Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(143,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([27, 34]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.bb (of order \(36\), degree \(12\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{36})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 393.1 | ||
Character | \(\chi\) | \(=\) | 950.393 |
Dual form | 950.2.bb.a.307.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.996195 | − | 0.0871557i | −0.704416 | − | 0.0616284i | ||||
\(3\) | −2.18554 | + | 1.01913i | −1.26182 | + | 0.588397i | −0.934314 | − | 0.356452i | \(-0.883986\pi\) |
−0.327507 | + | 0.944849i | \(0.606209\pi\) | |||||||
\(4\) | 0.984808 | + | 0.173648i | 0.492404 | + | 0.0868241i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.26604 | − | 0.824773i | 0.925109 | − | 0.336712i | ||||
\(7\) | −0.271245 | − | 1.01230i | −0.102521 | − | 0.382614i | 0.895531 | − | 0.444999i | \(-0.146796\pi\) |
−0.998052 | + | 0.0623853i | \(0.980129\pi\) | |||||||
\(8\) | −0.965926 | − | 0.258819i | −0.341506 | − | 0.0915064i | ||||
\(9\) | 1.80958 | − | 2.15657i | 0.603193 | − | 0.718858i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.152704 | + | 0.264490i | 0.0460419 | + | 0.0797469i | 0.888128 | − | 0.459596i | \(-0.152006\pi\) |
−0.842086 | + | 0.539343i | \(0.818673\pi\) | |||||||
\(12\) | −2.32931 | + | 0.624135i | −0.672412 | + | 0.180172i | ||||
\(13\) | −1.36365 | + | 2.92437i | −0.378210 | + | 0.811073i | 0.621410 | + | 0.783486i | \(0.286560\pi\) |
−0.999619 | + | 0.0275876i | \(0.991217\pi\) | |||||||
\(14\) | 0.181985 | + | 1.03209i | 0.0486376 | + | 0.275837i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.939693 | + | 0.342020i | 0.234923 | + | 0.0855050i | ||||
\(17\) | 0.171663 | − | 1.96212i | 0.0416345 | − | 0.475884i | −0.946544 | − | 0.322575i | \(-0.895451\pi\) |
0.988178 | − | 0.153309i | \(-0.0489930\pi\) | |||||||
\(18\) | −1.99065 | + | 1.99065i | −0.469201 | + | 0.469201i | ||||
\(19\) | 1.55007 | − | 4.07398i | 0.355609 | − | 0.934635i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.62449 | + | 1.93599i | 0.354492 | + | 0.422467i | ||||
\(22\) | −0.129071 | − | 0.276793i | −0.0275180 | − | 0.0590125i | ||||
\(23\) | 0.858480 | − | 0.601114i | 0.179005 | − | 0.125341i | −0.480640 | − | 0.876918i | \(-0.659595\pi\) |
0.659645 | + | 0.751577i | \(0.270707\pi\) | |||||||
\(24\) | 2.37484 | − | 0.418748i | 0.484762 | − | 0.0854766i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.61334 | − | 2.79439i | 0.316402 | − | 0.548025i | ||||
\(27\) | 0.115336 | − | 0.430438i | 0.0221963 | − | 0.0828379i | ||||
\(28\) | −0.0913401 | − | 1.04402i | −0.0172617 | − | 0.197302i | ||||
\(29\) | −2.09602 | − | 1.75877i | −0.389221 | − | 0.326595i | 0.427088 | − | 0.904210i | \(-0.359539\pi\) |
−0.816310 | + | 0.577614i | \(0.803984\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.31521 | + | 1.91404i | 0.595429 | + | 0.343771i | 0.767241 | − | 0.641359i | \(-0.221629\pi\) |
−0.171812 | + | 0.985130i | \(0.554962\pi\) | |||||||
\(32\) | −0.906308 | − | 0.422618i | −0.160214 | − | 0.0747091i | ||||
\(33\) | −0.603291 | − | 0.422429i | −0.105019 | − | 0.0735354i | ||||
\(34\) | −0.342020 | + | 1.93969i | −0.0586560 | + | 0.332655i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.15657 | − | 1.80958i | 0.359429 | − | 0.301597i | ||||
\(37\) | 0.822014 | + | 0.822014i | 0.135138 | + | 0.135138i | 0.771440 | − | 0.636302i | \(-0.219537\pi\) |
−0.636302 | + | 0.771440i | \(0.719537\pi\) | |||||||
\(38\) | −1.89924 | + | 3.92338i | −0.308097 | + | 0.636456i | ||||
\(39\) | − | 7.78106i | − | 1.24597i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.48886 | + | 6.83807i | −0.388694 | + | 1.06793i | 0.578896 | + | 0.815401i | \(0.303484\pi\) |
−0.967590 | + | 0.252526i | \(0.918739\pi\) | |||||||
\(42\) | −1.44957 | − | 2.07020i | −0.223674 | − | 0.319439i | ||||
\(43\) | 3.83759 | − | 5.48065i | 0.585227 | − | 0.835791i | −0.411924 | − | 0.911218i | \(-0.635143\pi\) |
0.997151 | + | 0.0754269i | \(0.0240320\pi\) | |||||||
\(44\) | 0.104455 | + | 0.286989i | 0.0157473 | + | 0.0432652i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.907604 | + | 0.524005i | −0.133819 | + | 0.0772604i | ||||
\(47\) | 0.570701 | − | 0.0499299i | 0.0832453 | − | 0.00728302i | −0.0454570 | − | 0.998966i | \(-0.514474\pi\) |
0.128702 | + | 0.991683i | \(0.458919\pi\) | |||||||
\(48\) | −2.40230 | + | 0.210174i | −0.346742 | + | 0.0303360i | ||||
\(49\) | 5.11100 | − | 2.95084i | 0.730143 | − | 0.421548i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.62449 | + | 4.46324i | 0.227473 | + | 0.624978i | ||||
\(52\) | −1.85075 | + | 2.64314i | −0.256653 | + | 0.366538i | ||||
\(53\) | 6.32502 | + | 9.03307i | 0.868809 | + | 1.24079i | 0.969308 | + | 0.245850i | \(0.0790672\pi\) |
−0.100499 | + | 0.994937i | \(0.532044\pi\) | |||||||
\(54\) | −0.152412 | + | 0.418748i | −0.0207406 | + | 0.0569844i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.04801i | 0.140046i | ||||||||
\(57\) | 0.764198 | + | 10.4836i | 0.101221 | + | 1.38858i | ||||
\(58\) | 1.93476 | + | 1.93476i | 0.254046 | + | 0.254046i | ||||
\(59\) | −5.85327 | + | 4.91147i | −0.762030 | + | 0.639419i | −0.938655 | − | 0.344859i | \(-0.887927\pi\) |
0.176624 | + | 0.984278i | \(0.443482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.34864 | + | 13.3198i | −0.300713 | + | 1.70543i | 0.342317 | + | 0.939585i | \(0.388788\pi\) |
−0.643030 | + | 0.765841i | \(0.722323\pi\) | |||||||
\(62\) | −3.13577 | − | 2.19569i | −0.398244 | − | 0.278853i | ||||
\(63\) | −2.67394 | − | 1.24688i | −0.336885 | − | 0.157092i | ||||
\(64\) | 0.866025 | + | 0.500000i | 0.108253 | + | 0.0625000i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.564178 | + | 0.473401i | 0.0694455 | + | 0.0582717i | ||||
\(67\) | 0.495049 | + | 5.65843i | 0.0604798 | + | 0.691287i | 0.964549 | + | 0.263902i | \(0.0850096\pi\) |
−0.904070 | + | 0.427385i | \(0.859435\pi\) | |||||||
\(68\) | 0.509774 | − | 1.90250i | 0.0618192 | − | 0.230712i | ||||
\(69\) | −1.26363 | + | 2.18866i | −0.152123 | + | 0.263484i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.34730 | + | 0.237565i | −0.159895 | + | 0.0281937i | −0.253022 | − | 0.967460i | \(-0.581425\pi\) |
0.0931277 | + | 0.995654i | \(0.470314\pi\) | |||||||
\(72\) | −2.30608 | + | 1.61474i | −0.271774 | + | 0.190299i | ||||
\(73\) | 6.26968 | + | 13.4454i | 0.733810 | + | 1.57366i | 0.816673 | + | 0.577100i | \(0.195816\pi\) |
−0.0828633 | + | 0.996561i | \(0.526406\pi\) | |||||||
\(74\) | −0.747243 | − | 0.890530i | −0.0868652 | − | 0.103522i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.23396 | − | 3.74292i | 0.256252 | − | 0.429342i | ||||
\(77\) | 0.226324 | − | 0.226324i | 0.0257920 | − | 0.0257920i | ||||
\(78\) | −0.678164 | + | 7.75145i | −0.0767870 | + | 0.877679i | ||||
\(79\) | −2.32099 | − | 0.844770i | −0.261131 | − | 0.0950441i | 0.208137 | − | 0.978100i | \(-0.433260\pi\) |
−0.469268 | + | 0.883056i | \(0.655482\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.65317 | + | 9.37560i | 0.183686 | + | 1.04173i | ||||
\(82\) | 3.07536 | − | 6.59514i | 0.339617 | − | 0.728311i | ||||
\(83\) | 7.19347 | − | 1.92749i | 0.789586 | − | 0.211569i | 0.158579 | − | 0.987346i | \(-0.449309\pi\) |
0.631007 | + | 0.775777i | \(0.282642\pi\) | |||||||
\(84\) | 1.26363 | + | 2.18866i | 0.137873 | + | 0.238803i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.30066 | + | 5.12533i | −0.463752 | + | 0.552678i | ||||
\(87\) | 6.37335 | + | 1.70774i | 0.683295 | + | 0.183088i | ||||
\(88\) | −0.0790452 | − | 0.295001i | −0.00842625 | − | 0.0314472i | ||||
\(89\) | 7.69475 | − | 2.80066i | 0.815642 | − | 0.296869i | 0.0996895 | − | 0.995019i | \(-0.468215\pi\) |
0.715952 | + | 0.698149i | \(0.245993\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.33022 | + | 0.587208i | 0.349102 | + | 0.0615561i | ||||
\(92\) | 0.949820 | − | 0.442908i | 0.0990256 | − | 0.0461764i | ||||
\(93\) | −9.19617 | − | 0.804560i | −0.953598 | − | 0.0834290i | ||||
\(94\) | −0.572881 | −0.0590882 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.41147 | 0.246120 | ||||||||
\(97\) | 12.8159 | + | 1.12124i | 1.30126 | + | 0.113845i | 0.716627 | − | 0.697456i | \(-0.245685\pi\) |
0.584628 | + | 0.811301i | \(0.301240\pi\) | |||||||
\(98\) | −5.34873 | + | 2.49416i | −0.540304 | + | 0.251948i | ||||
\(99\) | 0.846723 | + | 0.149300i | 0.0850988 | + | 0.0150052i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.23783 | + | 2.63435i | −0.720191 | + | 0.262128i | −0.676007 | − | 0.736895i | \(-0.736291\pi\) |
−0.0441839 | + | 0.999023i | \(0.514069\pi\) | |||||||
\(102\) | −1.22931 | − | 4.58784i | −0.121720 | − | 0.454263i | ||||
\(103\) | 12.3456 | + | 3.30798i | 1.21644 | + | 0.325945i | 0.809287 | − | 0.587413i | \(-0.199854\pi\) |
0.407157 | + | 0.913358i | \(0.366520\pi\) | |||||||
\(104\) | 2.07407 | − | 2.47178i | 0.203379 | − | 0.242378i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.51367 | − | 9.54996i | −0.535535 | − | 0.927574i | ||||
\(107\) | −8.85030 | + | 2.37143i | −0.855591 | + | 0.229255i | −0.659847 | − | 0.751400i | \(-0.729379\pi\) |
−0.195744 | + | 0.980655i | \(0.562712\pi\) | |||||||
\(108\) | 0.188328 | − | 0.403871i | 0.0181219 | − | 0.0388625i | ||||
\(109\) | 2.36986 | + | 13.4402i | 0.226992 | + | 1.28733i | 0.858841 | + | 0.512242i | \(0.171185\pi\) |
−0.631849 | + | 0.775091i | \(0.717704\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.63429 | − | 0.958801i | −0.250035 | − | 0.0910054i | ||||
\(112\) | 0.0913401 | − | 1.04402i | 0.00863083 | − | 0.0986509i | ||||
\(113\) | 0.317004 | − | 0.317004i | 0.0298212 | − | 0.0298212i | −0.692039 | − | 0.721860i | \(-0.743287\pi\) |
