Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(165,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.h (of order \(3\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 471.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.471 |
Dual form | 637.2.h.e.165.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | 1.22474 | 0.612372 | − | 0.790569i | \(-0.290215\pi\) | ||||
0.612372 | + | 0.790569i | \(0.290215\pi\) | |||||||
\(3\) | 1.36603 | − | 2.36603i | 0.788675 | − | 1.36603i | −0.138104 | − | 0.990418i | \(-0.544101\pi\) |
0.926779 | − | 0.375608i | \(-0.122566\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.866025 | − | 1.50000i | 0.387298 | − | 0.670820i | −0.604787 | − | 0.796387i | \(-0.706742\pi\) |
0.992085 | + | 0.125567i | \(0.0400750\pi\) | |||||||
\(6\) | 2.36603 | − | 4.09808i | 0.965926 | − | 1.67303i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.73205 | −0.612372 | ||||||||
\(9\) | −2.23205 | − | 3.86603i | −0.744017 | − | 1.28868i | ||||
\(10\) | 1.50000 | − | 2.59808i | 0.474342 | − | 0.821584i | ||||
\(11\) | −0.633975 | + | 1.09808i | −0.191151 | + | 0.331082i | −0.945632 | − | 0.325239i | \(-0.894555\pi\) |
0.754481 | + | 0.656322i | \(0.227889\pi\) | |||||||
\(12\) | 1.36603 | − | 2.36603i | 0.394338 | − | 0.683013i | ||||
\(13\) | −3.59808 | − | 0.232051i | −0.997927 | − | 0.0643593i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.36603 | − | 4.09808i | −0.610905 | − | 1.05812i | ||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 7.73205 | 1.87530 | 0.937649 | − | 0.347584i | \(-0.112998\pi\) | ||||
0.937649 | + | 0.347584i | \(0.112998\pi\) | |||||||
\(18\) | −3.86603 | − | 6.69615i | −0.911231 | − | 1.57830i | ||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | 0.866025 | − | 1.50000i | 0.193649 | − | 0.335410i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.09808 | + | 1.90192i | −0.234111 | + | 0.405492i | ||||
\(23\) | 4.73205 | 0.986701 | 0.493350 | − | 0.869831i | \(-0.335772\pi\) | ||||
0.493350 | + | 0.869831i | \(0.335772\pi\) | |||||||
\(24\) | −2.36603 | + | 4.09808i | −0.482963 | + | 0.836516i | ||||
\(25\) | 1.00000 | + | 1.73205i | 0.200000 | + | 0.346410i | ||||
\(26\) | −6.23205 | − | 0.401924i | −1.22221 | − | 0.0788237i | ||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.50000 | + | 2.59808i | 0.278543 | + | 0.482451i | 0.971023 | − | 0.238987i | \(-0.0768152\pi\) |
−0.692480 | + | 0.721437i | \(0.743482\pi\) | |||||||
\(30\) | −4.09808 | − | 7.09808i | −0.748203 | − | 1.29593i | ||||
\(31\) | 2.09808 | + | 3.63397i | 0.376826 | + | 0.652681i | 0.990598 | − | 0.136802i | \(-0.0436823\pi\) |
−0.613773 | + | 0.789483i | \(0.710349\pi\) | |||||||
\(32\) | −5.19615 | −0.918559 | ||||||||
\(33\) | 1.73205 | + | 3.00000i | 0.301511 | + | 0.522233i | ||||
\(34\) | 13.3923 | 2.29676 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.23205 | − | 3.86603i | −0.372008 | − | 0.644338i | ||||
\(37\) | −7.00000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | 1.73205 | + | 3.00000i | 0.280976 | + | 0.486664i | ||||
\(39\) | −5.46410 | + | 8.19615i | −0.874957 | + | 1.31243i | ||||
\(40\) | −1.50000 | + | 2.59808i | −0.237171 | + | 0.410792i | ||||
\(41\) | −2.59808 | − | 4.50000i | −0.405751 | − | 0.702782i | 0.588657 | − | 0.808383i | \(-0.299657\pi\) |
−0.994409 | + | 0.105601i | \(0.966323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0980762 | − | 0.169873i | 0.0149565 | − | 0.0259054i | −0.858450 | − | 0.512897i | \(-0.828572\pi\) |
0.873407 | + | 0.486991i | \(0.161906\pi\) | |||||||
\(44\) | −0.633975 | + | 1.09808i | −0.0955753 | + | 0.165541i | ||||
\(45\) | −7.73205 | −1.15263 | ||||||||
\(46\) | 8.19615 | 1.20846 | ||||||||
\(47\) | 6.46410 | − | 11.1962i | 0.942886 | − | 1.63313i | 0.182957 | − | 0.983121i | \(-0.441433\pi\) |
0.759929 | − | 0.650006i | \(-0.225234\pi\) | |||||||
\(48\) | −6.83013 | + | 11.8301i | −0.985844 | + | 1.70753i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.73205 | + | 3.00000i | 0.244949 | + | 0.424264i | ||||
\(51\) | 10.5622 | − | 18.2942i | 1.47900 | − | 2.56170i | ||||
\(52\) | −3.59808 | − | 0.232051i | −0.498963 | − | 0.0321797i | ||||
\(53\) | 4.96410 | + | 8.59808i | 0.681872 | + | 1.18104i | 0.974409 | + | 0.224782i | \(0.0721671\pi\) |
−0.292537 | + | 0.956254i | \(0.594500\pi\) | |||||||
\(54\) | −6.92820 | −0.942809 | ||||||||
\(55\) | 1.09808 | + | 1.90192i | 0.148065 | + | 0.256455i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.46410 | 0.723738 | ||||||||
\(58\) | 2.59808 | + | 4.50000i | 0.341144 | + | 0.590879i | ||||
\(59\) | −7.26795 | −0.946206 | −0.473103 | − | 0.881007i | \(-0.656866\pi\) | ||||
−0.473103 | + | 0.881007i | \(0.656866\pi\) | |||||||
\(60\) | −2.36603 | − | 4.09808i | −0.305453 | − | 0.529059i | ||||
\(61\) | −2.40192 | − | 4.16025i | −0.307535 | − | 0.532666i | 0.670288 | − | 0.742101i | \(-0.266171\pi\) |
−0.977822 | + | 0.209435i | \(0.932837\pi\) | |||||||
\(62\) | 3.63397 | + | 6.29423i | 0.461515 | + | 0.799368i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.46410 | + | 5.19615i | −0.429669 | + | 0.644503i | ||||
\(66\) | 3.00000 | + | 5.19615i | 0.369274 | + | 0.639602i | ||||
\(67\) | 3.09808 | − | 5.36603i | 0.378490 | − | 0.655564i | −0.612353 | − | 0.790585i | \(-0.709777\pi\) |
0.990843 | + | 0.135020i | \(0.0431100\pi\) | |||||||
\(68\) | 7.73205 | 0.937649 | ||||||||
\(69\) | 6.46410 | − | 11.1962i | 0.778186 | − | 1.34786i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | + | 5.19615i | −0.356034 | + | 0.616670i | −0.987294 | − | 0.158901i | \(-0.949205\pi\) |
0.631260 | + | 0.775571i | \(0.282538\pi\) | |||||||
\(72\) | 3.86603 | + | 6.69615i | 0.455615 | + | 0.789149i | ||||
\(73\) | −1.59808 | − | 2.76795i | −0.187041 | − | 0.323964i | 0.757222 | − | 0.653158i | \(-0.226556\pi\) |
−0.944262 | + | 0.329194i | \(0.893223\pi\) | |||||||
\(74\) | −12.1244 | −1.40943 | ||||||||
\(75\) | 5.46410 | 0.630940 | ||||||||
\(76\) | 1.00000 | + | 1.73205i | 0.114708 | + | 0.198680i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.46410 | + | 14.1962i | −1.07160 | + | 1.60740i | ||||
\(79\) | −8.09808 | + | 14.0263i | −0.911105 | + | 1.57808i | −0.0985985 | + | 0.995127i | \(0.531436\pi\) |
−0.812506 | + | 0.582952i | \(0.801897\pi\) | |||||||
\(80\) | −4.33013 | + | 7.50000i | −0.484123 | + | 0.838525i | ||||
\(81\) | 1.23205 | − | 2.13397i | 0.136895 | − | 0.237108i | ||||
\(82\) | −4.50000 | − | 7.79423i | −0.496942 | − | 0.860729i | ||||
\(83\) | 2.19615 | 0.241059 | 0.120530 | − | 0.992710i | \(-0.461541\pi\) | ||||
0.120530 | + | 0.992710i | \(0.461541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.69615 | − | 11.5981i | 0.726300 | − | 1.25799i | ||||
\(86\) | 0.169873 | − | 0.294229i | 0.0183179 | − | 0.0317275i | ||||
\(87\) | 8.19615 | 0.878720 | ||||||||
\(88\) | 1.09808 | − | 1.90192i | 0.117055 | − | 0.202746i | ||||
\(89\) | −12.9282 | −1.37039 | −0.685193 | − | 0.728361i | \(-0.740282\pi\) | ||||
−0.685193 | + | 0.728361i | \(0.740282\pi\) | |||||||
\(90\) | −13.3923 | −1.41167 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.73205 | 0.493350 | ||||||||
