Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [187,2,Mod(100,187)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(187, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("187.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.h (of order \(8\), degree \(4\), 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: | \(1.49320251780\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 100.8 | ||
Character | \(\chi\) | \(=\) | 187.100 |
Dual form | 187.2.h.a.144.8 |
$q$-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 \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(122\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.131056 | + | 0.131056i | 0.0926707 | + | 0.0926707i | 0.751922 | − | 0.659252i | \(-0.229127\pi\) |
−0.659252 | + | 0.751922i | \(0.729127\pi\) | |||||||
\(3\) | 0.554134 | + | 1.33780i | 0.319929 | + | 0.772378i | 0.999257 | + | 0.0385427i | \(0.0122716\pi\) |
−0.679328 | + | 0.733835i | \(0.737728\pi\) | |||||||
\(4\) | − | 1.96565i | − | 0.982824i | ||||||
\(5\) | 1.85179 | − | 0.767036i | 0.828145 | − | 0.343029i | 0.0719770 | − | 0.997406i | \(-0.477069\pi\) |
0.756168 | + | 0.654377i | \(0.227069\pi\) | |||||||
\(6\) | −0.102704 | + | 0.247949i | −0.0419287 | + | 0.101225i | ||||
\(7\) | −0.551118 | − | 0.228280i | −0.208303 | − | 0.0862819i | 0.276093 | − | 0.961131i | \(-0.410960\pi\) |
−0.484395 | + | 0.874849i | \(0.660960\pi\) | |||||||
\(8\) | 0.519723 | − | 0.519723i | 0.183750 | − | 0.183750i | ||||
\(9\) | 0.638682 | − | 0.638682i | 0.212894 | − | 0.212894i | ||||
\(10\) | 0.343213 | + | 0.142164i | 0.108534 | + | 0.0449561i | ||||
\(11\) | −0.382683 | + | 0.923880i | −0.115383 | + | 0.278560i | ||||
\(12\) | 2.62964 | − | 1.08923i | 0.759112 | − | 0.314434i | ||||
\(13\) | 2.18007i | 0.604643i | 0.953206 | + | 0.302322i | \(0.0977616\pi\) | ||||
−0.953206 | + | 0.302322i | \(0.902238\pi\) | |||||||
\(14\) | −0.0423098 | − | 0.102145i | −0.0113078 | − | 0.0272994i | ||||
\(15\) | 2.05228 | + | 2.05228i | 0.529896 | + | 0.529896i | ||||
\(16\) | −3.79507 | −0.948768 | ||||||||
\(17\) | −3.90011 | − | 1.33758i | −0.945916 | − | 0.324410i | ||||
\(18\) | 0.167407 | 0.0394581 | ||||||||
\(19\) | 6.03686 | + | 6.03686i | 1.38495 | + | 1.38495i | 0.835577 | + | 0.549373i | \(0.185134\pi\) |
0.549373 | + | 0.835577i | \(0.314866\pi\) | |||||||
\(20\) | −1.50772 | − | 3.63997i | −0.337137 | − | 0.813921i | ||||
\(21\) | − | 0.863782i | − | 0.188493i | ||||||
\(22\) | −0.171233 | + | 0.0709271i | −0.0365070 | + | 0.0151217i | ||||
\(23\) | 0.245547 | − | 0.592803i | 0.0512001 | − | 0.123608i | −0.896210 | − | 0.443630i | \(-0.853690\pi\) |
0.947410 | + | 0.320022i | \(0.103690\pi\) | |||||||
\(24\) | 0.983280 | + | 0.407288i | 0.200711 | + | 0.0831373i | ||||
\(25\) | −0.694756 | + | 0.694756i | −0.138951 | + | 0.138951i | ||||
\(26\) | −0.285712 | + | 0.285712i | −0.0560327 | + | 0.0560327i | ||||
\(27\) | 5.22174 | + | 2.16291i | 1.00492 | + | 0.416253i | ||||
\(28\) | −0.448719 | + | 1.08330i | −0.0847999 | + | 0.204725i | ||||
\(29\) | −7.81225 | + | 3.23594i | −1.45070 | + | 0.600899i | −0.962365 | − | 0.271759i | \(-0.912395\pi\) |
−0.488332 | + | 0.872658i | \(0.662395\pi\) | |||||||
\(30\) | 0.537928i | 0.0982117i | ||||||||
\(31\) | −3.47763 | − | 8.39575i | −0.624601 | − | 1.50792i | −0.846245 | − | 0.532793i | \(-0.821142\pi\) |
0.221644 | − | 0.975128i | \(-0.428858\pi\) | |||||||
\(32\) | −1.53681 | − | 1.53681i | −0.271673 | − | 0.271673i | ||||
\(33\) | −1.44802 | −0.252068 | ||||||||
\(34\) | −0.335836 | − | 0.686432i | −0.0575954 | − | 0.117722i | ||||
\(35\) | −1.19565 | −0.202102 | ||||||||
\(36\) | −1.25542 | − | 1.25542i | −0.209237 | − | 0.209237i | ||||
\(37\) | −1.36283 | − | 3.29015i | −0.224047 | − | 0.540898i | 0.771385 | − | 0.636369i | \(-0.219564\pi\) |
−0.995432 | + | 0.0954709i | \(0.969564\pi\) | |||||||
\(38\) | 1.58234i | 0.256689i | ||||||||
\(39\) | −2.91649 | + | 1.20805i | −0.467013 | + | 0.193443i | ||||
\(40\) | 0.563771 | − | 1.36106i | 0.0891400 | − | 0.215203i | ||||
\(41\) | −5.32899 | − | 2.20734i | −0.832249 | − | 0.344729i | −0.0744561 | − | 0.997224i | \(-0.523722\pi\) |
−0.757792 | + | 0.652496i | \(0.773722\pi\) | |||||||
\(42\) | 0.113204 | − | 0.113204i | 0.0174677 | − | 0.0174677i | ||||
\(43\) | 2.16470 | − | 2.16470i | 0.330113 | − | 0.330113i | −0.522516 | − | 0.852629i | \(-0.675007\pi\) |
0.852629 | + | 0.522516i | \(0.175007\pi\) | |||||||
\(44\) | 1.81602 | + | 0.752221i | 0.273776 | + | 0.113402i | ||||
\(45\) | 0.692812 | − | 1.67260i | 0.103278 | − | 0.249336i | ||||
\(46\) | 0.109871 | − | 0.0455101i | 0.0161996 | − | 0.00671009i | ||||
\(47\) | 10.6708i | 1.55650i | 0.627956 | + | 0.778249i | \(0.283892\pi\) | ||||
−0.627956 | + | 0.778249i | \(0.716108\pi\) | |||||||
\(48\) | −2.10298 | − | 5.07704i | −0.303539 | − | 0.732807i | ||||
\(49\) | −4.69813 | − | 4.69813i | −0.671161 | − | 0.671161i | ||||
\(50\) | −0.182104 | −0.0257534 | ||||||||
\(51\) | −0.371777 | − | 5.95876i | −0.0520591 | − | 0.834393i | ||||
\(52\) | 4.28525 | 0.594258 | ||||||||
\(53\) | 2.64883 | + | 2.64883i | 0.363845 | + | 0.363845i | 0.865226 | − | 0.501382i | \(-0.167175\pi\) |
−0.501382 | + | 0.865226i | \(0.667175\pi\) | |||||||
\(54\) | 0.400878 | + | 0.967804i | 0.0545525 | + | 0.131701i | ||||
\(55\) | 2.00436i | 0.270268i | ||||||||
\(56\) | −0.405071 | + | 0.167786i | −0.0541299 | + | 0.0224213i | ||||
\(57\) | −4.73087 | + | 11.4213i | −0.626619 | + | 1.51279i | ||||
\(58\) | −1.44793 | − | 0.599754i | −0.190123 | − | 0.0787515i | ||||
\(59\) | −4.38591 | + | 4.38591i | −0.570997 | + | 0.570997i | −0.932407 | − | 0.361410i | \(-0.882295\pi\) |
0.361410 | + | 0.932407i | \(0.382295\pi\) | |||||||
\(60\) | 4.03406 | − | 4.03406i | 0.520795 | − | 0.520795i | ||||
\(61\) | −0.0140470 | − | 0.00581845i | −0.00179853 | − | 0.000744977i | 0.381784 | − | 0.924252i | \(-0.375310\pi\) |
−0.383583 | + | 0.923507i | \(0.625310\pi\) | |||||||
\(62\) | 0.644550 | − | 1.55608i | 0.0818579 | − | 0.197622i | ||||
\(63\) | −0.497788 | + | 0.206190i | −0.0627153 | + | 0.0259775i | ||||
\(64\) | 7.18732i | 0.898416i | ||||||||
\(65\) | 1.67219 | + | 4.03703i | 0.207410 | + | 0.500732i | ||||
\(66\) | −0.189772 | − | 0.189772i | −0.0233594 | − | 0.0233594i | ||||
\(67\) | 6.00539 | 0.733675 | 0.366838 | − | 0.930285i | \(-0.380440\pi\) | ||||
0.366838 | + | 0.930285i | \(0.380440\pi\) | |||||||
\(68\) | −2.62921 | + | 7.66625i | −0.318838 | + | 0.929670i | ||||
\(69\) | 0.929117 | 0.111853 | ||||||||
\(70\) | −0.156698 | − | 0.156698i | −0.0187290 | − | 0.0187290i | ||||
\(71\) | −1.91924 | − | 4.63346i | −0.227772 | − | 0.549890i | 0.768134 | − | 0.640290i | \(-0.221186\pi\) |
−0.995906 | + | 0.0903994i | \(0.971186\pi\) | |||||||
\(72\) | − | 0.663876i | − | 0.0782385i | ||||||
\(73\) | 9.50711 | − | 3.93797i | 1.11272 | − | 0.460905i | 0.250848 | − | 0.968026i | \(-0.419291\pi\) |
0.861874 | + | 0.507122i | \(0.169291\pi\) | |||||||
\(74\) | 0.252588 | − | 0.609802i | 0.0293628 | − | 0.0708880i | ||||
\(75\) | −1.31443 | − | 0.544455i | −0.151777 | − | 0.0628683i | ||||
\(76\) | 11.8663 | − | 11.8663i | 1.36116 | − | 1.36116i | ||||
\(77\) | 0.421807 | − | 0.421807i | 0.0480694 | − | 0.0480694i | ||||
\(78\) | −0.540547 | − | 0.223902i | −0.0612049 | − | 0.0253519i | ||||
\(79\) | −3.73551 | + | 9.01833i | −0.420278 | + | 1.01464i | 0.561987 | + | 0.827146i | \(0.310037\pi\) |
−0.982266 | + | 0.187495i | \(0.939963\pi\) | |||||||
\(80\) | −7.02767 | + | 2.91096i | −0.785717 | + | 0.325455i | ||||
\(81\) | 5.47447i | 0.608275i | ||||||||
\(82\) | −0.409112 | − | 0.987683i | −0.0451788 | − | 0.109071i | ||||
\(83\) | 6.56549 | + | 6.56549i | 0.720657 | + | 0.720657i | 0.968739 | − | 0.248082i | \(-0.0798003\pi\) |
−0.248082 | + | 0.968739i | \(0.579800\pi\) | |||||||
\(84\) | −1.69789 | −0.185255 | ||||||||
\(85\) | −8.24816 | + | 0.514616i | −0.894638 | + | 0.0558179i | ||||
\(86\) | 0.567394 | 0.0611837 | ||||||||
\(87\) | −8.65806 | − | 8.65806i | −0.928242 | − | 0.928242i | ||||
\(88\) | 0.281272 | + | 0.679051i | 0.0299837 | + | 0.0723871i | ||||
\(89\) | − | 16.2031i | − | 1.71753i | −0.512370 | − | 0.858765i | \(-0.671232\pi\) | ||
0.512370 | − | 0.858765i | \(-0.328768\pi\) | |||||||
\(90\) | 0.310002 | − | 0.128407i | 0.0326770 | − | 0.0135353i | ||||
\(91\) | 0.497668 | − | 1.20148i | 0.0521697 | − | 0.125949i | ||||
\(92\) | −1.16524 | − | 0.482659i | −0.121485 | − | 0.0503207i | ||||
\(93\) | 9.30474 | − | 9.30474i | 0.964857 | − | 0.964857i | ||||
\(94\) | −1.39848 | + | 1.39848i | −0.144242 | + | 0.144242i | ||||
\(95\) | 15.8095 | + | 6.54850i | 1.62202 | + | 0.671862i | ||||
\(96\) | 1.20435 | − | 2.90755i | 0.122918 | − | 0.296750i | ||||
\(97\) | 12.9060 | − | 5.34582i | 1.31040 | − | 0.542786i | 0.385400 | − | 0.922750i | \(-0.374064\pi\) |
0.925001 | + | 0.379964i | \(0.124064\pi\) | |||||||
\(98\) | − | 1.23144i | − | 0.124394i | ||||||
\(99\) | 0.345652 | + | 0.834479i | 0.0347394 | + | 0.0838682i | ||||
\(100\) | 1.36565 | + | 1.36565i | 0.136565 | + | 0.136565i | ||||
\(101\) | 0.666064 | 0.0662759 | 0.0331379 | − | 0.999451i | \(-0.489450\pi\) | ||||
0.0331379 | + | 0.999451i | \(0.489450\pi\) | |||||||
\(102\) | 0.732209 | − | 0.829656i | 0.0724995 | − | 0.0821482i | ||||
\(103\) | 10.3950 | 1.02425 | 0.512126 | − | 0.858910i | \(-0.328858\pi\) | ||||
0.512126 | + | 0.858910i | \(0.328858\pi\) | |||||||
\(104\) | 1.13303 | + | 1.13303i | 0.111103 | + | 0.111103i | ||||
\(105\) | −0.662552 | − | 1.59954i | −0.0646584 | − | 0.156099i | ||||
\(106\) | 0.694291i | 0.0674355i | ||||||||
\(107\) | −5.24085 | + | 2.17083i | −0.506652 | + | 0.209862i | −0.621342 | − | 0.783539i | \(-0.713412\pi\) |
0.114690 | + | 0.993401i | \(0.463412\pi\) | |||||||
\(108\) | 4.25153 | − | 10.2641i | 0.409104 | − | 0.987663i | ||||
\(109\) | −1.18338 | − | 0.490174i | −0.113348 | − | 0.0469501i | 0.325289 | − | 0.945615i | \(-0.394538\pi\) |
−0.438637 | + | 0.898665i | \(0.644538\pi\) | |||||||
