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 | 79.1 | ||
Root | \(0.312819 + 1.16746i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.79 |
Dual form | 735.2.q.e.214.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
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 | \(-0.926055\pi\) |
−0.685948 | − | 0.727651i | \(-0.740612\pi\) | |||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 2.67009 | + | 4.62473i | 1.33504 | + | 2.31236i | ||||
\(5\) | −1.55199 | + | 1.60976i | −0.694073 | + | 0.719905i | ||||
\(6\) | −2.70928 | −1.10606 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 9.04945i | − | 3.19946i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 5.82208 | − | 1.67458i | 1.84110 | − | 0.529549i | ||||
\(11\) | −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 | \(0.0407935\pi\) | ||||
−0.991799 | + | 0.127806i | \(0.959207\pi\) | |||||||
\(14\) | 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 | −0.608959 | − | 0.793202i | \(-0.708412\pi\) |
0.382454 | + | 0.923975i | \(0.375079\pi\) | |||||||
\(18\) | −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 | 0.273597 | − | 0.961844i | \(-0.411786\pi\) |
−0.696183 | + | 0.717864i | \(0.745120\pi\) | |||||||
\(24\) | −4.52472 | − | 7.83705i | −0.923605 | − | 1.59973i | ||||
\(25\) | −0.182626 | − | 4.99666i | −0.0365252 | − | 0.999333i | ||||
\(26\) | 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 | \(0.287029\pi\) | |||||||
\(30\) | 4.20478 | − | 4.36127i | 0.767684 | − | 0.796256i | ||||
\(31\) | 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 | \(0.0165249\pi\) |
0.544265 | + | 0.838913i | \(0.316808\pi\) | |||||||
\(38\) | −7.22280 | + | 4.17009i | −1.17169 | + | 0.676477i | ||||
\(39\) | 0.460811 | + | 0.798148i | 0.0737888 | + | 0.127806i | ||||
\(40\) | 14.5674 | + | 14.0447i | 2.30331 | + | 2.22066i | ||||
\(41\) | 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 | \(-0.834281\pi\) | ||
0.867510 | − | 0.497419i | \(-0.165719\pi\) | |||||||
\(44\) | 5.34017 | − | 9.24945i | 0.805061 | − | 1.39441i | ||||
\(45\) | 0.618092 | + | 2.14894i | 0.0921397 | + | 0.320346i | ||||
\(46\) | 3.17009 | + | 5.49075i | 0.467404 | + | 0.809567i | ||||
\(47\) | 4.05330 | + | 2.34017i | 0.591234 | + | 0.341349i | 0.765585 | − | 0.643334i | \(-0.222449\pi\) |
−0.174351 | + | 0.984684i | \(0.555783\pi\) | |||||||
\(48\) | 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 | −0.259488 | − | 0.965746i | \(-0.583554\pi\) |
0.706617 | + | 0.707596i | \(0.250220\pi\) | |||||||
\(54\) | −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 | \(0.593124\pi\) | |||||||
\(60\) | −11.4757 | + | 3.30072i | −1.48151 | + | 0.426121i | ||||
\(61\) | 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 | ||||||||
\(65\) | −1.48359 | − | 1.43035i | −0.184016 | − | 0.177413i | ||||
\(66\) | 2.70928 | + | 4.69260i | 0.333489 | + | 0.577619i | ||||
\(67\) | −4.05330 | + | 2.34017i | −0.495189 | + | 0.285898i | −0.726725 | − | 0.686929i | \(-0.758958\pi\) |
0.231535 | + | 0.972826i | \(0.425625\pi\) | |||||||
\(68\) | −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 | −0.0963516 | − | 0.995347i | \(-0.530717\pi\) |
0.813820 | + | 0.581117i | \(0.197384\pi\) | |||||||
\(74\) | −14.6803 | − | 25.4271i | −1.70656 | − | 2.95584i | ||||
\(75\) | −2.65649 | − | 4.23592i | −0.306745 | − | 0.489122i | ||||
\(76\) | 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 | \(0.0540895\pi\) | |||||||
\(80\) | −8.55260 | − | 29.7352i | −0.956210 | − | 3.32449i | ||||
\(81\) | −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 | \(0.122438\pi\) | ||||
−0.926930 | + | 0.375235i | \(0.877562\pi\) | |||||||
\(84\) | 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 | ||||
\(95\) | 1.90272 | + | 6.61526i | 0.195215 | + | 0.678712i | ||||
\(96\) | 9.69481 | − | 16.7919i | 0.989472 | − | 1.71382i | ||||
\(97\) | 8.43907i | 0.856858i | 0.903576 | + | 0.428429i | \(0.140933\pi\) | ||||
−0.903576 | + | 0.428429i | \(0.859067\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 22.6206 | − | 14.1861i | 2.26206 | − | 1.41861i | ||||
\(101\) | 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 | 0.589190 | − | 0.807995i | \(-0.299447\pi\) |
−0.405149 | + | 0.914251i | \(0.632780\pi\) | |||||||
\(104\) | 8.34017 | 0.817821 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.1834 | −0.989101 | ||||||||
\(107\) | −14.2868 | − | 8.24846i | −1.38115 | − | 0.797409i | −0.388857 | − | 0.921298i | \(-0.627130\pi\) |
−0.992296 | + | 0.123889i | \(0.960463\pi\) | |||||||
\(108\) | 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 | \(-0.377424\pi\) | |||||||
\(110\) | −8.72254 | − | 8.40956i | −0.831662 | − | 0.801820i | ||||
