Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(293,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.w (of order \(4\), 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: | \(4.79102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 293.28 | ||
Character | \(\chi\) | \(=\) | 600.293 |
Dual form | 600.2.w.k.557.28 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.21574 | + | 0.722477i | 0.859659 | + | 0.510868i | ||||
\(3\) | −0.889875 | − | 1.48597i | −0.513770 | − | 0.857928i | ||||
\(4\) | 0.956054 | + | 1.75669i | 0.478027 | + | 0.878345i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.00827553 | − | 2.44948i | −0.00337847 | − | 0.999994i | ||||
\(7\) | −2.09015 | + | 2.09015i | −0.790001 | + | 0.790001i | −0.981494 | − | 0.191493i | \(-0.938667\pi\) |
0.191493 | + | 0.981494i | \(0.438667\pi\) | |||||||
\(8\) | −0.106854 | + | 2.82641i | −0.0377787 | + | 0.999286i | ||||
\(9\) | −1.41624 | + | 2.64467i | −0.472081 | + | 0.881555i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.65514 | 0.800553 | 0.400277 | − | 0.916394i | \(-0.368914\pi\) | ||||
0.400277 | + | 0.916394i | \(0.368914\pi\) | |||||||
\(12\) | 1.75963 | − | 2.98391i | 0.507961 | − | 0.861380i | ||||
\(13\) | −4.21638 | + | 4.21638i | −1.16941 | + | 1.16941i | −0.187065 | + | 0.982347i | \(0.559898\pi\) |
−0.982347 | + | 0.187065i | \(0.940102\pi\) | |||||||
\(14\) | −4.05116 | + | 1.03099i | −1.08272 | + | 0.275545i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.17192 | + | 3.35898i | −0.542981 | + | 0.839745i | ||||
\(17\) | 3.84954 | + | 3.84954i | 0.933651 | + | 0.933651i | 0.997932 | − | 0.0642808i | \(-0.0204753\pi\) |
−0.0642808 | + | 0.997932i | \(0.520475\pi\) | |||||||
\(18\) | −3.63250 | + | 2.19203i | −0.856187 | + | 0.516665i | ||||
\(19\) | 3.15804 | 0.724505 | 0.362252 | − | 0.932080i | \(-0.382008\pi\) | ||||
0.362252 | + | 0.932080i | \(0.382008\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.96588 | + | 1.24594i | 1.08364 | + | 0.271885i | ||||
\(22\) | 3.22796 | + | 1.91827i | 0.688203 | + | 0.408977i | ||||
\(23\) | 1.60962 | − | 1.60962i | 0.335629 | − | 0.335629i | −0.519090 | − | 0.854719i | \(-0.673729\pi\) |
0.854719 | + | 0.519090i | \(0.173729\pi\) | |||||||
\(24\) | 4.29506 | − | 2.35637i | 0.876725 | − | 0.480992i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.17226 | + | 2.07979i | −1.60271 | + | 0.407880i | ||||
\(27\) | 5.19019 | − | 0.248921i | 0.998852 | − | 0.0479048i | ||||
\(28\) | −5.67003 | − | 1.67345i | −1.07154 | − | 0.316252i | ||||
\(29\) | − | 4.35078i | − | 0.807919i | −0.914777 | − | 0.403959i | \(-0.867634\pi\) | ||
0.914777 | − | 0.403959i | \(-0.132366\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.56789 | 0.281602 | 0.140801 | − | 0.990038i | \(-0.455032\pi\) | ||||
0.140801 | + | 0.990038i | \(0.455032\pi\) | |||||||
\(32\) | −5.06728 | + | 2.51449i | −0.895777 | + | 0.444503i | ||||
\(33\) | −2.36274 | − | 3.94546i | −0.411300 | − | 0.686817i | ||||
\(34\) | 1.89884 | + | 7.46125i | 0.325649 | + | 1.27959i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.99986 | + | 0.0405414i | −0.999977 | + | 0.00675690i | ||||
\(37\) | −4.94127 | − | 4.94127i | −0.812339 | − | 0.812339i | 0.172645 | − | 0.984984i | \(-0.444769\pi\) |
−0.984984 | + | 0.172645i | \(0.944769\pi\) | |||||||
\(38\) | 3.83936 | + | 2.28161i | 0.622827 | + | 0.370127i | ||||
\(39\) | 10.0175 | + | 2.51338i | 1.60408 | + | 0.402463i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.6056i | 1.65631i | 0.560500 | + | 0.828154i | \(0.310609\pi\) | ||||
−0.560500 | + | 0.828154i | \(0.689391\pi\) | |||||||
\(42\) | 5.13706 | + | 5.10247i | 0.792666 | + | 0.787328i | ||||
\(43\) | −0.219791 | + | 0.219791i | −0.0335178 | + | 0.0335178i | −0.723667 | − | 0.690149i | \(-0.757545\pi\) |
0.690149 | + | 0.723667i | \(0.257545\pi\) | |||||||
\(44\) | 2.53845 | + | 4.66425i | 0.382686 | + | 0.703162i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.11979 | − | 0.793968i | 0.459989 | − | 0.117064i | ||||
\(47\) | −1.83256 | − | 1.83256i | −0.267306 | − | 0.267306i | 0.560708 | − | 0.828014i | \(-0.310529\pi\) |
−0.828014 | + | 0.560708i | \(0.810529\pi\) | |||||||
\(48\) | 6.92410 | + | 0.238347i | 0.999408 | + | 0.0344024i | ||||
\(49\) | − | 1.73743i | − | 0.248204i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.29471 | − | 9.14594i | 0.321324 | − | 1.28069i | ||||
\(52\) | −11.4380 | − | 3.37579i | −1.58616 | − | 0.468137i | ||||
\(53\) | −4.64119 | − | 4.64119i | −0.637516 | − | 0.637516i | 0.312426 | − | 0.949942i | \(-0.398858\pi\) |
−0.949942 | + | 0.312426i | \(0.898858\pi\) | |||||||
\(54\) | 6.48976 | + | 3.44717i | 0.883145 | + | 0.469100i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.68427 | − | 6.13095i | −0.759592 | − | 0.819283i | ||||
\(57\) | −2.81027 | − | 4.69277i | −0.372229 | − | 0.621573i | ||||
\(58\) | 3.14334 | − | 5.28942i | 0.412740 | − | 0.694535i | ||||
\(59\) | − | 9.93175i | − | 1.29300i | −0.762912 | − | 0.646502i | \(-0.776231\pi\) | ||
0.762912 | − | 0.646502i | \(-0.223769\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.9159i | 1.52568i | 0.646590 | + | 0.762838i | \(0.276195\pi\) | ||||
−0.646590 | + | 0.762838i | \(0.723805\pi\) | |||||||
\(62\) | 1.90615 | + | 1.13277i | 0.242082 | + | 0.143862i | ||||
\(63\) | −2.56758 | − | 8.48790i | −0.323485 | − | 1.06937i | ||||
\(64\) | −7.97716 | − | 0.604028i | −0.997146 | − | 0.0755035i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.0219726 | − | 6.50369i | −0.00270465 | − | 0.800549i | ||||
\(67\) | 8.80906 | + | 8.80906i | 1.07620 | + | 1.07620i | 0.996847 | + | 0.0793517i | \(0.0252850\pi\) |
0.0793517 | + | 0.996847i | \(0.474715\pi\) | |||||||
\(68\) | −3.08208 | + | 10.4428i | −0.373758 | + | 1.26638i | ||||
\(69\) | −3.82422 | − | 0.959493i | −0.460381 | − | 0.115509i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.89837i | − | 0.343973i | −0.985099 | − | 0.171986i | \(-0.944982\pi\) | ||
0.985099 | − | 0.171986i | \(-0.0550185\pi\) | |||||||
\(72\) | −7.32357 | − | 4.28548i | −0.863091 | − | 0.505048i | ||||
\(73\) | 2.29779 | + | 2.29779i | 0.268936 | + | 0.268936i | 0.828671 | − | 0.559736i | \(-0.189097\pi\) |
−0.559736 | + | 0.828671i | \(0.689097\pi\) | |||||||
\(74\) | −2.43735 | − | 9.57725i | −0.283336 | − | 1.11333i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.01926 | + | 5.54770i | 0.346333 | + | 0.636365i | ||||
\(77\) | −5.54962 | + | 5.54962i | −0.632438 | + | 0.632438i | ||||
\(78\) | 10.3628 | + | 10.2930i | 1.17336 | + | 1.16546i | ||||
\(79\) | − | 9.02676i | − | 1.01559i | −0.861478 | − | 0.507795i | \(-0.830461\pi\) | ||
0.861478 | − | 0.507795i | \(-0.169539\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.98851 | − | 7.49098i | −0.554279 | − | 0.832331i | ||||
\(82\) | −7.66227 | + | 12.8936i | −0.846156 | + | 1.42386i | ||||
\(83\) | −9.78801 | − | 9.78801i | −1.07437 | − | 1.07437i | −0.997002 | − | 0.0773719i | \(-0.975347\pi\) |
−0.0773719 | − | 0.997002i | \(-0.524653\pi\) | |||||||
\(84\) | 2.55892 | + | 9.91469i | 0.279201 | + | 1.08178i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.426003 | + | 0.108415i | −0.0459371 | + | 0.0116907i | ||||
\(87\) | −6.46515 | + | 3.87165i | −0.693136 | + | 0.415084i | ||||
\(88\) | −0.283713 | + | 7.50450i | −0.0302439 | + | 0.799982i | ||||
\(89\) | 2.83249 | 0.300243 | 0.150121 | − | 0.988668i | \(-0.452034\pi\) | ||||
0.150121 | + | 0.988668i | \(0.452034\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 17.6257i | − | 1.84768i | ||||||
\(92\) | 4.36649 | + | 1.28872i | 0.455238 | + | 0.134358i | ||||
\(93\) | −1.39523 | − | 2.32985i | −0.144679 | − | 0.241594i | ||||
\(94\) | −0.903936 | − | 3.55190i | −0.0932339 | − | 0.366351i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.24572 | + | 5.29227i | 0.841575 | + | 0.540140i | ||||
\(97\) | 9.26375 | − | 9.26375i | 0.940592 | − | 0.940592i | −0.0577400 | − | 0.998332i | \(-0.518389\pi\) |
0.998332 | + | 0.0577400i | \(0.0183894\pi\) | |||||||
\(98\) | 1.25525 | − | 2.11227i | 0.126800 | − | 0.213371i | ||||
\(99\) | −3.76032 | + | 7.02194i | −0.377926 | + | 0.705732i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.6797 | 1.06267 | 0.531337 | − | 0.847160i | \(-0.321690\pi\) | ||||
0.531337 | + | 0.847160i | \(0.321690\pi\) | |||||||
\(102\) | 9.39750 | − | 9.46122i | 0.930491 | − | 0.936800i | ||||
\(103\) | 10.3368 | + | 10.3368i | 1.01851 | + | 1.01851i | 0.999825 | + | 0.0186893i | \(0.00594934\pi\) |
0.0186893 | + | 0.999825i | \(0.494051\pi\) | |||||||
\(104\) | −11.4667 | − | 12.3677i | −1.12440 | − | 1.21276i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.28933 | − | 8.99563i | −0.222359 | − | 0.873733i | ||||
\(107\) | 3.47289 | − | 3.47289i | 0.335737 | − | 0.335737i | −0.519023 | − | 0.854760i | \(-0.673704\pi\) |
0.854760 | + | 0.519023i | \(0.173704\pi\) | |||||||
\(108\) | 5.39937 | + | 8.87957i | 0.519555 | + | 0.854437i | ||||
\(109\) | −2.67954 | −0.256654 | −0.128327 | − | 0.991732i | \(-0.540961\pi\) | ||||
−0.128327 | + | 0.991732i | \(0.540961\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.94549 | + | 11.7397i | −0.279573 | + | 1.11428i | ||||
\(112\) | −2.48113 | − | 11.5604i | −0.234445 | − | 1.09236i | ||||
\(113\) | 6.11636 | − | 6.11636i | 0.575379 | − | 0.575379i | −0.358248 | − | 0.933627i | \(-0.616626\pi\) |
0.933627 | + | 0.358248i | \(0.116626\pi\) | |||||||