\(110\) | −0.262684 | + | 0.262684i | −0.0250459 | + | 0.0250459i | ||||
\(111\) | 3.64637 | − | 3.64637i | 0.346098 | − | 0.346098i | ||||
\(112\) | 2.09153 | + | 0.866340i | 0.197631 | + | 0.0818615i | ||||
\(113\) | −2.79231 | + | 6.74122i | −0.262678 | + | 0.634161i | −0.999102 | − | 0.0423589i | \(-0.986513\pi\) |
0.736424 | + | 0.676520i | \(0.236513\pi\) | |||||||
\(114\) | −2.11685 | + | 0.876826i | −0.198261 | + | 0.0821223i | ||||
\(115\) | − | 1.28609i | − | 0.119929i | ||||||
\(116\) | 6.36072 | + | 15.3561i | 0.590578 | + | 1.42578i | ||||
\(117\) | 1.39237 | + | 1.39237i | 0.128725 | + | 0.128725i | ||||
\(118\) | −1.14960 | −0.105829 | ||||||||
\(119\) | 1.84408 | + | 1.62748i | 0.169046 | + | 0.149191i | ||||
\(120\) | 2.13323 | 0.194737 | ||||||||
\(121\) | −0.707107 | − | 0.707107i | −0.0642824 | − | 0.0642824i | ||||
\(122\) | −0.00107840 | − | 0.00260349i | −9.76338e−5 | − | 0.000235709i | ||||
\(123\) | − | 8.35227i | − | 0.753099i | ||||||
\(124\) | −16.5031 | + | 6.83580i | −1.48202 | + | 0.613873i | ||||
\(125\) | −4.58882 | + | 11.0784i | −0.410436 | + | 0.990881i | ||||
\(126\) | −0.0922607 | − | 0.0382156i | −0.00821924 | − | 0.00340452i | ||||
\(127\) | 4.86726 | − | 4.86726i | 0.431900 | − | 0.431900i | −0.457374 | − | 0.889274i | \(-0.651210\pi\) |
0.889274 | + | 0.457374i | \(0.151210\pi\) | |||||||
\(128\) | −4.01557 | + | 4.01557i | −0.354930 | + | 0.354930i | ||||
\(129\) | 4.09546 | + | 1.69639i | 0.360585 | + | 0.149359i | ||||
\(130\) | −0.309927 | + | 0.748230i | −0.0271824 | + | 0.0656241i | ||||
\(131\) | 1.96785 | − | 0.815109i | 0.171932 | − | 0.0712164i | −0.295057 | − | 0.955480i | \(-0.595339\pi\) |
0.466989 | + | 0.884263i | \(0.345339\pi\) | |||||||
\(132\) | 2.84630i | 0.247739i | ||||||||
\(133\) | −1.94892 | − | 4.70511i | −0.168993 | − | 0.407985i | ||||
\(134\) | 0.787044 | + | 0.787044i | 0.0679903 | + | 0.0679903i | ||||
\(135\) | 11.3286 | 0.975009 | ||||||||
\(136\) | −2.72215 | + | 1.33181i | −0.233422 | + | 0.114202i | ||||
\(137\) | −2.02146 | −0.172705 | −0.0863524 | − | 0.996265i | \(-0.527521\pi\) | ||||
−0.0863524 | + | 0.996265i | \(0.527521\pi\) | |||||||
\(138\) | 0.121767 | + | 0.121767i | 0.0103655 | + | 0.0103655i | ||||
\(139\) | −2.21678 | − | 5.35178i | −0.188025 | − | 0.453932i | 0.801554 | − | 0.597922i | \(-0.204007\pi\) |
−0.989579 | + | 0.143990i | \(0.954007\pi\) | |||||||
\(140\) | 2.35023i | 0.198631i | ||||||||
\(141\) | −14.2754 | + | 5.91306i | −1.20220 | + | 0.497969i | ||||
\(142\) | 0.355715 | − | 0.858772i | 0.0298509 | − | 0.0720665i | ||||
\(143\) | −2.01412 | − | 0.834277i | −0.168429 | − | 0.0697658i | ||||
\(144\) | −2.42384 | + | 2.42384i | −0.201987 | + | 0.201987i | ||||
\(145\) | −11.9845 | + | 11.9845i | −0.995263 | + | 0.995263i | ||||
\(146\) | 1.76206 | + | 0.729870i | 0.145829 | + | 0.0604044i | ||||
\(147\) | 3.68175 | − | 8.88854i | 0.303666 | − | 0.733114i | ||||
\(148\) | −6.46729 | + | 2.67884i | −0.531608 | + | 0.220199i | ||||
\(149\) | − | 1.27339i | − | 0.104320i | −0.998639 | − | 0.0521600i | \(-0.983389\pi\) | ||
0.998639 | − | 0.0521600i | \(-0.0166106\pi\) | |||||||
\(150\) | −0.100910 | − | 0.243619i | −0.00823928 | − | 0.0198914i | ||||
\(151\) | −9.13270 | − | 9.13270i | −0.743208 | − | 0.743208i | 0.229986 | − | 0.973194i | \(-0.426132\pi\) |
−0.973194 | + | 0.229986i | \(0.926132\pi\) | |||||||
\(152\) | 6.27499 | 0.508969 | ||||||||
\(153\) | −3.34522 | + | 1.63665i | −0.270445 | + | 0.132315i | ||||
\(154\) | 0.110561 | 0.00890925 | ||||||||
\(155\) | −12.8797 | − | 12.8797i | −1.03452 | − | 1.03452i | ||||
\(156\) | 2.37460 | + | 5.73280i | 0.190121 | + | 0.458992i | ||||
\(157\) | 8.79938i | 0.702267i | 0.936325 | + | 0.351133i | \(0.114204\pi\) | ||||
−0.936325 | + | 0.351133i | \(0.885796\pi\) | |||||||
\(158\) | −1.67147 | + | 0.692346i | −0.132975 | + | 0.0550801i | ||||
\(159\) | −2.07579 | + | 5.01141i | −0.164621 | + | 0.397430i | ||||
\(160\) | −4.02465 | − | 1.66706i | −0.318176 | − | 0.131793i | ||||
\(161\) | −0.270651 | + | 0.270651i | −0.0213303 | + | 0.0213303i | ||||
\(162\) | −0.717464 | + | 0.717464i | −0.0563693 | + | 0.0563693i | ||||
\(163\) | 15.3882 | + | 6.37402i | 1.20530 | + | 0.499252i | 0.892708 | − | 0.450636i | \(-0.148803\pi\) |
0.312592 | + | 0.949887i | \(0.398803\pi\) | |||||||
\(164\) | −4.33886 | + | 10.4749i | −0.338808 | + | 0.817954i | ||||
\(165\) | −2.68143 | + | 1.11068i | −0.208749 | + | 0.0864667i | ||||
\(166\) | 1.72090i | 0.133568i | ||||||||
\(167\) | −5.33570 | − | 12.8815i | −0.412889 | − | 0.996802i | −0.984358 | − | 0.176178i | \(-0.943626\pi\) |
0.571469 | − | 0.820623i | \(-0.306374\pi\) | |||||||
\(168\) | −0.448927 | − | 0.448927i | −0.0346355 | − | 0.0346355i | ||||
\(169\) | 8.24729 | 0.634407 | ||||||||
\(170\) | −1.14842 | − | 1.01353i | −0.0880795 | − | 0.0777341i | ||||
\(171\) | 7.71127 | 0.589695 | ||||||||
\(172\) | −4.25503 | − | 4.25503i | −0.324443 | − | 0.324443i | ||||
\(173\) | −6.78604 | − | 16.3829i | −0.515933 | − | 1.24557i | −0.940382 | − | 0.340120i | \(-0.889532\pi\) |
0.424449 | − | 0.905452i | \(-0.360468\pi\) | |||||||
\(174\) | − | 2.26939i | − | 0.172042i | ||||||
\(175\) | 0.541492 | − | 0.224293i | 0.0409329 | − | 0.0169550i | ||||
\(176\) | 1.45231 | − | 3.50619i | 0.109472 | − | 0.264289i | ||||
\(177\) | −8.29784 | − | 3.43708i | −0.623704 | − | 0.258347i | ||||
\(178\) | 2.12352 | − | 2.12352i | 0.159165 | − | 0.159165i | ||||
\(179\) | 2.70049 | − | 2.70049i | 0.201844 | − | 0.201844i | −0.598946 | − | 0.800790i | \(-0.704413\pi\) |
0.800790 | + | 0.598946i | \(0.204413\pi\) | |||||||
\(180\) | −3.28774 | − | 1.36183i | −0.245053 | − | 0.101504i | ||||
\(181\) | 5.13352 | − | 12.3934i | 0.381571 | − | 0.921194i | −0.610091 | − | 0.792331i | \(-0.708867\pi\) |
0.991662 | − | 0.128863i | \(-0.0411328\pi\) | |||||||
\(182\) | 0.222683 | − | 0.0922384i | 0.0165064 | − | 0.00683717i | ||||
\(183\) | − | 0.0220162i | − | 0.00162749i | ||||||
\(184\) | −0.180477 | − | 0.435710i | −0.0133049 | − | 0.0321210i | ||||
\(185\) | −5.04733 | − | 5.04733i | −0.371087 | − | 0.371087i | ||||
\(186\) | 2.43889 | 0.178828 | ||||||||
\(187\) | 2.72827 | − | 3.09137i | 0.199511 | − | 0.226063i | ||||
\(188\) | 20.9751 | 1.52976 | ||||||||
\(189\) | −2.38404 | − | 2.38404i | −0.173413 | − | 0.173413i | ||||
\(190\) | 1.21371 | + | 2.93015i | 0.0880517 | + | 0.212576i | ||||
\(191\) | − | 8.85486i | − | 0.640715i | −0.947297 | − | 0.320358i | \(-0.896197\pi\) | ||
0.947297 | − | 0.320358i | \(-0.103803\pi\) | |||||||
\(192\) | −9.61519 | + | 3.98274i | −0.693916 | + | 0.287430i | ||||
\(193\) | −4.47646 | + | 10.8071i | −0.322223 | + | 0.777914i | 0.676902 | + | 0.736073i | \(0.263322\pi\) |
−0.999124 | + | 0.0418407i | \(0.986678\pi\) | |||||||
\(194\) | 2.39201 | + | 0.990803i | 0.171736 | + | 0.0711355i | ||||
\(195\) | −4.47411 | + | 4.47411i | −0.320398 | + | 0.320398i | ||||
\(196\) | −9.23487 | + | 9.23487i | −0.659634 | + | 0.659634i | ||||
\(197\) | −12.5528 | − | 5.19954i | −0.894350 | − | 0.370452i | −0.112305 | − | 0.993674i | \(-0.535823\pi\) |
−0.782045 | + | 0.623222i | \(0.785823\pi\) | |||||||
\(198\) | −0.0640637 | + | 0.154663i | −0.00455281 | + | 0.0109915i | ||||
\(199\) | −12.9657 | + | 5.37059i | −0.919117 | + | 0.380711i | −0.791540 | − | 0.611118i | \(-0.790720\pi\) |
−0.127578 | + | 0.991829i | \(0.540720\pi\) | |||||||
\(200\) | 0.722162i | 0.0510645i | ||||||||
\(201\) | 3.32779 | + | 8.03400i | 0.234724 | + | 0.566675i | ||||
\(202\) | 0.0872919 | + | 0.0872919i | 0.00614183 | + | 0.00614183i | ||||
\(203\) | 5.04417 | 0.354031 | ||||||||
\(204\) | −11.7128 | + | 0.730782i | −0.820062 | + | 0.0511650i | ||||
\(205\) | −11.5613 | −0.807474 | ||||||||
\(206\) | 1.36233 | + | 1.36233i | 0.0949181 | + | 0.0949181i | ||||
\(207\) | −0.221786 | − | 0.535439i | −0.0154152 | − | 0.0372156i | ||||
\(208\) | − | 8.27353i | − | 0.573666i | ||||||
\(209\) | −7.88754 | + | 3.26712i | −0.545592 | + | 0.225992i | ||||
\(210\) | 0.122798 | − | 0.296461i | 0.00847389 | − | 0.0204578i | ||||
\(211\) | 12.2399 | + | 5.06994i | 0.842630 | + | 0.349029i | 0.761890 | − | 0.647706i | \(-0.224272\pi\) |
0.0807402 | + | 0.996735i | \(0.474272\pi\) | |||||||
\(212\) | 5.20667 | − | 5.20667i | 0.357595 | − | 0.357595i | ||||
\(213\) | 5.13511 | − | 5.13511i | 0.351852 | − | 0.351852i | ||||
\(214\) | −0.971347 | − | 0.402345i | −0.0663999 | − | 0.0275037i | ||||
\(215\) | 2.34816 | − | 5.66896i | 0.160143 | − | 0.386620i | ||||
\(216\) | 3.83797 | − | 1.58974i | 0.261141 | − | 0.108168i | ||||
\(217\) | 5.42092i | 0.367996i | ||||||||
\(218\) | −0.0908495 | − | 0.219330i | −0.00615310 | − | 0.0148549i | ||||
\(219\) | 10.5364 | + | 10.5364i | 0.711985 | + | 0.711985i | ||||
\(220\) | 3.93987 | 0.265626 | ||||||||
\(221\) | 2.91602 | − | 8.50253i | 0.196152 | − | 0.571942i | ||||
\(222\) | 0.955759 | 0.0641464 | ||||||||
\(223\) | −13.1660 | − | 13.1660i | −0.881662 | − | 0.881662i | 0.112042 | − | 0.993703i | \(-0.464261\pi\) |
−0.993703 | + | 0.112042i | \(0.964261\pi\) | |||||||
\(224\) | 0.496141 | + | 1.19779i | 0.0331498 | + | 0.0800307i | ||||
\(225\) | 0.887457i | 0.0591638i | ||||||||
\(226\) | −1.24943 | + | 0.517530i | −0.0831108 | + | 0.0344256i | ||||
\(227\) | −10.4777 | + | 25.2954i | −0.695430 | + | 1.67892i | 0.0381133 | + | 0.999273i | \(0.487865\pi\) |
−0.733543 | + | 0.679643i | \(0.762135\pi\) | |||||||
\(228\) | 22.4503 | + | 9.29922i | 1.48681 | + | 0.615856i | ||||
\(229\) | 12.1157 | − | 12.1157i | 0.800627 | − | 0.800627i | −0.182567 | − | 0.983193i | \(-0.558441\pi\) |
0.983193 | + | 0.182567i | \(0.0584405\pi\) | |||||||
\(230\) | 0.168550 | − | 0.168550i | 0.0111139 | − | 0.0111139i | ||||
\(231\) | 0.798030 | + | 0.330555i | 0.0525065 | + | 0.0217489i | ||||
\(232\) | −2.37841 | + | 5.74200i | −0.156150 | + | 0.376980i | ||||
\(233\) | −7.90060 | + | 3.27254i | −0.517586 | + | 0.214391i | −0.626156 | − | 0.779698i | \(-0.715373\pi\) |
0.108570 | + | 0.994089i | \(0.465373\pi\) | |||||||
\(234\) | 0.364958i | 0.0238581i | ||||||||
