Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(107,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([5, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.u (of order \(30\), degree \(8\), 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: | \(7.11467082010\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{30})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{30}]$ |
Embedding invariants
Embedding label | 134.4 | ||
Character | \(\chi\) | \(=\) | 891.134 |
Dual form | 891.2.u.c.512.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.29943 | − | 0.488759i | 1.62594 | − | 0.345604i | 0.697356 | − | 0.716725i | \(-0.254359\pi\) |
0.928585 | + | 0.371120i | \(0.121026\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.22139 | − | 1.43426i | 1.61070 | − | 0.717129i | ||||
\(5\) | 0.467414 | − | 2.19901i | 0.209034 | − | 0.983427i | −0.741054 | − | 0.671445i | \(-0.765674\pi\) |
0.950088 | − | 0.311982i | \(-0.100993\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.02888 | + | 0.423453i | 1.52277 | + | 0.160050i | 0.828634 | − | 0.559790i | \(-0.189118\pi\) |
0.694140 | + | 0.719840i | \(0.255785\pi\) | |||||||
\(8\) | 2.90269 | − | 2.10893i | 1.02626 | − | 0.745618i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 5.28492i | − | 1.67124i | ||||||
\(11\) | −1.67565 | − | 2.86220i | −0.505227 | − | 0.862986i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.45760 | + | 3.11324i | −0.958966 | + | 0.863457i | −0.990703 | − | 0.136039i | \(-0.956563\pi\) |
0.0317372 | + | 0.999496i | \(0.489896\pi\) | |||||||
\(14\) | 9.47109 | − | 0.995452i | 2.53126 | − | 0.266046i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.924716 | − | 1.02700i | 0.231179 | − | 0.256750i | ||||
\(17\) | 0.0235753 | + | 0.0725574i | 0.00571786 | + | 0.0175978i | 0.953875 | − | 0.300205i | \(-0.0970551\pi\) |
−0.948157 | + | 0.317803i | \(0.897055\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.40822 | + | 1.93825i | 0.323068 | + | 0.444665i | 0.939401 | − | 0.342821i | \(-0.111382\pi\) |
−0.616333 | + | 0.787486i | \(0.711382\pi\) | |||||||
\(20\) | −1.64822 | − | 7.75427i | −0.368553 | − | 1.73391i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.25196 | − | 5.76244i | −1.11972 | − | 1.22856i | ||||
\(23\) | −2.79482 | − | 1.61359i | −0.582759 | − | 0.336456i | 0.179470 | − | 0.983763i | \(-0.442562\pi\) |
−0.762229 | + | 0.647307i | \(0.775895\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0494405 | − | 0.0220123i | −0.00988810 | − | 0.00440247i | ||||
\(26\) | −6.42889 | + | 8.84860i | −1.26081 | + | 1.73535i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 13.5860 | − | 4.41435i | 2.56750 | − | 0.834233i | ||||
\(29\) | −0.192251 | + | 1.82914i | −0.0357001 | + | 0.339664i | 0.962064 | + | 0.272825i | \(0.0879579\pi\) |
−0.997764 | + | 0.0668387i | \(0.978709\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.12063 | + | 1.24459i | 0.201271 | + | 0.223534i | 0.835328 | − | 0.549752i | \(-0.185278\pi\) |
−0.634056 | + | 0.773287i | \(0.718611\pi\) | |||||||
\(32\) | −1.96356 | + | 3.40098i | −0.347111 | + | 0.601214i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0896728 | + | 0.155318i | 0.0153788 | + | 0.0266368i | ||||
\(35\) | 2.81433 | − | 8.66162i | 0.475709 | − | 1.46408i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.87906 | − | 4.27138i | −0.966511 | − | 0.702211i | −0.0118571 | − | 0.999930i | \(-0.503774\pi\) |
−0.954654 | + | 0.297718i | \(0.903774\pi\) | |||||||
\(38\) | 4.18544 | + | 3.76859i | 0.678968 | + | 0.611346i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.28079 | − | 7.36878i | −0.518739 | − | 1.16511i | ||||
\(41\) | 0.882440 | + | 8.39585i | 0.137814 | + | 1.31121i | 0.816740 | + | 0.577006i | \(0.195779\pi\) |
−0.678926 | + | 0.734206i | \(0.737554\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.70733 | − | 2.14043i | 0.565363 | − | 0.326413i | −0.189932 | − | 0.981797i | \(-0.560827\pi\) |
0.755295 | + | 0.655385i | \(0.227493\pi\) | |||||||
\(44\) | −9.50306 | − | 6.81697i | −1.43264 | − | 1.02770i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.21513 | − | 2.34434i | −1.06381 | − | 0.345654i | ||||
\(47\) | 2.52822 | − | 5.67848i | 0.368779 | − | 0.828291i | −0.629889 | − | 0.776686i | \(-0.716899\pi\) |
0.998668 | − | 0.0516056i | \(-0.0164339\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.20554 | + | 1.95670i | 1.31508 | + | 0.279528i | ||||
\(50\) | −0.124444 | − | 0.0264513i | −0.0175990 | − | 0.00374078i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.67312 | + | 14.9881i | −0.925395 | + | 2.07847i | ||||
\(53\) | −1.16884 | − | 0.379779i | −0.160552 | − | 0.0521666i | 0.227638 | − | 0.973746i | \(-0.426900\pi\) |
−0.388190 | + | 0.921579i | \(0.626900\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.07723 | + | 2.34694i | −0.954294 | + | 0.316461i | ||||
\(56\) | 12.5876 | − | 7.26746i | 1.68209 | − | 0.971156i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.451943 | + | 4.29995i | 0.0593430 | + | 0.564611i | ||||
\(59\) | 0.236025 | + | 0.530122i | 0.0307279 | + | 0.0690159i | 0.928257 | − | 0.371938i | \(-0.121307\pi\) |
−0.897530 | + | 0.440954i | \(0.854640\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.81073 | + | 2.53079i | 0.359877 | + | 0.324035i | 0.829158 | − | 0.559014i | \(-0.188820\pi\) |
−0.469281 | + | 0.883049i | \(0.655487\pi\) | |||||||
\(62\) | 3.18511 | + | 2.31412i | 0.404510 | + | 0.293893i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.70690 | + | 11.4087i | −0.463363 | + | 1.42608i | ||||
\(65\) | 5.22991 | + | 9.05847i | 0.648691 | + | 1.12357i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.49920 | + | 11.2569i | −0.794003 | + | 1.37525i | 0.129467 | + | 0.991584i | \(0.458673\pi\) |
−0.923470 | + | 0.383670i | \(0.874660\pi\) | |||||||
\(68\) | 0.180011 | + | 0.199923i | 0.0218296 | + | 0.0242442i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.23791 | − | 21.2923i | 0.267482 | − | 2.54492i | ||||
\(71\) | −1.06563 | + | 0.346245i | −0.126467 | + | 0.0410917i | −0.371567 | − | 0.928406i | \(-0.621179\pi\) |
0.245100 | + | 0.969498i | \(0.421179\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.82153 | − | 10.7654i | 0.915441 | − | 1.26000i | −0.0498335 | − | 0.998758i | \(-0.515869\pi\) |
0.965274 | − | 0.261239i | \(-0.0841309\pi\) | |||||||
\(74\) | −15.6061 | − | 6.94830i | −1.81418 | − | 0.807724i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.31639 | + | 4.22412i | 0.839247 | + | 0.484540i | ||||
\(77\) | −5.53899 | − | 12.2410i | −0.631226 | − | 1.39499i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.137193 | − | 0.645442i | −0.0154354 | − | 0.0726179i | 0.969756 | − | 0.244077i | \(-0.0784851\pi\) |
−0.985191 | + | 0.171459i | \(0.945152\pi\) | |||||||
\(80\) | −1.82616 | − | 2.51349i | −0.204171 | − | 0.281017i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.13265 | + | 18.8744i | 0.677238 | + | 2.08432i | ||||
\(83\) | 6.83259 | − | 7.58836i | 0.749974 | − | 0.832931i | −0.240497 | − | 0.970650i | \(-0.577310\pi\) |
0.990471 | + | 0.137719i | \(0.0439771\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.170574 | − | 0.0179280i | 0.0185013 | − | 0.00194457i | ||||
\(86\) | 7.47859 | − | 6.73376i | 0.806438 | − | 0.726120i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.9001 | − | 4.77426i | −1.16195 | − | 0.508937i | ||||
\(89\) | − | 6.58983i | − | 0.698520i | −0.937026 | − | 0.349260i | \(-0.886433\pi\) | ||
0.937026 | − | 0.349260i | \(-0.113567\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.2486 | + | 11.0787i | −1.59849 | + | 1.16137i | ||||
\(92\) | −11.3175 | − | 1.18952i | −1.17993 | − | 0.124016i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.03806 | − | 14.2929i | 0.313352 | − | 1.47420i | ||||
\(95\) | 4.92045 | − | 2.19073i | 0.504828 | − | 0.224764i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0853 | + | 3.41903i | −1.63321 | + | 0.347150i | −0.931058 | − | 0.364872i | \(-0.881113\pi\) |
−0.702157 | + | 0.712023i | \(0.747779\pi\) | |||||||
\(98\) | 22.1238 | 2.23485 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.190839 | −0.0190839 | ||||||||
\(101\) | 1.68427 | − | 0.358002i | 0.167591 | − | 0.0356226i | −0.123352 | − | 0.992363i | \(-0.539364\pi\) |
0.290943 | + | 0.956740i | \(0.406031\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.95154 | + | 1.31411i | −0.290824 | + | 0.129483i | −0.546963 | − | 0.837157i | \(-0.684216\pi\) |
0.256139 | + | 0.966640i | \(0.417549\pi\) | |||||||
\(104\) | −3.47075 | + | 16.3286i | −0.340335 | + | 1.60115i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.87328 | − | 0.301994i | −0.279078 | − | 0.0293323i | ||||
\(107\) | −11.9884 | + | 8.71006i | −1.15896 | + | 0.842034i | −0.989646 | − | 0.143529i | \(-0.954155\pi\) |
−0.169314 | + | 0.985562i | \(0.554155\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9258i | 1.42963i | 0.699313 | + | 0.714815i | \(0.253489\pi\) | ||||
−0.699313 | + | 0.714815i | \(0.746511\pi\) | |||||||
\(110\) | −15.1265 | + | 8.85567i | −1.44226 | + | 0.844355i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.16046 | − | 3.74609i | 0.393126 | − | 0.353972i | ||||
