Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(45,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.45");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.g (of order \(6\), 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: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 12x^{14} + 73x^{12} + 312x^{10} + 1045x^{8} + 2808x^{6} + 5913x^{4} + 8748x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 229.8 | ||
Root | \(0.956239 - 1.44416i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.229 |
Dual form | 322.2.g.b.45.8 |
$q$-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 \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 2.13508 | − | 1.23269i | 1.23269 | − | 0.711692i | 0.265098 | − | 0.964221i | \(-0.414596\pi\) |
0.967589 | + | 0.252529i | \(0.0812623\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.511122 | − | 0.885289i | 0.228581 | − | 0.395913i | −0.728807 | − | 0.684719i | \(-0.759925\pi\) |
0.957388 | + | 0.288806i | \(0.0932582\pi\) | |||||||
\(6\) | − | 2.46537i | − | 1.00649i | ||||||
\(7\) | −2.61593 | + | 0.396147i | −0.988727 | + | 0.149729i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.53904 | − | 2.66569i | 0.513012 | − | 0.888563i | ||||
\(10\) | −0.511122 | − | 0.885289i | −0.161631 | − | 0.279953i | ||||
\(11\) | 1.28679 | − | 0.742931i | 0.387983 | − | 0.224002i | −0.293303 | − | 0.956020i | \(-0.594754\pi\) |
0.681286 | + | 0.732018i | \(0.261421\pi\) | |||||||
\(12\) | −2.13508 | − | 1.23269i | −0.616344 | − | 0.355846i | ||||
\(13\) | − | 0.0815813i | − | 0.0226266i | −0.999936 | − | 0.0113133i | \(-0.996399\pi\) | ||
0.999936 | − | 0.0113133i | \(-0.00360121\pi\) | |||||||
\(14\) | −0.964890 | + | 2.46353i | −0.257878 | + | 0.658406i | ||||
\(15\) | − | 2.52021i | − | 0.650716i | ||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.20592 | + | 2.08871i | 0.292478 | + | 0.506587i | 0.974395 | − | 0.224842i | \(-0.0721867\pi\) |
−0.681917 | + | 0.731430i | \(0.738853\pi\) | |||||||
\(18\) | −1.53904 | − | 2.66569i | −0.362754 | − | 0.628309i | ||||
\(19\) | 1.03400 | − | 1.79095i | 0.237217 | − | 0.410872i | −0.722698 | − | 0.691164i | \(-0.757098\pi\) |
0.959915 | + | 0.280293i | \(0.0904315\pi\) | |||||||
\(20\) | −1.02224 | −0.228581 | ||||||||
\(21\) | −5.09688 | + | 4.07042i | −1.11223 | + | 0.888239i | ||||
\(22\) | − | 1.48586i | − | 0.316787i | ||||||
\(23\) | 3.64481 | + | 3.11694i | 0.759996 | + | 0.649927i | ||||
\(24\) | −2.13508 | + | 1.23269i | −0.435821 | + | 0.251621i | ||||
\(25\) | 1.97751 | + | 3.42515i | 0.395502 | + | 0.685029i | ||||
\(26\) | −0.0706515 | − | 0.0407907i | −0.0138559 | − | 0.00799971i | ||||
\(27\) | − | 0.192480i | − | 0.0370427i | ||||||
\(28\) | 1.65104 | + | 2.06738i | 0.312016 | + | 0.390699i | ||||
\(29\) | −0.342432 | −0.0635880 | −0.0317940 | − | 0.999494i | \(-0.510122\pi\) | ||||
−0.0317940 | + | 0.999494i | \(0.510122\pi\) | |||||||
\(30\) | −2.18257 | − | 1.26011i | −0.398481 | − | 0.230063i | ||||
\(31\) | −2.67411 | + | 1.54390i | −0.480285 | + | 0.277293i | −0.720535 | − | 0.693418i | \(-0.756104\pi\) |
0.240250 | + | 0.970711i | \(0.422770\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 1.83160 | − | 3.17243i | 0.318841 | − | 0.552249i | ||||
\(34\) | 2.41184 | 0.413627 | ||||||||
\(35\) | −0.986353 | + | 2.51833i | −0.166724 | + | 0.425675i | ||||
\(36\) | −3.07807 | −0.513012 | ||||||||
\(37\) | 0.135119 | + | 0.0780112i | 0.0222135 | + | 0.0128250i | 0.511066 | − | 0.859542i | \(-0.329251\pi\) |
−0.488852 | + | 0.872367i | \(0.662584\pi\) | |||||||
\(38\) | −1.03400 | − | 1.79095i | −0.167738 | − | 0.290530i | ||||
\(39\) | −0.100564 | − | 0.174182i | −0.0161032 | − | 0.0278915i | ||||
\(40\) | −0.511122 | + | 0.885289i | −0.0808155 | + | 0.139976i | ||||
\(41\) | 2.13767i | 0.333848i | 0.985970 | + | 0.166924i | \(0.0533834\pi\) | ||||
−0.985970 | + | 0.166924i | \(0.946617\pi\) | |||||||
\(42\) | 0.976650 | + | 6.44924i | 0.150700 | + | 0.995139i | ||||
\(43\) | − | 6.69764i | − | 1.02138i | −0.859765 | − | 0.510690i | \(-0.829390\pi\) | ||
0.859765 | − | 0.510690i | \(-0.170610\pi\) | |||||||
\(44\) | −1.28679 | − | 0.742931i | −0.193991 | − | 0.112001i | ||||
\(45\) | −1.57327 | − | 2.72498i | −0.234529 | − | 0.406217i | ||||
\(46\) | 4.52176 | − | 1.59803i | 0.666697 | − | 0.235617i | ||||
\(47\) | −3.72680 | − | 2.15167i | −0.543609 | − | 0.313853i | 0.202931 | − | 0.979193i | \(-0.434953\pi\) |
−0.746540 | + | 0.665340i | \(0.768287\pi\) | |||||||
\(48\) | 2.46537i | 0.355846i | ||||||||
\(49\) | 6.68614 | − | 2.07258i | 0.955162 | − | 0.296083i | ||||
\(50\) | 3.95502 | 0.559324 | ||||||||
\(51\) | 5.14946 | + | 2.97304i | 0.721069 | + | 0.416309i | ||||
\(52\) | −0.0706515 | + | 0.0407907i | −0.00979760 | + | 0.00565665i | ||||
\(53\) | −7.03856 | + | 4.06372i | −0.966821 | + | 0.558195i | −0.898266 | − | 0.439453i | \(-0.855172\pi\) |
−0.0685556 | + | 0.997647i | \(0.521839\pi\) | |||||||
\(54\) | −0.166692 | − | 0.0962398i | −0.0226839 | − | 0.0130966i | ||||
\(55\) | − | 1.51891i | − | 0.204810i | ||||||
\(56\) | 2.61593 | − | 0.396147i | 0.349568 | − | 0.0529373i | ||||
\(57\) | − | 5.09841i | − | 0.675302i | ||||||
\(58\) | −0.171216 | + | 0.296554i | −0.0224817 | + | 0.0389395i | ||||
\(59\) | 2.48203 | − | 1.43300i | 0.323133 | − | 0.186561i | −0.329655 | − | 0.944101i | \(-0.606932\pi\) |
0.652788 | + | 0.757540i | \(0.273599\pi\) | |||||||
\(60\) | −2.18257 | + | 1.26011i | −0.281768 | + | 0.162679i | ||||
\(61\) | 1.09121 | − | 1.89003i | 0.139715 | − | 0.241994i | −0.787674 | − | 0.616093i | \(-0.788715\pi\) |
0.927389 | + | 0.374099i | \(0.122048\pi\) | |||||||
\(62\) | 3.08780i | 0.392151i | ||||||||
\(63\) | −2.97000 | + | 7.58293i | −0.374185 | + | 0.955359i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.0722231 | − | 0.0416980i | −0.00895817 | − | 0.00517200i | ||||
\(66\) | −1.83160 | − | 3.17243i | −0.225455 | − | 0.390499i | ||||
\(67\) | −13.5852 | + | 7.84342i | −1.65970 | + | 0.958227i | −0.686844 | + | 0.726805i | \(0.741004\pi\) |
−0.972854 | + | 0.231422i | \(0.925662\pi\) | |||||||
\(68\) | 1.20592 | − | 2.08871i | 0.146239 | − | 0.253294i | ||||
\(69\) | 11.6242 | + | 2.16200i | 1.39939 | + | 0.260274i | ||||
\(70\) | 1.68776 | + | 2.11337i | 0.201726 | + | 0.252596i | ||||
\(71\) | −7.61259 | −0.903448 | −0.451724 | − | 0.892158i | \(-0.649191\pi\) | ||||
−0.451724 | + | 0.892158i | \(0.649191\pi\) | |||||||
\(72\) | −1.53904 | + | 2.66569i | −0.181377 | + | 0.314155i | ||||
\(73\) | 5.53281 | − | 3.19437i | 0.647567 | − | 0.373873i | −0.139957 | − | 0.990158i | \(-0.544696\pi\) |
0.787523 | + | 0.616285i | \(0.211363\pi\) | |||||||
\(74\) | 0.135119 | − | 0.0780112i | 0.0157073 | − | 0.00906862i | ||||
\(75\) | 8.44427 | + | 4.87530i | 0.975060 | + | 0.562951i | ||||
\(76\) | −2.06801 | −0.237217 | ||||||||
\(77\) | −3.07185 | + | 2.45321i | −0.350069 | + | 0.279569i | ||||
\(78\) | −0.201129 | −0.0227733 | ||||||||
\(79\) | 6.55870 | + | 3.78667i | 0.737911 | + | 0.426033i | 0.821309 | − | 0.570483i | \(-0.193244\pi\) |
−0.0833983 | + | 0.996516i | \(0.526577\pi\) | |||||||
\(80\) | 0.511122 | + | 0.885289i | 0.0571452 | + | 0.0989783i | ||||
\(81\) | 4.37984 | + | 7.58611i | 0.486649 | + | 0.842901i | ||||
\(82\) | 1.85128 | + | 1.06883i | 0.204439 | + | 0.118033i | ||||
\(83\) | −3.61313 | −0.396593 | −0.198296 | − | 0.980142i | \(-0.563541\pi\) | ||||
−0.198296 | + | 0.980142i | \(0.563541\pi\) | |||||||
\(84\) | 6.07353 | + | 2.37882i | 0.662676 | + | 0.259550i | ||||
\(85\) | 2.46549 | 0.267420 | ||||||||
\(86\) | −5.80033 | − | 3.34882i | −0.625465 | − | 0.361113i | ||||
\(87\) | −0.731118 | + | 0.422111i | −0.0783841 | + | 0.0452551i | ||||
\(88\) | −1.28679 | + | 0.742931i | −0.137173 | + | 0.0791967i | ||||
\(89\) | 7.27080 | − | 12.5934i | 0.770703 | − | 1.33490i | −0.166475 | − | 0.986046i | \(-0.553239\pi\) |
0.937178 | − | 0.348851i | \(-0.113428\pi\) | |||||||
\(90\) | −3.14654 | −0.331675 | ||||||||
\(91\) | 0.0323182 | + | 0.213411i | 0.00338787 | + | 0.0223715i | ||||
\(92\) | 0.876945 | − | 4.71497i | 0.0914278 | − | 0.491570i | ||||
\(93\) | −3.80629 | + | 6.59269i | −0.394694 | + | 0.683630i | ||||
\(94\) | −3.72680 | + | 2.15167i | −0.384390 | + | 0.221928i | ||||
\(95\) | −1.05700 | − | 1.83078i | −0.108446 | − | 0.187835i | ||||
\(96\) | 2.13508 | + | 1.23269i | 0.217910 | + | 0.125811i | ||||
\(97\) | 15.5010 | 1.57389 | 0.786946 | − | 0.617022i | \(-0.211661\pi\) | ||||
0.786946 | + | 0.617022i | \(0.211661\pi\) | |||||||
\(98\) | 1.54816 | − | 6.82665i | 0.156388 | − | 0.689596i | ||||
\(99\) | − | 4.57359i | − | 0.459663i | ||||||
\(100\) | 1.97751 | − | 3.42515i | 0.197751 | − | 0.342515i | ||||
\(101\) | −14.5106 | + | 8.37770i | −1.44386 | + | 0.833612i | −0.998104 | − | 0.0615432i | \(-0.980398\pi\) |
−0.445754 | + | 0.895155i | \(0.647064\pi\) | |||||||
\(102\) | 5.14946 | − | 2.97304i | 0.509873 | − | 0.294375i | ||||
\(103\) | 3.89407 | − | 6.74472i | 0.383694 | − | 0.664577i | −0.607893 | − | 0.794019i | \(-0.707985\pi\) |
0.991587 | + | 0.129441i | \(0.0413184\pi\) | |||||||
\(104\) | 0.0815813i | 0.00799971i | ||||||||
\(105\) | 0.998374 | + | 6.59269i | 0.0974314 | + | 0.643381i | ||||
\(106\) | 8.12743i | 0.789406i | ||||||||
\(107\) | −5.64261 | − | 3.25776i | −0.545491 | − | 0.314940i | 0.201810 | − | 0.979425i | \(-0.435318\pi\) |
−0.747302 | + | 0.664485i | \(0.768651\pi\) | |||||||
\(108\) | −0.166692 | + | 0.0962398i | −0.0160400 | + | 0.00926068i | ||||
\(109\) | −14.9835 | + | 8.65070i | −1.43515 | + | 0.828587i | −0.997508 | − | 0.0705599i | \(-0.977521\pi\) |
−0.437647 | + | 0.899147i | \(0.644188\pi\) | |||||||
\(110\) | −1.31542 | − | 0.759456i | −0.125420 | − | 0.0724113i | ||||
\(111\) | 0.384654 | 0.0365097 | ||||||||
\(112\) | 0.964890 | − | 2.46353i | 0.0911735 | − | 0.232782i | ||||
\(113\) | 15.6200i | 1.46941i | 0.678388 | + | 0.734703i | \(0.262679\pi\) | ||||