\(235\) | 8.18489 | + | 19.7601i | 0.533924 | + | 1.28901i | ||||
\(236\) | 8.62115 | + | 8.62115i | 0.561189 | + | 0.561189i | ||||
\(237\) | −14.1347 | −0.918146 | ||||||||
\(238\) | 0.0283863 | + | 0.454970i | 0.00184001 | + | 0.0294913i | ||||
\(239\) | −4.48889 | −0.290362 | −0.145181 | − | 0.989405i | \(-0.546376\pi\) | ||||
−0.145181 | + | 0.989405i | \(0.546376\pi\) | |||||||
\(240\) | −7.78854 | − | 7.78854i | −0.502748 | − | 0.502748i | ||||
\(241\) | −0.701006 | − | 1.69238i | −0.0451558 | − | 0.109016i | 0.899692 | − | 0.436525i | \(-0.143791\pi\) |
−0.944848 | + | 0.327509i | \(0.893791\pi\) | |||||||
\(242\) | − | 0.185341i | − | 0.0119142i | ||||||
\(243\) | 8.34147 | − | 3.45515i | 0.535106 | − | 0.221648i | ||||
\(244\) | −0.0114370 | + | 0.0276114i | −0.000732181 | + | 0.00176764i | ||||
\(245\) | −12.3036 | − | 5.09631i | −0.786047 | − | 0.325591i | ||||
\(246\) | 1.09462 | − | 1.09462i | 0.0697903 | − | 0.0697903i | ||||
\(247\) | −13.1608 | + | 13.1608i | −0.837401 | + | 0.837401i | ||||
\(248\) | −6.17087 | − | 2.55606i | −0.391851 | − | 0.162310i | ||||
\(249\) | −5.14514 | + | 12.4215i | −0.326060 | + | 0.787178i | ||||
\(250\) | −2.05329 | + | 0.850499i | −0.129861 | + | 0.0537903i | ||||
\(251\) | − | 12.7038i | − | 0.801858i | −0.916109 | − | 0.400929i | \(-0.868687\pi\) | ||
0.916109 | − | 0.400929i | \(-0.131313\pi\) | |||||||
\(252\) | 0.405298 | + | 0.978475i | 0.0255314 | + | 0.0616382i | ||||
\(253\) | 0.453712 | + | 0.453712i | 0.0285246 | + | 0.0285246i | ||||
\(254\) | 1.27577 | 0.0800490 | ||||||||
\(255\) | −5.25904 | − | 10.7492i | −0.329334 | − | 0.673141i | ||||
\(256\) | 13.3221 | 0.832632 | ||||||||
\(257\) | 15.2784 | + | 15.2784i | 0.953042 | + | 0.953042i | 0.998946 | − | 0.0459043i | \(-0.0146169\pi\) |
−0.0459043 | + | 0.998946i | \(0.514617\pi\) | |||||||
\(258\) | 0.314412 | + | 0.759058i | 0.0195745 | + | 0.0472569i | ||||
\(259\) | 2.12437i | 0.132002i | ||||||||
\(260\) | 7.93539 | − | 3.28694i | 0.492132 | − | 0.203848i | ||||
\(261\) | −2.92281 | + | 7.05628i | −0.180917 | + | 0.436773i | ||||
\(262\) | 0.364724 | + | 0.151074i | 0.0225327 | + | 0.00933336i | ||||
\(263\) | 10.8224 | − | 10.8224i | 0.667341 | − | 0.667341i | −0.289759 | − | 0.957100i | \(-0.593575\pi\) |
0.957100 | + | 0.289759i | \(0.0935751\pi\) | |||||||
\(264\) | −0.752570 | + | 0.752570i | −0.0463175 | + | 0.0463175i | ||||
\(265\) | 6.93682 | + | 2.87333i | 0.426126 | + | 0.176507i | ||||
\(266\) | 0.361216 | − | 0.872053i | 0.0221476 | − | 0.0534690i | ||||
\(267\) | 21.6765 | − | 8.97871i | 1.32658 | − | 0.549488i | ||||
\(268\) | − | 11.8045i | − | 0.721074i | ||||||
\(269\) | 0.495279 | + | 1.19571i | 0.0301977 | + | 0.0729036i | 0.938259 | − | 0.345934i | \(-0.112438\pi\) |
−0.908061 | + | 0.418837i | \(0.862438\pi\) | |||||||
\(270\) | 1.48468 | + | 1.48468i | 0.0903548 | + | 0.0903548i | ||||
\(271\) | 15.4512 | 0.938594 | 0.469297 | − | 0.883040i | \(-0.344507\pi\) | ||||
0.469297 | + | 0.883040i | \(0.344507\pi\) | |||||||
\(272\) | 14.8012 | + | 5.07620i | 0.897455 | + | 0.307790i | ||||
\(273\) | 1.88311 | 0.113971 | ||||||||
\(274\) | −0.264925 | − | 0.264925i | −0.0160047 | − | 0.0160047i | ||||
\(275\) | −0.375999 | − | 0.907743i | −0.0226736 | − | 0.0547390i | ||||
\(276\) | − | 1.82632i | − | 0.109931i | ||||||
\(277\) | 20.2729 | − | 8.39732i | 1.21808 | − | 0.504546i | 0.321282 | − | 0.946984i | \(-0.395886\pi\) |
0.896799 | + | 0.442438i | \(0.145886\pi\) | |||||||
\(278\) | 0.410861 | − | 0.991907i | 0.0246418 | − | 0.0594906i | ||||
\(279\) | −7.58332 | − | 3.14111i | −0.454001 | − | 0.188054i | ||||
\(280\) | −0.621408 | + | 0.621408i | −0.0371362 | + | 0.0371362i | ||||
\(281\) | 11.9930 | − | 11.9930i | 0.715445 | − | 0.715445i | −0.252224 | − | 0.967669i | \(-0.581162\pi\) |
0.967669 | + | 0.252224i | \(0.0811619\pi\) | |||||||
\(282\) | −2.64582 | − | 1.09593i | −0.157556 | − | 0.0652620i | ||||
\(283\) | 8.45391 | − | 20.4095i | 0.502533 | − | 1.21322i | −0.445567 | − | 0.895249i | \(-0.646998\pi\) |
0.948100 | − | 0.317973i | \(-0.103002\pi\) | |||||||
\(284\) | −9.10775 | + | 3.77255i | −0.540445 | + | 0.223860i | ||||
\(285\) | 24.7786i | 1.46776i | ||||||||
\(286\) | −0.154626 | − | 0.373301i | −0.00914324 | − | 0.0220737i | ||||
\(287\) | 2.43301 | + | 2.43301i | 0.143616 | + | 0.143616i | ||||
\(288\) | −1.96307 | −0.115675 | ||||||||
\(289\) | 13.4218 | + | 10.4334i | 0.789516 | + | 0.613730i | ||||
\(290\) | −3.14130 | −0.184463 | ||||||||
\(291\) | 14.3033 | + | 14.3033i | 0.838472 | + | 0.838472i | ||||
\(292\) | −7.74067 | − | 18.6876i | −0.452988 | − | 1.09361i | ||||
\(293\) | − | 30.6582i | − | 1.79107i | −0.444993 | − | 0.895534i | \(-0.646794\pi\) | ||
0.444993 | − | 0.895534i | \(-0.353206\pi\) | |||||||
\(294\) | 1.64741 | − | 0.682382i | 0.0960792 | − | 0.0397973i | ||||
\(295\) | −4.75763 | + | 11.4859i | −0.277000 | + | 0.668736i | ||||
\(296\) | −2.41826 | − | 1.00168i | −0.140559 | − | 0.0582212i | ||||
\(297\) | −3.99654 | + | 3.99654i | −0.231903 | + | 0.231903i | ||||
\(298\) | 0.166885 | − | 0.166885i | 0.00966741 | − | 0.00966741i | ||||
\(299\) | 1.29235 | + | 0.535310i | 0.0747387 | + | 0.0309578i | ||||
\(300\) | −1.07021 | + | 2.58371i | −0.0617885 | + | 0.149171i | ||||
\(301\) | −1.68716 | + | 0.698845i | −0.0972463 | + | 0.0402807i | ||||
\(302\) | − | 2.39379i | − | 0.137747i | ||||||
\(303\) | 0.369089 | + | 0.891059i | 0.0212036 | + | 0.0511900i | ||||
\(304\) | −22.9103 | − | 22.9103i | −1.31400 | − | 1.31400i | ||||
\(305\) | −0.0304750 | −0.00174499 | ||||||||
\(306\) | −0.652905 | − | 0.223919i | −0.0373241 | − | 0.0128006i | ||||
\(307\) | −0.553753 | −0.0316044 | −0.0158022 | − | 0.999875i | \(-0.505030\pi\) | ||||
−0.0158022 | + | 0.999875i | \(0.505030\pi\) | |||||||
\(308\) | −0.829124 | − | 0.829124i | −0.0472438 | − | 0.0472438i | ||||
\(309\) | 5.76023 | + | 13.9064i | 0.327688 | + | 0.791109i | ||||
\(310\) | − | 3.37593i | − | 0.191740i | ||||||
\(311\) | 7.29880 | − | 3.02326i | 0.413877 | − | 0.171433i | −0.166022 | − | 0.986122i | \(-0.553092\pi\) |
0.579899 | + | 0.814689i | \(0.303092\pi\) | |||||||
\(312\) | −0.887917 | + | 2.14362i | −0.0502684 | + | 0.121359i | ||||
\(313\) | 2.18052 | + | 0.903201i | 0.123250 | + | 0.0510520i | 0.443456 | − | 0.896296i | \(-0.353752\pi\) |
−0.320206 | + | 0.947348i | \(0.603752\pi\) | |||||||
\(314\) | −1.15321 | + | 1.15321i | −0.0650796 | + | 0.0650796i | ||||
\(315\) | −0.763642 | + | 0.763642i | −0.0430264 | + | 0.0430264i | ||||
\(316\) | 17.7269 | + | 7.34271i | 0.997214 | + | 0.413059i | ||||
\(317\) | 1.89179 | − | 4.56717i | 0.106253 | − | 0.256518i | −0.861807 | − | 0.507237i | \(-0.830667\pi\) |
0.968060 | + | 0.250719i | \(0.0806669\pi\) | |||||||
\(318\) | −0.928821 | + | 0.384730i | −0.0520857 | + | 0.0215746i | ||||
\(319\) | − | 8.45591i | − | 0.473440i | ||||||
\(320\) | 5.51294 | + | 13.3094i | 0.308183 | + | 0.744018i | ||||
\(321\) | −5.80826 | − | 5.80826i | −0.324186 | − | 0.324186i | ||||
\(322\) | −0.0709409 | −0.00395338 | ||||||||
\(323\) | −15.4697 | − | 31.6192i | −0.860755 | − | 1.75934i | ||||
\(324\) | 10.7609 | 0.597827 | ||||||||
\(325\) | −1.51462 | − | 1.51462i | −0.0840159 | − | 0.0840159i | ||||
\(326\) | 1.18137 | + | 2.85208i | 0.0654300 | + | 0.157962i | ||||
\(327\) | − | 1.85475i | − | 0.102568i | ||||||
\(328\) | −3.91680 | + | 1.62239i | −0.216269 | + | 0.0895817i | ||||
\(329\) | 2.43594 | − | 5.88087i | 0.134297 | − | 0.324223i | ||||
\(330\) | −0.496980 | − | 0.205856i | −0.0273579 | − | 0.0113320i | ||||
\(331\) | −19.1924 | + | 19.1924i | −1.05491 | + | 1.05491i | −0.0565075 | + | 0.998402i | \(0.517996\pi\) |
−0.998402 | + | 0.0565075i | \(0.982004\pi\) | |||||||
\(332\) | 12.9055 | − | 12.9055i | 0.708279 | − | 0.708279i | ||||
\(333\) | −2.97178 | − | 1.23095i | −0.162852 | − | 0.0674556i | ||||
\(334\) | 0.988926 | − | 2.38748i | 0.0541116 | − | 0.130637i | ||||
\(335\) | 11.1207 | − | 4.60635i | 0.607590 | − | 0.251672i | ||||
\(336\) | 3.27811i | 0.178836i | ||||||||
\(337\) | −10.2369 | − | 24.7140i | −0.557639 | − | 1.34626i | −0.911630 | − | 0.411011i | \(-0.865176\pi\) |
0.353991 | − | 0.935249i | \(-0.384824\pi\) | |||||||
\(338\) | 1.08086 | + | 1.08086i | 0.0587909 | + | 0.0587909i | ||||
\(339\) | −10.5657 | −0.573850 | ||||||||
\(340\) | 1.01155 | + | 16.2130i | 0.0548592 | + | 0.879272i | ||||
\(341\) | 9.08749 | 0.492115 | ||||||||
\(342\) | 1.01061 | + | 1.01061i | 0.0546475 | + | 0.0546475i | ||||
\(343\) | 3.11469 | + | 7.51953i | 0.168178 | + | 0.406017i | ||||
\(344\) | − | 2.25009i | − | 0.121316i | ||||||
\(345\) | 1.72053 | − | 0.712666i | 0.0926301 | − | 0.0383687i | ||||
\(346\) | 1.25773 | − | 3.03644i | 0.0676162 | − | 0.163240i | ||||
\(347\) | 13.2301 | + | 5.48008i | 0.710228 | + | 0.294186i | 0.708399 | − | 0.705812i | \(-0.249418\pi\) |
0.00182908 | + | 0.999998i | \(0.499418\pi\) | |||||||
\(348\) | −17.0187 | + | 17.0187i | −0.912298 | + | 0.912298i | ||||
\(349\) | −21.6075 | + | 21.6075i | −1.15662 | + | 1.15662i | −0.171423 | + | 0.985197i | \(0.554837\pi\) |
−0.985197 | + | 0.171423i | \(0.945163\pi\) | |||||||
\(350\) | 0.100361 | + | 0.0415708i | 0.00536451 | + | 0.00222205i | ||||
\(351\) | −4.71531 | + | 11.3838i | −0.251684 | + | 0.607620i | ||||
\(352\) | 2.00794 | − | 0.831718i | 0.107024 | − | 0.0443307i | ||||
\(353\) | 11.5249i | 0.613409i | 0.951805 | + | 0.306705i | \(0.0992264\pi\) | ||||
−0.951805 | + | 0.306705i | \(0.900774\pi\) | |||||||
\(354\) | −0.637033 | − | 1.53793i | −0.0338579 | − | 0.0817403i | ||||
\(355\) | −7.10806 | − | 7.10806i | −0.377256 | − | 0.377256i | ||||
\(356\) | −31.8497 | −1.68803 | ||||||||
\(357\) | −1.15538 | + | 3.36885i | −0.0611489 | + | 0.178298i | ||||
\(358\) | 0.707832 | 0.0374101 | ||||||||
\(359\) | 23.8971 | + | 23.8971i | 1.26124 | + | 1.26124i | 0.950493 | + | 0.310745i | \(0.100578\pi\) |
0.310745 | + | 0.950493i | \(0.399422\pi\) | |||||||
\(360\) | −0.509216 | − | 1.22936i | −0.0268381 | − | 0.0647928i | ||||
