Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(79,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.89539436150784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 79.6 | ||
Root | \(-1.16746 + 0.312819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.79 |
Dual form | 735.2.q.e.214.6 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.34630 | + | 1.35464i | 1.65909 | + | 0.957873i | 0.973138 | + | 0.230222i | \(0.0739454\pi\) |
0.685948 | + | 0.727651i | \(0.259388\pi\) | |||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 2.67009 | + | 4.62473i | 1.33504 | + | 2.31236i | ||||
\(5\) | −0.618092 | + | 2.14894i | −0.276419 | + | 0.961037i | ||||
\(6\) | −2.70928 | −1.10606 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 9.04945i | 3.19946i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −4.36127 | + | 4.20478i | −1.37916 | + | 1.32967i | ||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | −4.62473 | − | 2.67009i | −1.33504 | − | 0.770788i | ||||
\(13\) | − | 0.921622i | − | 0.255612i | −0.991799 | − | 0.127806i | \(-0.959207\pi\) | ||
0.991799 | − | 0.127806i | \(-0.0407935\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.539189 | − | 2.17009i | −0.139218 | − | 0.560314i | ||||
\(16\) | −6.91855 | + | 11.9833i | −1.72964 | + | 2.99582i | ||||
\(17\) | 0.933903 | − | 0.539189i | 0.226505 | − | 0.130773i | −0.382454 | − | 0.923975i | \(-0.624921\pi\) |
0.608959 | + | 0.793202i | \(0.291588\pi\) | |||||||
\(18\) | 2.34630 | − | 1.35464i | 0.553029 | − | 0.319291i | ||||
\(19\) | 1.53919 | − | 2.66595i | 0.353114 | − | 0.611612i | −0.633679 | − | 0.773596i | \(-0.718456\pi\) |
0.986793 | + | 0.161984i | \(0.0517894\pi\) | |||||||
\(20\) | −11.5886 | + | 2.87936i | −2.59130 | + | 0.643845i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 5.41855i | − | 1.15524i | ||||||
\(23\) | 2.02665 | + | 1.17009i | 0.422586 | + | 0.243980i | 0.696183 | − | 0.717864i | \(-0.254880\pi\) |
−0.273597 | + | 0.961844i | \(0.588214\pi\) | |||||||
\(24\) | −4.52472 | − | 7.83705i | −0.923605 | − | 1.59973i | ||||
\(25\) | −4.23592 | − | 2.65649i | −0.847185 | − | 0.531298i | ||||
\(26\) | 1.24846 | − | 2.16240i | 0.244844 | − | 0.424082i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.68035 | 1.24051 | 0.620255 | − | 0.784401i | \(-0.287029\pi\) | ||||
0.620255 | + | 0.784401i | \(0.287029\pi\) | |||||||
\(30\) | 1.67458 | − | 5.82208i | 0.305735 | − | 1.06296i | ||||
\(31\) | 3.87936 | + | 6.71925i | 0.696754 | + | 1.20681i | 0.969586 | + | 0.244752i | \(0.0787064\pi\) |
−0.272832 | + | 0.962062i | \(0.587960\pi\) | |||||||
\(32\) | −16.7919 | + | 9.69481i | −2.96842 | + | 1.71382i | ||||
\(33\) | 1.73205 | + | 1.00000i | 0.301511 | + | 0.174078i | ||||
\(34\) | 2.92162 | 0.501054 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.34017 | 0.890029 | ||||||||
\(37\) | −9.38521 | − | 5.41855i | −1.54292 | − | 0.890804i | −0.998653 | − | 0.0518912i | \(-0.983475\pi\) |
−0.544265 | − | 0.838913i | \(-0.683192\pi\) | |||||||
\(38\) | 7.22280 | − | 4.17009i | 1.17169 | − | 0.676477i | ||||
\(39\) | 0.460811 | + | 0.798148i | 0.0737888 | + | 0.127806i | ||||
\(40\) | −19.4468 | − | 5.59339i | −3.07480 | − | 0.884393i | ||||
\(41\) | 6.49693 | 1.01465 | 0.507325 | − | 0.861755i | \(-0.330634\pi\) | ||||
0.507325 | + | 0.861755i | \(0.330634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.52359i | 0.994838i | 0.867510 | + | 0.497419i | \(0.165719\pi\) | ||||
−0.867510 | + | 0.497419i | \(0.834281\pi\) | |||||||
\(44\) | 5.34017 | − | 9.24945i | 0.805061 | − | 1.39441i | ||||
\(45\) | 1.55199 | + | 1.60976i | 0.231358 | + | 0.239968i | ||||
\(46\) | 3.17009 | + | 5.49075i | 0.467404 | + | 0.809567i | ||||
\(47\) | −4.05330 | − | 2.34017i | −0.591234 | − | 0.341349i | 0.174351 | − | 0.984684i | \(-0.444217\pi\) |
−0.765585 | + | 0.643334i | \(0.777551\pi\) | |||||||
\(48\) | − | 13.8371i | − | 1.99721i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.34017 | − | 11.9711i | −0.896636 | − | 1.69297i | ||||
\(51\) | −0.539189 | + | 0.933903i | −0.0755015 | + | 0.130773i | ||||
\(52\) | 4.26225 | − | 2.46081i | 0.591068 | − | 0.341253i | ||||
\(53\) | −3.25515 | + | 1.87936i | −0.447129 | + | 0.258150i | −0.706617 | − | 0.707596i | \(-0.749780\pi\) |
0.259488 | + | 0.965746i | \(0.416446\pi\) | |||||||
\(54\) | −1.35464 | + | 2.34630i | −0.184343 | + | 0.319291i | ||||
\(55\) | 4.34017 | − | 1.07838i | 0.585229 | − | 0.145408i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.07838i | 0.407741i | ||||||||
\(58\) | 15.6741 | + | 9.04945i | 2.05811 | + | 1.18825i | ||||
\(59\) | 5.26180 | + | 9.11370i | 0.685027 | + | 1.18650i | 0.973428 | + | 0.228992i | \(0.0735431\pi\) |
−0.288401 | + | 0.957510i | \(0.593124\pi\) | |||||||
\(60\) | 8.59637 | − | 8.28792i | 1.10979 | − | 1.06997i | ||||
\(61\) | 2.07838 | − | 3.59986i | 0.266109 | − | 0.460914i | −0.701745 | − | 0.712429i | \(-0.747595\pi\) |
0.967854 | + | 0.251514i | \(0.0809286\pi\) | |||||||
\(62\) | 21.0205i | 2.66961i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −24.8576 | −3.10720 | ||||||||
\(65\) | 1.98052 | + | 0.569647i | 0.245653 | + | 0.0706561i | ||||
\(66\) | 2.70928 | + | 4.69260i | 0.333489 | + | 0.577619i | ||||
\(67\) | 4.05330 | − | 2.34017i | 0.495189 | − | 0.285898i | −0.231535 | − | 0.972826i | \(-0.574375\pi\) |
0.726725 | + | 0.686929i | \(0.241042\pi\) | |||||||
\(68\) | 4.98720 | + | 2.87936i | 0.604787 | + | 0.349174i | ||||
\(69\) | −2.34017 | −0.281724 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 7.83705 | + | 4.52472i | 0.923605 | + | 0.533244i | ||||
\(73\) | −6.13005 | + | 3.53919i | −0.717469 | + | 0.414231i | −0.813820 | − | 0.581117i | \(-0.802616\pi\) |
0.0963516 | + | 0.995347i | \(0.469283\pi\) | |||||||
\(74\) | −14.6803 | − | 25.4271i | −1.70656 | − | 2.95584i | ||||
\(75\) | 4.99666 | + | 0.182626i | 0.576965 | + | 0.0210878i | ||||
\(76\) | 16.4391 | 1.88569 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.49693i | 0.282721i | ||||||||
\(79\) | 3.07838 | − | 5.33191i | 0.346345 | − | 0.599886i | −0.639253 | − | 0.768997i | \(-0.720756\pi\) |
0.985597 | + | 0.169111i | \(0.0540895\pi\) | |||||||
\(80\) | −21.4751 | − | 22.2744i | −2.40099 | − | 2.49035i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 15.2438 | + | 8.80098i | 1.68339 | + | 0.971906i | ||||
\(83\) | − | 6.83710i | − | 0.750469i | −0.926930 | − | 0.375235i | \(-0.877562\pi\) | ||
0.926930 | − | 0.375235i | \(-0.122438\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.581449 | + | 2.34017i | 0.0630670 | + | 0.253827i | ||||
\(86\) | −8.83710 | + | 15.3063i | −0.952929 | + | 1.65052i | ||||
\(87\) | −5.78535 | + | 3.34017i | −0.620255 | + | 0.358104i | ||||
\(88\) | 15.6741 | − | 9.04945i | 1.67087 | − | 0.964674i | ||||
\(89\) | 4.17009 | − | 7.22280i | 0.442028 | − | 0.765615i | −0.555812 | − | 0.831308i | \(-0.687592\pi\) |
0.997840 | + | 0.0656928i | \(0.0209257\pi\) | |||||||
\(90\) | 1.46081 | + | 5.87936i | 0.153983 | + | 0.619739i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.4969i | 1.30289i | ||||||||
\(93\) | −6.71925 | − | 3.87936i | −0.696754 | − | 0.402271i | ||||
\(94\) | −6.34017 | − | 10.9815i | −0.653939 | − | 1.13266i | ||||
\(95\) | 4.77763 | + | 4.95544i | 0.490174 | + | 0.508417i | ||||
\(96\) | 9.69481 | − | 16.7919i | 0.989472 | − | 1.71382i | ||||
\(97\) | − | 8.43907i | − | 0.856858i | −0.903576 | − | 0.428429i | \(-0.859067\pi\) | ||
0.903576 | − | 0.428429i | \(-0.140933\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0.975255 | − | 26.6830i | 0.0975255 | − | 2.66830i | ||||
\(101\) | 2.90829 | + | 5.03731i | 0.289386 | + | 0.501231i | 0.973663 | − | 0.227991i | \(-0.0732156\pi\) |
−0.684277 | + | 0.729222i | \(0.739882\pi\) | |||||||
\(102\) | −2.53020 | + | 1.46081i | −0.250527 | + | 0.144642i | ||||
\(103\) | −1.86781 | − | 1.07838i | −0.184040 | − | 0.106256i | 0.405149 | − | 0.914251i | \(-0.367220\pi\) |
−0.589190 | + | 0.807995i | \(0.700553\pi\) | |||||||
\(104\) | 8.34017 | 0.817821 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.1834 | −0.989101 | ||||||||
\(107\) | 14.2868 | + | 8.24846i | 1.38115 | + | 0.797409i | 0.992296 | − | 0.123889i | \(-0.0395367\pi\) |
0.388857 | + | 0.921298i | \(0.372870\pi\) | |||||||
\(108\) | −4.62473 | + | 2.67009i | −0.445014 | + | 0.256929i | ||||
\(109\) | −6.41855 | − | 11.1173i | −0.614786 | − | 1.06484i | −0.990422 | − | 0.138073i | \(-0.955909\pi\) |
0.375636 | − | 0.926767i | \(-0.377424\pi\) | |||||||
\(110\) | 11.6442 | + | 3.34916i | 1.11023 | + | 0.319330i | ||||
\(111\) | 10.8371 | 1.02861 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.23513i | 0.492480i | 0.969209 | + | 0.246240i | \(0.0791951\pi\) | ||||
−0.969209 | + | 0.246240i | \(0.920805\pi\) | |||||||
\(114\) | −4.17009 | + | 7.22280i | −0.390564 | + | 0.676477i | ||||
\(115\) | −3.76711 | + | 3.63194i | −0.351284 | + | 0.338680i | ||||
\(116\) | 17.8371 | + | 30.8948i | 1.65613 | + | 2.86851i | ||||
\(117\) | −0.798148 | − | 0.460811i | −0.0737888 | − | 0.0426020i | ||||
\(118\) | 28.5113i | 2.62468i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 19.6381 | − | 4.87936i | 1.79270 | − | 0.445423i | ||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 9.75300 | − | 5.63090i | 0.882995 | − | 0.509798i | ||||
\(123\) | −5.62651 | + | 3.24846i | −0.507325 | + | 0.292904i | ||||
