Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(41,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 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("315.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bl (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.5 | ||
Character | \(\chi\) | \(=\) | 315.41 |
Dual form | 315.2.bl.i.146.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.334847 | + | 0.193324i | −0.236773 | + | 0.136701i | −0.613693 | − | 0.789545i | \(-0.710317\pi\) |
0.376920 | + | 0.926246i | \(0.376983\pi\) | |||||||
\(3\) | −0.454500 | − | 1.67136i | −0.262406 | − | 0.964958i | ||||
\(4\) | −0.925251 | + | 1.60258i | −0.462626 | + | 0.801291i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0.475302 | + | 0.471783i | 0.194041 | + | 0.192605i | ||||
\(7\) | 1.56056 | + | 2.13651i | 0.589835 | + | 0.807524i | ||||
\(8\) | − | 1.48879i | − | 0.526367i | ||||||
\(9\) | −2.58686 | + | 1.51926i | −0.862286 | + | 0.506421i | ||||
\(10\) | 0.386648i | 0.122269i | ||||||||
\(11\) | 3.67564 | − | 2.12213i | 1.10825 | − | 0.639847i | 0.169873 | − | 0.985466i | \(-0.445664\pi\) |
0.938375 | + | 0.345619i | \(0.112331\pi\) | |||||||
\(12\) | 3.09901 | + | 0.818050i | 0.894608 | + | 0.236151i | ||||
\(13\) | 3.15051 | + | 1.81895i | 0.873793 | + | 0.504485i | 0.868607 | − | 0.495502i | \(-0.165016\pi\) |
0.00518619 | + | 0.999987i | \(0.498349\pi\) | |||||||
\(14\) | −0.935587 | − | 0.413710i | −0.250046 | − | 0.110569i | ||||
\(15\) | −1.67469 | − | 0.442069i | −0.432402 | − | 0.114142i | ||||
\(16\) | −1.56268 | − | 2.70665i | −0.390671 | − | 0.676662i | ||||
\(17\) | 2.70345 | 0.655683 | 0.327841 | − | 0.944733i | \(-0.393679\pi\) | ||||
0.327841 | + | 0.944733i | \(0.393679\pi\) | |||||||
\(18\) | 0.572492 | − | 1.00882i | 0.134938 | − | 0.237782i | ||||
\(19\) | − | 5.17685i | − | 1.18765i | −0.804594 | − | 0.593825i | \(-0.797617\pi\) | ||
0.804594 | − | 0.593825i | \(-0.202383\pi\) | |||||||
\(20\) | 0.925251 | + | 1.60258i | 0.206893 | + | 0.358348i | ||||
\(21\) | 2.86159 | − | 3.57929i | 0.624450 | − | 0.781065i | ||||
\(22\) | −0.820519 | + | 1.42118i | −0.174935 | + | 0.302997i | ||||
\(23\) | 3.29639 | + | 1.90317i | 0.687345 | + | 0.396839i | 0.802616 | − | 0.596495i | \(-0.203441\pi\) |
−0.115272 | + | 0.993334i | \(0.536774\pi\) | |||||||
\(24\) | −2.48830 | + | 0.676656i | −0.507922 | + | 0.138122i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −1.40658 | −0.275854 | ||||||||
\(27\) | 3.71496 | + | 3.63306i | 0.714944 | + | 0.699182i | ||||
\(28\) | −4.86784 | + | 0.524116i | −0.919935 | + | 0.0990487i | ||||
\(29\) | 3.67289 | − | 2.12054i | 0.682038 | − | 0.393775i | −0.118584 | − | 0.992944i | \(-0.537836\pi\) |
0.800622 | + | 0.599169i | \(0.204502\pi\) | |||||||
\(30\) | 0.646227 | − | 0.175732i | 0.117984 | − | 0.0320841i | ||||
\(31\) | 0.652414 | + | 0.376671i | 0.117177 | + | 0.0676522i | 0.557443 | − | 0.830215i | \(-0.311783\pi\) |
−0.440266 | + | 0.897867i | \(0.645116\pi\) | |||||||
\(32\) | 3.62518 | + | 2.09300i | 0.640848 | + | 0.369994i | ||||
\(33\) | −5.21742 | − | 5.17879i | −0.908236 | − | 0.901512i | ||||
\(34\) | −0.905243 | + | 0.522642i | −0.155248 | + | 0.0896324i | ||||
\(35\) | 2.63055 | − | 0.283229i | 0.444644 | − | 0.0478745i | ||||
\(36\) | −0.0412499 | − | 5.55136i | −0.00687498 | − | 0.925226i | ||||
\(37\) | −4.23308 | −0.695914 | −0.347957 | − | 0.937510i | \(-0.613124\pi\) | ||||
−0.347957 | + | 0.937510i | \(0.613124\pi\) | |||||||
\(38\) | 1.00081 | + | 1.73345i | 0.162353 | + | 0.281203i | ||||
\(39\) | 1.60820 | − | 6.09233i | 0.257518 | − | 0.975553i | ||||
\(40\) | −1.28933 | − | 0.744395i | −0.203861 | − | 0.117699i | ||||
\(41\) | −0.143256 | + | 0.248127i | −0.0223728 | + | 0.0387509i | −0.876995 | − | 0.480499i | \(-0.840455\pi\) |
0.854622 | + | 0.519250i | \(0.173789\pi\) | |||||||
\(42\) | −0.266232 | + | 1.75173i | −0.0410805 | + | 0.270298i | ||||
\(43\) | 5.08515 | + | 8.80773i | 0.775477 | + | 1.34317i | 0.934526 | + | 0.355895i | \(0.115824\pi\) |
−0.159048 | + | 0.987271i | \(0.550843\pi\) | |||||||
\(44\) | 7.85402i | 1.18404i | ||||||||
\(45\) | 0.0222912 | + | 2.99992i | 0.00332297 | + | 0.447201i | ||||
\(46\) | −1.47172 | −0.216993 | ||||||||
\(47\) | −4.82756 | − | 8.36159i | −0.704173 | − | 1.21966i | −0.966989 | − | 0.254817i | \(-0.917985\pi\) |
0.262817 | − | 0.964846i | \(-0.415349\pi\) | |||||||
\(48\) | −3.81353 | + | 3.84197i | −0.550436 | + | 0.554541i | ||||
\(49\) | −2.12932 | + | 6.66828i | −0.304189 | + | 0.952612i | ||||
\(50\) | 0.334847 | + | 0.193324i | 0.0473546 | + | 0.0273402i | ||||
\(51\) | −1.22872 | − | 4.51842i | −0.172055 | − | 0.632706i | ||||
\(52\) | −5.83002 | + | 3.36596i | −0.808478 | + | 0.466775i | ||||
\(53\) | 2.71745i | 0.373271i | 0.982429 | + | 0.186635i | \(0.0597583\pi\) | ||||
−0.982429 | + | 0.186635i | \(0.940242\pi\) | |||||||
\(54\) | −1.94630 | − | 0.498328i | −0.264858 | − | 0.0678138i | ||||
\(55\) | − | 4.24426i | − | 0.572296i | ||||||
\(56\) | 3.18081 | − | 2.32334i | 0.425054 | − | 0.310470i | ||||
\(57\) | −8.65235 | + | 2.35288i | −1.14603 | + | 0.311646i | ||||
\(58\) | −0.819904 | + | 1.42012i | −0.107659 | + | 0.186470i | ||||
\(59\) | −4.44145 | + | 7.69282i | −0.578228 | + | 1.00152i | 0.417455 | + | 0.908698i | \(0.362922\pi\) |
−0.995683 | + | 0.0928220i | \(0.970411\pi\) | |||||||
\(60\) | 2.25796 | − | 2.27480i | 0.291501 | − | 0.293675i | ||||
\(61\) | −10.5052 | + | 6.06518i | −1.34505 | + | 0.776567i | −0.987544 | − | 0.157342i | \(-0.949707\pi\) |
−0.357510 | + | 0.933909i | \(0.616374\pi\) | |||||||
\(62\) | −0.291279 | −0.0369924 | ||||||||
\(63\) | −7.28286 | − | 3.15594i | −0.917554 | − | 0.397611i | ||||
\(64\) | 4.63222 | 0.579028 | ||||||||
\(65\) | 3.15051 | − | 1.81895i | 0.390772 | − | 0.225612i | ||||
\(66\) | 2.74822 | + | 0.725452i | 0.338283 | + | 0.0892970i | ||||
\(67\) | −4.74849 | + | 8.22463i | −0.580120 | + | 1.00480i | 0.415344 | + | 0.909664i | \(0.363661\pi\) |
−0.995465 | + | 0.0951336i | \(0.969672\pi\) | |||||||
\(68\) | −2.50137 | + | 4.33250i | −0.303336 | + | 0.525393i | ||||
\(69\) | 1.68267 | − | 6.37443i | 0.202569 | − | 0.767391i | ||||
\(70\) | −0.826077 | + | 0.603387i | −0.0987351 | + | 0.0721186i | ||||
\(71\) | − | 11.7148i | − | 1.39029i | −0.718869 | − | 0.695146i | \(-0.755340\pi\) | ||
0.718869 | − | 0.695146i | \(-0.244660\pi\) | |||||||
\(72\) | 2.26187 | + | 3.85129i | 0.266563 | + | 0.453879i | ||||
\(73\) | − | 15.7249i | − | 1.84046i | −0.391381 | − | 0.920229i | \(-0.628002\pi\) | ||
0.391381 | − | 0.920229i | \(-0.371998\pi\) | |||||||
\(74\) | 1.41744 | − | 0.818357i | 0.164774 | − | 0.0951320i | ||||
\(75\) | −1.22019 | + | 1.22929i | −0.140895 | + | 0.141946i | ||||
\(76\) | 8.29632 | + | 4.78988i | 0.951653 | + | 0.549437i | ||||
\(77\) | 10.2700 | + | 4.54132i | 1.17037 | + | 0.517532i | ||||
\(78\) | 0.639293 | + | 2.35090i | 0.0723857 | + | 0.266187i | ||||
\(79\) | −1.05648 | − | 1.82988i | −0.118864 | − | 0.205878i | 0.800454 | − | 0.599394i | \(-0.204592\pi\) |
−0.919318 | + | 0.393516i | \(0.871258\pi\) | |||||||
\(80\) | −3.12537 | −0.349427 | ||||||||
\(81\) | 4.38368 | − | 7.86024i | 0.487075 | − | 0.873360i | ||||
\(82\) | − | 0.110779i | − | 0.0122335i | ||||||
\(83\) | 6.95521 | + | 12.0468i | 0.763433 | + | 1.32231i | 0.941071 | + | 0.338210i | \(0.109821\pi\) |
−0.177637 | + | 0.984096i | \(0.556845\pi\) | |||||||
\(84\) | 3.08842 | + | 7.89767i | 0.336974 | + | 0.861707i | ||||
\(85\) | 1.35172 | − | 2.34126i | 0.146615 | − | 0.253945i | ||||
\(86\) | −3.40549 | − | 1.96616i | −0.367224 | − | 0.212017i | ||||
\(87\) | −5.21351 | − | 5.17491i | −0.558947 | − | 0.554809i | ||||
\(88\) | −3.15941 | − | 5.47226i | −0.336794 | − | 0.583345i | ||||
\(89\) | −6.28517 | −0.666226 | −0.333113 | − | 0.942887i | \(-0.608099\pi\) | ||||
−0.333113 | + | 0.942887i | \(0.608099\pi\) | |||||||
\(90\) | −0.587421 | − | 1.00020i | −0.0619196 | − | 0.105431i | ||||
\(91\) | 1.03036 | + | 9.56964i | 0.108011 | + | 1.00317i | ||||
\(92\) | −6.09998 | + | 3.52182i | −0.635967 | + | 0.367175i | ||||
\(93\) | 0.333029 | − | 1.26161i | 0.0345335 | − | 0.130823i | ||||
\(94\) | 3.23299 | + | 1.86657i | 0.333458 | + | 0.192522i | ||||
\(95\) | −4.48328 | − | 2.58842i | −0.459975 | − | 0.265567i | ||||
\(96\) | 1.85050 | − | 7.01024i | 0.188866 | − | 0.715479i | ||||
\(97\) | −11.7467 | + | 6.78195i | −1.19270 | + | 0.688603i | −0.958917 | − | 0.283687i | \(-0.908442\pi\) |
−0.233778 | + | 0.972290i | \(0.575109\pi\) | |||||||
\(98\) | −0.576143 | − | 2.64451i | −0.0581993 | − | 0.267135i | ||||
\(99\) | −6.28429 | + | 11.0739i | −0.631595 | + | 1.11297i | ||||
\(100\) | 1.85050 | 0.185050 | ||||||||
\(101\) | −9.57767 | − | 16.5890i | −0.953014 | − | 1.65067i | −0.738849 | − | 0.673871i | \(-0.764631\pi\) |
−0.214164 | − | 0.976798i | \(-0.568703\pi\) | |||||||
\(102\) | 1.28495 | + | 1.27544i | 0.127229 | + | 0.126288i | ||||
\(103\) | 1.97678 | + | 1.14129i | 0.194778 | + | 0.112455i | 0.594217 | − | 0.804305i | \(-0.297462\pi\) |
−0.399440 | + | 0.916759i | \(0.630795\pi\) | |||||||
\(104\) | 2.70803 | − | 4.69044i | 0.265544 | − | 0.459936i | ||||
\(105\) | −1.66896 | − | 4.26785i | −0.162874 | − | 0.416500i | ||||
\(106\) | −0.525350 | − | 0.909932i | −0.0510265 | − | 0.0883804i | ||||
\(107\) | − | 4.49066i | − | 0.434128i | −0.976157 | − | 0.217064i | \(-0.930352\pi\) | ||
0.976157 | − | 0.217064i | \(-0.0696481\pi\) | |||||||
\(108\) | −9.25954 | + | 2.59204i | −0.891000 | + | 0.249419i | ||||
\(109\) | 2.76774 | 0.265102 | 0.132551 | − | 0.991176i | \(-0.457683\pi\) | ||||
0.132551 | + | 0.991176i | \(0.457683\pi\) | |||||||
\(110\) | 0.820519 | + | 1.42118i | 0.0782334 | + | 0.135504i | ||||
\(111\) | 1.92394 | + | 7.07498i | 0.182612 | + | 0.671527i | ||||
\(112\) | 3.34411 | − | 7.56256i | 0.315989 | − | 0.714595i | ||||
\(113\) | −4.02691 | − | 2.32494i | −0.378820 | − | 0.218712i | 0.298485 | − | 0.954414i | \(-0.403519\pi\) |
−0.677305 | + | 0.735702i | \(0.736852\pi\) | |||||||
\(114\) | 2.44235 | − | 2.46056i | 0.228747 | − | 0.230453i | ||||