0.721860 | + | 0.692039i | \(0.243287\pi\) | |||||||
\(114\) | 0.152412 | − | 10.5103i | 0.0142747 | − | 0.984377i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.75877 | − | 2.09602i | −0.163298 | − | 0.194611i | ||||
\(117\) | 3.83897 | + | 8.23270i | 0.354913 | + | 0.761113i | ||||
\(118\) | 6.25906 | − | 4.38264i | 0.576193 | − | 0.403455i | ||||
\(119\) | −2.03282 | + | 0.358441i | −0.186348 | + | 0.0328582i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.45336 | − | 9.44550i | 0.495760 | − | 0.858682i | ||||
\(122\) | 3.50060 | − | 13.0644i | 0.316929 | − | 1.18280i | ||||
\(123\) | −1.52942 | − | 17.4813i | −0.137903 | − | 1.57624i | ||||
\(124\) | 2.93247 | + | 2.46064i | 0.263344 | + | 0.220972i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.55509 | + | 1.47518i | 0.227626 | + | 0.131420i | ||||
\(127\) | 8.39560 | + | 3.91493i | 0.744989 | + | 0.347394i | 0.757768 | − | 0.652524i | \(-0.226290\pi\) |
−0.0127789 | + | 0.999918i | \(0.504068\pi\) | |||||||
\(128\) | −0.819152 | − | 0.573576i | −0.0724035 | − | 0.0506975i | ||||
\(129\) | −2.80169 | + | 15.8892i | −0.246675 | + | 1.39896i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.03074 | − | 6.73859i | 0.701649 | − | 0.588754i | −0.220593 | − | 0.975366i | \(-0.570799\pi\) |
0.922242 | + | 0.386612i | \(0.126355\pi\) | |||||||
\(132\) | −0.520771 | − | 0.520771i | −0.0453273 | − | 0.0453273i | ||||
\(133\) | −4.54454 | − | 0.464086i | −0.394061 | − | 0.0402413i | ||||
\(134\) | − | 5.68004i | − | 0.490681i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.673648 | + | 1.85083i | −0.0577649 | + | 0.158708i | ||||
\(137\) | −12.8224 | − | 18.3122i | −1.09549 | − | 1.56452i | −0.790808 | − | 0.612065i | \(-0.790339\pi\) |
−0.304681 | − | 0.952455i | \(-0.598550\pi\) | |||||||
\(138\) | 1.44957 | − | 2.07020i | 0.123396 | − | 0.176227i | ||||
\(139\) | 4.46556 | + | 12.2690i | 0.378764 | + | 1.04065i | 0.971869 | + | 0.235521i | \(0.0756797\pi\) |
−0.593105 | + | 0.805125i | \(0.702098\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.19640 | + | 0.690744i | −0.100755 | + | 0.0581711i | ||||
\(142\) | 1.36287 | − | 0.119236i | 0.114370 | − | 0.0100061i | ||||
\(143\) | −0.981702 | + | 0.0858878i | −0.0820941 | + | 0.00718230i | ||||
\(144\) | 2.43804 | − | 1.40760i | 0.203170 | − | 0.117300i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.07398 | − | 13.9406i | −0.419925 | − | 1.15374i | ||||
\(147\) | −8.16299 | + | 11.6580i | −0.673272 | + | 0.961532i | ||||
\(148\) | 0.666785 | + | 0.952267i | 0.0548094 | + | 0.0782759i | ||||
\(149\) | −5.45475 | + | 14.9868i | −0.446870 | + | 1.22777i | 0.488021 | + | 0.872832i | \(0.337719\pi\) |
−0.934891 | + | 0.354934i | \(0.884503\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 19.9589i | − | 1.62423i | −0.583495 | − | 0.812117i | \(-0.698315\pi\) | ||
0.583495 | − | 0.812117i | \(-0.301685\pi\) | |||||||
\(152\) | −2.55167 | + | 3.53397i | −0.206968 | + | 0.286643i | ||||
\(153\) | −3.92082 | − | 3.92082i | −0.316979 | − | 0.316979i | ||||
\(154\) | −0.245188 | + | 0.205737i | −0.0197578 | + | 0.0165788i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.35117 | − | 7.66285i | 0.108180 | − | 0.613519i | ||||
\(157\) | −0.409844 | − | 0.286976i | −0.0327091 | − | 0.0229032i | 0.557108 | − | 0.830440i | \(-0.311911\pi\) |
−0.589817 | + | 0.807537i | \(0.700800\pi\) | |||||||
\(158\) | 2.23853 | + | 1.04384i | 0.178088 | + | 0.0830437i | ||||
\(159\) | −23.0295 | − | 13.2961i | −1.82636 | − | 1.05445i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.841367 | − | 0.705990i | −0.0663090 | − | 0.0556398i | ||||
\(162\) | −0.829743 | − | 9.48400i | −0.0651907 | − | 0.745134i | ||||
\(163\) | 2.19389 | − | 8.18771i | 0.171839 | − | 0.641311i | −0.825230 | − | 0.564797i | \(-0.808954\pi\) |
0.997069 | − | 0.0765138i | \(-0.0243789\pi\) | |||||||
\(164\) | −3.63846 | + | 6.30200i | −0.284116 | + | 0.492104i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.33409 | + | 1.29320i | −0.569236 | + | 0.100372i | ||||
\(167\) | −6.51890 | + | 4.56458i | −0.504448 | + | 0.353218i | −0.797934 | − | 0.602745i | \(-0.794074\pi\) |
0.293486 | + | 0.955963i | \(0.405185\pi\) | |||||||
\(168\) | −1.06806 | − | 2.29047i | −0.0824028 | − | 0.176713i | ||||
\(169\) | 1.66387 | + | 1.98293i | 0.127990 | + | 0.152533i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.98087 | − | 10.7150i | −0.457368 | − | 0.819398i | ||||
\(172\) | 4.73100 | − | 4.73100i | 0.360735 | − | 0.360735i | ||||
\(173\) | −0.916898 | + | 10.4802i | −0.0697105 | + | 0.796795i | 0.878207 | + | 0.478280i | \(0.158740\pi\) |
−0.947918 | + | 0.318515i | \(0.896816\pi\) | |||||||
\(174\) | −6.20026 | − | 2.25671i | −0.470041 | − | 0.171081i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.0530334 | + | 0.300767i | 0.00399754 | + | 0.0226712i | ||||
\(177\) | 7.78709 | − | 16.6995i | 0.585314 | − | 1.25521i | ||||
\(178\) | −7.90956 | + | 2.11936i | −0.592847 | + | 0.158853i | ||||
\(179\) | 10.5178 | + | 18.2173i | 0.786137 | + | 1.36163i | 0.928318 | + | 0.371788i | \(0.121255\pi\) |
−0.142181 | + | 0.989841i | \(0.545412\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.21213 | − | 3.82807i | 0.238756 | − | 0.284538i | −0.633339 | − | 0.773874i | \(-0.718316\pi\) |
0.872095 | + | 0.489336i | \(0.162761\pi\) | |||||||
\(182\) | −3.26637 | − | 0.875222i | −0.242120 | − | 0.0648757i | ||||
\(183\) | −8.44161 | − | 31.5045i | −0.624022 | − | 2.32888i | ||||
\(184\) | −0.984808 | + | 0.358441i | −0.0726010 | + | 0.0264246i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.09105 | + | 1.60300i | 0.666588 | + | 0.117537i | ||||
\(187\) | 0.545176 | − | 0.254220i | 0.0398672 | − | 0.0185904i | ||||
\(188\) | 0.570701 | + | 0.0499299i | 0.0416227 | + | 0.00364151i | ||||
\(189\) | −0.467017 | −0.0339705 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.7638 | −0.851200 | −0.425600 | − | 0.904911i | \(-0.639937\pi\) | ||||
−0.425600 | + | 0.904911i | \(0.639937\pi\) | |||||||
\(192\) | −2.40230 | − | 0.210174i | −0.173371 | − | 0.0151680i | ||||
\(193\) | −9.40261 | + | 4.38451i | −0.676815 | + | 0.315604i | −0.730459 | − | 0.682956i | \(-0.760694\pi\) |
0.0536444 | + | 0.998560i | \(0.482916\pi\) | |||||||
\(194\) | −12.6694 | − | 2.23396i | −0.909609 | − | 0.160389i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.54576 | − | 2.01849i | 0.396126 | − | 0.144178i | ||||
\(197\) | 1.29079 | + | 4.81731i | 0.0919652 | + | 0.343219i | 0.996542 | − | 0.0830922i | \(-0.0264796\pi\) |
−0.904577 | + | 0.426311i | \(0.859813\pi\) | |||||||
\(198\) | −0.830488 | − | 0.222529i | −0.0590202 | − | 0.0158144i | ||||
\(199\) | 17.2195 | − | 20.5214i | 1.22066 | − | 1.45472i | 0.369979 | − | 0.929040i | \(-0.379365\pi\) |
0.850680 | − | 0.525684i | \(-0.176191\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.84864 | − | 11.8622i | −0.483066 | − | 0.836695i | ||||
\(202\) | 7.43988 | − | 1.99351i | 0.523468 | − | 0.140263i | ||||
\(203\) | −1.21187 | + | 2.59886i | −0.0850565 | + | 0.182404i | ||||
\(204\) | 0.824773 | + | 4.67752i | 0.0577456 | + | 0.327492i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.0103 | − | 4.37138i | −0.836795 | − | 0.304568i | ||||
\(207\) | 0.257141 | − | 2.93914i | 0.0178726 | − | 0.204284i | ||||
\(208\) | −2.28161 | + | 2.28161i | −0.158201 | + | 0.158201i | ||||
\(209\) | 1.31423 | − | 0.212134i | 0.0909071 | − | 0.0146736i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.368241 | − | 0.438852i | −0.0253507 | − | 0.0302118i | 0.753220 | − | 0.657769i | \(-0.228500\pi\) |
−0.778571 | + | 0.627557i | \(0.784055\pi\) | |||||||
\(212\) | 4.66036 | + | 9.99417i | 0.320075 | + | 0.686402i | ||||
\(213\) | 2.70246 | − | 1.89228i | 0.185169 | − | 0.129657i | ||||
\(214\) | 9.02330 | − | 1.59105i | 0.616820 | − | 0.108762i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.222811 | + | 0.385920i | −0.0151604 | + | 0.0262586i | ||||
\(217\) | 1.03835 | − | 3.87516i | 0.0704875 | − | 0.263063i | ||||
\(218\) | −1.18946 | − | 13.5956i | −0.0805602 | − | 0.920808i | ||||
\(219\) | −27.4052 | − | 22.9957i | −1.85187 | − | 1.55391i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.50387 | + | 3.17766i | 0.370230 | + | 0.213753i | ||||
\(222\) | 2.54070 | + | 1.18475i | 0.170520 | + | 0.0795149i | ||||
\(223\) | −2.22968 | − | 1.56124i | −0.149310 | − | 0.104548i | 0.496534 | − | 0.868017i | \(-0.334606\pi\) |
−0.645845 | + | 0.763469i | \(0.723495\pi\) | |||||||
\(224\) | −0.181985 | + | 1.03209i | −0.0121594 | + | 0.0689593i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.343426 | + | 0.288169i | −0.0228444 | + | 0.0191687i | ||||
\(227\) | −13.4598 | − | 13.4598i | −0.893361 | − | 0.893361i | 0.101477 | − | 0.994838i | \(-0.467643\pi\) |
−0.994838 | + | 0.101477i | \(0.967643\pi\) | |||||||
\(228\) | −1.06786 | + | 10.4570i | −0.0707209 | + | 0.692531i | ||||
\(229\) | − | 9.44562i | − | 0.624184i | −0.950052 | − | 0.312092i | \(-0.898970\pi\) | ||
0.950052 | − | 0.312092i | \(-0.101030\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.263985 | + | 0.725293i | −0.0173689 | + | 0.0477208i | ||||
\(232\) | 1.56940 | + | 2.24133i | 0.103036 | + | 0.147151i | ||||
\(233\) | 13.4185 | − | 19.1635i | 0.879072 | − | 1.25545i | −0.0867473 | − | 0.996230i | \(-0.527647\pi\) |
0.965820 | − | 0.259215i | \(-0.0834638\pi\) | |||||||
\(234\) | −3.10684 | − | 8.53596i | −0.203100 | − | 0.558013i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.61721 | + | 3.82045i | −0.430744 | + | 0.248690i | ||||
\(237\) | 5.93354 | − | 0.519117i | 0.385425 | − | 0.0337203i | ||||
\(238\) | 2.05632 | − | 0.179905i | 0.133292 | − | 0.0116615i | ||||
