Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(230,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.230");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.p (of order \(6\), degree \(2\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 230.3 | ||
Character | \(\chi\) | \(=\) | 429.230 |
Dual form | 429.2.p.b.263.3 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.23621 | + | 2.14118i | −0.874135 | + | 1.51405i | −0.0164538 | + | 0.999865i | \(0.505238\pi\) |
−0.857681 | + | 0.514182i | \(0.828096\pi\) | |||||||
\(3\) | −1.16044 | + | 1.28584i | −0.669980 | + | 0.742379i | ||||
\(4\) | −2.05645 | − | 3.56187i | −1.02822 | − | 1.78094i | ||||
\(5\) | 2.31580i | 1.03566i | 0.855484 | + | 0.517830i | \(0.173260\pi\) | ||||
−0.855484 | + | 0.517830i | \(0.826740\pi\) | |||||||
\(6\) | −1.31867 | − | 4.07429i | −0.538343 | − | 1.66332i | ||||
\(7\) | −3.20654 | + | 1.85129i | −1.21196 | + | 0.699723i | −0.963185 | − | 0.268839i | \(-0.913360\pi\) |
−0.248771 | + | 0.968562i | \(0.580027\pi\) | |||||||
\(8\) | 5.22398 | 1.84696 | ||||||||
\(9\) | −0.306758 | − | 2.98428i | −0.102253 | − | 0.994758i | ||||
\(10\) | −4.95856 | − | 2.86283i | −1.56804 | − | 0.905306i | ||||
\(11\) | −0.00334847 | + | 3.31662i | −0.00100960 | + | 0.999999i | ||||
\(12\) | 6.96638 | + | 1.48908i | 2.01102 | + | 0.429860i | ||||
\(13\) | −2.99673 | − | 2.00489i | −0.831144 | − | 0.556058i | ||||
\(14\) | − | 9.15438i | − | 2.44661i | ||||||
\(15\) | −2.97775 | − | 2.68735i | −0.768851 | − | 0.693871i | ||||
\(16\) | −2.34506 | + | 4.06177i | −0.586266 | + | 1.01544i | ||||
\(17\) | 1.81821 | + | 3.14922i | 0.440979 | + | 0.763799i | 0.997762 | − | 0.0668592i | \(-0.0212978\pi\) |
−0.556783 | + | 0.830658i | \(0.687964\pi\) | |||||||
\(18\) | 6.76910 | + | 3.03238i | 1.59549 | + | 0.714738i | ||||
\(19\) | 1.23762 | − | 0.714538i | 0.283929 | − | 0.163926i | −0.351272 | − | 0.936273i | \(-0.614251\pi\) |
0.635201 | + | 0.772347i | \(0.280917\pi\) | |||||||
\(20\) | 8.24860 | − | 4.76233i | 1.84444 | − | 1.06489i | ||||
\(21\) | 1.34053 | − | 6.27140i | 0.292527 | − | 1.36853i | ||||
\(22\) | −7.09736 | − | 4.10722i | −1.51316 | − | 0.875663i | ||||
\(23\) | −4.95627 | − | 2.86150i | −1.03345 | − | 0.596664i | −0.115481 | − | 0.993310i | \(-0.536841\pi\) |
−0.917972 | + | 0.396645i | \(0.870174\pi\) | |||||||
\(24\) | −6.06212 | + | 6.71720i | −1.23743 | + | 1.37114i | ||||
\(25\) | −0.362948 | −0.0725897 | ||||||||
\(26\) | 7.99745 | − | 3.93808i | 1.56843 | − | 0.772320i | ||||
\(27\) | 4.19327 | + | 3.06863i | 0.806995 | + | 0.590558i | ||||
\(28\) | 13.1881 | + | 7.61418i | 2.49233 | + | 1.43895i | ||||
\(29\) | 0.195179 | − | 0.338060i | 0.0362439 | − | 0.0627762i | −0.847334 | − | 0.531060i | \(-0.821794\pi\) |
0.883578 | + | 0.468283i | \(0.155127\pi\) | |||||||
\(30\) | 9.43525 | − | 3.05377i | 1.72263 | − | 0.557540i | ||||
\(31\) | 7.44153 | 1.33654 | 0.668269 | − | 0.743920i | \(-0.267035\pi\) | ||||
0.668269 | + | 0.743920i | \(0.267035\pi\) | |||||||
\(32\) | −0.574015 | − | 0.994224i | −0.101473 | − | 0.175756i | ||||
\(33\) | −4.26075 | − | 3.85305i | −0.741702 | − | 0.670729i | ||||
\(34\) | −8.99076 | −1.54190 | ||||||||
\(35\) | −4.28723 | − | 7.42571i | −0.724675 | − | 1.25517i | ||||
\(36\) | −9.99878 | + | 7.22964i | −1.66646 | + | 1.20494i | ||||
\(37\) | −2.18584 | + | 3.78599i | −0.359350 | + | 0.622413i | −0.987852 | − | 0.155395i | \(-0.950335\pi\) |
0.628502 | + | 0.777808i | \(0.283668\pi\) | |||||||
\(38\) | 3.53329i | 0.573175i | ||||||||
\(39\) | 6.05550 | − | 1.52675i | 0.969655 | − | 0.244476i | ||||
\(40\) | 12.0977i | 1.91282i | ||||||||
\(41\) | 2.49288 | − | 4.31779i | 0.389322 | − | 0.674326i | −0.603036 | − | 0.797714i | \(-0.706043\pi\) |
0.992359 | + | 0.123388i | \(0.0393759\pi\) | |||||||
\(42\) | 11.7710 | + | 10.6231i | 1.81631 | + | 1.63918i | ||||
\(43\) | −6.34232 | + | 3.66174i | −0.967194 | + | 0.558410i | −0.898380 | − | 0.439220i | \(-0.855255\pi\) |
−0.0688144 | + | 0.997629i | \(0.521922\pi\) | |||||||
\(44\) | 11.8203 | − | 6.80854i | 1.78197 | − | 1.02643i | ||||
\(45\) | 6.91100 | − | 0.710392i | 1.03023 | − | 0.105899i | ||||
\(46\) | 12.2540 | − | 7.07485i | 1.80675 | − | 1.04313i | ||||
\(47\) | 9.51675i | 1.38816i | 0.719897 | + | 0.694081i | \(0.244189\pi\) | ||||
−0.719897 | + | 0.694081i | \(0.755811\pi\) | |||||||
\(48\) | −2.50147 | − | 7.72881i | −0.361056 | − | 1.11556i | ||||
\(49\) | 3.35458 | − | 5.81030i | 0.479226 | − | 0.830043i | ||||
\(50\) | 0.448682 | − | 0.777140i | 0.0634532 | − | 0.109904i | ||||
\(51\) | −6.15931 | − | 1.31657i | −0.862476 | − | 0.184356i | ||||
\(52\) | −0.978559 | + | 14.7969i | −0.135702 | + | 2.05197i | ||||
\(53\) | − | 4.53927i | − | 0.623517i | −0.950161 | − | 0.311759i | \(-0.899082\pi\) | ||
0.950161 | − | 0.311759i | \(-0.100918\pi\) | |||||||
\(54\) | −11.7543 | + | 5.18508i | −1.59956 | + | 0.705600i | ||||
\(55\) | −7.68065 | − | 0.00775439i | −1.03566 | − | 0.00104560i | ||||
\(56\) | −16.7509 | + | 9.67113i | −2.23843 | + | 1.29236i | ||||
\(57\) | −0.517399 | + | 2.42055i | −0.0685312 | + | 0.320610i | ||||
\(58\) | 0.482567 | + | 0.835830i | 0.0633641 | + | 0.109750i | ||||
\(59\) | −1.96442 | + | 1.13416i | −0.255746 | + | 0.147655i | −0.622392 | − | 0.782705i | \(-0.713839\pi\) |
0.366646 | + | 0.930360i | \(0.380506\pi\) | |||||||
\(60\) | −3.44842 | + | 16.1328i | −0.445189 | + | 2.08273i | ||||
\(61\) | 7.11598 | − | 4.10841i | 0.911108 | − | 0.526029i | 0.0303207 | − | 0.999540i | \(-0.490347\pi\) |
0.880788 | + | 0.473512i | \(0.157014\pi\) | |||||||
\(62\) | −9.19932 | + | 15.9337i | −1.16831 | + | 2.02358i | ||||
\(63\) | 6.50840 | + | 9.00128i | 0.819982 | + | 1.13406i | ||||
\(64\) | −6.54183 | −0.817729 | ||||||||
\(65\) | 4.64294 | − | 6.93984i | 0.575886 | − | 0.860781i | ||||
\(66\) | 13.5173 | − | 4.35987i | 1.66386 | − | 0.536663i | ||||
\(67\) | 1.25601 | − | 2.17547i | 0.153446 | − | 0.265776i | −0.779046 | − | 0.626967i | \(-0.784296\pi\) |
0.932492 | + | 0.361191i | \(0.117630\pi\) | |||||||
\(68\) | 7.47809 | − | 12.9524i | 0.906852 | − | 1.57071i | ||||
\(69\) | 9.43088 | − | 3.05235i | 1.13534 | − | 0.367460i | ||||
\(70\) | 21.1998 | 2.53385 | ||||||||
\(71\) | −12.1268 | + | 7.00140i | −1.43918 | + | 0.830913i | −0.997793 | − | 0.0664013i | \(-0.978848\pi\) |
−0.441391 | + | 0.897315i | \(0.645515\pi\) | |||||||
\(72\) | −1.60250 | − | 15.5898i | −0.188857 | − | 1.83728i | ||||
\(73\) | − | 13.6341i | − | 1.59575i | −0.602822 | − | 0.797875i | \(-0.705957\pi\) | ||
0.602822 | − | 0.797875i | \(-0.294043\pi\) | |||||||
\(74\) | −5.40433 | − | 9.36058i | −0.628241 | − | 1.08815i | ||||
\(75\) | 0.421180 | − | 0.466693i | 0.0486337 | − | 0.0538891i | ||||
\(76\) | −5.09019 | − | 2.93882i | −0.583885 | − | 0.337106i | ||||
\(77\) | −6.12931 | − | 10.6411i | −0.698499 | − | 1.21266i | ||||
\(78\) | −4.21683 | + | 14.8533i | −0.477462 | + | 1.68181i | ||||
\(79\) | − | 9.28575i | − | 1.04473i | −0.852723 | − | 0.522364i | \(-0.825050\pi\) | ||
0.852723 | − | 0.522364i | \(-0.174950\pi\) | |||||||
\(80\) | −9.40626 | − | 5.43071i | −1.05165 | − | 0.607172i | ||||
\(81\) | −8.81180 | + | 1.83090i | −0.979089 | + | 0.203434i | ||||
\(82\) | 6.16346 | + | 10.6754i | 0.680641 | + | 1.17890i | ||||
\(83\) | −1.73616 | −0.190569 | −0.0952843 | − | 0.995450i | \(-0.530376\pi\) | ||||
−0.0952843 | + | 0.995450i | \(0.530376\pi\) | |||||||
\(84\) | −25.0947 | + | 8.12202i | −2.73805 | + | 0.886185i | ||||
\(85\) | −7.29298 | + | 4.21061i | −0.791035 | + | 0.456704i | ||||
\(86\) | − | 18.1068i | − | 1.95250i | ||||||
\(87\) | 0.208197 | + | 0.643268i | 0.0223211 | + | 0.0689655i | ||||
\(88\) | −0.0174923 | + | 17.3260i | −0.00186469 | + | 1.84696i | ||||
\(89\) | −9.51379 | − | 5.49279i | −1.00846 | − | 0.582234i | −0.0977191 | − | 0.995214i | \(-0.531155\pi\) |
−0.910740 | + | 0.412980i | \(0.864488\pi\) | |||||||
\(90\) | −7.02239 | + | 15.6759i | −0.740225 | + | 1.65239i | ||||
\(91\) | 13.3208 | + | 0.880936i | 1.39640 | + | 0.0923472i | ||||
\(92\) | 23.5381i | 2.45402i | ||||||||
\(93\) | −8.63545 | + | 9.56860i | −0.895454 | + | 0.992218i | ||||
\(94\) | −20.3771 | − | 11.7647i | −2.10174 | − | 1.21344i | ||||
\(95\) | 1.65473 | + | 2.86608i | 0.169772 | + | 0.294053i | ||||
\(96\) | 1.94452 | + | 0.415646i | 0.198462 | + | 0.0424217i | ||||
\(97\) | −8.03552 | − | 13.9179i | −0.815884 | − | 1.41315i | −0.908692 | − | 0.417468i | \(-0.862918\pi\) |
0.0928080 | − | 0.995684i | \(-0.470416\pi\) | |||||||
\(98\) | 8.29395 | + | 14.3656i | 0.837816 | + | 1.45114i | ||||
\(99\) | 9.89874 | − | 1.00741i | 0.994861 | − | 0.101248i | ||||
\(100\) | 0.746385 | + | 1.29278i | 0.0746385 | + | 0.129278i | ||||
\(101\) | −3.58744 | + | 6.21363i | −0.356964 | + | 0.618279i | −0.987452 | − | 0.157920i | \(-0.949521\pi\) |
0.630488 | + | 0.776199i | \(0.282855\pi\) | |||||||
\(102\) | 10.4332 | − | 11.5607i | 1.03304 | − | 1.14468i | ||||
\(103\) | −14.0291 | −1.38233 | −0.691164 | − | 0.722698i | \(-0.742902\pi\) | ||||
−0.691164 | + | 0.722698i | \(0.742902\pi\) | |||||||
\(104\) | −15.6549 | − | 10.4735i | −1.53509 | − | 1.02702i | ||||
\(105\) | 14.5233 | + | 3.10440i | 1.41733 | + | 0.302958i | ||||
\(106\) | 9.71942 | + | 5.61151i | 0.944034 | + | 0.545038i | ||||
\(107\) | 6.17838 | − | 10.7013i | 0.597286 | − | 1.03453i | −0.395934 | − | 0.918279i | \(-0.629579\pi\) |
0.993220 | − | 0.116251i | \(-0.0370877\pi\) | |||||||
\(108\) | 2.30683 | − | 21.2464i | 0.221975 | − | 2.04443i | ||||
\(109\) | 9.25995i | 0.886942i | 0.896289 | + | 0.443471i | \(0.146253\pi\) | ||||
−0.896289 | + | 0.443471i | \(0.853747\pi\) | |||||||
\(110\) | 9.51153 | − | 16.4361i | 0.906889 | − | 1.56712i | ||||
\(111\) | −2.33163 | − | 7.20405i | −0.221309 | − | 0.683778i | ||||
\(112\) | − | 17.3656i | − | 1.64090i | ||||||
\(113\) | 6.38795 | − | 3.68809i | 0.600928 | − | 0.346946i | −0.168479 | − | 0.985705i | \(-0.553885\pi\) |
0.769407 | + | 0.638759i | \(0.220552\pi\) | |||||||
\(114\) | −4.54323 | − | 4.10017i | −0.425513 | − | 0.384016i | ||||
