | −415.319 | − | 842.146i | −0.542900 | − | 1.10084i | ||||
\(766\) | 374.405 | + | 648.489i | 0.488780 | + | 0.846591i | ||||
\(767\) | −29.3939 | + | 16.9706i | −0.0383232 | + | 0.0221259i | ||||
\(768\) | 1.57009 | − | 47.9743i | 0.00204439 | − | 0.0624666i | ||||
\(769\) | −1089.32 | −1.41654 | −0.708271 | − | 0.705941i | \(-0.750524\pi\) | ||||
−0.708271 | + | 0.705941i | \(0.750524\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 316.627 | + | 592.356i | 0.410671 | + | 0.768295i | ||||
\(772\) | 270.494 | − | 468.510i | 0.350381 | − | 0.606878i | ||||
\(773\) | −882.985 | + | 509.792i | −1.14228 | + | 0.659498i | −0.946995 | − | 0.321248i | \(-0.895898\pi\) |
−0.195288 | + | 0.980746i | \(0.562564\pi\) | |||||||
\(774\) | 43.0667 | − | 657.248i | 0.0556417 | − | 0.849158i | ||||
\(775\) | −50.3424 | + | 87.1957i | −0.0649580 | + | 0.112511i | ||||
\(776\) | 194.692i | 0.250892i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 337.579 | 0.433906 | ||||||||
\(779\) | −1054.49 | − | 608.811i | −1.35365 | − | 0.781528i | ||||
\(780\) | 428.464 | − | 689.040i | 0.549313 | − | 0.883385i | ||||
\(781\) | 18.0850 | + | 31.3241i | 0.0231562 | + | 0.0401077i | ||||
\(782\) | −700.202 | − | 404.262i | −0.895399 | − | 0.516959i | ||||
\(783\) | −558.923 | − | 55.0342i | −0.713822 | − | 0.0702863i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 714.464i | − | 0.910146i | ||||||
\(786\) | 0.572108 | − | 17.4808i | 0.000727872 | − | 0.0222402i | ||||
\(787\) | 633.501 | + | 1097.26i | 0.804956 | + | 1.39423i | 0.916321 | + | 0.400445i | \(0.131145\pi\) |
−0.111364 | + | 0.993780i | \(0.535522\pi\) | |||||||
\(788\) | −110.019 | + | 63.5194i | −0.139618 | + | 0.0806084i | ||||
\(789\) | 642.957 | + | 21.0425i | 0.814901 | + | 0.0266699i | ||||
\(790\) | 788.988 | 0.998719 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.83005 | − | 8.72562i | 0.00736118 | − | 0.0110172i | ||||
\(793\) | 688.656 | − | 1192.79i | 0.868419 | − | 1.50415i | ||||
\(794\) | 392.632 | − | 226.686i | 0.494499 | − | 0.285499i | ||||
\(795\) | 852.164 | + | 529.899i | 1.07190 | + | 0.666540i | ||||
\(796\) | −88.0000 | + | 152.420i | −0.110553 | + | 0.191483i | ||||
\(797\) | − | 922.123i | − | 1.15699i | −0.815685 | − | 0.578496i | \(-0.803640\pi\) | ||
0.815685 | − | 0.578496i | \(-0.196360\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 134.745 | 0.168642 | ||||||||
\(800\) | 88.9949 | + | 51.3812i | 0.111244 | + | 0.0642265i | ||||
\(801\) | 18.3611 | − | 280.212i | 0.0229227 | − | 0.349828i | ||||
\(802\) | −164.125 | − | 284.274i | −0.204645 | − | 0.354456i | ||||
\(803\) | 4.40273 | + | 2.54192i | 0.00548286 | + | 0.00316553i | ||||
\(804\) | 261.490 | − | 139.772i | 0.325237 | − | 0.173846i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 161.335i | − | 0.200167i | ||||||
