Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(49,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.j (of order \(6\), degree \(2\), not 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: | \(3.79289409601\) |
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: | \( x^{16} - 11x^{14} + 82x^{12} - 337x^{10} + 1006x^{8} - 1596x^{6} + 1765x^{4} - 414x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-1.87040 + 1.07988i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.49 |
Dual form | 475.2.j.c.349.2 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.44154 | − | 0.832272i | −1.01932 | − | 0.588506i | −0.105414 | − | 0.994428i | \(-0.533617\pi\) |
−0.913907 | + | 0.405923i | \(0.866950\pi\) | |||||||
\(3\) | 1.00438 | + | 0.579878i | 0.579878 | + | 0.334793i | 0.761085 | − | 0.648652i | \(-0.224667\pi\) |
−0.181207 | + | 0.983445i | \(0.558000\pi\) | |||||||
\(4\) | 0.385355 | + | 0.667454i | 0.192677 | + | 0.333727i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.965233 | − | 1.67183i | −0.394055 | − | 0.682523i | ||||
\(7\) | 2.43525i | 0.920440i | 0.887805 | + | 0.460220i | \(0.152229\pi\) | ||||
−0.887805 | + | 0.460220i | \(0.847771\pi\) | |||||||
\(8\) | 2.04621i | 0.723444i | ||||||||
\(9\) | −0.827483 | − | 1.43324i | −0.275828 | − | 0.477748i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.75477 | −1.73513 | −0.867564 | − | 0.497326i | \(-0.834315\pi\) | ||||
−0.867564 | + | 0.497326i | \(0.834315\pi\) | |||||||
\(12\) | 0.893835i | 0.258028i | ||||||||
\(13\) | −1.38132 | + | 0.797505i | −0.383109 | + | 0.221188i | −0.679170 | − | 0.733981i | \(-0.737660\pi\) |
0.296061 | + | 0.955169i | \(0.404327\pi\) | |||||||
\(14\) | 2.02680 | − | 3.51051i | 0.541684 | − | 0.938224i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.47371 | − | 4.28460i | 0.618428 | − | 1.07115i | ||||
\(17\) | −5.18234 | − | 2.99203i | −1.25690 | − | 0.725673i | −0.284432 | − | 0.958696i | \(-0.591805\pi\) |
−0.972471 | + | 0.233023i | \(0.925138\pi\) | |||||||
\(18\) | 2.75477i | 0.649305i | ||||||||
\(19\) | −0.149412 | − | 4.35634i | −0.0342775 | − | 0.999412i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41215 | + | 2.44592i | −0.308156 | + | 0.533743i | ||||
\(22\) | 8.29572 | + | 4.78953i | 1.76865 | + | 1.02113i | ||||
\(23\) | −0.814102 | + | 0.470022i | −0.169752 | + | 0.0980064i | −0.582469 | − | 0.812853i | \(-0.697913\pi\) |
0.412717 | + | 0.910859i | \(0.364580\pi\) | |||||||
\(24\) | −1.18655 | + | 2.05517i | −0.242204 | + | 0.419509i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.65497 | 0.520682 | ||||||||
\(27\) | − | 5.39862i | − | 1.03897i | ||||||
\(28\) | −1.62542 | + | 0.938437i | −0.307176 | + | 0.177348i | ||||
\(29\) | 1.30917 | + | 2.26755i | 0.243106 | + | 0.421073i | 0.961598 | − | 0.274463i | \(-0.0885002\pi\) |
−0.718491 | + | 0.695536i | \(0.755167\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.26913 | −0.946364 | −0.473182 | − | 0.880965i | \(-0.656895\pi\) | ||||
−0.473182 | + | 0.880965i | \(0.656895\pi\) | |||||||
\(32\) | −3.58777 | + | 2.07140i | −0.634233 | + | 0.366175i | ||||
\(33\) | −5.77996 | − | 3.33706i | −1.00616 | − | 0.580908i | ||||
\(34\) | 4.98037 | + | 8.62625i | 0.854126 | + | 1.47939i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.637749 | − | 1.10461i | 0.106292 | − | 0.184102i | ||||
\(37\) | 2.89384i | 0.475744i | 0.971297 | + | 0.237872i | \(0.0764498\pi\) | ||||
−0.971297 | + | 0.237872i | \(0.923550\pi\) | |||||||
\(38\) | −3.41028 | + | 6.40418i | −0.553220 | + | 1.03889i | ||||
\(39\) | −1.84982 | −0.296209 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.15767 | − | 5.46925i | 0.493145 | − | 0.854153i | −0.506823 | − | 0.862050i | \(-0.669180\pi\) |
0.999969 | + | 0.00789701i | \(0.00251372\pi\) | |||||||
\(42\) | 4.07134 | − | 2.35059i | 0.628221 | − | 0.362704i | ||||
\(43\) | −3.93108 | − | 2.26961i | −0.599485 | − | 0.346113i | 0.169354 | − | 0.985555i | \(-0.445832\pi\) |
−0.768839 | + | 0.639443i | \(0.779165\pi\) | |||||||
\(44\) | −2.21763 | − | 3.84104i | −0.334320 | − | 0.579059i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.56475 | 0.230709 | ||||||||
\(47\) | −7.75471 | + | 4.47718i | −1.13114 | + | 0.653064i | −0.944221 | − | 0.329311i | \(-0.893184\pi\) |
−0.186919 | + | 0.982375i | \(0.559850\pi\) | |||||||
\(48\) | 4.96909 | − | 2.86890i | 0.717226 | − | 0.414090i | ||||
\(49\) | 1.06953 | 0.152791 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.47002 | − | 6.01025i | −0.485900 | − | 0.841604i | ||||
\(52\) | −1.06460 | − | 0.614645i | −0.147633 | − | 0.0852359i | ||||
\(53\) | −1.90213 | + | 1.09819i | −0.261277 | + | 0.150848i | −0.624917 | − | 0.780691i | \(-0.714867\pi\) |
0.363640 | + | 0.931540i | \(0.381534\pi\) | |||||||
\(54\) | −4.49313 | + | 7.78232i | −0.611437 | + | 1.05904i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.98304 | −0.665887 | ||||||||
\(57\) | 2.37608 | − | 4.46205i | 0.314719 | − | 0.591013i | ||||
\(58\) | − | 4.35834i | − | 0.572278i | ||||||
\(59\) | −5.39939 | + | 9.35202i | −0.702941 | + | 1.21753i | 0.264489 | + | 0.964389i | \(0.414797\pi\) |
−0.967430 | + | 0.253140i | \(0.918537\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.26434 | + | 9.11811i | 0.674030 | + | 1.16745i | 0.976751 | + | 0.214375i | \(0.0687716\pi\) |
−0.302721 | + | 0.953079i | \(0.597895\pi\) | |||||||
\(62\) | 7.59566 | + | 4.38535i | 0.964649 | + | 0.556941i | ||||
\(63\) | 3.49031 | − | 2.01513i | 0.439738 | − | 0.253883i | ||||
\(64\) | −2.99898 | −0.374873 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.55469 | + | 9.62100i | 0.683735 | + | 1.18426i | ||||
\(67\) | −0.874320 | + | 0.504789i | −0.106815 | + | 0.0616698i | −0.552456 | − | 0.833542i | \(-0.686309\pi\) |
0.445641 | + | 0.895212i | \(0.352976\pi\) | |||||||
\(68\) | − | 4.61197i | − | 0.559284i | ||||||
\(69\) | −1.09022 | −0.131247 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.41694 | + | 7.65036i | −0.524194 | + | 0.907931i | 0.475409 | + | 0.879765i | \(0.342300\pi\) |
−0.999603 | + | 0.0281662i | \(0.991033\pi\) | |||||||
\(72\) | 2.93271 | − | 1.69320i | 0.345624 | − | 0.199546i | ||||
\(73\) | 8.87674 | + | 5.12499i | 1.03894 | + | 0.599835i | 0.919534 | − | 0.393011i | \(-0.128566\pi\) |
0.119410 | + | 0.992845i | \(0.461900\pi\) | |||||||
\(74\) | 2.40846 | − | 4.17157i | 0.279978 | − | 0.484936i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.85008 | − | 1.77846i | 0.326927 | − | 0.204004i | ||||
\(77\) | − | 14.0143i | − | 1.59708i | ||||||
\(78\) | 2.66659 | + | 1.53956i | 0.301932 | + | 0.174320i | ||||
\(79\) | 3.80229 | − | 6.58577i | 0.427792 | − | 0.740957i | −0.568885 | − | 0.822417i | \(-0.692625\pi\) |
0.996677 | + | 0.0814604i | \(0.0259584\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.648093 | − | 1.12253i | 0.0720103 | − | 0.124726i | ||||
\(82\) | −9.10381 | + | 5.25609i | −1.00535 | + | 0.580438i | ||||
\(83\) | 3.11355i | 0.341756i | 0.985292 | + | 0.170878i | \(0.0546604\pi\) | ||||
−0.985292 | + | 0.170878i | \(0.945340\pi\) | |||||||
\(84\) | −2.17672 | −0.237499 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.77787 | + | 6.54346i | 0.407378 | + | 0.705600i | ||||
\(87\) | 3.03663i | 0.325561i | ||||||||
\(88\) | − | 11.7755i | − | 1.25527i | ||||||
\(89\) | −5.55706 | − | 9.62511i | −0.589047 | − | 1.02026i | −0.994358 | − | 0.106081i | \(-0.966170\pi\) |
0.405310 | − | 0.914179i | \(-0.367163\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.94213 | − | 3.36387i | −0.203590 | − | 0.352629i | ||||
\(92\) | −0.627436 | − | 0.362251i | −0.0654148 | − | 0.0377672i | ||||
\(93\) | −5.29220 | − | 3.05545i | −0.548776 | − | 0.316836i | ||||
\(94\) | 14.9049 | 1.53733 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.80463 | −0.490371 | ||||||||
\(97\) | 3.51412 | + | 2.02888i | 0.356805 | + | 0.206002i | 0.667678 | − | 0.744450i | \(-0.267288\pi\) |
−0.310873 | + | 0.950451i | \(0.600621\pi\) | |||||||
\(98\) | −1.54177 | − | 0.890144i | −0.155743 | − | 0.0899181i | ||||
\(99\) | 4.76197 | + | 8.24798i | 0.478596 | + | 0.828953i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.56503 | + | 9.63892i | 0.553741 | + | 0.959108i | 0.998000 | + | 0.0632098i | \(0.0201337\pi\) |
−0.444259 | + | 0.895898i | \(0.646533\pi\) | |||||||
\(102\) | 11.5520i | 1.14382i | ||||||||
\(103\) | 11.5791i | 1.14092i | 0.821326 | + | 0.570460i | \(0.193235\pi\) | ||||
−0.821326 | + | 0.570460i | \(0.806765\pi\) | |||||||
\(104\) | −1.63186 | − | 2.82647i | −0.160017 | − | 0.277158i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.65598 | 0.355101 | ||||||||
\(107\) | − | 17.9177i | − | 1.73217i | −0.499894 | − | 0.866086i | \(-0.666628\pi\) | ||
0.499894 | − | 0.866086i | \(-0.333372\pi\) | |||||||
\(108\) | 3.60333 | − | 2.08039i | 0.346731 | − | 0.200185i | ||||
\(109\) | 2.81235 | − | 4.87113i | 0.269374 | − | 0.466570i | −0.699326 | − | 0.714803i | \(-0.746516\pi\) |
0.968700 | + | 0.248233i | \(0.0798498\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.67807 | + | 2.90650i | −0.159275 | + | 0.275873i | ||||