\(361\) | 53.8873i | 2.83617i | ||||||||
\(362\) | 2.29701 | − | 0.951453i | 0.120728 | − | 0.0500073i | ||||
\(363\) | 0.554134 | − | 1.33780i | 0.0290845 | − | 0.0702162i | ||||
\(364\) | −2.36168 | − | 0.978239i | −0.123786 | − | 0.0512737i | ||||
\(365\) | 14.5846 | − | 14.5846i | 0.763392 | − | 0.763392i | ||||
\(366\) | 0.00288536 | − | 0.00288536i | 0.000150820 | − | 0.000150820i | ||||
\(367\) | 4.73463 | + | 1.96115i | 0.247145 | + | 0.102371i | 0.502818 | − | 0.864393i | \(-0.332297\pi\) |
−0.255672 | + | 0.966764i | \(0.582297\pi\) | |||||||
\(368\) | −0.931869 | + | 2.24973i | −0.0485770 | + | 0.117275i | ||||
\(369\) | −4.81332 | + | 1.99374i | −0.250571 | + | 0.103790i | ||||
\(370\) | − | 1.32297i | − | 0.0687779i | ||||||
\(371\) | −0.855141 | − | 2.06449i | −0.0443967 | − | 0.107183i | ||||
\(372\) | −18.2898 | − | 18.2898i | −0.948284 | − | 0.948284i | ||||
\(373\) | −13.4961 | −0.698802 | −0.349401 | − | 0.936973i | \(-0.613615\pi\) | ||||
−0.349401 | + | 0.936973i | \(0.613615\pi\) | |||||||
\(374\) | 0.762700 | − | 0.0475860i | 0.0394383 | − | 0.00246062i | ||||
\(375\) | −17.3635 | −0.896645 | ||||||||
\(376\) | 5.54586 | + | 5.54586i | 0.286006 | + | 0.286006i | ||||
\(377\) | −7.05458 | − | 17.0313i | −0.363329 | − | 0.877154i | ||||
\(378\) | − | 0.624886i | − | 0.0321407i | ||||||
\(379\) | −21.3590 | + | 8.84719i | −1.09714 | + | 0.454450i | −0.856491 | − | 0.516163i | \(-0.827360\pi\) |
−0.240648 | + | 0.970612i | \(0.577360\pi\) | |||||||
\(380\) | 12.8720 | − | 31.0759i | 0.660322 | − | 1.59416i | ||||
\(381\) | 9.20853 | + | 3.81430i | 0.471767 | + | 0.195412i | ||||
\(382\) | 1.16048 | − | 1.16048i | 0.0593756 | − | 0.0593756i | ||||
\(383\) | −14.4275 | + | 14.4275i | −0.737209 | + | 0.737209i | −0.972037 | − | 0.234828i | \(-0.924547\pi\) |
0.234828 | + | 0.972037i | \(0.424547\pi\) | |||||||
\(384\) | −7.59719 | − | 3.14686i | −0.387692 | − | 0.160587i | ||||
\(385\) | 0.457556 | − | 1.10464i | 0.0233192 | − | 0.0562976i | ||||
\(386\) | −2.00301 | + | 0.829674i | −0.101950 | + | 0.0422293i | ||||
\(387\) | − | 2.76511i | − | 0.140558i | ||||||
\(388\) | −10.5080 | − | 25.3686i | −0.533463 | − | 1.28789i | ||||
\(389\) | 12.1700 | + | 12.1700i | 0.617043 | + | 0.617043i | 0.944772 | − | 0.327729i | \(-0.106283\pi\) |
−0.327729 | + | 0.944772i | \(0.606283\pi\) | |||||||
\(390\) | −1.17272 | −0.0593830 | ||||||||
\(391\) | −1.75058 | + | 1.98356i | −0.0885308 | + | 0.100313i | ||||
\(392\) | −4.88345 | −0.246652 | ||||||||
\(393\) | 2.18090 | + | 2.18090i | 0.110012 | + | 0.110012i | ||||
\(394\) | −0.963690 | − | 2.32655i | −0.0485500 | − | 0.117210i | ||||
\(395\) | 19.5653i | 0.984438i | ||||||||
\(396\) | 1.64029 | − | 0.679431i | 0.0824277 | − | 0.0341427i | ||||
\(397\) | −3.76439 | + | 9.08803i | −0.188929 | + | 0.456115i | −0.989754 | − | 0.142783i | \(-0.954395\pi\) |
0.800825 | + | 0.598899i | \(0.204395\pi\) | |||||||
\(398\) | −2.40309 | − | 0.995393i | −0.120456 | − | 0.0498945i | ||||
\(399\) | 5.21453 | − | 5.21453i | 0.261053 | − | 0.261053i | ||||
\(400\) | 2.63665 | − | 2.63665i | 0.131833 | − | 0.131833i | ||||
\(401\) | −16.1173 | − | 6.67600i | −0.804859 | − | 0.333383i | −0.0579581 | − | 0.998319i | \(-0.518459\pi\) |
−0.746901 | + | 0.664936i | \(0.768459\pi\) | |||||||
\(402\) | −0.616778 | + | 1.48903i | −0.0307621 | + | 0.0742662i | ||||
\(403\) | 18.3033 | − | 7.58149i | 0.911754 | − | 0.377661i | ||||
\(404\) | − | 1.30925i | − | 0.0651375i | ||||||
\(405\) | 4.19912 | + | 10.1376i | 0.208656 | + | 0.503740i | ||||
\(406\) | 0.661070 | + | 0.661070i | 0.0328083 | + | 0.0328083i | ||||
\(407\) | 3.56124 | 0.176524 | ||||||||
\(408\) | −3.29012 | − | 2.90368i | −0.162885 | − | 0.143754i | ||||
\(409\) | −23.0150 | −1.13802 | −0.569008 | − | 0.822332i | \(-0.692673\pi\) | ||||
−0.569008 | + | 0.822332i | \(0.692673\pi\) | |||||||
\(410\) | −1.51518 | − | 1.51518i | −0.0748293 | − | 0.0748293i | ||||
\(411\) | −1.12016 | − | 2.70430i | −0.0552533 | − | 0.133393i | ||||
\(412\) | − | 20.4330i | − | 1.00666i | ||||||
\(413\) | 3.41837 | − | 1.41593i | 0.168207 | − | 0.0696736i | ||||
\(414\) | 0.0411062 | − | 0.0992392i | 0.00202026 | − | 0.00487734i | ||||
\(415\) | 17.1939 | + | 7.12194i | 0.844014 | + | 0.349602i | ||||
\(416\) | 3.35036 | − | 3.35036i | 0.164265 | − | 0.164265i | ||||
\(417\) | 5.93121 | − | 5.93121i | 0.290452 | − | 0.290452i | ||||
\(418\) | −1.46189 | − | 0.605534i | −0.0715033 | − | 0.0296176i | ||||
\(419\) | −12.6943 | + | 30.6467i | −0.620156 | + | 1.49719i | 0.231365 | + | 0.972867i | \(0.425681\pi\) |
−0.851520 | + | 0.524321i | \(0.824319\pi\) | |||||||
\(420\) | −3.14414 | + | 1.30234i | −0.153418 | + | 0.0635479i | ||||
\(421\) | − | 20.4782i | − | 0.998045i | −0.866589 | − | 0.499023i | \(-0.833692\pi\) | ||
0.866589 | − | 0.499023i | \(-0.166308\pi\) | |||||||
\(422\) | 0.939670 | + | 2.26856i | 0.0457424 | + | 0.110432i | ||||
\(423\) | 6.81526 | + | 6.81526i | 0.331369 | + | 0.331369i | ||||
\(424\) | 2.75332 | 0.133713 | ||||||||
\(425\) | 3.63892 | − | 1.78034i | 0.176514 | − | 0.0863591i | ||||
\(426\) | 1.34598 | 0.0652128 | ||||||||
\(427\) | 0.00641330 | + | 0.00641330i | 0.000310362 | + | 0.000310362i | ||||
\(428\) | 4.26709 | + | 10.3017i | 0.206258 | + | 0.497950i | ||||
\(429\) | − | 3.15679i | − | 0.152411i | ||||||
\(430\) | 1.05069 | − | 0.435212i | 0.0506690 | − | 0.0209878i | ||||
\(431\) | 2.04914 | − | 4.94706i | 0.0987035 | − | 0.238291i | −0.866813 | − | 0.498633i | \(-0.833835\pi\) |
0.965516 | + | 0.260342i | \(0.0838354\pi\) | |||||||
\(432\) | −19.8169 | − | 8.20841i | −0.953439 | − | 0.394927i | ||||
\(433\) | −22.3708 | + | 22.3708i | −1.07507 | + | 1.07507i | −0.0781293 | + | 0.996943i | \(0.524895\pi\) |
−0.996943 | + | 0.0781293i | \(0.975105\pi\) | |||||||
\(434\) | −0.710445 | + | 0.710445i | −0.0341025 | + | 0.0341025i | ||||
\(435\) | −22.6739 | − | 9.39186i | −1.08713 | − | 0.450305i | ||||
\(436\) | −0.963509 | + | 2.32612i | −0.0461437 | + | 0.111401i | ||||
\(437\) | 5.06100 | − | 2.09634i | 0.242101 | − | 0.100281i | ||||
\(438\) | 2.76173i | 0.131960i | ||||||||
\(439\) | −9.30329 | − | 22.4601i | −0.444022 | − | 1.07196i | −0.974525 | − | 0.224281i | \(-0.927997\pi\) |
0.530503 | − | 0.847683i | \(-0.322003\pi\) | |||||||
\(440\) | 1.04171 | + | 1.04171i | 0.0496617 | + | 0.0496617i | ||||
\(441\) | −6.00122 | −0.285773 | ||||||||
\(442\) | 1.49647 | − | 0.732147i | 0.0711799 | − | 0.0348247i | ||||
\(443\) | −3.68500 | −0.175080 | −0.0875399 | − | 0.996161i | \(-0.527901\pi\) | ||||
−0.0875399 | + | 0.996161i | \(0.527901\pi\) | |||||||
\(444\) | −7.16748 | − | 7.16748i | −0.340154 | − | 0.340154i | ||||
\(445\) | −12.4284 | − | 30.0048i | −0.589162 | − | 1.42236i | ||||
\(446\) | − | 3.45098i | − | 0.163408i | ||||||
\(447\) | 1.70353 | − | 0.705627i | 0.0805744 | − | 0.0333750i | ||||
\(448\) | 1.64072 | − | 3.96106i | 0.0775170 | − | 0.187143i | ||||
\(449\) | 0.792880 | + | 0.328422i | 0.0374183 | + | 0.0154992i | 0.401314 | − | 0.915940i | \(-0.368554\pi\) |
−0.363896 | + | 0.931440i | \(0.618554\pi\) | |||||||
\(450\) | −0.116307 | + | 0.116307i | −0.00548275 | + | 0.00548275i | ||||
\(451\) | 4.07863 | − | 4.07863i | 0.192055 | − | 0.192055i | ||||
\(452\) | 13.2509 | + | 5.48869i | 0.623269 | + | 0.258166i | ||||
\(453\) | 7.15696 | − | 17.2784i | 0.336264 | − | 0.811812i | ||||
\(454\) | −4.68829 | + | 1.94195i | −0.220032 | + | 0.0911404i | ||||
\(455\) | − | 2.60661i | − | 0.122200i | ||||||
\(456\) | 3.47718 | + | 8.39466i | 0.162834 | + | 0.393116i | ||||
\(457\) | 27.2529 | + | 27.2529i | 1.27484 | + | 1.27484i | 0.943518 | + | 0.331320i | \(0.107494\pi\) |
0.331320 | + | 0.943518i | \(0.392506\pi\) | |||||||
\(458\) | 3.17567 | 0.148389 | ||||||||
\(459\) | −17.4723 | − | 15.4201i | −0.815537 | − | 0.719748i | ||||
\(460\) | −2.52800 | −0.117869 | ||||||||
\(461\) | −9.57279 | − | 9.57279i | −0.445849 | − | 0.445849i | 0.448123 | − | 0.893972i | \(-0.352093\pi\) |
−0.893972 | + | 0.448123i | \(0.852093\pi\) | |||||||
\(462\) | 0.0612655 | + | 0.147908i | 0.00285033 | + | 0.00688131i | ||||
\(463\) | 15.7275i | 0.730921i | 0.930827 | + | 0.365461i | \(0.119088\pi\) | ||||
−0.930827 | + | 0.365461i | \(0.880912\pi\) | |||||||
\(464\) | 29.6480 | − | 12.2806i | 1.37638 | − | 0.570113i | ||||
\(465\) | 10.0933 | − | 24.3675i | 0.468068 | − | 1.13001i | ||||
\(466\) | −1.46431 | − | 0.606537i | −0.0678328 | − | 0.0280973i | ||||
\(467\) | −23.4310 | + | 23.4310i | −1.08426 | + | 1.08426i | −0.0881526 | + | 0.996107i | \(0.528096\pi\) |
−0.996107 | + | 0.0881526i | \(0.971904\pi\) | |||||||
\(468\) | 2.73692 | − | 2.73692i | 0.126514 | − | 0.126514i | ||||
\(469\) | −3.30968 | − | 1.37091i | −0.152827 | − | 0.0633029i | ||||
\(470\) | −1.51700 | + | 3.66236i | −0.0699740 | + | 0.168932i | ||||
\(471\) | −11.7718 | + | 4.87603i | −0.542415 | + | 0.224676i | ||||
\(472\) | 4.55891i | 0.209841i | ||||||||
\(473\) | 1.17153 | + | 2.82831i | 0.0538668 | + | 0.130046i | ||||
\(474\) | −1.85244 | − | 1.85244i | −0.0850852 | − | 0.0850852i | ||||
\(475\) | −8.38829 | −0.384881 | ||||||||
\(476\) | 3.19906 | − | 3.62481i | 0.146629 | − | 0.166143i | ||||
\(477\) | 3.38352 | 0.154921 | ||||||||
\(478\) | −0.588297 | − | 0.588297i | −0.0269081 | − | 0.0269081i | ||||
\(479\) | 1.38279 | + | 3.33835i | 0.0631812 | + | 0.152533i | 0.952317 | − | 0.305111i | \(-0.0986935\pi\) |
−0.889136 | + | 0.457644i | \(0.848694\pi\) | |||||||
\(480\) | − | 6.30794i | − | 0.287917i | ||||||
\(481\) | 7.17277 | − | 2.97106i | 0.327050 | − | 0.135469i | ||||
\(482\) | 0.129926 | − | 0.313668i | 0.00591795 | − | 0.0142872i | ||||
\(483\) | −0.512053 | − | 0.212099i | −0.0232992 | − | 0.00965084i | ||||
\(484\) | −1.38992 | + | 1.38992i | −0.0631783 | + | 0.0631783i | ||||
\(485\) | 19.7987 | − | 19.7987i | 0.899011 | − | 0.899011i | ||||
\(486\) | 1.54602 | + | 0.640383i | 0.0701289 | + | 0.0290484i | ||||
\(487\) | −13.9298 | + | 33.6295i | −0.631219 | + | 1.52390i | 0.206872 | + | 0.978368i | \(0.433672\pi\) |
