Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(81,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.u (of order \(5\), degree \(4\), not 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: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 12 x^{14} - 18 x^{13} + 100 x^{12} + 23 x^{11} + 567 x^{10} + 556 x^{9} + 3841 x^{8} + 1155 x^{7} + 7575 x^{6} - 875 x^{5} + 7485 x^{4} + 900 x^{3} + 2000 x^{2} + \cdots + 6400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 161.2 | ||
Root | \(0.372462 - 1.14632i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.161 |
Dual form | 400.2.u.g.241.2 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −0.372462 | + | 1.14632i | −0.215041 | + | 0.661829i | 0.784109 | + | 0.620623i | \(0.213120\pi\) |
−0.999151 | + | 0.0412064i | \(0.986880\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.388572 | + | 2.20205i | 0.173775 | + | 0.984785i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.59935 | −0.604498 | −0.302249 | − | 0.953229i | \(-0.597737\pi\) | ||||
−0.302249 | + | 0.953229i | \(0.597737\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.25173 | + | 0.909432i | 0.417242 | + | 0.303144i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.86042 | + | 2.07822i | −0.862449 | + | 0.626606i | −0.928550 | − | 0.371207i | \(-0.878944\pi\) |
0.0661014 | + | 0.997813i | \(0.478944\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.38530 | − | 1.73302i | −0.661563 | − | 0.480654i | 0.205627 | − | 0.978630i | \(-0.434076\pi\) |
−0.867190 | + | 0.497977i | \(0.834076\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.66898 | − | 0.374751i | −0.689128 | − | 0.0967604i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.357732 | − | 1.10099i | −0.0867628 | − | 0.267028i | 0.898257 | − | 0.439471i | \(-0.144834\pi\) |
−0.985020 | + | 0.172443i | \(0.944834\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.866689 | + | 2.66739i | 0.198832 | + | 0.611942i | 0.999910 | + | 0.0133828i | \(0.00425999\pi\) |
−0.801078 | + | 0.598559i | \(0.795740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.595698 | − | 1.83337i | 0.129992 | − | 0.400074i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.55625 | − | 1.85723i | 0.533015 | − | 0.387258i | −0.288469 | − | 0.957489i | \(-0.593146\pi\) |
0.821484 | + | 0.570231i | \(0.193146\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.69802 | + | 1.71131i | −0.939605 | + | 0.342262i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.43408 | + | 3.22155i | −0.853339 | + | 0.619987i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.04006 | + | 9.35636i | −0.564526 | + | 1.73743i | 0.104830 | + | 0.994490i | \(0.466570\pi\) |
−0.669356 | + | 0.742942i | \(0.733430\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.572270 | − | 1.76126i | −0.102783 | − | 0.316332i | 0.886421 | − | 0.462880i | \(-0.153184\pi\) |
−0.989204 | + | 0.146547i | \(0.953184\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.31690 | − | 4.05302i | −0.229244 | − | 0.705540i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.621463 | − | 3.52185i | −0.105046 | − | 0.595301i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.63802 | − | 2.64318i | −0.598087 | − | 0.434535i | 0.247112 | − | 0.968987i | \(-0.420518\pi\) |
−0.845199 | + | 0.534451i | \(0.820518\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.87503 | − | 2.08883i | 0.460374 | − | 0.334481i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.49601 | + | 4.71963i | 1.01451 | + | 0.737082i | 0.965149 | − | 0.261699i | \(-0.0842829\pi\) |
0.0493568 | + | 0.998781i | \(0.484283\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.5345 | 1.75899 | 0.879496 | − | 0.475906i | \(-0.157880\pi\) | ||||
0.879496 | + | 0.475906i | \(0.157880\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.51623 | + | 3.10974i | −0.226026 | + | 0.463573i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.728491 | + | 2.24207i | −0.106261 | + | 0.327039i | −0.990024 | − | 0.140896i | \(-0.955002\pi\) |
0.883763 | + | 0.467935i | \(0.155002\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.44208 | −0.634583 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.39533 | 0.195385 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.15111 | − | 6.62042i | 0.295477 | − | 0.909385i | −0.687584 | − | 0.726105i | \(-0.741329\pi\) |
0.983061 | − | 0.183280i | \(-0.0586714\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.68781 | − | 5.49124i | −0.766944 | − | 0.740439i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.38050 | −0.447758 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.1170 | + | 8.07696i | 1.44731 | + | 1.05153i | 0.986451 | + | 0.164055i | \(0.0524574\pi\) |
0.460856 | + | 0.887475i | \(0.347543\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.96004 | − | 1.42405i | 0.250958 | − | 0.182331i | −0.455194 | − | 0.890393i | \(-0.650430\pi\) |
0.706151 | + | 0.708061i | \(0.250430\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.00195 | − | 1.45450i | −0.252222 | − | 0.183250i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.88933 | − | 5.92594i | 0.358378 | − | 0.735023i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.27388 | + | 13.1537i | 0.522138 | + | 1.60698i | 0.769907 | + | 0.638156i | \(0.220303\pi\) |
−0.247769 | + | 0.968819i | \(0.579697\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.17687 | + | 3.62203i | 0.141678 | + | 0.436042i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.07380 | − | 3.30482i | 0.127437 | − | 0.392210i | −0.866900 | − | 0.498482i | \(-0.833891\pi\) |
0.994337 | + | 0.106271i | \(0.0338912\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.63248 | − | 1.91261i | 0.308108 | − | 0.223854i | −0.422976 | − | 0.906141i | \(-0.639015\pi\) |
0.731084 | + | 0.682287i | \(0.239015\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.211872 | − | 6.02284i | −0.0244649 | − | 0.695458i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.57481 | − | 3.32380i | 0.521348 | − | 0.378782i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.06650 | − | 9.43770i | 0.345008 | − | 1.06182i | −0.616572 | − | 0.787299i | \(-0.711479\pi\) |
0.961580 | − | 0.274526i | \(-0.0885210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.607051 | − | 1.86831i | −0.0674501 | − | 0.207590i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.97495 | − | 12.2336i | −0.436307 | − | 1.34282i | −0.891741 | − | 0.452546i | \(-0.850516\pi\) |
0.455434 | − | 0.890270i | \(-0.349484\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.28542 | − | 1.21556i | 0.247888 | − | 0.131845i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.59308 | − | 6.96978i | −1.02849 | − | 0.747239i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.85248 | − | 6.43171i | 0.938361 | − | 0.681759i | −0.00966436 | − | 0.999953i | \(-0.503076\pi\) |
0.948026 | + | 0.318194i | \(0.103076\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.81493 | + | 2.77171i | 0.399913 | + | 0.290554i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.23212 | 0.231461 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.53696 | + | 2.94497i | −0.568080 | + | 0.302147i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.21345 | + | 6.81231i | −0.224742 | + | 0.691685i | 0.773576 | + | 0.633704i | \(0.218466\pi\) |
−0.998318 | + | 0.0579809i | \(0.981534\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.47046 | −0.549802 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.4139 | 1.83225 | 0.916124 | − | 0.400896i | \(-0.131301\pi\) | ||||
0.916124 | + | 0.400896i | \(0.131301\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.579455 | + | 1.78338i | −0.0570954 | + | 0.175722i | −0.975537 | − | 0.219835i | \(-0.929448\pi\) |
0.918442 | + | 0.395556i | \(0.129448\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.26864 | + | 0.599359i | 0.416577 | + | 0.0584914i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.86223 | 0.663397 | 0.331699 | − | 0.943385i | \(-0.392378\pi\) | ||||
0.331699 | + | 0.943385i | \(0.392378\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.56393 | − | 1.86280i | −0.245580 | − | 0.178424i | 0.458186 | − | 0.888857i | \(-0.348499\pi\) |