\(124\) | −20.7165 | + | 35.8820i | −1.86039 | + | 3.22230i | ||||
\(125\) | 8.32684 | − | 7.46081i | 0.744775 | − | 0.667315i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.84324i | 0.163562i | 0.996650 | + | 0.0817808i | \(0.0260607\pi\) | ||||
−0.996650 | + | 0.0817808i | \(0.973939\pi\) | |||||||
\(128\) | −24.7397 | − | 14.2834i | −2.18670 | − | 1.26249i | ||||
\(129\) | −3.26180 | − | 5.64960i | −0.287185 | − | 0.497419i | ||||
\(130\) | 3.87522 | + | 4.01944i | 0.339879 | + | 0.352529i | ||||
\(131\) | −0.738205 | + | 1.27861i | −0.0644973 | + | 0.111713i | −0.896471 | − | 0.443103i | \(-0.853878\pi\) |
0.831974 | + | 0.554815i | \(0.187211\pi\) | |||||||
\(132\) | 10.6803i | 0.929605i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.6803 | 1.09542 | ||||||||
\(135\) | −2.14894 | − | 0.618092i | −0.184952 | − | 0.0531969i | ||||
\(136\) | 4.87936 | + | 8.45130i | 0.418402 | + | 0.724693i | ||||
\(137\) | 3.84435 | − | 2.21953i | 0.328445 | − | 0.189628i | −0.326706 | − | 0.945126i | \(-0.605939\pi\) |
0.655150 | + | 0.755498i | \(0.272605\pi\) | |||||||
\(138\) | −5.49075 | − | 3.17009i | −0.467404 | − | 0.269856i | ||||
\(139\) | −13.6020 | −1.15370 | −0.576852 | − | 0.816849i | \(-0.695719\pi\) | ||||
−0.576852 | + | 0.816849i | \(0.695719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.68035 | 0.394156 | ||||||||
\(142\) | 4.69260 | + | 2.70928i | 0.393794 | + | 0.227357i | ||||
\(143\) | −1.59630 | + | 0.921622i | −0.133489 | + | 0.0770699i | ||||
\(144\) | 6.91855 | + | 11.9833i | 0.576546 | + | 0.998607i | ||||
\(145\) | −4.12907 | + | 14.3557i | −0.342900 | + | 1.19218i | ||||
\(146\) | −19.1773 | −1.58712 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 57.8720i | − | 4.75705i | ||||||
\(149\) | 7.83710 | − | 13.5743i | 0.642040 | − | 1.11205i | −0.342936 | − | 0.939359i | \(-0.611421\pi\) |
0.984977 | − | 0.172688i | \(-0.0552452\pi\) | |||||||
\(150\) | 11.4763 | + | 7.19716i | 0.937035 | + | 0.587646i | ||||
\(151\) | −2.92162 | − | 5.06040i | −0.237758 | − | 0.411809i | 0.722312 | − | 0.691567i | \(-0.243079\pi\) |
−0.960071 | + | 0.279757i | \(0.909746\pi\) | |||||||
\(152\) | 24.1254 | + | 13.9288i | 1.95683 | + | 1.12978i | ||||
\(153\) | − | 1.07838i | − | 0.0871817i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.8371 | + | 4.18342i | −1.35239 | + | 0.336020i | ||||
\(156\) | −2.46081 | + | 4.26225i | −0.197023 | + | 0.341253i | ||||
\(157\) | 4.26225 | − | 2.46081i | 0.340165 | − | 0.196394i | −0.320180 | − | 0.947357i | \(-0.603743\pi\) |
0.660345 | + | 0.750963i | \(0.270410\pi\) | |||||||
\(158\) | 14.4456 | − | 8.34017i | 1.14923 | − | 0.663509i | ||||
\(159\) | 1.87936 | − | 3.25515i | 0.149043 | − | 0.258150i | ||||
\(160\) | −10.4547 | − | 42.0772i | −0.826514 | − | 3.32649i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 2.70928i | − | 0.212861i | ||||||
\(163\) | −8.52450 | − | 4.92162i | −0.667690 | − | 0.385491i | 0.127511 | − | 0.991837i | \(-0.459301\pi\) |
−0.795201 | + | 0.606346i | \(0.792635\pi\) | |||||||
\(164\) | 17.3474 | + | 30.0465i | 1.35460 | + | 2.34624i | ||||
\(165\) | −3.21951 | + | 3.10399i | −0.250639 | + | 0.241645i | ||||
\(166\) | 9.26180 | − | 16.0419i | 0.718855 | − | 1.24509i | ||||
\(167\) | − | 19.2039i | − | 1.48605i | −0.669266 | − | 0.743023i | \(-0.733391\pi\) | ||
0.669266 | − | 0.743023i | \(-0.266609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1506 | 0.934662 | ||||||||
\(170\) | −1.80583 | + | 6.27840i | −0.138501 | + | 0.481532i | ||||
\(171\) | −1.53919 | − | 2.66595i | −0.117705 | − | 0.203871i | ||||
\(172\) | −30.1698 | + | 17.4186i | −2.30043 | + | 1.32815i | ||||
\(173\) | −19.4328 | − | 11.2195i | −1.47745 | − | 0.853005i | −0.477773 | − | 0.878483i | \(-0.658556\pi\) |
−0.999675 | + | 0.0254777i | \(0.991889\pi\) | |||||||
\(174\) | −18.0989 | −1.37207 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 27.6742 | 2.08602 | ||||||||
\(177\) | −9.11370 | − | 5.26180i | −0.685027 | − | 0.395501i | ||||
\(178\) | 19.5686 | − | 11.2979i | 1.46673 | − | 0.846814i | ||||
\(179\) | 5.00000 | + | 8.66025i | 0.373718 | + | 0.647298i | 0.990134 | − | 0.140122i | \(-0.0447496\pi\) |
−0.616417 | + | 0.787420i | \(0.711416\pi\) | |||||||
\(180\) | −3.30072 | + | 11.4757i | −0.246021 | + | 0.855351i | ||||
\(181\) | −8.52359 | −0.633553 | −0.316777 | − | 0.948500i | \(-0.602601\pi\) | ||||
−0.316777 | + | 0.948500i | \(0.602601\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.15676i | 0.307276i | ||||||||
\(184\) | −10.5886 | + | 18.3401i | −0.780605 | + | 1.35205i | ||||
\(185\) | 17.4451 | − | 16.8191i | 1.28259 | − | 1.23657i | ||||
\(186\) | −10.5103 | − | 18.2043i | −0.770650 | − | 1.33480i | ||||
\(187\) | −1.86781 | − | 1.07838i | −0.136587 | − | 0.0788588i | ||||
\(188\) | − | 24.9939i | − | 1.82286i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.49693 | + | 18.0989i | 0.326241 | + | 1.31303i | ||||
\(191\) | −7.68035 | + | 13.3027i | −0.555730 | + | 0.962553i | 0.442116 | + | 0.896958i | \(0.354228\pi\) |
−0.997846 | + | 0.0655953i | \(0.979105\pi\) | |||||||
\(192\) | 21.5273 | − | 12.4288i | 1.55360 | − | 0.896972i | ||||
\(193\) | −7.24589 | + | 4.18342i | −0.521571 | + | 0.301129i | −0.737577 | − | 0.675263i | \(-0.764030\pi\) |
0.216006 | + | 0.976392i | \(0.430697\pi\) | |||||||
\(194\) | 11.4319 | − | 19.8006i | 0.820761 | − | 1.42160i | ||||
\(195\) | −2.00000 | + | 0.496928i | −0.143223 | + | 0.0355858i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 11.7587i | − | 0.837774i | −0.908038 | − | 0.418887i | \(-0.862420\pi\) | ||
0.908038 | − | 0.418887i | \(-0.137580\pi\) | |||||||
\(198\) | −4.69260 | − | 2.70928i | −0.333489 | − | 0.192540i | ||||
\(199\) | −11.2979 | − | 19.5686i | −0.800888 | − | 1.38718i | −0.919032 | − | 0.394182i | \(-0.871028\pi\) |
0.118145 | − | 0.992996i | \(-0.462305\pi\) | |||||||
\(200\) | 24.0398 | − | 38.3328i | 1.69987 | − | 2.71054i | ||||
\(201\) | −2.34017 | + | 4.05330i | −0.165063 | + | 0.285898i | ||||
\(202\) | 15.7587i | 1.10878i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.75872 | −0.403191 | ||||||||
\(205\) | −4.01570 | + | 13.9615i | −0.280469 | + | 0.975116i | ||||
\(206\) | −2.92162 | − | 5.06040i | −0.203559 | − | 0.352575i | ||||
\(207\) | 2.02665 | − | 1.17009i | 0.140862 | − | 0.0813266i | ||||
\(208\) | 11.0441 | + | 6.37629i | 0.765768 | + | 0.442116i | ||||
\(209\) | −6.15676 | −0.425872 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.6742 | −0.941371 | −0.470685 | − | 0.882301i | \(-0.655993\pi\) | ||||
−0.470685 | + | 0.882301i | \(0.655993\pi\) | |||||||
\(212\) | −17.3831 | − | 10.0361i | −1.19387 | − | 0.689283i | ||||
\(213\) | −1.73205 | + | 1.00000i | −0.118678 | + | 0.0685189i | ||||
\(214\) | 22.3474 | + | 38.7068i | 1.52763 | + | 2.64594i | ||||
\(215\) | −14.0188 | − | 4.03218i | −0.956077 | − | 0.274992i | ||||
\(216\) | −9.04945 | −0.615737 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 34.7792i | − | 2.35555i | ||||||
\(219\) | 3.53919 | − | 6.13005i | 0.239156 | − | 0.414231i | ||||
\(220\) | 16.5758 | + | 17.1927i | 1.11754 | + | 1.15913i | ||||
\(221\) | −0.496928 | − | 0.860705i | −0.0334270 | − | 0.0578973i | ||||
\(222\) | 25.4271 | + | 14.6803i | 1.70656 | + | 0.985280i | ||||
\(223\) | 21.6742i | 1.45141i | 0.688005 | + | 0.725706i | \(0.258487\pi\) | ||||
−0.688005 | + | 0.725706i | \(0.741513\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.41855 | + | 2.34017i | −0.294570 | + | 0.156012i | ||||
\(226\) | −7.09171 | + | 12.2832i | −0.471733 | + | 0.817066i | ||||
\(227\) | −9.97440 | + | 5.75872i | −0.662024 | + | 0.382220i | −0.793048 | − | 0.609159i | \(-0.791507\pi\) |
0.131024 | + | 0.991379i | \(0.458174\pi\) | |||||||
\(228\) | −14.2367 | + | 8.21953i | −0.942845 | + | 0.544352i | ||||
\(229\) | 6.41855 | − | 11.1173i | 0.424150 | − | 0.734649i | −0.572191 | − | 0.820121i | \(-0.693906\pi\) |
0.996341 | + | 0.0854716i | \(0.0272397\pi\) | |||||||
\(230\) | −13.7587 | + | 3.41855i | −0.907223 | + | 0.225413i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 60.4534i | 3.96896i | ||||||||
\(233\) | −5.85855 | − | 3.38243i | −0.383806 | − | 0.221591i | 0.295667 | − | 0.955291i | \(-0.404458\pi\) |
−0.679473 | + | 0.733701i | \(0.737792\pi\) | |||||||
\(234\) | −1.24846 | − | 2.16240i | −0.0816147 | − | 0.141361i | ||||
\(235\) | 7.53421 | − | 7.26387i | 0.491478 | − | 0.473843i | ||||
\(236\) | −28.0989 | + | 48.6687i | −1.82908 | + | 3.16806i | ||||
\(237\) | 6.15676i | 0.399924i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.3607 | 1.51108 | 0.755539 | − | 0.655104i | \(-0.227375\pi\) | ||||
0.755539 | + | 0.655104i | \(0.227375\pi\) | |||||||
\(240\) | 29.7352 | + | 8.55260i | 1.91940 | + | 0.552068i | ||||
\(241\) | 7.34017 | + | 12.7136i | 0.472822 | + | 0.818952i | 0.999516 | − | 0.0311030i | \(-0.00990199\pi\) |
−0.526694 | + | 0.850055i | \(0.676569\pi\) | |||||||
\(242\) | 16.4241 | − | 9.48246i | 1.05578 | − | 0.609556i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 22.1978 | 1.42107 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −17.6020 | −1.12226 | ||||||||
\(247\) | −2.45700 | − | 1.41855i | −0.156335 | − | 0.0902602i | ||||
\(248\) | −60.8055 | + | 35.1061i | −3.86115 | + | 2.22924i | ||||
\(249\) | 3.41855 | + | 5.92110i | 0.216642 | + | 0.375235i | ||||
\(250\) | 29.6440 | − | 6.22546i | 1.87485 | − | 0.393732i | ||||
