Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(647,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2394.647");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.by (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: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 647.13 | ||
Character | \(\chi\) | \(=\) | 2394.647 |
Dual form | 2394.2.by.b.2357.13 |
$q$-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 \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.75570 | − | 3.04097i | −0.785175 | − | 1.35996i | −0.928895 | − | 0.370344i | \(-0.879240\pi\) |
0.143720 | − | 0.989618i | \(-0.454094\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64573 | − | 0.00972055i | 0.999993 | − | 0.00367402i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.04097 | − | 1.75570i | −0.961639 | − | 0.555202i | ||||
\(11\) | −2.13849 | − | 1.23466i | −0.644779 | − | 0.372263i | 0.141674 | − | 0.989913i | \(-0.454751\pi\) |
−0.786453 | + | 0.617650i | \(0.788085\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.595217i | 0.165083i | 0.996588 | + | 0.0825417i | \(0.0263038\pi\) | ||||
−0.996588 | + | 0.0825417i | \(0.973696\pi\) | |||||||
\(14\) | 2.28641 | − | 1.33128i | 0.611069 | − | 0.355801i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.856393 | − | 1.48332i | 0.207706 | − | 0.359757i | −0.743286 | − | 0.668974i | \(-0.766734\pi\) |
0.950991 | + | 0.309217i | \(0.100067\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.866025 | + | 0.500000i | −0.198680 | + | 0.114708i | ||||
\(20\) | −3.51141 | −0.785175 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.46932 | −0.526460 | ||||||||
\(23\) | 3.47984 | − | 2.00908i | 0.725596 | − | 0.418923i | −0.0912129 | − | 0.995831i | \(-0.529074\pi\) |
0.816809 | + | 0.576908i | \(0.195741\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.66500 | + | 6.34796i | −0.732999 | + | 1.26959i | ||||
\(26\) | 0.297608 | + | 0.515473i | 0.0583658 | + | 0.101093i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.31445 | − | 2.29613i | 0.248407 | − | 0.433928i | ||||
\(29\) | − | 8.62608i | − | 1.60182i | −0.598783 | − | 0.800911i | \(-0.704349\pi\) | ||
0.598783 | − | 0.800911i | \(-0.295651\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.78011 | − | 1.60510i | −0.499322 | − | 0.288284i | 0.229111 | − | 0.973400i | \(-0.426418\pi\) |
−0.728434 | + | 0.685116i | \(0.759751\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.71279i | − | 0.293740i | ||||||
\(35\) | −4.67469 | − | 8.02853i | −0.790166 | − | 1.35707i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.06702 | − | 1.84813i | −0.175416 | − | 0.303830i | 0.764889 | − | 0.644162i | \(-0.222794\pi\) |
−0.940305 | + | 0.340332i | \(0.889461\pi\) | |||||||
\(38\) | −0.500000 | + | 0.866025i | −0.0811107 | + | 0.140488i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.04097 | + | 1.75570i | −0.480819 | + | 0.277601i | ||||
\(41\) | −1.84541 | −0.288205 | −0.144102 | − | 0.989563i | \(-0.546029\pi\) | ||||
−0.144102 | + | 0.989563i | \(0.546029\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.168078 | 0.0256317 | 0.0128158 | − | 0.999918i | \(-0.495920\pi\) | ||||
0.0128158 | + | 0.999918i | \(0.495920\pi\) | |||||||
\(44\) | −2.13849 | + | 1.23466i | −0.322389 | + | 0.186132i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00908 | − | 3.47984i | 0.296223 | − | 0.513074i | ||||
\(47\) | −2.33889 | − | 4.05108i | −0.341163 | − | 0.590911i | 0.643486 | − | 0.765458i | \(-0.277487\pi\) |
−0.984649 | + | 0.174546i | \(0.944154\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99981 | − | 0.0514360i | 0.999973 | − | 0.00734799i | ||||
\(50\) | 7.32999i | 1.03662i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.515473 | + | 0.297608i | 0.0714832 | + | 0.0412709i | ||||
\(53\) | −0.675185 | − | 0.389819i | −0.0927439 | − | 0.0535457i | 0.452911 | − | 0.891556i | \(-0.350386\pi\) |
−0.545655 | + | 0.838010i | \(0.683719\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.67078i | 1.16917i | ||||||||
\(56\) | −0.00972055 | − | 2.64573i | −0.00129896 | − | 0.353551i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.31304 | − | 7.47040i | −0.566330 | − | 0.980912i | ||||
\(59\) | −6.28968 | + | 10.8940i | −0.818846 | + | 1.41828i | 0.0876865 | + | 0.996148i | \(0.472053\pi\) |
−0.906533 | + | 0.422135i | \(0.861281\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.7145 | + | 6.18602i | −1.37185 | + | 0.792039i | −0.991161 | − | 0.132664i | \(-0.957647\pi\) |
−0.380690 | + | 0.924703i | \(0.624314\pi\) | |||||||
\(62\) | −3.21019 | −0.407695 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.81004 | − | 1.04502i | 0.224507 | − | 0.129619i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.56133 | + | 2.70431i | −0.190747 | + | 0.330384i | −0.945498 | − | 0.325628i | \(-0.894424\pi\) |
0.754751 | + | 0.656012i | \(0.227758\pi\) | |||||||
\(68\) | −0.856393 | − | 1.48332i | −0.103853 | − | 0.179879i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.06266 | − | 4.61557i | −0.963672 | − | 0.551666i | ||||
\(71\) | 8.22648i | 0.976304i | 0.872759 | + | 0.488152i | \(0.162329\pi\) | ||||
−0.872759 | + | 0.488152i | \(0.837671\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.84116 | + | 1.06300i | 0.215492 | + | 0.124414i | 0.603861 | − | 0.797090i | \(-0.293628\pi\) |
−0.388369 | + | 0.921504i | \(0.626961\pi\) | |||||||
\(74\) | −1.84813 | − | 1.06702i | −0.214840 | − | 0.124038i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000i | 0.114708i | ||||||||
\(77\) | −5.66988 | − | 3.24579i | −0.646142 | − | 0.369892i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.36502 | − | 4.09633i | −0.266085 | − | 0.460873i | 0.701762 | − | 0.712411i | \(-0.252397\pi\) |
−0.967847 | + | 0.251538i | \(0.919064\pi\) | |||||||
\(80\) | −1.75570 | + | 3.04097i | −0.196294 | + | 0.339991i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.59817 | + | 0.922706i | −0.176489 | + | 0.101896i | ||||
\(83\) | 3.01650 | 0.331104 | 0.165552 | − | 0.986201i | \(-0.447059\pi\) | ||||
0.165552 | + | 0.986201i | \(0.447059\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.01429 | −0.652342 | ||||||||
\(86\) | 0.145560 | − | 0.0840390i | 0.0156961 | − | 0.00906216i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.23466 | + | 2.13849i | −0.131615 | + | 0.227964i | ||||
\(89\) | −1.73166 | − | 2.99933i | −0.183556 | − | 0.317928i | 0.759533 | − | 0.650469i | \(-0.225427\pi\) |
−0.943089 | + | 0.332541i | \(0.892094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.00578583 | + | 1.57479i | 0.000606520 | + | 0.165082i | ||||
\(92\) | − | 4.01817i | − | 0.418923i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.05108 | − | 2.33889i | −0.417837 | − | 0.241239i | ||||
\(95\) | 3.04097 | + | 1.75570i | 0.311997 | + | 0.180131i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.53619i | − | 0.663650i | −0.943341 | − | 0.331825i | \(-0.892336\pi\) | ||
0.943341 | − | 0.331825i | \(-0.107664\pi\) | |||||||
\(98\) | 6.03630 | − | 3.54445i | 0.609758 | − | 0.358044i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.66500 | + | 6.34796i | 0.366500 | + | 0.634796i | ||||
\(101\) | −2.38358 | + | 4.12849i | −0.237176 | + | 0.410800i | −0.959903 | − | 0.280333i | \(-0.909555\pi\) |
0.722727 | + | 0.691133i | \(0.242888\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.32073 | − | 3.64927i | 0.622800 | − | 0.359574i | −0.155159 | − | 0.987890i | \(-0.549589\pi\) |
0.777958 | + | 0.628316i | \(0.216255\pi\) | |||||||
\(104\) | 0.595217 | 0.0583658 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.779637 | −0.0757250 | ||||||||
\(107\) | −3.76674 | + | 2.17473i | −0.364145 | + | 0.210239i | −0.670897 | − | 0.741550i | \(-0.734091\pi\) |
0.306753 | + | 0.951789i | \(0.400758\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.94523 | − | 3.36924i | 0.186320 | − | 0.322715i | −0.757701 | − | 0.652602i | \(-0.773677\pi\) |
0.944020 | + | 0.329887i | \(0.107011\pi\) | |||||||
\(110\) | 4.33539 | + | 7.50911i | 0.413363 | + | 0.715966i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.33128 | − | 2.28641i | −0.125795 | − | 0.216046i | ||||
\(113\) | − | 2.54003i | − | 0.238946i | −0.992837 | − | 0.119473i | \(-0.961880\pi\) | ||
0.992837 | − | 0.119473i | \(-0.0381205\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.2191 | − | 7.05472i | −1.13944 | − | 0.657856i | ||||
