Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(17,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.br (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.5 | ||
Character | \(\chi\) | \(=\) | 273.257 |
Dual form | 273.2.br.b.17.5 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.13558 | −1.51008 | −0.755042 | − | 0.655676i | \(-0.772384\pi\) | ||||
−0.755042 | + | 0.655676i | \(0.772384\pi\) | |||||||
\(3\) | −1.59741 | + | 0.669547i | −0.922263 | + | 0.386563i | ||||
\(4\) | 2.56071 | 1.28036 | ||||||||
\(5\) | −3.07271 | − | 1.77403i | −1.37416 | − | 0.793370i | −0.382709 | − | 0.923869i | \(-0.625009\pi\) |
−0.991448 | + | 0.130499i | \(0.958342\pi\) | |||||||
\(6\) | 3.41139 | − | 1.42987i | 1.39270 | − | 0.583743i | ||||
\(7\) | −1.82045 | − | 1.91989i | −0.688064 | − | 0.725650i | ||||
\(8\) | −1.19745 | −0.423362 | ||||||||
\(9\) | 2.10341 | − | 2.13908i | 0.701138 | − | 0.713026i | ||||
\(10\) | 6.56202 | + | 3.78859i | 2.07509 | + | 1.19806i | ||||
\(11\) | 0.843639 | − | 1.46123i | 0.254367 | − | 0.440576i | −0.710357 | − | 0.703842i | \(-0.751466\pi\) |
0.964723 | + | 0.263266i | \(0.0847997\pi\) | |||||||
\(12\) | −4.09050 | + | 1.71452i | −1.18083 | + | 0.494939i | ||||
\(13\) | −0.905061 | + | 3.49011i | −0.251019 | + | 0.967982i | ||||
\(14\) | 3.88771 | + | 4.10008i | 1.03903 | + | 1.09579i | ||||
\(15\) | 6.09616 | + | 0.776521i | 1.57402 | + | 0.200497i | ||||
\(16\) | −2.56418 | −0.641044 | ||||||||
\(17\) | −2.50797 | −0.608273 | −0.304136 | − | 0.952628i | \(-0.598368\pi\) | ||||
−0.304136 | + | 0.952628i | \(0.598368\pi\) | |||||||
\(18\) | −4.49201 | + | 4.56818i | −1.05878 | + | 1.07673i | ||||
\(19\) | −1.66686 | − | 2.88709i | −0.382404 | − | 0.662343i | 0.609001 | − | 0.793169i | \(-0.291570\pi\) |
−0.991405 | + | 0.130826i | \(0.958237\pi\) | |||||||
\(20\) | −7.86833 | − | 4.54278i | −1.75941 | − | 1.01580i | ||||
\(21\) | 4.19345 | + | 1.84797i | 0.915086 | + | 0.403260i | ||||
\(22\) | −1.80166 | + | 3.12057i | −0.384115 | + | 0.665307i | ||||
\(23\) | 7.63380i | 1.59176i | 0.605457 | + | 0.795878i | \(0.292991\pi\) | ||||
−0.605457 | + | 0.795878i | \(0.707009\pi\) | |||||||
\(24\) | 1.91281 | − | 0.801748i | 0.390451 | − | 0.163656i | ||||
\(25\) | 3.79436 | + | 6.57203i | 0.758872 | + | 1.31441i | ||||
\(26\) | 1.93283 | − | 7.45342i | 0.379060 | − | 1.46174i | ||||
\(27\) | −1.92779 | + | 4.82531i | −0.371003 | + | 0.928631i | ||||
\(28\) | −4.66164 | − | 4.91629i | −0.880967 | − | 0.929091i | ||||
\(29\) | 3.85641 | − | 2.22650i | 0.716117 | − | 0.413450i | −0.0972050 | − | 0.995264i | \(-0.530990\pi\) |
0.813322 | + | 0.581814i | \(0.197657\pi\) | |||||||
\(30\) | −13.0189 | − | 1.65833i | −2.37691 | − | 0.302767i | ||||
\(31\) | 5.26838 | + | 9.12510i | 0.946229 | + | 1.63892i | 0.753271 | + | 0.657710i | \(0.228475\pi\) |
0.192958 | + | 0.981207i | \(0.438192\pi\) | |||||||
\(32\) | 7.87091 | 1.39139 | ||||||||
\(33\) | −0.369274 | + | 2.89903i | −0.0642824 | + | 0.504656i | ||||
\(34\) | 5.35598 | 0.918544 | ||||||||
\(35\) | 2.18776 | + | 9.12879i | 0.369799 | + | 1.54305i | ||||
\(36\) | 5.38624 | − | 5.47756i | 0.897706 | − | 0.912927i | ||||
\(37\) | − | 5.55358i | − | 0.913002i | −0.889723 | − | 0.456501i | \(-0.849102\pi\) | ||
0.889723 | − | 0.456501i | \(-0.150898\pi\) | |||||||
\(38\) | 3.55972 | + | 6.16561i | 0.577463 | + | 1.00019i | ||||
\(39\) | −0.891044 | − | 6.18110i | −0.142681 | − | 0.989769i | ||||
\(40\) | 3.67941 | + | 2.12431i | 0.581766 | + | 0.335883i | ||||
\(41\) | −2.89982 | + | 1.67421i | −0.452875 | + | 0.261468i | −0.709044 | − | 0.705165i | \(-0.750873\pi\) |
0.256169 | + | 0.966632i | \(0.417540\pi\) | |||||||
\(42\) | −8.95546 | − | 3.94649i | −1.38186 | − | 0.608957i | ||||
\(43\) | −0.303610 | + | 0.525869i | −0.0463002 | + | 0.0801942i | −0.888247 | − | 0.459367i | \(-0.848076\pi\) |
0.841947 | + | 0.539561i | \(0.181410\pi\) | |||||||
\(44\) | 2.16032 | − | 3.74178i | 0.325680 | − | 0.564094i | ||||
\(45\) | −10.2580 | + | 2.84125i | −1.52917 | + | 0.423548i | ||||
\(46\) | − | 16.3026i | − | 2.40369i | ||||||
\(47\) | 1.95815 | + | 1.13054i | 0.285626 | + | 0.164906i | 0.635968 | − | 0.771716i | \(-0.280601\pi\) |
−0.350342 | + | 0.936622i | \(0.613935\pi\) | |||||||
\(48\) | 4.09603 | − | 1.71684i | 0.591211 | − | 0.247804i | ||||
\(49\) | −0.371952 | + | 6.99011i | −0.0531360 | + | 0.998587i | ||||
\(50\) | −8.10317 | − | 14.0351i | −1.14596 | − | 1.98486i | ||||
\(51\) | 4.00625 | − | 1.67921i | 0.560988 | − | 0.235136i | ||||
\(52\) | −2.31760 | + | 8.93717i | −0.321393 | + | 1.23936i | ||||
\(53\) | 4.84067 | − | 2.79476i | 0.664918 | − | 0.383890i | −0.129230 | − | 0.991615i | \(-0.541251\pi\) |
0.794148 | + | 0.607724i | \(0.207917\pi\) | |||||||
\(54\) | 4.11696 | − | 10.3048i | 0.560247 | − | 1.40231i | ||||
\(55\) | −5.18451 | + | 2.99328i | −0.699080 | + | 0.403614i | ||||
\(56\) | 2.17989 | + | 2.29897i | 0.291300 | + | 0.307213i | ||||
\(57\) | 4.59570 | + | 3.49581i | 0.608715 | + | 0.463031i | ||||
\(58\) | −8.23567 | + | 4.75487i | −1.08140 | + | 0.624345i | ||||
\(59\) | − | 5.72753i | − | 0.745660i | −0.927900 | − | 0.372830i | \(-0.878387\pi\) | ||
0.927900 | − | 0.372830i | \(-0.121613\pi\) | |||||||
\(60\) | 15.6105 | + | 1.98845i | 2.01531 | + | 0.256708i | ||||
\(61\) | 7.83288 | − | 4.52232i | 1.00290 | − | 0.579023i | 0.0937934 | − | 0.995592i | \(-0.470101\pi\) |
0.909104 | + | 0.416568i | \(0.136767\pi\) | |||||||
\(62\) | −11.2511 | − | 19.4874i | −1.42889 | − | 2.47490i | ||||
\(63\) | −7.93594 | − | 0.144244i | −0.999835 | − | 0.0181730i | ||||
\(64\) | −11.6806 | −1.46008 | ||||||||
\(65\) | 8.97255 | − | 9.11849i | 1.11291 | − | 1.13101i | ||||
\(66\) | 0.788616 | − | 6.19111i | 0.0970719 | − | 0.762073i | ||||
\(67\) | 0.411700 | + | 0.237695i | 0.0502972 | + | 0.0290391i | 0.524938 | − | 0.851141i | \(-0.324089\pi\) |
−0.474641 | + | 0.880180i | \(0.657422\pi\) | |||||||
\(68\) | −6.42220 | −0.778806 | ||||||||
\(69\) | −5.11119 | − | 12.1943i | −0.615315 | − | 1.46802i | ||||
\(70\) | −4.67214 | − | 19.4953i | −0.558428 | − | 2.33013i | ||||
\(71\) | −3.84488 | + | 6.65953i | −0.456304 | + | 0.790341i | −0.998762 | − | 0.0497414i | \(-0.984160\pi\) |
0.542458 | + | 0.840083i | \(0.317494\pi\) | |||||||
\(72\) | −2.51873 | + | 2.56144i | −0.296835 | + | 0.301868i | ||||
\(73\) | −1.61834 | − | 2.80304i | −0.189412 | − | 0.328072i | 0.755642 | − | 0.654985i | \(-0.227325\pi\) |
−0.945054 | + | 0.326913i | \(0.893992\pi\) | |||||||
\(74\) | 11.8601i | 1.37871i | ||||||||
\(75\) | −10.4614 | − | 7.95769i | −1.20798 | − | 0.918875i | ||||
\(76\) | −4.26835 | − | 7.39300i | −0.489613 | − | 0.848035i | ||||
\(77\) | −4.34119 | + | 1.04039i | −0.494725 | + | 0.118563i | ||||
\(78\) | 1.90290 | + | 13.2003i | 0.215461 | + | 1.49463i | ||||
\(79\) | −3.65659 | + | 6.33341i | −0.411399 | + | 0.712564i | −0.995043 | − | 0.0994457i | \(-0.968293\pi\) |
0.583644 | + | 0.812010i | \(0.301626\pi\) | |||||||
\(80\) | 7.87897 | + | 4.54892i | 0.880895 | + | 0.508585i | ||||
\(81\) | −0.151310 | − | 8.99873i | −0.0168122 | − | 0.999859i | ||||
\(82\) | 6.19280 | − | 3.57541i | 0.683880 | − | 0.394838i | ||||
\(83\) | 15.7624i | 1.73014i | 0.501647 | + | 0.865072i | \(0.332728\pi\) | ||||
−0.501647 | + | 0.865072i | \(0.667272\pi\) | |||||||
\(84\) | 10.7382 | + | 4.73212i | 1.17164 | + | 0.516316i | ||||
\(85\) | 7.70627 | + | 4.44922i | 0.835863 | + | 0.482586i | ||||
\(86\) | 0.648385 | − | 1.12304i | 0.0699172 | − | 0.121100i | ||||
\(87\) | −4.66950 | + | 6.13867i | −0.500623 | + | 0.658134i | ||||
\(88\) | −1.01021 | + | 1.74974i | −0.107689 | + | 0.186523i | ||||
\(89\) | 5.07815i | 0.538282i | 0.963101 | + | 0.269141i | \(0.0867398\pi\) | ||||
−0.963101 | + | 0.269141i | \(0.913260\pi\) | |||||||
\(90\) | 21.9067 | − | 6.06772i | 2.30917 | − | 0.639594i | ||||
\(91\) | 8.34824 | − | 4.61594i | 0.875133 | − | 0.483882i | ||||
\(92\) | 19.5480i | 2.03802i | ||||||||
\(93\) | −14.5254 | − | 11.0491i | −1.50622 | − | 1.14573i | ||||
\(94\) | −4.18179 | − | 2.41436i | −0.431319 | − | 0.249022i | ||||
\(95\) | 11.8282i | 1.21355i | ||||||||
\(96\) | −12.5730 | + | 5.26994i | −1.28323 | + | 0.537861i | ||||
\(97\) | 4.00591 | − | 6.93845i | 0.406739 | − | 0.704493i | −0.587783 | − | 0.809019i | \(-0.699999\pi\) |
0.994522 | + | 0.104526i | \(0.0333325\pi\) | |||||||
\(98\) | 0.794334 | − | 14.9280i | 0.0802399 | − | 1.50795i | ||||
\(99\) | −1.35115 | − | 4.87817i | −0.135796 | − | 0.490274i | ||||
\(100\) | 9.71627 | + | 16.8291i | 0.971627 | + | 1.68291i | ||||
\(101\) | 2.10689 | − | 3.64925i | 0.209644 | − | 0.363113i | −0.741959 | − | 0.670446i | \(-0.766103\pi\) |
0.951602 | + | 0.307332i | \(0.0994363\pi\) | |||||||
\(102\) | −8.55568 | + | 3.58609i | −0.847139 | + | 0.355075i | ||||
\(103\) | −0.762161 | − | 0.440034i | −0.0750980 | − | 0.0433578i | 0.461981 | − | 0.886890i | \(-0.347139\pi\) |
−0.537079 | + | 0.843532i | \(0.680472\pi\) | |||||||
\(104\) | 1.08376 | − | 4.17923i | 0.106272 | − | 0.409807i | ||||
\(105\) | −9.60690 | − | 13.1176i | −0.937537 | − | 1.28014i | ||||
\(106\) | −10.3377 | + | 5.96845i | −1.00408 | + | 0.579707i | ||||
\(107\) | 5.12617i | 0.495565i | 0.968816 | + | 0.247783i | \(0.0797019\pi\) | ||||
−0.968816 | + | 0.247783i | \(0.920298\pi\) | |||||||
\(108\) | −4.93652 | + | 12.3562i | −0.475017 | + | 1.18898i | ||||
\(109\) | 3.50485 | − | 2.02352i | 0.335703 | − | 0.193818i | −0.322667 | − | 0.946513i | \(-0.604579\pi\) |
0.658370 | + | 0.752694i | \(0.271246\pi\) | |||||||
\(110\) | 11.0720 | − | 6.39240i | 1.05567 | − | 0.609491i | ||||
\(111\) | 3.71838 | + | 8.87132i | 0.352933 | + | 0.842028i | ||||
\(112\) | 4.66794 | + | 4.92293i | 0.441079 | + | 0.465174i | ||||
\(113\) | −1.99095 | − | 1.14947i | −0.187292 | − | 0.108133i | 0.403422 | − | 0.915014i | \(-0.367821\pi\) |
−0.590714 | + | 0.806881i | \(0.701154\pi\) | |||||||
\(114\) | −9.81449 | − | 7.46559i | −0.919211 | − | 0.699216i | ||||
\(115\) | 13.5426 | − | 23.4564i | 1.26285 | − | 2.18732i | ||||