\(93\) | 11.4641 | 1.18877 | ||||||||
\(94\) | 11.1962 | − | 19.3923i | 1.15479 | − | 2.00016i | ||||
\(95\) | 3.46410 | 0.355409 | ||||||||
\(96\) | −7.09808 | + | 12.2942i | −0.724444 | + | 1.25477i | ||||
\(97\) | 3.19615 | − | 5.53590i | 0.324520 | − | 0.562085i | −0.656895 | − | 0.753982i | \(-0.728131\pi\) |
0.981415 | + | 0.191897i | \(0.0614639\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.66025 | 0.568877 | ||||||||
\(100\) | 1.00000 | + | 1.73205i | 0.100000 | + | 0.173205i | ||||
\(101\) | −3.86603 | + | 6.69615i | −0.384684 | + | 0.666292i | −0.991725 | − | 0.128378i | \(-0.959023\pi\) |
0.607041 | + | 0.794670i | \(0.292356\pi\) | |||||||
\(102\) | 18.2942 | − | 31.6865i | 1.81140 | − | 3.13743i | ||||
\(103\) | −7.19615 | + | 12.4641i | −0.709058 | + | 1.22812i | 0.256149 | + | 0.966637i | \(0.417546\pi\) |
−0.965207 | + | 0.261487i | \(0.915787\pi\) | |||||||
\(104\) | 6.23205 | + | 0.401924i | 0.611103 | + | 0.0394119i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.59808 | + | 14.8923i | 0.835119 | + | 1.44647i | ||||
\(107\) | −7.85641 | −0.759507 | −0.379754 | − | 0.925088i | \(-0.623991\pi\) | ||||
−0.379754 | + | 0.925088i | \(0.623991\pi\) | |||||||
\(108\) | −4.00000 | −0.384900 | ||||||||
\(109\) | 4.19615 | + | 7.26795i | 0.401919 | + | 0.696143i | 0.993957 | − | 0.109766i | \(-0.0350102\pi\) |
−0.592039 | + | 0.805909i | \(0.701677\pi\) | |||||||
\(110\) | 1.90192 | + | 3.29423i | 0.181341 | + | 0.314092i | ||||
\(111\) | −9.56218 | + | 16.5622i | −0.907602 | + | 1.57201i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.69615 | + | 11.5981i | −0.629921 | + | 1.09106i | 0.357646 | + | 0.933857i | \(0.383579\pi\) |
−0.987567 | + | 0.157198i | \(0.949754\pi\) | |||||||
\(114\) | 9.46410 | 0.886394 | ||||||||
\(115\) | 4.09808 | − | 7.09808i | 0.382148 | − | 0.661899i | ||||
\(116\) | 1.50000 | + | 2.59808i | 0.139272 | + | 0.241225i | ||||
\(117\) | 7.13397 | + | 14.4282i | 0.659536 | + | 1.33389i | ||||
\(118\) | −12.5885 | −1.15886 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.09808 | + | 7.09808i | 0.374101 | + | 0.647963i | ||||
\(121\) | 4.69615 | + | 8.13397i | 0.426923 | + | 0.739452i | ||||
\(122\) | −4.16025 | − | 7.20577i | −0.376652 | − | 0.652380i | ||||
\(123\) | −14.1962 | −1.28002 | ||||||||
\(124\) | 2.09808 | + | 3.63397i | 0.188413 | + | 0.326341i | ||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.19615 | − | 15.9282i | −0.816027 | − | 1.41340i | −0.908588 | − | 0.417693i | \(-0.862839\pi\) |
0.0925619 | − | 0.995707i | \(-0.470494\pi\) | |||||||
\(128\) | 12.1244 | 1.07165 | ||||||||
\(129\) | −0.267949 | − | 0.464102i | −0.0235916 | − | 0.0408619i | ||||
\(130\) | −6.00000 | + | 9.00000i | −0.526235 | + | 0.789352i | ||||
\(131\) | −1.73205 | + | 3.00000i | −0.151330 | + | 0.262111i | −0.931717 | − | 0.363186i | \(-0.881689\pi\) |
0.780387 | + | 0.625297i | \(0.215022\pi\) | |||||||
\(132\) | 1.73205 | + | 3.00000i | 0.150756 | + | 0.261116i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.36603 | − | 9.29423i | 0.463554 | − | 0.802899i | ||||
\(135\) | −3.46410 | + | 6.00000i | −0.298142 | + | 0.516398i | ||||
\(136\) | −13.3923 | −1.14838 | ||||||||
\(137\) | 8.07180 | 0.689620 | 0.344810 | − | 0.938672i | \(-0.387943\pi\) | ||||
0.344810 | + | 0.938672i | \(0.387943\pi\) | |||||||
\(138\) | 11.1962 | − | 19.3923i | 0.953080 | − | 1.65078i | ||||
\(139\) | −5.29423 | + | 9.16987i | −0.449051 | + | 0.777778i | −0.998324 | − | 0.0578639i | \(-0.981571\pi\) |
0.549274 | + | 0.835642i | \(0.314904\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.6603 | − | 30.5885i | −1.48726 | − | 2.57601i | ||||
\(142\) | −5.19615 | + | 9.00000i | −0.436051 | + | 0.755263i | ||||
\(143\) | 2.53590 | − | 3.80385i | 0.212062 | − | 0.318094i | ||||
\(144\) | 11.1603 | + | 19.3301i | 0.930021 | + | 1.61084i | ||||
\(145\) | 5.19615 | 0.431517 | ||||||||
\(146\) | −2.76795 | − | 4.79423i | −0.229077 | − | 0.396773i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.00000 | −0.575396 | ||||||||
\(149\) | 3.23205 | + | 5.59808i | 0.264780 | + | 0.458612i | 0.967506 | − | 0.252848i | \(-0.0813674\pi\) |
−0.702726 | + | 0.711461i | \(0.748034\pi\) | |||||||
\(150\) | 9.46410 | 0.772741 | ||||||||
\(151\) | −1.00000 | − | 1.73205i | −0.0813788 | − | 0.140952i | 0.822464 | − | 0.568818i | \(-0.192599\pi\) |
−0.903842 | + | 0.427865i | \(0.859266\pi\) | |||||||
\(152\) | −1.73205 | − | 3.00000i | −0.140488 | − | 0.243332i | ||||
\(153\) | −17.2583 | − | 29.8923i | −1.39525 | − | 2.41665i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.26795 | 0.583776 | ||||||||
\(156\) | −5.46410 | + | 8.19615i | −0.437478 | + | 0.656217i | ||||
\(157\) | 0.598076 | + | 1.03590i | 0.0477317 | + | 0.0826737i | 0.888904 | − | 0.458093i | \(-0.151467\pi\) |
−0.841172 | + | 0.540767i | \(0.818134\pi\) | |||||||
\(158\) | −14.0263 | + | 24.2942i | −1.11587 | + | 1.93275i | ||||
\(159\) | 27.1244 | 2.15110 | ||||||||
\(160\) | −4.50000 | + | 7.79423i | −0.355756 | + | 0.616188i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.13397 | − | 3.69615i | 0.167661 | − | 0.290397i | ||||
\(163\) | −8.09808 | − | 14.0263i | −0.634290 | − | 1.09862i | −0.986665 | − | 0.162764i | \(-0.947959\pi\) |
0.352375 | − | 0.935859i | \(-0.385374\pi\) | |||||||
\(164\) | −2.59808 | − | 4.50000i | −0.202876 | − | 0.351391i | ||||
\(165\) | 6.00000 | 0.467099 | ||||||||
\(166\) | 3.80385 | 0.295236 | ||||||||
\(167\) | −3.29423 | − | 5.70577i | −0.254915 | − | 0.441526i | 0.709957 | − | 0.704245i | \(-0.248714\pi\) |
−0.964872 | + | 0.262719i | \(0.915381\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8923 | + | 1.66987i | 0.991716 | + | 0.128452i | ||||
\(170\) | 11.5981 | − | 20.0885i | 0.889532 | − | 1.54071i | ||||
\(171\) | 4.46410 | − | 7.73205i | 0.341378 | − | 0.591285i | ||||
\(172\) | 0.0980762 | − | 0.169873i | 0.00747824 | − | 0.0129527i | ||||
\(173\) | 4.26795 | + | 7.39230i | 0.324486 | + | 0.562027i | 0.981408 | − | 0.191932i | \(-0.0614753\pi\) |
−0.656922 | + | 0.753958i | \(0.728142\pi\) | |||||||
\(174\) | 14.1962 | 1.07621 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.16987 | − | 5.49038i | 0.238938 | − | 0.413853i | ||||
\(177\) | −9.92820 | + | 17.1962i | −0.746249 | + | 1.29254i | ||||
\(178\) | −22.3923 | −1.67837 | ||||||||
\(179\) | 3.46410 | − | 6.00000i | 0.258919 | − | 0.448461i | −0.707034 | − | 0.707180i | \(-0.749967\pi\) |
0.965953 | + | 0.258719i | \(0.0833004\pi\) | |||||||
\(180\) | −7.73205 | −0.576313 | ||||||||
\(181\) | −5.58846 | −0.415387 | −0.207693 | − | 0.978194i | \(-0.566596\pi\) | ||||
−0.207693 | + | 0.978194i | \(0.566596\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.1244 | −0.970180 | ||||||||
\(184\) | −8.19615 | −0.604228 | ||||||||
\(185\) | −6.06218 | + | 10.5000i | −0.445700 | + | 0.771975i | ||||
\(186\) | 19.8564 | 1.45594 | ||||||||
\(187\) | −4.90192 | + | 8.49038i | −0.358464 | + | 0.620878i | ||||
\(188\) | 6.46410 | − | 11.1962i | 0.471443 | − | 0.816563i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | −2.36603 | − | 4.09808i | −0.171200 | − | 0.296526i | 0.767640 | − | 0.640881i | \(-0.221431\pi\) |