−0.678388 | + | 0.734703i | \(0.737321\pi\) | |||||||
\(114\) | −4.41536 | − | 2.54921i | −0.413536 | − | 0.238755i | ||||
\(115\) | 4.62234 | − | 1.63358i | 0.431035 | − | 0.152332i | ||||
\(116\) | 0.171216 | + | 0.296554i | 0.0158970 | + | 0.0275344i | ||||
\(117\) | −0.217471 | − | 0.125557i | −0.0201052 | − | 0.0116077i | ||||
\(118\) | − | 2.86600i | − | 0.263837i | ||||||
\(119\) | −3.98203 | − | 4.98620i | −0.365032 | − | 0.457084i | ||||
\(120\) | 2.52021i | 0.230063i | ||||||||
\(121\) | −4.39611 | + | 7.61428i | −0.399646 | + | 0.692207i | ||||
\(122\) | −1.09121 | − | 1.89003i | −0.0987936 | − | 0.171116i | ||||
\(123\) | 2.63508 | + | 4.56409i | 0.237597 | + | 0.411530i | ||||
\(124\) | 2.67411 | + | 1.54390i | 0.240143 | + | 0.138646i | ||||
\(125\) | 9.15421 | 0.818778 | ||||||||
\(126\) | 5.08201 | + | 6.36356i | 0.452741 | + | 0.566911i | ||||
\(127\) | 6.12885 | 0.543848 | 0.271924 | − | 0.962319i | \(-0.412340\pi\) | ||||
0.271924 | + | 0.962319i | \(0.412340\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −8.25610 | − | 14.3000i | −0.726909 | − | 1.25904i | ||||
\(130\) | −0.0722231 | + | 0.0416980i | −0.00633438 | + | 0.00365716i | ||||
\(131\) | −11.3272 | − | 6.53974i | −0.989658 | − | 0.571380i | −0.0844863 | − | 0.996425i | \(-0.526925\pi\) |
−0.905172 | + | 0.425045i | \(0.860258\pi\) | |||||||
\(132\) | −3.66321 | −0.318841 | ||||||||
\(133\) | −1.99540 | + | 5.09460i | −0.173023 | + | 0.441758i | ||||
\(134\) | 15.6868i | 1.35514i | ||||||||
\(135\) | −0.170400 | − | 0.0983805i | −0.0146657 | − | 0.00846725i | ||||
\(136\) | −1.20592 | − | 2.08871i | −0.103407 | − | 0.179106i | ||||
\(137\) | −9.11197 | + | 5.26080i | −0.778488 | + | 0.449460i | −0.835894 | − | 0.548891i | \(-0.815050\pi\) |
0.0574061 | + | 0.998351i | \(0.481717\pi\) | |||||||
\(138\) | 7.68443 | − | 8.98583i | 0.654142 | − | 0.764925i | ||||
\(139\) | − | 16.5716i | − | 1.40558i | −0.711396 | − | 0.702791i | \(-0.751937\pi\) | ||
0.711396 | − | 0.702791i | \(-0.248063\pi\) | |||||||
\(140\) | 2.67411 | − | 0.404958i | 0.226004 | − | 0.0342252i | ||||
\(141\) | −10.6093 | −0.893467 | ||||||||
\(142\) | −3.80629 | + | 6.59269i | −0.319417 | + | 0.553247i | ||||
\(143\) | −0.0606093 | − | 0.104978i | −0.00506840 | − | 0.00877873i | ||||
\(144\) | 1.53904 | + | 2.66569i | 0.128253 | + | 0.222141i | ||||
\(145\) | −0.175024 | + | 0.303151i | −0.0145350 | + | 0.0251753i | ||||
\(146\) | − | 6.38874i | − | 0.528736i | ||||||
\(147\) | 11.7206 | − | 12.6670i | 0.966696 | − | 1.04476i | ||||
\(148\) | − | 0.156022i | − | 0.0128250i | ||||||
\(149\) | −9.44175 | − | 5.45120i | −0.773498 | − | 0.446580i | 0.0606227 | − | 0.998161i | \(-0.480691\pi\) |
−0.834121 | + | 0.551581i | \(0.814025\pi\) | |||||||
\(150\) | 8.44427 | − | 4.87530i | 0.689472 | − | 0.398067i | ||||
\(151\) | −8.58387 | − | 14.8677i | −0.698545 | − | 1.20992i | −0.968971 | − | 0.247175i | \(-0.920498\pi\) |
0.270425 | − | 0.962741i | \(-0.412836\pi\) | |||||||
\(152\) | −1.03400 | + | 1.79095i | −0.0838688 | + | 0.145265i | ||||
\(153\) | 7.42382 | 0.600180 | ||||||||
\(154\) | 0.588619 | + | 3.88690i | 0.0474323 | + | 0.313216i | ||||
\(155\) | 3.15648i | 0.253535i | ||||||||
\(156\) | −0.100564 | + | 0.174182i | −0.00805159 | + | 0.0139458i | ||||
\(157\) | −0.180567 | − | 0.312751i | −0.0144108 | − | 0.0249602i | 0.858730 | − | 0.512428i | \(-0.171254\pi\) |
−0.873141 | + | 0.487468i | \(0.837921\pi\) | |||||||
\(158\) | 6.55870 | − | 3.78667i | 0.521782 | − | 0.301251i | ||||
\(159\) | −10.0186 | + | 17.3527i | −0.794526 | + | 1.37616i | ||||
\(160\) | 1.02224 | 0.0808155 | ||||||||
\(161\) | −10.7693 | − | 6.70981i | −0.848742 | − | 0.528807i | ||||
\(162\) | 8.75969 | 0.688226 | ||||||||
\(163\) | 12.1574 | − | 21.0573i | 0.952243 | − | 1.64933i | 0.211687 | − | 0.977338i | \(-0.432104\pi\) |
0.740556 | − | 0.671995i | \(-0.234562\pi\) | |||||||
\(164\) | 1.85128 | − | 1.06883i | 0.144560 | − | 0.0834619i | ||||
\(165\) | −1.87234 | − | 3.24300i | −0.145762 | − | 0.252467i | ||||
\(166\) | −1.80657 | + | 3.12907i | −0.140217 | + | 0.242863i | ||||
\(167\) | − | 13.1624i | − | 1.01854i | −0.860607 | − | 0.509270i | \(-0.829915\pi\) | ||
0.860607 | − | 0.509270i | \(-0.170085\pi\) | |||||||
\(168\) | 5.09688 | − | 4.07042i | 0.393233 | − | 0.314040i | ||||
\(169\) | 12.9933 | 0.999488 | ||||||||
\(170\) | 1.23274 | − | 2.13517i | 0.0945471 | − | 0.163760i | ||||
\(171\) | −3.18274 | − | 5.51267i | −0.243390 | − | 0.421564i | ||||
\(172\) | −5.80033 | + | 3.34882i | −0.442271 | + | 0.255345i | ||||
\(173\) | −12.8768 | − | 7.43442i | −0.979005 | − | 0.565229i | −0.0770351 | − | 0.997028i | \(-0.524545\pi\) |
−0.901969 | + | 0.431800i | \(0.857879\pi\) | |||||||
\(174\) | 0.844222i | 0.0640003i | ||||||||
\(175\) | −6.52988 | − | 8.17654i | −0.493612 | − | 0.618089i | ||||
\(176\) | 1.48586i | 0.112001i | ||||||||
\(177\) | 3.53289 | − | 6.11914i | 0.265548 | − | 0.459943i | ||||
\(178\) | −7.27080 | − | 12.5934i | −0.544969 | − | 0.943914i | ||||
\(179\) | −8.23112 | − | 14.2567i | −0.615223 | − | 1.06560i | −0.990345 | − | 0.138622i | \(-0.955733\pi\) |
0.375123 | − | 0.926975i | \(-0.377601\pi\) | |||||||
\(180\) | −1.57327 | + | 2.72498i | −0.117265 | + | 0.203108i | ||||
\(181\) | 20.9810 | 1.55950 | 0.779751 | − | 0.626090i | \(-0.215346\pi\) | ||||
0.779751 | + | 0.626090i | \(0.215346\pi\) | |||||||
\(182\) | 0.200978 | + | 0.0787170i | 0.0148975 | + | 0.00583489i | ||||
\(183\) | − | 5.38049i | − | 0.397737i | ||||||
\(184\) | −3.64481 | − | 3.11694i | −0.268699 | − | 0.229784i | ||||
\(185\) | 0.138125 | − | 0.0797465i | 0.0101551 | − | 0.00586308i | ||||
\(186\) | 3.80629 | + | 6.59269i | 0.279091 | + | 0.483400i | ||||
\(187\) | 3.10354 | + | 1.79183i | 0.226953 | + | 0.131032i | ||||
\(188\) | 4.30334i | 0.313853i | ||||||||
\(189\) | 0.0762501 | + | 0.503512i | 0.00554638 | + | 0.0366251i | ||||
\(190\) | −2.11401 | −0.153366 | ||||||||
\(191\) | 8.61942 | + | 4.97643i | 0.623680 | + | 0.360082i | 0.778300 | − | 0.627892i | \(-0.216082\pi\) |
−0.154621 | + | 0.987974i | \(0.549416\pi\) | |||||||
\(192\) | 2.13508 | − | 1.23269i | 0.154086 | − | 0.0889616i | ||||
\(193\) | 5.53019 | + | 9.57857i | 0.398072 | + | 0.689481i | 0.993488 | − | 0.113937i | \(-0.0363461\pi\) |
−0.595416 | + | 0.803418i | \(0.703013\pi\) | |||||||
\(194\) | 7.75052 | − | 13.4243i | 0.556455 | − | 0.963808i | ||||
\(195\) | −0.205602 | −0.0147235 | ||||||||
\(196\) | −5.13798 | − | 4.75407i | −0.366998 | − | 0.339577i | ||||
\(197\) | −11.3061 | −0.805526 | −0.402763 | − | 0.915304i | \(-0.631950\pi\) | ||||
−0.402763 | + | 0.915304i | \(0.631950\pi\) | |||||||
\(198\) | −3.96085 | − | 2.28680i | −0.281485 | − | 0.162515i | ||||
\(199\) | −6.69299 | − | 11.5926i | −0.474454 | − | 0.821778i | 0.525118 | − | 0.851029i | \(-0.324021\pi\) |
−0.999572 | + | 0.0292512i | \(0.990688\pi\) | |||||||
\(200\) | −1.97751 | − | 3.42515i | −0.139831 | − | 0.242194i | ||||
\(201\) | −19.3370 | + | 33.4926i | −1.36393 | + | 2.36239i | ||||
\(202\) | 16.7554i | 1.17891i | ||||||||
\(203\) | 0.895776 | − | 0.135653i | 0.0628711 | − | 0.00952098i | ||||
\(204\) | − | 5.94609i | − | 0.416309i | ||||||
\(205\) | 1.89245 | + | 1.09261i | 0.132175 | + | 0.0763111i | ||||
\(206\) | −3.89407 | − | 6.74472i | −0.271313 | − | 0.469927i | ||||
\(207\) | 13.9183 | − | 4.91885i | 0.967389 | − | 0.341884i | ||||
\(208\) | 0.0706515 | + | 0.0407907i | 0.00489880 | + | 0.00282832i | ||||
\(209\) | − | 3.07277i | − | 0.212548i | ||||||
\(210\) | 6.20863 | + | 2.43173i | 0.428436 | + | 0.167805i | ||||
\(211\) | −13.3090 | −0.916232 | −0.458116 | − | 0.888892i | \(-0.651476\pi\) | ||||
−0.458116 | + | 0.888892i | \(0.651476\pi\) | |||||||
\(212\) | 7.03856 | + | 4.06372i | 0.483411 | + | 0.279097i | ||||
\(213\) | −16.2535 | + | 9.38394i | −1.11367 | + | 0.642977i | ||||
\(214\) | −5.64261 | + | 3.25776i | −0.385721 | + | 0.222696i | ||||
\(215\) | −5.92935 | − | 3.42331i | −0.404378 | − | 0.233468i | ||||
\(216\) | 0.192480i | 0.0130966i | ||||||||
\(217\) | 6.38367 | − | 5.09807i | 0.433352 | − | 0.346080i | ||||
\(218\) | 17.3014i | 1.17180i | ||||||||
\(219\) | 7.87532 | − | 13.6405i | 0.532165 | − | 0.921736i | ||||
\(220\) | −1.31542 | + | 0.759456i | −0.0886854 | + | 0.0512025i | ||||
\(221\) | 0.170400 | − | 0.0983805i | 0.0114623 | − | 0.00661779i | ||||
\(222\) | 0.192327 | − | 0.333120i | 0.0129081 | − | 0.0223575i | ||||
\(223\) | 13.7849i | 0.923103i | 0.887113 | + | 0.461551i | \(0.152707\pi\) | ||||
−0.887113 | + | 0.461551i | \(0.847293\pi\) | |||||||
\(224\) | −1.65104 | − | 2.06738i | −0.110314 | − | 0.138133i | ||||
\(225\) | 12.1738 | 0.811589 | ||||||||
\(226\) | 13.5273 | + | 7.81001i | 0.899824 | + | 0.519514i | ||||
\(227\) | 4.99408 | + | 8.65000i | 0.331469 | + | 0.574120i | 0.982800 | − | 0.184673i | \(-0.0591226\pi\) |
−0.651331 | + | 0.758793i | \(0.725789\pi\) | |||||||
\(228\) | −4.41536 | + | 2.54921i | −0.292414 | + | 0.168825i | ||||
\(229\) | −7.15920 | + | 12.4001i | −0.473093 | + | 0.819421i | −0.999526 | − | 0.0307956i | \(-0.990196\pi\) |
0.526433 | + | 0.850217i | \(0.323529\pi\) | |||||||
\(230\) | 0.896451 | − | 4.81985i | 0.0591102 | − | 0.317812i | ||||
\(231\) | −3.53459 | + | 9.02442i | −0.232559 | + | 0.593763i | ||||
\(232\) | 0.342432 | 0.0224817 | ||||||||
\(233\) | −9.06280 | + | 15.6972i | −0.593724 | + | 1.02836i | 0.400002 | + | 0.916514i | \(0.369009\pi\) |
−0.993726 | + | 0.111845i | \(0.964324\pi\) | |||||||
\(234\) | −0.217471 | + | 0.125557i | −0.0142165 | + | 0.00820790i | ||||
\(235\) | −3.80970 | + | 2.19953i | −0.248517 | + | 0.143481i | ||||
\(236\) | −2.48203 | − | 1.43300i | −0.161567 | − | 0.0932805i | ||||
\(237\) | 18.6711 | 1.21282 | ||||||||
\(238\) | −6.30919 | + | 0.955442i | −0.408964 | + | 0.0619321i | ||||
\(239\) | 0.994204 | 0.0643097 | 0.0321549 | − | 0.999483i | \(-0.489763\pi\) | ||||
