Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(34,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.i (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 35x^{8} + 295x^{4} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 34.6 | ||
Root | \(-1.33026 + 1.33026i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.34 |
Dual form | 91.2.i.a.83.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.854638 | + | 0.854638i | 0.604320 | + | 0.604320i | 0.941456 | − | 0.337136i | \(-0.109458\pi\) |
−0.337136 | + | 0.941456i | \(0.609458\pi\) | |||||||
\(3\) | 2.27378i | 1.31277i | 0.754427 | + | 0.656384i | \(0.227915\pi\) | ||||
−0.754427 | + | 0.656384i | \(0.772085\pi\) | |||||||
\(4\) | − | 0.539189i | − | 0.269594i | ||||||
\(5\) | 0.612999 | − | 0.612999i | 0.274142 | − | 0.274142i | −0.556623 | − | 0.830765i | \(-0.687903\pi\) |
0.830765 | + | 0.556623i | \(0.187903\pi\) | |||||||
\(6\) | −1.94326 | + | 1.94326i | −0.793333 | + | 0.793333i | ||||
\(7\) | −2.64571 | − | 0.0148122i | −0.999984 | − | 0.00559850i | ||||
\(8\) | 2.17009 | − | 2.17009i | 0.767241 | − | 0.767241i | ||||
\(9\) | −2.17009 | −0.723362 | ||||||||
\(10\) | 1.04778 | 0.331338 | ||||||||
\(11\) | −1.85464 | + | 1.85464i | −0.559194 | + | 0.559194i | −0.929078 | − | 0.369884i | \(-0.879398\pi\) |
0.369884 | + | 0.929078i | \(0.379398\pi\) | |||||||
\(12\) | 1.22600 | 0.353915 | ||||||||
\(13\) | 0.104263 | − | 3.60404i | 0.0289173 | − | 0.999582i | ||||
\(14\) | −2.24846 | − | 2.27378i | −0.600927 | − | 0.607694i | ||||
\(15\) | 1.39383 | + | 1.39383i | 0.359884 | + | 0.359884i | ||||
\(16\) | 2.63090 | 0.657724 | ||||||||
\(17\) | 3.04726 | 0.739070 | 0.369535 | − | 0.929217i | \(-0.379517\pi\) | ||||
0.369535 | + | 0.929217i | \(0.379517\pi\) | |||||||
\(18\) | −1.85464 | − | 1.85464i | −0.437142 | − | 0.437142i | ||||
\(19\) | −0.104263 | + | 0.104263i | −0.0239195 | + | 0.0239195i | −0.718965 | − | 0.695046i | \(-0.755384\pi\) |
0.695046 | + | 0.718965i | \(0.255384\pi\) | |||||||
\(20\) | −0.330522 | − | 0.330522i | −0.0739070 | − | 0.0739070i | ||||
\(21\) | 0.0336798 | − | 6.01577i | 0.00734953 | − | 1.31275i | ||||
\(22\) | −3.17009 | −0.675865 | ||||||||
\(23\) | − | 6.51026i | − | 1.35748i | −0.734377 | − | 0.678741i | \(-0.762526\pi\) | ||
0.734377 | − | 0.678741i | \(-0.237474\pi\) | |||||||
\(24\) | 4.93430 | + | 4.93430i | 1.00721 | + | 1.00721i | ||||
\(25\) | 4.24846i | 0.849693i | ||||||||
\(26\) | 3.16926 | − | 2.99104i | 0.621543 | − | 0.586592i | ||||
\(27\) | 1.88704i | 0.363162i | ||||||||
\(28\) | −0.00798659 | + | 1.42654i | −0.00150932 | + | 0.269590i | ||||
\(29\) | −3.78765 | −0.703350 | −0.351675 | − | 0.936122i | \(-0.614388\pi\) | ||||
−0.351675 | + | 0.936122i | \(0.614388\pi\) | |||||||
\(30\) | 2.38243i | 0.434971i | ||||||||
\(31\) | −6.77330 | + | 6.77330i | −1.21652 | + | 1.21652i | −0.247679 | + | 0.968842i | \(0.579668\pi\) |
−0.968842 | + | 0.247679i | \(0.920332\pi\) | |||||||
\(32\) | −2.09171 | − | 2.09171i | −0.369765 | − | 0.369765i | ||||
\(33\) | −4.21704 | − | 4.21704i | −0.734093 | − | 0.734093i | ||||
\(34\) | 2.60430 | + | 2.60430i | 0.446635 | + | 0.446635i | ||||
\(35\) | −1.63090 | + | 1.61274i | −0.275672 | + | 0.272602i | ||||
\(36\) | 1.17009i | 0.195014i | ||||||||
\(37\) | −2.02472 | + | 2.02472i | −0.332863 | + | 0.332863i | −0.853673 | − | 0.520810i | \(-0.825630\pi\) |
0.520810 | + | 0.853673i | \(0.325630\pi\) | |||||||
\(38\) | −0.178214 | −0.0289101 | ||||||||
\(39\) | 8.19481 | + | 0.237071i | 1.31222 | + | 0.0379618i | ||||
\(40\) | − | 2.66052i | − | 0.420665i | ||||||
\(41\) | 2.27378 | − | 2.27378i | 0.355105 | − | 0.355105i | −0.506900 | − | 0.862005i | \(-0.669209\pi\) |
0.862005 | + | 0.506900i | \(0.169209\pi\) | |||||||
\(42\) | 5.17009 | − | 5.11252i | 0.797762 | − | 0.788879i | ||||
\(43\) | 3.18342i | 0.485467i | 0.970093 | + | 0.242733i | \(0.0780440\pi\) | ||||
−0.970093 | + | 0.242733i | \(0.921956\pi\) | |||||||
\(44\) | 1.00000 | + | 1.00000i | 0.150756 | + | 0.150756i | ||||
\(45\) | −1.33026 | + | 1.33026i | −0.198304 | + | 0.198304i | ||||
\(46\) | 5.56391 | − | 5.56391i | 0.820354 | − | 0.820354i | ||||
\(47\) | −5.21678 | − | 5.21678i | −0.760946 | − | 0.760946i | 0.215548 | − | 0.976493i | \(-0.430846\pi\) |
−0.976493 | + | 0.215548i | \(0.930846\pi\) | |||||||
\(48\) | 5.98209i | 0.863440i | ||||||||
\(49\) | 6.99956 | + | 0.0783777i | 0.999937 | + | 0.0111968i | ||||
\(50\) | −3.63090 | + | 3.63090i | −0.513486 | + | 0.513486i | ||||
\(51\) | 6.92881i | 0.970227i | ||||||||
\(52\) | −1.94326 | − | 0.0562174i | −0.269482 | − | 0.00779595i | ||||
\(53\) | 3.43188 | 0.471405 | 0.235703 | − | 0.971825i | \(-0.424261\pi\) | ||||
0.235703 | + | 0.971825i | \(0.424261\pi\) | |||||||
\(54\) | −1.61274 | + | 1.61274i | −0.219466 | + | 0.219466i | ||||
\(55\) | 2.27378i | 0.306597i | ||||||||
\(56\) | −5.77356 | + | 5.70928i | −0.771525 | + | 0.762934i | ||||
\(57\) | −0.237071 | − | 0.237071i | −0.0314008 | − | 0.0314008i | ||||
\(58\) | −3.23707 | − | 3.23707i | −0.425048 | − | 0.425048i | ||||
\(59\) | 9.15135 | + | 9.15135i | 1.19140 | + | 1.19140i | 0.976673 | + | 0.214731i | \(0.0688873\pi\) |
0.214731 | + | 0.976673i | \(0.431113\pi\) | |||||||
\(60\) | 0.751536 | − | 0.751536i | 0.0970229 | − | 0.0970229i | ||||
\(61\) | 9.20756i | 1.17891i | 0.807802 | + | 0.589454i | \(0.200657\pi\) | ||||
−0.807802 | + | 0.589454i | \(0.799343\pi\) | |||||||
\(62\) | −11.5774 | −1.47034 | ||||||||
\(63\) | 5.74142 | + | 0.0321438i | 0.723351 | + | 0.00404974i | ||||
\(64\) | − | 8.83710i | − | 1.10464i | ||||||
\(65\) | −2.14536 | − | 2.27319i | −0.266099 | − | 0.281954i | ||||
\(66\) | − | 7.20809i | − | 0.887254i | ||||||
\(67\) | −1.04945 | − | 1.04945i | −0.128211 | − | 0.128211i | 0.640090 | − | 0.768300i | \(-0.278897\pi\) |
−0.768300 | + | 0.640090i | \(0.778897\pi\) | |||||||
\(68\) | − | 1.64305i | − | 0.199249i | ||||||
\(69\) | 14.8029 | 1.78206 | ||||||||
\(70\) | −2.77213 | − | 0.0155200i | −0.331333 | − | 0.00185500i | ||||
\(71\) | −4.10310 | − | 4.10310i | −0.486949 | − | 0.486949i | 0.420393 | − | 0.907342i | \(-0.361892\pi\) |
−0.907342 | + | 0.420393i | \(0.861892\pi\) | |||||||
\(72\) | −4.70928 | + | 4.70928i | −0.554993 | + | 0.554993i | ||||
\(73\) | −6.92561 | − | 6.92561i | −0.810581 | − | 0.810581i | 0.174140 | − | 0.984721i | \(-0.444286\pi\) |
−0.984721 | + | 0.174140i | \(0.944286\pi\) | |||||||
\(74\) | −3.46081 | −0.402311 | ||||||||
\(75\) | −9.66008 | −1.11545 | ||||||||
\(76\) | 0.0562174 | + | 0.0562174i | 0.00644858 | + | 0.00644858i | ||||
\(77\) | 4.93430 | − | 4.87936i | 0.562316 | − | 0.556055i | ||||
\(78\) | 6.80098 | + | 7.20620i | 0.770060 | + | 0.815942i | ||||
\(79\) | 17.5958 | 1.97968 | 0.989842 | − | 0.142168i | \(-0.0454074\pi\) | ||||
0.989842 | + | 0.142168i | \(0.0454074\pi\) | |||||||
\(80\) | 1.61274 | − | 1.61274i | 0.180310 | − | 0.180310i | ||||
\(81\) | −10.8010 | −1.20011 | ||||||||
\(82\) | 3.88652 | 0.429194 | ||||||||
\(83\) | 10.5474 | − | 10.5474i | 1.15773 | − | 1.15773i | 0.172763 | − | 0.984963i | \(-0.444731\pi\) |
0.984963 | − | 0.172763i | \(-0.0552694\pi\) | |||||||
\(84\) | −3.24364 | − | 0.0181598i | −0.353910 | − | 0.00198139i | ||||
\(85\) | 1.86797 | − | 1.86797i | 0.202610 | − | 0.202610i | ||||
\(86\) | −2.72067 | + | 2.72067i | −0.293377 | + | 0.293377i | ||||
\(87\) | − | 8.61230i | − | 0.923335i | ||||||
\(88\) | 8.04945i | 0.858074i | ||||||||
\(89\) | −3.39552 | − | 3.39552i | −0.359924 | − | 0.359924i | 0.503861 | − | 0.863785i | \(-0.331912\pi\) |
−0.863785 | + | 0.503861i | \(0.831912\pi\) | |||||||
\(90\) | −2.27378 | −0.239678 | ||||||||
\(91\) | −0.329233 | + | 9.53371i | −0.0345130 | + | 0.999404i | ||||
\(92\) | −3.51026 | −0.365970 | ||||||||
\(93\) | −15.4010 | − | 15.4010i | −1.59701 | − | 1.59701i | ||||
\(94\) | − | 8.91692i | − | 0.919710i | ||||||
\(95\) | 0.127826i | 0.0131147i | ||||||||
\(96\) | 4.75609 | − | 4.75609i | 0.485416 | − | 0.485416i | ||||
\(97\) | −4.44330 | + | 4.44330i | −0.451149 | + | 0.451149i | −0.895736 | − | 0.444587i | \(-0.853351\pi\) |
0.444587 | + | 0.895736i | \(0.353351\pi\) | |||||||
\(98\) | 5.91510 | + | 6.04907i | 0.597516 | + | 0.611049i | ||||
\(99\) | 4.02472 | − | 4.02472i | 0.404500 | − | 0.404500i | ||||
\(100\) | 2.29072 | 0.229072 | ||||||||
\(101\) | −1.16022 | −0.115446 | −0.0577231 | − | 0.998333i | \(-0.518384\pi\) | ||||
−0.0577231 | + | 0.998333i | \(0.518384\pi\) | |||||||
\(102\) | −5.92162 | + | 5.92162i | −0.586328 | + | 0.586328i | ||||
\(103\) | 5.32104 | 0.524298 | 0.262149 | − | 0.965027i | \(-0.415569\pi\) | ||||
0.262149 | + | 0.965027i | \(0.415569\pi\) | |||||||
\(104\) | −7.59483 | − | 8.04735i | −0.744734 | − | 0.789107i | ||||
\(105\) | −3.66701 | − | 3.70831i | −0.357864 | − | 0.361894i | ||||
\(106\) | 2.93302 | + | 2.93302i | 0.284880 | + | 0.284880i | ||||
\(107\) | 10.2485 | 0.990756 | 0.495378 | − | 0.868677i | \(-0.335029\pi\) | ||||
0.495378 | + | 0.868677i | \(0.335029\pi\) | |||||||
\(108\) | 1.01747 | 0.0979063 | ||||||||
\(109\) | −5.85464 | − | 5.85464i | −0.560773 | − | 0.560773i | 0.368754 | − | 0.929527i | \(-0.379784\pi\) |
−0.929527 | + | 0.368754i | \(0.879784\pi\) | |||||||
\(110\) | −1.94326 | + | 1.94326i | −0.185283 | + | 0.185283i | ||||
\(111\) | −4.60378 | − | 4.60378i | −0.436972 | − | 0.436972i | ||||
\(112\) | −6.96059 | − | 0.0389695i | −0.657714 | − | 0.00368227i | ||||
\(113\) | 5.74539 | 0.540481 | 0.270241 | − | 0.962793i | \(-0.412897\pi\) | ||||
0.270241 | + | 0.962793i | \(0.412897\pi\) | |||||||