\(111\) | 10.8371 | 1.02861 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.23513i | − | 0.492480i | −0.969209 | − | 0.246240i | \(-0.920805\pi\) | ||
0.969209 | − | 0.246240i | \(-0.0791951\pi\) | |||||||
\(114\) | −4.17009 | + | 7.22280i | −0.390564 | + | 0.676477i | ||||
\(115\) | 5.02890 | − | 1.44644i | 0.468948 | − | 0.134881i | ||||
\(116\) | 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 | \(-0.973939\pi\) | ||
0.996650 | − | 0.0817808i | \(-0.0260607\pi\) | |||||||
\(128\) | 24.7397 | + | 14.2834i | 2.18670 | + | 1.26249i | ||||
\(129\) | −3.26180 | − | 5.64960i | −0.287185 | − | 0.497419i | ||||
\(130\) | 1.54333 | + | 5.36576i | 0.135359 | + | 0.470608i | ||||
\(131\) | −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 | ||||||||
\(135\) | 1.60976 | + | 1.55199i | 0.138546 | + | 0.133574i | ||||
\(136\) | 4.87936 | + | 8.45130i | 0.418402 | + | 0.724693i | ||||
\(137\) | −3.84435 | + | 2.21953i | −0.328445 | + | 0.189628i | −0.655150 | − | 0.755498i | \(-0.727395\pi\) |
0.326706 | + | 0.945126i | \(0.394061\pi\) | |||||||
\(138\) | 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 | ||||
\(145\) | −10.3679 | + | 10.7537i | −0.861004 | + | 0.893048i | ||||
\(146\) | −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 | \(-0.0552452\pi\) | |||||||
\(150\) | 0.494784 | + | 13.5373i | 0.0403990 | + | 1.10532i | ||||
\(151\) | −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 | −0.660345 | − | 0.750963i | \(-0.729590\pi\) |
0.320180 | + | 0.947357i | \(0.396257\pi\) | |||||||
\(158\) | −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 | 0.795201 | − | 0.606346i | \(-0.207365\pi\) |
−0.127511 | + | 0.991837i | \(0.540699\pi\) | |||||||
\(164\) | 17.3474 | + | 30.0465i | 1.35460 | + | 2.34624i | ||||
\(165\) | 4.29789 | − | 1.23618i | 0.334590 | − | 0.0962368i | ||||
\(166\) | 9.26180 | − | 16.0419i | 0.718855 | − | 1.24509i | ||||
\(167\) | 19.2039i | 1.48605i | 0.669266 | + | 0.743023i | \(0.266609\pi\) | ||||
−0.669266 | + | 0.743023i | \(0.733391\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1506 | 0.934662 | ||||||||
\(170\) | −4.53434 | + | 4.70310i | −0.347768 | + | 0.360711i | ||||
\(171\) | −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 | 0.999675 | − | 0.0254777i | \(-0.00811068\pi\) |
0.477773 | + | 0.878483i | \(0.341444\pi\) | |||||||
\(174\) | −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 | \(0.711416\pi\) | |||||||
\(180\) | −8.28792 | + | 8.59637i | −0.617745 | + | 0.640736i | ||||
\(181\) | −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 | ||||
\(185\) | −23.2883 | + | 6.69833i | −1.71219 | + | 0.492471i | ||||
\(186\) | −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 | −0.216006 | − | 0.976392i | \(-0.569303\pi\) |
0.737577 | + | 0.675263i | \(0.235970\pi\) | |||||||
\(194\) | 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 | \(0.137580\pi\) | ||||
−0.908038 | + | 0.418887i | \(0.862420\pi\) | |||||||
\(198\) | 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 | \(-0.462305\pi\) | |||||||
\(200\) | −45.2170 | + | 1.65267i | −3.19733 | + | 0.116861i | ||||
\(201\) | −2.34017 | + | 4.05330i | −0.165063 | + | 0.285898i | ||||
\(202\) | − | 15.7587i | − | 1.10878i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.75872 | −0.403191 | ||||||||
\(205\) | −10.0832 | + | 10.4585i | −0.704241 | + | 0.730451i | ||||
\(206\) | −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 | ||||
\(215\) | 10.5014 | + | 10.1246i | 0.716189 | + | 0.690490i | ||||
\(216\) | −9.04945 | −0.615737 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 34.7792i | 2.35555i | ||||||||
\(219\) | 3.53919 | − | 6.13005i | 0.239156 | − | 0.414231i | ||||
\(220\) | 6.60144 | + | 22.9515i | 0.445069 | + | 1.54739i | ||||
\(221\) | −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 | \(-0.741513\pi\) | ||
0.688005 | − | 0.725706i | \(-0.258487\pi\) | |||||||
\(224\) | 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 | −0.131024 | − | 0.991379i | \(-0.541826\pi\) |
0.793048 | + | 0.609159i | \(0.208493\pi\) | |||||||
\(228\) | 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 | 0.679473 | − | 0.733701i | \(-0.262208\pi\) |
−0.295667 | + | 0.955291i | \(0.595542\pi\) | |||||||
\(234\) | −1.24846 | − | 2.16240i | −0.0816147 | − | 0.141361i | ||||
\(235\) | −10.0578 | + | 2.89288i | −0.656099 | + | 0.188711i | ||||
\(236\) | −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 | \(0.227375\pi\) | |||||||
\(240\) | −22.2744 | − | 21.4751i | −1.43780 | − | 1.38621i | ||||
\(241\) | 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 | ||||
\(250\) | −9.43058 | − | 28.7852i | −0.596443 | − | 1.82053i | ||||
\(251\) | 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 | ||||