\(239\) | 16.6235 | − | 9.59761i | 1.07529 | − | 0.620818i | 0.145667 | − | 0.989334i | \(-0.453467\pi\) |
0.929621 | + | 0.368516i | \(0.120134\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.36618 | + | 6.50103i | 0.152419 | + | 0.418768i | 0.992278 | − | 0.124037i | \(-0.0395843\pi\) |
−0.839858 | + | 0.542806i | \(0.817362\pi\) | |||||||
\(242\) | −6.25584 | + | 8.93427i | −0.402141 | + | 0.574316i | ||||
\(243\) | −12.4012 | − | 17.7108i | −0.795541 | − | 1.13615i | ||||
\(244\) | −4.62592 | + | 12.7096i | −0.296144 | + | 0.813649i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 17.5481i | 1.11883i | ||||||||
\(247\) | 9.80005 | + | 10.0885i | 0.623562 | + | 0.641913i | ||||
\(248\) | −2.70686 | − | 2.70686i | −0.171886 | − | 0.171886i | ||||
\(249\) | −13.7572 | + | 11.5437i | −0.871830 | + | 0.731552i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.448311 | − | 2.54250i | 0.0282971 | − | 0.160481i | −0.967385 | − | 0.253311i | \(-0.918480\pi\) |
0.995682 | + | 0.0928303i | \(0.0295914\pi\) | |||||||
\(252\) | −2.41680 | − | 1.69226i | −0.152244 | − | 0.106602i | ||||
\(253\) | 0.290082 | + | 0.135267i | 0.0182373 | + | 0.00850419i | ||||
\(254\) | −8.02244 | − | 4.63176i | −0.503373 | − | 0.290622i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.766044 | + | 0.642788i | 0.0478778 | + | 0.0401742i | ||||
\(257\) | −0.554471 | − | 6.33764i | −0.0345870 | − | 0.395331i | −0.993681 | − | 0.112243i | \(-0.964197\pi\) |
0.959094 | − | 0.283088i | \(-0.0913589\pi\) | |||||||
\(258\) | 4.17586 | − | 15.5845i | 0.259978 | − | 0.970251i | ||||
\(259\) | 0.609158 | − | 1.05509i | 0.0378512 | − | 0.0655603i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.58584 | + | 1.33759i | −0.469552 | + | 0.0827946i | ||||
\(262\) | −8.58749 | + | 6.01303i | −0.530537 | + | 0.371486i | ||||
\(263\) | 8.72779 | + | 18.7168i | 0.538179 | + | 1.15413i | 0.967939 | + | 0.251185i | \(0.0808202\pi\) |
−0.429761 | + | 0.902943i | \(0.641402\pi\) | |||||||
\(264\) | 0.473401 | + | 0.564178i | 0.0291358 | + | 0.0347227i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.48680 | + | 0.858402i | 0.275103 | + | 0.0526320i | ||||
\(267\) | −13.9629 | + | 13.9629i | −0.854517 | + | 0.854517i | ||||
\(268\) | −0.495049 | + | 5.65843i | −0.0302399 | + | 0.345644i | ||||
\(269\) | −19.9303 | − | 7.25402i | −1.21517 | − | 0.442286i | −0.346676 | − | 0.937985i | \(-0.612690\pi\) |
−0.868494 | + | 0.495700i | \(0.834912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.678701 | + | 3.84910i | 0.0412281 | + | 0.233816i | 0.998458 | − | 0.0555121i | \(-0.0176791\pi\) |
−0.957230 | + | 0.289328i | \(0.906568\pi\) | |||||||
\(272\) | 0.832395 | − | 1.78508i | 0.0504714 | − | 0.108236i | ||||
\(273\) | −7.87677 | + | 2.11057i | −0.476724 | + | 0.127738i | ||||
\(274\) | 11.1776 | + | 19.3601i | 0.675261 | + | 1.16959i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.62449 | + | 1.93599i | −0.0977825 | + | 0.116533i | ||||
\(277\) | 11.2376 | + | 3.01110i | 0.675200 | + | 0.180919i | 0.580096 | − | 0.814548i | \(-0.303015\pi\) |
0.0951037 | + | 0.995467i | \(0.469682\pi\) | |||||||
\(278\) | −3.37925 | − | 12.6115i | −0.202674 | − | 0.756390i | ||||
\(279\) | 10.1269 | − | 3.68589i | 0.606281 | − | 0.220668i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.46064 | − | 0.962858i | −0.325754 | − | 0.0574393i | 0.00837959 | − | 0.999965i | \(-0.497333\pi\) |
−0.334134 | + | 0.942526i | \(0.608444\pi\) | |||||||
\(282\) | 1.25205 | − | 0.583842i | 0.0745587 | − | 0.0347673i | ||||
\(283\) | −16.0648 | − | 1.40549i | −0.954955 | − | 0.0835477i | −0.400985 | − | 0.916085i | \(-0.631332\pi\) |
−0.553970 | + | 0.832537i | \(0.686888\pi\) | |||||||
\(284\) | −1.36808 | −0.0811806 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.985452 | 0.0582710 | ||||||||
\(287\) | 7.59728 | + | 0.664676i | 0.448453 | + | 0.0392346i | ||||
\(288\) | −2.55144 | + | 1.18976i | −0.150345 | + | 0.0701072i | ||||
\(289\) | 12.9213 | + | 2.27837i | 0.760075 | + | 0.134022i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −29.1523 | + | 10.6106i | −1.70894 | + | 0.622002i | ||||
\(292\) | 3.83966 | + | 14.3298i | 0.224699 | + | 0.838589i | ||||
\(293\) | 30.7180 | + | 8.23086i | 1.79456 | + | 0.480852i | 0.993108 | − | 0.117203i | \(-0.0373927\pi\) |
0.801456 | + | 0.598054i | \(0.204059\pi\) | |||||||
\(294\) | 9.14798 | − | 10.9021i | 0.533521 | − | 0.635826i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.581252 | − | 1.00676i | −0.0337846 | − | 0.0585166i | ||||
\(297\) | 0.131459 | − | 0.0352243i | 0.00762802 | − | 0.00204392i | ||||
\(298\) | 6.74018 | − | 14.4544i | 0.390448 | − | 0.837318i | ||||
\(299\) | 0.587208 | + | 3.33022i | 0.0339591 | + | 0.192592i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.58899 | − | 2.39820i | −0.379783 | − | 0.138230i | ||||
\(302\) | −1.73953 | + | 19.8830i | −0.100099 | + | 1.14414i | ||||
\(303\) | 13.1338 | − | 13.1338i | 0.754516 | − | 0.754516i | ||||
\(304\) | 2.84997 | − | 3.29813i | 0.163457 | − | 0.189161i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.56418 | + | 4.24762i | 0.203750 | + | 0.242820i | ||||
\(307\) | 13.7125 | + | 29.4066i | 0.782614 | + | 1.67832i | 0.733656 | + | 0.679521i | \(0.237812\pi\) |
0.0489576 | + | 0.998801i | \(0.484410\pi\) | |||||||
\(308\) | 0.262186 | − | 0.183585i | 0.0149394 | − | 0.0104607i | ||||
\(309\) | −30.3530 | + | 5.35204i | −1.72672 | + | 0.304467i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.06165 | + | 10.4991i | −0.343725 | + | 0.595349i | −0.985121 | − | 0.171861i | \(-0.945022\pi\) |
0.641397 | + | 0.767210i | \(0.278355\pi\) | |||||||
\(312\) | −2.01389 | + | 7.51593i | −0.114014 | + | 0.425506i | ||||
\(313\) | 0.728931 | + | 8.33172i | 0.0412016 | + | 0.470936i | 0.988567 | + | 0.150782i | \(0.0481792\pi\) |
−0.947365 | + | 0.320154i | \(0.896265\pi\) | |||||||
\(314\) | 0.383273 | + | 0.321604i | 0.0216293 | + | 0.0181492i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.13903 | − | 1.23497i | −0.120330 | − | 0.0694726i | ||||
\(317\) | −0.366753 | − | 0.171020i | −0.0205989 | − | 0.00960542i | 0.412292 | − | 0.911052i | \(-0.364729\pi\) |
−0.432890 | + | 0.901447i | \(0.642506\pi\) | |||||||
\(318\) | 21.7830 | + | 15.2526i | 1.22153 | + | 0.855325i | ||||
\(319\) | 0.145108 | − | 0.822948i | 0.00812449 | − | 0.0460763i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.9259 | − | 14.2025i | 0.944709 | − | 0.792705i | ||||
\(322\) | 0.776634 | + | 0.776634i | 0.0432801 | + | 0.0432801i | ||||
\(323\) | −7.72755 | − | 3.74077i | −0.429972 | − | 0.208142i | ||||
\(324\) | 9.52023i | 0.528902i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.89915 | + | 7.96534i | −0.160569 | + | 0.441160i | ||||
\(327\) | −18.8767 | − | 26.9588i | −1.04389 | − | 1.49082i | ||||
\(328\) | 4.17387 | − | 5.96091i | 0.230464 | − | 0.329136i | ||||
\(329\) | −0.205344 | − | 0.564178i | −0.0113210 | − | 0.0311041i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.5861 | − | 11.3080i | 1.07655 | − | 0.621545i | 0.146584 | − | 0.989198i | \(-0.453172\pi\) |
0.929963 | + | 0.367654i | \(0.119839\pi\) | |||||||
\(332\) | 7.41889 | − | 0.649069i | 0.407165 | − | 0.0356223i | ||||
\(333\) | 3.26024 | − | 0.285234i | 0.178660 | − | 0.0156307i | ||||
\(334\) | 6.89193 | − | 3.97906i | 0.377109 | − | 0.217724i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.864370 | + | 2.37484i | 0.0471553 | + | 0.129558i | ||||
\(337\) | −6.37906 | + | 9.11024i | −0.347489 | + | 0.496266i | −0.954411 | − | 0.298495i | \(-0.903515\pi\) |
0.606922 | + | 0.794762i | \(0.292404\pi\) | |||||||
\(338\) | −1.48472 | − | 2.12040i | −0.0807580 | − | 0.115334i | ||||
\(339\) | −0.369754 | + | 1.01589i | −0.0200823 | + | 0.0551757i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.16912i | 0.0633115i | ||||||||
\(342\) | 5.02423 | + | 11.1955i | 0.271679 | + | 0.605384i | ||||
\(343\) | −9.56085 | − | 9.56085i | −0.516238 | − | 0.516238i | ||||
\(344\) | −5.12533 | + | 4.30066i | −0.276339 | + | 0.231876i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.82682 | − | 10.3604i | 0.0982104 | − | 0.556979i | ||||
\(347\) | −8.21756 | − | 5.75400i | −0.441142 | − | 0.308891i | 0.331821 | − | 0.943342i | \(-0.392337\pi\) |
−0.772963 | + | 0.634452i | \(0.781226\pi\) | |||||||
\(348\) | 5.97998 | + | 2.78851i | 0.320561 | + | 0.149480i | ||||
\(349\) | 12.5667 | + | 7.25537i | 0.672678 | + | 0.388371i | 0.797091 | − | 0.603860i | \(-0.206371\pi\) |
−0.124413 | + | 0.992231i | \(0.539705\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.10148 | + | 0.924252i | 0.0587927 | + | 0.0493329i | ||||
\(352\) | −0.0266180 | − | 0.304245i | −0.00141874 | − | 0.0162163i | ||||
\(353\) | −2.65443 | + | 9.90648i | −0.141281 | + | 0.527269i | 0.858611 | + | 0.512627i | \(0.171328\pi\) |
−0.999893 | + | 0.0146421i | \(0.995339\pi\) | |||||||
\(354\) | −9.21291 | + | 15.9572i | −0.489661 | + | 0.848117i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.06418 | − | 1.42193i | 0.427401 | − | 0.0753623i | ||||
\(357\) | 4.07750 | − | 2.85510i | 0.215804 | − | 0.151108i | ||||
\(358\) | −8.89002 | − | 19.0647i | −0.469852 | − | 1.00760i | ||||
\(359\) | −13.6779 | − | 16.3007i | −0.721891 | − | 0.860316i | 0.272922 | − | 0.962036i | \(-0.412010\pi\) |
−0.994813 | + | 0.101720i | \(0.967565\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.1946 | − | 12.6299i | −0.747084 | − | 0.664730i | ||||
\(362\) | −3.53355 | + | 3.53355i | −0.185719 | + | 0.185719i | ||||
\(363\) | −2.29231 | + | 26.2012i | −0.120315 | + | 1.37521i | ||||
\(364\) | 3.17766 | + | 1.15657i | 0.166555 | + | 0.0606210i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.66369 | + | 32.1204i | 0.296046 | + | 1.67896i | ||||