\(116\) | 9.87515 | − | 5.70142i | 0.916885 | − | 0.529364i | ||||
\(117\) | 5.56190 | + | 9.27714i | 0.514198 | + | 0.857672i | ||||
\(118\) | 12.2316i | 1.12601i | ||||||||
\(119\) | 4.56563 | + | 4.81503i | 0.418531 | + | 0.441393i | ||||
\(120\) | −7.29984 | − | 0.929844i | −0.666381 | − | 0.0848828i | ||||
\(121\) | 4.07655 | + | 7.06079i | 0.370595 | + | 0.641890i | ||||
\(122\) | −16.7278 | + | 9.65778i | −1.51446 | + | 0.874374i | ||||
\(123\) | 3.51122 | − | 4.61596i | 0.316596 | − | 0.416207i | ||||
\(124\) | 13.4908 | + | 23.3668i | 1.21151 | + | 2.09840i | ||||
\(125\) | − | 9.18493i | − | 0.821526i | ||||||
\(126\) | 16.9479 | + | 0.308045i | 1.50984 | + | 0.0274428i | ||||
\(127\) | 5.96488 | + | 10.3315i | 0.529298 | + | 0.916771i | 0.999416 | + | 0.0341673i | \(0.0108779\pi\) |
−0.470118 | + | 0.882603i | \(0.655789\pi\) | |||||||
\(128\) | 9.20311 | 0.813448 | ||||||||
\(129\) | 0.132895 | − | 1.04331i | 0.0117008 | − | 0.0918581i | ||||
\(130\) | −19.1616 | + | 19.4733i | −1.68058 | + | 1.70792i | ||||
\(131\) | −4.43745 | + | 7.68588i | −0.387701 | + | 0.671519i | −0.992140 | − | 0.125133i | \(-0.960064\pi\) |
0.604438 | + | 0.796652i | \(0.293398\pi\) | |||||||
\(132\) | −0.945605 | + | 7.42357i | −0.0823044 | + | 0.646139i | ||||
\(133\) | −2.50846 | + | 8.45598i | −0.217511 | + | 0.733226i | ||||
\(134\) | −0.879220 | − | 0.507618i | −0.0759531 | − | 0.0438515i | ||||
\(135\) | 14.4838 | − | 11.4068i | 1.24657 | − | 0.981743i | ||||
\(136\) | 3.00317 | 0.257520 | ||||||||
\(137\) | −19.9783 | −1.70686 | −0.853432 | − | 0.521204i | \(-0.825483\pi\) | ||||
−0.853432 | + | 0.521204i | \(0.825483\pi\) | |||||||
\(138\) | 10.9154 | + | 26.0419i | 0.929177 | + | 2.21683i | ||||
\(139\) | −4.45338 | − | 2.57116i | −0.377730 | − | 0.218083i | 0.299100 | − | 0.954222i | \(-0.403314\pi\) |
−0.676830 | + | 0.736139i | \(0.736647\pi\) | |||||||
\(140\) | 5.60223 | + | 23.3762i | 0.473475 | + | 1.97565i | ||||
\(141\) | −3.88491 | − | 0.494855i | −0.327169 | − | 0.0416743i | ||||
\(142\) | 8.21107 | − | 14.2220i | 0.689057 | − | 1.19348i | ||||
\(143\) | 4.33629 | + | 4.26689i | 0.362619 | + | 0.356815i | ||||
\(144\) | −5.39352 | + | 5.48497i | −0.449460 | + | 0.457081i | ||||
\(145\) | −15.7995 | −1.31208 | ||||||||
\(146\) | 3.45610 | + | 5.98613i | 0.286028 | + | 0.495416i | ||||
\(147\) | −4.08605 | − | 11.4151i | −0.337012 | − | 0.941500i | ||||
\(148\) | − | 14.2211i | − | 1.16897i | ||||||
\(149\) | 9.13529 | + | 15.8228i | 0.748392 | + | 1.29625i | 0.948593 | + | 0.316498i | \(0.102507\pi\) |
−0.200201 | + | 0.979755i | \(0.564160\pi\) | |||||||
\(150\) | 22.3412 | + | 16.9943i | 1.82415 | + | 1.38758i | ||||
\(151\) | −2.70900 | + | 1.56404i | −0.220455 | + | 0.127280i | −0.606161 | − | 0.795342i | \(-0.707291\pi\) |
0.385706 | + | 0.922622i | \(0.373958\pi\) | |||||||
\(152\) | 1.99598 | + | 3.45714i | 0.161895 | + | 0.280411i | ||||
\(153\) | −5.27530 | + | 5.36475i | −0.426483 | + | 0.433714i | ||||
\(154\) | 9.27097 | − | 2.22184i | 0.747076 | − | 0.179041i | ||||
\(155\) | − | 37.3851i | − | 3.00284i | ||||||
\(156\) | −2.28171 | − | 15.8280i | −0.182683 | − | 1.26726i | ||||
\(157\) | −0.319245 | + | 0.184316i | −0.0254786 | + | 0.0147101i | −0.512685 | − | 0.858577i | \(-0.671349\pi\) |
0.487207 | + | 0.873287i | \(0.338016\pi\) | |||||||
\(158\) | 7.80896 | − | 13.5255i | 0.621247 | − | 1.07603i | ||||
\(159\) | −5.86130 | + | 7.70543i | −0.464831 | + | 0.611081i | ||||
\(160\) | −24.1850 | − | 13.9632i | −1.91199 | − | 1.10389i | ||||
\(161\) | 14.6560 | − | 13.8969i | 1.15506 | − | 1.09523i | ||||
\(162\) | 0.323135 | + | 19.2175i | 0.0253879 | + | 1.50987i | ||||
\(163\) | −9.90372 | + | 5.71791i | −0.775719 | + | 0.447862i | −0.834911 | − | 0.550385i | \(-0.814481\pi\) |
0.0591919 | + | 0.998247i | \(0.481148\pi\) | |||||||
\(164\) | −7.42560 | + | 4.28717i | −0.579842 | + | 0.334772i | ||||
\(165\) | 6.27763 | − | 8.25276i | 0.488713 | − | 0.642477i | ||||
\(166\) | − | 33.6618i | − | 2.61267i | ||||||
\(167\) | 5.65236 | − | 3.26339i | 0.437393 | − | 0.252529i | −0.265098 | − | 0.964221i | \(-0.585404\pi\) |
0.702491 | + | 0.711693i | \(0.252071\pi\) | |||||||
\(168\) | −5.02144 | − | 2.21285i | −0.387412 | − | 0.170725i | ||||
\(169\) | −11.3617 | − | 6.31752i | −0.873979 | − | 0.485963i | ||||
\(170\) | −16.4574 | − | 9.50167i | −1.26222 | − | 0.728745i | ||||
\(171\) | −9.68180 | − | 2.50719i | −0.740386 | − | 0.191730i | ||||
\(172\) | −0.777459 | + | 1.34660i | −0.0592807 | + | 0.102677i | ||||
\(173\) | −5.27550 | − | 9.13743i | −0.401089 | − | 0.694706i | 0.592769 | − | 0.805373i | \(-0.298035\pi\) |
−0.993858 | + | 0.110667i | \(0.964701\pi\) | |||||||
\(174\) | 9.97211 | − | 13.1096i | 0.755983 | − | 0.993838i | ||||
\(175\) | 5.71013 | − | 19.2488i | 0.431646 | − | 1.45507i | ||||
\(176\) | −2.16324 | + | 3.74684i | −0.163060 | + | 0.282429i | ||||
\(177\) | 3.83485 | + | 9.14919i | 0.288245 | + | 0.687695i | ||||
\(178\) | − | 10.8448i | − | 0.812852i | ||||||
\(179\) | 12.0328 | + | 6.94712i | 0.899371 | + | 0.519252i | 0.876996 | − | 0.480497i | \(-0.159544\pi\) |
0.0223753 | + | 0.999750i | \(0.492877\pi\) | |||||||
\(180\) | −26.2677 | + | 7.27562i | −1.95788 | + | 0.542293i | ||||
\(181\) | 2.10285i | 0.156304i | 0.996941 | + | 0.0781518i | \(0.0249019\pi\) | ||||
−0.996941 | + | 0.0781518i | \(0.975098\pi\) | |||||||
\(182\) | −17.8284 | + | 9.85772i | −1.32153 | + | 0.730703i | ||||
\(183\) | −9.48439 | + | 12.4685i | −0.701106 | + | 0.921695i | ||||
\(184\) | − | 9.14108i | − | 0.673889i | ||||||
\(185\) | −9.85221 | + | 17.0645i | −0.724349 | + | 1.25461i | ||||
\(186\) | 31.0203 | + | 23.5962i | 2.27452 | + | 1.73016i | ||||
\(187\) | −2.11582 | + | 3.66471i | −0.154724 | + | 0.267990i | ||||
\(188\) | 5.01426 | + | 2.89499i | 0.365703 | + | 0.211139i | ||||
\(189\) | 12.7735 | − | 5.08307i | 0.929136 | − | 0.369739i | ||||
\(190\) | − | 25.2602i | − | 1.83257i | ||||||
\(191\) | 5.47817 | − | 3.16282i | 0.396386 | − | 0.228854i | −0.288537 | − | 0.957469i | \(-0.593169\pi\) |
0.684924 | + | 0.728615i | \(0.259836\pi\) | |||||||
\(192\) | 18.6587 | − | 7.82073i | 1.34657 | − | 0.564412i | ||||
\(193\) | −8.85145 | − | 5.11039i | −0.637141 | − | 0.367854i | 0.146371 | − | 0.989230i | \(-0.453241\pi\) |
−0.783512 | + | 0.621376i | \(0.786574\pi\) | |||||||
\(194\) | −8.55496 | + | 14.8176i | −0.614210 | + | 1.06384i | ||||
\(195\) | −8.22754 | + | 20.5735i | −0.589186 | + | 1.47330i | ||||
\(196\) | −0.952462 | + | 17.8997i | −0.0680330 | + | 1.27855i | ||||
\(197\) | −4.35582 | − | 7.54450i | −0.310339 | − | 0.537524i | 0.668096 | − | 0.744075i | \(-0.267109\pi\) |
−0.978436 | + | 0.206551i | \(0.933776\pi\) | |||||||
\(198\) | 2.88550 | + | 10.4177i | 0.205064 | + | 0.740356i | ||||
\(199\) | 18.8883i | 1.33896i | 0.742831 | + | 0.669478i | \(0.233482\pi\) | ||||
−0.742831 | + | 0.669478i | \(0.766518\pi\) | |||||||
\(200\) | −4.54355 | − | 7.86966i | −0.321278 | − | 0.556469i | ||||
\(201\) | −0.816801 | − | 0.104043i | −0.0576127 | − | 0.00733863i | ||||
\(202\) | −4.49944 | + | 7.79326i | −0.316580 | + | 0.548332i | ||||
\(203\) | −11.2950 | − | 3.35066i | −0.792754 | − | 0.235170i | ||||
\(204\) | 10.2589 | − | 4.29997i | 0.718264 | − | 0.301058i | ||||
\(205\) | 11.8804 | 0.829762 | ||||||||
\(206\) | 1.62766 | + | 0.939729i | 0.113404 | + | 0.0654740i | ||||
\(207\) | 16.3293 | + | 16.0570i | 1.13496 | + | 1.11604i | ||||
\(208\) | 2.32074 | − | 8.94925i | 0.160914 | − | 0.620519i | ||||
\(209\) | −5.62491 | −0.389083 | ||||||||
\(210\) | 20.5163 | + | 28.0137i | 1.41576 | + | 1.93313i | ||||
\(211\) | 1.94065 | + | 3.36131i | 0.133600 | + | 0.231402i | 0.925062 | − | 0.379817i | \(-0.124013\pi\) |
−0.791462 | + | 0.611219i | \(0.790680\pi\) | |||||||
\(212\) | 12.3956 | − | 7.15659i | 0.851332 | − | 0.491517i | ||||
\(213\) | 1.68297 | − | 13.2123i | 0.115315 | − | 0.905293i | ||||
\(214\) | − | 10.9474i | − | 0.748346i | ||||||
\(215\) | 1.86581 | − | 1.07723i | 0.127247 | − | 0.0734663i | ||||
\(216\) | 2.30843 | − | 5.77806i | 0.157069 | − | 0.393147i | ||||
\(217\) | 7.92839 | − | 26.7265i | 0.538214 | − | 1.81431i | ||||
\(218\) | −7.48489 | + | 4.32140i | −0.506941 | + | 0.292682i | ||||
\(219\) | 4.46191 | + | 3.39405i | 0.301508 | + | 0.229348i | ||||
\(220\) | −13.2760 | + | 7.66493i | −0.895071 | + | 0.516769i | ||||
\(221\) | 2.26987 | − | 8.75310i | 0.152688 | − | 0.588797i | ||||
\(222\) | −7.94091 | − | 18.9454i | −0.532959 | − | 1.27153i | ||||
\(223\) | 7.59002 | + | 13.1463i | 0.508265 | + | 0.880341i | 0.999954 | + | 0.00957007i | \(0.00304630\pi\) |
−0.491689 | + | 0.870771i | \(0.663620\pi\) | |||||||
\(224\) | −14.3286 | − | 15.1113i | −0.957367 | − | 1.00966i | ||||
\(225\) | 22.0392 | + | 5.70725i | 1.46928 | + | 0.380483i | ||||
\(226\) | 4.25183 | + | 2.45479i | 0.282827 | + | 0.163290i | ||||
\(227\) | − | 22.5870i | − | 1.49915i | −0.661918 | − | 0.749577i | \(-0.730257\pi\) | ||
0.661918 | − | 0.749577i | \(-0.269743\pi\) | |||||||
\(228\) | 11.7683 | + | 8.95176i | 0.779372 | + | 0.592845i | ||||
\(229\) | −12.3908 | + | 21.4614i | −0.818804 | + | 1.41821i | 0.0877595 | + | 0.996142i | \(0.472029\pi\) |
−0.906564 | + | 0.422069i | \(0.861304\pi\) | |||||||
\(230\) | −28.9213 | + | 50.0932i | −1.90701 | + | 3.30304i | ||||
\(231\) | 6.23805 | − | 4.56856i | 0.410434 | − | 0.300589i | ||||
\(232\) | −4.61785 | + | 2.66612i | −0.303177 | + | 0.175039i | ||||
\(233\) | −3.08386 | − | 1.78047i | −0.202030 | − | 0.116642i | 0.395572 | − | 0.918435i | \(-0.370546\pi\) |
−0.597602 | + | 0.801793i | \(0.703880\pi\) | |||||||
\(234\) | −11.8779 | − | 19.8121i | −0.776482 | − | 1.29516i | ||||
\(235\) | −4.01122 | − | 6.94764i | −0.261663 | − | 0.453214i | ||||
\(236\) | − | 14.6666i | − | 0.954711i | ||||||
\(237\) | 1.60055 | − | 12.5653i | 0.103967 | − | 0.816203i | ||||
\(238\) | −9.75028 | − | 10.2829i | −0.632017 | − | 0.666541i | ||||
\(239\) | −3.20668 | −0.207423 | −0.103711 | − | 0.994607i | \(-0.533072\pi\) | ||||
−0.103711 | + | 0.994607i | \(0.533072\pi\) | |||||||