\(115\) | 3.29639 | − | 1.90317i | 0.307390 | − | 0.177472i | ||||
\(116\) | 7.84814i | 0.728681i | ||||||||
\(117\) | −10.9134 | + | 0.0810928i | −1.00894 | + | 0.00749703i | ||||
\(118\) | − | 3.43456i | − | 0.316177i | ||||||
\(119\) | 4.21889 | + | 5.77594i | 0.386745 | + | 0.529479i | ||||
\(120\) | −0.658148 | + | 2.49326i | −0.0600804 | + | 0.227602i | ||||
\(121\) | 3.50689 | − | 6.07411i | 0.318808 | − | 0.552192i | ||||
\(122\) | 2.34509 | − | 4.06182i | 0.212315 | − | 0.367740i | ||||
\(123\) | 0.479818 | + | 0.126658i | 0.0432637 | + | 0.0114204i | ||||
\(124\) | −1.20729 | + | 0.697032i | −0.108418 | + | 0.0625953i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.04877 | − | 0.351194i | 0.271606 | − | 0.0312868i | ||||
\(127\) | 14.6254 | 1.29779 | 0.648896 | − | 0.760877i | \(-0.275231\pi\) | ||||
0.648896 | + | 0.760877i | \(0.275231\pi\) | |||||||
\(128\) | −8.80145 | + | 5.08152i | −0.777946 | + | 0.449147i | ||||
\(129\) | 12.4096 | − | 12.5022i | 1.09261 | − | 1.10076i | ||||
\(130\) | −0.703292 | + | 1.21814i | −0.0616828 | + | 0.106838i | ||||
\(131\) | 5.64780 | − | 9.78227i | 0.493450 | − | 0.854681i | −0.506521 | − | 0.862228i | \(-0.669069\pi\) |
0.999972 | + | 0.00754645i | \(0.00240213\pi\) | |||||||
\(132\) | 13.1269 | − | 3.56966i | 1.14255 | − | 0.310699i | ||||
\(133\) | 11.0604 | − | 8.07877i | 0.959055 | − | 0.700518i | ||||
\(134\) | − | 3.67199i | − | 0.317212i | ||||||
\(135\) | 5.00380 | − | 1.40072i | 0.430658 | − | 0.120555i | ||||
\(136\) | − | 4.02487i | − | 0.345130i | ||||||
\(137\) | −14.4550 | + | 8.34559i | −1.23497 | + | 0.713012i | −0.968062 | − | 0.250710i | \(-0.919336\pi\) |
−0.266910 | + | 0.963721i | \(0.586003\pi\) | |||||||
\(138\) | 0.668895 | + | 2.45976i | 0.0569402 | + | 0.209389i | ||||
\(139\) | 7.61828 | + | 4.39842i | 0.646174 | + | 0.373069i | 0.786989 | − | 0.616967i | \(-0.211639\pi\) |
−0.140815 | + | 0.990036i | \(0.544972\pi\) | |||||||
\(140\) | −1.98002 | + | 4.47773i | −0.167342 | + | 0.378437i | ||||
\(141\) | −11.7811 | + | 11.8689i | −0.992144 | + | 0.999543i | ||||
\(142\) | 2.26476 | + | 3.92267i | 0.190054 | + | 0.329183i | ||||
\(143\) | 15.4402 | 1.29117 | ||||||||
\(144\) | 8.15455 | + | 4.62759i | 0.679546 | + | 0.385632i | ||||
\(145\) | − | 4.24108i | − | 0.352203i | ||||||
\(146\) | 3.04000 | + | 5.26543i | 0.251592 | + | 0.435770i | ||||
\(147\) | 12.1128 | + | 0.528115i | 0.999051 | + | 0.0435582i | ||||
\(148\) | 3.91666 | − | 6.78386i | 0.321948 | − | 0.557630i | ||||
\(149\) | −7.63089 | − | 4.40570i | −0.625147 | − | 0.360929i | 0.153723 | − | 0.988114i | \(-0.450874\pi\) |
−0.778870 | + | 0.627185i | \(0.784207\pi\) | |||||||
\(150\) | 0.170925 | − | 0.647515i | 0.0139560 | − | 0.0528694i | ||||
\(151\) | 0.632340 | + | 1.09524i | 0.0514591 | + | 0.0891297i | 0.890608 | − | 0.454773i | \(-0.150279\pi\) |
−0.839148 | + | 0.543902i | \(0.816946\pi\) | |||||||
\(152\) | −7.70724 | −0.625140 | ||||||||
\(153\) | −6.99344 | + | 4.10725i | −0.565386 | + | 0.332052i | ||||
\(154\) | −4.31683 | + | 0.464790i | −0.347860 | + | 0.0374538i | ||||
\(155\) | 0.652414 | − | 0.376671i | 0.0524032 | − | 0.0302550i | ||||
\(156\) | 8.27547 | + | 8.21421i | 0.662568 | + | 0.657663i | ||||
\(157\) | 0.850530 | + | 0.491054i | 0.0678797 | + | 0.0391903i | 0.533556 | − | 0.845765i | \(-0.320855\pi\) |
−0.465676 | + | 0.884955i | \(0.654189\pi\) | |||||||
\(158\) | 0.707521 | + | 0.408488i | 0.0562874 | + | 0.0324975i | ||||
\(159\) | 4.54183 | − | 1.23508i | 0.360191 | − | 0.0979485i | ||||
\(160\) | 3.62518 | − | 2.09300i | 0.286596 | − | 0.165466i | ||||
\(161\) | 1.07807 | + | 10.0128i | 0.0849636 | + | 0.789116i | ||||
\(162\) | 0.0517116 | + | 3.47945i | 0.00406285 | + | 0.273372i | ||||
\(163\) | 9.90775 | 0.776035 | 0.388018 | − | 0.921652i | \(-0.373160\pi\) | ||||
0.388018 | + | 0.921652i | \(0.373160\pi\) | |||||||
\(164\) | −0.265096 | − | 0.459159i | −0.0207005 | − | 0.0358543i | ||||
\(165\) | −7.09367 | + | 1.92902i | −0.552242 | + | 0.150174i | ||||
\(166\) | −4.65787 | − | 2.68922i | −0.361521 | − | 0.208724i | ||||
\(167\) | 0.932410 | − | 1.61498i | 0.0721521 | − | 0.124971i | −0.827692 | − | 0.561182i | \(-0.810347\pi\) |
0.899844 | + | 0.436211i | \(0.143680\pi\) | |||||||
\(168\) | −5.32881 | − | 4.26031i | −0.411127 | − | 0.328690i | ||||
\(169\) | 0.117124 | + | 0.202864i | 0.00900953 | + | 0.0156050i | ||||
\(170\) | 1.04528i | 0.0801696i | ||||||||
\(171\) | 7.86499 | + | 13.3918i | 0.601451 | + | 1.02409i | ||||
\(172\) | −18.8202 | −1.43502 | ||||||||
\(173\) | 3.93230 | + | 6.81094i | 0.298967 | + | 0.517826i | 0.975900 | − | 0.218219i | \(-0.0700246\pi\) |
−0.676933 | + | 0.736045i | \(0.736691\pi\) | |||||||
\(174\) | 2.74617 | + | 0.724908i | 0.208186 | + | 0.0549552i | ||||
\(175\) | 1.06999 | − | 2.41974i | 0.0808837 | − | 0.182915i | ||||
\(176\) | −11.4877 | − | 6.63244i | −0.865920 | − | 0.499939i | ||||
\(177\) | 14.8761 | + | 3.92685i | 1.11815 | + | 0.295160i | ||||
\(178\) | 2.10457 | − | 1.21507i | 0.157744 | − | 0.0910737i | ||||
\(179\) | 4.21069i | 0.314722i | 0.987541 | + | 0.157361i | \(0.0502986\pi\) | ||||
−0.987541 | + | 0.157361i | \(0.949701\pi\) | |||||||
\(180\) | −4.82824 | − | 2.73995i | −0.359876 | − | 0.204224i | ||||
\(181\) | 1.38290i | 0.102790i | 0.998678 | + | 0.0513951i | \(0.0163668\pi\) | ||||
−0.998678 | + | 0.0513951i | \(0.983633\pi\) | |||||||
\(182\) | −2.19506 | − | 3.00518i | −0.162708 | − | 0.222759i | ||||
\(183\) | 14.9117 | + | 14.8013i | 1.10230 | + | 1.09414i | ||||
\(184\) | 2.83342 | − | 4.90763i | 0.208883 | − | 0.361796i | ||||
\(185\) | −2.11654 | + | 3.66595i | −0.155611 | + | 0.269526i | ||||
\(186\) | 0.132386 | + | 0.486830i | 0.00970704 | + | 0.0356961i | ||||
\(187\) | 9.93691 | − | 5.73708i | 0.726659 | − | 0.419537i | ||||
\(188\) | 17.8668 | 1.30307 | ||||||||
\(189\) | −1.96464 | + | 13.6066i | −0.142907 | + | 0.989736i | ||||
\(190\) | 2.00162 | 0.145213 | ||||||||
\(191\) | 4.94345 | − | 2.85410i | 0.357695 | − | 0.206515i | −0.310374 | − | 0.950614i | \(-0.600454\pi\) |
0.668069 | + | 0.744099i | \(0.267121\pi\) | |||||||
\(192\) | −2.10535 | − | 7.74209i | −0.151940 | − | 0.558737i | ||||
\(193\) | −0.515538 | + | 0.892938i | −0.0371093 | + | 0.0642751i | −0.883984 | − | 0.467518i | \(-0.845148\pi\) |
0.846874 | + | 0.531793i | \(0.178482\pi\) | |||||||
\(194\) | 2.62223 | − | 4.54184i | 0.188265 | − | 0.326085i | ||||
\(195\) | −4.47201 | − | 4.43890i | −0.320247 | − | 0.317877i | ||||
\(196\) | −8.71632 | − | 9.58225i | −0.622594 | − | 0.684446i | ||||
\(197\) | − | 16.2023i | − | 1.15437i | −0.816615 | − | 0.577183i | \(-0.804152\pi\) | ||
0.816615 | − | 0.577183i | \(-0.195848\pi\) | |||||||
\(198\) | −0.0365807 | − | 4.92298i | −0.00259967 | − | 0.349861i | ||||
\(199\) | 17.6156i | 1.24874i | 0.781129 | + | 0.624370i | \(0.214644\pi\) | ||||
−0.781129 | + | 0.624370i | \(0.785356\pi\) | |||||||
\(200\) | −1.28933 | + | 0.744395i | −0.0911695 | + | 0.0526367i | ||||
\(201\) | 15.9045 | + | 4.19832i | 1.12181 | + | 0.296127i | ||||
\(202\) | 6.41411 | + | 3.70319i | 0.451296 | + | 0.260556i | ||||
\(203\) | 10.2623 | + | 4.53792i | 0.720272 | + | 0.318499i | ||||
\(204\) | 8.37802 | + | 2.21156i | 0.586579 | + | 0.154840i | ||||
\(205\) | 0.143256 | + | 0.248127i | 0.0100054 | + | 0.0173299i | ||||
\(206\) | −0.882558 | −0.0614907 | ||||||||
\(207\) | −11.4187 | + | 0.0848478i | −0.793655 | + | 0.00589733i | ||||
\(208\) | − | 11.3697i | − | 0.788350i | ||||||
\(209\) | −10.9860 | − | 19.0282i | −0.759914 | − | 1.31621i | ||||
\(210\) | 1.38393 | + | 1.10643i | 0.0955000 | + | 0.0763508i | ||||
\(211\) | 3.36761 | − | 5.83288i | 0.231836 | − | 0.401552i | −0.726512 | − | 0.687153i | \(-0.758860\pi\) |
0.958348 | + | 0.285602i | \(0.0921934\pi\) | |||||||
\(212\) | −4.35494 | − | 2.51433i | −0.299099 | − | 0.172685i | ||||
\(213\) | −19.5796 | + | 5.32438i | −1.34157 | + | 0.364821i | ||||
\(214\) | 0.868153 | + | 1.50368i | 0.0593457 | + | 0.102790i | ||||
\(215\) | 10.1703 | 0.693608 | ||||||||
\(216\) | 5.40886 | − | 5.53079i | 0.368026 | − | 0.376323i | ||||
\(217\) | 0.213369 | + | 1.98170i | 0.0144844 | + | 0.134527i | ||||
\(218\) | −0.926771 | + | 0.535072i | −0.0627689 | + | 0.0362396i | ||||
\(219\) | −26.2819 | + | 7.14696i | −1.77596 | + | 0.482947i | ||||
\(220\) | 6.80178 | + | 3.92701i | 0.458576 | + | 0.264759i | ||||
\(221\) | 8.51723 | + | 4.91743i | 0.572931 | + | 0.330782i | ||||
\(222\) | −2.01199 | − | 1.99710i | −0.135036 | − | 0.134036i | ||||
\(223\) | −4.86430 | + | 2.80840i | −0.325737 | + | 0.188065i | −0.653947 | − | 0.756540i | \(-0.726888\pi\) |
0.328210 | + | 0.944605i | \(0.393555\pi\) | |||||||
\(224\) | 1.18560 | + | 11.0115i | 0.0792161 | + | 0.735735i | ||||
\(225\) | 2.60915 | + | 1.48065i | 0.173943 | + | 0.0987103i | ||||
\(226\) | 1.79787 | 0.119592 | ||||||||
\(227\) | 7.27122 | + | 12.5941i | 0.482608 | + | 0.835901i | 0.999801 | − | 0.0199678i | \(-0.00635638\pi\) |
−0.517193 | + | 0.855869i | \(0.673023\pi\) | |||||||
\(228\) | 4.23492 | − | 16.0431i | 0.280464 | − | 1.06248i | ||||
\(229\) | −18.6640 | − | 10.7757i | −1.23335 | − | 0.712076i | −0.265624 | − | 0.964077i | \(-0.585578\pi\) |
−0.967727 | + | 0.252001i | \(0.918911\pi\) | |||||||
\(230\) | −0.735858 | + | 1.27454i | −0.0485210 | + | 0.0840409i | ||||
\(231\) | 2.92244 | − | 19.2289i | 0.192283 | − | 1.26517i | ||||
\(232\) | −3.15704 | − | 5.46816i | −0.207270 | − | 0.359002i | ||||
\(233\) | − | 8.01672i | − | 0.525193i | −0.964906 | − | 0.262596i | \(-0.915421\pi\) | ||
0.964906 | − | 0.262596i | \(-0.0845788\pi\) | |||||||
\(234\) | 3.63864 | − | 2.13697i | 0.237865 | − | 0.139698i | ||||
\(235\) | −9.65513 | −0.629831 | ||||||||
\(236\) | −8.21892 | − | 14.2356i | −0.535006 | − | 0.926657i | ||||
\(237\) | −2.57821 | + | 2.59744i | −0.167473 | + | 0.168722i | ||||
\(238\) | −2.52931 | − | 1.11844i | −0.163951 | − | 0.0724979i | ||||
\(239\) | −24.4549 | − | 14.1190i | −1.58185 | − | 0.913284i | −0.994589 | − | 0.103889i | \(-0.966871\pi\) |
−0.587265 | − | 0.809395i | \(-0.699795\pi\) | |||||||