\(367\) | 10.3782 | − | 22.2562i | 0.541739 | − | 1.16176i | −0.424810 | − | 0.905283i | \(-0.639659\pi\) |
0.966549 | − | 0.256481i | \(-0.0825632\pi\) | |||||||
\(368\) | 1.01230 | − | 0.271245i | 0.0527698 | − | 0.0141396i | ||||
\(369\) | 10.2430 | + | 17.7414i | 0.533231 | + | 0.923583i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.42855 | − | 8.85300i | 0.385671 | − | 0.459625i | ||||
\(372\) | −8.91675 | − | 2.38924i | −0.462312 | − | 0.123876i | ||||
\(373\) | −3.18418 | − | 11.8835i | −0.164870 | − | 0.615305i | −0.998057 | − | 0.0623125i | \(-0.980152\pi\) |
0.833186 | − | 0.552993i | \(-0.186514\pi\) | |||||||
\(374\) | −0.565258 | + | 0.205737i | −0.0292288 | + | 0.0106384i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.564178 | − | 0.0994798i | −0.0290952 | − | 0.00513028i | ||||
\(377\) | 8.00154 | − | 3.73118i | 0.412100 | − | 0.192165i | ||||
\(378\) | 0.465240 | + | 0.0407032i | 0.0239294 | + | 0.00209355i | ||||
\(379\) | 23.8642 | 1.22582 | 0.612911 | − | 0.790152i | \(-0.289998\pi\) | ||||
0.612911 | + | 0.790152i | \(0.289998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.3387 | −1.14445 | ||||||||
\(382\) | 11.7191 | + | 1.02528i | 0.599599 | + | 0.0524581i | ||||
\(383\) | −1.69629 | + | 0.790991i | −0.0866762 | + | 0.0404178i | −0.465473 | − | 0.885062i | \(-0.654116\pi\) |
0.378797 | + | 0.925480i | \(0.376338\pi\) | |||||||
\(384\) | 2.37484 | + | 0.418748i | 0.121190 | + | 0.0213691i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.74897 | − | 3.54834i | 0.496210 | − | 0.180605i | ||||
\(387\) | −4.87500 | − | 18.1937i | −0.247810 | − | 0.924839i | ||||
\(388\) | 12.4265 | + | 3.32966i | 0.630859 | + | 0.169038i | ||||
\(389\) | 12.7689 | − | 15.2173i | 0.647407 | − | 0.771550i | −0.338113 | − | 0.941105i | \(-0.609789\pi\) |
0.985521 | + | 0.169555i | \(0.0542331\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.03209 | − | 1.78763i | −0.0521950 | − | 0.0904044i | ||||
\(392\) | −5.70058 | + | 1.52747i | −0.287923 | + | 0.0771487i | ||||
\(393\) | −10.6840 | + | 22.9119i | −0.538935 | + | 1.15575i | ||||
\(394\) | −0.866025 | − | 4.91147i | −0.0436297 | − | 0.247436i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.807934 | + | 0.294064i | 0.0406002 | + | 0.0147773i | ||||
\(397\) | −0.998258 | + | 11.4101i | −0.0501011 | + | 0.572658i | 0.929108 | + | 0.369807i | \(0.120576\pi\) |
−0.979210 | + | 0.202851i | \(0.934979\pi\) | |||||||
\(398\) | −18.9425 | + | 18.9425i | −0.949504 | + | 0.949504i | ||||
\(399\) | 10.4052 | − | 3.61721i | 0.520913 | − | 0.181087i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.65095 | − | 10.3098i | −0.432008 | − | 0.514847i | 0.505493 | − | 0.862831i | \(-0.331311\pi\) |
−0.937500 | + | 0.347984i | \(0.886866\pi\) | |||||||
\(402\) | 5.78872 | + | 12.4140i | 0.288715 | + | 0.619152i | ||||
\(403\) | −10.1181 | + | 7.08480i | −0.504020 | + | 0.352919i | ||||
\(404\) | −7.58532 | + | 1.33750i | −0.377384 | + | 0.0665429i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.43376 | − | 2.48335i | 0.0711565 | − | 0.123247i | ||||
\(407\) | −0.0918904 | + | 0.342940i | −0.00455484 | + | 0.0169989i | ||||
\(408\) | −0.413962 | − | 4.73160i | −0.0204942 | − | 0.234249i | ||||
\(409\) | −20.2354 | − | 16.9795i | −1.00058 | − | 0.839583i | −0.0135122 | − | 0.999909i | \(-0.504301\pi\) |
−0.987064 | + | 0.160325i | \(0.948746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 46.6864 | + | 26.9544i | 2.30287 | + | 1.32956i | ||||
\(412\) | 11.5836 | + | 5.40151i | 0.570682 | + | 0.266113i | ||||
\(413\) | 6.55956 | + | 4.59305i | 0.322775 | + | 0.226009i | ||||
\(414\) | −0.512326 | + | 2.90554i | −0.0251794 | + | 0.142800i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.47178 | − | 2.07407i | 0.121189 | − | 0.101690i | ||||
\(417\) | −22.2634 | − | 22.2634i | −1.09025 | − | 1.09025i | ||||
\(418\) | −1.32772 | + | 0.0967838i | −0.0649407 | + | 0.00473385i | ||||
\(419\) | 19.5466i | 0.954916i | 0.878655 | + | 0.477458i | \(0.158442\pi\) | ||||
−0.878655 | + | 0.477458i | \(0.841558\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.98246 | − | 19.1841i | 0.340304 | − | 0.934978i | −0.645002 | − | 0.764181i | \(-0.723143\pi\) |
0.985306 | − | 0.170797i | \(-0.0546343\pi\) | |||||||
\(422\) | 0.328591 | + | 0.469277i | 0.0159956 | + | 0.0228440i | ||||
\(423\) | 0.925052 | − | 1.32111i | 0.0449776 | − | 0.0642346i | ||||
\(424\) | −3.77157 | − | 10.3623i | −0.183164 | − | 0.503238i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.85710 | + | 1.64955i | −0.138427 | + | 0.0799207i | ||||
\(427\) | 14.1207 | − | 1.23540i | 0.683349 | − | 0.0597852i | ||||
\(428\) | −9.12764 | + | 0.798565i | −0.441201 | + | 0.0386001i | ||||
\(429\) | 2.05802 | − | 1.18820i | 0.0993619 | − | 0.0573666i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.30706 | + | 11.8335i | 0.207464 | + | 0.570002i | 0.999163 | − | 0.0409095i | \(-0.0130255\pi\) |
−0.791699 | + | 0.610911i | \(0.790803\pi\) | |||||||
\(432\) | 0.255599 | − | 0.365033i | 0.0122975 | − | 0.0175626i | ||||
\(433\) | 14.6480 | + | 20.9196i | 0.703940 | + | 1.00533i | 0.998760 | + | 0.0497776i | \(0.0158512\pi\) |
−0.294821 | + | 0.955553i | \(0.595260\pi\) | |||||||
\(434\) | −1.37214 | + | 3.76991i | −0.0658647 | + | 0.180962i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.6475i | 0.653596i | ||||||||
\(437\) | −1.11823 | − | 4.42919i | −0.0534920 | − | 0.211877i | ||||
\(438\) | 25.2967 | + | 25.2967i | 1.20872 | + | 1.20872i | ||||
\(439\) | 20.7222 | − | 17.3880i | 0.989017 | − | 0.829884i | 0.00359221 | − | 0.999994i | \(-0.498857\pi\) |
0.985425 | + | 0.170109i | \(0.0544121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.88507 | − | 16.3620i | 0.137384 | − | 0.779144i | ||||
\(442\) | −5.20598 | − | 3.64526i | −0.247623 | − | 0.173387i | ||||
\(443\) | −12.0283 | − | 5.60888i | −0.571481 | − | 0.266486i | 0.115324 | − | 0.993328i | \(-0.463209\pi\) |
−0.686805 | + | 0.726842i | \(0.740987\pi\) | |||||||
\(444\) | −2.42777 | − | 1.40167i | −0.115217 | − | 0.0665205i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.08512 | + | 1.74963i | 0.0987334 | + | 0.0828472i | ||||
\(447\) | −3.35198 | − | 38.3133i | −0.158543 | − | 1.81216i | ||||
\(448\) | 0.271245 | − | 1.01230i | 0.0128151 | − | 0.0478267i | ||||
\(449\) | 3.78417 | − | 6.55438i | 0.178586 | − | 0.309320i | −0.762810 | − | 0.646622i | \(-0.776181\pi\) |
0.941396 | + | 0.337302i | \(0.109514\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.18866 | + | 0.385920i | −0.103060 | + | 0.0181723i | ||||
\(452\) | 0.367235 | − | 0.257140i | 0.0172733 | − | 0.0120949i | ||||
\(453\) | 20.3408 | + | 43.6210i | 0.955694 | + | 2.04949i | ||||
\(454\) | 12.2355 | + | 14.5817i | 0.574241 | + | 0.684354i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.97519 | − | 10.3241i | 0.0924965 | − | 0.483472i | ||||
\(457\) | 2.69607 | − | 2.69607i | 0.126117 | − | 0.126117i | −0.641231 | − | 0.767348i | \(-0.721576\pi\) |
0.767348 | + | 0.641231i | \(0.221576\pi\) | |||||||
\(458\) | −0.823240 | + | 9.40968i | −0.0384675 | + | 0.439685i | ||||
\(459\) | −0.824773 | − | 0.300193i | −0.0384971 | − | 0.0140118i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.73870 | + | 38.2171i | 0.313853 | + | 1.77995i | 0.578582 | + | 0.815624i | \(0.303606\pi\) |
−0.264729 | + | 0.964323i | \(0.585283\pi\) | |||||||
\(462\) | 0.326194 | − | 0.699525i | 0.0151759 | − | 0.0325449i | ||||
\(463\) | −29.2831 | + | 7.84638i | −1.36090 | + | 0.364652i | −0.864147 | − | 0.503240i | \(-0.832141\pi\) |
−0.496753 | + | 0.867892i | \(0.665475\pi\) | |||||||
\(464\) | −1.36808 | − | 2.36959i | −0.0635115 | − | 0.110005i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.0376 | + | 17.9211i | −0.696604 | + | 0.830180i | ||||
\(467\) | −34.0060 | − | 9.11187i | −1.57361 | − | 0.421647i | −0.636668 | − | 0.771138i | \(-0.719688\pi\) |
−0.936940 | + | 0.349491i | \(0.886355\pi\) | |||||||
\(468\) | 2.35105 | + | 8.77426i | 0.108678 | + | 0.405590i | ||||
\(469\) | 5.59375 | − | 2.03596i | 0.258295 | − | 0.0940119i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.18820 | + | 0.209511i | 0.0547492 | + | 0.00965376i | ||||
\(472\) | 6.92500 | − | 3.22918i | 0.318749 | − | 0.148635i | ||||
\(473\) | 2.03559 | + | 0.178091i | 0.0935967 | + | 0.00818865i | ||||
\(474\) | −5.95620 | −0.273577 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.06418 | −0.0946114 | ||||||||
\(477\) | 30.9261 | + | 2.70568i | 1.41601 | + | 0.123885i | ||||
\(478\) | −17.3968 | + | 8.11225i | −0.795710 | + | 0.371046i | ||||
\(479\) | 34.1491 | + | 6.02141i | 1.56031 | + | 0.275125i | 0.886129 | − | 0.463438i | \(-0.153384\pi\) |
0.674184 | + | 0.738564i | \(0.264496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.52481 | + | 1.28293i | −0.160718 | + | 0.0584965i | ||||
\(482\) | −1.79058 | − | 6.68252i | −0.0815585 | − | 0.304380i | ||||
\(483\) | 2.55834 | + | 0.685504i | 0.116408 | + | 0.0311915i | ||||
\(484\) | 7.01071 | − | 8.35504i | 0.318669 | − | 0.379774i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10.8105 | + | 18.7243i | 0.490372 | + | 0.849350i | ||||
\(487\) | −16.4190 | + | 4.39947i | −0.744018 | + | 0.199359i | −0.610863 | − | 0.791736i | \(-0.709177\pi\) |
−0.133155 | + | 0.991095i | \(0.542511\pi\) | |||||||
\(488\) | 5.71603 | − | 12.2581i | 0.258753 | − | 0.554897i | ||||
\(489\) | 3.54954 | + | 20.1304i | 0.160516 | + | 0.910329i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.0471 | + | 5.84067i | 0.724196 | + | 0.263586i | 0.677706 | − | 0.735333i | \(-0.262974\pi\) |
0.0464898 | + | 0.998919i | \(0.485197\pi\) | |||||||