−0.703766 | + | 0.710432i | \(0.748499\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.38496 | − | 3.18586i | 0.416202 | − | 0.302388i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.108692 | + | 0.0789696i | 0.0102249 | + | 0.00742883i | 0.592886 | − | 0.805286i | \(-0.297988\pi\) |
−0.582661 | + | 0.812715i | \(0.697988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.08299 | + | 4.90732i | 0.473991 | + | 0.457610i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.40968 | − | 4.33854i | −0.130325 | − | 0.401098i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.572139 | + | 1.76086i | 0.0524479 | + | 0.161418i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.463826 | − | 1.42751i | 0.0421660 | − | 0.129774i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.82973 | + | 5.68863i | −0.705983 | + | 0.512927i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.59390 | − | 9.68030i | −0.500334 | − | 0.865833i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.49674 | + | 6.89978i | −0.842699 | + | 0.612257i | −0.923123 | − | 0.384504i | \(-0.874373\pi\) |
0.0804241 | + | 0.996761i | \(0.474373\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.29616 | + | 13.2222i | −0.378256 | + | 1.16415i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.664422 | − | 2.04488i | −0.0580508 | − | 0.178662i | 0.917826 | − | 0.396982i | \(-0.129942\pi\) |
−0.975877 | + | 0.218320i | \(0.929942\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.38614 | − | 4.26610i | −0.120194 | − | 0.369918i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.81696 | − | 8.51225i | −0.758843 | − | 0.732618i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.7949 | + | 9.29605i | 1.09314 | + | 0.794215i | 0.979927 | − | 0.199355i | \(-0.0638847\pi\) |
0.113216 | + | 0.993570i | \(0.463885\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.0382 | + | 11.6525i | −1.36035 | + | 0.988349i | −0.361924 | + | 0.932208i | \(0.617880\pi\) |
−0.998423 | + | 0.0561417i | \(0.982120\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.29879 | − | 1.67017i | −0.193593 | − | 0.140654i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.4245 | 0.871744 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.7844 | − | 3.05875i | −1.80910 | − | 0.254015i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.65451 | − | 5.09205i | 0.136461 | − | 0.419985i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.45736 | 0.774777 | 0.387388 | − | 0.921917i | \(-0.373377\pi\) | ||||
0.387388 | + | 0.921917i | \(0.373377\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.5082 | 1.58755 | 0.793777 | − | 0.608209i | \(-0.208112\pi\) | ||||
0.793777 | + | 0.608209i | \(0.208112\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.553490 | − | 1.70347i | 0.0447470 | − | 0.137717i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.65602 | − | 1.94454i | 0.293659 | − | 0.156189i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.9261 | −1.19123 | −0.595616 | − | 0.803270i | \(-0.703092\pi\) | ||||
−0.595616 | + | 0.803270i | \(0.703092\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.78793 | + | 4.93172i | 0.538317 | + | 0.391111i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.08834 | + | 2.97035i | −0.322207 | + | 0.234097i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.73705 | − | 6.34784i | −0.684339 | − | 0.497201i | 0.190456 | − | 0.981696i | \(-0.439004\pi\) |
−0.874794 | + | 0.484495i | \(0.839004\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.41322 | − | 4.47478i | 0.654968 | − | 0.348361i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.99854 | − | 12.3062i | −0.309416 | − | 0.952285i | −0.977992 | − | 0.208642i | \(-0.933096\pi\) |
0.668576 | − | 0.743644i | \(-0.266904\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.33093 | − | 4.09619i | −0.102379 | − | 0.315091i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.34096 | + | 4.12704i | −0.102546 | + | 0.315603i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.5346 | + | 12.7396i | −1.33313 | + | 0.968575i | −0.333463 | + | 0.942763i | \(0.608217\pi\) |
−0.999667 | + | 0.0258121i | \(0.991783\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.51379 | − | 2.73698i | 0.567989 | − | 0.206896i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.3994 | + | 9.73527i | −1.00716 | + | 0.731747i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.49437 | + | 4.59920i | −0.111694 | + | 0.343760i | −0.991243 | − | 0.132048i | \(-0.957845\pi\) |
0.879549 | + | 0.475809i | \(0.157845\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.992136 | − | 3.05348i | −0.0737449 | − | 0.226963i | 0.907389 | − | 0.420291i | \(-0.138072\pi\) |
−0.981134 | + | 0.193328i | \(0.938072\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.902381 | + | 2.77724i | 0.0667059 | + | 0.205300i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.40677 | − | 9.03816i | 0.323992 | − | 0.664498i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.31135 | + | 2.40584i | 0.242150 | + | 0.175932i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.09165 | − | 5.15239i | 0.515842 | − | 0.374781i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.0932 | + | 8.05971i | 0.802679 | + | 0.583180i | 0.911699 | − | 0.410859i | \(-0.134771\pi\) |
−0.109020 | + | 0.994040i | \(0.534771\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.7184 | 1.41936 | 0.709682 | − | 0.704522i | \(-0.248838\pi\) | ||||
0.709682 | + | 0.704522i | \(0.248838\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.71687 | + | 5.51930i | 0.409394 | + | 0.395245i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.67522 | + | 20.5442i | −0.475589 | + | 1.46371i | 0.369572 | + | 0.929202i | \(0.379504\pi\) |
−0.845161 | + | 0.534512i | \(0.820496\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.2188 | −1.71683 | −0.858413 | − | 0.512960i | \(-0.828549\pi\) | ||||
−0.858413 | + | 0.512960i | \(0.828549\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.6702 | −1.17582 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.86213 | − | 14.9641i | 0.341255 | − | 1.05027i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.86867 | + | 16.1384i | −0.549572 | + | 1.12716i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.88875 | 0.339791 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.02251 | − | 5.82870i | −0.554929 | − | 0.403179i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.68226 | − | 1.22223i | 0.115812 | − | 0.0841421i | −0.528372 | − | 0.849013i | \(-0.677197\pi\) |
0.644184 | + | 0.764871i | \(0.277197\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.38844 | + | 2.46185i | 0.232172 | + | 0.168683i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.48198 | + | 25.3995i | 0.305668 | + | 1.73223i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.915260 | + | 2.81688i | 0.0621319 | + | 0.191222i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.21196 | + | 3.73004i | 0.0818970 | + | 0.252053i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.05473 | + | 3.24614i | −0.0709491 | + | 0.218359i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.8396 | + | 11.5081i | −1.06070 | + | 0.770642i | −0.974217 | − | 0.225611i | \(-0.927562\pi\) |
−0.0864809 | + | 0.996254i | \(0.527562\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.43696 | − | 2.13044i | −0.495797 | − | 0.142030i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.30621 | − | 3.85518i | 0.352185 | − | 0.255878i | −0.397600 | − | 0.917559i | \(-0.630157\pi\) |
0.749785 | + | 0.661681i | \(0.230157\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.68231 | + | 14.4107i | −0.309416 | + | 0.952285i | 0.668576 | + | 0.743644i | \(0.266904\pi\) |
−0.977992 | + | 0.208641i | \(0.933096\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.10619 | + | 6.48219i | 0.138577 | + | 0.426497i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.532402 | − | 1.63857i | −0.0348788 | − | 0.107346i | 0.932101 | − | 0.362198i | \(-0.117973\pi\) |