\(116\) | −7.47040 | − | 4.31304i | −0.693610 | − | 0.400456i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.5794i | 1.15802i | ||||||||
\(119\) | 2.25137 | − | 3.93278i | 0.206383 | − | 0.360518i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.45124 | − | 4.24567i | −0.222840 | − | 0.385970i | ||||
\(122\) | −6.18602 | + | 10.7145i | −0.560056 | + | 0.970046i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.78011 | + | 1.60510i | −0.249661 | + | 0.144142i | ||||
\(125\) | 8.18156 | 0.731781 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.8932 | 1.23282 | 0.616410 | − | 0.787425i | \(-0.288586\pi\) | ||||
0.616410 | + | 0.787425i | \(0.288586\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.04502 | − | 1.81004i | 0.0916548 | − | 0.158751i | ||||
\(131\) | −5.20576 | − | 9.01664i | −0.454830 | − | 0.787788i | 0.543849 | − | 0.839183i | \(-0.316966\pi\) |
−0.998678 | + | 0.0513953i | \(0.983633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.28641 | + | 1.33128i | −0.198257 | + | 0.115437i | ||||
\(134\) | 3.12267i | 0.269758i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.48332 | − | 0.856393i | −0.127193 | − | 0.0734351i | ||||
\(137\) | −5.54140 | − | 3.19933i | −0.473433 | − | 0.273337i | 0.244242 | − | 0.969714i | \(-0.421461\pi\) |
−0.717676 | + | 0.696377i | \(0.754794\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.6426i | 1.49643i | 0.663457 | + | 0.748214i | \(0.269088\pi\) | ||||
−0.663457 | + | 0.748214i | \(0.730912\pi\) | |||||||
\(140\) | −9.29025 | + | 0.0341328i | −0.785170 | + | 0.00288475i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.11324 | + | 7.12434i | 0.345176 | + | 0.597862i | ||||
\(143\) | 0.734889 | − | 1.27287i | 0.0614545 | − | 0.106442i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.2316 | + | 15.1448i | −2.17842 | + | 1.25771i | ||||
\(146\) | 2.12599 | 0.175948 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.13403 | −0.175416 | ||||||||
\(149\) | 5.31374 | − | 3.06789i | 0.435318 | − | 0.251331i | −0.266292 | − | 0.963893i | \(-0.585798\pi\) |
0.701610 | + | 0.712561i | \(0.252465\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.87298 | − | 17.1005i | 0.803451 | − | 1.39162i | −0.113880 | − | 0.993494i | \(-0.536328\pi\) |
0.917332 | − | 0.398124i | \(-0.130339\pi\) | |||||||
\(152\) | 0.500000 | + | 0.866025i | 0.0405554 | + | 0.0702439i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.53315 | + | 0.0240031i | −0.526456 | + | 0.00193422i | ||||
\(155\) | 11.2723i | 0.905413i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.0864 | − | 11.0195i | −1.52326 | − | 0.879456i | −0.999621 | − | 0.0275164i | \(-0.991240\pi\) |
−0.523641 | − | 0.851939i | \(-0.675427\pi\) | |||||||
\(158\) | −4.09633 | − | 2.36502i | −0.325886 | − | 0.188151i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.51141i | 0.277601i | ||||||||
\(161\) | 9.18719 | − | 5.34933i | 0.724052 | − | 0.421586i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.39949 | + | 9.35218i | 0.422920 | + | 0.732519i | 0.996224 | − | 0.0868237i | \(-0.0276717\pi\) |
−0.573303 | + | 0.819343i | \(0.694338\pi\) | |||||||
\(164\) | −0.922706 | + | 1.59817i | −0.0720512 | + | 0.124796i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.61237 | − | 1.50825i | 0.202759 | − | 0.117063i | ||||
\(167\) | 16.7805 | 1.29852 | 0.649259 | − | 0.760568i | \(-0.275079\pi\) | ||||
0.649259 | + | 0.760568i | \(0.275079\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6457 | 0.972747 | ||||||||
\(170\) | −5.20853 | + | 3.00715i | −0.399476 | + | 0.230638i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.0840390 | − | 0.145560i | 0.00640791 | − | 0.0110988i | ||||
\(173\) | −10.5495 | − | 18.2723i | −0.802065 | − | 1.38922i | −0.918255 | − | 0.395990i | \(-0.870402\pi\) |
0.116190 | − | 0.993227i | \(-0.462932\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.63490 | + | 16.8306i | −0.728330 | + | 1.27228i | ||||
\(176\) | 2.46932i | 0.186132i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.99933 | − | 1.73166i | −0.224809 | − | 0.129793i | ||||
\(179\) | 4.81969 | + | 2.78265i | 0.360241 | + | 0.207985i | 0.669186 | − | 0.743095i | \(-0.266643\pi\) |
−0.308946 | + | 0.951080i | \(0.599976\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6398i | 1.38549i | 0.721184 | + | 0.692744i | \(0.243598\pi\) | ||||
−0.721184 | + | 0.692744i | \(0.756402\pi\) | |||||||
\(182\) | 0.792403 | + | 1.36091i | 0.0587368 | + | 0.100877i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.00908 | − | 3.47984i | −0.148112 | − | 0.256537i | ||||
\(185\) | −3.74673 | + | 6.48953i | −0.275465 | + | 0.477120i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.66278 | + | 2.11470i | −0.267849 | + | 0.154643i | ||||
\(188\) | −4.67779 | −0.341163 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.51141 | 0.254744 | ||||||||
\(191\) | 12.7116 | − | 7.33902i | 0.919776 | − | 0.531033i | 0.0362121 | − | 0.999344i | \(-0.488471\pi\) |
0.883563 | + | 0.468311i | \(0.155137\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.74286 | − | 6.48283i | 0.269417 | − | 0.466644i | −0.699294 | − | 0.714834i | \(-0.746502\pi\) |
0.968711 | + | 0.248190i | \(0.0798357\pi\) | |||||||
\(194\) | −3.26810 | − | 5.66051i | −0.234636 | − | 0.406401i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.45536 | − | 6.08773i | 0.246811 | − | 0.434838i | ||||
\(197\) | − | 0.755615i | − | 0.0538354i | −0.999638 | − | 0.0269177i | \(-0.991431\pi\) | ||
0.999638 | − | 0.0269177i | \(-0.00856920\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.97321 | − | 1.71658i | −0.210765 | − | 0.121685i | 0.390902 | − | 0.920432i | \(-0.372163\pi\) |
−0.601667 | + | 0.798747i | \(0.705497\pi\) | |||||||
\(200\) | 6.34796 | + | 3.66500i | 0.448869 | + | 0.259154i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.76717i | 0.335417i | ||||||||
\(203\) | −0.0838502 | − | 22.8223i | −0.00588513 | − | 1.60181i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.24000 | + | 5.61184i | 0.226291 | + | 0.391948i | ||||
\(206\) | 3.64927 | − | 6.32073i | 0.254257 | − | 0.440386i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.515473 | − | 0.297608i | 0.0357416 | − | 0.0206354i | ||||
\(209\) | 2.46932 | 0.170806 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.83114 | 0.126061 | 0.0630304 | − | 0.998012i | \(-0.479923\pi\) | ||||
0.0630304 | + | 0.998012i | \(0.479923\pi\) | |||||||
\(212\) | −0.675185 | + | 0.389819i | −0.0463719 | + | 0.0267728i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.17473 | + | 3.76674i | −0.148662 | + | 0.257489i | ||||
\(215\) | −0.295095 | − | 0.511120i | −0.0201253 | − | 0.0348581i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.37103 | − | 4.21963i | −0.500378 | − | 0.286447i | ||||
\(218\) | − | 3.89047i | − | 0.263496i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.50911 | + | 4.33539i | 0.506264 | + | 0.292292i | ||||
\(221\) | 0.882895 | + | 0.509740i | 0.0593899 | + | 0.0342888i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.7812i | − | 0.922858i | −0.887177 | − | 0.461429i | \(-0.847337\pi\) | ||
0.887177 | − | 0.461429i | \(-0.152663\pi\) | |||||||
\(224\) | −2.29613 | − | 1.31445i | −0.153417 | − | 0.0878253i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.27001 | − | 2.19973i | −0.0844801 | − | 0.146324i | ||||
\(227\) | 6.32021 | − | 10.9469i | 0.419487 | − | 0.726572i | −0.576401 | − | 0.817167i | \(-0.695543\pi\) |
0.995888 | + | 0.0905945i | \(0.0288767\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.62930 | + | 4.98213i | −0.570240 | + | 0.329228i | −0.757245 | − | 0.653131i | \(-0.773455\pi\) |
0.187005 | + | 0.982359i | \(0.440122\pi\) | |||||||
\(230\) | −14.1094 | −0.930348 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.62608 | −0.566330 | ||||||||
\(233\) | 15.6790 | − | 9.05228i | 1.02717 | − | 0.593035i | 0.110995 | − | 0.993821i | \(-0.464596\pi\) |
0.916172 | + | 0.400786i | \(0.131263\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.21281 | + | 14.2250i | −0.535745 | + | 0.927937i | ||||
\(236\) | 6.28968 | + | 10.8940i | 0.409423 | + | 0.709142i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.0166492 | − | 4.53158i | −0.00107921 | − | 0.293738i | ||||
\(239\) | − | 11.8112i | − | 0.764001i | −0.924162 | − | 0.382001i | \(-0.875235\pi\) | ||