−0.938840 | + | 0.344355i | \(0.888098\pi\) | |||||||
\(192\) | 1.36603 | − | 2.36603i | 0.0985844 | − | 0.170753i | ||||
\(193\) | −2.50000 | + | 4.33013i | −0.179954 | + | 0.311689i | −0.941865 | − | 0.335993i | \(-0.890928\pi\) |
0.761911 | + | 0.647682i | \(0.224262\pi\) | |||||||
\(194\) | 5.53590 | − | 9.58846i | 0.397454 | − | 0.688411i | ||||
\(195\) | 7.56218 | + | 15.2942i | 0.541539 | + | 1.09524i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | − | 10.3923i | −0.427482 | − | 0.740421i | 0.569166 | − | 0.822222i | \(-0.307266\pi\) |
−0.996649 | + | 0.0818013i | \(0.973933\pi\) | |||||||
\(198\) | 9.80385 | 0.696729 | ||||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | −1.73205 | − | 3.00000i | −0.122474 | − | 0.212132i | ||||
\(201\) | −8.46410 | − | 14.6603i | −0.597012 | − | 1.03405i | ||||
\(202\) | −6.69615 | + | 11.5981i | −0.471140 | + | 0.816038i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 10.5622 | − | 18.2942i | 0.739500 | − | 1.28085i | ||||
\(205\) | −9.00000 | −0.628587 | ||||||||
\(206\) | −12.4641 | + | 21.5885i | −0.868415 | + | 1.50414i | ||||
\(207\) | −10.5622 | − | 18.2942i | −0.734122 | − | 1.27154i | ||||
\(208\) | 17.9904 | + | 1.16025i | 1.24741 | + | 0.0804491i | ||||
\(209\) | −2.53590 | −0.175412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.901924 | + | 1.56218i | 0.0620910 | + | 0.107545i | 0.895400 | − | 0.445263i | \(-0.146890\pi\) |
−0.833309 | + | 0.552808i | \(0.813556\pi\) | |||||||
\(212\) | 4.96410 | + | 8.59808i | 0.340936 | + | 0.590518i | ||||
\(213\) | 8.19615 | + | 14.1962i | 0.561591 | + | 0.972704i | ||||
\(214\) | −13.6077 | −0.930203 | ||||||||
\(215\) | −0.169873 | − | 0.294229i | −0.0115852 | − | 0.0200662i | ||||
\(216\) | 6.92820 | 0.471405 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.26795 | + | 12.5885i | 0.492248 | + | 0.852598i | ||||
\(219\) | −8.73205 | −0.590057 | ||||||||
\(220\) | 1.09808 | + | 1.90192i | 0.0740323 | + | 0.128228i | ||||
\(221\) | −27.8205 | − | 1.79423i | −1.87141 | − | 0.120693i | ||||
\(222\) | −16.5622 | + | 28.6865i | −1.11158 | + | 1.92531i | ||||
\(223\) | −5.00000 | − | 8.66025i | −0.334825 | − | 0.579934i | 0.648626 | − | 0.761107i | \(-0.275344\pi\) |
−0.983451 | + | 0.181173i | \(0.942010\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.46410 | − | 7.73205i | 0.297607 | − | 0.515470i | ||||
\(226\) | −11.5981 | + | 20.0885i | −0.771493 | + | 1.33626i | ||||
\(227\) | −5.66025 | −0.375684 | −0.187842 | − | 0.982199i | \(-0.560149\pi\) | ||||
−0.187842 | + | 0.982199i | \(0.560149\pi\) | |||||||
\(228\) | 5.46410 | 0.361869 | ||||||||
\(229\) | −7.19615 | + | 12.4641i | −0.475535 | + | 0.823651i | −0.999607 | − | 0.0280229i | \(-0.991079\pi\) |
0.524072 | + | 0.851674i | \(0.324412\pi\) | |||||||
\(230\) | 7.09808 | − | 12.2942i | 0.468033 | − | 0.810657i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.59808 | − | 4.50000i | −0.170572 | − | 0.295439i | ||||
\(233\) | 0.928203 | − | 1.60770i | 0.0608086 | − | 0.105324i | −0.834018 | − | 0.551737i | \(-0.813965\pi\) |
0.894827 | + | 0.446413i | \(0.147299\pi\) | |||||||
\(234\) | 12.3564 | + | 24.9904i | 0.807764 | + | 1.63367i | ||||
\(235\) | −11.1962 | − | 19.3923i | −0.730356 | − | 1.26501i | ||||
\(236\) | −7.26795 | −0.473103 | ||||||||
\(237\) | 22.1244 | + | 38.3205i | 1.43713 | + | 2.48918i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.8038 | −1.02227 | −0.511133 | − | 0.859502i | \(-0.670774\pi\) | ||||
−0.511133 | + | 0.859502i | \(0.670774\pi\) | |||||||
\(240\) | 11.8301 | + | 20.4904i | 0.763631 | + | 1.32265i | ||||
\(241\) | 21.1962 | 1.36536 | 0.682682 | − | 0.730716i | \(-0.260813\pi\) | ||||
0.682682 | + | 0.730716i | \(0.260813\pi\) | |||||||
\(242\) | 8.13397 | + | 14.0885i | 0.522872 | + | 0.905640i | ||||
\(243\) | −9.36603 | − | 16.2224i | −0.600831 | − | 1.04067i | ||||
\(244\) | −2.40192 | − | 4.16025i | −0.153767 | − | 0.266333i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −24.5885 | −1.56770 | ||||||||
\(247\) | −3.19615 | − | 6.46410i | −0.203366 | − | 0.411301i | ||||
\(248\) | −3.63397 | − | 6.29423i | −0.230758 | − | 0.399684i | ||||
\(249\) | 3.00000 | − | 5.19615i | 0.190117 | − | 0.329293i | ||||
\(250\) | 21.0000 | 1.32816 | ||||||||
\(251\) | −0.803848 | + | 1.39230i | −0.0507384 | + | 0.0878815i | −0.890279 | − | 0.455415i | \(-0.849491\pi\) |
0.839541 | + | 0.543297i | \(0.182824\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.00000 | + | 5.19615i | −0.188608 | + | 0.326679i | ||||
\(254\) | −15.9282 | − | 27.5885i | −0.999424 | − | 1.73105i | ||||
\(255\) | −18.2942 | − | 31.6865i | −1.14563 | − | 1.98429i | ||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −6.12436 | −0.382027 | −0.191013 | − | 0.981587i | \(-0.561177\pi\) | ||||
−0.191013 | + | 0.981587i | \(0.561177\pi\) | |||||||
\(258\) | −0.464102 | − | 0.803848i | −0.0288937 | − | 0.0500454i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.46410 | + | 5.19615i | −0.214834 | + | 0.322252i | ||||
\(261\) | 6.69615 | − | 11.5981i | 0.414481 | − | 0.717903i | ||||
\(262\) | −3.00000 | + | 5.19615i | −0.185341 | + | 0.321019i | ||||
\(263\) | −0.633975 | + | 1.09808i | −0.0390925 | + | 0.0677103i | −0.884910 | − | 0.465763i | \(-0.845780\pi\) |
0.845817 | + | 0.533473i | \(0.179113\pi\) | |||||||
\(264\) | −3.00000 | − | 5.19615i | −0.184637 | − | 0.319801i | ||||
\(265\) | 17.1962 | 1.05635 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.6603 | + | 30.5885i | −1.08079 | + | 1.87198i | ||||
\(268\) | 3.09808 | − | 5.36603i | 0.189245 | − | 0.327782i | ||||
\(269\) | −5.07180 | −0.309233 | −0.154616 | − | 0.987975i | \(-0.549414\pi\) | ||||
−0.154616 | + | 0.987975i | \(0.549414\pi\) | |||||||
\(270\) | −6.00000 | + | 10.3923i | −0.365148 | + | 0.632456i | ||||
\(271\) | −5.80385 | −0.352559 | −0.176279 | − | 0.984340i | \(-0.556406\pi\) | ||||
−0.176279 | + | 0.984340i | \(0.556406\pi\) | |||||||
\(272\) | −38.6603 | −2.34412 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.9808 | 0.844609 | ||||||||
\(275\) | −2.53590 | −0.152920 | ||||||||
\(276\) | 6.46410 | − | 11.1962i | 0.389093 | − | 0.673929i | ||||
\(277\) | 17.0000 | 1.02143 | 0.510716 | − | 0.859750i | \(-0.329381\pi\) | ||||
0.510716 | + | 0.859750i | \(0.329381\pi\) | |||||||
\(278\) | −9.16987 | + | 15.8827i | −0.549972 | + | 0.952580i | ||||
\(279\) | 9.36603 | − | 16.2224i | 0.560729 | − | 0.971212i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.3923 | 0.798918 | 0.399459 | − | 0.916751i | \(-0.369198\pi\) | ||||
0.399459 | + | 0.916751i | \(0.369198\pi\) | |||||||
\(282\) | −30.5885 | − | 52.9808i | −1.82152 | − | 3.15496i | ||||
\(283\) | 5.09808 | − | 8.83013i | 0.303049 | − | 0.524897i | −0.673776 | − | 0.738936i | \(-0.735329\pi\) |
0.976825 | + | 0.214039i | \(0.0686620\pi\) | |||||||
\(284\) | −3.00000 | + | 5.19615i | −0.178017 | + | 0.308335i | ||||
\(285\) | 4.73205 | − | 8.19615i | 0.280302 | − | 0.485498i | ||||
\(286\) | 4.39230 | − | 6.58846i | 0.259722 | − | 0.389584i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 11.5981 | + | 20.0885i | 0.683423 | + | 1.18372i | ||||