\(112\) | 10.4341 | + | 6.02412i | 0.985928 | + | 0.569226i | ||||
\(113\) | − | 15.6789i | − | 1.47494i | −0.675378 | − | 0.737472i | \(-0.736019\pi\) | ||
0.675378 | − | 0.737472i | \(-0.263981\pi\) | |||||||
\(114\) | −7.13885 | + | 4.45467i | −0.668614 | + | 0.417218i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00899 | + | 1.74762i | −0.0936822 | + | 0.162262i | ||||
\(117\) | 2.28604 | + | 1.31984i | 0.211344 | + | 0.122020i | ||||
\(118\) | 15.5669 | − | 8.98753i | 1.43304 | − | 0.827369i | ||||
\(119\) | 7.28635 | − | 12.6203i | 0.667939 | − | 1.15690i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.1173 | 2.01067 | ||||||||
\(122\) | − | 17.5255i | − | 1.58668i | ||||||
\(123\) | 6.34299 | − | 3.66213i | 0.571928 | − | 0.330203i | ||||
\(124\) | −2.03049 | − | 3.51691i | −0.182343 | − | 0.315827i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.70856 | −0.597646 | ||||||||
\(127\) | −5.30000 | + | 3.05996i | −0.470299 | + | 0.271527i | −0.716365 | − | 0.697726i | \(-0.754195\pi\) |
0.246066 | + | 0.969253i | \(0.420862\pi\) | |||||||
\(128\) | 11.4987 | + | 6.63877i | 1.01635 | + | 0.586790i | ||||
\(129\) | −2.63220 | − | 4.55910i | −0.231752 | − | 0.401406i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.44055 | − | 12.8874i | 0.650084 | − | 1.12598i | −0.333018 | − | 0.942920i | \(-0.608067\pi\) |
0.983102 | − | 0.183058i | \(-0.0585997\pi\) | |||||||
\(132\) | − | 5.14381i | − | 0.447711i | ||||||
\(133\) | 10.6088 | − | 0.363857i | 0.919899 | − | 0.0315504i | ||||
\(134\) | 1.68049 | 0.145172 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.12231 | − | 10.6042i | 0.524984 | − | 0.909299i | ||||
\(137\) | −15.0258 | + | 8.67518i | −1.28374 | + | 0.741170i | −0.977531 | − | 0.210793i | \(-0.932396\pi\) |
−0.306214 | + | 0.951963i | \(0.599062\pi\) | |||||||
\(138\) | 1.57160 | + | 0.907361i | 0.133783 | + | 0.0772397i | ||||
\(139\) | −3.35267 | − | 5.80700i | −0.284370 | − | 0.492543i | 0.688086 | − | 0.725629i | \(-0.258451\pi\) |
−0.972456 | + | 0.233086i | \(0.925118\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.3849 | −0.874564 | ||||||||
\(142\) | 12.7344 | − | 7.35219i | 1.06864 | − | 0.616982i | ||||
\(143\) | 7.94917 | − | 4.58946i | 0.664743 | − | 0.383790i | ||||
\(144\) | −8.18782 | −0.682319 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.53077 | − | 14.7757i | −0.706012 | − | 1.22285i | ||||
\(147\) | 1.07422 | + | 0.620199i | 0.0885999 | + | 0.0511532i | ||||
\(148\) | −1.93150 | + | 1.11515i | −0.158769 | + | 0.0916651i | ||||
\(149\) | 7.19642 | − | 12.4646i | 0.589553 | − | 1.02114i | −0.404737 | − | 0.914433i | \(-0.632637\pi\) |
0.994291 | − | 0.106704i | \(-0.0340296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.7219 | 1.03529 | 0.517645 | − | 0.855595i | \(-0.326809\pi\) | ||||
0.517645 | + | 0.855595i | \(0.326809\pi\) | |||||||
\(152\) | 8.91398 | − | 0.305729i | 0.723019 | − | 0.0247979i | ||||
\(153\) | 9.90341i | 0.800644i | ||||||||
\(154\) | −11.6637 | + | 20.2022i | −0.939890 | + | 1.62794i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.712838 | − | 1.23467i | −0.0570727 | − | 0.0988529i | ||||
\(157\) | −2.92309 | − | 1.68765i | −0.233288 | − | 0.134689i | 0.378800 | − | 0.925479i | \(-0.376337\pi\) |
−0.612088 | + | 0.790790i | \(0.709670\pi\) | |||||||
\(158\) | −10.9623 | + | 6.32909i | −0.872114 | + | 0.503515i | ||||
\(159\) | −2.54727 | −0.202012 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.14462 | − | 1.98255i | −0.0902089 | − | 0.156246i | ||||
\(162\) | −1.86850 | + | 1.07878i | −0.146803 | + | 0.0847569i | ||||
\(163\) | 0.307960i | 0.0241213i | 0.999927 | + | 0.0120607i | \(0.00383912\pi\) | ||||
−0.999927 | + | 0.0120607i | \(0.996161\pi\) | |||||||
\(164\) | 4.86730 | 0.380072 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.59132 | − | 4.48830i | 0.201125 | − | 0.348359i | ||||
\(167\) | −12.3532 | + | 7.13215i | −0.955923 | + | 0.551902i | −0.894916 | − | 0.446235i | \(-0.852765\pi\) |
−0.0610070 | + | 0.998137i | \(0.519431\pi\) | |||||||
\(168\) | −5.00486 | − | 2.88955i | −0.386133 | − | 0.222934i | ||||
\(169\) | −5.22797 | + | 9.05511i | −0.402152 | + | 0.696547i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.12005 | + | 3.81894i | −0.468012 | + | 0.292042i | ||||
\(172\) | − | 3.49842i | − | 0.266752i | ||||||
\(173\) | −11.5590 | − | 6.67357i | −0.878811 | − | 0.507382i | −0.00854514 | − | 0.999963i | \(-0.502720\pi\) |
−0.870266 | + | 0.492581i | \(0.836053\pi\) | |||||||
\(174\) | 2.52730 | − | 4.37742i | 0.191594 | − | 0.331851i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.2356 | + | 24.6569i | −1.07305 | + | 1.85858i | ||||
\(177\) | −10.8461 | + | 6.26197i | −0.815239 | + | 0.470679i | ||||
\(178\) | 18.5000i | 1.38663i | ||||||||
\(179\) | 14.2207 | 1.06291 | 0.531454 | − | 0.847087i | \(-0.321646\pi\) | ||||
0.531454 | + | 0.847087i | \(0.321646\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.94132 | − | 8.55861i | −0.367285 | − | 0.636157i | 0.621855 | − | 0.783133i | \(-0.286379\pi\) |
−0.989140 | + | 0.146976i | \(0.953046\pi\) | |||||||
\(182\) | 6.46552i | 0.479256i | ||||||||
\(183\) | 12.2107i | 0.902641i | ||||||||
\(184\) | −0.961763 | − | 1.66582i | −0.0709021 | − | 0.122806i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.08594 | + | 8.80911i | 0.372919 | + | 0.645915i | ||||
\(187\) | 29.8232 | + | 17.2184i | 2.18089 | + | 1.25914i | ||||
\(188\) | −5.97663 | − | 3.45061i | −0.435891 | − | 0.251661i | ||||
\(189\) | 13.1470 | 0.956305 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.9942 | −0.940228 | −0.470114 | − | 0.882606i | \(-0.655787\pi\) | ||||
−0.470114 | + | 0.882606i | \(0.655787\pi\) | |||||||
\(192\) | −3.01211 | − | 1.73904i | −0.217380 | − | 0.125505i | ||||
\(193\) | −12.5711 | − | 7.25795i | −0.904890 | − | 0.522439i | −0.0261066 | − | 0.999659i | \(-0.508311\pi\) |
−0.878784 | + | 0.477221i | \(0.841644\pi\) | |||||||
\(194\) | −3.37716 | − | 5.84942i | −0.242466 | − | 0.419964i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.412150 | + | 0.713865i | 0.0294393 | + | 0.0509904i | ||||
\(197\) | 25.0010i | 1.78125i | 0.454740 | + | 0.890624i | \(0.349732\pi\) | ||||
−0.454740 | + | 0.890624i | \(0.650268\pi\) | |||||||
\(198\) | − | 15.8530i | − | 1.12663i | ||||||
\(199\) | −1.12769 | − | 1.95322i | −0.0799401 | − | 0.138460i | 0.823284 | − | 0.567630i | \(-0.192140\pi\) |
−0.903224 | + | 0.429170i | \(0.858806\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.17086 | −0.0825864 | ||||||||
\(202\) | − | 18.5265i | − | 1.30352i | ||||||
\(203\) | −5.52205 | + | 3.18816i | −0.387572 | + | 0.223765i | ||||
\(204\) | 2.67438 | − | 4.63216i | 0.187244 | − | 0.324316i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.63694 | − | 16.6917i | 0.671437 | − | 1.16296i | ||||
\(207\) | 1.34731 | + | 0.777871i | 0.0936446 | + | 0.0540657i | ||||
\(208\) | 7.89120i | 0.547156i | ||||||||
\(209\) | 0.859833 | + | 25.0697i | 0.0594759 | + | 1.73411i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1081 | + | 19.2397i | −0.764710 | + | 1.32452i | 0.175689 | + | 0.984446i | \(0.443785\pi\) |
−0.940400 | + | 0.340071i | \(0.889549\pi\) | |||||||
\(212\) | −1.46599 | − | 0.846388i | −0.100684 | − | 0.0581302i | ||||
\(213\) | −8.87255 | + | 5.12257i | −0.607937 | + | 0.350993i | ||||
\(214\) | −14.9124 | + | 25.8291i | −1.01939 | + | 1.76564i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.0467 | 0.751634 | ||||||||
\(217\) | − | 12.8317i | − | 0.871071i | ||||||
\(218\) | −8.10822 | + | 4.68128i | −0.549158 | + | 0.317057i | ||||
\(219\) | 5.94373 | + | 10.2949i | 0.401640 | + | 0.695662i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.54463 | 0.642041 | ||||||||
\(222\) | 4.83801 | − | 2.79322i | 0.324706 | − | 0.187469i | ||||
\(223\) | −8.84730 | − | 5.10799i | −0.592459 | − | 0.342056i | 0.173610 | − | 0.984814i | \(-0.444457\pi\) |
−0.766069 | + | 0.642758i | \(0.777790\pi\) | |||||||
\(224\) | −5.04438 | − | 8.73712i | −0.337042 | − | 0.583774i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.0491 | + | 22.6017i | −0.868012 | + | 1.50344i | ||||
\(227\) | − | 4.15180i | − | 0.275565i | −0.990463 | − | 0.137782i | \(-0.956003\pi\) | ||
0.990463 | − | 0.137782i | \(-0.0439974\pi\) | |||||||
\(228\) | 3.89385 | − | 0.133550i | 0.257876 | − | 0.00884456i | ||||
\(229\) | −6.53286 | −0.431703 | −0.215852 | − | 0.976426i | \(-0.569253\pi\) | ||||
−0.215852 | + | 0.976426i | \(0.569253\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.12660 | − | 14.0757i | 0.534691 | − | 0.926111i | ||||
\(232\) | −4.63987 | + | 2.67883i | −0.304623 | + | 0.175874i | ||||
\(233\) | −4.45848 | − | 2.57410i | −0.292084 | − | 0.168635i | 0.346797 | − | 0.937940i | \(-0.387269\pi\) |
−0.638882 | + | 0.769305i | \(0.720603\pi\) | |||||||
\(234\) | −2.19694 | − | 3.80521i | −0.143618 | − | 0.248755i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.32272 | −0.541763 | ||||||||
\(237\) | 7.63788 | − | 4.40973i | 0.496134 | − | 0.286443i | ||||