\(251\) | 9.16290 | 0.578357 | 0.289179 | − | 0.957275i | \(-0.406618\pi\) | ||||
0.289179 | + | 0.957275i | \(0.406618\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.68035i | − | 0.294251i | ||||||
\(254\) | −2.49693 | + | 4.32481i | −0.156671 | + | 0.271363i | ||||
\(255\) | −1.67364 | − | 1.73592i | −0.104807 | − | 0.108708i | ||||
\(256\) | −13.8402 | − | 23.9719i | −0.865011 | − | 1.49824i | ||||
\(257\) | 4.39800 | + | 2.53919i | 0.274340 | + | 0.158390i | 0.630858 | − | 0.775898i | \(-0.282703\pi\) |
−0.356518 | + | 0.934288i | \(0.616036\pi\) | |||||||
\(258\) | − | 17.6742i | − | 1.10035i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.65368 | + | 10.6803i | 0.164574 | + | 0.662367i | ||||
\(261\) | 3.34017 | − | 5.78535i | 0.206752 | − | 0.358104i | ||||
\(262\) | −3.46410 | + | 2.00000i | −0.214013 | + | 0.123560i | ||||
\(263\) | −4.90155 | + | 2.82991i | −0.302243 | + | 0.174500i | −0.643450 | − | 0.765488i | \(-0.722498\pi\) |
0.341207 | + | 0.939988i | \(0.389164\pi\) | |||||||
\(264\) | −9.04945 | + | 15.6741i | −0.556955 | + | 0.964674i | ||||
\(265\) | −2.02666 | − | 8.15676i | −0.124497 | − | 0.501066i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.34017i | 0.510410i | ||||||||
\(268\) | 21.6453 | + | 12.4969i | 1.32220 | + | 0.763371i | ||||
\(269\) | −13.9288 | − | 24.1254i | −0.849255 | − | 1.47095i | −0.881875 | − | 0.471484i | \(-0.843718\pi\) |
0.0326200 | − | 0.999468i | \(-0.489615\pi\) | |||||||
\(270\) | −4.20478 | − | 4.36127i | −0.255895 | − | 0.265419i | ||||
\(271\) | −12.5597 | + | 21.7541i | −0.762948 | + | 1.32146i | 0.178377 | + | 0.983962i | \(0.442915\pi\) |
−0.941325 | + | 0.337502i | \(0.890418\pi\) | |||||||
\(272\) | 14.9216i | 0.904756i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0267 | 0.726557 | ||||||||
\(275\) | −0.365252 | + | 9.99333i | −0.0220255 | + | 0.602620i | ||||
\(276\) | −6.24846 | − | 10.8227i | −0.376113 | − | 0.651447i | ||||
\(277\) | −24.4200 | + | 14.0989i | −1.46726 | + | 0.847121i | −0.999328 | − | 0.0366462i | \(-0.988333\pi\) |
−0.467928 | + | 0.883767i | \(0.654999\pi\) | |||||||
\(278\) | −31.9143 | − | 18.4257i | −1.91409 | − | 1.10510i | ||||
\(279\) | 7.75872 | 0.464503 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.3545 | −1.21425 | −0.607125 | − | 0.794606i | \(-0.707677\pi\) | ||||
−0.607125 | + | 0.794606i | \(0.707677\pi\) | |||||||
\(282\) | 10.9815 | + | 6.34017i | 0.653939 | + | 0.377552i | ||||
\(283\) | −20.3667 | + | 11.7587i | −1.21068 | + | 0.698984i | −0.962906 | − | 0.269836i | \(-0.913031\pi\) |
−0.247769 | + | 0.968819i | \(0.579697\pi\) | |||||||
\(284\) | 5.34017 | + | 9.24945i | 0.316881 | + | 0.548854i | ||||
\(285\) | −6.61526 | − | 1.90272i | −0.391854 | − | 0.112707i | ||||
\(286\) | −4.99386 | −0.295293 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 19.3896i | 1.14254i | ||||||||
\(289\) | −7.91855 | + | 13.7153i | −0.465797 | + | 0.806784i | ||||
\(290\) | −29.1348 | + | 28.0894i | −1.71085 | + | 1.64947i | ||||
\(291\) | 4.21953 | + | 7.30845i | 0.247354 | + | 0.428429i | ||||
\(292\) | −32.7356 | − | 18.8999i | −1.91570 | − | 1.10603i | ||||
\(293\) | 2.92162i | 0.170683i | 0.996352 | + | 0.0853415i | \(0.0271981\pi\) | ||||
−0.996352 | + | 0.0853415i | \(0.972802\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.8371 | + | 5.67420i | −1.32963 | + | 0.330365i | ||||
\(296\) | 49.0349 | − | 84.9309i | 2.85010 | − | 4.93651i | ||||
\(297\) | 1.73205 | − | 1.00000i | 0.100504 | − | 0.0580259i | ||||
\(298\) | 36.7764 | − | 21.2329i | 2.13040 | − | 1.22999i | ||||
\(299\) | 1.07838 | − | 1.86781i | 0.0623642 | − | 0.108018i | ||||
\(300\) | 12.4969 | + | 23.5958i | 0.721511 | + | 1.36231i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 15.8310i | − | 0.910969i | ||||||
\(303\) | −5.03731 | − | 2.90829i | −0.289386 | − | 0.167077i | ||||
\(304\) | 21.2979 | + | 36.8891i | 1.22152 | + | 2.11573i | ||||
\(305\) | 6.45126 | + | 6.69136i | 0.369398 | + | 0.383146i | ||||
\(306\) | 1.46081 | − | 2.53020i | 0.0835090 | − | 0.144642i | ||||
\(307\) | − | 10.4703i | − | 0.597570i | −0.954321 | − | 0.298785i | \(-0.903419\pi\) | ||
0.954321 | − | 0.298785i | \(-0.0965813\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.15676 | 0.122694 | ||||||||
\(310\) | −45.1719 | − | 12.9926i | −2.56559 | − | 0.737931i | ||||
\(311\) | −11.9155 | − | 20.6382i | −0.675665 | − | 1.17029i | −0.976274 | − | 0.216538i | \(-0.930523\pi\) |
0.300609 | − | 0.953747i | \(-0.402810\pi\) | |||||||
\(312\) | −7.22280 | + | 4.17009i | −0.408911 | + | 0.236085i | ||||
\(313\) | 28.3646 | + | 16.3763i | 1.60326 | + | 0.925643i | 0.990829 | + | 0.135118i | \(0.0431415\pi\) |
0.612431 | + | 0.790524i | \(0.290192\pi\) | |||||||
\(314\) | 13.3340 | 0.752483 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.8781 | 1.84954 | ||||||||
\(317\) | 15.5153 | + | 8.95774i | 0.871424 | + | 0.503117i | 0.867821 | − | 0.496877i | \(-0.165520\pi\) |
0.00360269 | + | 0.999994i | \(0.498853\pi\) | |||||||
\(318\) | 8.81910 | − | 5.09171i | 0.494550 | − | 0.285529i | ||||
\(319\) | −6.68035 | − | 11.5707i | −0.374028 | − | 0.647835i | ||||
\(320\) | 15.3643 | − | 53.4176i | 0.858890 | − | 2.98614i | ||||
\(321\) | −16.4969 | −0.920769 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.31965i | − | 0.184710i | ||||||
\(324\) | 2.67009 | − | 4.62473i | 0.148338 | − | 0.256929i | ||||
\(325\) | −2.44828 | + | 3.90392i | −0.135806 | + | 0.216551i | ||||
\(326\) | −13.3340 | − | 23.0952i | −0.738504 | − | 1.27913i | ||||
\(327\) | 11.1173 | + | 6.41855i | 0.614786 | + | 0.354947i | ||||
\(328\) | 58.7936i | 3.24633i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −11.7587 | + | 2.92162i | −0.647296 | + | 0.160830i | ||||
\(331\) | 0.680346 | − | 1.17839i | 0.0373952 | − | 0.0647704i | −0.846722 | − | 0.532035i | \(-0.821427\pi\) |
0.884117 | + | 0.467265i | \(0.154761\pi\) | |||||||
\(332\) | 31.6197 | − | 18.2557i | 1.73536 | − | 1.00191i | ||||
\(333\) | −9.38521 | + | 5.41855i | −0.514306 | + | 0.296935i | ||||
\(334\) | 26.0144 | − | 45.0582i | 1.42344 | − | 2.46548i | ||||
\(335\) | 2.52359 | + | 10.1568i | 0.137878 | + | 0.554923i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 25.3607i | − | 1.38148i | −0.723101 | − | 0.690742i | \(-0.757284\pi\) | ||
0.723101 | − | 0.690742i | \(-0.242716\pi\) | |||||||
\(338\) | 28.5090 | + | 16.4597i | 1.55069 | + | 0.895288i | ||||
\(339\) | −2.61757 | − | 4.53376i | −0.142167 | − | 0.246240i | ||||
\(340\) | −9.27014 | + | 8.93751i | −0.502744 | + | 0.484704i | ||||
\(341\) | 7.75872 | − | 13.4385i | 0.420158 | − | 0.727736i | ||||
\(342\) | − | 8.34017i | − | 0.450985i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −59.0349 | −3.18295 | ||||||||
\(345\) | 1.44644 | − | 5.02890i | 0.0778738 | − | 0.270747i | ||||
\(346\) | −30.3968 | − | 52.6488i | −1.63414 | − | 2.83042i | ||||
\(347\) | 14.6044 | − | 8.43188i | 0.784008 | − | 0.452647i | −0.0538410 | − | 0.998550i | \(-0.517146\pi\) |
0.837849 | + | 0.545902i | \(0.183813\pi\) | |||||||
\(348\) | −30.8948 | − | 17.8371i | −1.65613 | − | 0.956169i | ||||
\(349\) | −9.51745 | −0.509457 | −0.254729 | − | 0.967013i | \(-0.581986\pi\) | ||||
−0.254729 | + | 0.967013i | \(0.581986\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.921622 | 0.0491926 | ||||||||
\(352\) | 33.5838 | + | 19.3896i | 1.79002 | + | 1.03347i | ||||
\(353\) | 31.0035 | − | 17.8999i | 1.65015 | − | 0.952715i | 0.673142 | − | 0.739514i | \(-0.264944\pi\) |
0.977008 | − | 0.213201i | \(-0.0683889\pi\) | |||||||
\(354\) | −14.2557 | − | 24.6915i | −0.757679 | − | 1.31234i | ||||
\(355\) | −1.23618 | + | 4.29789i | −0.0656098 | + | 0.228108i | ||||
\(356\) | 44.5380 | 2.36051 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 27.0928i | 1.43190i | ||||||||
\(359\) | −11.1568 | + | 19.3241i | −0.588831 | + | 1.01989i | 0.405555 | + | 0.914071i | \(0.367078\pi\) |
−0.994386 | + | 0.105815i | \(0.966255\pi\) | |||||||
\(360\) | −14.5674 | + | 14.0447i | −0.767769 | + | 0.740220i | ||||
\(361\) | 4.76180 | + | 8.24767i | 0.250621 | + | 0.434088i | ||||
\(362\) | −19.9989 | − | 11.5464i | −1.05112 | − | 0.606864i | ||||
\(363\) | 7.00000i | 0.367405i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.81658 | − | 15.3607i | −0.199769 | − | 0.804015i | ||||
\(366\) | −5.63090 | + | 9.75300i | −0.294332 | + | 0.509798i | ||||
\(367\) | 17.5920 | − | 10.1568i | 0.918296 | − | 0.530178i | 0.0352048 | − | 0.999380i | \(-0.488792\pi\) |
0.883091 | + | 0.469202i | \(0.155458\pi\) | |||||||
\(368\) | −28.0430 | + | 16.1906i | −1.46184 | + | 0.843994i | ||||
\(369\) | 3.24846 | − | 5.62651i | 0.169108 | − | 0.292904i | ||||
\(370\) | 63.7152 | − | 15.8310i | 3.31240 | − | 0.823012i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 41.4329i | − | 2.14820i | ||||||
\(373\) | −13.8564 | − | 8.00000i | −0.717458 | − | 0.414224i | 0.0963587 | − | 0.995347i | \(-0.469280\pi\) |
−0.813816 | + | 0.581122i | \(0.802614\pi\) | |||||||
\(374\) | −2.92162 | − | 5.06040i | −0.151073 | − | 0.261667i | ||||
\(375\) | −3.48085 | + | 10.6247i | −0.179750 | + | 0.548656i | ||||
\(376\) | 21.1773 | − | 36.6801i | 1.09213 | − | 1.89163i | ||||
\(377\) | − | 6.15676i | − | 0.317089i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.15676 | −0.316251 | −0.158126 | − | 0.987419i | \(-0.550545\pi\) | ||||