\(240\) | 1.42048 | + | 5.22360i | 0.0916916 | + | 0.337182i | ||||
\(241\) | −12.4500 | + | 7.18803i | −0.801977 | + | 0.463022i | −0.844162 | − | 0.536088i | \(-0.819901\pi\) |
0.0421850 | + | 0.999110i | \(0.486568\pi\) | |||||||
\(242\) | 2.71187i | 0.174325i | ||||||||
\(243\) | −15.1296 | − | 3.75420i | −0.970567 | − | 0.240832i | ||||
\(244\) | − | 22.4473i | − | 1.43704i | ||||||
\(245\) | 4.71024 | + | 5.17819i | 0.300926 | + | 0.330822i | ||||
\(246\) | −0.185152 | + | 0.0503493i | −0.0118048 | + | 0.00321015i | ||||
\(247\) | 9.41640 | − | 16.3097i | 0.599151 | − | 1.03776i | ||||
\(248\) | 0.560785 | − | 0.971308i | 0.0356099 | − | 0.0616781i | ||||
\(249\) | 16.9733 | − | 17.0999i | 1.07564 | − | 1.08366i | ||||
\(250\) | 0.334847 | − | 0.193324i | 0.0211776 | − | 0.0122269i | ||||
\(251\) | −28.7546 | −1.81498 | −0.907488 | − | 0.420078i | \(-0.862003\pi\) | ||||
−0.907488 | + | 0.420078i | \(0.862003\pi\) | |||||||
\(252\) | 11.7961 | − | 8.75134i | 0.743087 | − | 0.551283i | ||||
\(253\) | 16.1551 | 1.01566 | ||||||||
\(254\) | −4.89727 | + | 2.82744i | −0.307282 | + | 0.177409i | ||||
\(255\) | −4.52743 | − | 1.19511i | −0.283519 | − | 0.0748407i | ||||
\(256\) | −2.66746 | + | 4.62018i | −0.166716 | + | 0.288761i | ||||
\(257\) | −7.94503 | + | 13.7612i | −0.495598 | + | 0.858400i | −0.999987 | − | 0.00507607i | \(-0.998384\pi\) |
0.504390 | + | 0.863476i | \(0.331718\pi\) | |||||||
\(258\) | −1.73836 | + | 6.58541i | −0.108226 | + | 0.409990i | ||||
\(259\) | −6.60596 | − | 9.04400i | −0.410475 | − | 0.561967i | ||||
\(260\) | 6.73193i | 0.417496i | ||||||||
\(261\) | −6.27958 | + | 11.0656i | −0.388696 | + | 0.684945i | ||||
\(262\) | 4.36742i | 0.269820i | ||||||||
\(263\) | −1.02433 | + | 0.591398i | −0.0631629 | + | 0.0364671i | −0.531249 | − | 0.847216i | \(-0.678277\pi\) |
0.468086 | + | 0.883683i | \(0.344944\pi\) | |||||||
\(264\) | −7.71014 | + | 7.76764i | −0.474526 | + | 0.478065i | ||||
\(265\) | 2.35338 | + | 1.35873i | 0.144567 | + | 0.0834659i | ||||
\(266\) | −2.14171 | + | 4.84339i | −0.131317 | + | 0.296967i | ||||
\(267\) | 2.85661 | + | 10.5047i | 0.174822 | + | 0.642880i | ||||
\(268\) | −8.78710 | − | 15.2197i | −0.536757 | − | 0.929691i | ||||
\(269\) | −10.8395 | −0.660895 | −0.330448 | − | 0.943824i | \(-0.607200\pi\) | ||||
−0.330448 | + | 0.943824i | \(0.607200\pi\) | |||||||
\(270\) | −1.40472 | + | 1.43638i | −0.0854882 | + | 0.0874155i | ||||
\(271\) | 21.6099i | 1.31271i | 0.754453 | + | 0.656354i | \(0.227902\pi\) | ||||
−0.754453 | + | 0.656354i | \(0.772098\pi\) | |||||||
\(272\) | −4.22464 | − | 7.31728i | −0.256156 | − | 0.443675i | ||||
\(273\) | 15.5260 | − | 6.07150i | 0.939675 | − | 0.367464i | ||||
\(274\) | 3.22681 | − | 5.58900i | 0.194939 | − | 0.337644i | ||||
\(275\) | −3.67564 | − | 2.12213i | −0.221649 | − | 0.127969i | ||||
\(276\) | 8.65866 | + | 8.59456i | 0.521190 | + | 0.517332i | ||||
\(277\) | −2.76756 | − | 4.79355i | −0.166286 | − | 0.288017i | 0.770825 | − | 0.637047i | \(-0.219844\pi\) |
−0.937111 | + | 0.349030i | \(0.886511\pi\) | |||||||
\(278\) | −3.40128 | −0.203995 | ||||||||
\(279\) | −2.25997 | + | 0.0167929i | −0.135301 | + | 0.00100536i | ||||
\(280\) | −0.421669 | − | 3.91634i | −0.0251995 | − | 0.234046i | ||||
\(281\) | −15.4759 | + | 8.93502i | −0.923215 | + | 0.533019i | −0.884659 | − | 0.466238i | \(-0.845609\pi\) |
−0.0385558 | + | 0.999256i | \(0.512276\pi\) | |||||||
\(282\) | 1.65031 | − | 6.25184i | 0.0982743 | − | 0.372292i | ||||
\(283\) | −6.12953 | − | 3.53888i | −0.364363 | − | 0.210365i | 0.306630 | − | 0.951829i | \(-0.400799\pi\) |
−0.670993 | + | 0.741464i | \(0.734132\pi\) | |||||||
\(284\) | 18.7739 | + | 10.8391i | 1.11403 | + | 0.643185i | ||||
\(285\) | −2.28852 | + | 8.66959i | −0.135560 | + | 0.513542i | ||||
\(286\) | −5.17010 | + | 2.98496i | −0.305714 | + | 0.176504i | ||||
\(287\) | −0.753683 | + | 0.0811485i | −0.0444885 | + | 0.00479005i | ||||
\(288\) | −12.5577 | + | 0.0933108i | −0.739967 | + | 0.00549839i | ||||
\(289\) | −9.69137 | −0.570080 | ||||||||
\(290\) | 0.819904 | + | 1.42012i | 0.0481464 | + | 0.0833921i | ||||
\(291\) | 16.6739 | + | 16.5505i | 0.977443 | + | 0.970207i | ||||
\(292\) | 25.2004 | + | 14.5495i | 1.47474 | + | 0.851443i | ||||
\(293\) | −7.41171 | + | 12.8375i | −0.432997 | + | 0.749972i | −0.997130 | − | 0.0757117i | \(-0.975877\pi\) |
0.564133 | + | 0.825684i | \(0.309210\pi\) | |||||||
\(294\) | −4.15805 | + | 2.16487i | −0.242503 | + | 0.126258i | ||||
\(295\) | 4.44145 | + | 7.69282i | 0.258591 | + | 0.447893i | ||||
\(296\) | 6.30217i | 0.366306i | ||||||||
\(297\) | 21.3647 | + | 5.47018i | 1.23970 | + | 0.317412i | ||||
\(298\) | 3.40691 | 0.197357 | ||||||||
\(299\) | 6.92353 | + | 11.9919i | 0.400398 | + | 0.693510i | ||||
\(300\) | −0.841054 | − | 3.09285i | −0.0485583 | − | 0.178566i | ||||
\(301\) | −10.8821 | + | 24.6094i | −0.627234 | + | 1.41846i | ||||
\(302\) | −0.423475 | − | 0.244493i | −0.0243682 | − | 0.0140690i | ||||
\(303\) | −23.3731 | + | 23.5474i | −1.34275 | + | 1.35276i | ||||
\(304\) | −14.0119 | + | 8.08977i | −0.803637 | + | 0.463980i | ||||
\(305\) | 12.1304i | 0.694583i | ||||||||
\(306\) | 1.54770 | − | 2.72730i | 0.0884764 | − | 0.155910i | ||||
\(307\) | − | 6.07854i | − | 0.346921i | −0.984841 | − | 0.173460i | \(-0.944505\pi\) | ||
0.984841 | − | 0.173460i | \(-0.0554949\pi\) | |||||||
\(308\) | −16.7802 | + | 12.2567i | −0.956139 | + | 0.698388i | ||||
\(309\) | 1.00906 | − | 3.82261i | 0.0574034 | − | 0.217461i | ||||
\(310\) | −0.145639 | + | 0.252255i | −0.00827176 | + | 0.0143271i | ||||
\(311\) | 5.13664 | − | 8.89692i | 0.291272 | − | 0.504498i | −0.682839 | − | 0.730569i | \(-0.739255\pi\) |
0.974111 | + | 0.226071i | \(0.0725881\pi\) | |||||||
\(312\) | −9.07020 | − | 2.39427i | −0.513499 | − | 0.135549i | ||||
\(313\) | 14.0962 | − | 8.13844i | 0.796764 | − | 0.460012i | −0.0455747 | − | 0.998961i | \(-0.514512\pi\) |
0.842338 | + | 0.538949i | \(0.181179\pi\) | |||||||
\(314\) | −0.379730 | −0.0214294 | ||||||||
\(315\) | −6.37456 | + | 4.72917i | −0.359166 | + | 0.266458i | ||||
\(316\) | 3.91005 | 0.219958 | ||||||||
\(317\) | 28.8682 | − | 16.6671i | 1.62140 | − | 0.936115i | 0.634853 | − | 0.772633i | \(-0.281061\pi\) |
0.986546 | − | 0.163482i | \(-0.0522725\pi\) | |||||||
\(318\) | −1.28205 | + | 1.29161i | −0.0718937 | + | 0.0724299i | ||||
\(319\) | 9.00014 | − | 15.5887i | 0.503911 | − | 0.872800i | ||||
\(320\) | 2.31611 | − | 4.01162i | 0.129475 | − | 0.224257i | ||||
\(321\) | −7.50549 | + | 2.04101i | −0.418915 | + | 0.113918i | ||||
\(322\) | −2.29670 | − | 3.14433i | −0.127990 | − | 0.175227i | ||||
\(323\) | − | 13.9953i | − | 0.778721i | ||||||
\(324\) | 8.54068 | + | 14.2979i | 0.474482 | + | 0.794328i | ||||
\(325\) | − | 3.63789i | − | 0.201794i | ||||||
\(326\) | −3.31758 | + | 1.91541i | −0.183744 | + | 0.106085i | ||||
\(327\) | −1.25794 | − | 4.62588i | −0.0695642 | − | 0.255812i | ||||
\(328\) | 0.369409 | + | 0.213278i | 0.0203972 | + | 0.0117763i | ||||
\(329\) | 10.3309 | − | 23.3629i | 0.569561 | − | 1.28804i | ||||
\(330\) | 2.00237 | − | 2.01731i | 0.110227 | − | 0.111049i | ||||
\(331\) | 12.9962 | + | 22.5101i | 0.714336 | + | 1.23727i | 0.963215 | + | 0.268732i | \(0.0866046\pi\) |
−0.248879 | + | 0.968535i | \(0.580062\pi\) | |||||||
\(332\) | −25.7413 | −1.41274 | ||||||||
\(333\) | 10.9504 | − | 6.43116i | 0.600077 | − | 0.352426i | ||||
\(334\) | 0.721030i | 0.0394530i | ||||||||
\(335\) | 4.74849 | + | 8.22463i | 0.259438 | + | 0.449359i | ||||
\(336\) | −14.1596 | − | 2.15201i | −0.772471 | − | 0.117402i | ||||
\(337\) | 2.76544 | − | 4.78989i | 0.150643 | − | 0.260922i | −0.780821 | − | 0.624755i | \(-0.785199\pi\) |
0.931464 | + | 0.363833i | \(0.118532\pi\) | |||||||
\(338\) | −0.0784372 | − | 0.0452858i | −0.00426642 | − | 0.00246322i | ||||
\(339\) | −2.05557 | + | 7.78709i | −0.111643 | + | 0.422937i | ||||
\(340\) | 2.50137 | + | 4.33250i | 0.135656 | + | 0.234963i | ||||
\(341\) | 3.19739 | 0.173148 | ||||||||
\(342\) | −5.22252 | − | 2.96371i | −0.282402 | − | 0.160259i | ||||
\(343\) | −17.5698 | + | 5.85693i | −0.948678 | + | 0.316245i | ||||
\(344\) | 13.1129 | − | 7.57072i | 0.706998 | − | 0.408186i | ||||
\(345\) | −4.67909 | − | 4.64445i | −0.251913 | − | 0.250049i | ||||
\(346\) | −2.63344 | − | 1.52042i | −0.141575 | − | 0.0817381i | ||||
\(347\) | −16.1976 | − | 9.35170i | −0.869534 | − | 0.502026i | −0.00234075 | − | 0.999997i | \(-0.500745\pi\) |
−0.867193 | + | 0.497971i | \(0.834078\pi\) | |||||||
\(348\) | 13.1170 | − | 3.56698i | 0.703147 | − | 0.191210i | ||||
\(349\) | −17.6313 | + | 10.1794i | −0.943780 | + | 0.544892i | −0.891143 | − | 0.453722i | \(-0.850096\pi\) |
−0.0526367 | + | 0.998614i | \(0.516763\pi\) | |||||||
\(350\) | 0.109510 | + | 1.01710i | 0.00585356 | + | 0.0543661i | ||||
\(351\) | 5.09567 | + | 18.2033i | 0.271986 | + | 0.971618i | ||||
\(352\) | 17.7665 | 0.946957 | ||||||||
\(353\) | 3.80931 | + | 6.59791i | 0.202749 | + | 0.351171i | 0.949413 | − | 0.314030i | \(-0.101679\pi\) |
−0.746664 | + | 0.665201i | \(0.768346\pi\) | |||||||
\(354\) | −5.74037 | + | 1.56101i | −0.305097 | + | 0.0829667i | ||||
\(355\) | −10.1453 | − | 5.85740i | −0.538458 | − | 0.310879i | ||||
\(356\) | 5.81536 | − | 10.0725i | 0.308213 | − | 0.533841i | ||||
\(357\) | 7.73616 | − | 9.67643i | 0.409441 | − | 0.512131i | ||||
\(358\) | −0.814028 | − | 1.40994i | −0.0430227 | − | 0.0745175i | ||||
\(359\) | − | 13.5305i | − | 0.714114i | −0.934083 | − | 0.357057i | \(-0.883780\pi\) | ||
0.934083 | − | 0.357057i | \(-0.116220\pi\) | |||||||
\(360\) | 4.46625 | − | 0.0331869i | 0.235392 | − | 0.00174910i | ||||
\(361\) | −7.79973 | −0.410512 | ||||||||
\(362\) | −0.267348 | − | 0.463061i | −0.0140515 | − | 0.0243379i | ||||
\(363\) | −11.7459 | − | 3.10057i | −0.616499 | − | 0.162738i | ||||
\(364\) | −16.2895 | − | 7.20310i | −0.853801 | − | 0.377545i | ||||
\(365\) | −13.6181 | − | 7.86244i | −0.712806 | − | 0.411539i | ||||
\(366\) | −7.85459 | − | 2.07339i | −0.410566 | − | 0.108378i | ||||
