Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [152,2,Mod(77,152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("152.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 152.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.21372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 77.15 | ||
Root | \(-0.466170 + 1.33517i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 152.77 |
Dual form | 152.2.c.b.77.16 |
$q$-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 \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).
\(n\) | \(39\) | \(77\) | \(97\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.33517 | − | 0.466170i | 0.944109 | − | 0.329632i | ||||
\(3\) | 0.579017i | 0.334296i | 0.985932 | + | 0.167148i | \(0.0534557\pi\) | ||||
−0.985932 | + | 0.167148i | \(0.946544\pi\) | |||||||
\(4\) | 1.56537 | − | 1.24484i | 0.782685 | − | 0.622418i | ||||
\(5\) | − | 2.10882i | − | 0.943091i | −0.881842 | − | 0.471546i | \(-0.843696\pi\) | ||
0.881842 | − | 0.471546i | \(-0.156304\pi\) | |||||||
\(6\) | 0.269921 | + | 0.773088i | 0.110195 | + | 0.315612i | ||||
\(7\) | −2.73436 | −1.03349 | −0.516745 | − | 0.856140i | \(-0.672856\pi\) | ||||
−0.516745 | + | 0.856140i | \(0.672856\pi\) | |||||||
\(8\) | 1.50973 | − | 2.39180i | 0.533772 | − | 0.845629i | ||||
\(9\) | 2.66474 | 0.888246 | ||||||||
\(10\) | −0.983067 | − | 2.81563i | −0.310873 | − | 0.890381i | ||||
\(11\) | 4.66474i | 1.40647i | 0.710957 | + | 0.703236i | \(0.248262\pi\) | ||||
−0.710957 | + | 0.703236i | \(0.751738\pi\) | |||||||
\(12\) | 0.720781 | + | 0.906377i | 0.208072 | + | 0.261648i | ||||
\(13\) | 4.47791i | 1.24195i | 0.783831 | + | 0.620974i | \(0.213263\pi\) | ||||
−0.783831 | + | 0.620974i | \(0.786737\pi\) | |||||||
\(14\) | −3.65084 | + | 1.27468i | −0.975727 | + | 0.340671i | ||||
\(15\) | 1.22104 | 0.315271 | ||||||||
\(16\) | 0.900771 | − | 3.89726i | 0.225193 | − | 0.974314i | ||||
\(17\) | −6.85237 | −1.66194 | −0.830972 | − | 0.556314i | \(-0.812215\pi\) | ||||
−0.830972 | + | 0.556314i | \(0.812215\pi\) | |||||||
\(18\) | 3.55789 | − | 1.24222i | 0.838602 | − | 0.292795i | ||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | −2.62513 | − | 3.30108i | −0.586997 | − | 0.738144i | ||||
\(21\) | − | 1.58324i | − | 0.345491i | ||||||
\(22\) | 2.17456 | + | 6.22823i | 0.463618 | + | 1.32786i | ||||
\(23\) | −1.20416 | −0.251085 | −0.125543 | − | 0.992088i | \(-0.540067\pi\) | ||||
−0.125543 | + | 0.992088i | \(0.540067\pi\) | |||||||
\(24\) | 1.38489 | + | 0.874162i | 0.282690 | + | 0.178438i | ||||
\(25\) | 0.552894 | 0.110579 | ||||||||
\(26\) | 2.08747 | + | 5.97878i | 0.409386 | + | 1.17254i | ||||
\(27\) | 3.27998i | 0.631233i | ||||||||
\(28\) | −4.28028 | + | 3.40382i | −0.808897 | + | 0.643262i | ||||
\(29\) | − | 9.57484i | − | 1.77800i | −0.457904 | − | 0.889002i | \(-0.651400\pi\) | ||
0.457904 | − | 0.889002i | \(-0.348600\pi\) | |||||||
\(30\) | 1.63030 | − | 0.569213i | 0.297651 | − | 0.103924i | ||||
\(31\) | −5.35842 | −0.962400 | −0.481200 | − | 0.876611i | \(-0.659799\pi\) | ||||
−0.481200 | + | 0.876611i | \(0.659799\pi\) | |||||||
\(32\) | −0.614101 | − | 5.62342i | −0.108559 | − | 0.994090i | ||||
\(33\) | −2.70096 | −0.470178 | ||||||||
\(34\) | −9.14909 | + | 3.19437i | −1.56906 | + | 0.547830i | ||||
\(35\) | 5.76625i | 0.974675i | ||||||||
\(36\) | 4.17130 | − | 3.31716i | 0.695217 | − | 0.552860i | ||||
\(37\) | 1.09693i | 0.180335i | 0.995927 | + | 0.0901674i | \(0.0287402\pi\) | ||||
−0.995927 | + | 0.0901674i | \(0.971260\pi\) | |||||||
\(38\) | −0.466170 | − | 1.33517i | −0.0756228 | − | 0.216594i | ||||
\(39\) | −2.59279 | −0.415178 | ||||||||
\(40\) | −5.04386 | − | 3.18375i | −0.797505 | − | 0.503396i | ||||
\(41\) | 7.33797 | 1.14600 | 0.573000 | − | 0.819556i | \(-0.305780\pi\) | ||||
0.573000 | + | 0.819556i | \(0.305780\pi\) | |||||||
\(42\) | −0.738059 | − | 2.11390i | −0.113885 | − | 0.326181i | ||||
\(43\) | 7.64408i | 1.16571i | 0.812576 | + | 0.582856i | \(0.198065\pi\) | ||||
−0.812576 | + | 0.582856i | \(0.801935\pi\) | |||||||
\(44\) | 5.80683 | + | 7.30205i | 0.875413 | + | 1.10082i | ||||
\(45\) | − | 5.61945i | − | 0.837697i | ||||||
\(46\) | −1.60777 | + | 0.561345i | −0.237052 | + | 0.0827658i | ||||
\(47\) | 7.56486 | 1.10345 | 0.551724 | − | 0.834027i | \(-0.313970\pi\) | ||||
0.551724 | + | 0.834027i | \(0.313970\pi\) | |||||||
\(48\) | 2.25658 | + | 0.521562i | 0.325709 | + | 0.0752810i | ||||
\(49\) | 0.476702 | 0.0681003 | ||||||||
\(50\) | 0.738208 | − | 0.257743i | 0.104398 | − | 0.0364503i | ||||
\(51\) | − | 3.96764i | − | 0.555581i | ||||||
\(52\) | 5.57426 | + | 7.00959i | 0.773011 | + | 0.972055i | ||||
\(53\) | 3.11949i | 0.428495i | 0.976779 | + | 0.214248i | \(0.0687300\pi\) | ||||
−0.976779 | + | 0.214248i | \(0.931270\pi\) | |||||||
\(54\) | 1.52903 | + | 4.37934i | 0.208075 | + | 0.595953i | ||||
\(55\) | 9.83708 | 1.32643 | ||||||||
\(56\) | −4.12815 | + | 6.54003i | −0.551648 | + | 0.873948i | ||||
\(57\) | 0.579017 | 0.0766927 | ||||||||
\(58\) | −4.46351 | − | 12.7841i | −0.586087 | − | 1.67863i | ||||
\(59\) | − | 10.2442i | − | 1.33368i | −0.745201 | − | 0.666840i | \(-0.767646\pi\) | ||
0.745201 | − | 0.666840i | \(-0.232354\pi\) | |||||||
\(60\) | 1.91138 | − | 1.51999i | 0.246758 | − | 0.196230i | ||||
\(61\) | 0.722061i | 0.0924504i | 0.998931 | + | 0.0462252i | \(0.0147192\pi\) | ||||
−0.998931 | + | 0.0462252i | \(0.985281\pi\) | |||||||
\(62\) | −7.15441 | + | 2.49793i | −0.908611 | + | 0.317238i | ||||
\(63\) | −7.28634 | −0.917993 | ||||||||
\(64\) | −3.44140 | − | 7.22196i | −0.430175 | − | 0.902745i | ||||
\(65\) | 9.44309 | 1.17127 | ||||||||
\(66\) | −3.60625 | + | 1.25911i | −0.443899 | + | 0.154986i | ||||
\(67\) | − | 6.13698i | − | 0.749752i | −0.927075 | − | 0.374876i | \(-0.877685\pi\) | ||
0.927075 | − | 0.374876i | \(-0.122315\pi\) | |||||||
\(68\) | −10.7265 | + | 8.53007i | −1.30078 | + | 1.03442i | ||||
\(69\) | − | 0.697232i | − | 0.0839368i | ||||||
\(70\) | 2.68806 | + | 7.69894i | 0.321284 | + | 0.920200i | ||||
\(71\) | 4.62247 | 0.548587 | 0.274293 | − | 0.961646i | \(-0.411556\pi\) | ||||
0.274293 | + | 0.961646i | \(0.411556\pi\) | |||||||
\(72\) | 4.02305 | − | 6.37352i | 0.474121 | − | 0.751126i | ||||
\(73\) | −6.19270 | −0.724801 | −0.362400 | − | 0.932022i | \(-0.618043\pi\) | ||||
−0.362400 | + | 0.932022i | \(0.618043\pi\) | |||||||
\(74\) | 0.511358 | + | 1.46460i | 0.0594441 | + | 0.170256i | ||||
\(75\) | 0.320135i | 0.0369660i | ||||||||
\(76\) | −1.24484 | − | 1.56537i | −0.142792 | − | 0.179560i | ||||
\(77\) | − | 12.7551i | − | 1.45357i | ||||||
\(78\) | −3.46182 | + | 1.20868i | −0.391974 | + | 0.136856i | ||||
\(79\) | −3.26723 | −0.367592 | −0.183796 | − | 0.982964i | \(-0.558839\pi\) | ||||
−0.183796 | + | 0.982964i | \(0.558839\pi\) | |||||||
\(80\) | −8.21860 | − | 1.89956i | −0.918867 | − | 0.212377i | ||||
\(81\) | 6.09505 | 0.677228 | ||||||||
\(82\) | 9.79746 | − | 3.42075i | 1.08195 | − | 0.377758i | ||||
\(83\) | − | 8.97934i | − | 0.985611i | −0.870140 | − | 0.492805i | \(-0.835971\pi\) | ||
0.870140 | − | 0.492805i | \(-0.164029\pi\) | |||||||
\(84\) | −1.97087 | − | 2.47836i | −0.215040 | − | 0.270411i | ||||
\(85\) | 14.4504i | 1.56736i | ||||||||
\(86\) | 3.56344 | + | 10.2062i | 0.384256 | + | 1.10056i | ||||
\(87\) | 5.54400 | 0.594379 | ||||||||
\(88\) | 11.1571 | + | 7.04252i | 1.18935 | + | 0.750735i | ||||
\(89\) | 0.620707 | 0.0657948 | 0.0328974 | − | 0.999459i | \(-0.489527\pi\) | ||||
0.0328974 | + | 0.999459i | \(0.489527\pi\) | |||||||
\(90\) | −2.61962 | − | 7.50293i | −0.276132 | − | 0.790878i | ||||
\(91\) | − | 12.2442i | − | 1.28354i | ||||||
\(92\) | −1.88496 | + | 1.49899i | −0.196521 | + | 0.156280i | ||||
\(93\) | − | 3.10262i | − | 0.321726i | ||||||
\(94\) | 10.1004 | − | 3.52651i | 1.04178 | − | 0.363732i | ||||
\(95\) | −2.10882 | −0.216360 | ||||||||
\(96\) | 3.25606 | − | 0.355575i | 0.332320 | − | 0.0362907i | ||||
\(97\) | −1.67284 | −0.169851 | −0.0849257 | − | 0.996387i | \(-0.527065\pi\) | ||||
−0.0849257 | + | 0.996387i | \(0.527065\pi\) | |||||||
\(98\) | 0.636479 | − | 0.222224i | 0.0642941 | − | 0.0224480i | ||||
\(99\) | 12.4303i | 1.24929i | ||||||||
\(100\) | 0.865484 | − | 0.688261i | 0.0865484 | − | 0.0688261i | ||||
\(101\) | 7.30571i | 0.726946i | 0.931605 | + | 0.363473i | \(0.118409\pi\) | ||||
−0.931605 | + | 0.363473i | \(0.881591\pi\) | |||||||
\(102\) | −1.84960 | − | 5.29748i | −0.183137 | − | 0.524529i | ||||
\(103\) | −8.77332 | −0.864461 | −0.432231 | − | 0.901763i | \(-0.642273\pi\) | ||||
−0.432231 | + | 0.901763i | \(0.642273\pi\) | |||||||
\(104\) | 10.7103 | + | 6.76045i | 1.05023 | + | 0.662917i | ||||
\(105\) | −3.33876 | −0.325830 | ||||||||
\(106\) | 1.45421 | + | 4.16506i | 0.141246 | + | 0.404546i | ||||
\(107\) | − | 9.91355i | − | 0.958379i | −0.877711 | − | 0.479190i | \(-0.840931\pi\) | ||
0.877711 | − | 0.479190i | \(-0.159069\pi\) | |||||||
\(108\) | 4.08304 | + | 5.13439i | 0.392890 | + | 0.494057i | ||||
\(109\) | 2.84589i | 0.272587i | 0.990669 | + | 0.136293i | \(0.0435189\pi\) | ||||
−0.990669 | + | 0.136293i | \(0.956481\pi\) | |||||||