\(492\) | 1.52942 | − | 17.4813i | 0.0689516 | − | 0.788120i | ||||
\(493\) | −3.81073 | + | 3.81073i | −0.171627 | + | 0.171627i | ||||
\(494\) | −8.88349 | − | 10.9042i | −0.399687 | − | 0.490603i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.46064 | + | 2.93247i | 0.110486 | + | 0.131672i | ||||
\(497\) | 0.605934 | + | 1.29943i | 0.0271799 | + | 0.0582874i | ||||
\(498\) | 14.7110 | − | 10.3007i | 0.659215 | − | 0.461588i | ||||
\(499\) | −8.96275 | + | 1.58037i | −0.401228 | + | 0.0707473i | −0.370621 | − | 0.928784i | \(-0.620855\pi\) |
−0.0306068 | + | 0.999532i | \(0.509744\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.59539 | − | 16.6197i | 0.428690 | − | 0.742514i | ||||
\(502\) | −0.668198 | + | 2.49375i | −0.0298231 | + | 0.111301i | ||||
\(503\) | 3.66588 | + | 41.9012i | 0.163453 | + | 1.86828i | 0.427828 | + | 0.903860i | \(0.359279\pi\) |
−0.264375 | + | 0.964420i | \(0.585166\pi\) | |||||||
\(504\) | 2.26011 | + | 1.89646i | 0.100673 | + | 0.0844750i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.277189 | − | 0.160035i | −0.0123225 | − | 0.00711442i | ||||
\(507\) | −5.65732 | − | 2.63805i | −0.251250 | − | 0.117160i | ||||
\(508\) | 7.58823 | + | 5.31334i | 0.336673 | + | 0.235741i | ||||
\(509\) | −3.21951 | + | 18.2588i | −0.142702 | + | 0.809306i | 0.826481 | + | 0.562965i | \(0.190339\pi\) |
−0.969183 | + | 0.246341i | \(0.920772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9101 | − | 9.99379i | 0.526873 | − | 0.442099i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −1.57482 | − | 1.13708i | −0.0695299 | − | 0.0502034i | ||||
\(514\) | 6.36184i | 0.280609i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.51826 | + | 15.1613i | −0.242928 | + | 0.667438i | ||||
\(517\) | 0.100354 | + | 0.143321i | 0.00441357 | + | 0.00630323i | ||||
\(518\) | −0.698797 | + | 0.997986i | −0.0307034 | + | 0.0438490i | ||||
\(519\) | −8.67680 | − | 23.8393i | −0.380869 | − | 1.04643i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.7995 | − | 21.2462i | 1.61222 | − | 0.930814i | 0.623362 | − | 0.781934i | \(-0.285766\pi\) |
0.988855 | − | 0.148880i | \(-0.0475669\pi\) | |||||||
\(522\) | 7.67355 | − | 0.671349i | 0.335862 | − | 0.0293841i | ||||
\(523\) | −23.4603 | + | 2.05251i | −1.02585 | + | 0.0897501i | −0.587639 | − | 0.809123i | \(-0.699943\pi\) |
−0.438209 | + | 0.898873i | \(0.644387\pi\) | |||||||
\(524\) | 9.07888 | − | 5.24170i | 0.396613 | − | 0.228985i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.06330 | − | 19.4063i | −0.307975 | − | 0.846153i | ||||
\(527\) | 4.32467 | − | 6.17627i | 0.188386 | − | 0.269042i | ||||
\(528\) | −0.422429 | − | 0.603291i | −0.0183838 | − | 0.0262549i | ||||
\(529\) | −7.49081 | + | 20.5808i | −0.325688 | + | 0.894819i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.5107i | 0.933485i | ||||||||
\(532\) | −4.39491 | − | 1.24619i | −0.190543 | − | 0.0540290i | ||||
\(533\) | −16.6031 | − | 16.6031i | −0.719160 | − | 0.719160i | ||||
\(534\) | 15.1267 | − | 12.6928i | 0.654598 | − | 0.549273i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.986329 | − | 5.59375i | 0.0426029 | − | 0.241613i | ||||
\(537\) | −41.5529 | − | 29.0957i | −1.79314 | − | 1.25557i | ||||
\(538\) | 19.2222 | + | 8.96346i | 0.828728 | + | 0.386442i | ||||
\(539\) | 1.56094 | + | 0.901207i | 0.0672343 | + | 0.0388177i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.44949 | + | 7.08997i | 0.363272 | + | 0.304821i | 0.806093 | − | 0.591788i | \(-0.201578\pi\) |
−0.442821 | + | 0.896610i | \(0.646022\pi\) | |||||||
\(542\) | −0.340647 | − | 3.89361i | −0.0146320 | − | 0.167245i | ||||
\(543\) | −3.11893 | + | 11.6400i | −0.133846 | + | 0.499520i | ||||
\(544\) | −0.984808 | + | 1.70574i | −0.0422233 | + | 0.0731329i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.03074 | − | 1.41604i | 0.343684 | − | 0.0606008i | ||||
\(547\) | −36.2732 | + | 25.3987i | −1.55093 | + | 1.08597i | −0.590651 | + | 0.806927i | \(0.701129\pi\) |
−0.960278 | + | 0.279045i | \(0.909982\pi\) | |||||||
\(548\) | −9.44768 | − | 20.2606i | −0.403585 | − | 0.865490i | ||||
\(549\) | 24.4751 | + | 29.1683i | 1.04457 | + | 1.24487i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.4142 | + | 5.81293i | −0.443658 | + | 0.247639i | ||||
\(552\) | 1.78704 | − | 1.78704i | 0.0760613 | − | 0.0760613i | ||||
\(553\) | −0.225605 | + | 2.57868i | −0.00959370 | + | 0.109656i | ||||
\(554\) | −10.9324 | − | 3.97906i | −0.464472 | − | 0.169054i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.26723 | + | 12.8581i | 0.0961518 | + | 0.545304i | ||||
\(557\) | 16.6892 | − | 35.7902i | 0.707145 | − | 1.51648i | −0.142883 | − | 0.989740i | \(-0.545637\pi\) |
0.850028 | − | 0.526738i | \(-0.176585\pi\) | |||||||
\(558\) | −10.4096 | + | 2.78925i | −0.440674 | + | 0.118078i | ||||
\(559\) | 10.7943 | + | 18.6962i | 0.456549 | + | 0.790767i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.932419 | + | 1.11121i | −0.0393667 | + | 0.0469155i | ||||
\(562\) | 5.35594 | + | 1.43512i | 0.225927 | + | 0.0605369i | ||||
\(563\) | −2.76551 | − | 10.3210i | −0.116552 | − | 0.434979i | 0.882846 | − | 0.469662i | \(-0.155624\pi\) |
−0.999398 | + | 0.0346836i | \(0.988958\pi\) | |||||||
\(564\) | −1.29817 | + | 0.472497i | −0.0546630 | + | 0.0198957i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.8812 | + | 2.80028i | 0.667536 | + | 0.117705i | ||||
\(567\) | 9.04251 | − | 4.21659i | 0.379750 | − | 0.177080i | ||||
\(568\) | 1.36287 | + | 0.119236i | 0.0571849 | + | 0.00500303i | ||||
\(569\) | −30.8012 | −1.29125 | −0.645626 | − | 0.763654i | \(-0.723403\pi\) | ||||
−0.645626 | + | 0.763654i | \(0.723403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.0310 | 0.796421 | 0.398211 | − | 0.917294i | \(-0.369631\pi\) | ||||
0.398211 | + | 0.917294i | \(0.369631\pi\) | |||||||
\(572\) | −0.981702 | − | 0.0858878i | −0.0410470 | − | 0.00359115i | ||||
\(573\) | 25.7103 | − | 11.9889i | 1.07406 | − | 0.500843i | ||||
\(574\) | −7.51044 | − | 1.32429i | −0.313480 | − | 0.0552749i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.64543 | − | 0.962858i | 0.110226 | − | 0.0401191i | ||||
\(577\) | −1.96625 | − | 7.33814i | −0.0818560 | − | 0.305491i | 0.912844 | − | 0.408308i | \(-0.133881\pi\) |
−0.994700 | + | 0.102817i | \(0.967214\pi\) | |||||||
\(578\) | −12.6735 | − | 3.39586i | −0.527150 | − | 0.141249i | ||||
\(579\) | 16.0814 | − | 19.1650i | 0.668319 | − | 0.796471i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.90239 | − | 6.75914i | −0.161898 | − | 0.280416i | ||||
\(582\) | 29.9661 | − | 8.02940i | 1.24214 | − | 0.332829i | ||||
\(583\) | −1.42331 | + | 3.05229i | −0.0589473 | + | 0.126413i | ||||
\(584\) | −2.57613 | − | 14.6099i | −0.106601 | − | 0.604564i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.8837 | − | 10.8768i | −1.23449 | − | 0.449316i | ||||
\(587\) | −2.10433 | + | 24.0526i | −0.0868549 | + | 0.992757i | 0.820293 | + | 0.571944i | \(0.193811\pi\) |
−0.907148 | + | 0.420813i | \(0.861745\pi\) | |||||||
\(588\) | −10.0634 | + | 10.0634i | −0.415006 | + | 0.415006i | ||||
\(589\) | 12.9365 | − | 10.5392i | 0.533040 | − | 0.434260i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.73055 | − | 9.21291i | −0.317992 | − | 0.378969i | ||||
\(592\) | 0.491295 | + | 1.05359i | 0.0201921 | + | 0.0433021i | ||||
\(593\) | −8.33458 | + | 5.83594i | −0.342260 | + | 0.239653i | −0.732050 | − | 0.681251i | \(-0.761436\pi\) |
0.389790 | + | 0.920904i | \(0.372548\pi\) | |||||||
\(594\) | −0.134029 | + | 0.0236329i | −0.00549927 | + | 0.000969669i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.97431 | + | 13.8119i | −0.326640 | + | 0.565758i | ||||
\(597\) | −16.7198 | + | 62.3993i | −0.684297 | + | 2.55383i | ||||
\(598\) | −0.294726 | − | 3.36873i | −0.0120522 | − | 0.137758i | ||||
\(599\) | −27.7768 | − | 23.3075i | −1.13493 | − | 0.952320i | −0.135669 | − | 0.990754i | \(-0.543318\pi\) |
−0.999261 | + | 0.0384346i | \(0.987763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.39141 | − | 1.38068i | −0.0975475 | − | 0.0563191i | 0.450433 | − | 0.892810i | \(-0.351270\pi\) |
−0.547980 | + | 0.836491i | \(0.684603\pi\) | |||||||
\(602\) | 6.35490 | + | 2.96334i | 0.259007 | + | 0.120777i | ||||
\(603\) | 13.0987 | + | 9.17178i | 0.533418 | + | 0.373504i | ||||
\(604\) | 3.46583 | − | 19.6557i | 0.141023 | − | 0.799779i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.2285 | + | 11.9391i | −0.577993 | + | 0.484994i | ||||
\(607\) | 8.95776 | + | 8.95776i | 0.363584 | + | 0.363584i | 0.865131 | − | 0.501546i | \(-0.167235\pi\) |
−0.501546 | + | 0.865131i | \(0.667235\pi\) | |||||||
\(608\) | −3.12657 | + | 3.03719i | −0.126799 | + | 0.123174i | ||||
\(609\) | − | 6.91496i | − | 0.280208i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.632226 | + | 1.73703i | −0.0255771 | + | 0.0702726i | ||||
\(612\) | −3.18041 | − | 4.54210i | −0.128560 | − | 0.183603i | ||||
\(613\) | 19.0274 | − | 27.1740i | 0.768511 | − | 1.09755i | −0.223903 | − | 0.974611i | \(-0.571880\pi\) |
0.992415 | − | 0.122937i | \(-0.0392312\pi\) | |||||||
\(614\) | −11.0974 | − | 30.4898i | −0.447854 | − | 1.23047i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.277189 | + | 0.160035i | −0.0111683 | + | 0.00644799i | ||||
\(617\) | 12.3621 | − | 1.08154i | 0.497678 | − | 0.0435411i | 0.164446 | − | 0.986386i | \(-0.447416\pi\) |
0.333232 | + | 0.942845i | \(0.391861\pi\) | |||||||
\(618\) | 30.7039 | − | 2.68624i | 1.23509 | − | 0.108057i | ||||
\(619\) | −3.37305 | + | 1.94743i | −0.135574 | + | 0.0782740i | −0.566253 | − | 0.824231i | \(-0.691608\pi\) |
0.430679 | + | 0.902505i | \(0.358274\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.159729 | − | 0.438852i | −0.00640971 | − | 0.0176105i | ||||