0.0321549 | + | 0.999483i | \(0.489763\pi\) | |||||||
\(240\) | 2.18257 | + | 1.26011i | 0.140884 | + | 0.0813396i | ||||
\(241\) | −8.98769 | − | 15.5671i | −0.578948 | − | 1.00277i | −0.995600 | − | 0.0937016i | \(-0.970130\pi\) |
0.416652 | − | 0.909066i | \(-0.363203\pi\) | |||||||
\(242\) | 4.39611 | + | 7.61428i | 0.282593 | + | 0.489465i | ||||
\(243\) | 19.2027 | + | 11.0867i | 1.23185 | + | 0.711210i | ||||
\(244\) | −2.18242 | −0.139715 | ||||||||
\(245\) | 1.58260 | − | 6.97850i | 0.101108 | − | 0.445840i | ||||
\(246\) | 5.27015 | 0.336013 | ||||||||
\(247\) | −0.146108 | − | 0.0843554i | −0.00929662 | − | 0.00536741i | ||||
\(248\) | 2.67411 | − | 1.54390i | 0.169806 | − | 0.0980378i | ||||
\(249\) | −7.71432 | + | 4.45386i | −0.488875 | + | 0.282252i | ||||
\(250\) | 4.57711 | − | 7.92778i | 0.289482 | − | 0.501397i | ||||
\(251\) | −20.0434 | −1.26513 | −0.632564 | − | 0.774508i | \(-0.717997\pi\) | ||||
−0.632564 | + | 0.774508i | \(0.717997\pi\) | |||||||
\(252\) | 8.05201 | − | 1.21937i | 0.507229 | − | 0.0768130i | ||||
\(253\) | 7.00580 | + | 1.30302i | 0.440451 | + | 0.0819200i | ||||
\(254\) | 3.06443 | − | 5.30774i | 0.192279 | − | 0.333037i | ||||
\(255\) | 5.26401 | − | 3.03917i | 0.329645 | − | 0.190321i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 20.5193 | + | 11.8468i | 1.27996 | + | 0.738984i | 0.976841 | − | 0.213969i | \(-0.0686391\pi\) |
0.303118 | + | 0.952953i | \(0.401972\pi\) | |||||||
\(258\) | −16.5122 | −1.02800 | ||||||||
\(259\) | −0.384366 | − | 0.150544i | −0.0238834 | − | 0.00935438i | ||||
\(260\) | 0.0833960i | 0.00517200i | ||||||||
\(261\) | −0.527015 | + | 0.912816i | −0.0326214 | + | 0.0565019i | ||||
\(262\) | −11.3272 | + | 6.53974i | −0.699794 | + | 0.404026i | ||||
\(263\) | −3.14002 | + | 1.81289i | −0.193622 | + | 0.111788i | −0.593677 | − | 0.804703i | \(-0.702324\pi\) |
0.400055 | + | 0.916491i | \(0.368991\pi\) | |||||||
\(264\) | −1.83160 | + | 3.17243i | −0.112727 | + | 0.195249i | ||||
\(265\) | 8.30822i | 0.510370i | ||||||||
\(266\) | 3.41436 | + | 4.27537i | 0.209348 | + | 0.262140i | ||||
\(267\) | − | 35.8505i | − | 2.19401i | ||||||
\(268\) | 13.5852 | + | 7.84342i | 0.829849 | + | 0.479113i | ||||
\(269\) | 17.0267 | − | 9.83038i | 1.03814 | − | 0.599369i | 0.118832 | − | 0.992914i | \(-0.462085\pi\) |
0.919305 | + | 0.393546i | \(0.128752\pi\) | |||||||
\(270\) | −0.170400 | + | 0.0983805i | −0.0103702 | + | 0.00598725i | ||||
\(271\) | 6.85141 | + | 3.95566i | 0.416193 | + | 0.240289i | 0.693447 | − | 0.720507i | \(-0.256091\pi\) |
−0.277254 | + | 0.960797i | \(0.589424\pi\) | |||||||
\(272\) | −2.41184 | −0.146239 | ||||||||
\(273\) | 0.332071 | + | 0.415810i | 0.0200978 | + | 0.0251660i | ||||
\(274\) | 10.5216i | 0.635633i | ||||||||
\(275\) | 5.08929 | + | 2.93830i | 0.306896 | + | 0.177186i | ||||
\(276\) | −3.93974 | − | 11.1478i | −0.237145 | − | 0.671020i | ||||
\(277\) | 7.97446 | + | 13.8122i | 0.479139 | + | 0.829893i | 0.999714 | − | 0.0239230i | \(-0.00761567\pi\) |
−0.520575 | + | 0.853816i | \(0.674282\pi\) | |||||||
\(278\) | −14.3514 | − | 8.28579i | −0.860740 | − | 0.496949i | ||||
\(279\) | 9.50448i | 0.569018i | ||||||||
\(280\) | 0.986353 | − | 2.51833i | 0.0589458 | − | 0.150499i | ||||
\(281\) | 9.47524i | 0.565246i | 0.959231 | + | 0.282623i | \(0.0912045\pi\) | ||||
−0.959231 | + | 0.282623i | \(0.908796\pi\) | |||||||
\(282\) | −5.30467 | + | 9.18795i | −0.315888 | + | 0.547135i | ||||
\(283\) | 9.94962 | + | 17.2332i | 0.591443 | + | 1.02441i | 0.994038 | + | 0.109032i | \(0.0347750\pi\) |
−0.402595 | + | 0.915378i | \(0.631892\pi\) | |||||||
\(284\) | 3.80629 | + | 6.59269i | 0.225862 | + | 0.391204i | ||||
\(285\) | −4.51357 | − | 2.60591i | −0.267361 | − | 0.154361i | ||||
\(286\) | −0.121219 | −0.00716780 | ||||||||
\(287\) | −0.846830 | − | 5.59198i | −0.0499868 | − | 0.330084i | ||||
\(288\) | 3.07807 | 0.181377 | ||||||||
\(289\) | 5.59152 | − | 9.68479i | 0.328913 | − | 0.569694i | ||||
\(290\) | 0.175024 | + | 0.303151i | 0.0102778 | + | 0.0178016i | ||||
\(291\) | 33.0959 | − | 19.1079i | 1.94012 | − | 1.12013i | ||||
\(292\) | −5.53281 | − | 3.19437i | −0.323783 | − | 0.186936i | ||||
\(293\) | −5.49722 | −0.321151 | −0.160576 | − | 0.987024i | \(-0.551335\pi\) | ||||
−0.160576 | + | 0.987024i | \(0.551335\pi\) | |||||||
\(294\) | −5.10969 | − | 16.4838i | −0.298003 | − | 0.961357i | ||||
\(295\) | − | 2.92975i | − | 0.170577i | ||||||
\(296\) | −0.135119 | − | 0.0780112i | −0.00785366 | − | 0.00453431i | ||||
\(297\) | −0.142999 | − | 0.247681i | −0.00829764 | − | 0.0143719i | ||||
\(298\) | −9.44175 | + | 5.45120i | −0.546946 | + | 0.315779i | ||||
\(299\) | 0.254284 | − | 0.297349i | 0.0147056 | − | 0.0171961i | ||||
\(300\) | − | 9.75060i | − | 0.562951i | ||||||
\(301\) | 2.65325 | + | 17.5205i | 0.152931 | + | 1.00987i | ||||
\(302\) | −17.1677 | −0.987892 | ||||||||
\(303\) | −20.6542 | + | 35.7741i | −1.18655 | + | 2.05517i | ||||
\(304\) | 1.03400 | + | 1.79095i | 0.0593042 | + | 0.102718i | ||||
\(305\) | −1.11548 | − | 1.93208i | −0.0638724 | − | 0.110630i | ||||
\(306\) | 3.71191 | − | 6.42921i | 0.212196 | − | 0.367534i | ||||
\(307\) | − | 13.1660i | − | 0.751426i | −0.926736 | − | 0.375713i | \(-0.877398\pi\) | ||
0.926736 | − | 0.375713i | \(-0.122602\pi\) | |||||||
\(308\) | 3.66047 | + | 1.43369i | 0.208574 | + | 0.0816922i | ||||
\(309\) | − | 19.2007i | − | 1.09229i | ||||||
\(310\) | 2.73360 | + | 1.57824i | 0.155258 | + | 0.0896381i | ||||
\(311\) | −7.00742 | + | 4.04574i | −0.397354 | + | 0.229413i | −0.685342 | − | 0.728222i | \(-0.740347\pi\) |
0.287987 | + | 0.957634i | \(0.407014\pi\) | |||||||
\(312\) | 0.100564 | + | 0.174182i | 0.00569333 | + | 0.00986114i | ||||
\(313\) | 9.29473 | − | 16.0989i | 0.525369 | − | 0.909966i | −0.474194 | − | 0.880420i | \(-0.657261\pi\) |
0.999563 | − | 0.0295456i | \(-0.00940604\pi\) | |||||||
\(314\) | −0.361133 | −0.0203799 | ||||||||
\(315\) | 5.19505 | + | 6.50511i | 0.292708 | + | 0.366522i | ||||
\(316\) | − | 7.57333i | − | 0.426033i | ||||||
\(317\) | 2.54483 | − | 4.40778i | 0.142932 | − | 0.247566i | −0.785667 | − | 0.618649i | \(-0.787680\pi\) |
0.928600 | + | 0.371083i | \(0.121014\pi\) | |||||||
\(318\) | 10.0186 | + | 17.3527i | 0.561814 | + | 0.973091i | ||||
\(319\) | −0.440639 | + | 0.254403i | −0.0246710 | + | 0.0142438i | ||||
\(320\) | 0.511122 | − | 0.885289i | 0.0285726 | − | 0.0494892i | ||||
\(321\) | −16.0632 | −0.896560 | ||||||||
\(322\) | −11.1955 | + | 5.97161i | −0.623903 | + | 0.332785i | ||||
\(323\) | 4.98770 | 0.277523 | ||||||||
\(324\) | 4.37984 | − | 7.58611i | 0.243325 | − | 0.421451i | ||||
\(325\) | 0.279428 | − | 0.161328i | 0.0154999 | − | 0.00894886i | ||||
\(326\) | −12.1574 | − | 21.0573i | −0.673337 | − | 1.16625i | ||||
\(327\) | −21.3272 | + | 36.9398i | −1.17940 | + | 2.04278i | ||||
\(328\) | − | 2.13767i | − | 0.118033i | ||||||
\(329\) | 10.6014 | + | 4.15224i | 0.584474 | + | 0.228921i | ||||
\(330\) | −3.74469 | −0.206138 | ||||||||
\(331\) | −4.57645 | + | 7.92664i | −0.251544 | + | 0.435688i | −0.963951 | − | 0.266079i | \(-0.914272\pi\) |
0.712407 | + | 0.701767i | \(0.247605\pi\) | |||||||
\(332\) | 1.80657 | + | 3.12907i | 0.0991482 | + | 0.171730i | ||||
\(333\) | 0.415907 | − | 0.240124i | 0.0227916 | − | 0.0131587i | ||||
\(334\) | −11.3990 | − | 6.58122i | −0.623726 | − | 0.360108i | ||||
\(335\) | 16.0358i | 0.876128i | ||||||||
\(336\) | −0.976650 | − | 6.44924i | −0.0532806 | − | 0.351835i | ||||
\(337\) | − | 20.4152i | − | 1.11209i | −0.831153 | − | 0.556044i | \(-0.812319\pi\) | ||
0.831153 | − | 0.556044i | \(-0.187681\pi\) | |||||||
\(338\) | 6.49667 | − | 11.2526i | 0.353372 | − | 0.612059i | ||||
\(339\) | 19.2546 | + | 33.3499i | 1.04577 | + | 1.81132i | ||||
\(340\) | −1.23274 | − | 2.13517i | −0.0668549 | − | 0.115796i | ||||
\(341\) | −2.29402 | + | 3.97336i | −0.124228 | + | 0.215170i | ||||
\(342\) | −6.36548 | −0.344206 | ||||||||
\(343\) | −16.6694 | + | 8.07041i | −0.900062 | + | 0.435761i | ||||
\(344\) | 6.69764i | 0.361113i | ||||||||
\(345\) | 7.85536 | − | 9.18571i | 0.422919 | − | 0.494542i | ||||
\(346\) | −12.8768 | + | 7.43442i | −0.692261 | + | 0.399677i | ||||
\(347\) | 15.5611 | + | 26.9526i | 0.835364 | + | 1.44689i | 0.893734 | + | 0.448597i | \(0.148076\pi\) |
−0.0583706 | + | 0.998295i | \(0.518591\pi\) | |||||||
\(348\) | 0.731118 | + | 0.422111i | 0.0391920 | + | 0.0226275i | ||||
\(349\) | − | 10.4339i | − | 0.558517i | −0.960216 | − | 0.279258i | \(-0.909911\pi\) | ||
0.960216 | − | 0.279258i | \(-0.0900886\pi\) | |||||||
\(350\) | −10.3460 | + | 1.56677i | −0.553019 | + | 0.0837472i | ||||
\(351\) | −0.0157027 | −0.000838150 | ||||||||
\(352\) | 1.28679 | + | 0.742931i | 0.0685863 | + | 0.0395983i | ||||
\(353\) | −5.09731 | + | 2.94294i | −0.271303 | + | 0.156637i | −0.629479 | − | 0.777017i | \(-0.716732\pi\) |
0.358177 | + | 0.933654i | \(0.383398\pi\) | |||||||
\(354\) | −3.53289 | − | 6.11914i | −0.187771 | − | 0.325229i | ||||
\(355\) | −3.89096 | + | 6.73934i | −0.206511 | + | 0.357687i | ||||
\(356\) | −14.5416 | −0.770703 | ||||||||
\(357\) | −14.6484 | − | 5.73732i | −0.775274 | − | 0.303651i | ||||
\(358\) | −16.4622 | −0.870056 | ||||||||
\(359\) | 3.49303 | + | 2.01670i | 0.184355 | + | 0.106437i | 0.589337 | − | 0.807887i | \(-0.299389\pi\) |
−0.404982 | + | 0.914325i | \(0.632722\pi\) | |||||||
\(360\) | 1.57327 | + | 2.72498i | 0.0829186 | + | 0.143619i | ||||
\(361\) | 7.36167 | + | 12.7508i | 0.387456 | + | 0.671094i | ||||
\(362\) | 10.4905 | − | 18.1700i | 0.551367 | − | 0.954996i | ||||
\(363\) | 21.6761i | 1.13770i | ||||||||
\(364\) | 0.168660 | − | 0.134694i | 0.00884019 | − | 0.00705987i | ||||
\(365\) | − | 6.53085i | − | 0.341840i | ||||||
\(366\) | −4.65964 | − | 2.69025i | −0.243563 | − | 0.140621i | ||||