\(110\) | 13.1342 | − | 4.58575i | 1.25230 | − | 0.437234i | ||||
\(111\) | −0.635143 | −0.0602851 | ||||||||
\(112\) | −2.46303 | + | 10.6565i | −0.232734 | + | 1.00694i | ||||
\(113\) | −1.58487 | −0.149092 | −0.0745462 | − | 0.997218i | \(-0.523751\pi\) | ||||
−0.0745462 | + | 0.997218i | \(0.523751\pi\) | |||||||
\(114\) | 0.773088 | − | 0.269921i | 0.0724063 | − | 0.0252804i | ||||
\(115\) | 2.53936i | 0.236797i | ||||||||
\(116\) | −11.9191 | − | 14.9882i | −1.10666 | − | 1.39162i | ||||
\(117\) | 11.9325i | 1.10316i | ||||||||
\(118\) | −4.77554 | − | 13.6778i | −0.439624 | − | 1.25914i | ||||
\(119\) | 18.7368 | 1.71760 | ||||||||
\(120\) | 1.84345 | − | 2.92048i | 0.168283 | − | 0.266603i | ||||
\(121\) | −10.7598 | −0.978163 | ||||||||
\(122\) | 0.336603 | + | 0.964075i | 0.0304746 | + | 0.0872833i | ||||
\(123\) | 4.24881i | 0.383103i | ||||||||
\(124\) | −8.38791 | + | 6.67034i | −0.753256 | + | 0.599015i | ||||
\(125\) | − | 11.7100i | − | 1.04738i | ||||||
\(126\) | −9.72853 | + | 3.39668i | −0.866686 | + | 0.302600i | ||||
\(127\) | 14.2933 | 1.26833 | 0.634163 | − | 0.773199i | \(-0.281345\pi\) | ||||
0.634163 | + | 0.773199i | \(0.281345\pi\) | |||||||
\(128\) | −7.96153 | − | 8.03829i | −0.703706 | − | 0.710491i | ||||
\(129\) | −4.42605 | −0.389692 | ||||||||
\(130\) | 12.6081 | − | 4.40209i | 1.10581 | − | 0.386088i | ||||
\(131\) | − | 0.609006i | − | 0.0532091i | −0.999646 | − | 0.0266046i | \(-0.991531\pi\) | ||
0.999646 | − | 0.0266046i | \(-0.00846949\pi\) | |||||||
\(132\) | −4.22801 | + | 3.36226i | −0.368001 | + | 0.292647i | ||||
\(133\) | 2.73436i | 0.237099i | ||||||||
\(134\) | −2.86088 | − | 8.19393i | −0.247142 | − | 0.707848i | ||||
\(135\) | 6.91688 | 0.595310 | ||||||||
\(136\) | −10.3453 | + | 16.3895i | −0.887099 | + | 1.40539i | ||||
\(137\) | 18.1589 | 1.55142 | 0.775710 | − | 0.631089i | \(-0.217392\pi\) | ||||
0.775710 | + | 0.631089i | \(0.217392\pi\) | |||||||
\(138\) | −0.325029 | − | 0.930924i | −0.0276683 | − | 0.0792455i | ||||
\(139\) | 1.93421i | 0.164058i | 0.996630 | + | 0.0820289i | \(0.0261400\pi\) | ||||
−0.996630 | + | 0.0820289i | \(0.973860\pi\) | |||||||
\(140\) | 7.17804 | + | 9.02633i | 0.606655 | + | 0.762864i | ||||
\(141\) | 4.38018i | 0.368878i | ||||||||
\(142\) | 6.17180 | − | 2.15486i | 0.517926 | − | 0.180832i | ||||
\(143\) | −20.8883 | −1.74677 | ||||||||
\(144\) | 2.40032 | − | 10.3852i | 0.200027 | − | 0.865431i | ||||
\(145\) | −20.1916 | −1.67682 | ||||||||
\(146\) | −8.26832 | + | 2.88685i | −0.684291 | + | 0.238918i | ||||
\(147\) | 0.276019i | 0.0227656i | ||||||||
\(148\) | 1.36550 | + | 1.71711i | 0.112244 | + | 0.141145i | ||||
\(149\) | 15.5775i | 1.27616i | 0.769970 | + | 0.638080i | \(0.220271\pi\) | ||||
−0.769970 | + | 0.638080i | \(0.779729\pi\) | |||||||
\(150\) | 0.149237 | + | 0.427435i | 0.0121852 | + | 0.0349000i | ||||
\(151\) | −19.9746 | −1.62551 | −0.812756 | − | 0.582605i | \(-0.802034\pi\) | ||||
−0.812756 | + | 0.582605i | \(0.802034\pi\) | |||||||
\(152\) | −2.39180 | − | 1.50973i | −0.194000 | − | 0.122456i | ||||
\(153\) | −18.2598 | −1.47622 | ||||||||
\(154\) | −5.94603 | − | 17.0302i | −0.479145 | − | 1.37233i | ||||
\(155\) | 11.2999i | 0.907631i | ||||||||
\(156\) | −4.05867 | + | 3.22759i | −0.324954 | + | 0.258414i | ||||
\(157\) | 20.8872i | 1.66698i | 0.552536 | + | 0.833489i | \(0.313660\pi\) | ||||
−0.552536 | + | 0.833489i | \(0.686340\pi\) | |||||||
\(158\) | −4.36232 | + | 1.52309i | −0.347047 | + | 0.121170i | ||||
\(159\) | −1.80624 | −0.143244 | ||||||||
\(160\) | −11.8588 | + | 1.29503i | −0.937518 | + | 0.102381i | ||||
\(161\) | 3.29261 | 0.259494 | ||||||||
\(162\) | 8.13794 | − | 2.84133i | 0.639377 | − | 0.223236i | ||||
\(163\) | 2.54835i | 0.199602i | 0.995007 | + | 0.0998010i | \(0.0318206\pi\) | ||||
−0.995007 | + | 0.0998010i | \(0.968179\pi\) | |||||||
\(164\) | 11.4867 | − | 9.13457i | 0.896957 | − | 0.713290i | ||||
\(165\) | 5.69584i | 0.443420i | ||||||||
\(166\) | −4.18590 | − | 11.9890i | −0.324889 | − | 0.930524i | ||||
\(167\) | −18.6644 | −1.44429 | −0.722146 | − | 0.691740i | \(-0.756844\pi\) | ||||
−0.722146 | + | 0.691740i | \(0.756844\pi\) | |||||||
\(168\) | −3.78679 | − | 2.39027i | −0.292157 | − | 0.184413i | ||||
\(169\) | −7.05167 | −0.542436 | ||||||||
\(170\) | 6.73634 | + | 19.2938i | 0.516654 | + | 1.47976i | ||||
\(171\) | − | 2.66474i | − | 0.203778i | ||||||
\(172\) | 9.51562 | + | 11.9658i | 0.725559 | + | 0.912385i | ||||
\(173\) | 8.42370i | 0.640442i | 0.947343 | + | 0.320221i | \(0.103757\pi\) | ||||
−0.947343 | + | 0.320221i | \(0.896243\pi\) | |||||||
\(174\) | 7.40219 | − | 2.58445i | 0.561159 | − | 0.195926i | ||||
\(175\) | −1.51181 | −0.114282 | ||||||||
\(176\) | 18.1797 | + | 4.20186i | 1.37035 | + | 0.316727i | ||||
\(177\) | 5.93157 | 0.445844 | ||||||||
\(178\) | 0.828751 | − | 0.289355i | 0.0621175 | − | 0.0216881i | ||||
\(179\) | − | 16.6809i | − | 1.24679i | −0.781908 | − | 0.623394i | \(-0.785753\pi\) | ||
0.781908 | − | 0.623394i | \(-0.214247\pi\) | |||||||
\(180\) | −6.99528 | − | 8.79651i | −0.521398 | − | 0.655654i | ||||
\(181\) | 4.65888i | 0.346292i | 0.984896 | + | 0.173146i | \(0.0553932\pi\) | ||||
−0.984896 | + | 0.173146i | \(0.944607\pi\) | |||||||
\(182\) | −5.70788 | − | 16.3481i | −0.423096 | − | 1.21180i | ||||
\(183\) | −0.418086 | −0.0309058 | ||||||||
\(184\) | −1.81797 | + | 2.88012i | −0.134022 | + | 0.212325i | ||||
\(185\) | 2.31323 | 0.170072 | ||||||||
\(186\) | −1.44635 | − | 4.14253i | −0.106051 | − | 0.303745i | ||||
\(187\) | − | 31.9645i | − | 2.33748i | ||||||
\(188\) | 11.8418 | − | 9.41700i | 0.863653 | − | 0.686805i | ||||
\(189\) | − | 8.96864i | − | 0.652372i | ||||||
\(190\) | −2.81563 | + | 0.983067i | −0.204268 | + | 0.0713192i | ||||
\(191\) | 20.0609 | 1.45155 | 0.725777 | − | 0.687930i | \(-0.241480\pi\) | ||||
0.725777 | + | 0.687930i | \(0.241480\pi\) | |||||||
\(192\) | 4.18164 | − | 1.99263i | 0.301784 | − | 0.143806i | ||||
\(193\) | 1.85117 | 0.133250 | 0.0666251 | − | 0.997778i | \(-0.478777\pi\) | ||||
0.0666251 | + | 0.997778i | \(0.478777\pi\) | |||||||
\(194\) | −2.23353 | + | 0.779829i | −0.160358 | + | 0.0559885i | ||||
\(195\) | 5.46771i | 0.391551i | ||||||||
\(196\) | 0.746215 | − | 0.593416i | 0.0533011 | − | 0.0423868i | ||||
\(197\) | 0.224883i | 0.0160222i | 0.999968 | + | 0.00801112i | \(0.00255005\pi\) | ||||
−0.999968 | + | 0.00801112i | \(0.997450\pi\) | |||||||
\(198\) | 5.79464 | + | 16.5966i | 0.411807 | + | 1.17947i | ||||
\(199\) | −1.77685 | −0.125957 | −0.0629787 | − | 0.998015i | \(-0.520060\pi\) | ||||
−0.0629787 | + | 0.998015i | \(0.520060\pi\) | |||||||
\(200\) | 0.834723 | − | 1.32241i | 0.0590238 | − | 0.0935085i | ||||
\(201\) | 3.55342 | 0.250639 | ||||||||
\(202\) | 3.40571 | + | 9.75439i | 0.239625 | + | 0.686316i | ||||
\(203\) | 26.1810i | 1.83755i | ||||||||
\(204\) | −4.93906 | − | 6.21083i | −0.345803 | − | 0.434845i | ||||
\(205\) | − | 15.4744i | − | 1.08078i | ||||||
\(206\) | −11.7139 | + | 4.08986i | −0.816146 | + | 0.284954i | ||||
\(207\) | −3.20878 | −0.223026 | ||||||||
\(208\) | 17.4516 | + | 4.03357i | 1.21005 | + | 0.279678i | ||||
\(209\) | 4.66474 | 0.322667 | ||||||||
\(210\) | −4.45782 | + | 1.55643i | −0.307619 | + | 0.107404i | ||||
\(211\) | 17.0194i | 1.17166i | 0.810433 | + | 0.585831i | \(0.199232\pi\) | ||||
−0.810433 | + | 0.585831i | \(0.800768\pi\) | |||||||
\(212\) | 3.88325 | + | 4.88316i | 0.266703 | + | 0.335377i | ||||
\(213\) | 2.67649i | 0.183390i | ||||||||
\(214\) | −4.62140 | − | 13.2363i | −0.315913 | − | 0.904815i | ||||
\(215\) | 16.1200 | 1.09937 | ||||||||
\(216\) | 7.84506 | + | 4.95190i | 0.533788 | + | 0.336934i | ||||
\(217\) | 14.6518 | 0.994630 | ||||||||
\(218\) | 1.32667 | + | 3.79975i | 0.0898533 | + | 0.257352i | ||||
\(219\) | − | 3.58568i | − | 0.242298i | ||||||
\(220\) | 15.3987 | − | 12.2455i | 1.03818 | − | 0.825594i | ||||
\(221\) | − | 30.6843i | − | 2.06405i | ||||||
\(222\) | −0.848026 | + | 0.296085i | −0.0569158 | + | 0.0198719i | ||||
\(223\) | 13.6634 | 0.914971 | 0.457486 | − | 0.889217i | \(-0.348750\pi\) | ||||
0.457486 | + | 0.889217i | \(0.348750\pi\) | |||||||
\(224\) | 1.67917 | + | 15.3764i | 0.112194 | + | 1.02738i | ||||
\(225\) | 1.47332 | 0.0982212 | ||||||||
\(226\) | −2.11608 | + | 0.738821i | −0.140760 | + | 0.0491457i | ||||
\(227\) | − | 5.46152i | − | 0.362494i | −0.983438 | − | 0.181247i | \(-0.941987\pi\) | ||
0.983438 | − | 0.181247i | \(-0.0580133\pi\) | |||||||
\(228\) | 0.906377 | − | 0.720781i | 0.0600263 | − | 0.0477349i | ||||
\(229\) | 3.22791i | 0.213306i | 0.994296 | + | 0.106653i | \(0.0340135\pi\) | ||||
−0.994296 | + | 0.106653i | \(0.965987\pi\) | |||||||
\(230\) | 1.18377 | + | 3.39048i | 0.0780557 | + | 0.223562i | ||||
\(231\) | 7.38540 | 0.485923 | ||||||||
\(232\) | −22.9011 | − | 14.4555i | −1.50353 | − | 0.949048i | ||||
\(233\) | −17.8344 | −1.16837 | −0.584185 | − | 0.811621i | \(-0.698586\pi\) | ||||
−0.584185 | + | 0.811621i | \(0.698586\pi\) | |||||||
\(234\) | 5.56256 | + | 15.9319i | 0.363636 | + | 1.04150i | ||||
\(235\) | − | 15.9529i | − | 1.04065i | ||||||
\(236\) | −12.7523 | − | 16.0360i | −0.830106 | − | 1.04385i | ||||