\(114\) | −0.0261345 | − | 7.73555i | −0.00244772 | − | 0.724501i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.64297 | − | 4.15958i | 0.709632 | − | 0.386207i | ||||
\(117\) | −5.17949 | − | 17.1223i | −0.478844 | − | 1.58296i | ||||
\(118\) | 7.17546 | − | 12.0744i | 0.660555 | − | 1.11154i | ||||
\(119\) | −16.0922 | −1.47517 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.95026 | −0.359114 | ||||||||
\(122\) | −8.60897 | + | 14.4867i | −0.779420 | + | 1.31156i | ||||
\(123\) | 15.7596 | − | 9.43762i | 1.42099 | − | 0.850962i | ||||
\(124\) | 1.49899 | + | 2.75430i | 0.134613 | + | 0.247344i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.01079 | − | 12.1741i | 0.268223 | − | 1.08456i | ||||
\(127\) | 11.2254 | − | 11.2254i | 0.996089 | − | 0.996089i | −0.00390306 | − | 0.999992i | \(-0.501242\pi\) |
0.999992 | + | 0.00390306i | \(0.00124239\pi\) | |||||||
\(128\) | −9.26177 | − | 6.49766i | −0.818633 | − | 0.574317i | ||||
\(129\) | 0.522191 | + | 0.131017i | 0.0459763 | + | 0.0115354i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.55577 | −0.572780 | −0.286390 | − | 0.958113i | \(-0.592455\pi\) | ||||
−0.286390 | + | 0.958113i | \(0.592455\pi\) | |||||||
\(132\) | 4.67205 | − | 7.92268i | 0.406650 | − | 0.689581i | ||||
\(133\) | −6.60078 | + | 6.60078i | −0.572360 | + | 0.572360i | ||||
\(134\) | 4.34520 | + | 17.0739i | 0.375368 | + | 1.47496i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.2917 | + | 10.4690i | −0.968257 | + | 0.897712i | ||||
\(137\) | −1.63651 | − | 1.63651i | −0.139817 | − | 0.139817i | 0.633734 | − | 0.773551i | \(-0.281521\pi\) |
−0.773551 | + | 0.633734i | \(0.781521\pi\) | |||||||
\(138\) | −3.95604 | − | 3.92940i | −0.336761 | − | 0.334493i | ||||
\(139\) | −1.03173 | −0.0875104 | −0.0437552 | − | 0.999042i | \(-0.513932\pi\) | ||||
−0.0437552 | + | 0.999042i | \(0.513932\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.09239 | + | 4.35389i | −0.0919956 | + | 0.366663i | ||||
\(142\) | 2.09400 | − | 3.52366i | 0.175725 | − | 0.295699i | ||||
\(143\) | −11.1951 | + | 11.1951i | −0.936177 | + | 0.936177i | ||||
\(144\) | −5.80741 | − | 10.5011i | −0.483951 | − | 0.875095i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.13342 | + | 4.45361i | 0.0938022 | + | 0.368583i | ||||
\(147\) | −2.58178 | + | 1.54610i | −0.212942 | + | 0.127520i | ||||
\(148\) | 3.95616 | − | 13.4044i | 0.325194 | − | 1.10183i | ||||
\(149\) | 3.60278i | 0.295151i | 0.989051 | + | 0.147576i | \(0.0471470\pi\) | ||||
−0.989051 | + | 0.147576i | \(0.952853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.6985 | 1.11476 | 0.557382 | − | 0.830256i | \(-0.311806\pi\) | ||||
0.557382 | + | 0.830256i | \(0.311806\pi\) | |||||||
\(152\) | −0.337451 | + | 8.92592i | −0.0273709 | + | 0.723988i | ||||
\(153\) | −15.6326 | + | 4.72886i | −1.26382 | + | 0.382306i | ||||
\(154\) | −10.7564 | + | 2.73743i | −0.866774 | + | 0.220588i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.16202 | + | 20.0005i | 0.413292 | + | 1.60132i | ||||
\(157\) | −7.26828 | − | 7.26828i | −0.580072 | − | 0.580072i | 0.354851 | − | 0.934923i | \(-0.384532\pi\) |
−0.934923 | + | 0.354851i | \(0.884532\pi\) | |||||||
\(158\) | 6.52163 | − | 10.9742i | 0.518833 | − | 0.873061i | ||||
\(159\) | −2.76661 | + | 11.0268i | −0.219406 | + | 0.874479i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.72868i | 0.530295i | ||||||||
\(162\) | −0.652676 | − | 12.7112i | −0.0512791 | − | 0.998684i | ||||
\(163\) | 9.50622 | − | 9.50622i | 0.744585 | − | 0.744585i | −0.228872 | − | 0.973457i | \(-0.573504\pi\) |
0.973457 | + | 0.228872i | \(0.0735036\pi\) | |||||||
\(164\) | −18.6307 | + | 10.1395i | −1.45481 | + | 0.791760i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.82808 | − | 18.9713i | −0.374732 | − | 1.47246i | ||||
\(167\) | 14.4143 | + | 14.4143i | 1.11541 | + | 1.11541i | 0.992406 | + | 0.123005i | \(0.0392532\pi\) |
0.123005 | + | 0.992406i | \(0.460747\pi\) | |||||||
\(168\) | −4.05215 | + | 13.9025i | −0.312630 | + | 1.07260i | ||||
\(169\) | − | 22.5557i | − | 1.73505i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.47256 | + | 8.35197i | −0.342025 | + | 0.638691i | ||||
\(172\) | −0.596237 | − | 0.175973i | −0.0454626 | − | 0.0134178i | ||||
\(173\) | 18.0907 | + | 18.0907i | 1.37541 | + | 1.37541i | 0.852209 | + | 0.523202i | \(0.175262\pi\) |
0.523202 | + | 0.852209i | \(0.324738\pi\) | |||||||
\(174\) | −10.6571 | + | 0.0360050i | −0.807914 | + | 0.00272953i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.76675 | + | 8.91855i | −0.434685 | + | 0.672261i | ||||
\(177\) | −14.7583 | + | 8.83802i | −1.10930 | + | 0.664307i | ||||
\(178\) | 3.44357 | + | 2.04641i | 0.258107 | + | 0.153385i | ||||
\(179\) | 5.81962i | 0.434979i | 0.976063 | + | 0.217489i | \(0.0697868\pi\) | ||||
−0.976063 | + | 0.217489i | \(0.930213\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.58348i | 0.266358i | 0.991092 | + | 0.133179i | \(0.0425185\pi\) | ||||
−0.991092 | + | 0.133179i | \(0.957481\pi\) | |||||||
\(182\) | 12.7342 | − | 21.4283i | 0.943919 | − | 1.58837i | ||||
\(183\) | 17.7067 | − | 10.6037i | 1.30892 | − | 0.783846i | ||||
\(184\) | 4.37745 | + | 4.72144i | 0.322710 | + | 0.348069i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0129752 | − | 3.84052i | −0.000951384 | − | 0.281601i | ||||
\(187\) | 10.2211 | + | 10.2211i | 0.747437 | + | 0.747437i | ||||
\(188\) | 1.46721 | − | 4.97126i | 0.107008 | − | 0.362567i | ||||
\(189\) | −10.3280 | + | 11.3685i | −0.751250 | + | 0.826939i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.6034i | − | 0.839591i | −0.907619 | − | 0.419796i | \(-0.862102\pi\) | ||
0.907619 | − | 0.419796i | \(-0.137898\pi\) | |||||||
\(192\) | 6.20111 | + | 12.3914i | 0.447527 | + | 0.894271i | ||||
\(193\) | 9.83073 | + | 9.83073i | 0.707632 | + | 0.707632i | 0.966037 | − | 0.258405i | \(-0.0831969\pi\) |
−0.258405 | + | 0.966037i | \(0.583197\pi\) | |||||||
\(194\) | 17.9552 | − | 4.56948i | 1.28911 | − | 0.328069i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.05213 | − | 1.66108i | 0.218009 | − | 0.118648i | ||||
\(197\) | −1.97306 | + | 1.97306i | −0.140574 | + | 0.140574i | −0.773892 | − | 0.633318i | \(-0.781693\pi\) |
0.633318 | + | 0.773892i | \(0.281693\pi\) | |||||||
\(198\) | −9.64477 | + | 5.82012i | −0.685424 | + | 0.413618i | ||||
\(199\) | 4.09303i | 0.290147i | 0.989421 | + | 0.145074i | \(0.0463419\pi\) | ||||
−0.989421 | + | 0.145074i | \(0.953658\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.25108 | − | 20.9290i | 0.370383 | − | 1.47622i | ||||
\(202\) | 12.9838 | + | 7.71587i | 0.913538 | + | 0.542887i | ||||
\(203\) | 9.09376 | + | 9.09376i | 0.638257 | + | 0.638257i | ||||
\(204\) | 18.2604 | − | 4.71291i | 1.27849 | − | 0.329970i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.09877 | + | 20.0350i | 0.355248 | + | 1.39590i | ||||
\(207\) | 1.97729 | + | 6.53652i | 0.137431 | + | 0.454319i | ||||
\(208\) | −5.00509 | − | 23.3204i | −0.347040 | − | 1.61698i | ||||
\(209\) | 8.38503 | 0.580005 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.39432i | 0.371361i | 0.982610 | + | 0.185680i | \(0.0594489\pi\) | ||||
−0.982610 | + | 0.185680i | \(0.940551\pi\) | |||||||
\(212\) | 3.71590 | − | 12.5903i | 0.255209 | − | 0.864709i | ||||
\(213\) | −4.30690 | + | 2.57918i | −0.295104 | + | 0.176723i | ||||
\(214\) | 6.73123 | − | 1.71305i | 0.460137 | − | 0.117102i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.148957 | + | 14.6962i | 0.0101353 | + | 0.999949i | ||||
\(217\) | −3.27713 | + | 3.27713i | −0.222466 | + | 0.222466i | ||||
\(218\) | −3.25763 | − | 1.93591i | −0.220635 | − | 0.131116i | ||||
\(219\) | 1.36971 | − | 5.45920i | 0.0925564 | − | 0.368898i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −32.4622 | −2.18365 | ||||||||
\(222\) | −12.0626 | + | 12.1444i | −0.809590 | + | 0.815079i | ||||
\(223\) | 2.63896 | + | 2.63896i | 0.176718 | + | 0.176718i | 0.789923 | − | 0.613206i | \(-0.210120\pi\) |
−0.613206 | + | 0.789923i | \(0.710120\pi\) | |||||||
\(224\) | 5.33572 | − | 15.8470i | 0.356507 | − | 1.05882i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.8548 | − | 3.01698i | 0.788572 | − | 0.200687i | ||||
\(227\) | −5.62771 | + | 5.62771i | −0.373524 | + | 0.373524i | −0.868759 | − | 0.495235i | \(-0.835082\pi\) |
0.495235 | + | 0.868759i | \(0.335082\pi\) | |||||||
\(228\) | 5.55699 | − | 9.42331i | 0.368020 | − | 0.624074i | ||||
\(229\) | 11.2319 | 0.742225 | 0.371113 | − | 0.928588i | \(-0.378976\pi\) | ||||
0.371113 | + | 0.928588i | \(0.378976\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.1851 | + | 3.30813i | 0.867514 | + | 0.217659i | ||||
\(232\) | 12.2971 | + | 0.464899i | 0.807342 | + | 0.0305221i | ||||
\(233\) | 15.0715 | − | 15.0715i | 0.987366 | − | 0.987366i | −0.0125551 | − | 0.999921i | \(-0.503997\pi\) |
0.999921 | + | 0.0125551i | \(0.00399652\pi\) | |||||||
\(234\) | 6.07357 | − | 24.5584i | 0.397041 | − | 1.60543i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 17.4470 | − | 9.49529i | 1.13570 | − | 0.618091i | ||||
\(237\) | −13.4135 | + | 8.03269i | −0.871303 | + | 0.521780i | ||||
\(238\) | −19.5640 | − | 11.6263i | −1.26814 | − | 0.753618i | ||||
\(239\) | −2.89837 | −0.187480 | −0.0937398 | − | 0.995597i | \(-0.529882\pi\) | ||||
−0.0937398 | + | 0.995597i | \(0.529882\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.551900 | 0.0355510 | 0.0177755 | − | 0.999842i | \(-0.494342\pi\) | ||||
0.0177755 | + | 0.999842i | \(0.494342\pi\) | |||||||