\(255\) | −0.666537 | − | 2.31737i | −0.0417401 | − | 0.145120i | ||||
\(256\) | −13.8402 | − | 23.9719i | −0.865011 | − | 1.49824i | ||||
\(257\) | −4.39800 | − | 2.53919i | −0.274340 | − | 0.158390i | 0.356518 | − | 0.934288i | \(-0.383964\pi\) |
−0.630858 | + | 0.775898i | \(0.717297\pi\) | |||||||
\(258\) | 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 | −0.341207 | − | 0.939988i | \(-0.610836\pi\) |
0.643450 | + | 0.765488i | \(0.277502\pi\) | |||||||
\(264\) | −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 | \(-0.489615\pi\) | |||||||
\(270\) | −1.67458 | − | 5.82208i | −0.101912 | − | 0.354321i | ||||
\(271\) | −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 | ||||||||
\(275\) | −8.47185 | + | 5.31298i | −0.510872 | + | 0.320385i | ||||
\(276\) | −6.24846 | − | 10.8227i | −0.376113 | − | 0.651447i | ||||
\(277\) | 24.4200 | − | 14.0989i | 1.46726 | − | 0.847121i | 0.467928 | − | 0.883767i | \(-0.345001\pi\) |
0.999328 | + | 0.0366462i | \(0.0116675\pi\) | |||||||
\(278\) | 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 | 0.247769 | − | 0.968819i | \(-0.420303\pi\) |
0.962906 | + | 0.269836i | \(0.0869694\pi\) | |||||||
\(284\) | 5.34017 | + | 9.24945i | 0.316881 | + | 0.548854i | ||||
\(285\) | 4.95544 | + | 4.77763i | 0.293535 | + | 0.283002i | ||||
\(286\) | −4.99386 | −0.295293 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 19.3896i | − | 1.14254i | ||||||
\(289\) | −7.91855 | + | 13.7153i | −0.465797 | + | 0.806784i | ||||
\(290\) | 38.8935 | − | 11.1868i | 2.28391 | − | 0.656911i | ||||
\(291\) | 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 | \(-0.972802\pi\) | ||
0.996352 | − | 0.0853415i | \(-0.0271981\pi\) | |||||||
\(294\) | 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 | ||||
\(305\) | 2.56926 | + | 8.93264i | 0.147115 | + | 0.511481i | ||||
\(306\) | 1.46081 | − | 2.53020i | 0.0835090 | − | 0.144642i | ||||
\(307\) | 10.4703i | 0.597570i | 0.954321 | + | 0.298785i | \(0.0965813\pi\) | ||||
−0.954321 | + | 0.298785i | \(0.903419\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.15676 | 0.122694 | ||||||||
\(310\) | 33.8379 | + | 32.6237i | 1.92186 | + | 1.85290i | ||||
\(311\) | −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 | \(-0.956859\pi\) |
−0.612431 | − | 0.790524i | \(-0.709808\pi\) | |||||||
\(314\) | 13.3340 | 0.752483 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.8781 | 1.84954 | ||||||||
\(317\) | −15.5153 | − | 8.95774i | −0.871424 | − | 0.503117i | −0.00360269 | − | 0.999994i | \(-0.501147\pi\) |
−0.867821 | + | 0.496877i | \(0.834480\pi\) | |||||||
\(318\) | −8.81910 | + | 5.09171i | −0.494550 | + | 0.285529i | ||||
\(319\) | −6.68035 | − | 11.5707i | −0.374028 | − | 0.647835i | ||||
\(320\) | 38.5789 | − | 40.0147i | 2.15663 | − | 2.23689i | ||||
\(321\) | −16.4969 | −0.920769 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.31965i | 0.184710i | ||||||||
\(324\) | 2.67009 | − | 4.62473i | 0.148338 | − | 0.256929i | ||||
\(325\) | 4.60504 | − | 0.168312i | 0.255441 | − | 0.00933629i | ||||
\(326\) | −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 | \(0.242716\pi\) | ||||
−0.723101 | + | 0.690742i | \(0.757284\pi\) | |||||||
\(338\) | −28.5090 | − | 16.4597i | −1.55069 | − | 0.895288i | ||||
\(339\) | −2.61757 | − | 4.53376i | −0.142167 | − | 0.246240i | ||||
\(340\) | 12.3752 | − | 3.55942i | 0.671138 | − | 0.193037i | ||||
\(341\) | 7.75872 | − | 13.4385i | 0.420158 | − | 0.727736i | ||||
\(342\) | 8.34017i | 0.450985i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −59.0349 | −3.18295 | ||||||||
\(345\) | 3.63194 | − | 3.76711i | 0.195537 | − | 0.202814i | ||||
\(346\) | −30.3968 | − | 52.6488i | −1.63414 | − | 2.83042i | ||||
\(347\) | −14.6044 | + | 8.43188i | −0.784008 | + | 0.452647i | −0.837849 | − | 0.545902i | \(-0.816187\pi\) |
0.0538410 | + | 0.998550i | \(0.482854\pi\) | |||||||
\(348\) | 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 | \(0.735056\pi\) |
−0.977008 | + | 0.213201i | \(0.931611\pi\) | |||||||
\(354\) | −14.2557 | − | 24.6915i | −0.757679 | − | 1.31234i | ||||
\(355\) | −3.10399 | + | 3.21951i | −0.164743 | + | 0.170874i | ||||
\(356\) | 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 | \(0.966255\pi\) | |||||||
\(360\) | 19.4468 | − | 5.59339i | 1.02493 | − | 0.294798i | ||||
\(361\) | 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 | −0.883091 | − | 0.469202i | \(-0.844542\pi\) |
−0.0352048 | + | 0.999380i | \(0.511208\pi\) | |||||||
\(368\) | 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 | 0.813816 | − | 0.581122i | \(-0.197386\pi\) |
−0.0963587 | + | 0.995347i | \(0.530720\pi\) | |||||||