\(237\) | − | 1.89178i | − | 0.122884i | ||||||
\(238\) | 25.0169 | − | 8.73455i | 1.62160 | − | 0.566176i | ||||
\(239\) | 1.82556 | 0.118086 | 0.0590428 | − | 0.998255i | \(-0.481195\pi\) | ||||
0.0590428 | + | 0.998255i | \(0.481195\pi\) | |||||||
\(240\) | 1.09988 | − | 4.75871i | 0.0709968 | − | 0.307173i | ||||
\(241\) | 6.47608 | 0.417161 | 0.208581 | − | 0.978005i | \(-0.433116\pi\) | ||||
0.208581 | + | 0.978005i | \(0.433116\pi\) | |||||||
\(242\) | −14.3662 | + | 5.01589i | −0.923493 | + | 0.322434i | ||||
\(243\) | 13.3691i | 0.857627i | ||||||||
\(244\) | 0.898846 | + | 1.13029i | 0.0575427 | + | 0.0723596i | ||||
\(245\) | − | 1.00528i | − | 0.0642248i | ||||||
\(246\) | 1.98067 | + | 5.67290i | 0.126283 | + | 0.361691i | ||||
\(247\) | 4.47791 | 0.284923 | ||||||||
\(248\) | −8.08979 | + | 12.8163i | −0.513702 | + | 0.813833i | ||||
\(249\) | 5.19919 | 0.329485 | ||||||||
\(250\) | −5.45887 | − | 15.6349i | −0.345249 | − | 0.988839i | ||||
\(251\) | 3.10899i | 0.196238i | 0.995175 | + | 0.0981189i | \(0.0312825\pi\) | ||||
−0.995175 | + | 0.0981189i | \(0.968717\pi\) | |||||||
\(252\) | −11.4058 | + | 9.07030i | −0.718500 | + | 0.571375i | ||||
\(253\) | − | 5.61711i | − | 0.353145i | ||||||
\(254\) | 19.0840 | − | 6.66312i | 1.19744 | − | 0.418081i | ||||
\(255\) | −8.36702 | −0.523963 | ||||||||
\(256\) | −14.3772 | − | 7.02107i | −0.898576 | − | 0.438817i | ||||
\(257\) | 5.75606 | 0.359053 | 0.179526 | − | 0.983753i | \(-0.442543\pi\) | ||||
0.179526 | + | 0.983753i | \(0.442543\pi\) | |||||||
\(258\) | −5.90955 | + | 2.06329i | −0.367912 | + | 0.128455i | ||||
\(259\) | − | 2.99941i | − | 0.186374i | ||||||
\(260\) | 14.7819 | − | 11.7551i | 0.916737 | − | 0.729020i | ||||
\(261\) | − | 25.5145i | − | 1.57931i | ||||||
\(262\) | −0.283900 | − | 0.813128i | −0.0175394 | − | 0.0502352i | ||||
\(263\) | −4.58595 | −0.282782 | −0.141391 | − | 0.989954i | \(-0.545157\pi\) | ||||
−0.141391 | + | 0.989954i | \(0.545157\pi\) | |||||||
\(264\) | −4.07774 | + | 6.46016i | −0.250968 | + | 0.397596i | ||||
\(265\) | 6.57844 | 0.404110 | ||||||||
\(266\) | 1.27468 | + | 3.65084i | 0.0781554 | + | 0.223847i | ||||
\(267\) | 0.359400i | 0.0219949i | ||||||||
\(268\) | −7.63953 | − | 9.60665i | −0.466659 | − | 0.586820i | ||||
\(269\) | − | 11.3913i | − | 0.694542i | −0.937765 | − | 0.347271i | \(-0.887108\pi\) | ||
0.937765 | − | 0.347271i | \(-0.112892\pi\) | |||||||
\(270\) | 9.23523 | − | 3.22444i | 0.562038 | − | 0.196233i | ||||
\(271\) | 25.1252 | 1.52625 | 0.763124 | − | 0.646252i | \(-0.223664\pi\) | ||||
0.763124 | + | 0.646252i | \(0.223664\pi\) | |||||||
\(272\) | −6.17241 | + | 26.7054i | −0.374258 | + | 1.61926i | ||||
\(273\) | 7.08960 | 0.429082 | ||||||||
\(274\) | 24.2453 | − | 8.46514i | 1.46471 | − | 0.511398i | ||||
\(275\) | 2.57910i | 0.155526i | ||||||||
\(276\) | −0.867938 | − | 1.09143i | −0.0522437 | − | 0.0656961i | ||||
\(277\) | 18.2998i | 1.09953i | 0.835321 | + | 0.549763i | \(0.185282\pi\) | ||||
−0.835321 | + | 0.549763i | \(0.814718\pi\) | |||||||
\(278\) | 0.901672 | + | 2.58251i | 0.0540787 | + | 0.154888i | ||||
\(279\) | −14.2788 | −0.854848 | ||||||||
\(280\) | 13.7917 | + | 8.70551i | 0.824213 | + | 0.520254i | ||||
\(281\) | −18.0708 | −1.07802 | −0.539008 | − | 0.842301i | \(-0.681201\pi\) | ||||
−0.539008 | + | 0.842301i | \(0.681201\pi\) | |||||||
\(282\) | 2.04191 | + | 5.84830i | 0.121594 | + | 0.348261i | ||||
\(283\) | 15.3972i | 0.915269i | 0.889140 | + | 0.457634i | \(0.151303\pi\) | ||||
−0.889140 | + | 0.457634i | \(0.848697\pi\) | |||||||
\(284\) | 7.23589 | − | 5.75422i | 0.429371 | − | 0.341450i | ||||
\(285\) | − | 1.22104i | − | 0.0723282i | ||||||
\(286\) | −27.8894 | + | 9.73749i | −1.64914 | + | 0.575790i | ||||
\(287\) | −20.0646 | −1.18438 | ||||||||
\(288\) | −1.63642 | − | 14.9850i | −0.0964269 | − | 0.882997i | ||||
\(289\) | 29.9550 | 1.76206 | ||||||||
\(290\) | −26.9592 | + | 9.41271i | −1.58310 | + | 0.552734i | ||||
\(291\) | − | 0.968605i | − | 0.0567806i | ||||||
\(292\) | −9.69387 | + | 7.70889i | −0.567291 | + | 0.451129i | ||||
\(293\) | 11.4407i | 0.668374i | 0.942507 | + | 0.334187i | \(0.108462\pi\) | ||||
−0.942507 | + | 0.334187i | \(0.891538\pi\) | |||||||
\(294\) | 0.128672 | + | 0.368533i | 0.00750429 | + | 0.0214933i | ||||
\(295\) | −21.6031 | −1.25778 | ||||||||
\(296\) | 2.62364 | + | 1.65608i | 0.152496 | + | 0.0962576i | ||||
\(297\) | −15.3003 | −0.887811 | ||||||||
\(298\) | 7.26178 | + | 20.7987i | 0.420664 | + | 1.20484i | ||||
\(299\) | − | 5.39214i | − | 0.311835i | ||||||
\(300\) | 0.398515 | + | 0.501130i | 0.0230083 | + | 0.0289327i | ||||
\(301\) | − | 20.9016i | − | 1.20475i | ||||||
\(302\) | −26.6696 | + | 9.31157i | −1.53466 | + | 0.535821i | ||||
\(303\) | −4.23013 | −0.243015 | ||||||||
\(304\) | −3.89726 | − | 0.900771i | −0.223523 | − | 0.0516628i | ||||
\(305\) | 1.52269 | 0.0871892 | ||||||||
\(306\) | −24.3799 | + | 8.51216i | −1.39371 | + | 0.486608i | ||||
\(307\) | − | 21.3453i | − | 1.21824i | −0.793077 | − | 0.609122i | \(-0.791522\pi\) | ||
0.793077 | − | 0.609122i | \(-0.208478\pi\) | |||||||
\(308\) | −15.8779 | − | 19.9664i | −0.904730 | − | 1.13769i | ||||
\(309\) | − | 5.07991i | − | 0.288986i | ||||||
\(310\) | 5.26768 | + | 15.0873i | 0.299184 | + | 0.856903i | ||||
\(311\) | −21.7295 | −1.23216 | −0.616082 | − | 0.787682i | \(-0.711281\pi\) | ||||
−0.616082 | + | 0.787682i | \(0.711281\pi\) | |||||||
\(312\) | −3.91442 | + | 6.20142i | −0.221610 | + | 0.351086i | ||||
\(313\) | 34.1009 | 1.92750 | 0.963748 | − | 0.266814i | \(-0.0859710\pi\) | ||||
0.963748 | + | 0.266814i | \(0.0859710\pi\) | |||||||
\(314\) | 9.73698 | + | 27.8880i | 0.549490 | + | 1.57381i | ||||
\(315\) | 15.3656i | 0.865751i | ||||||||
\(316\) | −5.11443 | + | 4.06716i | −0.287709 | + | 0.228796i | ||||
\(317\) | − | 22.2281i | − | 1.24845i | −0.781244 | − | 0.624226i | \(-0.785414\pi\) | ||
0.781244 | − | 0.624226i | \(-0.214586\pi\) | |||||||
\(318\) | −2.41164 | + | 0.842015i | −0.135238 | + | 0.0472179i | ||||
\(319\) | 44.6641 | 2.50071 | ||||||||
\(320\) | −15.2298 | + | 7.25729i | −0.851371 | + | 0.405695i | ||||
\(321\) | 5.74012 | 0.320382 | ||||||||
\(322\) | 4.39620 | − | 1.53492i | 0.244991 | − | 0.0855376i | ||||
\(323\) | 6.85237i | 0.381276i | ||||||||
\(324\) | 9.54101 | − | 7.58733i | 0.530056 | − | 0.421519i | ||||
\(325\) | 2.47581i | 0.137333i | ||||||||
\(326\) | 1.18796 | + | 3.40248i | 0.0657952 | + | 0.188446i | ||||
\(327\) | −1.64782 | −0.0911245 | ||||||||
\(328\) | 11.0784 | − | 17.5510i | 0.611702 | − | 0.969090i | ||||
\(329\) | −20.6850 | −1.14040 | ||||||||
\(330\) | 2.65523 | + | 7.60493i | 0.146166 | + | 0.418637i | ||||
\(331\) | 24.1969i | 1.32998i | 0.746852 | + | 0.664991i | \(0.231564\pi\) | ||||
−0.746852 | + | 0.664991i | \(0.768436\pi\) | |||||||
\(332\) | −11.1778 | − | 14.0560i | −0.613461 | − | 0.771423i | ||||
\(333\) | 2.92304i | 0.160182i | ||||||||
\(334\) | −24.9202 | + | 8.70077i | −1.36357 | + | 0.476085i | ||||
\(335\) | −12.9418 | −0.707084 | ||||||||
\(336\) | −6.17029 | − | 1.42614i | −0.336617 | − | 0.0778021i | ||||
\(337\) | −34.2735 | −1.86700 | −0.933498 | − | 0.358583i | \(-0.883260\pi\) | ||||
−0.933498 | + | 0.358583i | \(0.883260\pi\) | |||||||
\(338\) | −9.41519 | + | 3.28728i | −0.512119 | + | 0.178804i | ||||
\(339\) | − | 0.917670i | − | 0.0498410i | ||||||
\(340\) | 17.9884 | + | 22.6202i | 0.975555 | + | 1.22675i | ||||
\(341\) | − | 24.9956i | − | 1.35359i | ||||||
\(342\) | −1.24222 | − | 3.55789i | −0.0671717 | − | 0.192388i | ||||
\(343\) | 17.8370 | 0.963108 | ||||||||
\(344\) | 18.2831 | + | 11.5405i | 0.985759 | + | 0.622224i | ||||
\(345\) | −1.47033 | −0.0791601 | ||||||||
\(346\) | 3.92688 | + | 11.2471i | 0.211110 | + | 0.604647i | ||||
\(347\) | 26.9233i | 1.44532i | 0.691206 | + | 0.722658i | \(0.257080\pi\) | ||||
−0.691206 | + | 0.722658i | \(0.742920\pi\) | |||||||
\(348\) | 8.67841 | − | 6.90136i | 0.465212 | − | 0.369952i | ||||
\(349\) | 8.65769i | 0.463436i | 0.972783 | + | 0.231718i | \(0.0744346\pi\) | ||||
−0.972783 | + | 0.231718i | \(0.925565\pi\) | |||||||
\(350\) | −2.01852 | + | 0.704760i | −0.107895 | + | 0.0376710i | ||||
\(351\) | −14.6875 | −0.783959 | ||||||||
\(352\) | 26.2318 | − | 2.86462i | 1.39816 | − | 0.152685i | ||||
\(353\) | −9.11265 | −0.485018 | −0.242509 | − | 0.970149i | \(-0.577970\pi\) | ||||
−0.242509 | + | 0.970149i | \(0.577970\pi\) | |||||||
\(354\) | 7.91966 | − | 2.76512i | 0.420925 | − | 0.146964i | ||||
\(355\) | − | 9.74795i | − | 0.517367i | ||||||
\(356\) | 0.971636 | − | 0.772678i | 0.0514966 | − | 0.0409518i | ||||
\(357\) | 10.8489i | 0.574187i | ||||||||
\(358\) | −7.77613 | − | 22.2719i | −0.410981 | − | 1.17710i | ||||
\(359\) | 4.29978 | 0.226934 | 0.113467 | − | 0.993542i | \(-0.463804\pi\) | ||||
0.113467 | + | 0.993542i | \(0.463804\pi\) | |||||||
\(360\) | −13.4406 | − | 8.48387i | −0.708381 | − | 0.447139i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 2.17183 | + | 6.22041i | 0.114149 | + | 0.326938i | ||||
\(363\) | − | 6.23010i | − | 0.326996i | ||||||
\(364\) | −15.2420 | − | 19.1667i | −0.798898 | − | 1.00461i | ||||