\(622\) | 6.95364 | − | 9.93083i | 0.278816 | − | 0.398190i | ||||
\(623\) | −4.92227 | − | 7.02973i | −0.197207 | − | 0.281640i | ||||
\(624\) | 2.66128 | − | 7.31180i | 0.106536 | − | 0.292706i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 8.36354i | − | 0.334274i | ||||||
\(627\) | −2.65610 | + | 1.80300i | −0.106075 | + | 0.0720049i | ||||
\(628\) | −0.353785 | − | 0.353785i | −0.0141175 | − | 0.0141175i | ||||
\(629\) | 1.75400 | − | 1.47178i | 0.0699366 | − | 0.0586838i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.68820 | + | 9.57424i | −0.0672060 | + | 0.381144i | 0.932590 | + | 0.360938i | \(0.117543\pi\) |
−0.999796 | + | 0.0202063i | \(0.993568\pi\) | |||||||
\(632\) | 2.02326 | + | 1.41670i | 0.0804809 | + | 0.0563533i | ||||
\(633\) | 1.25205 | + | 0.583842i | 0.0497647 | + | 0.0232056i | ||||
\(634\) | 0.350452 | + | 0.202333i | 0.0139182 | + | 0.00803569i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −20.3708 | − | 17.0931i | −0.807753 | − | 0.677786i | ||||
\(637\) | 1.65969 | + | 18.9704i | 0.0657594 | + | 0.751633i | ||||
\(638\) | −0.216280 | + | 0.807170i | −0.00856263 | + | 0.0319562i | ||||
\(639\) | −1.92572 | + | 3.33544i | −0.0761801 | + | 0.131948i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.45589 | + | 1.66733i | −0.373485 | + | 0.0658555i | −0.357240 | − | 0.934013i | \(-0.616282\pi\) |
−0.0162449 | + | 0.999868i | \(0.505171\pi\) | |||||||
\(642\) | −18.0993 | + | 12.6733i | −0.714322 | + | 0.500173i | ||||
\(643\) | 6.26598 | + | 13.4374i | 0.247106 | + | 0.529921i | 0.990265 | − | 0.139194i | \(-0.0444512\pi\) |
−0.743159 | + | 0.669115i | \(0.766673\pi\) | |||||||
\(644\) | −0.705990 | − | 0.841367i | −0.0278199 | − | 0.0331545i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.37211 | + | 4.40003i | 0.290052 | + | 0.173117i | ||||
\(647\) | −29.2043 | + | 29.2043i | −1.14814 | + | 1.14814i | −0.161223 | + | 0.986918i | \(0.551544\pi\) |
−0.986918 | + | 0.161223i | \(0.948456\pi\) | |||||||
\(648\) | 0.829743 | − | 9.48400i | 0.0325954 | − | 0.372567i | ||||
\(649\) | −2.19285 | − | 0.798133i | −0.0860770 | − | 0.0313295i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.67996 | + | 9.52752i | 0.0658428 | + | 0.373413i | ||||
\(652\) | 3.58234 | − | 7.68236i | 0.140295 | − | 0.300864i | ||||
\(653\) | 21.0887 | − | 5.65070i | 0.825264 | − | 0.221129i | 0.178618 | − | 0.983919i | \(-0.442838\pi\) |
0.646647 | + | 0.762790i | \(0.276171\pi\) | |||||||
\(654\) | 16.4553 | + | 28.5014i | 0.643453 | + | 1.11449i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.67752 | + | 5.57445i | −0.182626 | + | 0.217646i | ||||
\(657\) | 40.3414 | + | 10.8094i | 1.57387 | + | 0.421717i | ||||
\(658\) | 0.155391 | + | 0.579928i | 0.00605778 | + | 0.0226079i | ||||
\(659\) | 3.10013 | − | 1.12836i | 0.120764 | − | 0.0439545i | −0.280931 | − | 0.959728i | \(-0.590643\pi\) |
0.401695 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.3410 | − | 5.17360i | −1.14123 | − | 0.201230i | −0.429087 | − | 0.903263i | \(-0.641165\pi\) |
−0.712144 | + | 0.702033i | \(0.752276\pi\) | |||||||
\(662\) | −20.4971 | + | 9.55795i | −0.796642 | + | 0.371480i | ||||
\(663\) | −15.2674 | − | 1.33572i | −0.592936 | − | 0.0518752i | ||||
\(664\) | −7.44723 | −0.289009 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.27269 | −0.126814 | ||||||||
\(667\) | −2.85661 | − | 0.249921i | −0.110609 | − | 0.00967699i | ||||
\(668\) | −7.21250 | + | 3.36324i | −0.279060 | + | 0.130128i | ||||
\(669\) | 6.46415 | + | 1.13980i | 0.249919 | + | 0.0440674i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.88161 | + | 1.41279i | −0.149848 | + | 0.0545401i | ||||
\(672\) | −0.654100 | − | 2.44114i | −0.0252325 | − | 0.0941689i | ||||
\(673\) | −39.6237 | − | 10.6171i | −1.52738 | − | 0.409261i | −0.605217 | − | 0.796060i | \(-0.706914\pi\) |
−0.922164 | + | 0.386800i | \(0.873580\pi\) | |||||||
\(674\) | 7.14879 | − | 8.51960i | 0.275361 | − | 0.328163i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.29426 | + | 2.24173i | 0.0497793 | + | 0.0862204i | ||||
\(677\) | 21.8743 | − | 5.86119i | 0.840696 | − | 0.225264i | 0.187321 | − | 0.982299i | \(-0.440019\pi\) |
0.653374 | + | 0.757035i | \(0.273353\pi\) | |||||||
\(678\) | 0.456888 | − | 0.979800i | 0.0175467 | − | 0.0376290i | ||||
\(679\) | −2.34121 | − | 13.2777i | −0.0898474 | − | 0.509550i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 43.1343 | + | 15.6996i | 1.65291 | + | 0.601611i | ||||
\(682\) | 0.101896 | − | 1.16467i | 0.00390178 | − | 0.0445976i | ||||
\(683\) | 24.0893 | − | 24.0893i | 0.921753 | − | 0.921753i | −0.0754003 | − | 0.997153i | \(-0.524023\pi\) |
0.997153 | + | 0.0754003i | \(0.0240234\pi\) | |||||||
\(684\) | −4.02936 | − | 11.5908i | −0.154066 | − | 0.443185i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.69119 | + | 10.3578i | 0.331831 | + | 0.395461i | ||||
\(687\) | 9.62635 | + | 20.6438i | 0.367268 | + | 0.787609i | ||||
\(688\) | 5.48065 | − | 3.83759i | 0.208948 | − | 0.146307i | ||||
\(689\) | −35.0412 | + | 6.17870i | −1.33496 | + | 0.235390i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.21941 | + | 15.9685i | −0.350723 | + | 0.607470i | −0.986376 | − | 0.164505i | \(-0.947397\pi\) |
0.635653 | + | 0.771975i | \(0.280731\pi\) | |||||||
\(692\) | −2.72284 | + | 10.1618i | −0.103507 | + | 0.386292i | ||||
\(693\) | −0.0785329 | − | 0.897635i | −0.00298322 | − | 0.0340983i | ||||
\(694\) | 7.68480 | + | 6.44831i | 0.291711 | + | 0.244775i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.71419 | − | 3.29909i | −0.216596 | − | 0.125052i | ||||
\(697\) | 12.9899 | + | 6.05728i | 0.492027 | + | 0.229436i | ||||
\(698\) | −11.8865 | − | 8.32302i | −0.449911 | − | 0.315031i | ||||
\(699\) | −9.79635 | + | 55.5578i | −0.370532 | + | 2.10139i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.47700 | + | 3.75665i | −0.169094 | + | 0.141887i | −0.723408 | − | 0.690421i | \(-0.757425\pi\) |
0.554314 | + | 0.832308i | \(0.312981\pi\) | |||||||
\(702\) | −1.01674 | − | 1.01674i | −0.0383742 | − | 0.0383742i | ||||
\(703\) | 4.62304 | − | 2.07469i | 0.174361 | − | 0.0782485i | ||||
\(704\) | 0.305407i | 0.0115105i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.50774 | − | 9.63744i | 0.132016 | − | 0.362710i | ||||
\(707\) | 4.62998 | + | 6.61230i | 0.174128 | + | 0.248681i | ||||
\(708\) | 10.5686 | − | 15.0936i | 0.397193 | − | 0.567250i | ||||
\(709\) | −10.1395 | − | 27.8580i | −0.380797 | − | 1.04623i | −0.971022 | − | 0.238991i | \(-0.923183\pi\) |
0.590225 | − | 0.807239i | \(-0.299039\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.02182 | + | 3.47670i | −0.225836 | + | 0.130386i | ||||
\(712\) | −8.15742 | + | 0.713682i | −0.305712 | + | 0.0267464i | ||||
\(713\) | 3.99659 | − | 0.349657i | 0.149674 | − | 0.0130947i | ||||
\(714\) | −4.31082 | + | 2.48886i | −0.161329 | + | 0.0931431i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.19459 | + | 19.7670i | 0.268875 | + | 0.738727i | ||||
\(717\) | −26.5502 | + | 37.9175i | −0.991534 | + | 1.41606i | ||||
\(718\) | 12.2051 | + | 17.4307i | 0.455492 | + | 0.650509i | ||||
\(719\) | 14.3373 | − | 39.3915i | 0.534692 | − | 1.46905i | −0.318736 | − | 0.947843i | \(-0.603258\pi\) |
0.853428 | − | 0.521210i | \(-0.174519\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 13.3947i | − | 0.498844i | ||||||
\(722\) | 13.0398 | + | 13.8189i | 0.485292 | + | 0.514288i | ||||
\(723\) | −11.7968 | − | 11.7968i | −0.438727 | − | 0.438727i | ||||
\(724\) | 3.82807 | − | 3.21213i | 0.142269 | − | 0.119378i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.56717 | − | 25.9017i | 0.169504 | − | 0.961303i | ||||
\(727\) | 27.6836 | + | 19.3843i | 1.02673 | + | 0.718922i | 0.960329 | − | 0.278871i | \(-0.0899601\pi\) |
0.0663988 | + | 0.997793i | \(0.478849\pi\) | |||||||
\(728\) | −3.06477 | − | 1.42912i | −0.113588 | − | 0.0529669i | ||||
\(729\) | 20.4188 | + | 11.7888i | 0.756252 | + | 0.436622i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.0949 | − | 8.47065i | −0.373374 | − | 0.313298i | ||||
\(732\) | −2.84266 | − | 32.4918i | −0.105068 | − | 1.20093i | ||||
\(733\) | −7.13547 | + | 26.6299i | −0.263554 | + | 0.983599i | 0.699575 | + | 0.714559i | \(0.253373\pi\) |
−0.963129 | + | 0.269039i | \(0.913294\pi\) | |||||||
\(734\) | −12.2785 | + | 21.2670i | −0.453208 | + | 0.784978i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.03209 | + | 0.181985i | −0.0380433 | + | 0.00670806i | ||||
\(737\) | −1.42101 | + | 0.994999i | −0.0523434 | + | 0.0366512i | ||||
\(738\) | −8.65778 | − | 18.5667i | −0.318697 | − | 0.683449i | ||||
\(739\) | −0.0819052 | − | 0.0976108i | −0.00301293 | − | 0.00359067i | 0.764536 | − | 0.644581i | \(-0.222968\pi\) |
−0.767549 | + | 0.640991i | \(0.778524\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −31.6999 | − | 12.0612i | −1.16452 | − | 0.443078i | ||||
\(742\) | −8.17187 | + | 8.17187i | −0.299999 | + | 0.299999i | ||||
\(743\) | 2.25026 | − | 25.7206i | 0.0825540 | − | 0.943597i | −0.836111 | − | 0.548560i | \(-0.815176\pi\) |
0.918665 | − | 0.395037i | \(-0.129268\pi\) | |||||||
\(744\) | 8.67458 | + | 3.15729i | 0.318026 | + | 0.115752i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.13634 | + | 12.1158i | 0.0782171 | + | 0.443591i | ||||
\(747\) | 8.86041 | − | 19.0012i | 0.324185 | − | 0.695218i | ||||
\(748\) | 0.581038 | − | 0.155689i | 0.0212449 | − | 0.00569254i | ||||
\(749\) | 4.80120 | + | 8.31592i | 0.175432 | + | 0.303857i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.9402 | + | 21.3802i | −0.654646 | + | 0.780176i | −0.986607 | − | 0.163117i | \(-0.947845\pi\) |
0.331961 | + | 0.943293i | \(0.392290\pi\) | |||||||