\(242\) | −4.80249 | − | 2.85397i | −0.308716 | − | 0.183460i | ||||
\(243\) | −6.69226 | + | 14.0788i | −0.429308 | + | 0.903158i | ||||
\(244\) | −20.9326 | + | 11.3923i | −1.34007 | + | 0.729314i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 25.9780 | − | 0.0877665i | 1.65630 | − | 0.00559579i | ||||
\(247\) | −13.3155 | + | 13.3155i | −0.847245 | + | 0.847245i | ||||
\(248\) | −0.167536 | + | 4.43151i | −0.0106386 | + | 0.281401i | ||||
\(249\) | −5.83463 | + | 23.2549i | −0.369755 | + | 1.47372i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.29691 | −0.397457 | −0.198729 | − | 0.980055i | \(-0.563681\pi\) | ||||
−0.198729 | + | 0.980055i | \(0.563681\pi\) | |||||||
\(252\) | 12.4559 | − | 12.6253i | 0.784645 | − | 0.795321i | ||||
\(253\) | 4.27376 | − | 4.27376i | 0.268689 | − | 0.268689i | ||||
\(254\) | 21.7572 | − | 5.53707i | 1.36517 | − | 0.347426i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56551 | − | 14.5909i | −0.410344 | − | 0.911931i | ||||
\(257\) | −10.9183 | − | 10.9183i | −0.681066 | − | 0.681066i | 0.279174 | − | 0.960240i | \(-0.409939\pi\) |
−0.960240 | + | 0.279174i | \(0.909939\pi\) | |||||||
\(258\) | 0.540192 | + | 0.536554i | 0.0336309 | + | 0.0334044i | ||||
\(259\) | 20.6559 | 1.28350 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.5063 | + | 6.16176i | 0.712225 | + | 0.381403i | ||||
\(262\) | −7.97012 | − | 4.73639i | −0.492396 | − | 0.292615i | ||||
\(263\) | −21.0955 | + | 21.0955i | −1.30081 | + | 1.30081i | −0.372959 | + | 0.927848i | \(0.621657\pi\) |
−0.927848 | + | 0.372959i | \(0.878343\pi\) | |||||||
\(264\) | 11.4040 | − | 6.25648i | 0.701865 | − | 0.385059i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.7937 | + | 3.25593i | −0.784435 | + | 0.199634i | ||||
\(267\) | −2.52056 | − | 4.20900i | −0.154256 | − | 0.257587i | ||||
\(268\) | −7.05286 | + | 23.8967i | −0.430822 | + | 1.45973i | ||||
\(269\) | 20.6115i | 1.25671i | 0.777929 | + | 0.628353i | \(0.216271\pi\) | ||||
−0.777929 | + | 0.628353i | \(0.783729\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.2931 | −1.47570 | −0.737851 | − | 0.674964i | \(-0.764159\pi\) | ||||
−0.737851 | + | 0.674964i | \(0.764159\pi\) | |||||||
\(272\) | −21.2914 | + | 4.56963i | −1.29098 | + | 0.277075i | ||||
\(273\) | −26.1913 | + | 15.6847i | −1.58517 | + | 0.949280i | ||||
\(274\) | −0.807234 | − | 3.17192i | −0.0487668 | − | 0.191623i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.97062 | − | 7.63529i | −0.118618 | − | 0.459590i | ||||
\(277\) | 12.6491 | + | 12.6491i | 0.760013 | + | 0.760013i | 0.976324 | − | 0.216312i | \(-0.0694027\pi\) |
−0.216312 | + | 0.976324i | \(0.569403\pi\) | |||||||
\(278\) | −1.25432 | − | 0.745403i | −0.0752291 | − | 0.0447063i | ||||
\(279\) | −2.22052 | + | 4.14656i | −0.132939 | + | 0.248248i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.81745i | − | 0.526005i | −0.964795 | − | 0.263002i | \(-0.915287\pi\) | ||
0.964795 | − | 0.263002i | \(-0.0847127\pi\) | |||||||
\(282\) | −4.47364 | + | 4.50397i | −0.266402 | + | 0.268208i | ||||
\(283\) | −13.4928 | + | 13.4928i | −0.802061 | + | 0.802061i | −0.983417 | − | 0.181357i | \(-0.941951\pi\) |
0.181357 | + | 0.983417i | \(0.441951\pi\) | |||||||
\(284\) | 5.09153 | − | 2.77099i | 0.302127 | − | 0.164428i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −21.6985 | + | 5.52212i | −1.28306 | + | 0.326530i | ||||
\(287\) | −22.1672 | − | 22.1672i | −1.30849 | − | 1.30849i | ||||
\(288\) | 0.526525 | − | 16.9624i | 0.0310258 | − | 0.999519i | ||||
\(289\) | 12.6379i | 0.743409i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.0093 | − | 5.52212i | −1.29021 | − | 0.323712i | ||||
\(292\) | −1.83969 | + | 6.23331i | −0.107660 | + | 0.364777i | ||||
\(293\) | −6.84294 | − | 6.84294i | −0.399769 | − | 0.399769i | 0.478383 | − | 0.878151i | \(-0.341223\pi\) |
−0.878151 | + | 0.478383i | \(0.841223\pi\) | |||||||
\(294\) | −4.25579 | + | 0.0143782i | −0.248203 | + | 0.000838551i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 14.4940 | − | 13.4380i | 0.842448 | − | 0.781070i | ||||
\(297\) | 13.7806 | − | 0.660918i | 0.799634 | − | 0.0383503i | ||||
\(298\) | −2.60293 | + | 4.38005i | −0.150784 | + | 0.253730i | ||||
\(299\) | 13.5735i | 0.784977i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 0.918791i | − | 0.0529583i | ||||||
\(302\) | 16.6538 | + | 9.89682i | 0.958317 | + | 0.569498i | ||||
\(303\) | −9.50365 | − | 15.8698i | −0.545970 | − | 0.911698i | ||||
\(304\) | −6.85902 | + | 10.6078i | −0.393392 | + | 0.608400i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −22.4217 | − | 5.54515i | −1.28177 | − | 0.316995i | ||||
\(307\) | −5.31757 | − | 5.31757i | −0.303490 | − | 0.303490i | 0.538888 | − | 0.842378i | \(-0.318845\pi\) |
−0.842378 | + | 0.538888i | \(0.818845\pi\) | |||||||
\(308\) | −15.0547 | − | 4.44323i | −0.857822 | − | 0.253177i | ||||
\(309\) | 6.16176 | − | 24.5587i | 0.350530 | − | 1.39709i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 31.3649i | − | 1.77854i | −0.457382 | − | 0.889270i | \(-0.651213\pi\) | ||
0.457382 | − | 0.889270i | \(-0.348787\pi\) | |||||||
\(312\) | −8.17425 | + | 28.0449i | −0.462776 | + | 1.58773i | ||||
\(313\) | −5.42321 | − | 5.42321i | −0.306538 | − | 0.306538i | 0.537027 | − | 0.843565i | \(-0.319547\pi\) |
−0.843565 | + | 0.537027i | \(0.819547\pi\) | |||||||
\(314\) | −3.58518 | − | 14.0875i | −0.202324 | − | 0.795005i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.8572 | − | 8.63007i | 0.892039 | − | 0.485479i | ||||
\(317\) | 12.8513 | − | 12.8513i | 0.721799 | − | 0.721799i | −0.247172 | − | 0.968972i | \(-0.579501\pi\) |
0.968972 | + | 0.247172i | \(0.0795013\pi\) | |||||||
\(318\) | −11.3301 | + | 11.4069i | −0.635358 | + | 0.639666i | ||||
\(319\) | − | 11.5519i | − | 0.646782i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.25108 | − | 2.07019i | −0.460530 | − | 0.115547i | ||||
\(322\) | −4.86132 | + | 8.18034i | −0.270911 | + | 0.455872i | ||||
\(323\) | 12.1570 | + | 12.1570i | 0.676435 | + | 0.676435i | ||||
\(324\) | 8.39005 | − | 15.9250i | 0.466114 | − | 0.884725i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 18.4251 | − | 4.68908i | 1.02047 | − | 0.259704i | ||||
\(327\) | 2.38446 | + | 3.98173i | 0.131861 | + | 0.220190i | ||||
\(328\) | −29.9756 | − | 1.13325i | −1.65513 | − | 0.0625732i | ||||
\(329\) | 7.66064 | 0.422345 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6434i | 0.585016i | 0.956263 | + | 0.292508i | \(0.0944899\pi\) | ||||
−0.956263 | + | 0.292508i | \(0.905510\pi\) | |||||||
\(332\) | 7.83664 | − | 26.5524i | 0.430092 | − | 1.45725i | ||||
\(333\) | 20.0660 | − | 6.06996i | 1.09961 | − | 0.332632i | ||||
\(334\) | 7.11005 | + | 27.9380i | 0.389045 | + | 1.52870i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −14.9706 | + | 13.9742i | −0.816712 | + | 0.762356i | ||||
\(337\) | −0.581584 | + | 0.581584i | −0.0316809 | + | 0.0316809i | −0.722770 | − | 0.691089i | \(-0.757131\pi\) |
0.691089 | + | 0.722770i | \(0.257131\pi\) | |||||||
\(338\) | 16.2960 | − | 27.4219i | 0.886383 | − | 1.49155i | ||||
\(339\) | −14.5316 | − | 3.64596i | −0.789246 | − | 0.198021i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.16297 | 0.225438 | ||||||||
\(342\) | −11.4716 | + | 6.92251i | −0.620312 | + | 0.374327i | ||||
\(343\) | −10.9995 | − | 10.9995i | −0.593920 | − | 0.593920i | ||||
\(344\) | −0.597734 | − | 0.644705i | −0.0322276 | − | 0.0347602i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.92350 | + | 35.0637i | 0.479730 | + | 1.88504i | ||||
\(347\) | −1.90948 | + | 1.90948i | −0.102506 | + | 0.102506i | −0.756500 | − | 0.653994i | \(-0.773092\pi\) |
0.653994 | + | 0.756500i | \(0.273092\pi\) | |||||||
\(348\) | −12.9823 | − | 7.65575i | −0.695925 | − | 0.410391i | ||||
\(349\) | 16.3562 | 0.875528 | 0.437764 | − | 0.899090i | \(-0.355771\pi\) | ||||
0.437764 | + | 0.899090i | \(0.355771\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.8342 | + | 22.9333i | −1.11205 | + | 1.22409i | ||||
\(352\) | −13.4543 | + | 6.67631i | −0.717118 | + | 0.355848i | ||||
\(353\) | −0.326679 | + | 0.326679i | −0.0173874 | + | 0.0173874i | −0.715747 | − | 0.698360i | \(-0.753914\pi\) |
0.698360 | + | 0.715747i | \(0.253914\pi\) | |||||||
\(354\) | −24.3276 | + | 0.0821905i | −1.29300 | + | 0.00436838i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.70801 | + | 4.97580i | 0.143524 | + | 0.263717i | ||||
\(357\) | 14.3201 | + | 23.9126i | 0.757898 | + | 1.26559i | ||||
\(358\) | −4.20454 | + | 7.07515i | −0.222217 | + | 0.373934i | ||||
\(359\) | 16.0922 | 0.849315 | 0.424657 | − | 0.905354i | \(-0.360395\pi\) | ||||
0.424657 | + | 0.905354i | \(0.360395\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.02676 | −0.475093 | ||||||||
\(362\) | −2.58898 | + | 4.35658i | −0.136074 | + | 0.228977i | ||||
\(363\) | 3.51524 | + | 5.86998i | 0.184502 | + | 0.308094i | ||||
\(364\) | 30.9629 | − | 16.8511i | 1.62290 | − | 0.883239i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 29.1877 | − | 0.0986104i | 1.52567 | − | 0.00515445i | ||||
\(367\) | 17.3259 | − | 17.3259i | 0.904406 | − | 0.904406i | −0.0914078 | − | 0.995814i | \(-0.529137\pi\) |
0.995814 | + | 0.0914078i | \(0.0291367\pi\) | |||||||
\(368\) | 1.91071 | + | 8.90265i | 0.0996028 | + | 0.464083i | ||||
\(369\) | −28.0481 | − | 15.0200i | −1.46013 | − | 0.781912i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.4015 | 1.00728 | ||||||||