\(238\) | −21.0071 | + | 12.1285i | −1.36169 | + | 0.786171i | ||||
\(239\) | −13.9962 | −0.905338 | −0.452669 | − | 0.891679i | \(-0.649528\pi\) | ||||
−0.452669 | + | 0.891679i | \(0.649528\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.61285 | − | 13.1858i | −0.490387 | − | 0.849375i | 0.509552 | − | 0.860440i | \(-0.329811\pi\) |
−0.999939 | + | 0.0110652i | \(0.996478\pi\) | |||||||
\(242\) | −31.8830 | − | 18.4076i | −2.04952 | − | 1.18329i | ||||
\(243\) | −12.7242 | + | 7.34631i | −0.816256 | + | 0.471266i | ||||
\(244\) | −4.05728 | + | 7.02742i | −0.259741 | + | 0.449884i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −12.1916 | −0.777305 | ||||||||
\(247\) | 3.68059 | + | 5.89834i | 0.234190 | + | 0.375302i | ||||
\(248\) | − | 10.7817i | − | 0.684642i | ||||||
\(249\) | −1.80548 | + | 3.12718i | −0.114417 | + | 0.198177i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.05630 | + | 5.29366i | 0.192912 | + | 0.334133i | 0.946214 | − | 0.323542i | \(-0.104874\pi\) |
−0.753302 | + | 0.657674i | \(0.771540\pi\) | |||||||
\(252\) | 2.69002 | + | 1.55308i | 0.169455 | + | 0.0978350i | ||||
\(253\) | 4.68497 | − | 2.70487i | 0.294541 | − | 0.170053i | ||||
\(254\) | 10.1869 | 0.639181 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.05154 | − | 13.9457i | −0.503221 | − | 0.871605i | ||||
\(257\) | −0.106246 | + | 0.0613414i | −0.00662747 | + | 0.00382637i | −0.503310 | − | 0.864106i | \(-0.667885\pi\) |
0.496683 | + | 0.867932i | \(0.334551\pi\) | |||||||
\(258\) | 8.76281i | 0.545549i | ||||||||
\(259\) | −7.04723 | −0.437893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.16663 | − | 3.75271i | 0.134111 | − | 0.232287i | ||||
\(262\) | −21.4517 | + | 12.3851i | −1.32529 | + | 0.765156i | ||||
\(263\) | 8.71267 | + | 5.03027i | 0.537247 | + | 0.310179i | 0.743962 | − | 0.668222i | \(-0.232944\pi\) |
−0.206716 | + | 0.978401i | \(0.566278\pi\) | |||||||
\(264\) | 6.82832 | − | 11.8270i | 0.420254 | − | 0.727902i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −15.5958 | − | 8.30489i | −0.956240 | − | 0.509206i | ||||
\(267\) | − | 12.8897i | − | 0.788835i | ||||||
\(268\) | −0.673847 | − | 0.389046i | −0.0411618 | − | 0.0237648i | ||||
\(269\) | 2.85614 | − | 4.94698i | 0.174142 | − | 0.301623i | −0.765722 | − | 0.643172i | \(-0.777618\pi\) |
0.939864 | + | 0.341549i | \(0.110951\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.35560 | − | 11.0082i | 0.386075 | − | 0.668702i | −0.605843 | − | 0.795585i | \(-0.707164\pi\) |
0.991918 | + | 0.126883i | \(0.0404972\pi\) | |||||||
\(272\) | −25.6393 | + | 14.8028i | −1.55461 | + | 0.897554i | ||||
\(273\) | − | 4.50479i | − | 0.272642i | ||||||
\(274\) | 28.8804 | 1.74473 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.420122 | − | 0.727673i | −0.0252884 | − | 0.0438008i | ||||
\(277\) | − | 17.6019i | − | 1.05760i | −0.848747 | − | 0.528799i | \(-0.822642\pi\) | ||
0.848747 | − | 0.528799i | \(-0.177358\pi\) | |||||||
\(278\) | 11.1613i | 0.669413i | ||||||||
\(279\) | 4.36012 | + | 7.55195i | 0.261034 | + | 0.452123i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.2502 | + | 17.7539i | 0.611476 | + | 1.05911i | 0.990992 | + | 0.133922i | \(0.0427571\pi\) |
−0.379516 | + | 0.925185i | \(0.623910\pi\) | |||||||
\(282\) | 14.9702 | + | 8.64305i | 0.891462 | + | 0.514686i | ||||
\(283\) | 10.2677 | + | 5.92805i | 0.610350 | + | 0.352386i | 0.773103 | − | 0.634281i | \(-0.218704\pi\) |
−0.162752 | + | 0.986667i | \(0.552037\pi\) | |||||||
\(284\) | −6.80836 | −0.404002 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.2787 | −0.903449 | ||||||||
\(287\) | 13.3190 | + | 7.68973i | 0.786196 | + | 0.453911i | ||||
\(288\) | 5.93763 | + | 3.42809i | 0.349878 | + | 0.202002i | ||||
\(289\) | 9.40447 | + | 16.2890i | 0.553204 | + | 0.958177i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.35301 | + | 4.07552i | 0.137936 | + | 0.238911i | ||||
\(292\) | 7.89976i | 0.462298i | ||||||||
\(293\) | − | 24.9814i | − | 1.45943i | −0.683751 | − | 0.729715i | \(-0.739653\pi\) | ||
0.683751 | − | 0.729715i | \(-0.260347\pi\) | |||||||
\(294\) | −1.03235 | − | 1.78808i | −0.0602079 | − | 0.104283i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.92139 | −0.344174 | ||||||||
\(297\) | 31.0678i | 1.80274i | ||||||||
\(298\) | −20.7478 | + | 11.9788i | −1.20189 | + | 0.693911i | ||||
\(299\) | 0.749690 | − | 1.29850i | 0.0433557 | − | 0.0750943i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.52708 | − | 9.57319i | 0.318576 | − | 0.551789i | ||||
\(302\) | −18.3391 | − | 10.5881i | −1.05529 | − | 0.609274i | ||||
\(303\) | 12.9082i | 0.741554i | ||||||||
\(304\) | −19.0348 | − | 10.1362i | −1.09172 | − | 0.581348i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.24234 | − | 14.2761i | 0.471183 | − | 0.816113i | ||||
\(307\) | 14.6531 | + | 8.45997i | 0.836296 | + | 0.482836i | 0.856003 | − | 0.516970i | \(-0.172940\pi\) |
−0.0197074 | + | 0.999806i | \(0.506273\pi\) | |||||||
\(308\) | 9.35392 | − | 5.40049i | 0.532989 | − | 0.307721i | ||||
\(309\) | −6.71444 | + | 11.6298i | −0.381971 | + | 0.661594i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.2133 | −0.862670 | −0.431335 | − | 0.902192i | \(-0.641957\pi\) | ||||
−0.431335 | + | 0.902192i | \(0.641957\pi\) | |||||||
\(312\) | − | 3.78512i | − | 0.214290i | ||||||
\(313\) | 21.5877 | − | 12.4637i | 1.22021 | − | 0.704488i | 0.255246 | − | 0.966876i | \(-0.417844\pi\) |
0.964962 | + | 0.262389i | \(0.0845102\pi\) | |||||||
\(314\) | 2.80917 | + | 4.86562i | 0.158531 | + | 0.274583i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.86093 | 0.329703 | ||||||||
\(317\) | 21.8502 | − | 12.6152i | 1.22723 | − | 0.708541i | 0.260780 | − | 0.965398i | \(-0.416020\pi\) |
0.966449 | + | 0.256857i | \(0.0826869\pi\) | |||||||
\(318\) | 3.67199 | + | 2.12002i | 0.205915 | + | 0.118885i | ||||
\(319\) | −7.53396 | − | 13.0492i | −0.421821 | − | 0.730615i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.3901 | − | 17.9962i | 0.579919 | − | 1.00445i | ||||
\(322\) | 3.81055i | 0.212354i | ||||||||
\(323\) | −12.2600 | + | 23.0231i | −0.682163 | + | 1.28104i | ||||
\(324\) | 0.998983 | 0.0554991 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.256307 | − | 0.443937i | 0.0141955 | − | 0.0245874i | ||||
\(327\) | 5.64933 | − | 3.26164i | 0.312408 | − | 0.180369i | ||||
\(328\) | 11.1912 | + | 6.46125i | 0.617932 | + | 0.356763i | ||||
\(329\) | −10.9031 | − | 18.8847i | −0.601106 | − | 1.04115i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.2063 | −1.11064 | −0.555320 | − | 0.831637i | \(-0.687404\pi\) | ||||
−0.555320 | + | 0.831637i | \(0.687404\pi\) | |||||||
\(332\) | −2.07815 | + | 1.19982i | −0.114053 | + | 0.0658487i | ||||
\(333\) | 4.14757 | − | 2.39460i | 0.227285 | − | 0.131223i | ||||
\(334\) | 23.7436 | 1.29919 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.98651 | + | 12.1010i | 0.381145 | + | 0.660163i | ||||
\(337\) | −27.5610 | − | 15.9123i | −1.50134 | − | 0.866800i | −0.999999 | − | 0.00155051i | \(-0.999506\pi\) |
−0.501342 | − | 0.865249i | \(-0.667160\pi\) | |||||||
\(338\) | 15.0726 | − | 8.70219i | 0.819843 | − | 0.473337i | ||||
\(339\) | 9.09183 | − | 15.7475i | 0.493800 | − | 0.855287i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.3226 | 1.64206 | ||||||||
\(342\) | 12.0007 | − | 0.411596i | 0.648923 | − | 0.0222566i | ||||
\(343\) | 19.6514i | 1.06107i | ||||||||
\(344\) | 4.64410 | − | 8.04382i | 0.250393 | − | 0.433693i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.1085 | + | 19.2404i | 0.597194 | + | 1.03437i | ||||
\(347\) | −2.86009 | − | 1.65128i | −0.153538 | − | 0.0886451i | 0.421263 | − | 0.906939i | \(-0.361587\pi\) |
−0.574801 | + | 0.818294i | \(0.694920\pi\) | |||||||
\(348\) | −2.02681 | + | 1.17018i | −0.108649 | + | 0.0627283i | ||||
\(349\) | −17.8486 | −0.955416 | −0.477708 | − | 0.878519i | \(-0.658532\pi\) | ||||
−0.477708 | + | 0.878519i | \(0.658532\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.30543 | + | 7.45723i | 0.229807 | + | 0.398037i | ||||
\(352\) | 20.6468 | − | 11.9204i | 1.10048 | − | 0.635360i | ||||
\(353\) | − | 8.29523i | − | 0.441511i | −0.975329 | − | 0.220755i | \(-0.929148\pi\) | ||
0.975329 | − | 0.220755i | \(-0.0708522\pi\) | |||||||
\(354\) | 20.8467 | 1.10799 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.28288 | − | 7.41817i | 0.226992 | − | 0.393162i | ||||
\(357\) | 14.6365 | − | 8.45039i | 0.774646 | − | 0.447242i | ||||
\(358\) | −20.4997 | − | 11.8355i | −1.08344 | − | 0.625527i | ||||
\(359\) | 4.17511 | − | 7.23150i | 0.220354 | − | 0.381664i | −0.734562 | − | 0.678542i | \(-0.762612\pi\) |
0.954915 | + | 0.296878i | \(0.0959455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9554 | + | 1.30178i | −0.997650 | + | 0.0685148i | ||||
\(362\) | 16.4501i | 0.864598i | ||||||||
\(363\) | 22.2142 | + | 12.8254i | 1.16594 | + | 0.673156i | ||||
\(364\) | 1.49682 | − | 2.59256i | 0.0784545 | − | 0.135887i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.1626 | − | 17.6022i | 0.531209 | − | 0.920082i | ||||