\(115\) | 6.62668 | − | 11.4777i | 0.617941 | − | 1.07030i | ||||
\(116\) | −1.60550 | −0.149067 | ||||||||
\(117\) | −5.06389 | + | 9.55809i | −0.468156 | + | 0.883646i | ||||
\(118\) | − | 5.60825i | − | 0.516282i | ||||||
\(119\) | −11.6603 | − | 6.73206i | −1.06890 | − | 0.617127i | ||||
\(120\) | −15.5557 | − | 14.0387i | −1.42004 | − | 1.28155i | ||||
\(121\) | −11.0000 | − | 0.0222112i | −0.999998 | − | 0.00201920i | ||||
\(122\) | 20.3155i | 1.83928i | ||||||||
\(123\) | 2.65915 | + | 8.21598i | 0.239767 | + | 0.740810i | ||||
\(124\) | −15.3031 | − | 26.5058i | −1.37426 | − | 2.38029i | ||||
\(125\) | 10.7385i | 0.960481i | ||||||||
\(126\) | −27.3192 | + | 2.80818i | −2.43379 | + | 0.250173i | ||||
\(127\) | 4.58910 | + | 2.64952i | 0.407216 | + | 0.235107i | 0.689593 | − | 0.724197i | \(-0.257789\pi\) |
−0.282377 | + | 0.959304i | \(0.591123\pi\) | |||||||
\(128\) | 9.23513 | − | 15.9957i | 0.816278 | − | 1.41384i | ||||
\(129\) | 2.65148 | − | 12.4044i | 0.233449 | − | 1.09215i | ||||
\(130\) | 9.11981 | + | 18.5205i | 0.799861 | + | 1.62436i | ||||
\(131\) | −13.4978 | −1.17931 | −0.589653 | − | 0.807657i | \(-0.700735\pi\) | ||||
−0.589653 | + | 0.807657i | \(0.700735\pi\) | |||||||
\(132\) | −4.96205 | + | 23.0999i | −0.431891 | + | 2.01058i | ||||
\(133\) | −2.64564 | + | 4.58238i | −0.229406 | + | 0.397343i | ||||
\(134\) | 3.10539 | + | 5.37869i | 0.268265 | + | 0.464648i | ||||
\(135\) | −7.10635 | + | 9.71079i | −0.611617 | + | 0.835772i | ||||
\(136\) | 9.49827 | + | 16.4515i | 0.814470 | + | 1.41070i | ||||
\(137\) | −1.54454 | + | 0.891738i | −0.131959 | + | 0.0761863i | −0.564526 | − | 0.825415i | \(-0.690941\pi\) |
0.432567 | + | 0.901602i | \(0.357608\pi\) | |||||||
\(138\) | −5.12292 | + | 23.9666i | −0.436092 | + | 2.04017i | ||||
\(139\) | −5.31782 | + | 3.07024i | −0.451052 | + | 0.260415i | −0.708274 | − | 0.705937i | \(-0.750526\pi\) |
0.257223 | + | 0.966352i | \(0.417193\pi\) | |||||||
\(140\) | −17.6330 | + | 30.5412i | −1.49026 | + | 2.58120i | ||||
\(141\) | −12.2370 | − | 11.0436i | −1.03054 | − | 0.930041i | ||||
\(142\) | − | 34.6209i | − | 2.90532i | ||||||
\(143\) | 6.65952 | − | 9.93231i | 0.556897 | − | 0.830582i | ||||
\(144\) | 12.8408 | + | 5.75233i | 1.07007 | + | 0.479361i | ||||
\(145\) | 0.782882 | + | 0.451997i | 0.0650148 | + | 0.0375363i | ||||
\(146\) | 29.1931 | + | 16.8547i | 2.41604 | + | 1.39490i | ||||
\(147\) | 3.57832 | + | 11.0560i | 0.295135 | + | 0.911880i | ||||
\(148\) | 17.9803 | 1.47797 | ||||||||
\(149\) | −1.90432 | − | 3.29837i | −0.156008 | − | 0.270213i | 0.777418 | − | 0.628985i | \(-0.216529\pi\) |
−0.933425 | + | 0.358771i | \(0.883196\pi\) | |||||||
\(150\) | 0.478607 | + | 1.47876i | 0.0390781 | + | 0.120740i | ||||
\(151\) | 6.89118i | 0.560797i | 0.959884 | + | 0.280398i | \(0.0904665\pi\) | ||||
−0.959884 | + | 0.280398i | \(0.909533\pi\) | |||||||
\(152\) | 6.46529 | − | 3.73274i | 0.524404 | − | 0.302765i | ||||
\(153\) | 8.84040 | − | 6.39208i | 0.714704 | − | 0.516769i | ||||
\(154\) | 30.3616 | + | 0.0306531i | 2.44661 | + | 0.00247010i | ||||
\(155\) | 17.2331i | 1.38420i | ||||||||
\(156\) | −17.8909 | − | 18.4292i | −1.43242 | − | 1.47552i | ||||
\(157\) | −6.66314 | −0.531776 | −0.265888 | − | 0.964004i | \(-0.585665\pi\) | ||||
−0.265888 | + | 0.964004i | \(0.585665\pi\) | |||||||
\(158\) | 19.8825 | + | 11.4792i | 1.58177 | + | 0.913234i | ||||
\(159\) | 5.83677 | + | 5.26755i | 0.462886 | + | 0.417744i | ||||
\(160\) | 2.30243 | − | 1.32931i | 0.182023 | − | 0.105091i | ||||
\(161\) | 21.1899 | 1.67000 | ||||||||
\(162\) | 6.97296 | − | 21.1311i | 0.547848 | − | 1.66021i | ||||
\(163\) | 11.5455 | + | 19.9975i | 0.904316 | + | 1.56632i | 0.821833 | + | 0.569729i | \(0.192952\pi\) |
0.0824833 | + | 0.996592i | \(0.473715\pi\) | |||||||
\(164\) | −20.5059 | −1.60124 | ||||||||
\(165\) | 8.92290 | − | 9.86707i | 0.694647 | − | 0.768150i | ||||
\(166\) | 2.14627 | − | 3.71744i | 0.166583 | − | 0.288530i | ||||
\(167\) | 0.132034 | − | 0.228690i | 0.0102171 | − | 0.0176966i | −0.860872 | − | 0.508822i | \(-0.830081\pi\) |
0.871089 | + | 0.491126i | \(0.163414\pi\) | |||||||
\(168\) | 7.00289 | − | 32.7617i | 0.540285 | − | 2.52762i | ||||
\(169\) | 4.96079 | + | 12.0163i | 0.381599 | + | 0.924328i | ||||
\(170\) | − | 20.8208i | − | 1.59689i | ||||||
\(171\) | −2.51203 | − | 3.47420i | −0.192100 | − | 0.265678i | ||||
\(172\) | 26.0853 | + | 15.0604i | 1.98898 | + | 1.14834i | ||||
\(173\) | 11.7184 | + | 20.2968i | 0.890932 | + | 1.54314i | 0.838760 | + | 0.544501i | \(0.183281\pi\) |
0.0521714 | + | 0.998638i | \(0.483386\pi\) | |||||||
\(174\) | −1.63473 | − | 0.349428i | −0.123929 | − | 0.0264901i | ||||
\(175\) | 1.16381 | − | 0.671924i | 0.0879755 | − | 0.0507927i | ||||
\(176\) | −13.4635 | − | 7.79129i | −1.01485 | − | 0.587291i | ||||
\(177\) | 0.821248 | − | 3.84205i | 0.0617288 | − | 0.288786i | ||||
\(178\) | 23.5221 | − | 13.5805i | 1.76306 | − | 1.01790i | ||||
\(179\) | 16.7444 | + | 9.66739i | 1.25154 | + | 0.722575i | 0.971414 | − | 0.237390i | \(-0.0762919\pi\) |
0.280122 | + | 0.959965i | \(0.409625\pi\) | |||||||
\(180\) | −16.7424 | − | 23.1552i | −1.24791 | − | 1.72589i | ||||
\(181\) | −23.8199 | −1.77052 | −0.885258 | − | 0.465100i | \(-0.846018\pi\) | ||||
−0.885258 | + | 0.465100i | \(0.846018\pi\) | |||||||
\(182\) | −18.3536 | + | 27.4332i | −1.36046 | + | 2.03349i | ||||
\(183\) | −2.97492 | + | 13.9176i | −0.219912 | + | 1.02882i | ||||
\(184\) | −25.8915 | − | 14.9484i | −1.90874 | − | 1.10201i | ||||
\(185\) | −8.76761 | − | 5.06198i | −0.644607 | − | 0.372164i | ||||
\(186\) | −9.81288 | − | 30.3189i | −0.719516 | − | 2.22309i | ||||
\(187\) | −10.4509 | + | 6.01976i | −0.764244 | + | 0.440208i | ||||
\(188\) | 33.8975 | − | 19.5707i | 2.47223 | − | 1.42734i | ||||
\(189\) | −19.1268 | − | 2.07670i | −1.39127 | − | 0.151058i | ||||
\(190\) | −8.18240 | −0.593614 | ||||||||
\(191\) | −5.49010 | + | 3.16971i | −0.397250 | + | 0.229352i | −0.685297 | − | 0.728264i | \(-0.740327\pi\) |
0.288047 | + | 0.957616i | \(0.406994\pi\) | |||||||
\(192\) | 7.59140 | − | 8.41174i | 0.547862 | − | 0.607065i | ||||
\(193\) | −1.12988 | − | 0.652334i | −0.0813302 | − | 0.0469560i | 0.458783 | − | 0.888548i | \(-0.348285\pi\) |
−0.540114 | + | 0.841592i | \(0.681619\pi\) | |||||||
\(194\) | 39.7345 | 2.85277 | ||||||||
\(195\) | 3.53565 | + | 14.0233i | 0.253193 | + | 1.00423i | ||||
\(196\) | −27.5941 | −1.97101 | ||||||||
\(197\) | −2.11756 | + | 3.66773i | −0.150870 | + | 0.261315i | −0.931548 | − | 0.363619i | \(-0.881541\pi\) |
0.780677 | + | 0.624934i | \(0.214874\pi\) | |||||||
\(198\) | −10.0799 | + | 22.4404i | −0.716348 | + | 1.59477i | ||||
\(199\) | 8.81144 | + | 15.2619i | 0.624626 | + | 1.08188i | 0.988613 | + | 0.150481i | \(0.0480821\pi\) |
−0.363987 | + | 0.931404i | \(0.618585\pi\) | |||||||
\(200\) | −1.89604 | −0.134070 | ||||||||
\(201\) | 1.33978 | + | 4.13953i | 0.0945008 | + | 0.291980i | ||||
\(202\) | −8.86968 | − | 15.3627i | −0.624069 | − | 1.08092i | ||||
\(203\) | 1.44534i | 0.101443i | ||||||||
\(204\) | 7.97685 | + | 24.6461i | 0.558491 | + | 1.72557i | ||||
\(205\) | 9.99916 | + | 5.77302i | 0.698372 | + | 0.403205i | ||||
\(206\) | 17.3430 | − | 30.0389i | 1.20834 | − | 2.09291i | ||||
\(207\) | −7.01913 | + | 15.6687i | −0.487863 | + | 1.08905i | ||||
\(208\) | 15.1709 | − | 7.47042i | 1.05192 | − | 0.517981i | ||||
\(209\) | 2.36571 | + | 4.10710i | 0.163640 | + | 0.284094i | ||||
\(210\) | −24.6010 | + | 27.2594i | −1.69763 | + | 1.88108i | ||||
\(211\) | −0.446183 | − | 0.257604i | −0.0307165 | − | 0.0177342i | 0.484563 | − | 0.874756i | \(-0.338979\pi\) |
−0.515280 | + | 0.857022i | \(0.672312\pi\) | |||||||
\(212\) | −16.1683 | + | 9.33478i | −1.11044 | + | 0.641116i | ||||
\(213\) | 5.06973 | − | 23.7178i | 0.347373 | − | 1.62512i | ||||
\(214\) | 15.2756 | + | 26.4581i | 1.04422 | + | 1.80864i | ||||
\(215\) | −8.47987 | − | 14.6876i | −0.578322 | − | 1.00168i | ||||
\(216\) | 21.9056 | + | 16.0305i | 1.49049 | + | 1.09074i | ||||
\(217\) | −23.8615 | + | 13.7765i | −1.61983 | + | 0.935207i | ||||
\(218\) | −19.8273 | − | 11.4473i | −1.34287 | − | 0.775307i | ||||
\(219\) | 17.5312 | + | 15.8216i | 1.18465 | + | 1.06912i | ||||
\(220\) | 15.7672 | + | 27.3734i | 1.06303 | + | 1.84552i | ||||
\(221\) | 0.865191 | − | 13.0827i | 0.0581990 | − | 0.880037i | ||||
\(222\) | 18.3076 | + | 3.91329i | 1.22873 | + | 0.262643i | ||||
\(223\) | 7.83072 | − | 13.5632i | 0.524384 | − | 0.908260i | −0.475213 | − | 0.879871i | \(-0.657629\pi\) |
0.999597 | − | 0.0283889i | \(-0.00903769\pi\) | |||||||
\(224\) | 3.68120 | + | 2.12534i | 0.245961 | + | 0.142005i | ||||
\(225\) | 0.111338 | + | 1.08314i | 0.00742250 | + | 0.0722092i | ||||
\(226\) | 18.2370i | 1.21311i | ||||||||
\(227\) | −10.9081 | − | 18.8934i | −0.723995 | − | 1.25400i | −0.959386 | − | 0.282096i | \(-0.908970\pi\) |
0.235391 | − | 0.971901i | \(-0.424363\pi\) | |||||||
\(228\) | 9.68571 | − | 3.13483i | 0.641452 | − | 0.207609i | ||||
\(229\) | 13.4538 | 0.889054 | 0.444527 | − | 0.895765i | \(-0.353372\pi\) | ||||
0.444527 | + | 0.895765i | \(0.353372\pi\) | |||||||
\(230\) | 16.3840 | + | 28.3779i | 1.08033 | + | 1.87118i | ||||
\(231\) | 20.7954 | + | 4.46702i | 1.36824 | + | 0.293909i | ||||
\(232\) | 1.01961 | − | 1.76602i | 0.0669409 | − | 0.115945i | ||||
\(233\) | −5.12618 | −0.335827 | −0.167913 | − | 0.985802i | \(-0.553703\pi\) | ||||
−0.167913 | + | 0.985802i | \(0.553703\pi\) | |||||||
\(234\) | −14.2056 | − | 22.6586i | −0.928648 | − | 1.48124i | ||||
\(235\) | −22.0389 | −1.43766 | ||||||||
\(236\) | 8.07947 | + | 4.66468i | 0.525928 | + | 0.303645i | ||||
\(237\) | 11.9400 | + | 10.7756i | 0.775584 | + | 0.699947i | ||||
\(238\) | 28.8292 | − | 16.6445i | 1.86872 | − | 1.07891i | ||||
\(239\) | −24.2427 | −1.56813 | −0.784066 | − | 0.620677i | \(-0.786858\pi\) | ||||
−0.784066 | + | 0.620677i | \(0.786858\pi\) | |||||||
\(240\) | 17.8984 | − | 5.79292i | 1.15534 | − | 0.373931i | ||||