−0.966980 | + | 0.254851i | \(0.917973\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.22021 | − | 0.732968i | −0.340529 | − | 0.0478136i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.67649 | + | 7.03038i | 0.628556 | + | 0.456672i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.55820 | − | 4.76481i | 0.424215 | − | 0.308210i | −0.355117 | − | 0.934822i | \(-0.615559\pi\) |
0.779331 | + | 0.626612i | \(0.215559\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.19595 | − | 2.32199i | −0.205869 | − | 0.149573i | 0.480074 | − | 0.877228i | \(-0.340610\pi\) |
−0.685943 | + | 0.727656i | \(0.740610\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.0747 | −0.902892 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.72607 | − | 9.78166i | −0.110274 | − | 0.624928i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.55534 | − | 7.86452i | 0.162592 | − | 0.500408i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.5042 | 0.982539 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.2264 | −1.33980 | −0.669899 | − | 0.742452i | \(-0.733663\pi\) | ||||
−0.669899 | + | 0.742452i | \(0.733663\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.45223 | + | 10.6249i | −0.217040 | + | 0.667981i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.542185 | + | 3.07257i | 0.0339529 | + | 0.192412i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.186373 | 0.0116256 | 0.00581282 | − | 0.999983i | \(-0.498150\pi\) | ||||
0.00581282 | + | 0.999983i | \(0.498150\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.81847 | + | 4.22737i | 0.361542 | + | 0.262676i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.3143 | + | 8.94686i | −0.762236 | + | 0.553797i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.03986 | + | 5.84130i | 0.495759 | + | 0.360190i | 0.807395 | − | 0.590012i | \(-0.200877\pi\) |
−0.311636 | + | 0.950202i | \(0.600877\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.4143 | + | 2.16432i | 0.946895 | + | 0.132953i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.07558 | + | 12.5434i | 0.249422 | + | 0.767641i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.72173 | − | 26.8427i | −0.531773 | − | 1.63663i | −0.750520 | − | 0.660848i | \(-0.770197\pi\) |
0.218747 | − | 0.975782i | \(-0.429803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.30854 | − | 4.02727i | 0.0794881 | − | 0.244639i | −0.903414 | − | 0.428770i | \(-0.858947\pi\) |
0.982902 | + | 0.184131i | \(0.0589470\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.59819 | + | 3.34078i | −0.278295 | + | 0.202193i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.88185 | − | 14.6586i | 0.595898 | − | 0.883945i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.0058 | − | 10.9024i | 0.901614 | − | 0.655061i | −0.0372663 | − | 0.999305i | \(-0.511865\pi\) |
0.938880 | + | 0.344245i | \(0.111865\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.885426 | − | 2.72506i | 0.0530091 | − | 0.163145i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.02897 | − | 3.16685i | −0.0613834 | − | 0.188919i | 0.915662 | − | 0.401948i | \(-0.131667\pi\) |
−0.977046 | + | 0.213030i | \(0.931667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.72318 | − | 20.6918i | −0.399651 | − | 1.23000i | −0.925279 | − | 0.379286i | \(-0.876170\pi\) |
0.525628 | − | 0.850714i | \(-0.323830\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.31357 | − | 7.44402i | −0.0778091 | − | 0.440946i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3894 | − | 7.54834i | −0.613267 | − | 0.445564i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.6691 | − | 9.20463i | 0.745241 | − | 0.541449i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.98466 | − | 5.07466i | −0.409448 | − | 0.297482i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.9801 | 1.34251 | 0.671257 | − | 0.741225i | \(-0.265755\pi\) | ||||
0.671257 | + | 0.741225i | \(0.265755\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.4661 | + | 27.6186i | −0.784026 | + | 1.60802i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.98825 | − | 18.4300i | 0.347474 | − | 1.06941i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.31604 | −0.538760 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.4477 | −1.06331 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.85847 | + | 21.1082i | −0.394009 | + | 1.21263i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.89745 | + | 3.76276i | 0.223167 | + | 0.215455i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.166588 | −0.00950768 | −0.00475384 | − | 0.999989i | \(-0.501513\pi\) | ||||
−0.00475384 | + | 0.999989i | \(0.501513\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.82850 | − | 1.32848i | −0.104020 | − | 0.0755748i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.42513 | + | 4.66813i | −0.364335 | + | 0.264705i | −0.754858 | − | 0.655888i | \(-0.772294\pi\) |
0.390523 | + | 0.920593i | \(0.372294\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.65596 | + | 7.01546i | 0.545787 | + | 0.396537i | 0.826230 | − | 0.563333i | \(-0.190481\pi\) |
−0.280443 | + | 0.959871i | \(0.590481\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.42498 | − | 4.97356i | 0.136632 | − | 0.280229i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.09875 | − | 9.53696i | −0.174043 | − | 0.535649i | 0.825546 | − | 0.564335i | \(-0.190868\pi\) |
−0.999588 | + | 0.0286866i | \(0.990868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.7487 | − | 33.0810i | −0.601810 | − | 1.85218i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.55592 | + | 7.86633i | −0.142658 | + | 0.439056i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.62672 | − | 1.90842i | 0.146155 | − | 0.106188i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.1719 | + | 4.05979i | 0.786117 | + | 0.225197i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.09034 | − | 2.24526i | 0.170896 | − | 0.124163i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.16511 | − | 3.58585i | 0.0642348 | − | 0.197694i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0080 | − | 30.8015i | −0.550090 | − | 1.69300i | −0.708570 | − | 0.705640i | \(-0.750660\pi\) |
0.158481 | − | 0.987362i | \(-0.449340\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.15001 | − | 6.61707i | −0.117820 | − | 0.362613i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −27.3043 | + | 14.5224i | −1.49179 | + | 0.793446i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.21206 | − | 5.96641i | −0.447339 | − | 0.325011i | 0.341205 | − | 0.939989i | \(-0.389165\pi\) |
−0.788544 | + | 0.614978i | \(0.789165\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.131008 | + | 0.0951831i | −0.00711540 | + | 0.00516964i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.29722 | + | 3.84865i | 0.286860 | + | 0.208416i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2999 | 0.988101 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.51859 | + | 3.99894i | −0.404787 | + | 0.215296i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.3220 | − | 31.7678i | 0.554114 | − | 1.70539i | −0.144158 | − | 0.989555i | \(-0.546047\pi\) |
0.698272 | − | 0.715832i | \(-0.253953\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.59021 | 0.299237 | 0.149619 | − | 0.988744i | \(-0.452195\pi\) | ||||
0.149619 | + | 0.988744i | \(0.452195\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.1596 | 0.862537 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.71318 | + | 23.7387i | −0.410531 | + | 1.26348i | 0.505656 | + | 0.862735i | \(0.331250\pi\) |
−0.916188 | + | 0.400750i | \(0.868750\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.69463 | + | 1.08040i | 0.408388 | + | 0.0573417i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.23161 | −0.118110 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.9147 | + | 21.7343i | 1.57884 | + | 1.14709i | 0.918009 | + | 0.396558i | \(0.129796\pi\) |
0.660830 | + | 0.750536i | \(0.270204\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00748 | − | 6.54432i | 0.474078 | − | 0.344438i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.46363 | + | 1.06339i | 0.0768206 | + | 0.0558134i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.23456 | + | 5.05366i | 0.273990 | + | 0.264521i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.07356 | − | 3.30408i | −0.0560394 | − | 0.172472i | 0.919119 | − | 0.393980i | \(-0.128902\pi\) |