\(113\) | 11.1849 | − | 1.17558i | 1.05219 | − | 0.110590i | 0.437389 | − | 0.899272i | \(-0.355903\pi\) |
0.614800 | + | 0.788683i | \(0.289237\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.85463 | + | 5.39161i | −0.452697 | + | 0.502771i | ||||
\(116\) | 2.00415 | + | 6.16813i | 0.186080 | + | 0.572697i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.801825 | + | 1.10362i | 0.0738139 | + | 0.101596i | ||||
\(119\) | 0.0642576 | + | 0.302308i | 0.00589048 | + | 0.0277125i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.38440 | + | 9.59209i | −0.489491 | + | 0.872009i | ||||
\(122\) | 7.70002 | + | 4.44561i | 0.697127 | + | 0.402487i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.39505 | + | 2.40203i | 0.484490 | + | 0.215709i | ||||
\(125\) | 6.53559 | − | 8.99547i | 0.584561 | − | 0.804580i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.76481 | + | 1.87310i | −0.511544 | + | 0.166211i | −0.553404 | − | 0.832913i | \(-0.686672\pi\) |
0.0418604 | + | 0.999123i | \(0.486672\pi\) | |||||||
\(128\) | −2.12668 | + | 20.2340i | −0.187974 | + | 1.78845i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 16.4532 | + | 18.2731i | 1.44304 | + | 1.60266i | ||||
\(131\) | −3.57541 | + | 6.19280i | −0.312385 | + | 0.541067i | −0.978878 | − | 0.204444i | \(-0.934461\pi\) |
0.666493 | + | 0.745511i | \(0.267795\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.85280 | + | 8.40530i | 0.420791 | + | 0.728832i | ||||
\(134\) | −9.44251 | + | 29.0611i | −0.815709 | + | 2.51049i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.221450 | + | 0.160893i | 0.0189892 | + | 0.0137964i | ||||
\(137\) | 7.89402 | + | 7.10781i | 0.674432 | + | 0.607261i | 0.933491 | − | 0.358600i | \(-0.116746\pi\) |
−0.259059 | + | 0.965861i | \(0.583413\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0215881 | − | 0.0484877i | −0.00183108 | − | 0.00411267i | 0.912628 | − | 0.408792i | \(-0.134050\pi\) |
−0.914459 | + | 0.404679i | \(0.867383\pi\) | |||||||
\(140\) | −3.35692 | − | 31.9390i | −0.283712 | − | 2.69934i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.28111 | + | 1.31700i | −0.191427 | + | 0.110520i | ||||
\(143\) | 14.7044 | + | 4.67966i | 1.22965 | + | 0.391333i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.93244 | + | 1.27773i | 0.326572 | + | 0.106110i | ||||
\(146\) | 12.7234 | − | 28.5771i | 1.05299 | − | 2.36506i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −25.0650 | − | 5.32773i | −2.06033 | − | 0.437937i | ||||
\(149\) | −19.9493 | − | 4.24035i | −1.63431 | − | 0.347383i | −0.702880 | − | 0.711309i | \(-0.748103\pi\) |
−0.931428 | + | 0.363926i | \(0.881436\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.483681 | − | 1.08637i | 0.0393614 | − | 0.0884072i | −0.892795 | − | 0.450464i | \(-0.851259\pi\) |
0.932156 | + | 0.362057i | \(0.117925\pi\) | |||||||
\(152\) | 8.17525 | + | 2.65630i | 0.663101 | + | 0.215454i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −18.7194 | − | 25.4401i | −1.50845 | − | 2.05003i | ||||
\(155\) | 3.26066 | − | 1.88254i | 0.261902 | − | 0.151209i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.181157 | + | 1.72359i | 0.0144579 | + | 0.137558i | 0.999370 | − | 0.0354993i | \(-0.0113022\pi\) |
−0.984912 | + | 0.173057i | \(0.944635\pi\) | |||||||
\(158\) | −0.630930 | − | 1.41709i | −0.0501941 | − | 0.112738i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.56100 | + | 5.90755i | 0.518692 | + | 0.467033i | ||||
\(161\) | −10.5767 | − | 7.68443i | −0.833561 | − | 0.605618i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.309821 | + | 0.953532i | −0.0242671 | + | 0.0746864i | −0.962457 | − | 0.271435i | \(-0.912502\pi\) |
0.938190 | + | 0.346122i | \(0.112502\pi\) | |||||||
\(164\) | 14.8845 | + | 25.7807i | 1.16228 | + | 2.01314i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0022 | − | 20.7884i | 0.931550 | − | 1.61349i | ||||
\(167\) | 9.04541 | + | 10.0459i | 0.699955 | + | 0.777379i | 0.983369 | − | 0.181619i | \(-0.0581338\pi\) |
−0.283414 | + | 0.958998i | \(0.591467\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.903886 | − | 8.59990i | 0.0695297 | − | 0.661531i | ||||
\(170\) | 0.383460 | − | 0.124594i | 0.0294100 | − | 0.00955590i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.87286 | − | 12.2124i | 0.676549 | − | 0.931190i | ||||
\(173\) | −6.87255 | − | 3.05986i | −0.522510 | − | 0.232637i | 0.128494 | − | 0.991710i | \(-0.458986\pi\) |
−0.651005 | + | 0.759074i | \(0.725652\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.189869 | − | 0.109621i | −0.0143527 | − | 0.00828655i | ||||
\(176\) | −4.48898 | − | 0.925829i | −0.338370 | − | 0.0697870i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.22083 | − | 15.1528i | −0.241412 | − | 1.13575i | ||||
\(179\) | −7.34750 | − | 10.1130i | −0.549178 | − | 0.755879i | 0.440722 | − | 0.897643i | \(-0.354722\pi\) |
−0.989900 | + | 0.141765i | \(0.954722\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.56261 | − | 17.1200i | −0.413466 | − | 1.27252i | −0.913616 | − | 0.406578i | \(-0.866722\pi\) |
0.500150 | − | 0.865939i | \(-0.333278\pi\) | |||||||
\(182\) | −29.6482 | + | 32.9276i | −2.19767 | + | 2.44076i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.5154 | + | 1.21032i | −0.848928 | + | 0.0892259i | ||||
\(185\) | −12.1408 | + | 10.9316i | −0.892607 | + | 0.803707i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.168170 | − | 0.189058i | 0.0122978 | − | 0.0138253i | ||||
\(188\) | − | 21.9187i | − | 1.59859i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.2435 | − | 7.44233i | 0.743141 | − | 0.539924i | ||||
\(191\) | −21.5383 | − | 2.26377i | −1.55846 | − | 0.163801i | −0.714280 | − | 0.699861i | \(-0.753245\pi\) |
−0.844180 | + | 0.536060i | \(0.819912\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.07842 | − | 5.07358i | 0.0776266 | − | 0.365204i | −0.922139 | − | 0.386859i | \(-0.873560\pi\) |
0.999766 | + | 0.0216545i | \(0.00689339\pi\) | |||||||
\(194\) | −35.3159 | + | 15.7237i | −2.53553 | + | 1.12889i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 32.4611 | − | 6.89982i | 2.31865 | − | 0.492844i | ||||
\(197\) | 5.14679 | 0.366693 | 0.183347 | − | 0.983048i | \(-0.441307\pi\) | ||||
0.183347 | + | 0.983048i | \(0.441307\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.2595 | 1.71971 | 0.859855 | − | 0.510539i | \(-0.170554\pi\) | ||||
0.859855 | + | 0.510539i | \(0.170554\pi\) | |||||||
\(200\) | −0.189933 | + | 0.0403715i | −0.0134303 | + | 0.00285469i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.69788 | − | 1.64640i | 0.260182 | − | 0.115840i | ||||
\(203\) | −1.54911 | + | 7.28800i | −0.108726 | + | 0.511517i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.8750 | + | 1.98385i | 1.31829 | + | 0.138558i | ||||
\(206\) | −6.14457 | + | 4.46429i | −0.428113 | + | 0.311042i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.42982i | 0.445828i | ||||||||
\(209\) | 3.18798 | − | 7.27844i | 0.220517 | − | 0.503460i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.9292 | − | 12.5419i | 0.958927 | − | 0.863422i | −0.0317716 | − | 0.999495i | \(-0.510115\pi\) |
0.990699 | + | 0.136073i | \(0.0434483\pi\) | |||||||
\(212\) | −4.30999 | + | 0.452998i | −0.296011 | + | 0.0311121i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23.3093 | + | 25.8876i | −1.59339 | + | 1.76964i | ||||
\(215\) | −2.97397 | − | 9.15293i | −0.202823 | − | 0.624225i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.98787 | + | 5.48883i | 0.270714 | + | 0.372606i | ||||
\(218\) | 7.29511 | + | 34.3208i | 0.494087 | + | 2.32450i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −19.4324 | + | 17.7110i | −1.31013 | + | 1.19407i | ||||
\(221\) | −0.307403 | − | 0.177479i | −0.0206781 | − | 0.0119385i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.01408 | − | 2.23241i | −0.335768 | − | 0.149493i | 0.231926 | − | 0.972734i | \(-0.425497\pi\) |
−0.567693 | + | 0.823240i | \(0.692164\pi\) | |||||||
\(224\) | −9.35109 | + | 12.8707i | −0.624796 | + | 0.859958i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 25.1444 | − | 8.16990i | 1.67258 | − | 0.543454i | ||||
\(227\) | 1.43871 | − | 13.6884i | 0.0954905 | − | 0.908531i | −0.836967 | − | 0.547253i | \(-0.815674\pi\) |
0.932458 | − | 0.361279i | \(-0.117660\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.1405 | − | 15.7046i | −0.934431 | − | 1.03779i | −0.999204 | − | 0.0398904i | \(-0.987299\pi\) |
0.0647734 | − | 0.997900i | \(-0.479368\pi\) | |||||||
\(230\) | −8.52768 | + | 14.7704i | −0.562298 | + | 0.973929i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.29949 | + | 5.71488i | 0.216622 | + | 0.375200i | ||||
\(233\) | 4.62458 | − | 14.2330i | 0.302967 | − | 0.932435i | −0.677462 | − | 0.735558i | \(-0.736920\pi\) |
0.980428 | − | 0.196877i | \(-0.0630800\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.3053 | − | 8.21378i | −0.737477 | − | 0.535808i | ||||
\(236\) | 1.52066 | + | 1.36921i | 0.0989866 | + | 0.0891280i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.295511 | + | 0.663730i | 0.0191552 | + | 0.0430232i | ||||
\(239\) | −0.564976 | − | 5.37539i | −0.0365453 | − | 0.347705i | −0.997481 | − | 0.0709336i | \(-0.977402\pi\) |