\(367\) | 16.5648 | + | 28.6912i | 0.864678 | + | 1.49767i | 0.867367 | + | 0.497670i | \(0.165811\pi\) |
−0.00268854 | + | 0.999996i | \(0.500856\pi\) | |||||||
\(368\) | −4.52176 | + | 1.59803i | −0.235713 | + | 0.0833031i | ||||
\(369\) | 5.69836 | + | 3.28995i | 0.296645 | + | 0.171268i | ||||
\(370\) | − | 0.159493i | − | 0.00829164i | ||||||
\(371\) | 16.8025 | − | 13.4187i | 0.872344 | − | 0.696664i | ||||
\(372\) | 7.61259 | 0.394694 | ||||||||
\(373\) | 2.62443 | + | 1.51522i | 0.135888 | + | 0.0784549i | 0.566403 | − | 0.824129i | \(-0.308335\pi\) |
−0.430515 | + | 0.902583i | \(0.641668\pi\) | |||||||
\(374\) | 3.10354 | − | 1.79183i | 0.160480 | − | 0.0926533i | ||||
\(375\) | 19.5449 | − | 11.2843i | 1.00930 | − | 0.582718i | ||||
\(376\) | 3.72680 | + | 2.15167i | 0.192195 | + | 0.110964i | ||||
\(377\) | 0.0279360i | 0.00143878i | ||||||||
\(378\) | 0.474179 | + | 0.185722i | 0.0243892 | + | 0.00955249i | ||||
\(379\) | − | 20.8285i | − | 1.06989i | −0.844888 | − | 0.534943i | \(-0.820333\pi\) | ||
0.844888 | − | 0.534943i | \(-0.179667\pi\) | |||||||
\(380\) | −1.05700 | + | 1.83078i | −0.0542232 | + | 0.0939173i | ||||
\(381\) | 13.0856 | − | 7.55496i | 0.670394 | − | 0.387052i | ||||
\(382\) | 8.61942 | − | 4.97643i | 0.441008 | − | 0.254616i | ||||
\(383\) | 14.8397 | − | 25.7031i | 0.758272 | − | 1.31337i | −0.185458 | − | 0.982652i | \(-0.559377\pi\) |
0.943731 | − | 0.330714i | \(-0.107290\pi\) | |||||||
\(384\) | − | 2.46537i | − | 0.125811i | ||||||
\(385\) | 0.601712 | + | 3.97336i | 0.0306661 | + | 0.202501i | ||||
\(386\) | 11.0604 | 0.562959 | ||||||||
\(387\) | −17.8538 | − | 10.3079i | −0.907561 | − | 0.523981i | ||||
\(388\) | −7.75052 | − | 13.4243i | −0.393473 | − | 0.681515i | ||||
\(389\) | 8.91834 | − | 5.14901i | 0.452178 | − | 0.261065i | −0.256572 | − | 0.966525i | \(-0.582593\pi\) |
0.708750 | + | 0.705460i | \(0.249260\pi\) | |||||||
\(390\) | −0.102801 | + | 0.178057i | −0.00520554 | + | 0.00901626i | ||||
\(391\) | −2.11505 | + | 11.3718i | −0.106963 | + | 0.575094i | ||||
\(392\) | −6.68614 | + | 2.07258i | −0.337701 | + | 0.104681i | ||||
\(393\) | −32.2458 | −1.62659 | ||||||||
\(394\) | −5.65304 | + | 9.79136i | −0.284796 | + | 0.493282i | ||||
\(395\) | 6.70459 | − | 3.87089i | 0.337344 | − | 0.194766i | ||||
\(396\) | −3.96085 | + | 2.28680i | −0.199040 | + | 0.114916i | ||||
\(397\) | 24.4139 | + | 14.0954i | 1.22530 | + | 0.707427i | 0.966043 | − | 0.258381i | \(-0.0831891\pi\) |
0.259257 | + | 0.965808i | \(0.416522\pi\) | |||||||
\(398\) | −13.3860 | −0.670979 | ||||||||
\(399\) | 2.01972 | + | 13.3371i | 0.101112 | + | 0.667689i | ||||
\(400\) | −3.95502 | −0.197751 | ||||||||
\(401\) | −8.50199 | − | 4.90863i | −0.424569 | − | 0.245125i | 0.272461 | − | 0.962167i | \(-0.412162\pi\) |
−0.697030 | + | 0.717042i | \(0.745496\pi\) | |||||||
\(402\) | 19.3370 | + | 33.4926i | 0.964441 | + | 1.67046i | ||||
\(403\) | 0.125953 | + | 0.218158i | 0.00627419 | + | 0.0108672i | ||||
\(404\) | 14.5106 | + | 8.37770i | 0.721929 | + | 0.416806i | ||||
\(405\) | 8.95453 | 0.444954 | ||||||||
\(406\) | 0.330409 | − | 0.843591i | 0.0163979 | − | 0.0418667i | ||||
\(407\) | 0.231828 | 0.0114913 | ||||||||
\(408\) | −5.14946 | − | 2.97304i | −0.254936 | − | 0.147188i | ||||
\(409\) | 6.44300 | − | 3.71987i | 0.318586 | − | 0.183936i | −0.332176 | − | 0.943217i | \(-0.607783\pi\) |
0.650762 | + | 0.759282i | \(0.274450\pi\) | |||||||
\(410\) | 1.89245 | − | 1.09261i | 0.0934617 | − | 0.0539601i | ||||
\(411\) | −12.9698 | + | 22.4644i | −0.639755 | + | 1.10809i | ||||
\(412\) | −7.78814 | −0.383694 | ||||||||
\(413\) | −5.92513 | + | 4.73188i | −0.291557 | + | 0.232840i | ||||
\(414\) | 2.69930 | − | 14.5130i | 0.132663 | − | 0.713277i | ||||
\(415\) | −1.84675 | + | 3.19867i | −0.0906535 | + | 0.157016i | ||||
\(416\) | 0.0706515 | − | 0.0407907i | 0.00346398 | − | 0.00199993i | ||||
\(417\) | −20.4276 | − | 35.3816i | −1.00034 | − | 1.73264i | ||||
\(418\) | −2.66110 | − | 1.53639i | −0.130159 | − | 0.0751471i | ||||
\(419\) | −32.1651 | −1.57137 | −0.785684 | − | 0.618628i | \(-0.787689\pi\) | ||||
−0.785684 | + | 0.618628i | \(0.787689\pi\) | |||||||
\(420\) | 5.21025 | − | 4.16096i | 0.254234 | − | 0.203034i | ||||
\(421\) | − | 0.626009i | − | 0.0305098i | −0.999884 | − | 0.0152549i | \(-0.995144\pi\) | ||
0.999884 | − | 0.0152549i | \(-0.00485597\pi\) | |||||||
\(422\) | −6.65452 | + | 11.5260i | −0.323937 | + | 0.561075i | ||||
\(423\) | −11.4714 | + | 6.62299i | −0.557756 | + | 0.322021i | ||||
\(424\) | 7.03856 | − | 4.06372i | 0.341823 | − | 0.197352i | ||||
\(425\) | −4.76943 | + | 8.26090i | −0.231351 | + | 0.400712i | ||||
\(426\) | 18.7679i | 0.909307i | ||||||||
\(427\) | −2.10580 | + | 5.37647i | −0.101907 | + | 0.260186i | ||||
\(428\) | 6.51552i | 0.314940i | ||||||||
\(429\) | −0.258811 | − | 0.149425i | −0.0124955 | − | 0.00721429i | ||||
\(430\) | −5.92935 | + | 3.42331i | −0.285939 | + | 0.165087i | ||||
\(431\) | 31.1064 | − | 17.9593i | 1.49834 | − | 0.865068i | 0.498343 | − | 0.866980i | \(-0.333942\pi\) |
0.999998 | + | 0.00191218i | \(0.000608667\pi\) | |||||||
\(432\) | 0.166692 | + | 0.0962398i | 0.00801998 | + | 0.00463034i | ||||
\(433\) | −9.42386 | −0.452882 | −0.226441 | − | 0.974025i | \(-0.572709\pi\) | ||||
−0.226441 | + | 0.974025i | \(0.572709\pi\) | |||||||
\(434\) | −1.22322 | − | 8.07746i | −0.0587165 | − | 0.387730i | ||||
\(435\) | 0.863001i | 0.0413777i | ||||||||
\(436\) | 14.9835 | + | 8.65070i | 0.717577 | + | 0.414293i | ||||
\(437\) | 9.35103 | − | 3.30474i | 0.447321 | − | 0.158087i | ||||
\(438\) | −7.87532 | − | 13.6405i | −0.376297 | − | 0.651766i | ||||
\(439\) | −21.4226 | − | 12.3684i | −1.02245 | − | 0.590309i | −0.107634 | − | 0.994191i | \(-0.534328\pi\) |
−0.914811 | + | 0.403881i | \(0.867661\pi\) | |||||||
\(440\) | 1.51891i | 0.0724113i | ||||||||
\(441\) | 4.76535 | − | 21.0129i | 0.226921 | − | 1.00062i | ||||
\(442\) | − | 0.196761i | − | 0.00935897i | ||||||
\(443\) | −3.93090 | + | 6.80852i | −0.186763 | + | 0.323483i | −0.944169 | − | 0.329461i | \(-0.893133\pi\) |
0.757406 | + | 0.652944i | \(0.226466\pi\) | |||||||
\(444\) | −0.192327 | − | 0.333120i | −0.00912743 | − | 0.0158092i | ||||
\(445\) | −7.43253 | − | 12.8735i | −0.352336 | − | 0.610263i | ||||
\(446\) | 11.9380 | + | 6.89243i | 0.565283 | + | 0.326366i | ||||
\(447\) | −26.8785 | −1.27131 | ||||||||
\(448\) | −2.61593 | + | 0.396147i | −0.123591 | + | 0.0187162i | ||||
\(449\) | 19.7956 | 0.934213 | 0.467107 | − | 0.884201i | \(-0.345296\pi\) | ||||
0.467107 | + | 0.884201i | \(0.345296\pi\) | |||||||
\(450\) | 6.08692 | − | 10.5428i | 0.286940 | − | 0.496995i | ||||
\(451\) | 1.58814 | + | 2.75074i | 0.0747826 | + | 0.129527i | ||||
\(452\) | 13.5273 | − | 7.81001i | 0.636272 | − | 0.367352i | ||||
\(453\) | −36.6544 | − | 21.1625i | −1.72218 | − | 0.994299i | ||||
\(454\) | 9.98815 | 0.468767 | ||||||||
\(455\) | 0.205449 | + | 0.0804680i | 0.00963158 | + | 0.00377240i | ||||
\(456\) | 5.09841i | 0.238755i | ||||||||
\(457\) | −6.77168 | − | 3.90963i | −0.316766 | − | 0.182885i | 0.333184 | − | 0.942862i | \(-0.391877\pi\) |
−0.649950 | + | 0.759977i | \(0.725210\pi\) | |||||||
\(458\) | 7.15920 | + | 12.4001i | 0.334527 | + | 0.579418i | ||||
\(459\) | 0.402035 | − | 0.232115i | 0.0187654 | − | 0.0108342i | ||||
\(460\) | −3.72589 | − | 3.18628i | −0.173720 | − | 0.148561i | ||||
\(461\) | − | 5.25112i | − | 0.244569i | −0.992495 | − | 0.122284i | \(-0.960978\pi\) | ||
0.992495 | − | 0.122284i | \(-0.0390220\pi\) | |||||||
\(462\) | 6.04808 | + | 7.57326i | 0.281382 | + | 0.352340i | ||||
\(463\) | −6.73239 | −0.312881 | −0.156440 | − | 0.987687i | \(-0.550002\pi\) | ||||
−0.156440 | + | 0.987687i | \(0.550002\pi\) | |||||||
\(464\) | 0.171216 | − | 0.296554i | 0.00794849 | − | 0.0137672i | ||||
\(465\) | 3.89096 | + | 6.73934i | 0.180439 | + | 0.312529i | ||||
\(466\) | 9.06280 | + | 15.6972i | 0.419826 | + | 0.727160i | ||||
\(467\) | 6.40963 | − | 11.1018i | 0.296602 | − | 0.513730i | −0.678754 | − | 0.734366i | \(-0.737480\pi\) |
0.975356 | + | 0.220636i | \(0.0708131\pi\) | |||||||
\(468\) | 0.251113i | 0.0116077i | ||||||||
\(469\) | 32.4308 | − | 25.8995i | 1.49751 | − | 1.19593i | ||||
\(470\) | 4.39906i | 0.202913i | ||||||||
\(471\) | −0.771048 | − | 0.445165i | −0.0355280 | − | 0.0205121i | ||||
\(472\) | −2.48203 | + | 1.43300i | −0.114245 | + | 0.0659593i | ||||
\(473\) | −4.97588 | − | 8.61848i | −0.228791 | − | 0.396278i | ||||
\(474\) | 9.33555 | − | 16.1696i | 0.428796 | − | 0.742696i | ||||
\(475\) | 8.17901 | 0.375279 | ||||||||
\(476\) | −2.32716 | + | 5.94164i | −0.106665 | + | 0.272335i | ||||
\(477\) | 25.0168i | 1.14544i | ||||||||
\(478\) | 0.497102 | − | 0.861006i | 0.0227369 | − | 0.0393815i | ||||
\(479\) | 3.59812 | + | 6.23212i | 0.164402 | + | 0.284753i | 0.936443 | − | 0.350820i | \(-0.114097\pi\) |
−0.772041 | + | 0.635573i | \(0.780764\pi\) | |||||||
\(480\) | 2.18257 | − | 1.26011i | 0.0996202 | − | 0.0575158i | ||||
\(481\) | 0.00636426 | − | 0.0110232i | 0.000290185 | − | 0.000502616i | ||||
\(482\) | −17.9754 | −0.818756 | ||||||||
\(483\) | −31.2644 | − | 1.05075i | −1.42258 | − | 0.0478106i | ||||
\(484\) | 8.79222 | 0.399646 | ||||||||
\(485\) | 7.92292 | − | 13.7229i | 0.359761 | − | 0.623125i | ||||
\(486\) | 19.2027 | − | 11.0867i | 0.871051 | − | 0.502902i | ||||
\(487\) | −7.22065 | − | 12.5065i | −0.327199 | − | 0.566725i | 0.654756 | − | 0.755840i | \(-0.272771\pi\) |
−0.981955 | + | 0.189115i | \(0.939438\pi\) | |||||||
\(488\) | −1.09121 | + | 1.89003i | −0.0493968 | + | 0.0855578i | ||||
\(489\) | − | 59.9452i | − | 2.71082i | ||||||
\(490\) | −5.25226 | − | 4.85982i | −0.237273 | − | 0.219544i | ||||
\(491\) | 36.8916 | 1.66490 | 0.832448 | − | 0.554103i | \(-0.186939\pi\) | ||||
0.832448 | + | 0.554103i | \(0.186939\pi\) | |||||||
\(492\) | 2.63508 | − | 4.56409i | 0.118798 | − | 0.205765i | ||||