\(365\) | 13.0593i | 0.683553i | ||||||||
\(366\) | −0.558216 | + | 0.194899i | −0.0291784 | + | 0.0101875i | ||||
\(367\) | −21.2873 | −1.11119 | −0.555594 | − | 0.831454i | \(-0.687509\pi\) | ||||
−0.555594 | + | 0.831454i | \(0.687509\pi\) | |||||||
\(368\) | −1.08468 | + | 4.69294i | −0.0565426 | + | 0.244636i | ||||
\(369\) | 19.5538 | 1.01793 | ||||||||
\(370\) | 3.08856 | − | 1.07836i | 0.160567 | − | 0.0560612i | ||||
\(371\) | − | 8.52980i | − | 0.442845i | ||||||
\(372\) | −3.86224 | − | 4.85674i | −0.200248 | − | 0.251810i | ||||
\(373\) | − | 11.1076i | − | 0.575129i | −0.957761 | − | 0.287565i | \(-0.907154\pi\) | ||
0.957761 | − | 0.287565i | \(-0.0928456\pi\) | |||||||
\(374\) | −14.9009 | − | 42.6781i | −0.770507 | − | 2.20683i | ||||
\(375\) | 6.78031 | 0.350134 | ||||||||
\(376\) | 11.4209 | − | 18.0936i | 0.588990 | − | 0.933107i | ||||
\(377\) | 42.8753 | 2.20819 | ||||||||
\(378\) | −4.18091 | − | 11.9747i | −0.215043 | − | 0.615911i | ||||
\(379\) | − | 20.6908i | − | 1.06281i | −0.847117 | − | 0.531407i | \(-0.821664\pi\) | ||
0.847117 | − | 0.531407i | \(-0.178336\pi\) | |||||||
\(380\) | −3.30108 | + | 2.62513i | −0.169342 | + | 0.134666i | ||||
\(381\) | 8.27608i | 0.423996i | ||||||||
\(382\) | 26.7847 | − | 9.35178i | 1.37043 | − | 0.478479i | ||||
\(383\) | −12.1869 | −0.622720 | −0.311360 | − | 0.950292i | \(-0.600785\pi\) | ||||
−0.311360 | + | 0.950292i | \(0.600785\pi\) | |||||||
\(384\) | 4.65431 | − | 4.60986i | 0.237514 | − | 0.235246i | ||||
\(385\) | −26.8981 | −1.37085 | ||||||||
\(386\) | 2.47163 | − | 0.862960i | 0.125803 | − | 0.0439235i | ||||
\(387\) | 20.3695i | 1.03544i | ||||||||
\(388\) | −2.61862 | + | 2.08241i | −0.132940 | + | 0.105719i | ||||
\(389\) | 26.1769i | 1.32722i | 0.748078 | + | 0.663611i | \(0.230977\pi\) | ||||
−0.748078 | + | 0.663611i | \(0.769023\pi\) | |||||||
\(390\) | 2.54888 | + | 7.30034i | 0.129068 | + | 0.369667i | ||||
\(391\) | 8.25137 | 0.417290 | ||||||||
\(392\) | 0.719694 | − | 1.14018i | 0.0363500 | − | 0.0575876i | ||||
\(393\) | 0.352625 | 0.0177876 | ||||||||
\(394\) | 0.104834 | + | 0.300257i | 0.00528145 | + | 0.0151268i | ||||
\(395\) | 6.88999i | 0.346673i | ||||||||
\(396\) | 15.4737 | + | 19.4580i | 0.777582 | + | 0.977804i | ||||
\(397\) | − | 14.8451i | − | 0.745055i | −0.928021 | − | 0.372528i | \(-0.878491\pi\) | ||
0.928021 | − | 0.372528i | \(-0.121509\pi\) | |||||||
\(398\) | −2.37240 | + | 0.828314i | −0.118918 | + | 0.0415196i | ||||
\(399\) | −1.58324 | −0.0792611 | ||||||||
\(400\) | 0.498030 | − | 2.15477i | 0.0249015 | − | 0.107738i | ||||
\(401\) | 34.4111 | 1.71841 | 0.859205 | − | 0.511632i | \(-0.170959\pi\) | ||||
0.859205 | + | 0.511632i | \(0.170959\pi\) | |||||||
\(402\) | 4.74443 | − | 1.65650i | 0.236630 | − | 0.0826186i | ||||
\(403\) | − | 23.9945i | − | 1.19525i | ||||||
\(404\) | 9.09441 | + | 11.4361i | 0.452464 | + | 0.568970i | ||||
\(405\) | − | 12.8533i | − | 0.638688i | ||||||
\(406\) | 12.2048 | + | 34.9562i | 0.605715 | + | 1.73485i | ||||
\(407\) | −5.11691 | −0.253636 | ||||||||
\(408\) | −9.48980 | − | 5.99008i | −0.469815 | − | 0.296553i | ||||
\(409\) | 1.43283 | 0.0708487 | 0.0354243 | − | 0.999372i | \(-0.488722\pi\) | ||||
0.0354243 | + | 0.999372i | \(0.488722\pi\) | |||||||
\(410\) | −7.21372 | − | 20.6610i | −0.356260 | − | 1.02038i | ||||
\(411\) | 10.5143i | 0.518633i | ||||||||
\(412\) | −13.7335 | + | 10.9213i | −0.676601 | + | 0.538056i | ||||
\(413\) | 28.0113i | 1.37834i | ||||||||
\(414\) | −4.28428 | + | 1.49584i | −0.210561 | + | 0.0735165i | ||||
\(415\) | −18.9358 | −0.929521 | ||||||||
\(416\) | 25.1812 | − | 2.74989i | 1.23461 | − | 0.134824i | ||||
\(417\) | −1.11994 | −0.0548438 | ||||||||
\(418\) | 6.22823 | − | 2.17456i | 0.304633 | − | 0.106361i | ||||
\(419\) | 33.6886i | 1.64579i | 0.568190 | + | 0.822897i | \(0.307644\pi\) | ||||
−0.568190 | + | 0.822897i | \(0.692356\pi\) | |||||||
\(420\) | −5.22640 | + | 4.15621i | −0.255022 | + | 0.202802i | ||||
\(421\) | 0.237430i | 0.0115716i | 0.999983 | + | 0.00578582i | \(0.00184169\pi\) | ||||
−0.999983 | + | 0.00578582i | \(0.998158\pi\) | |||||||
\(422\) | 7.93393 | + | 22.7238i | 0.386218 | + | 1.10618i | ||||
\(423\) | 20.1584 | 0.980134 | ||||||||
\(424\) | 7.46120 | + | 4.70961i | 0.362348 | + | 0.228719i | ||||
\(425\) | −3.78863 | −0.183776 | ||||||||
\(426\) | 1.24770 | + | 3.57358i | 0.0604513 | + | 0.173140i | ||||
\(427\) | − | 1.97437i | − | 0.0955465i | ||||||
\(428\) | −12.3407 | − | 15.5184i | −0.596512 | − | 0.750109i | ||||
\(429\) | − | 12.0947i | − | 0.583936i | ||||||
\(430\) | 21.5229 | − | 7.51464i | 1.03793 | − | 0.362388i | ||||
\(431\) | 13.0743 | 0.629766 | 0.314883 | − | 0.949130i | \(-0.398035\pi\) | ||||
0.314883 | + | 0.949130i | \(0.398035\pi\) | |||||||
\(432\) | 12.7829 | + | 2.95451i | 0.615019 | + | 0.142149i | ||||
\(433\) | −9.67718 | −0.465056 | −0.232528 | − | 0.972590i | \(-0.574700\pi\) | ||||
−0.232528 | + | 0.972590i | \(0.574700\pi\) | |||||||
\(434\) | 19.5627 | − | 6.83024i | 0.939040 | − | 0.327862i | ||||
\(435\) | − | 11.6913i | − | 0.560554i | ||||||
\(436\) | 3.54266 | + | 4.45487i | 0.169663 | + | 0.213350i | ||||
\(437\) | 1.20416i | 0.0576030i | ||||||||
\(438\) | −1.67154 | − | 4.78750i | −0.0798692 | − | 0.228756i | ||||
\(439\) | 17.7983 | 0.849468 | 0.424734 | − | 0.905318i | \(-0.360368\pi\) | ||||
0.424734 | + | 0.905318i | \(0.360368\pi\) | |||||||
\(440\) | 14.8514 | − | 23.5283i | 0.708012 | − | 1.12167i | ||||
\(441\) | 1.27029 | 0.0604898 | ||||||||
\(442\) | −14.3041 | − | 40.9688i | −0.680377 | − | 1.94869i | ||||
\(443\) | − | 3.30468i | − | 0.157010i | −0.996914 | − | 0.0785050i | \(-0.974985\pi\) | ||
0.996914 | − | 0.0785050i | \(-0.0250147\pi\) | |||||||
\(444\) | −0.994235 | + | 0.790649i | −0.0471843 | + | 0.0375225i | ||||
\(445\) | − | 1.30896i | − | 0.0620505i | ||||||
\(446\) | 18.2430 | − | 6.36949i | 0.863833 | − | 0.301604i | ||||
\(447\) | −9.01966 | −0.426615 | ||||||||
\(448\) | 9.41002 | + | 19.7474i | 0.444582 | + | 0.932978i | ||||
\(449\) | −29.6543 | −1.39947 | −0.699735 | − | 0.714402i | \(-0.746699\pi\) | ||||
−0.699735 | + | 0.714402i | \(0.746699\pi\) | |||||||
\(450\) | 1.96713 | − | 0.686817i | 0.0927315 | − | 0.0323768i | ||||
\(451\) | 34.2297i | 1.61182i | ||||||||
\(452\) | −2.48092 | + | 1.97291i | −0.116692 | + | 0.0927978i | ||||
\(453\) | − | 11.5656i | − | 0.543402i | ||||||
\(454\) | −2.54600 | − | 7.29207i | −0.119490 | − | 0.342234i | ||||
\(455\) | −25.8208 | −1.21050 | ||||||||
\(456\) | 0.874162 | − | 1.38489i | 0.0409364 | − | 0.0648535i | ||||
\(457\) | −20.2310 | −0.946368 | −0.473184 | − | 0.880964i | \(-0.656895\pi\) | ||||
−0.473184 | + | 0.880964i | \(0.656895\pi\) | |||||||
\(458\) | 1.50476 | + | 4.30982i | 0.0703126 | + | 0.201385i | ||||
\(459\) | − | 22.4756i | − | 1.04907i | ||||||
\(460\) | 3.16108 | + | 3.97504i | 0.147386 | + | 0.185337i | ||||
\(461\) | − | 41.2429i | − | 1.92087i | −0.278502 | − | 0.960436i | \(-0.589838\pi\) | ||
0.278502 | − | 0.960436i | \(-0.410162\pi\) | |||||||
\(462\) | 9.86078 | − | 3.44285i | 0.458765 | − | 0.160176i | ||||
\(463\) | −16.5232 | −0.767896 | −0.383948 | − | 0.923355i | \(-0.625436\pi\) | ||||
−0.383948 | + | 0.923355i | \(0.625436\pi\) | |||||||
\(464\) | −37.3156 | − | 8.62474i | −1.73233 | − | 0.400393i | ||||
\(465\) | −6.54285 | −0.303417 | ||||||||
\(466\) | −23.8120 | + | 8.31386i | −1.10307 | + | 0.385132i | ||||
\(467\) | − | 24.9967i | − | 1.15671i | −0.815786 | − | 0.578355i | \(-0.803695\pi\) | ||
0.815786 | − | 0.578355i | \(-0.196305\pi\) | |||||||
\(468\) | 14.8539 | + | 18.6787i | 0.686624 | + | 0.863424i | ||||
\(469\) | 16.7807i | 0.774860i | ||||||||
\(470\) | −7.43677 | − | 21.2999i | −0.343032 | − | 0.982490i | ||||
\(471\) | −12.0940 | −0.557264 | ||||||||
\(472\) | −24.5021 | − | 15.4660i | −1.12780 | − | 0.711881i | ||||
\(473\) | −35.6576 | −1.63954 | ||||||||
\(474\) | −0.881893 | − | 2.52586i | −0.0405067 | − | 0.116016i | ||||
\(475\) | − | 0.552894i | − | 0.0253685i | ||||||
\(476\) | 29.3301 | − | 23.3242i | 1.34434 | − | 1.06907i | ||||
\(477\) | 8.31263i | 0.380609i | ||||||||
\(478\) | 2.43744 | − | 0.851022i | 0.111486 | − | 0.0389248i | ||||
\(479\) | 10.0298 | 0.458273 | 0.229137 | − | 0.973394i | \(-0.426410\pi\) | ||||
0.229137 | + | 0.973394i | \(0.426410\pi\) | |||||||
\(480\) | −0.749842 | − | 6.86643i | −0.0342255 | − | 0.313408i | ||||
\(481\) | −4.91197 | −0.223966 | ||||||||
\(482\) | 8.64669 | − | 3.01896i | 0.393846 | − | 0.137510i | ||||
\(483\) | 1.90648i | 0.0867478i | ||||||||
\(484\) | −16.8431 | + | 13.3942i | −0.765594 | + | 0.608826i | ||||
\(485\) | 3.52772i | 0.160185i | ||||||||
\(486\) | 6.23227 | + | 17.8500i | 0.282701 | + | 0.809694i | ||||
\(487\) | 41.6248 | 1.88620 | 0.943101 | − | 0.332508i | \(-0.107895\pi\) | ||||
0.943101 | + | 0.332508i | \(0.107895\pi\) | |||||||
\(488\) | 1.72702 | + | 1.09012i | 0.0781787 | + | 0.0493474i | ||||
\(489\) | −1.47554 | −0.0667261 | ||||||||
\(490\) | −0.468630 | − | 1.34222i | −0.0211706 | − | 0.0606352i | ||||
\(491\) | 34.6939i | 1.56572i | 0.622200 | + | 0.782858i | \(0.286239\pi\) | ||||