0.960936 | − | 0.276772i | \(-0.0892645\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.1404 | − | 5.85457i | 0.653202 | − | 0.377126i | −0.136480 | − | 0.990643i | \(-0.543579\pi\) |
0.789682 | + | 0.613517i | \(0.210246\pi\) | |||||||
\(242\) | −7.69281 | + | 24.6880i | −0.494513 | + | 1.58700i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.6843 | + | 4.12137i | 0.812028 | + | 0.263844i | ||||
\(245\) | 8.60560 | − | 19.3285i | 0.549792 | − | 1.23485i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.9033 | − | 2.31757i | −0.693761 | − | 0.147463i | ||||
\(248\) | 5.87758 | + | 1.24932i | 0.373227 | + | 0.0793318i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.6315 | − | 23.8788i | 0.672396 | − | 1.51023i | ||||
\(251\) | −21.4920 | − | 6.98319i | −1.35657 | − | 0.440775i | −0.461671 | − | 0.887051i | \(-0.652750\pi\) |
−0.894895 | + | 0.446276i | \(0.852750\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0647190 | + | 10.7031i | 0.00406885 | + | 0.672900i | ||||
\(254\) | −12.3403 | + | 7.12466i | −0.774297 | + | 0.447041i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.49159 | + | 23.7059i | 0.155725 | + | 1.48162i | ||||
\(257\) | −11.1919 | − | 25.1375i | −0.698133 | − | 1.56803i | −0.817985 | − | 0.575240i | \(-0.804909\pi\) |
0.119852 | − | 0.992792i | \(-0.461758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.8773 | − | 19.6984i | −1.35939 | − | 1.22400i | ||||
\(260\) | 29.8398 | + | 21.6799i | 1.85059 | + | 1.34453i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.19462 | + | 15.9874i | −0.320925 | + | 0.987705i | ||||
\(263\) | 16.0193 | + | 27.7463i | 0.987793 | + | 1.71091i | 0.628800 | + | 0.777567i | \(0.283547\pi\) |
0.358993 | + | 0.933340i | \(0.383120\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.38147 | + | 2.39277i | −0.0848630 | + | 0.146987i | ||||
\(266\) | 15.2668 | + | 16.9555i | 0.936069 | + | 1.03961i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.79113 | + | 45.5846i | −0.292665 | + | 2.78452i | ||||
\(269\) | 25.7177 | − | 8.35619i | 1.56804 | − | 0.509486i | 0.609097 | − | 0.793096i | \(-0.291532\pi\) |
0.958940 | + | 0.283610i | \(0.0915322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.74690 | − | 12.0391i | 0.531336 | − | 0.731322i | −0.455997 | − | 0.889981i | \(-0.650717\pi\) |
0.987333 | + | 0.158660i | \(0.0507172\pi\) | |||||||
\(272\) | 0.0963170 | + | 0.0428831i | 0.00584008 | + | 0.00260017i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.6257 | + | 12.4856i | 1.30646 | + | 0.754284i | ||||
\(275\) | 0.0198412 | + | 0.178394i | 0.00119647 | + | 0.0107575i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.63831 | + | 7.70765i | 0.0984366 | + | 0.463108i | 0.999563 | + | 0.0295520i | \(0.00940805\pi\) |
−0.901127 | + | 0.433556i | \(0.857259\pi\) | |||||||
\(278\) | −0.0733391 | − | 0.100943i | −0.00439859 | − | 0.00605414i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.0976 | − | 31.0772i | −0.603447 | − | 1.85722i | ||||
\(281\) | −14.2054 | + | 15.7767i | −0.847426 | + | 0.941161i | −0.998881 | − | 0.0473027i | \(-0.984937\pi\) |
0.151455 | + | 0.988464i | \(0.451604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.27158 | − | 0.448961i | 0.253919 | − | 0.0266880i | 0.0232863 | − | 0.999729i | \(-0.492587\pi\) |
0.230633 | + | 0.973041i | \(0.425920\pi\) | |||||||
\(284\) | −2.93622 | + | 2.64378i | −0.174232 | + | 0.156880i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 36.0990 | + | 3.57361i | 2.13458 | + | 0.211312i | ||||
\(287\) | 34.1996i | 2.01874i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7486 | − | 9.98893i | 0.808740 | − | 0.587584i | ||||
\(290\) | 9.66688 | + | 1.01603i | 0.567658 | + | 0.0596633i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.75586 | − | 45.8977i | 0.570919 | − | 2.68596i | ||||
\(293\) | 17.4446 | − | 7.76685i | 1.01913 | − | 0.453744i | 0.171978 | − | 0.985101i | \(-0.444984\pi\) |
0.847148 | + | 0.531356i | \(0.178317\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.27606 | − | 0.271236i | 0.0742953 | − | 0.0157920i | ||||
\(296\) | −26.0731 | −1.51547 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −47.9444 | −2.77735 | ||||||||
\(299\) | 14.6868 | − | 3.12178i | 0.849362 | − | 0.180537i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.8428 | − | 7.05366i | 0.913163 | − | 0.406566i | ||||
\(302\) | 0.581220 | − | 2.73442i | 0.0334454 | − | 0.157348i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.29279 | + | 0.346086i | 0.188854 | + | 0.0198494i | ||||
\(305\) | 6.87902 | − | 4.99790i | 0.393891 | − | 0.286179i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.86240i | 0.106293i | 0.998587 | + | 0.0531463i | \(0.0169250\pi\) | ||||
−0.998587 | + | 0.0531463i | \(0.983075\pi\) | |||||||
\(308\) | −35.4001 | − | 31.4889i | −2.01711 | − | 1.79424i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.57754 | − | 5.92244i | 0.373579 | − | 0.336372i | ||||
\(311\) | 8.90556 | − | 0.936012i | 0.504988 | − | 0.0530763i | 0.151390 | − | 0.988474i | \(-0.451625\pi\) |
0.353597 | + | 0.935398i | \(0.384958\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.4668 | − | 12.7352i | 0.648142 | − | 0.719834i | −0.326101 | − | 0.945335i | \(-0.605735\pi\) |
0.974243 | + | 0.225501i | \(0.0724017\pi\) | |||||||
\(314\) | 1.25898 | + | 3.87474i | 0.0710483 | + | 0.218664i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.36768 | − | 1.88245i | −0.0769381 | − | 0.105896i | ||||
\(317\) | −5.67686 | − | 26.7075i | −0.318844 | − | 1.50004i | −0.787307 | − | 0.616561i | \(-0.788525\pi\) |
0.468463 | − | 0.883483i | \(-0.344808\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.55752 | − | 2.51474i | 0.311162 | − | 0.140799i | ||||
\(320\) | 23.3551 | + | 13.4841i | 1.30559 | + | 0.753783i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −28.0762 | − | 12.5003i | −1.56463 | − | 0.696616i | ||||
\(323\) | −0.107435 | + | 0.147872i | −0.00597785 | + | 0.00822781i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.239475 | − | 0.0778102i | 0.0132837 | − | 0.00431614i | ||||
\(326\) | −0.246365 | + | 2.34401i | −0.0136449 | + | 0.129823i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20.2677 | + | 22.5095i | 1.11910 | + | 1.24288i | ||||
\(329\) | 12.5905 | − | 21.8073i | 0.694135 | − | 1.20228i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.93609 | + | 5.08545i | 0.161382 | + | 0.279522i | 0.935365 | − | 0.353685i | \(-0.115072\pi\) |
−0.773983 | + | 0.633207i | \(0.781738\pi\) | |||||||
\(332\) | 11.1268 | − | 34.2448i | 0.610663 | − | 1.87943i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 25.7093 | + | 18.6789i | 1.40675 | + | 1.02206i | ||||
\(335\) | 21.7163 | + | 19.5534i | 1.18649 | + | 1.06832i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.73993 | − | 15.1381i | −0.367147 | − | 0.824627i | −0.998781 | − | 0.0493597i | \(-0.984282\pi\) |
0.631634 | − | 0.775267i | \(-0.282385\pi\) | |||||||
\(338\) | −2.12485 | − | 20.2166i | −0.115577 | − | 1.09964i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.523772 | − | 0.302400i | 0.0284055 | − | 0.0163999i | ||||
\(341\) | 1.68447 | − | 5.29296i | 0.0912193 | − | 0.286630i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.28988 | + | 3.01847i | 0.501606 | + | 0.162982i | ||||
\(344\) | 6.24722 | − | 14.0315i | 0.336828 | − | 0.756527i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.2985 | − | 3.67690i | −0.929972 | − | 0.197672i | ||||
\(347\) | 2.46314 | + | 0.523557i | 0.132228 | + | 0.0281060i | 0.273550 | − | 0.961858i | \(-0.411802\pi\) |
−0.141322 | + | 0.989964i | \(0.545135\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.55059 | − | 7.97475i | 0.190059 | − | 0.426879i | −0.793232 | − | 0.608919i | \(-0.791603\pi\) |
0.983291 | + | 0.182040i | \(0.0582701\pi\) | |||||||
\(350\) | −0.490168 | − | 0.159265i | −0.0262006 | − | 0.00851308i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.0245 | − | 0.0787558i | 0.694210 | − | 0.00419770i | ||||
\(353\) | 0.464623 | − | 0.268250i | 0.0247294 | − | 0.0142775i | −0.487584 | − | 0.873076i | \(-0.662122\pi\) |
0.512314 | + | 0.858798i | \(0.328789\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.263304 | + | 2.50517i | 0.0139748 | + | 0.132961i | ||||
\(356\) | −9.45151 | − | 21.2284i | −0.500929 | − | 1.12510i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.8379 | − | 19.6629i | −1.15417 | − | 1.03922i | ||||
\(359\) | 12.7871 | + | 9.29040i | 0.674880 | + | 0.490329i | 0.871655 | − | 0.490120i | \(-0.163047\pi\) |
−0.196775 | + | 0.980449i | \(0.563047\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.09760 | − | 12.6111i | 0.215663 | − | 0.663742i | ||||
\(362\) | −21.1584 | − | 36.6474i | −1.11206 | − | 1.92614i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −33.2319 | + | 57.5594i | −1.74183 | + | 3.01693i | ||||
\(365\) | −20.0174 | − | 22.2315i | −1.04776 | − | 1.16365i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.02435 | + | 28.7747i | −0.157870 | + | 1.50203i | 0.573024 | + | 0.819538i | \(0.305770\pi\) |
−0.730894 | + | 0.682491i | \(0.760897\pi\) | |||||||
