Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,2,Mod(11,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.k (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: | \(0.383281929702\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.163368480538624.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 35.1 | ||
Root | \(0.204810 + 1.39930i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.35 |
Dual form | 48.2.k.a.11.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.39930 | − | 0.204810i | −0.989458 | − | 0.144822i | ||||
\(3\) | −0.814141 | + | 1.52878i | −0.470045 | + | 0.882643i | ||||
\(4\) | 1.91611 | + | 0.573183i | 0.958053 | + | 0.286591i | ||||
\(5\) | 2.08397 | + | 2.08397i | 0.931979 | + | 0.931979i | 0.997829 | − | 0.0658506i | \(-0.0209761\pi\) |
−0.0658506 | + | 0.997829i | \(0.520976\pi\) | |||||||
\(6\) | 1.45234 | − | 1.97249i | 0.592916 | − | 0.805265i | ||||
\(7\) | −1.14637 | −0.433285 | −0.216643 | − | 0.976251i | \(-0.569511\pi\) | ||||
−0.216643 | + | 0.976251i | \(0.569511\pi\) | |||||||
\(8\) | −2.56382 | − | 1.19449i | −0.906448 | − | 0.422318i | ||||
\(9\) | −1.67435 | − | 2.48929i | −0.558116 | − | 0.829763i | ||||
\(10\) | −2.48929 | − | 3.34292i | −0.787182 | − | 1.05713i | ||||
\(11\) | 1.67435 | − | 1.67435i | 0.504835 | − | 0.504835i | −0.408102 | − | 0.912937i | \(-0.633809\pi\) |
0.912937 | + | 0.408102i | \(0.133809\pi\) | |||||||
\(12\) | −2.43625 | + | 2.46266i | −0.703285 | + | 0.710908i | ||||
\(13\) | 0.146365 | + | 0.146365i | 0.0405945 | + | 0.0405945i | 0.727113 | − | 0.686518i | \(-0.240862\pi\) |
−0.686518 | + | 0.727113i | \(0.740862\pi\) | |||||||
\(14\) | 1.60411 | + | 0.234787i | 0.428718 | + | 0.0627495i | ||||
\(15\) | −4.88258 | + | 1.48929i | −1.26068 | + | 0.384533i | ||||
\(16\) | 3.34292 | + | 2.19656i | 0.835731 | + | 0.549139i | ||||
\(17\) | − | 5.59722i | − | 1.35752i | −0.734358 | − | 0.678762i | \(-0.762517\pi\) | ||
0.734358 | − | 0.678762i | \(-0.237483\pi\) | |||||||
\(18\) | 1.83309 | + | 3.82620i | 0.432064 | + | 0.901843i | ||||
\(19\) | 1.48929 | − | 1.48929i | 0.341666 | − | 0.341666i | −0.515327 | − | 0.856993i | \(-0.672330\pi\) |
0.856993 | + | 0.515327i | \(0.172330\pi\) | |||||||
\(20\) | 2.79861 | + | 5.18760i | 0.625788 | + | 1.15998i | ||||
\(21\) | 0.933303 | − | 1.75254i | 0.203663 | − | 0.382436i | ||||
\(22\) | −2.68585 | + | 2.00000i | −0.572624 | + | 0.426401i | ||||
\(23\) | 3.34870i | 0.698252i | 0.937076 | + | 0.349126i | \(0.113521\pi\) | ||||
−0.937076 | + | 0.349126i | \(0.886479\pi\) | |||||||
\(24\) | 3.91343 | − | 2.94704i | 0.798826 | − | 0.601561i | ||||
\(25\) | 3.68585i | 0.737169i | ||||||||
\(26\) | −0.174833 | − | 0.234787i | −0.0342875 | − | 0.0460455i | ||||
\(27\) | 5.16874 | − | 0.533081i | 0.994724 | − | 0.102592i | ||||
\(28\) | −2.19656 | − | 0.657077i | −0.415110 | − | 0.124176i | ||||
\(29\) | −3.51325 | + | 3.51325i | −0.652394 | + | 0.652394i | −0.953569 | − | 0.301175i | \(-0.902621\pi\) |
0.301175 | + | 0.953569i | \(0.402621\pi\) | |||||||
\(30\) | 7.13723 | − | 1.08397i | 1.30307 | − | 0.197905i | ||||
\(31\) | − | 5.83221i | − | 1.04750i | −0.851873 | − | 0.523748i | \(-0.824533\pi\) | ||
0.851873 | − | 0.523748i | \(-0.175467\pi\) | |||||||
\(32\) | −4.22789 | − | 3.75832i | −0.747392 | − | 0.664383i | ||||
\(33\) | 1.19656 | + | 3.92287i | 0.208294 | + | 0.682884i | ||||
\(34\) | −1.14637 | + | 7.83221i | −0.196600 | + | 1.34321i | ||||
\(35\) | −2.38899 | − | 2.38899i | −0.403813 | − | 0.403813i | ||||
\(36\) | −1.78141 | − | 5.72945i | −0.296902 | − | 0.954908i | ||||
\(37\) | −4.83221 | + | 4.83221i | −0.794411 | + | 0.794411i | −0.982208 | − | 0.187797i | \(-0.939865\pi\) |
0.187797 | + | 0.982208i | \(0.439865\pi\) | |||||||
\(38\) | −2.38899 | + | 1.77895i | −0.387545 | + | 0.288583i | ||||
\(39\) | −0.342923 | + | 0.104599i | −0.0549116 | + | 0.0167492i | ||||
\(40\) | −2.85363 | − | 7.83221i | −0.451199 | − | 1.23838i | ||||
\(41\) | 0.610042 | 0.0952726 | 0.0476363 | − | 0.998865i | \(-0.484831\pi\) | ||||
0.0476363 | + | 0.998865i | \(0.484831\pi\) | |||||||
\(42\) | −1.66491 | + | 2.26119i | −0.256902 | + | 0.348909i | ||||
\(43\) | −1.48929 | − | 1.48929i | −0.227114 | − | 0.227114i | 0.584372 | − | 0.811486i | \(-0.301341\pi\) |
−0.811486 | + | 0.584372i | \(0.801341\pi\) | |||||||
\(44\) | 4.16794 | − | 2.24852i | 0.628340 | − | 0.338977i | ||||
\(45\) | 1.69831 | − | 8.67689i | 0.253169 | − | 1.29347i | ||||
\(46\) | 0.685846 | − | 4.68585i | 0.101123 | − | 0.690890i | ||||
\(47\) | 6.41646 | 0.935936 | 0.467968 | − | 0.883745i | \(-0.344986\pi\) | ||||
0.467968 | + | 0.883745i | \(0.344986\pi\) | |||||||
\(48\) | −6.07967 | + | 3.32229i | −0.877525 | + | 0.479532i | ||||
\(49\) | −5.68585 | −0.812264 | ||||||||
\(50\) | 0.754898 | − | 5.15762i | 0.106759 | − | 0.729398i | ||||
\(51\) | 8.55693 | + | 4.55693i | 1.19821 | + | 0.638097i | ||||
\(52\) | 0.196558 | + | 0.364346i | 0.0272576 | + | 0.0505257i | ||||
\(53\) | 0.164553 | + | 0.164553i | 0.0226031 | + | 0.0226031i | 0.718318 | − | 0.695715i | \(-0.244912\pi\) |
−0.695715 | + | 0.718318i | \(0.744912\pi\) | |||||||
\(54\) | −7.34181 | − | 0.312665i | −0.999094 | − | 0.0425483i | ||||
\(55\) | 6.97858 | 0.940991 | ||||||||
\(56\) | 2.93908 | + | 1.36933i | 0.392751 | + | 0.182984i | ||||
\(57\) | 1.06431 | + | 3.48929i | 0.140971 | + | 0.462168i | ||||
\(58\) | 5.63565 | − | 4.19656i | 0.739998 | − | 0.551035i | ||||
\(59\) | −9.05051 | + | 9.05051i | −1.17828 | + | 1.17828i | −0.198093 | + | 0.980183i | \(0.563475\pi\) |
−0.980183 | + | 0.198093i | \(0.936525\pi\) | |||||||
\(60\) | −10.2092 | + | 0.0550256i | −1.31800 | + | 0.00710378i | ||||
\(61\) | 4.53948 | + | 4.53948i | 0.581221 | + | 0.581221i | 0.935239 | − | 0.354018i | \(-0.115185\pi\) |
−0.354018 | + | 0.935239i | \(0.615185\pi\) | |||||||
\(62\) | −1.19449 | + | 8.16104i | −0.151701 | + | 1.03645i | ||||
\(63\) | 1.91942 | + | 2.85363i | 0.241824 | + | 0.359524i | ||||
\(64\) | 5.14637 | + | 6.12494i | 0.643296 | + | 0.765618i | ||||
\(65\) | 0.610042i | 0.0756664i | ||||||||
\(66\) | −0.870906 | − | 5.73436i | −0.107201 | − | 0.705850i | ||||
\(67\) | −0.635654 | + | 0.635654i | −0.0776575 | + | 0.0776575i | −0.744869 | − | 0.667211i | \(-0.767488\pi\) |
0.667211 | + | 0.744869i | \(0.267488\pi\) | |||||||
\(68\) | 3.20823 | − | 10.7249i | 0.389055 | − | 1.30058i | ||||
\(69\) | −5.11943 | − | 2.72631i | −0.616307 | − | 0.328209i | ||||
\(70\) | 2.85363 | + | 3.83221i | 0.341075 | + | 0.458037i | ||||
\(71\) | − | 6.90659i | − | 0.819662i | −0.912162 | − | 0.409831i | \(-0.865588\pi\) | ||
0.912162 | − | 0.409831i | \(-0.134412\pi\) | |||||||
\(72\) | 1.31929 | + | 8.38209i | 0.155480 | + | 0.987839i | ||||
\(73\) | − | 7.07896i | − | 0.828530i | −0.910156 | − | 0.414265i | \(-0.864039\pi\) | ||
0.910156 | − | 0.414265i | \(-0.135961\pi\) | |||||||
\(74\) | 7.75142 | − | 5.77205i | 0.901084 | − | 0.670987i | ||||
\(75\) | −5.63485 | − | 3.00080i | −0.650657 | − | 0.346502i | ||||
\(76\) | 3.70727 | − | 2.00000i | 0.425253 | − | 0.229416i | ||||
\(77\) | −1.91942 | + | 1.91942i | −0.218738 | + | 0.218738i | ||||
\(78\) | 0.501277 | − | 0.0761315i | 0.0567584 | − | 0.00862019i | ||||
\(79\) | 9.83221i | 1.10621i | 0.833111 | + | 0.553105i | \(0.186557\pi\) | ||||
−0.833111 | + | 0.553105i | \(0.813443\pi\) | |||||||
\(80\) | 2.38899 | + | 11.5441i | 0.267097 | + | 1.29067i | ||||
\(81\) | −3.39312 | + | 8.33587i | −0.377013 | + | 0.926208i | ||||
\(82\) | −0.853635 | − | 0.124943i | −0.0942682 | − | 0.0137976i | ||||
\(83\) | −8.09081 | − | 8.09081i | −0.888081 | − | 0.888081i | 0.106257 | − | 0.994339i | \(-0.466113\pi\) |
−0.994339 | + | 0.106257i | \(0.966113\pi\) | |||||||
\(84\) | 2.79284 | − | 2.82310i | 0.304723 | − | 0.308026i | ||||
\(85\) | 11.6644 | − | 11.6644i | 1.26518 | − | 1.26518i | ||||
\(86\) | 1.77895 | + | 2.38899i | 0.191829 | + | 0.257611i | ||||
\(87\) | −2.51071 | − | 8.23127i | −0.269177 | − | 0.882485i | ||||
\(88\) | −6.29273 | + | 2.29273i | −0.670807 | + | 0.244406i | ||||
\(89\) | 0.490134 | 0.0519541 | 0.0259770 | − | 0.999663i | \(-0.491730\pi\) | ||||
0.0259770 | + | 0.999663i | \(0.491730\pi\) | |||||||
\(90\) | −4.15356 | + | 11.7938i | −0.437824 | + | 1.24317i | ||||
\(91\) | −0.167788 | − | 0.167788i | −0.0175890 | − | 0.0175890i | ||||
\(92\) | −1.91942 | + | 6.41646i | −0.200113 | + | 0.668962i | ||||
\(93\) | 8.91618 | + | 4.74824i | 0.924565 | + | 0.492370i | ||||
\(94\) | −8.97858 | − | 1.31415i | −0.926070 | − | 0.135545i | ||||
\(95\) | 6.20726 | 0.636851 | ||||||||
\(96\) | 9.18775 | − | 3.40372i | 0.937720 | − | 0.347391i | ||||
\(97\) | 12.3503 | 1.25398 | 0.626990 | − | 0.779027i | \(-0.284287\pi\) | ||||
0.626990 | + | 0.779027i | \(0.284287\pi\) | |||||||
\(98\) | 7.95623 | + | 1.16452i | 0.803701 | + | 0.117634i | ||||
\(99\) | −6.97138 | − | 1.36449i | −0.700650 | − | 0.137137i | ||||
\(100\) | −2.11266 | + | 7.06247i | −0.211266 | + | 0.706247i | ||||
\(101\) | −8.29123 | − | 8.29123i | −0.825008 | − | 0.825008i | 0.161813 | − | 0.986821i | \(-0.448266\pi\) |
−0.986821 | + | 0.161813i | \(0.948266\pi\) | |||||||
\(102\) | −11.0404 | − | 8.12907i | −1.09317 | − | 0.804898i | ||||
\(103\) | −12.2253 | −1.20460 | −0.602299 | − | 0.798271i | \(-0.705748\pi\) | ||||
−0.602299 | + | 0.798271i | \(0.705748\pi\) | |||||||
\(104\) | −0.200422 | − | 0.550088i | −0.0196530 | − | 0.0539405i | ||||
\(105\) | 5.59722 | − | 1.70727i | 0.546233 | − | 0.166612i | ||||
\(106\) | −0.196558 | − | 0.263962i | −0.0190914 | − | 0.0256382i | ||||
\(107\) | −0.714641 | + | 0.714641i | −0.0690869 | + | 0.0690869i | −0.740806 | − | 0.671719i | \(-0.765556\pi\) |
0.671719 | + | 0.740806i | \(0.265556\pi\) | |||||||
\(108\) | 10.2094 | + | 1.94119i | 0.982400 | + | 0.186791i | ||||
\(109\) | −12.4966 | − | 12.4966i | −1.19696 | − | 1.19696i | −0.975072 | − | 0.221888i | \(-0.928778\pi\) |
−0.221888 | − | 0.975072i | \(-0.571222\pi\) | |||||||
\(110\) | −9.76515 | − | 1.42928i | −0.931071 | − | 0.136277i | ||||
\(111\) | −3.45330 | − | 11.3215i | −0.327772 | − | 1.07459i | ||||
\(112\) | −3.83221 | − | 2.51806i | −0.362110 | − | 0.237934i | ||||
\(113\) | 5.47731i | 0.515262i | 0.966243 | + | 0.257631i | \(0.0829419\pi\) | ||||
−0.966243 | + | 0.257631i | \(0.917058\pi\) | |||||||