\(372\) | 2.75891 | − | 4.67845i | 0.143043 | − | 0.242566i | ||||
\(373\) | −4.04391 | + | 4.04391i | −0.209386 | + | 0.209386i | −0.804006 | − | 0.594621i | \(-0.797302\pi\) |
0.594621 | + | 0.804006i | \(0.297302\pi\) | |||||||
\(374\) | 5.04168 | + | 19.8106i | 0.260699 | + | 1.02438i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.37538 | − | 4.98374i | 0.277214 | − | 0.257017i | ||||
\(377\) | 18.3445 | + | 18.3445i | 0.944791 | + | 0.944791i | ||||
\(378\) | −20.7696 | + | 6.35947i | −1.06828 | + | 0.327096i | ||||
\(379\) | −9.37395 | −0.481507 | −0.240754 | − | 0.970586i | \(-0.577395\pi\) | ||||
−0.240754 | + | 0.970586i | \(0.577395\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.6698 | − | 6.69143i | −1.36633 | − | 0.342812i | ||||
\(382\) | 8.38318 | − | 14.1067i | 0.428921 | − | 0.721762i | ||||
\(383\) | −1.94014 | + | 1.94014i | −0.0991364 | + | 0.0991364i | −0.754935 | − | 0.655799i | \(-0.772332\pi\) |
0.655799 | + | 0.754935i | \(0.272332\pi\) | |||||||
\(384\) | −1.41354 | + | 19.5449i | −0.0721342 | + | 0.997395i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.84915 | + | 19.0541i | 0.246815 | + | 0.969829i | ||||
\(387\) | −0.269996 | − | 0.892551i | −0.0137247 | − | 0.0453709i | ||||
\(388\) | 25.1302 | + | 7.41690i | 1.27579 | + | 0.376536i | ||||
\(389\) | − | 15.7785i | − | 0.800003i | −0.916515 | − | 0.400001i | \(-0.869010\pi\) | ||
0.916515 | − | 0.400001i | \(-0.130990\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.3926 | 0.626721 | ||||||||
\(392\) | 4.91069 | + | 0.185652i | 0.248027 | + | 0.00937684i | ||||
\(393\) | 5.83382 | + | 9.74171i | 0.294277 | + | 0.491404i | ||||
\(394\) | −3.82422 | + | 0.973239i | −0.192661 | + | 0.0490310i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −15.9304 | + | 0.107643i | −0.800535 | + | 0.00540926i | ||||
\(397\) | 16.1961 | + | 16.1961i | 0.812858 | + | 0.812858i | 0.985061 | − | 0.172204i | \(-0.0550887\pi\) |
−0.172204 | + | 0.985061i | \(0.555089\pi\) | |||||||
\(398\) | −2.95712 | + | 4.97607i | −0.148227 | + | 0.249428i | ||||
\(399\) | 15.6825 | + | 3.93472i | 0.785105 | + | 0.196982i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.9532i | 1.69554i | 0.530362 | + | 0.847771i | \(0.322056\pi\) | ||||
−0.530362 | + | 0.847771i | \(0.677944\pi\) | |||||||
\(402\) | 21.5047 | − | 21.6505i | 1.07256 | − | 1.07983i | ||||
\(403\) | −6.61083 | + | 6.61083i | −0.329309 | + | 0.329309i | ||||
\(404\) | 10.2104 | + | 18.7610i | 0.507987 | + | 0.933395i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.48563 | + | 17.6257i | 0.222618 | + | 0.874749i | ||||
\(407\) | −13.1197 | − | 13.1197i | −0.650321 | − | 0.650321i | ||||
\(408\) | 25.6049 | + | 7.46307i | 1.26763 | + | 0.369477i | ||||
\(409\) | 11.9177i | 0.589294i | 0.955606 | + | 0.294647i | \(0.0952021\pi\) | ||||
−0.955606 | + | 0.294647i | \(0.904798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.975525 | + | 3.88811i | −0.0481191 | + | 0.191786i | ||||
\(412\) | −8.27602 | + | 28.0411i | −0.407730 | + | 1.38148i | ||||
\(413\) | 20.7588 | + | 20.7588i | 1.02148 | + | 1.02148i | ||||
\(414\) | −2.31861 | + | 9.37526i | −0.113953 | + | 0.460769i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.7635 | − | 31.9676i | 0.527726 | − | 1.56734i | ||||
\(417\) | 0.918113 | + | 1.53313i | 0.0449602 | + | 0.0750776i | ||||
\(418\) | 10.1940 | + | 6.05799i | 0.498606 | + | 0.296306i | ||||
\(419\) | − | 0.494053i | − | 0.0241361i | −0.999927 | − | 0.0120680i | \(-0.996159\pi\) | ||
0.999927 | − | 0.0120680i | \(-0.00384147\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 28.0844i | − | 1.36875i | −0.729129 | − | 0.684376i | \(-0.760075\pi\) | ||
0.729129 | − | 0.684376i | \(-0.239925\pi\) | |||||||
\(422\) | −3.89727 | + | 6.55810i | −0.189716 | + | 0.319243i | ||||
\(423\) | 7.44186 | − | 2.25116i | 0.361835 | − | 0.109455i | ||||
\(424\) | 13.6138 | − | 12.6220i | 0.661145 | − | 0.612976i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.09948 | + | 0.0239855i | −0.343971 | + | 0.00116210i | ||||
\(427\) | −24.9060 | − | 24.9060i | −1.20529 | − | 1.20529i | ||||
\(428\) | 9.42108 | + | 2.78053i | 0.455385 | + | 0.134402i | ||||
\(429\) | 26.5978 | + | 6.67337i | 1.28415 | + | 0.322193i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8.20673i | − | 0.395304i | −0.980272 | − | 0.197652i | \(-0.936668\pi\) | ||
0.980272 | − | 0.197652i | \(-0.0633316\pi\) | |||||||
\(432\) | −10.4366 | + | 17.9744i | −0.502129 | + | 0.864793i | ||||
\(433\) | −8.09993 | − | 8.09993i | −0.389258 | − | 0.389258i | 0.485165 | − | 0.874423i | \(-0.338760\pi\) |
−0.874423 | + | 0.485165i | \(0.838760\pi\) | |||||||
\(434\) | −6.35179 | + | 1.61649i | −0.304896 | + | 0.0775941i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.56179 | − | 4.70713i | −0.122687 | − | 0.225431i | ||||
\(437\) | 5.08325 | − | 5.08325i | 0.243165 | − | 0.243165i | ||||
\(438\) | 5.60936 | − | 5.64739i | 0.268025 | − | 0.269843i | ||||
\(439\) | 5.21928i | 0.249103i | 0.992213 | + | 0.124551i | \(0.0397491\pi\) | ||||
−0.992213 | + | 0.124551i | \(0.960251\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.59492 | + | 2.46062i | 0.218806 | + | 0.117173i | ||||
\(442\) | −39.4657 | − | 23.4532i | −1.87719 | − | 1.11556i | ||||
\(443\) | −21.7308 | − | 21.7308i | −1.03246 | − | 1.03246i | −0.999455 | − | 0.0330087i | \(-0.989491\pi\) |
−0.0330087 | − | 0.999455i | \(-0.510509\pi\) | |||||||
\(444\) | −23.4391 | + | 6.04949i | −1.11237 | + | 0.287096i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.30170 | + | 5.11487i | 0.0616374 | + | 0.242196i | ||||
\(447\) | 5.35364 | − | 3.20603i | 0.253219 | − | 0.151640i | ||||
\(448\) | 17.9360 | − | 15.4109i | 0.847394 | − | 0.728099i | ||||
\(449\) | −0.611967 | −0.0288805 | −0.0144403 | − | 0.999896i | \(-0.504597\pi\) | ||||
−0.0144403 | + | 0.999896i | \(0.504597\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.1592i | 1.32596i | ||||||||
\(452\) | 16.5921 | + | 4.89698i | 0.780428 | + | 0.230335i | ||||
\(453\) | −12.1899 | − | 20.3556i | −0.572732 | − | 0.956388i | ||||
\(454\) | −10.9077 | + | 2.77595i | −0.511925 | + | 0.130282i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.5640 | − | 7.44151i | 0.635192 | − | 0.348481i | ||||
\(457\) | −3.44344 | + | 3.44344i | −0.161077 | + | 0.161077i | −0.783044 | − | 0.621967i | \(-0.786334\pi\) |
0.621967 | + | 0.783044i | \(0.286334\pi\) | |||||||
\(458\) | 13.6551 | + | 8.11480i | 0.638061 | + | 0.379180i | ||||
\(459\) | 20.9381 | + | 19.0216i | 0.977305 | + | 0.887853i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.294401 | −0.0137116 | −0.00685580 | − | 0.999976i | \(-0.502182\pi\) | ||||
−0.00685580 | + | 0.999976i | \(0.502182\pi\) | |||||||
\(462\) | 13.6396 | + | 13.5477i | 0.634571 | + | 0.630298i | ||||
\(463\) | 9.79796 | + | 9.79796i | 0.455350 | + | 0.455350i | 0.897126 | − | 0.441776i | \(-0.145651\pi\) |
−0.441776 | + | 0.897126i | \(0.645651\pi\) | |||||||
\(464\) | 14.6142 | + | 9.44955i | 0.678446 | + | 0.438684i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 29.2118 | − | 7.43423i | 1.35321 | − | 0.344384i | ||||
\(467\) | 18.8562 | − | 18.8562i | 0.872561 | − | 0.872561i | −0.120190 | − | 0.992751i | \(-0.538350\pi\) |
0.992751 | + | 0.120190i | \(0.0383504\pi\) | |||||||
\(468\) | 25.1268 | − | 25.4686i | 1.16148 | − | 1.17729i | ||||
\(469\) | −36.8245 | −1.70040 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.33262 | + | 17.2684i | −0.199637 | + | 0.795684i | ||||
\(472\) | 28.0712 | + | 1.06125i | 1.29208 | + | 0.0488480i | ||||
\(473\) | −0.583575 | + | 0.583575i | −0.0268328 | + | 0.0268328i | ||||
\(474\) | −22.1108 | + | 0.0747012i | −1.01558 | + | 0.00343114i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15.3850 | − | 28.2690i | −0.705172 | − | 1.29571i | ||||
\(477\) | 18.8474 | − | 5.70133i | 0.862964 | − | 0.261046i | ||||
\(478\) | −3.52366 | − | 2.09400i | −0.161169 | − | 0.0957774i | ||||
\(479\) | −18.9906 | −0.867702 | −0.433851 | − | 0.900985i | \(-0.642846\pi\) | ||||
−0.433851 | + | 0.900985i | \(0.642846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 41.6685 | 1.89992 | ||||||||
\(482\) | 0.670968 | + | 0.398735i | 0.0305617 | + | 0.0181619i | ||||
\(483\) | 9.99866 | − | 5.98769i | 0.454955 | − | 0.272449i | ||||
\(484\) | −3.77666 | − | 6.93938i | −0.171666 | − | 0.315426i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −18.3077 | + | 12.2812i | −0.830454 | + | 0.557088i | ||||
\(487\) | −12.0580 | + | 12.0580i | −0.546399 | + | 0.546399i | −0.925397 | − | 0.378998i | \(-0.876269\pi\) |
0.378998 | + | 0.925397i | \(0.376269\pi\) | |||||||
\(488\) | −33.6792 | − | 1.27327i | −1.52459 | − | 0.0576381i | ||||
\(489\) | −22.5854 | − | 5.66666i | −1.02135 | − | 0.256255i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.1797 | 0.820439 | 0.410219 | − | 0.911987i | \(-0.365452\pi\) | ||||
0.410219 | + | 0.911987i | \(0.365452\pi\) | |||||||
\(492\) | 31.6460 | + | 18.6618i | 1.42671 | + | 0.841341i | ||||
\(493\) | 16.7485 | − | 16.7485i | 0.754314 | − | 0.754314i | ||||
\(494\) | −25.8084 | + | 6.56806i | −1.16117 | + | 0.295511i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.40534 | + | 5.26653i | −0.152904 | + | 0.236474i | ||||
\(497\) | 6.05801 | + | 6.05801i | 0.271739 | + | 0.271739i | ||||
\(498\) | −23.8945 | + | 24.0565i | −1.07074 | + | 1.07800i | ||||
\(499\) | −24.8457 | −1.11225 | −0.556124 | − | 0.831100i | \(-0.687712\pi\) | ||||