\(368\) | −4.24157 | + | 1.37817i | −0.221107 | + | 0.0718420i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −22.5739 | + | 31.0703i | −1.17356 | + | 1.61527i | ||||
\(371\) | −4.54830 | − | 2.02503i | −0.236136 | − | 0.105134i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.72386 | + | 3.30467i | 0.296370 | + | 0.171109i | 0.640811 | − | 0.767699i | \(-0.278598\pi\) |
−0.344441 | + | 0.938808i | \(0.611931\pi\) | |||||||
\(374\) | 0.294291 | − | 0.516920i | 0.0152174 | − | 0.0267293i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.63685 | − | 21.8147i | −0.239127 | − | 1.12501i | ||||
\(377\) | −5.02984 | − | 6.92297i | −0.259050 | − | 0.356551i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.478524 | + | 1.47275i | 0.0245801 | + | 0.0756498i | 0.962594 | − | 0.270948i | \(-0.0873370\pi\) |
−0.938014 | + | 0.346597i | \(0.887337\pi\) | |||||||
\(380\) | 12.7087 | − | 14.1144i | 0.651940 | − | 0.724053i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −50.6323 | + | 5.32167i | −2.59057 | + | 0.272280i | ||||
\(383\) | −10.0383 | + | 9.03850i | −0.512932 | + | 0.461846i | −0.884487 | − | 0.466565i | \(-0.845491\pi\) |
0.371555 | + | 0.928411i | \(0.378825\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −29.5071 | + | 6.45866i | −1.50382 | + | 0.329164i | ||||
\(386\) | − | 12.1934i | − | 0.620629i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −46.9133 | + | 34.0845i | −2.38166 | + | 1.73038i | ||||
\(389\) | −14.8974 | − | 1.56578i | −0.755329 | − | 0.0793882i | −0.280966 | − | 0.959718i | \(-0.590655\pi\) |
−0.474363 | + | 0.880330i | \(0.657321\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0511890 | − | 0.240825i | 0.00258874 | − | 0.0121791i | ||||
\(392\) | 30.8474 | − | 13.7341i | 1.55803 | − | 0.693678i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.8347 | − | 2.51554i | 0.596222 | − | 0.126731i | ||||
\(395\) | −1.48346 | −0.0746409 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.7132 | −1.03956 | −0.519782 | − | 0.854299i | \(-0.673987\pi\) | ||||
−0.519782 | + | 0.854299i | \(0.673987\pi\) | |||||||
\(398\) | 55.7829 | − | 11.8570i | 2.79615 | − | 0.594339i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.0683251 | + | 0.0304203i | −0.00341626 | + | 0.00152101i | ||||
\(401\) | −5.62292 | + | 26.4538i | −0.280795 | + | 1.32104i | 0.581050 | + | 0.813868i | \(0.302642\pi\) |
−0.861845 | + | 0.507171i | \(0.830691\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.74939 | − | 0.814494i | −0.386025 | − | 0.0405728i | ||||
\(404\) | 4.91223 | − | 3.56894i | 0.244392 | − | 0.177561i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.5154i | 0.869273i | ||||||||
\(407\) | −2.37432 | + | 23.9844i | −0.117691 | + | 1.18886i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.53727 | − | 4.08538i | 0.224354 | − | 0.202009i | −0.549287 | − | 0.835634i | \(-0.685100\pi\) |
0.773640 | + | 0.633625i | \(0.218434\pi\) | |||||||
\(410\) | 44.3714 | − | 4.66362i | 2.19135 | − | 0.230320i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.62330 | + | 8.46653i | −0.375573 | + | 0.417116i | ||||
\(413\) | 0.726437 | + | 2.23574i | 0.0357456 | + | 0.110014i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.4932 | − | 18.5718i | −0.662357 | − | 0.911656i | ||||
\(416\) | −3.79887 | − | 17.8723i | −0.186255 | − | 0.876260i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.77313 | − | 18.2944i | 0.184550 | − | 0.894809i | ||||
\(419\) | 30.8841 | + | 17.8309i | 1.50879 | + | 0.871098i | 0.999948 | + | 0.0102354i | \(0.00325810\pi\) |
0.508838 | + | 0.860862i | \(0.330075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0707 | + | 5.81944i | 0.637026 | + | 0.283622i | 0.699727 | − | 0.714410i | \(-0.253305\pi\) |
−0.0627012 | + | 0.998032i | \(0.519972\pi\) | |||||||
\(422\) | 25.8993 | − | 35.6473i | 1.26076 | − | 1.73528i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.19370 | + | 1.36262i | −0.203664 | + | 0.0661745i | ||||
\(425\) | 0.000431581 | − | 0.00410622i | 2.09348e−5 | − | 0.000199181i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.2524 | + | 11.3865i | 0.496150 | + | 0.551031i | ||||
\(428\) | −26.1268 | + | 45.2530i | −1.26289 | + | 2.18738i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.3120 | − | 19.5930i | −0.545513 | − | 0.944856i | ||||
\(431\) | 2.68944 | − | 8.27725i | 0.129546 | − | 0.398701i | −0.865156 | − | 0.501503i | \(-0.832781\pi\) |
0.994702 | + | 0.102802i | \(0.0327807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.3812 | + | 22.0733i | 1.46003 | + | 1.06077i | 0.983355 | + | 0.181693i | \(0.0581576\pi\) |
0.476673 | + | 0.879080i | \(0.341842\pi\) | |||||||
\(434\) | 11.8525 | + | 10.6721i | 0.568939 | + | 0.512275i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.4074 | + | 48.0818i | 1.02523 | + | 2.30270i | ||||
\(437\) | −0.808182 | − | 7.68934i | −0.0386606 | − | 0.367831i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.1171 | + | 16.2334i | −1.34196 | + | 0.774779i | −0.987094 | − | 0.160139i | \(-0.948806\pi\) |
−0.354863 | + | 0.934918i | \(0.615472\pi\) | |||||||
\(440\) | −15.5935 | + | 21.7378i | −0.743390 | + | 1.03631i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.793595 | − | 0.257855i | −0.0377474 | − | 0.0122649i | ||||
\(443\) | −7.65538 | + | 17.1943i | −0.363718 | + | 0.816924i | 0.635285 | + | 0.772278i | \(0.280883\pi\) |
−0.999003 | + | 0.0446461i | \(0.985784\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.4911 | − | 3.08018i | −0.686944 | − | 0.146014i | ||||
\(446\) | −12.6206 | − | 2.68260i | −0.597604 | − | 0.127025i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19.7657 | + | 44.3945i | −0.933842 | + | 2.09744i | ||||
\(449\) | −6.86840 | − | 2.23168i | −0.324140 | − | 0.105319i | 0.142427 | − | 0.989805i | \(-0.454509\pi\) |
−0.466567 | + | 0.884486i | \(0.654509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.5520 | − | 16.5942i | 1.06193 | − | 0.781392i | ||||
\(452\) | 34.3450 | − | 19.8291i | 1.61545 | − | 0.932681i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.38212 | − | 32.1787i | −0.158731 | − | 1.51022i | ||||
\(455\) | 17.2349 | + | 38.7101i | 0.807983 | + | 1.81476i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.13770 | − | 2.82520i | −0.146775 | − | 0.132157i | 0.592472 | − | 0.805591i | \(-0.298152\pi\) |
−0.739248 | + | 0.673434i | \(0.764819\pi\) | |||||||
\(458\) | −40.1908 | − | 29.2004i | −1.87799 | − | 1.36444i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.90572 | + | 24.3313i | −0.368606 | + | 1.13445i | ||||
\(461\) | −7.09611 | − | 12.2908i | −0.330499 | − | 0.572441i | 0.652111 | − | 0.758123i | \(-0.273884\pi\) |
−0.982610 | + | 0.185683i | \(0.940550\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.1892 | − | 34.9687i | 0.938271 | − | 1.62513i | 0.169576 | − | 0.985517i | \(-0.445760\pi\) |
0.768695 | − | 0.639616i | \(-0.220906\pi\) | |||||||
\(464\) | 1.70076 | + | 1.88888i | 0.0789556 | + | 0.0876891i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.67740 | − | 34.9881i | 0.170352 | − | 1.62079i | ||||
\(467\) | −10.7476 | + | 3.49210i | −0.497338 | + | 0.161595i | −0.546936 | − | 0.837174i | \(-0.684206\pi\) |
0.0495980 | + | 0.998769i | \(0.484206\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.9513 | + | 42.6008i | −1.42920 | + | 1.96712i | ||||
\(470\) | −30.0103 | − | 13.3614i | −1.38427 | − | 0.616317i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.80309 | + | 1.04102i | 0.0829942 | + | 0.0479167i | ||||
\(473\) | −12.3385 | − | 7.02453i | −0.567326 | − | 0.322988i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0269578 | − | 0.126826i | −0.00123691 | − | 0.00581919i | ||||
\(476\) | 0.640587 | + | 0.881692i | 0.0293612 | + | 0.0404123i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.92639 | − | 12.0842i | −0.179589 | − | 0.552718i | ||||
\(479\) | 15.3220 | − | 17.0168i | 0.700079 | − | 0.777516i | −0.283310 | − | 0.959028i | \(-0.591433\pi\) |
0.983389 | + | 0.181512i | \(0.0580992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.6253 | − | 3.53416i | 1.53318 | − | 0.161144i | ||||
\(482\) | 20.4557 | − | 18.4184i | 0.931731 | − | 0.838935i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.58773 | + | 38.6225i | −0.163079 | + | 1.75557i | ||||
\(485\) | 36.9698i | 1.67871i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.10169 | − | 4.43314i | 0.276494 | − | 0.200885i | −0.440893 | − | 0.897560i | \(-0.645338\pi\) |
0.717387 | + | 0.696675i | \(0.245338\pi\) | |||||||
\(488\) | 13.4959 | + | 1.41848i | 0.610932 | + | 0.0642116i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.3410 | − | 48.6505i | 0.467158 | − | 2.19781i | ||||
\(491\) | −34.8885 | + | 15.5333i | −1.57449 | + | 0.701010i | −0.993599 | − | 0.112967i | \(-0.963964\pi\) |
−0.580896 | + | 0.813978i | \(0.697298\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.137250 | + | 0.0291735i | −0.00618144 | + | 0.00131391i | ||||
\(494\) | −26.2041 | −1.17898 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.31446 | 0.103922 | ||||||||
\(497\) | −4.43992 | + | 0.943735i | −0.199158 | + | 0.0423323i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.36234 | + | 3.27793i | −0.329584 | + | 0.146740i | −0.564856 | − | 0.825189i | \(-0.691068\pi\) |