\(114\) | − | 0.405220i | − | 0.0379523i | ||||||
\(115\) | −3.99078 | − | 3.99078i | −0.372142 | − | 0.372142i | ||||
\(116\) | 2.04226i | 0.189619i | ||||||||
\(117\) | −0.226259 | + | 7.82109i | −0.0209177 | + | 0.723060i | ||||
\(118\) | 15.6422i | 1.43998i | ||||||||
\(119\) | −8.06217 | − | 0.0451368i | −0.739058 | − | 0.00413768i | ||||
\(120\) | 6.04945 | 0.552237 | ||||||||
\(121\) | 4.12064i | 0.374603i | ||||||||
\(122\) | −7.86913 | + | 7.86913i | −0.712438 | + | 0.712438i | ||||
\(123\) | 5.17009 | + | 5.17009i | 0.466171 | + | 0.466171i | ||||
\(124\) | 3.65209 | + | 3.65209i | 0.327967 | + | 0.327967i | ||||
\(125\) | 5.66930 | + | 5.66930i | 0.507078 | + | 0.507078i | ||||
\(126\) | 4.87936 | + | 4.93430i | 0.434688 | + | 0.439583i | ||||
\(127\) | 7.37629i | 0.654540i | 0.944931 | + | 0.327270i | \(0.106129\pi\) | ||||
−0.944931 | + | 0.327270i | \(0.893871\pi\) | |||||||
\(128\) | 3.36910 | − | 3.36910i | 0.297789 | − | 0.297789i | ||||
\(129\) | −7.23840 | −0.637305 | ||||||||
\(130\) | 0.109245 | − | 3.77626i | 0.00958142 | − | 0.331200i | ||||
\(131\) | 11.9642i | 1.04532i | 0.852543 | + | 0.522658i | \(0.175059\pi\) | ||||
−0.852543 | + | 0.522658i | \(0.824941\pi\) | |||||||
\(132\) | −2.27378 | + | 2.27378i | −0.197907 | + | 0.197907i | ||||
\(133\) | 0.277394 | − | 0.274305i | 0.0240531 | − | 0.0237853i | ||||
\(134\) | − | 1.79380i | − | 0.154960i | ||||||
\(135\) | 1.15676 | + | 1.15676i | 0.0995577 | + | 0.0995577i | ||||
\(136\) | 6.61282 | − | 6.61282i | 0.567045 | − | 0.567045i | ||||
\(137\) | 1.88357 | − | 1.88357i | 0.160924 | − | 0.160924i | −0.622052 | − | 0.782976i | \(-0.713701\pi\) |
0.782976 | + | 0.622052i | \(0.213701\pi\) | |||||||
\(138\) | 12.6511 | + | 12.6511i | 1.07694 | + | 1.07694i | ||||
\(139\) | − | 6.36883i | − | 0.540197i | −0.962833 | − | 0.270098i | \(-0.912944\pi\) | ||
0.962833 | − | 0.270098i | \(-0.0870563\pi\) | |||||||
\(140\) | 0.869570 | + | 0.879362i | 0.0734921 | + | 0.0743196i | ||||
\(141\) | 11.8618 | − | 11.8618i | 0.998946 | − | 0.998946i | ||||
\(142\) | − | 7.01333i | − | 0.588546i | ||||||
\(143\) | 6.49082 | + | 6.87756i | 0.542790 | + | 0.575131i | ||||
\(144\) | −5.70928 | −0.475773 | ||||||||
\(145\) | −2.32183 | + | 2.32183i | −0.192817 | + | 0.192817i | ||||
\(146\) | − | 11.8378i | − | 0.979701i | ||||||
\(147\) | −0.178214 | + | 15.9155i | −0.0146988 | + | 1.31269i | ||||
\(148\) | 1.09171 | + | 1.09171i | 0.0897379 | + | 0.0897379i | ||||
\(149\) | 13.3360 | + | 13.3360i | 1.09253 | + | 1.09253i | 0.995258 | + | 0.0972667i | \(0.0310100\pi\) |
0.0972667 | + | 0.995258i | \(0.468990\pi\) | |||||||
\(150\) | −8.25587 | − | 8.25587i | −0.674089 | − | 0.674089i | ||||
\(151\) | 7.64229 | − | 7.64229i | 0.621921 | − | 0.621921i | −0.324102 | − | 0.946022i | \(-0.605062\pi\) |
0.946022 | + | 0.324102i | \(0.105062\pi\) | |||||||
\(152\) | 0.452519i | 0.0367041i | ||||||||
\(153\) | −6.61282 | −0.534615 | ||||||||
\(154\) | 8.38713 | + | 0.0469561i | 0.675854 | + | 0.00378383i | ||||
\(155\) | 8.30406i | 0.666998i | ||||||||
\(156\) | 0.127826 | − | 4.41855i | 0.0102343 | − | 0.353767i | ||||
\(157\) | − | 21.0290i | − | 1.67830i | −0.543903 | − | 0.839148i | \(-0.683054\pi\) | ||
0.543903 | − | 0.839148i | \(-0.316946\pi\) | |||||||
\(158\) | 15.0381 | + | 15.0381i | 1.19636 | + | 1.19636i | ||||
\(159\) | 7.80335i | 0.618846i | ||||||||
\(160\) | −2.56443 | −0.202736 | ||||||||
\(161\) | −0.0964315 | + | 17.2243i | −0.00759987 | + | 1.35746i | ||||
\(162\) | −9.23093 | − | 9.23093i | −0.725250 | − | 0.725250i | ||||
\(163\) | −7.03612 | + | 7.03612i | −0.551111 | + | 0.551111i | −0.926762 | − | 0.375650i | \(-0.877419\pi\) |
0.375650 | + | 0.926762i | \(0.377419\pi\) | |||||||
\(164\) | −1.22600 | − | 1.22600i | −0.0957344 | − | 0.0957344i | ||||
\(165\) | −5.17009 | −0.402491 | ||||||||
\(166\) | 18.0284 | 1.39927 | ||||||||
\(167\) | −12.0684 | − | 12.0684i | −0.933884 | − | 0.933884i | 0.0640620 | − | 0.997946i | \(-0.479594\pi\) |
−0.997946 | + | 0.0640620i | \(0.979594\pi\) | |||||||
\(168\) | −12.9816 | − | 13.1278i | −1.00156 | − | 1.01283i | ||||
\(169\) | −12.9783 | − | 0.751536i | −0.998328 | − | 0.0578104i | ||||
\(170\) | 3.19287 | 0.244882 | ||||||||
\(171\) | 0.226259 | − | 0.226259i | 0.0173025 | − | 0.0173025i | ||||
\(172\) | 1.71646 | 0.130879 | ||||||||
\(173\) | 7.48239 | 0.568876 | 0.284438 | − | 0.958694i | \(-0.408193\pi\) | ||||
0.284438 | + | 0.958694i | \(0.408193\pi\) | |||||||
\(174\) | 7.36040 | − | 7.36040i | 0.557990 | − | 0.557990i | ||||
\(175\) | 0.0629292 | − | 11.2402i | 0.00475700 | − | 0.849680i | ||||
\(176\) | −4.87936 | + | 4.87936i | −0.367796 | + | 0.367796i | ||||
\(177\) | −20.8082 | + | 20.8082i | −1.56404 | + | 1.56404i | ||||
\(178\) | − | 5.80387i | − | 0.435019i | ||||||
\(179\) | − | 22.7009i | − | 1.69674i | −0.529402 | − | 0.848371i | \(-0.677584\pi\) | ||
0.529402 | − | 0.848371i | \(-0.322416\pi\) | |||||||
\(180\) | 0.717262 | + | 0.717262i | 0.0534615 | + | 0.0534615i | ||||
\(181\) | 1.91735 | 0.142516 | 0.0712579 | − | 0.997458i | \(-0.477299\pi\) | ||||
0.0712579 | + | 0.997458i | \(0.477299\pi\) | |||||||
\(182\) | −8.42924 | + | 7.86649i | −0.624817 | + | 0.583103i | ||||
\(183\) | −20.9360 | −1.54763 | ||||||||
\(184\) | −14.1278 | − | 14.1278i | −1.04152 | − | 1.04152i | ||||
\(185\) | 2.48231i | 0.182503i | ||||||||
\(186\) | − | 26.3246i | − | 1.93021i | ||||||
\(187\) | −5.65157 | + | 5.65157i | −0.413283 | + | 0.413283i | ||||
\(188\) | −2.81283 | + | 2.81283i | −0.205147 | + | 0.205147i | ||||
\(189\) | 0.0279513 | − | 4.99257i | 0.00203316 | − | 0.363156i | ||||
\(190\) | −0.109245 | + | 0.109245i | −0.00792546 | + | 0.00792546i | ||||
\(191\) | −10.0072 | −0.724095 | −0.362047 | − | 0.932160i | \(-0.617922\pi\) | ||||
−0.362047 | + | 0.932160i | \(0.617922\pi\) | |||||||
\(192\) | 20.0936 | 1.45013 | ||||||||
\(193\) | −10.2351 | + | 10.2351i | −0.736741 | + | 0.736741i | −0.971946 | − | 0.235205i | \(-0.924424\pi\) |
0.235205 | + | 0.971946i | \(0.424424\pi\) | |||||||
\(194\) | −7.59483 | −0.545277 | ||||||||
\(195\) | 5.16874 | − | 4.87809i | 0.370141 | − | 0.349327i | ||||
\(196\) | 0.0422604 | − | 3.77409i | 0.00301860 | − | 0.269578i | ||||
\(197\) | 15.2690 | + | 15.2690i | 1.08787 | + | 1.08787i | 0.995748 | + | 0.0921223i | \(0.0293651\pi\) |
0.0921223 | + | 0.995748i | \(0.470635\pi\) | |||||||
\(198\) | 6.87936 | 0.488895 | ||||||||
\(199\) | −22.4635 | −1.59240 | −0.796198 | − | 0.605036i | \(-0.793159\pi\) | ||||
−0.796198 | + | 0.605036i | \(0.793159\pi\) | |||||||
\(200\) | 9.21953 | + | 9.21953i | 0.651920 | + | 0.651920i | ||||
\(201\) | 2.38622 | − | 2.38622i | 0.168311 | − | 0.168311i | ||||
\(202\) | −0.991567 | − | 0.991567i | −0.0697664 | − | 0.0697664i | ||||
\(203\) | 10.0210 | + | 0.0561036i | 0.703339 | + | 0.00393770i | ||||
\(204\) | 3.73594 | 0.261568 | ||||||||
\(205\) | − | 2.78765i | − | 0.194698i | ||||||
\(206\) | 4.54756 | + | 4.54756i | 0.316844 | + | 0.316844i | ||||
\(207\) | 14.1278i | 0.981952i | ||||||||
\(208\) | 0.274305 | − | 9.48187i | 0.0190196 | − | 0.657449i | ||||
\(209\) | − | 0.386740i | − | 0.0267513i | ||||||
\(210\) | 0.0352892 | − | 6.30323i | 0.00243518 | − | 0.434964i | ||||
\(211\) | −18.8504 | −1.29772 | −0.648859 | − | 0.760909i | \(-0.724753\pi\) | ||||
−0.648859 | + | 0.760909i | \(0.724753\pi\) | |||||||
\(212\) | − | 1.85043i | − | 0.127088i | ||||||
\(213\) | 9.32956 | − | 9.32956i | 0.639251 | − | 0.639251i | ||||
\(214\) | 8.75872 | + | 8.75872i | 0.598734 | + | 0.598734i | ||||
\(215\) | 1.95143 | + | 1.95143i | 0.133087 | + | 0.133087i | ||||
\(216\) | 4.09505 | + | 4.09505i | 0.278633 | + | 0.278633i | ||||
\(217\) | 18.0205 | − | 17.8199i | 1.22331 | − | 1.20969i | ||||
\(218\) | − | 10.0072i | − | 0.677772i | ||||||
\(219\) | 15.7473 | − | 15.7473i | 1.06411 | − | 1.06411i | ||||
\(220\) | 1.22600 | 0.0826568 | ||||||||
\(221\) | 0.317716 | − | 10.9825i | 0.0213719 | − | 0.738760i | ||||
\(222\) | − | 7.86913i | − | 0.528142i | ||||||
\(223\) | −4.32131 | + | 4.32131i | −0.289376 | + | 0.289376i | −0.836833 | − | 0.547457i | \(-0.815596\pi\) |
0.547457 | + | 0.836833i | \(0.315596\pi\) | |||||||
\(224\) | 5.50307 | + | 5.56504i | 0.367689 | + | 0.371830i | ||||
\(225\) | − | 9.21953i | − | 0.614636i | ||||||
\(226\) | 4.91023 | + | 4.91023i | 0.326624 | + | 0.326624i | ||||
\(227\) | 4.69031 | − | 4.69031i | 0.311307 | − | 0.311307i | −0.534109 | − | 0.845416i | \(-0.679353\pi\) |
0.845416 | + | 0.534109i | \(0.179353\pi\) | |||||||
\(228\) | −0.127826 | + | 0.127826i | −0.00846549 | + | 0.00846549i | ||||
\(229\) | 0.264743 | + | 0.264743i | 0.0174947 | + | 0.0174947i | 0.715800 | − | 0.698305i | \(-0.246062\pi\) |
−0.698305 | + | 0.715800i | \(0.746062\pi\) | |||||||
\(230\) | − | 6.82135i | − | 0.449786i | ||||||
\(231\) | 11.0946 | + | 11.2195i | 0.729972 | + | 0.738191i | ||||
\(232\) | −8.21953 | + | 8.21953i | −0.539639 | + | 0.539639i | ||||
\(233\) | − | 6.16290i | − | 0.403745i | −0.979412 | − | 0.201872i | \(-0.935297\pi\) | ||
0.979412 | − | 0.201872i | \(-0.0647026\pi\) | |||||||
\(234\) | −6.87756 | + | 6.49082i | −0.449600 | + | 0.424319i | ||||
\(235\) | −6.39576 | −0.417214 | ||||||||
\(236\) | 4.93430 | − | 4.93430i | 0.321196 | − | 0.321196i | ||||
\(237\) | 40.0091i | 2.59887i | ||||||||
\(238\) | −6.85166 | − | 6.92881i | −0.444127 | − | 0.449128i | ||||
\(239\) | −5.63090 | − | 5.63090i | −0.364232 | − | 0.364232i | 0.501136 | − | 0.865369i | \(-0.332916\pi\) |
−0.865369 | + | 0.501136i | \(0.832916\pi\) | |||||||