−0.158126 | + | 0.987419i | \(0.550545\pi\) | |||||||
\(380\) | −10.1609 | + | 35.3266i | −0.521241 | + | 1.81222i | ||||
\(381\) | −0.921622 | − | 1.59630i | −0.0472161 | − | 0.0817808i | ||||
\(382\) | −36.0408 | + | 20.8082i | −1.84401 | + | 1.06464i | ||||
\(383\) | 23.2416 | + | 13.4186i | 1.18759 | + | 0.685656i | 0.957758 | − | 0.287574i | \(-0.0928488\pi\) |
0.229833 | + | 0.973230i | \(0.426182\pi\) | |||||||
\(384\) | 28.5669 | 1.45780 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.6681 | −1.15377 | ||||||||
\(387\) | 5.64960 | + | 3.26180i | 0.287185 | + | 0.165806i | ||||
\(388\) | 39.0284 | − | 22.5330i | 1.98137 | − | 1.14394i | ||||
\(389\) | −2.81658 | − | 4.87846i | −0.142806 | − | 0.247348i | 0.785746 | − | 0.618549i | \(-0.212279\pi\) |
−0.928552 | + | 0.371201i | \(0.878946\pi\) | |||||||
\(390\) | −5.36576 | − | 1.54333i | −0.271706 | − | 0.0781496i | ||||
\(391\) | 2.52359 | 0.127623 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1.47641i | − | 0.0744750i | ||||||
\(394\) | 15.9288 | − | 27.5895i | 0.802482 | − | 1.38994i | ||||
\(395\) | 9.55525 | + | 9.91087i | 0.480777 | + | 0.498670i | ||||
\(396\) | −5.34017 | − | 9.24945i | −0.268354 | − | 0.464802i | ||||
\(397\) | −32.7356 | − | 18.8999i | −1.64295 | − | 0.948558i | −0.979777 | − | 0.200092i | \(-0.935876\pi\) |
−0.663173 | − | 0.748466i | \(-0.730791\pi\) | |||||||
\(398\) | − | 61.2183i | − | 3.06860i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 61.1399 | − | 32.3812i | 3.05700 | − | 1.61906i | ||||
\(401\) | 6.81658 | − | 11.8067i | 0.340404 | − | 0.589597i | −0.644104 | − | 0.764938i | \(-0.722770\pi\) |
0.984508 | + | 0.175341i | \(0.0561029\pi\) | |||||||
\(402\) | −10.9815 | + | 6.34017i | −0.547708 | + | 0.316219i | ||||
\(403\) | 6.19261 | − | 3.57531i | 0.308476 | − | 0.178099i | ||||
\(404\) | −15.5308 | + | 26.9001i | −0.772685 | + | 1.33833i | ||||
\(405\) | 2.17009 | − | 0.539189i | 0.107832 | − | 0.0267925i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.6742i | 1.07435i | ||||||||
\(408\) | −8.45130 | − | 4.87936i | −0.418402 | − | 0.241564i | ||||
\(409\) | 6.17727 | + | 10.6994i | 0.305447 | + | 0.529049i | 0.977361 | − | 0.211580i | \(-0.0678609\pi\) |
−0.671914 | + | 0.740629i | \(0.734528\pi\) | |||||||
\(410\) | −28.3349 | + | 27.3182i | −1.39936 | + | 1.34915i | ||||
\(411\) | −2.21953 | + | 3.84435i | −0.109482 | + | 0.189628i | ||||
\(412\) | − | 11.5174i | − | 0.567424i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.34017 | 0.311603 | ||||||||
\(415\) | 14.6926 | + | 4.22596i | 0.721229 | + | 0.207444i | ||||
\(416\) | 8.93495 | + | 15.4758i | 0.438072 | + | 0.758763i | ||||
\(417\) | 11.7797 | − | 6.80098i | 0.576852 | − | 0.333046i | ||||
\(418\) | −14.4456 | − | 8.34017i | −0.706558 | − | 0.407931i | ||||
\(419\) | −28.9939 | −1.41644 | −0.708221 | − | 0.705991i | \(-0.750502\pi\) | ||||
−0.708221 | + | 0.705991i | \(0.750502\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1629 | −0.738994 | −0.369497 | − | 0.929232i | \(-0.620470\pi\) | ||||
−0.369497 | + | 0.929232i | \(0.620470\pi\) | |||||||
\(422\) | −32.0838 | − | 18.5236i | −1.56181 | − | 0.901714i | ||||
\(423\) | −4.05330 | + | 2.34017i | −0.197078 | + | 0.113783i | ||||
\(424\) | −17.0072 | − | 29.4573i | −0.825942 | − | 1.43057i | ||||
\(425\) | −5.38829 | − | 0.196940i | −0.261370 | − | 0.00955299i | ||||
\(426\) | −5.41855 | −0.262530 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 88.0965i | 4.25830i | ||||||||
\(429\) | 0.921622 | − | 1.59630i | 0.0444963 | − | 0.0770699i | ||||
\(430\) | −27.4303 | − | 28.4511i | −1.32280 | − | 1.37204i | ||||
\(431\) | 5.15676 | + | 8.93176i | 0.248392 | + | 0.430228i | 0.963080 | − | 0.269216i | \(-0.0867645\pi\) |
−0.714688 | + | 0.699444i | \(0.753431\pi\) | |||||||
\(432\) | −11.9833 | − | 6.91855i | −0.576546 | − | 0.332869i | ||||
\(433\) | − | 20.4391i | − | 0.982239i | −0.871092 | − | 0.491120i | \(-0.836588\pi\) | ||
0.871092 | − | 0.491120i | \(-0.163412\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.60197 | − | 14.4969i | −0.172701 | − | 0.695075i | ||||
\(436\) | 34.2762 | − | 59.3681i | 1.64153 | − | 2.84321i | ||||
\(437\) | 6.23879 | − | 3.60197i | 0.298442 | − | 0.172306i | ||||
\(438\) | 16.6080 | − | 9.58864i | 0.793561 | − | 0.458163i | ||||
\(439\) | −8.46081 | + | 14.6546i | −0.403812 | + | 0.699424i | −0.994182 | − | 0.107709i | \(-0.965649\pi\) |
0.590370 | + | 0.807133i | \(0.298982\pi\) | |||||||
\(440\) | 9.75872 | + | 39.2762i | 0.465229 | + | 1.87242i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 2.69263i | − | 0.128075i | ||||||
\(443\) | −11.0942 | − | 6.40522i | −0.527100 | − | 0.304321i | 0.212735 | − | 0.977110i | \(-0.431763\pi\) |
−0.739835 | + | 0.672789i | \(0.765096\pi\) | |||||||
\(444\) | 28.9360 | + | 50.1186i | 1.37324 | + | 2.37852i | ||||
\(445\) | 12.9439 | + | 13.4256i | 0.613600 | + | 0.636436i | ||||
\(446\) | −29.3607 | + | 50.8542i | −1.39027 | + | 2.40802i | ||||
\(447\) | 15.6742i | 0.741364i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.6270 | 0.690292 | 0.345146 | − | 0.938549i | \(-0.387829\pi\) | ||||
0.345146 | + | 0.938549i | \(0.387829\pi\) | |||||||
\(450\) | −13.5373 | − | 0.494784i | −0.638156 | − | 0.0233244i | ||||
\(451\) | −6.49693 | − | 11.2530i | −0.305928 | − | 0.529884i | ||||
\(452\) | −24.2111 | + | 13.9783i | −1.13879 | + | 0.657482i | ||||
\(453\) | 5.06040 | + | 2.92162i | 0.237758 | + | 0.137270i | ||||
\(454\) | −31.2039 | −1.46447 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −27.8576 | −1.30455 | ||||||||
\(457\) | −12.2601 | − | 7.07838i | −0.573504 | − | 0.331113i | 0.185044 | − | 0.982730i | \(-0.440757\pi\) |
−0.758548 | + | 0.651618i | \(0.774091\pi\) | |||||||
\(458\) | 30.1197 | − | 17.3896i | 1.40740 | − | 0.812564i | ||||
\(459\) | 0.539189 | + | 0.933903i | 0.0251672 | + | 0.0435908i | ||||
\(460\) | −26.8552 | − | 7.72425i | −1.25213 | − | 0.360145i | ||||
\(461\) | 0.340173 | 0.0158434 | 0.00792172 | − | 0.999969i | \(-0.497478\pi\) | ||||
0.00792172 | + | 0.999969i | \(0.497478\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.84324i | 0.457454i | 0.973491 | + | 0.228727i | \(0.0734564\pi\) | ||||
−0.973491 | + | 0.228727i | \(0.926544\pi\) | |||||||
\(464\) | −46.2183 | + | 80.0525i | −2.14563 | + | 3.71634i | ||||
\(465\) | 12.4896 | − | 12.0415i | 0.579194 | − | 0.558411i | ||||
\(466\) | −9.16394 | − | 15.8724i | −0.424511 | − | 0.735275i | ||||
\(467\) | 9.97440 | + | 5.75872i | 0.461560 | + | 0.266482i | 0.712700 | − | 0.701469i | \(-0.247472\pi\) |
−0.251140 | + | 0.967951i | \(0.580805\pi\) | |||||||
\(468\) | − | 4.92162i | − | 0.227502i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 27.5174 | − | 6.83710i | 1.26929 | − | 0.315372i | ||||
\(471\) | −2.46081 | + | 4.26225i | −0.113388 | + | 0.196394i | ||||
\(472\) | −82.4739 | + | 47.6163i | −3.79617 | + | 2.19172i | ||||
\(473\) | 11.2992 | − | 6.52359i | 0.519537 | − | 0.299955i | ||||
\(474\) | −8.34017 | + | 14.4456i | −0.383077 | + | 0.663509i | ||||
\(475\) | −13.6020 | + | 7.20394i | −0.624101 | + | 0.330539i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.75872i | 0.172100i | ||||||||
\(478\) | 54.8112 | + | 31.6453i | 2.50701 | + | 1.44742i | ||||
\(479\) | −9.75872 | − | 16.9026i | −0.445887 | − | 0.772300i | 0.552226 | − | 0.833694i | \(-0.313779\pi\) |
−0.998114 | + | 0.0613946i | \(0.980445\pi\) | |||||||
\(480\) | 30.0926 | + | 31.2126i | 1.37353 | + | 1.42465i | ||||
\(481\) | −4.99386 | + | 8.64961i | −0.227700 | + | 0.394388i | ||||
\(482\) | 39.7731i | 1.81162i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 37.3812 | 1.69915 | ||||||||
\(485\) | 18.1351 | + | 5.21612i | 0.823472 | + | 0.236852i | ||||
\(486\) | 1.35464 | + | 2.34630i | 0.0614476 | + | 0.106430i | ||||
\(487\) | 20.0490 | − | 11.5753i | 0.908508 | − | 0.524527i | 0.0285570 | − | 0.999592i | \(-0.490909\pi\) |
0.879951 | + | 0.475065i | \(0.157575\pi\) | |||||||
\(488\) | 32.5767 | + | 18.8082i | 1.47468 | + | 0.851406i | ||||
\(489\) | 9.84324 | 0.445127 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.00000 | 0.0902587 | 0.0451294 | − | 0.998981i | \(-0.485630\pi\) | ||||
0.0451294 | + | 0.998981i | \(0.485630\pi\) | |||||||
\(492\) | −30.0465 | − | 17.3474i | −1.35460 | − | 0.782079i | ||||
\(493\) | 6.23879 | − | 3.60197i | 0.280981 | − | 0.162224i | ||||
\(494\) | −3.84324 | − | 6.65669i | −0.172916 | − | 0.299499i | ||||
\(495\) | 1.23618 | − | 4.29789i | 0.0555623 | − | 0.193176i | ||||
\(496\) | −107.358 | −4.82053 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 18.5236i | 0.830062i | ||||||||
\(499\) | 13.6020 | − | 23.5593i | 0.608908 | − | 1.05466i | −0.382513 | − | 0.923950i | \(-0.624941\pi\) |
0.991421 | − | 0.130709i | \(-0.0417254\pi\) | |||||||
\(500\) | 56.7376 | + | 18.5883i | 2.53738 | + | 0.831296i | ||||
\(501\) | 9.60197 | + | 16.6311i | 0.428984 | + | 0.743023i | ||||
\(502\) | 21.4989 | + | 12.4124i | 0.959544 | + | 0.553993i | ||||
\(503\) | 18.8371i | 0.839905i | 0.907546 | + | 0.419952i | \(0.137953\pi\) | ||||
−0.907546 | + | 0.419952i | \(0.862047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.6225 | + | 3.13624i | −0.561693 | + | 0.139561i | ||||
\(506\) | 6.34017 | − | 10.9815i | 0.281855 | − | 0.488187i | ||||
\(507\) | −10.5227 | + | 6.07531i | −0.467331 | + | 0.269814i | ||||