\(367\) | −12.4879 | + | 7.20988i | −0.651862 | + | 0.376353i | −0.789169 | − | 0.614176i | \(-0.789489\pi\) |
0.137307 | + | 0.990528i | \(0.456155\pi\) | |||||||
\(368\) | 4.65080i | 0.242440i | ||||||||
\(369\) | −10.4517 | −0.544093 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.67438 | − | 4.63216i | −0.138847 | − | 0.240490i | ||||
\(372\) | − | 4.70974i | − | 0.244188i | ||||||
\(373\) | − | 24.1157i | − | 1.24866i | −0.781159 | − | 0.624332i | \(-0.785371\pi\) | ||
0.781159 | − | 0.624332i | \(-0.214629\pi\) | |||||||
\(374\) | −28.6608 | − | 49.6420i | −1.48202 | − | 2.56693i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.16125 | − | 15.8678i | −0.472455 | − | 0.818317i | ||||
\(377\) | −3.61676 | − | 2.08814i | −0.186273 | − | 0.107545i | ||||
\(378\) | −18.9519 | − | 10.9419i | −0.974783 | − | 0.562791i | ||||
\(379\) | −16.6757 | −0.856571 | −0.428285 | − | 0.903644i | \(-0.640882\pi\) | ||||
−0.428285 | + | 0.903644i | \(0.640882\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.09760 | −0.363621 | ||||||||
\(382\) | 18.7316 | + | 10.8147i | 0.958395 | + | 0.553329i | ||||
\(383\) | 9.42053 | + | 5.43895i | 0.481367 | + | 0.277917i | 0.720986 | − | 0.692950i | \(-0.243689\pi\) |
−0.239619 | + | 0.970867i | \(0.577023\pi\) | |||||||
\(384\) | 7.69935 | + | 13.3357i | 0.392906 | + | 0.680533i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.0812 | + | 20.9252i | 0.614916 | + | 1.06507i | ||||
\(387\) | 7.51226i | 0.381870i | ||||||||
\(388\) | 3.12736i | 0.158767i | ||||||||
\(389\) | 18.2272 | + | 31.5704i | 0.924154 | + | 1.60068i | 0.792917 | + | 0.609330i | \(0.208562\pi\) |
0.131237 | + | 0.991351i | \(0.458105\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.62528 | 0.284482 | ||||||||
\(392\) | 2.18849i | 0.110535i | ||||||||
\(393\) | 14.9463 | − | 8.62922i | 0.753939 | − | 0.435287i | ||||
\(394\) | 20.8077 | − | 36.0399i | 1.04827 | − | 1.81566i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.67010 | + | 6.35680i | −0.184429 | + | 0.319441i | ||||
\(397\) | 7.43380 | + | 4.29191i | 0.373092 | + | 0.215405i | 0.674808 | − | 0.737993i | \(-0.264226\pi\) |
−0.301717 | + | 0.953398i | \(0.597560\pi\) | |||||||
\(398\) | 3.75419i | 0.188181i | ||||||||
\(399\) | 10.8662 | + | 5.78635i | 0.543992 | + | 0.289680i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.52785 | − | 14.7707i | 0.425860 | − | 0.737612i | −0.570640 | − | 0.821200i | \(-0.693305\pi\) |
0.996500 | + | 0.0835885i | \(0.0266381\pi\) | |||||||
\(402\) | 1.68785 | + | 0.974478i | 0.0841821 | + | 0.0486026i | ||||
\(403\) | 7.27836 | − | 4.20216i | 0.362561 | − | 0.209325i | ||||
\(404\) | −4.28903 | + | 7.42881i | −0.213387 | + | 0.369597i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.6137 | 0.526747 | ||||||||
\(407\) | − | 16.6533i | − | 0.825476i | ||||||
\(408\) | 12.2982 | − | 7.10039i | 0.608853 | − | 0.351522i | ||||
\(409\) | −5.89702 | − | 10.2139i | −0.291589 | − | 0.505047i | 0.682597 | − | 0.730795i | \(-0.260851\pi\) |
−0.974186 | + | 0.225749i | \(0.927517\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.1222 | −0.992553 | ||||||||
\(412\) | −7.72850 | + | 4.46205i | −0.380756 | + | 0.219829i | ||||
\(413\) | −22.7745 | − | 13.1489i | −1.12066 | − | 0.647015i | ||||
\(414\) | −1.29480 | − | 2.24266i | −0.0636360 | − | 0.110221i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.30390 | − | 5.72252i | 0.161987 | − | 0.280570i | ||||
\(417\) | − | 7.77656i | − | 0.380820i | ||||||
\(418\) | 19.6253 | − | 36.8546i | 0.959907 | − | 1.80261i | ||||
\(419\) | −1.14280 | −0.0558292 | −0.0279146 | − | 0.999610i | \(-0.508887\pi\) | ||||
−0.0279146 | + | 0.999610i | \(0.508887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.75944 | + | 16.9039i | −0.475646 | + | 0.823843i | −0.999611 | − | 0.0278967i | \(-0.991119\pi\) |
0.523965 | + | 0.851740i | \(0.324452\pi\) | |||||||
\(422\) | 32.0254 | − | 18.4899i | 1.55897 | − | 0.900072i | ||||
\(423\) | 12.8338 | + | 7.40959i | 0.624000 | + | 0.360266i | ||||
\(424\) | −2.24713 | − | 3.89215i | −0.109130 | − | 0.189019i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 17.0535 | 0.826245 | ||||||||
\(427\) | −22.2049 | + | 12.8200i | −1.07457 | + | 0.620404i | ||||
\(428\) | 11.9593 | − | 6.90469i | 0.578073 | − | 0.333751i | ||||
\(429\) | 10.6453 | 0.513960 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.4392 | + | 31.9377i | 0.888187 | + | 1.53838i | 0.842017 | + | 0.539451i | \(0.181368\pi\) |
0.0461694 | + | 0.998934i | \(0.485299\pi\) | |||||||
\(432\) | −23.1309 | − | 13.3546i | −1.11289 | − | 0.642526i | ||||
\(433\) | 0.319506 | − | 0.184467i | 0.0153545 | − | 0.00886490i | −0.492303 | − | 0.870424i | \(-0.663845\pi\) |
0.507658 | + | 0.861559i | \(0.330512\pi\) | |||||||
\(434\) | −10.6795 | + | 18.4974i | −0.512630 | + | 0.887902i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.33501 | 0.207609 | ||||||||
\(437\) | 2.16921 | + | 3.47628i | 0.103767 | + | 0.166293i | ||||
\(438\) | − | 19.7872i | − | 0.945470i | ||||||
\(439\) | −1.13220 | + | 1.96102i | −0.0540367 | + | 0.0935944i | −0.891778 | − | 0.452472i | \(-0.850542\pi\) |
0.837742 | + | 0.546067i | \(0.183875\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.885022 | − | 1.53290i | −0.0421439 | − | 0.0729954i | ||||
\(442\) | −13.7590 | − | 7.94373i | −0.654447 | − | 0.377845i | ||||
\(443\) | −14.2572 | + | 8.23137i | −0.677378 | + | 0.391084i | −0.798866 | − | 0.601508i | \(-0.794567\pi\) |
0.121488 | + | 0.992593i | \(0.461233\pi\) | |||||||
\(444\) | −2.58661 | −0.122755 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.50248 | + | 14.7267i | 0.402604 | + | 0.697331i | ||||
\(447\) | 14.4558 | − | 8.34609i | 0.683738 | − | 0.394756i | ||||
\(448\) | − | 7.30329i | − | 0.345048i | ||||||
\(449\) | −14.1613 | −0.668315 | −0.334158 | − | 0.942517i | \(-0.608452\pi\) | ||||
−0.334158 | + | 0.942517i | \(0.608452\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.1717 | + | 31.4742i | −0.855670 | + | 1.48206i | ||||
\(452\) | 10.4649 | − | 6.04193i | 0.492229 | − | 0.284188i | ||||
\(453\) | 12.7776 | + | 7.37713i | 0.600342 | + | 0.346608i | ||||
\(454\) | −3.45543 | + | 5.98498i | −0.162171 | + | 0.280889i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.13029 | + | 4.86195i | 0.427565 | + | 0.227682i | ||||
\(457\) | − | 1.22073i | − | 0.0571033i | −0.999592 | − | 0.0285516i | \(-0.990910\pi\) | ||
0.999592 | − | 0.0285516i | \(-0.00908950\pi\) | |||||||
\(458\) | 9.41736 | + | 5.43712i | 0.440045 | + | 0.254060i | ||||
\(459\) | −16.1528 | + | 27.9775i | −0.753950 | + | 1.30588i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.34580 | − | 7.52714i | 0.202404 | − | 0.350574i | −0.746898 | − | 0.664938i | \(-0.768458\pi\) |
0.949303 | + | 0.314364i | \(0.101791\pi\) | |||||||
\(462\) | −23.4296 | + | 13.5271i | −1.09004 | + | 0.629337i | ||||
\(463\) | − | 19.7149i | − | 0.916229i | −0.888893 | − | 0.458114i | \(-0.848525\pi\) | ||
0.888893 | − | 0.458114i | \(-0.151475\pi\) | |||||||
\(464\) | 12.9540 | 0.601375 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.28471 | + | 7.42133i | 0.198485 | + | 0.343787i | ||||
\(467\) | 11.4795i | 0.531207i | 0.964082 | + | 0.265604i | \(0.0855713\pi\) | ||||
−0.964082 | + | 0.265604i | \(0.914429\pi\) | |||||||
\(468\) | 2.03443i | 0.0940418i | ||||||||
\(469\) | −1.22929 | − | 2.12919i | −0.0567633 | − | 0.0983170i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.95726 | − | 3.39008i | −0.0901858 | − | 0.156206i | ||||
\(472\) | −19.1362 | − | 11.0483i | −0.880814 | − | 0.508538i | ||||
\(473\) | 22.6225 | + | 13.0611i | 1.04018 | + | 0.600549i | ||||
\(474\) | −14.6804 | −0.674293 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.2313 | 0.514787 | ||||||||
\(477\) | 3.14796 | + | 1.81747i | 0.144135 | + | 0.0832164i | ||||
\(478\) | 20.1760 | + | 11.6486i | 0.922830 | + | 0.532796i | ||||
\(479\) | 19.6316 | + | 34.0029i | 0.896989 | + | 1.55363i | 0.831324 | + | 0.555789i | \(0.187584\pi\) |
0.0656652 | + | 0.997842i | \(0.479083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.30785 | − | 3.99731i | −0.105229 | − | 0.182262i | ||||
\(482\) | 25.3439i | 1.15438i | ||||||||
\(483\) | − | 2.65497i | − | 0.120805i | ||||||
\(484\) | 8.52302 | + | 14.7623i | 0.387410 | + | 0.671014i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 24.4565 | 1.10937 | ||||||||
\(487\) | − | 31.5943i | − | 1.43168i | −0.698266 | − | 0.715838i | \(-0.746045\pi\) | ||
0.698266 | − | 0.715838i | \(-0.253955\pi\) | |||||||
\(488\) | −18.6576 | + | 10.7719i | −0.844588 | + | 0.487623i | ||||
\(489\) | −0.178579 | + | 0.309309i | −0.00807564 | + | 0.0139874i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.53187 | − | 9.58148i | 0.249650 | − | 0.432406i | −0.713779 | − | 0.700371i | \(-0.753018\pi\) |
0.963429 | + | 0.267965i | \(0.0863511\pi\) | |||||||
\(492\) | 4.88861 | + | 2.82244i | 0.220395 | + | 0.127245i | ||||
\(493\) | − | 15.6683i | − | 0.705663i | ||||||