−0.838091 | + | 0.545530i | \(0.816328\pi\) | |||||||
\(488\) | −0.0103245 | + | 0.00427656i | −0.000467369 | + | 0.000193591i | ||||
\(489\) | 24.1184i | 1.09067i | ||||||||
\(490\) | −0.944557 | − | 2.28036i | −0.0426708 | − | 0.103016i | ||||
\(491\) | −7.13805 | − | 7.13805i | −0.322136 | − | 0.322136i | 0.527450 | − | 0.849586i | \(-0.323148\pi\) |
−0.849586 | + | 0.527450i | \(0.823148\pi\) | |||||||
\(492\) | −16.4176 | −0.740164 | ||||||||
\(493\) | 34.7970 | − | 2.17104i | 1.56718 | − | 0.0977786i | ||||
\(494\) | −3.44961 | −0.155205 | ||||||||
\(495\) | 1.28015 | + | 1.28015i | 0.0575385 | + | 0.0575385i | ||||
\(496\) | 13.1979 | + | 31.8625i | 0.592602 | + | 1.43067i | ||||
\(497\) | 2.99170i | 0.134196i | ||||||||
\(498\) | −2.30221 | + | 0.953608i | −0.103165 | + | 0.0427322i | ||||
\(499\) | 2.75253 | − | 6.64519i | 0.123220 | − | 0.297480i | −0.850218 | − | 0.526431i | \(-0.823530\pi\) |
0.973438 | + | 0.228952i | \(0.0735298\pi\) | |||||||
\(500\) | 21.7762 | + | 9.02001i | 0.973862 | + | 0.403387i | ||||
\(501\) | 14.2762 | − | 14.2762i | 0.637812 | − | 0.637812i | ||||
\(502\) | 1.66491 | − | 1.66491i | 0.0743088 | − | 0.0743088i | ||||
\(503\) | −35.5675 | − | 14.7325i | −1.58588 | − | 0.656891i | −0.596545 | − | 0.802580i | \(-0.703460\pi\) |
−0.989331 | + | 0.145688i | \(0.953460\pi\) | |||||||
\(504\) | −0.151550 | + | 0.365873i | −0.00675056 | + | 0.0162973i | ||||
\(505\) | 1.23341 | − | 0.510895i | 0.0548860 | − | 0.0227345i | ||||
\(506\) | 0.118924i | 0.00528680i | ||||||||
\(507\) | 4.57010 | + | 11.0332i | 0.202965 | + | 0.490002i | ||||
\(508\) | −9.56733 | − | 9.56733i | −0.424482 | − | 0.424482i | ||||
\(509\) | 30.6548 | 1.35875 | 0.679376 | − | 0.733790i | \(-0.262251\pi\) | ||||
0.679376 | + | 0.733790i | \(0.262251\pi\) | |||||||
\(510\) | 0.719520 | − | 2.09798i | 0.0318609 | − | 0.0929001i | ||||
\(511\) | −6.13849 | −0.271551 | ||||||||
\(512\) | 9.77709 | + | 9.77709i | 0.432090 | + | 0.432090i | ||||
\(513\) | 18.4657 | + | 44.5801i | 0.815280 | + | 1.96826i | ||||
\(514\) | 4.00466i | 0.176638i | ||||||||
\(515\) | 19.2494 | − | 7.97335i | 0.848229 | − | 0.351348i | ||||
\(516\) | 3.33452 | − | 8.05023i | 0.146794 | − | 0.354392i | ||||
\(517\) | −9.85854 | − | 4.08354i | −0.433578 | − | 0.179594i | ||||
\(518\) | −0.278412 | + | 0.278412i | −0.0122327 | + | 0.0122327i | ||||
\(519\) | 18.1567 | − | 18.1567i | 0.796990 | − | 0.796990i | ||||
\(520\) | 2.96722 | + | 1.22906i | 0.130121 | + | 0.0538979i | ||||
\(521\) | 11.6188 | − | 28.0502i | 0.509027 | − | 1.22890i | −0.435418 | − | 0.900229i | \(-0.643399\pi\) |
0.944444 | − | 0.328671i | \(-0.106601\pi\) | |||||||
\(522\) | −1.30782 | + | 0.541717i | −0.0572418 | + | 0.0237103i | ||||
\(523\) | 13.9575i | 0.610317i | 0.952302 | + | 0.305158i | \(0.0987094\pi\) | ||||
−0.952302 | + | 0.305158i | \(0.901291\pi\) | |||||||
\(524\) | −1.60222 | − | 3.86810i | −0.0699932 | − | 0.168979i | ||||
\(525\) | 0.600118 | + | 0.600118i | 0.0261913 | + | 0.0261913i | ||||
\(526\) | 2.83670 | 0.123686 | ||||||||
\(527\) | 2.33319 | + | 37.3960i | 0.101636 | + | 1.62899i | ||||
\(528\) | 5.49535 | 0.239154 | ||||||||
\(529\) | 15.9723 | + | 15.9723i | 0.694449 | + | 0.694449i | ||||
\(530\) | 0.532546 | + | 1.28568i | 0.0231323 | + | 0.0558464i | ||||
\(531\) | 5.60240i | 0.243124i | ||||||||
\(532\) | −9.24860 | + | 3.83090i | −0.400978 | + | 0.166090i | ||||
\(533\) | 4.81216 | − | 11.6176i | 0.208438 | − | 0.503213i | ||||
\(534\) | 4.01756 | + | 1.66413i | 0.173857 | + | 0.0720139i | ||||
\(535\) | −8.03984 | + | 8.03984i | −0.347593 | + | 0.347593i | ||||
\(536\) | 3.12114 | − | 3.12114i | 0.134813 | − | 0.134813i | ||||
\(537\) | 5.10914 | + | 2.11628i | 0.220476 | + | 0.0913240i | ||||
\(538\) | −0.0917957 | + | 0.221614i | −0.00395759 | + | 0.00955447i | ||||
\(539\) | 6.13840 | − | 2.54261i | 0.264400 | − | 0.109518i | ||||
\(540\) | − | 22.2680i | − | 0.958263i | ||||||
\(541\) | −5.28478 | − | 12.7586i | −0.227210 | − | 0.548534i | 0.768626 | − | 0.639699i | \(-0.220941\pi\) |
−0.995836 | + | 0.0911648i | \(0.970941\pi\) | |||||||
\(542\) | 2.02498 | + | 2.02498i | 0.0869802 | + | 0.0869802i | ||||
\(543\) | 19.4245 | 0.833586 | ||||||||
\(544\) | 3.93814 | + | 8.04936i | 0.168846 | + | 0.345113i | ||||
\(545\) | −2.56736 | −0.109974 | ||||||||
\(546\) | 0.246793 | + | 0.246793i | 0.0105618 | + | 0.0105618i | ||||
\(547\) | −1.70168 | − | 4.10823i | −0.0727587 | − | 0.175655i | 0.883316 | − | 0.468778i | \(-0.155306\pi\) |
−0.956075 | + | 0.293123i | \(0.905306\pi\) | |||||||
\(548\) | 3.97348i | 0.169738i | ||||||||
\(549\) | −0.0126877 | + | 0.00525542i | −0.000541498 | + | 0.000224296i | ||||
\(550\) | 0.0696883 | − | 0.168242i | 0.00297152 | − | 0.00717388i | ||||
\(551\) | −66.6963 | − | 27.6265i | −2.84136 | − | 1.17693i | ||||
\(552\) | 0.482883 | − | 0.482883i | 0.0205529 | − | 0.0205529i | ||||
\(553\) | 4.11741 | − | 4.11741i | 0.175090 | − | 0.175090i | ||||
\(554\) | 3.75741 | + | 1.55637i | 0.159637 | + | 0.0661239i | ||||
\(555\) | 3.95541 | − | 9.54921i | 0.167898 | − | 0.405341i | ||||
\(556\) | −10.5197 | + | 4.35741i | −0.446136 | + | 0.184795i | ||||
\(557\) | − | 0.297000i | − | 0.0125843i | −0.999980 | − | 0.00629215i | \(-0.997997\pi\) | ||
0.999980 | − | 0.00629215i | \(-0.00200287\pi\) | |||||||
\(558\) | −0.582179 | − | 1.40550i | −0.0246456 | − | 0.0594997i | ||||
\(559\) | 4.71919 | + | 4.71919i | 0.199601 | + | 0.199601i | ||||
\(560\) | 4.53759 | 0.191748 | ||||||||
\(561\) | 5.64745 | + | 1.93684i | 0.238435 | + | 0.0817735i | ||||
\(562\) | 3.14353 | 0.132602 | ||||||||
\(563\) | −15.1680 | − | 15.1680i | −0.639255 | − | 0.639255i | 0.311117 | − | 0.950372i | \(-0.399297\pi\) |
−0.950372 | + | 0.311117i | \(0.899297\pi\) | |||||||
\(564\) | 11.6230 | + | 28.0604i | 0.489416 | + | 1.18156i | ||||
\(565\) | 14.6251i | 0.615284i | ||||||||
\(566\) | 3.78274 | − | 1.56686i | 0.159000 | − | 0.0658601i | ||||
\(567\) | 1.24971 | − | 3.01708i | 0.0524831 | − | 0.126705i | ||||
\(568\) | −3.40559 | − | 1.41064i | −0.142895 | − | 0.0591892i | ||||
\(569\) | 11.9519 | − | 11.9519i | 0.501050 | − | 0.501050i | −0.410714 | − | 0.911764i | \(-0.634721\pi\) |
0.911764 | + | 0.410714i | \(0.134721\pi\) | |||||||
\(570\) | −3.24739 | + | 3.24739i | −0.136018 | + | 0.136018i | ||||
\(571\) | −2.52953 | − | 1.04777i | −0.105858 | − | 0.0438477i | 0.329126 | − | 0.944286i | \(-0.393246\pi\) |
−0.434984 | + | 0.900438i | \(0.643246\pi\) | |||||||
\(572\) | −1.63990 | + | 3.95906i | −0.0685675 | + | 0.165537i | ||||
\(573\) | 11.8460 | − | 4.90678i | 0.494874 | − | 0.204984i | ||||
\(574\) | 0.637722i | 0.0266180i | ||||||||
\(575\) | 0.241258 | + | 0.582449i | 0.0100612 | + | 0.0242898i | ||||
\(576\) | 4.59042 | + | 4.59042i | 0.191267 | + | 0.191267i | ||||
\(577\) | −23.0499 | −0.959580 | −0.479790 | − | 0.877383i | \(-0.659287\pi\) | ||||
−0.479790 | + | 0.877383i | \(0.659287\pi\) | |||||||
\(578\) | 0.391643 | + | 3.12637i | 0.0162902 | + | 0.130040i | ||||
\(579\) | −16.9383 | −0.703932 | ||||||||
\(580\) | 23.5574 | + | 23.5574i | 0.978168 | + | 0.978168i | ||||
\(581\) | −2.11959 | − | 5.11713i | −0.0879352 | − | 0.212294i | ||||
\(582\) | 3.74906i | 0.155404i | ||||||||
\(583\) | −3.46086 | + | 1.43354i | −0.143334 | + | 0.0593710i | ||||
\(584\) | 2.89441 | − | 6.98772i | 0.119771 | − | 0.289154i | ||||
\(585\) | 3.64638 | + | 1.51038i | 0.150759 | + | 0.0624465i | ||||
\(586\) | 4.01794 | − | 4.01794i | 0.165980 | − | 0.165980i | ||||
\(587\) | 23.1412 | − | 23.1412i | 0.955139 | − | 0.955139i | −0.0438970 | − | 0.999036i | \(-0.513977\pi\) |
0.999036 | + | 0.0438970i | \(0.0139773\pi\) | |||||||
\(588\) | −17.4717 | − | 7.23703i | −0.720523 | − | 0.298450i | ||||
\(589\) | 29.6900 | − | 71.6779i | 1.22335 | − | 2.95344i | ||||
\(590\) | −2.12882 | + | 0.881785i | −0.0876421 | + | 0.0363025i | ||||
\(591\) | − | 19.6743i | − | 0.809294i | ||||||
\(592\) | 5.17202 | + | 12.4864i | 0.212569 | + | 0.513187i | ||||
\(593\) | 25.5524 | + | 25.5524i | 1.04931 | + | 1.04931i | 0.998719 | + | 0.0505934i | \(0.0161112\pi\) |
0.0505934 | + | 0.998719i | \(0.483889\pi\) | |||||||
\(594\) | −1.04754 | −0.0429812 | ||||||||
\(595\) | 4.66318 | + | 1.59928i | 0.191172 | + | 0.0655640i | ||||
\(596\) | −2.50303 | −0.102528 | ||||||||
\(597\) | −14.3695 | − | 14.3695i | −0.588105 | − | 0.588105i | ||||
\(598\) | 0.0992152 | + | 0.239527i | 0.00405721 | + | 0.00979498i | ||||
\(599\) | 46.1615i | 1.88611i | 0.332642 | + | 0.943053i | \(0.392060\pi\) | ||||
−0.332642 | + | 0.943053i | \(0.607940\pi\) | |||||||
\(600\) | −0.966106 | + | 0.400174i | −0.0394411 | + | 0.0163370i | ||||
\(601\) | −1.11299 | + | 2.68700i | −0.0453999 | + | 0.109605i | −0.944953 | − | 0.327207i | \(-0.893893\pi\) |
0.899553 | + | 0.436812i | \(0.143893\pi\) | |||||||
\(602\) | −0.312701 | − | 0.129525i | −0.0127447 | − | 0.00527904i | ||||
\(603\) | 3.83554 | − | 3.83554i | 0.156195 | − | 0.156195i | ||||
\(604\) | −17.9517 | + | 17.9517i | −0.730443 | + | 0.730443i | ||||
\(605\) | −1.85179 | − | 0.767036i | −0.0752859 | − | 0.0311844i | ||||
\(606\) | −0.0684075 | + | 0.165150i | −0.00277886 | + | 0.00670877i | ||||
\(607\) | 27.8846 | − | 11.5502i | 1.13180 | − | 0.468807i | 0.263409 | − | 0.964684i | \(-0.415153\pi\) |
0.868393 | + | 0.495877i | \(0.165153\pi\) | |||||||
\(608\) | − | 18.5551i | − | 0.752507i | ||||||
\(609\) | 2.79514 | + | 6.74807i | 0.113265 | + | 0.273446i | ||||
\(610\) | −0.00399394 | − | 0.00399394i | −0.000161710 | − | 0.000161710i | ||||
\(611\) | −23.2631 | −0.941125 | ||||||||
\(612\) | 3.21707 | + | 6.57553i | 0.130042 | + | 0.265800i | ||||
\(613\) | −22.3208 | −0.901529 | −0.450765 | − | 0.892643i | \(-0.648849\pi\) | ||||
−0.450765 | + | 0.892643i | \(0.648849\pi\) | |||||||
\(614\) | −0.0725728 | − | 0.0725728i | −0.00292880 | − | 0.00292880i | ||||
\(615\) | −6.40649 | − | 15.4666i | −0.258335 | − | 0.623675i | ||||
\(616\) | − | 0.438446i | − | 0.0176655i | ||||||