\(241\) | 15.6267 | − | 9.02205i | 1.00660 | − | 0.581161i | 0.0964064 | − | 0.995342i | \(-0.469265\pi\) |
0.910195 | + | 0.414181i | \(0.135932\pi\) | |||||||
\(242\) | 13.6459 | − | 23.5255i | 0.877190 | − | 1.51228i | ||||
\(243\) | 7.87132 | − | 13.4552i | 0.504945 | − | 0.863151i | ||||
\(244\) | −29.2673 | − | 16.8975i | −1.87365 | − | 1.08175i | ||||
\(245\) | 13.4555 | + | 7.76855i | 0.859642 | + | 0.496314i | ||||
\(246\) | −20.8792 | − | 4.46298i | −1.33121 | − | 0.284549i | ||||
\(247\) | −5.14138 | − | 0.340012i | −0.327138 | − | 0.0216345i | ||||
\(248\) | 38.8744 | 2.46853 | ||||||||
\(249\) | 2.01471 | − | 2.23242i | 0.127677 | − | 0.141474i | ||||
\(250\) | −22.9931 | − | 13.2751i | −1.45421 | − | 0.839590i | ||||
\(251\) | 5.01922 | − | 2.89785i | 0.316810 | − | 0.182911i | −0.333160 | − | 0.942870i | \(-0.608115\pi\) |
0.649970 | + | 0.759960i | \(0.274781\pi\) | |||||||
\(252\) | 18.6772 | − | 41.6928i | 1.17656 | − | 2.62640i | ||||
\(253\) | 9.50712 | − | 16.4285i | 0.597707 | − | 1.03285i | ||||
\(254\) | −11.3462 | + | 6.55074i | −0.711924 | + | 0.411030i | ||||
\(255\) | 3.04891 | − | 14.2638i | 0.190930 | − | 0.893231i | ||||
\(256\) | 16.2914 | + | 28.2175i | 1.01821 | + | 1.76359i | ||||
\(257\) | −21.7456 | − | 12.5548i | −1.35645 | − | 0.783150i | −0.367311 | − | 0.930098i | \(-0.619721\pi\) |
−0.989144 | + | 0.146949i | \(0.953055\pi\) | |||||||
\(258\) | 23.2824 | + | 21.0118i | 1.44950 | + | 1.30814i | ||||
\(259\) | − | 16.1865i | − | 1.00578i | ||||||
\(260\) | −34.2668 | − | 2.26615i | −2.12514 | − | 0.140541i | ||||
\(261\) | −1.06874 | − | 0.478766i | −0.0661532 | − | 0.0296349i | ||||
\(262\) | 16.6861 | − | 28.9012i | 1.03087 | − | 1.78552i | ||||
\(263\) | −4.85093 | + | 8.40205i | −0.299121 | + | 0.518093i | −0.975935 | − | 0.218061i | \(-0.930027\pi\) |
0.676814 | + | 0.736154i | \(0.263360\pi\) | |||||||
\(264\) | −22.2581 | − | 20.1283i | −1.36989 | − | 1.23881i | ||||
\(265\) | 10.5121 | 0.645751 | ||||||||
\(266\) | −6.54115 | − | 11.3296i | −0.401064 | − | 0.694663i | ||||
\(267\) | 18.1030 | − | 5.85914i | 1.10789 | − | 0.358573i | ||||
\(268\) | −10.3317 | −0.631107 | ||||||||
\(269\) | −9.27986 | + | 5.35773i | −0.565803 | + | 0.326666i | −0.755471 | − | 0.655182i | \(-0.772592\pi\) |
0.189668 | + | 0.981848i | \(0.439259\pi\) | |||||||
\(270\) | −12.0076 | − | 27.2206i | −0.730761 | − | 1.65659i | ||||
\(271\) | −2.68341 | − | 1.54927i | −0.163005 | − | 0.0941113i | 0.416278 | − | 0.909237i | \(-0.363334\pi\) |
−0.579284 | + | 0.815126i | \(0.696668\pi\) | |||||||
\(272\) | −17.0552 | −1.03413 | ||||||||
\(273\) | −16.5907 | + | 16.1061i | −1.00411 | + | 0.974785i | ||||
\(274\) | − | 4.40952i | − | 0.266389i | ||||||
\(275\) | 0.00121532 | − | 1.20376i | 7.32866e−5 | − | 0.0725897i | ||||
\(276\) | −30.2662 | − | 27.3146i | −1.82181 | − | 1.64414i | ||||
\(277\) | 12.4789 | − | 7.20471i | 0.749786 | − | 0.432889i | −0.0758306 | − | 0.997121i | \(-0.524161\pi\) |
0.825617 | + | 0.564232i | \(0.190827\pi\) | |||||||
\(278\) | − | 15.1819i | − | 0.910551i | ||||||
\(279\) | −2.28275 | − | 22.2076i | −0.136665 | − | 1.32953i | ||||
\(280\) | −22.3964 | − | 38.7918i | −1.33844 | − | 2.31825i | ||||
\(281\) | −1.82943 | −0.109135 | −0.0545675 | − | 0.998510i | \(-0.517378\pi\) | ||||
−0.0545675 | + | 0.998510i | \(0.517378\pi\) | |||||||
\(282\) | 38.7740 | − | 12.5494i | 2.30896 | − | 0.747307i | ||||
\(283\) | 4.76401 | + | 2.75050i | 0.283191 | + | 0.163500i | 0.634867 | − | 0.772621i | \(-0.281055\pi\) |
−0.351676 | + | 0.936122i | \(0.614388\pi\) | |||||||
\(284\) | 49.8762 | + | 28.7960i | 2.95961 | + | 1.70873i | ||||
\(285\) | −5.60553 | − | 1.19820i | −0.332043 | − | 0.0709749i | ||||
\(286\) | 13.0343 | + | 26.5377i | 0.770736 | + | 1.56921i | ||||
\(287\) | 18.4602i | 1.08967i | ||||||||
\(288\) | −2.79095 | + | 2.01801i | −0.164459 | + | 0.118912i | ||||
\(289\) | 1.88826 | − | 3.27056i | 0.111074 | − | 0.192386i | ||||
\(290\) | −1.93562 | + | 1.11753i | −0.113663 | + | 0.0656236i | ||||
\(291\) | 27.2209 | + | 5.81855i | 1.59572 | + | 0.341089i | ||||
\(292\) | −48.5629 | + | 28.0378i | −2.84193 | + | 1.64079i | ||||
\(293\) | 0.387256 | + | 0.670747i | 0.0226237 | + | 0.0391855i | 0.877116 | − | 0.480279i | \(-0.159465\pi\) |
−0.854492 | + | 0.519465i | \(0.826131\pi\) | |||||||
\(294\) | −28.0964 | − | 6.00568i | −1.63862 | − | 0.350258i | ||||
\(295\) | −2.62649 | − | 4.54922i | −0.152920 | − | 0.264866i | ||||
\(296\) | −11.4188 | + | 19.7779i | −0.663704 | + | 1.14957i | ||||
\(297\) | −10.1915 | + | 13.8972i | −0.591373 | + | 0.806398i | ||||
\(298\) | 9.41657 | 0.545487 | ||||||||
\(299\) | 9.11559 | + | 18.5119i | 0.527168 | + | 1.07057i | ||||
\(300\) | −2.52844 | − | 0.540459i | −0.145979 | − | 0.0312034i | ||||
\(301\) | 13.5579 | − | 23.4830i | 0.781465 | − | 1.35354i | ||||
\(302\) | −14.7553 | − | 8.51898i | −0.849072 | − | 0.490212i | ||||
\(303\) | −3.82671 | − | 11.8234i | −0.219839 | − | 0.679237i | ||||
\(304\) | 6.70255i | 0.384418i | ||||||||
\(305\) | 9.51428 | + | 16.4792i | 0.544786 | + | 0.943598i | ||||
\(306\) | 2.75799 | + | 26.8309i | 0.157664 | + | 1.53382i | ||||
\(307\) | 25.7122i | 1.46747i | 0.679434 | + | 0.733737i | \(0.262225\pi\) | ||||
−0.679434 | + | 0.733737i | \(0.737775\pi\) | |||||||
\(308\) | −25.2975 | + | 43.7146i | −1.44146 | + | 2.49087i | ||||
\(309\) | 16.2799 | − | 18.0392i | 0.926133 | − | 1.02621i | ||||
\(310\) | −36.8993 | − | 21.3038i | −2.09574 | − | 1.20998i | ||||
\(311\) | − | 2.62026i | − | 0.148581i | −0.997237 | − | 0.0742905i | \(-0.976331\pi\) | ||
0.997237 | − | 0.0742905i | \(-0.0236692\pi\) | |||||||
\(312\) | 31.6338 | − | 7.97572i | 1.79091 | − | 0.451536i | ||||
\(313\) | 4.89272 | 0.276553 | 0.138276 | − | 0.990394i | \(-0.455844\pi\) | ||||
0.138276 | + | 0.990394i | \(0.455844\pi\) | |||||||
\(314\) | 8.23706 | − | 14.2670i | 0.464844 | − | 0.805134i | ||||
\(315\) | −20.8452 | + | 15.0722i | −1.17449 | + | 0.849222i | ||||
\(316\) | −33.0747 | + | 19.0957i | −1.86059 | + | 1.07421i | ||||
\(317\) | 4.04149i | 0.226993i | 0.993538 | + | 0.113496i | \(0.0362050\pi\) | ||||
−0.993538 | + | 0.113496i | \(0.963795\pi\) | |||||||
\(318\) | −18.4943 | + | 5.98578i | −1.03711 | + | 0.335666i | ||||
\(319\) | 1.12057 | + | 0.648468i | 0.0627396 | + | 0.0363072i | ||||
\(320\) | − | 15.1496i | − | 0.846888i | ||||||
\(321\) | 6.59046 | + | 20.3626i | 0.367843 | + | 1.13653i | ||||
\(322\) | −26.1953 | + | 45.3715i | −1.45981 | + | 2.52846i | ||||
\(323\) | 4.50048 | + | 2.59835i | 0.250413 | + | 0.144576i | ||||
\(324\) | 24.6425 | + | 27.6214i | 1.36903 | + | 1.53452i | ||||
\(325\) | 1.08766 | + | 0.727673i | 0.0603325 | + | 0.0403641i | ||||
\(326\) | −57.0910 | −3.16198 | ||||||||
\(327\) | −11.9068 | − | 10.7456i | −0.658447 | − | 0.594234i | ||||
\(328\) | 13.0228 | − | 22.5561i | 0.719062 | − | 1.24545i | ||||
\(329\) | −17.6183 | − | 30.5158i | −0.971329 | − | 1.68239i | ||||
\(330\) | 10.0966 | + | 31.3034i | 0.555800 | + | 1.72320i | ||||
\(331\) | −0.779830 | − | 1.35071i | −0.0428633 | − | 0.0742415i | 0.843798 | − | 0.536661i | \(-0.180315\pi\) |
−0.886661 | + | 0.462420i | \(0.846981\pi\) | |||||||
\(332\) | 3.57033 | + | 6.18399i | 0.195947 | + | 0.339391i | ||||
\(333\) | 11.9690 | + | 5.36177i | 0.655895 | + | 0.293823i | ||||
\(334\) | 0.326446 | + | 0.565420i | 0.0178623 | + | 0.0309384i | ||||
\(335\) | 5.03796 | + | 2.90867i | 0.275253 | + | 0.158918i | ||||
\(336\) | 22.3294 | + | 20.1517i | 1.21817 | + | 1.09937i | ||||
\(337\) | 27.2822i | 1.48616i | 0.669204 | + | 0.743079i | \(0.266635\pi\) | ||||
−0.669204 | + | 0.743079i | \(0.733365\pi\) | |||||||
\(338\) | −31.8616 | − | 4.23269i | −1.73304 | − | 0.230228i | ||||
\(339\) | −2.67055 | + | 12.4937i | −0.145045 | + | 0.678563i | ||||
\(340\) | 29.9953 | + | 17.3178i | 1.62672 | + | 0.939189i | ||||
\(341\) | −0.0249177 | + | 24.6807i | −0.00134937 | + | 1.33654i | ||||
\(342\) | 10.5443 | − | 1.08387i | 0.570171 | − | 0.0586087i | ||||
\(343\) | − | 1.07686i | − | 0.0581451i | ||||||
\(344\) | −33.1322 | + | 19.1289i | −1.78637 | + | 1.03136i | ||||
\(345\) | 7.06865 | + | 21.8401i | 0.380564 | + | 1.17583i | ||||
\(346\) | −57.9457 | −3.11518 | ||||||||
\(347\) | 3.08735 | + | 5.34746i | 0.165738 | + | 0.287066i | 0.936917 | − | 0.349552i | \(-0.113666\pi\) |
−0.771179 | + | 0.636618i | \(0.780333\pi\) | |||||||
\(348\) | 1.86309 | − | 2.06442i | 0.0998722 | − | 0.110664i | ||||
\(349\) | −18.1454 | − | 10.4763i | −0.971301 | − | 0.560781i | −0.0716686 | − | 0.997428i | \(-0.522832\pi\) |
−0.899633 | + | 0.436647i | \(0.856166\pi\) | |||||||
\(350\) | 3.32257i | 0.177599i | ||||||||
\(351\) | −6.41382 | − | 17.6029i | −0.342344 | − | 0.939575i | ||||
\(352\) | 3.29939 | − | 1.90046i | 0.175858 | − | 0.101295i | ||||
\(353\) | 19.3547 | + | 11.1744i | 1.03015 | + | 0.594755i | 0.917027 | − | 0.398826i | \(-0.130582\pi\) |
0.113120 | + | 0.993581i | \(0.463916\pi\) | |||||||
\(354\) | 7.21131 | + | 6.50804i | 0.383277 | + | 0.345899i | ||||
\(355\) | −16.2139 | − | 28.0833i | −0.860543 | − | 1.49050i | ||||
\(356\) | 45.1825i | 2.39467i | ||||||||
\(357\) | 22.1874 | − | 7.18107i | 1.17428 | − | 0.380063i | ||||
\(358\) | −41.3993 | + | 23.9019i | −2.18802 | + | 1.26326i | ||||
\(359\) | 2.14210 | 0.113056 | 0.0565279 | − | 0.998401i | \(-0.481997\pi\) | ||||
0.0565279 | + | 0.998401i | \(0.481997\pi\) | |||||||
\(360\) | 36.1029 | − | 3.71108i | 1.90279 | − | 0.195591i | ||||
\(361\) | −8.47887 | + | 14.6858i | −0.446256 | + | 0.772939i | ||||
\(362\) | 29.4464 | − | 51.0027i | 1.54767 | − | 2.68064i | ||||
\(363\) | 12.7934 | − | 14.1184i | 0.671478 | − | 0.741025i | ||||
\(364\) | −24.2557 | − | 49.2585i | −1.27134 | − | 2.58185i | ||||
\(365\) | 31.5739 | 1.65265 | ||||||||
\(366\) | −26.1225 | − | 23.5749i | −1.36544 | − | 1.23228i | ||||
\(367\) | 4.96066 | − | 8.59211i | 0.258944 | − | 0.448505i | −0.707015 | − | 0.707198i | \(-0.749959\pi\) |
0.965959 | + | 0.258694i | \(0.0832921\pi\) | |||||||