−0.556124 | + | 0.831100i | \(0.687712\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.59235 | − | 34.2462i | 0.383878 | − | 1.53001i | ||||
\(502\) | −7.65541 | − | 4.54937i | −0.341678 | − | 0.203048i | ||||
\(503\) | 17.0078 | − | 17.0078i | 0.758340 | − | 0.758340i | −0.217680 | − | 0.976020i | \(-0.569849\pi\) |
0.976020 | + | 0.217680i | \(0.0698490\pi\) | |||||||
\(504\) | 24.2646 | − | 6.35007i | 1.08083 | − | 0.282855i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.28347 | − | 2.10809i | 0.368245 | − | 0.0937161i | ||||
\(507\) | −33.5172 | + | 20.0717i | −1.48855 | + | 0.891418i | ||||
\(508\) | 30.4515 | + | 8.98743i | 1.35107 | + | 0.398753i | ||||
\(509\) | 26.1925i | 1.16096i | 0.814274 | + | 0.580481i | \(0.197135\pi\) | ||||
−0.814274 | + | 0.580481i | \(0.802865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.60542 | −0.424919 | ||||||||
\(512\) | 2.55962 | − | 22.4822i | 0.113120 | − | 0.993581i | ||||
\(513\) | 16.3908 | − | 0.786102i | 0.723673 | − | 0.0347073i | ||||
\(514\) | −5.38562 | − | 21.1621i | −0.237549 | − | 0.933420i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.269086 | + | 1.04259i | 0.0118458 | + | 0.0458973i | ||||
\(517\) | −4.86569 | − | 4.86569i | −0.213993 | − | 0.213993i | ||||
\(518\) | 25.1123 | + | 14.9234i | 1.10337 | + | 0.655699i | ||||
\(519\) | 10.7839 | − | 42.9808i | 0.473359 | − | 1.88665i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.5789i | 0.945388i | 0.881227 | + | 0.472694i | \(0.156718\pi\) | ||||
−0.881227 | + | 0.472694i | \(0.843282\pi\) | |||||||
\(522\) | 9.53701 | + | 15.8042i | 0.417424 | + | 0.691730i | ||||
\(523\) | 1.75051 | − | 1.75051i | 0.0765445 | − | 0.0765445i | −0.667798 | − | 0.744343i | \(-0.732763\pi\) |
0.744343 | + | 0.667798i | \(0.232763\pi\) | |||||||
\(524\) | −6.26767 | − | 11.5165i | −0.273804 | − | 0.503099i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −40.8878 | + | 10.4057i | −1.78279 | + | 0.453709i | ||||
\(527\) | 6.03567 | + | 6.03567i | 0.262918 | + | 0.262918i | ||||
\(528\) | 18.3844 | + | 0.632844i | 0.800079 | + | 0.0275410i | ||||
\(529\) | 17.8182i | 0.774707i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.2662 | + | 14.0658i | 1.13985 | + | 0.610403i | ||||
\(532\) | −17.9062 | − | 5.28482i | −0.776333 | − | 0.229126i | ||||
\(533\) | −44.7170 | − | 44.7170i | −1.93691 | − | 1.93691i | ||||
\(534\) | −0.0234403 | − | 6.93811i | −0.00101436 | − | 0.300241i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −25.8393 | + | 23.9567i | −1.11609 | + | 1.03477i | ||||
\(537\) | 8.64781 | − | 5.17874i | 0.373181 | − | 0.223479i | ||||
\(538\) | −14.8913 | + | 25.0583i | −0.642011 | + | 1.08034i | ||||
\(539\) | − | 4.61311i | − | 0.198701i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 22.6515i | − | 0.973864i | −0.873440 | − | 0.486932i | \(-0.838116\pi\) | ||
0.873440 | − | 0.486932i | \(-0.161884\pi\) | |||||||
\(542\) | −29.5341 | − | 17.5512i | −1.26860 | − | 0.753889i | ||||
\(543\) | 5.32496 | − | 3.18885i | 0.228516 | − | 0.136847i | ||||
\(544\) | −29.1863 | − | 9.82709i | −1.25135 | − | 0.421333i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −43.1737 | + | 0.145862i | −1.84766 | + | 0.00624232i | ||||
\(547\) | −24.2626 | − | 24.2626i | −1.03739 | − | 1.03739i | −0.999273 | − | 0.0381200i | \(-0.987863\pi\) |
−0.0381200 | − | 0.999273i | \(-0.512137\pi\) | |||||||
\(548\) | 1.31025 | − | 4.43944i | 0.0559712 | − | 0.189644i | ||||
\(549\) | −31.5136 | − | 16.8758i | −1.34497 | − | 0.720243i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.7399i | − | 0.585341i | ||||||
\(552\) | 3.12055 | − | 10.7063i | 0.132820 | − | 0.455689i | ||||
\(553\) | 18.8673 | + | 18.8673i | 0.802318 | + | 0.802318i | ||||
\(554\) | 6.23937 | + | 24.5168i | 0.265085 | + | 1.04162i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.986391 | − | 1.81243i | −0.0418323 | − | 0.0768643i | ||||
\(557\) | −14.5141 | + | 14.5141i | −0.614984 | + | 0.614984i | −0.944240 | − | 0.329257i | \(-0.893202\pi\) |
0.329257 | + | 0.944240i | \(0.393202\pi\) | |||||||
\(558\) | −5.69537 | + | 3.43686i | −0.241104 | + | 0.145494i | ||||
\(559\) | − | 1.85344i | − | 0.0783923i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.09277 | − | 24.2837i | 0.257237 | − | 1.02526i | ||||
\(562\) | 6.37040 | − | 10.7197i | 0.268719 | − | 0.452185i | ||||
\(563\) | 4.09672 | + | 4.09672i | 0.172656 | + | 0.172656i | 0.788145 | − | 0.615489i | \(-0.211042\pi\) |
−0.615489 | + | 0.788145i | \(0.711042\pi\) | |||||||
\(564\) | −8.69281 | + | 2.24356i | −0.366033 | + | 0.0944710i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −26.1519 | + | 6.65549i | −1.09925 | + | 0.279751i | ||||
\(567\) | 26.0840 | + | 5.23053i | 1.09542 | + | 0.219662i | ||||
\(568\) | 8.19196 | + | 0.309703i | 0.343727 | + | 0.0129948i | ||||
\(569\) | 27.6005 | 1.15707 | 0.578536 | − | 0.815657i | \(-0.303624\pi\) | ||||
0.578536 | + | 0.815657i | \(0.303624\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.2742i | 1.35063i | 0.737528 | + | 0.675317i | \(0.235993\pi\) | ||||
−0.737528 | + | 0.675317i | \(0.764007\pi\) | |||||||
\(572\) | −30.3693 | − | 8.96317i | −1.26980 | − | 0.374769i | ||||
\(573\) | −17.2423 | + | 10.3256i | −0.720309 | + | 0.431357i | ||||
\(574\) | −10.9343 | − | 42.9648i | −0.456388 | − | 1.79332i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.8951 | − | 20.2415i | 0.537294 | − | 0.843395i | ||||
\(577\) | 5.10163 | − | 5.10163i | 0.212384 | − | 0.212384i | −0.592896 | − | 0.805279i | \(-0.702015\pi\) |
0.805279 | + | 0.592896i | \(0.202015\pi\) | |||||||
\(578\) | −9.13063 | + | 15.3645i | −0.379784 | + | 0.639078i | ||||
\(579\) | 5.86010 | − | 23.3564i | 0.243537 | − | 0.970657i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.9168 | 1.69751 | ||||||||
\(582\) | −22.7680 | − | 22.6147i | −0.943764 | − | 0.937409i | ||||
\(583\) | −12.3230 | − | 12.3230i | −0.510365 | − | 0.510365i | ||||
\(584\) | −6.74001 | + | 6.24895i | −0.278904 | + | 0.258584i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.37538 | − | 13.2631i | −0.139436 | − | 0.547894i | ||||
\(587\) | 3.37004 | − | 3.37004i | 0.139097 | − | 0.139097i | −0.634130 | − | 0.773227i | \(-0.718642\pi\) |
0.773227 | + | 0.634130i | \(0.218642\pi\) | |||||||
\(588\) | −5.18433 | − | 3.05723i | −0.213798 | − | 0.126078i | ||||
\(589\) | 4.95148 | 0.204022 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.68769 | + | 1.17614i | 0.192826 | + | 0.0483799i | ||||
\(592\) | 27.3297 | − | 5.86557i | 1.12324 | − | 0.241074i | ||||
\(593\) | 16.9693 | − | 16.9693i | 0.696844 | − | 0.696844i | −0.266884 | − | 0.963729i | \(-0.585994\pi\) |
0.963729 | + | 0.266884i | \(0.0859941\pi\) | |||||||
\(594\) | 17.2312 | + | 9.15270i | 0.707005 | + | 0.375540i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.32897 | + | 3.44445i | −0.259245 | + | 0.141090i | ||||
\(597\) | 6.08214 | − | 3.64229i | 0.248926 | − | 0.149069i | ||||
\(598\) | −9.80656 | + | 16.5019i | −0.401020 | + | 0.674813i | ||||
\(599\) | 1.04438 | 0.0426723 | 0.0213361 | − | 0.999772i | \(-0.493208\pi\) | ||||
0.0213361 | + | 0.999772i | \(0.493208\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.244816 | 0.00998624 | 0.00499312 | − | 0.999988i | \(-0.498411\pi\) | ||||
0.00499312 | + | 0.999988i | \(0.498411\pi\) | |||||||
\(602\) | 0.663806 | − | 1.11701i | 0.0270547 | − | 0.0455260i | ||||
\(603\) | −35.7728 | + | 10.8212i | −1.45678 | + | 0.440675i | ||||
\(604\) | 13.0965 | + | 24.0639i | 0.532887 | + | 0.979148i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.0883806 | − | 26.1598i | −0.00359021 | − | 1.06267i | ||||
\(607\) | −3.95241 | + | 3.95241i | −0.160423 | + | 0.160423i | −0.782754 | − | 0.622331i | \(-0.786186\pi\) |
0.622331 | + | 0.782754i | \(0.286186\pi\) | |||||||
\(608\) | −16.0027 | + | 7.94086i | −0.648995 | + | 0.322045i | ||||
\(609\) | 5.42079 | − | 21.6054i | 0.219661 | − | 0.875496i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.4535 | 0.625183 | ||||||||
\(612\) | −23.2528 | − | 22.9407i | −0.939938 | − | 0.927321i | ||||
\(613\) | 21.0245 | − | 21.0245i | 0.849172 | − | 0.849172i | −0.140858 | − | 0.990030i | \(-0.544986\pi\) |
0.990030 | + | 0.140858i | \(0.0449861\pi\) | |||||||
\(614\) | −2.62297 | − | 10.3066i | −0.105854 | − | 0.415941i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.0925 | − | 16.2785i | −0.608094 | − | 0.655879i | ||||
\(617\) | −18.7366 | − | 18.7366i | −0.754307 | − | 0.754307i | 0.220973 | − | 0.975280i | \(-0.429077\pi\) |
−0.975280 | + | 0.220973i | \(0.929077\pi\) | |||||||
\(618\) | 25.2342 | − | 25.4053i | 1.01507 | − | 1.02195i | ||||
\(619\) | −8.66233 | −0.348169 | −0.174084 | − | 0.984731i | \(-0.555697\pi\) | ||||
−0.174084 | + | 0.984731i | \(0.555697\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.95356 | − | 8.75489i | 0.319165 | − | 0.351322i | ||||
\(622\) | 22.6604 | − | 38.1316i | 0.908600 | − | 1.52894i | ||||
\(623\) | −5.92031 | + | 5.92031i | −0.237192 | + | 0.237192i | ||||
\(624\) | −30.1996 | + | 28.1897i | −1.20895 | + | 1.12849i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.67508 | − | 10.5114i | −0.106918 | − | 0.420119i | ||||
\(627\) | −7.46163 | − | 12.4599i | −0.297989 | − | 0.497602i | ||||
\(628\) | 5.81925 | − | 19.7170i | 0.232214 | − | 0.786794i | ||||
\(629\) | − | 38.0432i | − | 1.51688i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.38183 | −0.0550097 | −0.0275049 | − | 0.999622i | \(-0.508756\pi\) | ||||