\(289\) | 42.7846 | 2.51674 | ||||||||
\(290\) | 9.00000 | 0.528498 | ||||||||
\(291\) | −8.73205 | − | 15.1244i | −0.511882 | − | 0.886605i | ||||
\(292\) | −1.59808 | − | 2.76795i | −0.0935203 | − | 0.161982i | ||||
\(293\) | −0.401924 | + | 0.696152i | −0.0234806 | + | 0.0406697i | −0.877527 | − | 0.479527i | \(-0.840808\pi\) |
0.854046 | + | 0.520197i | \(0.174141\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.29423 | + | 10.9019i | −0.366464 | + | 0.634735i | ||||
\(296\) | 12.1244 | 0.704714 | ||||||||
\(297\) | 2.53590 | − | 4.39230i | 0.147148 | − | 0.254867i | ||||
\(298\) | 5.59808 | + | 9.69615i | 0.324288 | + | 0.561683i | ||||
\(299\) | −17.0263 | − | 1.09808i | −0.984655 | − | 0.0635034i | ||||
\(300\) | 5.46410 | 0.315470 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.73205 | − | 3.00000i | −0.0996683 | − | 0.172631i | ||||
\(303\) | 10.5622 | + | 18.2942i | 0.606781 | + | 1.05098i | ||||
\(304\) | −5.00000 | − | 8.66025i | −0.286770 | − | 0.496700i | ||||
\(305\) | −8.32051 | −0.476431 | ||||||||
\(306\) | −29.8923 | − | 51.7750i | −1.70883 | − | 2.95978i | ||||
\(307\) | 4.58846 | 0.261877 | 0.130939 | − | 0.991390i | \(-0.458201\pi\) | ||||
0.130939 | + | 0.991390i | \(0.458201\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.6603 | + | 34.0526i | 1.11843 | + | 1.93718i | ||||
\(310\) | 12.5885 | 0.714976 | ||||||||
\(311\) | 0.633975 | + | 1.09808i | 0.0359494 | + | 0.0622662i | 0.883440 | − | 0.468544i | \(-0.155221\pi\) |
−0.847491 | + | 0.530810i | \(0.821888\pi\) | |||||||
\(312\) | 9.46410 | − | 14.1962i | 0.535799 | − | 0.803699i | ||||
\(313\) | 14.3923 | − | 24.9282i | 0.813501 | − | 1.40903i | −0.0968980 | − | 0.995294i | \(-0.530892\pi\) |
0.910399 | − | 0.413731i | \(-0.135775\pi\) | |||||||
\(314\) | 1.03590 | + | 1.79423i | 0.0584591 | + | 0.101254i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.09808 | + | 14.0263i | −0.455552 | + | 0.789040i | ||||
\(317\) | 3.23205 | − | 5.59808i | 0.181530 | − | 0.314419i | −0.760872 | − | 0.648902i | \(-0.775228\pi\) |
0.942402 | + | 0.334483i | \(0.108562\pi\) | |||||||
\(318\) | 46.9808 | 2.63455 | ||||||||
\(319\) | −3.80385 | −0.212975 | ||||||||
\(320\) | 0.866025 | − | 1.50000i | 0.0484123 | − | 0.0838525i | ||||
\(321\) | −10.7321 | + | 18.5885i | −0.599005 | + | 1.03751i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.73205 | + | 13.3923i | 0.430223 | + | 0.745168i | ||||
\(324\) | 1.23205 | − | 2.13397i | 0.0684473 | − | 0.118554i | ||||
\(325\) | −3.19615 | − | 6.46410i | −0.177291 | − | 0.358564i | ||||
\(326\) | −14.0263 | − | 24.2942i | −0.776844 | − | 1.34553i | ||||
\(327\) | 22.9282 | 1.26793 | ||||||||
\(328\) | 4.50000 | + | 7.79423i | 0.248471 | + | 0.430364i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 10.3923 | 0.572078 | ||||||||
\(331\) | −12.4904 | − | 21.6340i | −0.686533 | − | 1.18911i | −0.972952 | − | 0.231006i | \(-0.925798\pi\) |
0.286419 | − | 0.958105i | \(-0.407535\pi\) | |||||||
\(332\) | 2.19615 | 0.120530 | ||||||||
\(333\) | 15.6244 | + | 27.0622i | 0.856209 | + | 1.48300i | ||||
\(334\) | −5.70577 | − | 9.88269i | −0.312206 | − | 0.540757i | ||||
\(335\) | −5.36603 | − | 9.29423i | −0.293177 | − | 0.507798i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | 0.599208 | 0.299604 | − | 0.954064i | \(-0.403145\pi\) | ||||
0.299604 | + | 0.954064i | \(0.403145\pi\) | |||||||
\(338\) | 22.3301 | + | 2.89230i | 1.21460 | + | 0.157321i | ||||
\(339\) | 18.2942 | + | 31.6865i | 0.993606 | + | 1.72098i | ||||
\(340\) | 6.69615 | − | 11.5981i | 0.363150 | − | 0.628994i | ||||
\(341\) | −5.32051 | −0.288122 | ||||||||
\(342\) | 7.73205 | − | 13.3923i | 0.418101 | − | 0.724173i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.169873 | + | 0.294229i | −0.00915894 | + | 0.0158637i | ||||
\(345\) | −11.1962 | − | 19.3923i | −0.602781 | − | 1.04405i | ||||
\(346\) | 7.39230 | + | 12.8038i | 0.397413 | + | 0.688339i | ||||
\(347\) | 7.26795 | 0.390164 | 0.195082 | − | 0.980787i | \(-0.437503\pi\) | ||||
0.195082 | + | 0.980787i | \(0.437503\pi\) | |||||||
\(348\) | 8.19615 | 0.439360 | ||||||||
\(349\) | −12.3923 | − | 21.4641i | −0.663345 | − | 1.14895i | −0.979731 | − | 0.200317i | \(-0.935803\pi\) |
0.316386 | − | 0.948630i | \(-0.397530\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.3923 | + | 0.928203i | 0.768204 | + | 0.0495438i | ||||
\(352\) | 3.29423 | − | 5.70577i | 0.175583 | − | 0.304119i | ||||
\(353\) | 10.3301 | − | 17.8923i | 0.549817 | − | 0.952311i | −0.448469 | − | 0.893798i | \(-0.648031\pi\) |
0.998287 | − | 0.0585131i | \(-0.0186360\pi\) | |||||||
\(354\) | −17.1962 | + | 29.7846i | −0.913965 | + | 1.58303i | ||||
\(355\) | 5.19615 | + | 9.00000i | 0.275783 | + | 0.477670i | ||||
\(356\) | −12.9282 | −0.685193 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000 | − | 10.3923i | 0.317110 | − | 0.549250i | ||||
\(359\) | −9.46410 | + | 16.3923i | −0.499496 | + | 0.865153i | −1.00000 | 0.000581665i | \(-0.999815\pi\) | |
0.500504 | + | 0.865734i | \(0.333148\pi\) | |||||||
\(360\) | 13.3923 | 0.705836 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | −9.67949 | −0.508743 | ||||||||
\(363\) | 25.6603 | 1.34681 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.53590 | −0.289762 | ||||||||
\(366\) | −22.7321 | −1.18822 | ||||||||
\(367\) | 2.09808 | − | 3.63397i | 0.109519 | − | 0.189692i | −0.806057 | − | 0.591838i | \(-0.798402\pi\) |
0.915575 | + | 0.402146i | \(0.131736\pi\) | |||||||
\(368\) | −23.6603 | −1.23338 | ||||||||
\(369\) | −11.5981 | + | 20.0885i | −0.603772 | + | 1.04576i | ||||
\(370\) | −10.5000 | + | 18.1865i | −0.545869 | + | 0.945473i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 11.4641 | 0.594386 | ||||||||
\(373\) | 5.69615 | + | 9.86603i | 0.294936 | + | 0.510843i | 0.974970 | − | 0.222337i | \(-0.0713685\pi\) |
−0.680034 | + | 0.733180i | \(0.738035\pi\) | |||||||
\(374\) | −8.49038 | + | 14.7058i | −0.439027 | + | 0.760417i | ||||
\(375\) | 16.5622 | − | 28.6865i | 0.855267 | − | 1.48137i | ||||
\(376\) | −11.1962 | + | 19.3923i | −0.577397 | + | 1.00008i | ||||
\(377\) | −4.79423 | − | 9.69615i | −0.246915 | − | 0.499377i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.2942 | − | 23.0263i | −0.682879 | − | 1.18278i | −0.974098 | − | 0.226124i | \(-0.927394\pi\) |
0.291220 | − | 0.956656i | \(-0.405939\pi\) | |||||||
\(380\) | 3.46410 | 0.177705 | ||||||||
\(381\) | −50.2487 | −2.57432 | ||||||||
\(382\) | −4.09808 | − | 7.09808i | −0.209676 | − | 0.363169i | ||||
\(383\) | −5.83013 | − | 10.0981i | −0.297906 | − | 0.515988i | 0.677751 | − | 0.735291i | \(-0.262955\pi\) |
−0.975657 | + | 0.219304i | \(0.929621\pi\) | |||||||
\(384\) | 16.5622 | − | 28.6865i | 0.845185 | − | 1.46390i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.33013 | + | 7.50000i | −0.220398 | + | 0.381740i | ||||
\(387\) | −0.875644 | −0.0445115 | ||||||||
\(388\) | 3.19615 | − | 5.53590i | 0.162260 | − | 0.281043i | ||||
\(389\) | 11.7679 | + | 20.3827i | 0.596659 | + | 1.03344i | 0.993310 | + | 0.115474i | \(0.0368387\pi\) |
−0.396652 | + | 0.917969i | \(0.629828\pi\) | |||||||