\(240\) | 3.66701 | + | 3.66701i | 0.236705 | + | 0.236705i | ||||
\(241\) | −1.11217 | − | 1.11217i | −0.0716414 | − | 0.0716414i | 0.670378 | − | 0.742020i | \(-0.266132\pi\) |
−0.742020 | + | 0.670378i | \(0.766132\pi\) | |||||||
\(242\) | −3.52165 | + | 3.52165i | −0.226380 | + | 0.226380i | ||||
\(243\) | − | 18.8980i | − | 1.21230i | ||||||
\(244\) | 4.96462 | 0.317827 | ||||||||
\(245\) | 4.33877 | − | 4.24268i | 0.277194 | − | 0.271055i | ||||
\(246\) | 8.83710i | 0.563433i | ||||||||
\(247\) | 0.364897 | + | 0.386639i | 0.0232178 | + | 0.0246012i | ||||
\(248\) | 29.3973i | 1.86673i | ||||||||
\(249\) | 23.9825 | + | 23.9825i | 1.51983 | + | 1.51983i | ||||
\(250\) | 9.69040i | 0.612874i | ||||||||
\(251\) | −12.1069 | −0.764182 | −0.382091 | − | 0.924125i | \(-0.624796\pi\) | ||||
−0.382091 | + | 0.924125i | \(0.624796\pi\) | |||||||
\(252\) | 0.0173316 | − | 3.09571i | 0.00109179 | − | 0.195011i | ||||
\(253\) | 12.0742 | + | 12.0742i | 0.759097 | + | 0.759097i | ||||
\(254\) | −6.30406 | + | 6.30406i | −0.395552 | + | 0.395552i | ||||
\(255\) | 4.24735 | + | 4.24735i | 0.265980 | + | 0.265980i | ||||
\(256\) | −11.9155 | −0.744717 | ||||||||
\(257\) | −17.5759 | −1.09635 | −0.548176 | − | 0.836363i | \(-0.684678\pi\) | ||||
−0.548176 | + | 0.836363i | \(0.684678\pi\) | |||||||
\(258\) | −6.18621 | − | 6.18621i | −0.385137 | − | 0.385137i | ||||
\(259\) | 5.38682 | − | 5.32684i | 0.334721 | − | 0.330994i | ||||
\(260\) | −1.22568 | + | 1.15676i | −0.0760133 | + | 0.0717389i | ||||
\(261\) | 8.21953 | 0.508776 | ||||||||
\(262\) | −10.2250 | + | 10.2250i | −0.631705 | + | 0.631705i | ||||
\(263\) | −14.5259 | −0.895703 | −0.447851 | − | 0.894108i | \(-0.647811\pi\) | ||||
−0.447851 | + | 0.894108i | \(0.647811\pi\) | |||||||
\(264\) | −18.3027 | −1.12645 | ||||||||
\(265\) | 2.10374 | − | 2.10374i | 0.129232 | − | 0.129232i | ||||
\(266\) | 0.471502 | + | 0.00263975i | 0.0289097 | + | 0.000161853i | ||||
\(267\) | 7.72067 | − | 7.72067i | 0.472497 | − | 0.472497i | ||||
\(268\) | −0.565851 | + | 0.565851i | −0.0345648 | + | 0.0345648i | ||||
\(269\) | 23.4152i | 1.42765i | 0.700324 | + | 0.713825i | \(0.253039\pi\) | ||||
−0.700324 | + | 0.713825i | \(0.746961\pi\) | |||||||
\(270\) | 1.97721i | 0.120329i | ||||||||
\(271\) | −2.41653 | − | 2.41653i | −0.146794 | − | 0.146794i | 0.629890 | − | 0.776684i | \(-0.283100\pi\) |
−0.776684 | + | 0.629890i | \(0.783100\pi\) | |||||||
\(272\) | 8.01703 | 0.486104 | ||||||||
\(273\) | −21.6776 | − | 0.748605i | −1.31199 | − | 0.0453076i | ||||
\(274\) | 3.21953 | 0.194499 | ||||||||
\(275\) | −7.87936 | − | 7.87936i | −0.475143 | − | 0.475143i | ||||
\(276\) | − | 7.98157i | − | 0.480434i | ||||||
\(277\) | − | 29.0722i | − | 1.74678i | −0.487020 | − | 0.873391i | \(-0.661916\pi\) | ||
0.487020 | − | 0.873391i | \(-0.338084\pi\) | |||||||
\(278\) | 5.44304 | − | 5.44304i | 0.326452 | − | 0.326452i | ||||
\(279\) | 14.6987 | − | 14.6987i | 0.879985 | − | 0.879985i | ||||
\(280\) | −0.0394083 | + | 7.03897i | −0.00235509 | + | 0.420659i | ||||
\(281\) | 9.68455 | − | 9.68455i | 0.577732 | − | 0.577732i | −0.356546 | − | 0.934278i | \(-0.616046\pi\) |
0.934278 | + | 0.356546i | \(0.116046\pi\) | |||||||
\(282\) | 20.2751 | 1.20737 | ||||||||
\(283\) | 4.30357 | 0.255821 | 0.127910 | − | 0.991786i | \(-0.459173\pi\) | ||||
0.127910 | + | 0.991786i | \(0.459173\pi\) | |||||||
\(284\) | −2.21235 | + | 2.21235i | −0.131279 | + | 0.131279i | ||||
\(285\) | −0.290649 | −0.0172165 | ||||||||
\(286\) | −0.330522 | + | 11.4251i | −0.0195442 | + | 0.675582i | ||||
\(287\) | −6.04945 | + | 5.98209i | −0.357088 | + | 0.353112i | ||||
\(288\) | 4.53919 | + | 4.53919i | 0.267474 | + | 0.267474i | ||||
\(289\) | −7.71420 | −0.453776 | ||||||||
\(290\) | −3.96864 | −0.233047 | ||||||||
\(291\) | −10.1031 | − | 10.1031i | −0.592254 | − | 0.592254i | ||||
\(292\) | −3.73421 | + | 3.73421i | −0.218528 | + | 0.218528i | ||||
\(293\) | −3.57373 | − | 3.57373i | −0.208780 | − | 0.208780i | 0.594969 | − | 0.803749i | \(-0.297164\pi\) |
−0.803749 | + | 0.594969i | \(0.797164\pi\) | |||||||
\(294\) | −13.7543 | + | 13.4497i | −0.802166 | + | 0.784400i | ||||
\(295\) | 11.2195 | 0.653227 | ||||||||
\(296\) | 8.78765i | 0.510772i | ||||||||
\(297\) | −3.49978 | − | 3.49978i | −0.203078 | − | 0.203078i | ||||
\(298\) | 22.7948i | 1.32047i | ||||||||
\(299\) | −23.4633 | − | 0.678778i | −1.35692 | − | 0.0392548i | ||||
\(300\) | 5.20861i | 0.300719i | ||||||||
\(301\) | 0.0471535 | − | 8.42240i | 0.00271788 | − | 0.485459i | ||||
\(302\) | 13.0628 | 0.751678 | ||||||||
\(303\) | − | 2.63809i | − | 0.151554i | ||||||
\(304\) | −0.274305 | + | 0.274305i | −0.0157325 | + | 0.0157325i | ||||
\(305\) | 5.64423 | + | 5.64423i | 0.323188 | + | 0.323188i | ||||
\(306\) | −5.65157 | − | 5.65157i | −0.323079 | − | 0.323079i | ||||
\(307\) | 8.59457 | + | 8.59457i | 0.490518 | + | 0.490518i | 0.908469 | − | 0.417952i | \(-0.137252\pi\) |
−0.417952 | + | 0.908469i | \(0.637252\pi\) | |||||||
\(308\) | −2.63090 | − | 2.66052i | −0.149909 | − | 0.151597i | ||||
\(309\) | 12.0989i | 0.688282i | ||||||||
\(310\) | −7.09696 | + | 7.09696i | −0.403080 | + | 0.403080i | ||||
\(311\) | 22.5405 | 1.27815 | 0.639077 | − | 0.769143i | \(-0.279317\pi\) | ||||
0.639077 | + | 0.769143i | \(0.279317\pi\) | |||||||
\(312\) | 18.2979 | − | 17.2690i | 1.03592 | − | 0.977664i | ||||
\(313\) | 4.30873i | 0.243544i | 0.992558 | + | 0.121772i | \(0.0388576\pi\) | ||||
−0.992558 | + | 0.121772i | \(0.961142\pi\) | |||||||
\(314\) | 17.9722 | − | 17.9722i | 1.01423 | − | 1.01423i | ||||
\(315\) | 3.53919 | − | 3.49978i | 0.199411 | − | 0.197190i | ||||
\(316\) | − | 9.48747i | − | 0.533712i | ||||||
\(317\) | 3.97107 | + | 3.97107i | 0.223038 | + | 0.223038i | 0.809776 | − | 0.586739i | \(-0.199588\pi\) |
−0.586739 | + | 0.809776i | \(0.699588\pi\) | |||||||
\(318\) | −6.66904 | + | 6.66904i | −0.373981 | + | 0.373981i | ||||
\(319\) | 7.02472 | − | 7.02472i | 0.393309 | − | 0.393309i | ||||
\(320\) | −5.41714 | − | 5.41714i | −0.302827 | − | 0.302827i | ||||
\(321\) | 23.3028i | 1.30063i | ||||||||
\(322\) | −14.8029 | + | 14.6381i | −0.824934 | + | 0.815749i | ||||
\(323\) | −0.317716 | + | 0.317716i | −0.0176782 | + | 0.0176782i | ||||
\(324\) | 5.82377i | 0.323543i | ||||||||
\(325\) | 15.3116 | + | 0.442957i | 0.849338 | + | 0.0245708i | ||||
\(326\) | −12.0267 | −0.666095 | ||||||||
\(327\) | 13.3122 | − | 13.3122i | 0.736165 | − | 0.736165i | ||||
\(328\) | − | 9.86861i | − | 0.544903i | ||||||
\(329\) | 13.7248 | + | 13.8794i | 0.756674 | + | 0.765194i | ||||
\(330\) | −4.41855 | − | 4.41855i | −0.243233 | − | 0.243233i | ||||
\(331\) | 1.70928 | + | 1.70928i | 0.0939503 | + | 0.0939503i | 0.752520 | − | 0.658570i | \(-0.228838\pi\) |
−0.658570 | + | 0.752520i | \(0.728838\pi\) | |||||||
\(332\) | −5.68703 | − | 5.68703i | −0.312117 | − | 0.312117i | ||||
\(333\) | 4.39383 | − | 4.39383i | 0.240780 | − | 0.240780i | ||||
\(334\) | − | 20.6283i | − | 1.12873i | ||||||
\(335\) | −1.28662 | −0.0702957 | ||||||||
\(336\) | 0.0886081 | − | 15.8269i | 0.00483397 | − | 0.863427i | ||||
\(337\) | − | 23.1327i | − | 1.26012i | −0.776546 | − | 0.630061i | \(-0.783030\pi\) | ||
0.776546 | − | 0.630061i | \(-0.216970\pi\) | |||||||
\(338\) | −10.4494 | − | 11.7340i | −0.568373 | − | 0.638245i | ||||
\(339\) | 13.0638i | 0.709527i | ||||||||
\(340\) | −1.00719 | − | 1.00719i | −0.0546224 | − | 0.0546224i | ||||
\(341\) | − | 25.1240i | − | 1.36054i | ||||||
\(342\) | 0.386740 | 0.0209125 | ||||||||
\(343\) | −18.5176 | − | 0.311044i | −0.999859 | − | 0.0167948i | ||||
\(344\) | 6.90829 | + | 6.90829i | 0.372470 | + | 0.372470i | ||||
\(345\) | 9.07417 | − | 9.07417i | 0.488537 | − | 0.488537i | ||||
\(346\) | 6.39473 | + | 6.39473i | 0.343783 | + | 0.343783i | ||||
\(347\) | −8.60424 | −0.461900 | −0.230950 | − | 0.972966i | \(-0.574183\pi\) | ||||
−0.230950 | + | 0.972966i | \(0.574183\pi\) | |||||||
\(348\) | −4.64366 | −0.248926 | ||||||||
\(349\) | 19.0680 | + | 19.0680i | 1.02069 | + | 1.02069i | 0.999781 | + | 0.0209053i | \(0.00665484\pi\) |
0.0209053 | + | 0.999781i | \(0.493345\pi\) | |||||||
\(350\) | 9.66008 | − | 9.55252i | 0.516353 | − | 0.510604i | ||||
\(351\) | 6.80098 | + | 0.196748i | 0.363010 | + | 0.0105017i | ||||
\(352\) | 7.75872 | 0.413541 | ||||||||
\(353\) | 4.81231 | − | 4.81231i | 0.256133 | − | 0.256133i | −0.567346 | − | 0.823479i | \(-0.692030\pi\) |
0.823479 | + | 0.567346i | \(0.192030\pi\) | |||||||
\(354\) | −35.5669 | −1.89036 | ||||||||
\(355\) | −5.03040 | −0.266986 | ||||||||
\(356\) | −1.83083 | + | 1.83083i | −0.0970336 | + | 0.0970336i | ||||
\(357\) | 0.102631 | − | 18.3316i | 0.00543182 | − | 0.970212i | ||||
\(358\) | 19.4010 | − | 19.4010i | 1.02538 | − | 1.02538i | ||||
\(359\) | −12.5506 | + | 12.5506i | −0.662394 | + | 0.662394i | −0.955944 | − | 0.293549i | \(-0.905163\pi\) |
0.293549 | + | 0.955944i | \(0.405163\pi\) | |||||||
\(360\) | 5.77356i | 0.304293i | ||||||||
\(361\) | 18.9783i | 0.998856i | ||||||||
\(362\) | 1.63864 | + | 1.63864i | 0.0861252 | + | 0.0861252i | ||||
\(363\) | −9.36943 | −0.491768 | ||||||||
\(364\) | 5.14047 | + | 0.177519i | 0.269434 | + | 0.00930452i | ||||
\(365\) | −8.49079 | −0.444428 | ||||||||
\(366\) | −17.8927 | − | 17.8927i | −0.935266 | − | 0.935266i | ||||
\(367\) | 22.8806i | 1.19436i | 0.802109 | + | 0.597178i | \(0.203711\pi\) | ||||
−0.802109 | + | 0.597178i | \(0.796289\pi\) | |||||||
\(368\) | − | 17.1278i | − | 0.892850i | ||||||