\(807\) | −1145.85 | − | 37.5012i | −1.41989 | − | 0.0464699i | ||||
\(808\) | 198.207 | + | 343.304i | 0.245305 | + | 0.424881i | ||||
\(809\) | 612.155 | − | 353.428i | 0.756681 | − | 0.436870i | −0.0714221 | − | 0.997446i | \(-0.522754\pi\) |
0.828103 | + | 0.560576i | \(0.189420\pi\) | |||||||
\(810\) | −746.176 | − | 98.2092i | −0.921206 | − | 0.121246i | ||||
\(811\) | 833.778 | 1.02809 | 0.514043 | − | 0.857764i | \(-0.328147\pi\) | ||||
0.514043 | + | 0.857764i | \(0.328147\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −302.826 | + | 161.867i | −0.372480 | + | 0.199099i | ||||
\(814\) | 5.83005 | − | 10.0979i | 0.00716223 | − | 0.0124053i | ||||
\(815\) | 73.9906 | − | 42.7185i | 0.0907860 | − | 0.0524153i | ||||
\(816\) | −100.626 | + | 161.823i | −0.123317 | + | 0.198313i | ||||
\(817\) | 413.992 | − | 717.055i | 0.506722 | − | 0.877669i | ||||
\(818\) | 748.091i | 0.914537i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −999.984 | −1.21949 | ||||||||
\(821\) | −217.598 | − | 125.630i | −0.265040 | − | 0.153021i | 0.361591 | − | 0.932337i | \(-0.382234\pi\) |
−0.626632 | + | 0.779316i | \(0.715567\pi\) | |||||||
\(822\) | −358.998 | − | 223.235i | −0.436737 | − | 0.271575i | ||||
\(823\) | −19.4615 | − | 33.7082i | −0.0236470 | − | 0.0409577i | 0.853960 | − | 0.520339i | \(-0.174194\pi\) |
−0.877607 | + | 0.479381i | \(0.840861\pi\) | |||||||
\(824\) | 96.4426 | + | 55.6812i | 0.117042 | + | 0.0675742i | ||||
\(825\) | 10.5909 | + | 19.8137i | 0.0128374 | + | 0.0240166i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 108.007i | − | 0.130601i | −0.997866 | − | 0.0653005i | \(-0.979199\pi\) | ||
0.997866 | − | 0.0653005i | \(-0.0208006\pi\) | |||||||
\(828\) | −581.207 | + | 286.632i | −0.701940 | + | 0.346174i | ||||
\(829\) | 705.288 | + | 1221.59i | 0.850769 | + | 1.47358i | 0.880515 | + | 0.474018i | \(0.157197\pi\) |
−0.0297462 | + | 0.999557i | \(0.509470\pi\) | |||||||
\(830\) | −33.1722 | + | 19.1520i | −0.0399665 | + | 0.0230747i | ||||
\(831\) | −22.6186 | + | 691.112i | −0.0272185 | + | 0.831663i | ||||
\(832\) | −164.664 | −0.197914 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −187.085 | − | 350.004i | −0.224323 | − | 0.419669i | ||||
\(835\) | −515.284 | + | 892.497i | −0.617106 | + | 1.06886i | ||||
\(836\) | 11.4245 | − | 6.59595i | 0.0136657 | − | 0.00788989i | ||||
\(837\) | −136.307 | + | 61.7640i | −0.162851 | + | 0.0737922i | ||||
\(838\) | 63.4980 | − | 109.982i | 0.0757733 | − | 0.131243i | ||||
\(839\) | − | 299.906i | − | 0.357456i | −0.983899 | − | 0.178728i | \(-0.942802\pi\) | ||
0.983899 | − | 0.178728i | \(-0.0571982\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 408.320 | 0.485517 | ||||||||
\(842\) | 951.811 | + | 549.528i | 1.13042 | + | 0.652646i | ||||