0.924162 | − | 0.382001i | \(-0.124765\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.48526 | + | 4.89897i | 0.546583 | + | 0.315570i | 0.747743 | − | 0.663988i | \(-0.231138\pi\) |
−0.201159 | + | 0.979559i | \(0.564471\pi\) | |||||||
\(242\) | −4.24567 | − | 2.45124i | −0.272922 | − | 0.157572i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.3720i | 0.792039i | ||||||||
\(245\) | −12.4460 | − | 21.1959i | −0.795147 | − | 1.35416i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.297608 | − | 0.515473i | −0.0189364 | − | 0.0327988i | ||||
\(248\) | −1.60510 | + | 2.78011i | −0.101924 | + | 0.176537i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.08544 | − | 4.09078i | 0.448122 | − | 0.258724i | ||||
\(251\) | −9.52680 | −0.601326 | −0.300663 | − | 0.953730i | \(-0.597208\pi\) | ||||
−0.300663 | + | 0.953730i | \(0.597208\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.92212 | −0.623799 | ||||||||
\(254\) | 12.0318 | − | 6.94659i | 0.754945 | − | 0.435868i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 4.27855 | + | 7.41067i | 0.266889 | + | 0.462265i | 0.968057 | − | 0.250731i | \(-0.0806711\pi\) |
−0.701168 | + | 0.712996i | \(0.747338\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.84101 | − | 4.87928i | −0.176532 | − | 0.303184i | ||||
\(260\) | − | 2.09005i | − | 0.129619i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.01664 | − | 5.20576i | −0.557050 | − | 0.321613i | ||||
\(263\) | −19.2672 | − | 11.1239i | −1.18806 | − | 0.685929i | −0.230198 | − | 0.973144i | \(-0.573937\pi\) |
−0.957866 | + | 0.287214i | \(0.907271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.73762i | 0.168171i | ||||||||
\(266\) | −1.31445 | + | 2.29613i | −0.0805940 | + | 0.140785i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.56133 | + | 2.70431i | 0.0953737 | + | 0.165192i | ||||
\(269\) | −0.475904 | + | 0.824289i | −0.0290164 | + | 0.0502578i | −0.880169 | − | 0.474661i | \(-0.842571\pi\) |
0.851153 | + | 0.524918i | \(0.175904\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.5345 | − | 9.54618i | 1.00440 | − | 0.579889i | 0.0948509 | − | 0.995491i | \(-0.469763\pi\) |
0.909546 | + | 0.415602i | \(0.136429\pi\) | |||||||
\(272\) | −1.71279 | −0.103853 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.39865 | −0.386557 | ||||||||
\(275\) | 15.6751 | − | 9.05003i | 0.945245 | − | 0.545737i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.4005 | − | 24.9423i | 0.865239 | − | 1.49864i | −0.00156997 | − | 0.999999i | \(-0.500500\pi\) |
0.866809 | − | 0.498640i | \(-0.166167\pi\) | |||||||
\(278\) | 8.82131 | + | 15.2790i | 0.529067 | + | 0.916371i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.02853 | + | 4.67469i | −0.479796 | + | 0.279366i | ||||
\(281\) | 24.0917i | 1.43719i | 0.695427 | + | 0.718597i | \(0.255215\pi\) | ||||
−0.695427 | + | 0.718597i | \(0.744785\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.3568 | + | 11.1756i | 1.15064 | + | 0.664322i | 0.949043 | − | 0.315146i | \(-0.102054\pi\) |
0.201597 | + | 0.979469i | \(0.435387\pi\) | |||||||
\(284\) | 7.12434 | + | 4.11324i | 0.422752 | + | 0.244076i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1.46978i | − | 0.0869098i | ||||||
\(287\) | −4.88247 | + | 0.0179384i | −0.288203 | + | 0.00105887i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.03318 | + | 12.1818i | 0.413717 | + | 0.716578i | ||||
\(290\) | −15.1448 | + | 26.2316i | −0.889336 | + | 1.54037i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.84116 | − | 1.06300i | 0.107746 | − | 0.0622071i | ||||
\(293\) | 28.6949 | 1.67637 | 0.838186 | − | 0.545384i | \(-0.183616\pi\) | ||||
0.838186 | + | 0.545384i | \(0.183616\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 44.1713 | 2.57175 | ||||||||
\(296\) | −1.84813 | + | 1.06702i | −0.107420 | + | 0.0620191i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.06789 | − | 5.31374i | 0.177718 | − | 0.307816i | ||||
\(299\) | 1.19584 | + | 2.07126i | 0.0691573 | + | 0.119784i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.444690 | − | 0.00163381i | 0.0256315 | − | 9.41712e-5i | ||||
\(302\) | − | 19.7460i | − | 1.13625i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.866025 | + | 0.500000i | 0.0496700 | + | 0.0286770i | ||||
\(305\) | 37.6230 | + | 21.7217i | 2.15429 | + | 1.24378i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.9150i | 0.794171i | 0.917782 | + | 0.397085i | \(0.129978\pi\) | ||||
−0.917782 | + | 0.397085i | \(0.870022\pi\) | |||||||
\(308\) | −5.64587 | + | 3.28736i | −0.321703 | + | 0.187315i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.63615 | + | 9.76210i | 0.320112 | + | 0.554450i | ||||
\(311\) | 1.72103 | − | 2.98091i | 0.0975907 | − | 0.169032i | −0.813096 | − | 0.582129i | \(-0.802220\pi\) |
0.910687 | + | 0.413097i | \(0.135553\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.17108 | − | 1.83082i | 0.179240 | − | 0.103484i | −0.407696 | − | 0.913118i | \(-0.633668\pi\) |
0.586935 | + | 0.809634i | \(0.300334\pi\) | |||||||
\(314\) | −22.0391 | −1.24374 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.73003 | −0.266085 | ||||||||
\(317\) | 5.27797 | − | 3.04724i | 0.296440 | − | 0.171150i | −0.344402 | − | 0.938822i | \(-0.611918\pi\) |
0.640843 | + | 0.767672i | \(0.278585\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.6503 | + | 18.4468i | −0.596300 | + | 1.03282i | ||||
\(320\) | 1.75570 | + | 3.04097i | 0.0981469 | + | 0.169995i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.28168 | − | 9.22625i | 0.294336 | − | 0.514159i | ||||
\(323\) | 1.71279i | 0.0953020i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.77841 | − | 2.18147i | −0.209589 | − | 0.121006i | ||||
\(326\) | 9.35218 | + | 5.39949i | 0.517969 | + | 0.299050i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.84541i | 0.101896i | ||||||||
\(329\) | −6.22747 | − | 10.6954i | −0.343331 | − | 0.589654i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.4336 | − | 18.0715i | −0.573480 | − | 0.993297i | −0.996205 | − | 0.0870390i | \(-0.972260\pi\) |
0.422724 | − | 0.906258i | \(-0.361074\pi\) | |||||||
\(332\) | 1.50825 | − | 2.61237i | 0.0827760 | − | 0.143372i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.5324 | − | 8.39027i | 0.795176 | − | 0.459095i | ||||
\(335\) | 10.9650 | 0.599080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.40622 | −0.512390 | −0.256195 | − | 0.966625i | \(-0.582469\pi\) | ||||
−0.256195 | + | 0.966625i | \(0.582469\pi\) | |||||||
\(338\) | 10.9515 | − | 6.32286i | 0.595684 | − | 0.343918i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.00715 | + | 5.20853i | −0.163085 | + | 0.282472i | ||||
\(341\) | 3.96349 | + | 6.86496i | 0.214635 | + | 0.371759i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5191 | − | 0.204128i | 0.999939 | − | 0.0110219i | ||||
\(344\) | − | 0.168078i | − | 0.00906216i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.2723 | − | 10.5495i | −0.982325 | − | 0.567145i | ||||
\(347\) | 24.7087 | + | 14.2656i | 1.32643 | + | 0.765815i | 0.984746 | − | 0.173999i | \(-0.0556689\pi\) |
0.341685 | + | 0.939814i | \(0.389002\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.9001i | − | 0.583471i | −0.956499 | − | 0.291735i | \(-0.905767\pi\) | ||
0.956499 | − | 0.291735i | \(-0.0942326\pi\) | |||||||
\(350\) | 0.0712515 | + | 19.3932i | 0.00380855 | + | 1.03661i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.23466 | + | 2.13849i | 0.0658075 | + | 0.113982i | ||||
\(353\) | 14.9806 | − | 25.9471i | 0.797334 | − | 1.38102i | −0.124012 | − | 0.992281i | \(-0.539576\pi\) |
0.921346 | − | 0.388743i | \(-0.127091\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.0165 | − | 14.4433i | 1.32774 | − | 0.766569i | ||||
\(356\) | −3.46332 | −0.183556 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.56530 | 0.294135 | ||||||||
\(359\) | −11.4065 | + | 6.58557i | −0.602014 | + | 0.347573i | −0.769833 | − | 0.638245i | \(-0.779661\pi\) |
0.167820 | + | 0.985818i | \(0.446327\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.500000 | − | 0.866025i | 0.0263158 | − | 0.0455803i | ||||
\(362\) | 9.31992 | + | 16.1426i | 0.489844 | + | 0.848435i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.36670 | + | 0.782382i | 0.0716344 | + | 0.0410080i | ||||
\(365\) | − | 7.46523i | − | 0.390748i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.3387 | − | 7.70112i | −0.696276 | − | 0.401995i | 0.109683 | − | 0.993967i | \(-0.465016\pi\) |