\(369\) | −4.93430 | + | 4.93430i | −0.256870 | + | 0.256870i | ||||
\(370\) | −2.12147 | + | 2.12147i | −0.110290 | + | 0.110290i | ||||
\(371\) | −9.07976 | − | 0.0508338i | −0.471398 | − | 0.00263916i | ||||
\(372\) | −8.30406 | + | 8.30406i | −0.430545 | + | 0.430545i | ||||
\(373\) | 10.5041 | 0.543883 | 0.271941 | − | 0.962314i | \(-0.412334\pi\) | ||||
0.271941 | + | 0.962314i | \(0.412334\pi\) | |||||||
\(374\) | −9.66008 | −0.499511 | ||||||||
\(375\) | −12.8908 | + | 12.8908i | −0.665676 | + | 0.665676i | ||||
\(376\) | −22.6417 | −1.16766 | ||||||||
\(377\) | −0.394912 | + | 13.6509i | −0.0203390 | + | 0.703055i | ||||
\(378\) | 4.29072 | − | 4.24295i | 0.220691 | − | 0.218234i | ||||
\(379\) | 3.64229 | + | 3.64229i | 0.187092 | + | 0.187092i | 0.794438 | − | 0.607346i | \(-0.207766\pi\) |
−0.607346 | + | 0.794438i | \(0.707766\pi\) | |||||||
\(380\) | 0.0689224 | 0.00353564 | ||||||||
\(381\) | −16.7721 | −0.859260 | ||||||||
\(382\) | −8.55252 | − | 8.55252i | −0.437585 | − | 0.437585i | ||||
\(383\) | 24.5591 | − | 24.5591i | 1.25491 | − | 1.25491i | 0.301419 | − | 0.953492i | \(-0.402540\pi\) |
0.953492 | − | 0.301419i | \(-0.0974603\pi\) | |||||||
\(384\) | 7.66061 | + | 7.66061i | 0.390929 | + | 0.390929i | ||||
\(385\) | 0.0336798 | − | 6.01577i | 0.00171648 | − | 0.306592i | ||||
\(386\) | −17.4947 | −0.890455 | ||||||||
\(387\) | − | 6.90829i | − | 0.351168i | ||||||
\(388\) | 2.39578 | + | 2.39578i | 0.121627 | + | 0.121627i | ||||
\(389\) | 6.48974i | 0.329043i | 0.986374 | + | 0.164521i | \(0.0526080\pi\) | ||||
−0.986374 | + | 0.164521i | \(0.947392\pi\) | |||||||
\(390\) | 8.58639 | + | 0.248399i | 0.434789 | + | 0.0125782i | ||||
\(391\) | − | 19.8385i | − | 1.00327i | ||||||
\(392\) | 15.3597 | − | 15.0196i | 0.775784 | − | 0.758603i | ||||
\(393\) | −27.2039 | −1.37226 | ||||||||
\(394\) | 26.0989i | 1.31484i | ||||||||
\(395\) | 10.7862 | − | 10.7862i | 0.542714 | − | 0.542714i | ||||
\(396\) | −2.17009 | − | 2.17009i | −0.109051 | − | 0.109051i | ||||
\(397\) | 6.89530 | + | 6.89530i | 0.346065 | + | 0.346065i | 0.858642 | − | 0.512576i | \(-0.171309\pi\) |
−0.512576 | + | 0.858642i | \(0.671309\pi\) | |||||||
\(398\) | −19.1982 | − | 19.1982i | −0.962317 | − | 0.962317i | ||||
\(399\) | 0.623710 | + | 0.630733i | 0.0312245 | + | 0.0315761i | ||||
\(400\) | 11.1773i | 0.558864i | ||||||||
\(401\) | 9.02279 | − | 9.02279i | 0.450576 | − | 0.450576i | −0.444969 | − | 0.895546i | \(-0.646785\pi\) |
0.895546 | + | 0.444969i | \(0.146785\pi\) | |||||||
\(402\) | 4.07870 | 0.203427 | ||||||||
\(403\) | 23.7051 | + | 25.1175i | 1.18083 | + | 1.25119i | ||||
\(404\) | 0.625577i | 0.0311236i | ||||||||
\(405\) | −6.62099 | + | 6.62099i | −0.329000 | + | 0.329000i | ||||
\(406\) | 8.51640 | + | 8.61230i | 0.422662 | + | 0.427421i | ||||
\(407\) | − | 7.51026i | − | 0.372270i | ||||||
\(408\) | 15.0361 | + | 15.0361i | 0.744399 | + | 0.744399i | ||||
\(409\) | −2.86088 | + | 2.86088i | −0.141461 | + | 0.141461i | −0.774291 | − | 0.632830i | \(-0.781893\pi\) |
0.632830 | + | 0.774291i | \(0.281893\pi\) | |||||||
\(410\) | 2.38243 | − | 2.38243i | 0.117660 | − | 0.117660i | ||||
\(411\) | 4.28282 | + | 4.28282i | 0.211256 | + | 0.211256i | ||||
\(412\) | − | 2.86905i | − | 0.141348i | ||||||
\(413\) | −24.0763 | − | 24.3474i | −1.18472 | − | 1.19806i | ||||
\(414\) | −12.0742 | + | 12.0742i | −0.593413 | + | 0.593413i | ||||
\(415\) | − | 12.9311i | − | 0.634762i | ||||||
\(416\) | −7.75670 | + | 7.32052i | −0.380303 | + | 0.358918i | ||||
\(417\) | 14.4813 | 0.709154 | ||||||||
\(418\) | 0.330522 | − | 0.330522i | 0.0161664 | − | 0.0161664i | ||||
\(419\) | − | 35.4097i | − | 1.72988i | −0.501878 | − | 0.864939i | \(-0.667357\pi\) | ||
0.501878 | − | 0.864939i | \(-0.332643\pi\) | |||||||
\(420\) | −1.99948 | + | 1.97721i | −0.0975645 | + | 0.0964781i | ||||
\(421\) | 18.9307 | + | 18.9307i | 0.922628 | + | 0.922628i | 0.997215 | − | 0.0745864i | \(-0.0237636\pi\) |
−0.0745864 | + | 0.997215i | \(0.523764\pi\) | |||||||
\(422\) | −16.1103 | − | 16.1103i | −0.784237 | − | 0.784237i | ||||
\(423\) | 11.3209 | + | 11.3209i | 0.550439 | + | 0.550439i | ||||
\(424\) | 7.44748 | − | 7.44748i | 0.361682 | − | 0.361682i | ||||
\(425\) | 12.9462i | 0.627982i | ||||||||
\(426\) | 15.9468 | 0.772624 | ||||||||
\(427\) | 0.136385 | − | 24.3605i | 0.00660011 | − | 1.17889i | ||||
\(428\) | − | 5.52586i | − | 0.267102i | ||||||
\(429\) | −15.6381 | + | 14.7587i | −0.755014 | + | 0.712558i | ||||
\(430\) | 3.33553i | 0.160854i | ||||||||
\(431\) | 12.6042 | + | 12.6042i | 0.607125 | + | 0.607125i | 0.942194 | − | 0.335069i | \(-0.108760\pi\) |
−0.335069 | + | 0.942194i | \(0.608760\pi\) | |||||||
\(432\) | 4.96462i | 0.238860i | ||||||||
\(433\) | −14.3392 | −0.689098 | −0.344549 | − | 0.938768i | \(-0.611968\pi\) | ||||
−0.344549 | + | 0.938768i | \(0.611968\pi\) | |||||||
\(434\) | 30.6305 | + | 0.171488i | 1.47031 | + | 0.00823167i | ||||
\(435\) | −5.27933 | − | 5.27933i | −0.253125 | − | 0.253125i | ||||
\(436\) | −3.15676 | + | 3.15676i | −0.151181 | + | 0.151181i | ||||
\(437\) | 0.678778 | + | 0.678778i | 0.0324704 | + | 0.0324704i | ||||
\(438\) | 26.9165 | 1.28612 | ||||||||
\(439\) | 19.9812 | 0.953651 | 0.476826 | − | 0.878998i | \(-0.341787\pi\) | ||||
0.476826 | + | 0.878998i | \(0.341787\pi\) | |||||||
\(440\) | 4.93430 | + | 4.93430i | 0.235234 | + | 0.235234i | ||||
\(441\) | −15.1897 | − | 0.170086i | −0.723317 | − | 0.00809936i | ||||
\(442\) | 9.65756 | − | 9.11450i | 0.459363 | − | 0.433532i | ||||
\(443\) | −5.63809 | −0.267874 | −0.133937 | − | 0.990990i | \(-0.542762\pi\) | ||||
−0.133937 | + | 0.990990i | \(0.542762\pi\) | |||||||
\(444\) | −2.48231 | + | 2.48231i | −0.117805 | + | 0.117805i | ||||
\(445\) | −4.16290 | −0.197340 | ||||||||
\(446\) | −7.38630 | −0.349751 | ||||||||
\(447\) | −30.3231 | + | 30.3231i | −1.43423 | + | 1.43423i | ||||
\(448\) | −0.130897 | + | 23.3804i | −0.00618431 | + | 1.10462i | ||||
\(449\) | −12.9060 | + | 12.9060i | −0.609073 | + | 0.609073i | −0.942704 | − | 0.333631i | \(-0.891726\pi\) |
0.333631 | + | 0.942704i | \(0.391726\pi\) | |||||||
\(450\) | 7.87936 | − | 7.87936i | 0.371437 | − | 0.371437i | ||||
\(451\) | 8.43409i | 0.397146i | ||||||||
\(452\) | − | 3.09785i | − | 0.145711i | ||||||
\(453\) | 17.3769 | + | 17.3769i | 0.816438 | + | 0.816438i | ||||
\(454\) | 8.01703 | 0.376258 | ||||||||
\(455\) | 5.64234 | + | 6.04597i | 0.264517 | + | 0.283440i | ||||
\(456\) | −1.02893 | −0.0481840 | ||||||||
\(457\) | 6.96687 | + | 6.96687i | 0.325896 | + | 0.325896i | 0.851024 | − | 0.525127i | \(-0.175982\pi\) |
−0.525127 | + | 0.851024i | \(0.675982\pi\) | |||||||
\(458\) | 0.452519i | 0.0211448i | ||||||||
\(459\) | 5.75031i | 0.268402i | ||||||||
\(460\) | −2.15179 | + | 2.15179i | −0.100328 | + | 0.100328i | ||||
\(461\) | −7.20809 | + | 7.20809i | −0.335714 | + | 0.335714i | −0.854752 | − | 0.519037i | \(-0.826291\pi\) |
0.519037 | + | 0.854752i | \(0.326291\pi\) | |||||||
\(462\) | −0.106768 | + | 19.0705i | −0.00496729 | + | 0.887240i | ||||
\(463\) | −4.06084 | + | 4.06084i | −0.188723 | + | 0.188723i | −0.795144 | − | 0.606421i | \(-0.792605\pi\) |
0.606421 | + | 0.795144i | \(0.292605\pi\) | |||||||
\(464\) | −9.96493 | −0.462610 | ||||||||
\(465\) | −18.8816 | −0.875614 | ||||||||
\(466\) | 5.26705 | − | 5.26705i | 0.243991 | − | 0.243991i | ||||
\(467\) | 17.3673 | 0.803665 | 0.401832 | − | 0.915713i | \(-0.368373\pi\) | ||||
0.401832 | + | 0.915713i | \(0.368373\pi\) | |||||||
\(468\) | 4.21704 | + | 0.121997i | 0.194933 | + | 0.00563929i | ||||
\(469\) | 2.76099 | + | 2.79208i | 0.127491 | + | 0.128926i | ||||
\(470\) | −5.46606 | − | 5.46606i | −0.252131 | − | 0.252131i | ||||
\(471\) | 47.8154 | 2.20322 | ||||||||
\(472\) | 39.7184 | 1.82819 | ||||||||
\(473\) | −5.90409 | − | 5.90409i | −0.271470 | − | 0.271470i | ||||
\(474\) | −34.1933 | + | 34.1933i | −1.57055 | + | 1.57055i | ||||
\(475\) | −0.442957 | − | 0.442957i | −0.0203243 | − | 0.0203243i | ||||
\(476\) | −0.0243372 | + | 4.34703i | −0.00111550 | + | 0.199246i | ||||
\(477\) | −7.44748 | −0.340997 | ||||||||
\(478\) | − | 9.62475i | − | 0.440226i | ||||||
\(479\) | −9.88634 | − | 9.88634i | −0.451719 | − | 0.451719i | 0.444206 | − | 0.895925i | \(-0.353486\pi\) |
−0.895925 | + | 0.444206i | \(0.853486\pi\) | |||||||
\(480\) | − | 5.83096i | − | 0.266146i | ||||||
\(481\) | 7.08609 | + | 7.50830i | 0.323098 | + | 0.342349i | ||||
\(482\) | − | 1.90101i | − | 0.0865887i | ||||||
\(483\) | −39.1642 | − | 0.219264i | −1.78203 | − | 0.00997687i | ||||
\(484\) | 2.22180 | 0.100991 | ||||||||
\(485\) | 5.44748i | 0.247357i | ||||||||
\(486\) | 16.1509 | − | 16.1509i | 0.732620 | − | 0.732620i | ||||
\(487\) | −12.6092 | − | 12.6092i | −0.571375 | − | 0.571375i | 0.361137 | − | 0.932513i | \(-0.382389\pi\) |
−0.932513 | + | 0.361137i | \(0.882389\pi\) | |||||||
\(488\) | 19.9812 | + | 19.9812i | 0.904507 | + | 0.904507i | ||||
\(489\) | −15.9986 | − | 15.9986i | −0.723482 | − | 0.723482i | ||||
\(490\) | 7.33403 | + | 0.0821230i | 0.331318 | + | 0.00370994i | ||||
\(491\) | 1.72487i | 0.0778425i | 0.999242 | + | 0.0389212i | \(0.0123921\pi\) | ||||
−0.999242 | + | 0.0389212i | \(0.987608\pi\) | |||||||
\(492\) | 2.78765 | − | 2.78765i | 0.125677 | − | 0.125677i | ||||
\(493\) | −11.5420 | −0.519824 | ||||||||
\(494\) | −0.0185811 | + | 0.642291i | −0.000836003 | + | 0.0288980i | ||||
\(495\) | − | 4.93430i | − | 0.221780i | ||||||
\(496\) | −17.8199 | + | 17.8199i | −0.800135 | + | 0.800135i | ||||