\(240\) | −15.6316 | − | 1.99114i | −1.00902 | − | 0.128527i | ||||
\(241\) | −22.4935 | −1.44893 | −0.724466 | − | 0.689310i | \(-0.757914\pi\) | ||||
−0.724466 | + | 0.689310i | \(0.757914\pi\) | |||||||
\(242\) | −8.70580 | − | 15.0789i | −0.559630 | − | 0.969308i | ||||
\(243\) | 6.26678 | + | 14.2733i | 0.402014 | + | 0.915634i | ||||
\(244\) | 20.0578 | − | 11.5804i | 1.28407 | − | 0.741356i | ||||
\(245\) | 13.5436 | − | 20.8187i | 0.865266 | − | 1.33006i | ||||
\(246\) | −7.49850 | + | 9.85776i | −0.478087 | + | 0.628508i | ||||
\(247\) | 11.5849 | − | 3.20454i | 0.737127 | − | 0.203900i | ||||
\(248\) | −6.30861 | − | 10.9268i | −0.400597 | − | 0.693855i | ||||
\(249\) | −10.5537 | − | 25.1789i | −0.668810 | − | 1.59565i | ||||
\(250\) | 19.6152i | 1.24057i | ||||||||
\(251\) | 1.50887 | − | 2.61345i | 0.0952393 | − | 0.164959i | −0.814469 | − | 0.580207i | \(-0.802972\pi\) |
0.909708 | + | 0.415248i | \(0.136305\pi\) | |||||||
\(252\) | −20.3217 | − | 0.369367i | −1.28014 | − | 0.0232679i | ||||
\(253\) | 11.1547 | + | 6.44017i | 0.701290 | + | 0.404890i | ||||
\(254\) | −12.7385 | − | 22.0637i | −0.799285 | − | 1.38440i | ||||
\(255\) | −15.2890 | − | 1.94749i | −0.957435 | − | 0.121957i | ||||
\(256\) | 3.70723 | 0.231702 | ||||||||
\(257\) | 1.82260 | 0.113691 | 0.0568453 | − | 0.998383i | \(-0.481896\pi\) | ||||
0.0568453 | + | 0.998383i | \(0.481896\pi\) | |||||||
\(258\) | −0.283809 | + | 2.22807i | −0.0176692 | + | 0.138714i | ||||
\(259\) | −10.6623 | + | 10.1100i | −0.662520 | + | 0.628204i | ||||
\(260\) | 22.9761 | − | 23.3498i | 1.42492 | − | 1.44809i | ||||
\(261\) | 3.34896 | − | 12.9324i | 0.207296 | − | 0.800495i | ||||
\(262\) | 9.47653 | − | 16.4138i | 0.585462 | − | 1.01405i | ||||
\(263\) | 13.1894 | + | 7.61491i | 0.813294 | + | 0.469556i | 0.848099 | − | 0.529839i | \(-0.177747\pi\) |
−0.0348044 | + | 0.999394i | \(0.511081\pi\) | |||||||
\(264\) | 0.442187 | − | 3.47143i | 0.0272147 | − | 0.213652i | ||||
\(265\) | −19.8320 | −1.21827 | ||||||||
\(266\) | 5.35702 | − | 18.0584i | 0.328460 | − | 1.10723i | ||||
\(267\) | −3.40006 | − | 8.11186i | −0.208080 | − | 0.496438i | ||||
\(268\) | 1.05425 | + | 0.608670i | 0.0643984 | + | 0.0371804i | ||||
\(269\) | −14.5592 | −0.887689 | −0.443845 | − | 0.896104i | \(-0.646386\pi\) | ||||
−0.443845 | + | 0.896104i | \(0.646386\pi\) | |||||||
\(270\) | −30.9313 | + | 24.3602i | −1.88242 | + | 1.48251i | ||||
\(271\) | 20.0397 | 1.21733 | 0.608663 | − | 0.793428i | \(-0.291706\pi\) | ||||
0.608663 | + | 0.793428i | \(0.291706\pi\) | |||||||
\(272\) | 6.43089 | 0.389930 | ||||||||
\(273\) | −10.2449 | + | 12.9631i | −0.620052 | + | 0.784561i | ||||
\(274\) | 42.6654 | 2.57751 | ||||||||
\(275\) | 12.8043 | 0.772127 | ||||||||
\(276\) | −13.0883 | − | 31.2260i | −0.787822 | − | 1.87959i | ||||
\(277\) | −2.59927 | −0.156175 | −0.0780875 | − | 0.996947i | \(-0.524881\pi\) | ||||
−0.0780875 | + | 0.996947i | \(0.524881\pi\) | |||||||
\(278\) | 9.51055 | + | 5.49092i | 0.570405 | + | 0.329323i | ||||
\(279\) | 30.6009 | + | 7.92438i | 1.83203 | + | 0.474420i | ||||
\(280\) | −2.61973 | − | 10.9312i | −0.156559 | − | 0.653267i | ||||
\(281\) | 9.72929 | 0.580401 | 0.290200 | − | 0.956966i | \(-0.406278\pi\) | ||||
0.290200 | + | 0.956966i | \(0.406278\pi\) | |||||||
\(282\) | 8.29655 | + | 1.05680i | 0.494052 | + | 0.0629318i | ||||
\(283\) | −23.5291 | − | 13.5845i | −1.39866 | − | 0.807517i | −0.404409 | − | 0.914578i | \(-0.632523\pi\) |
−0.994252 | + | 0.107061i | \(0.965856\pi\) | |||||||
\(284\) | −9.84564 | + | 17.0532i | −0.584231 | + | 1.01192i | ||||
\(285\) | −7.91957 | − | 18.8945i | −0.469115 | − | 1.11921i | ||||
\(286\) | −9.26051 | − | 9.11229i | −0.547585 | − | 0.538821i | ||||
\(287\) | 8.49326 | + | 2.51952i | 0.501341 | + | 0.148722i | ||||
\(288\) | 16.5558 | − | 16.8365i | 0.975558 | − | 0.992099i | ||||
\(289\) | −10.7101 | −0.630004 | ||||||||
\(290\) | 33.7411 | 1.98135 | ||||||||
\(291\) | −1.75345 | + | 13.7657i | −0.102789 | + | 0.806958i | ||||
\(292\) | −4.14410 | − | 7.17779i | −0.242515 | − | 0.420048i | ||||
\(293\) | 7.78612 | + | 4.49532i | 0.454870 | + | 0.262619i | 0.709885 | − | 0.704318i | \(-0.248747\pi\) |
−0.255015 | + | 0.966937i | \(0.582080\pi\) | |||||||
\(294\) | 8.72610 | + | 24.3779i | 0.508917 | + | 1.42175i | ||||
\(295\) | −10.1608 | + | 17.5990i | −0.591585 | + | 1.02465i | ||||
\(296\) | 6.65012i | 0.386530i | ||||||||
\(297\) | 5.42451 | + | 6.88776i | 0.314762 | + | 0.399668i | ||||
\(298\) | −19.5092 | − | 33.7908i | −1.13014 | − | 1.95745i | ||||
\(299\) | −26.6428 | − | 6.90905i | −1.54079 | − | 0.399561i | ||||
\(300\) | −26.7887 | − | 20.3774i | −1.54665 | − | 1.17649i | ||||
\(301\) | 1.56232 | − | 0.374417i | 0.0900504 | − | 0.0215810i | ||||
\(302\) | 5.78529 | − | 3.34014i | 0.332906 | − | 0.192204i | ||||
\(303\) | −0.922221 | + | 7.23999i | −0.0529802 | + | 0.415927i | ||||
\(304\) | 4.27412 | + | 7.40300i | 0.245138 | + | 0.424591i | ||||
\(305\) | −32.0909 | −1.83752 | ||||||||
\(306\) | 11.2658 | − | 11.4569i | 0.644026 | − | 0.654946i | ||||
\(307\) | −0.798820 | −0.0455911 | −0.0227955 | − | 0.999740i | \(-0.507257\pi\) | ||||
−0.0227955 | + | 0.999740i | \(0.507257\pi\) | |||||||
\(308\) | −11.1165 | + | 2.66414i | −0.633424 | + | 0.151803i | ||||
\(309\) | 1.51210 | + | 0.192610i | 0.0860206 | + | 0.0109572i | ||||
\(310\) | 79.8389i | 4.53454i | ||||||||
\(311\) | −11.1632 | − | 19.3352i | −0.633006 | − | 1.09640i | −0.986934 | − | 0.161126i | \(-0.948487\pi\) |
0.353928 | − | 0.935273i | \(-0.384846\pi\) | |||||||
\(312\) | 1.06698 | + | 7.40155i | 0.0604058 | + | 0.419030i | ||||
\(313\) | 26.6678 | + | 15.3966i | 1.50735 | + | 0.870269i | 0.999963 | + | 0.00855148i | \(0.00272205\pi\) |
0.507388 | + | 0.861718i | \(0.330611\pi\) | |||||||
\(314\) | 0.681775 | − | 0.393623i | 0.0384748 | − | 0.0222134i | ||||
\(315\) | 24.1290 | + | 14.5218i | 1.35951 | + | 0.818212i | ||||
\(316\) | −9.36349 | + | 16.2180i | −0.526737 | + | 0.912336i | ||||
\(317\) | 0.708095 | − | 1.22646i | 0.0397706 | − | 0.0688846i | −0.845455 | − | 0.534047i | \(-0.820671\pi\) |
0.885226 | + | 0.465162i | \(0.154004\pi\) | |||||||
\(318\) | 12.5173 | − | 16.4556i | 0.701934 | − | 0.922784i | ||||
\(319\) | − | 7.51344i | − | 0.420672i | ||||||
\(320\) | 35.8911 | + | 20.7218i | 2.00638 | + | 1.15838i | ||||
\(321\) | −3.43221 | − | 8.18857i | −0.191567 | − | 0.457041i | ||||
\(322\) | −31.2992 | + | 29.6780i | −1.74424 | + | 1.65389i | ||||
\(323\) | 4.18044 | + | 7.24074i | 0.232606 | + | 0.402886i | ||||
\(324\) | −0.387461 | − | 23.0432i | −0.0215256 | − | 1.28018i | ||||
\(325\) | −26.3712 | + | 7.29465i | −1.46281 | + | 0.404634i | ||||
\(326\) | 21.1502 | − | 12.2111i | 1.17140 | − | 0.676309i | ||||
\(327\) | −4.24382 | + | 5.57905i | −0.234684 | + | 0.308522i | ||||
\(328\) | 3.47238 | − | 2.00478i | 0.191730 | − | 0.110695i | ||||
\(329\) | −1.39420 | − | 5.81752i | −0.0768647 | − | 0.320730i | ||||
\(330\) | −13.4064 | + | 17.6245i | −0.737998 | + | 0.970194i | ||||
\(331\) | −10.0365 | + | 5.79460i | −0.551658 | + | 0.318500i | −0.749791 | − | 0.661675i | \(-0.769846\pi\) |
0.198132 | + | 0.980175i | \(0.436512\pi\) | |||||||
\(332\) | 40.3629i | 2.21520i | ||||||||
\(333\) | −11.8795 | − | 11.6815i | −0.650995 | − | 0.640140i | ||||
\(334\) | −12.0711 | + | 6.96924i | −0.660500 | + | 0.381340i | ||||
\(335\) | −0.843357 | − | 1.46074i | −0.0460775 | − | 0.0798086i | ||||
\(336\) | −10.7527 | − | 4.73852i | −0.586610 | − | 0.258507i | ||||
\(337\) | 36.3321 | 1.97914 | 0.989568 | − | 0.144065i | \(-0.0460175\pi\) | ||||
0.989568 | + | 0.144065i | \(0.0460175\pi\) | |||||||
\(338\) | 24.2639 | + | 13.4916i | 1.31978 | + | 0.733846i | ||||
\(339\) | 3.94997 | + | 0.503143i | 0.214533 | + | 0.0273270i | ||||
\(340\) | 19.7336 | + | 11.3932i | 1.07020 | + | 0.617881i | ||||
\(341\) | 17.7784 | 0.962757 | ||||||||
\(342\) | 20.6763 | + | 5.35431i | 1.11805 | + | 0.289528i | ||||
\(343\) | 14.0974 | − | 12.0110i | 0.761186 | − | 0.648534i | ||||
\(344\) | 0.363558 | − | 0.629701i | 0.0196017 | − | 0.0339512i | ||||
\(345\) | −5.92781 | + | 46.5369i | −0.319142 | + | 2.50546i | ||||
\(346\) | 11.2663 | + | 19.5137i | 0.605678 | + | 1.04906i | ||||
\(347\) | 16.6002i | 0.891143i | 0.895246 | + | 0.445571i | \(0.146999\pi\) | ||||
−0.895246 | + | 0.445571i | \(0.853001\pi\) | |||||||
\(348\) | −11.9573 | + | 15.7194i | −0.640976 | + | 0.842646i | ||||
\(349\) | 10.5915 | + | 18.3450i | 0.566948 | + | 0.981984i | 0.996865 | + | 0.0791151i | \(0.0252095\pi\) |
−0.429917 | + | 0.902868i | \(0.641457\pi\) | |||||||
\(350\) | −12.1945 | + | 41.1073i | −0.651821 | + | 2.19728i | ||||
\(351\) | −15.0961 | − | 11.0954i | −0.805770 | − | 0.592229i | ||||
\(352\) | 6.64020 | − | 11.5012i | 0.353924 | − | 0.613014i | ||||
\(353\) | 8.36039 | + | 4.82687i | 0.444978 | + | 0.256908i | 0.705707 | − | 0.708504i | \(-0.250629\pi\) |
−0.260729 | + | 0.965412i | \(0.583963\pi\) | |||||||
\(354\) | −8.18964 | − | 19.5388i | −0.435274 | − | 1.03848i | ||||
\(355\) | 23.6284 | − | 13.6419i | 1.25407 | − | 0.724035i | ||||
\(356\) | 13.0037i | 0.689193i | ||||||||
\(357\) | −10.5171 | − | 4.63466i | −0.556622 | − | 0.245292i | ||||
\(358\) | −25.6970 | − | 14.8362i | −1.35813 | − | 0.784115i | ||||
\(359\) | −16.8609 | + | 29.2039i | −0.889884 | + | 1.54132i | −0.0498728 | + | 0.998756i | \(0.515882\pi\) |
−0.840011 | + | 0.542569i | \(0.817452\pi\) | |||||||
\(360\) | 12.2834 | − | 3.40225i | 0.647391 | − | 0.179314i | ||||
\(361\) | 3.94315 | − | 6.82974i | 0.207534 | − | 0.359460i | ||||
\(362\) | − | 4.49081i | − | 0.236032i | ||||||
\(363\) | −11.2394 | − | 8.54950i | −0.589917 | − | 0.448733i | ||||
\(364\) | 21.3774 | − | 11.8201i | 1.12048 | − | 0.619541i | ||||
\(365\) | 11.4839i | 0.601096i | ||||||||
\(366\) | 20.2547 | − | 26.6274i | 1.05873 | − | 1.39184i | ||||
\(367\) | 27.9659 | + | 16.1461i | 1.45981 | + | 0.842821i | 0.999001 | − | 0.0446783i | \(-0.0142263\pi\) |
0.460808 | + | 0.887500i | \(0.347560\pi\) | |||||||