−0.805959 | + | 0.591972i | \(0.798350\pi\) | |||||||
\(368\) | −3.47984 | − | 2.00908i | −0.181399 | − | 0.104731i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.49346i | 0.389567i | ||||||||
\(371\) | −1.79015 | − | 1.02479i | −0.0929400 | − | 0.0532046i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.482656 | + | 0.835984i | 0.0249910 | + | 0.0432856i | 0.878250 | − | 0.478201i | \(-0.158711\pi\) |
−0.853259 | + | 0.521487i | \(0.825378\pi\) | |||||||
\(374\) | −2.11470 | + | 3.66278i | −0.109349 | + | 0.189398i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.05108 | + | 2.33889i | −0.208919 | + | 0.120619i | ||||
\(377\) | 5.13439 | 0.264434 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.8827 | 1.79180 | 0.895902 | − | 0.444251i | \(-0.146530\pi\) | ||||
0.895902 | + | 0.444251i | \(0.146530\pi\) | |||||||
\(380\) | 3.04097 | − | 1.75570i | 0.155998 | − | 0.0900657i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.33902 | − | 12.7116i | 0.375497 | − | 0.650380i | ||||
\(383\) | 7.87352 | + | 13.6373i | 0.402318 | + | 0.696836i | 0.994005 | − | 0.109332i | \(-0.0348712\pi\) |
−0.591687 | + | 0.806168i | \(0.701538\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0842847 | + | 22.9406i | 0.00429555 | + | 1.16916i | ||||
\(386\) | − | 7.48572i | − | 0.381013i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.66051 | − | 3.26810i | −0.287369 | − | 0.165912i | ||||
\(389\) | 1.05300 | + | 0.607951i | 0.0533893 | + | 0.0308244i | 0.526457 | − | 0.850202i | \(-0.323520\pi\) |
−0.473068 | + | 0.881026i | \(0.656853\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.88226i | − | 0.348051i | ||||||
\(392\) | −0.0514360 | − | 6.99981i | −0.00259791 | − | 0.353544i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.377808 | − | 0.654382i | −0.0190337 | − | 0.0329673i | ||||
\(395\) | −8.30454 | + | 14.3839i | −0.417847 | + | 0.723732i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.69826 | − | 0.980491i | 0.0852332 | − | 0.0492094i | −0.456778 | − | 0.889581i | \(-0.650996\pi\) |
0.542011 | + | 0.840371i | \(0.317663\pi\) | |||||||
\(398\) | −3.43317 | −0.172089 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.32999 | 0.366500 | ||||||||
\(401\) | 29.5213 | − | 17.0441i | 1.47422 | − | 0.851143i | 0.474645 | − | 0.880177i | \(-0.342576\pi\) |
0.999578 | + | 0.0290337i | \(0.00924300\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.955380 | − | 1.65477i | 0.0475909 | − | 0.0824298i | ||||
\(404\) | 2.38358 | + | 4.12849i | 0.118588 | + | 0.205400i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.4838 | − | 19.7228i | −0.569930 | − | 0.978825i | ||||
\(407\) | 5.26960i | 0.261204i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.6709 | − | 18.8625i | −1.61547 | − | 0.932692i | −0.988072 | − | 0.153995i | \(-0.950786\pi\) |
−0.627399 | − | 0.778698i | \(-0.715881\pi\) | |||||||
\(410\) | 5.61184 | + | 3.24000i | 0.277149 | + | 0.160012i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 7.29855i | − | 0.359574i | ||||||
\(413\) | −16.5349 | + | 28.8839i | −0.813630 | + | 1.42128i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.29608 | − | 9.17308i | −0.259974 | − | 0.450289i | ||||
\(416\) | 0.297608 | − | 0.515473i | 0.0145915 | − | 0.0252731i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.13849 | − | 1.23466i | 0.104597 | − | 0.0603891i | ||||
\(419\) | −14.1892 | −0.693189 | −0.346594 | − | 0.938015i | \(-0.612662\pi\) | ||||
−0.346594 | + | 0.938015i | \(0.612662\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.8221 | 1.35597 | 0.677984 | − | 0.735077i | \(-0.262854\pi\) | ||||
0.677984 | + | 0.735077i | \(0.262854\pi\) | |||||||
\(422\) | 1.58581 | − | 0.915570i | 0.0771962 | − | 0.0445692i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.389819 | + | 0.675185i | −0.0189313 | + | 0.0327899i | ||||
\(425\) | 6.27735 | + | 10.8727i | 0.304496 | + | 0.527403i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.2876 | + | 16.4707i | −1.36893 | + | 0.797074i | ||||
\(428\) | 4.34946i | 0.210239i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.511120 | − | 0.295095i | −0.0246484 | − | 0.0142308i | ||||
\(431\) | 17.4360 | + | 10.0667i | 0.839862 | + | 0.484894i | 0.857217 | − | 0.514955i | \(-0.172191\pi\) |
−0.0173556 | + | 0.999849i | \(0.505525\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.4757i | 0.743715i | 0.928290 | + | 0.371858i | \(0.121279\pi\) | ||||
−0.928290 | + | 0.371858i | \(0.878721\pi\) | |||||||
\(434\) | −8.49331 | + | 0.0312048i | −0.407692 | + | 0.00149788i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.94523 | − | 3.36924i | −0.0931598 | − | 0.161358i | ||||
\(437\) | −2.00908 | + | 3.47984i | −0.0961075 | + | 0.166463i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.0606 | − | 14.4687i | 1.19608 | − | 0.690555i | 0.236398 | − | 0.971656i | \(-0.424033\pi\) |
0.959678 | + | 0.281101i | \(0.0906997\pi\) | |||||||
\(440\) | 8.67078 | 0.413363 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.01948 | 0.0484917 | ||||||||
\(443\) | −31.6887 | + | 18.2955i | −1.50557 | + | 0.869244i | −0.505596 | + | 0.862771i | \(0.668727\pi\) |
−0.999979 | + | 0.00647350i | \(0.997939\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.08057 | + | 10.5319i | −0.288247 | + | 0.499258i | ||||
\(446\) | −6.89060 | − | 11.9349i | −0.326280 | − | 0.565133i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.64573 | + | 0.00972055i | −0.124999 | + | 0.000459253i | ||||
\(449\) | 39.6301i | 1.87026i | 0.354302 | + | 0.935131i | \(0.384719\pi\) | ||||
−0.354302 | + | 0.935131i | \(0.615281\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.94639 | + | 2.27845i | 0.185828 | + | 0.107288i | ||||
\(452\) | −2.19973 | − | 1.27001i | −0.103467 | − | 0.0597365i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 12.6404i | − | 0.593244i | ||||||
\(455\) | 4.77872 | − | 2.78245i | 0.224030 | − | 0.130443i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.20628 | + | 7.28548i | 0.196761 | + | 0.340800i | 0.947476 | − | 0.319825i | \(-0.103624\pi\) |
−0.750715 | + | 0.660626i | \(0.770291\pi\) | |||||||
\(458\) | −4.98213 | + | 8.62930i | −0.232800 | + | 0.403221i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.2191 | + | 7.05472i | −0.569720 | + | 0.328928i | ||||
\(461\) | −40.2269 | −1.87355 | −0.936776 | − | 0.349929i | \(-0.886206\pi\) | ||||
−0.936776 | + | 0.349929i | \(0.886206\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.8560 | 1.10868 | 0.554342 | − | 0.832289i | \(-0.312970\pi\) | ||||
0.554342 | + | 0.832289i | \(0.312970\pi\) | |||||||
\(464\) | −7.47040 | + | 4.31304i | −0.346805 | + | 0.200228i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.05228 | − | 15.6790i | 0.419339 | − | 0.726316i | ||||
\(467\) | −17.7826 | − | 30.8004i | −0.822881 | − | 1.42527i | −0.903528 | − | 0.428529i | \(-0.859032\pi\) |
0.0806471 | − | 0.996743i | \(-0.474301\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.10459 | + | 7.17006i | −0.189532 | + | 0.331083i | ||||
\(470\) | 16.4256i | 0.757658i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.8940 | + | 6.28968i | 0.501439 | + | 0.289506i | ||||
\(473\) | −0.359433 | − | 0.207519i | −0.0165267 | − | 0.00954172i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 7.32999i | − | 0.336323i | ||||||
\(476\) | −2.28021 | − | 3.91613i | −0.104513 | − | 0.179496i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.90559 | − | 10.2288i | −0.270115 | − | 0.467853i | ||||
\(479\) | −19.0260 | + | 32.9540i | −0.869321 | + | 1.50571i | −0.00662907 | + | 0.999978i | \(0.502110\pi\) |
−0.862692 | + | 0.505730i | \(0.831223\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.10004 | − | 0.635106i | 0.0501573 | − | 0.0289584i | ||||
\(482\) | 9.79793 | 0.446283 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.90248 | −0.222840 | ||||||||
\(485\) | −19.8764 | + | 11.4756i | −0.902539 | + | 0.521081i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.2268 | + | 24.6416i | −0.644680 | + | 1.11662i | 0.339695 | + | 0.940535i | \(0.389676\pi\) |
−0.984375 | + | 0.176083i | \(0.943657\pi\) | |||||||
\(488\) | 6.18602 | + | 10.7145i | 0.280028 | + | 0.485023i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.3765 | − | 12.1332i | −0.965693 | − | 0.548121i | ||||
\(491\) | − | 41.4753i | − | 1.87175i | −0.352327 | − | 0.935877i | \(-0.614609\pi\) | ||