\(374\) | −2.92162 | − | 5.06040i | −0.151073 | − | 0.261667i | ||||
\(375\) | 10.9417 | + | 2.29783i | 0.565025 | + | 0.118659i | ||||
\(376\) | 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 | \(0.550545\pi\) | |||||||
\(380\) | −25.5133 | + | 26.4629i | −1.30881 | + | 1.35752i | ||||
\(381\) | −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 | −0.229833 | − | 0.973230i | \(-0.573818\pi\) |
−0.957758 | + | 0.287574i | \(0.907151\pi\) | |||||||
\(384\) | 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 | \(0.878946\pi\) | |||||||
\(390\) | 4.01944 | + | 3.87522i | 0.203532 | + | 0.196229i | ||||
\(391\) | 2.52359 | 0.127623 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.47641i | 0.0744750i | ||||||||
\(394\) | 15.9288 | − | 27.5895i | 0.802482 | − | 1.38994i | ||||
\(395\) | 3.80544 | + | 13.2305i | 0.191473 | + | 0.665700i | ||||
\(396\) | −5.34017 | − | 9.24945i | −0.268354 | − | 0.464802i | ||||
\(397\) | 32.7356 | + | 18.8999i | 1.64295 | + | 0.948558i | 0.979777 | + | 0.200092i | \(0.0641241\pi\) |
0.663173 | + | 0.748466i | \(0.269209\pi\) | |||||||
\(398\) | 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 | \(0.734528\pi\) | |||||||
\(410\) | 37.8257 | − | 10.8796i | 1.86808 | − | 0.537307i | ||||
\(411\) | −2.21953 | + | 3.84435i | −0.109482 | + | 0.189628i | ||||
\(412\) | 11.5174i | 0.567424i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.34017 | 0.311603 | ||||||||
\(415\) | −11.0061 | − | 10.6111i | −0.540266 | − | 0.520881i | ||||
\(416\) | 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 | ||||
\(425\) | 2.86470 | + | 4.56793i | 0.138958 | + | 0.221577i | ||||
\(426\) | −5.41855 | −0.262530 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 88.0965i | − | 4.25830i | ||||||
\(429\) | 0.921622 | − | 1.59630i | 0.0444963 | − | 0.0770699i | ||||
\(430\) | −10.9243 | − | 37.9809i | −0.526816 | − | 1.83160i | ||||
\(431\) | 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 | \(0.163412\pi\) | ||||
−0.871092 | + | 0.491120i | \(0.836588\pi\) | |||||||
\(434\) | 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 | 0.739835 | − | 0.672789i | \(-0.234904\pi\) |
−0.212735 | + | 0.977110i | \(0.568237\pi\) | |||||||
\(444\) | 28.9360 | + | 50.1186i | 1.37324 | + | 2.37852i | ||||
\(445\) | 5.15499 | + | 17.9226i | 0.244370 | + | 0.849611i | ||||
\(446\) | −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 | \(0.387829\pi\) | |||||||
\(450\) | 7.19716 | + | 11.4763i | 0.339278 | + | 0.540997i | ||||
\(451\) | −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 | 0.758548 | − | 0.651618i | \(-0.225909\pi\) |
−0.185044 | + | 0.982730i | \(0.559243\pi\) | |||||||
\(458\) | −30.1197 | + | 17.3896i | −1.40740 | + | 0.812564i | ||||
\(459\) | 0.539189 | + | 0.933903i | 0.0251672 | + | 0.0435908i | ||||
\(460\) | 20.1170 | + | 19.3952i | 0.937960 | + | 0.904304i | ||||
\(461\) | 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 | \(-0.926544\pi\) | ||
0.973491 | − | 0.228727i | \(-0.0734564\pi\) | |||||||
\(464\) | −46.2183 | + | 80.0525i | −2.14563 | + | 3.71634i | ||||
\(465\) | −16.6731 | + | 4.79560i | −0.773195 | + | 0.222391i | ||||
\(466\) | −9.16394 | − | 15.8724i | −0.424511 | − | 0.735275i | ||||
\(467\) | −9.97440 | − | 5.75872i | −0.461560 | − | 0.266482i | 0.251140 | − | 0.967951i | \(-0.419195\pi\) |
−0.712700 | + | 0.701469i | \(0.752528\pi\) | |||||||
\(468\) | 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 | \(0.980445\pi\) | |||||||
\(480\) | 11.9846 | + | 41.6672i | 0.547018 | + | 1.90184i | ||||
\(481\) | −4.99386 | + | 8.64961i | −0.227700 | + | 0.394388i | ||||
\(482\) | − | 39.7731i | − | 1.81162i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 37.3812 | 1.69915 | ||||||||
\(485\) | −13.5848 | − | 13.0974i | −0.616856 | − | 0.594722i | ||||
\(486\) | 1.35464 | + | 2.34630i | 0.0614476 | + | 0.106430i | ||||
\(487\) | −20.0490 | + | 11.5753i | −0.908508 | + | 0.524527i | −0.879951 | − | 0.475065i | \(-0.842425\pi\) |
−0.0285570 | + | 0.999592i | \(0.509091\pi\) | |||||||
\(488\) | −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 | ||||
\(495\) | 3.10399 | − | 3.21951i | 0.139514 | − | 0.144706i | ||||
\(496\) | −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 | \(-0.0417254\pi\) | |||||||
\(500\) | −12.2708 | + | 58.4304i | −0.548768 | + | 2.61309i | ||||
\(501\) | 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 | \(-0.862047\pi\) | ||
0.907546 | − | 0.419952i | \(-0.137953\pi\) | |||||||
\(504\) | 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 | ||||
\(515\) | −4.63475 | + | 1.33307i | −0.204231 | + | 0.0587422i | ||||
\(516\) | 17.4186 | − | 30.1698i | 0.766809 | − | 1.32815i | ||||