\(114\) | −0.774648 | − | 5.10056i | −0.0725524 | − | 0.477711i | ||||
\(115\) | −6.97858 | + | 6.97858i | −0.650756 | + | 0.650756i | ||||
\(116\) | −8.74549 | + | 4.71802i | −0.811999 | + | 0.438058i | ||||
\(117\) | 0.119279 | − | 0.609413i | 0.0110274 | − | 0.0563402i | ||||
\(118\) | 14.5181 | − | 10.8108i | 1.33650 | − | 0.995214i | ||||
\(119\) | 6.41646i | 0.588196i | ||||||||
\(120\) | 14.2970 | + | 2.01394i | 1.30513 | + | 0.183847i | ||||
\(121\) | 5.39312i | 0.490283i | ||||||||
\(122\) | −5.42238 | − | 7.28185i | −0.490920 | − | 0.659267i | ||||
\(123\) | −0.496660 | + | 0.932621i | −0.0447824 | + | 0.0840916i | ||||
\(124\) | 3.34292 | − | 11.1751i | 0.300203 | − | 1.00356i | ||||
\(125\) | 2.73865 | − | 2.73865i | 0.244953 | − | 0.244953i | ||||
\(126\) | −2.10139 | − | 4.38622i | −0.187207 | − | 0.390755i | ||||
\(127\) | 7.20390i | 0.639243i | 0.947545 | + | 0.319622i | \(0.103556\pi\) | ||||
−0.947545 | + | 0.319622i | \(0.896444\pi\) | |||||||
\(128\) | −5.94688 | − | 9.62469i | −0.525635 | − | 0.850710i | ||||
\(129\) | 3.48929 | − | 1.06431i | 0.307215 | − | 0.0937069i | ||||
\(130\) | 0.124943 | − | 0.853635i | 0.0109582 | − | 0.0748687i | ||||
\(131\) | 9.05051 | + | 9.05051i | 0.790747 | + | 0.790747i | 0.981616 | − | 0.190869i | \(-0.0611304\pi\) |
−0.190869 | + | 0.981616i | \(0.561130\pi\) | |||||||
\(132\) | 0.0442099 | + | 8.20248i | 0.00384798 | + | 0.713934i | ||||
\(133\) | −1.70727 | + | 1.70727i | −0.148039 | + | 0.148039i | ||||
\(134\) | 1.01966 | − | 0.759285i | 0.0880854 | − | 0.0655923i | ||||
\(135\) | 11.8824 | + | 9.66056i | 1.02267 | + | 0.831448i | ||||
\(136\) | −6.68585 | + | 14.3503i | −0.573307 | + | 1.23053i | ||||
\(137\) | 13.4430 | 1.14851 | 0.574255 | − | 0.818677i | \(-0.305292\pi\) | ||||
0.574255 | + | 0.818677i | \(0.305292\pi\) | |||||||
\(138\) | 6.60526 | + | 4.86345i | 0.562277 | + | 0.414004i | ||||
\(139\) | 8.63565 | + | 8.63565i | 0.732467 | + | 0.732467i | 0.971108 | − | 0.238641i | \(-0.0767020\pi\) |
−0.238641 | + | 0.971108i | \(0.576702\pi\) | |||||||
\(140\) | −3.20823 | − | 5.94688i | −0.271145 | − | 0.502603i | ||||
\(141\) | −5.22390 | + | 9.80936i | −0.439932 | + | 0.826097i | ||||
\(142\) | −1.41454 | + | 9.66442i | −0.118705 | + | 0.811020i | ||||
\(143\) | 0.490134 | 0.0409870 | ||||||||
\(144\) | −0.129352 | − | 11.9993i | −0.0107793 | − | 0.999942i | ||||
\(145\) | −14.6430 | −1.21603 | ||||||||
\(146\) | −1.44984 | + | 9.90562i | −0.119990 | + | 0.819795i | ||||
\(147\) | 4.62908 | − | 8.69242i | 0.381800 | − | 0.716939i | ||||
\(148\) | −12.0288 | + | 6.48929i | −0.988759 | + | 0.533416i | ||||
\(149\) | 11.6399 | + | 11.6399i | 0.953580 | + | 0.953580i | 0.998969 | − | 0.0453896i | \(-0.0144529\pi\) |
−0.0453896 | + | 0.998969i | \(0.514453\pi\) | |||||||
\(150\) | 7.27028 | + | 5.35311i | 0.593616 | + | 0.437079i | ||||
\(151\) | −0.810789 | −0.0659811 | −0.0329905 | − | 0.999456i | \(-0.510503\pi\) | ||||
−0.0329905 | + | 0.999456i | \(0.510503\pi\) | |||||||
\(152\) | −5.59722 | + | 2.03932i | −0.453994 | + | 0.165411i | ||||
\(153\) | −13.9331 | + | 9.37169i | −1.12642 | + | 0.757656i | ||||
\(154\) | 3.07896 | − | 2.29273i | 0.248110 | − | 0.184754i | ||||
\(155\) | 12.1541 | − | 12.1541i | 0.976244 | − | 0.976244i | ||||
\(156\) | −0.717031 | + | 0.00386467i | −0.0574084 | + | 0.000309421i | ||||
\(157\) | 5.51806 | + | 5.51806i | 0.440389 | + | 0.440389i | 0.892143 | − | 0.451754i | \(-0.149201\pi\) |
−0.451754 | + | 0.892143i | \(0.649201\pi\) | |||||||
\(158\) | 2.01373 | − | 13.7583i | 0.160204 | − | 1.09455i | ||||
\(159\) | −0.385535 | + | 0.117596i | −0.0305749 | + | 0.00932599i | ||||
\(160\) | −0.978577 | − | 16.6430i | −0.0773633 | − | 1.31574i | ||||
\(161\) | − | 3.83883i | − | 0.302542i | ||||||
\(162\) | 6.45527 | − | 10.9695i | 0.507174 | − | 0.861844i | ||||
\(163\) | 10.0748 | − | 10.0748i | 0.789115 | − | 0.789115i | −0.192234 | − | 0.981349i | \(-0.561573\pi\) |
0.981349 | + | 0.192234i | \(0.0615732\pi\) | |||||||
\(164\) | 1.16891 | + | 0.349666i | 0.0912762 | + | 0.0273043i | ||||
\(165\) | −5.68155 | + | 10.6687i | −0.442308 | + | 0.830559i | ||||
\(166\) | 9.66442 | + | 12.9786i | 0.750105 | + | 1.00733i | ||||
\(167\) | − | 2.36843i | − | 0.183275i | −0.995792 | − | 0.0916373i | \(-0.970790\pi\) | ||
0.995792 | − | 0.0916373i | \(-0.0292100\pi\) | |||||||
\(168\) | −4.48623 | + | 3.37838i | −0.346120 | + | 0.260648i | ||||
\(169\) | − | 12.9572i | − | 0.996704i | ||||||
\(170\) | −18.7111 | + | 13.9331i | −1.43507 | + | 1.06862i | ||||
\(171\) | −6.20086 | − | 1.21368i | −0.474191 | − | 0.0928125i | ||||
\(172\) | −2.00000 | − | 3.70727i | −0.152499 | − | 0.282677i | ||||
\(173\) | 5.22347 | − | 5.22347i | 0.397133 | − | 0.397133i | −0.480088 | − | 0.877221i | \(-0.659395\pi\) |
0.877221 | + | 0.480088i | \(0.159395\pi\) | |||||||
\(174\) | 1.82740 | + | 12.0323i | 0.138535 | + | 0.912165i | ||||
\(175\) | − | 4.22533i | − | 0.319405i | ||||||
\(176\) | 9.27502 | − | 1.91942i | 0.699131 | − | 0.144681i | ||||
\(177\) | −6.46787 | − | 21.2047i | −0.486155 | − | 1.59384i | ||||
\(178\) | −0.685846 | − | 0.100384i | −0.0514063 | − | 0.00752411i | ||||
\(179\) | 7.13110 | + | 7.13110i | 0.533003 | + | 0.533003i | 0.921465 | − | 0.388462i | \(-0.126993\pi\) |
−0.388462 | + | 0.921465i | \(0.626993\pi\) | |||||||
\(180\) | 8.22758 | − | 15.6524i | 0.613248 | − | 1.16666i | ||||
\(181\) | −6.73183 | + | 6.73183i | −0.500373 | + | 0.500373i | −0.911554 | − | 0.411181i | \(-0.865116\pi\) |
0.411181 | + | 0.911554i | \(0.365116\pi\) | |||||||
\(182\) | 0.200422 | + | 0.269152i | 0.0148563 | + | 0.0199509i | ||||
\(183\) | −10.6357 | + | 3.24410i | −0.786210 | + | 0.239811i | ||||
\(184\) | 4.00000 | − | 8.58546i | 0.294884 | − | 0.632929i | ||||
\(185\) | −20.1403 | −1.48075 | ||||||||
\(186\) | −11.5040 | − | 8.47036i | −0.843511 | − | 0.621077i | ||||
\(187\) | −9.37169 | − | 9.37169i | −0.685326 | − | 0.685326i | ||||
\(188\) | 12.2946 | + | 3.67780i | 0.896677 | + | 0.268231i | ||||
\(189\) | −5.92526 | + | 0.611106i | −0.430999 | + | 0.0444514i | ||||
\(190\) | −8.68585 | − | 1.27131i | −0.630138 | − | 0.0922304i | ||||
\(191\) | −25.5284 | −1.84717 | −0.923584 | − | 0.383396i | \(-0.874754\pi\) | ||||
−0.923584 | + | 0.383396i | \(0.874754\pi\) | |||||||
\(192\) | −13.5536 | + | 2.88110i | −0.978145 | + | 0.207926i | ||||
\(193\) | 9.07896 | 0.653518 | 0.326759 | − | 0.945108i | \(-0.394043\pi\) | ||||
0.326759 | + | 0.945108i | \(0.394043\pi\) | |||||||
\(194\) | −17.2818 | − | 2.52946i | −1.24076 | − | 0.181604i | ||||
\(195\) | −0.932621 | − | 0.496660i | −0.0667864 | − | 0.0355666i | ||||
\(196\) | −10.8947 | − | 3.25903i | −0.778192 | − | 0.232788i | ||||
\(197\) | 3.18414 | + | 3.18414i | 0.226861 | + | 0.226861i | 0.811380 | − | 0.584519i | \(-0.198717\pi\) |
−0.584519 | + | 0.811380i | \(0.698717\pi\) | |||||||
\(198\) | 9.47562 | + | 3.33715i | 0.673403 | + | 0.237161i | ||||
\(199\) | 19.5542 | 1.38616 | 0.693079 | − | 0.720861i | \(-0.256254\pi\) | ||||
0.693079 | + | 0.720861i | \(0.256254\pi\) | |||||||
\(200\) | 4.40272 | − | 9.44985i | 0.311320 | − | 0.668206i | ||||
\(201\) | −0.454264 | − | 1.48929i | −0.0320413 | − | 0.105046i | ||||
\(202\) | 9.90383 | + | 13.3001i | 0.696831 | + | 0.935790i | ||||
\(203\) | 4.02747 | − | 4.02747i | 0.282673 | − | 0.282673i | ||||
\(204\) | 13.7840 | + | 13.6362i | 0.965075 | + | 0.954727i | ||||
\(205\) | 1.27131 | + | 1.27131i | 0.0887920 | + | 0.0887920i | ||||
\(206\) | 17.1070 | + | 2.50387i | 1.19190 | + | 0.174453i | ||||
\(207\) | 8.33587 | − | 5.60688i | 0.579383 | − | 0.389705i | ||||
\(208\) | 0.167788 | + | 0.810789i | 0.0116340 | + | 0.0562181i | ||||
\(209\) | − | 4.98718i | − | 0.344970i | ||||||
\(210\) | −8.18188 | + | 1.24262i | −0.564603 | + | 0.0857492i | ||||
\(211\) | −10.3429 | + | 10.3429i | −0.712036 | + | 0.712036i | −0.966961 | − | 0.254925i | \(-0.917949\pi\) |
0.254925 | + | 0.966961i | \(0.417949\pi\) | |||||||
\(212\) | 0.220982 | + | 0.409620i | 0.0151771 | + | 0.0281328i | ||||
\(213\) | 10.5587 | + | 5.62294i | 0.723468 | + | 0.385277i | ||||
\(214\) | 1.14637 | − | 0.853635i | 0.0783639 | − | 0.0583533i | ||||
\(215\) | − | 6.20726i | − | 0.423332i | ||||||
\(216\) | −13.8885 | − | 4.80730i | −0.944991 | − | 0.327095i | ||||
\(217\) | 6.68585i | 0.453865i | ||||||||
\(218\) | 14.9272 | + | 20.0460i | 1.01100 | + | 1.35769i | ||||
\(219\) | 10.8222 | + | 5.76327i | 0.731296 | + | 0.389446i | ||||
\(220\) | 13.3717 | + | 4.00000i | 0.901519 | + | 0.269680i | ||||
\(221\) | 0.819240 | − | 0.819240i | 0.0551080 | − | 0.0551080i | ||||
\(222\) | 2.51346 | + | 16.5495i | 0.168692 | + | 1.11073i | ||||
\(223\) | − | 22.6184i | − | 1.51464i | −0.653042 | − | 0.757321i | \(-0.726508\pi\) | ||
0.653042 | − | 0.757321i | \(-0.273492\pi\) | |||||||
\(224\) | 4.84671 | + | 4.30840i | 0.323834 | + | 0.287867i | ||||
\(225\) | 9.17513 | − | 6.17139i | 0.611676 | − | 0.411426i | ||||
\(226\) | 1.12181 | − | 7.66442i | 0.0746215 | − | 0.509830i | ||||
\(227\) | 1.46515 | + | 1.46515i | 0.0972455 | + | 0.0972455i | 0.754056 | − | 0.656810i | \(-0.228095\pi\) |
−0.656810 | + | 0.754056i | \(0.728095\pi\) | |||||||
\(228\) | 0.0393236 | + | 7.29589i | 0.00260427 | + | 0.483182i | ||||
\(229\) | −7.51806 | + | 7.51806i | −0.496807 | + | 0.496807i | −0.910443 | − | 0.413635i | \(-0.864259\pi\) |
0.413635 | + | 0.910443i | \(0.364259\pi\) | |||||||
\(230\) | 11.1944 | − | 8.33587i | 0.738139 | − | 0.549651i | ||||
\(231\) | −1.37169 | − | 4.49704i | −0.0902507 | − | 0.295884i | ||||
\(232\) | 13.2039 | − | 4.81079i | 0.866879 | − | 0.315844i | ||||
\(233\) | −18.3820 | −1.20424 | −0.602121 | − | 0.798405i | \(-0.705678\pi\) | ||||
−0.602121 | + | 0.798405i | \(0.705678\pi\) | |||||||
\(234\) | −0.291722 | + | 0.828324i | −0.0190704 | + | 0.0541493i | ||||
\(235\) | 13.3717 | + | 13.3717i | 0.872273 | + | 0.872273i | ||||
\(236\) | −22.5293 | + | 12.1541i | −1.46654 | + | 0.791167i | ||||
\(237\) | −15.0313 | − | 8.00481i | −0.976388 | − | 0.519968i | ||||
\(238\) | 1.31415 | − | 8.97858i | 0.0851839 | − | 0.581995i | ||||
\(239\) | −13.5322 | −0.875328 | −0.437664 | − | 0.899139i | \(-0.644194\pi\) | ||||
−0.437664 | + | 0.899139i | \(0.644194\pi\) | |||||||