−0.975159 | + | 0.221508i | \(0.928902\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.83904 | + | 11.8154i | 0.199853 | + | 0.615083i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.44037 | + | 10.5884i | −0.178615 | + | 0.549721i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.6934 | − | 8.49575i | 0.605461 | − | 0.439893i | −0.242352 | − | 0.970188i | \(-0.577919\pi\) |
0.847813 | + | 0.530295i | \(0.177919\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.1803 | − | 2.80686i | 0.680626 | − | 0.144946i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.4662 | − | 17.0492i | 1.20857 | − | 0.878079i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.37239 | − | 4.22379i | 0.0704950 | − | 0.216961i | −0.909602 | − | 0.415481i | \(-0.863613\pi\) |
0.980097 | + | 0.198519i | \(0.0636133\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.37219 | − | 13.4562i | −0.223994 | − | 0.689383i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.726319 | + | 2.23538i | 0.0371132 | + | 0.114223i | 0.967897 | − | 0.251348i | \(-0.0808739\pi\) |
−0.930784 | + | 0.365571i | \(0.880874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.09680 | + | 8.78242i | 0.463616 | + | 0.447593i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.4380 | + | 10.4898i | 0.733926 | + | 0.533228i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.70812 | + | 2.69411i | −0.188009 | + | 0.136597i | −0.677808 | − | 0.735239i | \(-0.737070\pi\) |
0.489799 | + | 0.871835i | \(0.337070\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.95923 | − | 2.15001i | −0.149655 | − | 0.108731i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.59156 | 0.130727 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.9738 | + | 3.08534i | 1.10562 | + | 0.155240i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.21194 | + | 3.72998i | −0.0608258 | + | 0.187202i | −0.976852 | − | 0.213916i | \(-0.931378\pi\) |
0.916026 | + | 0.401118i | \(0.131378\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.40661 | 0.270669 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.06725 | 0.203109 | 0.101554 | − | 0.994830i | \(-0.467618\pi\) | ||||
0.101554 | + | 0.994830i | \(0.467618\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.68727 | + | 5.19290i | −0.0840491 | + | 0.258677i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.87823 | − | 2.06273i | 0.192711 | − | 0.102498i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.8993 | 0.788101 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.51161 | − | 6.91059i | −0.470319 | − | 0.341707i | 0.327247 | − | 0.944939i | \(-0.393879\pi\) |
−0.797566 | + | 0.603232i | \(0.793879\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.4219 | + | 11.2047i | −0.760706 | + | 0.552685i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.7799 | − | 12.9179i | −0.874894 | − | 0.635648i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.3945 | − | 13.5067i | 1.24657 | − | 0.663017i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.38383 | − | 22.7251i | −0.361588 | − | 1.11285i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.97447 | − | 15.3098i | −0.243019 | − | 0.747934i | −0.995956 | − | 0.0898423i | \(-0.971364\pi\) |
0.752937 | − | 0.658092i | \(-0.228636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.159992 | + | 0.492406i | −0.00779756 | + | 0.0239984i | −0.954880 | − | 0.296993i | \(-0.904016\pi\) |
0.947082 | + | 0.320992i | \(0.104016\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.95088 | + | 2.14394i | −0.143477 | + | 0.104242i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.56476 | + | 4.56027i | 0.172916 | + | 0.221205i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.13479 | + | 2.27756i | −0.151703 | + | 0.110219i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.88275 | + | 11.9499i | −0.187461 | + | 0.576946i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.24332 | + | 19.2150i | 0.300730 | + | 0.925553i | 0.981236 | + | 0.192810i | \(0.0617601\pi\) |
−0.680506 | + | 0.732743i | \(0.738240\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.3203 | − | 31.7627i | −0.495963 | − | 1.52642i | −0.815451 | − | 0.578827i | \(-0.803511\pi\) |
0.319488 | − | 0.947590i | \(-0.396489\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.6202 | − | 23.8327i | 0.557145 | − | 1.14269i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.16943 | + | 5.20889i | 0.342960 | + | 0.249175i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.6723 | − | 14.2928i | 0.938909 | − | 0.682157i | −0.00924884 | − | 0.999957i | \(-0.502944\pi\) |
0.948158 | + | 0.317800i | \(0.102944\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.56026 | − | 4.03977i | −0.264775 | − | 0.192370i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.2746 | 0.868252 | 0.434126 | − | 0.900852i | \(-0.357057\pi\) | ||||
0.434126 | + | 0.900852i | \(0.357057\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.6027 | + | 16.9944i | 0.834450 | + | 0.805612i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.52251 | + | 10.8412i | −0.166609 | + | 0.512770i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.1354 | −1.70534 | −0.852668 | − | 0.522454i | \(-0.825017\pi\) | ||||
−0.852668 | + | 0.522454i | \(0.825017\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.3897 | −1.33682 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.26607 | + | 22.3627i | −0.341390 | + | 1.05069i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.62106 | + | 9.47766i | −0.216639 | + | 0.444320i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.25903 | 0.433119 | 0.216560 | − | 0.976269i | \(-0.430516\pi\) | ||||
0.216560 | + | 0.976269i | \(0.430516\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.13309 | + | 3.72941i | 0.239592 | + | 0.174074i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.65453 | + | 3.38171i | −0.216783 | + | 0.157502i | −0.690877 | − | 0.722972i | \(-0.742776\pi\) |
0.474094 | + | 0.880474i | \(0.342776\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.5798 | + | 16.4052i | 1.04937 | + | 0.762415i | 0.972093 | − | 0.234594i | \(-0.0753762\pi\) |
0.0772808 | + | 0.997009i | \(0.475376\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.867341 | + | 4.91524i | 0.0402220 | + | 0.227939i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.730903 | − | 2.24949i | −0.0338222 | − | 0.104094i | 0.932720 | − | 0.360601i | \(-0.117428\pi\) |
−0.966542 | + | 0.256507i | \(0.917428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.83544 | − | 21.0373i | −0.315631 | − | 0.971413i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.55941 | − | 17.1101i | 0.256164 | − | 0.788391i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.9935 | + | 23.9711i | −1.51704 | + | 1.10219i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.63646 | − | 11.0483i | −0.396268 | − | 0.506931i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.71342 | − | 6.33067i | 0.398960 | − | 0.289861i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.16821 | − | 9.75074i | 0.144759 | − | 0.445523i | −0.852221 | − | 0.523182i | \(-0.824745\pi\) |
0.996980 | + | 0.0776594i | \(0.0247447\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.09708 | + | 12.6095i | 0.186811 | + | 0.574945i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.88223 | − | 5.79290i | −0.0856443 | − | 0.263586i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.8611 | − | 2.22705i | −0.720216 | − | 0.101125i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.5930 | − | 9.87586i | −0.615955 | − | 0.447518i | 0.235551 | − | 0.971862i | \(-0.424311\pi\) |
−0.851506 | + | 0.524344i | \(0.824311\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.5309 | − | 7.65114i | 0.476223 | − | 0.345996i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.7142 | − | 16.5028i | −1.02508 | − | 0.744762i | −0.0577599 | − | 0.998331i | \(-0.518396\pi\) |