\(368\) | − | 19.5744i | − | 1.02039i | ||||||
\(369\) | −2.51824 | + | 9.72449i | −0.131095 | + | 0.506237i | ||||
\(370\) | 21.0402 | − | 36.4427i | 1.09383 | − | 1.89457i | ||||
\(371\) | −14.1778 | − | 4.20584i | −0.736076 | − | 0.218356i | ||||
\(372\) | −37.1955 | − | 28.2935i | −1.92849 | − | 1.46695i | ||||
\(373\) | −5.29795 | − | 9.17632i | −0.274317 | − | 0.475132i | 0.695645 | − | 0.718385i | \(-0.255119\pi\) |
−0.969963 | + | 0.243254i | \(0.921785\pi\) | |||||||
\(374\) | 4.51852 | − | 7.82630i | 0.233647 | − | 0.404688i | ||||
\(375\) | 6.14975 | + | 14.6721i | 0.317572 | + | 0.757662i | ||||
\(376\) | −2.34478 | − | 1.35376i | −0.120923 | − | 0.0698150i | ||||
\(377\) | 4.28044 | + | 15.4744i | 0.220454 | + | 0.796972i | ||||
\(378\) | −27.2789 | + | 10.8553i | −1.40307 | + | 0.558338i | ||||
\(379\) | −22.3310 | + | 12.8928i | −1.14707 | + | 0.662260i | −0.948171 | − | 0.317760i | \(-0.897069\pi\) |
−0.198897 | + | 0.980020i | \(0.563736\pi\) | |||||||
\(380\) | 30.2887i | 1.55378i | ||||||||
\(381\) | −16.4458 | − | 12.5098i | −0.842542 | − | 0.640896i | ||||
\(382\) | −11.6991 | + | 6.75447i | −0.598577 | + | 0.345589i | ||||
\(383\) | −25.3512 | + | 14.6365i | −1.29538 | + | 0.747890i | −0.979603 | − | 0.200942i | \(-0.935600\pi\) |
−0.315780 | + | 0.948832i | \(0.602266\pi\) | |||||||
\(384\) | −14.7011 | + | 6.16192i | −0.750213 | + | 0.314449i | ||||
\(385\) | 15.1849 | + | 4.50459i | 0.773894 | + | 0.229575i | ||||
\(386\) | 18.9030 | + | 10.9137i | 0.962137 | + | 0.555490i | ||||
\(387\) | 0.486256 | + | 1.75557i | 0.0247178 | + | 0.0892404i | ||||
\(388\) | 10.2580 | − | 17.7674i | 0.520771 | − | 0.902002i | ||||
\(389\) | 3.32347 | − | 1.91881i | 0.168507 | − | 0.0972873i | −0.413375 | − | 0.910561i | \(-0.635650\pi\) |
0.581881 | + | 0.813274i | \(0.302317\pi\) | |||||||
\(390\) | 17.5706 | − | 43.9363i | 0.889721 | − | 2.22480i | ||||
\(391\) | − | 19.1454i | − | 0.968222i | ||||||
\(392\) | 0.445393 | − | 8.37030i | 0.0224958 | − | 0.422764i | ||||
\(393\) | 1.94234 | − | 15.2486i | 0.0979782 | − | 0.769188i | ||||
\(394\) | 9.30221 | + | 16.1119i | 0.468639 | + | 0.811706i | ||||
\(395\) | 22.4713 | − | 12.9738i | 1.13065 | − | 0.652783i | ||||
\(396\) | −3.45992 | − | 12.4916i | −0.173867 | − | 0.627726i | ||||
\(397\) | −5.09509 | − | 8.82496i | −0.255715 | − | 0.442912i | 0.709374 | − | 0.704832i | \(-0.248978\pi\) |
−0.965090 | + | 0.261920i | \(0.915644\pi\) | |||||||
\(398\) | − | 40.3375i | − | 2.02194i | ||||||
\(399\) | −1.65465 | − | 15.1872i | −0.0828360 | − | 0.760309i | ||||
\(400\) | −9.72941 | − | 16.8518i | −0.486470 | − | 0.842591i | ||||
\(401\) | 21.6409 | 1.08069 | 0.540347 | − | 0.841442i | \(-0.318293\pi\) | ||||
0.540347 | + | 0.841442i | \(0.318293\pi\) | |||||||
\(402\) | 1.74435 | + | 0.222193i | 0.0870001 | + | 0.0110820i | ||||
\(403\) | −36.6158 | + | 10.1285i | −1.82396 | + | 0.504534i | ||||
\(404\) | 5.39515 | − | 9.34467i | 0.268419 | − | 0.464915i | ||||
\(405\) | −15.4991 | + | 27.9189i | −0.770155 | + | 1.38730i | ||||
\(406\) | 24.1214 | + | 7.15560i | 1.19713 | + | 0.355127i | ||||
\(407\) | −8.11503 | − | 4.68521i | −0.402247 | − | 0.232237i | ||||
\(408\) | −4.79728 | + | 2.01076i | −0.237501 | + | 0.0995476i | ||||
\(409\) | −20.4569 | −1.01153 | −0.505765 | − | 0.862671i | \(-0.668790\pi\) | ||||
−0.505765 | + | 0.862671i | \(0.668790\pi\) | |||||||
\(410\) | −25.3715 | −1.25301 | ||||||||
\(411\) | 31.9135 | − | 13.3764i | 1.57418 | − | 0.659811i | ||||
\(412\) | −1.95168 | − | 1.12680i | −0.0961522 | − | 0.0555135i | ||||
\(413\) | −10.9962 | + | 10.4267i | −0.541089 | + | 0.513062i | ||||
\(414\) | −34.8725 | − | 34.2911i | −1.71389 | − | 1.68532i | ||||
\(415\) | 27.9629 | − | 48.4332i | 1.37264 | − | 2.37749i | ||||
\(416\) | −7.12365 | + | 27.4703i | −0.349266 | + | 1.34684i | ||||
\(417\) | 8.83536 | + | 1.12544i | 0.432670 | + | 0.0551129i | ||||
\(418\) | 12.0125 | 0.587549 | ||||||||
\(419\) | −11.3846 | − | 19.7187i | −0.556174 | − | 0.963322i | −0.997811 | − | 0.0661280i | \(-0.978935\pi\) |
0.441637 | − | 0.897194i | \(-0.354398\pi\) | |||||||
\(420\) | −24.6005 | − | 33.5903i | −1.20038 | − | 1.63904i | ||||
\(421\) | 32.8307i | 1.60007i | 0.599955 | + | 0.800034i | \(0.295185\pi\) | ||||
−0.599955 | + | 0.800034i | \(0.704815\pi\) | |||||||
\(422\) | −4.14442 | − | 7.17835i | −0.201747 | − | 0.349437i | ||||
\(423\) | 6.53711 | − | 1.81065i | 0.317845 | − | 0.0880367i | ||||
\(424\) | −5.79646 | + | 3.34659i | −0.281501 | + | 0.162525i | ||||
\(425\) | −9.51616 | − | 16.4825i | −0.461601 | − | 0.799517i | ||||
\(426\) | −3.59412 | + | 28.2160i | −0.174135 | + | 1.36707i | ||||
\(427\) | −22.9417 | − | 6.80564i | −1.11023 | − | 0.329348i | ||||
\(428\) | 13.1266i | 0.634500i | ||||||||
\(429\) | −9.78370 | − | 3.91260i | −0.472362 | − | 0.188902i | ||||
\(430\) | −3.98460 | + | 2.30051i | −0.192154 | + | 0.110940i | ||||
\(431\) | 1.20506 | − | 2.08722i | 0.0580455 | − | 0.100538i | −0.835542 | − | 0.549426i | \(-0.814846\pi\) |
0.893588 | + | 0.448888i | \(0.148180\pi\) | |||||||
\(432\) | 4.94319 | − | 12.3729i | 0.237830 | − | 0.595294i | ||||
\(433\) | 23.5698 | + | 13.6081i | 1.13269 | + | 0.653961i | 0.944611 | − | 0.328192i | \(-0.106439\pi\) |
0.188083 | + | 0.982153i | \(0.439772\pi\) | |||||||
\(434\) | −16.9317 | + | 57.0766i | −0.812749 | + | 2.73976i | ||||
\(435\) | 25.2382 | − | 10.5785i | 1.21008 | − | 0.507200i | ||||
\(436\) | 8.97490 | − | 5.18166i | 0.429820 | − | 0.248157i | ||||
\(437\) | 22.0394 | − | 12.7245i | 1.05429 | − | 0.608694i | ||||
\(438\) | −9.52879 | − | 7.24827i | −0.455303 | − | 0.346336i | ||||
\(439\) | − | 12.6924i | − | 0.605775i | −0.953026 | − | 0.302888i | \(-0.902049\pi\) | ||
0.953026 | − | 0.302888i | \(-0.0979507\pi\) | |||||||
\(440\) | 6.20819 | − | 3.58430i | 0.295964 | − | 0.170875i | ||||
\(441\) | 14.1700 | + | 15.4987i | 0.674763 | + | 0.738034i | ||||
\(442\) | −4.84749 | + | 18.6930i | −0.230572 | + | 0.889134i | ||||
\(443\) | −16.6247 | − | 9.59826i | −0.789862 | − | 0.456027i | 0.0500520 | − | 0.998747i | \(-0.484061\pi\) |
−0.839914 | + | 0.542720i | \(0.817395\pi\) | |||||||
\(444\) | 9.52171 | + | 22.7169i | 0.451880 | + | 1.07810i | ||||
\(445\) | 9.00878 | − | 15.6037i | 0.427057 | − | 0.739685i | ||||
\(446\) | −16.2091 | − | 28.0750i | −0.767523 | − | 1.32939i | ||||
\(447\) | −25.1869 | − | 19.1589i | −1.19130 | − | 0.906185i | ||||
\(448\) | 21.2639 | + | 22.4255i | 1.00463 | + | 1.05951i | ||||
\(449\) | 0.228112 | − | 0.395102i | 0.0107653 | − | 0.0186460i | −0.860593 | − | 0.509294i | \(-0.829907\pi\) |
0.871358 | + | 0.490648i | \(0.163240\pi\) | |||||||
\(450\) | −47.0665 | − | 12.1883i | −2.21874 | − | 0.574562i | ||||
\(451\) | 5.64971i | 0.266035i | ||||||||
\(452\) | −5.09824 | − | 2.94347i | −0.239801 | − | 0.138449i | ||||
\(453\) | 3.28017 | − | 4.31221i | 0.154116 | − | 0.202606i | ||||
\(454\) | 48.2364i | 2.26385i | ||||||||
\(455\) | −33.8405 | − | 0.626583i | −1.58647 | − | 0.0293746i | ||||
\(456\) | −5.50311 | − | 4.18605i | −0.257707 | − | 0.196030i | ||||
\(457\) | 8.98951i | 0.420512i | 0.977646 | + | 0.210256i | \(0.0674297\pi\) | ||||
−0.977646 | + | 0.210256i | \(0.932570\pi\) | |||||||
\(458\) | 26.4615 | − | 45.8326i | 1.23646 | − | 2.14162i | ||||
\(459\) | 4.83485 | − | 12.1018i | 0.225671 | − | 0.564861i | ||||
\(460\) | 34.6787 | − | 60.0652i | 1.61690 | − | 2.80055i | ||||
\(461\) | 8.71427 | + | 5.03118i | 0.405864 | + | 0.234326i | 0.689011 | − | 0.724751i | \(-0.258045\pi\) |
−0.283147 | + | 0.959076i | \(0.591378\pi\) | |||||||
\(462\) | −13.3219 | + | 9.75653i | −0.619790 | + | 0.453915i | ||||
\(463\) | − | 21.3601i | − | 0.992687i | −0.868126 | − | 0.496344i | \(-0.834676\pi\) | ||
0.868126 | − | 0.496344i | \(-0.165324\pi\) | |||||||
\(464\) | −9.88850 | + | 5.70913i | −0.459062 | + | 0.265040i | ||||
\(465\) | 25.0311 | + | 59.7191i | 1.16079 | + | 2.76941i | ||||
\(466\) | 6.58583 | + | 3.80233i | 0.305083 | + | 0.176140i | ||||
\(467\) | −7.57811 | + | 13.1257i | −0.350673 | + | 0.607384i | −0.986368 | − | 0.164557i | \(-0.947381\pi\) |
0.635694 | + | 0.771941i | \(0.280714\pi\) | |||||||
\(468\) | 14.2424 | + | 23.7561i | 0.658357 | + | 1.09813i | ||||
\(469\) | −0.293130 | − | 1.22313i | −0.0135355 | − | 0.0564789i | ||||
\(470\) | 8.56629 | + | 14.8373i | 0.395134 | + | 0.684391i | ||||
\(471\) | 0.386556 | − | 0.508178i | 0.0178116 | − | 0.0234156i | ||||
\(472\) | 6.85842i | 0.315684i | ||||||||
\(473\) | 0.512275 | + | 0.887287i | 0.0235544 | + | 0.0407975i | ||||
\(474\) | −3.41811 | + | 26.8342i | −0.156999 | + | 1.23254i | ||||
\(475\) | 12.6493 | − | 21.9093i | 0.580392 | − | 1.00527i | ||||
\(476\) | 11.6913 | + | 12.3299i | 0.535868 | + | 0.565141i | ||||
\(477\) | 4.20372 | − | 16.2331i | 0.192475 | − | 0.743264i | ||||
\(478\) | 6.84813 | 0.313226 | ||||||||
\(479\) | 33.1761 | + | 19.1543i | 1.51586 | + | 0.875180i | 0.999827 | + | 0.0186099i | \(0.00592407\pi\) |
0.516030 | + | 0.856570i | \(0.327409\pi\) | |||||||
\(480\) | 47.9823 | + | 6.11193i | 2.19008 | + | 0.278970i | ||||
\(481\) | 19.3826 | + | 5.02633i | 0.883770 | + | 0.229181i | ||||
\(482\) | 48.0367 | 2.18801 | ||||||||
\(483\) | −14.1070 | + | 32.0119i | −0.641891 | + | 1.45659i | ||||
\(484\) | 10.4389 | + | 18.0806i | 0.474494 | + | 0.821848i | ||||
\(485\) | −24.6180 | + | 14.2132i | −1.11785 | + | 0.645389i | ||||
\(486\) | −13.3832 | − | 30.4818i | −0.607075 | − | 1.38268i | ||||
\(487\) | 22.6899i | 1.02818i | 0.857737 | + | 0.514090i | \(0.171870\pi\) | ||||
−0.857737 | + | 0.514090i | \(0.828130\pi\) | |||||||
\(488\) | −9.37947 | + | 5.41524i | −0.424589 | + | 0.245136i | ||||
\(489\) | 11.9918 | − | 15.7648i | 0.542290 | − | 0.712911i | ||||
\(490\) | −28.9234 | + | 44.4601i | −1.30663 | + | 2.00850i | ||||
\(491\) | 8.34055 | − | 4.81542i | 0.376404 | − | 0.217317i | −0.299849 | − | 0.953987i | \(-0.596936\pi\) |
0.676252 | + | 0.736670i | \(0.263603\pi\) | |||||||
\(492\) | 8.99123 | − | 11.8201i | 0.405356 | − | 0.532893i | ||||
\(493\) | −9.67177 | + | 5.58400i | −0.435594 | + | 0.251491i | ||||