\(240\) | −19.5934 | − | 5.74628i | −1.26475 | − | 0.370921i | ||||
\(241\) | 4.87819 | 0.314232 | 0.157116 | − | 0.987580i | \(-0.449780\pi\) | ||||
0.157116 | + | 0.987580i | \(0.449780\pi\) | |||||||
\(242\) | 1.10456 | − | 7.54661i | 0.0710040 | − | 0.485114i | ||||
\(243\) | −9.98126 | − | 11.9739i | −0.640298 | − | 0.768127i | ||||
\(244\) | 6.09617 | + | 11.3001i | 0.390268 | + | 0.723413i | ||||
\(245\) | −11.8491 | − | 11.8491i | −0.757013 | − | 0.757013i | ||||
\(246\) | 0.885989 | − | 1.20330i | 0.0564886 | − | 0.0767196i | ||||
\(247\) | 0.435961 | 0.0277395 | ||||||||
\(248\) | −6.96655 | + | 14.9528i | −0.442376 | + | 0.949501i | ||||
\(249\) | 18.9561 | − | 5.78202i | 1.20130 | − | 0.366421i | ||||
\(250\) | −4.39312 | + | 3.27131i | −0.277845 | + | 0.206896i | ||||
\(251\) | 5.23224 | − | 5.23224i | 0.330256 | − | 0.330256i | −0.522427 | − | 0.852684i | \(-0.674973\pi\) |
0.852684 | + | 0.522427i | \(0.174973\pi\) | |||||||
\(252\) | 2.04215 | + | 6.56804i | 0.128643 | + | 0.413748i | ||||
\(253\) | 5.60688 | + | 5.60688i | 0.352502 | + | 0.352502i | ||||
\(254\) | 1.47543 | − | 10.0805i | 0.0925768 | − | 0.632504i | ||||
\(255\) | 8.33587 | + | 27.3288i | 0.522013 | + | 1.71140i | ||||
\(256\) | 6.35027 | + | 14.6858i | 0.396892 | + | 0.917865i | ||||
\(257\) | 12.8329i | 0.800495i | 0.916407 | + | 0.400248i | \(0.131076\pi\) | ||||
−0.916407 | + | 0.400248i | \(0.868924\pi\) | |||||||
\(258\) | −5.10056 | + | 0.774648i | −0.317547 | + | 0.0482275i | ||||
\(259\) | 5.53948 | − | 5.53948i | 0.344207 | − | 0.344207i | ||||
\(260\) | −0.349666 | + | 1.16891i | −0.0216853 | + | 0.0724924i | ||||
\(261\) | 14.6279 | + | 2.86309i | 0.905444 | + | 0.177221i | ||||
\(262\) | −10.8108 | − | 14.5181i | −0.667893 | − | 0.896929i | ||||
\(263\) | 28.3152i | 1.74599i | 0.487729 | + | 0.872995i | \(0.337825\pi\) | ||||
−0.487729 | + | 0.872995i | \(0.662175\pi\) | |||||||
\(264\) | 1.61809 | − | 11.4868i | 0.0995863 | − | 0.706965i | ||||
\(265\) | 0.685846i | 0.0421312i | ||||||||
\(266\) | 2.73865 | − | 2.03932i | 0.167918 | − | 0.125039i | ||||
\(267\) | −0.399038 | + | 0.749307i | −0.0244207 | + | 0.0458569i | ||||
\(268\) | −1.58233 | + | 0.853635i | −0.0966560 | + | 0.0521440i | ||||
\(269\) | 6.58101 | − | 6.58101i | 0.401251 | − | 0.401251i | −0.477423 | − | 0.878674i | \(-0.658429\pi\) |
0.878674 | + | 0.477423i | \(0.158429\pi\) | |||||||
\(270\) | −14.6485 | − | 15.9517i | −0.891481 | − | 0.970789i | ||||
\(271\) | 8.66129i | 0.526136i | 0.964777 | + | 0.263068i | \(0.0847343\pi\) | ||||
−0.964777 | + | 0.263068i | \(0.915266\pi\) | |||||||
\(272\) | 12.2946 | − | 18.7111i | 0.745470 | − | 1.13453i | ||||
\(273\) | 0.393115 | − | 0.119908i | 0.0237924 | − | 0.00725719i | ||||
\(274\) | −18.8108 | − | 2.75325i | −1.13640 | − | 0.166330i | ||||
\(275\) | 6.17139 | + | 6.17139i | 0.372149 | + | 0.372149i | ||||
\(276\) | −8.24669 | − | 8.15827i | −0.496392 | − | 0.491070i | ||||
\(277\) | 13.1249 | − | 13.1249i | 0.788601 | − | 0.788601i | −0.192664 | − | 0.981265i | \(-0.561713\pi\) |
0.981265 | + | 0.192664i | \(0.0617126\pi\) | |||||||
\(278\) | −10.3152 | − | 13.8526i | −0.618667 | − | 0.830822i | ||||
\(279\) | −14.5181 | + | 9.76515i | −0.869173 | + | 0.584624i | ||||
\(280\) | 3.27131 | + | 8.97858i | 0.195498 | + | 0.536573i | ||||
\(281\) | 26.1560 | 1.56033 | 0.780167 | − | 0.625571i | \(-0.215134\pi\) | ||||
0.780167 | + | 0.625571i | \(0.215134\pi\) | |||||||
\(282\) | 9.31888 | − | 12.6564i | 0.554931 | − | 0.753676i | ||||
\(283\) | −17.9070 | − | 17.9070i | −1.06446 | − | 1.06446i | −0.997774 | − | 0.0666843i | \(-0.978758\pi\) |
−0.0666843 | − | 0.997774i | \(-0.521242\pi\) | |||||||
\(284\) | 3.95874 | − | 13.2338i | 0.234908 | − | 0.785279i | ||||
\(285\) | −5.05359 | + | 9.48955i | −0.299349 | + | 0.562112i | ||||
\(286\) | −0.685846 | − | 0.100384i | −0.0405549 | − | 0.00593584i | ||||
\(287\) | −0.699331 | −0.0412802 | ||||||||
\(288\) | −2.27657 | + | 16.8172i | −0.134148 | + | 0.990961i | ||||
\(289\) | −14.3288 | −0.842873 | ||||||||
\(290\) | 20.4900 | + | 2.99903i | 1.20322 | + | 0.176109i | ||||
\(291\) | −10.0549 | + | 18.8809i | −0.589426 | + | 1.10682i | ||||
\(292\) | 4.05754 | − | 13.5640i | 0.237449 | − | 0.793775i | ||||
\(293\) | −0.654687 | − | 0.654687i | −0.0382472 | − | 0.0382472i | 0.687725 | − | 0.725972i | \(-0.258610\pi\) |
−0.725972 | + | 0.687725i | \(0.758610\pi\) | |||||||
\(294\) | −8.25779 | + | 11.2153i | −0.481604 | + | 0.654087i | ||||
\(295\) | −37.7220 | −2.19626 | ||||||||
\(296\) | 18.1610 | − | 6.61688i | 1.05559 | − | 0.384598i | ||||
\(297\) | 7.76170 | − | 9.54683i | 0.450379 | − | 0.553963i | ||||
\(298\) | −13.9038 | − | 18.6718i | −0.805427 | − | 1.08163i | ||||
\(299\) | −0.490134 | + | 0.490134i | −0.0283452 | + | 0.0283452i | ||||
\(300\) | −9.07697 | − | 8.97965i | −0.524059 | − | 0.518440i | ||||
\(301\) | 1.70727 | + | 1.70727i | 0.0984054 | + | 0.0984054i | ||||
\(302\) | 1.13454 | + | 0.166058i | 0.0652855 | + | 0.00955554i | ||||
\(303\) | 19.4257 | − | 5.92525i | 1.11598 | − | 0.340397i | ||||
\(304\) | 8.24989 | − | 1.70727i | 0.473163 | − | 0.0979186i | ||||
\(305\) | 18.9203i | 1.08337i | ||||||||
\(306\) | 21.4161 | − | 10.2602i | 1.22427 | − | 0.586538i | ||||
\(307\) | −0.971231 | + | 0.971231i | −0.0554311 | + | 0.0554311i | −0.734279 | − | 0.678848i | \(-0.762480\pi\) |
0.678848 | + | 0.734279i | \(0.262480\pi\) | |||||||
\(308\) | −4.77798 | + | 2.57763i | −0.272251 | + | 0.146874i | ||||
\(309\) | 9.95314 | − | 18.6899i | 0.566214 | − | 1.06323i | ||||
\(310\) | −19.4966 | + | 14.5181i | −1.10733 | + | 0.824570i | ||||
\(311\) | − | 33.1343i | − | 1.87887i | −0.342723 | − | 0.939437i | \(-0.611349\pi\) | ||
0.342723 | − | 0.939437i | \(-0.388651\pi\) | |||||||
\(312\) | 1.00414 | + | 0.141447i | 0.0568480 | + | 0.00800787i | ||||
\(313\) | 13.2285i | 0.747717i | 0.927486 | + | 0.373858i | \(0.121965\pi\) | ||||
−0.927486 | + | 0.373858i | \(0.878035\pi\) | |||||||
\(314\) | −6.59129 | − | 8.85160i | −0.371968 | − | 0.499524i | ||||
\(315\) | −1.94688 | + | 9.94688i | −0.109694 | + | 0.560443i | ||||
\(316\) | −5.63565 | + | 18.8396i | −0.317030 | + | 1.05981i | ||||
\(317\) | −7.89038 | + | 7.89038i | −0.443168 | + | 0.443168i | −0.893075 | − | 0.449907i | \(-0.851457\pi\) |
0.449907 | + | 0.893075i | \(0.351457\pi\) | |||||||
\(318\) | 0.563566 | − | 0.0855916i | 0.0316032 | − | 0.00479974i | ||||
\(319\) | 11.7648i | 0.658703i | ||||||||
\(320\) | −2.03932 | + | 23.4890i | −0.114002 | + | 1.31308i | ||||
\(321\) | −0.510711 | − | 1.67435i | −0.0285051 | − | 0.0934530i | ||||
\(322\) | −0.786230 | + | 5.37169i | −0.0438149 | + | 0.299353i | ||||
\(323\) | −8.33587 | − | 8.33587i | −0.463820 | − | 0.463820i | ||||
\(324\) | −11.2795 | + | 14.0275i | −0.626641 | + | 0.779308i | ||||
\(325\) | −0.539481 | + | 0.539481i | −0.0299250 | + | 0.0299250i | ||||
\(326\) | −16.1611 | + | 12.0342i | −0.895078 | + | 0.666515i | ||||
\(327\) | 29.2787 | − | 8.93060i | 1.61911 | − | 0.493864i | ||||
\(328\) | −1.56404 | − | 0.728692i | −0.0863596 | − | 0.0402353i | ||||
\(329\) | −7.35561 | −0.405528 | ||||||||
\(330\) | 10.1353 | − | 13.7652i | 0.557928 | − | 0.757747i | ||||
\(331\) | −3.02877 | − | 3.02877i | −0.166476 | − | 0.166476i | 0.618952 | − | 0.785429i | \(-0.287557\pi\) |
−0.785429 | + | 0.618952i | \(0.787557\pi\) | |||||||
\(332\) | −10.8653 | − | 20.1403i | −0.596312 | − | 1.10535i | ||||
\(333\) | 20.1196 | + | 3.93796i | 1.10255 | + | 0.215799i | ||||
\(334\) | −0.485078 | + | 3.31415i | −0.0265423 | + | 0.181342i | ||||
\(335\) | −2.64937 | −0.144750 | ||||||||
\(336\) | 6.96952 | − | 3.80856i | 0.380219 | − | 0.207774i | ||||
\(337\) | 15.2285 | 0.829547 | 0.414774 | − | 0.909925i | \(-0.363861\pi\) | ||||
0.414774 | + | 0.909925i | \(0.363861\pi\) | |||||||
\(338\) | −2.65375 | + | 18.1310i | −0.144345 | + | 0.986197i | ||||
\(339\) | −8.37361 | − | 4.45930i | −0.454792 | − | 0.242196i | ||||
\(340\) | 29.0361 | − | 15.6644i | 1.57470 | − | 0.849523i | ||||
\(341\) | −9.76515 | − | 9.76515i | −0.528813 | − | 0.528813i | ||||
\(342\) | 8.42831 | + | 2.96831i | 0.455751 | + | 0.160508i | ||||
\(343\) | 14.5426 | 0.785227 | ||||||||
\(344\) | 2.03932 | + | 5.59722i | 0.109953 | + | 0.301782i | ||||
\(345\) | −4.98718 | − | 16.3503i | −0.268501 | − | 0.880269i | ||||
\(346\) | −8.37904 | + | 6.23940i | −0.450460 | + | 0.335432i | ||||
\(347\) | −16.2175 | + | 16.2175i | −0.870600 | + | 0.870600i | −0.992538 | − | 0.121938i | \(-0.961089\pi\) |
0.121938 | + | 0.992538i | \(0.461089\pi\) | |||||||
\(348\) | −0.0927648 | − | 17.2111i | −0.00497271 | − | 0.922611i | ||||
\(349\) | −6.14637 | − | 6.14637i | −0.329007 | − | 0.329007i | 0.523202 | − | 0.852209i | \(-0.324737\pi\) |
−0.852209 | + | 0.523202i | \(0.824737\pi\) | |||||||
\(350\) | −0.865389 | + | 5.91252i | −0.0462570 | + | 0.316037i | ||||
\(351\) | 0.834549 | + | 0.678500i | 0.0445449 | + | 0.0362156i | ||||
\(352\) | −13.3717 | + | 0.786230i | −0.712714 | + | 0.0419062i | ||||
\(353\) | 22.9507i | 1.22154i | 0.791806 | + | 0.610772i | \(0.209141\pi\) | ||||
−0.791806 | + | 0.610772i | \(0.790859\pi\) | |||||||
\(354\) | 4.70759 | + | 30.9965i | 0.250206 | + | 1.64744i | ||||
\(355\) | 14.3931 | − | 14.3931i | 0.763907 | − | 0.763907i | ||||
\(356\) | 0.939148 | + | 0.280936i | 0.0497747 | + | 0.0148896i | ||||
\(357\) | −9.80936 | − | 5.22390i | −0.519167 | − | 0.276478i | ||||
\(358\) | −8.51806 | − | 11.4391i | −0.450193 | − | 0.604575i | ||||
\(359\) | − | 18.3408i | − | 0.967993i | −0.875070 | − | 0.483996i | \(-0.839185\pi\) | ||
0.875070 | − | 0.483996i | \(-0.160815\pi\) | |||||||
\(360\) | −14.7187 | + | 20.2174i | −0.775741 | + | 1.06555i | ||||
\(361\) | 14.5640i | 0.766528i | ||||||||
\(362\) | 10.7986 | − | 8.04113i | 0.567563 | − | 0.422632i | ||||
\(363\) | −8.24490 | − | 4.39076i | −0.432745 | − | 0.230455i | ||||
\(364\) | −0.225327 | − | 0.417674i | −0.0118103 | − | 0.0218920i | ||||
\(365\) | 14.7523 | − | 14.7523i | 0.772172 | − | 0.772172i | ||||
\(366\) | 15.5469 | − | 2.36119i | 0.812652 | − | 0.123422i | ||||
\(367\) | − | 2.86833i | − | 0.149725i | −0.997194 | − | 0.0748627i | \(-0.976148\pi\) | ||
0.997194 | − | 0.0748627i | \(-0.0238519\pi\) | |||||||