−0.967318 | + | 0.253568i | \(0.918396\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.3887 | 0.512923 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.12567 | − | 12.0462i | −0.0955416 | − | 0.541437i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.71739 | + | 5.28557i | −0.0770353 | + | 0.237090i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.2059 | −1.30743 | −0.653717 | − | 0.756739i | \(-0.726791\pi\) | ||||
−0.653717 | + | 0.756739i | \(0.726791\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.5962 | 0.696787 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.53123 | + | 29.3341i | −0.424977 | + | 1.30794i | 0.478040 | + | 0.878338i | \(0.341347\pi\) |
−0.903017 | + | 0.429606i | \(0.858653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.15511 | + | 40.5482i | 0.318398 | + | 1.80437i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.19127 | 0.230552 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.55341 | − | 1.85516i | −0.113178 | − | 0.0822287i | 0.529757 | − | 0.848150i | \(-0.322283\pi\) |
−0.642935 | + | 0.765921i | \(0.722283\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.21026 | + | 3.05893i | −0.186251 | + | 0.135319i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.4361 | − | 9.03536i | −0.549068 | − | 0.398921i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.15225 | − | 0.583016i | −0.182970 | − | 0.0256908i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.57571 | − | 7.92721i | −0.113279 | − | 0.348638i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.07273 | − | 24.8453i | −0.354353 | − | 1.09059i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.57661 | − | 23.3184i | 0.331937 | − | 1.02160i | −0.636274 | − | 0.771464i | \(-0.719525\pi\) |
0.968211 | − | 0.250135i | \(-0.0804750\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.5366 | + | 7.65528i | −0.460733 | + | 0.334742i | −0.793819 | − | 0.608155i | \(-0.791910\pi\) |
0.333086 | + | 0.942896i | \(0.391910\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.338858 | + | 9.63264i | 0.0147890 | + | 0.420403i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.73441 | + | 1.26012i | −0.0755520 | + | 0.0548918i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.02226 | + | 12.3792i | −0.174881 | + | 0.538227i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.56996 | + | 20.2203i | 0.285112 | + | 0.877485i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.31571 | − | 22.5154i | −0.316879 | − | 0.975252i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.66647 | + | 15.1110i | 0.115282 | + | 0.653304i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.71556 | − | 3.42606i | −0.203492 | − | 0.147845i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.7062 | − | 9.23160i | 0.547295 | − | 0.397633i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0579 | − | 15.2995i | −0.905351 | − | 0.657776i | 0.0344839 | − | 0.999405i | \(-0.489021\pi\) |
−0.939835 | + | 0.341629i | \(0.889021\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.86980 | 0.166069 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.10571 | − | 6.36973i | 0.133034 | − | 0.272849i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.49421 | + | 23.0648i | −0.320429 | + | 0.986180i | 0.653032 | + | 0.757330i | \(0.273497\pi\) |
−0.973462 | + | 0.228850i | \(0.926503\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.74851 | 0.159983 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.5919 | −1.17545 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.90440 | + | 15.0942i | −0.208556 | + | 0.641871i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.71928 | + | 8.41794i | 0.370113 | + | 0.357322i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.7393 | 1.04824 | 0.524118 | − | 0.851646i | \(-0.324395\pi\) | ||||
0.524118 | + | 0.851646i | \(0.324395\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.5132 | − | 19.9895i | −1.16368 | − | 0.845466i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.99122 | + | 2.89979i | −0.168509 | + | 0.122429i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.10487 | − | 4.43545i | −0.257290 | − | 0.186932i | 0.451662 | − | 0.892189i | \(-0.350831\pi\) |
−0.708951 | + | 0.705257i | \(0.750831\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.131660 | + | 0.270031i | −0.00553898 | + | 0.0113603i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.970888 | + | 2.98808i | 0.0407734 | + | 0.125488i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.0729216 | + | 0.224430i | 0.00305703 | + | 0.00940858i | 0.952573 | − | 0.304309i | \(-0.0984255\pi\) |
−0.949516 | + | 0.313718i | \(0.898426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.31068 | + | 16.3446i | −0.222245 | + | 0.684001i | 0.776314 | + | 0.630346i | \(0.217087\pi\) |
−0.998560 | + | 0.0536545i | \(0.982913\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.3708 | + | 9.71448i | −0.558575 | + | 0.405828i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.83104 | + | 13.0998i | −0.368280 | + | 0.546300i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.15985 | + | 4.47539i | −0.256438 | + | 0.186313i | −0.708575 | − | 0.705635i | \(-0.750662\pi\) |
0.452137 | + | 0.891948i | \(0.350662\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.34438 | + | 22.6037i | −0.305222 | + | 0.939377i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.35734 | + | 19.5659i | 0.263747 | + | 0.811729i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.60560 | + | 23.4076i | 0.314992 | + | 0.969445i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.00590 | − | 4.79001i | 0.372348 | − | 0.198042i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.4411 | + | 11.9451i | 0.678596 | + | 0.493029i | 0.872892 | − | 0.487914i | \(-0.162242\pi\) |
−0.194296 | + | 0.980943i | \(0.562242\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.20201 | − | 3.05294i | 0.173141 | − | 0.125794i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.0640 | − | 15.3039i | −0.866457 | − | 0.629518i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.3712 | −0.713348 | −0.356674 | − | 0.934229i | \(-0.616089\pi\) | ||||
−0.356674 | + | 0.934229i | \(0.616089\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.65518 | + | 1.94410i | −0.149848 | + | 0.0797003i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.02059 | − | 27.7625i | 0.369188 | − | 1.13624i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.1550 | 0.455779 | 0.227890 | − | 0.973687i | \(-0.426817\pi\) | ||||
0.227890 | + | 0.973687i | \(0.426817\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.30269 | 0.338674 | 0.169337 | − | 0.985558i | \(-0.445837\pi\) | ||||
0.169337 | + | 0.985558i | \(0.445837\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.61263 | + | 20.3516i | −0.269287 | + | 0.828781i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.32368 | + | 0.466677i | 0.135127 | + | 0.0189731i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.56913 | −0.185455 | −0.0927275 | − | 0.995692i | \(-0.529559\pi\) | ||||
−0.0927275 | + | 0.995692i | \(0.529559\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.3427 | + | 11.1471i | 0.621718 | + | 0.451704i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.62322 | − | 4.08551i | 0.227491 | − | 0.165282i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.6078 | + | 17.1521i | 0.953510 | + | 0.692765i | 0.951634 | − | 0.307233i | \(-0.0994031\pi\) |
0.00187525 | + | 0.999998i | \(0.499403\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.5691 | − | 15.0310i | −0.627805 | − | 0.606108i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.42696 | + | 29.0132i | 0.379515 | + | 1.16803i | 0.940382 | + | 0.340121i | \(0.110468\pi\) |
−0.560866 | + | 0.827906i | \(0.689532\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.12667 | + | 12.7006i | 0.165865 | + | 0.510480i | 0.999099 | − | 0.0424406i | \(-0.0135133\pi\) |