\(843\) | −117.144 | + | 188.386i | −0.138960 | + | 0.223471i | ||||
\(844\) | −378.745 | − | 656.006i | −0.448750 | − | 0.777258i | ||||
\(845\) | −1448.98 | − | 836.569i | −1.71477 | − | 0.990023i | ||||
\(846\) | 60.0000 | − | 89.7998i | 0.0709220 | − | 0.106146i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 203.647i | − | 0.240149i | ||||||
\(849\) | 13.8527 | − | 423.271i | 0.0163165 | − | 0.498553i | ||||
\(850\) | −203.982 | − | 353.307i | −0.239978 | − | 0.415655i | ||||
\(851\) | −623.579 | + | 360.024i | −0.732760 | + | 0.423059i | ||||
\(852\) | −526.150 | − | 17.2197i | −0.617546 | − | 0.0202109i | ||||
\(853\) | −13.7648 | −0.0161369 | −0.00806844 | − | 0.999967i | \(-0.502568\pi\) | ||||
−0.00806844 | + | 0.999967i | \(0.502568\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −786.656 | − | 525.607i | −0.920066 | − | 0.614745i | ||||
\(856\) | −152.745 | + | 264.562i | −0.178441 | + | 0.309068i | ||||
\(857\) | −218.677 | + | 126.253i | −0.255166 | + | 0.147320i | −0.622127 | − | 0.782916i | \(-0.713731\pi\) |
0.366962 | + | 0.930236i | \(0.380398\pi\) | |||||||
\(858\) | −30.5714 | − | 19.0102i | −0.0356311 | − | 0.0221564i | ||||
\(859\) | −337.255 | + | 584.143i | −0.392613 | + | 0.680026i | −0.992793 | − | 0.119839i | \(-0.961762\pi\) |
0.600180 | + | 0.799865i | \(0.295096\pi\) | |||||||
\(860\) | − | 679.991i | − | 0.790687i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 347.757 | 0.403430 | ||||||||
\(863\) | 413.716 | + | 238.859i | 0.479392 | + | 0.276777i | 0.720163 | − | 0.693805i | \(-0.244067\pi\) |
−0.240771 | + | 0.970582i | \(0.577400\pi\) | |||||||
\(864\) | 63.0385 | + | 139.119i | 0.0729612 | + | 0.161018i | ||||
\(865\) | −17.9150 | − | 31.0297i | −0.0207110 | − | 0.0358725i | ||||
\(866\) | 976.117 | + | 563.561i | 1.12716 | + | 0.650764i | ||||
\(867\) | −97.4432 | + | 52.0856i | −0.112391 | + | 0.0600756i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 35.0060i | − | 0.0402830i | ||||||
\(870\) | −579.506 | − | 18.9659i | −0.666099 | − | 0.0217999i | ||||
\(871\) | −508.575 | − | 880.878i | −0.583898 | − | 1.01134i | ||||
\(872\) | 303.320 | − | 175.122i | 0.347845 | − | 0.200828i | ||||
\(873\) | −274.010 | − | 555.613i | −0.313872 | − | 0.636441i | ||||
\(874\) | −814.640 | −0.932083 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −65.2549 | + | 34.8802i | −0.0744919 | + | 0.0398176i | ||||
\(877\) | −766.571 | + | 1327.74i | −0.874083 | + | 1.51396i | −0.0163476 | + | 0.999866i | \(0.505204\pi\) |
−0.857736 | + | 0.514091i | \(0.828130\pi\) | |||||||
\(878\) | 678.301 | − | 391.617i | 0.772552 | − | 0.446033i | ||||
\(879\) | −522.138 | + | 839.683i | −0.594014 | + | 0.955271i | ||||
\(880\) | 5.41699 | − | 9.38251i | 0.00615568 | − | 0.0106619i | ||||