\(497\) | 10.7948 | + | 10.9164i | 0.484215 | + | 0.489667i | ||||
\(498\) | 40.9926i | 1.83692i | ||||||||
\(499\) | −27.5555 | − | 27.5555i | −1.23355 | − | 1.23355i | −0.962589 | − | 0.270964i | \(-0.912657\pi\) |
−0.270964 | − | 0.962589i | \(-0.587343\pi\) | |||||||
\(500\) | 3.05682 | − | 3.05682i | 0.136705 | − | 0.136705i | ||||
\(501\) | 27.4410 | − | 27.4410i | 1.22597 | − | 1.22597i | ||||
\(502\) | −10.3470 | − | 10.3470i | −0.461811 | − | 0.461811i | ||||
\(503\) | − | 20.8862i | − | 0.931272i | −0.884976 | − | 0.465636i | \(-0.845826\pi\) | ||
0.884976 | − | 0.465636i | \(-0.154174\pi\) | |||||||
\(504\) | 12.5291 | − | 12.3896i | 0.558092 | − | 0.551878i | ||||
\(505\) | −0.711213 | + | 0.711213i | −0.0316486 | + | 0.0316486i | ||||
\(506\) | 20.6381i | 0.917475i | ||||||||
\(507\) | 1.70883 | − | 29.5097i | 0.0758918 | − | 1.31057i | ||||
\(508\) | 3.97721 | 0.176460 | ||||||||
\(509\) | −15.2473 | + | 15.2473i | −0.675823 | + | 0.675823i | −0.959052 | − | 0.283229i | \(-0.908594\pi\) |
0.283229 | + | 0.959052i | \(0.408594\pi\) | |||||||
\(510\) | 7.25990i | 0.321474i | ||||||||
\(511\) | 18.2206 | + | 18.4257i | 0.806031 | + | 0.815107i | ||||
\(512\) | −16.9216 | − | 16.9216i | −0.747837 | − | 0.747837i | ||||
\(513\) | −0.196748 | − | 0.196748i | −0.00868666 | − | 0.00868666i | ||||
\(514\) | −15.0210 | − | 15.0210i | −0.662548 | − | 0.662548i | ||||
\(515\) | 3.26180 | − | 3.26180i | 0.143732 | − | 0.143732i | ||||
\(516\) | 3.90286i | 0.171814i | ||||||||
\(517\) | 19.3505 | 0.851033 | ||||||||
\(518\) | 9.15630 | + | 0.0512623i | 0.402305 | + | 0.00225234i | ||||
\(519\) | 17.0133i | 0.746802i | ||||||||
\(520\) | −9.58864 | − | 0.277394i | −0.420490 | − | 0.0121645i | ||||
\(521\) | − | 20.1543i | − | 0.882975i | −0.897268 | − | 0.441487i | \(-0.854451\pi\) | ||
0.897268 | − | 0.441487i | \(-0.145549\pi\) | |||||||
\(522\) | 7.02472 | + | 7.02472i | 0.307464 | + | 0.307464i | ||||
\(523\) | − | 11.3031i | − | 0.494251i | −0.968983 | − | 0.247126i | \(-0.920514\pi\) | ||
0.968983 | − | 0.247126i | \(-0.0794861\pi\) | |||||||
\(524\) | 6.45095 | 0.281811 | ||||||||
\(525\) | 25.5578 | + | 0.143087i | 1.11543 | + | 0.00624485i | ||||
\(526\) | −12.4143 | − | 12.4143i | −0.541291 | − | 0.541291i | ||||
\(527\) | −20.6400 | + | 20.6400i | −0.899094 | + | 0.899094i | ||||
\(528\) | −11.0946 | − | 11.0946i | −0.482831 | − | 0.482831i | ||||
\(529\) | −19.3835 | −0.842760 | ||||||||
\(530\) | 3.59587 | 0.156195 | ||||||||
\(531\) | −19.8592 | − | 19.8592i | −0.861817 | − | 0.861817i | ||||
\(532\) | −0.147902 | − | 0.149568i | −0.00641237 | − | 0.00648458i | ||||
\(533\) | −7.95774 | − | 8.43188i | −0.344688 | − | 0.365225i | ||||
\(534\) | 13.1967 | 0.571079 | ||||||||
\(535\) | 6.28230 | − | 6.28230i | 0.271607 | − | 0.271607i | ||||
\(536\) | −4.55479 | −0.196737 | ||||||||
\(537\) | 51.6168 | 2.22743 | ||||||||
\(538\) | −20.0115 | + | 20.0115i | −0.862758 | + | 0.862758i | ||||
\(539\) | −13.1270 | + | 12.8363i | −0.565420 | + | 0.552898i | ||||
\(540\) | 0.623710 | − | 0.623710i | 0.0268402 | − | 0.0268402i | ||||
\(541\) | −9.28879 | + | 9.28879i | −0.399356 | + | 0.399356i | −0.878006 | − | 0.478650i | \(-0.841126\pi\) |
0.478650 | + | 0.878006i | \(0.341126\pi\) | |||||||
\(542\) | − | 4.13051i | − | 0.177421i | ||||||
\(543\) | 4.35965i | 0.187090i | ||||||||
\(544\) | −6.37398 | − | 6.37398i | −0.273282 | − | 0.273282i | ||||
\(545\) | −7.17778 | −0.307462 | ||||||||
\(546\) | −17.8867 | − | 19.1663i | −0.765480 | − | 0.820240i | ||||
\(547\) | 12.8999 | 0.551559 | 0.275780 | − | 0.961221i | \(-0.411064\pi\) | ||||
0.275780 | + | 0.961221i | \(0.411064\pi\) | |||||||
\(548\) | −1.01560 | − | 1.01560i | −0.0433842 | − | 0.0433842i | ||||
\(549\) | − | 19.9812i | − | 0.852777i | ||||||
\(550\) | − | 13.4680i | − | 0.574277i | ||||||
\(551\) | 0.394912 | − | 0.394912i | 0.0168238 | − | 0.0168238i | ||||
\(552\) | 32.1236 | − | 32.1236i | 1.36727 | − | 1.36727i | ||||
\(553\) | −46.5534 | − | 0.260633i | −1.97965 | − | 0.0110833i | ||||
\(554\) | 24.8462 | − | 24.8462i | 1.05562 | − | 1.05562i | ||||
\(555\) | −5.64423 | −0.239584 | ||||||||
\(556\) | −3.43400 | −0.145634 | ||||||||
\(557\) | −16.6153 | + | 16.6153i | −0.704013 | + | 0.704013i | −0.965269 | − | 0.261257i | \(-0.915863\pi\) |
0.261257 | + | 0.965269i | \(0.415863\pi\) | |||||||
\(558\) | 25.1240 | 1.06359 | ||||||||
\(559\) | 11.4732 | + | 0.331912i | 0.485264 | + | 0.0140384i | ||||
\(560\) | −4.29072 | + | 4.24295i | −0.181316 | + | 0.179297i | ||||
\(561\) | −12.8504 | − | 12.8504i | −0.542546 | − | 0.542546i | ||||
\(562\) | 16.5536 | 0.698270 | ||||||||
\(563\) | 21.6761 | 0.913538 | 0.456769 | − | 0.889585i | \(-0.349007\pi\) | ||||
0.456769 | + | 0.889585i | \(0.349007\pi\) | |||||||
\(564\) | −6.39576 | − | 6.39576i | −0.269310 | − | 0.269310i | ||||
\(565\) | 3.52192 | − | 3.52192i | 0.148168 | − | 0.148168i | ||||
\(566\) | 3.67799 | + | 3.67799i | 0.154598 | + | 0.154598i | ||||
\(567\) | 28.5763 | + | 0.159987i | 1.20009 | + | 0.00671881i | ||||
\(568\) | −17.8082 | −0.747214 | ||||||||
\(569\) | − | 18.0738i | − | 0.757695i | −0.925459 | − | 0.378847i | \(-0.876321\pi\) | ||
0.925459 | − | 0.378847i | \(-0.123679\pi\) | |||||||
\(570\) | −0.248399 | − | 0.248399i | −0.0104043 | − | 0.0104043i | ||||
\(571\) | 8.53692i | 0.357259i | 0.983916 | + | 0.178630i | \(0.0571664\pi\) | ||||
−0.983916 | + | 0.178630i | \(0.942834\pi\) | |||||||
\(572\) | 3.70831 | − | 3.49978i | 0.155052 | − | 0.146333i | ||||
\(573\) | − | 22.7542i | − | 0.950569i | ||||||
\(574\) | −10.2826 | − | 0.0575680i | −0.429188 | − | 0.00240284i | ||||
\(575\) | 27.6586 | 1.15344 | ||||||||
\(576\) | 19.1773i | 0.799053i | ||||||||
\(577\) | 8.56564 | − | 8.56564i | 0.356592 | − | 0.356592i | −0.505963 | − | 0.862555i | \(-0.668863\pi\) |
0.862555 | + | 0.505963i | \(0.168863\pi\) | |||||||
\(578\) | −6.59284 | − | 6.59284i | −0.274226 | − | 0.274226i | ||||
\(579\) | −23.2725 | − | 23.2725i | −0.967171 | − | 0.967171i | ||||
\(580\) | 1.25190 | + | 1.25190i | 0.0519825 | + | 0.0519825i | ||||
\(581\) | −28.0616 | + | 27.7491i | −1.16419 | + | 1.15123i | ||||
\(582\) | − | 17.2690i | − | 0.715822i | ||||||
\(583\) | −6.36490 | + | 6.36490i | −0.263607 | + | 0.263607i | ||||
\(584\) | −30.0583 | −1.24382 | ||||||||
\(585\) | 4.65562 | + | 4.93302i | 0.192486 | + | 0.203955i | ||||
\(586\) | − | 6.10849i | − | 0.252339i | ||||||
\(587\) | 0.308382 | − | 0.308382i | 0.0127283 | − | 0.0127283i | −0.700714 | − | 0.713442i | \(-0.747135\pi\) |
0.713442 | + | 0.700714i | \(0.247135\pi\) | |||||||
\(588\) | 8.58145 | + | 0.0960910i | 0.353893 | + | 0.00396272i | ||||
\(589\) | − | 1.41241i | − | 0.0581972i | ||||||
\(590\) | 9.58864 | + | 9.58864i | 0.394758 | + | 0.394758i | ||||
\(591\) | −34.7183 | + | 34.7183i | −1.42812 | + | 1.42812i | ||||
\(592\) | −5.32684 | + | 5.32684i | −0.218932 | + | 0.218932i | ||||
\(593\) | 4.95204 | + | 4.95204i | 0.203356 | + | 0.203356i | 0.801436 | − | 0.598080i | \(-0.204070\pi\) |
−0.598080 | + | 0.801436i | \(0.704070\pi\) | |||||||
\(594\) | − | 5.98209i | − | 0.245448i | ||||||
\(595\) | −4.96977 | + | 4.91443i | −0.203741 | + | 0.201472i | ||||
\(596\) | 7.19061 | − | 7.19061i | 0.294539 | − | 0.294539i | ||||
\(597\) | − | 51.0772i | − | 2.09045i | ||||||
\(598\) | −19.4725 | − | 20.6327i | −0.796289 | − | 0.843734i | ||||
\(599\) | −17.6309 | −0.720379 | −0.360189 | − | 0.932879i | \(-0.617288\pi\) | ||||
−0.360189 | + | 0.932879i | \(0.617288\pi\) | |||||||
\(600\) | −20.9632 | + | 20.9632i | −0.855820 | + | 0.855820i | ||||
\(601\) | − | 7.14746i | − | 0.291551i | −0.989318 | − | 0.145776i | \(-0.953432\pi\) | ||
0.989318 | − | 0.145776i | \(-0.0465677\pi\) | |||||||
\(602\) | 7.23840 | − | 7.15780i | 0.295015 | − | 0.291730i | ||||
\(603\) | 2.27739 | + | 2.27739i | 0.0927426 | + | 0.0927426i | ||||
\(604\) | −4.12064 | − | 4.12064i | −0.167666 | − | 0.167666i | ||||
\(605\) | 2.52595 | + | 2.52595i | 0.102694 | + | 0.102694i | ||||
\(606\) | 2.25461 | − | 2.25461i | 0.0915872 | − | 0.0915872i | ||||
\(607\) | 29.8550i | 1.21178i | 0.795550 | + | 0.605888i | \(0.207182\pi\) | ||||
−0.795550 | + | 0.605888i | \(0.792818\pi\) | |||||||
\(608\) | 0.436175 | 0.0176892 | ||||||||
\(609\) | −0.127567 | + | 22.7856i | −0.00516929 | + | 0.923321i | ||||
\(610\) | 9.64754i | 0.390618i | ||||||||
\(611\) | −19.3454 | + | 18.2576i | −0.782632 | + | 0.738623i | ||||
\(612\) | 3.56556i | 0.144129i | ||||||||
\(613\) | −6.43907 | − | 6.43907i | −0.260072 | − | 0.260072i | 0.565011 | − | 0.825083i | \(-0.308872\pi\) |
−0.825083 | + | 0.565011i | \(0.808872\pi\) | |||||||
\(614\) | 14.6905i | 0.592859i | ||||||||
\(615\) | 6.33852 | 0.255594 | ||||||||
\(616\) | 0.119230 | − | 21.2965i | 0.00480393 | − | 0.858061i | ||||
\(617\) | 16.4908 | + | 16.4908i | 0.663894 | + | 0.663894i | 0.956296 | − | 0.292402i | \(-0.0944544\pi\) |
−0.292402 | + | 0.956296i | \(0.594454\pi\) | |||||||
\(618\) | −10.3402 | + | 10.3402i | −0.415943 | + | 0.415943i | ||||
\(619\) | 22.3208 | + | 22.3208i | 0.897148 | + | 0.897148i | 0.995183 | − | 0.0980353i | \(-0.0312558\pi\) |
−0.0980353 | + | 0.995183i | \(0.531256\pi\) | |||||||
\(620\) | 4.47745 | 0.179819 | ||||||||
\(621\) | 12.2851 | 0.492986 | ||||||||
\(622\) | 19.2639 | + | 19.2639i | 0.772414 | + | 0.772414i | ||||
\(623\) | 8.93326 | + | 9.03385i | 0.357903 | + | 0.361934i | ||||
\(624\) | 21.5597 | + | 0.623710i | 0.863079 | + | 0.0249684i | ||||
\(625\) | −14.2918 | −0.571671 | ||||||||
\(626\) | −3.68240 | + | 3.68240i | −0.147178 | + | 0.147178i | ||||