\(390\) | 13.0981 | + | 26.4904i | 0.663247 | + | 1.34139i | ||||
\(391\) | 36.5885 | 1.85036 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.73205 | + | 8.19615i | 0.238700 | + | 0.413441i | ||||
\(394\) | −10.3923 | − | 18.0000i | −0.523557 | − | 0.906827i | ||||
\(395\) | 14.0263 | + | 24.2942i | 0.705739 | + | 1.22238i | ||||
\(396\) | 5.66025 | 0.284438 | ||||||||
\(397\) | −9.39230 | − | 16.2679i | −0.471386 | − | 0.816465i | 0.528078 | − | 0.849196i | \(-0.322913\pi\) |
−0.999464 | + | 0.0327309i | \(0.989580\pi\) | |||||||
\(398\) | −3.46410 | −0.173640 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | − | 8.66025i | −0.250000 | − | 0.433013i | ||||
\(401\) | −10.8564 | −0.542143 | −0.271072 | − | 0.962559i | \(-0.587378\pi\) | ||||
−0.271072 | + | 0.962559i | \(0.587378\pi\) | |||||||
\(402\) | −14.6603 | − | 25.3923i | −0.731187 | − | 1.26645i | ||||
\(403\) | −6.70577 | − | 13.5622i | −0.334038 | − | 0.675580i | ||||
\(404\) | −3.86603 | + | 6.69615i | −0.192342 | + | 0.333146i | ||||
\(405\) | −2.13397 | − | 3.69615i | −0.106038 | − | 0.183663i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.43782 | − | 7.68653i | 0.219975 | − | 0.381007i | ||||
\(408\) | −18.2942 | + | 31.6865i | −0.905699 | + | 1.56872i | ||||
\(409\) | 16.8038 | 0.830897 | 0.415448 | − | 0.909617i | \(-0.363625\pi\) | ||||
0.415448 | + | 0.909617i | \(0.363625\pi\) | |||||||
\(410\) | −15.5885 | −0.769859 | ||||||||
\(411\) | 11.0263 | − | 19.0981i | 0.543886 | − | 0.942039i | ||||
\(412\) | −7.19615 | + | 12.4641i | −0.354529 | + | 0.614062i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −18.2942 | − | 31.6865i | −0.899112 | − | 1.55731i | ||||
\(415\) | 1.90192 | − | 3.29423i | 0.0933618 | − | 0.161707i | ||||
\(416\) | 18.6962 | + | 1.20577i | 0.916654 | + | 0.0591178i | ||||
\(417\) | 14.4641 | + | 25.0526i | 0.708310 | + | 1.22683i | ||||
\(418\) | −4.39230 | −0.214835 | ||||||||
\(419\) | −16.0981 | − | 27.8827i | −0.786442 | − | 1.36216i | −0.928134 | − | 0.372247i | \(-0.878587\pi\) |
0.141691 | − | 0.989911i | \(-0.454746\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.1769 | −1.56821 | −0.784103 | − | 0.620630i | \(-0.786877\pi\) | ||||
−0.784103 | + | 0.620630i | \(0.786877\pi\) | |||||||
\(422\) | 1.56218 | + | 2.70577i | 0.0760456 | + | 0.131715i | ||||
\(423\) | −57.7128 | −2.80609 | ||||||||
\(424\) | −8.59808 | − | 14.8923i | −0.417559 | − | 0.723234i | ||||
\(425\) | 7.73205 | + | 13.3923i | 0.375060 | + | 0.649622i | ||||
\(426\) | 14.1962 | + | 24.5885i | 0.687806 | + | 1.19131i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.85641 | −0.379754 | ||||||||
\(429\) | −5.53590 | − | 11.1962i | −0.267276 | − | 0.540555i | ||||
\(430\) | −0.294229 | − | 0.509619i | −0.0141890 | − | 0.0245760i | ||||
\(431\) | −0.339746 | + | 0.588457i | −0.0163650 | + | 0.0283450i | −0.874092 | − | 0.485761i | \(-0.838543\pi\) |
0.857727 | + | 0.514106i | \(0.171876\pi\) | |||||||
\(432\) | 20.0000 | 0.962250 | ||||||||
\(433\) | −6.79423 | + | 11.7679i | −0.326510 | + | 0.565532i | −0.981817 | − | 0.189831i | \(-0.939206\pi\) |
0.655307 | + | 0.755363i | \(0.272539\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.09808 | − | 12.2942i | 0.340327 | − | 0.589463i | ||||
\(436\) | 4.19615 | + | 7.26795i | 0.200959 | + | 0.348072i | ||||
\(437\) | 4.73205 | + | 8.19615i | 0.226365 | + | 0.392075i | ||||
\(438\) | −15.1244 | −0.722670 | ||||||||
\(439\) | −14.5885 | −0.696269 | −0.348135 | − | 0.937445i | \(-0.613185\pi\) | ||||
−0.348135 | + | 0.937445i | \(0.613185\pi\) | |||||||
\(440\) | −1.90192 | − | 3.29423i | −0.0906707 | − | 0.157046i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −48.1865 | − | 3.10770i | −2.29200 | − | 0.147818i | ||||
\(443\) | −11.6603 | + | 20.1962i | −0.553995 | + | 0.959548i | 0.443986 | + | 0.896034i | \(0.353564\pi\) |
−0.997981 | + | 0.0635142i | \(0.979769\pi\) | |||||||
\(444\) | −9.56218 | + | 16.5622i | −0.453801 | + | 0.786006i | ||||
\(445\) | −11.1962 | + | 19.3923i | −0.530749 | + | 0.919283i | ||||
\(446\) | −8.66025 | − | 15.0000i | −0.410075 | − | 0.710271i | ||||
\(447\) | 17.6603 | 0.835301 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | − | 10.3923i | 0.283158 | − | 0.490443i | −0.689003 | − | 0.724758i | \(-0.741951\pi\) |
0.972161 | + | 0.234315i | \(0.0752847\pi\) | |||||||
\(450\) | 7.73205 | − | 13.3923i | 0.364492 | − | 0.631319i | ||||
\(451\) | 6.58846 | 0.310238 | ||||||||
\(452\) | −6.69615 | + | 11.5981i | −0.314961 | + | 0.545528i | ||||
\(453\) | −5.46410 | −0.256726 | ||||||||
\(454\) | −9.80385 | −0.460117 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.46410 | −0.443197 | ||||||||
\(457\) | 11.0000 | 0.514558 | 0.257279 | − | 0.966337i | \(-0.417174\pi\) | ||||
0.257279 | + | 0.966337i | \(0.417174\pi\) | |||||||
\(458\) | −12.4641 | + | 21.5885i | −0.582409 | + | 1.00876i | ||||
\(459\) | −30.9282 | −1.44360 | ||||||||
\(460\) | 4.09808 | − | 7.09808i | 0.191074 | − | 0.330950i | ||||
\(461\) | −7.79423 | + | 13.5000i | −0.363013 | + | 0.628758i | −0.988455 | − | 0.151513i | \(-0.951585\pi\) |
0.625442 | + | 0.780271i | \(0.284919\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.58846 | −0.213244 | −0.106622 | − | 0.994300i | \(-0.534003\pi\) | ||||
−0.106622 | + | 0.994300i | \(0.534003\pi\) | |||||||
\(464\) | −7.50000 | − | 12.9904i | −0.348179 | − | 0.603063i | ||||
\(465\) | 9.92820 | − | 17.1962i | 0.460409 | − | 0.797452i | ||||
\(466\) | 1.60770 | − | 2.78461i | 0.0744750 | − | 0.128995i | ||||
\(467\) | 12.7583 | − | 22.0981i | 0.590385 | − | 1.02258i | −0.403795 | − | 0.914849i | \(-0.632309\pi\) |
0.994180 | − | 0.107728i | \(-0.0343575\pi\) | |||||||
\(468\) | 7.13397 | + | 14.4282i | 0.329768 | + | 0.666944i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −19.3923 | − | 33.5885i | −0.894500 | − | 1.54932i | ||||
\(471\) | 3.26795 | 0.150579 | ||||||||
\(472\) | 12.5885 | 0.579431 | ||||||||
\(473\) | 0.124356 | + | 0.215390i | 0.00571788 | + | 0.00990366i | ||||
\(474\) | 38.3205 | + | 66.3731i | 1.76012 | + | 3.04862i | ||||
\(475\) | −2.00000 | + | 3.46410i | −0.0917663 | + | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.1603 | − | 38.3827i | 1.01465 | − | 1.75742i | ||||
\(478\) | −27.3731 | −1.25201 | ||||||||
\(479\) | 0.633975 | − | 1.09808i | 0.0289670 | − | 0.0501724i | −0.851178 | − | 0.524876i | \(-0.824112\pi\) |
0.880146 | + | 0.474704i | \(0.157445\pi\) | |||||||
\(480\) | 12.2942 | + | 21.2942i | 0.561152 | + | 0.971944i | ||||
\(481\) | 25.1865 | + | 1.62436i | 1.14841 | + | 0.0740642i | ||||
\(482\) | 36.7128 | 1.67222 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.69615 | + | 8.13397i | 0.213461 | + | 0.369726i | ||||
\(485\) | −5.53590 | − | 9.58846i | −0.251372 | − | 0.435389i | ||||
\(486\) | −16.2224 | − | 28.0981i | −0.735864 | − | 1.27455i | ||||
\(487\) | 40.7846 | 1.84813 | 0.924064 | − | 0.382239i | \(-0.124847\pi\) | ||||
0.924064 | + | 0.382239i | \(0.124847\pi\) | |||||||
\(488\) | 4.16025 | + | 7.20577i | 0.188326 | + | 0.326190i | ||||
\(489\) | −44.2487 | −2.00100 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.80385 | − | 6.58846i | −0.171665 | − | 0.297333i | 0.767337 | − | 0.641244i | \(-0.221581\pi\) |