\(494\) | −24.7404 | + | 6.84355i | −1.11312 | + | 0.307906i | ||||
\(495\) | −4.50231 | + | 17.3862i | −0.202364 | + | 0.781451i | ||||
\(496\) | −13.5091 | − | 23.3984i | −0.606575 | − | 1.05062i | ||||
\(497\) | 19.7850 | − | 4.74157i | 0.887477 | − | 0.212688i | ||||
\(498\) | 22.5382 | + | 53.7716i | 1.00996 | + | 2.40956i | ||||
\(499\) | −3.42519 | − | 1.97754i | −0.153333 | − | 0.0885267i | 0.421371 | − | 0.906889i | \(-0.361549\pi\) |
−0.574703 | + | 0.818362i | \(0.694883\pi\) | |||||||
\(500\) | − | 23.5200i | − | 1.05185i | ||||||
\(501\) | −6.84412 | + | 8.99748i | −0.305773 | + | 0.401978i | ||||
\(502\) | −3.22232 | + | 5.58123i | −0.143819 | + | 0.249103i | ||||
\(503\) | 12.6346 | − | 21.8838i | 0.563350 | − | 0.975750i | −0.433851 | − | 0.900984i | \(-0.642846\pi\) |
0.997201 | − | 0.0747660i | \(-0.0238210\pi\) | |||||||
\(504\) | 9.50288 | + | 0.172724i | 0.423292 | + | 0.00769376i | ||||
\(505\) | −12.9477 | + | 7.47538i | −0.576167 | + | 0.332650i | ||||
\(506\) | −23.8218 | − | 13.7535i | −1.05901 | − | 0.611418i | ||||
\(507\) | 22.3792 | + | 2.48443i | 0.993894 | + | 0.110338i | ||||
\(508\) | 15.2744 | + | 26.4560i | 0.677690 | + | 1.17379i | ||||
\(509\) | 39.1820i | 1.73671i | 0.495940 | + | 0.868357i | \(0.334824\pi\) | ||||
−0.495940 | + | 0.868357i | \(0.665176\pi\) | |||||||
\(510\) | 32.6509 | + | 4.15904i | 1.44581 | + | 0.184165i | ||||
\(511\) | −2.43544 | + | 8.20982i | −0.107737 | + | 0.363181i | ||||
\(512\) | −26.3233 | −1.16334 | ||||||||
\(513\) | 17.1445 | − | 2.47742i | 0.756946 | − | 0.109381i | ||||
\(514\) | −3.89231 | −0.171683 | ||||||||
\(515\) | 1.56127 | + | 2.70419i | 0.0687976 | + | 0.119161i | ||||
\(516\) | 0.340306 | − | 2.67161i | 0.0149812 | − | 0.117611i | ||||
\(517\) | 3.30395 | − | 1.90753i | 0.145307 | − | 0.0838932i | ||||
\(518\) | 22.7701 | − | 21.5907i | 1.00046 | − | 0.948642i | ||||
\(519\) | 14.5451 | + | 11.0640i | 0.638457 | + | 0.485655i | ||||
\(520\) | −10.7442 | + | 10.9189i | −0.471163 | + | 0.478826i | ||||
\(521\) | −15.3554 | − | 26.5964i | −0.672733 | − | 1.16521i | −0.977126 | − | 0.212662i | \(-0.931787\pi\) |
0.304392 | − | 0.952547i | \(-0.401547\pi\) | |||||||
\(522\) | −7.15199 | + | 27.6182i | −0.313034 | + | 1.20882i | ||||
\(523\) | − | 6.38988i | − | 0.279410i | −0.990193 | − | 0.139705i | \(-0.955385\pi\) | ||
0.990193 | − | 0.139705i | \(-0.0446154\pi\) | |||||||
\(524\) | −11.3630 | + | 19.6813i | −0.496396 | + | 0.859783i | ||||
\(525\) | 3.76656 | + | 34.5713i | 0.164386 | + | 1.50882i | ||||
\(526\) | −28.1671 | − | 16.2623i | −1.22814 | − | 0.709069i | ||||
\(527\) | −13.2130 | − | 22.8855i | −0.575566 | − | 0.996909i | ||||
\(528\) | 0.946884 | − | 7.43361i | 0.0412078 | − | 0.323506i | ||||
\(529\) | −35.2748 | −1.53369 | ||||||||
\(530\) | 42.3528 | 1.83969 | ||||||||
\(531\) | −12.2516 | − | 12.0474i | −0.531675 | − | 0.522811i | ||||
\(532\) | −6.42344 | + | 21.6533i | −0.278492 | + | 0.938791i | ||||
\(533\) | −3.21867 | − | 11.6359i | −0.139416 | − | 0.504008i | ||||
\(534\) | 7.26111 | + | 17.3236i | 0.314219 | + | 0.749663i | ||||
\(535\) | 9.09397 | − | 15.7512i | 0.393167 | − | 0.680985i | ||||
\(536\) | −0.492990 | − | 0.284628i | −0.0212939 | − | 0.0122941i | ||||
\(537\) | −23.8726 | − | 3.04087i | −1.03018 | − | 0.131223i | ||||
\(538\) | 31.0923 | 1.34049 | ||||||||
\(539\) | 9.90033 | + | 6.44063i | 0.426438 | + | 0.277418i | ||||
\(540\) | 37.0888 | − | 29.2096i | 1.59605 | − | 1.25698i | ||||
\(541\) | −32.4487 | − | 18.7343i | −1.39508 | − | 0.805449i | −0.401207 | − | 0.915988i | \(-0.631409\pi\) |
−0.993872 | + | 0.110539i | \(0.964742\pi\) | |||||||
\(542\) | −42.7965 | −1.83827 | ||||||||
\(543\) | −1.40796 | − | 3.35911i | −0.0604213 | − | 0.144153i | ||||
\(544\) | −19.7400 | −0.846347 | ||||||||
\(545\) | −14.3592 | −0.615079 | ||||||||
\(546\) | 21.8789 | − | 27.6837i | 0.936331 | − | 1.18475i | ||||
\(547\) | −21.5999 | −0.923543 | −0.461771 | − | 0.886999i | \(-0.652786\pi\) | ||||
−0.461771 | + | 0.886999i | \(0.652786\pi\) | |||||||
\(548\) | −51.1588 | −2.18539 | ||||||||
\(549\) | 6.80220 | − | 26.2674i | 0.290311 | − | 1.12107i | ||||
\(550\) | −27.3446 | −1.16598 | ||||||||
\(551\) | −12.8562 | − | 7.42252i | −0.547692 | − | 0.316210i | ||||
\(552\) | 6.12038 | + | 14.6020i | 0.260501 | + | 0.621503i | ||||
\(553\) | 18.8161 | − | 4.50937i | 0.800141 | − | 0.191758i | ||||
\(554\) | 5.55095 | 0.235837 | ||||||||
\(555\) | 4.31247 | − | 33.8555i | 0.183054 | − | 1.43709i | ||||
\(556\) | −11.4038 | − | 6.58400i | −0.483630 | − | 0.279224i | ||||
\(557\) | 2.44610 | − | 4.23677i | 0.103645 | − | 0.179518i | −0.809539 | − | 0.587066i | \(-0.800283\pi\) |
0.913184 | + | 0.407548i | \(0.133616\pi\) | |||||||
\(558\) | −65.3507 | − | 16.9232i | −2.76652 | − | 0.716415i | ||||
\(559\) | −1.56055 | − | 1.53558i | −0.0660044 | − | 0.0649480i | ||||
\(560\) | −5.60980 | − | 23.4078i | −0.237057 | − | 0.989161i | ||||
\(561\) | 0.926130 | − | 7.27068i | 0.0391012 | − | 0.306968i | ||||
\(562\) | −20.7777 | −0.876454 | ||||||||
\(563\) | 20.1700 | 0.850063 | 0.425031 | − | 0.905179i | \(-0.360263\pi\) | ||||
0.425031 | + | 0.905179i | \(0.360263\pi\) | |||||||
\(564\) | −9.94815 | − | 1.26718i | −0.418892 | − | 0.0533580i | ||||
\(565\) | 4.07840 | + | 7.06399i | 0.171579 | + | 0.297184i | ||||
\(566\) | 50.2484 | + | 29.0109i | 2.11210 | + | 1.21942i | ||||
\(567\) | −17.0011 | + | 16.6722i | −0.713980 | + | 0.700166i | ||||
\(568\) | 4.60405 | − | 7.97445i | 0.193182 | − | 0.334600i | ||||
\(569\) | − | 4.28392i | − | 0.179591i | −0.995960 | − | 0.0897956i | \(-0.971379\pi\) | ||
0.995960 | − | 0.0897956i | \(-0.0286214\pi\) | |||||||
\(570\) | 16.9129 | + | 40.3508i | 0.708403 | + | 1.69011i | ||||
\(571\) | 17.4508 | + | 30.2256i | 0.730292 | + | 1.26490i | 0.956758 | + | 0.290884i | \(0.0939495\pi\) |
−0.226466 | + | 0.974019i | \(0.572717\pi\) | |||||||
\(572\) | 11.1040 | + | 10.9263i | 0.464281 | + | 0.456851i | ||||
\(573\) | −6.63320 | + | 8.72021i | −0.277106 | + | 0.364292i | ||||
\(574\) | −18.1380 | − | 5.38064i | −0.757068 | − | 0.224584i | ||||
\(575\) | −50.1695 | + | 28.9654i | −2.09221 | + | 1.20794i | ||||
\(576\) | −24.5692 | + | 24.9858i | −1.02371 | + | 1.04107i | ||||
\(577\) | 9.56256 | + | 16.5628i | 0.398095 | + | 0.689520i | 0.993491 | − | 0.113912i | \(-0.0363383\pi\) |
−0.595396 | + | 0.803432i | \(0.703005\pi\) | |||||||
\(578\) | 22.8722 | 0.951360 | ||||||||
\(579\) | 17.5610 | + | 2.23690i | 0.729810 | + | 0.0929623i | ||||
\(580\) | −40.4579 | −1.67992 | ||||||||
\(581\) | 30.2620 | − | 28.6945i | 1.25548 | − | 1.19045i | ||||
\(582\) | 3.74464 | − | 29.3977i | 0.155221 | − | 1.21857i | ||||
\(583\) | − | 9.43109i | − | 0.390596i | ||||||
\(584\) | 1.93788 | + | 3.35650i | 0.0801899 | + | 0.138893i | ||||
\(585\) | −0.632189 | − | 38.3729i | −0.0261378 | − | 1.58652i | ||||
\(586\) | −16.6279 | − | 9.60013i | −0.686893 | − | 0.396578i | ||||
\(587\) | 18.1693 | − | 10.4900i | 0.749926 | − | 0.432970i | −0.0757414 | − | 0.997127i | \(-0.524132\pi\) |
0.825667 | + | 0.564158i | \(0.190799\pi\) | |||||||
\(588\) | −10.4632 | − | 29.2308i | −0.431495 | − | 1.20546i | ||||
\(589\) | 17.5633 | − | 30.4206i | 0.723684 | − | 1.25346i | ||||
\(590\) | 21.6992 | − | 37.5842i | 0.893343 | − | 1.54732i | ||||
\(591\) | 12.0094 | + | 9.13521i | 0.494001 | + | 0.375772i | ||||
\(592\) | 14.2403i | 0.585275i | ||||||||
\(593\) | 23.4759 | + | 13.5538i | 0.964038 | + | 0.556588i | 0.897413 | − | 0.441191i | \(-0.145444\pi\) |
0.0666245 | + | 0.997778i | \(0.478777\pi\) | |||||||
\(594\) | −11.5845 | − | 14.7094i | −0.475317 | − | 0.603533i | ||||
\(595\) | −5.48685 | − | 22.8948i | −0.224939 | − | 0.938594i | ||||
\(596\) | 23.3928 | + | 40.5176i | 0.958208 | + | 1.65967i | ||||
\(597\) | −12.6466 | − | 30.1723i | −0.517592 | − | 1.23487i | ||||
\(598\) | 56.8979 | + | 14.7548i | 2.32673 | + | 0.603371i | ||||
\(599\) | −35.9228 | + | 20.7401i | −1.46777 | + | 0.847416i | −0.999349 | − | 0.0360905i | \(-0.988510\pi\) |
−0.468419 | + | 0.883506i | \(0.655176\pi\) | |||||||
\(600\) | 12.5270 | + | 9.52892i | 0.511413 | + | 0.389017i | ||||
\(601\) | −0.652926 | + | 0.376967i | −0.0266334 | + | 0.0153768i | −0.513258 | − | 0.858235i | \(-0.671561\pi\) |
0.486624 | + | 0.873611i | \(0.338228\pi\) | |||||||
\(602\) | −3.33646 | + | 0.799599i | −0.135984 | + | 0.0325892i | ||||
\(603\) | 1.37442 | − | 0.380688i | 0.0559709 | − | 0.0155028i | ||||
\(604\) | −6.93697 | + | 4.00506i | −0.282261 | + | 0.162964i | ||||
\(605\) | − | 28.9277i | − | 1.17608i | ||||||
\(606\) | 1.96948 | − | 15.4616i | 0.0800046 | − | 0.628085i | ||||
\(607\) | 7.80610 | − | 4.50685i | 0.316840 | − | 0.182928i | −0.333143 | − | 0.942876i | \(-0.608109\pi\) |
0.649983 | + | 0.759949i | \(0.274776\pi\) | |||||||
\(608\) | −13.1197 | − | 22.7240i | −0.532074 | − | 0.921580i | ||||
\(609\) | 20.2861 | − | 2.21018i | 0.822036 | − | 0.0895612i | ||||
\(610\) | 68.5327 | 2.77481 | ||||||||
\(611\) | −5.71795 | + | 5.81096i | −0.231324 | + | 0.235086i | ||||
\(612\) | −13.5085 | + | 13.7376i | −0.546050 | + | 0.555309i | ||||
\(613\) | 33.6925 | + | 19.4524i | 1.36083 | + | 0.785675i | 0.989734 | − | 0.142920i | \(-0.0456493\pi\) |
0.371094 | + | 0.928595i | \(0.378983\pi\) | |||||||
\(614\) | 1.70595 | 0.0688464 | ||||||||
\(615\) | −18.9778 | + | 7.95448i | −0.765259 | + | 0.320756i | ||||
\(616\) | 5.19835 | − | 1.24581i | 0.209448 | − | 0.0501952i | ||||
\(617\) | −19.1554 | + | 33.1781i | −0.771166 | + | 1.33570i | 0.165758 | + | 0.986166i | \(0.446993\pi\) |
−0.936924 | + | 0.349533i | \(0.886340\pi\) | |||||||
\(618\) | −3.22922 | − | 0.411335i | −0.129898 | − | 0.0165463i | ||||
\(619\) | −11.9878 | − | 20.7635i | −0.481832 | − | 0.834557i | 0.517951 | − | 0.855410i | \(-0.326695\pi\) |
−0.999783 | + | 0.0208535i | \(0.993362\pi\) | |||||||
\(620\) | − | 95.7324i | − | 3.84470i | ||||||
\(621\) | −36.8354 | − | 14.7164i | −1.47816 | − | 0.590547i | ||||
\(622\) | 23.8399 | + | 41.2919i | 0.955893 | + | 1.65566i | ||||