−0.833234 | + | 0.552921i | \(0.813513\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.35148 | + | 16.4702i | −0.214748 | + | 0.660925i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.1582 | + | 10.2866i | −0.567237 | + | 0.412122i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.1428 | − | 16.0795i | 0.765714 | − | 0.643181i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.66965 | − | 7.02541i | 0.386168 | − | 0.280568i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.60866 | + | 4.95096i | −0.0641416 | + | 0.197408i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.142339 | − | 0.438075i | −0.00566643 | − | 0.0174395i | 0.948183 | − | 0.317724i | \(-0.102918\pi\) |
−0.953850 | + | 0.300284i | \(0.902918\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.774495 | + | 2.38365i | 0.0307834 | + | 0.0947416i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.8838 | − | 18.2312i | −0.749382 | − | 0.723483i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.5957 | + | 7.69821i | 0.419816 | + | 0.305014i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.34962 | − | 3.16018i | 0.172068 | − | 0.125015i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.0956 | + | 16.0534i | 0.872724 | + | 0.634071i | 0.931316 | − | 0.364211i | \(-0.118661\pi\) |
−0.0585926 | + | 0.998282i | \(0.518661\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.8667 | 0.546848 | 0.273424 | − | 0.961894i | \(-0.411844\pi\) | ||||
0.273424 | + | 0.961894i | \(0.411844\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.7853 | − | 4.32256i | −1.21217 | − | 0.170201i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.54913 | + | 29.3892i | −0.375415 | + | 1.15541i | 0.567783 | + | 0.823178i | \(0.307801\pi\) |
−0.943198 | + | 0.332231i | \(0.892199\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.5849 | −1.90712 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.56995 | −0.139917 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.64737 | + | 14.3031i | −0.181866 | + | 0.559725i | −0.999880 | − | 0.0154722i | \(-0.995075\pi\) |
0.818015 | + | 0.575198i | \(0.195075\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.24475 | − | 2.25767i | 0.165856 | − | 0.0882146i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.03453 | 0.196416 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.112275 | + | 0.0815727i | 0.00437362 | + | 0.00317762i | 0.589970 | − | 0.807425i | \(-0.299140\pi\) |
−0.585596 | + | 0.810603i | \(0.699140\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.8045 | − | 17.2950i | 0.925888 | − | 0.672697i | −0.0190943 | − | 0.999818i | \(-0.506078\pi\) |
0.944983 | + | 0.327120i | \(0.106078\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.32827 | − | 2.41813i | −0.129259 | − | 0.0939123i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.85554 | − | 4.71003i | 0.343403 | − | 0.182647i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.60569 | + | 29.5633i | 0.371934 | + | 1.14470i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.29238 | − | 22.4436i | −0.281940 | − | 0.867721i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.64705 | + | 8.14678i | −0.102188 | + | 0.314503i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.1214 | − | 16.0722i | 0.852719 | − | 0.619537i | −0.0731753 | − | 0.997319i | \(-0.523313\pi\) |
0.925894 | + | 0.377782i | \(0.123313\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.3184 | − | 22.7230i | 0.589604 | − | 0.874608i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.5307 | + | 10.5571i | −0.558458 | + | 0.405744i | −0.830894 | − | 0.556430i | \(-0.812171\pi\) |
0.272436 | + | 0.962174i | \(0.412171\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.54009 | − | 10.8953i | 0.135856 | − | 0.418122i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.44292 | + | 7.51853i | 0.0936128 | + | 0.288111i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.43526 | − | 25.9611i | −0.322766 | − | 0.993372i | −0.972439 | − | 0.233158i | \(-0.925094\pi\) |
0.649673 | − | 0.760214i | \(-0.274906\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.4986 | + | 31.7872i | −0.592171 | + | 1.21453i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.7753 | − | 10.7349i | −0.563712 | − | 0.409561i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.6044 | + | 12.0638i | −0.632576 | + | 0.459593i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.5969 | + | 22.2300i | 1.16396 | + | 0.845667i | 0.990274 | − | 0.139134i | \(-0.0444317\pi\) |
0.173688 | + | 0.984801i | \(0.444432\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.74918 | 0.332354 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.8913 | − | 30.7892i | −1.20971 | − | 1.16790i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.87241 | − | 8.84038i | 0.108800 | − | 0.334853i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.07662 | 0.0785451 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.1068 | −1.28820 | −0.644098 | − | 0.764943i | \(-0.722767\pi\) | ||||
−0.644098 | + | 0.764943i | \(0.722767\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.89736 | − | 11.9948i | 0.146992 | − | 0.452394i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.78455 | − | 5.71103i | 0.104872 | − | 0.215090i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.4502 | −1.10759 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.2989 | + | 12.5684i | 0.649673 | + | 0.472015i | 0.863160 | − | 0.504931i | \(-0.168482\pi\) |
−0.213487 | + | 0.976946i | \(0.568482\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.4214 | − | 9.02465i | 0.465838 | − | 0.338451i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.73393 | − | 3.43940i | −0.177287 | − | 0.128807i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.05069 | + | 22.9553i | 0.151487 | + | 0.858481i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.01932 | + | 9.29252i | 0.112759 | + | 0.347036i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.20972 | + | 25.2669i | 0.306171 | + | 0.942298i | 0.979238 | + | 0.202716i | \(0.0649767\pi\) |
−0.673067 | + | 0.739582i | \(0.735023\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.926752 | − | 2.85225i | 0.0345140 | − | 0.106223i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.85212 | − | 2.79873i | 0.143262 | − | 0.104086i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.72932 | − | 49.1589i | −0.0642252 | − | 1.82571i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.12942 | + | 0.820574i | −0.0418880 | + | 0.0304334i | −0.608532 | − | 0.793529i | \(-0.708241\pi\) |
0.566644 | + | 0.823963i | \(0.308241\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.06345 | − | 21.7391i | 0.261609 | − | 0.805150i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.12625 | − | 12.6993i | −0.152615 | − | 0.469701i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.72195 | + | 14.5327i | 0.174409 | + | 0.536776i | 0.999606 | − | 0.0280692i | \(-0.00893587\pi\) |
−0.825197 | + | 0.564845i | \(0.808936\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.8558 | + | 1.66467i | 0.437309 | + | 0.0614024i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −39.5612 | − | 28.7429i | −1.45726 | − | 1.05876i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.0588 | − | 18.2063i | 0.921802 | − | 0.669728i | −0.0221698 | − | 0.999754i | \(-0.507057\pi\) |
0.943972 | + | 0.330026i | \(0.107057\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.06351 | + | 5.85848i | 0.296220 | + | 0.215217i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.18330 | −0.336902 | −0.168451 | − | 0.985710i | \(-0.553877\pi\) | ||||
−0.168451 | + | 0.985710i | \(0.553877\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.67486 | + | 20.8255i | 0.134637 | + | 0.762989i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.15012 | − | 18.9281i | 0.225021 | − | 0.692543i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.9751 | −0.401022 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.3438 | 1.65462 | 0.827309 | − | 0.561747i | \(-0.189871\pi\) | ||||
0.827309 | + | 0.561747i | \(0.189871\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.90604 | − | 24.3323i | 0.288112 | − | 0.886718i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.58034 | + | 42.9579i | 0.275877 | + | 1.56340i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.4782 | −1.65293 | −0.826467 | − | 0.562985i | \(-0.809653\pi\) | ||||