\(493\) | −0.412945 | − | 0.715242i | −0.0185981 | − | 0.0322129i | ||||
\(494\) | −0.146108 | + | 0.0843554i | −0.00657370 | + | 0.00379533i | ||||
\(495\) | −4.04895 | − | 2.33766i | −0.181987 | − | 0.105070i | ||||
\(496\) | − | 3.08780i | − | 0.138646i | ||||||
\(497\) | 19.9140 | − | 3.01570i | 0.893263 | − | 0.135273i | ||||
\(498\) | 8.90773i | 0.399165i | ||||||||
\(499\) | 2.83621 | − | 4.91245i | 0.126966 | − | 0.219912i | −0.795534 | − | 0.605909i | \(-0.792809\pi\) |
0.922500 | + | 0.385998i | \(0.126143\pi\) | |||||||
\(500\) | −4.57711 | − | 7.92778i | −0.204694 | − | 0.354541i | ||||
\(501\) | −16.2252 | − | 28.1028i | −0.724887 | − | 1.25554i | ||||
\(502\) | −10.0217 | + | 17.3581i | −0.447290 | + | 0.774729i | ||||
\(503\) | −27.9984 | −1.24839 | −0.624194 | − | 0.781269i | \(-0.714573\pi\) | ||||
−0.624194 | + | 0.781269i | \(0.714573\pi\) | |||||||
\(504\) | 2.97000 | − | 7.58293i | 0.132294 | − | 0.337771i | ||||
\(505\) | 17.1281i | 0.762190i | ||||||||
\(506\) | 4.63134 | − | 5.41569i | 0.205888 | − | 0.240757i | ||||
\(507\) | 27.7418 | − | 16.0167i | 1.23206 | − | 0.711328i | ||||
\(508\) | −3.06443 | − | 5.30774i | −0.135962 | − | 0.235493i | ||||
\(509\) | 27.6822 | + | 15.9823i | 1.22699 | + | 0.708403i | 0.966399 | − | 0.257046i | \(-0.0827491\pi\) |
0.260592 | + | 0.965449i | \(0.416082\pi\) | |||||||
\(510\) | − | 6.07835i | − | 0.269154i | ||||||
\(511\) | −13.2080 | + | 10.5480i | −0.584287 | + | 0.466618i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.344721 | − | 0.199025i | −0.0152198 | − | 0.00878715i | ||||
\(514\) | 20.5193 | − | 11.8468i | 0.905067 | − | 0.522541i | ||||
\(515\) | −3.98069 | − | 6.89475i | −0.175410 | − | 0.303819i | ||||
\(516\) | −8.25610 | + | 14.3000i | −0.363454 | + | 0.629522i | ||||
\(517\) | −6.39416 | −0.281215 | ||||||||
\(518\) | −0.322558 | + | 0.257599i | −0.0141724 | + | 0.0113182i | ||||
\(519\) | −36.6573 | −1.60908 | ||||||||
\(520\) | 0.0722231 | + | 0.0416980i | 0.00316719 | + | 0.00182858i | ||||
\(521\) | −15.6394 | − | 27.0883i | −0.685175 | − | 1.18676i | −0.973382 | − | 0.229190i | \(-0.926392\pi\) |
0.288207 | − | 0.957568i | \(-0.406941\pi\) | |||||||
\(522\) | 0.527015 | + | 0.912816i | 0.0230668 | + | 0.0399529i | ||||
\(523\) | 15.2538 | − | 26.4204i | 0.667004 | − | 1.15528i | −0.311734 | − | 0.950169i | \(-0.600910\pi\) |
0.978738 | − | 0.205115i | \(-0.0657569\pi\) | |||||||
\(524\) | 13.0795i | 0.571380i | ||||||||
\(525\) | −24.0209 | − | 9.40826i | −1.04836 | − | 0.410610i | ||||
\(526\) | 3.62578i | 0.158092i | ||||||||
\(527\) | −6.44953 | − | 3.72364i | −0.280946 | − | 0.162204i | ||||
\(528\) | 1.83160 | + | 3.17243i | 0.0797103 | + | 0.138062i | ||||
\(529\) | 3.56934 | + | 22.7214i | 0.155189 | + | 0.987885i | ||||
\(530\) | 7.19513 | + | 4.15411i | 0.312536 | + | 0.180443i | ||||
\(531\) | − | 8.82177i | − | 0.382832i | ||||||
\(532\) | 5.40976 | − | 0.819234i | 0.234543 | − | 0.0355183i | ||||
\(533\) | 0.174394 | 0.00755384 | ||||||||
\(534\) | −31.0474 | − | 17.9252i | −1.34355 | − | 0.775701i | ||||
\(535\) | −5.76812 | + | 3.33022i | −0.249378 | + | 0.143978i | ||||
\(536\) | 13.5852 | − | 7.84342i | 0.586792 | − | 0.338784i | ||||
\(537\) | −35.1481 | − | 20.2928i | −1.51675 | − | 0.875699i | ||||
\(538\) | − | 19.6608i | − | 0.847635i | ||||||
\(539\) | 7.06389 | − | 7.63432i | 0.304263 | − | 0.328833i | ||||
\(540\) | 0.196761i | 0.00846725i | ||||||||
\(541\) | 18.7925 | − | 32.5496i | 0.807953 | − | 1.39941i | −0.106327 | − | 0.994331i | \(-0.533909\pi\) |
0.914280 | − | 0.405084i | \(-0.132758\pi\) | |||||||
\(542\) | 6.85141 | − | 3.95566i | 0.294293 | − | 0.169910i | ||||
\(543\) | 44.7960 | − | 25.8630i | 1.92238 | − | 1.10989i | ||||
\(544\) | −1.20592 | + | 2.08871i | −0.0517034 | + | 0.0895529i | ||||
\(545\) | 17.6863i | 0.757596i | ||||||||
\(546\) | 0.526137 | − | 0.0796764i | 0.0225166 | − | 0.00340984i | ||||
\(547\) | 0.838058 | 0.0358328 | 0.0179164 | − | 0.999839i | \(-0.494297\pi\) | ||||
0.0179164 | + | 0.999839i | \(0.494297\pi\) | |||||||
\(548\) | 9.11197 | + | 5.26080i | 0.389244 | + | 0.224730i | ||||
\(549\) | −3.35883 | − | 5.81766i | −0.143351 | − | 0.248292i | ||||
\(550\) | 5.08929 | − | 2.93830i | 0.217008 | − | 0.125290i | ||||
\(551\) | −0.354076 | + | 0.613277i | −0.0150841 | + | 0.0261265i | ||||
\(552\) | −11.6242 | − | 2.16200i | −0.494758 | − | 0.0920207i | ||||
\(553\) | −18.6571 | − | 7.30743i | −0.793382 | − | 0.310744i | ||||
\(554\) | 15.9489 | 0.677605 | ||||||||
\(555\) | 0.196605 | − | 0.340530i | 0.00834542 | − | 0.0144547i | ||||
\(556\) | −14.3514 | + | 8.28579i | −0.608635 | + | 0.351396i | ||||
\(557\) | −14.2817 | + | 8.24557i | −0.605137 | + | 0.349376i | −0.771060 | − | 0.636763i | \(-0.780273\pi\) |
0.165923 | + | 0.986139i | \(0.446940\pi\) | |||||||
\(558\) | 8.23112 | + | 4.75224i | 0.348451 | + | 0.201178i | ||||
\(559\) | −0.546403 | −0.0231104 | ||||||||
\(560\) | −1.68776 | − | 2.11337i | −0.0713209 | − | 0.0893062i | ||||
\(561\) | 8.83506 | 0.373017 | ||||||||
\(562\) | 8.20580 | + | 4.73762i | 0.346141 | + | 0.199845i | ||||
\(563\) | 16.6530 | + | 28.8438i | 0.701840 | + | 1.21562i | 0.967820 | + | 0.251645i | \(0.0809714\pi\) |
−0.265979 | + | 0.963979i | \(0.585695\pi\) | |||||||
\(564\) | 5.30467 | + | 9.18795i | 0.223367 | + | 0.386883i | ||||
\(565\) | 13.8282 | + | 7.98373i | 0.581758 | + | 0.335878i | ||||
\(566\) | 19.8992 | 0.836427 | ||||||||
\(567\) | −14.4626 | − | 18.1096i | −0.607370 | − | 0.760533i | ||||
\(568\) | 7.61259 | 0.319417 | ||||||||
\(569\) | 19.6304 | + | 11.3336i | 0.822951 | + | 0.475131i | 0.851433 | − | 0.524463i | \(-0.175734\pi\) |
−0.0284820 | + | 0.999594i | \(0.509067\pi\) | |||||||
\(570\) | −4.51357 | + | 2.60591i | −0.189053 | + | 0.109150i | ||||
\(571\) | −4.61506 | + | 2.66451i | −0.193134 | + | 0.111506i | −0.593449 | − | 0.804872i | \(-0.702234\pi\) |
0.400315 | + | 0.916378i | \(0.368901\pi\) | |||||||
\(572\) | −0.0606093 | + | 0.104978i | −0.00253420 | + | 0.00438937i | ||||
\(573\) | 24.5375 | 1.02507 | ||||||||
\(574\) | −5.26621 | − | 2.06261i | −0.219808 | − | 0.0860919i | ||||
\(575\) | −3.46833 | + | 18.6478i | −0.144639 | + | 0.777667i | ||||
\(576\) | 1.53904 | − | 2.66569i | 0.0641265 | − | 0.111070i | ||||
\(577\) | 4.66357 | − | 2.69251i | 0.194147 | − | 0.112091i | −0.399776 | − | 0.916613i | \(-0.630912\pi\) |
0.593922 | + | 0.804522i | \(0.297579\pi\) | |||||||
\(578\) | −5.59152 | − | 9.68479i | −0.232576 | − | 0.402834i | ||||
\(579\) | 23.6148 | + | 13.6340i | 0.981397 | + | 0.566610i | ||||
\(580\) | 0.350049 | 0.0145350 | ||||||||
\(581\) | 9.45169 | − | 1.43133i | 0.392122 | − | 0.0593816i | ||||
\(582\) | − | 38.2159i | − | 1.58410i | ||||||
\(583\) | −6.03812 | + | 10.4583i | −0.250073 | + | 0.433140i | ||||
\(584\) | −5.53281 | + | 3.19437i | −0.228949 | + | 0.132184i | ||||
\(585\) | −0.222308 | + | 0.128350i | −0.00919130 | + | 0.00530660i | ||||
\(586\) | −2.74861 | + | 4.76074i | −0.113544 | + | 0.196664i | ||||
\(587\) | 29.0516i | 1.19909i | 0.800342 | + | 0.599543i | \(0.204651\pi\) | ||||
−0.800342 | + | 0.599543i | \(0.795349\pi\) | |||||||
\(588\) | −16.8303 | − | 3.81680i | −0.694068 | − | 0.157402i | ||||
\(589\) | 6.38560i | 0.263114i | ||||||||
\(590\) | −2.53724 | − | 1.46488i | −0.104457 | − | 0.0603081i | ||||
\(591\) | −24.1394 | + | 13.9369i | −0.992961 | + | 0.573286i | ||||
\(592\) | −0.135119 | + | 0.0780112i | −0.00555337 | + | 0.00320624i | ||||
\(593\) | −11.5856 | − | 6.68893i | −0.475762 | − | 0.274682i | 0.242886 | − | 0.970055i | \(-0.421906\pi\) |
−0.718649 | + | 0.695373i | \(0.755239\pi\) | |||||||
\(594\) | −0.285998 | −0.0117346 | ||||||||
\(595\) | −6.44953 | + | 0.976694i | −0.264405 | + | 0.0400406i | ||||
\(596\) | 10.9024i | 0.446580i | ||||||||
\(597\) | −28.5801 | − | 16.5007i | −1.16971 | − | 0.675330i | ||||
\(598\) | −0.130369 | − | 0.368891i | −0.00533120 | − | 0.0150851i | ||||
\(599\) | 13.1165 | + | 22.7184i | 0.535925 | + | 0.928249i | 0.999118 | + | 0.0419915i | \(0.0133702\pi\) |
−0.463193 | + | 0.886257i | \(0.653296\pi\) | |||||||
\(600\) | −8.44427 | − | 4.87530i | −0.344736 | − | 0.199033i | ||||
\(601\) | 6.64915i | 0.271225i | 0.990762 | + | 0.135612i | \(0.0433002\pi\) | ||||
−0.990762 | + | 0.135612i | \(0.956700\pi\) | |||||||
\(602\) | 16.4999 | + | 6.46249i | 0.672484 | + | 0.263391i | ||||
\(603\) | 48.2853i | 1.96633i | ||||||||
\(604\) | −8.58387 | + | 14.8677i | −0.349273 | + | 0.604958i | ||||
\(605\) | 4.49389 | + | 7.78365i | 0.182703 | + | 0.316450i | ||||
\(606\) | 20.6542 | + | 35.7741i | 0.839018 | + | 1.45322i | ||||
\(607\) | −7.01860 | − | 4.05219i | −0.284876 | − | 0.164473i | 0.350753 | − | 0.936468i | \(-0.385926\pi\) |
−0.635629 | + | 0.771995i | \(0.719259\pi\) | |||||||
\(608\) | 2.06801 | 0.0838688 | ||||||||
\(609\) | 1.74533 | − | 1.39384i | 0.0707244 | − | 0.0564813i | ||||
\(610\) | −2.23097 | −0.0903293 | ||||||||
\(611\) | −0.175536 | + | 0.304037i | −0.00710142 | + | 0.0123000i | ||||
\(612\) | −3.71191 | − | 6.42921i | −0.150045 | − | 0.259886i | ||||
\(613\) | −6.10873 | + | 3.52688i | −0.246729 | + | 0.142449i | −0.618266 | − | 0.785969i | \(-0.712164\pi\) |
0.371536 | + | 0.928418i | \(0.378831\pi\) | |||||||
\(614\) | −11.4021 | − | 6.58302i | −0.460153 | − | 0.265669i | ||||
\(615\) | 5.38738 | 0.217240 | ||||||||
\(616\) | 3.07185 | − | 2.45321i | 0.123768 | − | 0.0988427i | ||||
\(617\) | 25.1391i | 1.01206i | 0.862515 | + | 0.506032i | \(0.168888\pi\) | ||||
−0.862515 | + | 0.506032i | \(0.831112\pi\) | |||||||
\(618\) | −16.6283 | − | 9.60034i | −0.668887 | − | 0.386182i | ||||
\(619\) | 1.93440 | + | 3.35049i | 0.0777503 | + | 0.134667i | 0.902279 | − | 0.431153i | \(-0.141893\pi\) |
−0.824529 | + | 0.565820i | \(0.808560\pi\) | |||||||
\(620\) | 2.73360 | − | 1.57824i | 0.109784 | − | 0.0633837i | ||||