\(517\) | − | 9.36069i | − | 0.411683i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.4391 | 0.984966 | ||||||||
\(520\) | −12.9439 | + | 13.4256i | −0.567628 | + | 0.588753i | ||||
\(521\) | 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 | 0.422347 | − | 0.906434i | \(-0.361206\pi\) |
−0.573822 | + | 0.818980i | \(0.694540\pi\) | |||||||
\(524\) | −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 | ||||
\(530\) | 15.8046 | − | 16.3928i | 0.686508 | − | 0.712058i | ||||
\(531\) | 10.5236 | 0.456685 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.98771i | 0.259357i | ||||||||
\(534\) | −11.2979 | + | 19.5686i | −0.488908 | + | 0.846814i | ||||
\(535\) | 35.4510 | − | 10.1966i | 1.53268 | − | 0.440838i | ||||
\(536\) | 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 | \(-0.922198\pi\) | ||
0.970277 | − | 0.241997i | \(-0.0778023\pi\) | |||||||
\(548\) | −20.5295 | − | 11.8527i | −0.876976 | − | 0.506322i | ||||
\(549\) | −2.07838 | − | 3.59986i | −0.0887030 | − | 0.153638i | ||||
\(550\) | 27.0747 | − | 0.989569i | 1.15447 | − | 0.0421954i | ||||
\(551\) | 10.2823 | − | 17.8095i | 0.438041 | − | 0.758710i | ||||
\(552\) | 21.1773i | 0.901365i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −76.3956 | −3.24574 | ||||||||
\(555\) | −16.8191 | + | 17.4451i | −0.713932 | + | 0.740503i | ||||
\(556\) | −36.3184 | − | 62.9054i | −1.54024 | − | 2.66778i | ||||
\(557\) | 23.0788 | − | 13.3246i | 0.977882 | − | 0.564580i | 0.0762519 | − | 0.997089i | \(-0.475705\pi\) |
0.901630 | + | 0.432508i | \(0.142371\pi\) | |||||||
\(558\) | −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 | \(-0.235358\pi\) |
0.953002 | − | 0.302963i | \(-0.0979758\pi\) | |||||||
\(564\) | 12.4969 | + | 21.6453i | 0.526216 | + | 0.911432i | ||||
\(565\) | 8.42728 | + | 8.12490i | 0.354539 | + | 0.341817i | ||||
\(566\) | −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 | \(0.264035\pi\) | |||||||
\(570\) | −5.15499 | − | 17.9226i | −0.215919 | − | 0.750694i | ||||
\(571\) | −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 | \(0.693405\pi\) |
−0.996474 | + | 0.0839011i | \(0.973262\pi\) | |||||||
\(578\) | 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 | ||||
\(585\) | −1.98052 | + | 0.569647i | −0.0818842 | + | 0.0235520i | ||||
\(586\) | −3.95774 | + | 6.85501i | −0.163493 | + | 0.283178i | ||||
\(587\) | − | 36.0288i | − | 1.48707i | −0.668699 | − | 0.743533i | \(-0.733149\pi\) | ||
0.668699 | − | 0.743533i | \(-0.266851\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.8843 | 0.984135 | ||||||||
\(590\) | 45.8962 | + | 44.2494i | 1.88952 | + | 1.82172i | ||||
\(591\) | 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 | −0.178419 | − | 0.983955i | \(-0.557098\pi\) |
−0.941339 | + | 0.337462i | \(0.890432\pi\) | |||||||
\(594\) | 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 | \(0.631211\pi\) | |||||||
\(600\) | −38.3328 | + | 24.0398i | −1.56493 | + | 0.981420i | ||||
\(601\) | 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 | ||||
\(605\) | 4.32664 | + | 15.0426i | 0.175903 | + | 0.611569i | ||||
\(606\) | −7.87936 | − | 13.6475i | −0.320077 | − | 0.554390i | ||||
\(607\) | −11.2992 | − | 6.52359i | −0.458620 | − | 0.264784i | 0.252844 | − | 0.967507i | \(-0.418634\pi\) |
−0.711464 | + | 0.702723i | \(0.751967\pi\) | |||||||
\(608\) | − | 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 | −0.746203 | − | 0.665718i | \(-0.768125\pi\) |
0.203427 | + | 0.979090i | \(0.434792\pi\) | |||||||
\(614\) | 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 | \(0.151520\pi\) | ||||
−0.888829 | + | 0.458240i | \(0.848480\pi\) | |||||||
\(618\) | −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 | \(0.782403\pi\) | |||||||
\(620\) | −25.6094 | − | 89.0371i | −1.02850 | − | 3.57581i | ||||
\(621\) | −1.17009 | + | 2.02665i | −0.0469540 | + | 0.0813266i | ||||
\(622\) | 64.5646i | 2.58881i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −12.7526 | −0.510512 | ||||||||
\(625\) | −24.9333 | + | 1.82504i | −0.997332 | + | 0.0730017i | ||||
\(626\) | 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 | ||||
\(635\) | 2.96717 | + | 2.86071i | 0.117749 | + | 0.113524i | ||||
\(636\) | 20.0722 | 0.795916 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 36.1978i | 1.43308i | ||||||||
\(639\) | 1.00000 | − | 1.73205i | 0.0395594 | − | 0.0685189i | ||||
\(640\) | −61.3887 | + | 17.6570i | −2.42660 | + | 0.697953i | ||||
\(641\) | 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 | \(-0.791531\pi\) | ||
0.793094 | − | 0.609100i | \(-0.208469\pi\) | |||||||
\(644\) | 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 | −0.136088 | − | 0.990697i | \(-0.543453\pi\) |
0.789924 | + | 0.613204i | \(0.210120\pi\) | |||||||