−0.939002 | + | 0.343911i | \(0.888248\pi\) | |||||||
\(492\) | −14.1962 | −0.640012 | ||||||||
\(493\) | 11.5981 | + | 20.0885i | 0.522351 | + | 0.904739i | ||||
\(494\) | −5.53590 | − | 11.1962i | −0.249072 | − | 0.503739i | ||||
\(495\) | 4.90192 | − | 8.49038i | 0.220325 | − | 0.381614i | ||||
\(496\) | −10.4904 | − | 18.1699i | −0.471032 | − | 0.815851i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.19615 | − | 9.00000i | 0.232845 | − | 0.403300i | ||||
\(499\) | 19.4904 | − | 33.7583i | 0.872509 | − | 1.51123i | 0.0131168 | − | 0.999914i | \(-0.495825\pi\) |
0.859393 | − | 0.511316i | \(-0.170842\pi\) | |||||||
\(500\) | 12.1244 | 0.542218 | ||||||||
\(501\) | −18.0000 | −0.804181 | ||||||||
\(502\) | −1.39230 | + | 2.41154i | −0.0621416 | + | 0.107632i | ||||
\(503\) | −9.29423 | + | 16.0981i | −0.414409 | + | 0.717778i | −0.995366 | − | 0.0961565i | \(-0.969345\pi\) |
0.580957 | + | 0.813934i | \(0.302678\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.69615 | + | 11.5981i | 0.297975 | + | 0.516108i | ||||
\(506\) | −5.19615 | + | 9.00000i | −0.230997 | + | 0.400099i | ||||
\(507\) | 21.5622 | − | 28.2224i | 0.957610 | − | 1.25340i | ||||
\(508\) | −9.19615 | − | 15.9282i | −0.408013 | − | 0.706700i | ||||
\(509\) | −13.7321 | −0.608662 | −0.304331 | − | 0.952566i | \(-0.598433\pi\) | ||||
−0.304331 | + | 0.952566i | \(0.598433\pi\) | |||||||
\(510\) | −31.6865 | − | 54.8827i | −1.40310 | − | 2.43025i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8.66025 | 0.382733 | ||||||||
\(513\) | −4.00000 | − | 6.92820i | −0.176604 | − | 0.305888i | ||||
\(514\) | −10.6077 | −0.467885 | ||||||||
\(515\) | 12.4641 | + | 21.5885i | 0.549234 | + | 0.951301i | ||||
\(516\) | −0.267949 | − | 0.464102i | −0.0117958 | − | 0.0204309i | ||||
\(517\) | 8.19615 | + | 14.1962i | 0.360466 | + | 0.624346i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.3205 | 1.02366 | ||||||||
\(520\) | 6.00000 | − | 9.00000i | 0.263117 | − | 0.394676i | ||||
\(521\) | −12.0622 | − | 20.8923i | −0.528454 | − | 0.915308i | −0.999450 | − | 0.0331732i | \(-0.989439\pi\) |
0.470996 | − | 0.882135i | \(-0.343895\pi\) | |||||||
\(522\) | 11.5981 | − | 20.0885i | 0.507634 | − | 0.879248i | ||||
\(523\) | 29.1769 | 1.27582 | 0.637909 | − | 0.770112i | \(-0.279800\pi\) | ||||
0.637909 | + | 0.770112i | \(0.279800\pi\) | |||||||
\(524\) | −1.73205 | + | 3.00000i | −0.0756650 | + | 0.131056i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.09808 | + | 1.90192i | −0.0478784 | + | 0.0829278i | ||||
\(527\) | 16.2224 | + | 28.0981i | 0.706660 | + | 1.22397i | ||||
\(528\) | −8.66025 | − | 15.0000i | −0.376889 | − | 0.652791i | ||||
\(529\) | −0.607695 | −0.0264215 | ||||||||
\(530\) | 29.7846 | 1.29376 | ||||||||
\(531\) | 16.2224 | + | 28.0981i | 0.703994 | + | 1.21935i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.30385 | + | 16.7942i | 0.359680 | + | 0.727439i | ||||
\(534\) | −30.5885 | + | 52.9808i | −1.32369 | + | 2.29270i | ||||
\(535\) | −6.80385 | + | 11.7846i | −0.294156 | + | 0.509493i | ||||
\(536\) | −5.36603 | + | 9.29423i | −0.231777 | + | 0.401450i | ||||
\(537\) | −9.46410 | − | 16.3923i | −0.408406 | − | 0.707380i | ||||
\(538\) | −8.78461 | −0.378731 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.46410 | + | 6.00000i | −0.149071 | + | 0.258199i | ||||
\(541\) | 7.30385 | − | 12.6506i | 0.314017 | − | 0.543893i | −0.665211 | − | 0.746655i | \(-0.731658\pi\) |
0.979228 | + | 0.202762i | \(0.0649918\pi\) | |||||||
\(542\) | −10.0526 | −0.431794 | ||||||||
\(543\) | −7.63397 | + | 13.2224i | −0.327605 | + | 0.567429i | ||||
\(544\) | −40.1769 | −1.72257 | ||||||||
\(545\) | 14.5359 | 0.622649 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.8038 | 0.761238 | 0.380619 | − | 0.924732i | \(-0.375711\pi\) | ||||
0.380619 | + | 0.924732i | \(0.375711\pi\) | |||||||
\(548\) | 8.07180 | 0.344810 | ||||||||
\(549\) | −10.7224 | + | 18.5718i | −0.457622 | + | 0.792625i | ||||
\(550\) | −4.39230 | −0.187289 | ||||||||
\(551\) | −3.00000 | + | 5.19615i | −0.127804 | + | 0.221364i | ||||
\(552\) | −11.1962 | + | 19.3923i | −0.476540 | + | 0.825391i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 29.4449 | 1.25099 | ||||||||
\(555\) | 16.5622 | + | 28.6865i | 0.703025 | + | 1.21768i | ||||
\(556\) | −5.29423 | + | 9.16987i | −0.224525 | + | 0.388889i | ||||
\(557\) | −21.8205 | + | 37.7942i | −0.924565 | + | 1.60139i | −0.132305 | + | 0.991209i | \(0.542238\pi\) |
−0.792260 | + | 0.610184i | \(0.791096\pi\) | |||||||
\(558\) | 16.2224 | − | 28.0981i | 0.686750 | − | 1.18949i | ||||
\(559\) | −0.392305 | + | 0.588457i | −0.0165927 | + | 0.0248891i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.3923 | + | 23.1962i | 0.565424 | + | 0.979342i | ||||
\(562\) | 23.1962 | 0.978471 | ||||||||
\(563\) | −28.0526 | −1.18227 | −0.591137 | − | 0.806571i | \(-0.701321\pi\) | ||||
−0.591137 | + | 0.806571i | \(0.701321\pi\) | |||||||
\(564\) | −17.6603 | − | 30.5885i | −0.743631 | − | 1.28801i | ||||
\(565\) | 11.5981 | + | 20.0885i | 0.487935 | + | 0.845128i | ||||
\(566\) | 8.83013 | − | 15.2942i | 0.371158 | − | 0.642864i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.19615 | − | 9.00000i | 0.218026 | − | 0.377632i | ||||
\(569\) | 42.9282 | 1.79964 | 0.899822 | − | 0.436257i | \(-0.143696\pi\) | ||||
0.899822 | + | 0.436257i | \(0.143696\pi\) | |||||||
\(570\) | 8.19615 | − | 14.1962i | 0.343299 | − | 0.594611i | ||||
\(571\) | −8.39230 | − | 14.5359i | −0.351207 | − | 0.608308i | 0.635254 | − | 0.772303i | \(-0.280895\pi\) |
−0.986461 | + | 0.163995i | \(0.947562\pi\) | |||||||
\(572\) | 2.53590 | − | 3.80385i | 0.106031 | − | 0.159047i | ||||
\(573\) | −12.9282 | −0.540083 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.73205 | + | 8.19615i | 0.197340 | + | 0.341803i | ||||
\(576\) | −2.23205 | − | 3.86603i | −0.0930021 | − | 0.161084i | ||||
\(577\) | 21.5981 | + | 37.4090i | 0.899140 | + | 1.55736i | 0.828596 | + | 0.559847i | \(0.189140\pi\) |
0.0705436 | + | 0.997509i | \(0.477527\pi\) | |||||||
\(578\) | 74.1051 | 3.08237 | ||||||||
\(579\) | 6.83013 | + | 11.8301i | 0.283850 | + | 0.491643i | ||||
\(580\) | 5.19615 | 0.215758 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −15.1244 | − | 26.1962i | −0.626925 | − | 1.08587i | ||||
\(583\) | −12.5885 | −0.521361 | ||||||||
\(584\) | 2.76795 | + | 4.79423i | 0.114539 | + | 0.198387i | ||||
\(585\) | 27.8205 | + | 1.79423i | 1.15024 | + | 0.0741822i | ||||
\(586\) | −0.696152 | + | 1.20577i | −0.0287578 | + | 0.0498100i | ||||
\(587\) | 8.19615 | + | 14.1962i | 0.338291 | + | 0.585938i | 0.984111 | − | 0.177552i | \(-0.0568177\pi\) |
−0.645820 | + | 0.763490i | \(0.723484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.19615 | + | 7.26795i | −0.172899 | + | 0.299471i | ||||
\(590\) | −10.9019 | + | 18.8827i | −0.448825 | + | 0.777388i | ||||
\(591\) | −32.7846 | −1.34858 | ||||||||
\(592\) | 35.0000 | 1.43849 | ||||||||
\(593\) | −8.72243 | + | 15.1077i | −0.358187 | + | 0.620399i | −0.987658 | − | 0.156626i | \(-0.949938\pi\) |