\(368\) | −7.35561 | + | 11.1944i | −0.383437 | + | 0.583550i | ||||
\(369\) | −1.02142 | − | 1.51857i | −0.0531731 | − | 0.0790536i | ||||
\(370\) | 28.1825 | + | 4.12494i | 1.46514 | + | 0.214446i | ||||
\(371\) | −0.188638 | − | 0.188638i | −0.00979359 | − | 0.00979359i | ||||
\(372\) | 14.3627 | + | 14.2087i | 0.744673 | + | 0.736689i | ||||
\(373\) | −17.2253 | + | 17.2253i | −0.891894 | + | 0.891894i | −0.994701 | − | 0.102808i | \(-0.967217\pi\) |
0.102808 | + | 0.994701i | \(0.467217\pi\) | |||||||
\(374\) | 11.1944 | + | 15.0333i | 0.578850 | + | 0.777352i | ||||
\(375\) | 1.95715 | + | 6.41646i | 0.101067 | + | 0.331344i | ||||
\(376\) | −16.4507 | − | 7.66442i | −0.848378 | − | 0.395262i | ||||
\(377\) | −1.02844 | −0.0529672 | ||||||||
\(378\) | 8.41640 | + | 0.358429i | 0.432893 | + | 0.0184356i | ||||
\(379\) | 5.83956 | + | 5.83956i | 0.299958 | + | 0.299958i | 0.840997 | − | 0.541039i | \(-0.181969\pi\) |
−0.541039 | + | 0.840997i | \(0.681969\pi\) | |||||||
\(380\) | 11.8938 | + | 3.55789i | 0.610137 | + | 0.182516i | ||||
\(381\) | −11.0132 | − | 5.86499i | −0.564223 | − | 0.300473i | ||||
\(382\) | 35.7220 | + | 5.22846i | 1.82769 | + | 0.267511i | ||||
\(383\) | 30.7659 | 1.57206 | 0.786031 | − | 0.618187i | \(-0.212133\pi\) | ||||
0.786031 | + | 0.618187i | \(0.212133\pi\) | |||||||
\(384\) | 19.5556 | − | 1.25563i | 0.997945 | − | 0.0640763i | ||||
\(385\) | −8.00000 | −0.407718 | ||||||||
\(386\) | −12.7042 | − | 1.85946i | −0.646628 | − | 0.0946441i | ||||
\(387\) | −1.21368 | + | 6.20086i | −0.0616949 | + | 0.315207i | ||||
\(388\) | 23.6644 | + | 7.07896i | 1.20138 | + | 0.359380i | ||||
\(389\) | −11.0299 | − | 11.0299i | −0.559237 | − | 0.559237i | 0.369853 | − | 0.929090i | \(-0.379408\pi\) |
−0.929090 | + | 0.369853i | \(0.879408\pi\) | |||||||
\(390\) | 1.20330 | + | 0.885989i | 0.0609315 | + | 0.0448638i | ||||
\(391\) | 18.7434 | 0.947894 | ||||||||
\(392\) | 14.5775 | + | 6.79171i | 0.736275 | + | 0.343033i | ||||
\(393\) | −21.2047 | + | 6.46787i | −1.06963 | + | 0.326261i | ||||
\(394\) | −3.80344 | − | 5.10773i | −0.191615 | − | 0.257324i | ||||
\(395\) | −20.4900 | + | 20.4900i | −1.03096 | + | 1.03096i | ||||
\(396\) | −12.5758 | − | 6.61039i | −0.631957 | − | 0.332185i | ||||
\(397\) | −1.75325 | − | 1.75325i | −0.0879931 | − | 0.0879931i | 0.661740 | − | 0.749733i | \(-0.269818\pi\) |
−0.749733 | + | 0.661740i | \(0.769818\pi\) | |||||||
\(398\) | −27.3622 | − | 4.00489i | −1.37155 | − | 0.200747i | ||||
\(399\) | −1.22008 | − | 4.00000i | −0.0610806 | − | 0.200250i | ||||
\(400\) | −8.09617 | + | 12.3215i | −0.404809 | + | 0.616075i | ||||
\(401\) | − | 24.4693i | − | 1.22194i | −0.791654 | − | 0.610970i | \(-0.790780\pi\) | ||
0.791654 | − | 0.610970i | \(-0.209220\pi\) | |||||||
\(402\) | 0.330633 | + | 2.17701i | 0.0164905 | + | 0.108579i | ||||
\(403\) | 0.853635 | − | 0.853635i | 0.0425226 | − | 0.0425226i | ||||
\(404\) | −11.1345 | − | 20.6393i | −0.553961 | − | 1.02684i | ||||
\(405\) | −24.4428 | + | 10.3005i | −1.21457 | + | 0.511838i | ||||
\(406\) | −6.46052 | + | 4.81079i | −0.320630 | + | 0.238755i | ||||
\(407\) | 16.1816i | 0.802093i | ||||||||
\(408\) | −16.4952 | − | 21.9043i | −0.816635 | − | 1.08443i | ||||
\(409\) | − | 8.78623i | − | 0.434451i | −0.976121 | − | 0.217226i | \(-0.930299\pi\) | ||
0.976121 | − | 0.217226i | \(-0.0697007\pi\) | |||||||
\(410\) | −1.51857 | − | 2.03932i | −0.0749969 | − | 0.100715i | ||||
\(411\) | −10.9445 | + | 20.5513i | −0.539851 | + | 1.01372i | ||||
\(412\) | −23.4250 | − | 7.00735i | −1.15407 | − | 0.345227i | ||||
\(413\) | 10.3752 | − | 10.3752i | 0.510530 | − | 0.510530i | ||||
\(414\) | −12.8128 | + | 6.13847i | −0.629713 | + | 0.301689i | ||||
\(415\) | − | 33.7220i | − | 1.65535i | ||||||
\(416\) | −0.0687294 | − | 1.16891i | −0.00336974 | − | 0.0573103i | ||||
\(417\) | −20.2327 | + | 6.17139i | −0.990798 | + | 0.302214i | ||||
\(418\) | −1.02142 | + | 6.97858i | −0.0499594 | + | 0.341333i | ||||
\(419\) | 3.52202 | + | 3.52202i | 0.172062 | + | 0.172062i | 0.787885 | − | 0.615823i | \(-0.211176\pi\) |
−0.615823 | + | 0.787885i | \(0.711176\pi\) | |||||||
\(420\) | 11.7034 | − | 0.0630795i | 0.571069 | − | 0.00307796i | ||||
\(421\) | 11.2253 | − | 11.2253i | 0.547089 | − | 0.547089i | −0.378509 | − | 0.925598i | \(-0.623563\pi\) |
0.925598 | + | 0.378509i | \(0.123563\pi\) | |||||||
\(422\) | 16.5912 | − | 12.3546i | 0.807648 | − | 0.601411i | ||||
\(423\) | −10.7434 | − | 15.9724i | −0.522361 | − | 0.776605i | ||||
\(424\) | −0.225327 | − | 0.618442i | −0.0109428 | − | 0.0300342i | ||||
\(425\) | 20.6305 | 1.00073 | ||||||||
\(426\) | −13.6232 | − | 10.0307i | −0.660044 | − | 0.485990i | ||||
\(427\) | −5.20390 | − | 5.20390i | −0.251835 | − | 0.251835i | ||||
\(428\) | −1.77895 | + | 0.959708i | −0.0859887 | + | 0.0463892i | ||||
\(429\) | −0.399038 | + | 0.749307i | −0.0192657 | + | 0.0361769i | ||||
\(430\) | −1.27131 | + | 8.68585i | −0.0613079 | + | 0.418869i | ||||
\(431\) | 12.1336 | 0.584454 | 0.292227 | − | 0.956349i | \(-0.405604\pi\) | ||||
0.292227 | + | 0.956349i | \(0.405604\pi\) | |||||||
\(432\) | 18.4496 | + | 9.57138i | 0.887658 | + | 0.460503i | ||||
\(433\) | −12.1495 | −0.583868 | −0.291934 | − | 0.956439i | \(-0.594299\pi\) | ||||
−0.291934 | + | 0.956439i | \(0.594299\pi\) | |||||||
\(434\) | 1.36933 | − | 9.35553i | 0.0657298 | − | 0.449080i | ||||
\(435\) | 11.9215 | − | 22.3860i | 0.571591 | − | 1.07332i | ||||
\(436\) | −16.7820 | − | 31.1077i | −0.803713 | − | 1.48979i | ||||
\(437\) | 4.98718 | + | 4.98718i | 0.238569 | + | 0.238569i | ||||
\(438\) | −13.9632 | − | 10.2811i | −0.667186 | − | 0.491248i | ||||
\(439\) | 27.1035 | 1.29358 | 0.646790 | − | 0.762668i | \(-0.276111\pi\) | ||||
0.646790 | + | 0.762668i | \(0.276111\pi\) | |||||||
\(440\) | −17.8918 | − | 8.33587i | −0.852959 | − | 0.397397i | ||||
\(441\) | 9.52009 | + | 14.1537i | 0.453337 | + | 0.673986i | ||||
\(442\) | −1.31415 | + | 0.978577i | −0.0625079 | + | 0.0465462i | ||||
\(443\) | 28.8412 | − | 28.8412i | 1.37029 | − | 1.37029i | 0.510276 | − | 0.860011i | \(-0.329543\pi\) |
0.860011 | − | 0.510276i | \(-0.170457\pi\) | |||||||
\(444\) | −0.127591 | − | 23.6726i | −0.00605520 | − | 1.12345i | ||||
\(445\) | 1.02142 | + | 1.02142i | 0.0484201 | + | 0.0484201i | ||||
\(446\) | −4.63248 | + | 31.6501i | −0.219354 | + | 1.49868i | ||||
\(447\) | −27.2714 | + | 8.31836i | −1.28990 | + | 0.393445i | ||||
\(448\) | −5.89962 | − | 7.02142i | −0.278731 | − | 0.331731i | ||||
\(449\) | − | 9.67586i | − | 0.456632i | −0.973587 | − | 0.228316i | \(-0.926678\pi\) | ||
0.973587 | − | 0.228316i | \(-0.0733220\pi\) | |||||||
\(450\) | −14.1028 | + | 6.75650i | −0.664811 | + | 0.318504i | ||||
\(451\) | 1.02142 | − | 1.02142i | 0.0480969 | − | 0.0480969i | ||||
\(452\) | −3.13950 | + | 10.4951i | −0.147670 | + | 0.493648i | ||||
\(453\) | 0.660097 | − | 1.23952i | 0.0310140 | − | 0.0582377i | ||||
\(454\) | −1.75011 | − | 2.35027i | −0.0821370 | − | 0.110304i | ||||
\(455\) | − | 0.699331i | − | 0.0327851i | ||||||
\(456\) | 1.43924 | − | 10.2172i | 0.0673988 | − | 0.478465i | ||||
\(457\) | 4.20077i | 0.196504i | 0.995162 | + | 0.0982518i | \(0.0313251\pi\) | ||||
−0.995162 | + | 0.0982518i | \(0.968675\pi\) | |||||||
\(458\) | 12.0598 | − | 8.98028i | 0.563519 | − | 0.419621i | ||||
\(459\) | −2.98377 | − | 28.9305i | −0.139271 | − | 1.35036i | ||||
\(460\) | −17.3717 | + | 9.37169i | −0.809959 | + | 0.436957i | ||||
\(461\) | −27.5406 | + | 27.5406i | −1.28269 | + | 1.28269i | −0.343565 | + | 0.939129i | \(0.611634\pi\) |
−0.939129 | + | 0.343565i | \(0.888366\pi\) | |||||||
\(462\) | 0.998377 | + | 6.57367i | 0.0464487 | + | 0.305835i | ||||
\(463\) | 37.4109i | 1.73863i | 0.494255 | + | 0.869317i | \(0.335441\pi\) | ||||
−0.494255 | + | 0.869317i | \(0.664559\pi\) | |||||||
\(464\) | −19.4616 | + | 4.02747i | −0.903481 | + | 0.186971i | ||||
\(465\) | 8.68585 | + | 28.4762i | 0.402796 | + | 1.32055i | ||||
\(466\) | 25.7220 | + | 3.76481i | 1.19155 | + | 0.174401i | ||||
\(467\) | 16.9168 | + | 16.9168i | 0.782817 | + | 0.782817i | 0.980305 | − | 0.197489i | \(-0.0632785\pi\) |
−0.197489 | + | 0.980305i | \(0.563279\pi\) | |||||||
\(468\) | 0.577856 | − | 1.09933i | 0.0267114 | − | 0.0508166i | ||||
\(469\) | 0.728692 | − | 0.728692i | 0.0336479 | − | 0.0336479i | ||||
\(470\) | −15.9724 | − | 21.4497i | −0.736753 | − | 0.989402i | ||||
\(471\) | −12.9284 | + | 3.94343i | −0.595709 | + | 0.181704i | ||||
\(472\) | 34.0147 | − | 12.3931i | 1.56565 | − | 0.570439i | ||||
\(473\) | −4.98718 | −0.229311 | ||||||||
\(474\) | 19.3939 | + | 14.2797i | 0.890792 | + | 0.655889i | ||||
\(475\) | 5.48929 | + | 5.48929i | 0.251866 | + | 0.251866i | ||||
\(476\) | −3.67780 | + | 12.2946i | −0.168572 | + | 0.563523i | ||||
\(477\) | 0.134101 | − | 0.685139i | 0.00614005 | − | 0.0313703i | ||||
\(478\) | 18.9357 | + | 2.77154i | 0.866100 | + | 0.126767i | ||||
\(479\) | 18.5500 | 0.847573 | 0.423786 | − | 0.905762i | \(-0.360701\pi\) | ||||
0.423786 | + | 0.905762i | \(0.360701\pi\) | |||||||
\(480\) | 26.2402 | + | 12.0537i | 1.19770 | + | 0.550175i | ||||
\(481\) | −1.41454 | −0.0644974 | ||||||||
\(482\) | −6.82608 | − | 0.999102i | −0.310919 | − | 0.0455079i | ||||
\(483\) | 5.86873 | + | 3.12535i | 0.267037 | + | 0.142208i | ||||
\(484\) | −3.09124 | + | 10.3338i | −0.140511 | + | 0.469717i | ||||
\(485\) | 25.7376 | + | 25.7376i | 1.16868 | + | 1.16868i | ||||
\(486\) | 11.5144 | + | 18.7994i | 0.522306 | + | 0.852758i | ||||
\(487\) | −40.9259 | −1.85453 | −0.927264 | − | 0.374408i | \(-0.877846\pi\) | ||||
−0.927264 | + | 0.374408i | \(0.877846\pi\) | |||||||
\(488\) | −6.21604 | − | 17.0608i | −0.281387 | − | 0.772306i | ||||
\(489\) | 7.19983 | + | 23.6044i | 0.325587 | + | 1.06743i | ||||
\(490\) | 14.1537 | + | 19.0073i | 0.639400 | + | 0.858664i | ||||
\(491\) | 5.04360 | − | 5.04360i | 0.227615 | − | 0.227615i | −0.584081 | − | 0.811696i | \(-0.698545\pi\) |
0.811696 | + | 0.584081i | \(0.198545\pi\) | |||||||
\(492\) | −1.48622 | + | 1.50232i | −0.0670038 | + | 0.0677300i | ||||
\(493\) | 19.6644 | + | 19.6644i | 0.885641 | + | 0.885641i | ||||
\(494\) | −0.610042 | − | 0.0892891i | −0.0274471 | − | 0.00401731i | ||||
\(495\) | −11.6846 | − | 17.3717i | −0.525182 | − | 0.780800i | ||||