\(623\) | 9.74948 | − | 9.24449i | 0.390605 | − | 0.370373i | ||||
\(624\) | 2.28479 | + | 15.8494i | 0.0914649 | + | 0.634485i | ||||
\(625\) | 2.67746 | − | 4.63750i | 0.107098 | − | 0.185500i | ||||
\(626\) | −56.9512 | − | 32.8808i | −2.27623 | − | 1.31418i | ||||
\(627\) | 8.98527 | − | 3.76615i | 0.358837 | − | 0.150405i | ||||
\(628\) | −0.817496 | + | 0.471982i | −0.0326216 | + | 0.0188341i | ||||
\(629\) | 13.9282i | 0.555355i | ||||||||
\(630\) | −51.5294 | − | 31.0125i | −2.05298 | − | 1.23557i | ||||
\(631\) | −9.65365 | − | 5.57354i | −0.384306 | − | 0.221879i | 0.295384 | − | 0.955379i | \(-0.404552\pi\) |
−0.679690 | + | 0.733500i | \(0.737886\pi\) | |||||||
\(632\) | 4.37858 | − | 7.58393i | 0.174171 | − | 0.301672i | ||||
\(633\) | −5.35057 | − | 4.07002i | −0.212666 | − | 0.161769i | ||||
\(634\) | −1.51219 | + | 2.61920i | −0.0600569 | + | 0.104022i | ||||
\(635\) | − | 42.3275i | − | 1.67972i | ||||||
\(636\) | −15.0091 | + | 19.7314i | −0.595149 | + | 0.782401i | ||||
\(637\) | −24.0596 | − | 7.62463i | −0.953277 | − | 0.302099i | ||||
\(638\) | 16.0456i | 0.635250i | ||||||||
\(639\) | 6.15789 | + | 22.2323i | 0.243602 | + | 0.879494i | ||||
\(640\) | −28.2785 | − | 16.3266i | −1.11780 | − | 0.645365i | ||||
\(641\) | 43.7290i | 1.72719i | 0.504186 | + | 0.863595i | \(0.331792\pi\) | ||||
−0.504186 | + | 0.863595i | \(0.668208\pi\) | |||||||
\(642\) | 7.32977 | + | 17.4874i | 0.289283 | + | 0.690171i | ||||
\(643\) | 0.926927 | − | 1.60548i | 0.0365544 | − | 0.0633141i | −0.847169 | − | 0.531323i | \(-0.821695\pi\) |
0.883724 | + | 0.468009i | \(0.155028\pi\) | |||||||
\(644\) | 37.5299 | − | 35.5860i | 1.47889 | − | 1.40229i | ||||
\(645\) | −2.25921 | + | 2.97002i | −0.0889562 | + | 0.116944i | ||||
\(646\) | −8.92768 | − | 15.4632i | −0.351255 | − | 0.608391i | ||||
\(647\) | −4.91645 | + | 8.51554i | −0.193285 | + | 0.334780i | −0.946337 | − | 0.323181i | \(-0.895248\pi\) |
0.753052 | + | 0.657961i | \(0.228581\pi\) | |||||||
\(648\) | 0.181186 | + | 10.7755i | 0.00711765 | + | 0.423302i | ||||
\(649\) | −8.36921 | − | 4.83196i | −0.328520 | − | 0.189671i | ||||
\(650\) | 56.3179 | − | 15.5783i | 2.20897 | − | 0.611032i | ||||
\(651\) | 5.22978 | + | 48.0015i | 0.204971 | + | 1.88133i | ||||
\(652\) | −25.3606 | + | 14.6419i | −0.993197 | + | 0.573423i | ||||
\(653\) | 7.17275i | 0.280691i | 0.990103 | + | 0.140346i | \(0.0448214\pi\) | ||||
−0.990103 | + | 0.140346i | \(0.955179\pi\) | |||||||
\(654\) | 9.06302 | − | 11.9145i | 0.354392 | − | 0.465895i | ||||
\(655\) | 27.2700 | − | 15.7443i | 1.06553 | − | 0.615181i | ||||
\(656\) | 7.43564 | − | 4.29297i | 0.290313 | − | 0.167612i | ||||
\(657\) | −9.39996 | − | 2.43421i | −0.366728 | − | 0.0949675i | ||||
\(658\) | 2.97743 | + | 12.4238i | 0.116072 | + | 0.484330i | ||||
\(659\) | 25.1600 | + | 14.5261i | 0.980094 | + | 0.565858i | 0.902299 | − | 0.431112i | \(-0.141878\pi\) |
0.0777958 | + | 0.996969i | \(0.475212\pi\) | |||||||
\(660\) | 16.0752 | − | 21.1329i | 0.625727 | − | 0.822599i | ||||
\(661\) | −2.31494 | + | 4.00959i | −0.0900407 | + | 0.155955i | −0.907528 | − | 0.419991i | \(-0.862033\pi\) |
0.817487 | + | 0.575947i | \(0.195366\pi\) | |||||||
\(662\) | 21.4339 | − | 12.3748i | 0.833051 | − | 0.480962i | ||||
\(663\) | 2.23471 | + | 15.5020i | 0.0867891 | + | 0.602050i | ||||
\(664\) | − | 18.8746i | − | 0.732477i | ||||||
\(665\) | 22.7089 | − | 21.5327i | 0.880614 | − | 0.835001i | ||||
\(666\) | 25.3697 | + | 24.9467i | 0.983057 | + | 0.966666i | ||||
\(667\) | 16.9966 | + | 29.4390i | 0.658112 | + | 1.13988i | ||||
\(668\) | 14.4741 | − | 8.35660i | 0.560018 | − | 0.323327i | ||||
\(669\) | −20.9264 | − | 15.9181i | −0.809061 | − | 0.615429i | ||||
\(670\) | 1.80106 | + | 3.11953i | 0.0695810 | + | 0.120518i | ||||
\(671\) | − | 15.2608i | − | 0.589137i | ||||||
\(672\) | 33.0062 | + | 14.5452i | 1.27324 | + | 0.561093i | ||||
\(673\) | −5.59142 | − | 9.68463i | −0.215534 | − | 0.373315i | 0.737904 | − | 0.674906i | \(-0.235816\pi\) |
−0.953438 | + | 0.301591i | \(0.902482\pi\) | |||||||
\(674\) | −77.5902 | −2.98866 | ||||||||
\(675\) | −39.0268 | + | 5.63948i | −1.50214 | + | 0.217064i | ||||
\(676\) | −29.0941 | − | 16.1774i | −1.11900 | − | 0.622206i | ||||
\(677\) | 19.5293 | − | 33.8258i | 0.750574 | − | 1.30003i | −0.196971 | − | 0.980409i | \(-0.563111\pi\) |
0.947545 | − | 0.319623i | \(-0.103556\pi\) | |||||||
\(678\) | −8.43550 | − | 1.07450i | −0.323963 | − | 0.0412660i | ||||
\(679\) | −20.6136 | + | 4.94016i | −0.791078 | + | 0.189586i | ||||
\(680\) | −9.22786 | − | 5.32771i | −0.353872 | − | 0.204308i | ||||
\(681\) | 15.1231 | + | 36.0806i | 0.579518 | + | 1.38261i | ||||
\(682\) | −37.9673 | −1.45384 | ||||||||
\(683\) | −13.3992 | −0.512706 | −0.256353 | − | 0.966583i | \(-0.582521\pi\) | ||||
−0.256353 | + | 0.966583i | \(0.582521\pi\) | |||||||
\(684\) | −24.7923 | − | 6.42020i | −0.947958 | − | 0.245482i | ||||
\(685\) | 61.3876 | + | 35.4421i | 2.34550 | + | 1.35417i | ||||
\(686\) | −30.1061 | + | 25.6505i | −1.14946 | + | 0.979341i | ||||
\(687\) | 5.42363 | − | 42.5788i | 0.206925 | − | 1.62448i | ||||
\(688\) | 0.778511 | − | 1.34842i | 0.0296804 | − | 0.0514080i | ||||
\(689\) | 5.37293 | + | 19.4239i | 0.204692 | + | 0.739992i | ||||
\(690\) | 12.6593 | − | 99.3833i | 0.481932 | − | 3.78346i | ||||
\(691\) | −37.8925 | −1.44150 | −0.720749 | − | 0.693196i | \(-0.756202\pi\) | ||||
−0.720749 | + | 0.693196i | \(0.756202\pi\) | |||||||
\(692\) | −13.5090 | − | 23.3983i | −0.513536 | − | 0.889471i | ||||
\(693\) | −6.90584 | + | 11.4745i | −0.262331 | + | 0.435881i | ||||
\(694\) | − | 35.4510i | − | 1.34570i | ||||||
\(695\) | 9.12262 | + | 15.8008i | 0.346041 | + | 0.599360i | ||||
\(696\) | 5.59149 | − | 7.35074i | 0.211945 | − | 0.278629i | ||||
\(697\) | 7.27266 | − | 4.19887i | 0.275472 | − | 0.159044i | ||||
\(698\) | −22.6190 | − | 39.1772i | −0.856140 | − | 1.48288i | ||||
\(699\) | 6.11828 | + | 0.779339i | 0.231415 | + | 0.0294773i | ||||
\(700\) | 14.6220 | − | 49.2906i | 0.552660 | − | 1.86301i | ||||
\(701\) | 3.58407i | 0.135369i | 0.997707 | + | 0.0676843i | \(0.0215611\pi\) | ||||
−0.997707 | + | 0.0676843i | \(0.978439\pi\) | |||||||
\(702\) | 32.2390 | + | 23.6951i | 1.21678 | + | 0.894315i | ||||
\(703\) | −16.0337 | + | 9.25704i | −0.604721 | + | 0.349136i | ||||
\(704\) | −9.85422 | + | 17.0680i | −0.371395 | + | 0.643275i | ||||
\(705\) | 11.0593 | + | 8.41250i | 0.416518 | + | 0.316833i | ||||
\(706\) | −17.8543 | − | 10.3082i | −0.671955 | − | 0.387954i | ||||
\(707\) | −10.8416 | + | 2.59825i | −0.407742 | + | 0.0977174i | ||||
\(708\) | 9.81995 | + | 23.4284i | 0.369056 | + | 0.880495i | ||||
\(709\) | 31.3283 | − | 18.0874i | 1.17656 | − | 0.679286i | 0.221343 | − | 0.975196i | \(-0.428956\pi\) |
0.955216 | + | 0.295910i | \(0.0956227\pi\) | |||||||
\(710\) | −50.4604 | + | 29.1333i | −1.89375 | + | 1.09335i | ||||
\(711\) | 5.85633 | + | 21.1435i | 0.219629 | + | 0.792944i | ||||
\(712\) | − | 6.08082i | − | 0.227888i | ||||||
\(713\) | −69.6592 | + | 40.2178i | −2.60876 | + | 1.50617i | ||||
\(714\) | 22.4600 | + | 9.89769i | 0.840546 | + | 0.370412i | ||||
\(715\) | −5.75458 | − | 20.8036i | −0.215209 | − | 0.778011i | ||||
\(716\) | 30.8125 | + | 17.7896i | 1.15152 | + | 0.664828i | ||||
\(717\) | 5.12237 | − | 2.14702i | 0.191298 | − | 0.0801821i | ||||
\(718\) | 36.0078 | − | 62.3674i | 1.34380 | − | 2.32753i | ||||
\(719\) | −1.40930 | − | 2.44099i | −0.0525582 | − | 0.0910334i | 0.838549 | − | 0.544826i | \(-0.183404\pi\) |
−0.891108 | + | 0.453792i | \(0.850071\pi\) | |||||||
\(720\) | 26.3032 | − | 7.28546i | 0.980263 | − | 0.271513i | ||||
\(721\) | 0.542657 | + | 2.26432i | 0.0202096 | + | 0.0843278i | ||||
\(722\) | −8.42092 | + | 14.5855i | −0.313394 | + | 0.542815i | ||||
\(723\) | 35.9312 | − | 15.0604i | 1.33630 | − | 0.560104i | ||||
\(724\) | 5.38480i | 0.200124i | ||||||||
\(725\) | 29.2652 | + | 16.8963i | 1.08688 | + | 0.627512i | ||||
\(726\) | 24.0027 | + | 18.2582i | 0.890825 | + | 0.677624i | ||||
\(727\) | 10.8299i | 0.401657i | 0.979626 | + | 0.200829i | \(0.0643635\pi\) | ||||
−0.979626 | + | 0.200829i | \(0.935637\pi\) | |||||||
\(728\) | −9.99658 | + | 5.52735i | −0.370498 | + | 0.204857i | ||||
\(729\) | −19.5672 | − | 18.6044i | −0.724713 | − | 0.689051i | ||||
\(730\) | − | 24.5249i | − | 0.907706i | ||||||
\(731\) | 0.761447 | − | 1.31887i | 0.0281631 | − | 0.0487800i | ||||
\(732\) | −24.2868 | + | 31.9281i | −0.897666 | + | 1.18010i | ||||
\(733\) | 1.85550 | − | 3.21383i | 0.0685346 | − | 0.118705i | −0.829722 | − | 0.558177i | \(-0.811501\pi\) |
0.898256 | + | 0.439472i | \(0.144834\pi\) | |||||||
\(734\) | −59.7235 | − | 34.4814i | −2.20444 | − | 1.27273i | ||||
\(735\) | −7.69545 | + | 42.3240i | −0.283851 | + | 1.56114i | ||||
\(736\) | 60.0849i | 2.21476i | ||||||||
\(737\) | 0.694653 | − | 0.401058i | 0.0255879 | − | 0.0147732i | ||||
\(738\) | 5.37792 | − | 20.7674i | 0.197964 | − | 0.764460i | ||||
\(739\) | 16.4242 | + | 9.48254i | 0.604176 | + | 0.348821i | 0.770683 | − | 0.637219i | \(-0.219915\pi\) |
−0.166507 | + | 0.986040i | \(0.553249\pi\) | |||||||
\(740\) | −25.2287 | + | 43.6974i | −0.927425 | + | 1.60635i | ||||
\(741\) | −16.3601 | + | 12.8756i | −0.601005 | + | 0.472996i | ||||
\(742\) | 30.2779 | + | 8.98192i | 1.11154 | + | 0.329737i | ||||
\(743\) | −6.65239 | − | 11.5223i | −0.244053 | − | 0.422711i | 0.717812 | − | 0.696237i | \(-0.245144\pi\) |
−0.961865 | + | 0.273525i | \(0.911810\pi\) | |||||||
\(744\) | 17.3935 | + | 13.2307i | 0.637675 | + | 0.485060i | ||||
\(745\) | − | 64.8251i | − | 2.37501i | ||||||
\(746\) | 11.3142 | + | 19.5968i | 0.414243 | + | 0.717489i | ||||
\(747\) | 33.7169 | + | 33.1548i | 1.23364 | + | 1.21307i | ||||
\(748\) | −5.41802 | + | 9.38428i | −0.198102 | + | 0.343123i | ||||
\(749\) | 9.84167 | − | 9.33191i | 0.359607 | − | 0.340981i | ||||
\(750\) | −13.1333 | − | 31.3334i | −0.479560 | − | 1.14413i | ||||
\(751\) | −9.05463 | −0.330408 | −0.165204 | − | 0.986259i | \(-0.552828\pi\) | ||||