−0.0275049 | + | 0.999622i | \(0.508756\pi\) | |||||||
\(632\) | 25.5133 | + | 0.964549i | 1.01487 | + | 0.0383677i | ||||
\(633\) | 8.01583 | − | 4.80028i | 0.318601 | − | 0.190794i | ||||
\(634\) | 24.9086 | − | 6.33907i | 0.989246 | − | 0.251757i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −22.0156 | + | 5.68210i | −0.872977 | + | 0.225310i | ||||
\(637\) | 7.32566 | + | 7.32566i | 0.290253 | + | 0.290253i | ||||
\(638\) | 8.34598 | − | 14.0441i | 0.330421 | − | 0.556012i | ||||
\(639\) | 7.66521 | + | 4.10479i | 0.303231 | + | 0.162383i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 32.1844i | − | 1.27121i | −0.772015 | − | 0.635604i | \(-0.780751\pi\) | ||
0.772015 | − | 0.635604i | \(-0.219249\pi\) | |||||||
\(642\) | −8.53551 | − | 8.47803i | −0.336870 | − | 0.334601i | ||||
\(643\) | −13.8136 | + | 13.8136i | −0.544755 | + | 0.544755i | −0.924919 | − | 0.380164i | \(-0.875868\pi\) |
0.380164 | + | 0.924919i | \(0.375868\pi\) | |||||||
\(644\) | −11.8202 | + | 6.43298i | −0.465782 | + | 0.253495i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.99662 | + | 23.5630i | 0.235934 | + | 0.927072i | ||||
\(647\) | −15.5057 | − | 15.5057i | −0.609594 | − | 0.609594i | 0.333246 | − | 0.942840i | \(-0.391856\pi\) |
−0.942840 | + | 0.333246i | \(0.891856\pi\) | |||||||
\(648\) | 21.7056 | − | 13.2991i | 0.852677 | − | 0.522439i | ||||
\(649\) | − | 26.3701i | − | 1.03512i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.78597 | + | 1.95350i | 0.305156 | + | 0.0765635i | ||||
\(652\) | 25.7880 | + | 7.61103i | 1.00993 | + | 0.298071i | ||||
\(653\) | 17.9422 | + | 17.9422i | 0.702132 | + | 0.702132i | 0.964868 | − | 0.262736i | \(-0.0846248\pi\) |
−0.262736 | + | 0.964868i | \(0.584625\pi\) | |||||||
\(654\) | 0.0221746 | + | 6.56348i | 0.000867097 | + | 0.256652i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −35.6238 | − | 23.0344i | −1.39088 | − | 0.899343i | ||||
\(657\) | −9.33110 | + | 2.82265i | −0.364041 | + | 0.110122i | ||||
\(658\) | 9.31335 | + | 5.53463i | 0.363072 | + | 0.215763i | ||||
\(659\) | − | 39.4445i | − | 1.53654i | −0.640127 | − | 0.768269i | \(-0.721118\pi\) | ||
0.640127 | − | 0.768269i | \(-0.278882\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.69555i | 0.299322i | 0.988737 | + | 0.149661i | \(0.0478183\pi\) | ||||
−0.988737 | + | 0.149661i | \(0.952182\pi\) | |||||||
\(662\) | −7.68964 | + | 12.9397i | −0.298866 | + | 0.502915i | ||||
\(663\) | 28.8874 | + | 48.2381i | 1.12189 | + | 1.87341i | ||||
\(664\) | 28.7108 | − | 26.6190i | 1.11420 | − | 1.03302i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 28.7805 | + | 7.11775i | 1.11522 | + | 0.275807i | ||||
\(667\) | −7.00310 | − | 7.00310i | −0.271161 | − | 0.271161i | ||||
\(668\) | −11.5406 | + | 39.1023i | −0.446520 | + | 1.51291i | ||||
\(669\) | 1.57308 | − | 6.26976i | 0.0608188 | − | 0.242403i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.6383i | 1.22138i | ||||||||
\(672\) | −28.2964 | + | 6.17313i | −1.09156 | + | 0.238134i | ||||
\(673\) | 2.37397 | + | 2.37397i | 0.0915096 | + | 0.0915096i | 0.751380 | − | 0.659870i | \(-0.229389\pi\) |
−0.659870 | + | 0.751380i | \(0.729389\pi\) | |||||||
\(674\) | −1.12724 | + | 0.286875i | −0.0434196 | + | 0.0110500i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 39.6233 | − | 21.5644i | 1.52397 | − | 0.829402i | ||||
\(677\) | 6.61424 | − | 6.61424i | 0.254206 | − | 0.254206i | −0.568487 | − | 0.822693i | \(-0.692471\pi\) |
0.822693 | + | 0.568487i | \(0.192471\pi\) | |||||||
\(678\) | −15.0325 | − | 14.9313i | −0.577319 | − | 0.573431i | ||||
\(679\) | 38.7252i | 1.48614i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.3706 | + | 3.35468i | 0.512363 | + | 0.128552i | ||||
\(682\) | 5.06110 | + | 3.00765i | 0.193799 | + | 0.115169i | ||||
\(683\) | −14.3187 | − | 14.3187i | −0.547889 | − | 0.547889i | 0.377941 | − | 0.925830i | \(-0.376632\pi\) |
−0.925830 | + | 0.377941i | \(0.876632\pi\) | |||||||
\(684\) | −18.9478 | + | 0.128032i | −0.724488 | + | 0.00489541i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.42568 | − | 21.3195i | −0.207154 | − | 0.813983i | ||||
\(687\) | −9.99500 | − | 16.6903i | −0.381333 | − | 0.636776i | ||||
\(688\) | −0.260905 | − | 1.21564i | −0.00994691 | − | 0.0463460i | ||||
\(689\) | 39.1380 | 1.49104 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 36.4559i | − | 1.38685i | −0.720529 | − | 0.693425i | \(-0.756101\pi\) | ||
0.720529 | − | 0.693425i | \(-0.243899\pi\) | |||||||
\(692\) | −14.4841 | + | 49.0754i | −0.550602 | + | 1.86557i | ||||
\(693\) | −6.81728 | − | 22.5365i | −0.258967 | − | 0.856091i | ||||
\(694\) | −3.70098 | + | 0.941876i | −0.140487 | + | 0.0357531i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.2520 | − | 18.6868i | −0.388602 | − | 0.708323i | ||||
\(697\) | −40.8265 | + | 40.8265i | −1.54641 | + | 1.54641i | ||||
\(698\) | 19.8849 | + | 11.8170i | 0.752655 | + | 0.447279i | ||||
\(699\) | −35.8076 | − | 8.98411i | −1.35437 | − | 0.339810i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.0342 | −1.81423 | −0.907113 | − | 0.420887i | \(-0.861719\pi\) | ||||
−0.907113 | + | 0.420887i | \(0.861719\pi\) | |||||||
\(702\) | −41.8979 | + | 12.8287i | −1.58133 | + | 0.484189i | ||||
\(703\) | −15.6047 | − | 15.6047i | −0.588544 | − | 0.588544i | ||||
\(704\) | −21.1804 | − | 1.60378i | −0.798268 | − | 0.0604446i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.633175 | + | 0.161139i | −0.0238299 | + | 0.00606455i | ||||
\(707\) | −22.3222 | + | 22.3222i | −0.839515 | + | 0.839515i | ||||
\(708\) | −29.6354 | − | 17.4762i | −1.11377 | − | 0.656796i | ||||
\(709\) | 6.97929 | 0.262113 | 0.131056 | − | 0.991375i | \(-0.458163\pi\) | ||||
0.131056 | + | 0.991375i | \(0.458163\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.8728 | + | 12.7841i | 0.895299 | + | 0.479441i | ||||
\(712\) | −0.302663 | + | 8.00576i | −0.0113428 | + | 0.300029i | ||||
\(713\) | 2.52371 | − | 2.52371i | 0.0945138 | − | 0.0945138i | ||||
\(714\) | 0.133172 | + | 39.4175i | 0.00498382 | + | 1.47516i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.2233 | + | 5.56387i | −0.382062 | + | 0.207932i | ||||
\(717\) | 2.57918 | + | 4.30690i | 0.0963214 | + | 0.160844i | ||||
\(718\) | 19.5640 | + | 11.6263i | 0.730121 | + | 0.433888i | ||||
\(719\) | −2.63485 | −0.0982634 | −0.0491317 | − | 0.998792i | \(-0.515645\pi\) | ||||
−0.0491317 | + | 0.998792i | \(0.515645\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.2108 | −1.60926 | ||||||||
\(722\) | −10.9742 | − | 6.52163i | −0.408418 | − | 0.242710i | ||||
\(723\) | −0.491122 | − | 0.820109i | −0.0182650 | − | 0.0305002i | ||||
\(724\) | −6.29506 | + | 3.42600i | −0.233954 | + | 0.127326i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.0326905 | + | 9.67606i | 0.00121326 | + | 0.359112i | ||||
\(727\) | 5.55176 | − | 5.55176i | 0.205903 | − | 0.205903i | −0.596620 | − | 0.802524i | \(-0.703490\pi\) |
0.802524 | + | 0.596620i | \(0.203490\pi\) | |||||||
\(728\) | 49.8174 | + | 1.88338i | 1.84636 | + | 0.0698028i | ||||
\(729\) | 26.8761 | − | 2.58389i | 0.995410 | − | 0.0956996i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.69219 | −0.0625879 | ||||||||
\(732\) | 35.5560 | + | 20.9676i | 1.31419 | + | 0.774984i | ||||
\(733\) | 10.2051 | − | 10.2051i | 0.376934 | − | 0.376934i | −0.493061 | − | 0.869995i | \(-0.664122\pi\) |
0.869995 | + | 0.493061i | \(0.164122\pi\) | |||||||
\(734\) | 33.5814 | − | 8.54626i | 1.23951 | − | 0.315448i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.10903 | + | 12.2038i | −0.151461 | + | 0.449837i | ||||
\(737\) | 23.3893 | + | 23.3893i | 0.861554 | + | 0.861554i | ||||
\(738\) | −23.2476 | − | 38.5246i | −0.855757 | − | 1.41811i | ||||
\(739\) | −33.7165 | −1.24028 | −0.620141 | − | 0.784490i | \(-0.712925\pi\) | ||||
−0.620141 | + | 0.784490i | \(0.712925\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.6356 | + | 7.93737i | 1.16216 | + | 0.291586i | ||||
\(742\) | 23.5872 | + | 14.0172i | 0.865914 | + | 0.514586i | ||||
\(743\) | 14.9523 | − | 14.9523i | 0.548546 | − | 0.548546i | −0.377474 | − | 0.926020i | \(-0.623207\pi\) |
0.926020 | + | 0.377474i | \(0.123207\pi\) | |||||||
\(744\) | 6.73420 | − | 3.69454i | 0.246888 | − | 0.135448i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.83798 | + | 1.99472i | −0.286969 | + | 0.0730317i | ||||
\(747\) | 39.7482 | − | 12.0238i | 1.45431 | − | 0.439928i | ||||
\(748\) | −8.18335 | + | 27.7271i | −0.299213 | + | 1.01380i | ||||
\(749\) | 14.5177i | 0.530466i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.4194 | 1.07353 | 0.536764 | − | 0.843733i | \(-0.319647\pi\) | ||||
0.536764 | + | 0.843733i | \(0.319647\pi\) | |||||||
\(752\) | 10.1357 | − | 2.17536i | 0.369611 | − | 0.0793271i | ||||
\(753\) | 5.60346 | + | 9.35705i | 0.204202 | + | 0.340990i | ||||
\(754\) | 9.04869 | + | 35.5557i | 0.329534 | + | 1.29486i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −29.8451 | − | 7.27412i | −1.08546 | − | 0.264557i | ||||
\(757\) | 9.10219 | + | 9.10219i | 0.330825 | + | 0.330825i | 0.852900 | − | 0.522075i | \(-0.174842\pi\) |
−0.522075 | + | 0.852900i | \(0.674842\pi\) | |||||||
\(758\) | −11.3963 | − | 6.77246i | −0.413932 | − | 0.245987i | ||||
\(759\) | −10.1538 | − | 2.54758i | −0.368560 | − | 0.0924715i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.4230i | 0.704083i | 0.935984 | + | 0.352042i | \(0.114512\pi\) | ||||