\(367\) | 1.03813 | − | 0.599366i | 0.0541901 | − | 0.0312867i | −0.472660 | − | 0.881245i | \(-0.656706\pi\) |
0.526850 | + | 0.849958i | \(0.323373\pi\) | |||||||
\(368\) | − | 11.8962i | − | 0.620133i | ||||||
\(369\) | −0.00638668 | − | 0.859512i | −0.000332478 | − | 0.0447444i | ||||
\(370\) | − | 1.63671i | − | 0.0850887i | ||||||
\(371\) | −5.80586 | + | 4.24074i | −0.301425 | + | 0.220168i | ||||
\(372\) | 1.71370 | + | 1.70102i | 0.0888514 | + | 0.0881936i | ||||
\(373\) | −14.2091 | + | 24.6109i | −0.735721 | + | 1.27431i | 0.218685 | + | 0.975795i | \(0.429823\pi\) |
−0.954406 | + | 0.298511i | \(0.903510\pi\) | |||||||
\(374\) | −2.21823 | + | 3.84209i | −0.114702 | + | 0.198670i | ||||
\(375\) | 0.454500 | + | 1.67136i | 0.0234703 | + | 0.0863084i | ||||
\(376\) | −12.4487 | + | 7.18723i | −0.641990 | + | 0.370653i | ||||
\(377\) | 15.4286 | 0.794613 | ||||||||
\(378\) | −1.97263 | − | 4.93595i | −0.101461 | − | 0.253878i | ||||
\(379\) | 23.8261 | 1.22386 | 0.611931 | − | 0.790911i | \(-0.290393\pi\) | ||||
0.611931 | + | 0.790911i | \(0.290393\pi\) | |||||||
\(380\) | 8.29632 | − | 4.78988i | 0.425592 | − | 0.245716i | ||||
\(381\) | −6.64724 | − | 24.4442i | −0.340548 | − | 1.25231i | ||||
\(382\) | −1.10353 | + | 1.91138i | −0.0564617 | + | 0.0977945i | ||||
\(383\) | −7.72665 | + | 13.3830i | −0.394813 | + | 0.683837i | −0.993077 | − | 0.117462i | \(-0.962524\pi\) |
0.598264 | + | 0.801299i | \(0.295857\pi\) | |||||||
\(384\) | 12.4933 | + | 12.4008i | 0.637546 | + | 0.632826i | ||||
\(385\) | 9.06790 | − | 6.62342i | 0.462143 | − | 0.337561i | ||||
\(386\) | − | 0.398664i | − | 0.0202915i | ||||||
\(387\) | −26.5358 | − | 15.0587i | −1.34889 | − | 0.765476i | ||||
\(388\) | − | 25.1000i | − | 1.27426i | ||||||
\(389\) | 32.5077 | − | 18.7683i | 1.64821 | − | 0.951593i | 0.670423 | − | 0.741979i | \(-0.266113\pi\) |
0.977784 | − | 0.209614i | \(-0.0672207\pi\) | |||||||
\(390\) | 2.35559 | + | 0.621807i | 0.119280 | + | 0.0314864i | ||||
\(391\) | 8.91162 | + | 5.14512i | 0.450680 | + | 0.260200i | ||||
\(392\) | 9.92768 | + | 3.17011i | 0.501424 | + | 0.160115i | ||||
\(393\) | −18.9166 | − | 4.99343i | −0.954215 | − | 0.251885i | ||||
\(394\) | 3.13229 | + | 5.42529i | 0.157803 | + | 0.273322i | ||||
\(395\) | −2.11297 | −0.106315 | ||||||||
\(396\) | −11.9323 | − | 20.3173i | −0.599622 | − | 1.02098i | ||||
\(397\) | 12.7223i | 0.638513i | 0.947668 | + | 0.319257i | \(0.103433\pi\) | ||||
−0.947668 | + | 0.319257i | \(0.896567\pi\) | |||||||
\(398\) | −3.40553 | − | 5.89855i | −0.170704 | − | 0.295668i | ||||
\(399\) | −18.5294 | − | 14.8140i | −0.927632 | − | 0.741628i | ||||
\(400\) | −1.56268 | + | 2.70665i | −0.0781342 | + | 0.135332i | ||||
\(401\) | 12.6232 | + | 7.28802i | 0.630374 | + | 0.363946i | 0.780897 | − | 0.624660i | \(-0.214762\pi\) |
−0.150523 | + | 0.988607i | \(0.548096\pi\) | |||||||
\(402\) | −6.13720 | + | 1.66892i | −0.306096 | + | 0.0832383i | ||||
\(403\) | 1.37029 | + | 2.37341i | 0.0682590 | + | 0.118228i | ||||
\(404\) | 35.4470 | 1.76355 | ||||||||
\(405\) | −4.61533 | − | 7.72650i | −0.229338 | − | 0.383933i | ||||
\(406\) | −4.31359 | + | 0.464442i | −0.214080 | + | 0.0230499i | ||||
\(407\) | −15.5593 | + | 8.98315i | −0.771245 | + | 0.445278i | ||||
\(408\) | −6.72699 | + | 1.82930i | −0.333036 | + | 0.0905641i | ||||
\(409\) | 32.7144 | + | 18.8877i | 1.61762 | + | 0.933936i | 0.987532 | + | 0.157415i | \(0.0503162\pi\) |
0.630092 | + | 0.776520i | \(0.283017\pi\) | |||||||
\(410\) | −0.0959378 | − | 0.0553897i | −0.00473803 | − | 0.00273550i | ||||
\(411\) | 20.5182 | + | 20.3663i | 1.01209 | + | 1.00460i | ||||
\(412\) | −3.65803 | + | 2.11196i | −0.180218 | + | 0.104049i | ||||
\(413\) | −23.3669 | + | 2.51590i | −1.14981 | + | 0.123799i | ||||
\(414\) | 3.80712 | − | 2.23592i | 0.187110 | − | 0.109890i | ||||
\(415\) | 13.9104 | 0.682836 | ||||||||
\(416\) | 7.61411 | + | 13.1880i | 0.373312 | + | 0.646596i | ||||
\(417\) | 3.88881 | − | 14.7319i | 0.190436 | − | 0.721426i | ||||
\(418\) | 7.35723 | + | 4.24770i | 0.359854 | + | 0.207762i | ||||
\(419\) | −0.454552 | + | 0.787307i | −0.0222063 | + | 0.0384625i | −0.876915 | − | 0.480645i | \(-0.840402\pi\) |
0.854709 | + | 0.519108i | \(0.173736\pi\) | |||||||
\(420\) | 8.38380 | + | 1.27419i | 0.409087 | + | 0.0621740i | ||||
\(421\) | 2.13949 | + | 3.70571i | 0.104273 | + | 0.180605i | 0.913441 | − | 0.406972i | \(-0.133415\pi\) |
−0.809168 | + | 0.587577i | \(0.800082\pi\) | |||||||
\(422\) | 2.60416i | 0.126769i | ||||||||
\(423\) | 25.1917 | + | 14.2959i | 1.22486 | + | 0.695091i | ||||
\(424\) | 4.04572 | 0.196478 | ||||||||
\(425\) | −1.35172 | − | 2.34126i | −0.0655683 | − | 0.113568i | ||||
\(426\) | 5.52685 | − | 5.56807i | 0.267777 | − | 0.269774i | ||||
\(427\) | −29.3523 | − | 12.9794i | −1.42046 | − | 0.628116i | ||||
\(428\) | 7.19665 | + | 4.15499i | 0.347863 | + | 0.200839i | ||||
\(429\) | −7.01756 | − | 25.8060i | −0.338811 | − | 1.24593i | ||||
\(430\) | −3.40549 | + | 1.96616i | −0.164228 | + | 0.0948168i | ||||
\(431\) | − | 11.8641i | − | 0.571471i | −0.958308 | − | 0.285736i | \(-0.907762\pi\) | ||
0.958308 | − | 0.285736i | \(-0.0922380\pi\) | |||||||
\(432\) | 4.02810 | − | 15.7324i | 0.193802 | − | 0.756925i | ||||
\(433\) | − | 15.0802i | − | 0.724709i | −0.932040 | − | 0.362354i | \(-0.881973\pi\) | ||
0.932040 | − | 0.362354i | \(-0.118027\pi\) | |||||||
\(434\) | −0.454557 | − | 0.622319i | −0.0218195 | − | 0.0298723i | ||||
\(435\) | −7.08836 | + | 1.92757i | −0.339861 | + | 0.0924201i | ||||
\(436\) | −2.56086 | + | 4.43554i | −0.122643 | + | 0.212424i | ||||
\(437\) | 9.85242 | − | 17.0649i | 0.471305 | − | 0.816325i | ||||
\(438\) | 7.41873 | − | 7.47406i | 0.354481 | − | 0.357124i | ||||
\(439\) | 33.8067 | − | 19.5183i | 1.61350 | − | 0.931557i | 0.624955 | − | 0.780661i | \(-0.285117\pi\) |
0.988550 | − | 0.150897i | \(-0.0482161\pi\) | |||||||
\(440\) | −6.31882 | −0.301238 | ||||||||
\(441\) | −4.62263 | − | 20.4849i | −0.220125 | − | 0.975472i | ||||
\(442\) | −3.80263 | −0.180873 | ||||||||
\(443\) | −15.6110 | + | 9.01300i | −0.741700 | + | 0.428220i | −0.822687 | − | 0.568495i | \(-0.807526\pi\) |
0.0809874 | + | 0.996715i | \(0.474193\pi\) | |||||||
\(444\) | −13.1184 | − | 3.46287i | −0.622570 | − | 0.164341i | ||||
\(445\) | −3.14258 | + | 5.44311i | −0.148973 | + | 0.258028i | ||||
\(446\) | 1.08586 | − | 1.88077i | 0.0514172 | − | 0.0890572i | ||||
\(447\) | −3.89524 | + | 14.7563i | −0.184239 | + | 0.697950i | ||||
\(448\) | 7.22885 | + | 9.89678i | 0.341531 | + | 0.467579i | ||||
\(449\) | 17.5843i | 0.829856i | 0.909854 | + | 0.414928i | \(0.136193\pi\) | ||||
−0.909854 | + | 0.414928i | \(0.863807\pi\) | |||||||
\(450\) | −1.15991 | + | 0.00861884i | −0.0546788 | + | 0.000406296i | ||||
\(451\) | 1.21603i | 0.0572607i | ||||||||
\(452\) | 7.45182 | − | 4.30231i | 0.350504 | − | 0.202364i | ||||
\(453\) | 1.54314 | − | 1.55465i | 0.0725033 | − | 0.0730440i | ||||
\(454\) | −4.86950 | − | 2.81140i | −0.228537 | − | 0.131946i | ||||
\(455\) | 8.80273 | + | 3.89251i | 0.412679 | + | 0.182484i | ||||
\(456\) | 3.50294 | + | 12.8815i | 0.164040 | + | 0.603233i | ||||
\(457\) | 3.96531 | + | 6.86813i | 0.185490 | + | 0.321277i | 0.943741 | − | 0.330684i | \(-0.107280\pi\) |
−0.758252 | + | 0.651962i | \(0.773946\pi\) | |||||||
\(458\) | 8.33279 | 0.389365 | ||||||||
\(459\) | 10.0432 | + | 9.82178i | 0.468776 | + | 0.458441i | ||||
\(460\) | 7.04365i | 0.328412i | ||||||||
\(461\) | −4.02115 | − | 6.96483i | −0.187284 | − | 0.324385i | 0.757060 | − | 0.653345i | \(-0.226635\pi\) |
−0.944344 | + | 0.328961i | \(0.893302\pi\) | |||||||
\(462\) | 2.73883 | + | 7.00371i | 0.127422 | + | 0.325842i | ||||
\(463\) | 9.70541 | − | 16.8103i | 0.451049 | − | 0.781239i | −0.547403 | − | 0.836869i | \(-0.684383\pi\) |
0.998451 | + | 0.0556301i | \(0.0177168\pi\) | |||||||
\(464\) | −11.4791 | − | 6.62747i | −0.532905 | − | 0.307673i | ||||
\(465\) | −0.926074 | − | 0.919218i | −0.0429457 | − | 0.0426277i | ||||
\(466\) | 1.54983 | + | 2.68438i | 0.0717943 | + | 0.124351i | ||||
\(467\) | 15.5234 | 0.718337 | 0.359169 | − | 0.933273i | \(-0.383060\pi\) | ||||
0.359169 | + | 0.933273i | \(0.383060\pi\) | |||||||
\(468\) | 9.96765 | − | 17.5646i | 0.460755 | − | 0.811924i | ||||
\(469\) | −24.9823 | + | 2.68982i | −1.15357 | + | 0.124204i | ||||
\(470\) | 3.23299 | − | 1.86657i | 0.149127 | − | 0.0860985i | ||||
\(471\) | 0.434159 | − | 1.64472i | 0.0200050 | − | 0.0757848i | ||||
\(472\) | 11.4530 | + | 6.61239i | 0.527167 | + | 0.304360i | ||||
\(473\) | 37.3823 | + | 21.5827i | 1.71884 | + | 0.992374i | ||||
\(474\) | 0.361159 | − | 1.36818i | 0.0165886 | − | 0.0628425i | ||||
\(475\) | −4.48328 | + | 2.58842i | −0.205707 | + | 0.118765i | ||||
\(476\) | −13.1599 | + | 1.41692i | −0.603185 | + | 0.0649445i | ||||
\(477\) | −4.12853 | − | 7.02967i | −0.189032 | − | 0.321866i | ||||
\(478\) | 10.9182 | 0.499387 | ||||||||
\(479\) | −4.74982 | − | 8.22692i | −0.217025 | − | 0.375898i | 0.736872 | − | 0.676032i | \(-0.236302\pi\) |
−0.953897 | + | 0.300134i | \(0.902969\pi\) | |||||||
\(480\) | −5.14579 | − | 5.10770i | −0.234872 | − | 0.233134i | ||||
\(481\) | −13.3363 | − | 7.69974i | −0.608085 | − | 0.351078i | ||||
\(482\) | 2.77924 | − | 4.81378i | 0.126591 | − | 0.219262i | ||||
\(483\) | 16.2449 | − | 6.35264i | 0.739169 | − | 0.289055i | ||||
\(484\) | 6.48951 | + | 11.2402i | 0.294978 | + | 0.510916i | ||||
\(485\) | 13.5639i | 0.615905i | ||||||||
\(486\) | 5.79190 | − | 1.66784i | 0.262726 | − | 0.0756548i | ||||
\(487\) | −36.0106 | −1.63179 | −0.815897 | − | 0.578197i | \(-0.803756\pi\) | ||||
−0.815897 | + | 0.578197i | \(0.803756\pi\) | |||||||
\(488\) | 9.02979 | + | 15.6401i | 0.408759 | + | 0.707992i | ||||
\(489\) | −4.50308 | − | 16.5594i | −0.203636 | − | 0.748841i | ||||
\(490\) | −2.57828 | − | 0.823298i | −0.116475 | − | 0.0371928i | ||||
\(491\) | 26.0433 | + | 15.0361i | 1.17532 | + | 0.678571i | 0.954927 | − | 0.296840i | \(-0.0959328\pi\) |
0.220393 | + | 0.975411i | \(0.429266\pi\) | |||||||