0.235273 | + | 0.971929i | \(0.424402\pi\) | |||||||
\(500\) | 8.15190 | − | 38.3517i | 0.364564 | − | 1.71514i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −52.8325 | − | 5.55292i | −2.35803 | − | 0.247839i | ||||
\(503\) | −21.0846 | + | 15.3188i | −0.940115 | + | 0.683033i | −0.948448 | − | 0.316932i | \(-0.897347\pi\) |
0.00833362 | + | 0.999965i | \(0.497347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.87106i | − | 0.172260i | ||||||
\(506\) | 5.38006 | + | 24.5795i | 0.239173 | + | 1.09269i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.8842 | + | 14.3022i | −0.704748 | + | 0.634558i | ||||
\(509\) | −27.8101 | + | 2.92296i | −1.23266 | + | 0.129558i | −0.698367 | − | 0.715740i | \(-0.746089\pi\) |
−0.534295 | + | 0.845298i | \(0.679423\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.0707 | − | 40.0605i | 1.59567 | − | 1.77217i | ||||
\(512\) | 4.74153 | + | 14.5929i | 0.209548 | + | 0.644922i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −38.0212 | − | 52.3316i | −1.67704 | − | 2.30825i | ||||
\(515\) | 1.51015 | + | 7.10470i | 0.0665452 | + | 0.313070i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.4894 | + | 2.27886i | −0.901121 | + | 0.100224i | ||||
\(518\) | −59.9330 | − | 34.6024i | −2.63331 | − | 1.52034i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 34.2844 | + | 15.2644i | 1.50347 | + | 0.669389i | ||||
\(521\) | −18.9804 | + | 26.1242i | −0.831545 | + | 1.14452i | 0.156088 | + | 0.987743i | \(0.450112\pi\) |
−0.987633 | + | 0.156781i | \(0.949888\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.5104 | − | 5.36454i | 0.721948 | − | 0.234575i | 0.0750804 | − | 0.997177i | \(-0.476079\pi\) |
0.646868 | + | 0.762602i | \(0.276079\pi\) | |||||||
\(524\) | −2.63575 | + | 25.0775i | −0.115143 | + | 1.09552i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 50.3965 | + | 55.9710i | 2.19739 | + | 2.44045i | ||||
\(527\) | −0.0638847 | + | 0.110652i | −0.00278286 | + | 0.00482006i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.29267 | − | 10.8992i | −0.273594 | − | 0.473879i | ||||
\(530\) | −2.00710 | + | 6.17722i | −0.0871828 | + | 0.268321i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 27.6881 | + | 20.1166i | 1.20043 | + | 0.872166i | ||||
\(533\) | −29.1894 | − | 26.2823i | −1.26433 | − | 1.13841i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.5500 | + | 30.4338i | 0.585817 | + | 1.31577i | ||||
\(536\) | 4.87491 | + | 46.3817i | 0.210564 | + | 2.00338i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 55.0519 | − | 31.7842i | 2.37345 | − | 1.37031i | ||||
\(539\) | −9.82480 | − | 29.6269i | −0.423184 | − | 1.27612i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.58312 | − | 3.11375i | −0.412011 | − | 0.133870i | 0.0956753 | − | 0.995413i | \(-0.469499\pi\) |
−0.507686 | + | 0.861542i | \(0.669499\pi\) | |||||||
\(542\) | 14.2287 | − | 31.9581i | 0.611174 | − | 1.37272i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.293058 | − | 0.0622914i | −0.0125648 | − | 0.00267072i | ||||
\(545\) | 32.8219 | + | 6.97652i | 1.40594 | + | 0.298841i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.70462 | − | 21.7969i | 0.414939 | − | 0.931969i | −0.578293 | − | 0.815829i | \(-0.696281\pi\) |
0.993233 | − | 0.116140i | \(-0.0370522\pi\) | |||||||
\(548\) | 35.6242 | + | 11.5750i | 1.52179 | + | 0.494460i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.132815 | + | 0.400506i | 0.00566325 | + | 0.0170776i | ||||
\(551\) | −3.81607 | + | 2.20321i | −0.162570 | + | 0.0938599i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.279420 | − | 2.65850i | −0.0118821 | − | 0.113051i | ||||
\(554\) | 7.53436 | + | 16.9225i | 0.320104 | + | 0.718966i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.139088 | − | 0.125235i | −0.00589863 | − | 0.00531115i | ||||
\(557\) | −31.6776 | − | 23.0151i | −1.34222 | − | 0.975181i | −0.999359 | − | 0.0357950i | \(-0.988604\pi\) |
−0.342862 | − | 0.939386i | \(-0.611396\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.15482 | + | 18.9426i | −0.260321 | + | 0.801185i | ||||
\(560\) | −6.29304 | − | 10.8999i | −0.265929 | − | 0.460603i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.9534 | + | 43.2205i | −1.05259 | + | 1.82315i | ||||
\(563\) | 3.35948 | + | 3.73108i | 0.141585 | + | 0.157246i | 0.809767 | − | 0.586752i | \(-0.199594\pi\) |
−0.668181 | + | 0.743998i | \(0.732927\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.64287 | − | 25.1452i | 0.111186 | − | 1.05787i | ||||
\(566\) | 9.60276 | − | 3.12012i | 0.403634 | − | 0.131149i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.36299 | + | 3.25238i | −0.0991489 | + | 0.136467i | ||||
\(569\) | −8.68706 | − | 3.86773i | −0.364181 | − | 0.162144i | 0.216485 | − | 0.976286i | \(-0.430541\pi\) |
−0.580665 | + | 0.814142i | \(0.697208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.4930 | − | 19.9146i | −1.44349 | − | 0.833398i | −0.445408 | − | 0.895328i | \(-0.646941\pi\) |
−0.998081 | + | 0.0619297i | \(0.980275\pi\) | |||||||
\(572\) | 54.0807 | − | 6.01494i | 2.26123 | − | 0.251497i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16.7153 | + | 78.6395i | 0.697685 | + | 3.28235i | ||||
\(575\) | 0.102658 | + | 0.141297i | 0.00428115 | + | 0.00589249i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.03506 | − | 12.4186i | −0.167982 | − | 0.516994i | 0.831262 | − | 0.555881i | \(-0.187619\pi\) |
−0.999244 | + | 0.0388866i | \(0.987619\pi\) | |||||||
\(578\) | 26.7317 | − | 29.6886i | 1.11189 | − | 1.23488i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14.5005 | − | 1.52407i | 0.602102 | − | 0.0632835i | ||||
\(581\) | 30.7410 | − | 27.6793i | 1.27535 | − | 1.14833i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.871561 | + | 3.98183i | 0.0360964 | + | 0.164911i | ||||
\(584\) | − | 47.7437i | − | 1.97565i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.3166 | − | 26.3855i | 1.50022 | − | 1.08998i | ||||
\(587\) | 23.6214 | + | 2.48270i | 0.974958 | + | 0.102472i | 0.578589 | − | 0.815619i | \(-0.303604\pi\) |
0.396369 | + | 0.918091i | \(0.370270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.834224 | + | 3.92472i | −0.0343736 | + | 0.161715i | ||||
\(590\) | 2.80165 | − | 1.24737i | 0.115342 | − | 0.0513536i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.82317 | + | 2.08798i | −0.403730 | + | 0.0858154i | ||||
\(593\) | 37.1489 | 1.52552 | 0.762761 | − | 0.646680i | \(-0.223843\pi\) | ||||
0.762761 | + | 0.646680i | \(0.223843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.694814 | 0.0284846 | ||||||||
\(596\) | −70.3462 | + | 14.9525i | −2.88149 | + | 0.612480i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 32.2455 | − | 14.3566i | 1.31862 | − | 0.587087i | ||||
\(599\) | −0.496033 | + | 2.33365i | −0.0202673 | + | 0.0953503i | −0.987119 | − | 0.159989i | \(-0.948854\pi\) |
0.966851 | + | 0.255340i | \(0.0821873\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.75664 | − | 0.710152i | −0.275609 | − | 0.0289677i | −0.0342844 | − | 0.999412i | \(-0.510915\pi\) |
−0.241325 | + | 0.970444i | \(0.577582\pi\) | |||||||
\(602\) | 32.9818 | − | 23.9627i | 1.34424 | − | 0.976646i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 4.19334i | − | 0.170624i | ||||||
\(605\) | 18.5764 | + | 16.3238i | 0.755237 | + | 0.663658i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.0946 | − | 27.0973i | 1.22150 | − | 1.09985i | 0.229544 | − | 0.973298i | \(-0.426277\pi\) |
0.991960 | − | 0.126549i | \(-0.0403900\pi\) | |||||||
\(608\) | −9.35708 | + | 0.983468i | −0.379480 | + | 0.0398849i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.3750 | − | 14.8545i | 0.541540 | − | 0.601441i | ||||
\(611\) | 8.93688 | + | 27.5049i | 0.361547 | + | 1.11273i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.119072 | + | 0.163888i | 0.00480926 | + | 0.00661938i | 0.811415 | − | 0.584471i | \(-0.198698\pi\) |
−0.806606 | + | 0.591090i | \(0.798698\pi\) | |||||||
\(614\) | 0.910262 | + | 4.28245i | 0.0367352 | + | 0.172825i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −41.8934 | − | 23.8506i | −1.68793 | − | 0.960967i | ||||
\(617\) | 7.00117 | + | 4.04213i | 0.281857 | + | 0.162730i | 0.634264 | − | 0.773117i | \(-0.281303\pi\) |
−0.352407 | + | 0.935847i | \(0.614637\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.1722 | + | 8.53602i | 0.770597 | + | 0.343092i | 0.754089 | − | 0.656772i | \(-0.228079\pi\) |
0.0165075 | + | 0.999864i | \(0.494745\pi\) | |||||||
\(620\) | 7.80381 | − | 10.7410i | 0.313409 | − | 0.431370i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.0202 | − | 6.50496i | 0.802737 | − | 0.260825i | ||||
\(623\) | 2.79048 | − | 26.5496i | 0.111798 | − | 1.06369i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.9074 | − | 18.7775i | −0.676295 | − | 0.751101i | ||||
\(626\) | 20.1427 | − | 34.8881i | 0.805062 | − | 1.39441i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.05565 | + | 5.29255i | 0.121934 | + | 0.211196i | ||||
\(629\) | 0.171320 | − | 0.527268i | 0.00683097 | − | 0.0210236i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.6268 | + | 14.2597i | 0.781332 | + | 0.567671i | 0.905378 | − | 0.424606i | \(-0.139587\pi\) |