\(508\) | −8.52450 | + | 4.92162i | −0.378214 | + | 0.218362i | ||||
\(509\) | 3.40522 | − | 5.89801i | 0.150934 | − | 0.261425i | −0.780637 | − | 0.624984i | \(-0.785105\pi\) |
0.931571 | + | 0.363560i | \(0.118439\pi\) | |||||||
\(510\) | −1.57531 | − | 6.34017i | −0.0697557 | − | 0.280748i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 17.8599i | − | 0.789303i | ||||||
\(513\) | 2.66595 | + | 1.53919i | 0.117705 | + | 0.0679568i | ||||
\(514\) | 6.87936 | + | 11.9154i | 0.303436 | + | 0.525566i | ||||
\(515\) | 3.47185 | − | 3.34727i | 0.152988 | − | 0.147498i | ||||
\(516\) | 17.4186 | − | 30.1698i | 0.766809 | − | 1.32815i | ||||
\(517\) | 9.36069i | 0.411683i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.4391 | 0.984966 | ||||||||
\(520\) | −5.15499 | + | 17.9226i | −0.226061 | + | 0.785957i | ||||
\(521\) | 12.9083 | + | 22.3578i | 0.565523 | + | 0.979514i | 0.997001 | + | 0.0773904i | \(0.0246588\pi\) |
−0.431478 | + | 0.902123i | \(0.642008\pi\) | |||||||
\(522\) | 15.6741 | − | 9.04945i | 0.686037 | − | 0.396084i | ||||
\(523\) | 3.46410 | + | 2.00000i | 0.151475 | + | 0.0874539i | 0.573822 | − | 0.818980i | \(-0.305460\pi\) |
−0.422347 | + | 0.906434i | \(0.638794\pi\) | |||||||
\(524\) | −7.88428 | −0.344426 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.3340 | −0.668595 | ||||||||
\(527\) | 7.24589 | + | 4.18342i | 0.315636 | + | 0.182233i | ||||
\(528\) | −23.9666 | + | 13.8371i | −1.04301 | + | 0.602183i | ||||
\(529\) | −8.76180 | − | 15.1759i | −0.380948 | − | 0.659821i | ||||
\(530\) | 6.29429 | − | 21.8836i | 0.273406 | − | 0.950563i | ||||
\(531\) | 10.5236 | 0.456685 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.98771i | − | 0.259357i | ||||||
\(534\) | −11.2979 | + | 19.5686i | −0.488908 | + | 0.846814i | ||||
\(535\) | −26.5560 | + | 25.6031i | −1.14812 | + | 1.10692i | ||||
\(536\) | 21.1773 | + | 36.6801i | 0.914719 | + | 1.58434i | ||||
\(537\) | −8.66025 | − | 5.00000i | −0.373718 | − | 0.215766i | ||||
\(538\) | − | 75.4740i | − | 3.25391i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.87936 | − | 11.5886i | −0.123908 | − | 0.498696i | ||||
\(541\) | −12.9421 | + | 22.4164i | −0.556426 | + | 0.963758i | 0.441365 | + | 0.897328i | \(0.354494\pi\) |
−0.997791 | + | 0.0664306i | \(0.978839\pi\) | |||||||
\(542\) | −58.9377 | + | 34.0277i | −2.53159 | + | 1.46162i | ||||
\(543\) | 7.38165 | − | 4.26180i | 0.316777 | − | 0.182891i | ||||
\(544\) | −10.4547 | + | 18.1080i | −0.448240 | + | 0.776375i | ||||
\(545\) | 27.8576 | − | 6.92162i | 1.19329 | − | 0.296490i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.3197i | 0.483993i | 0.970277 | + | 0.241997i | \(0.0778023\pi\) | ||||
−0.970277 | + | 0.241997i | \(0.922198\pi\) | |||||||
\(548\) | 20.5295 | + | 11.8527i | 0.876976 | + | 0.506322i | ||||
\(549\) | −2.07838 | − | 3.59986i | −0.0887030 | − | 0.153638i | ||||
\(550\) | −14.3943 | + | 22.9526i | −0.613776 | + | 0.978701i | ||||
\(551\) | 10.2823 | − | 17.8095i | 0.438041 | − | 0.758710i | ||||
\(552\) | − | 21.1773i | − | 0.901365i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −76.3956 | −3.24574 | ||||||||
\(555\) | −6.69833 | + | 23.2883i | −0.284328 | + | 0.988535i | ||||
\(556\) | −36.3184 | − | 62.9054i | −1.54024 | − | 2.66778i | ||||
\(557\) | −23.0788 | + | 13.3246i | −0.977882 | + | 0.564580i | −0.901630 | − | 0.432508i | \(-0.857629\pi\) |
−0.0762519 | + | 0.997089i | \(0.524295\pi\) | |||||||
\(558\) | 18.2043 | + | 10.5103i | 0.770650 | + | 0.444935i | ||||
\(559\) | 6.01229 | 0.254293 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.15676 | 0.0910583 | ||||||||
\(562\) | −47.7579 | − | 27.5730i | −2.01455 | − | 1.16310i | ||||
\(563\) | −40.1442 | + | 23.1773i | −1.69188 | + | 0.976806i | −0.738875 | + | 0.673843i | \(0.764642\pi\) |
−0.953002 | + | 0.302963i | \(0.902024\pi\) | |||||||
\(564\) | 12.4969 | + | 21.6453i | 0.526216 | + | 0.911432i | ||||
\(565\) | −11.2500 | − | 3.23579i | −0.473292 | − | 0.136131i | ||||
\(566\) | −63.7152 | −2.67815 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.0989i | 0.759413i | ||||||||
\(569\) | −7.18342 | + | 12.4420i | −0.301145 | + | 0.521598i | −0.976395 | − | 0.215990i | \(-0.930702\pi\) |
0.675251 | + | 0.737588i | \(0.264035\pi\) | |||||||
\(570\) | −12.9439 | − | 13.4256i | −0.542160 | − | 0.562338i | ||||
\(571\) | −19.3607 | − | 33.5337i | −0.810220 | − | 1.40334i | −0.912710 | − | 0.408608i | \(-0.866014\pi\) |
0.102490 | − | 0.994734i | \(-0.467319\pi\) | |||||||
\(572\) | −8.52450 | − | 4.92162i | −0.356427 | − | 0.205783i | ||||
\(573\) | − | 15.3607i | − | 0.641702i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.47641 | − | 10.3402i | −0.228382 | − | 0.431215i | ||||
\(576\) | −12.4288 | + | 21.5273i | −0.517867 | + | 0.896972i | ||||
\(577\) | 37.6496 | − | 21.7370i | 1.56737 | − | 0.904922i | 0.570898 | − | 0.821021i | \(-0.306595\pi\) |
0.996474 | − | 0.0839011i | \(-0.0267380\pi\) | |||||||
\(578\) | −37.1586 | + | 21.4535i | −1.54559 | + | 0.892349i | ||||
\(579\) | 4.18342 | − | 7.24589i | 0.173857 | − | 0.301129i | ||||
\(580\) | −77.4161 | + | 19.2351i | −3.21453 | + | 0.798695i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 22.8638i | 0.947733i | ||||||||
\(583\) | 6.51030 | + | 3.75872i | 0.269629 | + | 0.155670i | ||||
\(584\) | −32.0277 | − | 55.4736i | −1.32532 | − | 2.29551i | ||||
\(585\) | 1.48359 | − | 1.43035i | 0.0613388 | − | 0.0591378i | ||||
\(586\) | −3.95774 | + | 6.85501i | −0.163493 | + | 0.283178i | ||||
\(587\) | 36.0288i | 1.48707i | 0.668699 | + | 0.743533i | \(0.266851\pi\) | ||||
−0.668699 | + | 0.743533i | \(0.733149\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.8843 | 0.984135 | ||||||||
\(590\) | −61.2692 | − | 17.6226i | −2.52241 | − | 0.725511i | ||||
\(591\) | 5.87936 | + | 10.1834i | 0.241845 | + | 0.418887i | ||||
\(592\) | 129.864 | − | 74.9770i | 5.33738 | − | 3.08154i | ||||
\(593\) | 27.2679 | + | 15.7431i | 1.11976 | + | 0.646493i | 0.941339 | − | 0.337462i | \(-0.109568\pi\) |
0.178419 | + | 0.983955i | \(0.442902\pi\) | |||||||
\(594\) | 5.41855 | 0.222326 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 83.7030 | 3.42861 | ||||||||
\(597\) | 19.5686 | + | 11.2979i | 0.800888 | + | 0.462393i | ||||
\(598\) | 5.06040 | − | 2.92162i | 0.206935 | − | 0.119474i | ||||
\(599\) | 14.5174 | + | 25.1450i | 0.593167 | + | 1.02740i | 0.993803 | + | 0.111158i | \(0.0354559\pi\) |
−0.400636 | + | 0.916237i | \(0.631211\pi\) | |||||||
\(600\) | −1.65267 | + | 45.2170i | −0.0674698 | + | 1.84598i | ||||
\(601\) | 15.3607 | 0.626576 | 0.313288 | − | 0.949658i | \(-0.398570\pi\) | ||||
0.313288 | + | 0.949658i | \(0.398570\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.68035i | − | 0.190598i | ||||||
\(604\) | 15.6020 | − | 27.0234i | 0.634835 | − | 1.09957i | ||||
\(605\) | 10.8640 | + | 11.2683i | 0.441683 | + | 0.458121i | ||||
\(606\) | −7.87936 | − | 13.6475i | −0.320077 | − | 0.554390i | ||||
\(607\) | 11.2992 | + | 6.52359i | 0.458620 | + | 0.264784i | 0.711464 | − | 0.702723i | \(-0.248033\pi\) |
−0.252844 | + | 0.967507i | \(0.581366\pi\) | |||||||
\(608\) | 59.6886i | 2.42069i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.07223 | + | 24.4391i | 0.245858 | + | 0.989509i | ||||
\(611\) | −2.15676 | + | 3.73561i | −0.0872530 | + | 0.151127i | ||||
\(612\) | 4.98720 | − | 2.87936i | 0.201596 | − | 0.116391i | ||||
\(613\) | 13.4385 | − | 7.75872i | 0.542776 | − | 0.313372i | −0.203427 | − | 0.979090i | \(-0.565208\pi\) |
0.746203 | + | 0.665718i | \(0.231875\pi\) | |||||||
\(614\) | 14.1834 | − | 24.5664i | 0.572396 | − | 0.991419i | ||||
\(615\) | −3.50307 | − | 14.0989i | −0.141257 | − | 0.568522i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.7649i | − | 0.916479i | −0.888829 | − | 0.458240i | \(-0.848480\pi\) | ||
0.888829 | − | 0.458240i | \(-0.151520\pi\) | |||||||
\(618\) | 5.06040 | + | 2.92162i | 0.203559 | + | 0.117525i | ||||
\(619\) | 3.96388 | + | 6.86565i | 0.159322 | + | 0.275954i | 0.934624 | − | 0.355637i | \(-0.115736\pi\) |
−0.775302 | + | 0.631590i | \(0.782403\pi\) | |||||||
\(620\) | −64.3037 | − | 66.6969i | −2.58250 | − | 2.67861i | ||||
\(621\) | −1.17009 | + | 2.02665i | −0.0469540 | + | 0.0813266i | ||||
\(622\) | − | 64.5646i | − | 2.58881i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −12.7526 | −0.510512 | ||||||||
\(625\) | 10.8861 | + | 22.5054i | 0.435445 | + | 0.900216i | ||||
\(626\) | 44.3679 | + | 76.8474i | 1.77330 | + | 3.07144i | ||||
\(627\) | 5.33191 | − | 3.07838i | 0.212936 | − | 0.122939i | ||||
\(628\) | 22.7612 | + | 13.1412i | 0.908269 | + | 0.524389i | ||||
\(629\) | −11.6865 | −0.465971 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.2039 | 0.764497 | 0.382248 | − | 0.924060i | \(-0.375150\pi\) | ||||
0.382248 | + | 0.924060i | \(0.375150\pi\) | |||||||
\(632\) | 48.2508 | + | 27.8576i | 1.91931 | + | 1.10812i | ||||
\(633\) | 11.8422 | − | 6.83710i | 0.470685 | − | 0.271750i | ||||
\(634\) | 24.2690 | + | 42.0351i | 0.963844 | + | 1.66943i | ||||
\(635\) | −3.96103 | − | 1.13929i | −0.157189 | − | 0.0452115i | ||||
\(636\) | 20.0722 | 0.795916 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 36.1978i | − | 1.43308i | ||||||
\(639\) | 1.00000 | − | 1.73205i | 0.0395594 | − | 0.0685189i | ||||
\(640\) | 45.9857 | − | 44.3357i | 1.81775 | − | 1.75252i | ||||