\(492\) | −0.646932 | + | 0.651757i | −0.0291659 | + | 0.0293835i | ||||
\(493\) | 9.92946 | − | 5.73278i | 0.447200 | − | 0.258191i | ||||
\(494\) | 7.28167i | 0.327618i | ||||||||
\(495\) | 6.44816 | + | 10.9793i | 0.289823 | + | 0.493483i | ||||
\(496\) | − | 2.35447i | − | 0.105719i | ||||||
\(497\) | 25.0288 | − | 18.2816i | 1.12269 | − | 0.820043i | ||||
\(498\) | −2.37764 | + | 9.00720i | −0.106545 | + | 0.403622i | ||||
\(499\) | −20.8184 | + | 36.0586i | −0.931961 | + | 1.61420i | −0.151994 | + | 0.988381i | \(0.548570\pi\) |
−0.779966 | + | 0.625822i | \(0.784764\pi\) | |||||||
\(500\) | 0.925251 | − | 1.60258i | 0.0413785 | − | 0.0716697i | ||||
\(501\) | −3.12299 | − | 0.824379i | −0.139525 | − | 0.0368306i | ||||
\(502\) | 9.62841 | − | 5.55897i | 0.429737 | − | 0.248109i | ||||
\(503\) | −1.37222 | −0.0611841 | −0.0305920 | − | 0.999532i | \(-0.509739\pi\) | ||||
−0.0305920 | + | 0.999532i | \(0.509739\pi\) | |||||||
\(504\) | −4.69854 | + | 10.8427i | −0.209290 | + | 0.482970i | ||||
\(505\) | −19.1553 | −0.852401 | ||||||||
\(506\) | −5.40950 | + | 3.12318i | −0.240482 | + | 0.138842i | ||||
\(507\) | 0.285826 | − | 0.287958i | 0.0126940 | − | 0.0127886i | ||||
\(508\) | −13.5321 | + | 23.4384i | −0.600392 | + | 1.03991i | ||||
\(509\) | −9.47184 | + | 16.4057i | −0.419832 | + | 0.727170i | −0.995922 | − | 0.0902160i | \(-0.971244\pi\) |
0.576090 | + | 0.817386i | \(0.304578\pi\) | |||||||
\(510\) | 1.74704 | − | 0.475082i | 0.0773603 | − | 0.0210370i | ||||
\(511\) | 33.5963 | − | 24.5396i | 1.48621 | − | 1.08557i | ||||
\(512\) | − | 22.3888i | − | 0.989456i | ||||||
\(513\) | 18.8078 | − | 19.2318i | 0.830383 | − | 0.849103i | ||||
\(514\) | − | 6.14387i | − | 0.270994i | ||||||
\(515\) | 1.97678 | − | 1.14129i | 0.0871072 | − | 0.0502914i | ||||
\(516\) | 8.55377 | + | 31.4552i | 0.376559 | + | 1.38474i | ||||
\(517\) | −35.4888 | − | 20.4895i | −1.56079 | − | 0.901125i | ||||
\(518\) | 3.96041 | + | 1.75127i | 0.174011 | + | 0.0769463i | ||||
\(519\) | 9.59627 | − | 9.66784i | 0.421229 | − | 0.424371i | ||||
\(520\) | −2.70803 | − | 4.69044i | −0.118755 | − | 0.205690i | ||||
\(521\) | 32.4326 | 1.42090 | 0.710448 | − | 0.703750i | \(-0.248492\pi\) | ||||
0.710448 | + | 0.703750i | \(0.248492\pi\) | |||||||
\(522\) | −0.0365532 | − | 4.91929i | −0.00159989 | − | 0.215311i | ||||
\(523\) | 40.2111i | 1.75831i | 0.476537 | + | 0.879154i | \(0.341892\pi\) | ||||
−0.476537 | + | 0.879154i | \(0.658108\pi\) | |||||||
\(524\) | 10.4513 | + | 18.1021i | 0.456566 | + | 0.790795i | ||||
\(525\) | −4.53055 | − | 0.688563i | −0.197729 | − | 0.0300514i | ||||
\(526\) | 0.228663 | − | 0.396056i | 0.00997018 | − | 0.0172689i | ||||
\(527\) | 1.76377 | + | 1.01831i | 0.0768309 | + | 0.0443584i | ||||
\(528\) | −5.86399 | + | 22.2145i | −0.255198 | + | 0.966763i | ||||
\(529\) | −4.25588 | − | 7.37140i | −0.185038 | − | 0.320496i | ||||
\(530\) | −1.05070 | −0.0456395 | ||||||||
\(531\) | −0.198010 | − | 26.6480i | −0.00859291 | − | 1.15642i | ||||
\(532\) | 2.71327 | + | 25.2000i | 0.117635 | + | 1.09256i | ||||
\(533\) | −0.902657 | + | 0.521149i | −0.0390984 | + | 0.0225735i | ||||
\(534\) | −2.98735 | − | 2.96523i | −0.129275 | − | 0.128318i | ||||
\(535\) | −3.88902 | − | 2.24533i | −0.168137 | − | 0.0970740i | ||||
\(536\) | 12.2447 | + | 7.06951i | 0.528893 | + | 0.305356i | ||||
\(537\) | 7.03756 | − | 1.91376i | 0.303693 | − | 0.0825848i | ||||
\(538\) | 3.62957 | − | 2.09553i | 0.156482 | − | 0.0903449i | ||||
\(539\) | 6.32436 | + | 29.0289i | 0.272409 | + | 1.25036i | ||||
\(540\) | −2.38500 | + | 9.31502i | −0.102634 | + | 0.400854i | ||||
\(541\) | −23.5961 | −1.01448 | −0.507239 | − | 0.861806i | \(-0.669334\pi\) | ||||
−0.507239 | + | 0.861806i | \(0.669334\pi\) | |||||||
\(542\) | −4.17772 | − | 7.23602i | −0.179448 | − | 0.310813i | ||||
\(543\) | 2.31132 | − | 0.628529i | 0.0991883 | − | 0.0269728i | ||||
\(544\) | 9.80049 | + | 5.65832i | 0.420193 | + | 0.242598i | ||||
\(545\) | 1.38387 | − | 2.39694i | 0.0592785 | − | 0.102673i | ||||
\(546\) | −4.02507 | + | 5.03457i | −0.172257 | + | 0.215460i | ||||
\(547\) | 4.43140 | + | 7.67540i | 0.189473 | + | 0.328176i | 0.945075 | − | 0.326855i | \(-0.105989\pi\) |
−0.755602 | + | 0.655031i | \(0.772655\pi\) | |||||||
\(548\) | − | 30.8871i | − | 1.31943i | ||||||
\(549\) | 17.9609 | − | 31.6499i | 0.766551 | − | 1.35079i | ||||
\(550\) | 1.64104 | 0.0699741 | ||||||||
\(551\) | −10.9777 | − | 19.0140i | −0.467667 | − | 0.810022i | ||||
\(552\) | −9.49019 | − | 2.50514i | −0.403929 | − | 0.106626i | ||||
\(553\) | 2.26085 | − | 5.11282i | 0.0961413 | − | 0.217419i | ||||
\(554\) | 1.85342 | + | 1.07007i | 0.0787442 | + | 0.0454630i | ||||
\(555\) | 7.08908 | + | 1.87131i | 0.300915 | + | 0.0794328i | ||||
\(556\) | −14.0977 | + | 8.13928i | −0.597874 | + | 0.345182i | ||||
\(557\) | 40.1442i | 1.70096i | 0.526005 | + | 0.850481i | \(0.323689\pi\) | ||||
−0.526005 | + | 0.850481i | \(0.676311\pi\) | |||||||
\(558\) | 0.753497 | − | 0.442529i | 0.0318981 | − | 0.0187338i | ||||
\(559\) | 36.9984i | 1.56487i | ||||||||
\(560\) | −4.87732 | − | 6.67737i | −0.206104 | − | 0.282170i | ||||
\(561\) | −14.1050 | − | 14.0006i | −0.595514 | − | 0.591106i | ||||
\(562\) | 3.45471 | − | 5.98374i | 0.145728 | − | 0.252409i | ||||
\(563\) | 1.30952 | − | 2.26815i | 0.0551895 | − | 0.0955910i | −0.837111 | − | 0.547033i | \(-0.815757\pi\) |
0.892300 | + | 0.451442i | \(0.149090\pi\) | |||||||
\(564\) | −8.12049 | − | 29.8618i | −0.341934 | − | 1.25741i | ||||
\(565\) | −4.02691 | + | 2.32494i | −0.169414 | + | 0.0978110i | ||||
\(566\) | 2.73661 | 0.115028 | ||||||||
\(567\) | 23.6344 | − | 2.90060i | 0.992553 | − | 0.121814i | ||||
\(568\) | −17.4409 | −0.731804 | ||||||||
\(569\) | −5.42169 | + | 3.13021i | −0.227289 | + | 0.131225i | −0.609321 | − | 0.792924i | \(-0.708558\pi\) |
0.382032 | + | 0.924149i | \(0.375224\pi\) | |||||||
\(570\) | −0.909737 | − | 3.34542i | −0.0381047 | − | 0.140124i | ||||
\(571\) | 0.966490 | − | 1.67401i | 0.0404464 | − | 0.0700552i | −0.845094 | − | 0.534618i | \(-0.820455\pi\) |
0.885540 | + | 0.464563i | \(0.153789\pi\) | |||||||
\(572\) | −14.2860 | + | 24.7441i | −0.597329 | + | 1.03460i | ||||
\(573\) | −7.01701 | − | 6.96507i | −0.293140 | − | 0.290970i | ||||
\(574\) | 0.236681 | − | 0.172878i | 0.00987887 | − | 0.00721577i | ||||
\(575\) | − | 3.80634i | − | 0.158735i | ||||||
\(576\) | −11.9829 | + | 7.03757i | −0.499288 | + | 0.293232i | ||||
\(577\) | − | 27.0058i | − | 1.12427i | −0.827047 | − | 0.562133i | \(-0.809981\pi\) | ||
0.827047 | − | 0.562133i | \(-0.190019\pi\) | |||||||
\(578\) | 3.24513 | − | 1.87358i | 0.134980 | − | 0.0779305i | ||||
\(579\) | 1.72673 | + | 0.455807i | 0.0717604 | + | 0.0189427i | ||||
\(580\) | 6.79669 | + | 3.92407i | 0.282217 | + | 0.162938i | ||||
\(581\) | −14.8840 | + | 33.6595i | −0.617493 | + | 1.39643i | ||||
\(582\) | −8.78283 | − | 2.31841i | −0.364060 | − | 0.0961014i | ||||
\(583\) | 5.76680 | + | 9.98838i | 0.238836 | + | 0.413677i | ||||
\(584\) | −23.4111 | −0.968756 | ||||||||
\(585\) | −5.38646 | + | 9.49180i | −0.222703 | + | 0.392438i | ||||
\(586\) | − | 5.73145i | − | 0.236764i | ||||||
\(587\) | −13.2537 | − | 22.9561i | −0.547038 | − | 0.947498i | −0.998476 | − | 0.0551950i | \(-0.982422\pi\) |
0.451438 | − | 0.892303i | \(-0.350911\pi\) | |||||||
\(588\) | −12.0538 | + | 18.9232i | −0.497089 | + | 0.780380i | ||||
\(589\) | 1.94997 | − | 3.37745i | 0.0803471 | − | 0.139165i | ||||
\(590\) | −2.97442 | − | 1.71728i | −0.122455 | − | 0.0706993i | ||||
\(591\) | −27.0798 | + | 7.36394i | −1.11391 | + | 0.302912i | ||||
\(592\) | 6.61496 | + | 11.4575i | 0.271873 | + | 0.470898i | ||||
\(593\) | 9.48706 | 0.389587 | 0.194793 | − | 0.980844i | \(-0.437596\pi\) | ||||
0.194793 | + | 0.980844i | \(0.437596\pi\) | |||||||
\(594\) | −8.21142 | + | 2.29863i | −0.336919 | + | 0.0943141i | ||||
\(595\) | 7.11155 | − | 0.765696i | 0.291545 | − | 0.0313905i | ||||
\(596\) | 14.1210 | − | 8.15275i | 0.578418 | − | 0.333950i | ||||
\(597\) | 29.4420 | − | 8.00632i | 1.20498 | − | 0.327677i | ||||
\(598\) | −4.63665 | − | 2.67697i | −0.189607 | − | 0.109469i | ||||
\(599\) | −24.3866 | − | 14.0796i | −0.996408 | − | 0.575276i | −0.0892244 | − | 0.996012i | \(-0.528439\pi\) |
−0.907184 | + | 0.420735i | \(0.861772\pi\) | |||||||
\(600\) | 1.83015 | + | 1.81660i | 0.0747156 | + | 0.0741625i | ||||
\(601\) | 31.7370 | − | 18.3234i | 1.29458 | − | 0.747425i | 0.315116 | − | 0.949053i | \(-0.397957\pi\) |
0.979462 | + | 0.201628i | \(0.0646232\pi\) | |||||||
\(602\) | −1.11375 | − | 10.3442i | −0.0453930 | − | 0.421597i | ||||
\(603\) | −0.211699 | − | 28.4902i | −0.00862104 | − | 1.16021i | ||||
\(604\) | −2.34029 | −0.0952252 | ||||||||
\(605\) | −3.50689 | − | 6.07411i | −0.142575 | − | 0.246948i | ||||
\(606\) | 3.27413 | − | 12.4034i | 0.133003 | − | 0.503852i | ||||
\(607\) | −21.6527 | − | 12.5012i | −0.878855 | − | 0.507407i | −0.00857405 | − | 0.999963i | \(-0.502729\pi\) |
−0.870281 | + | 0.492556i | \(0.836063\pi\) | |||||||
\(608\) | 10.8351 | − | 18.7670i | 0.439423 | − | 0.761103i | ||||
\(609\) | 2.92026 | − | 19.2144i | 0.118335 | − | 0.778609i | ||||
\(610\) | −2.34509 | − | 4.06182i | −0.0949501 | − | 0.164458i | ||||
\(611\) | − | 35.1243i | − | 1.42098i | ||||||
\(612\) | −0.111517 | − | 15.0078i | −0.00450780 | − | 0.606655i | ||||
\(613\) | 12.4336 | 0.502188 | 0.251094 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251094 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(614\) | 1.17513 | + | 2.03538i | 0.0474244 | + | 0.0821414i | ||||
\(615\) | 0.349598 | − | 0.352205i | 0.0140971 | − | 0.0142023i | ||||
\(616\) | 6.76108 | − | 15.2899i | 0.272412 | − | 0.616047i | ||||
\(617\) | 4.00794 | + | 2.31398i | 0.161353 | + | 0.0931575i | 0.578502 | − | 0.815681i | \(-0.303637\pi\) |
−0.417149 | + | 0.908838i | \(0.636971\pi\) | |||||||
\(618\) | 0.401123 | + | 1.47507i | 0.0161355 | + | 0.0593359i | ||||
\(619\) | 18.3309 | − | 10.5834i | 0.736783 | − | 0.425382i | −0.0841156 | − | 0.996456i | \(-0.526807\pi\) |