\(494\) | −0.396685 | − | 11.5659i | −0.0178477 | − | 0.520376i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.0343 | + | 22.5761i | −0.585258 | + | 1.01370i | ||||
\(497\) | −18.6306 | − | 10.7564i | −0.835696 | − | 0.482489i | ||||
\(498\) | 5.20533 | − | 3.00530i | 0.233256 | − | 0.134671i | ||||
\(499\) | −10.1868 | + | 17.6440i | −0.456023 | + | 0.789854i | −0.998746 | − | 0.0500570i | \(-0.984060\pi\) |
0.542724 | + | 0.839911i | \(0.317393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.5431 | −0.739091 | ||||||||
\(502\) | − | 10.1747i | − | 0.454118i | ||||||
\(503\) | −11.8407 | + | 6.83622i | −0.527950 | + | 0.304812i | −0.740181 | − | 0.672407i | \(-0.765260\pi\) |
0.212231 | + | 0.977219i | \(0.431927\pi\) | |||||||
\(504\) | 4.12338 | + | 7.14191i | 0.183670 | + | 0.318126i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.00474 | −0.400310 | ||||||||
\(507\) | −10.5017 | + | 6.06317i | −0.466398 | + | 0.269275i | ||||
\(508\) | −4.08476 | − | 2.35834i | −0.181232 | − | 0.104634i | ||||
\(509\) | −3.86196 | − | 6.68912i | −0.171179 | − | 0.296490i | 0.767654 | − | 0.640865i | \(-0.221424\pi\) |
−0.938832 | + | 0.344375i | \(0.888091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.4807 | + | 21.6171i | −0.552112 | + | 0.956285i | ||||
\(512\) | 0.249240i | 0.0110150i | ||||||||
\(513\) | −23.5182 | + | 0.806621i | −1.03836 | + | 0.0356132i | ||||
\(514\) | 0.204211 | 0.00900736 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.02866 | − | 3.51374i | 0.0893067 | − | 0.154684i | ||||
\(517\) | 44.6265 | − | 25.7651i | 1.96267 | − | 1.13315i | ||||
\(518\) | 10.1588 | + | 5.86521i | 0.446354 | + | 0.257703i | ||||
\(519\) | −7.73971 | − | 13.4056i | −0.339736 | − | 0.588439i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.16876 | −0.0950151 | −0.0475075 | − | 0.998871i | \(-0.515128\pi\) | ||||
−0.0475075 | + | 0.998871i | \(0.515128\pi\) | |||||||
\(522\) | −6.24656 | + | 3.60645i | −0.273404 | + | 0.157850i | ||||
\(523\) | −20.6921 | + | 11.9466i | −0.904804 | + | 0.522389i | −0.878756 | − | 0.477272i | \(-0.841626\pi\) |
−0.0260485 | + | 0.999661i | \(0.508292\pi\) | |||||||
\(524\) | 11.4690 | 0.501026 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.37310 | − | 14.5026i | −0.365085 | − | 0.632345i | ||||
\(527\) | 27.3065 | + | 15.7654i | 1.18949 | + | 0.686751i | ||||
\(528\) | −28.5959 | + | 16.5099i | −1.24448 | + | 0.718500i | ||||
\(529\) | −11.0582 | + | 19.1533i | −0.480790 | + | 0.832752i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.8716 | 0.775562 | ||||||||
\(532\) | 4.33101 | + | 6.94067i | 0.187773 | + | 0.300916i | ||||
\(533\) | 10.0730i | 0.436312i | ||||||||
\(534\) | −10.7277 | + | 18.5809i | −0.464234 | + | 0.804076i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.03290 | − | 1.78904i | −0.0446147 | − | 0.0772749i | ||||
\(537\) | 14.2830 | + | 8.24629i | 0.616356 | + | 0.355854i | ||||
\(538\) | −8.23448 | + | 4.75418i | −0.355013 | + | 0.204967i | ||||
\(539\) | −6.15492 | −0.265111 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.2275 | − | 36.7671i | −0.912641 | − | 1.58074i | −0.810319 | − | 0.585990i | \(-0.800706\pi\) |
−0.102323 | − | 0.994751i | \(-0.532627\pi\) | |||||||
\(542\) | −18.3237 | + | 10.5792i | −0.787069 | + | 0.454415i | ||||
\(543\) | − | 11.4614i | − | 0.491858i | ||||||
\(544\) | 24.7907 | 1.06289 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.74921 | + | 6.49383i | −0.160451 | + | 0.277910i | ||||
\(547\) | −10.4189 | + | 6.01535i | −0.445480 | + | 0.257198i | −0.705919 | − | 0.708292i | \(-0.749466\pi\) |
0.260439 | + | 0.965490i | \(0.416133\pi\) | |||||||
\(548\) | −11.5806 | − | 6.68604i | −0.494697 | − | 0.285614i | ||||
\(549\) | 8.71231 | − | 15.0902i | 0.371833 | − | 0.644033i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.68259 | − | 6.04198i | 0.412492 | − | 0.257397i | ||||
\(552\) | − | 2.23082i | − | 0.0949500i | ||||||
\(553\) | 16.0380 | + | 9.25956i | 0.682006 | + | 0.393756i | ||||
\(554\) | −14.6496 | + | 25.3739i | −0.622403 | + | 1.07803i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.58394 | − | 4.47551i | 0.109583 | − | 0.189804i | ||||
\(557\) | 7.58006 | − | 4.37635i | 0.321178 | − | 0.185432i | −0.330740 | − | 0.943722i | \(-0.607298\pi\) |
0.651917 | + | 0.758290i | \(0.273965\pi\) | |||||||
\(558\) | − | 14.5152i | − | 0.614479i | ||||||
\(559\) | 7.24011 | 0.306224 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.9692 | + | 34.5876i | 0.843099 | + | 1.46029i | ||||
\(562\) | − | 34.1238i | − | 1.43943i | ||||||
\(563\) | − | 35.9707i | − | 1.51598i | −0.652265 | − | 0.757991i | \(-0.726181\pi\) | ||
0.652265 | − | 0.757991i | \(-0.273819\pi\) | |||||||
\(564\) | −4.00186 | − | 6.93143i | −0.168509 | − | 0.291866i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.86750 | − | 17.0910i | −0.414762 | − | 0.718389i | ||||
\(567\) | 2.73365 | + | 1.57827i | 0.114802 | + | 0.0662812i | ||||
\(568\) | −15.6542 | − | 9.03798i | −0.656837 | − | 0.379225i | ||||
\(569\) | 20.3125 | 0.851543 | 0.425772 | − | 0.904831i | \(-0.360003\pi\) | ||||
0.425772 | + | 0.904831i | \(0.360003\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.1773 | 0.425906 | 0.212953 | − | 0.977062i | \(-0.431692\pi\) | ||||
0.212953 | + | 0.977062i | \(0.431692\pi\) | |||||||
\(572\) | 6.12650 | + | 3.53714i | 0.256162 | + | 0.147895i | ||||
\(573\) | −13.0511 | − | 7.53505i | −0.545217 | − | 0.314781i | ||||
\(574\) | −12.7999 | − | 22.1701i | −0.534258 | − | 0.925362i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.48161 | + | 4.29827i | 0.103400 | + | 0.179095i | ||||
\(577\) | 32.7441i | 1.36316i | 0.731745 | + | 0.681578i | \(0.238706\pi\) | ||||
−0.731745 | + | 0.681578i | \(0.761294\pi\) | |||||||
\(578\) | − | 31.3083i | − | 1.30225i | ||||||
\(579\) | −8.41745 | − | 14.5794i | −0.349817 | − | 0.605901i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.58228 | −0.314566 | ||||||||
\(582\) | − | 7.83337i | − | 0.324703i | ||||||
\(583\) | 10.9463 | − | 6.31984i | 0.453349 | − | 0.261741i | ||||
\(584\) | −10.4868 | + | 18.1637i | −0.433947 | + | 0.751618i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.7913 | + | 36.0117i | −0.858883 | + | 1.48763i | ||||
\(587\) | 7.59786 | + | 4.38663i | 0.313597 | + | 0.181056i | 0.648535 | − | 0.761185i | \(-0.275382\pi\) |
−0.334938 | + | 0.942240i | \(0.608715\pi\) | |||||||
\(588\) | 0.955987i | 0.0394243i | ||||||||
\(589\) | 0.787274 | + | 22.9541i | 0.0324390 | + | 0.945808i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.4975 | + | 25.1105i | −0.596349 | + | 1.03291i | ||||
\(592\) | 12.3989 | + | 7.15852i | 0.509592 | + | 0.294213i | ||||
\(593\) | −27.9905 | + | 16.1603i | −1.14943 | + | 0.663625i | −0.948749 | − | 0.316031i | \(-0.897650\pi\) |
−0.200684 | + | 0.979656i | \(0.564316\pi\) | |||||||
\(594\) | 25.8569 | − | 44.7855i | 1.06092 | − | 1.83757i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.0927 | 0.454375 | ||||||||
\(597\) | − | 2.61570i | − | 0.107053i | ||||||
\(598\) | −2.16141 | + | 1.24789i | −0.0883868 | + | 0.0510301i | ||||
\(599\) | −9.77520 | − | 16.9311i | −0.399404 | − | 0.691787i | 0.594249 | − | 0.804281i | \(-0.297449\pi\) |
−0.993652 | + | 0.112494i | \(0.964116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.401837 | −0.0163913 | −0.00819564 | − | 0.999966i | \(-0.502609\pi\) | ||||
−0.00819564 | + | 0.999966i | \(0.502609\pi\) | |||||||
\(602\) | −15.9350 | + | 9.20008i | −0.649462 | + | 0.374967i | ||||
\(603\) | 1.44697 | + | 0.835409i | 0.0589252 | + | 0.0340205i | ||||
\(604\) | 4.90243 | + | 8.49126i | 0.199477 | + | 0.345505i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.7431 | − | 18.6076i | 0.436409 | − | 0.755882i | ||||
\(607\) | − | 13.4453i | − | 0.545727i | −0.962053 | − | 0.272863i | \(-0.912029\pi\) | ||
0.962053 | − | 0.272863i | \(-0.0879707\pi\) | |||||||
\(608\) | 9.55976 | + | 15.3200i | 0.387700 | + | 0.621309i | ||||
\(609\) | −7.39497 | −0.299659 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.14115 | − | 12.3688i | 0.288900 | − | 0.500390i | ||||
\(612\) | −6.61008 | + | 3.81633i | −0.267196 | + | 0.154266i | ||||
\(613\) | 17.9313 | + | 10.3527i | 0.724239 | + | 0.418140i | 0.816311 | − | 0.577613i | \(-0.196016\pi\) |
−0.0920716 | + | 0.995752i | \(0.529349\pi\) | |||||||
\(614\) | −14.0820 | − | 24.3907i | −0.568303 | − | 0.984330i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28.6762 | 1.15540 | ||||||||
\(617\) | 8.03560 | − | 4.63936i | 0.323501 | − | 0.186773i | −0.329451 | − | 0.944173i | \(-0.606864\pi\) |
0.652952 | + | 0.757399i | \(0.273530\pi\) | |||||||
\(618\) | 19.3583 | − | 11.1765i | 0.778703 | − | 0.449585i | ||||
\(619\) | 2.89129 | 0.116211 | 0.0581053 | − | 0.998310i | \(-0.481494\pi\) | ||||
0.0581053 | + | 0.998310i | \(0.481494\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.53747 | + | 4.39503i | 0.101825 | + | 0.176366i | ||||
\(622\) | 21.9306 | + | 12.6616i | 0.879338 | + | 0.507686i | ||||
\(623\) | 23.4396 | − | 13.5329i | 0.939088 | − | 0.542183i | ||||