−0.124047 | + | 0.992276i | \(0.539587\pi\) | |||||||
\(632\) | −1.75942 | − | 1.58419i | −0.0699859 | − | 0.0630156i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −26.1071 | − | 58.6374i | −1.03684 | − | 2.32879i | ||||
\(635\) | 1.42441 | + | 13.5524i | 0.0565261 | + | 0.537810i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.9208 | + | 21.8936i | −1.50248 | + | 0.867455i | ||||
\(638\) | 11.5500 | − | 8.49876i | 0.457270 | − | 0.336469i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 43.5007 | + | 14.1342i | 1.71952 | + | 0.558705i | ||||
\(641\) | −6.56437 | + | 14.7438i | −0.259277 | + | 0.582346i | −0.995539 | − | 0.0943509i | \(-0.969922\pi\) |
0.736262 | + | 0.676697i | \(0.236589\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.3090 | − | 2.61635i | −0.485419 | − | 0.103179i | −0.0412999 | − | 0.999147i | \(-0.513150\pi\) |
−0.444119 | + | 0.895968i | \(0.646483\pi\) | |||||||
\(644\) | −45.0932 | − | 9.58485i | −1.77692 | − | 0.377696i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.174766 | + | 0.392530i | −0.00687607 | + | 0.0154439i | ||||
\(647\) | 28.7701 | + | 9.34797i | 1.13107 | + | 0.367507i | 0.813982 | − | 0.580890i | \(-0.197295\pi\) |
0.317087 | + | 0.948396i | \(0.397295\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.12182 | − | 1.56385i | 0.0440352 | − | 0.0613865i | ||||
\(650\) | 0.512626 | − | 0.295965i | 0.0201068 | − | 0.0116087i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.369553 | + | 3.51607i | 0.0144728 | + | 0.137700i | ||||
\(653\) | −7.96901 | − | 17.8987i | −0.311851 | − | 0.700430i | 0.687825 | − | 0.725877i | \(-0.258566\pi\) |
−0.999676 | + | 0.0254470i | \(0.991899\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.9468 | + | 10.7570i | 0.466801 | + | 0.420310i | ||||
\(656\) | 9.43855 | + | 6.85751i | 0.368514 | + | 0.267741i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.2924 | − | 56.2981i | 0.713111 | − | 2.19473i | ||||
\(659\) | −0.674716 | − | 1.16864i | −0.0262832 | − | 0.0455238i | 0.852585 | − | 0.522589i | \(-0.175034\pi\) |
−0.878868 | + | 0.477065i | \(0.841700\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.3929 | + | 24.9293i | −0.559821 | + | 0.969638i | 0.437690 | + | 0.899126i | \(0.355797\pi\) |
−0.997511 | + | 0.0705120i | \(0.977537\pi\) | |||||||
\(662\) | 9.23687 | + | 10.2586i | 0.359001 | + | 0.398711i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.82959 | − | 36.4361i | 0.148617 | − | 1.41399i | ||||
\(665\) | 20.7516 | − | 6.74260i | 0.804712 | − | 0.261467i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.48879 | − | 4.80191i | 0.135086 | − | 0.185931i | ||||
\(668\) | 43.5473 | + | 19.3885i | 1.68490 | + | 0.750164i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 59.4920 | + | 34.3477i | 2.29838 | + | 1.32697i | ||||
\(671\) | 2.53384 | − | 12.2856i | 0.0978179 | − | 0.474281i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.52227 | − | 21.2756i | −0.174321 | − | 0.820114i | −0.975206 | − | 0.221297i | \(-0.928971\pi\) |
0.800886 | − | 0.598817i | \(-0.204362\pi\) | |||||||
\(674\) | −22.8969 | − | 31.5149i | −0.881955 | − | 1.21391i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.42270 | − | 29.0001i | −0.362411 | − | 1.11539i | ||||
\(677\) | −12.6502 | + | 14.0494i | −0.486185 | + | 0.539963i | −0.935461 | − | 0.353430i | \(-0.885015\pi\) |
0.449276 | + | 0.893393i | \(0.351682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −66.2536 | + | 6.96353i | −2.54258 | + | 0.267236i | ||||
\(680\) | 0.457314 | − | 0.411767i | 0.0175372 | − | 0.0157905i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.28634 | − | 12.9941i | 0.0492567 | − | 0.497569i | ||||
\(683\) | 33.7466i | 1.29128i | 0.763642 | + | 0.645640i | \(0.223409\pi\) | ||||
−0.763642 | + | 0.645640i | \(0.776591\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.3199 | − | 14.0367i | 0.738176 | − | 0.536316i | ||||
\(686\) | 22.8367 | + | 2.40024i | 0.871910 | + | 0.0916414i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.23001 | − | 5.78672i | 0.0468936 | − | 0.220617i | ||||
\(689\) | 5.22372 | − | 2.32575i | 0.199008 | − | 0.0886041i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.9313 | − | 5.72442i | 1.02451 | − | 0.217767i | 0.335136 | − | 0.942170i | \(-0.391218\pi\) |
0.689377 | + | 0.724403i | \(0.257884\pi\) | |||||||
\(692\) | −26.5278 | −1.00844 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.91971 | 0.224709 | ||||||||
\(695\) | −0.116716 | + | 0.0248087i | −0.00442727 | + | 0.000941046i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.588377 | + | 0.261963i | −0.0222864 | + | 0.00992254i | ||||
\(698\) | 4.26659 | − | 20.0727i | 0.161493 | − | 0.759765i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.768867 | − | 0.0808112i | −0.0290604 | − | 0.00305437i | ||||
\(701\) | −8.43699 | + | 6.12983i | −0.318661 | + | 0.231521i | −0.735604 | − | 0.677412i | \(-0.763101\pi\) |
0.416943 | + | 0.908933i | \(0.363101\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 17.4101i | − | 0.656636i | ||||||
\(704\) | 38.8654 | − | 8.50704i | 1.46479 | − | 0.320621i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.937258 | − | 0.843911i | 0.0352742 | − | 0.0317610i | ||||
\(707\) | 6.93732 | − | 0.729141i | 0.260905 | − | 0.0274222i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.4139 | + | 14.8976i | −0.503768 | + | 0.559491i | −0.940365 | − | 0.340166i | \(-0.889517\pi\) |
0.436598 | + | 0.899657i | \(0.356183\pi\) | |||||||
\(710\) | 1.82988 | + | 5.63178i | 0.0686740 | + | 0.211357i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.8975 | − | 19.1282i | −0.520829 | − | 0.716860i | ||||
\(713\) | −1.12371 | − | 5.28663i | −0.0420832 | − | 0.197986i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.1637 | − | 30.1479i | 0.641885 | − | 1.12747i | ||||
\(716\) | −38.1738 | − | 22.0397i | −1.42662 | − | 0.823660i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 33.9439 | + | 15.1128i | 1.26677 | + | 0.564004i | ||||
\(719\) | −6.01752 | + | 8.28241i | −0.224416 | + | 0.308882i | −0.906347 | − | 0.422535i | \(-0.861140\pi\) |
0.681931 | + | 0.731417i | \(0.261140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.4479 | + | 4.04456i | −0.463583 | + | 0.150627i | ||||
\(722\) | 3.25834 | − | 31.0011i | 0.121263 | − | 1.15374i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −42.4738 | − | 47.1719i | −1.57853 | − | 1.75313i | ||||
\(725\) | 0.0497687 | − | 0.0862019i | 0.00184836 | − | 0.00320146i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.22282 | + | 12.5103i | 0.267880 | + | 0.463981i | 0.968314 | − | 0.249736i | \(-0.0803437\pi\) |
−0.700434 | + | 0.713717i | \(0.747010\pi\) | |||||||
\(728\) | −20.8976 | + | 64.3163i | −0.774517 | + | 2.38372i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −56.8943 | − | 41.3361i | −2.10575 | − | 1.52992i | ||||
\(731\) | 0.242706 | + | 0.218533i | 0.00897679 | + | 0.00808274i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.97291 | + | 6.67726i | 0.109807 | + | 0.246630i | 0.960088 | − | 0.279699i | \(-0.0902347\pi\) |
−0.850281 | + | 0.526329i | \(0.823568\pi\) | |||||||
\(734\) | 7.10963 | + | 67.6436i | 0.262421 | + | 2.49677i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.9756 | − | 6.33674i | 0.404565 | − | 0.233575i | ||||
\(737\) | 43.1100 | − | 0.260675i | 1.58798 | − | 0.00960207i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.4909 | − | 4.05854i | −0.459485 | − | 0.149296i | 0.0701229 | − | 0.997538i | \(-0.477661\pi\) |
−0.529608 | + | 0.848243i | \(0.677661\pi\) | |||||||
\(740\) | −23.4315 | + | 52.6280i | −0.861358 | + | 1.93464i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.4482 | − | 2.43340i | −0.420278 | − | 0.0893328i | ||||
\(743\) | 34.5995 | + | 7.35434i | 1.26933 | + | 0.269805i | 0.792870 | − | 0.609391i | \(-0.208586\pi\) |
0.476461 | + | 0.879196i | \(0.341919\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.6491 | + | 41.8866i | −0.683251 | + | 1.53461i | ||||
\(746\) | 14.7768 | + | 4.80127i | 0.541017 | + | 0.175787i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.270584 | − | 0.850230i | 0.00989352 | − | 0.0310875i | ||||
\(749\) | −51.9880 | + | 30.0153i | −1.89960 | + | 1.09674i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.41132 | + | 22.9422i | 0.0879905 | + | 0.837174i | 0.946137 | + | 0.323768i | \(0.104950\pi\) |
−0.858146 | + | 0.513406i | \(0.828384\pi\) | |||||||
\(752\) | −3.49392 | − | 7.84746i | −0.127410 | − | 0.286168i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −14.9494 | − | 13.4605i | −0.544425 | − | 0.490203i | ||||
\(755\) | −2.16285 | − | 1.57140i | −0.0787141 | − | 0.0571892i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.02640 | − | 9.31430i | 0.109996 | − | 0.338534i | −0.880874 | − | 0.473350i | \(-0.843044\pi\) |
0.990871 | + | 0.134816i | \(0.0430445\pi\) | |||||||
\(758\) | 1.82015 | + | 3.15259i | 0.0661108 | + | 0.114507i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.66246 | − | 16.7359i | 0.350494 | − | 0.607074i | ||||
\(761\) | −32.4027 | − | 35.9869i | −1.17460 | − | 1.30452i | −0.943415 | − | 0.331614i | \(-0.892407\pi\) |