\(617\) | −18.8814 | + | 7.82094i | −0.760138 | + | 0.314859i | −0.728870 | − | 0.684652i | \(-0.759954\pi\) |
−0.0312673 | + | 0.999511i | \(0.509954\pi\) | |||||||
\(618\) | −1.06761 | + | 2.57744i | −0.0429456 | + | 0.103680i | ||||
\(619\) | −3.40671 | − | 1.41111i | −0.136927 | − | 0.0567172i | 0.313168 | − | 0.949698i | \(-0.398610\pi\) |
−0.450095 | + | 0.892981i | \(0.648610\pi\) | |||||||
\(620\) | −25.3169 | + | 25.3169i | −1.01675 | + | 1.01675i | ||||
\(621\) | 2.56436 | − | 2.56436i | 0.102904 | − | 0.102904i | ||||
\(622\) | 1.35277 | + | 0.560336i | 0.0542412 | + | 0.0224674i | ||||
\(623\) | −3.69886 | + | 8.92984i | −0.148192 | + | 0.357766i | ||||
\(624\) | 11.0683 | − | 4.58464i | 0.443087 | − | 0.183533i | ||||
\(625\) | 19.1220i | 0.764878i | ||||||||
\(626\) | 0.167401 | + | 0.404141i | 0.00669068 | + | 0.0161527i | ||||
\(627\) | −8.74150 | − | 8.74150i | −0.349102 | − | 0.349102i | ||||
\(628\) | 17.2965 | 0.690205 | ||||||||
\(629\) | 0.914340 | + | 14.6549i | 0.0364571 | + | 0.584327i | ||||
\(630\) | −0.200160 | −0.00797457 | ||||||||
\(631\) | 8.23198 | + | 8.23198i | 0.327710 | + | 0.327710i | 0.851715 | − | 0.524005i | \(-0.175563\pi\) |
−0.524005 | + | 0.851715i | \(0.675563\pi\) | |||||||
\(632\) | 2.74560 | + | 6.62846i | 0.109214 | + | 0.263666i | ||||
\(633\) | 19.1840i | 0.762494i | ||||||||
\(634\) | 0.846487 | − | 0.350626i | 0.0336183 | − | 0.0139252i | ||||
\(635\) | 5.27978 | − | 12.7465i | 0.209522 | − | 0.505830i | ||||
\(636\) | 9.85066 | + | 4.08028i | 0.390604 | + | 0.161794i | ||||
\(637\) | 10.2423 | − | 10.2423i | 0.405813 | − | 0.405813i | ||||
\(638\) | 1.10820 | − | 1.10820i | 0.0438741 | − | 0.0438741i | ||||
\(639\) | −4.18509 | − | 1.73352i | −0.165560 | − | 0.0685771i | ||||
\(640\) | −4.35590 | + | 10.5161i | −0.172182 | + | 0.415684i | ||||
\(641\) | 7.56293 | − | 3.13267i | 0.298718 | − | 0.123733i | −0.228291 | − | 0.973593i | \(-0.573314\pi\) |
0.527008 | + | 0.849860i | \(0.323314\pi\) | |||||||
\(642\) | − | 1.52242i | − | 0.0600851i | ||||||
\(643\) | −3.43015 | − | 8.28111i | −0.135272 | − | 0.326575i | 0.841699 | − | 0.539946i | \(-0.181556\pi\) |
−0.976971 | + | 0.213371i | \(0.931556\pi\) | |||||||
\(644\) | 0.532004 | + | 0.532004i | 0.0209639 | + | 0.0209639i | ||||
\(645\) | 8.88512 | 0.349851 | ||||||||
\(646\) | 2.11650 | − | 6.17129i | 0.0832725 | − | 0.242806i | ||||
\(647\) | −12.5224 | −0.492306 | −0.246153 | − | 0.969231i | \(-0.579167\pi\) | ||||
−0.246153 | + | 0.969231i | \(0.579167\pi\) | |||||||
\(648\) | 2.84521 | + | 2.84521i | 0.111770 | + | 0.111770i | ||||
\(649\) | −2.37364 | − | 5.73047i | −0.0931734 | − | 0.224940i | ||||
\(650\) | − | 0.397000i | − | 0.0155716i | ||||||
\(651\) | −7.25209 | + | 3.00392i | −0.284232 | + | 0.117733i | ||||
\(652\) | 12.5291 | − | 30.2479i | 0.490677 | − | 1.18460i | ||||
\(653\) | 11.4043 | + | 4.72381i | 0.446285 | + | 0.184857i | 0.594496 | − | 0.804099i | \(-0.297352\pi\) |
−0.148211 | + | 0.988956i | \(0.547352\pi\) | |||||||
\(654\) | 0.243076 | − | 0.243076i | 0.00950504 | − | 0.00950504i | ||||
\(655\) | 3.01882 | − | 3.01882i | 0.117955 | − | 0.117955i | ||||
\(656\) | 20.2239 | + | 8.37701i | 0.789611 | + | 0.327067i | ||||
\(657\) | 3.55691 | − | 8.58713i | 0.138768 | − | 0.335016i | ||||
\(658\) | 1.08997 | − | 0.451480i | 0.0424914 | − | 0.0176005i | ||||
\(659\) | − | 29.3851i | − | 1.14468i | −0.820016 | − | 0.572340i | \(-0.806036\pi\) | ||
0.820016 | − | 0.572340i | \(-0.193964\pi\) | |||||||
\(660\) | 2.18322 | + | 5.27075i | 0.0849816 | + | 0.205164i | ||||
\(661\) | −20.4931 | − | 20.4931i | −0.797089 | − | 0.797089i | 0.185546 | − | 0.982636i | \(-0.440595\pi\) |
−0.982636 | + | 0.185546i | \(0.940595\pi\) | |||||||
\(662\) | −5.03057 | −0.195519 | ||||||||
\(663\) | 12.9905 | − | 0.810499i | 0.504510 | − | 0.0314772i | ||||
\(664\) | 6.82448 | 0.264841 | ||||||||
\(665\) | −7.21799 | − | 7.21799i | −0.279901 | − | 0.279901i | ||||
\(666\) | −0.228146 | − | 0.550793i | −0.00884048 | − | 0.0213428i | ||||
\(667\) | 5.42570i | 0.210084i | ||||||||
\(668\) | −25.3205 | + | 10.4881i | −0.979681 | + | 0.405797i | ||||
\(669\) | 10.3177 | − | 24.9092i | 0.398906 | − | 0.963045i | ||||
\(670\) | 2.06113 | + | 0.853748i | 0.0796284 | + | 0.0329832i | ||||
\(671\) | 0.0107511 | − | 0.0107511i | 0.000415042 | − | 0.000415042i | ||||
\(672\) | −1.32747 | + | 1.32747i | −0.0512083 | + | 0.0512083i | ||||
\(673\) | 19.5511 | + | 8.09834i | 0.753640 | + | 0.312168i | 0.726226 | − | 0.687456i | \(-0.241273\pi\) |
0.0274144 | + | 0.999624i | \(0.491273\pi\) | |||||||
\(674\) | 1.89732 | − | 4.58054i | 0.0730821 | − | 0.176436i | ||||
\(675\) | −5.13053 | + | 2.12514i | −0.197474 | + | 0.0817965i | ||||
\(676\) | − | 16.2113i | − | 0.623510i | ||||||
\(677\) | 8.89234 | + | 21.4680i | 0.341760 | + | 0.825082i | 0.997538 | + | 0.0701284i | \(0.0223409\pi\) |
−0.655778 | + | 0.754954i | \(0.727659\pi\) | |||||||
\(678\) | −1.38470 | − | 1.38470i | −0.0531791 | − | 0.0531791i | ||||
\(679\) | −8.33304 | −0.319793 | ||||||||
\(680\) | −4.01930 | + | 4.55421i | −0.154133 | + | 0.174646i | ||||
\(681\) | −39.6462 | −1.51925 | ||||||||
\(682\) | 1.19097 | + | 1.19097i | 0.0456047 | + | 0.0456047i | ||||
\(683\) | 8.77395 | + | 21.1822i | 0.335726 | + | 0.810514i | 0.998116 | + | 0.0613547i | \(0.0195421\pi\) |
−0.662390 | + | 0.749159i | \(0.730458\pi\) | |||||||
\(684\) | − | 15.1576i | − | 0.579567i | ||||||
\(685\) | −3.74331 | + | 1.55053i | −0.143025 | + | 0.0592427i | ||||
\(686\) | −0.577282 | + | 1.39368i | −0.0220407 | + | 0.0532110i | ||||
\(687\) | 22.9220 | + | 9.49462i | 0.874530 | + | 0.362242i | ||||
\(688\) | −8.21518 | + | 8.21518i | −0.313201 | + | 0.313201i | ||||
\(689\) | −5.77464 | + | 5.77464i | −0.219996 | + | 0.219996i | ||||
\(690\) | 0.318885 | + | 0.132087i | 0.0121398 | + | 0.00502845i | ||||
\(691\) | −9.03891 | + | 21.8218i | −0.343856 | + | 0.830142i | 0.653462 | + | 0.756959i | \(0.273316\pi\) |
−0.997319 | + | 0.0731832i | \(0.976684\pi\) | |||||||
\(692\) | −32.2031 | + | 13.3390i | −1.22418 | + | 0.507071i | ||||
\(693\) | − | 0.538801i | − | 0.0204674i | ||||||
\(694\) | 1.01569 | + | 2.45208i | 0.0385549 | + | 0.0930798i | ||||
\(695\) | −8.21002 | − | 8.21002i | −0.311424 | − | 0.311424i | ||||
\(696\) | −8.99959 | −0.341128 | ||||||||
\(697\) | 17.8312 | + | 15.7368i | 0.675404 | + | 0.596074i | ||||
\(698\) | −5.66358 | −0.214370 | ||||||||
\(699\) | −8.75599 | − | 8.75599i | −0.331182 | − | 0.331182i | ||||
\(700\) | −0.440882 | − | 1.06438i | −0.0166638 | − | 0.0402299i | ||||
\(701\) | 12.4090i | 0.468682i | 0.972155 | + | 0.234341i | \(0.0752932\pi\) | ||||
−0.972155 | + | 0.234341i | \(0.924707\pi\) | |||||||
\(702\) | −2.10988 | + | 0.873942i | −0.0796324 | + | 0.0329848i | ||||
\(703\) | 11.6350 | − | 28.0894i | 0.438822 | − | 1.05941i | ||||
\(704\) | −6.64022 | − | 2.75047i | −0.250263 | − | 0.103662i | ||||
\(705\) | −21.8995 | + | 21.8995i | −0.824782 | + | 0.824782i | ||||
\(706\) | −1.51041 | + | 1.51041i | −0.0568451 | + | 0.0568451i | ||||
\(707\) | −0.367080 | − | 0.152049i | −0.0138055 | − | 0.00571841i | ||||
\(708\) | −6.75609 | + | 16.3106i | −0.253909 | + | 0.612991i | ||||
\(709\) | 15.0811 | − | 6.24678i | 0.566381 | − | 0.234603i | −0.0810719 | − | 0.996708i | \(-0.525834\pi\) |
0.647453 | + | 0.762106i | \(0.275834\pi\) | |||||||
\(710\) | − | 1.86311i | − | 0.0699213i | ||||||
\(711\) | 3.37404 | + | 8.14565i | 0.126536 | + | 0.305486i | ||||
\(712\) | −8.42115 | − | 8.42115i | −0.315596 | − | 0.315596i | ||||
\(713\) | −5.83095 | −0.218371 | ||||||||
\(714\) | −0.592927 | + | 0.290089i | −0.0221898 | + | 0.0108563i | ||||
\(715\) | −4.36965 | −0.163416 | ||||||||
\(716\) | −5.30821 | − | 5.30821i | −0.198377 | − | 0.198377i | ||||
\(717\) | −2.48745 | − | 6.00523i | −0.0928954 | − | 0.224269i | ||||
\(718\) | 6.26371i | 0.233760i | ||||||||
\(719\) | 8.28958 | − | 3.43366i | 0.309149 | − | 0.128054i | −0.222715 | − | 0.974884i | \(-0.571492\pi\) |
0.531864 | + | 0.846830i | \(0.321492\pi\) | |||||||
\(720\) | −2.62927 | + | 6.34762i | −0.0979872 | + | 0.236562i | ||||
\(721\) | −5.72888 | − | 2.37298i | −0.213354 | − | 0.0883743i | ||||
\(722\) | −7.06227 | + | 7.06227i | −0.262830 | + | 0.262830i | ||||
\(723\) | 1.87561 | − | 1.87561i | 0.0697546 | − | 0.0697546i | ||||
\(724\) | −24.3611 | − | 10.0907i | −0.905372 | − | 0.375017i | ||||
\(725\) | 3.17942 | − | 7.67580i | 0.118081 | − | 0.285072i | ||||
\(726\) | 0.247949 | − | 0.102704i | 0.00920227 | − | 0.00381170i | ||||
\(727\) | − | 51.7088i | − | 1.91777i | −0.283791 | − | 0.958886i | \(-0.591592\pi\) | ||
0.283791 | − | 0.958886i | \(-0.408408\pi\) | |||||||
\(728\) | −0.365785 | − | 0.883084i | −0.0135569 | − | 0.0327293i | ||||
\(729\) | 20.8577 | + | 20.8577i | 0.772507 | + | 0.772507i | ||||
\(730\) | 3.82280 | 0.141488 | ||||||||
\(731\) | −11.3380 | + | 5.54711i | −0.419352 | + | 0.205167i | ||||
\(732\) | −0.0432762 | −0.00159953 | ||||||||
\(733\) | −14.7147 | − | 14.7147i | −0.543501 | − | 0.543501i | 0.381053 | − | 0.924553i | \(-0.375562\pi\) |
−0.924553 | + | 0.381053i | \(0.875562\pi\) | |||||||
\(734\) | 0.363482 | + | 0.877522i | 0.0134164 | + | 0.0323899i | ||||
\(735\) | − | 19.2837i | − | 0.711291i | ||||||
\(736\) | −1.28839 | + | 0.533668i | −0.0474906 | + | 0.0196713i | ||||
\(737\) | −2.29816 | + | 5.54826i | −0.0846540 | + | 0.204373i | ||||
\(738\) | −0.892108 | − | 0.369523i | −0.0328389 | − | 0.0136023i | ||||
\(739\) | −9.11969 | + | 9.11969i | −0.335473 | + | 0.335473i | −0.854660 | − | 0.519187i | \(-0.826235\pi\) |
0.519187 | + | 0.854660i | \(0.326235\pi\) | |||||||
\(740\) | −9.92128 | + | 9.92128i | −0.364714 | + | 0.364714i | ||||
\(741\) | −24.8993 | − | 10.3136i | −0.914699 | − | 0.378881i | ||||
\(742\) | 0.158493 | − | 0.382636i | 0.00581846 | − | 0.0140470i | ||||
\(743\) | −35.6986 | + | 14.7868i | −1.30965 | + | 0.542477i | −0.924784 | − | 0.380493i | \(-0.875754\pi\) |
−0.384871 | + | 0.922970i | \(0.625754\pi\) | |||||||
\(744\) | − | 9.67177i | − | 0.354584i | ||||||