\(881\) | − | 1368.30i | − | 1.55313i | −0.630039 | − | 0.776563i | \(-0.716961\pi\) | ||
0.630039 | − | 0.776563i | \(-0.283039\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 944.486 | 1.06963 | 0.534817 | − | 0.844968i | \(-0.320381\pi\) | ||||
0.534817 | + | 0.844968i | \(0.320381\pi\) | |||||||
\(884\) | 566.130 | + | 326.855i | 0.640418 | + | 0.369746i | ||||
\(885\) | 27.6009 | + | 17.1630i | 0.0311875 | + | 0.0193932i | ||||
\(886\) | 547.288 | + | 947.930i | 0.617706 | + | 1.06990i | ||||
\(887\) | 1149.10 | + | 663.432i | 1.29549 | + | 0.747951i | 0.979622 | − | 0.200852i | \(-0.0643711\pi\) |
0.315868 | + | 0.948803i | \(0.397704\pi\) | |||||||
\(888\) | 80.0000 | + | 149.666i | 0.0900901 | + | 0.168543i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 289.908i | − | 0.325740i | ||||||
\(891\) | −4.35736 | + | 33.1065i | −0.00489042 | + | 0.0371565i | ||||
\(892\) | −230.494 | − | 399.227i | −0.258401 | − | 0.447564i | ||||
\(893\) | 117.576 | − | 67.8823i | 0.131664 | − | 0.0760160i | ||||
\(894\) | 6.91764 | − | 211.369i | 0.00773785 | − | 0.236431i | ||||
\(895\) | −8.12549 | −0.00907876 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1047.98 | + | 1960.60i | 1.16832 | + | 2.18573i | ||||
\(898\) | 478.834 | − | 829.365i | 0.533223 | − | 0.923569i | ||||
\(899\) | −99.8432 | + | 57.6445i | −0.111060 | + | 0.0641207i | ||||
\(900\) | −326.288 | − | 21.3803i | −0.362543 | − | 0.0237559i | ||||
\(901\) | −404.235 | + | 700.156i | −0.448652 | + | 0.777088i | ||||
\(902\) | 44.3675i | 0.0491879i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −227.660 | −0.251836 | ||||||||
\(905\) | 1063.52 | + | 614.024i | 1.17516 | + | 0.678479i | ||||
\(906\) | −474.197 | + | 762.586i | −0.523396 | + | 0.841706i | ||||
\(907\) | 609.822 | + | 1056.24i | 0.672351 | + | 1.16455i | 0.977236 | + | 0.212157i | \(0.0680487\pi\) |
−0.304885 | + | 0.952389i | \(0.598618\pi\) | |||||||
\(908\) | 447.632 | + | 258.441i | 0.492987 | + | 0.284626i | ||||
\(909\) | −1048.81 | − | 700.766i | −1.15381 | − | 0.770920i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 63.8282i | − | 0.0700639i | −0.999386 | − | 0.0350320i | \(-0.988847\pi\) | ||
0.999386 | − | 0.0350320i | \(-0.0111533\pi\) | |||||||
\(912\) | −6.28037 | + | 191.897i | −0.00688637 | + | 0.210414i | ||||
\(913\) | 0.849738 | + | 1.47179i | 0.000930710 | + | 0.00161204i | ||||
\(914\) | 1022.25 | − | 590.197i | 1.11844 | − | 0.645729i | ||||
\(915\) | −1318.21 | − | 43.1420i | −1.44066 | − | 0.0471497i | ||||
\(916\) | 74.1699 | 0.0809716 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 59.4170 | − | 603.435i | 0.0647244 | − | 0.657336i | ||||
\(919\) | −490.693 | + | 849.905i | −0.533942 | + | 0.924815i | 0.465272 | + | 0.885168i | \(0.345957\pi\) |
−0.999214 | + | 0.0396468i | \(0.987377\pi\) | |||||||