0.352327 | − | 0.935877i | \(-0.385391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.7952 | − | 7.38731i | −0.576267 | − | 0.332708i | ||||
\(494\) | −0.515473 | − | 0.297608i | −0.0231922 | − | 0.0133900i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.21019i | 0.144142i | ||||||||
\(497\) | 0.0799659 | + | 21.7651i | 0.00358696 | + | 0.976298i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.7711 | − | 18.6560i | −0.482179 | − | 0.835158i | 0.517612 | − | 0.855616i | \(-0.326821\pi\) |
−0.999791 | + | 0.0204573i | \(0.993488\pi\) | |||||||
\(500\) | 4.09078 | − | 7.08544i | 0.182945 | − | 0.316870i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.25045 | + | 4.76340i | −0.368236 | + | 0.212601i | ||||
\(503\) | −0.949169 | −0.0423214 | −0.0211607 | − | 0.999776i | \(-0.506736\pi\) | ||||
−0.0211607 | + | 0.999776i | \(0.506736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.7395 | 0.744897 | ||||||||
\(506\) | −8.59281 | + | 4.96106i | −0.381997 | + | 0.220546i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.94659 | − | 12.0318i | 0.308205 | − | 0.533827i | ||||
\(509\) | 13.8688 | + | 24.0215i | 0.614724 | + | 1.06473i | 0.990433 | + | 0.137996i | \(0.0440661\pi\) |
−0.375708 | + | 0.926738i | \(0.622601\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.88156 | + | 2.79451i | 0.215947 | + | 0.123622i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.41067 | + | 4.27855i | 0.326870 | + | 0.188719i | ||||
\(515\) | −22.1947 | − | 12.8141i | −0.978013 | − | 0.564656i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.5509i | 0.508010i | ||||||||
\(518\) | −4.90002 | − | 2.80508i | −0.215295 | − | 0.123248i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.04502 | − | 1.81004i | −0.0458274 | − | 0.0793753i | ||||
\(521\) | −7.62372 | + | 13.2047i | −0.334001 | + | 0.578507i | −0.983292 | − | 0.182033i | \(-0.941732\pi\) |
0.649291 | + | 0.760540i | \(0.275066\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.85055 | − | 1.06842i | 0.0809190 | − | 0.0467186i | −0.458995 | − | 0.888439i | \(-0.651790\pi\) |
0.539914 | + | 0.841720i | \(0.318457\pi\) | |||||||
\(524\) | −10.4115 | −0.454830 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.2478 | −0.970051 | ||||||||
\(527\) | −4.76173 | + | 2.74919i | −0.207424 | + | 0.119756i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.42716 | + | 5.93602i | −0.149007 | + | 0.258088i | ||||
\(530\) | 1.36881 | + | 2.37085i | 0.0594574 | + | 0.102983i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.00972055 | + | 2.64573i | 0.000421439 | + | 0.114707i | ||||
\(533\) | − | 1.09842i | − | 0.0475779i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.2266 | + | 7.63637i | 0.571835 | + | 0.330149i | ||||
\(536\) | 2.70431 | + | 1.56133i | 0.116808 | + | 0.0674394i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.951807i | 0.0410353i | ||||||||
\(539\) | −15.0325 | − | 8.53237i | −0.647497 | − | 0.367515i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.26233 | − | 16.0428i | −0.398219 | − | 0.689735i | 0.595287 | − | 0.803513i | \(-0.297038\pi\) |
−0.993506 | + | 0.113778i | \(0.963705\pi\) | |||||||
\(542\) | 9.54618 | − | 16.5345i | 0.410043 | − | 0.710216i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.48332 | + | 0.856393i | −0.0635967 | + | 0.0367176i | ||||
\(545\) | −13.6610 | −0.585174 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.6461 | 1.48136 | 0.740680 | − | 0.671858i | \(-0.234503\pi\) | ||||
0.740680 | + | 0.671858i | \(0.234503\pi\) | |||||||
\(548\) | −5.54140 | + | 3.19933i | −0.236717 | + | 0.136668i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.05003 | − | 15.6751i | 0.385895 | − | 0.668389i | ||||
\(551\) | 4.31304 | + | 7.47040i | 0.183742 | + | 0.318250i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.29702 | − | 10.8148i | −0.267777 | − | 0.459892i | ||||
\(554\) | − | 28.8009i | − | 1.22363i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.2790 | + | 8.82131i | 0.647972 | + | 0.374107i | ||||
\(557\) | 37.8710 | + | 21.8649i | 1.60465 | + | 0.926444i | 0.990540 | + | 0.137221i | \(0.0438170\pi\) |
0.614107 | + | 0.789223i | \(0.289516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.100043i | 0.00423136i | ||||||||
\(560\) | −4.61557 | + | 8.06266i | −0.195043 | + | 0.340710i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.0459 | + | 20.8641i | 0.508125 | + | 0.880098i | ||||
\(563\) | 21.2955 | − | 36.8848i | 0.897497 | − | 1.55451i | 0.0668136 | − | 0.997765i | \(-0.478717\pi\) |
0.830683 | − | 0.556745i | \(-0.187950\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.72415 | + | 4.45954i | −0.324958 | + | 0.187614i | ||||
\(566\) | 22.3513 | 0.939494 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.22648 | 0.345176 | ||||||||
\(569\) | −37.1444 | + | 21.4454i | −1.55718 | + | 0.899036i | −0.559651 | + | 0.828729i | \(0.689065\pi\) |
−0.997525 | + | 0.0703073i | \(0.977602\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.8552 | − | 23.9980i | 0.579824 | − | 1.00428i | −0.415675 | − | 0.909513i | \(-0.636455\pi\) |
0.995499 | − | 0.0947712i | \(-0.0302120\pi\) | |||||||
\(572\) | −0.734889 | − | 1.27287i | −0.0307273 | − | 0.0532212i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.21937 | + | 2.45677i | −0.176113 | + | 0.102544i | ||||
\(575\) | 29.4531i | 1.22828i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.3272 | − | 7.11713i | −0.513189 | − | 0.296290i | 0.220954 | − | 0.975284i | \(-0.429083\pi\) |
−0.734144 | + | 0.678994i | \(0.762416\pi\) | |||||||
\(578\) | 12.1818 | + | 7.03318i | 0.506697 | + | 0.292542i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 30.2897i | 1.25771i | ||||||||
\(581\) | 7.98085 | − | 0.0293220i | 0.331102 | − | 0.00121648i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.962585 | + | 1.66725i | 0.0398662 | + | 0.0690503i | ||||
\(584\) | 1.06300 | − | 1.84116i | 0.0439871 | − | 0.0761879i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.8505 | − | 14.3474i | 1.02656 | − | 0.592687i | ||||
\(587\) | −24.0614 | −0.993120 | −0.496560 | − | 0.868002i | \(-0.665404\pi\) | ||||
−0.496560 | + | 0.868002i | \(0.665404\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.21019 | 0.132274 | ||||||||
\(590\) | 38.2534 | − | 22.0856i | 1.57487 | − | 0.909251i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.06702 | + | 1.84813i | −0.0438541 | + | 0.0759575i | ||||
\(593\) | −12.0326 | − | 20.8410i | −0.494119 | − | 0.855839i | 0.505858 | − | 0.862617i | \(-0.331176\pi\) |
−0.999977 | + | 0.00677788i | \(0.997843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.9122 | + | 0.0584622i | −0.652337 | + | 0.00239672i | ||||
\(596\) | − | 6.13577i | − | 0.251331i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.07126 | + | 1.19584i | 0.0847000 | + | 0.0489016i | ||||
\(599\) | −1.13337 | − | 0.654351i | −0.0463082 | − | 0.0267361i | 0.476667 | − | 0.879084i | \(-0.341845\pi\) |
−0.522975 | + | 0.852348i | \(0.675178\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.10485i | 0.330604i | 0.986243 | + | 0.165302i | \(0.0528598\pi\) | ||||
−0.986243 | + | 0.165302i | \(0.947140\pi\) | |||||||
\(602\) | 0.384296 | − | 0.223760i | 0.0156627 | − | 0.00911976i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.87298 | − | 17.1005i | −0.401726 | − | 0.695809i | ||||
\(605\) | −8.60731 | + | 14.9083i | −0.349937 | + | 0.606108i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0945 | − | 8.13749i | 0.572080 | − | 0.330291i | −0.185900 | − | 0.982569i | \(-0.559520\pi\) |
0.757980 | + | 0.652278i | \(0.226187\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 43.4433 | 1.75897 | ||||||||
\(611\) | 2.41127 | − | 1.39215i | 0.0975497 | − | 0.0563203i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0546 | − | 24.3434i | 0.567662 | − | 0.983219i | −0.429135 | − | 0.903241i | \(-0.641181\pi\) |
0.996797 | − | 0.0799787i | \(-0.0254852\pi\) | |||||||
\(614\) | 6.95750 | + | 12.0507i | 0.280782 | + | 0.486328i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.24579 | + | 5.66988i | −0.130777 | + | 0.228446i | ||||
\(617\) | 7.61122i | 0.306416i | 0.988194 | + | 0.153208i | \(0.0489605\pi\) | ||||
−0.988194 | + | 0.153208i | \(0.951040\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.51794 | + | 1.45373i | 0.101204 | + | 0.0584304i | 0.549748 | − | 0.835331i | \(-0.314724\pi\) |