−0.622200 | + | 0.782858i | \(0.713761\pi\) | |||||||
\(492\) | 5.28907 | + | 6.65097i | 0.238450 | + | 0.299849i | ||||
\(493\) | 65.6104i | 2.95494i | ||||||||
\(494\) | 5.97878 | − | 2.08747i | 0.268998 | − | 0.0939196i | ||||
\(495\) | 26.2132 | 1.17820 | ||||||||
\(496\) | −4.82671 | + | 20.8831i | −0.216725 | + | 0.937680i | ||||
\(497\) | −12.6395 | −0.566959 | ||||||||
\(498\) | 6.94182 | − | 2.42371i | 0.311070 | − | 0.108609i | ||||
\(499\) | − | 14.1270i | − | 0.632413i | −0.948690 | − | 0.316207i | \(-0.897591\pi\) | ||
0.948690 | − | 0.316207i | \(-0.102409\pi\) | |||||||
\(500\) | −14.5771 | − | 18.3305i | −0.651906 | − | 0.819767i | ||||
\(501\) | − | 10.8070i | − | 0.482821i | ||||||
\(502\) | 1.44932 | + | 4.15104i | 0.0646863 | + | 0.185270i | ||||
\(503\) | 3.01157 | 0.134279 | 0.0671395 | − | 0.997744i | \(-0.478613\pi\) | ||||
0.0671395 | + | 0.997744i | \(0.478613\pi\) | |||||||
\(504\) | −11.0004 | + | 17.4275i | −0.489999 | + | 0.776281i | ||||
\(505\) | 15.4064 | 0.685576 | ||||||||
\(506\) | −2.61853 | − | 7.49981i | −0.116408 | − | 0.333407i | ||||
\(507\) | − | 4.08304i | − | 0.181334i | ||||||
\(508\) | 22.3743 | − | 17.7928i | 0.992701 | − | 0.789429i | ||||
\(509\) | − | 2.38122i | − | 0.105546i | −0.998607 | − | 0.0527730i | \(-0.983194\pi\) | ||
0.998607 | − | 0.0527730i | \(-0.0168060\pi\) | |||||||
\(510\) | −11.1714 | + | 3.90046i | −0.494679 | + | 0.172715i | ||||
\(511\) | 16.9330 | 0.749074 | ||||||||
\(512\) | −22.4691 | − | 2.67211i | −0.993003 | − | 0.118092i | ||||
\(513\) | 3.27998 | 0.144815 | ||||||||
\(514\) | 7.68533 | − | 2.68330i | 0.338985 | − | 0.118355i | ||||
\(515\) | 18.5013i | 0.815266i | ||||||||
\(516\) | −6.92842 | + | 5.50971i | −0.305006 | + | 0.242551i | ||||
\(517\) | 35.2881i | 1.55197i | ||||||||
\(518\) | −1.39823 | − | 4.00472i | −0.0614349 | − | 0.175957i | ||||
\(519\) | −4.87747 | −0.214097 | ||||||||
\(520\) | 14.2566 | − | 22.5860i | 0.625191 | − | 0.990460i | ||||
\(521\) | 17.9133 | 0.784798 | 0.392399 | − | 0.919795i | \(-0.371645\pi\) | ||||
0.392399 | + | 0.919795i | \(0.371645\pi\) | |||||||
\(522\) | −11.8941 | − | 34.0662i | −0.520590 | − | 1.49104i | ||||
\(523\) | − | 18.9602i | − | 0.829071i | −0.910033 | − | 0.414536i | \(-0.863944\pi\) | ||
0.910033 | − | 0.414536i | \(-0.136056\pi\) | |||||||
\(524\) | −0.758112 | − | 0.953320i | −0.0331183 | − | 0.0416460i | ||||
\(525\) | − | 0.875363i | − | 0.0382040i | ||||||
\(526\) | −6.12304 | + | 2.13783i | −0.266977 | + | 0.0932140i | ||||
\(527\) | 36.7178 | 1.59945 | ||||||||
\(528\) | −2.43295 | + | 10.5264i | −0.105881 | + | 0.458101i | ||||
\(529\) | −21.5500 | −0.936956 | ||||||||
\(530\) | 8.78335 | − | 3.06667i | 0.381524 | − | 0.133208i | ||||
\(531\) | − | 27.2981i | − | 1.18464i | ||||||
\(532\) | 3.40382 | + | 4.28028i | 0.147574 | + | 0.185574i | ||||
\(533\) | 32.8588i | 1.42327i | ||||||||
\(534\) | 0.167542 | + | 0.479861i | 0.00725023 | + | 0.0207656i | ||||
\(535\) | −20.9059 | −0.903839 | ||||||||
\(536\) | −14.6784 | − | 9.26521i | −0.634011 | − | 0.400196i | ||||
\(537\) | 9.65852 | 0.416796 | ||||||||
\(538\) | −5.31030 | − | 15.2094i | −0.228943 | − | 0.655724i | ||||
\(539\) | 2.22369i | 0.0957811i | ||||||||
\(540\) | 10.8275 | − | 8.61037i | 0.465941 | − | 0.370531i | ||||
\(541\) | − | 34.2027i | − | 1.47049i | −0.677802 | − | 0.735245i | \(-0.737067\pi\) | ||
0.677802 | − | 0.735245i | \(-0.262933\pi\) | |||||||
\(542\) | 33.5465 | − | 11.7126i | 1.44095 | − | 0.503100i | ||||
\(543\) | −2.69757 | −0.115764 | ||||||||
\(544\) | 4.20804 | + | 38.5338i | 0.180418 | + | 1.65212i | ||||
\(545\) | 6.00145 | 0.257074 | ||||||||
\(546\) | 9.46584 | − | 3.30496i | 0.405101 | − | 0.141439i | ||||
\(547\) | − | 0.645113i | − | 0.0275830i | −0.999905 | − | 0.0137915i | \(-0.995610\pi\) | ||
0.999905 | − | 0.0137915i | \(-0.00439011\pi\) | |||||||
\(548\) | 28.4254 | − | 22.6049i | 1.21427 | − | 0.965632i | ||||
\(549\) | 1.92410i | 0.0821187i | ||||||||
\(550\) | 1.20230 | + | 3.44355i | 0.0512663 | + | 0.146833i | ||||
\(551\) | −9.57484 | −0.407902 | ||||||||
\(552\) | −1.66764 | − | 1.05263i | −0.0709794 | − | 0.0448031i | ||||
\(553\) | 8.93377 | 0.379903 | ||||||||
\(554\) | 8.53080 | + | 24.4333i | 0.362439 | + | 1.03807i | ||||
\(555\) | 1.33940i | 0.0568544i | ||||||||
\(556\) | 2.40778 | + | 3.02776i | 0.102112 | + | 0.128406i | ||||
\(557\) | 10.2596i | 0.434714i | 0.976092 | + | 0.217357i | \(0.0697436\pi\) | ||||
−0.976092 | + | 0.217357i | \(0.930256\pi\) | |||||||
\(558\) | −19.0646 | + | 6.65634i | −0.807070 | + | 0.281785i | ||||
\(559\) | −34.2295 | −1.44775 | ||||||||
\(560\) | 22.4726 | + | 5.19407i | 0.949640 | + | 0.219490i | ||||
\(561\) | 18.5080 | 0.781409 | ||||||||
\(562\) | −24.1277 | + | 8.42408i | −1.01776 | + | 0.355349i | ||||
\(563\) | − | 12.9293i | − | 0.544906i | −0.962169 | − | 0.272453i | \(-0.912165\pi\) | ||
0.962169 | − | 0.272453i | \(-0.0878350\pi\) | |||||||
\(564\) | 5.45261 | + | 6.85661i | 0.229596 | + | 0.288715i | ||||
\(565\) | 3.34221i | 0.140608i | ||||||||
\(566\) | 7.17772 | + | 20.5579i | 0.301702 | + | 0.864114i | ||||
\(567\) | −16.6660 | −0.699908 | ||||||||
\(568\) | 6.97871 | − | 11.0560i | 0.292820 | − | 0.463901i | ||||
\(569\) | 6.32637 | 0.265215 | 0.132608 | − | 0.991169i | \(-0.457665\pi\) | ||||
0.132608 | + | 0.991169i | \(0.457665\pi\) | |||||||
\(570\) | −0.569213 | − | 1.63030i | −0.0238417 | − | 0.0682858i | ||||
\(571\) | − | 31.1997i | − | 1.30566i | −0.757502 | − | 0.652832i | \(-0.773581\pi\) | ||
0.757502 | − | 0.652832i | \(-0.226419\pi\) | |||||||
\(572\) | −32.6979 | + | 26.0025i | −1.36717 | + | 1.08722i | ||||
\(573\) | 11.6156i | 0.485248i | ||||||||
\(574\) | −26.7897 | + | 9.35353i | −1.11818 | + | 0.390409i | ||||
\(575\) | −0.665774 | −0.0277647 | ||||||||
\(576\) | −9.17044 | − | 19.2446i | −0.382102 | − | 0.801860i | ||||
\(577\) | 5.48996 | 0.228550 | 0.114275 | − | 0.993449i | \(-0.463545\pi\) | ||||
0.114275 | + | 0.993449i | \(0.463545\pi\) | |||||||
\(578\) | 39.9950 | − | 13.9641i | 1.66357 | − | 0.580830i | ||||
\(579\) | 1.07186i | 0.0445450i | ||||||||
\(580\) | −31.6073 | + | 25.1352i | −1.31242 | + | 1.04368i | ||||
\(581\) | 24.5527i | 1.01862i | ||||||||
\(582\) | −0.451535 | − | 1.29325i | −0.0187167 | − | 0.0536071i | ||||
\(583\) | −14.5516 | −0.602666 | ||||||||
\(584\) | −9.34934 | + | 14.8117i | −0.386878 | + | 0.612912i | ||||
\(585\) | 25.1634 | 1.04038 | ||||||||
\(586\) | 5.33332 | + | 15.2753i | 0.220318 | + | 0.631018i | ||||
\(587\) | − | 17.4576i | − | 0.720552i | −0.932846 | − | 0.360276i | \(-0.882683\pi\) | ||
0.932846 | − | 0.360276i | \(-0.117317\pi\) | |||||||
\(588\) | 0.343598 | + | 0.432072i | 0.0141697 | + | 0.0178183i | ||||
\(589\) | 5.35842i | 0.220790i | ||||||||
\(590\) | −28.8439 | + | 10.0707i | −1.18748 | + | 0.414606i | ||||
\(591\) | −0.130211 | −0.00535617 | ||||||||
\(592\) | 4.27503 | + | 0.988086i | 0.175703 | + | 0.0406101i | ||||
\(593\) | −16.7657 | −0.688486 | −0.344243 | − | 0.938881i | \(-0.611864\pi\) | ||||
−0.344243 | + | 0.938881i | \(0.611864\pi\) | |||||||
\(594\) | −20.4285 | + | 7.13252i | −0.838191 | + | 0.292651i | ||||
\(595\) | − | 39.5125i | − | 1.61985i | ||||||
\(596\) | 19.3915 | + | 24.3846i | 0.794305 | + | 0.998832i | ||||
\(597\) | − | 1.02883i | − | 0.0421070i | ||||||
\(598\) | −2.51365 | − | 7.19943i | −0.102791 | − | 0.294407i | ||||
\(599\) | −0.357982 | −0.0146267 | −0.00731337 | − | 0.999973i | \(-0.502328\pi\) | ||||
−0.00731337 | + | 0.999973i | \(0.502328\pi\) | |||||||
\(600\) | 0.765698 | + | 0.483319i | 0.0312595 | + | 0.0197314i | ||||
\(601\) | 22.8949 | 0.933903 | 0.466952 | − | 0.884283i | \(-0.345352\pi\) | ||||
0.466952 | + | 0.884283i | \(0.345352\pi\) | |||||||
\(602\) | −9.74372 | − | 27.9073i | −0.397124 | − | 1.13742i | ||||
\(603\) | − | 16.3535i | − | 0.665964i | ||||||
\(604\) | −31.2677 | + | 24.8651i | −1.27226 | + | 1.01175i | ||||
\(605\) | 22.6904i | 0.922497i | ||||||||
\(606\) | −5.64796 | + | 1.97196i | −0.229433 | + | 0.0801055i | ||||
\(607\) | 1.33917 | 0.0543551 | 0.0271775 | − | 0.999631i | \(-0.491348\pi\) | ||||
0.0271775 | + | 0.999631i | \(0.491348\pi\) | |||||||
\(608\) | −5.62342 | + | 0.614101i | −0.228060 | + | 0.0249051i | ||||
\(609\) | −15.1593 | −0.614284 | ||||||||
\(610\) | 2.03306 | − | 0.709834i | 0.0823161 | − | 0.0287403i | ||||
\(611\) | 33.8747i | 1.37043i | ||||||||
\(612\) | −28.5833 | + | 22.7304i | −1.15541 | + | 0.918822i | ||||
\(613\) | − | 29.8667i | − | 1.20631i | −0.797625 | − | 0.603153i | \(-0.793911\pi\) | ||
0.797625 | − | 0.603153i | \(-0.206089\pi\) | |||||||
\(614\) | −9.95056 | − | 28.4997i | −0.401572 | − | 1.15015i | ||||
\(615\) | 8.95997 | 0.361301 | ||||||||
\(616\) | −30.5075 | − | 19.2568i | −1.22918 | − | 0.775877i | ||||
\(617\) | −36.4935 | −1.46917 | −0.734587 | − | 0.678514i | \(-0.762624\pi\) | ||||
−0.734587 | + | 0.678514i | \(0.762624\pi\) | |||||||
\(618\) | −2.36810 | − | 6.78255i | −0.0952590 | − | 0.272834i | ||||
\(619\) | − | 8.88669i | − | 0.357186i | −0.983923 | − | 0.178593i | \(-0.942845\pi\) | ||
0.983923 | − | 0.178593i | \(-0.0571546\pi\) | |||||||