\(624\) | −4.57593 | + | 7.92574i | −0.183184 | + | 0.317284i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −41.4926 | −1.65838 | ||||||||
\(627\) | −13.6738 | + | 25.6781i | −0.546078 | + | 1.02548i | ||||
\(628\) | − | 2.60138i | − | 0.103806i | ||||||
\(629\) | 8.65844 | − | 14.9969i | 0.345234 | − | 0.597964i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.2270 | − | 26.3740i | −0.606178 | − | 1.04993i | −0.991864 | − | 0.127301i | \(-0.959369\pi\) |
0.385686 | − | 0.922630i | \(-0.373965\pi\) | |||||||
\(632\) | 13.4759 | + | 7.78029i | 0.536041 | + | 0.309483i | ||||
\(633\) | −22.3134 | + | 12.8826i | −0.886877 | + | 0.512039i | ||||
\(634\) | −41.9972 | −1.66792 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.981604 | − | 1.70019i | −0.0389231 | − | 0.0674168i | ||||
\(637\) | −1.47737 | + | 0.852959i | −0.0585355 | + | 0.0337955i | ||||
\(638\) | 25.0812i | 0.992975i | ||||||||
\(639\) | 14.6198 | 0.578349 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.0369 | − | 17.3845i | 0.396434 | − | 0.686645i | −0.596849 | − | 0.802354i | \(-0.703581\pi\) |
0.993283 | + | 0.115709i | \(0.0369141\pi\) | |||||||
\(642\) | −29.9554 | + | 17.2948i | −1.18225 | + | 0.682571i | ||||
\(643\) | 1.80924 | + | 1.04457i | 0.0713496 | + | 0.0411937i | 0.535250 | − | 0.844693i | \(-0.320217\pi\) |
−0.463901 | + | 0.885887i | \(0.653551\pi\) | |||||||
\(644\) | 0.882172 | − | 1.52797i | 0.0347625 | − | 0.0602103i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36.8347 | − | 22.9850i | 1.44924 | − | 0.904334i | ||||
\(647\) | 2.10623i | 0.0828043i | 0.999143 | + | 0.0414021i | \(0.0131825\pi\) | ||||
−0.999143 | + | 0.0414021i | \(0.986818\pi\) | |||||||
\(648\) | 2.29693 | + | 1.32613i | 0.0902319 | + | 0.0520954i | ||||
\(649\) | 31.0722 | − | 53.8187i | 1.21969 | − | 2.11257i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.44081 | − | 12.8879i | 0.291628 | − | 0.505115i | ||||
\(652\) | −0.205549 | + | 0.118674i | −0.00804994 | + | 0.00464763i | ||||
\(653\) | 1.83067i | 0.0716395i | 0.999358 | + | 0.0358197i | \(0.0114042\pi\) | ||||
−0.999358 | + | 0.0358197i | \(0.988596\pi\) | |||||||
\(654\) | −10.8583 | −0.424593 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −15.6223 | − | 27.0587i | −0.609950 | − | 1.05646i | ||||
\(657\) | − | 16.9634i | − | 0.661804i | ||||||
\(658\) | 36.2973i | 1.41502i | ||||||||
\(659\) | 12.0268 | + | 20.8310i | 0.468497 | + | 0.811460i | 0.999352 | − | 0.0360024i | \(-0.0114624\pi\) |
−0.530855 | + | 0.847463i | \(0.678129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.72110 | + | 15.1054i | 0.339211 | + | 0.587531i | 0.984285 | − | 0.176589i | \(-0.0565065\pi\) |
−0.645073 | + | 0.764121i | \(0.723173\pi\) | |||||||
\(662\) | 29.1282 | + | 16.8172i | 1.13210 | + | 0.653617i | ||||
\(663\) | 9.58642 | + | 5.53472i | 0.372306 | + | 0.214951i | ||||
\(664\) | −6.37097 | −0.247241 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.97184 | −0.308902 | ||||||||
\(667\) | −2.13159 | − | 1.23068i | −0.0825356 | − | 0.0476519i | ||||
\(668\) | −9.52077 | − | 5.49682i | −0.368370 | − | 0.212678i | ||||
\(669\) | −5.92402 | − | 10.2607i | −0.229036 | − | 0.396702i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.2951 | − | 52.4726i | −1.16953 | − | 2.02568i | ||||
\(672\) | − | 11.7005i | − | 0.451357i | ||||||
\(673\) | 47.5187i | 1.83171i | 0.401506 | + | 0.915856i | \(0.368487\pi\) | ||||
−0.401506 | + | 0.915856i | \(0.631513\pi\) | |||||||
\(674\) | 26.4868 | + | 45.8765i | 1.02023 | + | 1.76709i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.05850 | −0.309942 | ||||||||
\(677\) | − | 14.5531i | − | 0.559321i | −0.960099 | − | 0.279661i | \(-0.909778\pi\) | ||
0.960099 | − | 0.279661i | \(-0.0902219\pi\) | |||||||
\(678\) | −26.2124 | + | 15.1338i | −1.00668 | + | 0.581208i | ||||
\(679\) | −4.94084 | + | 8.55778i | −0.189612 | + | 0.328418i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.40754 | − | 4.16998i | 0.0922570 | − | 0.159794i | ||||
\(682\) | −43.7112 | − | 25.2367i | −1.67379 | − | 0.966363i | ||||
\(683\) | 3.33714i | 0.127692i | 0.997960 | + | 0.0638460i | \(0.0203367\pi\) | ||||
−0.997960 | + | 0.0638460i | \(0.979663\pi\) | |||||||
\(684\) | −4.90736 | − | 2.61321i | −0.187638 | − | 0.0999185i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.3553 | − | 28.3282i | 0.624448 | − | 1.08158i | ||||
\(687\) | −6.56146 | − | 3.78826i | −0.250335 | − | 0.144531i | ||||
\(688\) | −19.4487 | + | 11.2287i | −0.741476 | + | 0.428092i | ||||
\(689\) | 1.75163 | − | 3.03391i | 0.0667318 | − | 0.115583i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.3318 | −0.735415 | −0.367708 | − | 0.929941i | \(-0.619857\pi\) | ||||
−0.367708 | + | 0.929941i | \(0.619857\pi\) | |||||||
\(692\) | − | 10.2868i | − | 0.391044i | ||||||
\(693\) | −20.0859 | + | 11.5966i | −0.763001 | + | 0.440519i | ||||
\(694\) | 2.74862 | + | 4.76075i | 0.104336 | + | 0.180716i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.21358 | −0.235525 | ||||||||
\(697\) | −32.7283 | + | 18.8957i | −1.23967 | + | 0.715725i | ||||
\(698\) | 25.7295 | + | 14.8549i | 0.973876 | + | 0.562268i | ||||
\(699\) | −2.98533 | − | 5.17074i | −0.112916 | − | 0.195575i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.96892 | + | 8.60643i | −0.187674 | + | 0.325060i | −0.944474 | − | 0.328586i | \(-0.893428\pi\) |
0.756801 | + | 0.653646i | \(0.226761\pi\) | |||||||
\(702\) | − | 14.3332i | − | 0.540971i | ||||||
\(703\) | 12.6065 | − | 0.432375i | 0.475464 | − | 0.0163073i | ||||
\(704\) | 17.2584 | 0.650452 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.90389 | + | 11.9579i | −0.259831 | + | 0.450041i | ||||
\(707\) | −23.4732 | + | 13.5523i | −0.882801 | + | 0.509686i | ||||
\(708\) | −8.35916 | − | 4.82616i | −0.314157 | − | 0.181378i | ||||
\(709\) | 18.6059 | + | 32.2264i | 0.698760 | + | 1.21029i | 0.968897 | + | 0.247466i | \(0.0795979\pi\) |
−0.270136 | + | 0.962822i | \(0.587069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.5853 | −0.471987 | ||||||||
\(712\) | 19.6950 | − | 11.3709i | 0.738101 | − | 0.426143i | ||||
\(713\) | 4.28961 | − | 2.47661i | 0.160647 | − | 0.0927497i | ||||
\(714\) | −28.1321 | −1.05282 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.48003 | + | 9.49169i | 0.204798 | + | 0.354721i | ||||
\(717\) | −14.0575 | − | 8.11608i | −0.524985 | − | 0.303100i | ||||
\(718\) | −12.0372 | + | 6.94966i | −0.449223 | + | 0.259359i | ||||
\(719\) | −1.32109 | + | 2.28819i | −0.0492683 | + | 0.0853351i | −0.889608 | − | 0.456725i | \(-0.849022\pi\) |
0.840340 | + | 0.542060i | \(0.182356\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.1980 | −1.05015 | ||||||||
\(722\) | 28.4083 | + | 13.8995i | 1.05725 | + | 0.517284i | ||||
\(723\) | − | 17.6581i | − | 0.656711i | ||||||
\(724\) | 3.80832 | − | 6.59621i | 0.141535 | − | 0.245146i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −21.3484 | − | 36.9765i | −0.792313 | − | 1.37233i | ||||
\(727\) | −8.81013 | − | 5.08653i | −0.326750 | − | 0.188649i | 0.327647 | − | 0.944800i | \(-0.393744\pi\) |
−0.654397 | + | 0.756151i | \(0.727077\pi\) | |||||||
\(728\) | 6.88317 | − | 3.97400i | 0.255107 | − | 0.147286i | ||||
\(729\) | −20.9284 | −0.775126 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.5815 | + | 23.5238i | 0.502329 | + | 0.870060i | ||||
\(732\) | −8.15009 | + | 4.70546i | −0.301236 | + | 0.173919i | ||||
\(733\) | 14.8222i | 0.547472i | 0.961805 | + | 0.273736i | \(0.0882594\pi\) | ||||
−0.961805 | + | 0.273736i | \(0.911741\pi\) | |||||||
\(734\) | 24.0023 | 0.885942 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.94720 | − | 3.37266i | 0.0717749 | − | 0.124318i | ||||
\(737\) | 5.03151 | − | 2.90494i | 0.185338 | − | 0.107005i | ||||
\(738\) | 15.0665 | + | 8.69865i | 0.554605 | + | 0.320202i | ||||
\(739\) | 17.7433 | − | 30.7323i | 0.652697 | − | 1.13050i | −0.329769 | − | 0.944062i | \(-0.606971\pi\) |
0.982466 | − | 0.186443i | \(-0.0596959\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.276386 | + | 8.05845i | 0.0101533 | + | 0.296035i | ||||
\(742\) | 8.90325i | 0.326849i | ||||||||
\(743\) | 7.56804 | + | 4.36941i | 0.277645 | + | 0.160298i | 0.632357 | − | 0.774677i | \(-0.282088\pi\) |
−0.354712 | + | 0.934976i | \(0.615421\pi\) | |||||||
\(744\) | 6.25210 | − | 10.8289i | 0.229213 | − | 0.397009i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.0708 | + | 34.7637i | −0.734846 | + | 1.27279i | ||||
\(747\) | 4.46247 | − | 2.57641i | 0.163273 | − | 0.0942658i | ||||
\(748\) | 26.5408i | 0.970428i | ||||||||
\(749\) | 43.6342 | 1.59436 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.54957 | − | 11.3442i | −0.238997 | − | 0.413955i | 0.721430 | − | 0.692488i | \(-0.243485\pi\) |
−0.960427 | + | 0.278533i | \(0.910152\pi\) | |||||||
\(752\) | 44.3011i | 1.61549i | ||||||||
\(753\) | 7.08911i | 0.258342i | ||||||||
\(754\) | 3.47580 | + | 6.02026i | 0.126581 | + | 0.219245i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.06627 | + | 8.77504i | 0.184258 | + | 0.319145i | ||||
\(757\) | −14.2357 | − | 8.21901i | −0.517407 | − | 0.298725i | 0.218466 | − | 0.975845i | \(-0.429895\pi\) |