\(496\) | 12.8108 | − | 19.4966i | 0.575221 | − | 0.875425i | ||||
\(497\) | 7.91748i | 0.355147i | ||||||||
\(498\) | −27.7096 | + | 4.20840i | −1.24170 | + | 0.188583i | ||||
\(499\) | −11.4647 | + | 11.4647i | −0.513232 | + | 0.513232i | −0.915515 | − | 0.402283i | \(-0.868217\pi\) |
0.402283 | + | 0.915515i | \(0.368217\pi\) | |||||||
\(500\) | 6.81730 | − | 3.67780i | 0.304879 | − | 0.164476i | ||||
\(501\) | 3.62081 | + | 1.92824i | 0.161766 | + | 0.0861472i | ||||
\(502\) | −8.39312 | + | 6.24989i | −0.374603 | + | 0.278946i | ||||
\(503\) | 32.7159i | 1.45873i | 0.684125 | + | 0.729365i | \(0.260184\pi\) | ||||
−0.684125 | + | 0.729365i | \(0.739816\pi\) | |||||||
\(504\) | −1.51239 | − | 9.60894i | −0.0673671 | − | 0.428016i | ||||
\(505\) | − | 34.5573i | − | 1.53778i | ||||||
\(506\) | −6.69739 | − | 8.99408i | −0.297735 | − | 0.399836i | ||||
\(507\) | 19.8087 | + | 10.5490i | 0.879734 | + | 0.468495i | ||||
\(508\) | −4.12915 | + | 13.8034i | −0.183202 | + | 0.612429i | ||||
\(509\) | 10.1389 | − | 10.1389i | 0.449399 | − | 0.449399i | −0.445756 | − | 0.895155i | \(-0.647065\pi\) |
0.895155 | + | 0.445756i | \(0.147065\pi\) | |||||||
\(510\) | −6.06721 | − | 39.9486i | −0.268660 | − | 1.76896i | ||||
\(511\) | 8.11508i | 0.358990i | ||||||||
\(512\) | −5.87815 | − | 21.8506i | −0.259780 | − | 0.965668i | ||||
\(513\) | 6.90383 | − | 8.49165i | 0.304811 | − | 0.374916i | ||||
\(514\) | 2.62831 | − | 17.9572i | 0.115930 | − | 0.792056i | ||||
\(515\) | −25.4772 | − | 25.4772i | −1.12266 | − | 1.12266i | ||||
\(516\) | 7.29589 | − | 0.0393236i | 0.321184 | − | 0.00173112i | ||||
\(517\) | 10.7434 | − | 10.7434i | 0.472494 | − | 0.472494i | ||||
\(518\) | −8.88596 | + | 6.61688i | −0.390427 | + | 0.290729i | ||||
\(519\) | 3.73290 | + | 12.2382i | 0.163856 | + | 0.537197i | ||||
\(520\) | 0.728692 | − | 1.56404i | 0.0319553 | − | 0.0685877i | ||||
\(521\) | 6.08735 | 0.266692 | 0.133346 | − | 0.991070i | \(-0.457428\pi\) | ||||
0.133346 | + | 0.991070i | \(0.457428\pi\) | |||||||
\(522\) | −19.8825 | − | 7.00227i | −0.870233 | − | 0.306481i | ||||
\(523\) | 15.8824 | + | 15.8824i | 0.694489 | + | 0.694489i | 0.963216 | − | 0.268727i | \(-0.0866030\pi\) |
−0.268727 | + | 0.963216i | \(0.586603\pi\) | |||||||
\(524\) | 12.1541 | + | 22.5293i | 0.530956 | + | 0.984199i | ||||
\(525\) | 6.45960 | + | 3.44001i | 0.281920 | + | 0.150134i | ||||
\(526\) | 5.79923 | − | 39.6216i | 0.252859 | − | 1.72758i | ||||
\(527\) | −32.6442 | −1.42200 | ||||||||
\(528\) | −4.61681 | + | 15.7422i | −0.200921 | + | 0.685090i | ||||
\(529\) | 11.7862 | 0.512445 | ||||||||
\(530\) | 0.140468 | − | 0.959708i | 0.00610154 | − | 0.0416870i | ||||
\(531\) | 37.6831 | + | 7.37563i | 1.63531 | + | 0.320075i | ||||
\(532\) | −4.24989 | + | 2.29273i | −0.184256 | + | 0.0994025i | ||||
\(533\) | 0.0892891 | + | 0.0892891i | 0.00386754 | + | 0.00386754i | ||||
\(534\) | 0.711841 | − | 0.966782i | 0.0308044 | − | 0.0418368i | ||||
\(535\) | −2.97858 | −0.128775 | ||||||||
\(536\) | 2.38899 | − | 0.870418i | 0.103189 | − | 0.0375964i | ||||
\(537\) | −16.7076 | + | 5.09617i | −0.720987 | + | 0.219916i | ||||
\(538\) | −10.5567 | + | 7.86098i | −0.455131 | + | 0.338911i | ||||
\(539\) | −9.52009 | + | 9.52009i | −0.410059 | + | 0.410059i | ||||
\(540\) | 17.2307 | + | 25.3214i | 0.741490 | + | 1.08966i | ||||
\(541\) | −25.6184 | − | 25.6184i | −1.10142 | − | 1.10142i | −0.994239 | − | 0.107184i | \(-0.965817\pi\) |
−0.107184 | − | 0.994239i | \(-0.534183\pi\) | |||||||
\(542\) | 1.77392 | − | 12.1198i | 0.0761963 | − | 0.520589i | ||||
\(543\) | −4.81084 | − | 15.7722i | −0.206453 | − | 0.676848i | ||||
\(544\) | −21.0361 | + | 23.6644i | −0.901916 | + | 1.01460i | ||||
\(545\) | − | 52.0852i | − | 2.23108i | ||||||
\(546\) | −0.574646 | + | 0.0872745i | −0.0245926 | + | 0.00373500i | ||||
\(547\) | −27.2113 | + | 27.2113i | −1.16347 | + | 1.16347i | −0.179758 | + | 0.983711i | \(0.557532\pi\) |
−0.983711 | + | 0.179758i | \(0.942468\pi\) | |||||||
\(548\) | 25.7581 | + | 7.70527i | 1.10033 | + | 0.329153i | ||||
\(549\) | 3.69941 | − | 18.9007i | 0.157887 | − | 0.806664i | ||||
\(550\) | −7.37169 | − | 9.89962i | −0.314330 | − | 0.422121i | ||||
\(551\) | 10.4645i | 0.445802i | ||||||||
\(552\) | 9.86873 | + | 13.1049i | 0.420041 | + | 0.557782i | ||||
\(553\) | − | 11.2713i | − | 0.479305i | ||||||
\(554\) | −21.0539 | + | 15.6777i | −0.894495 | + | 0.666080i | ||||
\(555\) | 16.3971 | − | 30.7902i | 0.696018 | − | 1.30697i | ||||
\(556\) | 11.5970 | + | 21.4966i | 0.491823 | + | 0.911660i | ||||
\(557\) | −26.1831 | + | 26.1831i | −1.10941 | + | 1.10941i | −0.116184 | + | 0.993228i | \(0.537066\pi\) |
−0.993228 | + | 0.116184i | \(0.962934\pi\) | |||||||
\(558\) | 22.3152 | − | 10.6910i | 0.944677 | − | 0.452585i | ||||
\(559\) | − | 0.435961i | − | 0.0184392i | ||||||
\(560\) | −2.73865 | − | 13.2338i | −0.115729 | − | 0.559228i | ||||
\(561\) | 21.9572 | − | 6.69739i | 0.927032 | − | 0.282764i | ||||
\(562\) | −36.6002 | − | 5.35700i | −1.54388 | − | 0.225971i | ||||
\(563\) | −25.0435 | − | 25.0435i | −1.05546 | − | 1.05546i | −0.998369 | − | 0.0570880i | \(-0.981818\pi\) |
−0.0570880 | − | 0.998369i | \(-0.518182\pi\) | |||||||
\(564\) | −15.6321 | + | 15.8015i | −0.658230 | + | 0.665364i | ||||
\(565\) | −11.4145 | + | 11.4145i | −0.480213 | + | 0.480213i | ||||
\(566\) | 21.3898 | + | 28.7248i | 0.899079 | + | 1.20739i | ||||
\(567\) | 3.88975 | − | 9.55596i | 0.163354 | − | 0.401312i | ||||
\(568\) | −8.24989 | + | 17.7073i | −0.346157 | + | 0.742981i | ||||
\(569\) | −12.5449 | −0.525911 | −0.262955 | − | 0.964808i | \(-0.584697\pi\) | ||||
−0.262955 | + | 0.964808i | \(0.584697\pi\) | |||||||
\(570\) | 9.01506 | − | 12.2437i | 0.377599 | − | 0.512834i | ||||
\(571\) | −4.48615 | − | 4.48615i | −0.187740 | − | 0.187740i | 0.606979 | − | 0.794718i | \(-0.292381\pi\) |
−0.794718 | + | 0.606979i | \(0.792381\pi\) | |||||||
\(572\) | 0.939148 | + | 0.280936i | 0.0392677 | + | 0.0117465i | ||||
\(573\) | 20.7837 | − | 39.0273i | 0.868251 | − | 1.63039i | ||||
\(574\) | 0.978577 | + | 0.143230i | 0.0408450 | + | 0.00597830i | ||||
\(575\) | −12.3428 | −0.514730 | ||||||||
\(576\) | 6.62994 | − | 23.0661i | 0.276248 | − | 0.961087i | ||||
\(577\) | 4.48508 | 0.186716 | 0.0933581 | − | 0.995633i | \(-0.470240\pi\) | ||||
0.0933581 | + | 0.995633i | \(0.470240\pi\) | |||||||
\(578\) | 20.0504 | + | 2.93469i | 0.833987 | + | 0.122067i | ||||
\(579\) | −7.39156 | + | 13.8798i | −0.307183 | + | 0.576823i | ||||
\(580\) | −28.0575 | − | 8.39312i | −1.16503 | − | 0.348505i | ||||
\(581\) | 9.27502 | + | 9.27502i | 0.384793 | + | 0.384793i | ||||
\(582\) | 17.9368 | − | 24.3607i | 0.743504 | − | 1.00979i | ||||
\(583\) | 0.551038 | 0.0228217 | ||||||||
\(584\) | −8.45578 | + | 18.1492i | −0.349903 | + | 0.751019i | ||||
\(585\) | 1.51857 | − | 1.02142i | 0.0627852 | − | 0.0422306i | ||||
\(586\) | 0.782020 | + | 1.05019i | 0.0323049 | + | 0.0433830i | ||||
\(587\) | 11.9808 | − | 11.9808i | 0.494501 | − | 0.494501i | −0.415220 | − | 0.909721i | \(-0.636295\pi\) |
0.909721 | + | 0.415220i | \(0.136295\pi\) | |||||||
\(588\) | 13.8522 | − | 14.0023i | 0.571253 | − | 0.577444i | ||||
\(589\) | −8.68585 | − | 8.68585i | −0.357894 | − | 0.357894i | ||||
\(590\) | 52.7845 | + | 7.72583i | 2.17310 | + | 0.318067i | ||||
\(591\) | −7.46020 | + | 2.27552i | −0.306872 | + | 0.0936023i | ||||
\(592\) | −26.7679 | + | 5.53948i | −1.10016 | + | 0.227671i | ||||
\(593\) | − | 3.27696i | − | 0.134569i | −0.997734 | − | 0.0672843i | \(-0.978567\pi\) | ||
0.997734 | − | 0.0672843i | \(-0.0214334\pi\) | |||||||
\(594\) | −12.8163 | + | 11.7692i | −0.525858 | + | 0.482898i | ||||
\(595\) | −13.3717 | + | 13.3717i | −0.548186 | + | 0.548186i | ||||
\(596\) | 15.6315 | + | 28.9751i | 0.640292 | + | 1.18687i | ||||
\(597\) | −15.9199 | + | 29.8941i | −0.651556 | + | 1.22348i | ||||
\(598\) | 0.786230 | − | 0.585462i | 0.0321514 | − | 0.0239413i | ||||
\(599\) | − | 38.9889i | − | 1.59304i | −0.604611 | − | 0.796521i | \(-0.706671\pi\) | ||
0.604611 | − | 0.796521i | \(-0.293329\pi\) | |||||||
\(600\) | 10.8623 | + | 14.4243i | 0.443453 | + | 0.588870i | ||||
\(601\) | − | 23.5787i | − | 0.961797i | −0.876776 | − | 0.480898i | \(-0.840311\pi\) | ||
0.876776 | − | 0.480898i | \(-0.159689\pi\) | |||||||
\(602\) | −2.03932 | − | 2.73865i | −0.0831166 | − | 0.111619i | ||||
\(603\) | 2.64663 | + | 0.518020i | 0.107779 | + | 0.0210954i | ||||
\(604\) | −1.55356 | − | 0.464730i | −0.0632133 | − | 0.0189096i | ||||
\(605\) | −11.2391 | + | 11.2391i | −0.456934 | + | 0.456934i | ||||
\(606\) | −28.3960 | + | 4.31265i | −1.15351 | + | 0.175189i | ||||
\(607\) | − | 22.2829i | − | 0.904434i | −0.891908 | − | 0.452217i | \(-0.850633\pi\) | ||
0.891908 | − | 0.452217i | \(-0.149367\pi\) | |||||||
\(608\) | −11.8938 | + | 0.699331i | −0.482356 | + | 0.0283616i | ||||
\(609\) | 2.87819 | + | 9.43605i | 0.116630 | + | 0.382368i | ||||
\(610\) | 3.87506 | − | 26.4752i | 0.156896 | − | 1.07195i | ||||
\(611\) | 0.939148 | + | 0.939148i | 0.0379939 | + | 0.0379939i | ||||
\(612\) | −32.0690 | + | 9.97095i | −1.29631 | + | 0.403052i | ||||
\(613\) | 22.1611 | − | 22.1611i | 0.895077 | − | 0.895077i | −0.0999189 | − | 0.994996i | \(-0.531858\pi\) |
0.994996 | + | 0.0999189i | \(0.0318583\pi\) | |||||||
\(614\) | 1.55797 | − | 1.16013i | 0.0628744 | − | 0.0468190i | ||||
\(615\) | −2.97858 | + | 0.908529i | −0.120108 | + | 0.0366354i | ||||
\(616\) | 7.21377 | − | 2.62831i | 0.290651 | − | 0.105898i | ||||
\(617\) | −25.7376 | −1.03616 | −0.518078 | − | 0.855334i | \(-0.673352\pi\) | ||||
−0.518078 | + | 0.855334i | \(0.673352\pi\) | |||||||
\(618\) | −17.7553 | + | 24.1143i | −0.714225 | + | 0.970019i | ||||
\(619\) | 7.71462 | + | 7.71462i | 0.310077 | + | 0.310077i | 0.844939 | − | 0.534863i | \(-0.179637\pi\) |
−0.534863 | + | 0.844939i | \(0.679637\pi\) | |||||||
\(620\) | 30.2552 | − | 16.3221i | 1.21508 | − | 0.655510i | ||||
\(621\) | 1.78513 | + | 17.3085i | 0.0716347 | + | 0.694567i | ||||
\(622\) | −6.78623 | + | 46.3650i | −0.272103 | + | 1.85907i | ||||
\(623\) | −0.561872 | −0.0225109 | ||||||||
\(624\) | −1.37612 | − | 0.403585i | −0.0550890 | − | 0.0161563i | ||||
\(625\) | 29.8438 | 1.19375 | ||||||||