−0.231183 | − | 0.972910i | \(-0.574260\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.32036 | + | 60.1342i | −0.228812 | + | 2.17701i | ||||
\(764\) | −72.6303 | + | 23.5990i | −2.62767 | + | 0.853783i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.6646 | + | 25.6897i | −0.674381 | + | 0.928205i | ||||
\(767\) | −2.46648 | − | 1.09815i | −0.0890593 | − | 0.0396518i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.9445 | + | 16.7111i | 1.04377 | + | 0.602619i | 0.920898 | − | 0.389804i | \(-0.127457\pi\) |
0.122869 | + | 0.992423i | \(0.460791\pi\) | |||||||
\(770\) | −64.6928 | + | 29.2731i | −2.33137 | + | 1.05493i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.80279 | − | 17.8907i | −0.136866 | − | 0.643902i | ||||
\(773\) | 3.82924 | + | 5.27050i | 0.137728 | + | 0.189567i | 0.872310 | − | 0.488954i | \(-0.162621\pi\) |
−0.734581 | + | 0.678521i | \(0.762621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.0280083 | − | 0.0862007i | −0.00100609 | − | 0.00309642i | ||||
\(776\) | −39.4801 | + | 43.8471i | −1.41725 | + | 1.57402i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.0208 | + | 3.68084i | −1.25556 | + | 0.131964i | ||||
\(779\) | −15.0306 | + | 13.5336i | −0.538527 | + | 0.484892i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.77665 | + | 2.46987i | 0.0993563 | + | 0.0883788i | ||||
\(782\) | − | 0.578780i | − | 0.0206971i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.5220 | − | 7.64471i | 0.375787 | − | 0.273025i | ||||
\(785\) | 3.87487 | + | 0.407266i | 0.138300 | + | 0.0145359i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.02818 | + | 28.3604i | −0.214881 | + | 1.01094i | 0.729980 | + | 0.683468i | \(0.239529\pi\) |
−0.944862 | + | 0.327470i | \(0.893804\pi\) | |||||||
\(788\) | 16.5798 | − | 7.38182i | 0.590632 | − | 0.262966i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.41111 | + | 0.725053i | −0.121362 | + | 0.0257962i | ||||
\(791\) | 45.5606 | 1.61995 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.5974 | −0.624901 | ||||||||
\(794\) | −47.6285 | + | 10.1237i | −1.69027 | + | 0.359278i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 78.1494 | − | 34.7943i | 2.76993 | − | 1.23325i | ||||
\(797\) | 5.62407 | − | 26.4592i | 0.199215 | − | 0.937232i | −0.758980 | − | 0.651114i | \(-0.774302\pi\) |
0.958194 | − | 0.286118i | \(-0.0923648\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.471619 | + | 0.0495692i | 0.0166847 | + | 0.00175363i | ||||
\(800\) | 0.171943 | − | 0.124924i | 0.00607910 | − | 0.00441672i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 63.5768i | 2.24498i | ||||||||
\(803\) | −43.9189 | − | 4.34774i | −1.54987 | − | 0.153428i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.8418 | + | 19.6665i | −0.769823 | + | 0.693152i | ||||
\(806\) | −18.2173 | + | 1.91471i | −0.641676 | + | 0.0674428i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.13391 | − | 4.59117i | 0.145430 | − | 0.161517i | ||||
\(809\) | −12.9385 | − | 39.8205i | −0.454892 | − | 1.40001i | −0.871262 | − | 0.490818i | \(-0.836698\pi\) |
0.416370 | − | 0.909195i | \(-0.363302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.51871 | − | 10.3486i | −0.264018 | − | 0.363389i | 0.656341 | − | 0.754464i | \(-0.272103\pi\) |
−0.920359 | + | 0.391075i | \(0.872103\pi\) | |||||||
\(812\) | 5.46256 | + | 25.6993i | 0.191698 | + | 0.901870i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.26299 | + | 56.3108i | 0.219518 | + | 1.97369i | ||||
\(815\) | 1.95201 | + | 1.12699i | 0.0683760 | + | 0.0394769i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.36944 | + | 4.17154i | 0.327795 | + | 0.145944i | ||||
\(818\) | 8.43637 | − | 11.6117i | 0.294971 | − | 0.405992i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 63.6493 | − | 20.6809i | 2.22273 | − | 0.722208i | ||||
\(821\) | −1.23995 | + | 11.7973i | −0.0432746 | + | 0.411730i | 0.951344 | + | 0.308130i | \(0.0997030\pi\) |
−0.994619 | + | 0.103601i | \(0.966964\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.5821 | + | 19.5269i | 0.612875 | + | 0.680666i | 0.967072 | − | 0.254505i | \(-0.0819124\pi\) |
−0.354197 | + | 0.935171i | \(0.615246\pi\) | |||||||
\(824\) | −5.79604 | + | 10.0390i | −0.201914 | + | 0.349726i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.76313 | + | 4.78588i | 0.0961415 | + | 0.166522i | ||||
\(827\) | −7.99992 | + | 24.6212i | −0.278184 | + | 0.856163i | 0.710175 | + | 0.704025i | \(0.248616\pi\) |
−0.988359 | + | 0.152138i | \(0.951384\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0195 | − | 10.1858i | −0.486918 | − | 0.353766i | 0.317080 | − | 0.948399i | \(-0.397298\pi\) |
−0.803998 | + | 0.594632i | \(0.797298\pi\) | |||||||
\(830\) | −40.1039 | − | 36.1097i | −1.39203 | − | 1.25339i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.7009 | − | 50.9871i | −0.787013 | − | 1.76766i | ||||
\(833\) | 0.0750507 | + | 0.714060i | 0.00260035 | + | 0.0247407i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.3191 | − | 15.1953i | 0.910809 | − | 0.525856i | ||||
\(836\) | −0.169424 | − | 28.0191i | −0.00585965 | − | 0.969061i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 79.7307 | + | 25.9061i | 2.75425 | + | 0.894911i | ||||
\(839\) | −12.6296 | + | 28.3664i | −0.436021 | + | 0.979318i | 0.553222 | + | 0.833034i | \(0.313398\pi\) |
−0.989243 | + | 0.146284i | \(0.953269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0575 | + | 5.32613i | 0.864051 | + | 0.183660i | ||||
\(842\) | 32.8994 | + | 6.99298i | 1.13379 | + | 0.240994i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 26.8832 | − | 60.3806i | 0.925357 | − | 2.07839i | ||||
\(845\) | −18.4888 | − | 6.00737i | −0.636033 | − | 0.206660i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.7549 | + | 36.3654i | −0.884949 | + | 1.24953i | ||||
\(848\) | −1.47088 | + | 0.849211i | −0.0505101 | + | 0.0291620i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.00101456 | − | 0.00965290i | −3.47992e−5 | − | 0.000331092i | ||||
\(851\) | 9.53862 | + | 21.4241i | 0.326980 | + | 0.734409i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.237337 | − | 0.213699i | −0.00812626 | − | 0.00731692i | 0.665057 | − | 0.746792i | \(-0.268407\pi\) |
−0.673184 | + | 0.739475i | \(0.735074\pi\) | |||||||
\(854\) | 29.1400 | + | 21.1714i | 0.997150 | + | 0.724472i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.4296 | + | 50.5652i | −0.561553 | + | 1.72828i | ||||
\(857\) | 6.62378 | + | 11.4727i | 0.226264 | + | 0.391901i | 0.956698 | − | 0.291083i | \(-0.0940154\pi\) |
−0.730434 | + | 0.682983i | \(0.760682\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.29076 | − | 7.43181i | 0.146399 | − | 0.253570i | −0.783495 | − | 0.621398i | \(-0.786565\pi\) |
0.929894 | + | 0.367828i | \(0.119898\pi\) | |||||||
\(860\) | −22.7080 | − | 25.2198i | −0.774336 | − | 0.859987i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.13860 | − | 20.3474i | 0.0728410 | − | 0.693036i | ||||
\(863\) | −51.0889 | + | 16.5998i | −1.73909 | + | 0.565063i | −0.994712 | − | 0.102700i | \(-0.967252\pi\) |
−0.744374 | + | 0.667763i | \(0.767252\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.94098 | + | 13.6826i | −0.338004 | + | 0.465222i | ||||
\(866\) | 80.6480 | + | 35.9068i | 2.74053 | + | 1.22016i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.7189 | + | 11.9620i | 0.703245 | + | 0.406018i | ||||
\(869\) | −1.61750 | + | 1.47421i | −0.0548698 | + | 0.0500091i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.5739 | − | 59.1556i | −0.426050 | − | 2.00441i | ||||
\(872\) | 31.4774 | + | 43.3249i | 1.06596 | + | 1.46717i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.61659 | − | 17.2861i | −0.189984 | − | 0.584710i | ||||
\(875\) | 30.1403 | − | 33.4742i | 1.01893 | − | 1.13163i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.7743 | − | 4.60087i | 1.47815 | − | 0.155360i | 0.669134 | − | 0.743142i | \(-0.266665\pi\) |
0.809020 | + | 0.587782i | \(0.199999\pi\) | |||||||
\(878\) | −56.7191 | + | 51.0701i | −1.91418 | + | 1.72353i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.13412 | + | 9.43857i | −0.139361 | + | 0.318174i | ||||
\(881\) | 7.44194i | 0.250725i | 0.992111 | + | 0.125363i | \(0.0400095\pi\) | ||||
−0.992111 | + | 0.125363i | \(0.959991\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.59369 | − | 5.51714i | 0.255548 | − | 0.185667i | −0.452634 | − | 0.891696i | \(-0.649516\pi\) |
0.708182 | + | 0.706030i | \(0.249516\pi\) | |||||||
\(884\) | −1.24482 | − | 0.130835i | −0.0418677 | − | 0.00440047i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.19915 | + | 43.2786i | −0.309052 | + | 1.45397i | ||||
\(887\) | −22.0938 | + | 9.83681i | −0.741838 | + | 0.330288i | −0.742621 | − | 0.669712i | \(-0.766418\pi\) |
0.000782633 | 1.00000i | \(0.499751\pi\) | ||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.0189 | + | 5.10537i | −0.805568 | + | 0.171229i | ||||
\(890\) | −34.8267 | −1.16739 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.3542 | −0.648026 | ||||||||
\(893\) | 14.5666 | − | 3.09623i | 0.487453 | − | 0.103611i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.6728 | + | 11.4303i | −0.858148 | + | 0.382072i | ||||