−0.735873 | + | 0.677119i | \(0.763228\pi\) | |||||||
\(758\) | 24.0386 | + | 13.8787i | 0.873121 | + | 0.504097i | ||||
\(759\) | 6.27397 | 0.227731 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.3918 | 0.594203 | 0.297101 | − | 0.954846i | \(-0.403980\pi\) | ||||
0.297101 | + | 0.954846i | \(0.403980\pi\) | |||||||
\(762\) | 10.2315 | + | 5.90714i | 0.370647 | + | 0.213993i | ||||
\(763\) | 11.8625 | + | 6.84879i | 0.429450 | + | 0.247943i | ||||
\(764\) | −5.00738 | − | 8.67304i | −0.181161 | − | 0.313780i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.05337 | − | 15.6809i | −0.327112 | − | 0.566574i | ||||
\(767\) | − | 17.2242i | − | 0.621929i | ||||||
\(768\) | − | 18.6756i | − | 0.673899i | ||||||
\(769\) | −25.0210 | − | 43.3377i | −0.902282 | − | 1.56280i | −0.824525 | − | 0.565825i | \(-0.808558\pi\) |
−0.0777564 | − | 0.996972i | \(-0.524776\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.142282 | −0.00512416 | ||||||||
\(772\) | − | 11.1875i | − | 0.402649i | ||||||
\(773\) | 42.1644 | − | 24.3436i | 1.51655 | − | 0.875580i | 0.516737 | − | 0.856144i | \(-0.327146\pi\) |
0.999811 | − | 0.0194356i | \(-0.00618693\pi\) | |||||||
\(774\) | 6.25225 | − | 10.8292i | 0.224732 | − | 0.389248i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.15151 | + | 7.19063i | −0.149031 | + | 0.258129i | ||||
\(777\) | −7.07808 | − | 4.08653i | −0.253925 | − | 0.146603i | ||||
\(778\) | − | 60.6799i | − | 2.17548i | ||||||
\(779\) | −24.2977 | − | 12.9387i | −0.870555 | − | 0.463577i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.4185 | − | 44.0261i | 0.909544 | − | 1.57538i | ||||
\(782\) | −8.10905 | − | 4.68176i | −0.289979 | − | 0.167419i | ||||
\(783\) | 12.2416 | − | 7.06771i | 0.437480 | − | 0.252579i | ||||
\(784\) | 2.64572 | − | 4.58252i | 0.0944900 | − | 0.163662i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −28.7275 | −1.02467 | ||||||||
\(787\) | − | 6.51678i | − | 0.232298i | −0.993232 | − | 0.116149i | \(-0.962945\pi\) | ||
0.993232 | − | 0.116149i | \(-0.0370550\pi\) | |||||||
\(788\) | −16.6870 | + | 9.63426i | −0.594451 | + | 0.343206i | ||||
\(789\) | 5.83388 | + | 10.1046i | 0.207692 | + | 0.359732i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.1820 | 1.35760 | ||||||||
\(792\) | −16.8771 | + | 9.74399i | −0.599701 | + | 0.346238i | ||||
\(793\) | −14.5435 | − | 8.39668i | −0.516454 | − | 0.298175i | ||||
\(794\) | −7.14407 | − | 12.3739i | −0.253534 | − | 0.439133i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.869124 | − | 1.50537i | 0.0308053 | − | 0.0533563i | ||||
\(797\) | − | 38.3796i | − | 1.35947i | −0.733456 | − | 0.679737i | \(-0.762094\pi\) | ||
0.733456 | − | 0.679737i | \(-0.237906\pi\) | |||||||
\(798\) | −10.8483 | − | 17.3849i | −0.384024 | − | 0.615419i | ||||
\(799\) | 53.5834 | 1.89565 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.19675 | + | 15.9292i | −0.324951 | + | 0.562832i | ||||
\(802\) | −24.5864 | + | 14.1950i | −0.868177 | + | 0.501242i | ||||
\(803\) | −51.0836 | − | 29.4931i | −1.80270 | − | 1.04079i | ||||
\(804\) | −0.451198 | − | 0.781498i | −0.0159125 | − | 0.0275613i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.9894 | −0.492755 | ||||||||
\(807\) | 5.73729 | − | 3.31243i | 0.201962 | − | 0.116603i | ||||
\(808\) | −19.7232 | + | 11.3872i | −0.693861 | + | 0.400601i | ||||
\(809\) | −25.1409 | −0.883906 | −0.441953 | − | 0.897038i | \(-0.645714\pi\) | ||||
−0.441953 | + | 0.897038i | \(0.645714\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.5053 | + | 40.7124i | 0.825383 | + | 1.42961i | 0.901626 | + | 0.432517i | \(0.142374\pi\) |
−0.0762426 | + | 0.997089i | \(0.524292\pi\) | |||||||
\(812\) | −4.25590 | − | 2.45714i | −0.149353 | − | 0.0862289i | ||||
\(813\) | 12.7668 | − | 7.37094i | 0.447753 | − | 0.258510i | ||||
\(814\) | −13.8601 | + | 24.0064i | −0.485797 | + | 0.841425i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −34.3354 | −1.20198 | ||||||||
\(817\) | −9.29984 | + | 17.4642i | −0.325360 | + | 0.610996i | ||||
\(818\) | 19.6317i | 0.686406i | ||||||||
\(819\) | −3.21416 | + | 5.56708i | −0.112312 | + | 0.194530i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.91021 | + | 17.1650i | 0.345869 | + | 0.599062i | 0.985511 | − | 0.169610i | \(-0.0542509\pi\) |
−0.639642 | + | 0.768673i | \(0.720918\pi\) | |||||||
\(822\) | 29.0069 | + | 16.7471i | 1.01173 | + | 0.584123i | ||||
\(823\) | −33.9627 | + | 19.6084i | −1.18387 | + | 0.683505i | −0.956906 | − | 0.290399i | \(-0.906212\pi\) |
−0.226960 | + | 0.973904i | \(0.572879\pi\) | |||||||
\(824\) | −23.6932 | −0.825391 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.8869 | + | 37.9092i | 0.761543 | + | 1.31903i | ||||
\(827\) | 10.2568 | − | 5.92176i | 0.356663 | − | 0.205920i | −0.310953 | − | 0.950425i | \(-0.600648\pi\) |
0.667616 | + | 0.744506i | \(0.267315\pi\) | |||||||
\(828\) | 1.19903i | 0.0416690i | ||||||||
\(829\) | −46.9321 | −1.63002 | −0.815010 | − | 0.579447i | \(-0.803269\pi\) | ||||
−0.815010 | + | 0.579447i | \(0.803269\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.2070 | − | 17.6790i | 0.354076 | − | 0.613278i | ||||
\(832\) | 4.14255 | − | 2.39170i | 0.143617 | − | 0.0829174i | ||||
\(833\) | −5.54270 | − | 3.20008i | −0.192043 | − | 0.110876i | ||||
\(834\) | −6.47222 | + | 11.2102i | −0.224115 | + | 0.388178i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −16.4015 | + | 10.2346i | −0.567259 | + | 0.353972i | ||||
\(837\) | 28.4461i | 0.983240i | ||||||||
\(838\) | 1.64738 | + | 0.951117i | 0.0569079 | + | 0.0328558i | ||||
\(839\) | −26.5669 | + | 46.0153i | −0.917192 | + | 1.58862i | −0.113532 | + | 0.993534i | \(0.536217\pi\) |
−0.803660 | + | 0.595089i | \(0.797117\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0722 | − | 19.1775i | 0.381799 | − | 0.661294i | ||||
\(842\) | 28.1372 | − | 16.2450i | 0.969673 | − | 0.559841i | ||||
\(843\) | 23.7755i | 0.818870i | ||||||||
\(844\) | −17.1222 | −0.589370 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.3336 | − | 21.3624i | −0.424038 | − | 0.734455i | ||||
\(847\) | 53.8613i | 1.85070i | ||||||||
\(848\) | 10.8665i | 0.373156i | ||||||||
\(849\) | 6.87509 | + | 11.9080i | 0.235952 | + | 0.408682i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.36017 | − | 2.35588i | −0.0466259 | − | 0.0807584i | ||||
\(852\) | −6.83816 | − | 3.94802i | −0.234272 | − | 0.135257i | ||||
\(853\) | −36.6327 | − | 21.1499i | −1.25428 | − | 0.724159i | −0.282324 | − | 0.959319i | \(-0.591105\pi\) |
−0.971957 | + | 0.235160i | \(0.924438\pi\) | |||||||
\(854\) | 42.6790 | 1.46045 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.6634 | 1.25313 | ||||||||
\(857\) | 20.3849 | + | 11.7692i | 0.696333 | + | 0.402028i | 0.805980 | − | 0.591942i | \(-0.201639\pi\) |
−0.109647 | + | 0.993971i | \(0.534972\pi\) | |||||||
\(858\) | −15.3456 | − | 8.85979i | −0.523890 | − | 0.302468i | ||||
\(859\) | 4.74062 | + | 8.21099i | 0.161748 | + | 0.280156i | 0.935496 | − | 0.353338i | \(-0.114954\pi\) |
−0.773748 | + | 0.633494i | \(0.781620\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.91821 | + | 15.4468i | 0.303932 | + | 0.526425i | ||||
\(862\) | − | 61.3859i | − | 2.09081i | ||||||
\(863\) | 22.8204i | 0.776816i | 0.921487 | + | 0.388408i | \(0.126975\pi\) | ||||
−0.921487 | + | 0.388408i | \(0.873025\pi\) | |||||||
\(864\) | 11.1827 | + | 19.3690i | 0.380443 | + | 0.658947i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.614106 | −0.0208682 | ||||||||
\(867\) | 21.8138i | 0.740834i | ||||||||
\(868\) | 8.56456 | − | 4.94475i | 0.290700 | − | 0.167836i | ||||
\(869\) | −21.8813 | + | 37.8996i | −0.742273 | + | 1.28565i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.805144 | − | 1.39455i | 0.0272813 | − | 0.0472525i | ||||
\(872\) | 9.96736 | + | 5.75466i | 0.337537 | + | 0.194877i | ||||
\(873\) | − | 6.71546i | − | 0.227284i | ||||||
\(874\) | −0.233792 | − | 6.81656i | −0.00790814 | − | 0.230574i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.58089 | + | 7.93434i | −0.154774 | + | 0.268077i | ||||
\(877\) | −21.9054 | − | 12.6471i | −0.739693 | − | 0.427062i | 0.0822647 | − | 0.996611i | \(-0.473785\pi\) |
−0.821958 | + | 0.569549i | \(0.807118\pi\) | |||||||
\(878\) | 3.26421 | − | 1.88459i | 0.110162 | − | 0.0636018i | ||||
\(879\) | 14.4862 | − | 25.0908i | 0.488606 | − | 0.846291i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.2871 | −1.12147 | −0.560736 | − | 0.827995i | \(-0.689482\pi\) | ||||
−0.560736 | + | 0.827995i | \(0.689482\pi\) | |||||||
\(882\) | 2.94632i | 0.0992077i | ||||||||
\(883\) | −13.2596 | + | 7.65544i | −0.446222 | + | 0.257626i | −0.706233 | − | 0.707979i | \(-0.749607\pi\) |
0.260011 | + | 0.965606i | \(0.416274\pi\) | |||||||
\(884\) | 3.67807 | + | 6.37061i | 0.123707 | + | 0.214267i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.4030 | 0.920621 | ||||||||
\(887\) | −37.4171 | + | 21.6027i | −1.25634 | + | 0.725349i | −0.972361 | − | 0.233481i | \(-0.924988\pi\) |
−0.283980 | + | 0.958830i | \(0.591655\pi\) | |||||||