\(920\) | −579.399 | + | 334.516i | −0.629781 | + | 0.363604i | ||||
\(921\) | −269.615 | − | 167.654i | −0.292741 | − | 0.182035i | ||||
\(922\) | −245.472 | + | 425.170i | −0.266238 | + | 0.461139i | ||||
\(923\) | 1805.92i | 1.95658i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −363.320 | −0.392779 | ||||||||
\(926\) | −389.062 | − | 224.625i | −0.420154 | − | 0.242576i | ||||
\(927\) | −353.595 | − | 23.1695i | −0.381440 | − | 0.0249941i | ||||
\(928\) | 58.8340 | + | 101.903i | 0.0633987 | + | 0.109810i | ||||
\(929\) | 295.255 | + | 170.465i | 0.317820 | + | 0.183493i | 0.650420 | − | 0.759574i | \(-0.274593\pi\) |
−0.332600 | + | 0.943068i | \(0.607926\pi\) | |||||||
\(930\) | −136.251 | + | 72.8292i | −0.146506 | + | 0.0783110i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 165.343i | 0.177406i | ||||||||
\(933\) | 1154.79 | + | 37.7937i | 1.23772 | + | 0.0405077i | ||||
\(934\) | 387.085 | + | 670.451i | 0.414438 | + | 0.717827i | ||||
\(935\) | −37.2482 | + | 21.5053i | −0.0398377 | + | 0.0230003i | ||||
\(936\) | 469.919 | − | 231.749i | 0.502051 | − | 0.247595i | ||||
\(937\) | 1010.00 | 1.07791 | 0.538954 | − | 0.842335i | \(-0.318820\pi\) | ||||
0.538954 | + | 0.842335i | \(0.318820\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 209.882 | − | 112.187i | 0.223517 | − | 0.119475i | ||||
\(940\) | 55.7490 | − | 96.5601i | 0.0593075 | − | 0.102724i | ||||
\(941\) | 250.331 | − | 144.529i | 0.266027 | − | 0.153591i | −0.361054 | − | 0.932545i | \(-0.617583\pi\) |
0.627081 | + | 0.778954i | \(0.284250\pi\) | |||||||
\(942\) | 243.629 | − | 391.795i | 0.258630 | − | 0.415919i | ||||
\(943\) | 1369.91 | − | 2372.76i | 1.45272 | − | 2.51618i | ||||
\(944\) | − | 6.59595i | − | 0.00698724i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −30.1699 | −0.0318921 | ||||||||
\(947\) | 717.116 | + | 414.027i | 0.757250 | + | 0.437199i | 0.828308 | − | 0.560274i | \(-0.189304\pi\) |
−0.0710573 | + | 0.997472i | \(0.522637\pi\) | |||||||
\(948\) | 432.663 | + | 269.042i | 0.456395 | + | 0.283799i | ||||
\(949\) | 126.915 | + | 219.823i | 0.133736 | + | 0.231637i | ||||
\(950\) | −355.980 | − | 205.525i | −0.374715 | − | 0.216342i | ||||
\(951\) | −581.490 | − | 1087.87i | −0.611451 | − | 1.14392i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 102.785i | 0.107854i | 0.998545 | + | 0.0539269i | \(0.0171738\pi\) | ||||
−0.998545 | + | 0.0539269i | \(0.982826\pi\) | |||||||
\(954\) | 286.613 | + | 581.168i | 0.300433 | + | 0.609191i | ||||
\(955\) | −1151.55 | − | 1994.53i | −1.20581 | − | 2.08852i | ||||
\(956\) | 291.797 | − | 168.469i | 0.305227 | − | 0.176223i | ||||
\(957\) | −0.841484 | + | 25.7116i | −0.000879294 | + | 0.0268669i | ||||
\(958\) | 191.660 | 0.200063 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 74.3320 | + | 139.062i | 0.0774292 | + | 0.144857i | ||||