0.629471 | + | 0.777024i | \(0.283272\pi\) | |||||||
\(594\) | 4.39230 | − | 7.60770i | 0.180218 | − | 0.312148i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.23205 | + | 5.59808i | 0.132390 | + | 0.229306i | ||||
\(597\) | −2.73205 | + | 4.73205i | −0.111815 | + | 0.193670i | ||||
\(598\) | −29.4904 | − | 1.90192i | −1.20595 | − | 0.0777754i | ||||
\(599\) | −21.9282 | − | 37.9808i | −0.895962 | − | 1.55185i | −0.832609 | − | 0.553861i | \(-0.813154\pi\) |
−0.0633527 | − | 0.997991i | \(-0.520179\pi\) | |||||||
\(600\) | −9.46410 | −0.386370 | ||||||||
\(601\) | −14.9904 | − | 25.9641i | −0.611470 | − | 1.05910i | −0.990993 | − | 0.133915i | \(-0.957245\pi\) |
0.379522 | − | 0.925183i | \(-0.376088\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.6603 | −1.12641 | ||||||||
\(604\) | −1.00000 | − | 1.73205i | −0.0406894 | − | 0.0704761i | ||||
\(605\) | 16.2679 | 0.661386 | ||||||||
\(606\) | 18.2942 | + | 31.6865i | 0.743152 | + | 1.28718i | ||||
\(607\) | −7.19615 | − | 12.4641i | −0.292083 | − | 0.505902i | 0.682219 | − | 0.731148i | \(-0.261015\pi\) |
−0.974302 | + | 0.225245i | \(0.927682\pi\) | |||||||
\(608\) | −5.19615 | − | 9.00000i | −0.210732 | − | 0.364998i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.4115 | −0.583506 | ||||||||
\(611\) | −25.8564 | + | 38.7846i | −1.04604 | + | 1.56906i | ||||
\(612\) | −17.2583 | − | 29.8923i | −0.697627 | − | 1.20832i | ||||
\(613\) | −1.69615 | + | 2.93782i | −0.0685070 | + | 0.118658i | −0.898244 | − | 0.439497i | \(-0.855157\pi\) |
0.829737 | + | 0.558154i | \(0.188490\pi\) | |||||||
\(614\) | 7.94744 | 0.320733 | ||||||||
\(615\) | −12.2942 | + | 21.2942i | −0.495751 | + | 0.858666i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.6962 | + | 42.7750i | −0.994230 | + | 1.72206i | −0.404214 | + | 0.914664i | \(0.632455\pi\) |
−0.590016 | + | 0.807392i | \(0.700878\pi\) | |||||||
\(618\) | 34.0526 | + | 58.9808i | 1.36979 | + | 2.37255i | ||||
\(619\) | 17.6865 | + | 30.6340i | 0.710882 | + | 1.23128i | 0.964527 | + | 0.263986i | \(0.0850373\pi\) |
−0.253645 | + | 0.967297i | \(0.581629\pi\) | |||||||
\(620\) | 7.26795 | 0.291888 | ||||||||
\(621\) | −18.9282 | −0.759563 | ||||||||
\(622\) | 1.09808 | + | 1.90192i | 0.0440288 | + | 0.0762602i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 27.3205 | − | 40.9808i | 1.09370 | − | 1.64054i | ||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 24.9282 | − | 43.1769i | 0.996331 | − | 1.72570i | ||||
\(627\) | −3.46410 | + | 6.00000i | −0.138343 | + | 0.239617i | ||||
\(628\) | 0.598076 | + | 1.03590i | 0.0238658 | + | 0.0413368i | ||||
\(629\) | −54.1244 | −2.15808 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.39230 | − | 11.0718i | 0.254474 | − | 0.440761i | −0.710279 | − | 0.703920i | \(-0.751431\pi\) |
0.964752 | + | 0.263159i | \(0.0847645\pi\) | |||||||
\(632\) | 14.0263 | − | 24.2942i | 0.557935 | − | 0.966373i | ||||
\(633\) | 4.92820 | 0.195878 | ||||||||
\(634\) | 5.59808 | − | 9.69615i | 0.222328 | − | 0.385083i | ||||
\(635\) | −31.8564 | −1.26418 | ||||||||
\(636\) | 27.1244 | 1.07555 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.58846 | −0.260840 | ||||||||
\(639\) | 26.7846 | 1.05958 | ||||||||
\(640\) | 10.5000 | − | 18.1865i | 0.415049 | − | 0.718886i | ||||
\(641\) | 28.8564 | 1.13976 | 0.569880 | − | 0.821728i | \(-0.306990\pi\) | ||||
0.569880 | + | 0.821728i | \(0.306990\pi\) | |||||||
\(642\) | −18.5885 | + | 32.1962i | −0.733628 | + | 1.27068i | ||||
\(643\) | −0.392305 | + | 0.679492i | −0.0154710 | + | 0.0267965i | −0.873657 | − | 0.486542i | \(-0.838258\pi\) |
0.858186 | + | 0.513338i | \(0.171591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.928203 | −0.0365480 | ||||||||
\(646\) | 13.3923 | + | 23.1962i | 0.526913 | + | 0.912640i | ||||
\(647\) | 22.5167 | − | 39.0000i | 0.885221 | − | 1.53325i | 0.0397614 | − | 0.999209i | \(-0.487340\pi\) |
0.845460 | − | 0.534039i | \(-0.179326\pi\) | |||||||
\(648\) | −2.13397 | + | 3.69615i | −0.0838304 | + | 0.145199i | ||||
\(649\) | 4.60770 | − | 7.98076i | 0.180868 | − | 0.313272i | ||||
\(650\) | −5.53590 | − | 11.1962i | −0.217136 | − | 0.439149i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.09808 | − | 14.0263i | −0.317145 | − | 0.549311i | ||||
\(653\) | −37.8564 | −1.48144 | −0.740718 | − | 0.671816i | \(-0.765514\pi\) | ||||
−0.740718 | + | 0.671816i | \(0.765514\pi\) | |||||||
\(654\) | 39.7128 | 1.55289 | ||||||||
\(655\) | 3.00000 | + | 5.19615i | 0.117220 | + | 0.203030i | ||||
\(656\) | 12.9904 | + | 22.5000i | 0.507189 | + | 0.878477i | ||||
\(657\) | −7.13397 | + | 12.3564i | −0.278323 | + | 0.482069i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.1962 | + | 24.5885i | −0.553004 | + | 0.957830i | 0.445052 | + | 0.895505i | \(0.353185\pi\) |
−0.998056 | + | 0.0623257i | \(0.980148\pi\) | |||||||
\(660\) | 6.00000 | 0.233550 | ||||||||
\(661\) | −16.5981 | + | 28.7487i | −0.645590 | + | 1.11820i | 0.338574 | + | 0.940940i | \(0.390055\pi\) |
−0.984165 | + | 0.177256i | \(0.943278\pi\) | |||||||
\(662\) | −21.6340 | − | 37.4711i | −0.840828 | − | 1.45636i | ||||
\(663\) | −42.2487 | + | 63.3731i | −1.64080 | + | 2.46121i | ||||
\(664\) | −3.80385 | −0.147618 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 27.0622 | + | 46.8731i | 1.04864 | + | 1.81629i | ||||
\(667\) | 7.09808 | + | 12.2942i | 0.274839 | + | 0.476034i | ||||
\(668\) | −3.29423 | − | 5.70577i | −0.127458 | − | 0.220763i | ||||
\(669\) | −27.3205 | −1.05627 | ||||||||
\(670\) | −9.29423 | − | 16.0981i | −0.359067 | − | 0.621923i | ||||
\(671\) | 6.09103 | 0.235142 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0885 | + | 38.2583i | 0.851447 | + | 1.47475i | 0.879902 | + | 0.475155i | \(0.157608\pi\) |
−0.0284546 | + | 0.999595i | \(0.509059\pi\) | |||||||
\(674\) | 19.0526 | 0.733877 | ||||||||
\(675\) | −4.00000 | − | 6.92820i | −0.153960 | − | 0.266667i | ||||
\(676\) | 12.8923 | + | 1.66987i | 0.495858 | + | 0.0642259i | ||||
\(677\) | −11.5359 | + | 19.9808i | −0.443361 | + | 0.767923i | −0.997936 | − | 0.0642101i | \(-0.979547\pi\) |
0.554576 | + | 0.832133i | \(0.312881\pi\) | |||||||
\(678\) | 31.6865 | + | 54.8827i | 1.21691 | + | 2.10776i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −11.5981 | + | 20.0885i | −0.444766 | + | 0.770357i | ||||
\(681\) | −7.73205 | + | 13.3923i | −0.296293 | + | 0.513194i | ||||
\(682\) | −9.21539 | −0.352876 | ||||||||
\(683\) | 15.4641 | 0.591717 | 0.295859 | − | 0.955232i | \(-0.404394\pi\) | ||||
0.295859 | + | 0.955232i | \(0.404394\pi\) | |||||||
\(684\) | 4.46410 | − | 7.73205i | 0.170689 | − | 0.295642i | ||||
\(685\) | 6.99038 | − | 12.1077i | 0.267089 | − | 0.462611i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.6603 | + | 34.0526i | 0.750085 | + | 1.29919i | ||||
\(688\) | −0.490381 | + | 0.849365i | −0.0186956 | + | 0.0323817i | ||||
\(689\) | −15.8660 | − | 32.0885i | −0.604447 | − | 1.22247i | ||||
\(690\) | −19.3923 | − | 33.5885i | −0.738252 | − | 1.27869i | ||||
\(691\) | −0.392305 | −0.0149240 | −0.00746199 | − | 0.999972i | \(-0.502375\pi\) | ||||
−0.00746199 | + | 0.999972i | \(0.502375\pi\) | |||||||