−0.448543 | + | 0.893761i | \(0.648057\pi\) | |||||||
\(620\) | 9.76210 | + | 5.63615i | 0.392055 | + | 0.226353i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 3.44206i | − | 0.138014i | ||||||
\(623\) | −4.61067 | − | 7.91858i | −0.184723 | − | 0.317251i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.96059 | + | 6.85994i | 0.158423 | + | 0.274398i | ||||
\(626\) | 1.83082 | − | 3.17108i | 0.0731744 | − | 0.126742i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.0864 | + | 11.0195i | −0.761631 | + | 0.439728i | ||||
\(629\) | −3.65514 | −0.145740 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.84789 | −0.0735633 | −0.0367817 | − | 0.999323i | \(-0.511711\pi\) | ||||
−0.0367817 | + | 0.999323i | \(0.511711\pi\) | |||||||
\(632\) | −4.09633 | + | 2.36502i | −0.162943 | + | 0.0940753i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.04724 | − | 5.27797i | 0.121021 | − | 0.209615i | ||||
\(635\) | −24.3923 | − | 42.2487i | −0.967979 | − | 1.67659i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0306155 | + | 4.16641i | 0.00121303 | + | 0.165079i | ||||
\(638\) | 21.3005i | 0.843295i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.04097 | + | 1.75570i | 0.120205 | + | 0.0694003i | ||||
\(641\) | 23.2092 | + | 13.3999i | 0.916710 | + | 0.529263i | 0.882584 | − | 0.470155i | \(-0.155802\pi\) |
0.0341261 | + | 0.999418i | \(0.489135\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.3736i | 0.527403i | 0.964604 | + | 0.263702i | \(0.0849434\pi\) | ||||
−0.964604 | + | 0.263702i | \(0.915057\pi\) | |||||||
\(644\) | −0.0390588 | − | 10.6310i | −0.00153913 | − | 0.418920i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.856393 | + | 1.48332i | 0.0336943 | + | 0.0583603i | ||||
\(647\) | 9.15663 | − | 15.8598i | 0.359984 | − | 0.623511i | −0.627973 | − | 0.778235i | \(-0.716115\pi\) |
0.987958 | + | 0.154724i | \(0.0494487\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.9008 | − | 15.5312i | 1.05595 | − | 0.609653i | ||||
\(650\) | −4.36294 | −0.171128 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.7990 | 0.422920 | ||||||||
\(653\) | −32.0199 | + | 18.4867i | −1.25304 | + | 0.723440i | −0.971711 | − | 0.236172i | \(-0.924107\pi\) |
−0.281324 | + | 0.959613i | \(0.590774\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.2796 | + | 31.6611i | −0.714241 | + | 1.23710i | ||||
\(656\) | 0.922706 | + | 1.59817i | 0.0360256 | + | 0.0623982i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.7408 | − | 6.14871i | −0.418721 | − | 0.239702i | ||||
\(659\) | − | 5.54025i | − | 0.215818i | −0.994161 | − | 0.107909i | \(-0.965585\pi\) | ||
0.994161 | − | 0.107909i | \(-0.0344155\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.8347 | + | 18.3798i | 1.23822 | + | 0.714890i | 0.968731 | − | 0.248113i | \(-0.0798103\pi\) |
0.269494 | + | 0.963002i | \(0.413144\pi\) | |||||||
\(662\) | −18.0715 | − | 10.4336i | −0.702367 | − | 0.405512i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 3.01650i | − | 0.117063i | ||||||
\(665\) | 8.06266 | + | 4.61557i | 0.312657 | + | 0.178984i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.3305 | − | 30.0173i | −0.671040 | − | 1.16228i | ||||
\(668\) | 8.39027 | − | 14.5324i | 0.324629 | − | 0.562274i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.49594 | − | 5.48248i | 0.366860 | − | 0.211807i | ||||
\(671\) | 30.5505 | 1.17939 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.9341 | 1.53935 | 0.769674 | − | 0.638437i | \(-0.220419\pi\) | ||||
0.769674 | + | 0.638437i | \(0.220419\pi\) | |||||||
\(674\) | −8.14603 | + | 4.70311i | −0.313773 | + | 0.181157i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.32286 | − | 10.9515i | 0.243187 | − | 0.421212i | ||||
\(677\) | 13.1842 | + | 22.8357i | 0.506709 | + | 0.877645i | 0.999970 | + | 0.00776410i | \(0.00247141\pi\) |
−0.493261 | + | 0.869881i | \(0.664195\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0635354 | − | 17.2930i | −0.00243826 | − | 0.663645i | ||||
\(680\) | 6.01429i | 0.230638i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.86496 | + | 3.96349i | 0.262873 | + | 0.151770i | ||||
\(683\) | −16.1103 | − | 9.30128i | −0.616443 | − | 0.355904i | 0.159040 | − | 0.987272i | \(-0.449160\pi\) |
−0.775483 | + | 0.631369i | \(0.782494\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.4683i | 0.858469i | ||||||||
\(686\) | 15.9360 | − | 9.43635i | 0.608438 | − | 0.360281i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.0840390 | − | 0.145560i | −0.00320396 | − | 0.00554942i | ||||
\(689\) | 0.232027 | − | 0.401882i | 0.00883951 | − | 0.0153105i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.9045 | − | 14.3786i | 0.947413 | − | 0.546989i | 0.0551367 | − | 0.998479i | \(-0.482441\pi\) |
0.892276 | + | 0.451490i | \(0.149107\pi\) | |||||||
\(692\) | −21.0990 | −0.802065 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.5311 | 1.08303 | ||||||||
\(695\) | 53.6507 | − | 30.9752i | 2.03509 | − | 1.17496i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.58040 | + | 2.73733i | −0.0598618 | + | 0.103684i | ||||
\(698\) | −5.45007 | − | 9.43979i | −0.206288 | − | 0.357301i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.75831 | + | 16.7594i | 0.368829 | + | 0.633445i | ||||
\(701\) | 28.8513i | 1.08970i | 0.838535 | + | 0.544848i | \(0.183413\pi\) | ||||
−0.838535 | + | 0.544848i | \(0.816587\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.84813 | + | 1.06702i | 0.0697034 | + | 0.0402433i | ||||
\(704\) | 2.13849 | + | 1.23466i | 0.0805974 | + | 0.0465329i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 29.9611i | − | 1.12760i | ||||||
\(707\) | −6.26620 | + | 10.9461i | −0.235665 | + | 0.411669i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.1282 | − | 29.6669i | −0.643263 | − | 1.11416i | −0.984700 | − | 0.174260i | \(-0.944247\pi\) |
0.341437 | − | 0.939905i | \(-0.389087\pi\) | |||||||
\(710\) | 14.4433 | − | 25.0165i | 0.542046 | − | 0.938852i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.99933 | + | 1.73166i | −0.112404 | + | 0.0648967i | ||||
\(713\) | −12.8991 | −0.483075 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.16099 | −0.193010 | ||||||||
\(716\) | 4.81969 | − | 2.78265i | 0.180120 | − | 0.103993i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.58557 | + | 11.4065i | −0.245771 | + | 0.425688i | ||||
\(719\) | −13.3470 | − | 23.1178i | −0.497761 | − | 0.862147i | 0.502236 | − | 0.864731i | \(-0.332511\pi\) |
−0.999997 | + | 0.00258353i | \(0.999178\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.6875 | − | 9.71645i | 0.621474 | − | 0.361859i | ||||
\(722\) | − | 1.00000i | − | 0.0372161i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.1426 | + | 9.31992i | 0.599934 | + | 0.346372i | ||||
\(725\) | 54.7580 | + | 31.6145i | 2.03366 | + | 1.17413i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 22.2729i | − | 0.826056i | −0.910718 | − | 0.413028i | \(-0.864471\pi\) | ||
0.910718 | − | 0.413028i | \(-0.135529\pi\) | |||||||
\(728\) | 1.57479 | − | 0.00578583i | 0.0583654 | − | 0.000214437i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.73261 | − | 6.46508i | −0.138150 | − | 0.239283i | ||||
\(731\) | 0.143941 | − | 0.249313i | 0.00532384 | − | 0.00922117i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.7349 | − | 19.4768i | 1.24603 | − | 0.719393i | 0.275711 | − | 0.961241i | \(-0.411087\pi\) |
0.970314 | + | 0.241847i | \(0.0777533\pi\) | |||||||
\(734\) | −15.4022 | −0.568507 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.01817 | −0.148112 | ||||||||
\(737\) | 6.67780 | − | 3.85543i | 0.245980 | − | 0.142016i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.5489 | + | 20.0033i | −0.424834 | + | 0.735834i | −0.996405 | − | 0.0847187i | \(-0.973001\pi\) |
0.571571 | + | 0.820553i | \(0.306334\pi\) | |||||||
\(740\) | 3.74673 | + | 6.48953i | 0.137733 | + | 0.238560i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.06271 | + | 0.00757850i | −0.0757245 | + | 0.000278215i | ||||
\(743\) | 8.62955i | 0.316587i | 0.987392 | + | 0.158294i | \(0.0505993\pi\) | ||||
−0.987392 | + | 0.158294i | \(0.949401\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.6587 | − | 10.7726i | −0.683602 | − | 0.394678i | ||||
\(746\) | 0.835984 | + | 0.482656i | 0.0306076 | + | 0.0176713i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.22941i | 0.154643i | ||||||||