\(752\) | 0.553361 | + | 0.148273i | 0.0201790 | + | 0.00540694i | ||||
\(753\) | 1.61134 | + | 6.01361i | 0.0587206 | + | 0.219148i | ||||
\(754\) | −8.29628 | + | 3.01960i | −0.302133 | + | 0.109967i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.459922 | − | 0.0810966i | −0.0167272 | − | 0.00294946i | ||||
\(757\) | −23.8409 | + | 11.1172i | −0.866511 | + | 0.404061i | −0.804456 | − | 0.594012i | \(-0.797543\pi\) |
−0.0620549 | + | 0.998073i | \(0.519765\pi\) | |||||||
\(758\) | −23.7734 | − | 2.07990i | −0.863488 | − | 0.0755454i | ||||
\(759\) | −0.771841 | −0.0280160 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.4620 | 0.850498 | 0.425249 | − | 0.905076i | \(-0.360186\pi\) | ||||
0.425249 | + | 0.905076i | \(0.360186\pi\) | |||||||
\(762\) | 22.2537 | + | 1.94695i | 0.806168 | + | 0.0705305i | ||||
\(763\) | 12.9627 | − | 6.04459i | 0.469280 | − | 0.218829i | ||||
\(764\) | −11.5851 | − | 2.04277i | −0.419134 | − | 0.0739047i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.75877 | − | 0.640140i | 0.0635470 | − | 0.0231292i | ||||
\(767\) | −6.38112 | − | 23.8147i | −0.230409 | − | 0.859897i | ||||
\(768\) | −2.32931 | − | 0.624135i | −0.0840516 | − | 0.0225215i | ||||
\(769\) | 3.70950 | − | 4.42081i | 0.133768 | − | 0.159418i | −0.695002 | − | 0.719008i | \(-0.744597\pi\) |
0.828770 | + | 0.559589i | \(0.189041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.67071 | + | 13.2861i | 0.276254 | + | 0.478486i | ||||
\(772\) | −10.0211 | + | 2.68515i | −0.360668 | + | 0.0966408i | ||||
\(773\) | 17.2425 | − | 36.9767i | 0.620170 | − | 1.32996i | −0.305705 | − | 0.952126i | \(-0.598892\pi\) |
0.925874 | − | 0.377832i | \(-0.123330\pi\) | |||||||
\(774\) | 3.27076 | + | 18.5494i | 0.117565 | + | 0.666744i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.0890 | − | 4.40003i | −0.433970 | − | 0.157952i | ||||
\(777\) | −0.256058 | + | 2.92676i | −0.00918604 | + | 0.104997i | ||||
\(778\) | −14.0466 | + | 14.0466i | −0.503594 | + | 0.503594i | ||||
\(779\) | 24.0003 | + | 20.7390i | 0.859899 | + | 0.743052i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.268571 | − | 0.320070i | −0.00961021 | − | 0.0114530i | ||||
\(782\) | 0.872359 | + | 1.87078i | 0.0311955 | + | 0.0668990i | ||||
\(783\) | −0.998788 | + | 0.699359i | −0.0356938 | + | 0.0249930i | ||||
\(784\) | 5.81201 | − | 1.02481i | 0.207572 | − | 0.0366005i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.6402 | − | 21.8935i | 0.450862 | − | 0.780915i | ||||
\(787\) | −8.78524 | + | 32.7870i | −0.313160 | + | 1.16873i | 0.612530 | + | 0.790447i | \(0.290152\pi\) |
−0.925690 | + | 0.378282i | \(0.876515\pi\) | |||||||
\(788\) | 0.434667 | + | 4.96826i | 0.0154844 | + | 0.176987i | ||||
\(789\) | −38.1498 | − | 32.0115i | −1.35817 | − | 1.13964i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.406889 | − | 0.234917i | −0.0144673 | − | 0.00835269i | ||||
\(792\) | −0.779230 | − | 0.363361i | −0.0276887 | − | 0.0129115i | ||||
\(793\) | −35.7493 | − | 25.0319i | −1.26949 | − | 0.888909i | ||||
\(794\) | 1.98892 | − | 11.2797i | 0.0705841 | − | 0.400302i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.5214 | − | 17.2195i | 0.727362 | − | 0.610329i | ||||
\(797\) | −8.82038 | − | 8.82038i | −0.312434 | − | 0.312434i | 0.533418 | − | 0.845852i | \(-0.320907\pi\) |
−0.845852 | + | 0.533418i | \(0.820907\pi\) | |||||||
\(798\) | −10.6809 | + | 2.69657i | −0.378099 | + | 0.0954576i | ||||
\(799\) | − | 1.12836i | − | 0.0399183i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.88444 | − | 21.6623i | 0.278583 | − | 0.765400i | ||||
\(802\) | 7.71947 | + | 11.0245i | 0.272584 | + | 0.389290i | ||||
\(803\) | −2.59877 | + | 3.71143i | −0.0917085 | + | 0.130973i | ||||
\(804\) | −4.68475 | − | 12.8712i | −0.165218 | − | 0.453933i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.6971 | − | 6.17598i | 0.376790 | − | 0.217540i | ||||
\(807\) | 50.9512 | − | 4.45765i | 1.79357 | − | 0.156917i | ||||
\(808\) | 7.67302 | − | 0.671303i | 0.269936 | − | 0.0236163i | ||||
\(809\) | −40.5542 | + | 23.4140i | −1.42581 | + | 0.823192i | −0.996787 | − | 0.0801005i | \(-0.974476\pi\) |
−0.429024 | + | 0.903293i | \(0.641143\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.441914 | + | 1.21415i | 0.0155177 | + | 0.0426345i | 0.947210 | − | 0.320615i | \(-0.103890\pi\) |
−0.931692 | + | 0.363249i | \(0.881667\pi\) | |||||||
\(812\) | −1.64475 | + | 2.34894i | −0.0577192 | + | 0.0824316i | ||||
\(813\) | −5.40607 | − | 7.72067i | −0.189599 | − | 0.270776i | ||||
\(814\) | 0.121430 | − | 0.333626i | 0.00425611 | − | 0.0116936i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.74968i | 0.166272i | ||||||||
\(817\) | −16.3795 | − | 24.1296i | −0.573047 | − | 0.844189i | ||||
\(818\) | 18.6785 | + | 18.6785i | 0.653080 | + | 0.653080i | ||||
\(819\) | 7.29266 | − | 6.11927i | 0.254826 | − | 0.213825i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.43036 | + | 42.1397i | −0.259321 | + | 1.47068i | 0.525410 | + | 0.850849i | \(0.323912\pi\) |
−0.784732 | + | 0.619835i | \(0.787199\pi\) | |||||||
\(822\) | −44.1595 | − | 30.9208i | −1.54024 | − | 1.07849i | ||||
\(823\) | −4.47539 | − | 2.08691i | −0.156002 | − | 0.0727451i | 0.343049 | − | 0.939318i | \(-0.388540\pi\) |
−0.499051 | + | 0.866572i | \(0.666318\pi\) | |||||||
\(824\) | −11.0687 | − | 6.39053i | −0.385597 | − | 0.222625i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.13429 | − | 5.14728i | −0.213439 | − | 0.179097i | ||||
\(827\) | −1.63390 | − | 18.6756i | −0.0568163 | − | 0.649413i | −0.970199 | − | 0.242311i | \(-0.922095\pi\) |
0.913382 | − | 0.407103i | \(-0.133461\pi\) | |||||||
\(828\) | 0.763611 | − | 2.84984i | 0.0265373 | − | 0.0990386i | ||||
\(829\) | 7.72076 | − | 13.3727i | 0.268153 | − | 0.464454i | −0.700232 | − | 0.713915i | \(-0.746920\pi\) |
0.968385 | + | 0.249461i | \(0.0802534\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.6288 | + | 4.87171i | −0.958433 | + | 0.168998i | ||||
\(832\) | −2.64314 | + | 1.85075i | −0.0916345 | + | 0.0641632i | ||||
\(833\) | −4.91253 | − | 10.5349i | −0.170209 | − | 0.365014i | ||||
\(834\) | 20.2383 | + | 24.1191i | 0.700796 | + | 0.835176i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.33110 | + | 0.0193026i | 0.0460370 | + | 0.000667594i | ||||
\(837\) | 1.20624 | − | 1.20624i | 0.0416936 | − | 0.0416936i | ||||
\(838\) | 1.70360 | − | 19.4723i | 0.0588499 | − | 0.672658i | ||||
\(839\) | 46.4177 | + | 16.8946i | 1.60252 | + | 0.583268i | 0.979940 | − | 0.199292i | \(-0.0638641\pi\) |
0.622576 | + | 0.782560i | \(0.286086\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.73577 | − | 21.1866i | −0.128820 | − | 0.730572i | ||||
\(842\) | −8.62790 | + | 18.5026i | −0.297337 | + | 0.637641i | ||||
\(843\) | 12.9157 | − | 3.46075i | 0.444841 | − | 0.119195i | ||||
\(844\) | −0.286441 | − | 0.496130i | −0.00985969 | − | 0.0170775i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.03667 | + | 1.23546i | −0.0356416 | + | 0.0424760i | ||||
\(847\) | −11.0409 | − | 2.95840i | −0.379369 | − | 0.101652i | ||||
\(848\) | 2.85409 | + | 10.6516i | 0.0980097 | + | 0.365777i | ||||
\(849\) | 36.5427 | − | 13.3004i | 1.25414 | − | 0.456470i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.19981 | + | 0.211558i | 0.0411289 | + | 0.00725213i | ||||
\(852\) | 2.98999 | − | 1.39426i | 0.102435 | − | 0.0477664i | ||||
\(853\) | 25.8602 | + | 2.26248i | 0.885438 | + | 0.0774658i | 0.520795 | − | 0.853682i | \(-0.325636\pi\) |
0.364643 | + | 0.931148i | \(0.381191\pi\) | |||||||
\(854\) | −14.1746 | −0.485046 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.16250 | 0.313168 | ||||||||
\(857\) | 40.2799 | + | 3.52403i | 1.37594 | + | 0.120379i | 0.751002 | − | 0.660300i | \(-0.229571\pi\) |
0.624933 | + | 0.780678i | \(0.285126\pi\) | |||||||
\(858\) | −2.15374 | + | 1.00431i | −0.0735276 | + | 0.0342865i | ||||
\(859\) | −8.58678 | − | 1.51408i | −0.292977 | − | 0.0516598i | 0.0252278 | − | 0.999682i | \(-0.491969\pi\) |
−0.318205 | + | 0.948022i | \(0.603080\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.2815 | + | 6.28996i | −0.588953 | + | 0.214361i | ||||
\(862\) | −3.25931 | − | 12.1639i | −0.111012 | − | 0.414304i | ||||
\(863\) | −20.7778 | − | 5.56739i | −0.707284 | − | 0.189516i | −0.112793 | − | 0.993619i | \(-0.535980\pi\) |
−0.594491 | + | 0.804102i | \(0.702646\pi\) | |||||||
\(864\) | −0.286441 | + | 0.341367i | −0.00974491 | + | 0.0116135i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −12.7690 | − | 22.1166i | −0.433910 | − | 0.751553i | ||||
\(867\) | −30.5619 | + | 8.18904i | −1.03794 | + | 0.278114i | ||||
\(868\) | 1.69549 | − | 3.63598i | 0.0575485 | − | 0.123413i | ||||
\(869\) | −0.130990 | − | 0.742878i | −0.00444351 | − | 0.0252004i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.2224 | − | 6.26844i | −0.583559 | − | 0.212398i | ||||
\(872\) | 1.18946 | − | 13.5956i | 0.0402801 | − | 0.460404i | ||||
\(873\) | 25.6094 | − | 25.6094i | 0.866747 | − | 0.866747i | ||||
\(874\) | 0.727940 | + | 4.50980i | 0.0246230 | + | 0.152546i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22.9957 | − | 27.4052i | −0.776953 | − | 0.925937i | ||||
\(877\) | −6.61953 | − | 14.1956i | −0.223526 | − | 0.479352i | 0.762279 | − | 0.647248i | \(-0.224080\pi\) |
−0.985805 | + | 0.167896i | \(0.946303\pi\) | |||||||
\(878\) | −22.1588 | + | 15.5158i | −0.747824 | + | 0.523632i | ||||
\(879\) | −75.5236 | + | 13.3169i | −2.54735 | + | 0.449166i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.80659 | − | 8.32526i | 0.161938 | − | 0.280485i | −0.773626 | − | 0.633643i | \(-0.781559\pi\) |
0.935564 | + | 0.353158i | \(0.114892\pi\) | |||||||