\(368\) | 23.2455 | − | 13.4208i | 1.21176 | − | 0.699608i | ||||
\(369\) | −13.6502 | − | 6.11492i | −0.710601 | − | 0.318330i | ||||
\(370\) | 21.6773 | − | 12.5154i | 1.12695 | − | 0.650644i | ||||
\(371\) | 8.40353 | + | 14.5553i | 0.436290 | + | 0.755676i | ||||
\(372\) | 51.8405 | + | 11.0810i | 2.68780 | + | 0.574525i | ||||
\(373\) | 15.3434 | − | 8.85854i | 0.794453 | − | 0.458678i | −0.0470748 | − | 0.998891i | \(-0.514990\pi\) |
0.841528 | + | 0.540214i | \(0.181657\pi\) | |||||||
\(374\) | 0.0301053 | − | 29.8190i | 0.00155671 | − | 1.54190i | ||||
\(375\) | −13.8080 | − | 12.4614i | −0.713041 | − | 0.643503i | ||||
\(376\) | 49.7154i | 2.56387i | ||||||||
\(377\) | −1.26268 | + | 0.621762i | −0.0650311 | + | 0.0320224i | ||||
\(378\) | 28.0914 | − | 38.3868i | 1.44487 | − | 1.97440i | ||||
\(379\) | −5.96882 | + | 10.3383i | −0.306598 | + | 0.531043i | −0.977616 | − | 0.210398i | \(-0.932524\pi\) |
0.671018 | + | 0.741441i | \(0.265857\pi\) | |||||||
\(380\) | 6.80573 | − | 11.7879i | 0.349127 | − | 0.604705i | ||||
\(381\) | −8.73222 | + | 2.82623i | −0.447365 | + | 0.144792i | ||||
\(382\) | − | 15.6738i | − | 0.801940i | ||||||
\(383\) | −29.8752 | + | 17.2485i | −1.52655 | + | 0.881356i | −0.527050 | + | 0.849834i | \(0.676702\pi\) |
−0.999503 | + | 0.0315212i | \(0.989965\pi\) | |||||||
\(384\) | 9.85109 | + | 30.4370i | 0.502711 | + | 1.55323i | ||||
\(385\) | 24.6426 | − | 14.1943i | 1.25590 | − | 0.723407i | ||||
\(386\) | 2.79353 | − | 1.61285i | 0.142187 | − | 0.0820918i | ||||
\(387\) | 12.8732 | + | 17.8039i | 0.654381 | + | 0.905026i | ||||
\(388\) | −33.0493 | + | 57.2430i | −1.67782 | + | 2.90607i | ||||
\(389\) | − | 8.07746i | − | 0.409543i | −0.978810 | − | 0.204772i | \(-0.934355\pi\) | ||
0.978810 | − | 0.204772i | \(-0.0656452\pi\) | |||||||
\(390\) | −34.3974 | − | 9.76536i | −1.74178 | − | 0.494488i | ||||
\(391\) | − | 20.8112i | − | 1.05247i | ||||||
\(392\) | 17.5243 | − | 30.3529i | 0.885109 | − | 1.53305i | ||||
\(393\) | 15.6633 | − | 17.3559i | 0.790111 | − | 0.875491i | ||||
\(394\) | −5.23552 | − | 9.06819i | −0.263762 | − | 0.456849i | ||||
\(395\) | 21.5040 | 1.08198 | ||||||||
\(396\) | −23.9445 | − | 33.1864i | −1.20326 | − | 1.66768i | ||||
\(397\) | 0.187144 | + | 0.324144i | 0.00939251 | + | 0.0162683i | 0.870683 | − | 0.491844i | \(-0.163677\pi\) |
−0.861291 | + | 0.508112i | \(0.830344\pi\) | |||||||
\(398\) | −43.5713 | −2.18403 | ||||||||
\(399\) | −2.82210 | − | 8.71945i | −0.141282 | − | 0.436518i | ||||
\(400\) | 0.851137 | − | 1.47421i | 0.0425569 | − | 0.0737106i | ||||
\(401\) | 0.872340 | + | 0.503646i | 0.0435626 | + | 0.0251509i | 0.521623 | − | 0.853176i | \(-0.325327\pi\) |
−0.478061 | + | 0.878327i | \(0.658660\pi\) | |||||||
\(402\) | −10.5197 | − | 2.24862i | −0.524677 | − | 0.112151i | ||||
\(403\) | −22.3003 | − | 14.9195i | −1.11086 | − | 0.743192i | ||||
\(404\) | 29.5095 | 1.46815 | ||||||||
\(405\) | −4.24001 | − | 20.4064i | −0.210688 | − | 1.01400i | ||||
\(406\) | −3.09473 | − | 1.78675i | −0.153589 | − | 0.0886747i | ||||
\(407\) | −12.5494 | − | 7.26229i | −0.622050 | − | 0.359978i | ||||
\(408\) | −32.1761 | − | 6.87773i | −1.59296 | − | 0.340498i | ||||
\(409\) | −13.6305 | + | 7.86959i | −0.673987 | + | 0.389126i | −0.797585 | − | 0.603206i | \(-0.793890\pi\) |
0.123599 | + | 0.992332i | \(0.460556\pi\) | |||||||
\(410\) | −24.7222 | + | 14.2734i | −1.22094 | + | 0.704912i | ||||
\(411\) | 0.645710 | − | 3.02083i | 0.0318505 | − | 0.149007i | ||||
\(412\) | 28.8501 | + | 49.9699i | 1.42134 | + | 2.46184i | ||||
\(413\) | 4.19933 | − | 7.27345i | 0.206635 | − | 0.357903i | ||||
\(414\) | −24.8723 | − | 34.3991i | −1.22241 | − | 1.69062i | ||||
\(415\) | − | 4.02061i | − | 0.197364i | ||||||
\(416\) | −0.273145 | + | 4.13026i | −0.0133920 | + | 0.202503i | ||||
\(417\) | 2.22317 | − | 10.4007i | 0.108869 | − | 0.509324i | ||||
\(418\) | −11.7186 | − | 0.0118311i | −0.573175 | − | 0.000578678i | ||||
\(419\) | 19.0181 | + | 10.9801i | 0.929093 | + | 0.536412i | 0.886525 | − | 0.462681i | \(-0.153113\pi\) |
0.0425684 | + | 0.999094i | \(0.486446\pi\) | |||||||
\(420\) | −18.8090 | − | 58.1143i | −0.917786 | − | 2.83569i | ||||
\(421\) | 5.93199 | 0.289108 | 0.144554 | − | 0.989497i | \(-0.453825\pi\) | ||||
0.144554 | + | 0.989497i | \(0.453825\pi\) | |||||||
\(422\) | 1.10316 | − | 0.636907i | 0.0537008 | − | 0.0310042i | ||||
\(423\) | 28.4006 | − | 2.91934i | 1.38089 | − | 0.141943i | ||||
\(424\) | − | 23.7131i | − | 1.15161i | ||||||
\(425\) | −0.659915 | − | 1.14301i | −0.0320106 | − | 0.0554439i | ||||
\(426\) | 44.5169 | + | 40.1755i | 2.15685 | + | 1.94651i | ||||
\(427\) | −15.2118 | + | 26.3476i | −0.736149 | + | 1.27505i | ||||
\(428\) | −50.8221 | −2.45658 | ||||||||
\(429\) | 5.04338 | + | 20.0889i | 0.243497 | + | 0.969902i | ||||
\(430\) | 41.9317 | 2.02213 | ||||||||
\(431\) | −14.5033 | + | 25.1205i | −0.698601 | + | 1.21001i | 0.270350 | + | 0.962762i | \(0.412860\pi\) |
−0.968952 | + | 0.247251i | \(0.920473\pi\) | |||||||
\(432\) | −22.2976 | + | 9.83596i | −1.07279 | + | 0.473233i | ||||
\(433\) | −0.286323 | − | 0.495926i | −0.0137598 | − | 0.0238327i | 0.859064 | − | 0.511869i | \(-0.171047\pi\) |
−0.872823 | + | 0.488036i | \(0.837713\pi\) | |||||||
\(434\) | − | 68.1226i | − | 3.26999i | ||||||
\(435\) | −1.48968 | + | 0.482144i | −0.0714248 | + | 0.0231170i | ||||
\(436\) | 32.9828 | − | 19.0426i | 1.57959 | − | 0.911975i | ||||
\(437\) | −8.17861 | −0.391236 | ||||||||
\(438\) | −55.5492 | + | 17.9788i | −2.65425 | + | 0.859061i | ||||
\(439\) | 0.649189 | + | 0.374810i | 0.0309841 | + | 0.0178887i | 0.515412 | − | 0.856942i | \(-0.327639\pi\) |
−0.484428 | + | 0.874831i | \(0.660972\pi\) | |||||||
\(440\) | −40.1236 | − | 0.0405088i | −1.91282 | − | 0.00193118i | ||||
\(441\) | −18.3686 | − | 8.22863i | −0.874695 | − | 0.391840i | ||||
\(442\) | 26.9429 | + | 18.0255i | 1.28154 | + | 0.857387i | ||||
\(443\) | 0.139797i | 0.00664197i | 0.999994 | + | 0.00332099i | \(0.00105710\pi\) | ||||
−0.999994 | + | 0.00332099i | \(0.998943\pi\) | |||||||
\(444\) | −20.8650 | + | 23.1197i | −0.990211 | + | 1.09721i | ||||
\(445\) | 12.7202 | − | 22.0321i | 0.602996 | − | 1.04442i | ||||
\(446\) | 19.3609 | + | 33.5341i | 0.916765 | + | 1.58788i | ||||
\(447\) | 6.45102 | + | 1.37892i | 0.305123 | + | 0.0652207i | ||||
\(448\) | 20.9766 | − | 12.1109i | 0.991052 | − | 0.572184i | ||||
\(449\) | 10.2530 | − | 5.91959i | 0.483870 | − | 0.279363i | −0.238158 | − | 0.971227i | \(-0.576543\pi\) |
0.722028 | + | 0.691864i | \(0.243210\pi\) | |||||||
\(450\) | −2.45684 | − | 1.10060i | −0.115816 | − | 0.0518826i | ||||
\(451\) | 14.3121 | + | 8.28240i | 0.673933 | + | 0.390003i | ||||
\(452\) | −26.2730 | − | 15.1687i | −1.23578 | − | 0.713476i | ||||
\(453\) | −8.86095 | − | 7.99680i | −0.416324 | − | 0.375723i | ||||
\(454\) | 53.9389 | 2.53148 | ||||||||
\(455\) | −2.04008 | + | 30.8483i | −0.0956402 | + | 1.44619i | ||||
\(456\) | −2.70288 | + | 12.6449i | −0.126574 | + | 0.592153i | ||||
\(457\) | 25.2592 | + | 14.5834i | 1.18158 | + | 0.682184i | 0.956379 | − | 0.292129i | \(-0.0943638\pi\) |
0.225198 | + | 0.974313i | \(0.427697\pi\) | |||||||
\(458\) | −16.6318 | + | 28.8071i | −0.777154 | + | 1.34607i | ||||
\(459\) | −2.03958 | + | 18.7849i | −0.0951995 | + | 0.876806i | ||||
\(460\) | −54.5097 | −2.54153 | ||||||||
\(461\) | −4.42794 | − | 7.66941i | −0.206230 | − | 0.357200i | 0.744294 | − | 0.667852i | \(-0.232786\pi\) |
−0.950524 | + | 0.310652i | \(0.899453\pi\) | |||||||
\(462\) | −35.2723 | + | 39.0046i | −1.64101 | + | 1.81466i | ||||
\(463\) | −26.3101 | −1.22273 | −0.611367 | − | 0.791347i | \(-0.709380\pi\) | ||||
−0.611367 | + | 0.791347i | \(0.709380\pi\) | |||||||
\(464\) | 0.915416 | + | 1.58555i | 0.0424971 | + | 0.0736071i | ||||
\(465\) | −22.1590 | − | 19.9980i | −1.02760 | − | 0.927385i | ||||
\(466\) | 6.33705 | − | 10.9761i | 0.293558 | − | 0.508458i | ||||
\(467\) | − | 29.3379i | − | 1.35760i | −0.734324 | − | 0.678799i | \(-0.762501\pi\) | ||
0.734324 | − | 0.678799i | \(-0.237499\pi\) | |||||||
\(468\) | 44.4583 | − | 1.61880i | 2.05509 | − | 0.0748290i | ||||
\(469\) | 9.30096i | 0.429479i | ||||||||
\(470\) | 27.2448 | − | 47.1894i | 1.25671 | − | 2.17669i | ||||
\(471\) | 7.73217 | − | 8.56771i | 0.356280 | − | 0.394779i | ||||
\(472\) | −10.2621 | + | 5.92483i | −0.472352 | + | 0.272713i | ||||
\(473\) | −12.1234 | − | 21.0473i | −0.557433 | − | 0.967757i | ||||
\(474\) | −37.8328 | + | 12.2448i | −1.73772 | + | 0.562422i | ||||
\(475\) | −0.449191 | + | 0.259340i | −0.0206103 | + | 0.0118994i | ||||
\(476\) | 55.3766i | 2.53818i | ||||||||
\(477\) | −13.5464 | + | 1.39246i | −0.620249 | + | 0.0637564i | ||||
\(478\) | 29.9692 | − | 51.9082i | 1.37076 | − | 2.37423i | ||||
\(479\) | −17.3828 | + | 30.1080i | −0.794242 | + | 1.37567i | 0.129077 | + | 0.991635i | \(0.458799\pi\) |
−0.923319 | + | 0.384033i | \(0.874535\pi\) | |||||||
\(480\) | −0.962555 | + | 4.50313i | −0.0439344 | + | 0.205539i | ||||
\(481\) | 14.1409 | − | 6.96321i | 0.644769 | − | 0.317495i | ||||
\(482\) | 44.6127i | 2.03205i | ||||||||
\(483\) | −24.5896 | + | 27.2468i | −1.11887 | + | 1.23977i | ||||
\(484\) | 22.5418 | + | 39.2262i | 1.02463 | + | 1.78301i | ||||
\(485\) | 32.2312 | − | 18.6087i | 1.46354 | − | 0.844977i | ||||
\(486\) | 19.0794 | + | 33.4874i | 0.865461 | + | 1.51902i | ||||
\(487\) | −8.12787 | − | 14.0779i | −0.368309 | − | 0.637929i | 0.620993 | − | 0.783816i | \(-0.286730\pi\) |
−0.989301 | + | 0.145887i | \(0.953396\pi\) | |||||||
\(488\) | 37.1738 | − | 21.4623i | 1.68278 | − | 0.971552i | ||||
\(489\) | −39.1114 | − | 8.36016i | −1.76868 | − | 0.378059i | ||||
\(490\) | −33.2678 | + | 19.2072i | −1.50289 | + | 0.867692i | ||||
\(491\) | 6.73824 | − | 11.6710i | 0.304093 | − | 0.526704i | −0.672966 | − | 0.739673i | \(-0.734980\pi\) |
0.977059 | + | 0.212969i | \(0.0683135\pi\) | |||||||
\(492\) | 23.7959 | − | 26.3673i | 1.07280 | − | 1.18873i | ||||
\(493\) | 1.41950 | 0.0639312 | ||||||||