0.820898 | + | 0.571074i | \(0.193473\pi\) | |||||||
\(620\) | 1.39406i | 0.0559869i | ||||||||
\(621\) | 5.33162 | + | 19.0462i | 0.213950 | + | 0.764296i | ||||
\(622\) | 3.97215i | 0.159269i | ||||||||
\(623\) | −9.80836 | − | 13.4283i | −0.392964 | − | 0.537993i | ||||
\(624\) | −19.0029 | + | 5.16755i | −0.760724 | + | 0.206868i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −3.14671 | + | 5.45027i | −0.125768 | + | 0.217837i | ||||
\(627\) | −26.8098 | + | 27.0098i | −1.07068 | + | 1.07867i | ||||
\(628\) | −1.57391 | + | 0.908696i | −0.0628058 | + | 0.0362609i | ||||
\(629\) | −11.4439 | −0.456299 | ||||||||
\(630\) | 1.22024 | − | 2.81591i | 0.0486155 | − | 0.112188i | ||||
\(631\) | 28.3793 | 1.12976 | 0.564882 | − | 0.825172i | \(-0.308922\pi\) | ||||
0.564882 | + | 0.825172i | \(0.308922\pi\) | |||||||
\(632\) | −2.72431 | + | 1.57288i | −0.108367 | + | 0.0625659i | ||||
\(633\) | −11.2794 | − | 2.97743i | −0.448316 | − | 0.118342i | ||||
\(634\) | −6.44429 | + | 11.1618i | −0.255935 | + | 0.443293i | ||||
\(635\) | 7.31269 | − | 12.6659i | 0.290195 | − | 0.502633i | ||||
\(636\) | −2.22301 | + | 8.42142i | −0.0881482 | + | 0.333931i | ||||
\(637\) | −18.8377 | + | 17.1353i | −0.746376 | + | 0.678927i | ||||
\(638\) | 6.95978i | 0.275540i | ||||||||
\(639\) | 17.7979 | + | 30.3045i | 0.704073 | + | 1.19883i | ||||
\(640\) | 10.1630i | 0.401730i | ||||||||
\(641\) | −23.6678 | + | 13.6646i | −0.934821 | + | 0.539719i | −0.888333 | − | 0.459200i | \(-0.848136\pi\) |
−0.0464877 | + | 0.998919i | \(0.514803\pi\) | |||||||
\(642\) | 2.11862 | − | 2.13442i | 0.0836151 | − | 0.0842387i | ||||
\(643\) | −33.1113 | − | 19.1168i | −1.30578 | − | 0.753894i | −0.324393 | − | 0.945922i | \(-0.605160\pi\) |
−0.981389 | + | 0.192029i | \(0.938493\pi\) | |||||||
\(644\) | −17.0438 | − | 7.53663i | −0.671618 | − | 0.296985i | ||||
\(645\) | −4.62240 | − | 16.9982i | −0.182007 | − | 0.669302i | ||||
\(646\) | 2.70564 | + | 4.68630i | 0.106452 | + | 0.184380i | ||||
\(647\) | 14.5947 | 0.573775 | 0.286887 | − | 0.957964i | \(-0.407379\pi\) | ||||
0.286887 | + | 0.957964i | \(0.407379\pi\) | |||||||
\(648\) | −11.7023 | − | 6.52638i | −0.459708 | − | 0.256380i | ||||
\(649\) | 37.7014i | 1.47991i | ||||||||
\(650\) | 0.703292 | + | 1.21814i | 0.0275854 | + | 0.0477793i | ||||
\(651\) | 3.21516 | − | 1.25730i | 0.126012 | − | 0.0492775i | ||||
\(652\) | −9.16716 | + | 15.8780i | −0.359014 | + | 0.621830i | ||||
\(653\) | 14.2573 | + | 8.23145i | 0.557931 | + | 0.322122i | 0.752315 | − | 0.658804i | \(-0.228937\pi\) |
−0.194384 | + | 0.980926i | \(0.562271\pi\) | |||||||
\(654\) | 1.31551 | + | 1.30577i | 0.0514406 | + | 0.0510598i | ||||
\(655\) | −5.64780 | − | 9.78227i | −0.220678 | − | 0.382225i | ||||
\(656\) | 0.895455 | 0.0349616 | ||||||||
\(657\) | 23.8902 | + | 40.6780i | 0.932047 | + | 1.58700i | ||||
\(658\) | 1.05733 | + | 9.82020i | 0.0412192 | + | 0.382831i | ||||
\(659\) | 15.9994 | − | 9.23728i | 0.623249 | − | 0.359833i | −0.154884 | − | 0.987933i | \(-0.549500\pi\) |
0.778133 | + | 0.628100i | \(0.216167\pi\) | |||||||
\(660\) | 3.47202 | − | 13.1530i | 0.135148 | − | 0.511981i | ||||
\(661\) | −19.0057 | − | 10.9729i | −0.739234 | − | 0.426797i | 0.0825565 | − | 0.996586i | \(-0.473692\pi\) |
−0.821791 | + | 0.569789i | \(0.807025\pi\) | |||||||
\(662\) | −8.70349 | − | 5.02496i | −0.338271 | − | 0.195301i | ||||
\(663\) | 4.34768 | − | 16.4703i | 0.168850 | − | 0.639653i | ||||
\(664\) | 17.9351 | − | 10.3549i | 0.696018 | − | 0.401846i | ||||
\(665\) | −1.46623 | − | 13.6179i | −0.0568581 | − | 0.528081i | ||||
\(666\) | −2.42341 | + | 4.27043i | −0.0939051 | + | 0.165476i | ||||
\(667\) | 16.1430 | 0.625060 | ||||||||
\(668\) | 1.72543 | + | 2.98853i | 0.0667588 | + | 0.115630i | ||||
\(669\) | 6.90467 | + | 6.85355i | 0.266950 | + | 0.264974i | ||||
\(670\) | −3.18004 | − | 1.83600i | −0.122856 | − | 0.0709307i | ||||
\(671\) | −25.7422 | + | 44.5869i | −0.993768 | + | 1.72126i | ||||
\(672\) | 17.8652 | − | 6.98627i | 0.689166 | − | 0.269501i | ||||
\(673\) | −6.33688 | − | 10.9758i | −0.244269 | − | 0.423086i | 0.717657 | − | 0.696397i | \(-0.245215\pi\) |
−0.961926 | + | 0.273311i | \(0.911881\pi\) | |||||||
\(674\) | 2.13851i | 0.0823722i | ||||||||
\(675\) | 1.28884 | − | 5.03378i | 0.0496075 | − | 0.193750i | ||||
\(676\) | −0.433476 | −0.0166722 | ||||||||
\(677\) | 24.0294 | + | 41.6202i | 0.923526 | + | 1.59959i | 0.793915 | + | 0.608028i | \(0.208039\pi\) |
0.129610 | + | 0.991565i | \(0.458627\pi\) | |||||||
\(678\) | −0.817132 | − | 3.00488i | −0.0313818 | − | 0.115402i | ||||
\(679\) | −32.8211 | − | 14.5132i | −1.25956 | − | 0.556967i | ||||
\(680\) | −3.48564 | − | 2.01243i | −0.133668 | − | 0.0771734i | ||||
\(681\) | 17.7445 | − | 17.8768i | 0.679970 | − | 0.685041i | ||||
\(682\) | −1.07064 | + | 0.618132i | −0.0409968 | + | 0.0236695i | ||||
\(683\) | − | 16.8700i | − | 0.645512i | −0.946482 | − | 0.322756i | \(-0.895391\pi\) | ||
0.946482 | − | 0.322756i | \(-0.104609\pi\) | |||||||
\(684\) | −28.7385 | + | 0.213544i | −1.09884 | + | 0.00816507i | ||||
\(685\) | 16.6912i | 0.637737i | ||||||||
\(686\) | 4.75090 | − | 5.35784i | 0.181390 | − | 0.204563i | ||||
\(687\) | −9.52717 | + | 36.0917i | −0.363484 | + | 1.37698i | ||||
\(688\) | 15.8929 | − | 27.5274i | 0.605913 | − | 1.04947i | ||||
\(689\) | −4.94290 | + | 8.56135i | −0.188309 | + | 0.326162i | ||||
\(690\) | 2.46466 | + | 0.650600i | 0.0938281 | + | 0.0247679i | ||||
\(691\) | 17.7426 | − | 10.2437i | 0.674959 | − | 0.389688i | −0.122994 | − | 0.992407i | \(-0.539250\pi\) |
0.797953 | + | 0.602720i | \(0.205916\pi\) | |||||||
\(692\) | −14.5535 | −0.553239 | ||||||||
\(693\) | −33.4665 | + | 3.85507i | −1.27129 | + | 0.146442i | ||||
\(694\) | 7.23164 | 0.274509 | ||||||||
\(695\) | 7.61828 | − | 4.39842i | 0.288978 | − | 0.166841i | ||||
\(696\) | −7.70436 | + | 7.76182i | −0.292033 | + | 0.294211i | ||||
\(697\) | −0.387285 | + | 0.670798i | −0.0146695 | + | 0.0254083i | ||||
\(698\) | 3.93585 | − | 6.81710i | 0.148974 | − | 0.258031i | ||||
\(699\) | −13.3988 | + | 3.64360i | −0.506789 | + | 0.137814i | ||||
\(700\) | 2.88782 | + | 3.95361i | 0.109149 | + | 0.149432i | ||||
\(701\) | − | 21.3800i | − | 0.807513i | −0.914867 | − | 0.403756i | \(-0.867704\pi\) | ||
0.914867 | − | 0.403756i | \(-0.132296\pi\) | |||||||
\(702\) | −5.22540 | − | 5.11020i | −0.197220 | − | 0.192872i | ||||
\(703\) | 21.9140i | 0.826502i | ||||||||
\(704\) | 17.0264 | − | 9.83019i | 0.641706 | − | 0.370489i | ||||
\(705\) | 4.38826 | + | 16.1372i | 0.165271 | + | 0.607760i | ||||
\(706\) | −2.55107 | − | 1.47286i | −0.0960109 | − | 0.0554319i | ||||
\(707\) | 20.4960 | − | 46.3509i | 0.770832 | − | 1.74320i | ||||
\(708\) | −20.0572 | + | 20.2068i | −0.753796 | + | 0.759418i | ||||
\(709\) | −11.1926 | − | 19.3862i | −0.420349 | − | 0.728065i | 0.575625 | − | 0.817714i | \(-0.304759\pi\) |
−0.995973 | + | 0.0896487i | \(0.971426\pi\) | |||||||
\(710\) | 4.52951 | 0.169990 | ||||||||
\(711\) | 5.51305 | + | 3.12857i | 0.206755 | + | 0.117331i | ||||
\(712\) | 9.35730i | 0.350680i | ||||||||
\(713\) | 1.43374 | + | 2.48331i | 0.0536940 | + | 0.0930007i | ||||
\(714\) | −0.719744 | + | 4.73571i | −0.0269358 | + | 0.177230i | ||||
\(715\) | 7.72008 | − | 13.3716i | 0.288715 | − | 0.500069i | ||||
\(716\) | −6.74798 | − | 3.89595i | −0.252184 | − | 0.145598i | ||||
\(717\) | −12.4832 | + | 47.2899i | −0.466192 | + | 1.76607i | ||||
\(718\) | 2.61578 | + | 4.53066i | 0.0976201 | + | 0.169083i | ||||
\(719\) | −29.8224 | −1.11219 | −0.556095 | − | 0.831119i | \(-0.687701\pi\) | ||||
−0.556095 | + | 0.831119i | \(0.687701\pi\) | |||||||
\(720\) | 8.08488 | − | 4.74826i | 0.301306 | − | 0.176957i | ||||
\(721\) | 0.646495 | + | 6.00445i | 0.0240767 | + | 0.223617i | ||||
\(722\) | 2.61172 | − | 1.50788i | 0.0971981 | − | 0.0561174i | ||||
\(723\) | 17.6723 | + | 17.5415i | 0.657240 | + | 0.652374i | ||||
\(724\) | −2.21621 | − | 1.27953i | −0.0823650 | − | 0.0475534i | ||||
\(725\) | −3.67289 | − | 2.12054i | −0.136408 | − | 0.0787550i | ||||
\(726\) | 4.53249 | − | 1.23254i | 0.168217 | − | 0.0457440i | ||||
\(727\) | 6.90885 | − | 3.98882i | 0.256235 | − | 0.147937i | −0.366381 | − | 0.930465i | \(-0.619403\pi\) |
0.622616 | + | 0.782528i | \(0.286070\pi\) | |||||||
\(728\) | 14.2472 | − | 1.53399i | 0.528036 | − | 0.0568533i | ||||
\(729\) | 0.601817 | + | 26.9933i | 0.0222895 | + | 0.999752i | ||||
\(730\) | 6.08000 | 0.225031 | ||||||||
\(731\) | 13.7474 | + | 23.8112i | 0.508467 | + | 0.880691i | ||||
\(732\) | −37.5174 | + | 10.2023i | −1.38668 | + | 0.377088i | ||||
\(733\) | −4.66110 | − | 2.69109i | −0.172162 | − | 0.0993975i | 0.411443 | − | 0.911435i | \(-0.365025\pi\) |
−0.583605 | + | 0.812038i | \(0.698358\pi\) | |||||||
\(734\) | −0.231744 | + | 0.401392i | −0.00855383 | + | 0.0148157i | ||||
\(735\) | 6.51379 | − | 10.2260i | 0.240265 | − | 0.377191i | ||||
\(736\) | 7.96667 | + | 13.7987i | 0.293655 | + | 0.508626i | ||||
\(737\) | 40.3077i | 1.48475i | ||||||||
\(738\) | 0.168303 | + | 0.286571i | 0.00619532 | + | 0.0105488i | ||||
\(739\) | 7.85381 | 0.288907 | 0.144453 | − | 0.989512i | \(-0.453858\pi\) | ||||
0.144453 | + | 0.989512i | \(0.453858\pi\) | |||||||
\(740\) | −3.91666 | − | 6.78386i | −0.143979 | − | 0.249380i | ||||
\(741\) | −31.5390 | − | 8.32540i | −1.15862 | − | 0.305841i | ||||
\(742\) | 1.12424 | − | 2.54241i | 0.0412721 | − | 0.0933350i | ||||
\(743\) | −40.8901 | − | 23.6079i | −1.50011 | − | 0.866089i | −1.00000 | 0.000128167i | \(-0.999959\pi\) | |
−0.500111 | − | 0.865961i | \(-0.666707\pi\) | |||||||
\(744\) | −1.87828 | − | 0.495811i | −0.0688610 | − | 0.0181773i | ||||
\(745\) | −7.63089 | + | 4.40570i | −0.279574 | + | 0.161412i | ||||
\(746\) | − | 10.9879i | − | 0.402295i | ||||||
\(747\) | −36.2944 | − | 20.5965i | −1.32794 | − | 0.753587i | ||||
\(748\) | 21.2330i | 0.776354i | ||||||||
\(749\) | 9.59432 | − | 7.00793i | 0.350569 | − | 0.256064i | ||||
\(750\) | −0.475302 | − | 0.471783i | −0.0173556 | − | 0.0172271i | ||||