\(620\) | 14.0665 | + | 17.6886i | 0.564926 | + | 0.710390i | ||||
\(621\) | − | 3.94963i | − | 0.158493i | ||||||
\(622\) | −29.0126 | + | 10.1296i | −1.16330 | + | 0.406161i | ||||
\(623\) | −1.69723 | −0.0679982 | ||||||||
\(624\) | −2.33551 | + | 10.1048i | −0.0934951 | + | 0.404514i | ||||
\(625\) | −21.9298 | −0.877194 | ||||||||
\(626\) | 45.5306 | − | 15.8968i | 1.81977 | − | 0.635365i | ||||
\(627\) | 2.70096i | 0.107866i | ||||||||
\(628\) | 26.0011 | + | 32.6962i | 1.03756 | + | 1.30472i | ||||
\(629\) | − | 7.51659i | − | 0.299706i | ||||||
\(630\) | 7.16297 | + | 20.5157i | 0.285379 | + | 0.817364i | ||||
\(631\) | −28.1724 | −1.12153 | −0.560763 | − | 0.827977i | \(-0.689492\pi\) | ||||
−0.560763 | + | 0.827977i | \(0.689492\pi\) | |||||||
\(632\) | −4.93265 | + | 7.81456i | −0.196210 | + | 0.310846i | ||||
\(633\) | −9.85452 | −0.391682 | ||||||||
\(634\) | −10.3621 | − | 29.6783i | −0.411530 | − | 1.17868i | ||||
\(635\) | − | 30.1420i | − | 1.19615i | ||||||
\(636\) | −2.82744 | + | 2.24847i | −0.112115 | + | 0.0891577i | ||||
\(637\) | 2.13463i | 0.0845771i | ||||||||
\(638\) | 59.6343 | − | 20.8211i | 2.36095 | − | 0.824315i | ||||
\(639\) | 12.3177 | 0.487280 | ||||||||
\(640\) | −16.9513 | + | 16.7894i | −0.670058 | + | 0.663659i | ||||
\(641\) | 3.58435 | 0.141573 | 0.0707867 | − | 0.997491i | \(-0.477449\pi\) | ||||
0.0707867 | + | 0.997491i | \(0.477449\pi\) | |||||||
\(642\) | 7.66405 | − | 2.67587i | 0.302476 | − | 0.105608i | ||||
\(643\) | 19.8837i | 0.784137i | 0.919936 | + | 0.392069i | \(0.128240\pi\) | ||||
−0.919936 | + | 0.392069i | \(0.871760\pi\) | |||||||
\(644\) | 5.15416 | − | 4.09876i | 0.203102 | − | 0.161514i | ||||
\(645\) | 9.33373i | 0.367515i | ||||||||
\(646\) | 3.19437 | + | 9.14909i | 0.125681 | + | 0.359966i | ||||
\(647\) | 35.7712 | 1.40631 | 0.703156 | − | 0.711036i | \(-0.251774\pi\) | ||||
0.703156 | + | 0.711036i | \(0.251774\pi\) | |||||||
\(648\) | 9.20191 | − | 14.5781i | 0.361485 | − | 0.572683i | ||||
\(649\) | 47.7865 | 1.87578 | ||||||||
\(650\) | 1.15415 | + | 3.30563i | 0.0452694 | + | 0.129657i | ||||
\(651\) | 8.48365i | 0.332501i | ||||||||
\(652\) | 3.17227 | + | 3.98911i | 0.124236 | + | 0.156226i | ||||
\(653\) | − | 8.57378i | − | 0.335518i | −0.985828 | − | 0.167759i | \(-0.946347\pi\) | ||
0.985828 | − | 0.167759i | \(-0.0536531\pi\) | |||||||
\(654\) | −2.20012 | + | 0.768164i | −0.0860315 | + | 0.0300376i | ||||
\(655\) | −1.28428 | −0.0501810 | ||||||||
\(656\) | 6.60983 | − | 28.5980i | 0.258071 | − | 1.11656i | ||||
\(657\) | −16.5019 | −0.643802 | ||||||||
\(658\) | −27.6181 | + | 9.64274i | −1.07666 | + | 0.375913i | ||||
\(659\) | − | 22.9993i | − | 0.895927i | −0.894052 | − | 0.447964i | \(-0.852149\pi\) | ||
0.894052 | − | 0.447964i | \(-0.147851\pi\) | |||||||
\(660\) | 7.09038 | + | 8.91610i | 0.275993 | + | 0.347059i | ||||
\(661\) | − | 28.4720i | − | 1.10743i | −0.832706 | − | 0.553716i | \(-0.813209\pi\) | ||
0.832706 | − | 0.553716i | \(-0.186791\pi\) | |||||||
\(662\) | 11.2799 | + | 32.3070i | 0.438405 | + | 1.25565i | ||||
\(663\) | 17.7667 | 0.690003 | ||||||||
\(664\) | −21.4768 | − | 13.5564i | −0.833461 | − | 0.526091i | ||||
\(665\) | 5.76625 | 0.223606 | ||||||||
\(666\) | 1.36263 | + | 3.90276i | 0.0528010 | + | 0.151229i | ||||
\(667\) | 11.5297i | 0.446431i | ||||||||
\(668\) | −29.2167 | + | 23.2341i | −1.13043 | + | 0.898953i | ||||
\(669\) | 7.91136i | 0.305871i | ||||||||
\(670\) | −17.2795 | + | 6.03307i | −0.667565 | + | 0.233078i | ||||
\(671\) | −3.36822 | −0.130029 | ||||||||
\(672\) | −8.90322 | + | 0.972268i | −0.343449 | + | 0.0375061i | ||||
\(673\) | 6.63685 | 0.255832 | 0.127916 | − | 0.991785i | \(-0.459171\pi\) | ||||
0.127916 | + | 0.991785i | \(0.459171\pi\) | |||||||
\(674\) | −45.7610 | + | 15.9773i | −1.76265 | + | 0.615422i | ||||
\(675\) | 1.81348i | 0.0698009i | ||||||||
\(676\) | −11.0385 | + | 8.77816i | −0.424557 | + | 0.337622i | ||||
\(677\) | 29.0823i | 1.11772i | 0.829261 | + | 0.558862i | \(0.188762\pi\) | ||||
−0.829261 | + | 0.558862i | \(0.811238\pi\) | |||||||
\(678\) | −0.427790 | − | 1.22525i | −0.0164292 | − | 0.0470553i | ||||
\(679\) | 4.57415 | 0.175540 | ||||||||
\(680\) | 34.5624 | + | 21.8163i | 1.32541 | + | 0.836615i | ||||
\(681\) | 3.16231 | 0.121180 | ||||||||
\(682\) | −11.6522 | − | 33.3735i | −0.446186 | − | 1.27794i | ||||
\(683\) | 4.63939i | 0.177521i | 0.996053 | + | 0.0887607i | \(0.0282906\pi\) | ||||
−0.996053 | + | 0.0887607i | \(0.971709\pi\) | |||||||
\(684\) | −3.31716 | − | 4.17130i | −0.126835 | − | 0.159494i | ||||
\(685\) | − | 38.2938i | − | 1.46313i | ||||||
\(686\) | 23.8155 | − | 8.31509i | 0.909280 | − | 0.317471i | ||||
\(687\) | −1.86902 | −0.0713074 | ||||||||
\(688\) | 29.7909 | + | 6.88556i | 1.13577 | + | 0.262510i | ||||
\(689\) | −13.9688 | −0.532169 | ||||||||
\(690\) | −1.96315 | + | 0.685426i | −0.0747358 | + | 0.0260937i | ||||
\(691\) | 5.11245i | 0.194487i | 0.995261 | + | 0.0972434i | \(0.0310025\pi\) | ||||
−0.995261 | + | 0.0972434i | \(0.968997\pi\) | |||||||
\(692\) | 10.4861 | + | 13.1862i | 0.398622 | + | 0.501264i | ||||
\(693\) | − | 33.9889i | − | 1.29113i | ||||||
\(694\) | 12.5508 | + | 35.9472i | 0.476423 | + | 1.36454i | ||||
\(695\) | 4.07890 | 0.154721 | ||||||||
\(696\) | 8.36997 | − | 13.2601i | 0.317263 | − | 0.502624i | ||||
\(697\) | −50.2825 | −1.90459 | ||||||||
\(698\) | 4.03596 | + | 11.5595i | 0.152763 | + | 0.437534i | ||||
\(699\) | − | 10.3264i | − | 0.390581i | ||||||
\(700\) | −2.36654 | + | 1.88195i | −0.0894468 | + | 0.0711311i | ||||
\(701\) | 5.27938i | 0.199399i | 0.995018 | + | 0.0996997i | \(0.0317882\pi\) | ||||
−0.995018 | + | 0.0996997i | \(0.968212\pi\) | |||||||
\(702\) | −19.6103 | + | 6.84686i | −0.740143 | + | 0.258418i | ||||
\(703\) | 1.09693 | 0.0413716 | ||||||||
\(704\) | 33.6886 | − | 16.0532i | 1.26969 | − | 0.605029i | ||||
\(705\) | 9.23700 | 0.347886 | ||||||||
\(706\) | −12.1670 | + | 4.24805i | −0.457910 | + | 0.159877i | ||||
\(707\) | − | 19.9764i | − | 0.751290i | ||||||
\(708\) | 9.28510 | − | 7.38382i | 0.348955 | − | 0.277501i | ||||
\(709\) | − | 28.1441i | − | 1.05697i | −0.848942 | − | 0.528486i | \(-0.822760\pi\) | ||
0.848942 | − | 0.528486i | \(-0.177240\pi\) | |||||||
\(710\) | −4.54420 | − | 13.0152i | −0.170541 | − | 0.488451i | ||||
\(711\) | −8.70632 | −0.326512 | ||||||||
\(712\) | 0.937103 | − | 1.48461i | 0.0351194 | − | 0.0556379i | ||||
\(713\) | 6.45241 | 0.241645 | ||||||||
\(714\) | 5.05745 | + | 14.4852i | 0.189270 | + | 0.542095i | ||||
\(715\) | 44.0495i | 1.64736i | ||||||||
\(716\) | −20.7650 | − | 26.1118i | −0.776023 | − | 0.975843i | ||||
\(717\) | 1.05703i | 0.0394755i | ||||||||
\(718\) | 5.74094 | − | 2.00443i | 0.214250 | − | 0.0748046i | ||||
\(719\) | 9.51160 | 0.354723 | 0.177361 | − | 0.984146i | \(-0.443244\pi\) | ||||
0.177361 | + | 0.984146i | \(0.443244\pi\) | |||||||
\(720\) | −21.9004 | − | 5.06183i | −0.816181 | − | 0.188643i | ||||
\(721\) | 23.9894 | 0.893412 | ||||||||
\(722\) | −1.33517 | + | 0.466170i | −0.0496900 | + | 0.0173491i | ||||
\(723\) | 3.74976i | 0.139455i | ||||||||
\(724\) | 5.79954 | + | 7.29288i | 0.215538 | + | 0.271038i | ||||
\(725\) | − | 5.29387i | − | 0.196609i | ||||||
\(726\) | −2.90429 | − | 8.31826i | −0.107788 | − | 0.308720i | ||||
\(727\) | 7.06196 | 0.261914 | 0.130957 | − | 0.991388i | \(-0.458195\pi\) | ||||
0.130957 | + | 0.991388i | \(0.458195\pi\) | |||||||
\(728\) | −29.2857 | − | 18.4855i | −1.08540 | − | 0.685118i | ||||
\(729\) | 10.5442 | 0.390527 | ||||||||
\(730\) | 6.08784 | + | 17.4364i | 0.225321 | + | 0.645349i | ||||
\(731\) | − | 52.3801i | − | 1.93735i | ||||||
\(732\) | −0.654459 | + | 0.520448i | −0.0241895 | + | 0.0192363i | ||||
\(733\) | 7.62443i | 0.281615i | 0.990037 | + | 0.140807i | \(0.0449698\pi\) | ||||
−0.990037 | + | 0.140807i | \(0.955030\pi\) | |||||||
\(734\) | −28.4222 | + | 9.92350i | −1.04908 | + | 0.366283i | ||||
\(735\) | 0.582073 | 0.0214701 | ||||||||
\(736\) | 0.739478 | + | 6.77152i | 0.0272575 | + | 0.249602i | ||||
\(737\) | 28.6274 | 1.05450 | ||||||||
\(738\) | 26.1077 | − | 9.11539i | 0.961037 | − | 0.335542i | ||||
\(739\) | 45.0131i | 1.65583i | 0.560851 | + | 0.827917i | \(0.310474\pi\) | ||||
−0.560851 | + | 0.827917i | \(0.689526\pi\) | |||||||
\(740\) | 3.62106 | − | 2.87959i | 0.133113 | − | 0.105856i | ||||
\(741\) | 2.59279i | 0.0952484i | ||||||||
\(742\) | −3.97634 | − | 11.3888i | −0.145976 | − | 0.418094i | ||||
\(743\) | 15.3137 | 0.561805 | 0.280903 | − | 0.959736i | \(-0.409366\pi\) | ||||
0.280903 | + | 0.959736i | \(0.409366\pi\) | |||||||
\(744\) | −7.42083 | − | 4.68413i | −0.272061 | − | 0.171728i | ||||
\(745\) | 32.8501 | 1.20354 | ||||||||
\(746\) | −5.17803 | − | 14.8306i | −0.189581 | − | 0.542985i | ||||
\(747\) | − | 23.9276i | − | 0.875465i | ||||||
\(748\) | −39.7906 | − | 50.0363i | −1.45489 | − | 1.82951i | ||||
\(749\) | 27.1072i | 0.990475i | ||||||||
\(750\) | 9.05288 | − | 3.16078i | 0.330565 | − | 0.115415i | ||||
\(751\) | 4.09580 | 0.149458 | 0.0747290 | − | 0.997204i | \(-0.476191\pi\) | ||||
0.0747290 | + | 0.997204i | \(0.476191\pi\) | |||||||
\(752\) | 6.81420 | − | 29.4822i | 0.248488 | − | 1.07511i | ||||