−0.826467 | + | 0.562985i | \(0.809653\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.8937 | − | 7.91474i | −0.395416 | − | 0.287287i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.515120 | − | 0.374257i | 0.0186731 | − | 0.0135668i | −0.578410 | − | 0.815747i | \(-0.696326\pi\) |
0.597083 | + | 0.802180i | \(0.296326\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.10062 | + | 2.97928i | 0.148453 | + | 0.107857i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.96618 | + | 0.556891i | 0.143398 | + | 0.0201344i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.5198 | − | 38.5319i | −0.452063 | − | 1.39131i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.87386 | + | 8.84482i | 0.103634 | + | 0.318952i | 0.989407 | − | 0.145165i | \(-0.0463714\pi\) |
−0.885774 | + | 0.464118i | \(0.846371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.0694170 | + | 0.213644i | −0.00249999 | + | 0.00769419i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.91821 | + | 4.29983i | −0.212863 | + | 0.154654i | −0.689108 | − | 0.724658i | \(-0.741998\pi\) |
0.476245 | + | 0.879313i | \(0.341998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.70260 | + | 7.29513i | 0.204844 | + | 0.262049i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.01308 | + | 5.09530i | −0.251593 | + | 0.182793i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.95909 | + | 21.4179i | −0.249335 | + | 0.767375i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.79661 | + | 11.6848i | 0.135853 | + | 0.418114i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.6621 | − | 51.2806i | −0.595454 | − | 1.83262i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.79986 | − | 32.8679i | −0.207006 | − | 1.17311i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.0553 | + | 16.7507i | 0.821833 | + | 0.597097i | 0.917237 | − | 0.398342i | \(-0.130414\pi\) |
−0.0954038 | + | 0.995439i | \(0.530414\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.69055 | + | 7.04060i | −0.344993 | + | 0.250652i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.173837 | − | 0.126300i | −0.00618094 | − | 0.00449071i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.14320 | −0.253662 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.22227 | + | 16.8637i | −0.291614 | + | 0.598092i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.53076 | + | 4.71121i | −0.0542225 | + | 0.166880i | −0.974500 | − | 0.224386i | \(-0.927962\pi\) |
0.920278 | + | 0.391265i | \(0.127962\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.72909 | 0.0965482 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.9301 | 0.598195 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.55518 | + | 10.9417i | −0.125460 | + | 0.386125i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.12948 | − | 7.84853i | −0.286526 | − | 0.276624i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.0189 | 1.19752 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.0656 | + | 16.0316i | 0.775787 | + | 0.563642i | 0.903712 | − | 0.428142i | \(-0.140832\pi\) |
−0.127925 | + | 0.991784i | \(0.540832\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.8986 | − | 29.7146i | 1.43614 | − | 1.04342i | 0.447313 | − | 0.894378i | \(-0.352381\pi\) |
0.988831 | − | 0.149042i | \(-0.0476189\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.12917 | + | 3.00002i | 0.144816 | + | 0.105215i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.5833 | − | 21.7060i | 0.370716 | − | 0.760328i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.99681 | + | 30.7670i | 0.349744 | + | 1.07640i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.25457 | + | 6.93884i | 0.0787809 | + | 0.242463i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.73239 | + | 14.5648i | −0.165162 | + | 0.508315i | −0.999048 | − | 0.0436206i | \(-0.986111\pi\) |
0.833886 | + | 0.551936i | \(0.186111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.6552 | − | 12.8272i | 0.615421 | − | 0.447129i | −0.235898 | − | 0.971778i | \(-0.575803\pi\) |
0.851319 | + | 0.524649i | \(0.175803\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.1228 | + | 16.7875i | 0.456878 | + | 0.584467i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.7315 | − | 17.2419i | 0.825224 | − | 0.599560i | −0.0929802 | − | 0.995668i | \(-0.529639\pi\) |
0.918204 | + | 0.396108i | \(0.129639\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.2985 | − | 40.9287i | 0.461877 | − | 1.42151i | −0.400990 | − | 0.916082i | \(-0.631334\pi\) |
0.862868 | − | 0.505430i | \(-0.168666\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.90852 | + | 21.2622i | 0.239654 | + | 0.737579i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.58907 | + | 4.89066i | 0.0550581 | + | 0.169451i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.5452 | − | 13.5868i | 0.884028 | − | 0.470192i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.21149 | + | 5.96600i | 0.283831 | + | 0.206215i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.4386 | + | 17.7556i | −0.843713 | + | 0.612993i | −0.923405 | − | 0.383826i | \(-0.874606\pi\) |
0.0796927 | + | 0.996819i | \(0.474606\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −54.8379 | − | 39.8421i | −1.89096 | − | 1.37387i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.01348 | 0.138232 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.50283 | − | 4.52244i | 0.292506 | − | 0.155577i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.741821 | + | 2.28309i | −0.0254893 | + | 0.0784479i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.2236 | 0.899992 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.2087 | −0.487067 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.8447 | − | 51.8426i | 0.576751 | − | 1.77506i | −0.0533875 | − | 0.998574i | \(-0.517002\pi\) |
0.630138 | − | 0.776483i | \(-0.282998\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.60900 | − | 1.34920i | −0.328621 | − | 0.0461416i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.3459 | 0.968276 | 0.484138 | − | 0.874992i | \(-0.339133\pi\) | ||||
0.484138 | + | 0.874992i | \(0.339133\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.62806 | + | 2.63594i | 0.123788 | + | 0.0899372i | 0.647957 | − | 0.761677i | \(-0.275624\pi\) |
−0.524169 | + | 0.851615i | \(0.675624\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.5225 | − | 9.09812i | 0.426765 | − | 0.310063i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.7437 | − | 13.6181i | −0.638044 | − | 0.463566i | 0.221133 | − | 0.975244i | \(-0.429024\pi\) |
−0.859178 | + | 0.511677i | \(0.829024\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.8667 | − | 33.6617i | −1.18550 | − | 1.14453i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.83271 | + | 17.9512i | 0.198089 | + | 0.609656i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.8421 | + | 33.3686i | 0.367794 | + | 1.13195i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.6011 | − | 38.7821i | 0.426971 | − | 1.31408i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.96597 | + | 6.51416i | −0.303452 | + | 0.220471i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.94661 | + | 15.4822i | 0.302451 | + | 0.523394i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.1415 | + | 19.7195i | −0.916505 | + | 0.665880i | −0.942652 | − | 0.333778i | \(-0.891676\pi\) |
0.0261468 | + | 0.999658i | \(0.491676\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.55924 | + | 26.3426i | −0.288696 | + | 0.888515i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.53650 | − | 7.80655i | −0.0854569 | − | 0.263009i | 0.899192 | − | 0.437553i | \(-0.144155\pi\) |
−0.984649 | + | 0.174544i | \(0.944155\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.81874 | − | 5.59752i | −0.0612056 | − | 0.188371i | 0.915778 | − | 0.401684i | \(-0.131575\pi\) |
−0.976984 | + | 0.213312i | \(0.931575\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.6442 | − | 25.7234i | −0.895634 | − | 0.864681i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.1004 | − | 15.3304i | −0.708484 | − | 0.514744i | 0.174200 | − | 0.984710i | \(-0.444266\pi\) |