\(896\) | −17.1363 | + | 80.6199i | −0.572483 | + | 2.69332i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.8842 | − | 1.77460i | −0.563431 | − | 0.0592190i | ||||
\(899\) | −2.49197 | + | 1.81052i | −0.0831119 | + | 0.0603843i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.0937613i | − | 0.00312364i | ||||||
\(902\) | 43.7461 | − | 49.1797i | 1.45658 | − | 1.63751i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29.9871 | − | 27.0005i | 0.997357 | − | 0.898024i | ||||
\(905\) | −40.2470 | + | 4.23013i | −1.33786 | + | 0.140614i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.9778 | + | 26.6300i | −0.796168 | + | 0.884234i | −0.995409 | − | 0.0957163i | \(-0.969486\pi\) |
0.199241 | + | 0.979951i | \(0.436152\pi\) | |||||||
\(908\) | −14.9980 | − | 46.1592i | −0.497728 | − | 1.53185i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 58.5502 | + | 80.5875i | 1.94092 | + | 2.67145i | ||||
\(911\) | 1.82117 | + | 8.56791i | 0.0603379 | + | 0.283868i | 0.997964 | − | 0.0637775i | \(-0.0203148\pi\) |
−0.937626 | + | 0.347645i | \(0.886981\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.1684 | − | 6.84082i | −1.09772 | − | 0.226398i | ||||
\(914\) | −8.59575 | − | 4.96276i | −0.284322 | − | 0.164154i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −68.0766 | − | 30.3097i | −2.24931 | − | 1.00146i | ||||
\(917\) | −17.0273 | + | 23.4360i | −0.562290 | + | 0.773926i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.4876 | + | 12.8303i | −1.30258 | + | 0.423233i | −0.876477 | − | 0.481443i | \(-0.840113\pi\) |
−0.426100 | + | 0.904676i | \(0.640113\pi\) | |||||||
\(920\) | −2.72096 | + | 25.8882i | −0.0897075 | + | 0.853510i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.3242 | − | 24.7936i | −0.735209 | − | 0.816533i | ||||
\(923\) | 2.60659 | − | 4.51474i | 0.0857969 | − | 0.148605i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.196640 | + | 0.340591i | 0.00646550 | + | 0.0111986i | ||||
\(926\) | 29.3323 | − | 90.2756i | 0.963920 | − | 2.96664i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.84339 | − | 4.24547i | −0.191819 | − | 0.139364i | ||||
\(929\) | 40.2699 | + | 36.2591i | 1.32121 | + | 1.18962i | 0.967093 | + | 0.254423i | \(0.0818855\pi\) |
0.354118 | + | 0.935201i | \(0.384781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.17087 | + | 20.5981i | 0.300563 | + | 0.675076i | ||||
\(932\) | −5.51618 | − | 52.4830i | −0.180689 | − | 1.71914i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23.0065 | + | 13.2828i | −0.752795 | + | 0.434626i | ||||
\(935\) | −0.337136 | − | 0.458176i | −0.0110255 | − | 0.0149839i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.5444 | − | 5.37559i | −0.540480 | − | 0.175613i | 0.0260393 | − | 0.999661i | \(-0.491710\pi\) |
−0.566520 | + | 0.824048i | \(0.691710\pi\) | |||||||
\(938\) | −50.3487 | + | 113.085i | −1.64394 | + | 3.69236i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −48.1995 | − | 10.2451i | −1.57209 | − | 0.334159i | ||||
\(941\) | −21.0404 | − | 4.47227i | −0.685896 | − | 0.145792i | −0.148234 | − | 0.988952i | \(-0.547359\pi\) |
−0.537662 | + | 0.843161i | \(0.680692\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.0812 | − | 24.8888i | 0.360853 | − | 0.810489i | ||||
\(944\) | 0.762692 | + | 0.247814i | 0.0248235 | + | 0.00806564i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.8049 | − | 10.1218i | −1.03407 | − | 0.329089i | ||||
\(947\) | −38.7882 | + | 22.3944i | −1.26045 | + | 0.727719i | −0.973161 | − | 0.230126i | \(-0.926086\pi\) |
−0.287286 | + | 0.957845i | \(0.592753\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.47156 | + | 61.5728i | 0.210076 | + | 1.99874i | ||||
\(950\) | −0.123975 | − | 0.278452i | −0.00402228 | − | 0.00903418i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.824065 | + | 0.741992i | 0.0267081 | + | 0.0240481i | ||||
\(953\) | −8.11741 | − | 5.89765i | −0.262949 | − | 0.191043i | 0.448497 | − | 0.893784i | \(-0.351959\pi\) |
−0.711446 | + | 0.702741i | \(0.751959\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0454 | + | 46.3049i | −0.486857 | + | 1.49839i | ||||
\(956\) | −9.52970 | − | 16.5059i | −0.308213 | − | 0.533840i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.9147 | − | 46.6176i | 0.869574 | − | 1.50615i | ||||
\(959\) | 28.7943 | + | 31.9793i | 0.929815 | + | 1.03266i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.94720 | − | 28.0407i | 0.0950710 | − | 0.904540i | ||||
\(962\) | 75.5916 | − | 24.5612i | 2.43717 | − | 0.791884i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.2693 | − | 33.4039i | 0.781662 | − | 1.07587i | ||||
\(965\) | −10.6528 | − | 4.74292i | −0.342925 | − | 0.152680i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.74268 | + | 2.16084i | 0.120356 | + | 0.0694878i | 0.558970 | − | 0.829188i | \(-0.311197\pi\) |
−0.438613 | + | 0.898676i | \(0.644530\pi\) | |||||||
\(968\) | 4.59980 | + | 39.1981i | 0.147843 | + | 1.25988i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18.0693 | + | 85.0095i | 0.580171 | + | 2.72949i | ||||
\(971\) | 33.7344 | + | 46.4314i | 1.08259 | + | 1.49005i | 0.856640 | + | 0.515914i | \(0.172548\pi\) |
0.225947 | + | 0.974140i | \(0.427452\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0664437 | − | 0.204493i | −0.00213009 | − | 0.00655574i | ||||
\(974\) | 11.8637 | − | 13.1759i | 0.380136 | − | 0.422184i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.19826 | − | 0.546359i | 0.166392 | − | 0.0174885i | ||||
\(977\) | −2.56397 | + | 2.30861i | −0.0820288 | + | 0.0738591i | −0.709125 | − | 0.705083i | \(-0.750910\pi\) |
0.627096 | + | 0.778942i | \(0.284243\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.8614 | + | 11.0422i | −0.602813 | + | 0.352912i | ||||
\(980\) | − | 74.6073i | − | 2.38324i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −72.6315 | + | 52.7699i | −2.31776 | + | 1.68395i | ||||
\(983\) | −1.02901 | − | 0.108153i | −0.0328203 | − | 0.00344955i | 0.0881041 | − | 0.996111i | \(-0.471919\pi\) |
−0.120924 | + | 0.992662i | \(0.538586\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.40568 | − | 11.3178i | 0.0766513 | − | 0.360616i | ||||
\(986\) | −0.301338 | + | 0.134165i | −0.00959657 | + | 0.00427267i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −38.4478 | + | 8.17234i | −1.22319 | + | 0.259997i | ||||
\(989\) | −13.8151 | −0.439294 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.78910 | 0.310961 | 0.155481 | − | 0.987839i | \(-0.450307\pi\) | ||||
0.155481 | + | 0.987839i | \(0.450307\pi\) | |||||||
\(992\) | −6.43324 | + | 1.36743i | −0.204255 | + | 0.0434158i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.74803 | + | 4.34010i | −0.309189 | + | 0.137660i | ||||
\(995\) | 11.3392 | − | 53.3468i | 0.359477 | − | 1.69121i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.5510 | + | 1.21406i | 0.365823 | + | 0.0384496i | 0.285657 | − | 0.958332i | \(-0.407788\pi\) |
0.0801664 | + | 0.996781i | \(0.474455\pi\) | |||||||
\(998\) | −15.3271 | + | 11.1358i | −0.485170 | + | 0.352496i | ||||
\(999\) | 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 | 891.2.u.c.134.4 | 32 | ||
3.2 | odd | 2 | inner | 891.2.u.c.134.1 | 32 | ||
9.2 | odd | 6 | inner | 891.2.u.c.431.4 | 32 | ||
9.4 | even | 3 | 99.2.j.a.35.1 | yes | 16 | ||
9.5 | odd | 6 | 99.2.j.a.35.4 | yes | 16 | ||
9.7 | even | 3 | inner | 891.2.u.c.431.1 | 32 | ||
11.6 | odd | 10 | inner | 891.2.u.c.215.4 | 32 | ||
33.17 | even | 10 | inner | 891.2.u.c.215.1 | 32 | ||
36.23 | even | 6 | 1584.2.cd.c.1025.4 | 16 | |||
36.31 | odd | 6 | 1584.2.cd.c.1025.1 | 16 | |||
99.4 | even | 15 | 1089.2.d.g.1088.4 | 16 | |||
99.40 | odd | 30 | 1089.2.d.g.1088.14 | 16 | |||
99.50 | even | 30 | 99.2.j.a.17.1 | ✓ | 16 | ||
99.59 | odd | 30 | 1089.2.d.g.1088.13 | 16 | |||
99.61 | odd | 30 | inner | 891.2.u.c.512.1 | 32 | ||
99.83 | even | 30 | inner | 891.2.u.c.512.4 | 32 | ||
99.94 | odd | 30 | 99.2.j.a.17.4 | yes | 16 | ||
99.95 | even | 30 | 1089.2.d.g.1088.3 | 16 | |||
396.347 | odd | 30 | 1584.2.cd.c.17.1 | 16 | |||
396.391 | even | 30 | 1584.2.cd.c.17.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.j.a.17.1 | ✓ | 16 | 99.50 | even | 30 | ||
99.2.j.a.17.4 | yes | 16 | 99.94 | odd | 30 | ||
99.2.j.a.35.1 | yes | 16 | 9.4 | even | 3 | ||
99.2.j.a.35.4 | yes | 16 | 9.5 | odd | 6 | ||
891.2.u.c.134.1 | 32 | 3.2 | odd | 2 | inner | ||
891.2.u.c.134.4 | 32 | 1.1 | even | 1 | trivial | ||
891.2.u.c.215.1 | 32 | 33.17 | even | 10 | inner | ||
891.2.u.c.215.4 | 32 | 11.6 | odd | 10 | inner | ||
891.2.u.c.431.1 | 32 | 9.7 | even | 3 | inner | ||
891.2.u.c.431.4 | 32 | 9.2 | odd | 6 | inner | ||
891.2.u.c.512.1 | 32 | 99.61 | odd | 30 | inner | ||
891.2.u.c.512.4 | 32 | 99.83 | even | 30 | inner | ||
1089.2.d.g.1088.3 | 16 | 99.95 | even | 30 | |||
1089.2.d.g.1088.4 | 16 | 99.4 | even | 15 | |||
1089.2.d.g.1088.13 | 16 | 99.59 | odd | 30 | |||
1089.2.d.g.1088.14 | 16 | 99.40 | odd | 30 | |||
1584.2.cd.c.17.1 | 16 | 396.347 | odd | 30 | |||
1584.2.cd.c.17.4 | 16 | 396.391 | even | 30 | |||
1584.2.cd.c.1025.1 | 16 | 36.31 | odd | 6 | |||
1584.2.cd.c.1025.4 | 16 | 36.23 | even | 6 |