−0.165204 | + | 0.986259i | \(0.552828\pi\) | |||||||
\(752\) | −5.02104 | − | 2.89890i | −0.183099 | − | 0.105712i | ||||
\(753\) | −0.660458 | + | 5.18500i | −0.0240684 | + | 0.188952i | ||||
\(754\) | −9.14123 | − | 33.0469i | −0.332904 | − | 1.20350i | ||||
\(755\) | 11.0986 | 0.403920 | ||||||||
\(756\) | 32.7093 | − | 13.0163i | 1.18962 | − | 0.473398i | ||||
\(757\) | −6.56272 | − | 11.3670i | −0.238526 | − | 0.413139i | 0.721766 | − | 0.692138i | \(-0.243331\pi\) |
−0.960292 | + | 0.278998i | \(0.909998\pi\) | |||||||
\(758\) | 47.6898 | − | 27.5337i | 1.73217 | − | 1.00007i | ||||
\(759\) | −22.1306 | − | 2.81896i | −0.803289 | − | 0.102322i | ||||
\(760\) | − | 14.1637i | − | 0.513772i | ||||||
\(761\) | −3.04726 | + | 1.75934i | −0.110463 | + | 0.0637760i | −0.554214 | − | 0.832374i | \(-0.686981\pi\) |
0.443751 | + | 0.896150i | \(0.353648\pi\) | |||||||
\(762\) | 35.1213 | + | 26.7157i | 1.27231 | + | 0.967808i | ||||
\(763\) | −10.2653 | − | 3.04520i | −0.371630 | − | 0.110244i | ||||
\(764\) | 14.0280 | − | 8.09908i | 0.507516 | − | 0.293014i | ||||
\(765\) | 25.7267 | − | 7.12578i | 0.930151 | − | 0.257633i | ||||
\(766\) | 54.1395 | − | 31.2574i | 1.95614 | − | 1.12938i | ||||
\(767\) | 19.9897 | + | 5.18376i | 0.721786 | + | 0.187175i | ||||
\(768\) | −5.92196 | + | 2.48217i | −0.213690 | + | 0.0895675i | ||||
\(769\) | −13.7311 | − | 23.7829i | −0.495155 | − | 0.857634i | 0.504829 | − | 0.863219i | \(-0.331555\pi\) |
−0.999984 | + | 0.00558526i | \(0.998222\pi\) | |||||||
\(770\) | −32.4286 | − | 9.61992i | −1.16865 | − | 0.346678i | ||||
\(771\) | −2.91143 | + | 1.22032i | −0.104853 | + | 0.0439486i | ||||
\(772\) | −22.6660 | − | 13.0862i | −0.815768 | − | 0.470984i | ||||
\(773\) | 22.3381i | 0.803445i | 0.915762 | + | 0.401722i | \(0.131588\pi\) | ||||
−0.915762 | + | 0.401722i | \(0.868412\pi\) | |||||||
\(774\) | −1.03844 | − | 3.74916i | −0.0373260 | − | 0.134761i | ||||
\(775\) | −39.9803 | + | 69.2479i | −1.43613 | + | 2.48746i | ||||
\(776\) | −4.79688 | + | 8.30843i | −0.172198 | + | 0.298255i | ||||
\(777\) | 10.2628 | − | 23.2886i | 0.368177 | − | 0.835475i | ||||
\(778\) | −7.09754 | + | 4.09777i | −0.254459 | + | 0.146912i | ||||
\(779\) | 9.66718 | + | 5.58135i | 0.346363 | + | 0.199973i | ||||
\(780\) | −21.0684 | + | 52.6827i | −0.754369 | + | 1.88634i | ||||
\(781\) | 6.48739 | + | 11.2365i | 0.232137 | + | 0.402073i | ||||
\(782\) | 40.8865i | 1.46210i | ||||||||
\(783\) | 3.30920 | + | 22.9006i | 0.118261 | + | 0.818400i | ||||
\(784\) | 0.953750 | − | 17.9239i | 0.0340625 | − | 0.640138i | ||||
\(785\) | 1.30793 | 0.0466821 | ||||||||
\(786\) | −4.14803 | + | 32.5645i | −0.147955 | + | 1.16154i | ||||
\(787\) | 22.9241 | 0.817155 | 0.408577 | − | 0.912724i | \(-0.366025\pi\) | ||||
0.408577 | + | 0.912724i | \(0.366025\pi\) | |||||||
\(788\) | −11.1540 | − | 19.3193i | −0.397345 | − | 0.688222i | ||||
\(789\) | −26.1674 | − | 3.33317i | −0.931584 | − | 0.118664i | ||||
\(790\) | −47.9893 | + | 27.7066i | −1.70738 | + | 0.985758i | ||||
\(791\) | 1.41755 | + | 5.91495i | 0.0504022 | + | 0.210311i | ||||
\(792\) | 1.61794 | + | 5.84135i | 0.0574909 | + | 0.207564i | ||||
\(793\) | 8.69415 | + | 31.4306i | 0.308738 | + | 1.11613i | ||||
\(794\) | 10.8810 | + | 18.8464i | 0.386152 | + | 0.668835i | ||||
\(795\) | 31.6797 | − | 13.2784i | 1.12356 | − | 0.470938i | ||||
\(796\) | 48.3675i | 1.71434i | ||||||||
\(797\) | −4.93237 | + | 8.54311i | −0.174713 | + | 0.302612i | −0.940062 | − | 0.341003i | \(-0.889233\pi\) |
0.765349 | + | 0.643616i | \(0.222567\pi\) | |||||||
\(798\) | 3.53364 | + | 32.4334i | 0.125089 | + | 1.14813i | ||||
\(799\) | −4.91099 | − | 2.83536i | −0.173738 | − | 0.100308i | ||||
\(800\) | 29.8651 | + | 51.7278i | 1.05589 | + | 1.82885i | ||||
\(801\) | 10.8626 | + | 10.6814i | 0.383809 | + | 0.377410i | ||||
\(802\) | −46.2159 | −1.63194 | ||||||||
\(803\) | −5.46117 | −0.192721 | ||||||||
\(804\) | −2.09159 | − | 0.266424i | −0.0737648 | − | 0.00939607i | ||||
\(805\) | −69.6873 | + | 16.7009i | −2.45615 | + | 0.588630i | ||||
\(806\) | 78.1961 | − | 21.6302i | 2.75434 | − | 0.761890i | ||||
\(807\) | 23.2569 | − | 9.74807i | 0.818683 | − | 0.343148i | ||||
\(808\) | −2.52290 | + | 4.36978i | −0.0887551 | + | 0.153728i | ||||
\(809\) | 11.5112 | + | 6.64600i | 0.404712 | + | 0.233661i | 0.688515 | − | 0.725222i | \(-0.258263\pi\) |
−0.283803 | + | 0.958883i | \(0.591596\pi\) | |||||||
\(810\) | 33.0996 | − | 59.6231i | 1.16300 | − | 2.09494i | ||||
\(811\) | −55.7173 | −1.95650 | −0.978249 | − | 0.207434i | \(-0.933489\pi\) | ||||
−0.978249 | + | 0.207434i | \(0.933489\pi\) | |||||||
\(812\) | −28.9233 | − | 8.58007i | −1.01501 | − | 0.301101i | ||||
\(813\) | −32.0116 | + | 13.4175i | −1.12270 | + | 0.470574i | ||||
\(814\) | 17.3303 | + | 10.0057i | 0.607427 | + | 0.350698i | ||||
\(815\) | 40.5750 | 1.42128 | ||||||||
\(816\) | −10.2727 | + | 4.30578i | −0.359618 | + | 0.150733i | ||||
\(817\) | 2.02431 | 0.0708215 | ||||||||
\(818\) | 43.6875 | 1.52750 | ||||||||
\(819\) | 7.68594 | − | 27.5668i | 0.268568 | − | 0.963261i | ||||
\(820\) | 30.4223 | 1.06239 | ||||||||
\(821\) | −31.0746 | −1.08451 | −0.542255 | − | 0.840214i | \(-0.682429\pi\) | ||||
−0.542255 | + | 0.840214i | \(0.682429\pi\) | |||||||
\(822\) | −68.1539 | + | 28.5665i | −2.37714 | + | 0.996371i | ||||
\(823\) | −49.6805 | −1.73175 | −0.865877 | − | 0.500257i | \(-0.833239\pi\) | ||||
−0.865877 | + | 0.500257i | \(0.833239\pi\) | |||||||
\(824\) | 0.912649 | + | 0.526918i | 0.0317936 | + | 0.0183561i | ||||
\(825\) | −20.4536 | + | 8.57307i | −0.712104 | + | 0.298476i | ||||
\(826\) | 23.4833 | − | 22.2670i | 0.817090 | − | 0.774767i | ||||
\(827\) | −12.5355 | −0.435902 | −0.217951 | − | 0.975960i | \(-0.569937\pi\) | ||||
−0.217951 | + | 0.975960i | \(0.569937\pi\) | |||||||
\(828\) | 41.8146 | + | 41.1174i | 1.45316 | + | 1.42893i | ||||
\(829\) | 38.6735 | + | 22.3281i | 1.34319 | + | 0.775488i | 0.987274 | − | 0.159031i | \(-0.0508371\pi\) |
0.355912 | + | 0.934520i | \(0.384170\pi\) | |||||||
\(830\) | −59.7171 | + | 103.433i | −2.07281 | + | 3.59021i | ||||
\(831\) | 4.15209 | − | 1.74033i | 0.144034 | − | 0.0603715i | ||||
\(832\) | 10.5717 | − | 40.7666i | 0.366507 | − | 1.41333i | ||||
\(833\) | 0.932846 | − | 17.5310i | 0.0323212 | − | 0.607414i | ||||
\(834\) | −18.8686 | − | 2.40346i | −0.653368 | − | 0.0832252i | ||||
\(835\) | −23.1574 | −0.801395 | ||||||||
\(836\) | −14.4038 | −0.498165 | ||||||||
\(837\) | −54.1878 | + | 7.83029i | −1.87300 | + | 0.270654i | ||||
\(838\) | 24.3128 | + | 42.1109i | 0.839870 | + | 1.45470i | ||||
\(839\) | 28.8735 | + | 16.6701i | 0.996824 | + | 0.575517i | 0.907307 | − | 0.420469i | \(-0.138134\pi\) |
0.0895168 | + | 0.995985i | \(0.471468\pi\) | |||||||
\(840\) | 11.5038 | + | 15.7076i | 0.396918 | + | 0.541964i | ||||
\(841\) | −4.58542 | + | 7.94218i | −0.158118 | + | 0.273868i | ||||
\(842\) | − | 70.1126i | − | 2.41624i | ||||||
\(843\) | −15.5416 | + | 6.51422i | −0.535282 | + | 0.224362i | ||||
\(844\) | 4.96945 | + | 8.60735i | 0.171056 | + | 0.296277i | ||||
\(845\) | 23.7038 | + | 39.5680i | 0.815436 | + | 1.36118i | ||||
\(846\) | −13.9605 | + | 3.86679i | −0.479973 | + | 0.132943i | ||||
\(847\) | 6.13480 | − | 20.6803i | 0.210794 | − | 0.710584i | ||||
\(848\) | −12.4123 | + | 7.16627i | −0.426241 | + | 0.246091i | ||||
\(849\) | 46.6811 | + | 5.94617i | 1.60209 | + | 0.204072i | ||||
\(850\) | 20.3225 | + | 35.1997i | 0.697057 | + | 1.20734i | ||||
\(851\) | 42.3949 | 1.45328 | ||||||||
\(852\) | 4.30960 | − | 33.8329i | 0.147644 | − | 1.15910i | ||||
\(853\) | 35.6443 | 1.22044 | 0.610219 | − | 0.792233i | \(-0.291082\pi\) | ||||
0.610219 | + | 0.792233i | \(0.291082\pi\) | |||||||
\(854\) | 48.9939 | + | 14.5340i | 1.67654 | + | 0.497343i | ||||
\(855\) | 25.3015 | + | 24.8797i | 0.865294 | + | 0.850867i | ||||
\(856\) | − | 6.13832i | − | 0.209803i | ||||||
\(857\) | −2.17917 | − | 3.77444i | −0.0744391 | − | 0.128932i | 0.826403 | − | 0.563079i | \(-0.190383\pi\) |
−0.900842 | + | 0.434147i | \(0.857050\pi\) | |||||||
\(858\) | 20.8939 | + | 8.35569i | 0.713306 | + | 0.285258i | ||||
\(859\) | 17.9240 | + | 10.3484i | 0.611557 | + | 0.353083i | 0.773575 | − | 0.633705i | \(-0.218467\pi\) |
−0.162017 | + | 0.986788i | \(0.551800\pi\) | |||||||
\(860\) | 4.77781 | − | 2.75847i | 0.162922 | − | 0.0940631i | ||||
\(861\) | −15.2541 | + | 1.66194i | −0.519859 | + | 0.0566389i | ||||
\(862\) | −2.57350 | + | 4.45743i | −0.0876537 | + | 0.151821i | ||||
\(863\) | −1.00841 | + | 1.74661i | −0.0343266 | + | 0.0594555i | −0.882678 | − | 0.469978i | \(-0.844262\pi\) |
0.848352 | + | 0.529433i | \(0.177595\pi\) | |||||||
\(864\) | −15.1735 | + | 37.9796i | −0.516211 | + | 1.29209i | ||||
\(865\) | 37.4355i | 1.27285i | ||||||||
\(866\) | −50.3354 | − | 29.0611i | −1.71046 | − | 0.987537i | ||||
\(867\) | 17.1083 | − | 7.17090i | 0.581029 | − | 0.243536i | ||||
\(868\) | 20.3023 | − | 68.4388i | 0.689106 | − | 2.32296i | ||||
\(869\) | 6.16969 | + | 10.6862i | 0.209292 | + | 0.362505i | ||||
\(870\) | −53.8983 | + | 22.5913i | −1.82732 | + | 0.765916i | ||||
\(871\) | −1.20220 | + | 1.22175i | −0.0407349 | + | 0.0413975i | ||||
\(872\) | −4.19687 | + | 2.42307i | −0.142124 | + | 0.0820553i | ||||
\(873\) | −6.41579 | − | 23.1634i | −0.217142 | − | 0.783962i | ||||
\(874\) | −47.0670 | + | 27.1742i | −1.59207 | + | 0.919180i | ||||
\(875\) | −17.6341 | + | 16.7207i | −0.596140 | + | 0.565262i | ||||
\(876\) | 11.4257 | + | 8.69118i | 0.386038 | + | 0.293648i | ||||
\(877\) | −4.75191 | + | 2.74352i | −0.160461 | + | 0.0926419i | −0.578080 | − | 0.815980i | \(-0.696198\pi\) |
0.417619 | + | 0.908622i | \(0.362865\pi\) | |||||||
\(878\) | 27.1057i | 0.914772i | ||||||||
\(879\) | −15.4474 | − | 1.96767i | −0.521029 | − | 0.0663680i | ||||
\(880\) | 13.2940 | − | 7.67530i | 0.448141 | − | 0.258734i | ||||
\(881\) | −11.5197 | − | 19.9528i | −0.388110 | − | 0.672227i | 0.604085 | − | 0.796920i | \(-0.293539\pi\) |
−0.992195 | + | 0.124693i | \(0.960205\pi\) | |||||||