\(745\) | −0.976734 | − | 2.35804i | −0.0357848 | − | 0.0863921i | ||||
\(746\) | −1.76875 | − | 1.76875i | −0.0647585 | − | 0.0647585i | ||||
\(747\) | 8.38653 | 0.306847 | ||||||||
\(748\) | −6.07654 | − | 5.36282i | −0.222180 | − | 0.196084i | ||||
\(749\) | 3.38388 | 0.123644 | ||||||||
\(750\) | −2.27559 | − | 2.27559i | −0.0830928 | − | 0.0830928i | ||||
\(751\) | 6.63762 | + | 16.0246i | 0.242210 | + | 0.584747i | 0.997502 | − | 0.0706420i | \(-0.0225048\pi\) |
−0.755292 | + | 0.655389i | \(0.772505\pi\) | |||||||
\(752\) | − | 40.4965i | − | 1.47675i | ||||||
\(753\) | 16.9951 | − | 7.03962i | 0.619337 | − | 0.256538i | ||||
\(754\) | 1.30751 | − | 3.15660i | 0.0476166 | − | 0.114957i | ||||
\(755\) | −23.9169 | − | 9.90672i | −0.870426 | − | 0.360542i | ||||
\(756\) | −4.68618 | + | 4.68618i | −0.170435 | + | 0.170435i | ||||
\(757\) | 1.42718 | − | 1.42718i | 0.0518716 | − | 0.0518716i | −0.680695 | − | 0.732567i | \(-0.738322\pi\) |
0.732567 | + | 0.680695i | \(0.238322\pi\) | |||||||
\(758\) | −3.95871 | − | 1.63975i | −0.143787 | − | 0.0595585i | ||||
\(759\) | −0.355558 | + | 0.858392i | −0.0129059 | + | 0.0311577i | ||||
\(760\) | 11.6200 | − | 4.81314i | 0.421500 | − | 0.174591i | ||||
\(761\) | − | 31.8985i | − | 1.15632i | −0.815924 | − | 0.578160i | \(-0.803771\pi\) | ||
0.815924 | − | 0.578160i | \(-0.196229\pi\) | |||||||
\(762\) | 0.706948 | + | 1.70672i | 0.0256100 | + | 0.0618280i | ||||
\(763\) | 0.540286 | + | 0.540286i | 0.0195597 | + | 0.0195597i | ||||
\(764\) | −17.4055 | −0.629711 | ||||||||
\(765\) | −4.93928 | + | 5.59663i | −0.178580 | + | 0.202346i | ||||
\(766\) | −3.78162 | −0.136635 | ||||||||
\(767\) | −9.56159 | − | 9.56159i | −0.345249 | − | 0.345249i | ||||
\(768\) | 7.38224 | + | 17.8223i | 0.266384 | + | 0.643107i | ||||
\(769\) | 25.7904i | 0.930026i | 0.885304 | + | 0.465013i | \(0.153950\pi\) | ||||
−0.885304 | + | 0.465013i | \(0.846050\pi\) | |||||||
\(770\) | 0.204735 | − | 0.0848042i | 0.00737815 | − | 0.00305613i | ||||
\(771\) | −11.9731 | + | 28.9057i | −0.431202 | + | 1.04101i | ||||
\(772\) | 21.2430 | + | 8.79915i | 0.764553 | + | 0.316688i | ||||
\(773\) | −23.2460 | + | 23.2460i | −0.836101 | + | 0.836101i | −0.988343 | − | 0.152243i | \(-0.951351\pi\) |
0.152243 | + | 0.988343i | \(0.451351\pi\) | |||||||
\(774\) | 0.362384 | − | 0.362384i | 0.0130256 | − | 0.0130256i | ||||
\(775\) | 8.24911 | + | 3.41689i | 0.296317 | + | 0.122738i | ||||
\(776\) | 3.92917 | − | 9.48587i | 0.141049 | − | 0.340523i | ||||
\(777\) | −2.84197 | + | 1.17718i | −0.101955 | + | 0.0422312i | ||||
\(778\) | 3.18990i | 0.114364i | ||||||||
\(779\) | −18.8450 | − | 45.4958i | −0.675191 | − | 1.63005i | ||||
\(780\) | 8.79453 | + | 8.79453i | 0.314895 | + | 0.314895i | ||||
\(781\) | 5.01522 | 0.179459 | ||||||||
\(782\) | −0.489383 | + | 0.0305334i | −0.0175003 | + | 0.00109187i | ||||
\(783\) | −47.7925 | −1.70797 | ||||||||
\(784\) | 17.8297 | + | 17.8297i | 0.636776 | + | 0.636776i | ||||
\(785\) | 6.74944 | + | 16.2946i | 0.240898 | + | 0.581579i | ||||
\(786\) | 0.571642i | 0.0203898i | ||||||||
\(787\) | −17.5631 | + | 7.27488i | −0.626058 | + | 0.259322i | −0.673077 | − | 0.739572i | \(-0.735028\pi\) |
0.0470194 | + | 0.998894i | \(0.485028\pi\) | |||||||
\(788\) | −10.2205 | + | 24.6744i | −0.364089 | + | 0.878989i | ||||
\(789\) | 20.4753 | + | 8.48116i | 0.728941 | + | 0.301937i | ||||
\(790\) | −2.56416 | + | 2.56416i | −0.0912286 | + | 0.0912286i | ||||
\(791\) | 3.07778 | − | 3.07778i | 0.109433 | − | 0.109433i | ||||
\(792\) | 0.613341 | + | 0.254054i | 0.0217941 | + | 0.00902742i | ||||
\(793\) | 0.0126846 | − | 0.0306234i | 0.000450445 | − | 0.00108747i | ||||
\(794\) | −1.68439 | + | 0.697697i | −0.0597767 | + | 0.0247603i | ||||
\(795\) | 10.8723i | 0.385600i | ||||||||
\(796\) | 10.5567 | + | 25.4861i | 0.374172 | + | 0.903331i | ||||
\(797\) | 13.5592 | + | 13.5592i | 0.480291 | + | 0.480291i | 0.905225 | − | 0.424933i | \(-0.139703\pi\) |
−0.424933 | + | 0.905225i | \(0.639703\pi\) | |||||||
\(798\) | 1.36679 | 0.0483839 | ||||||||
\(799\) | 14.2730 | − | 41.6174i | 0.504944 | − | 1.47232i | ||||
\(800\) | 2.13542 | 0.0754986 | ||||||||
\(801\) | −10.3487 | − | 10.3487i | −0.365652 | − | 0.365652i | ||||
\(802\) | −1.23734 | − | 2.98720i | −0.0436920 | − | 0.105482i | ||||
\(803\) | 10.2904i | 0.363141i | ||||||||
\(804\) | 15.7920 | − | 6.54127i | 0.556942 | − | 0.230693i | ||||
\(805\) | −0.293589 | + | 0.708787i | −0.0103477 | + | 0.0249814i | ||||
\(806\) | 3.39237 | + | 1.40516i | 0.119491 | + | 0.0494948i | ||||
\(807\) | −1.32517 | + | 1.32517i | −0.0466480 | + | 0.0466480i | ||||
\(808\) | 0.346169 | − | 0.346169i | 0.0121782 | − | 0.0121782i | ||||
\(809\) | −52.1544 | − | 21.6031i | −1.83365 | − | 0.759524i | −0.964023 | − | 0.265820i | \(-0.914357\pi\) |
−0.869630 | − | 0.493704i | \(-0.835643\pi\) | |||||||
\(810\) | −0.778271 | + | 1.87891i | −0.0273456 | + | 0.0660182i | ||||
\(811\) | −8.70390 | + | 3.60527i | −0.305635 | + | 0.126598i | −0.530230 | − | 0.847854i | \(-0.677894\pi\) |
0.224594 | + | 0.974452i | \(0.427894\pi\) | |||||||
\(812\) | − | 9.91506i | − | 0.347950i | ||||||
\(813\) | 8.56204 | + | 20.6706i | 0.300284 | + | 0.724949i | ||||
\(814\) | 0.466722 | + | 0.466722i | 0.0163586 | + | 0.0163586i | ||||
\(815\) | 33.3849 | 1.16942 | ||||||||
\(816\) | 1.41092 | + | 22.6139i | 0.0493920 | + | 0.791645i | ||||
\(817\) | 26.1359 | 0.914381 | ||||||||
\(818\) | −3.01625 | − | 3.01625i | −0.105461 | − | 0.105461i | ||||
\(819\) | −0.449510 | − | 1.08521i | −0.0157071 | − | 0.0379204i | ||||
\(820\) | 22.7254i | 0.793605i | ||||||||
\(821\) | 44.4602 | − | 18.4160i | 1.55167 | − | 0.642723i | 0.568053 | − | 0.822992i | \(-0.307697\pi\) |
0.983617 | + | 0.180269i | \(0.0576968\pi\) | |||||||
\(822\) | 0.207612 | − | 0.501219i | 0.00724129 | − | 0.0174820i | ||||
\(823\) | 10.8859 | + | 4.50911i | 0.379460 | + | 0.157178i | 0.564257 | − | 0.825599i | \(-0.309163\pi\) |
−0.184797 | + | 0.982777i | \(0.559163\pi\) | |||||||
\(824\) | 5.40253 | − | 5.40253i | 0.188206 | − | 0.188206i | ||||
\(825\) | 1.00602 | − | 1.00602i | 0.0350252 | − | 0.0350252i | ||||
\(826\) | 0.633565 | + | 0.262431i | 0.0220446 | + | 0.00913115i | ||||
\(827\) | −11.5802 | + | 27.9571i | −0.402683 | + | 0.972163i | 0.584329 | + | 0.811517i | \(0.301358\pi\) |
−0.987012 | + | 0.160646i | \(0.948642\pi\) | |||||||
\(828\) | −1.05249 | + | 0.435954i | −0.0365764 | + | 0.0151504i | ||||
\(829\) | − | 4.82405i | − | 0.167546i | −0.996485 | − | 0.0837731i | \(-0.973303\pi\) | ||
0.996485 | − | 0.0837731i | \(-0.0266971\pi\) | |||||||
\(830\) | 1.31999 | + | 3.18674i | 0.0458175 | + | 0.110613i | ||||
\(831\) | 22.4678 | + | 22.4678i | 0.779400 | + | 0.779400i | ||||
\(832\) | −15.6689 | −0.543221 | ||||||||
\(833\) | 12.0391 | + | 24.6073i | 0.417131 | + | 0.852594i | ||||
\(834\) | 1.55464 | 0.0538329 | ||||||||
\(835\) | −19.7612 | − | 19.7612i | −0.683864 | − | 0.683864i | ||||
\(836\) | 6.42202 | + | 15.5041i | 0.222110 | + | 0.536221i | ||||
\(837\) | − | 51.3622i | − | 1.77534i | ||||||
\(838\) | −5.68010 | + | 2.35278i | −0.196216 | + | 0.0812753i | ||||
\(839\) | −18.1179 | + | 43.7406i | −0.625501 | + | 1.51009i | 0.219658 | + | 0.975577i | \(0.429506\pi\) |
−0.845159 | + | 0.534516i | \(0.820494\pi\) | |||||||
\(840\) | −1.17566 | − | 0.486975i | −0.0405642 | − | 0.0168022i | ||||
\(841\) | 30.0538 | − | 30.0538i | 1.03634 | − | 1.03634i | ||||
\(842\) | 2.68379 | − | 2.68379i | 0.0924896 | − | 0.0924896i | ||||
\(843\) | 22.6900 | + | 9.39852i | 0.781486 | + | 0.323702i | ||||
\(844\) | 9.96572 | − | 24.0594i | 0.343034 | − | 0.828158i | ||||
\(845\) | 15.2722 | − | 6.32597i | 0.525381 | − | 0.217620i | ||||
\(846\) | 1.78636i | 0.0614164i | ||||||||
\(847\) | 0.228280 | + | 0.551118i | 0.00784381 | + | 0.0189366i | ||||
\(848\) | −10.0525 | − | 10.0525i | −0.345204 | − | 0.345204i | ||||
\(849\) | 31.9884 | 1.09784 | ||||||||
\(850\) | 0.710227 | + | 0.243579i | 0.0243606 | + | 0.00835468i | ||||
\(851\) | −2.28505 | −0.0783306 | ||||||||
\(852\) | −10.0938 | − | 10.0938i | −0.345809 | − | 0.345809i | ||||
\(853\) | −12.0474 | − | 29.0850i | −0.412495 | − | 0.995850i | −0.984466 | − | 0.175576i | \(-0.943821\pi\) |
0.571971 | − | 0.820274i | \(-0.306179\pi\) | |||||||
\(854\) | 0.00168101i | 5.75229e-5i | ||||||||
\(855\) | 14.2796 | − | 5.91482i | 0.488353 | − | 0.202283i | ||||
\(856\) | −1.59556 | + | 3.85202i | −0.0545351 | + | 0.131659i | ||||
\(857\) | 34.4497 | + | 14.2696i | 1.17678 | + | 0.487439i | 0.883429 | − | 0.468566i | \(-0.155229\pi\) |
0.293352 | + | 0.956004i | \(0.405229\pi\) | |||||||
\(858\) | 0.413717 | − | 0.413717i | 0.0141241 | − | 0.0141241i | ||||
\(859\) | 18.3048 | − | 18.3048i | 0.624552 | − | 0.624552i | −0.322140 | − | 0.946692i | \(-0.604402\pi\) |
0.946692 | + | 0.322140i | \(0.104402\pi\) | |||||||
\(860\) | −11.1432 | − | 4.61566i | −0.379980 | − | 0.157393i | ||||
\(861\) | −1.90666 | + | 4.60308i | −0.0649788 | + | 0.156873i | ||||
\(862\) | 0.916895 | − | 0.379790i | 0.0312296 | − | 0.0129357i | ||||
\(863\) | 7.00354i | 0.238403i | 0.992870 | + | 0.119202i | \(0.0380335\pi\) | ||||
−0.992870 | + | 0.119202i | \(0.961967\pi\) | |||||||
\(864\) | −4.70084 | − | 11.3488i | −0.159926 | − | 0.386095i | ||||
\(865\) | −25.1326 | − | 25.1326i | −0.854535 | − | 0.854535i | ||||
\(866\) | −5.86367 | −0.199256 | ||||||||
\(867\) | −6.52034 | + | 23.7371i | −0.221442 | + | 0.806155i | ||||
\(868\) | 10.6556 | 0.361675 | ||||||||
\(869\) | −6.90233 | − | 6.90233i | −0.234145 | − | 0.234145i | ||||
\(870\) | −1.74070 | − | 4.20242i | −0.0590153 | − | 0.142475i | ||||
\(871\) | 13.0922i | 0.443612i | ||||||||
\(872\) | −0.869786 | + | 0.360277i | −0.0294547 | + | 0.0122005i | ||||
\(873\) | 4.82852 | − | 11.6571i | 0.163421 | − | 0.394533i | ||||
\(874\) | 0.938014 | + | 0.388538i | 0.0317288 | + | 0.0131425i | ||||
\(875\) | 5.05796 | − | 5.05796i | 0.170990 | − | 0.170990i | ||||