\(648\) | −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 | 0.898543 | − | 0.438886i | \(-0.144627\pi\) |
0.0691846 | + | 0.997604i | \(0.477960\pi\) | |||||||
\(654\) | 17.3896 | + | 30.1197i | 0.679988 | + | 1.17777i | ||||
\(655\) | −0.912557 | − | 3.17272i | −0.0356565 | − | 0.123969i | ||||
\(656\) | −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 | \(0.316483\pi\) | |||||||
\(660\) | 17.1927 | + | 16.5758i | 0.669227 | + | 0.645214i | ||||
\(661\) | 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 | ||||
\(670\) | −19.6798 | + | 20.4123i | −0.760298 | + | 0.788594i | ||||
\(671\) | −8.31351 | −0.320940 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.21008i | 0.0851923i | 0.999092 | + | 0.0425962i | \(0.0135629\pi\) | ||||
−0.999092 | + | 0.0425962i | \(0.986437\pi\) | |||||||
\(674\) | 34.3545 | − | 59.5038i | 1.32329 | − | 2.29200i | ||||
\(675\) | −4.99666 | + | 0.182626i | −0.192322 | + | 0.00702928i | ||||
\(676\) | 32.4432 | + | 56.1932i | 1.24781 | + | 2.16128i | ||||
\(677\) | 16.9296 | + | 9.77432i | 0.650658 | + | 0.375658i | 0.788708 | − | 0.614768i | \(-0.210750\pi\) |
−0.138050 | + | 0.990425i | \(0.544084\pi\) | |||||||
\(678\) | 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 | −0.291269 | − | 0.956641i | \(-0.594077\pi\) |
0.682841 | + | 0.730567i | \(0.260744\pi\) | |||||||
\(684\) | 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 | ||||
\(690\) | −13.6247 | + | 3.91881i | −0.518683 | + | 0.149187i | ||||
\(691\) | −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 | ||||||||
\(695\) | 21.1102 | − | 21.8958i | 0.800755 | − | 0.830557i | ||||
\(696\) | −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 | ||||
\(705\) | −7.26387 | + | 7.53421i | −0.273573 | + | 0.283755i | ||||
\(706\) | 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 | \(0.233181\pi\) | |||||||
\(710\) | 11.6442 | − | 3.34916i | 0.436998 | − | 0.125692i | ||||
\(711\) | −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 | ||||
\(725\) | −1.22001 | − | 33.3794i | −0.0453099 | − | 1.23968i | ||||
\(726\) | −9.48246 | + | 16.4241i | −0.351927 | + | 0.609556i | ||||
\(727\) | − | 2.89043i | − | 0.107200i | −0.998562 | − | 0.0536000i | \(-0.982930\pi\) | ||
0.998562 | − | 0.0536000i | \(-0.0170696\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 29.7630 | − | 30.8707i | 1.10158 | − | 1.14258i | ||||
\(731\) | 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 | 0.852229 | − | 0.523168i | \(-0.175250\pi\) |
−0.0269626 | + | 0.999636i | \(0.508583\pi\) | |||||||
\(734\) | 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 | \(0.839465\pi\) | |||||||
\(740\) | −93.1598 | − | 89.8170i | −3.42462 | − | 3.30174i | ||||
\(741\) | 2.83710 | 0.104224 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 9.97334i | − | 0.365886i | −0.983123 | − | 0.182943i | \(-0.941438\pi\) | ||
0.983123 | − | 0.182943i | \(-0.0585624\pi\) | |||||||
\(744\) | 35.1061 | − | 60.8055i | 1.28705 | − | 2.22924i | ||||
\(745\) | 9.68810 | + | 33.6830i | 0.354944 | + | 1.23405i | ||||
\(746\) | −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 | \(0.362708\pi\) | ||||
−0.418065 | + | 0.908417i | \(0.637292\pi\) | |||||||
\(758\) | 14.4456 | + | 8.34017i | 0.524688 | + | 0.302929i | ||||
\(759\) | 2.34017 | + | 4.05330i | 0.0849429 | + | 0.147125i | ||||
\(760\) | 59.8645 | − | 17.2186i | 2.17151 | − | 0.624583i | ||||
\(761\) | −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 | ||||||||
\(765\) | −1.73592 | − | 1.67364i | −0.0627625 | − | 0.0605104i | ||||
\(766\) | 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 | −0.406742 | − | 0.913543i | \(-0.633335\pi\) |
0.587780 | + | 0.809021i | \(0.300002\pi\) | |||||||
\(774\) | 8.83710 | + | 15.3063i | 0.317643 | + | 0.550174i | ||||
\(775\) | 32.8654 | − | 20.6110i | 1.18056 | − | 0.740368i | ||||
\(776\) | 76.3689 | 2.74148 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.2618i | 0.547162i | ||||||||
\(779\) | 10.0000 | − | 17.3205i | 0.358287 | − | 0.620572i | ||||
\(780\) | −3.04202 | − | 10.5763i | −0.108922 | − | 0.378692i | ||||
\(781\) | −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 | −0.963780 | − | 0.266697i | \(-0.914068\pi\) |
−0.250924 | + | 0.968007i | \(0.580734\pi\) | |||||||
\(788\) | −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 | ||||
\(795\) | 2.32324 | + | 8.07729i | 0.0823967 | + | 0.286472i | ||||
\(796\) | 60.3328 | − | 104.499i | 2.13844 | − | 3.70389i | ||||
\(797\) | − | 28.2823i | − | 1.00181i | −0.865502 | − | 0.500905i | \(-0.833000\pi\) | ||
0.865502 | − | 0.500905i | \(-0.167000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.04718 | −0.178556 | ||||||||