\(621\) | 0.599948 | − | 0.701552i | 0.0240751 | − | 0.0281523i | ||||
\(622\) | 8.09147i | 0.324439i | ||||||||
\(623\) | −14.0310 | + | 35.8237i | −0.562142 | + | 1.43525i | ||||
\(624\) | 0.201129 | 0.00805159 | ||||||||
\(625\) | −5.20863 | + | 9.02161i | −0.208345 | + | 0.360864i | ||||
\(626\) | −9.29473 | − | 16.0989i | −0.371492 | − | 0.643443i | ||||
\(627\) | −3.78777 | − | 6.56061i | −0.151269 | − | 0.262005i | ||||
\(628\) | −0.180567 | + | 0.312751i | −0.00720539 | + | 0.0124801i | ||||
\(629\) | 0.376301i | 0.0150041i | ||||||||
\(630\) | 8.23112 | − | 1.24649i | 0.327936 | − | 0.0496614i | ||||
\(631\) | 9.33314i | 0.371546i | 0.982593 | + | 0.185773i | \(0.0594790\pi\) | ||||
−0.982593 | + | 0.185773i | \(0.940521\pi\) | |||||||
\(632\) | −6.55870 | − | 3.78667i | −0.260891 | − | 0.150625i | ||||
\(633\) | −28.4158 | + | 16.4059i | −1.12943 | + | 0.652076i | ||||
\(634\) | −2.54483 | − | 4.40778i | −0.101068 | − | 0.175055i | ||||
\(635\) | 3.13259 | − | 5.42581i | 0.124313 | − | 0.215317i | ||||
\(636\) | 20.0372 | 0.794526 | ||||||||
\(637\) | −0.169084 | − | 0.545464i | −0.00669935 | − | 0.0216121i | ||||
\(638\) | 0.508806i | 0.0201438i | ||||||||
\(639\) | −11.7160 | + | 20.2928i | −0.463480 | + | 0.802770i | ||||
\(640\) | −0.511122 | − | 0.885289i | −0.0202039 | − | 0.0349941i | ||||
\(641\) | 19.6315 | − | 11.3343i | 0.775398 | − | 0.447676i | −0.0593988 | − | 0.998234i | \(-0.518918\pi\) |
0.834797 | + | 0.550558i | \(0.185585\pi\) | |||||||
\(642\) | −8.03160 | + | 13.9111i | −0.316982 | + | 0.549029i | ||||
\(643\) | −2.18923 | −0.0863347 | −0.0431673 | − | 0.999068i | \(-0.513745\pi\) | ||||
−0.0431673 | + | 0.999068i | \(0.513745\pi\) | |||||||
\(644\) | −0.426201 | + | 12.6814i | −0.0167947 | + | 0.499718i | ||||
\(645\) | −16.8795 | −0.664629 | ||||||||
\(646\) | 2.49385 | − | 4.31948i | 0.0981192 | − | 0.169948i | ||||
\(647\) | −3.21752 | + | 1.85764i | −0.126494 | + | 0.0730313i | −0.561912 | − | 0.827197i | \(-0.689934\pi\) |
0.435418 | + | 0.900228i | \(0.356601\pi\) | |||||||
\(648\) | −4.37984 | − | 7.58611i | −0.172056 | − | 0.298011i | ||||
\(649\) | 2.12924 | − | 3.68796i | 0.0835801 | − | 0.144765i | ||||
\(650\) | − | 0.322656i | − | 0.0126556i | ||||||
\(651\) | 7.34531 | − | 18.7538i | 0.287885 | − | 0.735021i | ||||
\(652\) | −24.3148 | −0.952243 | ||||||||
\(653\) | −16.1362 | + | 27.9487i | −0.631458 | + | 1.09372i | 0.355795 | + | 0.934564i | \(0.384210\pi\) |
−0.987254 | + | 0.159154i | \(0.949123\pi\) | |||||||
\(654\) | 21.3272 | + | 36.9398i | 0.833960 | + | 1.44446i | ||||
\(655\) | −11.5791 | + | 6.68521i | −0.452434 | + | 0.261213i | ||||
\(656\) | −1.85128 | − | 1.06883i | −0.0722802 | − | 0.0417310i | ||||
\(657\) | − | 19.6650i | − | 0.767205i | ||||||
\(658\) | 8.89665 | − | 7.10496i | 0.346828 | − | 0.276980i | ||||
\(659\) | − | 21.0261i | − | 0.819060i | −0.912297 | − | 0.409530i | \(-0.865693\pi\) | ||
0.912297 | − | 0.409530i | \(-0.134307\pi\) | |||||||
\(660\) | −1.87234 | + | 3.24300i | −0.0728809 | + | 0.126233i | ||||
\(661\) | −1.01116 | − | 1.75138i | −0.0393295 | − | 0.0681207i | 0.845691 | − | 0.533674i | \(-0.179189\pi\) |
−0.885020 | + | 0.465553i | \(0.845856\pi\) | |||||||
\(662\) | 4.57645 | + | 7.92664i | 0.177869 | + | 0.308078i | ||||
\(663\) | 0.242545 | − | 0.420100i | 0.00941966 | − | 0.0163153i | ||||
\(664\) | 3.61313 | 0.140217 | ||||||||
\(665\) | 3.49030 | + | 4.37047i | 0.135348 | + | 0.169480i | ||||
\(666\) | − | 0.480248i | − | 0.0186093i | ||||||
\(667\) | −1.24810 | − | 1.06734i | −0.0483266 | − | 0.0413276i | ||||
\(668\) | −11.3990 | + | 6.58122i | −0.441041 | + | 0.254635i | ||||
\(669\) | 16.9924 | + | 29.4317i | 0.656965 | + | 1.13790i | ||||
\(670\) | 13.8874 | + | 8.01789i | 0.536517 | + | 0.309758i | ||||
\(671\) | − | 3.24278i | − | 0.125186i | ||||||
\(672\) | −6.07353 | − | 2.37882i | −0.234291 | − | 0.0917648i | ||||
\(673\) | −24.9185 | −0.960538 | −0.480269 | − | 0.877121i | \(-0.659461\pi\) | ||||
−0.480269 | + | 0.877121i | \(0.659461\pi\) | |||||||
\(674\) | −17.6801 | − | 10.2076i | −0.681012 | − | 0.393183i | ||||
\(675\) | 0.659271 | − | 0.380630i | 0.0253753 | − | 0.0146505i | ||||
\(676\) | −6.49667 | − | 11.2526i | −0.249872 | − | 0.432791i | ||||
\(677\) | 14.4527 | − | 25.0329i | 0.555464 | − | 0.962092i | −0.442403 | − | 0.896816i | \(-0.645874\pi\) |
0.997867 | − | 0.0652757i | \(-0.0207927\pi\) | |||||||
\(678\) | 38.5092 | 1.47894 | ||||||||
\(679\) | −40.5496 | + | 6.14068i | −1.55615 | + | 0.235658i | ||||
\(680\) | −2.46549 | −0.0945471 | ||||||||
\(681\) | 21.3255 | + | 12.3123i | 0.817194 | + | 0.471807i | ||||
\(682\) | 2.29402 | + | 3.97336i | 0.0878426 | + | 0.152148i | ||||
\(683\) | 14.6289 | + | 25.3379i | 0.559757 | + | 0.969528i | 0.997516 | + | 0.0704359i | \(0.0224390\pi\) |
−0.437759 | + | 0.899092i | \(0.644228\pi\) | |||||||
\(684\) | −3.18274 | + | 5.51267i | −0.121695 | + | 0.210782i | ||||
\(685\) | 10.7556i | 0.410952i | ||||||||
\(686\) | −1.34552 | + | 18.4713i | −0.0513721 | + | 0.705238i | ||||
\(687\) | 35.3002i | 1.34679i | ||||||||
\(688\) | 5.80033 | + | 3.34882i | 0.221135 | + | 0.127673i | ||||
\(689\) | 0.331524 | + | 0.574216i | 0.0126300 | + | 0.0218759i | ||||
\(690\) | −4.02738 | − | 11.3958i | −0.153320 | − | 0.433831i | ||||
\(691\) | −21.6346 | − | 12.4907i | −0.823018 | − | 0.475170i | 0.0284381 | − | 0.999596i | \(-0.490947\pi\) |
−0.851456 | + | 0.524426i | \(0.824280\pi\) | |||||||
\(692\) | 14.8688i | 0.565229i | ||||||||
\(693\) | 1.81181 | + | 11.9642i | 0.0688251 | + | 0.454481i | ||||
\(694\) | 31.1222 | 1.18138 | ||||||||
\(695\) | −14.6706 | − | 8.47009i | −0.556489 | − | 0.321289i | ||||
\(696\) | 0.731118 | − | 0.422111i | 0.0277130 | − | 0.0160001i | ||||
\(697\) | −4.46498 | + | 2.57786i | −0.169123 | + | 0.0976433i | ||||
\(698\) | −9.03607 | − | 5.21697i | −0.342020 | − | 0.197465i | ||||
\(699\) | 44.6864i | 1.69019i | ||||||||
\(700\) | −3.81616 | + | 9.74331i | −0.144237 | + | 0.368263i | ||||
\(701\) | 8.46507i | 0.319721i | 0.987140 | + | 0.159861i | \(0.0511045\pi\) | ||||
−0.987140 | + | 0.159861i | \(0.948896\pi\) | |||||||
\(702\) | −0.00785137 | + | 0.0135990i | −0.000296331 | + | 0.000513260i | ||||
\(703\) | 0.279428 | − | 0.161328i | 0.0105388 | − | 0.00608459i | ||||
\(704\) | 1.28679 | − | 0.742931i | 0.0484979 | − | 0.0280003i | ||||
\(705\) | −5.42266 | + | 9.39233i | −0.204229 | + | 0.353736i | ||||
\(706\) | 5.88587i | 0.221518i | ||||||||
\(707\) | 34.6399 | − | 27.6638i | 1.30277 | − | 1.04040i | ||||
\(708\) | −7.06577 | −0.265548 | ||||||||
\(709\) | −23.3960 | − | 13.5077i | −0.878655 | − | 0.507292i | −0.00844049 | − | 0.999964i | \(-0.502687\pi\) |
−0.870215 | + | 0.492673i | \(0.836020\pi\) | |||||||
\(710\) | 3.89096 | + | 6.73934i | 0.146025 | + | 0.252923i | ||||
\(711\) | 20.1881 | − | 11.6556i | 0.757115 | − | 0.437120i | ||||
\(712\) | −7.27080 | + | 12.5934i | −0.272485 | + | 0.471957i | ||||
\(713\) | −14.5589 | − | 2.70783i | −0.545235 | − | 0.101409i | ||||
\(714\) | −12.2928 | + | 9.81720i | −0.460048 | + | 0.367400i | ||||
\(715\) | −0.123915 | −0.00463416 | ||||||||
\(716\) | −8.23112 | + | 14.2567i | −0.307611 | + | 0.532798i | ||||
\(717\) | 2.12270 | − | 1.22554i | 0.0792738 | − | 0.0457687i | ||||
\(718\) | 3.49303 | − | 2.01670i | 0.130359 | − | 0.0752626i | ||||
\(719\) | 27.7231 | + | 16.0059i | 1.03390 | + | 0.596921i | 0.918099 | − | 0.396352i | \(-0.129724\pi\) |
0.115799 | + | 0.993273i | \(0.463057\pi\) | |||||||
\(720\) | 3.14654 | 0.117265 | ||||||||
\(721\) | −7.51469 | + | 19.1863i | −0.279862 | + | 0.714536i | ||||
\(722\) | 14.7233 | 0.547946 | ||||||||
\(723\) | −38.3788 | − | 22.1580i | −1.42732 | − | 0.824066i | ||||
\(724\) | −10.4905 | − | 18.1700i | −0.389876 | − | 0.675284i | ||||
\(725\) | −0.677162 | − | 1.17288i | −0.0251491 | − | 0.0435596i | ||||
\(726\) | 18.7721 | + | 10.8381i | 0.696696 | + | 0.402238i | ||||
\(727\) | 31.7477 | 1.17746 | 0.588728 | − | 0.808331i | \(-0.299629\pi\) | ||||
0.588728 | + | 0.808331i | \(0.299629\pi\) | |||||||
\(728\) | −0.0323182 | − | 0.213411i | −0.00119779 | − | 0.00790953i | ||||
\(729\) | 28.3866 | 1.05135 | ||||||||
\(730\) | −5.65588 | − | 3.26542i | −0.209334 | − | 0.120859i | ||||
\(731\) | 13.9895 | − | 8.07682i | 0.517419 | − | 0.298732i | ||||
\(732\) | −4.65964 | + | 2.69025i | −0.172225 | + | 0.0994343i | ||||
\(733\) | 19.2615 | − | 33.3619i | 0.711440 | − | 1.23225i | −0.252877 | − | 0.967498i | \(-0.581377\pi\) |
0.964317 | − | 0.264751i | \(-0.0852899\pi\) | |||||||
\(734\) | 33.1297 | 1.22284 | ||||||||
\(735\) | −5.22335 | − | 16.8505i | −0.192666 | − | 0.621540i | ||||
\(736\) | −0.876945 | + | 4.71497i | −0.0323246 | + | 0.173796i | ||||
\(737\) | −11.6542 | + | 20.1857i | −0.429289 | + | 0.743551i | ||||
\(738\) | 5.69836 | − | 3.28995i | 0.209760 | − | 0.121105i | ||||
\(739\) | −19.9020 | − | 34.4712i | −0.732106 | − | 1.26805i | −0.955981 | − | 0.293427i | \(-0.905204\pi\) |
0.223875 | − | 0.974618i | \(-0.428129\pi\) | |||||||
\(740\) | −0.138125 | − | 0.0797465i | −0.00507757 | − | 0.00293154i | ||||
\(741\) | −0.415936 | −0.0152798 | ||||||||
\(742\) | −3.21966 | − | 21.2608i | −0.118197 | − | 0.780507i | ||||
\(743\) | 39.5642i | 1.45147i | 0.687974 | + | 0.725735i | \(0.258500\pi\) | ||||
−0.687974 | + | 0.725735i | \(0.741500\pi\) | |||||||
\(744\) | 3.80629 | − | 6.59269i | 0.139545 | − | 0.241700i | ||||
\(745\) | −9.65177 | + | 5.57245i | −0.353614 | + | 0.204159i | ||||
\(746\) | 2.62443 | − | 1.51522i | 0.0960872 | − | 0.0554760i | ||||
\(747\) | −5.56075 | + | 9.63149i | −0.203457 | + | 0.352398i | ||||
\(748\) | − | 3.58366i | − | 0.131032i | ||||||
\(749\) | 16.0512 | + | 6.28676i | 0.586498 | + | 0.229713i | ||||
\(750\) | − | 22.5686i | − | 0.824087i | ||||||
\(751\) | −7.65953 | − | 4.42223i | −0.279500 | − | 0.161369i | 0.353697 | − | 0.935360i | \(-0.384924\pi\) |