\(882\) | −4.30013 | + | 16.0483i | −0.144793 | + | 0.540375i | ||||
\(883\) | −1.73826 | − | 19.8684i | −0.0584971 | − | 0.668625i | −0.967672 | − | 0.252211i | \(-0.918842\pi\) |
0.909175 | − | 0.416414i | \(-0.136713\pi\) | |||||||
\(884\) | 4.86846 | + | 4.08512i | 0.163744 | + | 0.137398i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.4937 | + | 6.63587i | 0.386137 | + | 0.222936i | ||||
\(887\) | −9.00491 | − | 4.19906i | −0.302355 | − | 0.140991i | 0.265520 | − | 0.964105i | \(-0.414457\pi\) |
−0.567875 | + | 0.823115i | \(0.692234\pi\) | |||||||
\(888\) | 2.29637 | + | 1.60793i | 0.0770611 | + | 0.0539587i | ||||
\(889\) | 1.68582 | − | 9.56077i | 0.0565407 | − | 0.320658i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.22731 | + | 1.86894i | −0.0746177 | + | 0.0626117i | ||||
\(892\) | −1.92470 | − | 1.92470i | −0.0644437 | − | 0.0644437i | ||||
\(893\) | 0.681211 | − | 2.40242i | 0.0227959 | − | 0.0803939i | ||||
\(894\) | 38.4597i | 1.28628i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.358441 | + | 0.984808i | −0.0119747 | + | 0.0329001i | ||||
\(897\) | −4.67730 | − | 6.67988i | −0.156171 | − | 0.223035i | ||||
\(898\) | −4.34102 | + | 6.19962i | −0.144862 | + | 0.206884i | ||||
\(899\) | −3.58239 | − | 9.84255i | −0.119480 | − | 0.328267i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.8097 | − | 10.8598i | 0.626643 | − | 0.361793i | ||||
\(902\) | 2.21397 | − | 0.193697i | 0.0737171 | − | 0.00644941i | ||||
\(903\) | 16.8446 | − | 1.47371i | 0.560552 | − | 0.0490420i | ||||
\(904\) | −0.388249 | + | 0.224155i | −0.0129130 | + | 0.00745530i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −16.4616 | − | 45.2278i | −0.546899 | − | 1.50259i | ||||
\(907\) | 10.7526 | − | 15.3563i | 0.357034 | − | 0.509898i | −0.599950 | − | 0.800037i | \(-0.704813\pi\) |
0.956984 | + | 0.290140i | \(0.0937018\pi\) | |||||||
\(908\) | −10.9181 | − | 15.5926i | −0.362329 | − | 0.517459i | ||||
\(909\) | −7.41625 | + | 20.3760i | −0.245982 | + | 0.675829i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 23.0503i | − | 0.763690i | −0.924226 | − | 0.381845i | \(-0.875289\pi\) | ||
0.924226 | − | 0.381845i | \(-0.124711\pi\) | |||||||
\(912\) | −2.86748 | + | 10.1127i | −0.0949516 | + | 0.334865i | ||||
\(913\) | 1.60827 | + | 1.60827i | 0.0532260 | + | 0.0532260i | ||||
\(914\) | −2.92079 | + | 2.45084i | −0.0966113 | + | 0.0810665i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.64022 | − | 9.30212i | 0.0541942 | − | 0.307351i | ||||
\(917\) | −8.99978 | − | 6.30172i | −0.297199 | − | 0.208101i | ||||
\(918\) | 0.795471 | + | 0.370934i | 0.0262544 | + | 0.0122426i | ||||
\(919\) | −18.6072 | − | 10.7429i | −0.613795 | − | 0.354375i | 0.160654 | − | 0.987011i | \(-0.448640\pi\) |
−0.774449 | + | 0.632636i | \(0.781973\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −59.9384 | − | 50.2943i | −1.97504 | − | 1.65725i | ||||
\(922\) | −3.38222 | − | 38.6590i | −0.111388 | − | 1.27317i | ||||
\(923\) | 1.14252 | − | 4.26394i | 0.0376065 | − | 0.140349i | ||||
\(924\) | −0.385920 | + | 0.668434i | −0.0126958 | + | 0.0219899i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 29.8555 | − | 5.26433i | 0.981113 | − | 0.172997i | ||||
\(927\) | 29.4742 | − | 20.6380i | 0.968059 | − | 0.677842i | ||||
\(928\) | 1.15635 | + | 2.47980i | 0.0379591 | + | 0.0814036i | ||||
\(929\) | 9.67809 | + | 11.5339i | 0.317528 | + | 0.378415i | 0.901074 | − | 0.433665i | \(-0.142780\pi\) |
−0.583546 | + | 0.812080i | \(0.698335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.09926 | − | 25.3961i | −0.134348 | − | 0.832323i | ||||
\(932\) | 16.5423 | − | 16.5423i | 0.541862 | − | 0.541862i | ||||
\(933\) | 2.54800 | − | 29.1238i | 0.0834178 | − | 0.953470i | ||||
\(934\) | 33.0824 | + | 12.0410i | 1.08249 | + | 0.393994i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.57738 | − | 8.94578i | −0.0515583 | − | 0.292402i | ||||
\(937\) | 18.1290 | − | 38.8778i | 0.592248 | − | 1.27008i | −0.350496 | − | 0.936564i | \(-0.613987\pi\) |
0.942744 | − | 0.333517i | \(-0.108235\pi\) | |||||||
\(938\) | −5.74991 | + | 1.54068i | −0.187741 | + | 0.0503051i | ||||
\(939\) | −10.0842 | − | 17.4664i | −0.329087 | − | 0.569995i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.4971 | + | 28.0027i | −0.765982 | + | 0.912862i | −0.998210 | − | 0.0597991i | \(-0.980954\pi\) |
0.232228 | + | 0.972661i | \(0.425398\pi\) | |||||||
\(942\) | −1.16541 | − | 0.312272i | −0.0379713 | − | 0.0101744i | ||||
\(943\) | 1.97383 | + | 7.36644i | 0.0642768 | + | 0.239884i | ||||
\(944\) | −7.18009 | + | 2.61334i | −0.233692 | + | 0.0850570i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.01233 | − | 0.354827i | −0.0654264 | − | 0.0115364i | ||||
\(947\) | 30.4041 | − | 14.1777i | 0.988002 | − | 0.460713i | 0.139682 | − | 0.990196i | \(-0.455392\pi\) |
0.848320 | + | 0.529483i | \(0.177614\pi\) | |||||||
\(948\) | 5.93354 | + | 0.519117i | 0.192712 | + | 0.0168601i | ||||
\(949\) | −47.8689 | −1.55389 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.975844 | 0.0316439 | ||||||||
\(952\) | 2.05632 | + | 0.179905i | 0.0666458 | + | 0.00583075i | ||||
\(953\) | 32.2501 | − | 15.0385i | 1.04468 | − | 0.487144i | 0.176974 | − | 0.984215i | \(-0.443369\pi\) |
0.867710 | + | 0.497071i | \(0.165591\pi\) | |||||||
\(954\) | −30.5726 | − | 5.39078i | −0.989825 | − | 0.174533i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 18.0376 | − | 6.56515i | 0.583378 | − | 0.212332i | ||||
\(957\) | 0.521555 | + | 1.94647i | 0.0168595 | + | 0.0629204i | ||||
\(958\) | −33.4944 | − | 8.97479i | −1.08215 | − | 0.289962i | ||||
\(959\) | −15.0595 | + | 17.9472i | −0.486296 | + | 0.579545i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.17293 | − | 14.1559i | −0.263643 | − | 0.456643i | ||||
\(962\) | 3.62322 | − | 0.970838i | 0.116817 | − | 0.0313011i | ||||
\(963\) | −10.9012 | + | 23.3776i | −0.351285 | + | 0.753333i | ||||
\(964\) | 1.20134 | + | 6.81315i | 0.0386926 | + | 0.219437i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.48886 | − | 0.905869i | −0.0800776 | − | 0.0291459i | ||||
\(967\) | −1.33516 | + | 15.2609i | −0.0429357 | + | 0.490758i | 0.944034 | + | 0.329849i | \(0.106998\pi\) |
−0.986969 | + | 0.160908i | \(0.948558\pi\) | |||||||
\(968\) | −7.71222 | + | 7.71222i | −0.247880 | + | 0.247880i | ||||
\(969\) | 20.7012 | + | 0.300193i | 0.665018 | + | 0.00964358i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.5780 | − | 29.2909i | −0.788746 | − | 0.939991i | 0.210547 | − | 0.977584i | \(-0.432475\pi\) |
−0.999293 | + | 0.0375929i | \(0.988031\pi\) | |||||||
\(972\) | −9.13740 | − | 19.5952i | −0.293082 | − | 0.628517i | ||||
\(973\) | 11.2087 | − | 7.84841i | 0.359334 | − | 0.251608i | ||||
\(974\) | 16.7400 | − | 2.95171i | 0.536384 | − | 0.0945790i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.76264 | + | 11.7132i | −0.216467 | + | 0.374932i | ||||
\(977\) | 7.23478 | − | 27.0006i | 0.231461 | − | 0.863825i | −0.748251 | − | 0.663416i | \(-0.769106\pi\) |
0.979712 | − | 0.200409i | \(-0.0642272\pi\) | |||||||
\(978\) | −1.78155 | − | 20.3632i | −0.0569676 | − | 0.651143i | ||||
\(979\) | 1.91576 | + | 1.60752i | 0.0612281 | + | 0.0513765i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.2732 | + | 19.2103i | 1.06233 | + | 0.613337i | ||||
\(982\) | −15.4770 | − | 7.21704i | −0.493891 | − | 0.230305i | ||||
\(983\) | −7.95470 | − | 5.56994i | −0.253716 | − | 0.177654i | 0.439799 | − | 0.898096i | \(-0.355050\pi\) |
−0.693514 | + | 0.720443i | \(0.743939\pi\) | |||||||
\(984\) | −3.04720 | + | 17.2815i | −0.0971412 | + | 0.550915i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.12836 | − | 3.46410i | 0.131474 | − | 0.110319i | ||||
\(987\) | 1.02376 | + | 1.02376i | 0.0325866 | + | 0.0325866i | ||||
\(988\) | 7.89932 | + | 11.6370i | 0.251311 | + | 0.370221i | ||||
\(989\) | − | 7.01186i | − | 0.222964i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.01249 | − | 2.78179i | 0.0321628 | − | 0.0883665i | −0.922572 | − | 0.385825i | \(-0.873917\pi\) |
0.954735 | + | 0.297459i | \(0.0961390\pi\) | |||||||
\(992\) | −2.19569 | − | 3.13577i | −0.0697133 | − | 0.0995609i | ||||
\(993\) | −31.2817 | + | 44.6749i | −0.992695 | + | 1.41771i | ||||
\(994\) | −0.490376 | − | 1.34730i | −0.0155538 | − | 0.0427336i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −15.5528 | + | 8.97940i | −0.492809 | + | 0.284523i | ||||
\(997\) | 40.0166 | − | 3.50100i | 1.26734 | − | 0.110878i | 0.566418 | − | 0.824118i | \(-0.308329\pi\) |
0.700920 | + | 0.713240i | \(0.252773\pi\) | |||||||
\(998\) | 9.06638 | − | 0.793206i | 0.286991 | − | 0.0251085i | ||||
\(999\) | 0.448634 | − | 0.259019i | 0.0141941 | − | 0.00819499i |
(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 | 950.2.bb.a.393.1 | yes | 24 | |
5.2 | odd | 4 | inner | 950.2.bb.a.507.2 | yes | 24 | |
5.3 | odd | 4 | inner | 950.2.bb.a.507.1 | yes | 24 | |
5.4 | even | 2 | inner | 950.2.bb.a.393.2 | yes | 24 | |
19.3 | odd | 18 | inner | 950.2.bb.a.193.2 | yes | 24 | |
95.3 | even | 36 | inner | 950.2.bb.a.307.2 | yes | 24 | |
95.22 | even | 36 | inner | 950.2.bb.a.307.1 | yes | 24 | |
95.79 | odd | 18 | inner | 950.2.bb.a.193.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.bb.a.193.1 | ✓ | 24 | 95.79 | odd | 18 | inner | |
950.2.bb.a.193.2 | yes | 24 | 19.3 | odd | 18 | inner | |
950.2.bb.a.307.1 | yes | 24 | 95.22 | even | 36 | inner | |
950.2.bb.a.307.2 | yes | 24 | 95.3 | even | 36 | inner | |
950.2.bb.a.393.1 | yes | 24 | 1.1 | even | 1 | trivial | |
950.2.bb.a.393.2 | yes | 24 | 5.4 | even | 2 | inner | |
950.2.bb.a.507.1 | yes | 24 | 5.3 | odd | 4 | inner | |
950.2.bb.a.507.2 | yes | 24 | 5.2 | odd | 4 | inner |