\(961\) | 465.140 | − | 805.647i | 0.484017 | − | 0.838342i | ||||
\(962\) | 504.179 | − | 291.088i | 0.524094 | − | 0.302586i | ||||
\(963\) | 63.5589 | − | 969.984i | 0.0660009 | − | 1.00725i | ||||
\(964\) | −130.000 | + | 225.167i | −0.134855 | + | 0.233575i | ||||
\(965\) | 1777.17i | 1.84163i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −184.753 | −0.191058 | −0.0955289 | − | 0.995427i | \(-0.530454\pi\) | ||||
−0.0955289 | + | 0.995427i | \(0.530454\pi\) | |||||||
\(968\) | 295.972 | + | 170.879i | 0.305756 | + | 0.176528i | ||||
\(969\) | 402.505 | − | 647.294i | 0.415382 | − | 0.668002i | ||||
\(970\) | −319.786 | − | 553.885i | −0.329676 | − | 0.571015i | ||||
\(971\) | −1272.48 | − | 734.664i | −1.31048 | − | 0.756606i | −0.328305 | − | 0.944572i | \(-0.606477\pi\) |
−0.982176 | + | 0.187966i | \(0.939811\pi\) | |||||||
\(972\) | −375.697 | − | 308.299i | −0.386519 | − | 0.317180i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 33.2312i | 0.0341183i | ||||||||
\(975\) | −36.6922 | + | 1121.13i | −0.0376330 | + | 1.14988i | ||||
\(976\) | 133.830 | + | 231.800i | 0.137121 | + | 0.237500i | ||||
\(977\) | 574.237 | − | 331.536i | 0.587756 | − | 0.339341i | −0.176454 | − | 0.984309i | \(-0.556463\pi\) |
0.764210 | + | 0.644968i | \(0.223129\pi\) | |||||||
\(978\) | 55.1415 | + | 1.80466i | 0.0563819 | + | 0.00184525i | ||||
\(979\) | −12.8627 | −0.0131386 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −619.150 | + | 926.659i | −0.631142 | + | 0.944607i | ||||
\(982\) | 73.1176 | − | 126.643i | 0.0744579 | − | 0.128965i | ||||
\(983\) | 1644.81 | − | 949.630i | 1.67325 | − | 0.966053i | 0.707456 | − | 0.706758i | \(-0.249843\pi\) |
0.965798 | − | 0.259296i | \(-0.0834904\pi\) | |||||||
\(984\) | −548.368 | − | 340.990i | −0.557284 | − | 0.346535i | ||||
\(985\) | 208.664 | − | 361.417i | 0.211842 | − | 0.366921i | ||||
\(986\) | − | 467.138i | − | 0.473771i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 658.656 | 0.666656 | ||||||||
\(989\) | 1613.48 | + | 931.543i | 1.63143 | + | 0.941904i | ||||
\(990\) | −2.25407 | + | 34.3998i | −0.00227684 | + | 0.0347472i | ||||
\(991\) | 128.863 | + | 223.197i | 0.130033 | + | 0.225224i | 0.923689 | − | 0.383143i | \(-0.125158\pi\) |
−0.793656 | + | 0.608367i | \(0.791825\pi\) | |||||||
\(992\) | 27.1525 | + | 15.6765i | 0.0273715 | + | 0.0158029i | ||||
\(993\) | 1295.07 | − | 692.244i | 1.30420 | − | 0.697123i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 578.167i | − | 0.581073i | ||||||
\(996\) | −24.7216 | − | 0.809082i | −0.0248209 | − | 0.000812332i | ||||
\(997\) | −617.871 | − | 1070.18i | −0.619730 | − | 1.07340i | −0.989535 | − | 0.144294i | \(-0.953909\pi\) |
0.369805 | − | 0.929109i | \(-0.379424\pi\) | |||||||