\(494\) | 7.08387 | − | 10.5883i | 0.318718 | − | 0.476391i | ||||
\(495\) | 2.33296 | + | 22.9236i | 0.104859 | + | 1.03034i | ||||
\(496\) | −17.4509 | + | 30.2258i | −0.783567 | + | 1.35718i | ||||
\(497\) | 25.9233 | − | 44.9005i | 1.16282 | − | 2.01406i | ||||
\(498\) | 2.28942 | + | 7.07362i | 0.102591 | + | 0.316977i | ||||
\(499\) | 8.03905 | 0.359877 | 0.179939 | − | 0.983678i | \(-0.442410\pi\) | ||||
0.179939 | + | 0.983678i | \(0.442410\pi\) | |||||||
\(500\) | 38.2492 | − | 22.0832i | 1.71056 | − | 0.987590i | ||||
\(501\) | 0.140841 | + | 0.435156i | 0.00629230 | + | 0.0194414i | ||||
\(502\) | 14.3294i | 0.639554i | ||||||||
\(503\) | −18.1322 | − | 31.4060i | −0.808477 | − | 1.40032i | −0.913919 | − | 0.405898i | \(-0.866959\pi\) |
0.105442 | − | 0.994425i | \(-0.466374\pi\) | |||||||
\(504\) | 33.9998 | + | 47.0226i | 1.51447 | + | 2.09455i | ||||
\(505\) | −14.3895 | − | 8.30781i | −0.640326 | − | 0.369693i | ||||
\(506\) | 23.4236 | + | 40.6656i | 1.04131 | + | 1.80781i | ||||
\(507\) | −21.2077 | − | 7.56537i | −0.941866 | − | 0.335990i | ||||
\(508\) | − | 21.7944i | − | 0.966969i | ||||||
\(509\) | 26.8544 | + | 15.5044i | 1.19030 | + | 0.687221i | 0.958375 | − | 0.285512i | \(-0.0921636\pi\) |
0.231927 | + | 0.972733i | \(0.425497\pi\) | |||||||
\(510\) | 26.7722 | + | 24.1613i | 1.18549 | + | 1.06988i | ||||
\(511\) | 25.2407 | + | 43.7182i | 1.11658 | + | 1.93398i | ||||
\(512\) | −43.6179 | −1.92766 | ||||||||
\(513\) | 7.38231 | + | 0.801537i | 0.325937 | + | 0.0353887i | ||||
\(514\) | 53.7645 | − | 31.0409i | 2.37145 | − | 1.36916i | ||||
\(515\) | − | 32.4887i | − | 1.43162i | ||||||
\(516\) | −49.6356 | + | 16.0648i | −2.18508 | + | 0.707215i | ||||
\(517\) | −31.5635 | − | 0.0318665i | −1.38816 | − | 0.00140149i | ||||
\(518\) | 34.6584 | + | 20.0100i | 1.52280 | + | 0.879190i | ||||
\(519\) | −39.6969 | − | 8.48531i | −1.74250 | − | 0.372464i | ||||
\(520\) | 24.2547 | − | 36.2536i | 1.06364 | − | 1.58983i | ||||
\(521\) | 15.3032i | 0.670444i | 0.942139 | + | 0.335222i | \(0.108811\pi\) | ||||
−0.942139 | + | 0.335222i | \(0.891189\pi\) | |||||||
\(522\) | 2.34631 | − | 1.69651i | 0.102695 | − | 0.0742542i | ||||
\(523\) | 25.8794 | + | 14.9415i | 1.13163 | + | 0.653345i | 0.944344 | − | 0.328961i | \(-0.106698\pi\) |
0.187283 | + | 0.982306i | \(0.440032\pi\) | |||||||
\(524\) | 27.7575 | + | 48.0773i | 1.21259 | + | 2.10027i | ||||
\(525\) | −0.486542 | + | 2.27620i | −0.0212344 | + | 0.0993413i | ||||
\(526\) | −11.9936 | − | 20.7735i | −0.522944 | − | 0.905766i | ||||
\(527\) | 13.5302 | + | 23.4350i | 0.589386 | + | 1.02085i | ||||
\(528\) | 25.6419 | − | 8.27056i | 1.11592 | − | 0.359930i | ||||
\(529\) | 4.87638 | + | 8.44614i | 0.212017 | + | 0.367224i | ||||
\(530\) | −12.9952 | + | 22.5083i | −0.564474 | + | 0.977697i | ||||
\(531\) | 3.98725 | + | 5.51446i | 0.173032 | + | 0.239307i | ||||
\(532\) | 21.7625 | 0.943524 | ||||||||
\(533\) | −16.1272 | + | 7.94130i | −0.698547 | + | 0.343976i | ||||
\(534\) | −9.83369 | + | 46.0050i | −0.425545 | + | 1.99083i | ||||
\(535\) | 24.7820 | + | 14.3079i | 1.07142 | + | 0.618585i | ||||
\(536\) | 6.56137 | − | 11.3646i | 0.283408 | − | 0.490877i | ||||
\(537\) | −31.8616 | + | 10.3122i | −1.37493 | + | 0.445003i | ||||
\(538\) | − | 26.4932i | − | 1.14220i | ||||||
\(539\) | 19.2594 | + | 11.1453i | 0.829559 | + | 0.480063i | ||||
\(540\) | 49.2024 | + | 5.34217i | 2.11734 | + | 0.229890i | ||||
\(541\) | − | 0.0554765i | − | 0.00238512i | −0.999999 | − | 0.00119256i | \(-0.999620\pi\) | ||
0.999999 | − | 0.00119256i | \(-0.000379604\pi\) | |||||||
\(542\) | 6.63453 | − | 3.83045i | 0.284978 | − | 0.164532i | ||||
\(543\) | 27.6415 | − | 30.6285i | 1.18621 | − | 1.31439i | ||||
\(544\) | 2.08736 | − | 3.61541i | 0.0894946 | − | 0.155009i | ||||
\(545\) | −21.4442 | −0.918569 | ||||||||
\(546\) | −13.9765 | − | 55.4343i | −0.598137 | − | 2.37237i | ||||
\(547\) | − | 1.16971i | − | 0.0500131i | −0.999687 | − | 0.0250066i | \(-0.992039\pi\) | ||
0.999687 | − | 0.0250066i | \(-0.00796067\pi\) | |||||||
\(548\) | 6.35252 | + | 3.66763i | 0.271366 | + | 0.156673i | ||||
\(549\) | −14.4435 | − | 19.9758i | −0.616435 | − | 0.852545i | ||||
\(550\) | 2.57598 | + | 1.49071i | 0.109840 | + | 0.0635641i | ||||
\(551\) | − | 0.557852i | − | 0.0237653i | ||||||
\(552\) | 49.2668 | − | 15.9455i | 2.09693 | − | 0.678683i | ||||
\(553\) | 17.1907 | + | 29.7751i | 0.731021 | + | 1.26617i | ||||
\(554\) | 35.6262i | 1.51361i | ||||||||
\(555\) | 16.6832 | − | 5.39960i | 0.708161 | − | 0.229200i | ||||
\(556\) | 21.8716 | + | 12.6276i | 0.927564 | + | 0.535530i | ||||
\(557\) | −10.7382 | + | 18.5991i | −0.454993 | + | 0.788071i | −0.998688 | − | 0.0512122i | \(-0.983692\pi\) |
0.543695 | + | 0.839283i | \(0.317025\pi\) | |||||||
\(558\) | 50.3725 | + | 22.5655i | 2.13244 | + | 0.955274i | ||||
\(559\) | 26.3476 | + | 1.74243i | 1.11439 | + | 0.0736971i | ||||
\(560\) | 40.2154 | 1.69941 | ||||||||
\(561\) | 4.38718 | − | 20.4237i | 0.185227 | − | 0.862289i | ||||
\(562\) | 2.26157 | − | 3.91716i | 0.0953987 | − | 0.165235i | ||||
\(563\) | −7.34568 | − | 12.7231i | −0.309583 | − | 0.536214i | 0.668688 | − | 0.743543i | \(-0.266856\pi\) |
−0.978271 | + | 0.207329i | \(0.933523\pi\) | |||||||
\(564\) | −14.1712 | + | 66.2973i | −0.596716 | + | 2.79162i | ||||
\(565\) | 8.54088 | + | 14.7932i | 0.359318 | + | 0.622356i | ||||
\(566\) | −11.7787 | + | 6.80042i | −0.495095 | + | 0.285843i | ||||
\(567\) | 24.8658 | − | 22.1841i | 1.04427 | − | 0.931644i | ||||
\(568\) | −63.3501 | + | 36.5752i | −2.65811 | + | 1.53466i | ||||
\(569\) | −2.01217 | + | 3.48518i | −0.0843546 | + | 0.146107i | −0.905116 | − | 0.425165i | \(-0.860216\pi\) |
0.820761 | + | 0.571271i | \(0.193550\pi\) | |||||||
\(570\) | 9.49518 | − | 10.5212i | 0.397709 | − | 0.440686i | ||||
\(571\) | − | 14.5414i | − | 0.608539i | −0.952586 | − | 0.304269i | \(-0.901588\pi\) | ||
0.952586 | − | 0.304269i | \(-0.0984123\pi\) | |||||||
\(572\) | −49.0726 | − | 3.29506i | −2.05183 | − | 0.137773i | ||||
\(573\) | 2.29520 | − | 10.7376i | 0.0958833 | − | 0.448572i | ||||
\(574\) | −39.5267 | − | 22.8208i | −1.64981 | − | 0.952520i | ||||
\(575\) | 1.79887 | + | 1.03858i | 0.0750180 | + | 0.0433117i | ||||
\(576\) | 2.00676 | + | 19.5226i | 0.0836151 | + | 0.813443i | ||||
\(577\) | −13.1988 | −0.549472 | −0.274736 | − | 0.961520i | \(-0.588591\pi\) | ||||
−0.274736 | + | 0.961520i | \(0.588591\pi\) | |||||||
\(578\) | 4.66859 | + | 8.08623i | 0.194188 | + | 0.336343i | ||||
\(579\) | 2.14995 | − | 0.695842i | 0.0893488 | − | 0.0289182i | ||||
\(580\) | − | 3.71803i | − | 0.154383i | ||||||
\(581\) | 5.56707 | − | 3.21415i | 0.230961 | − | 0.133345i | ||||
\(582\) | −46.1095 | + | 51.0921i | −1.91130 | + | 2.11784i | ||||
\(583\) | 15.0551 | + | 0.0151996i | 0.623517 | + | 0.000629504i | ||||
\(584\) | − | 71.2243i | − | 2.94728i | ||||||
\(585\) | −22.1347 | − | 11.7270i | −0.915156 | − | 0.484850i | ||||
\(586\) | −1.91492 | −0.0791048 | ||||||||
\(587\) | −39.5978 | − | 22.8618i | −1.63438 | − | 0.943608i | −0.982721 | − | 0.185092i | \(-0.940742\pi\) |
−0.651655 | − | 0.758515i | \(-0.725925\pi\) | |||||||
\(588\) | 32.0213 | − | 35.4815i | 1.32054 | − | 1.46323i | ||||
\(589\) | 9.20976 | − | 5.31726i | 0.379481 | − | 0.219094i | ||||
\(590\) | 12.9876 | 0.534692 | ||||||||
\(591\) | −2.25880 | − | 6.97902i | −0.0929145 | − | 0.287078i | ||||
\(592\) | −10.2519 | − | 17.7568i | −0.421350 | − | 0.729799i | ||||
\(593\) | 1.84220 | 0.0756500 | 0.0378250 | − | 0.999284i | \(-0.487957\pi\) | ||||
0.0378250 | + | 0.999284i | \(0.487957\pi\) | |||||||
\(594\) | −17.1576 | − | 39.0019i | −0.703985 | − | 1.60027i | ||||
\(595\) | 15.5901 | − | 27.0029i | 0.639134 | − | 1.10701i | ||||
\(596\) | −7.83226 | + | 13.5659i | −0.320822 | + | 0.555680i | ||||
\(597\) | −29.8494 | − | 6.38039i | −1.22166 | − | 0.261132i | ||||
\(598\) | −50.9063 | − | 3.36656i | −2.08171 | − | 0.137669i | ||||
\(599\) | − | 4.33911i | − | 0.177291i | −0.996063 | − | 0.0886457i | \(-0.971746\pi\) | ||
0.996063 | − | 0.0886457i | \(-0.0282539\pi\) | |||||||
\(600\) | 2.20024 | − | 2.43800i | 0.0898243 | − | 0.0995308i | ||||
\(601\) | −30.7221 | − | 17.7374i | −1.25318 | − | 0.723524i | −0.281441 | − | 0.959579i | \(-0.590812\pi\) |
−0.971740 | + | 0.236054i | \(0.924146\pi\) | |||||||
\(602\) | 33.5209 | + | 58.0600i | 1.36621 | + | 2.36635i | ||||
\(603\) | −6.87749 | − | 3.08093i | −0.280073 | − | 0.125465i | ||||
\(604\) | 24.5455 | − | 14.1714i | 0.998743 | − | 0.576625i | ||||
\(605\) | 0.0514368 | − | 25.4738i | 0.00209120 | − | 1.03566i | ||||
\(606\) | 30.0467 | + | 6.42256i | 1.22057 | + | 0.260899i | ||||
\(607\) | −2.88163 | + | 1.66371i | −0.116962 | + | 0.0675279i | −0.557340 | − | 0.830285i | \(-0.688178\pi\) |
0.440378 | + | 0.897813i | \(0.354845\pi\) | |||||||
\(608\) | −1.42082 | − | 0.820312i | −0.0576219 | − | 0.0332680i | ||||
\(609\) | −1.85847 | − | 1.67723i | −0.0753090 | − | 0.0679647i | ||||
\(610\) | −47.0467 | −1.90487 | ||||||||
\(611\) | 19.0801 | − | 28.5192i | 0.771898 | − | 1.15376i | ||||
\(612\) | −40.9476 | − | 18.3434i | −1.65521 | − | 0.741488i | ||||
\(613\) | −0.938235 | − | 0.541690i | −0.0378949 | − | 0.0218787i | 0.480933 | − | 0.876757i | \(-0.340298\pi\) |
−0.518828 | + | 0.854879i | \(0.673631\pi\) | |||||||
\(614\) | −55.0546 | − | 31.7858i | −2.22182 | − | 1.28277i | ||||
\(615\) | −19.0266 | + | 6.15806i | −0.767226 | + | 0.248317i | ||||
\(616\) | −32.0194 | − | 55.5888i | −1.29010 | − | 2.23974i | ||||
\(617\) | −21.0322 | + | 12.1430i | −0.846726 | + | 0.488857i | −0.859545 | − | 0.511061i | \(-0.829253\pi\) |
0.0128191 | + | 0.999918i | \(0.495919\pi\) | |||||||
\(618\) | 18.4997 | + | 57.1586i | 0.744167 | + | 2.29926i | ||||
\(619\) | 3.72197 | 0.149599 | 0.0747993 | − | 0.997199i | \(-0.476168\pi\) | ||||
0.0747993 | + | 0.997199i | \(0.476168\pi\) | |||||||
\(620\) | 61.3822 | − | 35.4390i | 2.46517 | − | 1.42327i | ||||
\(621\) | −12.0021 | − | 27.2080i | −0.481626 | − | 1.09182i | ||||