\(800\) | −51.5083 | − | 82.1330i | −1.82110 | − | 2.90384i | ||||
\(801\) | −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 | \(0.922189\pi\) | |||||||
\(810\) | −4.36127 | − | 4.20478i | −0.153239 | − | 0.147741i | ||||
\(811\) | −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 | ||||
\(815\) | −21.1526 | + | 6.08403i | −0.740943 | + | 0.213114i | ||||
\(816\) | −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 | −0.937217 | − | 0.348745i | \(-0.886608\pi\) |
−0.166586 | + | 0.986027i | \(0.553274\pi\) | |||||||
\(824\) | 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 | \(-0.662016\pi\) | ||
0.487294 | − | 0.873238i | \(-0.337984\pi\) | |||||||
\(828\) | −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 | \(0.640184\pi\) | |||||||
\(830\) | 11.4493 | + | 39.8062i | 0.397410 | + | 1.38169i | ||||
\(831\) | 14.0989 | − | 24.4200i | 0.489085 | − | 0.847121i | ||||
\(832\) | − | 22.9093i | − | 0.794238i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 36.8515 | 1.27606 | ||||||||
\(835\) | −30.9136 | − | 29.8044i | −1.06981 | − | 1.03142i | ||||
\(836\) | −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 | ||||
\(845\) | −18.8577 | + | 19.5595i | −0.648724 | + | 0.672868i | ||||
\(846\) | −12.6803 | −0.435959 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 52.0098i | 1.78603i | ||||||||
\(849\) | 11.7587 | − | 20.3667i | 0.403558 | − | 0.698984i | ||||
\(850\) | −0.533565 | − | 14.5984i | −0.0183011 | − | 0.500720i | ||||
\(851\) | −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 | \(-0.762554\pi\) | ||
0.734438 | − | 0.678675i | \(-0.237446\pi\) | |||||||
\(854\) | 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 | 0.00851788 | − | 0.999964i | \(-0.497289\pi\) |
0.870253 | + | 0.492605i | \(0.163955\pi\) | |||||||
\(858\) | −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 | 0.591270 | − | 0.806473i | \(-0.298627\pi\) |
−0.402791 | + | 0.915292i | \(0.631960\pi\) | |||||||
\(864\) | −9.69481 | − | 16.7919i | −0.329824 | − | 0.571272i | ||||
\(865\) | −48.2203 | + | 13.8694i | −1.63954 | + | 0.471574i | ||||
\(866\) | 27.6875 | − | 47.9562i | 0.940861 | − | 1.62962i | ||||
\(867\) | 15.8371i | 0.537856i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.3135 | −0.417707 | ||||||||
\(870\) | 28.0894 | − | 29.1348i | 0.952319 | − | 0.987762i | ||||
\(871\) | −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 | 0.482111 | − | 0.876110i | \(-0.339870\pi\) |
−0.517678 | + | 0.855576i | \(0.673203\pi\) | |||||||
\(878\) | 39.7032 | − | 22.9227i | 1.33992 | − | 0.773603i | ||||
\(879\) | −1.46081 | − | 2.53020i | −0.0492719 | − | 0.0853415i | ||||
\(880\) | −42.9502 | + | 44.5487i | −1.44785 | + | 1.50174i | ||||
\(881\) | 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 | \(0.0630033\pi\) | ||||
−0.980476 | + | 0.196641i | \(0.936997\pi\) | |||||||
\(884\) | 2.65368 | − | 4.59632i | 0.0892531 | − | 0.154591i | ||||
\(885\) | −22.6146 | + | 6.50455i | −0.760182 | + | 0.218648i | ||||
\(886\) | −17.3535 | − | 30.0572i | −0.583002 | − | 1.00979i | ||||
\(887\) | −22.1883 | − | 12.8104i | −0.745011 | − | 0.430132i | 0.0788773 | − | 0.996884i | \(-0.474866\pi\) |
−0.823889 | + | 0.566752i | \(0.808200\pi\) | |||||||
\(888\) | − | 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 | ||||
\(900\) | −0.975255 | − | 26.6830i | −0.0325085 | − | 0.889435i | ||||
\(901\) | −2.02666 | + | 3.51028i | −0.0675179 | + | 0.116944i | ||||
\(902\) | 35.2039i | 1.17216i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −47.3751 | −1.57567 | ||||||||
\(905\) | 13.2286 | − | 13.7209i | 0.439732 | − | 0.456098i | ||||
\(906\) | 7.91548 | + | 13.7100i | 0.262974 | + | 0.455485i | ||||
\(907\) | 50.0184 | − | 28.8781i | 1.66083 | − | 0.958883i | 0.688516 | − | 0.725221i | \(-0.258263\pi\) |
0.972318 | − | 0.233662i | \(-0.0750708\pi\) | |||||||
\(908\) | 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 | ||||
\(915\) | 6.69136 | + | 6.45126i | 0.221210 | + | 0.213272i | ||||
\(916\) | 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 | \(-0.113376\pi\) | |||||||
\(920\) | −13.0895 | − | 45.5088i | −0.431548 | − | 1.50038i | ||||
\(921\) | 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 | ||||
\(935\) | −4.63475 | + | 1.33307i | −0.151572 | + | 0.0435962i | ||||
\(936\) | 4.17009 | − | 7.22280i | 0.136304 | − | 0.236085i | ||||
\(937\) | 16.1256i | 0.526799i | 0.964687 | + | 0.263400i | \(0.0848437\pi\) | ||||
−0.964687 | + | 0.263400i | \(0.915156\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.7526 | −1.06884 | ||||||||
\(940\) | −40.2340 | − | 38.7903i | −1.31229 | − | 1.26520i | ||||
\(941\) | −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 | 0.405175 | − | 0.914239i | \(-0.367211\pi\) |