−0.633197 | + | 0.773991i | \(0.718258\pi\) | |||||||
\(752\) | 3.72680 | − | 2.15167i | 0.135902 | − | 0.0784632i | ||||
\(753\) | −42.7942 | + | 24.7072i | −1.55951 | + | 0.900382i | ||||
\(754\) | 0.0241933 | + | 0.0139680i | 0.000881068 | + | 0.000508685i | ||||
\(755\) | −17.5496 | −0.638696 | ||||||||
\(756\) | 0.397929 | − | 0.317791i | 0.0144725 | − | 0.0115579i | ||||
\(757\) | − | 19.5400i | − | 0.710195i | −0.934829 | − | 0.355098i | \(-0.884448\pi\) | ||
0.934829 | − | 0.355098i | \(-0.115552\pi\) | |||||||
\(758\) | −18.0380 | − | 10.4142i | −0.655169 | − | 0.378262i | ||||
\(759\) | 16.5641 | − | 5.85391i | 0.601240 | − | 0.212484i | ||||
\(760\) | 1.05700 | + | 1.83078i | 0.0383416 | + | 0.0664095i | ||||
\(761\) | −14.6407 | − | 8.45283i | −0.530726 | − | 0.306415i | 0.210586 | − | 0.977575i | \(-0.432463\pi\) |
−0.741312 | + | 0.671161i | \(0.765796\pi\) | |||||||
\(762\) | − | 15.1099i | − | 0.547375i | ||||||
\(763\) | 35.7687 | − | 28.5652i | 1.29491 | − | 1.03413i | ||||
\(764\) | − | 9.95285i | − | 0.360082i | ||||||
\(765\) | 3.79447 | − | 6.57222i | 0.137190 | − | 0.237619i | ||||
\(766\) | −14.8397 | − | 25.7031i | −0.536180 | − | 0.928690i | ||||
\(767\) | −0.116906 | − | 0.202488i | −0.00422124 | − | 0.00731140i | ||||
\(768\) | −2.13508 | − | 1.23269i | −0.0770430 | − | 0.0444808i | ||||
\(769\) | 44.2342 | 1.59513 | 0.797563 | − | 0.603236i | \(-0.206122\pi\) | ||||
0.797563 | + | 0.603236i | \(0.206122\pi\) | |||||||
\(770\) | 3.74189 | + | 1.46558i | 0.134848 | + | 0.0528160i | ||||
\(771\) | 58.4137 | 2.10372 | ||||||||
\(772\) | 5.53019 | − | 9.57857i | 0.199036 | − | 0.344740i | ||||
\(773\) | 19.1314 | + | 33.1365i | 0.688108 | + | 1.19184i | 0.972449 | + | 0.233115i | \(0.0748917\pi\) |
−0.284341 | + | 0.958723i | \(0.591775\pi\) | |||||||
\(774\) | −17.8538 | + | 10.3079i | −0.641743 | + | 0.370510i | ||||
\(775\) | −10.5762 | − | 6.10615i | −0.379907 | − | 0.219339i | ||||
\(776\) | −15.5010 | −0.556455 | ||||||||
\(777\) | −1.00623 | + | 0.152379i | −0.0360981 | + | 0.00546658i | ||||
\(778\) | − | 10.2980i | − | 0.369202i | ||||||
\(779\) | 3.82845 | + | 2.21036i | 0.137169 | + | 0.0791943i | ||||
\(780\) | 0.102801 | + | 0.178057i | 0.00368087 | + | 0.00637546i | ||||
\(781\) | −9.79583 | + | 5.65562i | −0.350522 | + | 0.202374i | ||||
\(782\) | 8.79070 | + | 7.51756i | 0.314355 | + | 0.268828i | ||||
\(783\) | 0.0659111i | 0.00235547i | ||||||||
\(784\) | −1.54816 | + | 6.82665i | −0.0552914 | + | 0.243809i | ||||
\(785\) | −0.369166 | −0.0131761 | ||||||||
\(786\) | −16.1229 | + | 27.9257i | −0.575085 | + | 0.996076i | ||||
\(787\) | 20.5080 | + | 35.5209i | 0.731031 | + | 1.26618i | 0.956443 | + | 0.291920i | \(0.0942940\pi\) |
−0.225412 | + | 0.974264i | \(0.572373\pi\) | |||||||
\(788\) | 5.65304 | + | 9.79136i | 0.201381 | + | 0.348803i | ||||
\(789\) | −4.46946 | + | 7.74132i | −0.159117 | + | 0.275598i | ||||
\(790\) | − | 7.74179i | − | 0.275441i | ||||||
\(791\) | −6.18782 | − | 40.8608i | −0.220013 | − | 1.45284i | ||||
\(792\) | 4.57359i | 0.162515i | ||||||||
\(793\) | −0.154191 | − | 0.0890225i | −0.00547550 | − | 0.00316128i | ||||
\(794\) | 24.4139 | − | 14.0954i | 0.866418 | − | 0.500227i | ||||
\(795\) | 10.2414 | + | 17.7387i | 0.363226 | + | 0.629127i | ||||
\(796\) | −6.69299 | + | 11.5926i | −0.237227 | + | 0.410889i | ||||
\(797\) | −32.1997 | −1.14057 | −0.570286 | − | 0.821446i | \(-0.693168\pi\) | ||||
−0.570286 | + | 0.821446i | \(0.693168\pi\) | |||||||
\(798\) | 12.5601 | + | 4.91941i | 0.444623 | + | 0.174145i | ||||
\(799\) | − | 10.3790i | − | 0.367181i | ||||||
\(800\) | −1.97751 | + | 3.42515i | −0.0699155 | + | 0.121097i | ||||
\(801\) | −22.3800 | − | 38.7634i | −0.790760 | − | 1.36964i | ||||
\(802\) | −8.50199 | + | 4.90863i | −0.300216 | + | 0.173330i | ||||
\(803\) | 4.74639 | − | 8.22099i | 0.167496 | − | 0.290112i | ||||
\(804\) | 38.6740 | 1.36393 | ||||||||
\(805\) | −11.4446 | + | 6.10444i | −0.403368 | + | 0.215153i | ||||
\(806\) | 0.251907 | 0.00887304 | ||||||||
\(807\) | 24.2356 | − | 41.9772i | 0.853132 | − | 1.47767i | ||||
\(808\) | 14.5106 | − | 8.37770i | 0.510481 | − | 0.294726i | ||||
\(809\) | −0.597463 | − | 1.03484i | −0.0210057 | − | 0.0363829i | 0.855331 | − | 0.518081i | \(-0.173353\pi\) |
−0.876337 | + | 0.481698i | \(0.840020\pi\) | |||||||
\(810\) | 4.47727 | − | 7.75485i | 0.157315 | − | 0.272478i | ||||
\(811\) | − | 32.5133i | − | 1.14170i | −0.821055 | − | 0.570849i | \(-0.806614\pi\) | ||
0.821055 | − | 0.570849i | \(-0.193386\pi\) | |||||||
\(812\) | −0.565367 | − | 0.707938i | −0.0198405 | − | 0.0248438i | ||||
\(813\) | 19.5044 | 0.684048 | ||||||||
\(814\) | 0.115914 | − | 0.200769i | 0.00406278 | − | 0.00703694i | ||||
\(815\) | −12.4278 | − | 21.5257i | −0.435328 | − | 0.754011i | ||||
\(816\) | −5.14946 | + | 2.97304i | −0.180267 | + | 0.104077i | ||||
\(817\) | −11.9951 | − | 6.92539i | −0.419656 | − | 0.242289i | ||||
\(818\) | − | 7.43973i | − | 0.260124i | ||||||
\(819\) | 0.618626 | + | 0.242297i | 0.0216165 | + | 0.00846653i | ||||
\(820\) | − | 2.18522i | − | 0.0763111i | ||||||
\(821\) | 13.0689 | − | 22.6360i | 0.456107 | − | 0.790000i | −0.542644 | − | 0.839963i | \(-0.682577\pi\) |
0.998751 | + | 0.0499623i | \(0.0159101\pi\) | |||||||
\(822\) | 12.9698 | + | 22.4644i | 0.452375 | + | 0.783537i | ||||
\(823\) | −8.14872 | − | 14.1140i | −0.284047 | − | 0.491983i | 0.688331 | − | 0.725397i | \(-0.258344\pi\) |
−0.972378 | + | 0.233414i | \(0.925010\pi\) | |||||||
\(824\) | −3.89407 | + | 6.74472i | −0.135656 | + | 0.234964i | ||||
\(825\) | 14.4880 | 0.504409 | ||||||||
\(826\) | 1.13536 | + | 7.49725i | 0.0395042 | + | 0.260863i | ||||
\(827\) | − | 0.742014i | − | 0.0258024i | −0.999917 | − | 0.0129012i | \(-0.995893\pi\) | ||
0.999917 | − | 0.0129012i | \(-0.00410669\pi\) | |||||||
\(828\) | −11.2190 | − | 9.59418i | −0.389887 | − | 0.333421i | ||||
\(829\) | 41.4331 | − | 23.9214i | 1.43903 | − | 0.830825i | 0.441248 | − | 0.897385i | \(-0.354536\pi\) |
0.997782 | + | 0.0665603i | \(0.0212025\pi\) | |||||||
\(830\) | 1.84675 | + | 3.19867i | 0.0641017 | + | 0.111027i | ||||
\(831\) | 34.0522 | + | 19.6600i | 1.18126 | + | 0.681999i | ||||
\(832\) | − | 0.0815813i | − | 0.00282832i | ||||||
\(833\) | 12.3920 | + | 11.4661i | 0.429356 | + | 0.397275i | ||||
\(834\) | −40.8551 | −1.41470 | ||||||||
\(835\) | −11.6526 | − | 6.72761i | −0.403254 | − | 0.232819i | ||||
\(836\) | −2.66110 | + | 1.53639i | −0.0920361 | + | 0.0531370i | ||||
\(837\) | 0.297169 | + | 0.514712i | 0.0102717 | + | 0.0177911i | ||||
\(838\) | −16.0825 | + | 27.8558i | −0.555562 | + | 0.962262i | ||||
\(839\) | −22.5059 | −0.776990 | −0.388495 | − | 0.921451i | \(-0.627005\pi\) | ||||
−0.388495 | + | 0.921451i | \(0.627005\pi\) | |||||||
\(840\) | −0.998374 | − | 6.59269i | −0.0344472 | − | 0.227470i | ||||
\(841\) | −28.8827 | −0.995957 | ||||||||
\(842\) | −0.542139 | − | 0.313004i | −0.0186834 | − | 0.0107868i | ||||
\(843\) | 11.6800 | + | 20.2304i | 0.402281 | + | 0.696771i | ||||
\(844\) | 6.65452 | + | 11.5260i | 0.229058 | + | 0.396740i | ||||
\(845\) | 6.64118 | − | 11.5029i | 0.228464 | − | 0.395711i | ||||
\(846\) | 13.2460i | 0.455406i | ||||||||
\(847\) | 8.48352 | − | 21.6599i | 0.291497 | − | 0.744243i | ||||
\(848\) | − | 8.12743i | − | 0.279097i | ||||||
\(849\) | 42.4864 | + | 24.5295i | 1.45813 | + | 0.841852i | ||||
\(850\) | 4.76943 | + | 8.26090i | 0.163590 | + | 0.283347i | ||||
\(851\) | 0.249329 | + | 0.705496i | 0.00854687 | + | 0.0241841i | ||||
\(852\) | 16.2535 | + | 9.38394i | 0.556834 | + | 0.321488i | ||||
\(853\) | − | 16.5459i | − | 0.566520i | −0.959043 | − | 0.283260i | \(-0.908584\pi\) | ||
0.959043 | − | 0.283260i | \(-0.0914159\pi\) | |||||||
\(854\) | 3.60326 | + | 4.51191i | 0.123301 | + | 0.154394i | ||||
\(855\) | −6.50707 | −0.222537 | ||||||||
\(856\) | 5.64261 | + | 3.25776i | 0.192860 | + | 0.111348i | ||||
\(857\) | −47.8740 | + | 27.6401i | −1.63535 | + | 0.944167i | −0.652940 | + | 0.757410i | \(0.726464\pi\) |
−0.982406 | + | 0.186757i | \(0.940202\pi\) | |||||||
\(858\) | −0.258811 | + | 0.149425i | −0.00883566 | + | 0.00510127i | ||||
\(859\) | −22.5929 | − | 13.0440i | −0.770860 | − | 0.445056i | 0.0623211 | − | 0.998056i | \(-0.480150\pi\) |
−0.833181 | + | 0.553000i | \(0.813483\pi\) | |||||||
\(860\) | 6.84662i | 0.233468i | ||||||||
\(861\) | −8.70121 | − | 10.8954i | −0.296537 | − | 0.371316i | ||||
\(862\) | − | 35.9185i | − | 1.22339i | ||||||
\(863\) | 21.4647 | − | 37.1780i | 0.730667 | − | 1.26555i | −0.225931 | − | 0.974143i | \(-0.572543\pi\) |
0.956598 | − | 0.291409i | \(-0.0941241\pi\) | |||||||
\(864\) | 0.166692 | − | 0.0962398i | 0.00567098 | − | 0.00327414i | ||||
\(865\) | −13.1632 | + | 7.59979i | −0.447563 | + | 0.258401i | ||||
\(866\) | −4.71193 | + | 8.16131i | −0.160118 | + | 0.277332i | ||||
\(867\) | − | 27.5704i | − | 0.936339i | ||||||
\(868\) | −7.60689 | − | 2.97939i | −0.258195 | − | 0.101127i | ||||
\(869\) | 11.2529 | 0.381729 | ||||||||
\(870\) | 0.747381 | + | 0.431500i | 0.0253386 | + | 0.0146292i | ||||
\(871\) | 0.639877 | + | 1.10830i | 0.0216814 | + | 0.0375533i | ||||
\(872\) | 14.9835 | − | 8.65070i | 0.507404 | − | 0.292950i | ||||
\(873\) | 23.8567 | − | 41.3210i | 0.807426 | − | 1.39850i | ||||
\(874\) | 1.81353 | − | 9.75060i | 0.0613435 | − | 0.329819i | ||||
\(875\) | −23.9467 | + | 3.62641i | −0.809547 | + | 0.122595i | ||||
\(876\) | −15.7506 | −0.532165 | ||||||||
\(877\) | −22.0658 | + | 38.2191i | −0.745110 | + | 1.29057i | 0.205033 | + | 0.978755i | \(0.434270\pi\) |
−0.950143 | + | 0.311814i | \(0.899064\pi\) | |||||||
\(878\) | −21.4226 | + | 12.3684i | −0.722978 | + | 0.417412i | ||||
\(879\) | −11.7370 | + | 6.77636i | −0.395879 | + | 0.228561i | ||||
\(880\) | 1.31542 | + | 0.759456i | 0.0443427 | + | 0.0256013i | ||||