\(753\) | −1.80016 | −0.0656015 | ||||||||
\(754\) | 57.2459 | − | 19.9872i | 2.08477 | − | 0.727890i | ||||
\(755\) | 42.1228i | 1.53301i | ||||||||
\(756\) | −11.1645 | − | 14.0392i | −0.406048 | − | 0.510602i | ||||
\(757\) | − | 9.51720i | − | 0.345909i | −0.984930 | − | 0.172954i | \(-0.944669\pi\) | ||
0.984930 | − | 0.172954i | \(-0.0553313\pi\) | |||||||
\(758\) | −9.64542 | − | 27.6258i | −0.350338 | − | 1.00341i | ||||
\(759\) | 3.25240 | 0.118055 | ||||||||
\(760\) | −3.18375 | + | 5.04386i | −0.115487 | + | 0.182960i | ||||
\(761\) | −38.4841 | −1.39505 | −0.697523 | − | 0.716562i | \(-0.745715\pi\) | ||||
−0.697523 | + | 0.716562i | \(0.745715\pi\) | |||||||
\(762\) | 3.85806 | + | 11.0500i | 0.139763 | + | 0.400299i | ||||
\(763\) | − | 7.78167i | − | 0.281715i | ||||||
\(764\) | 31.4027 | − | 24.9725i | 1.13611 | − | 0.903473i | ||||
\(765\) | 38.5065i | 1.39221i | ||||||||
\(766\) | −16.2716 | + | 5.68116i | −0.587916 | + | 0.205269i | ||||
\(767\) | 45.8726 | 1.65636 | ||||||||
\(768\) | 4.06532 | − | 8.32466i | 0.146695 | − | 0.300390i | ||||
\(769\) | 15.0210 | 0.541670 | 0.270835 | − | 0.962626i | \(-0.412700\pi\) | ||||
0.270835 | + | 0.962626i | \(0.412700\pi\) | |||||||
\(770\) | −35.9136 | + | 12.5391i | −1.29423 | + | 0.451877i | ||||
\(771\) | 3.33286i | 0.120030i | ||||||||
\(772\) | 2.89777 | − | 2.30440i | 0.104293 | − | 0.0829372i | ||||
\(773\) | − | 38.4471i | − | 1.38285i | −0.722451 | − | 0.691423i | \(-0.756984\pi\) | ||
0.722451 | − | 0.691423i | \(-0.243016\pi\) | |||||||
\(774\) | 9.49564 | + | 27.1968i | 0.341314 | + | 0.977568i | ||||
\(775\) | −2.96263 | −0.106421 | ||||||||
\(776\) | −2.52555 | + | 4.00110i | −0.0906619 | + | 0.143631i | ||||
\(777\) | 1.73671 | 0.0623040 | ||||||||
\(778\) | 12.2029 | + | 34.9507i | 0.437495 | + | 1.25304i | ||||
\(779\) | − | 7.33797i | − | 0.262910i | ||||||
\(780\) | 6.80640 | + | 8.55899i | 0.243708 | + | 0.306461i | ||||
\(781\) | 21.5626i | 0.771572i | ||||||||
\(782\) | 11.0170 | − | 3.84654i | 0.393967 | − | 0.137552i | ||||
\(783\) | 31.4053 | 1.12233 | ||||||||
\(784\) | 0.429399 | − | 1.85783i | 0.0153357 | − | 0.0663511i | ||||
\(785\) | 44.0472 | 1.57211 | ||||||||
\(786\) | 0.470815 | − | 0.164383i | 0.0167934 | − | 0.00586336i | ||||
\(787\) | − | 30.8457i | − | 1.09953i | −0.835319 | − | 0.549765i | \(-0.814717\pi\) | ||
0.835319 | − | 0.549765i | \(-0.185283\pi\) | |||||||
\(788\) | 0.279942 | + | 0.352025i | 0.00997253 | + | 0.0125404i | ||||
\(789\) | − | 2.65535i | − | 0.0945328i | ||||||
\(790\) | 3.21191 | + | 9.19932i | 0.114275 | + | 0.327297i | ||||
\(791\) | 4.33361 | 0.154085 | ||||||||
\(792\) | 29.7308 | + | 18.7665i | 1.05644 | + | 0.666838i | ||||
\(793\) | −3.23332 | −0.114819 | ||||||||
\(794\) | −6.92035 | − | 19.8208i | −0.245594 | − | 0.703414i | ||||
\(795\) | 3.80903i | 0.135092i | ||||||||
\(796\) | −2.78143 | + | 2.21188i | −0.0985850 | + | 0.0783981i | ||||
\(797\) | − | 34.1285i | − | 1.20889i | −0.796646 | − | 0.604446i | \(-0.793394\pi\) | ||
0.796646 | − | 0.604446i | \(-0.206606\pi\) | |||||||
\(798\) | −2.11390 | + | 0.738059i | −0.0748312 | + | 0.0261270i | ||||
\(799\) | −51.8372 | −1.83387 | ||||||||
\(800\) | −0.339532 | − | 3.10915i | −0.0120043 | − | 0.109925i | ||||
\(801\) | 1.65402 | 0.0584420 | ||||||||
\(802\) | 45.9448 | − | 16.0414i | 1.62237 | − | 0.566443i | ||||
\(803\) | − | 28.8873i | − | 1.01941i | ||||||
\(804\) | 5.56242 | − | 4.42342i | 0.196171 | − | 0.156002i | ||||
\(805\) | − | 6.94351i | − | 0.244727i | ||||||
\(806\) | −11.1855 | − | 32.0368i | −0.393993 | − | 1.12845i | ||||
\(807\) | 6.59578 | 0.232182 | ||||||||
\(808\) | 17.4738 | + | 11.0297i | 0.614726 | + | 0.388023i | ||||
\(809\) | −25.9170 | −0.911192 | −0.455596 | − | 0.890187i | \(-0.650574\pi\) | ||||
−0.455596 | + | 0.890187i | \(0.650574\pi\) | |||||||
\(810\) | −5.99185 | − | 17.1614i | −0.210532 | − | 0.602991i | ||||
\(811\) | 33.7874i | 1.18644i | 0.805041 | + | 0.593219i | \(0.202143\pi\) | ||||
−0.805041 | + | 0.593219i | \(0.797857\pi\) | |||||||
\(812\) | 32.5911 | + | 40.9830i | 1.14372 | + | 1.43822i | ||||
\(813\) | 14.5479i | 0.510218i | ||||||||
\(814\) | −6.83195 | + | 2.38535i | −0.239460 | + | 0.0836065i | ||||
\(815\) | 5.37400 | 0.188243 | ||||||||
\(816\) | −15.4629 | − | 3.57393i | −0.541310 | − | 0.125113i | ||||
\(817\) | 7.64408 | 0.267432 | ||||||||
\(818\) | 1.91307 | − | 0.667941i | 0.0668889 | − | 0.0233540i | ||||
\(819\) | − | 32.6276i | − | 1.14010i | ||||||
\(820\) | −19.2631 | − | 24.2232i | −0.672698 | − | 0.845912i | ||||
\(821\) | − | 27.6475i | − | 0.964903i | −0.875923 | − | 0.482451i | \(-0.839746\pi\) | ||
0.875923 | − | 0.482451i | \(-0.160254\pi\) | |||||||
\(822\) | 4.90146 | + | 14.0384i | 0.170958 | + | 0.489647i | ||||
\(823\) | −12.4983 | −0.435665 | −0.217832 | − | 0.975986i | \(-0.569899\pi\) | ||||
−0.217832 | + | 0.975986i | \(0.569899\pi\) | |||||||
\(824\) | −13.2454 | + | 20.9840i | −0.461425 | + | 0.731013i | ||||
\(825\) | −1.49335 | −0.0519916 | ||||||||
\(826\) | 13.0580 | + | 37.3999i | 0.454347 | + | 1.30131i | ||||
\(827\) | 9.03084i | 0.314033i | 0.987596 | + | 0.157017i | \(0.0501876\pi\) | ||||
−0.987596 | + | 0.157017i | \(0.949812\pi\) | |||||||
\(828\) | −5.02293 | + | 3.99440i | −0.174559 | + | 0.138815i | ||||
\(829\) | 55.7684i | 1.93692i | 0.249175 | + | 0.968458i | \(0.419841\pi\) | ||||
−0.249175 | + | 0.968458i | \(0.580159\pi\) | |||||||
\(830\) | −25.2825 | + | 8.82730i | −0.877569 | + | 0.306400i | ||||
\(831\) | −10.5959 | −0.367567 | ||||||||
\(832\) | 32.3393 | − | 15.4103i | 1.12116 | − | 0.534256i | ||||
\(833\) | −3.26654 | −0.113179 | ||||||||
\(834\) | −1.49532 | + | 0.522084i | −0.0517786 | + | 0.0180783i | ||||
\(835\) | 39.3597i | 1.36210i | ||||||||
\(836\) | 7.30205 | − | 5.80683i | 0.252547 | − | 0.200833i | ||||
\(837\) | − | 17.5755i | − | 0.607498i | ||||||
\(838\) | 15.7046 | + | 44.9800i | 0.542507 | + | 1.55381i | ||||
\(839\) | −14.3128 | −0.494134 | −0.247067 | − | 0.968998i | \(-0.579467\pi\) | ||||
−0.247067 | + | 0.968998i | \(0.579467\pi\) | |||||||
\(840\) | −5.04064 | + | 7.98564i | −0.173919 | + | 0.275531i | ||||
\(841\) | −62.6776 | −2.16130 | ||||||||
\(842\) | 0.110683 | + | 0.317010i | 0.00381438 | + | 0.0109249i | ||||
\(843\) | − | 10.4633i | − | 0.360376i | ||||||
\(844\) | 21.1863 | + | 26.6416i | 0.729264 | + | 0.917043i | ||||
\(845\) | 14.8707i | 0.511567i | ||||||||
\(846\) | 26.9149 | − | 9.39723i | 0.925354 | − | 0.323084i | ||||
\(847\) | 29.4211 | 1.01092 | ||||||||
\(848\) | 12.1575 | + | 2.80995i | 0.417489 | + | 0.0964940i | ||||
\(849\) | −8.91525 | −0.305971 | ||||||||
\(850\) | −5.05848 | + | 1.76615i | −0.173504 | + | 0.0605783i | ||||
\(851\) | − | 1.32089i | − | 0.0452794i | ||||||
\(852\) | 3.33179 | + | 4.18970i | 0.114145 | + | 0.143537i | ||||
\(853\) | − | 38.0325i | − | 1.30221i | −0.758988 | − | 0.651105i | \(-0.774306\pi\) | ||
0.758988 | − | 0.651105i | \(-0.225694\pi\) | |||||||
\(854\) | −0.920393 | − | 2.63612i | −0.0314952 | − | 0.0902063i | ||||
\(855\) | −5.61945 | −0.192181 | ||||||||
\(856\) | −23.7112 | − | 14.9668i | −0.810433 | − | 0.511556i | ||||
\(857\) | −23.1869 | −0.792048 | −0.396024 | − | 0.918240i | \(-0.629610\pi\) | ||||
−0.396024 | + | 0.918240i | \(0.629610\pi\) | |||||||
\(858\) | −5.63818 | − | 16.1485i | −0.192484 | − | 0.551300i | ||||
\(859\) | 46.5870i | 1.58953i | 0.606919 | + | 0.794764i | \(0.292405\pi\) | ||||
−0.606919 | + | 0.794764i | \(0.707595\pi\) | |||||||
\(860\) | 25.2337 | − | 20.0667i | 0.860462 | − | 0.684269i | ||||
\(861\) | − | 11.6178i | − | 0.395933i | ||||||
\(862\) | 17.4564 | − | 6.09484i | 0.594568 | − | 0.207591i | ||||
\(863\) | −54.3149 | −1.84890 | −0.924451 | − | 0.381301i | \(-0.875476\pi\) | ||||
−0.924451 | + | 0.381301i | \(0.875476\pi\) | |||||||
\(864\) | 18.4447 | − | 2.01424i | 0.627502 | − | 0.0685258i | ||||
\(865\) | 17.7640 | 0.603995 | ||||||||
\(866\) | −12.9207 | + | 4.51121i | −0.439063 | + | 0.153297i | ||||
\(867\) | 17.3444i | 0.589048i | ||||||||
\(868\) | 22.9355 | − | 18.2391i | 0.778482 | − | 0.619075i | ||||
\(869\) | − | 15.2408i | − | 0.517008i | ||||||
\(870\) | −5.45012 | − | 15.6099i | −0.184777 | − | 0.529224i | ||||
\(871\) | 27.4808 | 0.931153 | ||||||||
\(872\) | 6.80679 | + | 4.29653i | 0.230507 | + | 0.145499i | ||||
\(873\) | −4.45769 | −0.150870 | ||||||||
\(874\) | 0.561345 | + | 1.60777i | 0.0189878 | + | 0.0543835i | ||||
\(875\) | 32.0194i | 1.08245i | ||||||||
\(876\) | −4.46358 | − | 5.61292i | −0.150810 | − | 0.189643i | ||||
\(877\) | 1.80324i | 0.0608910i | 0.999536 | + | 0.0304455i | \(0.00969260\pi\) | ||||
−0.999536 | + | 0.0304455i | \(0.990307\pi\) | |||||||
\(878\) | 23.7639 | − | 8.29705i | 0.801991 | − | 0.280012i | ||||
\(879\) | −6.62438 | −0.223435 | ||||||||
\(880\) | 8.86095 | − | 38.3376i | 0.298703 | − | 1.29236i | ||||
\(881\) | 12.6372 | 0.425759 | 0.212880 | − | 0.977078i | \(-0.431716\pi\) | ||||
0.212880 | + | 0.977078i | \(0.431716\pi\) | |||||||
\(882\) | 1.69605 | − | 0.592170i | 0.0571090 | − | 0.0199394i | ||||
\(883\) | 39.9276i | 1.34367i | 0.740700 | + | 0.671835i | \(0.234494\pi\) | ||||