\(888\) | −5.94731 | − | 3.43368i | −0.199579 | − | 0.115227i | ||||
\(889\) | −7.45177 | − | 12.9068i | −0.249924 | − | 0.432882i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.72962 | + | 6.45990i | −0.124947 | + | 0.216415i | ||||
\(892\) | − | 7.87356i | − | 0.263626i | ||||||
\(893\) | 20.6628 | + | 33.1132i | 0.691453 | + | 1.10809i | ||||
\(894\) | −27.7849 | −0.929265 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −16.1671 | + | 28.0022i | −0.540104 | + | 0.935488i | ||||
\(897\) | 1.50594 | − | 0.869457i | 0.0502820 | − | 0.0290303i | ||||
\(898\) | 20.4141 | + | 11.7861i | 0.681228 | + | 0.393307i | ||||
\(899\) | −6.89818 | − | 11.9480i | −0.230067 | − | 0.398488i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.1433 | 0.437867 | ||||||||
\(902\) | 52.3903 | − | 30.2475i | 1.74441 | − | 1.00713i | ||||
\(903\) | 11.1026 | − | 6.41007i | 0.369470 | − | 0.213314i | ||||
\(904\) | 32.0822 | 1.06704 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −12.2796 | − | 21.2688i | −0.407961 | − | 0.706609i | ||||
\(907\) | 12.4083 | + | 7.16392i | 0.412010 | + | 0.237874i | 0.691653 | − | 0.722230i | \(-0.256883\pi\) |
−0.279643 | + | 0.960104i | \(0.590216\pi\) | |||||||
\(908\) | 2.77114 | − | 1.59992i | 0.0919634 | − | 0.0530951i | ||||
\(909\) | 9.20994 | − | 15.9521i | 0.305475 | − | 0.529097i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.61162 | −0.152790 | −0.0763949 | − | 0.997078i | \(-0.524341\pi\) | ||||
−0.0763949 | + | 0.997078i | \(0.524341\pi\) | |||||||
\(912\) | −13.2404 | − | 21.2184i | −0.438432 | − | 0.702610i | ||||
\(913\) | − | 17.9177i | − | 0.592990i | ||||||
\(914\) | −1.01598 | + | 1.75973i | −0.0336056 | + | 0.0582066i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.51747 | − | 4.36038i | −0.0831795 | − | 0.144071i | ||||
\(917\) | 31.3841 | + | 18.1196i | 1.03640 | + | 0.598363i | ||||
\(918\) | 46.5699 | − | 26.8871i | 1.53703 | − | 0.887407i | ||||
\(919\) | −26.4921 | −0.873892 | −0.436946 | − | 0.899488i | \(-0.643940\pi\) | ||||
−0.436946 | + | 0.899488i | \(0.643940\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.81149 | + | 16.9940i | 0.323300 | + | 0.559972i | ||||
\(922\) | −12.5293 | + | 7.23378i | −0.412630 | + | 0.238232i | ||||
\(923\) | − | 14.0901i | − | 0.463782i | ||||||
\(924\) | 12.5265 | 0.412091 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.4082 | + | 28.4198i | −0.539206 | + | 0.933932i | ||||
\(927\) | 16.5956 | − | 9.58148i | 0.545072 | − | 0.314697i | ||||
\(928\) | −9.39398 | − | 5.42362i | −0.308372 | − | 0.178039i | ||||
\(929\) | −2.37863 | + | 4.11990i | −0.0780402 | + | 0.135170i | −0.902404 | − | 0.430890i | \(-0.858200\pi\) |
0.824364 | + | 0.566060i | \(0.191533\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.159802 | − | 4.65925i | −0.00523729 | − | 0.152701i | ||||
\(932\) | − | 3.96777i | − | 0.129969i | ||||||
\(933\) | −15.2799 | − | 8.82188i | −0.500243 | − | 0.288815i | ||||
\(934\) | 9.55406 | − | 16.5481i | 0.312619 | − | 0.541471i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.70068 | + | 4.67771i | −0.0882744 | + | 0.152896i | ||||
\(937\) | 10.3375 | − | 5.96833i | 0.337710 | − | 0.194977i | −0.321549 | − | 0.946893i | \(-0.604203\pi\) |
0.659259 | + | 0.751916i | \(0.270870\pi\) | |||||||
\(938\) | 4.09242i | 0.133622i | ||||||||
\(939\) | 28.9096 | 0.943429 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.99715 | + | 15.5835i | 0.293299 | + | 0.508008i | 0.974588 | − | 0.224006i | \(-0.0719136\pi\) |
−0.681289 | + | 0.732015i | \(0.738580\pi\) | |||||||
\(942\) | 6.51590i | 0.212299i | ||||||||
\(943\) | 5.93670i | 0.193326i | ||||||||
\(944\) | 26.7131 | + | 46.2684i | 0.869437 | + | 1.50591i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21.7408 | − | 37.6561i | −0.706853 | − | 1.22431i | ||||
\(947\) | −21.8404 | − | 12.6096i | −0.709717 | − | 0.409755i | 0.101239 | − | 0.994862i | \(-0.467719\pi\) |
−0.810956 | + | 0.585107i | \(0.801053\pi\) | |||||||
\(948\) | 5.88659 | + | 3.39862i | 0.191188 | + | 0.110382i | ||||
\(949\) | −16.3488 | −0.530705 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.2611 | 0.948858 | ||||||||
\(952\) | 25.8238 | + | 14.9094i | 0.836955 | + | 0.483216i | ||||
\(953\) | −36.6484 | − | 21.1589i | −1.18716 | − | 0.685405i | −0.229498 | − | 0.973309i | \(-0.573708\pi\) |
−0.957659 | + | 0.287904i | \(0.907042\pi\) | |||||||
\(954\) | −3.02527 | − | 5.23991i | −0.0979466 | − | 0.169648i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.39350 | − | 9.34181i | −0.174438 | − | 0.302136i | ||||
\(957\) | − | 17.4751i | − | 0.564890i | ||||||
\(958\) | − | 65.3552i | − | 2.11153i | ||||||
\(959\) | −21.1263 | − | 36.5918i | −0.682203 | − | 1.18161i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.23623 | −0.104395 | ||||||||
\(962\) | 7.68304i | 0.247711i | ||||||||
\(963\) | −25.6805 | + | 14.8266i | −0.827542 | + | 0.477781i | ||||
\(964\) | 5.86730 | − | 10.1625i | 0.188973 | − | 0.327311i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.20966 | + | 3.82724i | −0.0710945 | + | 0.123139i | ||||
\(967\) | −11.8614 | − | 6.84820i | −0.381438 | − | 0.220223i | 0.297006 | − | 0.954876i | \(-0.404012\pi\) |
−0.678444 | + | 0.734652i | \(0.737345\pi\) | |||||||
\(968\) | 45.2567i | 1.45460i | ||||||||
\(969\) | −25.6642 | + | 16.0146i | −0.824454 | + | 0.514463i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.2906 | − | 33.4123i | 0.619065 | − | 1.07225i | −0.370591 | − | 0.928796i | \(-0.620845\pi\) |
0.989657 | − | 0.143457i | \(-0.0458217\pi\) | |||||||
\(972\) | −9.80665 | − | 5.66187i | −0.314548 | − | 0.181605i | ||||
\(973\) | 14.1415 | − | 8.16461i | 0.453356 | − | 0.261745i | ||||
\(974\) | −26.2951 | + | 45.5445i | −0.842549 | + | 1.45934i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 52.0899 | 1.66736 | ||||||||
\(977\) | 17.4592i | 0.558568i | 0.960209 | + | 0.279284i | \(0.0900971\pi\) | ||||
−0.960209 | + | 0.279284i | \(0.909903\pi\) | |||||||
\(978\) | 0.514858 | − | 0.297253i | 0.0164633 | − | 0.00950512i | ||||
\(979\) | 31.9796 | + | 55.3903i | 1.02207 | + | 1.77028i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.30869 | −0.297204 | ||||||||
\(982\) | −15.9488 | + | 9.20805i | −0.508947 | + | 0.293841i | ||||
\(983\) | −38.0325 | − | 21.9581i | −1.21305 | − | 0.700353i | −0.249625 | − | 0.968342i | \(-0.580308\pi\) |
−0.963422 | + | 0.267989i | \(0.913641\pi\) | |||||||
\(984\) | 7.49348 | + | 12.9791i | 0.238883 | + | 0.413758i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −13.0403 | + | 22.5864i | −0.415287 | + | 0.719298i | ||||
\(987\) | − | 25.2898i | − | 0.804984i | ||||||
\(988\) | −2.51854 | + | 4.72958i | −0.0801254 | + | 0.150468i | ||||
\(989\) | 4.26707 | 0.135685 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.1731 | + | 40.1370i | −0.736118 | + | 1.27499i | 0.218112 | + | 0.975924i | \(0.430010\pi\) |
−0.954231 | + | 0.299071i | \(0.903323\pi\) | |||||||
\(992\) | 18.9044 | − | 10.9145i | 0.600216 | − | 0.346535i | ||||
\(993\) | −20.2948 | − | 11.7172i | −0.644035 | − | 0.371834i | ||||
\(994\) | 17.9045 | + | 31.0114i | 0.567895 | + | 0.983623i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.78300 | −0.0881827 | ||||||||
\(997\) | −10.1647 | + | 5.86857i | −0.321918 | + | 0.185859i | −0.652247 | − | 0.758006i | \(-0.726174\pi\) |
0.330329 | + | 0.943866i | \(0.392840\pi\) | |||||||
\(998\) | 29.3692 | − | 16.9563i | 0.929667 | − | 0.536744i | ||||
\(999\) | 15.6227 | 0.494281 |
(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 | 475.2.j.c.49.2 | 16 | ||
5.2 | odd | 4 | 95.2.e.c.11.4 | ✓ | 8 | ||
5.3 | odd | 4 | 475.2.e.e.201.1 | 8 | |||
5.4 | even | 2 | inner | 475.2.j.c.49.7 | 16 | ||
15.2 | even | 4 | 855.2.k.h.676.1 | 8 | |||
19.7 | even | 3 | inner | 475.2.j.c.349.7 | 16 | ||
20.7 | even | 4 | 1520.2.q.o.961.1 | 8 | |||
95.7 | odd | 12 | 95.2.e.c.26.4 | yes | 8 | ||
95.8 | even | 12 | 9025.2.a.bp.1.1 | 4 | |||
95.27 | even | 12 | 1805.2.a.i.1.4 | 4 | |||
95.64 | even | 6 | inner | 475.2.j.c.349.2 | 16 | ||
95.68 | odd | 12 | 9025.2.a.bg.1.4 | 4 | |||
95.83 | odd | 12 | 475.2.e.e.26.1 | 8 | |||
95.87 | odd | 12 | 1805.2.a.o.1.1 | 4 | |||
285.197 | even | 12 | 855.2.k.h.406.1 | 8 | |||
380.7 | even | 12 | 1520.2.q.o.881.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.e.c.11.4 | ✓ | 8 | 5.2 | odd | 4 | ||
95.2.e.c.26.4 | yes | 8 | 95.7 | odd | 12 | ||
475.2.e.e.26.1 | 8 | 95.83 | odd | 12 | |||
475.2.e.e.201.1 | 8 | 5.3 | odd | 4 | |||
475.2.j.c.49.2 | 16 | 1.1 | even | 1 | trivial | ||
475.2.j.c.49.7 | 16 | 5.4 | even | 2 | inner | ||
475.2.j.c.349.2 | 16 | 95.64 | even | 6 | inner | ||
475.2.j.c.349.7 | 16 | 19.7 | even | 3 | inner | ||
855.2.k.h.406.1 | 8 | 285.197 | even | 12 | |||
855.2.k.h.676.1 | 8 | 15.2 | even | 4 | |||
1520.2.q.o.881.1 | 8 | 380.7 | even | 12 | |||
1520.2.q.o.961.1 | 8 | 20.7 | even | 4 | |||
1805.2.a.i.1.4 | 4 | 95.27 | even | 12 | |||
1805.2.a.o.1.1 | 4 | 95.87 | odd | 12 | |||
9025.2.a.bg.1.4 | 4 | 95.68 | odd | 12 | |||
9025.2.a.bp.1.1 | 4 | 95.8 | even | 12 |