\(627\) | 0.879362 | 0.0351183 | ||||||||
\(628\) | −11.3386 | −0.452459 | ||||||||
\(629\) | −6.16986 | + | 6.16986i | −0.246009 | + | 0.246009i | ||||
\(630\) | 6.01577 | + | 0.0336798i | 0.239674 | + | 0.00134184i | ||||
\(631\) | 3.75154 | − | 3.75154i | 0.149346 | − | 0.149346i | −0.628480 | − | 0.777826i | \(-0.716322\pi\) |
0.777826 | + | 0.628480i | \(0.216322\pi\) | |||||||
\(632\) | 38.1845 | − | 38.1845i | 1.51890 | − | 1.51890i | ||||
\(633\) | − | 42.8618i | − | 1.70360i | ||||||
\(634\) | 6.78765i | 0.269572i | ||||||||
\(635\) | 4.52166 | + | 4.52166i | 0.179437 | + | 0.179437i | ||||
\(636\) | 4.20748 | 0.166837 | ||||||||
\(637\) | 1.01227 | − | 25.2186i | 0.0401076 | − | 0.999195i | ||||
\(638\) | 12.0072 | 0.475369 | ||||||||
\(639\) | 8.90409 | + | 8.90409i | 0.352240 | + | 0.352240i | ||||
\(640\) | − | 4.13051i | − | 0.163273i | ||||||
\(641\) | 25.6947i | 1.01488i | 0.861687 | + | 0.507440i | \(0.169408\pi\) | ||||
−0.861687 | + | 0.507440i | \(0.830592\pi\) | |||||||
\(642\) | −19.9154 | + | 19.9154i | −0.785999 | + | 0.785999i | ||||
\(643\) | −22.1537 | + | 22.1537i | −0.873658 | + | 0.873658i | −0.992869 | − | 0.119211i | \(-0.961964\pi\) |
0.119211 | + | 0.992869i | \(0.461964\pi\) | |||||||
\(644\) | 9.28713 | + | 0.0519948i | 0.365964 | + | 0.00204888i | ||||
\(645\) | −4.43713 | + | 4.43713i | −0.174712 | + | 0.174712i | ||||
\(646\) | −0.543065 | −0.0213666 | ||||||||
\(647\) | −32.4446 | −1.27553 | −0.637764 | − | 0.770232i | \(-0.720140\pi\) | ||||
−0.637764 | + | 0.770232i | \(0.720140\pi\) | |||||||
\(648\) | −23.4391 | + | 23.4391i | −0.920774 | + | 0.920774i | ||||
\(649\) | −33.9449 | −1.33245 | ||||||||
\(650\) | 12.7073 | + | 13.4645i | 0.498423 | + | 0.528120i | ||||
\(651\) | 40.5185 | + | 40.9747i | 1.58804 | + | 1.60593i | ||||
\(652\) | 3.79380 | + | 3.79380i | 0.148577 | + | 0.148577i | ||||
\(653\) | 31.6514 | 1.23862 | 0.619308 | − | 0.785148i | \(-0.287413\pi\) | ||||
0.619308 | + | 0.785148i | \(0.287413\pi\) | |||||||
\(654\) | 22.7542 | 0.889758 | ||||||||
\(655\) | 7.33403 | + | 7.33403i | 0.286564 | + | 0.286564i | ||||
\(656\) | 5.98209 | − | 5.98209i | 0.233561 | − | 0.233561i | ||||
\(657\) | 15.0292 | + | 15.0292i | 0.586344 | + | 0.586344i | ||||
\(658\) | −0.132079 | + | 23.5916i | −0.00514899 | + | 0.919695i | ||||
\(659\) | 30.5330 | 1.18940 | 0.594699 | − | 0.803948i | \(-0.297271\pi\) | ||||
0.594699 | + | 0.803948i | \(0.297271\pi\) | |||||||
\(660\) | 2.78765i | 0.108509i | ||||||||
\(661\) | −9.20895 | − | 9.20895i | −0.358187 | − | 0.358187i | 0.504957 | − | 0.863144i | \(-0.331508\pi\) |
−0.863144 | + | 0.504957i | \(0.831508\pi\) | |||||||
\(662\) | 2.92162i | 0.113552i | ||||||||
\(663\) | 24.9717 | + | 0.722418i | 0.969822 | + | 0.0280564i | ||||
\(664\) | − | 45.7775i | − | 1.77651i | ||||||
\(665\) | 0.00189339 | − | 0.338191i | 7.34225e−5 | − | 0.0131145i | ||||
\(666\) | 7.51026 | 0.291017 | ||||||||
\(667\) | 24.6586i | 0.954785i | ||||||||
\(668\) | −6.50717 | + | 6.50717i | −0.251770 | + | 0.251770i | ||||
\(669\) | −9.82571 | − | 9.82571i | −0.379884 | − | 0.379884i | ||||
\(670\) | −1.09960 | − | 1.09960i | −0.0424811 | − | 0.0424811i | ||||
\(671\) | −17.0767 | − | 17.0767i | −0.659239 | − | 0.659239i | ||||
\(672\) | −12.6537 | + | 12.5128i | −0.488126 | + | 0.482691i | ||||
\(673\) | − | 22.6319i | − | 0.872397i | −0.899850 | − | 0.436199i | \(-0.856325\pi\) | ||
0.899850 | − | 0.436199i | \(-0.143675\pi\) | |||||||
\(674\) | 19.7701 | − | 19.7701i | 0.761516 | − | 0.761516i | ||||
\(675\) | −8.01703 | −0.308576 | ||||||||
\(676\) | −0.405220 | + | 6.99773i | −0.0155854 | + | 0.269144i | ||||
\(677\) | − | 10.7242i | − | 0.412165i | −0.978535 | − | 0.206082i | \(-0.933928\pi\) | ||
0.978535 | − | 0.206082i | \(-0.0660715\pi\) | |||||||
\(678\) | −11.1648 | + | 11.1648i | −0.428781 | + | 0.428781i | ||||
\(679\) | 11.8215 | − | 11.6899i | 0.453668 | − | 0.448616i | ||||
\(680\) | − | 8.10731i | − | 0.310901i | ||||||
\(681\) | 10.6647 | + | 10.6647i | 0.408674 | + | 0.408674i | ||||
\(682\) | 21.4720 | − | 21.4720i | 0.822204 | − | 0.822204i | ||||
\(683\) | −3.70701 | + | 3.70701i | −0.141845 | + | 0.141845i | −0.774463 | − | 0.632619i | \(-0.781980\pi\) |
0.632619 | + | 0.774463i | \(0.281980\pi\) | |||||||
\(684\) | −0.121997 | − | 0.121997i | −0.00466466 | − | 0.00466466i | ||||
\(685\) | − | 2.30925i | − | 0.0882319i | ||||||
\(686\) | −15.5600 | − | 16.0917i | −0.594085 | − | 0.614384i | ||||
\(687\) | −0.601968 | + | 0.601968i | −0.0229665 | + | 0.0229665i | ||||
\(688\) | 8.37525i | 0.319303i | ||||||||
\(689\) | 0.357818 | − | 12.3687i | 0.0136318 | − | 0.471208i | ||||
\(690\) | 15.5103 | 0.590465 | ||||||||
\(691\) | 0.266133 | − | 0.266133i | 0.0101242 | − | 0.0101242i | −0.702027 | − | 0.712151i | \(-0.747721\pi\) |
0.712151 | + | 0.702027i | \(0.247721\pi\) | |||||||
\(692\) | − | 4.03442i | − | 0.153366i | ||||||
\(693\) | −10.7079 | + | 10.5886i | −0.406758 | + | 0.402229i | ||||
\(694\) | −7.35350 | − | 7.35350i | −0.279135 | − | 0.279135i | ||||
\(695\) | −3.90409 | − | 3.90409i | −0.148090 | − | 0.148090i | ||||
\(696\) | −18.6894 | − | 18.6894i | −0.708421 | − | 0.708421i | ||||
\(697\) | 6.92881 | − | 6.92881i | 0.262447 | − | 0.262447i | ||||
\(698\) | 32.5925i | 1.23364i | ||||||||
\(699\) | 14.0131 | 0.530024 | ||||||||
\(700\) | −6.06059 | − | 0.0339307i | −0.229069 | − | 0.00128246i | ||||
\(701\) | 34.0349i | 1.28548i | 0.766084 | + | 0.642740i | \(0.222202\pi\) | ||||
−0.766084 | + | 0.642740i | \(0.777798\pi\) | |||||||
\(702\) | 5.64423 | + | 5.98053i | 0.213028 | + | 0.225720i | ||||
\(703\) | − | 0.422207i | − | 0.0159238i | ||||||
\(704\) | 16.3896 | + | 16.3896i | 0.617707 | + | 0.617707i | ||||
\(705\) | − | 14.5426i | − | 0.547705i | ||||||
\(706\) | 8.22556 | 0.309573 | ||||||||
\(707\) | 3.06960 | + | 0.0171854i | 0.115444 | + | 0.000646325i | ||||
\(708\) | 11.2195 | + | 11.2195i | 0.421656 | + | 0.421656i | ||||
\(709\) | 11.4989 | − | 11.4989i | 0.431849 | − | 0.431849i | −0.457408 | − | 0.889257i | \(-0.651222\pi\) |
0.889257 | + | 0.457408i | \(0.151222\pi\) | |||||||
\(710\) | −4.29917 | − | 4.29917i | −0.161345 | − | 0.161345i | ||||
\(711\) | −38.1845 | −1.43203 | ||||||||
\(712\) | −14.7371 | −0.552297 | ||||||||
\(713\) | 44.0960 | + | 44.0960i | 1.65141 | + | 1.65141i | ||||
\(714\) | 15.7546 | − | 15.5792i | 0.589601 | − | 0.583036i | ||||
\(715\) | 8.19481 | + | 0.237071i | 0.306469 | + | 0.00886596i | ||||
\(716\) | −12.2401 | −0.457432 | ||||||||
\(717\) | 12.8034 | − | 12.8034i | 0.478153 | − | 0.478153i | ||||
\(718\) | −21.4524 | −0.800596 | ||||||||
\(719\) | −35.0445 | −1.30694 | −0.653469 | − | 0.756953i | \(-0.726687\pi\) | ||||
−0.653469 | + | 0.756953i | \(0.726687\pi\) | |||||||
\(720\) | −3.49978 | + | 3.49978i | −0.130429 | + | 0.130429i | ||||
\(721\) | −14.0779 | − | 0.0788166i | −0.524290 | − | 0.00293528i | ||||
\(722\) | −16.2195 | + | 16.2195i | −0.603629 | + | 0.603629i | ||||
\(723\) | 2.52884 | − | 2.52884i | 0.0940486 | − | 0.0940486i | ||||
\(724\) | − | 1.03382i | − | 0.0384215i | ||||||
\(725\) | − | 16.0917i | − | 0.597631i | ||||||
\(726\) | −8.00747 | − | 8.00747i | −0.297185 | − | 0.297185i | ||||
\(727\) | −15.0936 | −0.559789 | −0.279895 | − | 0.960031i | \(-0.590300\pi\) | ||||
−0.279895 | + | 0.960031i | \(0.590300\pi\) | |||||||
\(728\) | 19.9745 | + | 21.4034i | 0.740305 | + | 0.793264i | ||||
\(729\) | 10.5669 | 0.391367 | ||||||||
\(730\) | −7.25655 | − | 7.25655i | −0.268577 | − | 0.268577i | ||||
\(731\) | 9.70071i | 0.358794i | ||||||||
\(732\) | 11.2885i | 0.417233i | ||||||||
\(733\) | 14.8155 | − | 14.8155i | 0.547223 | − | 0.547223i | −0.378414 | − | 0.925637i | \(-0.623530\pi\) |
0.925637 | + | 0.378414i | \(0.123530\pi\) | |||||||
\(734\) | −19.5546 | + | 19.5546i | −0.721773 | + | 0.721773i | ||||
\(735\) | 9.64693 | + | 9.86542i | 0.355832 | + | 0.363891i | ||||
\(736\) | −13.6176 | + | 13.6176i | −0.501950 | + | 0.501950i | ||||
\(737\) | 3.89269 | 0.143389 | ||||||||
\(738\) | −8.43409 | −0.310463 | ||||||||
\(739\) | 16.1370 | − | 16.1370i | 0.593607 | − | 0.593607i | −0.344997 | − | 0.938604i | \(-0.612120\pi\) |
0.938604 | + | 0.344997i | \(0.112120\pi\) | |||||||
\(740\) | 1.33843 | 0.0492018 | ||||||||
\(741\) | −0.879132 | + | 0.829697i | −0.0322957 | + | 0.0304797i | ||||
\(742\) | −7.71646 | − | 7.80335i | −0.283280 | − | 0.286470i | ||||
\(743\) | −24.1350 | − | 24.1350i | −0.885428 | − | 0.885428i | 0.108652 | − | 0.994080i | \(-0.465347\pi\) |
−0.994080 | + | 0.108652i | \(0.965347\pi\) | |||||||
\(744\) | −66.8431 | −2.45059 | ||||||||
\(745\) | 16.3499 | 0.599013 | ||||||||
\(746\) | 8.97721 | + | 8.97721i | 0.328679 | + | 0.328679i | ||||
\(747\) | −22.8887 | + | 22.8887i | −0.837455 | + | 0.837455i | ||||
\(748\) | 3.04726 | + | 3.04726i | 0.111419 | + | 0.111419i | ||||
\(749\) | −27.1145 | − | 0.151803i | −0.990741 | − | 0.00554675i | ||||
\(750\) | −22.0338 | −0.804562 | ||||||||
\(751\) | 16.7770i | 0.612201i | 0.951999 | + | 0.306100i | \(0.0990243\pi\) | ||||
−0.951999 | + | 0.306100i | \(0.900976\pi\) | |||||||
\(752\) | −13.7248 | − | 13.7248i | −0.500493 | − | 0.500493i | ||||
\(753\) | − | 27.5285i | − | 1.00319i | ||||||
\(754\) | −12.0041 | + | 11.3290i | −0.437162 | + | 0.412579i | ||||
\(755\) | − | 9.36943i | − | 0.340989i | ||||||
\(756\) | −2.69194 | − | 0.0150710i | −0.0979048 | − | 0.000548128i | ||||
\(757\) | −20.7321 | −0.753520 | −0.376760 | − | 0.926311i | \(-0.622962\pi\) | ||||