\(641\) | 2.97334 | + | 5.14997i | 0.117440 | + | 0.203412i | 0.918752 | − | 0.394834i | \(-0.129198\pi\) |
−0.801313 | + | 0.598246i | \(0.795865\pi\) | |||||||
\(642\) | −38.7068 | − | 22.3474i | −1.52763 | − | 0.881980i | ||||
\(643\) | 30.8904i | 1.21820i | 0.793094 | + | 0.609100i | \(0.208469\pi\) | ||||
−0.793094 | + | 0.609100i | \(0.791531\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.1568 | − | 3.51745i | 0.557422 | − | 0.138499i | ||||
\(646\) | 4.49693 | − | 7.78891i | 0.176929 | − | 0.306451i | ||||
\(647\) | −16.6311 | + | 9.60197i | −0.653836 | + | 0.377492i | −0.789924 | − | 0.613204i | \(-0.789880\pi\) |
0.136088 | + | 0.990697i | \(0.456547\pi\) | |||||||
\(648\) | 7.83705 | − | 4.52472i | 0.307868 | − | 0.177748i | ||||
\(649\) | 10.5236 | − | 18.2274i | 0.413087 | − | 0.715488i | ||||
\(650\) | −11.0328 | + | 5.84324i | −0.432742 | + | 0.229191i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 52.5646i | − | 2.05859i | ||||||
\(653\) | −24.7292 | − | 14.2774i | −0.967727 | − | 0.558718i | −0.0691846 | − | 0.997604i | \(-0.522040\pi\) |
−0.898543 | + | 0.438886i | \(0.855373\pi\) | |||||||
\(654\) | 17.3896 | + | 30.1197i | 0.679988 | + | 1.17777i | ||||
\(655\) | −2.29138 | − | 2.37666i | −0.0895316 | − | 0.0928637i | ||||
\(656\) | −44.9493 | + | 77.8545i | −1.75498 | + | 3.03971i | ||||
\(657\) | 7.07838i | 0.276154i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.9877 | 1.09025 | 0.545123 | − | 0.838356i | \(-0.316483\pi\) | ||||
0.545123 | + | 0.838356i | \(0.316483\pi\) | |||||||
\(660\) | −22.9515 | − | 6.60144i | −0.893385 | − | 0.256961i | ||||
\(661\) | 11.0722 | + | 19.1777i | 0.430660 | + | 0.745925i | 0.996930 | − | 0.0782946i | \(-0.0249475\pi\) |
−0.566270 | + | 0.824220i | \(0.691614\pi\) | |||||||
\(662\) | 3.19259 | − | 1.84324i | 0.124084 | − | 0.0716397i | ||||
\(663\) | 0.860705 | + | 0.496928i | 0.0334270 | + | 0.0192991i | ||||
\(664\) | 61.8720 | 2.40110 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −29.3607 | −1.13770 | ||||||||
\(667\) | 13.5387 | + | 7.81658i | 0.524221 | + | 0.302659i | ||||
\(668\) | 88.8129 | − | 51.2762i | 3.43628 | − | 1.98393i | ||||
\(669\) | −10.8371 | − | 18.7704i | −0.418987 | − | 0.725706i | ||||
\(670\) | −7.83762 | + | 27.2494i | −0.302794 | + | 1.05273i | ||||
\(671\) | −8.31351 | −0.320940 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.21008i | − | 0.0851923i | −0.999092 | − | 0.0425962i | \(-0.986437\pi\) | ||
0.999092 | − | 0.0425962i | \(-0.0135629\pi\) | |||||||
\(674\) | 34.3545 | − | 59.5038i | 1.32329 | − | 2.29200i | ||||
\(675\) | 2.65649 | − | 4.23592i | 0.102248 | − | 0.163041i | ||||
\(676\) | 32.4432 | + | 56.1932i | 1.24781 | + | 2.16128i | ||||
\(677\) | −16.9296 | − | 9.77432i | −0.650658 | − | 0.375658i | 0.138050 | − | 0.990425i | \(-0.455916\pi\) |
−0.788708 | + | 0.614768i | \(0.789250\pi\) | |||||||
\(678\) | − | 14.1834i | − | 0.544711i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −21.1773 | + | 5.26180i | −0.812111 | + | 0.201781i | ||||
\(681\) | 5.75872 | − | 9.97440i | 0.220675 | − | 0.382220i | ||||
\(682\) | 36.4086 | − | 21.0205i | 1.39416 | − | 0.804917i | ||||
\(683\) | −10.2335 | + | 5.90829i | −0.391572 | + | 0.226074i | −0.682841 | − | 0.730567i | \(-0.739256\pi\) |
0.291269 | + | 0.956641i | \(0.405923\pi\) | |||||||
\(684\) | 8.21953 | − | 14.2367i | 0.314282 | − | 0.544352i | ||||
\(685\) | 2.39350 | + | 9.63317i | 0.0914508 | + | 0.368064i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.8371i | 0.489766i | ||||||||
\(688\) | −78.1740 | − | 45.1338i | −2.98036 | − | 1.72071i | ||||
\(689\) | 1.73206 | + | 3.00002i | 0.0659863 | + | 0.114292i | ||||
\(690\) | 10.2061 | − | 9.83991i | 0.388541 | − | 0.374599i | ||||
\(691\) | −5.87936 | + | 10.1834i | −0.223661 | + | 0.387393i | −0.955917 | − | 0.293637i | \(-0.905134\pi\) |
0.732256 | + | 0.681030i | \(0.238468\pi\) | |||||||
\(692\) | − | 119.829i | − | 4.55520i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 45.6886 | 1.73431 | ||||||||
\(695\) | 8.40727 | − | 29.2299i | 0.318906 | − | 1.10875i | ||||
\(696\) | −30.2267 | − | 52.3542i | −1.14574 | − | 1.98448i | ||||
\(697\) | 6.06750 | − | 3.50307i | 0.229823 | − | 0.132688i | ||||
\(698\) | −22.3308 | − | 12.8927i | −0.845233 | − | 0.487996i | ||||
\(699\) | 6.76487 | 0.255871 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.94668 | 0.375681 | 0.187840 | − | 0.982200i | \(-0.439851\pi\) | ||||
0.187840 | + | 0.982200i | \(0.439851\pi\) | |||||||
\(702\) | 2.16240 | + | 1.24846i | 0.0816147 | + | 0.0471202i | ||||
\(703\) | −28.8912 | + | 16.6803i | −1.08965 | + | 0.629111i | ||||
\(704\) | 24.8576 | + | 43.0547i | 0.936857 | + | 1.62268i | ||||
\(705\) | −2.89288 | + | 10.0578i | −0.108952 | + | 0.378799i | ||||
\(706\) | 96.9914 | 3.65032 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 56.1978i | − | 2.11204i | ||||||
\(709\) | −5.52359 | + | 9.56714i | −0.207443 | + | 0.359301i | −0.950908 | − | 0.309473i | \(-0.899847\pi\) |
0.743465 | + | 0.668774i | \(0.233181\pi\) | |||||||
\(710\) | −8.72254 | + | 8.40956i | −0.327351 | + | 0.315605i | ||||
\(711\) | −3.07838 | − | 5.33191i | −0.115448 | − | 0.199962i | ||||
\(712\) | 65.3624 | + | 37.7370i | 2.44956 | + | 1.41425i | ||||
\(713\) | 18.1568i | 0.679976i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.993857 | − | 4.00000i | −0.0371681 | − | 0.149592i | ||||
\(716\) | −26.7009 | + | 46.2473i | −0.997858 | + | 1.72834i | ||||
\(717\) | −20.2310 | + | 11.6803i | −0.755539 | + | 0.436211i | ||||
\(718\) | −52.3542 | + | 30.2267i | −1.95384 | + | 1.12805i | ||||
\(719\) | −3.07838 | + | 5.33191i | −0.114804 | + | 0.198847i | −0.917701 | − | 0.397271i | \(-0.869957\pi\) |
0.802897 | + | 0.596117i | \(0.203291\pi\) | |||||||
\(720\) | −30.0277 | + | 7.46081i | −1.11907 | + | 0.278048i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 25.8020i | 0.960252i | ||||||||
\(723\) | −12.7136 | − | 7.34017i | −0.472822 | − | 0.272984i | ||||
\(724\) | −22.7587 | − | 39.4193i | −0.845821 | − | 1.46501i | ||||
\(725\) | −28.2974 | − | 17.7463i | −1.05094 | − | 0.659080i | ||||
\(726\) | −9.48246 | + | 16.4241i | −0.351927 | + | 0.609556i | ||||
\(727\) | 2.89043i | 0.107200i | 0.998562 | + | 0.0536000i | \(0.0170696\pi\) | ||||
−0.998562 | + | 0.0536000i | \(0.982930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 11.8533 | − | 41.2109i | 0.438711 | − | 1.52528i | ||||
\(731\) | 3.51745 | + | 6.09240i | 0.130097 | + | 0.225335i | ||||
\(732\) | −19.2239 | + | 11.0989i | −0.710534 | + | 0.410227i | ||||
\(733\) | −22.3432 | − | 12.8999i | −0.825267 | − | 0.476468i | 0.0269626 | − | 0.999636i | \(-0.491417\pi\) |
−0.852229 | + | 0.523168i | \(0.824750\pi\) | |||||||
\(734\) | 55.0349 | 2.03138 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −45.3751 | −1.67255 | ||||||||
\(737\) | −8.10660 | − | 4.68035i | −0.298610 | − | 0.172403i | ||||
\(738\) | 15.2438 | − | 8.80098i | 0.561130 | − | 0.323969i | ||||
\(739\) | −0.523590 | − | 0.906885i | −0.0192606 | − | 0.0333603i | 0.856234 | − | 0.516587i | \(-0.172798\pi\) |
−0.875495 | + | 0.483227i | \(0.839465\pi\) | |||||||
\(740\) | 124.364 | + | 35.7702i | 4.57170 | + | 1.31494i | ||||
\(741\) | 2.83710 | 0.104224 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.97334i | 0.365886i | 0.983123 | + | 0.182943i | \(0.0585624\pi\) | ||||
−0.983123 | + | 0.182943i | \(0.941438\pi\) | |||||||
\(744\) | 35.1061 | − | 60.8055i | 1.28705 | − | 2.22924i | ||||
\(745\) | 24.3263 | + | 25.2316i | 0.891246 | + | 0.924416i | ||||
\(746\) | −21.6742 | − | 37.5408i | −0.793549 | − | 1.37447i | ||||
\(747\) | −5.92110 | − | 3.41855i | −0.216642 | − | 0.125078i | ||||
\(748\) | − | 11.5174i | − | 0.421120i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −22.5597 | + | 20.2134i | −0.823764 | + | 0.738089i | ||||
\(751\) | −1.63317 | + | 2.82872i | −0.0595950 | + | 0.103222i | −0.894284 | − | 0.447501i | \(-0.852314\pi\) |
0.834689 | + | 0.550722i | \(0.185648\pi\) | |||||||
\(752\) | 56.0859 | − | 32.3812i | 2.04524 | − | 1.18082i | ||||
\(753\) | −7.93530 | + | 4.58145i | −0.289179 | + | 0.166957i | ||||
\(754\) | 8.34017 | − | 14.4456i | 0.303731 | − | 0.526078i | ||||
\(755\) | 12.6803 | − | 3.15061i | 0.461485 | − | 0.114663i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 49.9877i | − | 1.81683i | −0.418065 | − | 0.908417i | \(-0.637292\pi\) | ||
0.418065 | − | 0.908417i | \(-0.362708\pi\) | |||||||
\(758\) | −14.4456 | − | 8.34017i | −0.524688 | − | 0.302929i | ||||
\(759\) | 2.34017 | + | 4.05330i | 0.0849429 | + | 0.147125i | ||||
\(760\) | −44.8440 | + | 43.2349i | −1.62666 | + | 1.56829i | ||||
\(761\) | −1.30632 | + | 2.26262i | −0.0473542 | + | 0.0820198i | −0.888731 | − | 0.458429i | \(-0.848412\pi\) |
0.841377 | + | 0.540449i | \(0.181746\pi\) | |||||||
\(762\) | − | 4.99386i | − | 0.180908i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −82.0288 | −2.96770 | ||||||||
\(765\) | 2.31737 | + | 0.666537i | 0.0837848 | + | 0.0240987i | ||||
\(766\) | 36.3545 | + | 62.9679i | 1.31354 | + | 2.27512i | ||||
\(767\) | 8.39939 | − | 4.84939i | 0.303284 | − | 0.175101i | ||||
\(768\) | 23.9719 | + | 13.8402i | 0.865011 | + | 0.499414i | ||||
\(769\) | 15.6742 | 0.565226 | 0.282613 | − | 0.959234i | \(-0.408799\pi\) | ||||
0.282613 | + | 0.959234i | \(0.408799\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.07838 | −0.182893 | ||||||||