\(876\) | 20.7109 | − | 20.7109i | 0.699756 | − | 0.699756i | ||||
\(877\) | −17.5964 | − | 7.28866i | −0.594187 | − | 0.246120i | 0.0652637 | − | 0.997868i | \(-0.479211\pi\) |
−0.659451 | + | 0.751748i | \(0.729211\pi\) | |||||||
\(878\) | 1.72429 | − | 4.16279i | 0.0581918 | − | 0.140488i | ||||
\(879\) | 41.0144 | − | 16.9887i | 1.38338 | − | 0.573015i | ||||
\(880\) | − | 7.60670i | − | 0.256422i | ||||||
\(881\) | 3.60457 | + | 8.70221i | 0.121441 | + | 0.293185i | 0.972896 | − | 0.231243i | \(-0.0742792\pi\) |
−0.851455 | + | 0.524428i | \(0.824279\pi\) | |||||||
\(882\) | −0.786498 | − | 0.786498i | −0.0264828 | − | 0.0264828i | ||||
\(883\) | −9.67910 | −0.325728 | −0.162864 | − | 0.986649i | \(-0.552073\pi\) | ||||
−0.162864 | + | 0.986649i | \(0.552073\pi\) | |||||||
\(884\) | −16.7130 | − | 5.73186i | −0.562118 | − | 0.192783i | ||||
\(885\) | −18.0022 | −0.605138 | ||||||||
\(886\) | −0.482943 | − | 0.482943i | −0.0162248 | − | 0.0162248i | ||||
\(887\) | 14.3805 | + | 34.7176i | 0.482849 | + | 1.16570i | 0.958250 | + | 0.285932i | \(0.0923031\pi\) |
−0.475401 | + | 0.879769i | \(0.657697\pi\) | |||||||
\(888\) | − | 3.79021i | − | 0.127191i | ||||||
\(889\) | −3.79354 | + | 1.57133i | −0.127231 | + | 0.0527008i | ||||
\(890\) | 2.30350 | − | 5.56114i | 0.0772134 | − | 0.186410i | ||||
\(891\) | −5.05775 | − | 2.09499i | −0.169441 | − | 0.0701848i | ||||
\(892\) | −25.8798 | + | 25.8798i | −0.866518 | + | 0.866518i | ||||
\(893\) | −64.4182 | + | 64.4182i | −2.15567 | + | 2.15567i | ||||
\(894\) | 0.315736 | + | 0.130782i | 0.0105598 | + | 0.00437400i | ||||
\(895\) | 2.92936 | − | 7.07211i | 0.0979178 | − | 0.236395i | ||||
\(896\) | 3.12973 | − | 1.29638i | 0.104557 | − | 0.0433089i | ||||
\(897\) | 2.02554i | 0.0676309i | ||||||||
\(898\) | 0.0608702 | + | 0.146954i | 0.00203126 | + | 0.00490390i | ||||
\(899\) | 54.3363 | + | 54.3363i | 1.81222 | + | 1.81222i | ||||
\(900\) | 1.74443 | 0.0581476 | ||||||||
\(901\) | −6.78772 | − | 13.8738i | −0.226132 | − | 0.462202i | ||||
\(902\) | 1.06906 | 0.0355958 | ||||||||
\(903\) | −1.86983 | − | 1.86983i | −0.0622239 | − | 0.0622239i | ||||
\(904\) | 2.05234 | + | 4.95479i | 0.0682599 | + | 0.164794i | ||||
\(905\) | − | 26.8876i | − | 0.893773i | ||||||
\(906\) | 3.20241 | − | 1.32648i | 0.106393 | − | 0.0440694i | ||||
\(907\) | 13.3874 | − | 32.3200i | 0.444521 | − | 1.07317i | −0.529824 | − | 0.848108i | \(-0.677742\pi\) |
0.974345 | − | 0.225061i | \(-0.0722580\pi\) | |||||||
\(908\) | 49.7219 | + | 20.5955i | 1.65008 | + | 0.683485i | ||||
\(909\) | 0.425403 | − | 0.425403i | 0.0141097 | − | 0.0141097i | ||||
\(910\) | 0.341612 | − | 0.341612i | 0.0113243 | − | 0.0113243i | ||||
\(911\) | −24.2088 | − | 10.0276i | −0.802074 | − | 0.332230i | −0.0562874 | − | 0.998415i | \(-0.517926\pi\) |
−0.745787 | + | 0.666185i | \(0.767926\pi\) | |||||||
\(912\) | 17.9540 | − | 43.3447i | 0.594516 | − | 1.43529i | ||||
\(913\) | −8.57823 | + | 3.55322i | −0.283898 | + | 0.117594i | ||||
\(914\) | 7.14333i | 0.236281i | ||||||||
\(915\) | −0.0168872 | − | 0.0407694i | −0.000558275 | − | 0.00134780i | ||||
\(916\) | −23.8152 | − | 23.8152i | −0.786875 | − | 0.786875i | ||||
\(917\) | −1.27059 | −0.0419585 | ||||||||
\(918\) | −0.268955 | − | 4.31075i | −0.00887683 | − | 0.142276i | ||||
\(919\) | 6.09791 | 0.201152 | 0.100576 | − | 0.994929i | \(-0.467932\pi\) | ||||
0.100576 | + | 0.994929i | \(0.467932\pi\) | |||||||
\(920\) | −0.668410 | − | 0.668410i | −0.0220368 | − | 0.0220368i | ||||
\(921\) | −0.306853 | − | 0.740809i | −0.0101112 | − | 0.0244105i | ||||
\(922\) | − | 2.50915i | − | 0.0826344i | ||||||
\(923\) | 10.1013 | − | 4.18408i | 0.332487 | − | 0.137721i | ||||
\(924\) | 0.649755 | − | 1.56865i | 0.0213754 | − | 0.0516047i | ||||
\(925\) | 3.23269 | + | 1.33902i | 0.106290 | + | 0.0440268i | ||||
\(926\) | −2.06119 | + | 2.06119i | −0.0677350 | + | 0.0677350i | ||||
\(927\) | 6.63911 | − | 6.63911i | 0.218057 | − | 0.218057i | ||||
\(928\) | 16.9790 | + | 7.03293i | 0.557363 | + | 0.230867i | ||||
\(929\) | 14.6692 | − | 35.4145i | 0.481280 | − | 1.16191i | −0.477722 | − | 0.878511i | \(-0.658537\pi\) |
0.959002 | − | 0.283401i | \(-0.0914626\pi\) | |||||||
\(930\) | 4.51631 | − | 1.87071i | 0.148095 | − | 0.0613432i | ||||
\(931\) | − | 56.7239i | − | 1.85905i | ||||||
\(932\) | 6.43266 | + | 15.5298i | 0.210709 | + | 0.508696i | ||||
\(933\) | 8.08903 | + | 8.08903i | 0.264823 | + | 0.264823i | ||||
\(934\) | −6.14157 | −0.200958 | ||||||||
\(935\) | 2.68099 | − | 7.81724i | 0.0876778 | − | 0.255651i | ||||
\(936\) | 1.44730 | 0.0473064 | ||||||||
\(937\) | 40.8743 | + | 40.8743i | 1.33530 | + | 1.33530i | 0.900548 | + | 0.434756i | \(0.143166\pi\) |
0.434756 | + | 0.900548i | \(0.356834\pi\) | |||||||
\(938\) | −0.254087 | − | 0.613420i | −0.00829624 | − | 0.0200289i | ||||
\(939\) | 3.41759i | 0.111529i | ||||||||
\(940\) | 38.8414 | − | 16.0886i | 1.26687 | − | 0.524753i | ||||
\(941\) | −1.62183 | + | 3.91544i | −0.0528701 | + | 0.127640i | −0.948108 | − | 0.317949i | \(-0.897006\pi\) |
0.895238 | + | 0.445589i | \(0.147006\pi\) | |||||||
\(942\) | −2.18180 | − | 0.903731i | −0.0710869 | − | 0.0294452i | ||||
\(943\) | −2.61704 | + | 2.61704i | −0.0852225 | + | 0.0852225i | ||||
\(944\) | 16.6448 | − | 16.6448i | 0.541743 | − | 0.541743i | ||||
\(945\) | −6.24338 | − | 2.58609i | −0.203097 | − | 0.0841256i | ||||
\(946\) | −0.217132 | + | 0.524204i | −0.00705958 | + | 0.0170433i | ||||
\(947\) | 17.9207 | − | 7.42301i | 0.582345 | − | 0.241215i | −0.0720084 | − | 0.997404i | \(-0.522941\pi\) |
0.654354 | + | 0.756189i | \(0.272941\pi\) | |||||||
\(948\) | 27.7838i | 0.902376i | ||||||||
\(949\) | 8.58506 | + | 20.7262i | 0.278683 | + | 0.672800i | ||||
\(950\) | −1.09934 | − | 1.09934i | −0.0356672 | − | 0.0356672i | ||||
\(951\) | 7.15826 | 0.232122 | ||||||||
\(952\) | 1.80425 | − | 0.112570i | 0.0584761 | − | 0.00364841i | ||||
\(953\) | −8.61141 | −0.278951 | −0.139475 | − | 0.990226i | \(-0.544542\pi\) | ||||
−0.139475 | + | 0.990226i | \(0.544542\pi\) | |||||||
\(954\) | 0.443432 | + | 0.443432i | 0.0143566 | + | 0.0143566i | ||||
\(955\) | −6.79200 | − | 16.3973i | −0.219784 | − | 0.530605i | ||||
\(956\) | 8.82358i | 0.285375i | ||||||||
\(957\) | 11.3123 | − | 4.68571i | 0.365675 | − | 0.151467i | ||||
\(958\) | −0.256288 | + | 0.618734i | −0.00828029 | + | 0.0199904i | ||||
\(959\) | 1.11406 | + | 0.461459i | 0.0359749 | + | 0.0149013i | ||||
\(960\) | −14.7504 | + | 14.7504i | −0.476067 | + | 0.476067i | ||||
\(961\) | −36.4744 | + | 36.4744i | −1.17659 | + | 1.17659i | ||||
\(962\) | 1.32941 | + | 0.550660i | 0.0428620 | + | 0.0177540i | ||||
\(963\) | −1.96077 | + | 4.73371i | −0.0631848 | + | 0.152542i | ||||
\(964\) | −3.32662 | + | 1.37793i | −0.107143 | + | 0.0443802i | ||||
\(965\) | 23.4461i | 0.754757i | ||||||||
\(966\) | −0.0393108 | − | 0.0949046i | −0.00126480 | − | 0.00305350i | ||||
\(967\) | −36.0986 | − | 36.0986i | −1.16085 | − | 1.16085i | −0.984289 | − | 0.176563i | \(-0.943502\pi\) |
−0.176563 | − | 0.984289i | \(-0.556498\pi\) | |||||||
\(968\) | −0.734999 | −0.0236238 | ||||||||
\(969\) | 33.7278 | − | 38.2166i | 1.08349 | − | 1.22769i | ||||
\(970\) | 5.18948 | 0.166624 | ||||||||
\(971\) | −1.31533 | − | 1.31533i | −0.0422109 | − | 0.0422109i | 0.685686 | − | 0.727897i | \(-0.259502\pi\) |
−0.727897 | + | 0.685686i | \(0.759502\pi\) | |||||||
\(972\) | −6.79161 | − | 16.3964i | −0.217841 | − | 0.525915i | ||||
\(973\) | 3.45551i | 0.110778i | ||||||||
\(974\) | −6.23294 | + | 2.58177i | −0.199716 | + | 0.0827252i | ||||
\(975\) | 1.18695 | − | 2.86556i | 0.0380129 | − | 0.0917712i | ||||
\(976\) | 0.0533093 | + | 0.0220814i | 0.00170639 | + | 0.000706810i | ||||
\(977\) | −7.12449 | + | 7.12449i | −0.227933 | + | 0.227933i | −0.811829 | − | 0.583896i | \(-0.801528\pi\) |
0.583896 | + | 0.811829i | \(0.301528\pi\) | |||||||
\(978\) | −3.16087 | + | 3.16087i | −0.101073 | + | 0.101073i | ||||
\(979\) | 14.9698 | + | 6.20068i | 0.478435 | + | 0.198174i | ||||
\(980\) | −10.0176 | + | 24.1845i | −0.319999 | + | 0.772546i | ||||
\(981\) | −1.06887 | + | 0.442741i | −0.0341264 | + | 0.0141356i | ||||
\(982\) | − | 1.87097i | − | 0.0597051i | ||||||
\(983\) | −10.4310 | − | 25.1826i | −0.332697 | − | 0.803201i | −0.998376 | − | 0.0569632i | \(-0.981858\pi\) |
0.665680 | − | 0.746238i | \(-0.268142\pi\) | |||||||
\(984\) | −4.34087 | − | 4.34087i | −0.138382 | − | 0.138382i | ||||
\(985\) | −27.2334 | −0.867727 | ||||||||
\(986\) | 4.84489 | + | 4.27583i | 0.154293 | + | 0.136170i | ||||
\(987\) | 9.21725 | 0.293388 | ||||||||
\(988\) | 25.8695 | + | 25.8695i | 0.823018 | + | 0.823018i | ||||
\(989\) | −0.751704 | − | 1.81477i | −0.0239028 | − | 0.0577065i | ||||
\(990\) | 0.335543i | 0.0106643i | ||||||||
\(991\) | 2.89202 | − | 1.19791i | 0.0918680 | − | 0.0380530i | −0.336276 | − | 0.941763i | \(-0.609168\pi\) |
0.428144 | + | 0.903710i | \(0.359168\pi\) | |||||||
\(992\) | −7.55823 | + | 18.2472i | −0.239974 | + | 0.579348i | ||||
\(993\) | −36.3107 | − | 15.0404i | −1.15229 | − | 0.477292i | ||||
\(994\) | −0.392081 | + | 0.392081i | −0.0124361 | + | 0.0124361i | ||||
\(995\) | −19.8904 | + | 19.8904i | −0.630568 | + | 0.630568i | ||||
\(996\) | 24.4162 | + | 10.1135i | 0.773658 | + | 0.320460i | ||||
\(997\) | −8.98503 | + | 21.6918i | −0.284559 | + | 0.686986i | −0.999931 | − | 0.0117581i | \(-0.996257\pi\) |
0.715372 | + | 0.698744i | \(0.246257\pi\) | |||||||
\(998\) | 1.23163 | − | 0.510158i | 0.0389865 | − | 0.0161488i | ||||
\(999\) | − | 20.1280i | − | 0.636821i |
(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 | 187.2.h.a.100.8 | ✓ | 56 | |
17.5 | odd | 16 | 3179.2.a.bi.1.13 | 28 | |||
17.8 | even | 8 | inner | 187.2.h.a.144.8 | yes | 56 | |
17.12 | odd | 16 | 3179.2.a.bh.1.13 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.2.h.a.100.8 | ✓ | 56 | 1.1 | even | 1 | trivial | |
187.2.h.a.144.8 | yes | 56 | 17.8 | even | 8 | inner | |
3179.2.a.bh.1.13 | 28 | 17.12 | odd | 16 | |||
3179.2.a.bi.1.13 | 28 | 17.5 | odd | 16 |