\(626\) | 2.70932 | − | 18.5106i | 0.108286 | − | 0.739834i | ||||
\(627\) | 7.62430 | + | 4.06027i | 0.304485 | + | 0.162151i | ||||
\(628\) | 7.41033 | + | 13.7360i | 0.295704 | + | 0.548128i | ||||
\(629\) | 27.0469 | + | 27.0469i | 1.07843 | + | 1.07843i | ||||
\(630\) | 4.76150 | − | 13.5200i | 0.189703 | − | 0.538649i | ||||
\(631\) | 2.26817 | 0.0902945 | 0.0451473 | − | 0.998980i | \(-0.485624\pi\) | ||||
0.0451473 | + | 0.998980i | \(0.485624\pi\) | |||||||
\(632\) | 11.7445 | − | 25.2080i | 0.467172 | − | 1.00272i | ||||
\(633\) | −7.39147 | − | 24.2327i | −0.293785 | − | 0.963162i | ||||
\(634\) | 12.6571 | − | 9.42502i | 0.502677 | − | 0.374315i | ||||
\(635\) | −15.0127 | + | 15.0127i | −0.595761 | + | 0.595761i | ||||
\(636\) | −0.806130 | + | 0.00434490i | −0.0319651 | + | 0.000172286i | ||||
\(637\) | −0.832212 | − | 0.832212i | −0.0329734 | − | 0.0329734i | ||||
\(638\) | 2.40955 | − | 16.4625i | 0.0953950 | − | 0.651758i | ||||
\(639\) | −17.1925 | + | 11.5640i | −0.680125 | + | 0.457466i | ||||
\(640\) | 7.66442 | − | 32.4507i | 0.302963 | − | 1.28272i | ||||
\(641\) | − | 20.0686i | − | 0.792662i | −0.918108 | − | 0.396331i | \(-0.870283\pi\) | ||
0.918108 | − | 0.396331i | \(-0.129717\pi\) | |||||||
\(642\) | 0.371718 | + | 2.44752i | 0.0146705 | + | 0.0965960i | ||||
\(643\) | 14.0748 | − | 14.0748i | 0.555054 | − | 0.555054i | −0.372841 | − | 0.927895i | \(-0.621616\pi\) |
0.927895 | + | 0.372841i | \(0.121616\pi\) | |||||||
\(644\) | 2.20035 | − | 7.35561i | 0.0867060 | − | 0.289851i | ||||
\(645\) | 9.48955 | + | 5.05359i | 0.373651 | + | 0.198985i | ||||
\(646\) | 9.95715 | + | 13.3717i | 0.391759 | + | 0.526102i | ||||
\(647\) | 1.95003i | 0.0766638i | 0.999265 | + | 0.0383319i | \(0.0122044\pi\) | ||||
−0.999265 | + | 0.0383319i | \(0.987796\pi\) | |||||||
\(648\) | 18.6565 | − | 17.3186i | 0.732896 | − | 0.680340i | ||||
\(649\) | 30.3074i | 1.18967i | ||||||||
\(650\) | 0.865389 | − | 0.644407i | 0.0339433 | − | 0.0252757i | ||||
\(651\) | −10.2212 | − | 5.44322i | −0.400600 | − | 0.213337i | ||||
\(652\) | 25.0790 | − | 13.5296i | 0.982168 | − | 0.529861i | ||||
\(653\) | 5.80289 | − | 5.80289i | 0.227085 | − | 0.227085i | −0.584389 | − | 0.811474i | \(-0.698666\pi\) |
0.811474 | + | 0.584389i | \(0.198666\pi\) | |||||||
\(654\) | −42.7988 | + | 6.50008i | −1.67357 | + | 0.254173i | ||||
\(655\) | 37.7220i | 1.47392i | ||||||||
\(656\) | 2.03932 | + | 1.33999i | 0.0796222 | + | 0.0523179i | ||||
\(657\) | −17.6216 | + | 11.8526i | −0.687483 | + | 0.462416i | ||||
\(658\) | 10.2927 | + | 1.50650i | 0.401252 | + | 0.0587295i | ||||
\(659\) | 5.49262 | + | 5.49262i | 0.213962 | + | 0.213962i | 0.805948 | − | 0.591986i | \(-0.201656\pi\) |
−0.591986 | + | 0.805948i | \(0.701656\pi\) | |||||||
\(660\) | −17.0016 | + | 17.1858i | −0.661785 | + | 0.668958i | ||||
\(661\) | −5.86833 | + | 5.86833i | −0.228251 | + | 0.228251i | −0.811962 | − | 0.583710i | \(-0.801600\pi\) |
0.583710 | + | 0.811962i | \(0.301600\pi\) | |||||||
\(662\) | 3.61785 | + | 4.85849i | 0.140612 | + | 0.188831i | ||||
\(663\) | 0.585462 | + | 1.91942i | 0.0227375 | + | 0.0745439i | ||||
\(664\) | 11.0790 | + | 30.4078i | 0.429947 | + | 1.18005i | ||||
\(665\) | −7.11579 | −0.275938 | ||||||||
\(666\) | −27.3469 | − | 9.63110i | −1.05967 | − | 0.373197i | ||||
\(667\) | −11.7648 | − | 11.7648i | −0.455535 | − | 0.455535i | ||||
\(668\) | 1.35754 | − | 4.53816i | 0.0525249 | − | 0.175587i | ||||
\(669\) | 34.5787 | + | 18.4146i | 1.33689 | + | 0.711950i | ||||
\(670\) | 3.70727 | + | 0.542616i | 0.143224 | + | 0.0209631i | ||||
\(671\) | 15.2013 | 0.586841 | ||||||||
\(672\) | −10.5325 | + | 3.90191i | −0.406301 | + | 0.150519i | ||||
\(673\) | −22.8929 | −0.882456 | −0.441228 | − | 0.897395i | \(-0.645457\pi\) | ||||
−0.441228 | + | 0.897395i | \(0.645457\pi\) | |||||||
\(674\) | −21.3093 | − | 3.11894i | −0.820802 | − | 0.120137i | ||||
\(675\) | 1.96486 | + | 19.0512i | 0.0756273 | + | 0.733280i | ||||
\(676\) | 7.42682 | − | 24.8273i | 0.285647 | − | 0.954895i | ||||
\(677\) | −13.7685 | − | 13.7685i | −0.529168 | − | 0.529168i | 0.391156 | − | 0.920324i | \(-0.372075\pi\) |
−0.920324 | + | 0.391156i | \(0.872075\pi\) | |||||||
\(678\) | 10.8039 | + | 7.95492i | 0.414922 | + | 0.305507i | ||||
\(679\) | −14.1579 | −0.543331 | ||||||||
\(680\) | −43.8386 | + | 15.9724i | −1.68113 | + | 0.612514i | ||||
\(681\) | −3.43274 | + | 1.04706i | −0.131543 | + | 0.0401233i | ||||
\(682\) | 11.6644 | + | 15.6644i | 0.446654 | + | 0.599822i | ||||
\(683\) | −5.72238 | + | 5.72238i | −0.218961 | + | 0.218961i | −0.808060 | − | 0.589100i | \(-0.799483\pi\) |
0.589100 | + | 0.808060i | \(0.299483\pi\) | |||||||
\(684\) | −11.1858 | − | 5.87977i | −0.427701 | − | 0.224818i | ||||
\(685\) | 28.0147 | + | 28.0147i | 1.07039 | + | 1.07039i | ||||
\(686\) | −20.3495 | − | 2.97847i | −0.776949 | − | 0.113719i | ||||
\(687\) | −5.37271 | − | 17.6142i | −0.204982 | − | 0.672025i | ||||
\(688\) | −1.70727 | − | 8.24989i | −0.0650890 | − | 0.314524i | ||||
\(689\) | 0.0481697i | 0.00183512i | ||||||||
\(690\) | 3.62988 | + | 23.9004i | 0.138187 | + | 0.909874i | ||||
\(691\) | 24.2327 | − | 24.2327i | 0.921854 | − | 0.921854i | −0.0753061 | − | 0.997160i | \(-0.523993\pi\) |
0.997160 | + | 0.0753061i | \(0.0239934\pi\) | |||||||
\(692\) | 13.0027 | − | 7.01471i | 0.494289 | − | 0.266659i | ||||
\(693\) | 7.99175 | + | 1.56421i | 0.303581 | + | 0.0594194i | ||||
\(694\) | 26.0147 | − | 19.3717i | 0.987504 | − | 0.735339i | ||||
\(695\) | 35.9929i | 1.36529i | ||||||||
\(696\) | −3.39519 | + | 24.1026i | −0.128695 | + | 0.913605i | ||||
\(697\) | − | 3.41454i | − | 0.129335i | ||||||
\(698\) | 7.34180 | + | 9.85947i | 0.277891 | + | 0.373187i | ||||
\(699\) | 14.9655 | − | 28.1020i | 0.566048 | − | 1.06292i | ||||
\(700\) | 2.42188 | − | 8.09617i | 0.0915386 | − | 0.306007i | ||||
\(701\) | −10.9100 | + | 10.9100i | −0.412064 | + | 0.412064i | −0.882457 | − | 0.470393i | \(-0.844112\pi\) |
0.470393 | + | 0.882457i | \(0.344112\pi\) | |||||||
\(702\) | −1.02882 | − | 1.12035i | −0.0388305 | − | 0.0422849i | ||||
\(703\) | 14.3931i | 0.542847i | ||||||||
\(704\) | 18.8721 | + | 1.63848i | 0.711269 | + | 0.0617525i | ||||
\(705\) | −31.3288 | + | 9.55596i | −1.17991 | + | 0.359898i | ||||
\(706\) | 4.70054 | − | 32.1151i | 0.176907 | − | 1.20867i | ||||
\(707\) | 9.50478 | + | 9.50478i | 0.357464 | + | 0.357464i | ||||
\(708\) | −0.238972 | − | 44.3376i | −0.00898112 | − | 1.66631i | ||||
\(709\) | −14.0031 | + | 14.0031i | −0.525899 | + | 0.525899i | −0.919347 | − | 0.393448i | \(-0.871282\pi\) |
0.393448 | + | 0.919347i | \(0.371282\pi\) | |||||||
\(710\) | −23.0882 | + | 17.1925i | −0.866485 | + | 0.645223i | ||||
\(711\) | 24.4752 | − | 16.4625i | 0.917892 | − | 0.617394i | ||||
\(712\) | −1.25662 | − | 0.585462i | −0.0470937 | − | 0.0219411i | ||||
\(713\) | 19.5303 | 0.731416 | ||||||||
\(714\) | 12.6564 | + | 9.31888i | 0.473653 | + | 0.348750i | ||||
\(715\) | 1.02142 | + | 1.02142i | 0.0381990 | + | 0.0381990i | ||||
\(716\) | 9.57652 | + | 17.7514i | 0.357891 | + | 0.663400i | ||||
\(717\) | 11.0172 | − | 20.6879i | 0.411443 | − | 0.772602i | ||||
\(718\) | −3.75639 | + | 25.6644i | −0.140187 | + | 0.957788i | ||||
\(719\) | 30.0665 | 1.12129 | 0.560646 | − | 0.828055i | \(-0.310553\pi\) | ||||
0.560646 | + | 0.828055i | \(0.310553\pi\) | |||||||
\(720\) | 24.7366 | − | 25.2757i | 0.921879 | − | 0.941971i | ||||
\(721\) | 14.0147 | 0.521934 | ||||||||
\(722\) | 2.98286 | − | 20.3795i | 0.111011 | − | 0.758447i | ||||
\(723\) | −3.97154 | + | 7.45769i | −0.147703 | + | 0.277355i | ||||
\(724\) | −16.7575 | + | 9.04033i | −0.622786 | + | 0.335981i | ||||
\(725\) | −12.9493 | − | 12.9493i | −0.480925 | − | 0.480925i | ||||
\(726\) | 10.6379 | + | 7.83264i | 0.394808 | + | 0.290697i | ||||
\(727\) | 9.48194 | 0.351666 | 0.175833 | − | 0.984420i | \(-0.443738\pi\) | ||||
0.175833 | + | 0.984420i | \(0.443738\pi\) | |||||||
\(728\) | 0.229757 | + | 0.630602i | 0.00851537 | + | 0.0233717i | ||||
\(729\) | 26.4316 | − | 5.51071i | 0.978950 | − | 0.204100i | ||||
\(730\) | −23.6644 | + | 17.6216i | −0.875860 | + | 0.652204i | ||||
\(731\) | −8.33587 | + | 8.33587i | −0.308313 | + | 0.308313i | ||||
\(732\) | −22.2385 | + | 0.119862i | −0.821959 | + | 0.00443021i | ||||
\(733\) | −29.4752 | − | 29.4752i | −1.08869 | − | 1.08869i | −0.995663 | − | 0.0930283i | \(-0.970345\pi\) |
−0.0930283 | − | 0.995663i | \(-0.529655\pi\) | |||||||
\(734\) | −0.587462 | + | 4.01366i | −0.0216836 | + | 0.148147i | ||||
\(735\) | 27.7616 | − | 8.46787i | 1.02400 | − | 0.312342i | ||||
\(736\) | 12.5855 | − | 14.1579i | 0.463906 | − | 0.521868i | ||||
\(737\) | 2.12861i | 0.0784085i | ||||||||
\(738\) | 1.11826 | + | 2.33414i | 0.0411638 | + | 0.0859209i | ||||
\(739\) | 22.1077 | − | 22.1077i | 0.813246 | − | 0.813246i | −0.171873 | − | 0.985119i | \(-0.554982\pi\) |
0.985119 | + | 0.171873i | \(0.0549819\pi\) | |||||||
\(740\) | −38.5910 | − | 11.5441i | −1.41863 | − | 0.424370i | ||||
\(741\) | −0.354934 | + | 0.666489i | −0.0130388 | + | 0.0244841i | ||||
\(742\) | 0.225327 | + | 0.302597i | 0.00827201 | + | 0.0111087i | ||||
\(743\) | 0.908529i | 0.0333307i | 0.999861 | + | 0.0166653i | \(0.00530499\pi\) | ||||
−0.999861 | + | 0.0166653i | \(0.994695\pi\) | |||||||
\(744\) | −17.1877 | − | 22.8240i | −0.630133 | − | 0.836768i | ||||
\(745\) | 48.5145i | 1.77743i | ||||||||
\(746\) | 27.6314 | − | 20.5756i | 1.01166 | − | 0.753325i | ||||
\(747\) | −6.59352 | + | 33.6872i | −0.241244 | + | 1.23255i | ||||
\(748\) | −12.5855 | − | 23.3288i | −0.460170 | − | 0.852987i | ||||
\(749\) | 0.819240 | − | 0.819240i | 0.0299344 | − | 0.0299344i | ||||
\(750\) | −1.42450 | − | 9.37942i | −0.0520154 | − | 0.342488i | ||||
\(751\) | − | 39.1182i | − | 1.42744i | −0.700429 | − | 0.713722i | \(-0.747008\pi\) | ||
0.700429 | − | 0.713722i | \(-0.252992\pi\) | |||||||
\(752\) | 21.4497 | + | 14.0941i | 0.782191 | + | 0.513960i | ||||
\(753\) | 3.73917 | + | 12.2587i | 0.136263 | + | 0.446733i | ||||
\(754\) | 1.43910 | + | 0.210634i | 0.0524088 | + | 0.00767084i | ||||
\(755\) | −1.68966 | − | 1.68966i | −0.0614930 | − | 0.0614930i | ||||
\(756\) | −11.7037 | − | 2.22531i | −0.425659 | − | 0.0809339i | ||||