\(882\) | −30.2613 | − | 33.0988i | −1.01895 | − | 1.11449i | ||||
\(883\) | −35.1333 | −1.18233 | −0.591165 | − | 0.806551i | \(-0.701332\pi\) | ||||
−0.591165 | + | 0.806551i | \(0.701332\pi\) | |||||||
\(884\) | 5.81248 | − | 22.4142i | 0.195495 | − | 0.753870i | ||||
\(885\) | 4.44755 | − | 34.9159i | 0.149503 | − | 1.17369i | ||||
\(886\) | 35.5034 | + | 20.4979i | 1.19276 | + | 0.688640i | ||||
\(887\) | 21.0557 | 0.706980 | 0.353490 | − | 0.935438i | \(-0.384995\pi\) | ||||
0.353490 | + | 0.935438i | \(0.384995\pi\) | |||||||
\(888\) | −4.45257 | − | 10.6229i | −0.149418 | − | 0.356483i | ||||
\(889\) | 8.97655 | − | 30.2598i | 0.301064 | − | 1.01488i | ||||
\(890\) | −19.2390 | + | 33.3229i | −0.644893 | + | 1.11699i | ||||
\(891\) | −13.2768 | − | 7.37058i | −0.444790 | − | 0.246924i | ||||
\(892\) | 19.4358 | + | 33.6639i | 0.650760 | + | 1.12715i | ||||
\(893\) | − | 7.53781i | − | 0.252243i | ||||||
\(894\) | 53.7886 | + | 40.9154i | 1.79896 | + | 1.36842i | ||||
\(895\) | −24.6488 | − | 42.6930i | −0.823919 | − | 1.42707i | ||||
\(896\) | −16.7538 | − | 17.6690i | −0.559704 | − | 0.590278i | ||||
\(897\) | 47.1853 | − | 6.80205i | 1.57547 | − | 0.227114i | ||||
\(898\) | −0.487153 | + | 0.843773i | −0.0162565 | + | 0.0281571i | ||||
\(899\) | 40.6340 | + | 23.4601i | 1.35522 | + | 0.782437i | ||||
\(900\) | 56.4360 | + | 14.6146i | 1.88120 | + | 0.487154i | ||||
\(901\) | −12.1403 | + | 7.00920i | −0.404451 | + | 0.233510i | ||||
\(902\) | − | 12.0654i | − | 0.401735i | ||||||
\(903\) | −2.24496 | + | 1.64414i | −0.0747077 | + | 0.0547136i | ||||
\(904\) | 2.38405 | + | 1.37643i | 0.0792924 | + | 0.0457795i | ||||
\(905\) | 3.73052 | − | 6.46145i | 0.124007 | − | 0.214786i | ||||
\(906\) | −7.00508 | + | 9.20909i | −0.232728 | + | 0.305952i | ||||
\(907\) | 4.87928 | − | 8.45115i | 0.162014 | − | 0.280616i | −0.773577 | − | 0.633702i | \(-0.781534\pi\) |
0.935591 | + | 0.353086i | \(0.114868\pi\) | |||||||
\(908\) | − | 57.8389i | − | 1.91945i | ||||||
\(909\) | −3.37436 | − | 12.1827i | −0.111920 | − | 0.404074i | ||||
\(910\) | 72.2692 | + | 1.33812i | 2.39570 | + | 0.0443582i | ||||
\(911\) | 27.3053i | 0.904664i | 0.891850 | + | 0.452332i | \(0.149408\pi\) | ||||
−0.891850 | + | 0.452332i | \(0.850592\pi\) | |||||||
\(912\) | −11.7842 | − | 8.96387i | −0.390213 | − | 0.296823i | ||||
\(913\) | 23.0324 | + | 13.2977i | 0.762260 | + | 0.440091i | ||||
\(914\) | − | 19.1978i | − | 0.635008i | ||||||
\(915\) | 51.2622 | − | 21.4864i | 1.69468 | − | 0.710318i | ||||
\(916\) | −31.7292 | + | 54.9565i | −1.04836 | + | 1.81581i | ||||
\(917\) | 22.8342 | − | 5.47233i | 0.754051 | − | 0.180712i | ||||
\(918\) | −10.3252 | + | 25.8443i | −0.340783 | + | 0.852989i | ||||
\(919\) | −16.4746 | − | 28.5348i | −0.543446 | − | 0.941275i | −0.998703 | − | 0.0509154i | \(-0.983786\pi\) |
0.455257 | − | 0.890360i | \(-0.349547\pi\) | |||||||
\(920\) | −16.2165 | + | 28.0879i | −0.534643 | + | 0.926030i | ||||
\(921\) | 1.27604 | − | 0.534848i | 0.0420470 | − | 0.0176238i | ||||
\(922\) | −18.6100 | − | 10.7445i | −0.612889 | − | 0.353852i | ||||
\(923\) | −19.7626 | − | 19.4463i | −0.650496 | − | 0.640084i | ||||
\(924\) | 15.9739 | − | 11.6988i | 0.525502 | − | 0.384861i | ||||
\(925\) | 36.4983 | − | 21.0723i | 1.20006 | − | 0.692852i | ||||
\(926\) | 45.6162i | 1.49904i | ||||||||
\(927\) | −2.54441 | + | 0.704749i | −0.0835693 | + | 0.0231470i | ||||
\(928\) | 30.3534 | − | 17.5246i | 0.996400 | − | 0.575272i | ||||
\(929\) | 35.5445 | − | 20.5216i | 1.16618 | − | 0.673293i | 0.213402 | − | 0.976965i | \(-0.431546\pi\) |
0.952777 | + | 0.303671i | \(0.0982124\pi\) | |||||||
\(930\) | −53.4559 | − | 127.535i | −1.75289 | − | 4.18204i | ||||
\(931\) | 20.8011 | − | 10.5777i | 0.681727 | − | 0.346670i | ||||
\(932\) | −7.89687 | − | 4.55926i | −0.258671 | − | 0.149344i | ||||
\(933\) | 30.7780 | + | 23.4119i | 1.00763 | + | 0.766471i | ||||
\(934\) | 16.1837 | − | 28.0310i | 0.529546 | − | 0.917201i | ||||
\(935\) | 13.0026 | − | 7.50707i | 0.425231 | − | 0.245507i | ||||
\(936\) | −6.66009 | − | 11.1089i | −0.217692 | − | 0.363105i | ||||
\(937\) | − | 37.2279i | − | 1.21618i | −0.793867 | − | 0.608092i | \(-0.791935\pi\) | ||
0.793867 | − | 0.608092i | \(-0.208065\pi\) | |||||||
\(938\) | 0.626003 | + | 2.61210i | 0.0204397 | + | 0.0852880i | ||||
\(939\) | −52.9080 | − | 6.73936i | −1.72659 | − | 0.219931i | ||||
\(940\) | −10.2716 | − | 17.7909i | −0.335022 | − | 0.580275i | ||||
\(941\) | −22.9236 | + | 13.2350i | −0.747289 | + | 0.431448i | −0.824714 | − | 0.565551i | \(-0.808664\pi\) |
0.0774244 | + | 0.996998i | \(0.475330\pi\) | |||||||
\(942\) | −0.825522 | + | 1.08526i | −0.0268970 | + | 0.0353596i | ||||
\(943\) | −12.7806 | − | 22.1366i | −0.416193 | − | 0.720867i | ||||
\(944\) | 14.6864i | 0.478001i | ||||||||
\(945\) | −48.2668 | − | 7.04176i | −1.57012 | − | 0.229069i | ||||
\(946\) | −1.09401 | − | 1.89487i | −0.0355692 | − | 0.0616077i | ||||
\(947\) | 12.6629 | 0.411489 | 0.205745 | − | 0.978606i | \(-0.434038\pi\) | ||||
0.205745 | + | 0.978606i | \(0.434038\pi\) | |||||||
\(948\) | 4.09855 | − | 32.1761i | 0.133115 | − | 1.04503i | ||||
\(949\) | 11.2476 | − | 3.11125i | 0.365113 | − | 0.100996i | ||||
\(950\) | −27.0137 | + | 46.7891i | −0.876441 | + | 1.51804i | ||||
\(951\) | −0.309944 | + | 2.43325i | −0.0100506 | + | 0.0789036i | ||||
\(952\) | −5.46711 | − | 5.76575i | −0.177190 | − | 0.186869i | ||||
\(953\) | −49.2658 | − | 28.4436i | −1.59588 | − | 0.921380i | −0.992270 | − | 0.124097i | \(-0.960397\pi\) |
−0.603606 | − | 0.797282i | \(-0.706270\pi\) | |||||||
\(954\) | −8.97738 | + | 34.6672i | −0.290653 | + | 1.12239i | ||||
\(955\) | −22.4438 | −0.726263 | ||||||||
\(956\) | −8.21139 | −0.265575 | ||||||||
\(957\) | 5.03060 | + | 12.0020i | 0.162616 | + | 0.387970i | ||||
\(958\) | −70.8504 | − | 40.9055i | −2.28907 | − | 1.32160i | ||||
\(959\) | 36.3695 | + | 38.3562i | 1.17443 | + | 1.23859i | ||||
\(960\) | −71.2069 | − | 9.07025i | −2.29819 | − | 0.292741i | ||||
\(961\) | −40.0117 | + | 69.3023i | −1.29070 | + | 2.23556i | ||||
\(962\) | −41.3931 | − | 10.7341i | −1.33457 | − | 0.346082i | ||||
\(963\) | 10.9653 | + | 10.7824i | 0.353351 | + | 0.347459i | ||||
\(964\) | −57.5993 | −1.85515 | ||||||||
\(965\) | 18.1320 | + | 31.4055i | 0.583688 | + | 1.01098i | ||||
\(966\) | 30.1267 | − | 68.3641i | 0.969311 | − | 2.19958i | ||||
\(967\) | − | 12.2544i | − | 0.394076i | −0.980396 | − | 0.197038i | \(-0.936868\pi\) | ||
0.980396 | − | 0.197038i | \(-0.0631322\pi\) | |||||||
\(968\) | −4.88145 | − | 8.45493i | −0.156896 | − | 0.271752i | ||||
\(969\) | −11.5259 | − | 8.76740i | −0.370265 | − | 0.281649i | ||||
\(970\) | 52.5738 | − | 30.3535i | 1.68804 | − | 0.974592i | ||||
\(971\) | 6.17935 | + | 10.7029i | 0.198305 | + | 0.343474i | 0.947979 | − | 0.318333i | \(-0.103123\pi\) |
−0.749674 | + | 0.661807i | \(0.769790\pi\) | |||||||
\(972\) | 16.0474 | + | 36.5499i | 0.514721 | + | 1.17234i | ||||
\(973\) | 3.17079 | + | 13.2306i | 0.101651 | + | 0.424155i | ||||
\(974\) | − | 48.4562i | − | 1.55264i | ||||||
\(975\) | 37.2414 | − | 29.3093i | 1.19268 | − | 0.938649i | ||||
\(976\) | −20.0849 | + | 11.5960i | −0.642902 | + | 0.371179i | ||||
\(977\) | −13.4679 | + | 23.3271i | −0.430876 | + | 0.746300i | −0.996949 | − | 0.0780555i | \(-0.975129\pi\) |
0.566073 | + | 0.824355i | \(0.308462\pi\) | |||||||
\(978\) | −25.6096 | + | 33.6671i | −0.818904 | + | 1.07656i | ||||
\(979\) | 7.42032 | + | 4.28412i | 0.237154 | + | 0.136921i | ||||
\(980\) | 34.6812 | − | 53.3108i | 1.10785 | − | 1.70295i | ||||
\(981\) | 3.04366 | − | 11.7534i | 0.0971767 | − | 0.375259i | ||||
\(982\) | −17.8119 | + | 10.2837i | −0.568402 | + | 0.328167i | ||||
\(983\) | −27.8939 | + | 16.1045i | −0.889677 | + | 0.513655i | −0.873837 | − | 0.486219i | \(-0.838376\pi\) |
−0.0158400 | + | 0.999875i | \(0.505042\pi\) | |||||||
\(984\) | −4.20451 | + | 5.52737i | −0.134035 | + | 0.176206i | ||||
\(985\) | 30.9094i | 0.984856i | ||||||||
\(986\) | 20.6549 | − | 11.9251i | 0.657785 | − | 0.379772i | ||||
\(987\) | 6.12221 | + | 8.35946i | 0.194872 | + | 0.266085i | ||||
\(988\) | 29.6655 | − | 8.20590i | 0.943785 | − | 0.261064i | ||||
\(989\) | −4.01438 | − | 2.31770i | −0.127650 | − | 0.0736986i | ||||
\(990\) | 9.61506 | − | 37.1296i | 0.305587 | − | 1.18006i | ||||
\(991\) | 2.45118 | − | 4.24556i | 0.0778642 | − | 0.134865i | −0.824464 | − | 0.565914i | \(-0.808523\pi\) |
0.902328 | + | 0.431050i | \(0.141857\pi\) | |||||||
\(992\) | 41.4669 | + | 71.8228i | 1.31658 | + | 2.28038i | ||||
\(993\) | 12.1527 | − | 15.9763i | 0.385654 | − | 0.506992i | ||||
\(994\) | −42.2524 | + | 10.1260i | −1.34017 | + | 0.321178i | ||||
\(995\) | 33.5084 | − | 58.0383i | 1.06229 | − | 1.83994i | ||||
\(996\) | −27.0249 | − | 64.4759i | −0.856316 | − | 2.04300i | ||||
\(997\) | 22.7660i | 0.721008i | 0.932758 | + | 0.360504i | \(0.117395\pi\) | ||||
−0.932758 | + | 0.360504i | \(0.882605\pi\) | |||||||
\(998\) | 7.31478 | + | 4.22319i | 0.231545 | + | 0.133683i | ||||
\(999\) | 26.7977 | + | 10.7061i | 0.847843 | + | 0.338727i |
(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 | 273.2.br.b.257.5 | yes | 64 | |
3.2 | odd | 2 | inner | 273.2.br.b.257.28 | yes | 64 | |
7.3 | odd | 6 | 273.2.y.b.101.28 | yes | 64 | ||
13.4 | even | 6 | 273.2.y.b.173.5 | yes | 64 | ||
21.17 | even | 6 | 273.2.y.b.101.5 | ✓ | 64 | ||
39.17 | odd | 6 | 273.2.y.b.173.28 | yes | 64 | ||
91.17 | odd | 6 | inner | 273.2.br.b.17.28 | yes | 64 | |
273.17 | even | 6 | inner | 273.2.br.b.17.5 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.y.b.101.5 | ✓ | 64 | 21.17 | even | 6 | ||
273.2.y.b.101.28 | yes | 64 | 7.3 | odd | 6 | ||
273.2.y.b.173.5 | yes | 64 | 13.4 | even | 6 | ||
273.2.y.b.173.28 | yes | 64 | 39.17 | odd | 6 | ||
273.2.br.b.17.5 | yes | 64 | 273.17 | even | 6 | inner | |
273.2.br.b.17.28 | yes | 64 | 91.17 | odd | 6 | inner | |
273.2.br.b.257.5 | yes | 64 | 1.1 | even | 1 | trivial | |
273.2.br.b.257.28 | yes | 64 | 3.2 | odd | 2 | inner |