\(749\) | −9.94466 | + | 5.79037i | −0.363370 | + | 0.211576i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.46386 | − | 16.3919i | −0.345341 | − | 0.598148i | 0.640075 | − | 0.768313i | \(-0.278903\pi\) |
−0.985416 | + | 0.170164i | \(0.945570\pi\) | |||||||
\(752\) | −2.33889 | + | 4.05108i | −0.0852907 | + | 0.147728i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.44651 | − | 2.56719i | 0.161932 | − | 0.0934917i | ||||
\(755\) | −69.3361 | −2.52340 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.8603 | 0.431070 | 0.215535 | − | 0.976496i | \(-0.430850\pi\) | ||||
0.215535 | + | 0.976496i | \(0.430850\pi\) | |||||||
\(758\) | 30.2093 | − | 17.4414i | 1.09725 | − | 0.633499i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.75570 | − | 3.04097i | 0.0636861 | − | 0.110308i | ||||
\(761\) | −11.1902 | − | 19.3820i | −0.405644 | − | 0.702596i | 0.588752 | − | 0.808314i | \(-0.299619\pi\) |
−0.994396 | + | 0.105718i | \(0.966286\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.11382 | − | 8.93303i | 0.185133 | − | 0.323397i | ||||
\(764\) | − | 14.6780i | − | 0.531033i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.6373 | + | 7.87352i | 0.492737 | + | 0.284482i | ||||
\(767\) | −6.48432 | − | 3.74372i | −0.234135 | − | 0.135178i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.7566i | 1.46972i | 0.678218 | + | 0.734861i | \(0.262753\pi\) | ||||
−0.678218 | + | 0.734861i | \(0.737247\pi\) | |||||||
\(770\) | 11.5433 | + | 19.8250i | 0.415991 | + | 0.714442i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.74286 | − | 6.48283i | −0.134709 | − | 0.233322i | ||||
\(773\) | −3.96252 | + | 6.86328i | −0.142522 | + | 0.246855i | −0.928446 | − | 0.371468i | \(-0.878854\pi\) |
0.785924 | + | 0.618323i | \(0.212188\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.3782 | − | 11.7653i | 0.732005 | − | 0.422624i | ||||
\(776\) | −6.53619 | −0.234636 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.21590 | 0.0435922 | ||||||||
\(779\) | 1.59817 | − | 0.922706i | 0.0572605 | − | 0.0330594i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.1569 | − | 17.5923i | 0.363442 | − | 0.629500i | ||||
\(782\) | −3.44113 | − | 5.96021i | −0.123055 | − | 0.213137i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.54445 | − | 6.03630i | −0.126588 | − | 0.215582i | ||||
\(785\) | 77.3883i | 2.76211i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.7626 | + | 21.2249i | 1.31045 | + | 0.756587i | 0.982170 | − | 0.187995i | \(-0.0601988\pi\) |
0.328277 | + | 0.944582i | \(0.393532\pi\) | |||||||
\(788\) | −0.654382 | − | 0.377808i | −0.0233114 | − | 0.0134588i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.6091i | 0.590925i | ||||||||
\(791\) | −0.0246905 | − | 6.72024i | −0.000877892 | − | 0.238944i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.68202 | − | 6.37745i | −0.130753 | − | 0.226470i | ||||
\(794\) | 0.980491 | − | 1.69826i | 0.0347963 | − | 0.0602690i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.97321 | + | 1.71658i | −0.105383 | + | 0.0608427i | ||||
\(797\) | −19.7757 | −0.700491 | −0.350245 | − | 0.936658i | \(-0.613902\pi\) | ||||
−0.350245 | + | 0.936658i | \(0.613902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.01205 | −0.283446 | ||||||||
\(800\) | 6.34796 | − | 3.66500i | 0.224434 | − | 0.129577i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.0441 | − | 29.5213i | 0.601849 | − | 1.04243i | ||||
\(803\) | −2.62487 | − | 4.54641i | −0.0926297 | − | 0.160439i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.3971 | − | 18.5461i | −1.14185 | − | 0.653665i | ||||
\(806\) | − | 1.91076i | − | 0.0673037i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.12849 | + | 2.38358i | 0.145240 | + | 0.0838542i | ||||
\(809\) | 48.6212 | + | 28.0714i | 1.70943 | + | 0.986939i | 0.935261 | + | 0.353960i | \(0.115165\pi\) |
0.774168 | + | 0.632980i | \(0.218168\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 43.9345i | − | 1.54275i | −0.636381 | − | 0.771375i | \(-0.719569\pi\) | ||
0.636381 | − | 0.771375i | \(-0.280431\pi\) | |||||||
\(812\) | −19.8066 | − | 11.3385i | −0.695076 | − | 0.397905i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.63480 | + | 4.56361i | 0.0923497 | + | 0.159954i | ||||
\(815\) | 18.9598 | − | 32.8393i | 0.664133 | − | 1.15031i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.145560 | + | 0.0840390i | −0.00509249 | + | 0.00294015i | ||||
\(818\) | −37.7251 | −1.31903 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.48000 | 0.226291 | ||||||||
\(821\) | −25.3988 | + | 14.6640i | −0.886424 | + | 0.511777i | −0.872771 | − | 0.488129i | \(-0.837679\pi\) |
−0.0136531 | + | 0.999907i | \(0.504346\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.5361 | − | 18.2491i | 0.367267 | − | 0.636124i | −0.621871 | − | 0.783120i | \(-0.713627\pi\) |
0.989137 | + | 0.146996i | \(0.0469604\pi\) | |||||||
\(824\) | −3.64927 | − | 6.32073i | −0.127128 | − | 0.220193i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.122278 | + | 33.2816i | 0.00425460 | + | 1.15802i | ||||
\(827\) | − | 47.6743i | − | 1.65780i | −0.559397 | − | 0.828900i | \(-0.688967\pi\) | ||
0.559397 | − | 0.828900i | \(-0.311033\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.6003 | − | 7.85212i | −0.472357 | − | 0.272715i | 0.244869 | − | 0.969556i | \(-0.421255\pi\) |
−0.717226 | + | 0.696841i | \(0.754588\pi\) | |||||||
\(830\) | −9.17308 | − | 5.29608i | −0.318402 | − | 0.183830i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 0.595217i | − | 0.0206354i | ||||||
\(833\) | 5.91829 | − | 10.4270i | 0.205057 | − | 0.361274i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.4617 | − | 51.0291i | −1.01956 | − | 1.76593i | ||||
\(836\) | 1.23466 | − | 2.13849i | 0.0427015 | − | 0.0739612i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.2882 | + | 7.09461i | −0.424490 | + | 0.245079i | ||||
\(839\) | 33.2819 | 1.14902 | 0.574509 | − | 0.818498i | \(-0.305193\pi\) | ||||
0.574509 | + | 0.818498i | \(0.305193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −45.4092 | −1.56584 | ||||||||
\(842\) | 24.0947 | − | 13.9111i | 0.830357 | − | 0.479407i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.915570 | − | 1.58581i | 0.0315152 | − | 0.0545860i | ||||
\(845\) | −22.2021 | − | 38.4552i | −0.763777 | − | 1.32290i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.52660 | − | 11.2091i | −0.224257 | − | 0.385149i | ||||
\(848\) | 0.779637i | 0.0267728i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.8727 | + | 6.27735i | 0.372930 | + | 0.215311i | ||||
\(851\) | −7.42608 | − | 4.28745i | −0.254563 | − | 0.146972i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.7084i | 0.811760i | 0.913926 | + | 0.405880i | \(0.133035\pi\) | ||||
−0.913926 | + | 0.405880i | \(0.866965\pi\) | |||||||
\(854\) | −16.2624 | + | 28.4079i | −0.556488 | + | 0.972097i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.17473 | + | 3.76674i | 0.0743308 | + | 0.128745i | ||||
\(857\) | −5.33159 | + | 9.23459i | −0.182124 | + | 0.315448i | −0.942604 | − | 0.333914i | \(-0.891630\pi\) |
0.760480 | + | 0.649362i | \(0.224964\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.9964 | + | 10.3902i | −0.614028 | + | 0.354509i | −0.774540 | − | 0.632524i | \(-0.782019\pi\) |
0.160512 | + | 0.987034i | \(0.448685\pi\) | |||||||
\(860\) | −0.590190 | −0.0201253 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.1333 | 0.685744 | ||||||||
\(863\) | −3.81749 | + | 2.20403i | −0.129949 | + | 0.0750260i | −0.563565 | − | 0.826072i | \(-0.690571\pi\) |
0.433616 | + | 0.901098i | \(0.357237\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.0437 | + | 64.1615i | −1.25952 | + | 2.18156i | ||||
\(866\) | 7.73786 | + | 13.4024i | 0.262943 | + | 0.455431i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.33982 | + | 4.27368i | −0.249130 | + | 0.145058i | ||||
\(869\) | 11.6799i | 0.396215i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.60965 | − | 0.929333i | −0.0545410 | − | 0.0314892i | ||||
\(872\) | −3.36924 | − | 1.94523i | −0.114097 | − | 0.0658739i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.01817i | 0.135917i | ||||||||
\(875\) | 21.6462 | − | 0.0795292i | 0.731776 | − | 0.00268858i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.6203 | − | 20.1269i | −0.392388 | − | 0.679636i | 0.600376 | − | 0.799718i | \(-0.295018\pi\) |
−0.992764 | + | 0.120082i | \(0.961684\pi\) | |||||||