\(751\) | 17.4591 | − | 30.2400i | 0.637090 | − | 1.10347i | −0.348978 | − | 0.937131i | \(-0.613471\pi\) |
0.986068 | − | 0.166342i | \(-0.0531956\pi\) | |||||||
\(752\) | −15.0879 | + | 26.1330i | −0.550199 | + | 0.952973i | ||||
\(753\) | 13.0690 | + | 48.0592i | 0.476261 | + | 1.75138i | ||||
\(754\) | −5.16623 | + | 2.98272i | −0.188143 | + | 0.108624i | ||||
\(755\) | 1.26468 | 0.0460264 | ||||||||
\(756\) | −19.9879 | − | 15.7380i | −0.726955 | − | 0.572387i | ||||
\(757\) | −11.7811 | −0.428190 | −0.214095 | − | 0.976813i | \(-0.568680\pi\) | ||||
−0.214095 | + | 0.976813i | \(0.568680\pi\) | |||||||
\(758\) | −7.97809 | + | 4.60615i | −0.289777 | + | 0.167303i | ||||
\(759\) | −7.34251 | − | 27.0010i | −0.266516 | − | 0.980072i | ||||
\(760\) | −3.85362 | + | 6.67467i | −0.139786 | + | 0.242116i | ||||
\(761\) | 25.6257 | − | 44.3849i | 0.928929 | − | 1.60895i | 0.143813 | − | 0.989605i | \(-0.454064\pi\) |
0.785117 | − | 0.619348i | \(-0.212603\pi\) | |||||||
\(762\) | 6.95147 | + | 6.90000i | 0.251825 | + | 0.249961i | ||||
\(763\) | 4.31922 | + | 5.91330i | 0.156366 | + | 0.214076i | ||||
\(764\) | 10.5630i | 0.382157i | ||||||||
\(765\) | 0.0602630 | + | 8.11012i | 0.00217881 | + | 0.293222i | ||||
\(766\) | − | 5.97499i | − | 0.215885i | ||||||
\(767\) | −27.9856 | + | 16.1575i | −1.01050 | + | 0.583414i | ||||
\(768\) | 8.93433 | + | 2.35840i | 0.322390 | + | 0.0851016i | ||||
\(769\) | 3.05041 | + | 1.76116i | 0.110001 | + | 0.0635089i | 0.553991 | − | 0.832523i | \(-0.313104\pi\) |
−0.443990 | + | 0.896032i | \(0.646438\pi\) | |||||||
\(770\) | −1.75589 | + | 3.97088i | −0.0632781 | + | 0.143101i | ||||
\(771\) | 26.6109 | + | 7.02451i | 0.958367 | + | 0.252981i | ||||
\(772\) | −0.954005 | − | 1.65239i | −0.0343354 | − | 0.0594706i | ||||
\(773\) | −36.9128 | −1.32766 | −0.663831 | − | 0.747882i | \(-0.731071\pi\) | ||||
−0.663831 | + | 0.747882i | \(0.731071\pi\) | |||||||
\(774\) | 11.7967 | − | 0.0876561i | 0.424022 | − | 0.00315074i | ||||
\(775\) | − | 0.753343i | − | 0.0270609i | ||||||
\(776\) | 10.0969 | + | 17.4884i | 0.362458 | + | 0.627796i | ||||
\(777\) | −12.1133 | + | 15.1514i | −0.434563 | + | 0.543554i | ||||
\(778\) | −7.25675 | + | 12.5691i | −0.260167 | + | 0.450623i | ||||
\(779\) | 1.28451 | + | 0.741614i | 0.0460225 | + | 0.0265711i | ||||
\(780\) | 11.2514 | − | 3.05966i | 0.402866 | − | 0.109554i | ||||
\(781\) | −24.8604 | − | 43.0594i | −0.889574 | − | 1.54079i | ||||
\(782\) | −3.97871 | −0.142278 | ||||||||
\(783\) | 21.3487 | + | 5.46608i | 0.762939 | + | 0.195342i | ||||
\(784\) | 21.3761 | − | 4.65710i | 0.763434 | − | 0.166325i | ||||
\(785\) | 0.850530 | − | 0.491054i | 0.0303567 | − | 0.0175265i | ||||
\(786\) | 7.29952 | − | 1.98500i | 0.260365 | − | 0.0708024i | ||||
\(787\) | 20.1637 | + | 11.6415i | 0.718759 | + | 0.414976i | 0.814296 | − | 0.580450i | \(-0.197123\pi\) |
−0.0955367 | + | 0.995426i | \(0.530457\pi\) | |||||||
\(788\) | 25.9655 | + | 14.9912i | 0.924983 | + | 0.534039i | ||||
\(789\) | 1.45399 | + | 1.44323i | 0.0517636 | + | 0.0513804i | ||||
\(790\) | 0.707521 | − | 0.408488i | 0.0251725 | − | 0.0145333i | ||||
\(791\) | −1.31698 | − | 12.2317i | −0.0468265 | − | 0.434910i | ||||
\(792\) | 16.4868 | + | 9.35599i | 0.585831 | + | 0.332451i | ||||
\(793\) | −44.1289 | −1.56706 | ||||||||
\(794\) | −2.45953 | − | 4.26002i | −0.0872853 | − | 0.151183i | ||||
\(795\) | 1.20130 | − | 4.55088i | 0.0426058 | − | 0.161403i | ||||
\(796\) | −28.2305 | − | 16.2989i | −1.00060 | − | 0.577699i | ||||
\(797\) | 15.1425 | − | 26.2275i | 0.536373 | − | 0.929026i | −0.462722 | − | 0.886503i | \(-0.653127\pi\) |
0.999096 | − | 0.0425225i | \(-0.0135394\pi\) | |||||||
\(798\) | 9.06844 | + | 1.37824i | 0.321019 | + | 0.0487892i | ||||
\(799\) | −13.0511 | − | 22.6051i | −0.461714 | − | 0.799712i | ||||
\(800\) | − | 4.18600i | − | 0.147997i | ||||||
\(801\) | 16.2588 | − | 9.54882i | 0.574478 | − | 0.337391i | ||||
\(802\) | −5.63580 | −0.199007 | ||||||||
\(803\) | −33.3703 | − | 57.7990i | −1.17761 | − | 2.03968i | ||||
\(804\) | −21.4438 | + | 21.6037i | −0.756264 | + | 0.761904i | ||||
\(805\) | 9.21034 | + | 4.07275i | 0.324622 | + | 0.143546i | ||||
\(806\) | −0.917676 | − | 0.529820i | −0.0323237 | − | 0.0186621i | ||||
\(807\) | 4.92655 | + | 18.1166i | 0.173423 | + | 0.637736i | ||||
\(808\) | −24.6976 | + | 14.2591i | −0.868857 | + | 0.501635i | ||||
\(809\) | 28.5991i | 1.00549i | 0.864434 | + | 0.502746i | \(0.167677\pi\) | ||||
−0.864434 | + | 0.502746i | \(0.832323\pi\) | |||||||
\(810\) | 3.03915 | + | 1.69494i | 0.106785 | + | 0.0595542i | ||||
\(811\) | − | 30.1445i | − | 1.05852i | −0.848461 | − | 0.529258i | \(-0.822470\pi\) | ||
0.848461 | − | 0.529258i | \(-0.177530\pi\) | |||||||
\(812\) | −16.7676 | + | 12.2475i | −0.588427 | + | 0.429802i | ||||
\(813\) | 36.1178 | − | 9.82170i | 1.26671 | − | 0.344462i | ||||
\(814\) | 3.47332 | − | 6.01597i | 0.121740 | − | 0.210860i | ||||
\(815\) | 4.95388 | − | 8.58036i | 0.173527 | − | 0.300557i | ||||
\(816\) | −10.3097 | + | 10.3866i | −0.360911 | + | 0.363603i | ||||
\(817\) | 45.5963 | − | 26.3250i | 1.59521 | − | 0.920996i | ||||
\(818\) | −14.6058 | −0.510679 | ||||||||
\(819\) | −17.2042 | − | 23.1899i | −0.601163 | − | 0.810322i | ||||
\(820\) | −0.530191 | −0.0185151 | ||||||||
\(821\) | −32.7300 | + | 18.8967i | −1.14229 | + | 0.659499i | −0.946996 | − | 0.321246i | \(-0.895898\pi\) |
−0.195290 | + | 0.980745i | \(0.562565\pi\) | |||||||
\(822\) | −10.8078 | − | 2.85294i | −0.376965 | − | 0.0995078i | ||||
\(823\) | 25.9752 | − | 44.9904i | 0.905439 | − | 1.56827i | 0.0851124 | − | 0.996371i | \(-0.472875\pi\) |
0.820327 | − | 0.571895i | \(-0.193792\pi\) | |||||||
\(824\) | 1.69915 | − | 2.94301i | 0.0591925 | − | 0.102524i | ||||
\(825\) | −1.87626 | + | 7.10781i | −0.0653229 | + | 0.247462i | ||||
\(826\) | 7.33796 | − | 5.35983i | 0.255320 | − | 0.186492i | ||||
\(827\) | 16.7067i | 0.580949i | 0.956883 | + | 0.290475i | \(0.0938132\pi\) | ||||
−0.956883 | + | 0.290475i | \(0.906187\pi\) | |||||||
\(828\) | 10.4292 | − | 18.3779i | 0.362440 | − | 0.638677i | ||||
\(829\) | − | 43.0971i | − | 1.49682i | −0.663235 | − | 0.748411i | \(-0.730817\pi\) | ||
0.663235 | − | 0.748411i | \(-0.269183\pi\) | |||||||
\(830\) | −4.65787 | + | 2.68922i | −0.161677 | + | 0.0933442i | ||||
\(831\) | −6.75387 | + | 6.80424i | −0.234289 | + | 0.236037i | ||||
\(832\) | 14.5938 | + | 8.42576i | 0.505951 | + | 0.292111i | ||||
\(833\) | −5.75651 | + | 18.0274i | −0.199451 | + | 0.624611i | ||||
\(834\) | 1.54588 | + | 5.68475i | 0.0535296 | + | 0.196847i | ||||
\(835\) | −0.932410 | − | 1.61498i | −0.0322674 | − | 0.0558888i | ||||
\(836\) | 40.6591 | 1.40622 | ||||||||
\(837\) | 1.05522 | + | 3.76957i | 0.0364738 | + | 0.130296i | ||||
\(838\) | − | 0.351504i | − | 0.0121425i | ||||||
\(839\) | 3.43018 | + | 5.94125i | 0.118423 | + | 0.205115i | 0.919143 | − | 0.393924i | \(-0.128883\pi\) |
−0.800720 | + | 0.599039i | \(0.795549\pi\) | |||||||
\(840\) | −6.35394 | + | 2.48473i | −0.219232 | + | 0.0857315i | ||||
\(841\) | −5.50660 | + | 9.53771i | −0.189883 | + | 0.328887i | ||||
\(842\) | −1.43281 | − | 0.827232i | −0.0493778 | − | 0.0285083i | ||||
\(843\) | 21.9674 | + | 21.8048i | 0.756597 | + | 0.750996i | ||||
\(844\) | 6.23178 | + | 10.7938i | 0.214507 | + | 0.371536i | ||||
\(845\) | 0.234248 | 0.00805837 | ||||||||
\(846\) | −11.1991 | + | 0.0832160i | −0.385033 | + | 0.00286103i | ||||
\(847\) | 18.4501 | − | 1.98651i | 0.633952 | − | 0.0682572i | ||||
\(848\) | 7.35519 | − | 4.24652i | 0.252578 | − | 0.145826i | ||||
\(849\) | −3.12886 | + | 11.8530i | −0.107382 | + | 0.406795i | ||||
\(850\) | 0.905243 | + | 0.522642i | 0.0310496 | + | 0.0179265i | ||||
\(851\) | −13.9539 | − | 8.05627i | −0.478333 | − | 0.276166i | ||||
\(852\) | 9.58330 | − | 36.3043i | 0.328318 | − | 1.24377i | ||||
\(853\) | −15.8246 | + | 9.13635i | −0.541825 | + | 0.312823i | −0.745818 | − | 0.666150i | \(-0.767941\pi\) |
0.203994 | + | 0.978972i | \(0.434608\pi\) | |||||||
\(854\) | 12.3378 | − | 1.32840i | 0.422189 | − | 0.0454568i | ||||
\(855\) | 15.5301 | − | 0.115398i | 0.531118 | − | 0.00394653i | ||||
\(856\) | −6.68565 | −0.228511 | ||||||||
\(857\) | 6.20774 | + | 10.7521i | 0.212052 | + | 0.367285i | 0.952357 | − | 0.304986i | \(-0.0986519\pi\) |
−0.740304 | + | 0.672272i | \(0.765319\pi\) | |||||||
\(858\) | 7.33874 | + | 7.28441i | 0.250540 | + | 0.248686i | ||||
\(859\) | 3.69582 | + | 2.13378i | 0.126100 | + | 0.0728038i | 0.561723 | − | 0.827325i | \(-0.310139\pi\) |
−0.435623 | + | 0.900129i | \(0.643472\pi\) | |||||||
\(860\) | −9.41008 | + | 16.2987i | −0.320881 | + | 0.555782i | ||||
\(861\) | 0.478177 | + | 1.22279i | 0.0162962 | + | 0.0416726i | ||||
\(862\) | 2.29361 | + | 3.97265i | 0.0781206 | + | 0.135309i | ||||
\(863\) | 16.8919i | 0.575008i | 0.957779 | + | 0.287504i | \(0.0928255\pi\) | ||||
−0.957779 | + | 0.287504i | \(0.907175\pi\) | |||||||
\(864\) | 5.86341 | + | 20.9459i | 0.199477 | + | 0.712594i | ||||
\(865\) | 7.86459 | 0.267404 | ||||||||
\(866\) | 2.91537 | + | 5.04957i | 0.0990683 | + | 0.171591i | ||||
\(867\) | 4.40473 | + | 16.1977i | 0.149592 | + | 0.550103i | ||||
\(868\) | −3.37326 | − | 1.49163i | −0.114496 | − | 0.0506294i | ||||
\(869\) | −7.76651 | − | 4.48400i | −0.263461 | − | 0.152109i | ||||
\(870\) | 2.00087 | − | 2.01579i | 0.0678359 | − | 0.0683418i | ||||
\(871\) | −29.9203 | + | 17.2745i | −1.01381 | + | 0.585324i | ||||
\(872\) | − | 4.12059i | − | 0.139541i | ||||||
\(873\) | 20.0834 | − | 35.3903i | 0.679722 | − | 1.19778i | ||||
\(874\) | 7.61885i | 0.257711i | ||||||||
\(875\) | −1.56056 | − | 2.13651i | −0.0527565 | − | 0.0722271i | ||||
\(876\) | 12.8637 | − | 48.7316i | 0.434625 | − | 1.64649i | ||||
\(877\) | 5.91368 | − | 10.2428i | 0.199691 | − | 0.345875i | −0.748737 | − | 0.662867i | \(-0.769340\pi\) |
0.948428 | + | 0.316992i | \(0.102673\pi\) | |||||||
\(878\) | −7.54672 | + | 13.0713i | −0.254689 | + | 0.441135i | ||||
\(879\) | 24.8246 | + | 6.55297i | 0.837312 | + | 0.221026i | ||||
\(880\) | −11.4877 | + | 6.63244i | −0.387251 | + | 0.223580i | ||||