−0.589167 | + | 0.808011i | \(0.700544\pi\) | |||||||
\(948\) | 28.4733 | − | 16.4391i | 0.924770 | − | 0.533916i | ||||
\(949\) | 3.26180 | + | 5.64960i | 0.105882 | + | 0.183394i | ||||
\(950\) | 22.1556 | + | 35.3283i | 0.718822 | + | 1.14620i | ||||
\(951\) | −17.9155 | −0.580949 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.11327i | 0.198028i | 0.995086 | + | 0.0990142i | \(0.0315689\pi\) | ||||
−0.995086 | + | 0.0990142i | \(0.968431\pi\) | |||||||
\(954\) | −5.09171 | + | 8.81910i | −0.164850 | + | 0.285529i | ||||
\(955\) | −9.49432 | − | 33.0093i | −0.307229 | − | 1.06816i | ||||
\(956\) | 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 | \(0.135154\pi\) | ||||
−0.911204 | + | 0.411956i | \(0.864846\pi\) | |||||||
\(968\) | −54.8594 | − | 31.6731i | −1.76325 | − | 1.01801i | ||||
\(969\) | 1.65983 | + | 2.87490i | 0.0533213 | + | 0.0923552i | ||||
\(970\) | 14.1319 | + | 49.1330i | 0.453748 | + | 1.57756i | ||||
\(971\) | −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 | ||||||||
\(975\) | 3.90392 | − | 2.44828i | 0.125026 | − | 0.0784077i | ||||
\(976\) | 28.7587 | + | 49.8116i | 0.920544 | + | 1.59443i | ||||
\(977\) | 3.30133 | − | 1.90602i | 0.105619 | − | 0.0609791i | −0.446260 | − | 0.894903i | \(-0.647244\pi\) |
0.551879 | + | 0.833924i | \(0.313911\pi\) | |||||||
\(978\) | −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 | −0.130465 | − | 0.991453i | \(-0.541647\pi\) |
0.793391 | + | 0.608712i | \(0.208314\pi\) | |||||||
\(984\) | −29.3968 | − | 50.9168i | −0.937136 | − | 1.62317i | ||||
\(985\) | −18.9287 | − | 18.2495i | −0.603118 | − | 0.581477i | ||||
\(986\) | 19.5174 | 0.621562 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.1506i | 0.482005i | ||||||||
\(989\) | −7.63317 | + | 13.2210i | −0.242721 | + | 0.420404i | ||||
\(990\) | −11.6442 | + | 3.34916i | −0.370076 | + | 0.106443i | ||||
\(991\) | 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 | −0.958844 | − | 0.283933i | \(-0.908361\pi\) |
−0.233529 | + | 0.972350i | \(0.575027\pi\) | |||||||
\(998\) | −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.79.1 | 12 | ||
5.4 | even | 2 | inner | 735.2.q.e.79.6 | 12 | ||
7.2 | even | 3 | 105.2.d.b.64.6 | yes | 6 | ||
7.3 | odd | 6 | 735.2.q.f.214.6 | 12 | |||
7.4 | even | 3 | inner | 735.2.q.e.214.6 | 12 | ||
7.5 | odd | 6 | 735.2.d.b.589.6 | 6 | |||
7.6 | odd | 2 | 735.2.q.f.79.1 | 12 | |||
21.2 | odd | 6 | 315.2.d.e.64.1 | 6 | |||
21.5 | even | 6 | 2205.2.d.l.1324.1 | 6 | |||
28.23 | odd | 6 | 1680.2.t.k.1009.3 | 6 | |||
35.2 | odd | 12 | 525.2.a.j.1.1 | 3 | |||
35.4 | even | 6 | inner | 735.2.q.e.214.1 | 12 | ||
35.9 | even | 6 | 105.2.d.b.64.1 | ✓ | 6 | ||
35.12 | even | 12 | 3675.2.a.bi.1.1 | 3 | |||
35.19 | odd | 6 | 735.2.d.b.589.1 | 6 | |||
35.23 | odd | 12 | 525.2.a.k.1.3 | 3 | |||
35.24 | odd | 6 | 735.2.q.f.214.1 | 12 | |||
35.33 | even | 12 | 3675.2.a.bj.1.3 | 3 | |||
35.34 | odd | 2 | 735.2.q.f.79.6 | 12 | |||
84.23 | even | 6 | 5040.2.t.v.1009.1 | 6 | |||
105.2 | even | 12 | 1575.2.a.x.1.3 | 3 | |||
105.23 | even | 12 | 1575.2.a.w.1.1 | 3 | |||
105.44 | odd | 6 | 315.2.d.e.64.6 | 6 | |||
105.89 | even | 6 | 2205.2.d.l.1324.6 | 6 | |||
140.23 | even | 12 | 8400.2.a.dj.1.2 | 3 | |||
140.79 | odd | 6 | 1680.2.t.k.1009.6 | 6 | |||
140.107 | even | 12 | 8400.2.a.dg.1.2 | 3 | |||
420.359 | even | 6 | 5040.2.t.v.1009.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.b.64.1 | ✓ | 6 | 35.9 | even | 6 | ||
105.2.d.b.64.6 | yes | 6 | 7.2 | even | 3 | ||
315.2.d.e.64.1 | 6 | 21.2 | odd | 6 | |||
315.2.d.e.64.6 | 6 | 105.44 | odd | 6 | |||
525.2.a.j.1.1 | 3 | 35.2 | odd | 12 | |||
525.2.a.k.1.3 | 3 | 35.23 | odd | 12 | |||
735.2.d.b.589.1 | 6 | 35.19 | odd | 6 | |||
735.2.d.b.589.6 | 6 | 7.5 | odd | 6 | |||
735.2.q.e.79.1 | 12 | 1.1 | even | 1 | trivial | ||
735.2.q.e.79.6 | 12 | 5.4 | even | 2 | inner | ||
735.2.q.e.214.1 | 12 | 35.4 | even | 6 | inner | ||
735.2.q.e.214.6 | 12 | 7.4 | even | 3 | inner | ||
735.2.q.f.79.1 | 12 | 7.6 | odd | 2 | |||
735.2.q.f.79.6 | 12 | 35.34 | odd | 2 | |||
735.2.q.f.214.1 | 12 | 35.24 | odd | 6 | |||
735.2.q.f.214.6 | 12 | 7.3 | odd | 6 | |||
1575.2.a.w.1.1 | 3 | 105.23 | even | 12 | |||
1575.2.a.x.1.3 | 3 | 105.2 | even | 12 | |||
1680.2.t.k.1009.3 | 6 | 28.23 | odd | 6 | |||
1680.2.t.k.1009.6 | 6 | 140.79 | odd | 6 | |||
2205.2.d.l.1324.1 | 6 | 21.5 | even | 6 | |||
2205.2.d.l.1324.6 | 6 | 105.89 | even | 6 | |||
3675.2.a.bi.1.1 | 3 | 35.12 | even | 12 | |||
3675.2.a.bj.1.3 | 3 | 35.33 | even | 12 | |||
5040.2.t.v.1009.1 | 6 | 84.23 | even | 6 | |||
5040.2.t.v.1009.2 | 6 | 420.359 | even | 6 | |||
8400.2.a.dg.1.2 | 3 | 140.107 | even | 12 | |||
8400.2.a.dj.1.2 | 3 | 140.23 | even | 12 |