\(757\) | −8.97544 | + | 8.97544i | −0.326218 | + | 0.326218i | −0.851146 | − | 0.524928i | \(-0.824092\pi\) |
0.524928 | + | 0.851146i | \(0.324092\pi\) | |||||||
\(758\) | −6.97532 | − | 9.36732i | −0.253355 | − | 0.340236i | ||||
\(759\) | −13.1365 | + | 4.00691i | −0.476825 | + | 0.145442i | ||||
\(760\) | −15.9143 | − | 7.41454i | −0.577273 | − | 0.268954i | ||||
\(761\) | 30.6766 | 1.11202 | 0.556012 | − | 0.831174i | \(-0.312331\pi\) | ||||
0.556012 | + | 0.831174i | \(0.312331\pi\) | |||||||
\(762\) | 14.2096 | + | 10.4625i | 0.514760 | + | 0.379017i | ||||
\(763\) | 14.3257 | + | 14.3257i | 0.518626 | + | 0.518626i | ||||
\(764\) | −48.9151 | − | 14.6324i | −1.76968 | − | 0.529382i | ||||
\(765\) | −48.5664 | − | 9.50581i | −1.75592 | − | 0.343683i | ||||
\(766\) | −43.0508 | − | 6.30115i | −1.55549 | − | 0.227670i | ||||
\(767\) | −2.64937 | −0.0956630 | ||||||||
\(768\) | −27.6215 | − | 2.24817i | −0.996704 | − | 0.0811240i | ||||
\(769\) | −41.7795 | −1.50661 | −0.753304 | − | 0.657673i | \(-0.771541\pi\) | ||||
−0.753304 | + | 0.657673i | \(0.771541\pi\) | |||||||
\(770\) | 11.1944 | + | 1.63848i | 0.403419 | + | 0.0590467i | ||||
\(771\) | −19.6187 | − | 10.4478i | −0.706551 | − | 0.376268i | ||||
\(772\) | 17.3963 | + | 5.20390i | 0.626105 | + | 0.187293i | ||||
\(773\) | −17.6074 | − | 17.6074i | −0.633293 | − | 0.633293i | 0.315599 | − | 0.948892i | \(-0.397794\pi\) |
−0.948892 | + | 0.315599i | \(0.897794\pi\) | |||||||
\(774\) | 2.96831 | − | 8.42831i | 0.106694 | − | 0.302949i | ||||
\(775\) | 21.4966 | 0.772182 | ||||||||
\(776\) | −31.6639 | − | 14.7523i | −1.13667 | − | 0.529578i | ||||
\(777\) | 3.95874 | + | 12.9786i | 0.142019 | + | 0.465604i | ||||
\(778\) | 13.1751 | + | 17.6932i | 0.472351 | + | 0.634332i | ||||
\(779\) | 0.908529 | − | 0.908529i | 0.0325514 | − | 0.0325514i | ||||
\(780\) | −1.50232 | − | 1.48622i | −0.0537918 | − | 0.0532151i | ||||
\(781\) | −11.5640 | − | 11.5640i | −0.413794 | − | 0.413794i | ||||
\(782\) | −26.2277 | − | 3.83883i | −0.937901 | − | 0.137276i | ||||
\(783\) | −16.2862 | + | 20.0319i | −0.582022 | + | 0.715882i | ||||
\(784\) | −19.0073 | − | 12.4893i | −0.678834 | − | 0.446046i | ||||
\(785\) | 22.9989i | 0.820866i | ||||||||
\(786\) | 30.9965 | − | 4.70759i | 1.10561 | − | 0.167914i | ||||
\(787\) | 1.69006 | − | 1.69006i | 0.0602440 | − | 0.0602440i | −0.676343 | − | 0.736587i | \(-0.736436\pi\) |
0.736587 | + | 0.676343i | \(0.236436\pi\) | |||||||
\(788\) | 4.27606 | + | 7.92625i | 0.152328 | + | 0.282361i | ||||
\(789\) | −43.2878 | − | 23.0526i | −1.54108 | − | 0.820693i | ||||
\(790\) | 32.8683 | − | 24.4752i | 1.16940 | − | 0.870789i | ||||
\(791\) | − | 6.27900i | − | 0.223255i | ||||||
\(792\) | 16.2435 | + | 11.8256i | 0.577187 | + | 0.420204i | ||||
\(793\) | 1.32885i | 0.0471887i | ||||||||
\(794\) | 2.09425 | + | 2.81241i | 0.0743221 | + | 0.0998088i | ||||
\(795\) | −1.04851 | − | 0.558376i | −0.0371868 | − | 0.0198035i | ||||
\(796\) | 37.4679 | + | 11.2081i | 1.32801 | + | 0.397261i | ||||
\(797\) | 5.76177 | − | 5.76177i | 0.204092 | − | 0.204092i | −0.597658 | − | 0.801751i | \(-0.703902\pi\) |
0.801751 | + | 0.597658i | \(0.203902\pi\) | |||||||
\(798\) | 0.888030 | + | 5.84710i | 0.0314359 | + | 0.206985i | ||||
\(799\) | − | 35.9143i | − | 1.27056i | ||||||
\(800\) | 13.8526 | − | 15.5834i | 0.489763 | − | 0.550955i | ||||
\(801\) | −0.820654 | − | 1.22008i | −0.0289964 | − | 0.0431096i | ||||
\(802\) | −5.01156 | + | 34.2400i | −0.176964 | + | 1.20906i | ||||
\(803\) | −11.8526 | − | 11.8526i | −0.418271 | − | 0.418271i | ||||
\(804\) | −0.0167840 | − | 3.11401i | −0.000591925 | − | 0.109823i | ||||
\(805\) | 8.00000 | − | 8.00000i | 0.281963 | − | 0.281963i | ||||
\(806\) | −1.36933 | + | 1.01966i | −0.0482325 | + | 0.0359161i | ||||
\(807\) | 4.70306 | + | 15.4188i | 0.165555 | + | 0.542767i | ||||
\(808\) | 11.3534 | + | 31.1611i | 0.399411 | + | 1.09624i | ||||
\(809\) | −14.1012 | −0.495771 | −0.247885 | − | 0.968789i | \(-0.579736\pi\) | ||||
−0.247885 | + | 0.968789i | \(0.579736\pi\) | |||||||
\(810\) | 36.3126 | − | 9.40747i | 1.27590 | − | 0.330545i | ||||
\(811\) | −16.2327 | − | 16.2327i | −0.570006 | − | 0.570006i | 0.362124 | − | 0.932130i | \(-0.382052\pi\) |
−0.932130 | + | 0.362124i | \(0.882052\pi\) | |||||||
\(812\) | 10.0255 | − | 5.40858i | 0.351827 | − | 0.189804i | ||||
\(813\) | −13.2412 | − | 7.05151i | −0.464390 | − | 0.247307i | ||||
\(814\) | 3.31415 | − | 22.6430i | 0.116161 | − | 0.793637i | ||||
\(815\) | 41.9909 | 1.47088 | ||||||||
\(816\) | 18.5956 | + | 34.0292i | 0.650976 | + | 1.19126i | ||||
\(817\) | −4.43596 | −0.155195 | ||||||||
\(818\) | −1.79951 | + | 12.2946i | −0.0629183 | + | 0.429871i | ||||
\(819\) | −0.136737 | + | 0.698610i | −0.00477799 | + | 0.0244114i | ||||
\(820\) | 1.70727 | + | 3.16465i | 0.0596204 | + | 0.110514i | ||||
\(821\) | −17.2853 | − | 17.2853i | −0.603262 | − | 0.603262i | 0.337915 | − | 0.941177i | \(-0.390278\pi\) |
−0.941177 | + | 0.337915i | \(0.890278\pi\) | |||||||
\(822\) | 19.5238 | − | 26.5161i | 0.680969 | − | 0.924854i | ||||
\(823\) | 7.35341 | 0.256324 | 0.128162 | − | 0.991753i | \(-0.459092\pi\) | ||||
0.128162 | + | 0.991753i | \(0.459092\pi\) | |||||||
\(824\) | 31.3436 | + | 14.6031i | 1.09190 | + | 0.508723i | ||||
\(825\) | −14.4591 | + | 4.41033i | −0.503401 | + | 0.153548i | ||||
\(826\) | −16.6430 | + | 12.3931i | −0.579084 | + | 0.431212i | ||||
\(827\) | 0.224507 | − | 0.224507i | 0.00780688 | − | 0.00780688i | −0.703193 | − | 0.710999i | \(-0.748243\pi\) |
0.710999 | + | 0.703193i | \(0.248243\pi\) | |||||||
\(828\) | 19.1862 | − | 5.96541i | 0.666766 | − | 0.207312i | ||||
\(829\) | 29.5181 | + | 29.5181i | 1.02520 | + | 1.02520i | 0.999674 | + | 0.0255305i | \(0.00812749\pi\) |
0.0255305 | + | 0.999674i | \(0.491873\pi\) | |||||||
\(830\) | −6.90659 | + | 47.1873i | −0.239731 | + | 1.63789i | ||||
\(831\) | 9.37962 | + | 30.7507i | 0.325375 | + | 1.06673i | ||||
\(832\) | −0.143230 | + | 1.64973i | −0.00496560 | + | 0.0571941i | ||||
\(833\) | 31.8249i | 1.10267i | ||||||||
\(834\) | 29.5756 | − | 4.49180i | 1.02412 | − | 0.155538i | ||||
\(835\) | 4.93573 | − | 4.93573i | 0.170808 | − | 0.170808i | ||||
\(836\) | 2.85856 | − | 9.55596i | 0.0988655 | − | 0.330500i | ||||
\(837\) | −3.10904 | − | 30.1452i | −0.107464 | − | 1.04197i | ||||
\(838\) | −4.20704 | − | 5.64973i | −0.145330 | − | 0.195167i | ||||
\(839\) | − | 14.0224i | − | 0.484106i | −0.970263 | − | 0.242053i | \(-0.922179\pi\) | ||
0.970263 | − | 0.242053i | \(-0.0778208\pi\) | |||||||
\(840\) | −16.3896 | − | 2.30871i | −0.565495 | − | 0.0796581i | ||||
\(841\) | 4.31415i | 0.148764i | ||||||||
\(842\) | −18.0067 | + | 13.4086i | −0.620552 | + | 0.462091i | ||||
\(843\) | −21.2946 | + | 39.9868i | −0.733427 | + | 1.37722i | ||||
\(844\) | −25.7465 | + | 13.8898i | −0.886232 | + | 0.478105i | ||||
\(845\) | 27.0023 | − | 27.0023i | 0.928907 | − | 0.928907i | ||||
\(846\) | 11.7620 | + | 24.5506i | 0.404384 | + | 0.844068i | ||||
\(847\) | − | 6.18248i | − | 0.212433i | ||||||
\(848\) | 0.188638 | + | 0.911538i | 0.00647785 | + | 0.0313023i | ||||
\(849\) | 41.9546 | − | 12.7970i | 1.43988 | − | 0.439193i | ||||
\(850\) | −28.8683 | − | 4.22533i | −0.990175 | − | 0.144928i | ||||
\(851\) | −16.1816 | − | 16.1816i | −0.554698 | − | 0.554698i | ||||
\(852\) | 17.0086 | + | 16.8262i | 0.582704 | + | 0.576456i | ||||
\(853\) | −8.55417 | + | 8.55417i | −0.292889 | + | 0.292889i | −0.838221 | − | 0.545331i | \(-0.816404\pi\) |
0.545331 | + | 0.838221i | \(0.316404\pi\) | |||||||
\(854\) | 6.21604 | + | 8.34766i | 0.212708 | + | 0.285651i | ||||
\(855\) | −10.3931 | − | 15.4517i | −0.355437 | − | 0.528436i | ||||
\(856\) | 2.68585 | − | 0.978577i | 0.0918003 | − | 0.0334471i | ||||
\(857\) | 43.5095 | 1.48626 | 0.743128 | − | 0.669149i | \(-0.233341\pi\) | ||||
0.743128 | + | 0.669149i | \(0.233341\pi\) | |||||||
\(858\) | 0.711841 | − | 0.966782i | 0.0243019 | − | 0.0330054i | ||||
\(859\) | −8.70306 | − | 8.70306i | −0.296945 | − | 0.296945i | 0.542871 | − | 0.839816i | \(-0.317337\pi\) |
−0.839816 | + | 0.542871i | \(0.817337\pi\) | |||||||
\(860\) | 3.55789 | − | 11.8938i | 0.121323 | − | 0.405574i | ||||
\(861\) | 0.569354 | − | 1.06912i | 0.0194035 | − | 0.0364357i | ||||
\(862\) | −16.9786 | − | 2.48508i | −0.578293 | − | 0.0846421i | ||||
\(863\) | −26.9270 | −0.916607 | −0.458303 | − | 0.888796i | \(-0.651543\pi\) | ||||
−0.458303 | + | 0.888796i | \(0.651543\pi\) | |||||||
\(864\) | −23.8563 | − | 17.1719i | −0.811609 | − | 0.584201i | ||||
\(865\) | 21.7711 | 0.740239 | ||||||||
\(866\) | 17.0009 | + | 2.48834i | 0.577712 | + | 0.0845572i | ||||
\(867\) | 11.6657 | − | 21.9057i | 0.396188 | − | 0.743956i | ||||
\(868\) | −3.83221 | + | 12.8108i | −0.130074 | + | 0.434827i | ||||
\(869\) | 16.4625 | + | 16.4625i | 0.558454 | + | 0.558454i | ||||
\(870\) | −21.2666 | + | 28.8831i | −0.721006 | + | 0.979230i | ||||
\(871\) | −0.186076 | −0.00630493 | ||||||||
\(872\) | 17.1120 | + | 46.9663i | 0.579485 | + | 1.59048i | ||||
\(873\) | −20.6787 | − | 30.7434i | −0.699866 | − | 1.04051i | ||||
\(874\) | −5.95715 | − | 8.00000i | −0.201504 | − | 0.270604i | ||||
\(875\) | −3.13950 | + | 3.13950i | −0.106134 | + | 0.106134i | ||||
\(876\) | 17.4330 | + | 17.2461i | 0.589008 | + | 0.582693i | ||||
\(877\) | 39.7251 | + | 39.7251i | 1.34142 | + | 1.34142i | 0.894646 | + | 0.446775i | \(0.147427\pi\) |
0.446775 | + | 0.894646i | \(0.352573\pi\) | |||||||
\(878\) | −37.9261 | − | 5.55107i | −1.27994 | − | 0.187339i | ||||
\(879\) | 1.53388 | − | 0.467866i | 0.0517365 | − | 0.0157807i | ||||
\(880\) | 23.3288 | + | 15.3288i | 0.786415 | + | 0.516735i | ||||
\(881\) | − | 1.63848i | − | 0.0552018i | −0.999619 | − | 0.0276009i | \(-0.991213\pi\) | ||
0.999619 | − | 0.0276009i | \(-0.00878675\pi\) | |||||||
\(882\) | −10.4227 | − | 21.7552i | −0.350950 | − | 0.732534i | ||||
\(883\) | −31.7967 | + | 31.7967i | −1.07004 | + | 1.07004i | −0.0726900 | + | 0.997355i | \(0.523158\pi\) |
−0.997355 | + | 0.0726900i | \(0.976842\pi\) | |||||||
\(884\) | 2.03932 | − | 1.10018i | 0.0685899 | − | 0.0370029i | ||||
\(885\) | 30.7110 | − | 57.6687i | 1.03234 | − | 1.93851i | ||||
\(886\) | −46.2646 | + | 34.4507i | −1.55429 | + | 1.15739i | ||||