\(881\) | 2.38825 | 0.0804622 | 0.0402311 | − | 0.999190i | \(-0.487191\pi\) | ||||
0.0402311 | + | 0.999190i | \(0.487191\pi\) | |||||||
\(882\) | 5.50810 | + | 5.96565i | 0.185467 | + | 0.200874i | ||||
\(883\) | −6.82573 | −0.229704 | −0.114852 | − | 0.993383i | \(-0.536639\pi\) | ||||
−0.114852 | + | 0.993383i | \(0.536639\pi\) | |||||||
\(884\) | −15.7612 | + | 9.09971i | −0.530105 | + | 0.306056i | ||||
\(885\) | 10.8388 | − | 10.9196i | 0.364342 | − | 0.367059i | ||||
\(886\) | 3.48486 | − | 6.03596i | 0.117076 | − | 0.202782i | ||||
\(887\) | −13.5359 | + | 23.4449i | −0.454492 | + | 0.787203i | −0.998659 | − | 0.0517739i | \(-0.983512\pi\) |
0.544167 | + | 0.838977i | \(0.316846\pi\) | |||||||
\(888\) | 10.5332 | − | 2.86434i | 0.353470 | − | 0.0961209i | ||||
\(889\) | 22.8237 | + | 31.2472i | 0.765484 | + | 1.04800i | ||||
\(890\) | − | 2.43015i | − | 0.0814588i | ||||||
\(891\) | −0.567642 | − | 38.1942i | −0.0190167 | − | 1.27955i | ||||
\(892\) | − | 10.3939i | − | 0.348014i | ||||||
\(893\) | −43.2866 | + | 24.9916i | −1.44853 | + | 0.836310i | ||||
\(894\) | −1.54844 | − | 5.69416i | −0.0517877 | − | 0.190441i | ||||
\(895\) | 3.64656 | + | 2.10534i | 0.121891 | + | 0.0703739i | ||||
\(896\) | −24.5919 | − | 10.8744i | −0.821557 | − | 0.363287i | ||||
\(897\) | 16.8960 | − | 17.0220i | 0.564141 | − | 0.568348i | ||||
\(898\) | −3.39948 | − | 5.88807i | −0.113442 | − | 0.196487i | ||||
\(899\) | 3.19499 | 0.106559 | ||||||||
\(900\) | −4.78699 | + | 2.81140i | −0.159566 | + | 0.0937134i | ||||
\(901\) | 7.34650i | 0.244747i | ||||||||
\(902\) | −0.235088 | − | 0.407185i | −0.00782759 | − | 0.0135578i | ||||
\(903\) | 46.0770 | + | 7.00289i | 1.53335 | + | 0.233042i | ||||
\(904\) | −3.46135 | + | 5.99523i | −0.115123 | + | 0.199398i | ||||
\(905\) | 1.19763 | + | 0.691451i | 0.0398105 | + | 0.0229846i | ||||
\(906\) | −0.216166 | + | 0.818899i | −0.00718162 | + | 0.0272061i | ||||
\(907\) | −10.3947 | − | 18.0042i | −0.345151 | − | 0.597820i | 0.640230 | − | 0.768183i | \(-0.278839\pi\) |
−0.985381 | + | 0.170364i | \(0.945506\pi\) | |||||||
\(908\) | −26.9108 | −0.893067 | ||||||||
\(909\) | 49.9792 | + | 28.3624i | 1.65770 | + | 0.940722i | ||||
\(910\) | −3.70009 | + | 0.398386i | −0.122657 | + | 0.0132064i | ||||
\(911\) | −33.8775 | + | 19.5592i | −1.12241 | + | 0.648024i | −0.942015 | − | 0.335570i | \(-0.891071\pi\) |
−0.180396 | + | 0.983594i | \(0.557738\pi\) | |||||||
\(912\) | 19.8893 | + | 19.7421i | 0.658600 | + | 0.653725i | ||||
\(913\) | 51.1297 | + | 29.5198i | 1.69215 | + | 0.976961i | ||||
\(914\) | −2.65555 | − | 1.53318i | −0.0878378 | − | 0.0507132i | ||||
\(915\) | 20.2742 | − | 5.51326i | 0.670243 | − | 0.182263i | ||||
\(916\) | 34.5378 | − | 19.9404i | 1.14116 | − | 0.658849i | ||||
\(917\) | 29.7136 | − | 3.19924i | 0.981230 | − | 0.105648i | ||||
\(918\) | −5.26173 | − | 1.34720i | −0.173663 | − | 0.0444643i | ||||
\(919\) | 0.643554 | 0.0212289 | 0.0106144 | − | 0.999944i | \(-0.496621\pi\) | ||||
0.0106144 | + | 0.999944i | \(0.496621\pi\) | |||||||
\(920\) | −2.83342 | − | 4.90763i | −0.0934152 | − | 0.161800i | ||||
\(921\) | −10.1594 | + | 2.76270i | −0.334764 | + | 0.0910341i | ||||
\(922\) | 2.69294 | + | 1.55477i | 0.0886873 | + | 0.0512036i | ||||
\(923\) | 21.3086 | − | 36.9076i | 0.701381 | − | 1.21483i | ||||
\(924\) | 28.1118 | + | 22.4750i | 0.924811 | + | 0.739373i | ||||
\(925\) | 2.11654 | + | 3.66595i | 0.0695914 | + | 0.120536i | ||||
\(926\) | 7.50516i | 0.246635i | ||||||||
\(927\) | −6.84757 | + | 0.0508815i | −0.224904 | + | 0.00167117i | ||||
\(928\) | 17.7532 | 0.582777 | ||||||||
\(929\) | 0.117189 | + | 0.202978i | 0.00384486 | + | 0.00665950i | 0.867941 | − | 0.496667i | \(-0.165443\pi\) |
−0.864097 | + | 0.503326i | \(0.832109\pi\) | |||||||
\(930\) | 0.487801 | + | 0.128765i | 0.0159956 | + | 0.00422238i | ||||
\(931\) | 34.5207 | + | 11.0232i | 1.13137 | + | 0.361270i | ||||
\(932\) | 12.8475 | + | 7.41748i | 0.420832 | + | 0.242968i | ||||
\(933\) | −17.2045 | − | 4.54150i | −0.563251 | − | 0.148682i | ||||
\(934\) | −5.19797 | + | 3.00105i | −0.170083 | + | 0.0981973i | ||||
\(935\) | − | 11.4742i | − | 0.375245i | ||||||
\(936\) | 0.120730 | + | 16.2477i | 0.00394619 | + | 0.531074i | ||||
\(937\) | − | 18.1699i | − | 0.593584i | −0.954942 | − | 0.296792i | \(-0.904083\pi\) | ||
0.954942 | − | 0.296792i | \(-0.0959167\pi\) | |||||||
\(938\) | 7.84524 | − | 5.73036i | 0.256156 | − | 0.187103i | ||||
\(939\) | −20.0089 | − | 19.8608i | −0.652967 | − | 0.648133i | ||||
\(940\) | 8.93342 | − | 15.4731i | 0.291376 | − | 0.504678i | ||||
\(941\) | 0.276744 | − | 0.479335i | 0.00902160 | − | 0.0156259i | −0.861479 | − | 0.507793i | \(-0.830462\pi\) |
0.870501 | + | 0.492167i | \(0.163795\pi\) | |||||||
\(942\) | 0.172587 | + | 0.634664i | 0.00562320 | + | 0.0206785i | ||||
\(943\) | −0.944455 | + | 0.545281i | −0.0307557 | + | 0.0177568i | ||||
\(944\) | 27.7623 | 0.903587 | ||||||||
\(945\) | 10.8014 | + | 8.50474i | 0.351368 | + | 0.276659i | ||||
\(946\) | −16.6898 | −0.542633 | ||||||||
\(947\) | 20.8441 | − | 12.0343i | 0.677341 | − | 0.391063i | −0.121511 | − | 0.992590i | \(-0.538774\pi\) |
0.798852 | + | 0.601527i | \(0.205441\pi\) | |||||||
\(948\) | −1.77712 | − | 6.53509i | −0.0577182 | − | 0.212250i | ||||
\(949\) | 28.6027 | − | 49.5413i | 0.928483 | − | 1.60818i | ||||
\(950\) | 1.00081 | − | 1.73345i | 0.0324706 | − | 0.0562406i | ||||
\(951\) | −40.9772 | − | 40.6738i | −1.32878 | − | 1.31894i | ||||
\(952\) | 8.59916 | − | 6.28104i | 0.278700 | − | 0.203570i | ||||
\(953\) | 10.9096i | 0.353398i | 0.984265 | + | 0.176699i | \(0.0565418\pi\) | ||||
−0.984265 | + | 0.176699i | \(0.943458\pi\) | |||||||
\(954\) | 2.74143 | + | 1.55572i | 0.0887571 | + | 0.0503684i | ||||
\(955\) | − | 5.70820i | − | 0.184713i | ||||||
\(956\) | 45.2538 | − | 26.1273i | 1.46361 | − | 0.845017i | ||||
\(957\) | −30.1448 | − | 7.95737i | −0.974444 | − | 0.257225i | ||||
\(958\) | 3.18093 | + | 1.83651i | 0.102771 | + | 0.0593349i | ||||
\(959\) | −40.3882 | − | 17.8594i | −1.30420 | − | 0.576710i | ||||
\(960\) | −7.75752 | − | 2.04776i | −0.250373 | − | 0.0660913i | ||||
\(961\) | −15.2162 | − | 26.3553i | −0.490846 | − | 0.850171i | ||||
\(962\) | 5.95418 | 0.191971 | ||||||||
\(963\) | 6.82249 | + | 11.6167i | 0.219852 | + | 0.374343i | ||||
\(964\) | − | 26.6029i | − | 0.856823i | ||||||
\(965\) | 0.515538 | + | 0.892938i | 0.0165958 | + | 0.0287447i | ||||
\(966\) | −4.21145 | + | 5.26770i | −0.135501 | + | 0.169485i | ||||
\(967\) | −8.30830 | + | 14.3904i | −0.267177 | + | 0.462764i | −0.968132 | − | 0.250442i | \(-0.919424\pi\) |
0.700955 | + | 0.713206i | \(0.252757\pi\) | |||||||
\(968\) | −9.04308 | − | 5.22103i | −0.290656 | − | 0.167810i | ||||
\(969\) | −23.3912 | + | 6.36088i | −0.751433 | + | 0.204341i | ||||
\(970\) | −2.62223 | − | 4.54184i | −0.0841948 | − | 0.145830i | ||||
\(971\) | 31.5538 | 1.01261 | 0.506305 | − | 0.862354i | \(-0.331011\pi\) | ||||
0.506305 | + | 0.862354i | \(0.331011\pi\) | |||||||
\(972\) | 20.0151 | − | 20.7729i | 0.641986 | − | 0.666292i | ||||
\(973\) | 2.49152 | + | 23.1405i | 0.0798745 | + | 0.741850i | ||||
\(974\) | 12.0580 | − | 6.96171i | 0.386365 | − | 0.223068i | ||||
\(975\) | −6.08021 | + | 1.65342i | −0.194723 | + | 0.0529519i | ||||
\(976\) | 32.8326 | + | 18.9559i | 1.05095 | + | 0.606764i | ||||
\(977\) | −18.5295 | − | 10.6980i | −0.592810 | − | 0.342259i | 0.173398 | − | 0.984852i | \(-0.444525\pi\) |
−0.766208 | + | 0.642593i | \(0.777859\pi\) | |||||||
\(978\) | 4.70917 | + | 4.67431i | 0.150583 | + | 0.149468i | ||||
\(979\) | −23.1020 | + | 13.3380i | −0.738343 | + | 0.426283i | ||||
\(980\) | −12.6566 | + | 2.75743i | −0.404301 | + | 0.0880828i | ||||
\(981\) | −7.15976 | + | 4.20493i | −0.228594 | + | 0.134253i | ||||
\(982\) | −11.6274 | −0.371045 | ||||||||
\(983\) | −20.6637 | − | 35.7906i | −0.659070 | − | 1.14154i | −0.980857 | − | 0.194730i | \(-0.937617\pi\) |
0.321787 | − | 0.946812i | \(-0.395716\pi\) | |||||||
\(984\) | 0.188567 | − | 0.714348i | 0.00601131 | − | 0.0227726i | ||||
\(985\) | −14.0316 | − | 8.10114i | −0.447084 | − | 0.258124i | ||||
\(986\) | −2.21657 | + | 3.83921i | −0.0705899 | + | 0.122265i | ||||
\(987\) | −43.7430 | − | 6.64817i | −1.39236 | − | 0.211613i | ||||
\(988\) | 17.4251 | + | 30.1811i | 0.554365 | + | 0.960189i | ||||
\(989\) | 38.7116i | 1.23096i | ||||||||
\(990\) | −4.28171 | − | 2.42981i | −0.136082 | − | 0.0772244i | ||||
\(991\) | 50.6454 | 1.60880 | 0.804402 | − | 0.594085i | \(-0.202486\pi\) | ||||
0.804402 | + | 0.594085i | \(0.202486\pi\) | |||||||
\(992\) | 1.57675 | + | 2.73101i | 0.0500618 | + | 0.0867095i | ||||
\(993\) | 31.7156 | − | 31.9521i | 1.00646 | − | 1.01397i | ||||
\(994\) | −4.84653 | + | 10.9602i | −0.153723 | + | 0.347637i | ||||
\(995\) | 15.2556 | + | 8.80782i | 0.483635 | + | 0.279227i | ||||
\(996\) | 11.6994 | + | 43.0228i | 0.370710 | + | 1.36323i | ||||
\(997\) | 0.0982245 | − | 0.0567099i | 0.00311080 | − | 0.00179602i | −0.498444 | − | 0.866922i | \(-0.666095\pi\) |
0.501555 | + | 0.865126i | \(0.332762\pi\) | |||||||
\(998\) | − | 16.0988i | − | 0.509599i | ||||||
\(999\) | −15.7257 | − | 15.3790i | −0.497539 | − | 0.486570i |
(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 | 315.2.bl.i.41.5 | ✓ | 24 | |
3.2 | odd | 2 | 945.2.bl.i.881.8 | 24 | |||
7.6 | odd | 2 | 315.2.bl.j.41.5 | yes | 24 | ||
9.2 | odd | 6 | 315.2.bl.j.146.5 | yes | 24 | ||
9.7 | even | 3 | 945.2.bl.j.251.8 | 24 | |||
21.20 | even | 2 | 945.2.bl.j.881.8 | 24 | |||
63.20 | even | 6 | inner | 315.2.bl.i.146.5 | yes | 24 | |
63.34 | odd | 6 | 945.2.bl.i.251.8 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bl.i.41.5 | ✓ | 24 | 1.1 | even | 1 | trivial | |
315.2.bl.i.146.5 | yes | 24 | 63.20 | even | 6 | inner | |
315.2.bl.j.41.5 | yes | 24 | 7.6 | odd | 2 | ||
315.2.bl.j.146.5 | yes | 24 | 9.2 | odd | 6 | ||
945.2.bl.i.251.8 | 24 | 63.34 | odd | 6 | |||
945.2.bl.i.881.8 | 24 | 3.2 | odd | 2 | |||
945.2.bl.j.251.8 | 24 | 9.7 | even | 3 | |||
945.2.bl.j.881.8 | 24 | 21.20 | even | 2 |