−0.935984 | + | 0.352042i | \(0.885488\pi\) | |||||||
\(762\) | −27.5891 | − | 27.4033i | −0.999449 | − | 0.992718i | ||||
\(763\) | 5.60064 | − | 5.60064i | 0.202757 | − | 0.202757i | ||||
\(764\) | 20.3836 | − | 11.0935i | 0.737451 | − | 0.401347i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.76041 | + | 0.957001i | −0.135869 | + | 0.0345778i | ||||
\(767\) | 41.8760 | + | 41.8760i | 1.51206 | + | 1.51206i | ||||
\(768\) | −15.8392 | + | 22.7403i | −0.571548 | + | 0.820568i | ||||
\(769\) | 1.26203i | 0.0455101i | 0.999741 | + | 0.0227551i | \(0.00724379\pi\) | ||||
−0.999741 | + | 0.0227551i | \(0.992756\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.50841 | + | 25.9403i | −0.234395 | + | 0.934217i | ||||
\(772\) | −7.87085 | + | 26.6683i | −0.283278 | + | 0.959812i | ||||
\(773\) | −13.6782 | − | 13.6782i | −0.491971 | − | 0.491971i | 0.416956 | − | 0.908927i | \(-0.363097\pi\) |
−0.908927 | + | 0.416956i | \(0.863097\pi\) | |||||||
\(774\) | 0.316602 | − | 1.28018i | 0.0113800 | − | 0.0460150i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 25.1933 | + | 27.1730i | 0.904386 | + | 0.975455i | ||||
\(777\) | −18.3812 | − | 30.6942i | −0.659423 | − | 1.10115i | ||||
\(778\) | 11.3996 | − | 19.1826i | 0.408696 | − | 0.687729i | ||||
\(779\) | 33.4928i | 1.20000i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 7.69555i | − | 0.275368i | ||||||
\(782\) | 15.0662 | + | 8.95337i | 0.538766 | + | 0.320172i | ||||
\(783\) | −1.08300 | − | 22.5813i | −0.0387032 | − | 0.806991i | ||||
\(784\) | 5.83600 | + | 3.77356i | 0.208428 | + | 0.134770i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.0542525 | + | 16.0582i | 0.00193512 | + | 0.572777i | ||||
\(787\) | −1.64945 | − | 1.64945i | −0.0587966 | − | 0.0587966i | 0.677097 | − | 0.735894i | \(-0.263238\pi\) |
−0.735894 | + | 0.677097i | \(0.763238\pi\) | |||||||
\(788\) | −5.35240 | − | 1.57970i | −0.190671 | − | 0.0562745i | ||||
\(789\) | 50.1199 | + | 12.5750i | 1.78431 | + | 0.447683i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.5682i | 0.909100i | ||||||||
\(792\) | −19.4451 | − | 11.3785i | −0.690951 | − | 0.404318i | ||||
\(793\) | −50.2420 | − | 50.2420i | −1.78414 | − | 1.78414i | ||||
\(794\) | 7.98895 | + | 31.3915i | 0.283517 | + | 1.11404i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.19019 | + | 3.91316i | −0.254850 | + | 0.138698i | ||||
\(797\) | 15.2015 | − | 15.2015i | 0.538466 | − | 0.538466i | −0.384612 | − | 0.923078i | \(-0.625665\pi\) |
0.923078 | + | 0.384612i | \(0.125665\pi\) | |||||||
\(798\) | 16.2231 | + | 16.1138i | 0.574290 | + | 0.570423i | ||||
\(799\) | − | 14.1090i | − | 0.499141i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.01149 | + | 7.49098i | −0.141739 | + | 0.264681i | ||||
\(802\) | −24.5304 | + | 41.2783i | −0.866199 | + | 1.45759i | ||||
\(803\) | 6.10093 | + | 6.10093i | 0.215297 | + | 0.215297i | ||||
\(804\) | 41.7861 | − | 10.7847i | 1.47368 | − | 0.380349i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.8132 | + | 3.26089i | −0.451327 | + | 0.114860i | ||||
\(807\) | 30.6282 | − | 18.3417i | 1.07816 | − | 0.645657i | ||||
\(808\) | −1.14118 | + | 30.1853i | −0.0401465 | + | 1.06192i | ||||
\(809\) | −44.9347 | −1.57982 | −0.789910 | − | 0.613223i | \(-0.789873\pi\) | ||||
−0.789910 | + | 0.613223i | \(0.789873\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.8947i | − | 0.839055i | −0.907743 | − | 0.419528i | \(-0.862196\pi\) | ||
0.907743 | − | 0.419528i | \(-0.137804\pi\) | |||||||
\(812\) | −7.28080 | + | 24.6691i | −0.255506 | + | 0.865714i | ||||
\(813\) | 21.6178 | + | 36.0990i | 0.758171 | + | 1.26605i | ||||
\(814\) | −6.47149 | − | 25.4289i | −0.226826 | − | 0.891282i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 25.7371 | + | 27.5721i | 0.900979 | + | 0.965218i | ||||
\(817\) | −0.694110 | + | 0.694110i | −0.0242838 | + | 0.0242838i | ||||
\(818\) | −8.61029 | + | 14.4889i | −0.301052 | + | 0.506592i | ||||
\(819\) | 46.6141 | + | 24.9623i | 1.62883 | + | 0.872253i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.1420 | 1.50567 | 0.752833 | − | 0.658212i | \(-0.228687\pi\) | ||||
0.752833 | + | 0.658212i | \(0.228687\pi\) | |||||||
\(822\) | −3.99506 | + | 4.02215i | −0.139344 | + | 0.140288i | ||||
\(823\) | −29.4978 | − | 29.4978i | −1.02823 | − | 1.02823i | −0.999590 | − | 0.0286405i | \(-0.990882\pi\) |
−0.0286405 | − | 0.999590i | \(-0.509118\pi\) | |||||||
\(824\) | −30.3205 | + | 28.1115i | −1.05627 | + | 0.979309i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.2396 | + | 40.2351i | 0.356281 | + | 1.39996i | ||||
\(827\) | −32.6568 | + | 32.6568i | −1.13559 | + | 1.13559i | −0.146357 | + | 0.989232i | \(0.546755\pi\) |
−0.989232 | + | 0.146357i | \(0.953245\pi\) | |||||||
\(828\) | −9.59224 | + | 9.72275i | −0.333353 | + | 0.337889i | ||||
\(829\) | 19.3767 | 0.672980 | 0.336490 | − | 0.941687i | \(-0.390760\pi\) | ||||
0.336490 | + | 0.941687i | \(0.390760\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.54014 | − | 30.0524i | 0.261565 | − | 1.04251i | ||||
\(832\) | 36.1815 | − | 31.0879i | 1.25437 | − | 1.07778i | ||||
\(833\) | 6.68831 | − | 6.68831i | 0.231736 | − | 0.231736i | ||||
\(834\) | 0.00853813 | + | 2.52720i | 0.000295651 | + | 0.0875099i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.01654 | + | 14.7299i | 0.277258 | + | 0.509444i | ||||
\(837\) | 8.13766 | − | 0.390281i | 0.281279 | − | 0.0134901i | ||||
\(838\) | 0.356942 | − | 0.600640i | 0.0123304 | − | 0.0207488i | ||||
\(839\) | −38.4795 | −1.32846 | −0.664229 | − | 0.747529i | \(-0.731240\pi\) | ||||
−0.664229 | + | 0.747529i | \(0.731240\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0707 | 0.347267 | ||||||||
\(842\) | 20.2904 | − | 34.1434i | 0.699252 | − | 1.17666i | ||||
\(843\) | −13.1025 | + | 7.84643i | −0.451274 | + | 0.270245i | ||||
\(844\) | −9.47616 | + | 5.15726i | −0.326183 | + | 0.177520i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.6738 | + | 2.63975i | 0.366972 | + | 0.0907564i | ||||
\(847\) | 8.25662 | − | 8.25662i | 0.283701 | − | 0.283701i | ||||
\(848\) | 25.6699 | − | 5.50936i | 0.881510 | − | 0.189192i | ||||
\(849\) | 32.0568 | + | 8.04302i | 1.10019 | + | 0.276036i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.9071 | −0.545289 | ||||||||
\(852\) | −8.64845 | − | 5.10005i | −0.296291 | − | 0.174725i | ||||
\(853\) | −20.0303 | + | 20.0303i | −0.685823 | + | 0.685823i | −0.961306 | − | 0.275483i | \(-0.911162\pi\) |
0.275483 | + | 0.961306i | \(0.411162\pi\) | |||||||
\(854\) | −12.2852 | − | 48.2733i | −0.420392 | − | 1.65188i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.44472 | + | 10.1869i | 0.322814 | + | 0.348181i | ||||
\(857\) | −24.3417 | − | 24.3417i | −0.831496 | − | 0.831496i | 0.156226 | − | 0.987721i | \(-0.450067\pi\) |
−0.987721 | + | 0.156226i | \(0.950067\pi\) | |||||||
\(858\) | 27.5147 | + | 27.3294i | 0.939335 | + | 0.933009i | ||||
\(859\) | 43.4501 | 1.48250 | 0.741249 | − | 0.671230i | \(-0.234234\pi\) | ||||
0.741249 | + | 0.671230i | \(0.234234\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.2138 | + | 52.6659i | −0.450326 | + | 1.79485i | ||||
\(862\) | 5.92917 | − | 9.97726i | 0.201948 | − | 0.339827i | ||||
\(863\) | −16.6773 | + | 16.6773i | −0.567701 | + | 0.567701i | −0.931484 | − | 0.363783i | \(-0.881485\pi\) |
0.363783 | + | 0.931484i | \(0.381485\pi\) | |||||||
\(864\) | −25.6742 | + | 14.3120i | −0.873455 | + | 0.486905i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.99541 | − | 15.6994i | −0.135769 | − | 0.533488i | ||||
\(867\) | 18.7797 | − | 11.2462i | 0.637791 | − | 0.381941i | ||||
\(868\) | −8.89002 | − | 2.62379i | −0.301747 | − | 0.0890572i | ||||
\(869\) | − | 23.9673i | − | 0.813034i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −74.2847 | −2.51704 | ||||||||
\(872\) | 0.286321 | − | 7.57348i | 0.00969604 | − | 0.256470i | ||||
\(873\) | 11.3798 | + | 37.6193i | 0.385148 | + | 1.27322i | ||||
\(874\) | 9.85245 | − | 2.50738i | 0.333264 | − | 0.0848136i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.8996 | − | 2.81313i | 0.368264 | − | 0.0950469i | ||||
\(877\) | −0.209733 | − | 0.209733i | −0.00708216 | − | 0.00708216i | 0.703557 | − | 0.710639i | \(-0.251594\pi\) |
−0.710639 | + | 0.703557i | \(0.751594\pi\) | |||||||
\(878\) | −3.77081 | + | 6.34529i | −0.127259 | + | 0.214143i | ||||
\(879\) | −4.07907 | + | 16.2578i | −0.137584 | + | 0.548362i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.66064i | 0.258093i | 0.991639 | + | 0.129047i | \(0.0411917\pi\) | ||||
−0.991639 | + | 0.129047i | \(0.958808\pi\) | |||||||
\(882\) | 3.80849 | + | 6.31121i | 0.128239 | + | 0.212509i | ||||
\(883\) | 7.44439 | − | 7.44439i | 0.250524 | − | 0.250524i | −0.570662 | − | 0.821185i | \(-0.693313\pi\) |
0.821185 | + | 0.570662i | \(0.193313\pi\) | |||||||
\(884\) | −31.0357 | − | 57.0261i | −1.04384 | − | 1.91800i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.7191 | − | 42.1191i | −0.360114 | − | 1.41502i | ||||
\(887\) | 15.8208 | + | 15.8208i | 0.531211 | + | 0.531211i | 0.920933 | − | 0.389722i | \(-0.127429\pi\) |
−0.389722 | + | 0.920933i | \(0.627429\pi\) | |||||||
\(888\) | −32.8665 | − | 9.57959i | −1.10293 | − | 0.321470i | ||||
\(889\) | 46.9253i | 1.57382i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.2452 | − | 19.8896i | −0.443730 | − | 0.666325i | ||||
\(892\) | −2.11284 | + | 7.15881i | −0.0707433 | + | 0.239695i | ||||