−0.740700 | + | 0.671835i | \(0.765506\pi\) | |||||||
\(884\) | −38.1969 | − | 48.0323i | −1.28470 | − | 1.61550i | ||||
\(885\) | − | 12.5086i | − | 0.420471i | ||||||
\(886\) | −1.54054 | − | 4.41232i | −0.0517555 | − | 0.148235i | ||||
\(887\) | −14.3642 | −0.482304 | −0.241152 | − | 0.970487i | \(-0.577525\pi\) | ||||
−0.241152 | + | 0.970487i | \(0.577525\pi\) | |||||||
\(888\) | −0.958898 | + | 1.51913i | −0.0321785 | + | 0.0509788i | ||||
\(889\) | −39.0830 | −1.31080 | ||||||||
\(890\) | −0.610197 | − | 1.74768i | −0.0204538 | − | 0.0585825i | ||||
\(891\) | 28.4318i | 0.952502i | ||||||||
\(892\) | 21.3883 | − | 17.0087i | 0.716135 | − | 0.569494i | ||||
\(893\) | − | 7.56486i | − | 0.253148i | ||||||
\(894\) | −12.0428 | + | 4.20470i | −0.402771 | + | 0.140626i | ||||
\(895\) | −35.1769 | −1.17584 | ||||||||
\(896\) | 21.7697 | + | 21.9795i | 0.727273 | + | 0.734285i | ||||
\(897\) | 3.12214 | 0.104245 | ||||||||
\(898\) | −39.5935 | + | 13.8239i | −1.32125 | + | 0.461311i | ||||
\(899\) | 51.3060i | 1.71115i | ||||||||
\(900\) | 2.30629 | − | 1.83404i | 0.0768763 | − | 0.0611346i | ||||
\(901\) | − | 21.3759i | − | 0.712135i | ||||||
\(902\) | 15.9569 | + | 45.7026i | 0.531306 | + | 1.52173i | ||||
\(903\) | 12.1024 | 0.402743 | ||||||||
\(904\) | −2.39274 | + | 3.79070i | −0.0795814 | + | 0.126077i | ||||
\(905\) | 9.82473 | 0.326585 | ||||||||
\(906\) | −5.39156 | − | 15.4421i | −0.179123 | − | 0.513031i | ||||
\(907\) | − | 3.32787i | − | 0.110500i | −0.998473 | − | 0.0552501i | \(-0.982404\pi\) | ||
0.998473 | − | 0.0552501i | \(-0.0175956\pi\) | |||||||
\(908\) | −6.79869 | − | 8.54930i | −0.225623 | − | 0.283719i | ||||
\(909\) | 19.4678i | 0.645707i | ||||||||
\(910\) | −34.4752 | + | 12.0369i | −1.14284 | + | 0.399018i | ||||
\(911\) | −35.8252 | −1.18694 | −0.593471 | − | 0.804855i | \(-0.702243\pi\) | ||||
−0.593471 | + | 0.804855i | \(0.702243\pi\) | |||||||
\(912\) | 0.521562 | − | 2.25658i | 0.0172706 | − | 0.0747228i | ||||
\(913\) | 41.8863 | 1.38623 | ||||||||
\(914\) | −27.0119 | + | 9.43111i | −0.893475 | + | 0.311953i | ||||
\(915\) | 0.881666i | 0.0291470i | ||||||||
\(916\) | 4.01822 | + | 5.05288i | 0.132766 | + | 0.166952i | ||||
\(917\) | 1.66524i | 0.0549910i | ||||||||
\(918\) | −10.4775 | − | 30.0089i | −0.345808 | − | 0.990440i | ||||
\(919\) | −48.3186 | −1.59388 | −0.796942 | − | 0.604055i | \(-0.793551\pi\) | ||||
−0.796942 | + | 0.604055i | \(0.793551\pi\) | |||||||
\(920\) | 6.07364 | + | 3.83376i | 0.200242 | + | 0.126395i | ||||
\(921\) | 12.3593 | 0.407254 | ||||||||
\(922\) | −19.2262 | − | 55.0663i | −0.633181 | − | 1.81351i | ||||
\(923\) | 20.6990i | 0.681316i | ||||||||
\(924\) | 11.5609 | − | 9.19360i | 0.380325 | − | 0.302447i | ||||
\(925\) | 0.606487i | 0.0199412i | ||||||||
\(926\) | −22.0613 | + | 7.70261i | −0.724978 | + | 0.253123i | ||||
\(927\) | −23.3786 | −0.767855 | ||||||||
\(928\) | −53.8434 | + | 5.87992i | −1.76750 | + | 0.193018i | ||||
\(929\) | −23.2127 | −0.761585 | −0.380792 | − | 0.924661i | \(-0.624349\pi\) | ||||
−0.380792 | + | 0.924661i | \(0.624349\pi\) | |||||||
\(930\) | −8.73583 | + | 3.05008i | −0.286459 | + | 0.100016i | ||||
\(931\) | − | 0.476702i | − | 0.0156233i | ||||||
\(932\) | −27.9174 | + | 22.2009i | −0.914466 | + | 0.727214i | ||||
\(933\) | − | 12.5817i | − | 0.411908i | ||||||
\(934\) | −11.6527 | − | 33.3749i | −0.381288 | − | 1.09206i | ||||
\(935\) | −67.4073 | −2.20445 | ||||||||
\(936\) | 28.5400 | + | 18.0148i | 0.932860 | + | 0.588834i | ||||
\(937\) | 7.10467 | 0.232099 | 0.116050 | − | 0.993243i | \(-0.462977\pi\) | ||||
0.116050 | + | 0.993243i | \(0.462977\pi\) | |||||||
\(938\) | 7.82266 | + | 22.4051i | 0.255419 | + | 0.731553i | ||||
\(939\) | 19.7450i | 0.644354i | ||||||||
\(940\) | −19.8587 | − | 24.9722i | −0.647720 | − | 0.814503i | ||||
\(941\) | 55.5352i | 1.81040i | 0.424989 | + | 0.905199i | \(0.360278\pi\) | ||||
−0.424989 | + | 0.905199i | \(0.639722\pi\) | |||||||
\(942\) | −16.1476 | + | 5.63788i | −0.526118 | + | 0.183692i | ||||
\(943\) | −8.83612 | −0.287744 | ||||||||
\(944\) | −39.9243 | − | 9.22767i | −1.29942 | − | 0.300335i | ||||
\(945\) | −18.9132 | −0.615247 | ||||||||
\(946\) | −47.6091 | + | 16.6225i | −1.54791 | + | 0.540445i | ||||
\(947\) | − | 15.5988i | − | 0.506894i | −0.967349 | − | 0.253447i | \(-0.918436\pi\) | ||
0.967349 | − | 0.253447i | \(-0.0815643\pi\) | |||||||
\(948\) | −2.35496 | − | 2.96134i | −0.0764855 | − | 0.0961799i | ||||
\(949\) | − | 27.7304i | − | 0.900165i | ||||||
\(950\) | −0.257743 | − | 0.738208i | −0.00836227 | − | 0.0239506i | ||||
\(951\) | 12.8704 | 0.417352 | ||||||||
\(952\) | 28.2876 | − | 44.8147i | 0.916807 | − | 1.45245i | ||||
\(953\) | 21.1243 | 0.684282 | 0.342141 | − | 0.939649i | \(-0.388848\pi\) | ||||
0.342141 | + | 0.939649i | \(0.388848\pi\) | |||||||
\(954\) | 3.87510 | + | 11.0988i | 0.125461 | + | 0.359337i | ||||
\(955\) | − | 42.3047i | − | 1.36895i | ||||||
\(956\) | 2.85768 | − | 2.27252i | 0.0924239 | − | 0.0734986i | ||||
\(957\) | 25.8613i | 0.835977i | ||||||||
\(958\) | 13.3915 | − | 4.67560i | 0.432660 | − | 0.151062i | ||||
\(959\) | −49.6529 | −1.60338 | ||||||||
\(960\) | −4.20209 | − | 8.81831i | −0.135622 | − | 0.284610i | ||||
\(961\) | −2.28738 | −0.0737863 | ||||||||
\(962\) | −6.55832 | + | 2.28981i | −0.211449 | + | 0.0738265i | ||||
\(963\) | − | 26.4170i | − | 0.851277i | ||||||
\(964\) | 10.1375 | − | 8.06165i | 0.326506 | − | 0.259648i | ||||
\(965\) | − | 3.90378i | − | 0.125667i | ||||||
\(966\) | 0.888744 | + | 2.54548i | 0.0285949 | + | 0.0818994i | ||||
\(967\) | 46.1207 | 1.48314 | 0.741570 | − | 0.670875i | \(-0.234081\pi\) | ||||
0.741570 | + | 0.670875i | \(0.234081\pi\) | |||||||
\(968\) | −16.2444 | + | 25.7353i | −0.522116 | + | 0.827162i | ||||
\(969\) | −3.96764 | −0.127459 | ||||||||
\(970\) | 1.64452 | + | 4.71011i | 0.0528022 | + | 0.151233i | ||||
\(971\) | 22.3253i | 0.716454i | 0.933635 | + | 0.358227i | \(0.116619\pi\) | ||||
−0.933635 | + | 0.358227i | \(0.883381\pi\) | |||||||
\(972\) | 16.6423 | + | 20.9276i | 0.533802 | + | 0.671252i | ||||
\(973\) | − | 5.28882i | − | 0.169552i | ||||||
\(974\) | 55.5763 | − | 19.4043i | 1.78078 | − | 0.621752i | ||||
\(975\) | −1.43354 | −0.0459099 | ||||||||
\(976\) | 2.81406 | + | 0.650411i | 0.0900757 | + | 0.0208192i | ||||
\(977\) | 14.2650 | 0.456379 | 0.228190 | − | 0.973617i | \(-0.426719\pi\) | ||||
0.228190 | + | 0.973617i | \(0.426719\pi\) | |||||||
\(978\) | −1.97010 | + | 0.687851i | −0.0629967 | + | 0.0219951i | ||||
\(979\) | 2.89544i | 0.0925385i | ||||||||
\(980\) | −1.25140 | − | 1.57363i | −0.0399746 | − | 0.0502678i | ||||
\(981\) | 7.58355i | 0.242124i | ||||||||
\(982\) | 16.1733 | + | 46.3224i | 0.516110 | + | 1.47821i | ||||
\(983\) | 12.7242 | 0.405838 | 0.202919 | − | 0.979196i | \(-0.434957\pi\) | ||||
0.202919 | + | 0.979196i | \(0.434957\pi\) | |||||||
\(984\) | 10.1623 | + | 6.41458i | 0.323963 | + | 0.204489i | ||||
\(985\) | 0.474237 | 0.0151104 | ||||||||
\(986\) | 30.5856 | + | 87.6011i | 0.974044 | + | 2.78979i | ||||
\(987\) | − | 11.9770i | − | 0.381232i | ||||||
\(988\) | 7.00959 | − | 5.57426i | 0.223005 | − | 0.177341i | ||||
\(989\) | − | 9.20472i | − | 0.292693i | ||||||
\(990\) | 34.9992 | − | 12.2198i | 1.11235 | − | 0.388372i | ||||
\(991\) | −10.8169 | −0.343611 | −0.171806 | − | 0.985131i | \(-0.554960\pi\) | ||||
−0.171806 | + | 0.985131i | \(0.554960\pi\) | |||||||
\(992\) | 3.29061 | + | 30.1326i | 0.104477 | + | 0.956712i | ||||
\(993\) | −14.0104 | −0.444607 | ||||||||
\(994\) | −16.8759 | + | 5.89215i | −0.535271 | + | 0.186888i | ||||
\(995\) | 3.74705i | 0.118789i | ||||||||
\(996\) | 8.13866 | − | 6.47214i | 0.257883 | − | 0.205078i | ||||
\(997\) | 5.39134i | 0.170746i | 0.996349 | + | 0.0853728i | \(0.0272081\pi\) | ||||
−0.996349 | + | 0.0853728i | \(0.972792\pi\) | |||||||
\(998\) | −6.58561 | − | 18.8620i | −0.208464 | − | 0.597067i | ||||
\(999\) | −3.59792 | −0.113833 |
(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 | 152.2.c.b.77.15 | ✓ | 16 | |
3.2 | odd | 2 | 1368.2.g.b.685.2 | 16 | |||
4.3 | odd | 2 | 608.2.c.b.305.8 | 16 | |||
8.3 | odd | 2 | 608.2.c.b.305.9 | 16 | |||
8.5 | even | 2 | inner | 152.2.c.b.77.16 | yes | 16 | |
12.11 | even | 2 | 5472.2.g.b.2737.12 | 16 | |||
16.3 | odd | 4 | 4864.2.a.bp.1.5 | 8 | |||
16.5 | even | 4 | 4864.2.a.bo.1.5 | 8 | |||
16.11 | odd | 4 | 4864.2.a.bn.1.4 | 8 | |||
16.13 | even | 4 | 4864.2.a.bq.1.4 | 8 | |||
24.5 | odd | 2 | 1368.2.g.b.685.1 | 16 | |||
24.11 | even | 2 | 5472.2.g.b.2737.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.15 | ✓ | 16 | 1.1 | even | 1 | trivial | |
152.2.c.b.77.16 | yes | 16 | 8.5 | even | 2 | inner | |
608.2.c.b.305.8 | 16 | 4.3 | odd | 2 | |||
608.2.c.b.305.9 | 16 | 8.3 | odd | 2 | |||
1368.2.g.b.685.1 | 16 | 24.5 | odd | 2 | |||
1368.2.g.b.685.2 | 16 | 3.2 | odd | 2 | |||
4864.2.a.bn.1.4 | 8 | 16.11 | odd | 4 | |||
4864.2.a.bo.1.5 | 8 | 16.5 | even | 4 | |||
4864.2.a.bp.1.5 | 8 | 16.3 | odd | 4 | |||
4864.2.a.bq.1.4 | 8 | 16.13 | even | 4 | |||
5472.2.g.b.2737.5 | 16 | 24.11 | even | 2 | |||
5472.2.g.b.2737.12 | 16 | 12.11 | even | 2 |