\(622\) | 5.61045 | + | 3.23920i | 0.224959 | + | 0.129880i | ||||
\(623\) | 40.6751 | 1.62961 | ||||||||
\(624\) | −7.99922 | + | 28.1764i | −0.320225 | + | 1.12796i | ||||
\(625\) | −26.6830 | −1.06732 | ||||||||
\(626\) | −6.04844 | + | 10.4762i | −0.241744 | + | 0.418714i | ||||
\(627\) | −8.02633 | − | 1.72412i | −0.320541 | − | 0.0688548i | ||||
\(628\) | 13.7024 | + | 23.7332i | 0.546785 | + | 0.947060i | ||||
\(629\) | −15.8972 | −0.633864 | ||||||||
\(630\) | −6.50320 | − | 63.2659i | −0.259094 | − | 2.52057i | ||||
\(631\) | 10.8592 | + | 18.8086i | 0.432297 | + | 0.748760i | 0.997071 | − | 0.0764859i | \(-0.0243700\pi\) |
−0.564774 | + | 0.825246i | \(0.691037\pi\) | |||||||
\(632\) | − | 48.5086i | − | 1.92957i | ||||||
\(633\) | 0.849006 | − | 0.274785i | 0.0337450 | − | 0.0109217i | ||||
\(634\) | −8.65358 | − | 4.99615i | −0.343678 | − | 0.198422i | ||||
\(635\) | −6.13576 | + | 10.6274i | −0.243490 | + | 0.421737i | ||||
\(636\) | 6.75934 | − | 31.6223i | 0.268025 | − | 1.25391i | ||||
\(637\) | −21.7018 | + | 10.6863i | −0.859857 | + | 0.423408i | ||||
\(638\) | −2.77375 | + | 1.59769i | −0.109814 | + | 0.0632533i | ||||
\(639\) | 24.6141 | + | 34.0419i | 0.973719 | + | 1.34668i | ||||
\(640\) | 37.0430 | + | 21.3868i | 1.46425 | + | 0.845386i | ||||
\(641\) | 23.1524 | − | 13.3670i | 0.914463 | − | 0.527966i | 0.0325988 | − | 0.999469i | \(-0.489622\pi\) |
0.881865 | + | 0.471503i | \(0.156288\pi\) | |||||||
\(642\) | −51.7472 | − | 11.0611i | −2.04230 | − | 0.436547i | ||||
\(643\) | −7.20749 | − | 12.4837i | −0.284236 | − | 0.492311i | 0.688188 | − | 0.725533i | \(-0.258407\pi\) |
−0.972424 | + | 0.233222i | \(0.925073\pi\) | |||||||
\(644\) | −43.5760 | − | 75.4758i | −1.71713 | − | 2.97416i | ||||
\(645\) | 28.7262 | + | 6.14030i | 1.13109 | + | 0.241774i | ||||
\(646\) | −11.1271 | + | 6.42424i | −0.437790 | + | 0.252758i | ||||
\(647\) | −5.74259 | − | 3.31548i | −0.225764 | − | 0.130345i | 0.382852 | − | 0.923810i | \(-0.374942\pi\) |
−0.608617 | + | 0.793464i | \(0.708275\pi\) | |||||||
\(648\) | −46.0327 | + | 9.56461i | −1.80834 | + | 0.375733i | ||||
\(649\) | −3.75500 | − | 6.51905i | −0.147397 | − | 0.255895i | ||||
\(650\) | −2.90266 | + | 1.42932i | −0.113852 | + | 0.0560625i | ||||
\(651\) | 9.97557 | − | 46.6688i | 0.390974 | − | 1.82909i | ||||
\(652\) | 47.4856 | − | 82.2475i | 1.85968 | − | 3.22106i | ||||
\(653\) | 11.4843 | + | 6.63046i | 0.449415 | + | 0.259470i | 0.707583 | − | 0.706630i | \(-0.249785\pi\) |
−0.258168 | + | 0.966100i | \(0.583119\pi\) | |||||||
\(654\) | 37.7277 | − | 12.2108i | 1.47527 | − | 0.477479i | ||||
\(655\) | − | 31.2582i | − | 1.22136i | ||||||
\(656\) | 11.6919 | + | 20.2510i | 0.456493 | + | 0.790669i | ||||
\(657\) | −40.6879 | + | 4.18238i | −1.58739 | + | 0.163170i | ||||
\(658\) | 87.1200 | 3.39629 | ||||||||
\(659\) | 9.07488 | + | 15.7182i | 0.353507 | + | 0.612293i | 0.986861 | − | 0.161570i | \(-0.0516556\pi\) |
−0.633354 | + | 0.773862i | \(0.718322\pi\) | |||||||
\(660\) | −53.4947 | − | 11.4911i | −2.08228 | − | 0.447291i | ||||
\(661\) | −22.5077 | + | 38.9844i | −0.875447 | + | 1.51632i | −0.0191618 | + | 0.999816i | \(0.506100\pi\) |
−0.856286 | + | 0.516503i | \(0.827234\pi\) | |||||||
\(662\) | 3.85615 | 0.149873 | ||||||||
\(663\) | 15.8182 | + | 16.2942i | 0.614328 | + | 0.632813i | ||||
\(664\) | −9.06969 | −0.351972 | ||||||||
\(665\) | −10.6119 | − | 6.12678i | −0.411512 | − | 0.237587i | ||||
\(666\) | −26.2767 | + | 18.9995i | −1.01820 | + | 0.736214i | ||||
\(667\) | −1.93472 | + | 1.11701i | −0.0749127 | + | 0.0432509i | ||||
\(668\) | −1.08609 | −0.0420220 | ||||||||
\(669\) | 8.35301 | + | 25.8083i | 0.322946 | + | 0.997808i | ||||
\(670\) | −12.4560 | + | 7.19147i | −0.481217 | + | 0.277831i | ||||
\(671\) | 13.6022 | + | 23.6148i | 0.525108 | + | 0.911639i | ||||
\(672\) | −7.00466 | + | 2.26710i | −0.270211 | + | 0.0874551i | ||||
\(673\) | 19.2627 | + | 11.1213i | 0.742523 | + | 0.428696i | 0.822986 | − | 0.568062i | \(-0.192307\pi\) |
−0.0804630 | + | 0.996758i | \(0.525640\pi\) | |||||||
\(674\) | −58.4163 | − | 33.7267i | −2.25011 | − | 1.29910i | ||||
\(675\) | −1.52194 | − | 1.11375i | −0.0585795 | − | 0.0428684i | ||||
\(676\) | 32.5988 | − | 42.3805i | 1.25380 | − | 1.63002i | ||||
\(677\) | 39.8731 | 1.53245 | 0.766224 | − | 0.642574i | \(-0.222133\pi\) | ||||
0.766224 | + | 0.642574i | \(0.222133\pi\) | |||||||
\(678\) | −23.4499 | − | 21.1630i | −0.900587 | − | 0.812760i | ||||
\(679\) | 51.5324 | + | 29.7522i | 1.97763 | + | 1.14179i | ||||
\(680\) | −38.0984 | + | 21.9961i | −1.46101 | + | 0.843514i | ||||
\(681\) | 36.9520 | + | 7.89858i | 1.41600 | + | 0.302674i | ||||
\(682\) | −52.8152 | − | 30.5640i | −2.02240 | − | 1.17036i | ||||
\(683\) | 18.6392 | − | 10.7613i | 0.713208 | − | 0.411771i | −0.0990400 | − | 0.995083i | \(-0.531577\pi\) |
0.812248 | + | 0.583313i | \(0.198244\pi\) | |||||||
\(684\) | −7.20879 | + | 16.0920i | −0.275635 | + | 0.615294i | ||||
\(685\) | −2.06509 | − | 3.57684i | −0.0789031 | − | 0.136664i | ||||
\(686\) | 2.30576 | + | 1.33123i | 0.0880344 | + | 0.0508267i | ||||
\(687\) | −15.6124 | + | 17.2995i | −0.595649 | + | 0.660015i | ||||
\(688\) | − | 34.3480i | − | 1.30951i | ||||||
\(689\) | −9.10077 | + | 13.6030i | −0.346712 | + | 0.518232i | ||||
\(690\) | −55.5020 | − | 11.8637i | −2.11292 | − | 0.451643i | ||||
\(691\) | 9.36312 | − | 16.2174i | 0.356190 | − | 0.616939i | −0.631131 | − | 0.775676i | \(-0.717409\pi\) |
0.987321 | + | 0.158737i | \(0.0507423\pi\) | |||||||
\(692\) | 48.1965 | − | 83.4787i | 1.83216 | − | 3.17339i | ||||
\(693\) | −29.8757 | + | 21.5558i | −1.13488 | + | 0.818836i | ||||
\(694\) | −15.2665 | −0.579509 | ||||||||
\(695\) | −7.11009 | − | 12.3150i | −0.269701 | − | 0.467136i | ||||
\(696\) | 1.08762 | + | 3.36042i | 0.0412261 | + | 0.127376i | ||||
\(697\) | 18.1303 | 0.686733 | ||||||||
\(698\) | 44.8632 | − | 25.9018i | 1.69810 | − | 0.980397i | ||||
\(699\) | 5.94862 | − | 6.59143i | 0.224997 | − | 0.249311i | ||||
\(700\) | −4.78662 | − | 2.76356i | −0.180917 | − | 0.104453i | ||||
\(701\) | −42.5649 | −1.60766 | −0.803828 | − | 0.594862i | \(-0.797207\pi\) | ||||
−0.803828 | + | 0.594862i | \(0.797207\pi\) | |||||||
\(702\) | 45.6200 | + | 8.02781i | 1.72181 | + | 0.302990i | ||||
\(703\) | 6.24747i | 0.235628i | ||||||||
\(704\) | 0.0219051 | − | 21.6968i | 0.000825580 | − | 0.817729i | ||||
\(705\) | 25.5749 | − | 28.3385i | 0.963205 | − | 1.06729i | ||||
\(706\) | −47.8531 | + | 27.6280i | −1.80097 | + | 1.03979i | ||||
\(707\) | − | 26.5656i | − | 0.999103i | ||||||
\(708\) | −15.3738 | + | 4.97580i | −0.577781 | + | 0.187002i | ||||
\(709\) | −15.0049 | − | 25.9892i | −0.563519 | − | 0.976044i | −0.997186 | − | 0.0749705i | \(-0.976114\pi\) |
0.433667 | − | 0.901073i | \(-0.357220\pi\) | |||||||
\(710\) | 80.1752 | 3.00892 | ||||||||
\(711\) | −27.7112 | + | 2.84848i | −1.03925 | + | 0.106826i | ||||
\(712\) | −49.6999 | − | 28.6942i | −1.86258 | − | 1.07536i | ||||
\(713\) | −36.8822 | − | 21.2939i | −1.38125 | − | 0.797465i | ||||
\(714\) | −12.0524 | + | 56.3847i | −0.451048 | + | 2.11014i | ||||
\(715\) | 23.0013 | + | 15.4221i | 0.860200 | + | 0.576755i | ||||
\(716\) | − | 79.5220i | − | 2.97188i | ||||||
\(717\) | 28.1323 | − | 31.1722i | 1.05062 | − | 1.16415i | ||||
\(718\) | −2.64810 | + | 4.58664i | −0.0988261 | + | 0.171172i | ||||
\(719\) | −42.9331 | + | 24.7874i | −1.60113 | + | 0.924415i | −0.609873 | + | 0.792499i | \(0.708779\pi\) |
−0.991261 | + | 0.131916i | \(0.957887\pi\) | |||||||
\(720\) | −13.3213 | + | 29.7368i | −0.496455 | + | 1.10822i | ||||
\(721\) | 44.9848 | − | 25.9720i | 1.67532 | − | 0.967248i | ||||
\(722\) | −20.9634 | − | 36.3097i | −0.780177 | − | 1.35131i | ||||
\(723\) | −6.53289 | + | 30.5629i | −0.242961 | + | 1.13665i | ||||
\(724\) | 48.9843 | + | 84.8433i | 1.82049 | + | 3.15318i | ||||
\(725\) | −0.0708400 | + | 0.122699i | −0.00263093 | + | 0.00455691i | ||||
\(726\) | 14.4148 | + | 44.8464i | 0.534983 | + | 1.66440i | ||||
\(727\) | −0.679238 | −0.0251915 | −0.0125958 | − | 0.999921i | \(-0.504009\pi\) | ||||
−0.0125958 | + | 0.999921i | \(0.504009\pi\) | |||||||
\(728\) | 69.5875 | + | 4.60200i | 2.57908 | + | 0.170561i | ||||
\(729\) | 8.16701 | + | 25.7352i | 0.302482 | + | 0.953155i | ||||
\(730\) | −39.0321 | + | 67.6056i | −1.44464 | + | 2.50219i | ||||
\(731\) | −23.0633 | − | 13.3156i | −0.853026 | − | 0.492495i | ||||
\(732\) | 55.6904 | − | 18.0245i | 2.05838 | − | 0.666204i | ||||
\(733\) | 23.3555i | 0.862654i | 0.902196 | + | 0.431327i | \(0.141954\pi\) | ||||
−0.902196 | + | 0.431327i | \(0.858046\pi\) | |||||||
\(734\) | 12.2649 | + | 21.2434i | 0.452705 | + | 0.784107i | ||||
\(735\) | −25.6034 | + | 8.28669i | −0.944396 | + | 0.305659i | ||||
\(736\) | 6.57019i | 0.242180i | ||||||||
\(737\) | 7.21101 | + | 4.17299i | 0.265621 | + | 0.153714i | ||||
\(738\) | 29.9677 | − | 21.6682i | 1.10313 | − | 0.797619i | ||||
\(739\) | 19.2960 | + | 11.1405i | 0.709814 | + | 0.409811i | 0.810992 | − | 0.585057i | \(-0.198928\pi\) |
−0.101178 | + | 0.994868i | \(0.532261\pi\) | |||||||
\(740\) | 41.6388i | 1.53067i | ||||||||
\(741\) | 6.40346 | − | 6.21641i | 0.235237 | − | 0.228366i | ||||
\(742\) | −41.5542 | −1.52550 | ||||||||
\(743\) | 4.30681 | − | 7.45961i | 0.158002 | − | 0.273667i | −0.776146 | − | 0.630553i | \(-0.782828\pi\) |
0.934148 | + | 0.356886i | \(0.116162\pi\) | |||||||
\(744\) | −45.1114 | + | 49.9862i | −1.65387 | + | 1.83258i | ||||
\(745\) | 7.63839 | − | 4.41002i | 0.279849 | − | 0.161571i | ||||
\(746\) | 43.8042i | 1.60379i | ||||||||
\(747\) | 0.532583 | + | 5.18119i | 0.0194862 | + | 0.189570i | ||||
\(748\) | 42.9333 | + | 24.8454i | 1.56980 | + | 0.908437i | ||||
\(749\) | 45.7520i | 1.67174i | ||||||||
\(750\) | 43.7517 | − | 14.1605i | 1.59759 | − | 0.517068i | ||||
\(751\) | 1.46013 | − | 2.52902i | 0.0532809 | − | 0.0922853i | −0.838155 | − | 0.545432i | \(-0.816365\pi\) |
0.891436 | + | 0.453147i | \(0.149699\pi\) | |||||||