\(878\) | 14.4687 | − | 25.0606i | 0.488296 | − | 0.845754i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.50911 | − | 4.33539i | 0.253132 | − | 0.146146i | ||||
\(881\) | −39.9137 | −1.34473 | −0.672363 | − | 0.740222i | \(-0.734720\pi\) | ||||
−0.672363 | + | 0.740222i | \(0.734720\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.7953 | −1.20461 | −0.602305 | − | 0.798266i | \(-0.705751\pi\) | ||||
−0.602305 | + | 0.798266i | \(0.705751\pi\) | |||||||
\(884\) | 0.882895 | − | 0.509740i | 0.0296950 | − | 0.0171444i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.2955 | + | 31.6887i | −0.614648 | + | 1.06460i | ||||
\(887\) | 6.00830 | + | 10.4067i | 0.201739 | + | 0.349422i | 0.949089 | − | 0.315009i | \(-0.102007\pi\) |
−0.747350 | + | 0.664431i | \(0.768674\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.7576 | − | 0.135049i | 1.23281 | − | 0.00452941i | ||||
\(890\) | 12.1611i | 0.407642i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.9349 | − | 6.89060i | −0.399609 | − | 0.230714i | ||||
\(893\) | 4.05108 | + | 2.33889i | 0.135564 | + | 0.0782681i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 19.5420i | − | 0.653219i | ||||||
\(896\) | −2.28641 | + | 1.33128i | −0.0763837 | + | 0.0444751i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.8151 | + | 34.3207i | 0.661238 | + | 1.14530i | ||||
\(899\) | −13.8457 | + | 23.9814i | −0.461779 | + | 0.799825i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.15645 | + | 0.667676i | −0.0385269 | + | 0.0222435i | ||||
\(902\) | 4.55690 | 0.151728 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.54003 | −0.0844801 | ||||||||
\(905\) | 56.6832 | − | 32.7260i | 1.88421 | − | 1.08785i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.9526 | + | 36.2910i | −0.695720 | + | 1.20502i | 0.274217 | + | 0.961668i | \(0.411581\pi\) |
−0.969937 | + | 0.243355i | \(0.921752\pi\) | |||||||
\(908\) | −6.32021 | − | 10.9469i | −0.209743 | − | 0.363286i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.74726 | − | 4.79903i | 0.0910709 | − | 0.159086i | ||||
\(911\) | − | 12.1167i | − | 0.401445i | −0.979648 | − | 0.200723i | \(-0.935671\pi\) | ||
0.979648 | − | 0.200723i | \(-0.0643290\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.45075 | − | 3.72434i | −0.213489 | − | 0.123258i | ||||
\(914\) | 7.28548 | + | 4.20628i | 0.240982 | + | 0.139131i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.96426i | 0.329228i | ||||||||
\(917\) | −13.8607 | − | 23.8050i | −0.457721 | − | 0.786112i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.6700 | − | 27.1412i | −0.516904 | − | 0.895304i | −0.999807 | − | 0.0196305i | \(-0.993751\pi\) |
0.482903 | − | 0.875674i | \(-0.339582\pi\) | |||||||
\(920\) | −7.05472 | + | 12.2191i | −0.232587 | + | 0.402853i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.8375 | + | 20.1134i | −1.14731 | + | 0.662401i | ||||
\(923\) | −4.89654 | −0.161172 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.6424 | 0.514320 | ||||||||
\(926\) | 20.6599 | − | 11.9280i | 0.678927 | − | 0.391979i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.31304 | + | 7.47040i | −0.141582 | + | 0.245228i | ||||
\(929\) | −10.4378 | − | 18.0788i | −0.342454 | − | 0.593148i | 0.642434 | − | 0.766341i | \(-0.277925\pi\) |
−0.984888 | + | 0.173194i | \(0.944591\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.03630 | + | 3.54445i | −0.197832 | + | 0.116165i | ||||
\(932\) | − | 18.1046i | − | 0.593035i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −30.8004 | − | 17.7826i | −1.00782 | − | 0.581865i | ||||
\(935\) | 12.8615 | + | 7.42559i | 0.420616 | + | 0.242843i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.69948i | − | 0.120857i | −0.998173 | − | 0.0604283i | \(-0.980753\pi\) | ||
0.998173 | − | 0.0604283i | \(-0.0192467\pi\) | |||||||
\(938\) | 0.0303541 | + | 8.26175i | 0.000991095 | + | 0.269756i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.21281 | + | 14.2250i | 0.267872 | + | 0.463969i | ||||
\(941\) | 16.4609 | − | 28.5111i | 0.536610 | − | 0.929436i | −0.462473 | − | 0.886633i | \(-0.653038\pi\) |
0.999084 | − | 0.0428029i | \(-0.0136288\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.42173 | + | 3.70759i | −0.209120 | + | 0.120736i | ||||
\(944\) | 12.5794 | 0.409423 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.415038 | −0.0134940 | ||||||||
\(947\) | 23.7686 | − | 13.7228i | 0.772377 | − | 0.445932i | −0.0613449 | − | 0.998117i | \(-0.519539\pi\) |
0.833722 | + | 0.552185i | \(0.186206\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.632713 | + | 1.09589i | −0.0205387 | + | 0.0355741i | ||||
\(950\) | −3.66500 | − | 6.34796i | −0.118908 | − | 0.205955i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.93278 | − | 2.25137i | −0.127462 | − | 0.0729673i | ||||
\(953\) | 41.1355i | 1.33251i | 0.745725 | + | 0.666254i | \(0.232103\pi\) | ||||
−0.745725 | + | 0.666254i | \(0.767897\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44.6355 | − | 25.7703i | −1.44437 | − | 0.833907i | ||||
\(956\) | −10.2288 | − | 5.90559i | −0.330822 | − | 0.191000i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 38.0520i | 1.22941i | ||||||||
\(959\) | −14.6922 | − | 8.41070i | −0.474434 | − | 0.271596i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.3473 | − | 17.9221i | −0.333785 | − | 0.578132i | ||||
\(962\) | 0.635106 | − | 1.10004i | 0.0204766 | − | 0.0354666i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.48526 | − | 4.89897i | 0.273292 | − | 0.157785i | ||||
\(965\) | −26.2854 | −0.846158 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.9162 | −0.736934 | −0.368467 | − | 0.929641i | \(-0.620117\pi\) | ||||
−0.368467 | + | 0.929641i | \(0.620117\pi\) | |||||||
\(968\) | −4.24567 | + | 2.45124i | −0.136461 | + | 0.0787859i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.4756 | + | 19.8764i | −0.368460 | + | 0.638191i | ||||
\(971\) | 8.29489 | + | 14.3672i | 0.266196 | + | 0.461064i | 0.967876 | − | 0.251427i | \(-0.0808999\pi\) |
−0.701680 | + | 0.712492i | \(0.747567\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.171496 | + | 46.6777i | 0.00549791 | + | 1.49642i | ||||
\(974\) | 28.4537i | 0.911715i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.7145 | + | 6.18602i | 0.342963 | + | 0.198010i | ||||
\(977\) | −25.5981 | − | 14.7790i | −0.818954 | − | 0.472824i | 0.0311013 | − | 0.999516i | \(-0.490099\pi\) |
−0.850056 | + | 0.526693i | \(0.823432\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.55204i | 0.273324i | ||||||||
\(980\) | −24.5792 | + | 0.180613i | −0.785154 | + | 0.00576946i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20.7376 | − | 35.9187i | −0.661765 | − | 1.14621i | ||||
\(983\) | −0.150054 | + | 0.259900i | −0.00478596 | + | 0.00828953i | −0.868408 | − | 0.495850i | \(-0.834857\pi\) |
0.863623 | + | 0.504139i | \(0.168190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.29780 | + | 1.32664i | −0.0732141 | + | 0.0422702i | ||||
\(986\) | −14.7746 | −0.470520 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.595217 | −0.0189364 | ||||||||
\(989\) | 0.584884 | − | 0.337683i | 0.0185982 | − | 0.0107377i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.57216 | − | 7.91922i | 0.145240 | − | 0.251562i | −0.784223 | − | 0.620479i | \(-0.786938\pi\) |
0.929462 | + | 0.368917i | \(0.120271\pi\) | |||||||
\(992\) | 1.60510 | + | 2.78011i | 0.0509619 | + | 0.0882685i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.9518 | + | 18.8091i | 0.347370 | + | 0.596590i | ||||
\(995\) | 12.0553i | 0.382177i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.45887 | − | 1.99698i | −0.109544 | − | 0.0632450i | 0.444227 | − | 0.895914i | \(-0.353478\pi\) |
−0.553771 | + | 0.832669i | \(0.686812\pi\) | |||||||
\(998\) | −18.6560 | − | 10.7711i | −0.590546 | − | 0.340952i | ||||
\(999\) | 0 | 0 |
(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 | 2394.2.by.b.647.13 | yes | 48 | |
3.2 | odd | 2 | 2394.2.by.a.647.12 | ✓ | 48 | ||
7.5 | odd | 6 | 2394.2.by.a.2357.12 | yes | 48 | ||
21.5 | even | 6 | inner | 2394.2.by.b.2357.13 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2394.2.by.a.647.12 | ✓ | 48 | 3.2 | odd | 2 | ||
2394.2.by.a.2357.12 | yes | 48 | 7.5 | odd | 6 | ||
2394.2.by.b.647.13 | yes | 48 | 1.1 | even | 1 | trivial | |
2394.2.by.b.2357.13 | yes | 48 | 21.5 | even | 6 | inner |