\(772\) | −38.6943 | − | 22.3402i | −1.39264 | − | 0.804040i | ||||
\(773\) | −5.03338 | + | 2.90602i | −0.181038 | + | 0.104522i | −0.587780 | − | 0.809021i | \(-0.699998\pi\) |
0.406742 | + | 0.913543i | \(0.366665\pi\) | |||||||
\(774\) | 8.83710 | + | 15.3063i | 0.317643 | + | 0.550174i | ||||
\(775\) | 1.41695 | − | 38.7677i | 0.0508982 | − | 1.39258i | ||||
\(776\) | 76.3689 | 2.74148 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 15.2618i | − | 0.547162i | ||||||
\(779\) | 10.0000 | − | 17.3205i | 0.358287 | − | 0.620572i | ||||
\(780\) | −7.63833 | − | 7.92261i | −0.273496 | − | 0.283675i | ||||
\(781\) | −2.00000 | − | 3.46410i | −0.0715656 | − | 0.123955i | ||||
\(782\) | 5.92110 | + | 3.41855i | 0.211738 | + | 0.122247i | ||||
\(783\) | 6.68035i | 0.238736i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.65368 | + | 10.6803i | 0.0947140 | + | 0.381198i | ||||
\(786\) | 2.00000 | − | 3.46410i | 0.0713376 | − | 0.123560i | ||||
\(787\) | 34.0767 | − | 19.6742i | 1.21470 | − | 0.701310i | 0.250924 | − | 0.968007i | \(-0.419266\pi\) |
0.963780 | + | 0.266697i | \(0.0859324\pi\) | |||||||
\(788\) | 54.3809 | − | 31.3968i | 1.93724 | − | 1.11847i | ||||
\(789\) | 2.82991 | − | 4.90155i | 0.100748 | − | 0.174500i | ||||
\(790\) | 8.99386 | + | 36.1978i | 0.319987 | + | 1.28786i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 18.0989i | − | 0.643116i | ||||||
\(793\) | −3.31771 | − | 1.91548i | −0.117815 | − | 0.0680207i | ||||
\(794\) | −51.2050 | − | 88.6896i | −1.81720 | − | 3.14748i | ||||
\(795\) | 5.83352 | + | 6.05063i | 0.206894 | + | 0.214594i | ||||
\(796\) | 60.3328 | − | 104.499i | 2.13844 | − | 3.70389i | ||||
\(797\) | 28.2823i | 1.00181i | 0.865502 | + | 0.500905i | \(0.167000\pi\) | ||||
−0.865502 | + | 0.500905i | \(0.833000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.04718 | −0.178556 | ||||||||
\(800\) | 96.8834 | + | 3.54105i | 3.42535 | + | 0.125195i | ||||
\(801\) | −4.17009 | − | 7.22280i | −0.147343 | − | 0.255205i | ||||
\(802\) | 31.9875 | − | 18.4680i | 1.12952 | − | 0.652128i | ||||
\(803\) | 12.2601 | + | 7.07838i | 0.432650 | + | 0.249791i | ||||
\(804\) | −24.9939 | −0.881465 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19.3730 | 0.682384 | ||||||||
\(807\) | 24.1254 | + | 13.9288i | 0.849255 | + | 0.490317i | ||||
\(808\) | −45.5849 | + | 26.3184i | −1.60367 | + | 0.925879i | ||||
\(809\) | −7.83710 | − | 13.5743i | −0.275538 | − | 0.477245i | 0.694733 | − | 0.719268i | \(-0.255523\pi\) |
−0.970271 | + | 0.242022i | \(0.922189\pi\) | |||||||
\(810\) | 5.82208 | + | 1.67458i | 0.204567 | + | 0.0588388i | ||||
\(811\) | −42.1666 | −1.48067 | −0.740335 | − | 0.672238i | \(-0.765333\pi\) | ||||
−0.740335 | + | 0.672238i | \(0.765333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 25.1194i | − | 0.880976i | ||||||
\(814\) | −29.3607 | + | 50.8542i | −1.02909 | + | 1.78244i | ||||
\(815\) | 15.8452 | − | 15.2767i | 0.555034 | − | 0.535118i | ||||
\(816\) | −7.46081 | − | 12.9225i | −0.261181 | − | 0.452378i | ||||
\(817\) | 17.3916 | + | 10.0410i | 0.608455 | + | 0.351291i | ||||
\(818\) | 33.4719i | 1.17032i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −75.2905 | + | 18.7070i | −2.62926 | + | 0.653277i | ||||
\(821\) | 19.5236 | − | 33.8159i | 0.681378 | − | 1.18018i | −0.293182 | − | 0.956057i | \(-0.594714\pi\) |
0.974560 | − | 0.224125i | \(-0.0719523\pi\) | |||||||
\(822\) | −10.4154 | + | 6.01333i | −0.363279 | + | 0.209739i | ||||
\(823\) | 31.6659 | − | 18.2823i | 1.10380 | − | 0.637281i | 0.166586 | − | 0.986027i | \(-0.446726\pi\) |
0.937217 | + | 0.348745i | \(0.113392\pi\) | |||||||
\(824\) | 9.75872 | − | 16.9026i | 0.339961 | − | 0.588830i | ||||
\(825\) | −4.68035 | − | 8.83710i | −0.162949 | − | 0.307668i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.2245i | 1.74648i | 0.487294 | + | 0.873238i | \(0.337984\pi\) | ||||
−0.487294 | + | 0.873238i | \(0.662016\pi\) | |||||||
\(828\) | 10.8227 | + | 6.24846i | 0.376113 | + | 0.217149i | ||||
\(829\) | 16.4186 | + | 28.4378i | 0.570240 | + | 0.987684i | 0.996541 | + | 0.0831031i | \(0.0264831\pi\) |
−0.426301 | + | 0.904581i | \(0.640184\pi\) | |||||||
\(830\) | 28.7485 | + | 29.8185i | 0.997875 | + | 1.03501i | ||||
\(831\) | 14.0989 | − | 24.4200i | 0.489085 | − | 0.847121i | ||||
\(832\) | 22.9093i | 0.794238i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 36.8515 | 1.27606 | ||||||||
\(835\) | 41.2682 | + | 11.8698i | 1.42814 | + | 0.410771i | ||||
\(836\) | −16.4391 | − | 28.4733i | −0.568557 | − | 0.984770i | ||||
\(837\) | −6.71925 | + | 3.87936i | −0.232251 | + | 0.134090i | ||||
\(838\) | −68.0283 | − | 39.2762i | −2.35000 | − | 1.35677i | ||||
\(839\) | 13.3607 | 0.461262 | 0.230631 | − | 0.973041i | \(-0.425921\pi\) | ||||
0.230631 | + | 0.973041i | \(0.425921\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6270 | 0.538863 | ||||||||
\(842\) | −35.5767 | − | 20.5402i | −1.22606 | − | 0.707863i | ||||
\(843\) | 17.6276 | − | 10.1773i | 0.607125 | − | 0.350524i | ||||
\(844\) | −36.5113 | − | 63.2394i | −1.25677 | − | 2.17679i | ||||
\(845\) | −7.51020 | + | 26.1110i | −0.258359 | + | 0.898245i | ||||
\(846\) | −12.6803 | −0.435959 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 52.0098i | − | 1.78603i | ||||||
\(849\) | 11.7587 | − | 20.3667i | 0.403558 | − | 0.698984i | ||||
\(850\) | −12.3758 | − | 7.76126i | −0.424485 | − | 0.266209i | ||||
\(851\) | −12.6803 | − | 21.9630i | −0.434677 | − | 0.752882i | ||||
\(852\) | −9.24945 | − | 5.34017i | −0.316881 | − | 0.182951i | ||||
\(853\) | 39.6430i | 1.35735i | 0.734438 | + | 0.678675i | \(0.237446\pi\) | ||||
−0.734438 | + | 0.678675i | \(0.762554\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.68035 | − | 1.65983i | 0.228463 | − | 0.0567649i | ||||
\(856\) | −74.6441 | + | 129.287i | −2.55128 | + | 4.41895i | ||||
\(857\) | −25.7256 | + | 14.8527i | −0.878771 | + | 0.507359i | −0.870253 | − | 0.492605i | \(-0.836045\pi\) |
−0.00851788 | + | 0.999964i | \(0.502711\pi\) | |||||||
\(858\) | 4.32481 | − | 2.49693i | 0.147646 | − | 0.0852437i | ||||
\(859\) | −1.53919 | + | 2.66595i | −0.0525164 | + | 0.0909612i | −0.891089 | − | 0.453829i | \(-0.850058\pi\) |
0.838572 | + | 0.544791i | \(0.183391\pi\) | |||||||
\(860\) | −18.7838 | − | 75.5995i | −0.640521 | − | 2.57792i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.9421i | 0.951713i | ||||||||
\(863\) | −5.53693 | − | 3.19675i | −0.188479 | − | 0.108819i | 0.402791 | − | 0.915292i | \(-0.368040\pi\) |
−0.591270 | + | 0.806473i | \(0.701373\pi\) | |||||||
\(864\) | −9.69481 | − | 16.7919i | −0.329824 | − | 0.571272i | ||||
\(865\) | 36.1214 | − | 34.8253i | 1.22817 | − | 1.18410i | ||||
\(866\) | 27.6875 | − | 47.9562i | 0.940861 | − | 1.62962i | ||||
\(867\) | − | 15.8371i | − | 0.537856i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.3135 | −0.417707 | ||||||||
\(870\) | 11.1868 | − | 38.8935i | 0.379267 | − | 1.31861i | ||||
\(871\) | −2.15676 | − | 3.73561i | −0.0730789 | − | 0.126576i | ||||
\(872\) | 100.605 | − | 58.0843i | 3.40692 | − | 1.96698i | ||||
\(873\) | −7.30845 | − | 4.21953i | −0.247354 | − | 0.142810i | ||||
\(874\) | 19.5174 | 0.660188 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 37.7998 | 1.27714 | ||||||||
\(877\) | 1.05328 | + | 0.608111i | 0.0355667 | + | 0.0205345i | 0.517678 | − | 0.855576i | \(-0.326797\pi\) |
−0.482111 | + | 0.876110i | \(0.660130\pi\) | |||||||
\(878\) | −39.7032 | + | 22.9227i | −1.33992 | + | 0.773603i | ||||
\(879\) | −1.46081 | − | 2.53020i | −0.0492719 | − | 0.0853415i | ||||
\(880\) | −17.1052 | + | 59.4703i | −0.576616 | + | 2.00474i | ||||
\(881\) | 15.9733 | 0.538155 | 0.269078 | − | 0.963118i | \(-0.413281\pi\) | ||||
0.269078 | + | 0.963118i | \(0.413281\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 11.6865i | − | 0.393282i | −0.980476 | − | 0.196641i | \(-0.936997\pi\) | ||
0.980476 | − | 0.196641i | \(-0.0630033\pi\) | |||||||
\(884\) | 2.65368 | − | 4.59632i | 0.0892531 | − | 0.154591i | ||||
\(885\) | 16.9404 | − | 16.3326i | 0.569446 | − | 0.549013i | ||||
\(886\) | −17.3535 | − | 30.0572i | −0.583002 | − | 1.00979i | ||||
\(887\) | 22.1883 | + | 12.8104i | 0.745011 | + | 0.430132i | 0.823889 | − | 0.566752i | \(-0.191800\pi\) |
−0.0788773 | + | 0.996884i | \(0.525134\pi\) | |||||||
\(888\) | 98.0698i | 3.29101i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 12.1834 | + | 49.0349i | 0.408389 | + | 1.64365i | ||||
\(891\) | −1.00000 | + | 1.73205i | −0.0335013 | + | 0.0580259i | ||||
\(892\) | −100.237 | + | 57.8720i | −3.35619 | + | 1.93770i | ||||
\(893\) | −12.4776 | + | 7.20394i | −0.417546 | + | 0.241071i | ||||
\(894\) | −21.2329 | + | 36.7764i | −0.710133 | + | 1.22999i | ||||
\(895\) | −21.7009 | + | 5.39189i | −0.725380 | + | 0.180231i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.15676i | 0.0720120i | ||||||||
\(898\) | 34.3194 | + | 19.8143i | 1.14525 | + | 0.661212i | ||||
\(899\) | 25.9155 | + | 44.8869i | 0.864330 | + | 1.49706i | ||||
\(900\) | −22.6206 | − | 14.1861i | −0.754019 | − | 0.472871i | ||||
\(901\) | −2.02666 | + | 3.51028i | −0.0675179 | + | 0.116944i | ||||
\(902\) | − | 35.2039i | − | 1.17216i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −47.3751 | −1.57567 | ||||||||
\(905\) | 5.26836 | − | 18.3167i | 0.175126 | − | 0.608868i | ||||