\(893\) | −5.78730 | − | 5.78730i | −0.193665 | − | 0.193665i | ||||
\(894\) | 8.82493 | − | 0.0298149i | 0.295150 | − | 0.000997160i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 32.9395 | − | 5.77740i | 1.10043 | − | 0.193009i | ||||
\(897\) | 20.1699 | − | 12.0787i | 0.673454 | − | 0.403298i | ||||
\(898\) | −0.743993 | − | 0.442132i | −0.0248274 | − | 0.0147541i | ||||
\(899\) | − | 6.82156i | − | 0.227512i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 35.7329i | − | 1.19043i | ||||||
\(902\) | −20.3444 | + | 34.2343i | −0.677393 | + | 1.13988i | ||||
\(903\) | −1.36530 | + | 0.817610i | −0.0454344 | + | 0.0272084i | ||||
\(904\) | 16.6338 | + | 17.9409i | 0.553231 | + | 0.596705i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.113362 | − | 33.5540i | −0.00376620 | − | 1.11476i | ||||
\(907\) | 33.9035 | + | 33.9035i | 1.12575 | + | 1.12575i | 0.990861 | + | 0.134886i | \(0.0430668\pi\) |
0.134886 | + | 0.990861i | \(0.456933\pi\) | |||||||
\(908\) | −15.2665 | − | 4.50575i | −0.506638 | − | 0.149529i | ||||
\(909\) | −15.1251 | + | 28.2444i | −0.501669 | + | 0.936806i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.75281i | 0.289994i | 0.989432 | + | 0.144997i | \(0.0463172\pi\) | ||||
−0.989432 | + | 0.144997i | \(0.953683\pi\) | |||||||
\(912\) | 21.8666 | + | 0.752710i | 0.724076 | + | 0.0249247i | ||||
\(913\) | −25.9885 | − | 25.9885i | −0.860094 | − | 0.860094i | ||||
\(914\) | −6.67413 | + | 1.69852i | −0.220761 | + | 0.0561822i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.7383 | + | 19.7310i | 0.354804 | + | 0.651930i | ||||
\(917\) | 13.7025 | − | 13.7025i | 0.452497 | − | 0.452497i | ||||
\(918\) | 11.7126 | + | 38.2526i | 0.386573 | + | 1.26253i | ||||
\(919\) | 27.0428i | 0.892058i | 0.895018 | + | 0.446029i | \(0.147162\pi\) | ||||
−0.895018 | + | 0.446029i | \(0.852838\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.16980 | + | 12.6338i | −0.104449 | + | 0.416297i | ||||
\(922\) | −0.357915 | − | 0.212698i | −0.0117873 | − | 0.00700483i | ||||
\(923\) | 12.2206 | + | 12.2206i | 0.402246 | + | 0.402246i | ||||
\(924\) | 6.79429 | + | 26.3248i | 0.223516 | + | 0.866024i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.83298 | + | 18.9906i | 0.158822 | + | 0.624069i | ||||
\(927\) | −41.9768 | + | 12.6979i | −1.37870 | + | 0.417055i | ||||
\(928\) | 10.9400 | + | 22.0466i | 0.359122 | + | 0.723716i | ||||
\(929\) | −41.2267 | −1.35261 | −0.676303 | − | 0.736624i | \(-0.736419\pi\) | ||||
−0.676303 | + | 0.736624i | \(0.736419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 5.48688i | − | 0.179825i | ||||||
\(932\) | 40.8851 | + | 12.0668i | 1.33924 | + | 0.395261i | ||||
\(933\) | −46.6075 | + | 27.9109i | −1.52586 | + | 0.913761i | ||||
\(934\) | 36.5474 | − | 9.30109i | 1.19587 | − | 0.304341i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 48.9481 | − | 12.8098i | 1.59992 | − | 0.418700i | ||||
\(937\) | 37.7773 | − | 37.7773i | 1.23413 | − | 1.23413i | 0.271766 | − | 0.962363i | \(-0.412392\pi\) |
0.962363 | − | 0.271766i | \(-0.0876078\pi\) | |||||||
\(938\) | −44.7690 | − | 26.6048i | −1.46176 | − | 0.868679i | ||||
\(939\) | −3.23277 | + | 12.8847i | −0.105498 | + | 0.420478i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.4869 | −1.74362 | −0.871812 | − | 0.489841i | \(-0.837055\pi\) | ||||
−0.871812 | + | 0.489841i | \(0.837055\pi\) | |||||||
\(942\) | −17.7433 | + | 17.8636i | −0.578109 | + | 0.582029i | ||||
\(943\) | 17.0709 | + | 17.0709i | 0.555905 | + | 0.555905i | ||||
\(944\) | 33.3606 | + | 21.5710i | 1.08579 | + | 0.702076i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.13110 | + | 0.287857i | −0.0367751 | + | 0.00935903i | ||||
\(947\) | 23.8152 | − | 23.8152i | 0.773891 | − | 0.773891i | −0.204893 | − | 0.978784i | \(-0.565685\pi\) |
0.978784 | + | 0.204893i | \(0.0656846\pi\) | |||||||
\(948\) | −26.9350 | − | 15.8838i | −0.874809 | − | 0.515880i | ||||
\(949\) | −19.3767 | −0.628993 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.5327 | − | 7.66064i | −0.990091 | − | 0.248413i | ||||
\(952\) | 1.71952 | − | 45.4832i | 0.0557301 | − | 1.47412i | ||||
\(953\) | −31.8333 | + | 31.8333i | −1.03118 | + | 1.03118i | −0.0316832 | + | 0.999498i | \(0.510087\pi\) |
−0.999498 | + | 0.0316832i | \(0.989913\pi\) | |||||||
\(954\) | 27.0327 | + | 6.68549i | 0.875215 | + | 0.216451i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.77099 | − | 5.09153i | −0.0896203 | − | 0.164672i | ||||
\(957\) | −17.1658 | + | 10.2798i | −0.554893 | + | 0.332297i | ||||
\(958\) | −23.0876 | − | 13.7203i | −0.745928 | − | 0.443282i | ||||
\(959\) | 6.84111 | 0.220911 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5417 | −0.920700 | ||||||||
\(962\) | 50.6581 | + | 30.1045i | 1.63328 | + | 0.970609i | ||||
\(963\) | 4.26618 | + | 14.1031i | 0.137476 | + | 0.454466i | ||||
\(964\) | 0.527646 | + | 0.969517i | 0.0169943 | + | 0.0312260i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.4817 | − | 0.0556834i | 0.530292 | − | 0.00179158i | ||||
\(967\) | −21.7712 | + | 21.7712i | −0.700115 | + | 0.700115i | −0.964435 | − | 0.264320i | \(-0.914852\pi\) |
0.264320 | + | 0.964435i | \(0.414852\pi\) | |||||||
\(968\) | 0.422102 | − | 11.1650i | 0.0135669 | − | 0.358858i | ||||
\(969\) | 7.24679 | − | 28.8833i | 0.232801 | − | 0.927864i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.19315 | −0.0703814 | −0.0351907 | − | 0.999381i | \(-0.511204\pi\) | ||||
−0.0351907 | + | 0.999381i | \(0.511204\pi\) | |||||||
\(972\) | −31.1303 | + | 1.70391i | −0.998505 | + | 0.0546528i | ||||
\(973\) | 2.15647 | − | 2.15647i | 0.0691333 | − | 0.0691333i | ||||
\(974\) | −23.3710 | + | 5.94777i | −0.748855 | + | 0.190579i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −40.0253 | − | 25.8804i | −1.28118 | − | 0.828412i | ||||
\(977\) | −2.26226 | − | 2.26226i | −0.0723760 | − | 0.0723760i | 0.669992 | − | 0.742368i | \(-0.266297\pi\) |
−0.742368 | + | 0.669992i | \(0.766297\pi\) | |||||||
\(978\) | −23.3639 | − | 23.2066i | −0.747096 | − | 0.742065i | ||||
\(979\) | 7.52063 | 0.240361 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.79488 | − | 7.08649i | 0.121161 | − | 0.226254i | ||||
\(982\) | 22.1018 | + | 13.1344i | 0.705298 | + | 0.419136i | ||||
\(983\) | −39.9359 | + | 39.9359i | −1.27376 | + | 1.27376i | −0.329656 | + | 0.944101i | \(0.606933\pi\) |
−0.944101 | + | 0.329656i | \(0.893067\pi\) | |||||||
\(984\) | 24.9906 | + | 45.5515i | 0.796671 | + | 1.45213i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 32.4622 | − | 8.26144i | 1.03381 | − | 0.263098i | ||||
\(987\) | −6.81701 | − | 11.3835i | −0.216988 | − | 0.362341i | ||||
\(988\) | −36.1216 | − | 10.6609i | −1.14918 | − | 0.339168i | ||||
\(989\) | 0.707560i | 0.0224991i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.1776 | 0.831560 | 0.415780 | − | 0.909465i | \(-0.363509\pi\) | ||||
0.415780 | + | 0.909465i | \(0.363509\pi\) | |||||||
\(992\) | −7.94496 | + | 3.94245i | −0.252253 | + | 0.125173i | ||||
\(993\) | 15.8159 | − | 9.47134i | 0.501902 | − | 0.300564i | ||||
\(994\) | 2.98820 | + | 11.7417i | 0.0947799 | + | 0.372426i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −46.4298 | + | 11.9833i | −1.47118 | + | 0.379704i | ||||
\(997\) | −28.1978 | − | 28.1978i | −0.893034 | − | 0.893034i | 0.101774 | − | 0.994808i | \(-0.467548\pi\) |
−0.994808 | + | 0.101774i | \(0.967548\pi\) | |||||||
\(998\) | −30.2060 | − | 17.9505i | −0.956153 | − | 0.568212i | ||||
\(999\) | −26.8761 | − | 24.4161i | −0.850321 | − | 0.772492i |
(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 | 600.2.w.k.293.28 | yes | 64 | |
3.2 | odd | 2 | inner | 600.2.w.k.293.6 | yes | 64 | |
5.2 | odd | 4 | inner | 600.2.w.k.557.11 | yes | 64 | |
5.3 | odd | 4 | inner | 600.2.w.k.557.22 | yes | 64 | |
5.4 | even | 2 | inner | 600.2.w.k.293.5 | ✓ | 64 | |
8.5 | even | 2 | inner | 600.2.w.k.293.21 | yes | 64 | |
15.2 | even | 4 | inner | 600.2.w.k.557.21 | yes | 64 | |
15.8 | even | 4 | inner | 600.2.w.k.557.12 | yes | 64 | |
15.14 | odd | 2 | inner | 600.2.w.k.293.27 | yes | 64 | |
24.5 | odd | 2 | inner | 600.2.w.k.293.11 | yes | 64 | |
40.13 | odd | 4 | inner | 600.2.w.k.557.27 | yes | 64 | |
40.29 | even | 2 | inner | 600.2.w.k.293.12 | yes | 64 | |
40.37 | odd | 4 | inner | 600.2.w.k.557.6 | yes | 64 | |
120.29 | odd | 2 | inner | 600.2.w.k.293.22 | yes | 64 | |
120.53 | even | 4 | inner | 600.2.w.k.557.5 | yes | 64 | |
120.77 | even | 4 | inner | 600.2.w.k.557.28 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.2.w.k.293.5 | ✓ | 64 | 5.4 | even | 2 | inner | |
600.2.w.k.293.6 | yes | 64 | 3.2 | odd | 2 | inner | |
600.2.w.k.293.11 | yes | 64 | 24.5 | odd | 2 | inner | |
600.2.w.k.293.12 | yes | 64 | 40.29 | even | 2 | inner | |
600.2.w.k.293.21 | yes | 64 | 8.5 | even | 2 | inner | |
600.2.w.k.293.22 | yes | 64 | 120.29 | odd | 2 | inner | |
600.2.w.k.293.27 | yes | 64 | 15.14 | odd | 2 | inner | |
600.2.w.k.293.28 | yes | 64 | 1.1 | even | 1 | trivial | |
600.2.w.k.557.5 | yes | 64 | 120.53 | even | 4 | inner | |
600.2.w.k.557.6 | yes | 64 | 40.37 | odd | 4 | inner | |
600.2.w.k.557.11 | yes | 64 | 5.2 | odd | 4 | inner | |
600.2.w.k.557.12 | yes | 64 | 15.8 | even | 4 | inner | |
600.2.w.k.557.21 | yes | 64 | 15.2 | even | 4 | inner | |
600.2.w.k.557.22 | yes | 64 | 5.3 | odd | 4 | inner | |
600.2.w.k.557.27 | yes | 64 | 40.13 | odd | 4 | inner | |
600.2.w.k.557.28 | yes | 64 | 120.77 | even | 4 | inner |