−0.882684 | + | 0.469967i | \(0.844266\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.1886 | − | 11.0352i | 0.509410 | − | 0.370108i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.61917 | + | 4.08257i | 0.188249 | + | 0.136771i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.61185 | −0.221257 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.7083 | − | 1.50355i | −0.357940 | − | 0.0502583i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.46987 | − | 10.6792i | 0.115856 | − | 0.356567i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.2188 | 0.607630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.05851 | −0.268468 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.87107 | − | 21.1470i | 0.228655 | − | 0.703727i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.33839 | − | 3.37123i | 0.210695 | − | 0.112063i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.9049 | −1.85629 | −0.928146 | − | 0.372216i | \(-0.878598\pi\) | ||||
−0.928146 | + | 0.372216i | \(0.878598\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.0491 | + | 16.7462i | 0.764491 | + | 0.555435i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.01861 | − | 6.55240i | 0.298800 | − | 0.217091i | −0.428276 | − | 0.903648i | \(-0.640879\pi\) |
0.727076 | + | 0.686557i | \(0.240879\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.7941 | + | 26.7325i | 1.21771 | + | 0.884717i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.76498 | + | 3.06625i | −0.190584 | + | 0.101367i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.06264 | + | 3.27048i | 0.0350916 | + | 0.108001i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.0872351 | + | 0.268482i | 0.00287762 | + | 0.00885640i | 0.952485 | − | 0.304585i | \(-0.0985179\pi\) |
−0.949607 | + | 0.313442i | \(0.898518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.0620478 | − | 0.190964i | 0.00204454 | − | 0.00629246i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.28867 | + | 6.02207i | −0.272825 | + | 0.198219i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.6148 | + | 6.19193i | 0.710690 | + | 0.203589i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.34718 | + | 1.70533i | −0.0770916 | + | 0.0560103i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.82070 | − | 5.60354i | 0.0597353 | − | 0.183846i | −0.916736 | − | 0.399493i | \(-0.869186\pi\) |
0.976471 | + | 0.215647i | \(0.0691861\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.84990 | − | 11.8488i | −0.126175 | − | 0.388328i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.95806 | − | 9.10396i | −0.0968424 | − | 0.298050i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.01107 | + | 8.22659i | −0.131176 | + | 0.269038i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.83443 | − | 2.78588i | −0.125265 | − | 0.0910107i | 0.523388 | − | 0.852094i | \(-0.324668\pi\) |
−0.648654 | + | 0.761084i | \(0.724668\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.6385 | + | 8.45583i | −0.379807 | + | 0.275946i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.49301 | + | 6.89708i | 0.309463 | + | 0.224838i | 0.731666 | − | 0.681663i | \(-0.238743\pi\) |
−0.422203 | + | 0.906501i | \(0.638743\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.3708 | 0.826188 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.1014 | + | 13.6141i | 0.458719 | + | 0.442866i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.35893 | − | 25.7261i | 0.271629 | − | 0.835987i | −0.718463 | − | 0.695565i | \(-0.755154\pi\) |
0.990092 | − | 0.140422i | \(-0.0448460\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.59384 | −0.311429 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.0866 | 0.391934 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.12461 | − | 9.61655i | 0.101216 | − | 0.311511i | −0.887608 | − | 0.460600i | \(-0.847634\pi\) |
0.988824 | + | 0.149089i | \(0.0476342\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.4373 | + | 27.5596i | −0.434822 | + | 0.891808i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 41.9249 | 1.35524 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.4636 | − | 14.8676i | −0.660803 | − | 0.480101i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.3050 | − | 16.2055i | 0.719515 | − | 0.522758i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.58964 | + | 6.24074i | 0.276797 | + | 0.201105i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.66204 | + | 43.4210i | 0.246650 | + | 1.39777i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.0533 | − | 52.4847i | −0.548398 | − | 1.68780i | −0.712771 | − | 0.701397i | \(-0.752560\pi\) |
0.164373 | − | 0.986398i | \(-0.447440\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.20931 | + | 3.72188i | 0.0388487 | + | 0.119564i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.6530 | + | 38.9419i | −0.406054 | + | 1.24971i | 0.513957 | + | 0.857816i | \(0.328179\pi\) |
−0.920012 | + | 0.391891i | \(0.871821\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.6508 | − | 18.6364i | 0.822326 | − | 0.597455i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.93234 | + | 14.7335i | −0.318089 | + | 0.471848i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.9047 | + | 9.37583i | −0.412859 | + | 0.299959i | −0.774758 | − | 0.632258i | \(-0.782128\pi\) |
0.361900 | + | 0.932217i | \(0.382128\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.9553 | + | 36.7947i | −0.382094 | + | 1.17596i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.51524 | − | 4.66344i | −0.0483780 | − | 0.148892i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.3748 | − | 41.1633i | −0.426588 | − | 1.31290i | −0.901465 | − | 0.432852i | \(-0.857507\pi\) |
0.474877 | − | 0.880052i | \(-0.342493\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −47.8331 | − | 6.71624i | −1.52409 | − | 0.213997i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.67658 | + | 2.67119i | 0.117027 | + | 0.0850249i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.4850 | − | 21.4221i | 0.937570 | − | 0.681184i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.5901 | − | 8.42071i | −0.368172 | − | 0.267493i | 0.388281 | − | 0.921541i | \(-0.373069\pi\) |
−0.756452 | + | 0.654049i | \(0.773069\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 39.0360 | 1.23877 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.41075 | − | 53.3309i | −0.298341 | − | 1.69070i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.34905 | + | 22.6180i | −0.232747 | + | 0.716321i | 0.764666 | + | 0.644427i | \(0.222904\pi\) |
−0.997412 | + | 0.0718934i | \(0.977096\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.6464 | 0.779777 |
(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 | 400.2.u.g.161.2 | 16 | ||
4.3 | odd | 2 | 200.2.m.c.161.3 | yes | 16 | ||
20.3 | even | 4 | 1000.2.q.d.449.5 | 32 | |||
20.7 | even | 4 | 1000.2.q.d.449.4 | 32 | |||
20.19 | odd | 2 | 1000.2.m.c.801.2 | 16 | |||
25.4 | even | 10 | 10000.2.a.bh.1.6 | 8 | |||
25.16 | even | 5 | inner | 400.2.u.g.241.2 | 16 | ||
25.21 | even | 5 | 10000.2.a.bk.1.3 | 8 | |||
100.59 | odd | 10 | 1000.2.m.c.201.2 | 16 | |||
100.63 | even | 20 | 1000.2.q.d.49.4 | 32 | |||
100.71 | odd | 10 | 5000.2.a.l.1.6 | 8 | |||
100.79 | odd | 10 | 5000.2.a.m.1.3 | 8 | |||
100.87 | even | 20 | 1000.2.q.d.49.5 | 32 | |||
100.91 | odd | 10 | 200.2.m.c.41.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.2.m.c.41.3 | ✓ | 16 | 100.91 | odd | 10 | ||
200.2.m.c.161.3 | yes | 16 | 4.3 | odd | 2 | ||
400.2.u.g.161.2 | 16 | 1.1 | even | 1 | trivial | ||
400.2.u.g.241.2 | 16 | 25.16 | even | 5 | inner | ||
1000.2.m.c.201.2 | 16 | 100.59 | odd | 10 | |||
1000.2.m.c.801.2 | 16 | 20.19 | odd | 2 | |||
1000.2.q.d.49.4 | 32 | 100.63 | even | 20 | |||
1000.2.q.d.49.5 | 32 | 100.87 | even | 20 | |||
1000.2.q.d.449.4 | 32 | 20.7 | even | 4 | |||
1000.2.q.d.449.5 | 32 | 20.3 | even | 4 | |||
5000.2.a.l.1.6 | 8 | 100.71 | odd | 10 | |||
5000.2.a.m.1.3 | 8 | 100.79 | odd | 10 | |||
10000.2.a.bh.1.6 | 8 | 25.4 | even | 10 | |||
10000.2.a.bk.1.3 | 8 | 25.21 | even | 5 |