\(906\) | 7.91548 | + | 13.7100i | 0.262974 | + | 0.455485i | ||||
\(907\) | −50.0184 | + | 28.8781i | −1.66083 | + | 0.958883i | −0.688516 | + | 0.725221i | \(0.741737\pi\) |
−0.972318 | + | 0.233662i | \(0.924929\pi\) | |||||||
\(908\) | −53.2650 | − | 30.7526i | −1.76766 | − | 1.02056i | ||||
\(909\) | 5.81658 | 0.192924 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.9877 | −1.19233 | −0.596163 | − | 0.802863i | \(-0.703309\pi\) | ||||
−0.596163 | + | 0.802863i | \(0.703309\pi\) | |||||||
\(912\) | −36.8891 | − | 21.2979i | −1.22152 | − | 0.705244i | ||||
\(913\) | −11.8422 | + | 6.83710i | −0.391920 | + | 0.226275i | ||||
\(914\) | −19.1773 | − | 33.2160i | −0.634328 | − | 1.09869i | ||||
\(915\) | −8.93264 | − | 2.56926i | −0.295304 | − | 0.0849370i | ||||
\(916\) | 68.5523 | 2.26503 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.92162i | 0.0964279i | ||||||||
\(919\) | 23.3607 | − | 40.4619i | 0.770598 | − | 1.33472i | −0.166637 | − | 0.986018i | \(-0.553291\pi\) |
0.937236 | − | 0.348697i | \(-0.113376\pi\) | |||||||
\(920\) | −32.8670 | − | 34.0902i | −1.08359 | − | 1.12392i | ||||
\(921\) | 5.23513 | + | 9.06752i | 0.172504 | + | 0.298785i | ||||
\(922\) | 0.798148 | + | 0.460811i | 0.0262856 | + | 0.0151760i | ||||
\(923\) | − | 1.84324i | − | 0.0606711i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.3607 | + | 47.8843i | 0.833854 | + | 1.57443i | ||||
\(926\) | −13.3340 | + | 23.0952i | −0.438183 | + | 0.758956i | ||||
\(927\) | −1.86781 | + | 1.07838i | −0.0613468 | + | 0.0354186i | ||||
\(928\) | −112.176 | + | 64.7647i | −3.68235 | + | 2.12601i | ||||
\(929\) | −26.5246 | + | 45.9420i | −0.870245 | + | 1.50731i | −0.00850190 | + | 0.999964i | \(0.502706\pi\) |
−0.861743 | + | 0.507345i | \(0.830627\pi\) | |||||||
\(930\) | 45.6163 | − | 11.3340i | 1.49582 | − | 0.371657i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 36.1256i | − | 1.18333i | ||||||
\(933\) | 20.6382 | + | 11.9155i | 0.675665 | + | 0.390095i | ||||
\(934\) | 15.6020 | + | 27.0234i | 0.510512 | + | 0.884233i | ||||
\(935\) | 3.47185 | − | 3.34727i | 0.113542 | − | 0.109468i | ||||
\(936\) | 4.17009 | − | 7.22280i | 0.136304 | − | 0.236085i | ||||
\(937\) | − | 16.1256i | − | 0.526799i | −0.964687 | − | 0.263400i | \(-0.915156\pi\) | ||
0.964687 | − | 0.263400i | \(-0.0848437\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.7526 | −1.06884 | ||||||||
\(940\) | 53.7104 | + | 15.4485i | 1.75184 | + | 0.503875i | ||||
\(941\) | −12.3535 | − | 21.3969i | −0.402713 | − | 0.697519i | 0.591340 | − | 0.806423i | \(-0.298599\pi\) |
−0.994052 | + | 0.108904i | \(0.965266\pi\) | |||||||
\(942\) | −11.5476 | + | 6.66701i | −0.376241 | + | 0.217223i | ||||
\(943\) | 13.1670 | + | 7.60197i | 0.428776 | + | 0.247554i | ||||
\(944\) | −145.616 | −4.73940 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.3484 | 1.14928 | ||||||||
\(947\) | 5.66204 | + | 3.26898i | 0.183992 | + | 0.106228i | 0.589167 | − | 0.808011i | \(-0.299456\pi\) |
−0.405175 | + | 0.914239i | \(0.632789\pi\) | |||||||
\(948\) | −28.4733 | + | 16.4391i | −0.924770 | + | 0.533916i | ||||
\(949\) | 3.26180 | + | 5.64960i | 0.105882 | + | 0.183394i | ||||
\(950\) | −41.6730 | − | 1.52313i | −1.35205 | − | 0.0494170i | ||||
\(951\) | −17.9155 | −0.580949 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 6.11327i | − | 0.198028i | −0.995086 | − | 0.0990142i | \(-0.968431\pi\) | ||
0.995086 | − | 0.0990142i | \(-0.0315689\pi\) | |||||||
\(954\) | −5.09171 | + | 8.81910i | −0.164850 | + | 0.285529i | ||||
\(955\) | −23.8397 | − | 24.7270i | −0.771435 | − | 0.800146i | ||||
\(956\) | 62.3751 | + | 108.037i | 2.01735 | + | 3.49416i | ||||
\(957\) | 11.5707 | + | 6.68035i | 0.374028 | + | 0.215945i | ||||
\(958\) | − | 52.8781i | − | 1.70842i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13.4030 | + | 53.9432i | 0.432578 | + | 1.74101i | ||||
\(961\) | −14.5989 | + | 25.2860i | −0.470932 | + | 0.815678i | ||||
\(962\) | −23.4342 | + | 13.5297i | −0.755548 | + | 0.436216i | ||||
\(963\) | 14.2868 | − | 8.24846i | 0.460384 | − | 0.265803i | ||||
\(964\) | −39.1978 | + | 67.8926i | −1.26248 | + | 2.18667i | ||||
\(965\) | −4.51130 | − | 18.1568i | −0.145224 | − | 0.584487i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 25.6209i | − | 0.823912i | −0.911204 | − | 0.411956i | \(-0.864846\pi\) | ||
0.911204 | − | 0.411956i | \(-0.135154\pi\) | |||||||
\(968\) | 54.8594 | + | 31.6731i | 1.76325 | + | 1.01801i | ||||
\(969\) | 1.65983 | + | 2.87490i | 0.0533213 | + | 0.0923552i | ||||
\(970\) | 35.4844 | + | 36.8051i | 1.13934 | + | 1.18174i | ||||
\(971\) | −2.02666 | + | 3.51028i | −0.0650387 | + | 0.112650i | −0.896711 | − | 0.442616i | \(-0.854050\pi\) |
0.831672 | + | 0.555267i | \(0.187384\pi\) | |||||||
\(972\) | 5.34017i | 0.171286i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 62.7214 | 2.00972 | ||||||||
\(975\) | 0.168312 | − | 4.60504i | 0.00539031 | − | 0.147479i | ||||
\(976\) | 28.7587 | + | 49.8116i | 0.920544 | + | 1.59443i | ||||
\(977\) | −3.30133 | + | 1.90602i | −0.105619 | + | 0.0609791i | −0.551879 | − | 0.833924i | \(-0.686089\pi\) |
0.446260 | + | 0.894903i | \(0.352756\pi\) | |||||||
\(978\) | 23.0952 | + | 13.3340i | 0.738504 | + | 0.426375i | ||||
\(979\) | −16.6803 | −0.533106 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.8371 | −0.409857 | ||||||||
\(982\) | 4.69260 | + | 2.70928i | 0.149747 | + | 0.0864565i | ||||
\(983\) | −20.7846 | + | 12.0000i | −0.662926 | + | 0.382741i | −0.793391 | − | 0.608712i | \(-0.791686\pi\) |
0.130465 | + | 0.991453i | \(0.458353\pi\) | |||||||
\(984\) | −29.3968 | − | 50.9168i | −0.937136 | − | 1.62317i | ||||
\(985\) | 25.2688 | + | 7.26797i | 0.805132 | + | 0.231577i | ||||
\(986\) | 19.5174 | 0.621562 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 15.1506i | − | 0.482005i | ||||||
\(989\) | −7.63317 | + | 13.2210i | −0.242721 | + | 0.420404i | ||||
\(990\) | 8.72254 | − | 8.40956i | 0.277221 | − | 0.267273i | ||||
\(991\) | 21.2039 | + | 36.7263i | 0.673565 | + | 1.16665i | 0.976886 | + | 0.213761i | \(0.0685713\pi\) |
−0.303321 | + | 0.952888i | \(0.598095\pi\) | |||||||
\(992\) | −130.284 | − | 75.2194i | −4.13651 | − | 2.38822i | ||||
\(993\) | 1.36069i | 0.0431803i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 49.0349 | − | 12.1834i | 1.55451 | − | 0.386240i | ||||
\(996\) | −18.2557 | + | 31.6197i | −0.578452 | + | 1.00191i | ||||
\(997\) | 37.6496 | − | 21.7370i | 1.19237 | − | 0.688417i | 0.233529 | − | 0.972350i | \(-0.424973\pi\) |
0.958844 | + | 0.283933i | \(0.0916392\pi\) | |||||||
\(998\) | 63.8286 | − | 36.8515i | 2.02046 | − | 1.16651i | ||||
\(999\) | 5.41855 | − | 9.38521i | 0.171435 | − | 0.296935i |
(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 | 735.2.q.e.79.6 | 12 | ||
5.4 | even | 2 | inner | 735.2.q.e.79.1 | 12 | ||
7.2 | even | 3 | 105.2.d.b.64.1 | ✓ | 6 | ||
7.3 | odd | 6 | 735.2.q.f.214.1 | 12 | |||
7.4 | even | 3 | inner | 735.2.q.e.214.1 | 12 | ||
7.5 | odd | 6 | 735.2.d.b.589.1 | 6 | |||
7.6 | odd | 2 | 735.2.q.f.79.6 | 12 | |||
21.2 | odd | 6 | 315.2.d.e.64.6 | 6 | |||
21.5 | even | 6 | 2205.2.d.l.1324.6 | 6 | |||
28.23 | odd | 6 | 1680.2.t.k.1009.6 | 6 | |||
35.2 | odd | 12 | 525.2.a.k.1.3 | 3 | |||
35.4 | even | 6 | inner | 735.2.q.e.214.6 | 12 | ||
35.9 | even | 6 | 105.2.d.b.64.6 | yes | 6 | ||
35.12 | even | 12 | 3675.2.a.bj.1.3 | 3 | |||
35.19 | odd | 6 | 735.2.d.b.589.6 | 6 | |||
35.23 | odd | 12 | 525.2.a.j.1.1 | 3 | |||
35.24 | odd | 6 | 735.2.q.f.214.6 | 12 | |||
35.33 | even | 12 | 3675.2.a.bi.1.1 | 3 | |||
35.34 | odd | 2 | 735.2.q.f.79.1 | 12 | |||
84.23 | even | 6 | 5040.2.t.v.1009.2 | 6 | |||
105.2 | even | 12 | 1575.2.a.w.1.1 | 3 | |||
105.23 | even | 12 | 1575.2.a.x.1.3 | 3 | |||
105.44 | odd | 6 | 315.2.d.e.64.1 | 6 | |||
105.89 | even | 6 | 2205.2.d.l.1324.1 | 6 | |||
140.23 | even | 12 | 8400.2.a.dg.1.2 | 3 | |||
140.79 | odd | 6 | 1680.2.t.k.1009.3 | 6 | |||
140.107 | even | 12 | 8400.2.a.dj.1.2 | 3 | |||
420.359 | even | 6 | 5040.2.t.v.1009.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.b.64.1 | ✓ | 6 | 7.2 | even | 3 | ||
105.2.d.b.64.6 | yes | 6 | 35.9 | even | 6 | ||
315.2.d.e.64.1 | 6 | 105.44 | odd | 6 | |||
315.2.d.e.64.6 | 6 | 21.2 | odd | 6 | |||
525.2.a.j.1.1 | 3 | 35.23 | odd | 12 | |||
525.2.a.k.1.3 | 3 | 35.2 | odd | 12 | |||
735.2.d.b.589.1 | 6 | 7.5 | odd | 6 | |||
735.2.d.b.589.6 | 6 | 35.19 | odd | 6 | |||
735.2.q.e.79.1 | 12 | 5.4 | even | 2 | inner | ||
735.2.q.e.79.6 | 12 | 1.1 | even | 1 | trivial | ||
735.2.q.e.214.1 | 12 | 7.4 | even | 3 | inner | ||
735.2.q.e.214.6 | 12 | 35.4 | even | 6 | inner | ||
735.2.q.f.79.1 | 12 | 35.34 | odd | 2 | |||
735.2.q.f.79.6 | 12 | 7.6 | odd | 2 | |||
735.2.q.f.214.1 | 12 | 7.3 | odd | 6 | |||
735.2.q.f.214.6 | 12 | 35.24 | odd | 6 | |||
1575.2.a.w.1.1 | 3 | 105.2 | even | 12 | |||
1575.2.a.x.1.3 | 3 | 105.23 | even | 12 | |||
1680.2.t.k.1009.3 | 6 | 140.79 | odd | 6 | |||
1680.2.t.k.1009.6 | 6 | 28.23 | odd | 6 | |||
2205.2.d.l.1324.1 | 6 | 105.89 | even | 6 | |||
2205.2.d.l.1324.6 | 6 | 21.5 | even | 6 | |||
3675.2.a.bi.1.1 | 3 | 35.33 | even | 12 | |||
3675.2.a.bj.1.3 | 3 | 35.12 | even | 12 | |||
5040.2.t.v.1009.1 | 6 | 420.359 | even | 6 | |||
5040.2.t.v.1009.2 | 6 | 84.23 | even | 6 | |||
8400.2.a.dg.1.2 | 3 | 140.23 | even | 12 | |||
8400.2.a.dj.1.2 | 3 | 140.107 | even | 12 |