\(752\) | −38.6549 | − | 22.3174i | −1.40960 | − | 0.813832i | ||||
\(753\) | −2.09834 | + | 9.81668i | −0.0764678 | + | 0.357740i | ||||
\(754\) | 0.229629 | − | 3.47225i | 0.00836258 | − | 0.126452i | ||||
\(755\) | −15.9586 | −0.580794 | ||||||||
\(756\) | 31.9364 | + | 72.3979i | 1.16151 | + | 2.63309i | ||||
\(757\) | −11.2830 | + | 19.5427i | −0.410088 | + | 0.710293i | −0.994899 | − | 0.100877i | \(-0.967835\pi\) |
0.584811 | + | 0.811170i | \(0.301169\pi\) | |||||||
\(758\) | −14.7575 | − | 25.5607i | −0.536016 | − | 0.928407i | ||||
\(759\) | 10.0919 | + | 31.2889i | 0.366314 | + | 1.13571i | ||||
\(760\) | 8.64428 | + | 14.9723i | 0.313561 | + | 0.543104i | ||||
\(761\) | −2.92561 | − | 5.06731i | −0.106053 | − | 0.183690i | 0.808115 | − | 0.589025i | \(-0.200488\pi\) |
−0.914168 | + | 0.405335i | \(0.867155\pi\) | |||||||
\(762\) | 4.74341 | − | 22.1911i | 0.171836 | − | 0.803899i | ||||
\(763\) | −17.1429 | − | 29.6923i | −0.620614 | − | 1.07494i | ||||
\(764\) | 22.5802 | + | 13.0367i | 0.816924 | + | 0.471651i | ||||
\(765\) | 14.8028 | + | 20.4726i | 0.535196 | + | 0.740190i | ||||
\(766\) | − | 85.2912i | − | 3.08170i | ||||||
\(767\) | 8.16072 | + | 0.539689i | 0.294666 | + | 0.0194870i | ||||
\(768\) | −55.1882 | − | 11.7966i | −1.99143 | − | 0.425674i | ||||
\(769\) | 35.9163 | + | 20.7363i | 1.29517 | + | 0.747769i | 0.979566 | − | 0.201121i | \(-0.0644583\pi\) |
0.315608 | + | 0.948890i | \(0.397792\pi\) | |||||||
\(770\) | −0.0709867 | + | 70.3116i | −0.00255818 | + | 2.53385i | ||||
\(771\) | 41.3780 | − | 13.3922i | 1.49019 | − | 0.482309i | ||||
\(772\) | 5.36596i | 0.193125i | ||||||||
\(773\) | −5.92843 | + | 3.42278i | −0.213231 | + | 0.123109i | −0.602812 | − | 0.797883i | \(-0.705953\pi\) |
0.389581 | + | 0.920992i | \(0.372620\pi\) | |||||||
\(774\) | −54.0356 | + | 5.55440i | −1.94227 | + | 0.199649i | ||||
\(775\) | −2.70089 | −0.0970189 | ||||||||
\(776\) | −41.9774 | − | 72.7071i | −1.50690 | − | 2.61003i | ||||
\(777\) | 20.8133 | + | 18.7835i | 0.746672 | + | 0.673855i | ||||
\(778\) | 17.2953 | + | 9.98546i | 0.620068 | + | 0.357996i | ||||
\(779\) | − | 7.12503i | − | 0.255281i | ||||||
\(780\) | 42.6785 | − | 41.4318i | 1.52813 | − | 1.48350i | ||||
\(781\) | −23.1804 | − | 40.2434i | −0.829460 | − | 1.44002i | ||||
\(782\) | 44.5606 | + | 25.7271i | 1.59348 | + | 0.919998i | ||||
\(783\) | 1.85582 | − | 0.818645i | 0.0663217 | − | 0.0292560i | ||||
\(784\) | 15.7334 | + | 27.2511i | 0.561907 | + | 0.973252i | ||||
\(785\) | − | 15.4305i | − | 0.550739i | ||||||
\(786\) | 17.7990 | + | 54.9938i | 0.634870 | + | 1.96156i | ||||
\(787\) | −46.6245 | + | 26.9186i | −1.66198 | + | 0.959546i | −0.690215 | + | 0.723604i | \(0.742484\pi\) |
−0.971767 | + | 0.235942i | \(0.924183\pi\) | |||||||
\(788\) | 17.4186 | 0.620513 | ||||||||
\(789\) | −5.17447 | − | 15.9876i | −0.184216 | − | 0.569173i | ||||
\(790\) | −26.5835 | + | 46.0440i | −0.945799 | + | 1.63817i | ||||
\(791\) | −13.6555 | + | 23.6520i | −0.485532 | + | 0.840967i | ||||
\(792\) | 51.7109 | − | 5.26269i | 1.83747 | − | 0.187002i | ||||
\(793\) | −29.5616 | − | 1.95498i | −1.04976 | − | 0.0694235i | ||||
\(794\) | −0.925402 | −0.0328413 | ||||||||
\(795\) | −12.1986 | + | 13.5168i | −0.432641 | + | 0.479392i | ||||
\(796\) | 36.2405 | − | 62.7705i | 1.28451 | − | 2.22484i | ||||
\(797\) | −11.9010 | + | 6.87106i | −0.421556 | + | 0.243386i | −0.695743 | − | 0.718291i | \(-0.744925\pi\) |
0.274187 | + | 0.961676i | \(0.411591\pi\) | |||||||
\(798\) | 22.1587 | + | 4.73647i | 0.784408 | + | 0.167669i | ||||
\(799\) | −29.9704 | + | 17.3034i | −1.06028 | + | 0.612151i | ||||
\(800\) | 0.208338 | + | 0.360852i | 0.00736586 | + | 0.0127580i | ||||
\(801\) | −13.4736 | + | 30.0767i | −0.476065 | + | 1.06271i | ||||
\(802\) | −2.15680 | + | 1.24523i | −0.0761591 | + | 0.0439705i | ||||
\(803\) | 45.2192 | + | 0.0456533i | 1.59575 | + | 0.00161107i | ||||
\(804\) | 11.9893 | − | 13.2848i | 0.422829 | − | 0.468520i | ||||
\(805\) | 49.0717i | 1.72955i | ||||||||
\(806\) | 59.5133 | − | 29.3053i | 2.09627 | − | 1.03224i | ||||
\(807\) | 3.87955 | − | 18.1497i | 0.136567 | − | 0.638900i | ||||
\(808\) | −18.7407 | + | 32.4599i | −0.659297 | + | 1.14194i | ||||
\(809\) | −11.8217 | + | 20.4757i | −0.415627 | + | 0.719888i | −0.995494 | − | 0.0948235i | \(-0.969771\pi\) |
0.579867 | + | 0.814711i | \(0.303105\pi\) | |||||||
\(810\) | 48.9354 | + | 16.1480i | 1.71942 | + | 0.567383i | ||||
\(811\) | 4.85443i | 0.170462i | 0.996361 | + | 0.0852311i | \(0.0271629\pi\) | ||||
−0.996361 | + | 0.0852311i | \(0.972837\pi\) | |||||||
\(812\) | 5.14811 | − | 2.97226i | 0.180663 | − | 0.104306i | ||||
\(813\) | 5.10604 | − | 1.65260i | 0.179077 | − | 0.0579591i | ||||
\(814\) | 31.0636 | − | 17.8928i | 1.08878 | − | 0.627142i | ||||
\(815\) | −46.3102 | + | 26.7372i | −1.62217 | + | 0.936563i | ||||
\(816\) | 19.7916 | − | 21.9303i | 0.692843 | − | 0.767713i | ||||
\(817\) | −5.23290 | + | 9.06365i | −0.183076 | + | 0.317097i | ||||
\(818\) | − | 38.9140i | − | 1.36060i | ||||||
\(819\) | −1.45730 | − | 40.0231i | −0.0509223 | − | 1.39852i | ||||
\(820\) | − | 47.4877i | − | 1.65834i | ||||||
\(821\) | −23.5087 | + | 40.7182i | −0.820458 | + | 1.42107i | 0.0848840 | + | 0.996391i | \(0.472948\pi\) |
−0.905342 | + | 0.424684i | \(0.860385\pi\) | |||||||
\(822\) | 5.66992 | + | 5.11698i | 0.197761 | + | 0.178475i | ||||
\(823\) | −17.7481 | − | 30.7406i | −0.618659 | − | 1.07155i | −0.989731 | − | 0.142945i | \(-0.954343\pi\) |
0.371072 | − | 0.928604i | \(-0.378990\pi\) | |||||||
\(824\) | −73.2878 | −2.55310 | ||||||||
\(825\) | 1.54643 | + | 1.39846i | 0.0538399 | + | 0.0486880i | ||||
\(826\) | 10.3825 | + | 17.9831i | 0.361254 | + | 0.625711i | ||||
\(827\) | −0.0190957 | −0.000664022 | −0.000332011 | − | 1.00000i | \(-0.500106\pi\) | ||||
−0.000332011 | 1.00000i | \(0.500106\pi\) | ||||||||
\(828\) | 70.2442 | − | 7.22052i | 2.44116 | − | 0.250930i | ||||
\(829\) | −5.22732 | + | 9.05399i | −0.181552 | + | 0.314458i | −0.942409 | − | 0.334462i | \(-0.891446\pi\) |
0.760857 | + | 0.648920i | \(0.224779\pi\) | |||||||
\(830\) | 8.60887 | + | 4.97034i | 0.298818 | + | 0.172523i | ||||
\(831\) | −5.21695 | + | 24.4065i | −0.180974 | + | 0.846652i | ||||
\(832\) | 19.6041 | + | 13.1157i | 0.679650 | + | 0.454705i | ||||
\(833\) | 24.3973 | 0.845315 | ||||||||
\(834\) | 19.5215 | + | 17.6177i | 0.675974 | + | 0.610051i | ||||
\(835\) | 0.529602 | + | 0.305766i | 0.0183276 | + | 0.0105815i | ||||
\(836\) | 9.76401 | − | 16.8724i | 0.337695 | − | 0.583544i | ||||
\(837\) | 31.2043 | + | 22.8353i | 1.07858 | + | 0.789304i | ||||
\(838\) | −47.0208 | + | 27.1475i | −1.62431 | + | 0.937793i | ||||
\(839\) | 2.54653 | − | 1.47024i | 0.0879159 | − | 0.0507583i | −0.455398 | − | 0.890288i | \(-0.650503\pi\) |
0.543313 | + | 0.839530i | \(0.317170\pi\) | |||||||
\(840\) | 75.8697 | + | 16.2173i | 2.61775 | + | 0.559551i | ||||
\(841\) | 14.4238 | + | 24.9828i | 0.497373 | + | 0.861475i | ||||
\(842\) | −7.33321 | + | 12.7015i | −0.252719 | + | 0.437722i | ||||
\(843\) | 2.12295 | − | 2.35236i | 0.0731182 | − | 0.0810195i | ||||
\(844\) | 2.11900i | 0.0729389i | ||||||||
\(845\) | −27.8273 | + | 11.4882i | −0.957288 | + | 0.395207i | ||||
\(846\) | −28.8584 | + | 64.4199i | −0.992171 | + | 2.21480i | ||||
\(847\) | 35.3129 | − | 20.2930i | 1.21337 | − | 0.697275i | ||||
\(848\) | 18.4375 | + | 10.6449i | 0.633146 | + | 0.365547i | ||||
\(849\) | −9.06505 | + | 2.93395i | −0.311112 | + | 0.100693i | ||||
\(850\) | 3.26318 | 0.111926 | ||||||||
\(851\) | 21.6672 | − | 12.5096i | 0.742743 | − | 0.428823i | ||||
\(852\) | −94.9054 | + | 30.7166i | −3.25140 | + | 1.05233i | ||||
\(853\) | − | 15.6357i | − | 0.535356i | −0.963508 | − | 0.267678i | \(-0.913744\pi\) | ||
0.963508 | − | 0.267678i | \(-0.0862563\pi\) | |||||||
\(854\) | −37.6100 | − | 65.1424i | −1.28699 | − | 2.22913i | ||||
\(855\) | 8.04556 | − | 5.81736i | 0.275152 | − | 0.198950i | ||||
\(856\) | 32.2757 | − | 55.9032i | 1.10316 | − | 1.91073i | ||||
\(857\) | −29.0261 | −0.991514 | −0.495757 | − | 0.868461i | \(-0.665109\pi\) | ||||
−0.495757 | + | 0.868461i | \(0.665109\pi\) | |||||||
\(858\) | −49.2488 | − | 14.0354i | −1.68133 | − | 0.479160i | ||||
\(859\) | 18.6927 | 0.637785 | 0.318893 | − | 0.947791i | \(-0.396689\pi\) | ||||
0.318893 | + | 0.947791i | \(0.396689\pi\) | |||||||
\(860\) | −34.8768 | + | 60.4084i | −1.18929 | + | 2.05991i | ||||
\(861\) | −23.7368 | − | 21.4220i | −0.808949 | − | 0.730059i | ||||
\(862\) | −35.8584 | − | 62.1086i | −1.22134 | − | 2.11543i | ||||
\(863\) | 39.6741i | 1.35052i | 0.737579 | + | 0.675260i | \(0.235969\pi\) | ||||
−0.737579 | + | 0.675260i | \(0.764031\pi\) | |||||||
\(864\) | 0.643905 | − | 5.93049i | 0.0219061 | − | 0.201759i | ||||
\(865\) | −47.0035 | + | 27.1375i | −1.59817 | + | 0.922701i | ||||
\(866\) | 1.41583 | 0.0481117 | ||||||||
\(867\) | 2.01420 | + | 6.22329i | 0.0684059 | + | 0.211354i | ||||
\(868\) | 98.1400 | + | 56.6612i | 3.33109 | + | 1.92321i | ||||
\(869\) | 30.7973 | + | 0.0310930i | 1.04473 | + | 0.00105476i | ||||
\(870\) | 0.809206 | − | 3.78572i | 0.0274347 | − | 0.128348i | ||||
\(871\) | −8.12551 | + | 4.00113i | −0.275322 | + | 0.135573i | ||||
\(872\) | 48.3738i | 1.63814i | ||||||||
\(873\) | −39.0700 | + | 28.2497i | −1.32232 | + | 0.956106i | ||||
\(874\) | 10.1105 | − | 17.5119i | 0.341993 | − | 0.592349i | ||||
\(875\) | −19.8801 | − | 34.4334i | −0.672071 | − | 1.16406i | ||||
\(876\) | 20.3023 | − | 94.9803i | 0.685950 | − | 3.20909i | ||||
\(877\) | −4.33737 | + | 2.50418i | −0.146462 | + | 0.0845601i | −0.571440 | − | 0.820644i | \(-0.693615\pi\) |
0.424978 | + | 0.905204i | \(0.360282\pi\) | |||||||
\(878\) | −1.60507 | + | 0.926690i | −0.0541686 | + | 0.0312743i | ||||
\(879\) | −1.31186 | − | 0.280413i | −0.0442479 | − | 0.00945810i | ||||
\(880\) | 18.0431 | − | 31.1788i | 0.608233 | − | 1.05104i | ||||
\(881\) | −40.3122 | − | 23.2742i | −1.35815 | − | 0.784129i | −0.368776 | − | 0.929518i | \(-0.620223\pi\) |