\(998\) | −78.8000 | + | 45.4952i | −0.0789579 | + | 0.0455863i | ||||
\(999\) | −438.946 | − | 314.526i | −0.439385 | − | 0.314841i |
(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 | 294.3.h.d.275.2 | 8 | ||
3.2 | odd | 2 | inner | 294.3.h.d.275.4 | 8 | ||
7.2 | even | 3 | 42.3.b.a.29.3 | yes | 4 | ||
7.3 | odd | 6 | 294.3.h.g.263.3 | 8 | |||
7.4 | even | 3 | inner | 294.3.h.d.263.4 | 8 | ||
7.5 | odd | 6 | 294.3.b.h.197.4 | 4 | |||
7.6 | odd | 2 | 294.3.h.g.275.1 | 8 | |||
21.2 | odd | 6 | 42.3.b.a.29.1 | ✓ | 4 | ||
21.5 | even | 6 | 294.3.b.h.197.2 | 4 | |||
21.11 | odd | 6 | inner | 294.3.h.d.263.2 | 8 | ||
21.17 | even | 6 | 294.3.h.g.263.1 | 8 | |||
21.20 | even | 2 | 294.3.h.g.275.3 | 8 | |||
28.23 | odd | 6 | 336.3.d.b.113.3 | 4 | |||
35.2 | odd | 12 | 1050.3.c.a.449.3 | 8 | |||
35.9 | even | 6 | 1050.3.e.a.701.2 | 4 | |||
35.23 | odd | 12 | 1050.3.c.a.449.5 | 8 | |||
56.37 | even | 6 | 1344.3.d.c.449.3 | 4 | |||
56.51 | odd | 6 | 1344.3.d.e.449.2 | 4 | |||
63.2 | odd | 6 | 1134.3.q.a.701.2 | 8 | |||
63.16 | even | 3 | 1134.3.q.a.701.3 | 8 | |||
63.23 | odd | 6 | 1134.3.q.a.1079.3 | 8 | |||
63.58 | even | 3 | 1134.3.q.a.1079.2 | 8 | |||
84.23 | even | 6 | 336.3.d.b.113.4 | 4 | |||
105.2 | even | 12 | 1050.3.c.a.449.8 | 8 | |||
105.23 | even | 12 | 1050.3.c.a.449.2 | 8 | |||
105.44 | odd | 6 | 1050.3.e.a.701.4 | 4 | |||
168.107 | even | 6 | 1344.3.d.e.449.1 | 4 | |||
168.149 | odd | 6 | 1344.3.d.c.449.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.b.a.29.1 | ✓ | 4 | 21.2 | odd | 6 | ||
42.3.b.a.29.3 | yes | 4 | 7.2 | even | 3 | ||
294.3.b.h.197.2 | 4 | 21.5 | even | 6 | |||
294.3.b.h.197.4 | 4 | 7.5 | odd | 6 | |||
294.3.h.d.263.2 | 8 | 21.11 | odd | 6 | inner | ||
294.3.h.d.263.4 | 8 | 7.4 | even | 3 | inner | ||
294.3.h.d.275.2 | 8 | 1.1 | even | 1 | trivial | ||
294.3.h.d.275.4 | 8 | 3.2 | odd | 2 | inner | ||
294.3.h.g.263.1 | 8 | 21.17 | even | 6 | |||
294.3.h.g.263.3 | 8 | 7.3 | odd | 6 | |||
294.3.h.g.275.1 | 8 | 7.6 | odd | 2 | |||
294.3.h.g.275.3 | 8 | 21.20 | even | 2 | |||
336.3.d.b.113.3 | 4 | 28.23 | odd | 6 | |||
336.3.d.b.113.4 | 4 | 84.23 | even | 6 | |||
1050.3.c.a.449.2 | 8 | 105.23 | even | 12 | |||
1050.3.c.a.449.3 | 8 | 35.2 | odd | 12 | |||
1050.3.c.a.449.5 | 8 | 35.23 | odd | 12 | |||
1050.3.c.a.449.8 | 8 | 105.2 | even | 12 | |||
1050.3.e.a.701.2 | 4 | 35.9 | even | 6 | |||
1050.3.e.a.701.4 | 4 | 105.44 | odd | 6 | |||
1134.3.q.a.701.2 | 8 | 63.2 | odd | 6 | |||
1134.3.q.a.701.3 | 8 | 63.16 | even | 3 | |||
1134.3.q.a.1079.2 | 8 | 63.58 | even | 3 | |||
1134.3.q.a.1079.3 | 8 | 63.23 | odd | 6 | |||
1344.3.d.c.449.3 | 4 | 56.37 | even | 6 | |||
1344.3.d.c.449.4 | 4 | 168.149 | odd | 6 | |||
1344.3.d.e.449.1 | 4 | 168.107 | even | 6 | |||
1344.3.d.e.449.2 | 4 | 56.51 | odd | 6 |