\(881\) | −2.81759 | −0.0949270 | −0.0474635 | − | 0.998873i | \(-0.515114\pi\) | ||||
−0.0474635 | + | 0.998873i | \(0.515114\pi\) | |||||||
\(882\) | −15.8151 | − | 14.6334i | −0.532521 | − | 0.492732i | ||||
\(883\) | 11.0067 | 0.370403 | 0.185202 | − | 0.982701i | \(-0.440706\pi\) | ||||
0.185202 | + | 0.982701i | \(0.440706\pi\) | |||||||
\(884\) | −0.170400 | − | 0.0983805i | −0.00573117 | − | 0.00330889i | ||||
\(885\) | −3.61147 | − | 6.25525i | −0.121398 | − | 0.210268i | ||||
\(886\) | 3.93090 | + | 6.80852i | 0.132061 | + | 0.228737i | ||||
\(887\) | 7.71627 | + | 4.45499i | 0.259087 | + | 0.149584i | 0.623918 | − | 0.781490i | \(-0.285540\pi\) |
−0.364831 | + | 0.931074i | \(0.618873\pi\) | |||||||
\(888\) | −0.384654 | −0.0129081 | ||||||||
\(889\) | −16.0326 | + | 2.42792i | −0.537717 | + | 0.0814300i | ||||
\(890\) | −14.8651 | −0.498278 | ||||||||
\(891\) | 11.2719 | + | 6.50784i | 0.377623 | + | 0.218021i | ||||
\(892\) | 11.9380 | − | 6.89243i | 0.399715 | − | 0.230776i | ||||
\(893\) | −7.70705 | + | 4.44967i | −0.257907 | + | 0.148902i | ||||
\(894\) | −13.4392 | + | 23.2775i | −0.449476 | + | 0.778515i | ||||
\(895\) | −16.8284 | −0.562512 | ||||||||
\(896\) | −0.964890 | + | 2.46353i | −0.0322347 | + | 0.0823008i | ||||
\(897\) | 0.176379 | − | 0.948316i | 0.00588911 | − | 0.0316633i | ||||
\(898\) | 9.89781 | − | 17.1435i | 0.330294 | − | 0.572086i | ||||
\(899\) | 0.915701 | − | 0.528680i | 0.0305403 | − | 0.0176325i | ||||
\(900\) | −6.08692 | − | 10.5428i | −0.202897 | − | 0.351428i | ||||
\(901\) | −16.9759 | − | 9.80103i | −0.565549 | − | 0.326520i | ||||
\(902\) | 3.17628 | 0.105759 | ||||||||
\(903\) | 27.2622 | + | 34.1371i | 0.907230 | + | 1.13601i | ||||
\(904\) | − | 15.6200i | − | 0.519514i | ||||||
\(905\) | 10.7238 | − | 18.5742i | 0.356472 | − | 0.617428i | ||||
\(906\) | −36.6544 | + | 21.1625i | −1.21776 | + | 0.703075i | ||||
\(907\) | −19.4132 | + | 11.2082i | −0.644603 | + | 0.372162i | −0.786385 | − | 0.617736i | \(-0.788050\pi\) |
0.141782 | + | 0.989898i | \(0.454717\pi\) | |||||||
\(908\) | 4.99408 | − | 8.65000i | 0.165734 | − | 0.287060i | ||||
\(909\) | 51.5743i | 1.71061i | ||||||||
\(910\) | 0.172412 | − | 0.137690i | 0.00571539 | − | 0.00456437i | ||||
\(911\) | 45.4326i | 1.50525i | 0.658450 | + | 0.752624i | \(0.271212\pi\) | ||||
−0.658450 | + | 0.752624i | \(0.728788\pi\) | |||||||
\(912\) | 4.41536 | + | 2.54921i | 0.146207 | + | 0.0844127i | ||||
\(913\) | −4.64936 | + | 2.68431i | −0.153871 | + | 0.0888376i | ||||
\(914\) | −6.77168 | + | 3.90963i | −0.223987 | + | 0.129319i | ||||
\(915\) | −4.76329 | − | 2.75009i | −0.157469 | − | 0.0909151i | ||||
\(916\) | 14.3184 | 0.473093 | ||||||||
\(917\) | 32.2217 | + | 12.6203i | 1.06405 | + | 0.416757i | ||||
\(918\) | − | 0.464230i | − | 0.0153219i | ||||||
\(919\) | 45.5151 | + | 26.2782i | 1.50141 | + | 0.866837i | 0.999999 | + | 0.00162549i | \(0.000517409\pi\) |
0.501407 | + | 0.865212i | \(0.332816\pi\) | |||||||
\(920\) | −4.62234 | + | 1.63358i | −0.152394 | + | 0.0538574i | ||||
\(921\) | −16.2296 | − | 28.1105i | −0.534784 | − | 0.926273i | ||||
\(922\) | −4.54760 | − | 2.62556i | −0.149767 | − | 0.0864682i | ||||
\(923\) | 0.621045i | 0.0204419i | ||||||||
\(924\) | 9.58267 | − | 1.45117i | 0.315247 | − | 0.0477399i | ||||
\(925\) | 0.617071i | 0.0202892i | ||||||||
\(926\) | −3.36620 | + | 5.83042i | −0.110620 | + | 0.191600i | ||||
\(927\) | −11.9862 | − | 20.7608i | −0.393679 | − | 0.681873i | ||||
\(928\) | −0.171216 | − | 0.296554i | −0.00562043 | − | 0.00973488i | ||||
\(929\) | 3.52984 | + | 2.03795i | 0.115810 | + | 0.0668631i | 0.556786 | − | 0.830656i | \(-0.312034\pi\) |
−0.440976 | + | 0.897519i | \(0.645368\pi\) | |||||||
\(930\) | 7.78192 | 0.255179 | ||||||||
\(931\) | 3.20161 | − | 14.1176i | 0.104928 | − | 0.462685i | ||||
\(932\) | 18.1256 | 0.593724 | ||||||||
\(933\) | −9.97426 | + | 17.2759i | −0.326543 | + | 0.565588i | ||||
\(934\) | −6.40963 | − | 11.1018i | −0.209729 | − | 0.363262i | ||||
\(935\) | 3.17257 | − | 1.83169i | 0.103754 | − | 0.0599025i | ||||
\(936\) | 0.217471 | + | 0.125557i | 0.00710825 | + | 0.00410395i | ||||
\(937\) | −18.5316 | −0.605402 | −0.302701 | − | 0.953086i | \(-0.597888\pi\) | ||||
−0.302701 | + | 0.953086i | \(0.597888\pi\) | |||||||
\(938\) | −6.21429 | − | 41.0356i | −0.202904 | − | 1.33986i | ||||
\(939\) | − | 45.8300i | − | 1.49560i | ||||||
\(940\) | 3.80970 | + | 2.19953i | 0.124259 | + | 0.0717407i | ||||
\(941\) | −18.1217 | − | 31.3878i | −0.590752 | − | 1.02321i | −0.994131 | − | 0.108179i | \(-0.965498\pi\) |
0.403380 | − | 0.915033i | \(-0.367835\pi\) | |||||||
\(942\) | −0.771048 | + | 0.445165i | −0.0251221 | + | 0.0145042i | ||||
\(943\) | −6.66299 | + | 7.79140i | −0.216977 | + | 0.253723i | ||||
\(944\) | 2.86600i | 0.0932805i | ||||||||
\(945\) | 0.484727 | + | 0.189853i | 0.0157682 | + | 0.00617591i | ||||
\(946\) | −9.95177 | −0.323560 | ||||||||
\(947\) | −8.25770 | + | 14.3028i | −0.268339 | + | 0.464777i | −0.968433 | − | 0.249274i | \(-0.919808\pi\) |
0.700094 | + | 0.714051i | \(0.253141\pi\) | |||||||
\(948\) | −9.33555 | − | 16.1696i | −0.303205 | − | 0.525166i | ||||
\(949\) | −0.260601 | − | 0.451374i | −0.00845947 | − | 0.0146522i | ||||
\(950\) | 4.08950 | − | 7.08323i | 0.132681 | − | 0.229810i | ||||
\(951\) | − | 12.5479i | − | 0.406895i | ||||||
\(952\) | 3.98203 | + | 4.98620i | 0.129058 | + | 0.161604i | ||||
\(953\) | − | 55.5834i | − | 1.80052i | −0.435349 | − | 0.900262i | \(-0.643375\pi\) | ||
0.435349 | − | 0.900262i | \(-0.356625\pi\) | |||||||
\(954\) | 21.6652 | + | 12.5084i | 0.701437 | + | 0.404975i | ||||
\(955\) | 8.81115 | − | 5.08712i | 0.285122 | − | 0.164615i | ||||
\(956\) | −0.497102 | − | 0.861006i | −0.0160774 | − | 0.0278469i | ||||
\(957\) | −0.627199 | + | 1.08634i | −0.0202745 | + | 0.0351164i | ||||
\(958\) | 7.19624 | 0.232500 | ||||||||
\(959\) | 21.7522 | − | 17.3715i | 0.702415 | − | 0.560956i | ||||
\(960\) | − | 2.52021i | − | 0.0813396i | ||||||
\(961\) | −10.7327 | + | 18.5897i | −0.346218 | + | 0.599666i | ||||
\(962\) | −0.00636426 | − | 0.0110232i | −0.000205192 | − | 0.000355403i | ||||
\(963\) | −17.3684 | + | 10.0276i | −0.559687 | + | 0.323136i | ||||
\(964\) | −8.98769 | + | 15.5671i | −0.289474 | + | 0.501384i | ||||
\(965\) | 11.3064 | 0.363966 | ||||||||
\(966\) | −16.5422 | + | 26.5504i | −0.532236 | + | 0.854246i | ||||
\(967\) | −17.2521 | −0.554789 | −0.277394 | − | 0.960756i | \(-0.589471\pi\) | ||||
−0.277394 | + | 0.960756i | \(0.589471\pi\) | |||||||
\(968\) | 4.39611 | − | 7.61428i | 0.141296 | − | 0.244732i | ||||
\(969\) | 10.6491 | − | 6.14828i | 0.342099 | − | 0.197511i | ||||
\(970\) | −7.92292 | − | 13.7229i | −0.254390 | − | 0.440616i | ||||
\(971\) | −0.288764 | + | 0.500154i | −0.00926687 | + | 0.0160507i | −0.870622 | − | 0.491953i | \(-0.836283\pi\) |
0.861355 | + | 0.508004i | \(0.169616\pi\) | |||||||
\(972\) | − | 22.1733i | − | 0.711210i | ||||||
\(973\) | 6.56477 | + | 43.3500i | 0.210457 | + | 1.38974i | ||||
\(974\) | −14.4413 | −0.462729 | ||||||||
\(975\) | 0.397734 | − | 0.688895i | 0.0127377 | − | 0.0220623i | ||||
\(976\) | 1.09121 | + | 1.89003i | 0.0349288 | + | 0.0604985i | ||||
\(977\) | −6.76955 | + | 3.90840i | −0.216577 | + | 0.125041i | −0.604364 | − | 0.796708i | \(-0.706573\pi\) |
0.387787 | + | 0.921749i | \(0.373240\pi\) | |||||||
\(978\) | −51.9141 | − | 29.9726i | −1.66003 | − | 0.958418i | ||||
\(979\) | − | 21.6068i | − | 0.690556i | ||||||
\(980\) | −6.83486 | + | 2.11868i | −0.218332 | + | 0.0676788i | ||||
\(981\) | 53.2550i | 1.70030i | ||||||||
\(982\) | 18.4458 | − | 31.9491i | 0.588630 | − | 1.01954i | ||||
\(983\) | −24.1184 | − | 41.7743i | −0.769258 | − | 1.33239i | −0.937966 | − | 0.346728i | \(-0.887293\pi\) |
0.168708 | − | 0.985666i | \(-0.446041\pi\) | |||||||
\(984\) | −2.63508 | − | 4.56409i | −0.0840032 | − | 0.145498i | ||||
\(985\) | −5.77879 | + | 10.0092i | −0.184128 | + | 0.318918i | ||||
\(986\) | −0.825890 | −0.0263017 | ||||||||
\(987\) | 27.7532 | − | 4.20285i | 0.883395 | − | 0.133778i | ||||
\(988\) | 0.168711i | 0.00536741i | ||||||||
\(989\) | 20.8762 | − | 24.4117i | 0.663823 | − | 0.776245i | ||||
\(990\) | −4.04895 | + | 2.33766i | −0.128684 | + | 0.0742958i | ||||
\(991\) | 8.92320 | + | 15.4554i | 0.283455 | + | 0.490958i | 0.972233 | − | 0.234014i | \(-0.0751861\pi\) |
−0.688779 | + | 0.724972i | \(0.741853\pi\) | |||||||
\(992\) | −2.67411 | − | 1.54390i | −0.0849032 | − | 0.0490189i | ||||
\(993\) | 22.5653i | 0.716089i | ||||||||
\(994\) | 7.34531 | − | 18.7538i | 0.232979 | − | 0.594836i | ||||
\(995\) | −13.6837 | −0.433804 | ||||||||
\(996\) | 7.71432 | + | 4.45386i | 0.244438 | + | 0.141126i | ||||
\(997\) | −2.81054 | + | 1.62267i | −0.0890107 | + | 0.0513903i | −0.543845 | − | 0.839186i | \(-0.683032\pi\) |
0.454834 | + | 0.890576i | \(0.349699\pi\) | |||||||
\(998\) | −2.83621 | − | 4.91245i | −0.0897785 | − | 0.155501i | ||||
\(999\) | 0.0150156 | − | 0.0260077i | 0.000475071 | − | 0.000822848i |
(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 | 322.2.g.b.229.8 | yes | 16 | |
7.2 | even | 3 | 2254.2.c.b.2253.13 | 16 | |||
7.3 | odd | 6 | inner | 322.2.g.b.45.7 | ✓ | 16 | |
7.5 | odd | 6 | 2254.2.c.b.2253.4 | 16 | |||
23.22 | odd | 2 | inner | 322.2.g.b.229.7 | yes | 16 | |
161.45 | even | 6 | inner | 322.2.g.b.45.8 | yes | 16 | |
161.68 | even | 6 | 2254.2.c.b.2253.3 | 16 | |||
161.114 | odd | 6 | 2254.2.c.b.2253.14 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.g.b.45.7 | ✓ | 16 | 7.3 | odd | 6 | inner | |
322.2.g.b.45.8 | yes | 16 | 161.45 | even | 6 | inner | |
322.2.g.b.229.7 | yes | 16 | 23.22 | odd | 2 | inner | |
322.2.g.b.229.8 | yes | 16 | 1.1 | even | 1 | trivial | |
2254.2.c.b.2253.3 | 16 | 161.68 | even | 6 | |||
2254.2.c.b.2253.4 | 16 | 7.5 | odd | 6 | |||
2254.2.c.b.2253.13 | 16 | 7.2 | even | 3 | |||
2254.2.c.b.2253.14 | 16 | 161.114 | odd | 6 |