−0.376760 | + | 0.926311i | \(0.622962\pi\) | |||||||
\(758\) | 6.22568i | 0.226127i | ||||||||
\(759\) | −27.4540 | + | 27.4540i | −0.996519 | + | 0.996519i | ||||
\(760\) | 0.277394 | + | 0.277394i | 0.0100621 | + | 0.0100621i | ||||
\(761\) | 2.11330 | + | 2.11330i | 0.0766071 | + | 0.0766071i | 0.744372 | − | 0.667765i | \(-0.232749\pi\) |
−0.667765 | + | 0.744372i | \(0.732749\pi\) | |||||||
\(762\) | −14.3341 | − | 14.3341i | −0.519268 | − | 0.519268i | ||||
\(763\) | 15.4030 | + | 15.5764i | 0.557624 | + | 0.563903i | ||||
\(764\) | 5.39576i | 0.195212i | ||||||||
\(765\) | −4.05365 | + | 4.05365i | −0.146560 | + | 0.146560i | ||||
\(766\) | 41.9782 | 1.51674 | ||||||||
\(767\) | 33.9360 | − | 32.0277i | 1.22536 | − | 1.15645i | ||||
\(768\) | − | 27.0932i | − | 0.977642i | ||||||
\(769\) | 25.9456 | − | 25.9456i | 0.935621 | − | 0.935621i | −0.0624284 | − | 0.998049i | \(-0.519885\pi\) |
0.998049 | + | 0.0624284i | \(0.0198845\pi\) | |||||||
\(770\) | 5.17009 | − | 5.11252i | 0.186317 | − | 0.184242i | ||||
\(771\) | − | 39.9637i | − | 1.43926i | ||||||
\(772\) | 5.51867 | + | 5.51867i | 0.198621 | + | 0.198621i | ||||
\(773\) | 0.951693 | − | 0.951693i | 0.0342300 | − | 0.0342300i | −0.689785 | − | 0.724015i | \(-0.742295\pi\) |
0.724015 | + | 0.689785i | \(0.242295\pi\) | |||||||
\(774\) | 5.90409 | − | 5.90409i | 0.212218 | − | 0.212218i | ||||
\(775\) | −28.7761 | − | 28.7761i | −1.03367 | − | 1.03367i | ||||
\(776\) | 19.2847i | 0.692280i | ||||||||
\(777\) | 12.1121 | + | 12.2485i | 0.434518 | + | 0.439411i | ||||
\(778\) | −5.54638 | + | 5.54638i | −0.198847 | + | 0.198847i | ||||
\(779\) | 0.474142i | 0.0169879i | ||||||||
\(780\) | −2.63021 | − | 2.78692i | −0.0941766 | − | 0.0997879i | ||||
\(781\) | 15.2195 | 0.544598 | ||||||||
\(782\) | 16.9547 | − | 16.9547i | 0.606299 | − | 0.606299i | ||||
\(783\) | − | 7.14746i | − | 0.255430i | ||||||
\(784\) | 18.4151 | + | 0.206204i | 0.657683 | + | 0.00736442i | ||||
\(785\) | −12.8908 | − | 12.8908i | −0.460091 | − | 0.460091i | ||||
\(786\) | −23.2495 | − | 23.2495i | −0.829283 | − | 0.829283i | ||||
\(787\) | 24.8017 | + | 24.8017i | 0.884085 | + | 0.884085i | 0.993947 | − | 0.109862i | \(-0.0350409\pi\) |
−0.109862 | + | 0.993947i | \(0.535041\pi\) | |||||||
\(788\) | 8.23287 | − | 8.23287i | 0.293284 | − | 0.293284i | ||||
\(789\) | − | 33.0286i | − | 1.17585i | ||||||
\(790\) | 18.4366 | 0.655946 | ||||||||
\(791\) | −15.2006 | − | 0.0851021i | −0.540473 | − | 0.00302588i | ||||
\(792\) | − | 17.4680i | − | 0.620698i | ||||||
\(793\) | 33.1845 | + | 0.960007i | 1.17841 | + | 0.0340908i | ||||
\(794\) | 11.7860i | 0.418268i | ||||||||
\(795\) | 4.78345 | + | 4.78345i | 0.169651 | + | 0.169651i | ||||
\(796\) | 12.1121i | 0.429301i | ||||||||
\(797\) | −34.9017 | −1.23628 | −0.618141 | − | 0.786067i | \(-0.712114\pi\) | ||||
−0.618141 | + | 0.786067i | \(0.712114\pi\) | |||||||
\(798\) | −0.00600221 | + | 1.07209i | −0.000212476 | + | 0.0379517i | ||||
\(799\) | −15.8969 | − | 15.8969i | −0.562392 | − | 0.562392i | ||||
\(800\) | 8.88655 | − | 8.88655i | 0.314187 | − | 0.314187i | ||||
\(801\) | 7.36857 | + | 7.36857i | 0.260356 | + | 0.260356i | ||||
\(802\) | 15.4224 | 0.544585 | ||||||||
\(803\) | 25.6890 | 0.906545 | ||||||||
\(804\) | −1.28662 | − | 1.28662i | −0.0453757 | − | 0.0453757i | ||||
\(805\) | 10.4993 | + | 10.6176i | 0.370053 | + | 0.374220i | ||||
\(806\) | −1.20710 | + | 41.7256i | −0.0425182 | + | 1.46972i | ||||
\(807\) | −53.2411 | −1.87418 | ||||||||
\(808\) | −2.51778 | + | 2.51778i | −0.0885750 | + | 0.0885750i | ||||
\(809\) | 10.2618 | 0.360786 | 0.180393 | − | 0.983595i | \(-0.442263\pi\) | ||||
0.180393 | + | 0.983595i | \(0.442263\pi\) | |||||||
\(810\) | −11.3171 | −0.397642 | ||||||||
\(811\) | 13.3684 | − | 13.3684i | 0.469428 | − | 0.469428i | −0.432301 | − | 0.901729i | \(-0.642298\pi\) |
0.901729 | + | 0.432301i | \(0.142298\pi\) | |||||||
\(812\) | 0.0302504 | − | 5.40323i | 0.00106158 | − | 0.189616i | ||||
\(813\) | 5.49466 | − | 5.49466i | 0.192706 | − | 0.192706i | ||||
\(814\) | 6.41855 | − | 6.41855i | 0.224970 | − | 0.224970i | ||||
\(815\) | 8.62627i | 0.302165i | ||||||||
\(816\) | 18.2290i | 0.638142i | ||||||||
\(817\) | −0.331912 | − | 0.331912i | −0.0116121 | − | 0.0116121i | ||||
\(818\) | −4.89002 | −0.170976 | ||||||||
\(819\) | 0.714465 | − | 20.6890i | 0.0249654 | − | 0.722931i | ||||
\(820\) | −1.50307 | −0.0524895 | ||||||||
\(821\) | 17.3074 | + | 17.3074i | 0.604031 | + | 0.604031i | 0.941380 | − | 0.337349i | \(-0.109530\pi\) |
−0.337349 | + | 0.941380i | \(0.609530\pi\) | |||||||
\(822\) | 7.32052i | 0.255333i | ||||||||
\(823\) | − | 35.0772i | − | 1.22271i | −0.791355 | − | 0.611356i | \(-0.790624\pi\) | ||
0.791355 | − | 0.611356i | \(-0.209376\pi\) | |||||||
\(824\) | 11.5471 | − | 11.5471i | 0.402263 | − | 0.402263i | ||||
\(825\) | 17.9160 | − | 17.9160i | 0.623753 | − | 0.623753i | ||||
\(826\) | 0.231696 | − | 41.3846i | 0.00806172 | − | 1.43996i | ||||
\(827\) | −19.4173 | + | 19.4173i | −0.675207 | + | 0.675207i | −0.958912 | − | 0.283705i | \(-0.908436\pi\) |
0.283705 | + | 0.958912i | \(0.408436\pi\) | |||||||
\(828\) | 7.61757 | 0.264729 | ||||||||
\(829\) | −9.16091 | −0.318172 | −0.159086 | − | 0.987265i | \(-0.550855\pi\) | ||||
−0.159086 | + | 0.987265i | \(0.550855\pi\) | |||||||
\(830\) | 11.0514 | − | 11.0514i | 0.383599 | − | 0.383599i | ||||
\(831\) | 66.1039 | 2.29312 | ||||||||
\(832\) | −31.8493 | − | 0.921381i | −1.10418 | − | 0.0319432i | ||||
\(833\) | 21.3295 | + | 0.238838i | 0.739023 | + | 0.00827523i | ||||
\(834\) | 12.3763 | + | 12.3763i | 0.428556 | + | 0.428556i | ||||
\(835\) | −14.7959 | −0.512033 | ||||||||
\(836\) | −0.208526 | −0.00721201 | ||||||||
\(837\) | −12.7815 | − | 12.7815i | −0.441794 | − | 0.441794i | ||||
\(838\) | 30.2625 | − | 30.2625i | 1.04540 | − | 1.04540i | ||||
\(839\) | 26.1882 | + | 26.1882i | 0.904116 | + | 0.904116i | 0.995789 | − | 0.0916731i | \(-0.0292215\pi\) |
−0.0916731 | + | 0.995789i | \(0.529221\pi\) | |||||||
\(840\) | −16.0051 | − | 0.0896058i | −0.552228 | − | 0.00309170i | ||||
\(841\) | −14.6537 | −0.505299 | ||||||||
\(842\) | 32.3579i | 1.11513i | ||||||||
\(843\) | 22.0206 | + | 22.0206i | 0.758428 | + | 0.758428i | ||||
\(844\) | 10.1639i | 0.349857i | ||||||||
\(845\) | −8.41635 | + | 7.49497i | −0.289531 | + | 0.257835i | ||||
\(846\) | 19.3505i | 0.665283i | ||||||||
\(847\) | 0.0610359 | − | 10.9020i | 0.00209722 | − | 0.374598i | ||||
\(848\) | 9.02893 | 0.310055 | ||||||||
\(849\) | 9.78539i | 0.335834i | ||||||||
\(850\) | −11.0643 | + | 11.0643i | −0.379502 | + | 0.379502i | ||||
\(851\) | 13.1815 | + | 13.1815i | 0.451855 | + | 0.451855i | ||||
\(852\) | −5.03040 | − | 5.03040i | −0.172339 | − | 0.172339i | ||||
\(853\) | −7.70865 | − | 7.70865i | −0.263939 | − | 0.263939i | 0.562713 | − | 0.826652i | \(-0.309758\pi\) |
−0.826652 | + | 0.562713i | \(0.809758\pi\) | |||||||
\(854\) | 20.9360 | − | 20.7029i | 0.716415 | − | 0.708438i | ||||
\(855\) | − | 0.277394i | − | 0.00948666i | ||||||
\(856\) | 22.2401 | − | 22.2401i | 0.760149 | − | 0.760149i | ||||
\(857\) | −22.4141 | −0.765651 | −0.382825 | − | 0.923821i | \(-0.625049\pi\) | ||||
−0.382825 | + | 0.923821i | \(0.625049\pi\) | |||||||
\(858\) | −25.9783 | − | 0.751536i | −0.886883 | − | 0.0256570i | ||||
\(859\) | 43.5695i | 1.48657i | 0.668974 | + | 0.743286i | \(0.266734\pi\) | ||||
−0.668974 | + | 0.743286i | \(0.733266\pi\) | |||||||
\(860\) | 1.05219 | − | 1.05219i | 0.0358794 | − | 0.0358794i | ||||
\(861\) | −13.6020 | − | 13.7551i | −0.463554 | − | 0.468774i | ||||
\(862\) | 21.5441i | 0.733795i | ||||||||
\(863\) | −9.02893 | − | 9.02893i | −0.307348 | − | 0.307348i | 0.536532 | − | 0.843880i | \(-0.319734\pi\) |
−0.843880 | + | 0.536532i | \(0.819734\pi\) | |||||||
\(864\) | 3.94714 | − | 3.94714i | 0.134285 | − | 0.134285i | ||||
\(865\) | 4.58670 | − | 4.58670i | 0.155952 | − | 0.155952i | ||||
\(866\) | −12.2548 | − | 12.2548i | −0.416436 | − | 0.416436i | ||||
\(867\) | − | 17.5404i | − | 0.595703i | ||||||
\(868\) | −9.60827 | − | 9.71646i | −0.326126 | − | 0.329798i | ||||
\(869\) | −32.6339 | + | 32.6339i | −1.10703 | + | 1.10703i | ||||
\(870\) | − | 9.02383i | − | 0.305937i | ||||||
\(871\) | −3.89168 | + | 3.67284i | −0.131864 | + | 0.124449i | ||||
\(872\) | −25.4101 | −0.860496 | ||||||||
\(873\) | 9.64235 | − | 9.64235i | 0.326344 | − | 0.326344i | ||||
\(874\) | 1.16022i | 0.0392450i | ||||||||
\(875\) | −14.9153 | − | 15.0833i | −0.504231 | − | 0.509909i | ||||
\(876\) | −8.49079 | − | 8.49079i | −0.286877 | − | 0.286877i | ||||
\(877\) | −4.81957 | − | 4.81957i | −0.162745 | − | 0.162745i | 0.621036 | − | 0.783782i | \(-0.286712\pi\) |
−0.783782 | + | 0.621036i | \(0.786712\pi\) | |||||||
\(878\) | 17.0767 | + | 17.0767i | 0.576311 | + | 0.576311i | ||||
\(879\) | 8.12589 | − | 8.12589i | 0.274079 | − | 0.274079i | ||||
\(880\) | 5.98209i | 0.201656i | ||||||||
\(881\) | −3.46947 | −0.116889 | −0.0584447 | − | 0.998291i | \(-0.518614\pi\) | ||||
−0.0584447 | + | 0.998291i | \(0.518614\pi\) | |||||||
\(882\) | −12.8363 | − | 13.1270i | −0.432220 | − | 0.442009i | ||||
\(883\) | 47.0772i | 1.58427i | 0.610344 | + | 0.792136i | \(0.291031\pi\) | ||||
−0.610344 | + | 0.792136i | \(0.708969\pi\) | |||||||
\(884\) | −5.92162 | − | 0.171309i | −0.199166 | − | 0.00576175i | ||||
\(885\) | 25.5108i | 0.857536i | ||||||||
\(886\) | −4.81852 | − | 4.81852i | −0.161881 | − | 0.161881i | ||||
\(887\) | 5.75722i | 0.193309i | 0.995318 | + | 0.0966543i | \(0.0308141\pi\) | ||||