−0.989375 | + | 0.145389i | \(0.953557\pi\) | |||||||
\(882\) | 40.3265 | − | 29.1582i | 1.35786 | − | 0.981808i | ||||
\(883\) | −26.4621 | −0.890522 | −0.445261 | − | 0.895401i | \(-0.646889\pi\) | ||||
−0.445261 | + | 0.895401i | \(0.646889\pi\) | |||||||
\(884\) | −48.3781 | + | 23.8222i | −1.62713 | + | 0.801226i | ||||
\(885\) | 8.89744 | + | 1.90185i | 0.299084 | + | 0.0639300i | ||||
\(886\) | −0.299332 | − | 0.172819i | −0.0100563 | − | 0.00580598i | ||||
\(887\) | 11.1436 | − | 19.3013i | 0.374166 | − | 0.648075i | −0.616036 | − | 0.787718i | \(-0.711262\pi\) |
0.990202 | + | 0.139643i | \(0.0445956\pi\) | |||||||
\(888\) | −12.1804 | − | 37.6338i | −0.408747 | − | 1.26291i | ||||
\(889\) | −19.6201 | −0.658038 | ||||||||
\(890\) | 31.4498 | + | 54.4727i | 1.05420 | + | 1.82593i | ||||
\(891\) | −6.04291 | − | 29.2315i | −0.202445 | − | 0.979294i | ||||
\(892\) | −64.4139 | −2.15674 | ||||||||
\(893\) | 6.80008 | + | 11.7781i | 0.227556 | + | 0.394139i | ||||
\(894\) | −10.9274 | + | 12.1082i | −0.365466 | + | 0.404958i | ||||
\(895\) | −22.3878 | + | 38.7768i | −0.748341 | + | 1.29616i | ||||
\(896\) | 68.3878i | 2.28468i | ||||||||
\(897\) | −34.3814 | − | 9.76083i | −1.14796 | − | 0.325905i | ||||
\(898\) | 29.2715i | 0.976803i | ||||||||
\(899\) | 1.45243 | − | 2.51569i | 0.0484413 | − | 0.0839028i | ||||
\(900\) | 3.62904 | − | 2.62399i | 0.120968 | − | 0.0874663i | ||||
\(901\) | 14.2952 | − | 8.25333i | 0.476242 | − | 0.274958i | ||||
\(902\) | −35.4270 | + | 20.4061i | −1.17959 | + | 0.679450i | ||||
\(903\) | 14.4622 | + | 44.6839i | 0.481271 | + | 1.48699i | ||||
\(904\) | 33.3706 | − | 19.2665i | 1.10989 | − | 0.640794i | ||||
\(905\) | − | 55.1621i | − | 1.83365i | ||||||
\(906\) | 28.0767 | − | 9.08716i | 0.932784 | − | 0.301901i | ||||
\(907\) | 8.12560 | − | 14.0740i | 0.269806 | − | 0.467318i | −0.699006 | − | 0.715116i | \(-0.746374\pi\) |
0.968812 | + | 0.247798i | \(0.0797071\pi\) | |||||||
\(908\) | −44.8638 | + | 77.7065i | −1.48886 | + | 2.57878i | ||||
\(909\) | 19.6437 | + | 8.79983i | 0.651539 | + | 0.291872i | ||||
\(910\) | −63.5300 | − | 42.5033i | −2.10600 | − | 1.40897i | ||||
\(911\) | − | 30.1340i | − | 0.998383i | −0.866492 | − | 0.499191i | \(-0.833630\pi\) | ||
0.866492 | − | 0.499191i | \(-0.166370\pi\) | |||||||
\(912\) | −8.61839 | − | 7.77791i | −0.285383 | − | 0.257552i | ||||
\(913\) | 0.00581348 | − | 5.75820i | 0.000192398 | − | 0.190568i | ||||
\(914\) | −62.4516 | + | 36.0565i | −2.06572 | + | 1.19264i | ||||
\(915\) | −32.2304 | − | 6.88932i | −1.06550 | − | 0.227754i | ||||
\(916\) | −27.6671 | − | 47.9209i | −0.914147 | − | 1.58335i | ||||
\(917\) | 43.2811 | − | 24.9883i | 1.42927 | − | 0.825187i | ||||
\(918\) | −37.7007 | − | 27.5893i | −1.24431 | − | 0.910583i | ||||
\(919\) | 0.220789 | − | 0.127473i | 0.00728315 | − | 0.00420493i | −0.496354 | − | 0.868120i | \(-0.665328\pi\) |
0.503637 | + | 0.863915i | \(0.331995\pi\) | |||||||
\(920\) | 34.6177 | − | 59.9595i | 1.14131 | − | 1.97681i | ||||
\(921\) | −33.0617 | − | 29.8375i | −1.08942 | − | 0.983178i | ||||
\(922\) | 21.8955 | 0.721090 | ||||||||
\(923\) | 50.3778 | + | 3.33161i | 1.65820 | + | 0.109661i | ||||
\(924\) | −26.8537 | − | 83.2567i | −0.883421 | − | 2.73895i | ||||
\(925\) | 0.793348 | − | 1.37412i | 0.0260851 | − | 0.0451807i | ||||
\(926\) | 32.5249 | − | 56.3348i | 1.06883 | − | 1.85128i | ||||
\(927\) | 4.30355 | + | 41.8667i | 0.141347 | + | 1.37508i | ||||
\(928\) | −0.448144 | −0.0147110 | ||||||||
\(929\) | 40.3841 | − | 23.3158i | 1.32496 | − | 0.764966i | 0.340445 | − | 0.940264i | \(-0.389422\pi\) |
0.984515 | + | 0.175298i | \(0.0560889\pi\) | |||||||
\(930\) | 70.2127 | − | 22.7247i | 2.30236 | − | 0.745173i | ||||
\(931\) | − | 9.58790i | − | 0.314231i | ||||||
\(932\) | 10.5417 | + | 18.2588i | 0.345305 | + | 0.598086i | ||||
\(933\) | 3.36922 | + | 3.04065i | 0.110303 | + | 0.0995464i | ||||
\(934\) | 62.8180 | + | 36.2680i | 2.05547 | + | 1.18672i | ||||
\(935\) | −13.9406 | − | 24.2022i | −0.455906 | − | 0.791496i | ||||
\(936\) | −26.4537 | + | 49.9313i | −0.864665 | + | 1.63206i | ||||
\(937\) | 9.76109i | 0.318881i | 0.987208 | + | 0.159441i | \(0.0509690\pi\) | ||||
−0.987208 | + | 0.159441i | \(0.949031\pi\) | |||||||
\(938\) | −19.9151 | − | 11.4980i | −0.650251 | − | 0.375422i | ||||
\(939\) | −5.67770 | + | 6.29124i | −0.185285 | + | 0.205307i | ||||
\(940\) | 45.3219 | + | 78.4999i | 1.47824 | + | 2.56038i | ||||
\(941\) | 26.4931 | 0.863650 | 0.431825 | − | 0.901957i | \(-0.357870\pi\) | ||||
0.431825 | + | 0.901957i | \(0.357870\pi\) | |||||||
\(942\) | 8.78645 | + | 27.1475i | 0.286278 | + | 0.884514i | ||||
\(943\) | −24.7107 | + | 14.2668i | −0.804693 | + | 0.464589i | ||||
\(944\) | − | 10.6387i | − | 0.346260i | ||||||
\(945\) | 4.80923 | − | 44.2939i | 0.156444 | − | 1.44088i | ||||
\(946\) | 60.0533 | + | 0.0606299i | 1.95250 | + | 0.00197125i | ||||
\(947\) | −1.22181 | − | 0.705411i | −0.0397034 | − | 0.0229228i | 0.480017 | − | 0.877259i | \(-0.340631\pi\) |
−0.519720 | + | 0.854336i | \(0.673964\pi\) | |||||||
\(948\) | 13.8272 | − | 64.6880i | 0.449087 | − | 2.10097i | ||||
\(949\) | −27.3349 | + | 40.8577i | −0.887330 | + | 1.32630i | ||||
\(950\) | − | 1.28240i | − | 0.0416066i | ||||||
\(951\) | −5.19670 | − | 4.68991i | −0.168515 | − | 0.152081i | ||||
\(952\) | −60.9131 | − | 35.1682i | −1.97421 | − | 1.13981i | ||||
\(953\) | 24.2967 | + | 42.0831i | 0.787048 | + | 1.36321i | 0.927768 | + | 0.373157i | \(0.121725\pi\) |
−0.140721 | + | 0.990049i | \(0.544942\pi\) | |||||||
\(954\) | 13.7648 | − | 30.7268i | 0.445651 | − | 0.994818i | ||||
\(955\) | −7.34043 | − | 12.7140i | −0.237531 | − | 0.411416i | ||||
\(956\) | 49.8540 | + | 86.3496i | 1.61239 | + | 2.79275i | ||||
\(957\) | −2.13417 | + | 0.688357i | −0.0689880 | + | 0.0222514i | ||||
\(958\) | −42.9778 | − | 74.4397i | −1.38855 | − | 2.40504i | ||||
\(959\) | 3.30174 | − | 5.71878i | 0.106619 | − | 0.184669i | ||||
\(960\) | 19.4799 | + | 17.5802i | 0.628712 | + | 0.567399i | ||||
\(961\) | 24.3764 | 0.786334 | ||||||||
\(962\) | −2.57165 | + | 38.8863i | −0.0829132 | + | 1.25374i | ||||
\(963\) | −33.8308 | − | 15.1553i | −1.09018 | − | 0.488372i | ||||
\(964\) | −64.2708 | − | 37.1068i | −2.07002 | − | 1.19513i | ||||
\(965\) | 1.51068 | − | 2.61657i | 0.0486304 | − | 0.0842304i | ||||
\(966\) | −27.9424 | − | 86.3338i | −0.899032 | − | 2.77775i | ||||
\(967\) | 44.3067i | 1.42481i | 0.701770 | + | 0.712404i | \(0.252393\pi\) | ||||
−0.701770 | + | 0.712404i | \(0.747607\pi\) | |||||||
\(968\) | −57.4637 | − | 0.116031i | −1.84695 | − | 0.00372938i | ||||
\(969\) | −8.56360 | + | 2.77166i | −0.275102 | + | 0.0890384i | ||||
\(970\) | 92.0173i | 2.95450i | ||||||||
\(971\) | 18.5387 | − | 10.7033i | 0.594935 | − | 0.343486i | −0.172111 | − | 0.985077i | \(-0.555059\pi\) |
0.767046 | + | 0.641592i | \(0.221726\pi\) | |||||||
\(972\) | −64.1127 | − | 0.366714i | −2.05641 | − | 0.0117624i | ||||
\(973\) | 11.3679 | − | 19.6897i | 0.364437 | − | 0.631223i | ||||
\(974\) | 40.1911 | 1.28781 | ||||||||
\(975\) | −2.19783 | + | 0.554132i | −0.0703870 | + | 0.0177464i | ||||
\(976\) | 38.5380i | 1.23357i | ||||||||
\(977\) | 33.0568 | + | 19.0853i | 1.05758 | + | 0.610594i | 0.924762 | − | 0.380546i | \(-0.124264\pi\) |
0.132818 | + | 0.991140i | \(0.457597\pi\) | |||||||
\(978\) | 66.2507 | − | 73.4098i | 2.11846 | − | 2.34739i | ||||
\(979\) | 18.2494 | − | 31.5352i | 0.583252 | − | 1.00787i | ||||
\(980\) | − | 63.9025i | − | 2.04129i | ||||||
\(981\) | 27.6342 | − | 2.84057i | 0.882293 | − | 0.0906923i | ||||
\(982\) | 16.6598 | + | 28.8556i | 0.531636 | + | 0.920820i | ||||
\(983\) | − | 20.6274i | − | 0.657911i | −0.944346 | − | 0.328955i | \(-0.893303\pi\) | ||
0.944346 | − | 0.328955i | \(-0.106697\pi\) | |||||||
\(984\) | 13.8913 | + | 42.9201i | 0.442840 | + | 1.36824i | ||||
\(985\) | −8.49374 | − | 4.90386i | −0.270633 | − | 0.156250i | ||||
\(986\) | −1.75481 | + | 3.03942i | −0.0558845 | + | 0.0967948i | ||||
\(987\) | 59.6834 | + | 12.7575i | 1.89974 | + | 0.406075i | ||||
\(988\) | 9.36190 | + | 19.0122i | 0.297842 | + | 0.604857i | ||||
\(989\) | 41.9123 | 1.33273 | ||||||||
\(990\) | −51.9676 | − | 23.3431i | −1.65164 | − | 0.741892i | ||||
\(991\) | 6.40435 | − | 11.0927i | 0.203441 | − | 0.352370i | −0.746194 | − | 0.665729i | \(-0.768121\pi\) |
0.949635 | + | 0.313359i | \(0.101454\pi\) | |||||||
\(992\) | −4.27155 | − | 7.39855i | −0.135622 | − | 0.234904i | ||||
\(993\) | 2.64173 | + | 0.564677i | 0.0838329 | + | 0.0179195i | ||||
\(994\) | 64.0935 | + | 111.013i | 2.03292 | + | 3.52112i | ||||
\(995\) | −35.3435 | + | 20.4056i | −1.12046 | + | 0.646900i | ||||
\(996\) | −12.0948 | − | 2.58529i | −0.383237 | − | 0.0819179i | ||||
\(997\) | 38.7630 | − | 22.3798i | 1.22764 | − | 0.708776i | 0.261101 | − | 0.965311i | \(-0.415914\pi\) |
0.966535 | + | 0.256536i | \(0.0825811\pi\) | |||||||
\(998\) | −9.93798 | + | 17.2131i | −0.314581 | + | 0.544871i | ||||
\(999\) | −20.7836 | + | 9.16813i | −0.657565 | + | 0.290067i |
(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 | 429.2.p.b.230.3 | ✓ | 96 | |
3.2 | odd | 2 | inner | 429.2.p.b.230.46 | yes | 96 | |
11.10 | odd | 2 | inner | 429.2.p.b.230.45 | yes | 96 | |
13.3 | even | 3 | inner | 429.2.p.b.263.4 | yes | 96 | |
33.32 | even | 2 | inner | 429.2.p.b.230.4 | yes | 96 | |
39.29 | odd | 6 | inner | 429.2.p.b.263.45 | yes | 96 | |
143.120 | odd | 6 | inner | 429.2.p.b.263.46 | yes | 96 | |
429.263 | even | 6 | inner | 429.2.p.b.263.3 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.p.b.230.3 | ✓ | 96 | 1.1 | even | 1 | trivial | |
429.2.p.b.230.4 | yes | 96 | 33.32 | even | 2 | inner | |
429.2.p.b.230.45 | yes | 96 | 11.10 | odd | 2 | inner | |
429.2.p.b.230.46 | yes | 96 | 3.2 | odd | 2 | inner | |
429.2.p.b.263.3 | yes | 96 | 429.263 | even | 6 | inner | |
429.2.p.b.263.4 | yes | 96 | 13.3 | even | 3 | inner | |
429.2.p.b.263.45 | yes | 96 | 39.29 | odd | 6 | inner | |
429.2.p.b.263.46 | yes | 96 | 143.120 | odd | 6 | inner |