\(887\) | − | 29.8573i | − | 1.00251i | −0.865299 | − | 0.501256i | \(-0.832872\pi\) | ||
0.865299 | − | 0.501256i | \(-0.167128\pi\) | |||||||
\(888\) | −4.66984 | + | 33.1513i | −0.156709 | + | 1.11248i | ||||
\(889\) | − | 8.25831i | − | 0.276975i | ||||||
\(890\) | −1.22008 | − | 1.63848i | −0.0408973 | − | 0.0549219i | ||||
\(891\) | 8.27590 | + | 19.6384i | 0.277253 | + | 0.657912i | ||||
\(892\) | 12.9645 | − | 43.3393i | 0.434084 | − | 1.45111i | ||||
\(893\) | 9.55596 | − | 9.55596i | 0.319778 | − | 0.319778i | ||||
\(894\) | 39.8647 | − | 6.05446i | 1.33328 | − | 0.202492i | ||||
\(895\) | 29.7220i | 0.993496i | ||||||||
\(896\) | 6.81730 | + | 11.0334i | 0.227750 | + | 0.368600i | ||||
\(897\) | −0.350269 | − | 1.14835i | −0.0116952 | − | 0.0383421i | ||||
\(898\) | −1.98171 | + | 13.5395i | −0.0661306 | + | 0.451818i | ||||
\(899\) | 20.4900 | + | 20.4900i | 0.683380 | + | 0.683380i | ||||
\(900\) | 21.1179 | − | 6.56601i | 0.703929 | − | 0.218867i | ||||
\(901\) | 0.921039 | − | 0.921039i | 0.0306842 | − | 0.0306842i | ||||
\(902\) | −1.63848 | + | 1.22008i | −0.0545554 | + | 0.0406244i | ||||
\(903\) | −4.00000 | + | 1.22008i | −0.133112 | + | 0.0406019i | ||||
\(904\) | 6.54262 | − | 14.0428i | 0.217604 | − | 0.467058i | ||||
\(905\) | −28.0578 | −0.932674 | ||||||||
\(906\) | −1.17754 | + | 1.59927i | −0.0391212 | + | 0.0531322i | ||||
\(907\) | −12.1176 | − | 12.1176i | −0.402358 | − | 0.402358i | 0.476705 | − | 0.879063i | \(-0.341831\pi\) |
−0.879063 | + | 0.476705i | \(0.841831\pi\) | |||||||
\(908\) | 1.96758 | + | 3.64718i | 0.0652966 | + | 0.121036i | ||||
\(909\) | −6.75686 | + | 34.5217i | −0.224111 | + | 1.14501i | ||||
\(910\) | −0.143230 | + | 0.978577i | −0.00474803 | + | 0.0324395i | ||||
\(911\) | 4.53816 | 0.150356 | 0.0751780 | − | 0.997170i | \(-0.476048\pi\) | ||||
0.0751780 | + | 0.997170i | \(0.476048\pi\) | |||||||
\(912\) | −4.10653 | + | 14.0022i | −0.135981 | + | 0.463660i | ||||
\(913\) | −27.0937 | −0.896669 | ||||||||
\(914\) | 0.860359 | − | 5.87815i | 0.0284581 | − | 0.194432i | ||||
\(915\) | −28.9250 | − | 15.4038i | −0.956230 | − | 0.509233i | ||||
\(916\) | −18.7146 | + | 10.0962i | −0.618348 | + | 0.333587i | ||||
\(917\) | −10.3752 | − | 10.3752i | −0.342619 | − | 0.342619i | ||||
\(918\) | −1.75005 | + | 41.0937i | −0.0577604 | + | 1.35630i | ||||
\(919\) | −33.6461 | −1.10988 | −0.554942 | − | 0.831889i | \(-0.687259\pi\) | ||||
−0.554942 | + | 0.831889i | \(0.687259\pi\) | |||||||
\(920\) | 26.2277 | − | 9.55596i | 0.864702 | − | 0.315051i | ||||
\(921\) | −0.694081 | − | 2.27552i | −0.0228707 | − | 0.0749809i | ||||
\(922\) | 44.1783 | − | 32.8971i | 1.45493 | − | 1.08341i | ||||
\(923\) | 1.01089 | − | 1.01089i | 0.0332737 | − | 0.0332737i | ||||
\(924\) | −0.0506807 | − | 9.40304i | −0.00166727 | − | 0.309337i | ||||
\(925\) | −17.8108 | − | 17.8108i | −0.585615 | − | 0.585615i | ||||
\(926\) | 7.66213 | − | 52.3493i | 0.251793 | − | 1.72030i | ||||
\(927\) | 20.4695 | + | 30.4324i | 0.672305 | + | 0.999530i | ||||
\(928\) | 28.0575 | − | 1.64973i | 0.921034 | − | 0.0541551i | ||||
\(929\) | 27.1844i | 0.891891i | 0.895060 | + | 0.445946i | \(0.147133\pi\) | ||||
−0.895060 | + | 0.445946i | \(0.852867\pi\) | |||||||
\(930\) | −6.32193 | − | 41.6259i | −0.207304 | − | 1.36497i | ||||
\(931\) | −8.46787 | + | 8.46787i | −0.277523 | + | 0.277523i | ||||
\(932\) | −35.2218 | − | 10.5362i | −1.15373 | − | 0.345125i | ||||
\(933\) | 50.6551 | + | 26.9760i | 1.65837 | + | 0.883154i | ||||
\(934\) | −20.2070 | − | 27.1365i | −0.661195 | − | 0.887933i | ||||
\(935\) | − | 39.0606i | − | 1.27742i | ||||||
\(936\) | −1.03375 | + | 1.41995i | −0.0337892 | + | 0.0464124i | ||||
\(937\) | − | 22.1495i | − | 0.723593i | −0.932257 | − | 0.361796i | \(-0.882164\pi\) | ||
0.932257 | − | 0.361796i | \(-0.117836\pi\) | |||||||
\(938\) | −1.16891 | + | 0.870418i | −0.0381661 | + | 0.0284202i | ||||
\(939\) | −20.2234 | − | 10.7698i | −0.659967 | − | 0.351460i | ||||
\(940\) | 17.9572 | + | 33.2860i | 0.585698 | + | 1.08567i | ||||
\(941\) | −7.35208 | + | 7.35208i | −0.239671 | + | 0.239671i | −0.816714 | − | 0.577043i | \(-0.804207\pi\) |
0.577043 | + | 0.816714i | \(0.304207\pi\) | |||||||
\(942\) | 18.8984 | − | 2.87020i | 0.615743 | − | 0.0935161i | ||||
\(943\) | 2.04285i | 0.0665242i | ||||||||
\(944\) | −50.1351 | + | 10.3752i | −1.63176 | + | 0.337684i | ||||
\(945\) | −13.6216 | − | 11.0745i | −0.443110 | − | 0.360254i | ||||
\(946\) | 6.97858 | + | 1.02142i | 0.226893 | + | 0.0332093i | ||||
\(947\) | 9.29033 | + | 9.29033i | 0.301895 | + | 0.301895i | 0.841755 | − | 0.539860i | \(-0.181523\pi\) |
−0.539860 | + | 0.841755i | \(0.681523\pi\) | |||||||
\(948\) | −24.2134 | − | 23.9537i | −0.786413 | − | 0.777981i | ||||
\(949\) | 1.03612 | − | 1.03612i | 0.0336337 | − | 0.0336337i | ||||
\(950\) | −6.55693 | − | 8.80545i | −0.212735 | − | 0.285686i | ||||
\(951\) | −5.63879 | − | 18.4866i | −0.182850 | − | 0.599468i | ||||
\(952\) | 7.66442 | − | 16.4507i | 0.248405 | − | 0.533169i | ||||
\(953\) | 12.6413 | 0.409491 | 0.204745 | − | 0.978815i | \(-0.434363\pi\) | ||||
0.204745 | + | 0.978815i | \(0.434363\pi\) | |||||||
\(954\) | −0.327971 | + | 0.931252i | −0.0106185 | + | 0.0301504i | ||||
\(955\) | −53.2003 | − | 53.2003i | −1.72152 | − | 1.72152i | ||||
\(956\) | −25.9292 | − | 7.75645i | −0.838611 | − | 0.250862i | ||||
\(957\) | −17.9858 | − | 9.57821i | −0.581399 | − | 0.309620i | ||||
\(958\) | −25.9572 | − | 3.79923i | −0.838638 | − | 0.122748i | ||||
\(959\) | −15.4105 | −0.497632 | ||||||||
\(960\) | −34.2493 | − | 22.2411i | −1.10539 | − | 0.717828i | ||||
\(961\) | −3.01469 | −0.0972482 | ||||||||
\(962\) | 1.97937 | + | 0.289711i | 0.0638174 | + | 0.00934067i | ||||
\(963\) | 2.97550 | + | 0.582390i | 0.0958843 | + | 0.0187672i | ||||
\(964\) | 9.34713 | + | 2.79610i | 0.301051 | + | 0.0900562i | ||||
\(965\) | 18.9203 | + | 18.9203i | 0.609065 | + | 0.609065i | ||||
\(966\) | −7.57204 | − | 5.57529i | −0.243627 | − | 0.179382i | ||||
\(967\) | 23.3043 | 0.749415 | 0.374708 | − | 0.927143i | \(-0.377743\pi\) | ||||
0.374708 | + | 0.927143i | \(0.377743\pi\) | |||||||
\(968\) | 6.44205 | − | 13.8270i | 0.207055 | − | 0.444416i | ||||
\(969\) | 19.5303 | − | 5.95715i | 0.627404 | − | 0.191371i | ||||
\(970\) | −30.7434 | − | 41.2860i | −0.987111 | − | 1.32561i | ||||
\(971\) | 6.17139 | − | 6.17139i | 0.198049 | − | 0.198049i | −0.601114 | − | 0.799163i | \(-0.705276\pi\) |
0.799163 | + | 0.601114i | \(0.205276\pi\) | |||||||
\(972\) | −12.2619 | − | 28.6644i | −0.393301 | − | 0.919410i | ||||
\(973\) | −9.89962 | − | 9.89962i | −0.317367 | − | 0.317367i | ||||
\(974\) | 57.2677 | + | 8.38202i | 1.83498 | + | 0.268577i | ||||
\(975\) | −0.385535 | − | 1.26396i | −0.0123470 | − | 0.0404792i | ||||
\(976\) | 5.20390 | + | 25.1464i | 0.166573 | + | 0.804916i | ||||
\(977\) | 9.43605i | 0.301886i | 0.988542 | + | 0.150943i | \(0.0482310\pi\) | ||||
−0.988542 | + | 0.150943i | \(0.951769\pi\) | |||||||
\(978\) | −5.24034 | − | 34.5043i | −0.167568 | − | 1.10333i | ||||
\(979\) | 0.820654 | − | 0.820654i | 0.0262282 | − | 0.0262282i | ||||
\(980\) | −15.9125 | − | 29.4959i | −0.508305 | − | 0.942211i | ||||
\(981\) | −10.1840 | + | 52.0315i | −0.325150 | + | 1.66124i | ||||
\(982\) | −8.09052 | + | 6.02456i | −0.258179 | + | 0.192251i | ||||
\(983\) | 25.8750i | 0.825285i | 0.910893 | + | 0.412643i | \(0.135394\pi\) | ||||
−0.910893 | + | 0.412643i | \(0.864606\pi\) | |||||||
\(984\) | 2.38736 | − | 1.79782i | 0.0761062 | − | 0.0573123i | ||||
\(985\) | 13.2713i | 0.422859i | ||||||||
\(986\) | −23.4890 | − | 31.5440i | −0.748044 | − | 1.00457i | ||||
\(987\) | 5.98850 | − | 11.2451i | 0.190616 | − | 0.357936i | ||||
\(988\) | 0.835347 | + | 0.249885i | 0.0265759 | + | 0.00794991i | ||||
\(989\) | 4.98718 | − | 4.98718i | 0.158583 | − | 0.158583i | ||||
\(990\) | 12.7924 | + | 26.7014i | 0.406568 | + | 0.848626i | ||||
\(991\) | 23.5886i | 0.749316i | 0.927163 | + | 0.374658i | \(0.122240\pi\) | ||||
−0.927163 | + | 0.374658i | \(0.877760\pi\) | |||||||
\(992\) | −21.9193 | + | 24.6580i | −0.695938 | + | 0.782891i | ||||
\(993\) | 7.09617 | − | 2.16448i | 0.225190 | − | 0.0686878i | ||||
\(994\) | 1.62158 | − | 11.0790i | 0.0514333 | − | 0.351403i | ||||
\(995\) | 40.7503 | + | 40.7503i | 1.29187 | + | 1.29187i | ||||
\(996\) | 39.6361 | − | 0.213632i | 1.25592 | − | 0.00676918i | ||||
\(997\) | 3.16779 | − | 3.16779i | 0.100325 | − | 0.100325i | −0.655163 | − | 0.755488i | \(-0.727400\pi\) |
0.755488 | + | 0.655163i | \(0.227400\pi\) | |||||||
\(998\) | 18.3907 | − | 13.6946i | 0.582149 | − | 0.433494i | ||||
\(999\) | −22.4005 | + | 27.5524i | −0.708719 | + | 0.871719i |
(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 | 48.2.k.a.35.1 | yes | 12 | |
3.2 | odd | 2 | inner | 48.2.k.a.35.6 | yes | 12 | |
4.3 | odd | 2 | 192.2.k.a.47.4 | 12 | |||
8.3 | odd | 2 | 384.2.k.a.95.3 | 12 | |||
8.5 | even | 2 | 384.2.k.b.95.4 | 12 | |||
12.11 | even | 2 | 192.2.k.a.47.6 | 12 | |||
16.3 | odd | 4 | 384.2.k.b.287.6 | 12 | |||
16.5 | even | 4 | 192.2.k.a.143.6 | 12 | |||
16.11 | odd | 4 | inner | 48.2.k.a.11.6 | yes | 12 | |
16.13 | even | 4 | 384.2.k.a.287.1 | 12 | |||
24.5 | odd | 2 | 384.2.k.b.95.6 | 12 | |||
24.11 | even | 2 | 384.2.k.a.95.1 | 12 | |||
48.5 | odd | 4 | 192.2.k.a.143.4 | 12 | |||
48.11 | even | 4 | inner | 48.2.k.a.11.1 | ✓ | 12 | |
48.29 | odd | 4 | 384.2.k.a.287.3 | 12 | |||
48.35 | even | 4 | 384.2.k.b.287.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.k.a.11.1 | ✓ | 12 | 48.11 | even | 4 | inner | |
48.2.k.a.11.6 | yes | 12 | 16.11 | odd | 4 | inner | |
48.2.k.a.35.1 | yes | 12 | 1.1 | even | 1 | trivial | |
48.2.k.a.35.6 | yes | 12 | 3.2 | odd | 2 | inner | |
192.2.k.a.47.4 | 12 | 4.3 | odd | 2 | |||
192.2.k.a.47.6 | 12 | 12.11 | even | 2 | |||
192.2.k.a.143.4 | 12 | 48.5 | odd | 4 | |||
192.2.k.a.143.6 | 12 | 16.5 | even | 4 | |||
384.2.k.a.95.1 | 12 | 24.11 | even | 2 | |||
384.2.k.a.95.3 | 12 | 8.3 | odd | 2 | |||
384.2.k.a.287.1 | 12 | 16.13 | even | 4 | |||
384.2.k.a.287.3 | 12 | 48.29 | odd | 4 | |||
384.2.k.b.95.4 | 12 | 8.5 | even | 2 | |||
384.2.k.b.95.6 | 12 | 24.5 | odd | 2 | |||
384.2.k.b.287.4 | 12 | 48.35 | even | 4 | |||
384.2.k.b.287.6 | 12 | 16.3 | odd | 4 |