−0.995318 | + | 0.0966543i | \(0.969186\pi\) | |||||||
\(888\) | −19.9812 | −0.670526 | ||||||||
\(889\) | 0.109259 | − | 19.5155i | 0.00366444 | − | 0.654530i | ||||
\(890\) | −3.55777 | − | 3.55777i | −0.119257 | − | 0.119257i | ||||
\(891\) | 20.0319 | − | 20.0319i | 0.671094 | − | 0.671094i | ||||
\(892\) | 2.33000 | + | 2.33000i | 0.0780142 | + | 0.0780142i | ||||
\(893\) | 1.08783 | 0.0364029 | ||||||||
\(894\) | −51.8305 | −1.73347 | ||||||||
\(895\) | −13.9156 | − | 13.9156i | −0.465148 | − | 0.465148i | ||||
\(896\) | −8.96357 | + | 8.86376i | −0.299452 | + | 0.296118i | ||||
\(897\) | 1.54339 | − | 53.3503i | 0.0515324 | − | 1.78132i | ||||
\(898\) | −22.0599 | −0.736150 | ||||||||
\(899\) | 25.6549 | − | 25.6549i | 0.855639 | − | 0.855639i | ||||
\(900\) | −4.97107 | −0.165702 | ||||||||
\(901\) | 10.4578 | 0.348401 | ||||||||
\(902\) | −7.20809 | + | 7.20809i | −0.240003 | + | 0.240003i | ||||
\(903\) | 19.1507 | + | 0.107217i | 0.637295 | + | 0.00356795i | ||||
\(904\) | 12.4680 | − | 12.4680i | 0.414679 | − | 0.414679i | ||||
\(905\) | 1.17534 | − | 1.17534i | 0.0390695 | − | 0.0390695i | ||||
\(906\) | 29.7019i | 0.986780i | ||||||||
\(907\) | 13.1412i | 0.436345i | 0.975910 | + | 0.218172i | \(0.0700095\pi\) | ||||
−0.975910 | + | 0.218172i | \(0.929990\pi\) | |||||||
\(908\) | −2.52896 | − | 2.52896i | −0.0839266 | − | 0.0839266i | ||||
\(909\) | 2.51778 | 0.0835093 | ||||||||
\(910\) | −0.344965 | + | 9.98927i | −0.0114355 | + | 0.331141i | ||||
\(911\) | 22.8394 | 0.756702 | 0.378351 | − | 0.925662i | \(-0.376491\pi\) | ||||
0.378351 | + | 0.925662i | \(0.376491\pi\) | |||||||
\(912\) | −0.623710 | − | 0.623710i | −0.0206531 | − | 0.0206531i | ||||
\(913\) | 39.1232i | 1.29479i | ||||||||
\(914\) | 11.9083i | 0.393891i | ||||||||
\(915\) | −12.8337 | + | 12.8337i | −0.424271 | + | 0.424271i | ||||
\(916\) | 0.142747 | − | 0.142747i | 0.00471648 | − | 0.00471648i | ||||
\(917\) | 0.177216 | − | 31.6537i | 0.00585219 | − | 1.04530i | ||||
\(918\) | −4.91443 | + | 4.91443i | −0.162201 | + | 0.162201i | ||||
\(919\) | 35.0265 | 1.15542 | 0.577709 | − | 0.816243i | \(-0.303947\pi\) | ||||
0.577709 | + | 0.816243i | \(0.303947\pi\) | |||||||
\(920\) | −17.3207 | −0.571046 | ||||||||
\(921\) | −19.5422 | + | 19.5422i | −0.643936 | + | 0.643936i | ||||
\(922\) | −12.3206 | −0.405758 | ||||||||
\(923\) | −15.2156 | + | 14.3600i | −0.500826 | + | 0.472664i | ||||
\(924\) | 6.04945 | − | 5.98209i | 0.199012 | − | 0.196796i | ||||
\(925\) | −8.60197 | − | 8.60197i | −0.282831 | − | 0.282831i | ||||
\(926\) | −6.94110 | −0.228099 | ||||||||
\(927\) | −11.5471 | −0.379257 | ||||||||
\(928\) | 7.92267 | + | 7.92267i | 0.260074 | + | 0.260074i | ||||
\(929\) | 16.0163 | − | 16.0163i | 0.525479 | − | 0.525479i | −0.393742 | − | 0.919221i | \(-0.628820\pi\) |
0.919221 | + | 0.393742i | \(0.128820\pi\) | |||||||
\(930\) | −16.1369 | − | 16.1369i | −0.529151 | − | 0.529151i | ||||
\(931\) | −0.737966 | + | 0.721622i | −0.0241859 | + | 0.0236502i | ||||
\(932\) | −3.32297 | −0.108847 | ||||||||
\(933\) | 51.2522i | 1.67792i | ||||||||
\(934\) | 14.8428 | + | 14.8428i | 0.485671 | + | 0.485671i | ||||
\(935\) | 6.92881i | 0.226596i | ||||||||
\(936\) | 16.4814 | + | 17.4634i | 0.538712 | + | 0.570810i | ||||
\(937\) | 39.2356i | 1.28177i | 0.767636 | + | 0.640886i | \(0.221433\pi\) | ||||
−0.767636 | + | 0.640886i | \(0.778567\pi\) | |||||||
\(938\) | −0.0265701 | + | 4.74586i | −0.000867545 | + | 0.154958i | ||||
\(939\) | −9.79711 | −0.319717 | ||||||||
\(940\) | 3.44852i | 0.112478i | ||||||||
\(941\) | 31.6697 | − | 31.6697i | 1.03240 | − | 1.03240i | 0.0329454 | − | 0.999457i | \(-0.489511\pi\) |
0.999457 | − | 0.0329454i | \(-0.0104887\pi\) | |||||||
\(942\) | 40.8648 | + | 40.8648i | 1.33145 | + | 1.33145i | ||||
\(943\) | −14.8029 | − | 14.8029i | −0.482049 | − | 0.482049i | ||||
\(944\) | 24.0763 | + | 24.0763i | 0.783615 | + | 0.783615i | ||||
\(945\) | −3.04331 | − | 3.07757i | −0.0989987 | − | 0.100113i | ||||
\(946\) | − | 10.0917i | − | 0.328110i | ||||||
\(947\) | −11.5948 | + | 11.5948i | −0.376780 | + | 0.376780i | −0.869939 | − | 0.493159i | \(-0.835842\pi\) |
0.493159 | + | 0.869939i | \(0.335842\pi\) | |||||||
\(948\) | 21.5724 | 0.700641 | ||||||||
\(949\) | −25.6823 | + | 24.2381i | −0.833682 | + | 0.786803i | ||||
\(950\) | − | 0.757136i | − | 0.0245647i | ||||||
\(951\) | −9.02935 | + | 9.02935i | −0.292797 | + | 0.292797i | ||||
\(952\) | −17.5936 | + | 17.3977i | −0.570210 | + | 0.563861i | ||||
\(953\) | − | 37.1939i | − | 1.20483i | −0.798183 | − | 0.602415i | \(-0.794205\pi\) | ||
0.798183 | − | 0.602415i | \(-0.205795\pi\) | |||||||
\(954\) | −6.36490 | − | 6.36490i | −0.206071 | − | 0.206071i | ||||
\(955\) | −6.13440 | + | 6.13440i | −0.198504 | + | 0.198504i | ||||
\(956\) | −3.03612 | + | 3.03612i | −0.0981951 | + | 0.0981951i | ||||
\(957\) | 15.9727 | + | 15.9727i | 0.516324 | + | 0.516324i | ||||
\(958\) | − | 16.8985i | − | 0.545965i | ||||||
\(959\) | −5.01127 | + | 4.95547i | −0.161822 | + | 0.160021i | ||||
\(960\) | 12.3174 | − | 12.3174i | 0.397542 | − | 0.397542i | ||||
\(961\) | − | 60.7552i | − | 1.95985i | ||||||
\(962\) | −0.360834 | + | 12.4729i | −0.0116338 | + | 0.402143i | ||||
\(963\) | −22.2401 | −0.716676 | ||||||||
\(964\) | −0.599672 | + | 0.599672i | −0.0193141 | + | 0.0193141i | ||||
\(965\) | 12.5483i | 0.403943i | ||||||||
\(966\) | −33.2838 | − | 33.6586i | −1.07089 | − | 1.08295i | ||||
\(967\) | 34.8785 | + | 34.8785i | 1.12162 | + | 1.12162i | 0.991499 | + | 0.130117i | \(0.0415354\pi\) |
0.130117 | + | 0.991499i | \(0.458465\pi\) | |||||||
\(968\) | 8.94214 | + | 8.94214i | 0.287411 | + | 0.287411i | ||||
\(969\) | −0.722418 | − | 0.722418i | −0.0232074 | − | 0.0232074i | ||||
\(970\) | −4.65562 | + | 4.65562i | −0.149483 | + | 0.149483i | ||||
\(971\) | 13.7033i | 0.439760i | 0.975527 | + | 0.219880i | \(0.0705666\pi\) | ||||
−0.975527 | + | 0.219880i | \(0.929433\pi\) | |||||||
\(972\) | −10.1896 | −0.326831 | ||||||||
\(973\) | −0.0943366 | + | 16.8501i | −0.00302429 | + | 0.540189i | ||||
\(974\) | − | 21.5525i | − | 0.690587i | ||||||
\(975\) | −1.00719 | + | 34.8154i | −0.0322558 | + | 1.11498i | ||||
\(976\) | 24.2242i | 0.775396i | ||||||||
\(977\) | 5.81011 | + | 5.81011i | 0.185882 | + | 0.185882i | 0.793913 | − | 0.608031i | \(-0.208040\pi\) |
−0.608031 | + | 0.793913i | \(0.708040\pi\) | |||||||
\(978\) | − | 27.3460i | − | 0.874429i | ||||||
\(979\) | 12.5949 | 0.402535 | ||||||||
\(980\) | −2.28761 | − | 2.33942i | −0.0730749 | − | 0.0747299i | ||||
\(981\) | 12.7051 | + | 12.7051i | 0.405642 | + | 0.405642i | ||||
\(982\) | −1.47414 | + | 1.47414i | −0.0470418 | + | 0.0470418i | ||||
\(983\) | −12.2658 | − | 12.2658i | −0.391218 | − | 0.391218i | 0.483904 | − | 0.875121i | \(-0.339218\pi\) |
−0.875121 | + | 0.483904i | \(0.839218\pi\) | |||||||
\(984\) | 22.4391 | 0.715331 | ||||||||
\(985\) | 18.7197 | 0.596461 | ||||||||
\(986\) | −9.86420 | − | 9.86420i | −0.314140 | − | 0.314140i | ||||
\(987\) | −31.5586 | + | 31.2072i | −1.00452 | + | 0.993338i | ||||
\(988\) | 0.208471 | − | 0.196748i | 0.00663235 | − | 0.00625940i | ||||
\(989\) | 20.7249 | 0.659013 | ||||||||
\(990\) | 4.21704 | − | 4.21704i | 0.134026 | − | 0.134026i | ||||
\(991\) | 40.5574 | 1.28835 | 0.644175 | − | 0.764878i | \(-0.277201\pi\) | ||||
0.644175 | + | 0.764878i | \(0.277201\pi\) | |||||||
\(992\) | 28.3355 | 0.899655 | ||||||||
\(993\) | −3.88652 | + | 3.88652i | −0.123335 | + | 0.123335i | ||||
\(994\) | −0.103883 | + | 18.5552i | −0.00329497 | + | 0.588536i | ||||
\(995\) | −13.7701 | + | 13.7701i | −0.436542 | + | 0.436542i | ||||
\(996\) | 12.9311 | − | 12.9311i | 0.409737 | − | 0.409737i | ||||
\(997\) | 17.4686i | 0.553236i | 0.960980 | + | 0.276618i | \(0.0892136\pi\) | ||||
−0.960980 | + | 0.276618i | \(0.910786\pi\) | |||||||
\(998\) | − | 47.0999i | − | 1.49092i | ||||||
\(999\) | −3.82074 | − | 3.82074i | −0.120883 | − | 0.120883i |
(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 | 91.2.i.a.34.6 | yes | 12 | |
3.2 | odd | 2 | 819.2.y.h.307.1 | 12 | |||
7.2 | even | 3 | 637.2.bc.a.619.5 | 24 | |||
7.3 | odd | 6 | 637.2.bc.a.411.1 | 24 | |||
7.4 | even | 3 | 637.2.bc.a.411.2 | 24 | |||
7.5 | odd | 6 | 637.2.bc.a.619.6 | 24 | |||
7.6 | odd | 2 | inner | 91.2.i.a.34.5 | ✓ | 12 | |
13.5 | odd | 4 | inner | 91.2.i.a.83.6 | yes | 12 | |
21.20 | even | 2 | 819.2.y.h.307.2 | 12 | |||
39.5 | even | 4 | 819.2.y.h.811.2 | 12 | |||
91.5 | even | 12 | 637.2.bc.a.31.2 | 24 | |||
91.18 | odd | 12 | 637.2.bc.a.460.6 | 24 | |||
91.31 | even | 12 | 637.2.bc.a.460.5 | 24 | |||
91.44 | odd | 12 | 637.2.bc.a.31.1 | 24 | |||
91.83 | even | 4 | inner | 91.2.i.a.83.5 | yes | 12 | |
273.83 | odd | 4 | 819.2.y.h.811.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.i.a.34.5 | ✓ | 12 | 7.6 | odd | 2 | inner | |
91.2.i.a.34.6 | yes | 12 | 1.1 | even | 1 | trivial | |
91.2.i.a.83.5 | yes | 12 | 91.83 | even | 4 | inner | |
91.2.i.a.83.6 | yes | 12 | 13.5 | odd | 4 | inner | |
637.2.bc.a.31.1 | 24 | 91.44 | odd | 12 | |||
637.2.bc.a.31.2 | 24 | 91.5 | even | 12 | |||
637.2.bc.a.411.1 | 24 | 7.3 | odd | 6 | |||
637.2.bc.a.411.2 | 24 | 7.4 | even | 3 | |||
637.2.bc.a.460.5 | 24 | 91.31 | even | 12 | |||
637.2.bc.a.460.6 | 24 | 91.18 | odd | 12 | |||
637.2.bc.a.619.5 | 24 | 7.2 | even | 3 | |||
637.2.bc.a.619.6 | 24 | 7.5 | odd | 6 | |||
819.2.y.h.307.1 | 12 | 3.2 | odd | 2 | |||
819.2.y.h.307.2 | 12 | 21.20 | even | 2 | |||
819.2.y.h.811.1 | 12 | 273.83 | odd | 4 | |||
819.2.y.h.811.2 | 12 | 39.5 | even | 4 |