\(692\) | 4.26795 | + | 7.39230i | 0.162243 | + | 0.281013i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.5885 | 0.477851 | ||||||||
\(695\) | 9.16987 | + | 15.8827i | 0.347833 | + | 0.602465i | ||||
\(696\) | −14.1962 | −0.538104 | ||||||||
\(697\) | −20.0885 | − | 34.7942i | −0.760905 | − | 1.31793i | ||||
\(698\) | −21.4641 | − | 37.1769i | −0.812428 | − | 1.40717i | ||||
\(699\) | −2.53590 | − | 4.39230i | −0.0959165 | − | 0.166132i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7846 | 0.785024 | 0.392512 | − | 0.919747i | \(-0.371606\pi\) | ||||
0.392512 | + | 0.919747i | \(0.371606\pi\) | |||||||
\(702\) | 24.9282 | + | 1.60770i | 0.940854 | + | 0.0606785i | ||||
\(703\) | −7.00000 | − | 12.1244i | −0.264010 | − | 0.457279i | ||||
\(704\) | −0.633975 | + | 1.09808i | −0.0238938 | + | 0.0413853i | ||||
\(705\) | −61.1769 | −2.30406 | ||||||||
\(706\) | 17.8923 | − | 30.9904i | 0.673386 | − | 1.16634i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.92820 | + | 17.1962i | −0.373125 | + | 0.646271i | ||||
\(709\) | −15.0885 | − | 26.1340i | −0.566659 | − | 0.981482i | −0.996893 | − | 0.0787648i | \(-0.974902\pi\) |
0.430234 | − | 0.902717i | \(-0.358431\pi\) | |||||||
\(710\) | 9.00000 | + | 15.5885i | 0.337764 | + | 0.585024i | ||||
\(711\) | 72.3013 | 2.71151 | ||||||||
\(712\) | 22.3923 | 0.839187 | ||||||||
\(713\) | 9.92820 | + | 17.1962i | 0.371814 | + | 0.644001i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.50962 | − | 7.09808i | −0.131252 | − | 0.265453i | ||||
\(716\) | 3.46410 | − | 6.00000i | 0.129460 | − | 0.224231i | ||||
\(717\) | −21.5885 | + | 37.3923i | −0.806236 | + | 1.39644i | ||||
\(718\) | −16.3923 | + | 28.3923i | −0.611755 | + | 1.05959i | ||||
\(719\) | −3.63397 | − | 6.29423i | −0.135524 | − | 0.234735i | 0.790273 | − | 0.612755i | \(-0.209939\pi\) |
−0.925798 | + | 0.378019i | \(0.876605\pi\) | |||||||
\(720\) | 38.6603 | 1.44078 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.9904 | − | 22.5000i | 0.483452 | − | 0.837363i | ||||
\(723\) | 28.9545 | − | 50.1506i | 1.07683 | − | 1.86512i | ||||
\(724\) | −5.58846 | −0.207693 | ||||||||
\(725\) | −3.00000 | + | 5.19615i | −0.111417 | + | 0.192980i | ||||
\(726\) | 44.4449 | 1.64950 | ||||||||
\(727\) | 41.1769 | 1.52717 | 0.763584 | − | 0.645709i | \(-0.223438\pi\) | ||||
0.763584 | + | 0.645709i | \(0.223438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | −9.58846 | −0.354885 | ||||||||
\(731\) | 0.758330 | − | 1.31347i | 0.0280479 | − | 0.0485803i | ||||
\(732\) | −13.1244 | −0.485090 | ||||||||
\(733\) | 11.7942 | − | 20.4282i | 0.435630 | − | 0.754533i | −0.561717 | − | 0.827329i | \(-0.689859\pi\) |
0.997347 | + | 0.0727965i | \(0.0231924\pi\) | |||||||
\(734\) | 3.63397 | − | 6.29423i | 0.134132 | − | 0.232324i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.5885 | −0.906343 | ||||||||
\(737\) | 3.92820 | + | 6.80385i | 0.144697 | + | 0.250623i | ||||
\(738\) | −20.0885 | + | 34.7942i | −0.739466 | + | 1.28079i | ||||
\(739\) | −20.3923 | + | 35.3205i | −0.750143 | + | 1.29929i | 0.197610 | + | 0.980281i | \(0.436682\pi\) |
−0.947753 | + | 0.319005i | \(0.896651\pi\) | |||||||
\(740\) | −6.06218 | + | 10.5000i | −0.222850 | + | 0.385988i | ||||
\(741\) | −19.6603 | − | 1.26795i | −0.722237 | − | 0.0465793i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.80385 | + | 6.58846i | 0.139550 | + | 0.241707i | 0.927326 | − | 0.374254i | \(-0.122101\pi\) |
−0.787777 | + | 0.615961i | \(0.788768\pi\) | |||||||
\(744\) | −19.8564 | −0.727971 | ||||||||
\(745\) | 11.1962 | 0.410195 | ||||||||
\(746\) | 9.86603 | + | 17.0885i | 0.361221 | + | 0.625653i | ||||
\(747\) | −4.90192 | − | 8.49038i | −0.179352 | − | 0.310647i | ||||
\(748\) | −4.90192 | + | 8.49038i | −0.179232 | + | 0.310439i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 28.6865 | − | 49.6865i | 1.04748 | − | 1.81430i | ||||
\(751\) | 35.8038 | 1.30650 | 0.653250 | − | 0.757142i | \(-0.273405\pi\) | ||||
0.653250 | + | 0.757142i | \(0.273405\pi\) | |||||||
\(752\) | −32.3205 | + | 55.9808i | −1.17861 | + | 2.04141i | ||||
\(753\) | 2.19615 | + | 3.80385i | 0.0800322 | + | 0.138620i | ||||
\(754\) | −8.30385 | − | 16.7942i | −0.302408 | − | 0.611610i | ||||
\(755\) | −3.46410 | −0.126072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.00000 | + | 13.8564i | 0.290765 | + | 0.503620i | 0.973991 | − | 0.226587i | \(-0.0727569\pi\) |
−0.683226 | + | 0.730207i | \(0.739424\pi\) | |||||||
\(758\) | −23.0263 | − | 39.8827i | −0.836352 | − | 1.44860i | ||||
\(759\) | 8.19615 | + | 14.1962i | 0.297501 | + | 0.515288i | ||||
\(760\) | −6.00000 | −0.217643 | ||||||||
\(761\) | 20.6603 | + | 35.7846i | 0.748934 | + | 1.29719i | 0.948334 | + | 0.317273i | \(0.102767\pi\) |
−0.199401 | + | 0.979918i | \(0.563900\pi\) | |||||||
\(762\) | −87.0333 | −3.15288 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.36603 | − | 4.09808i | −0.0855998 | − | 0.148263i | ||||
\(765\) | −59.7846 | −2.16152 | ||||||||
\(766\) | −10.0981 | − | 17.4904i | −0.364858 | − | 0.631953i | ||||
\(767\) | 26.1506 | + | 1.68653i | 0.944245 | + | 0.0608972i | ||||
\(768\) | 25.9545 | − | 44.9545i | 0.936552 | − | 1.62216i | ||||
\(769\) | 7.58846 | + | 13.1436i | 0.273647 | + | 0.473970i | 0.969793 | − | 0.243930i | \(-0.0784367\pi\) |
−0.696146 | + | 0.717900i | \(0.745103\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.36603 | + | 14.4904i | −0.301295 | + | 0.521858i | ||||
\(772\) | −2.50000 | + | 4.33013i | −0.0899770 | + | 0.155845i | ||||
\(773\) | 12.9282 | 0.464995 | 0.232498 | − | 0.972597i | \(-0.425310\pi\) | ||||
0.232498 | + | 0.972597i | \(0.425310\pi\) | |||||||
\(774\) | −1.51666 | −0.0545152 | ||||||||
\(775\) | −4.19615 | + | 7.26795i | −0.150730 | + | 0.261072i | ||||
\(776\) | −5.53590 | + | 9.58846i | −0.198727 | + | 0.344206i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.3827 | + | 35.3038i | 0.730755 | + | 1.26570i | ||||
\(779\) | 5.19615 | − | 9.00000i | 0.186171 | − | 0.322458i | ||||
\(780\) | 7.56218 | + | 15.2942i | 0.270769 | + | 0.547621i | ||||
\(781\) | −3.80385 | − | 6.58846i | −0.136112 | − | 0.235754i | ||||
\(782\) | 63.3731 | 2.26622 | ||||||||
\(783\) | −6.00000 | − | 10.3923i | −0.214423 | − | 0.371391i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.07180 | 0.0739456 | ||||||||
\(786\) | 8.19615 | + | 14.1962i | 0.292347 | + | 0.506360i | ||||
\(787\) | −12.9808 | −0.462714 | −0.231357 | − | 0.972869i | \(-0.574317\pi\) | ||||
−0.231357 | + | 0.972869i | \(0.574317\pi\) | |||||||
\(788\) | −6.00000 | − | 10.3923i | −0.213741 | − | 0.370211i | ||||
\(789\) | 1.73205 | + | 3.00000i | 0.0616626 | + | 0.106803i | ||||
\(790\) | 24.2942 | + | 42.0788i | 0.864350 | + | 1.49710i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −9.80385 | −0.348365 | ||||||||
\(793\) | 7.67691 | + | 15.5263i | 0.272615 | + | 0.551354i | ||||
\(794\) | −16.2679 | − | 28.1769i | −0.577328 | − | 0.999961i | ||||
\(795\) | 23.4904 | − | 40.6865i | 0.833118 | − | 1.44300i | ||||
\(796\) | −2.00000 | −0.0708881 | ||||||||
\(797\) | −17.1962 | + | 29.7846i | −0.609119 | + | 1.05503i | 0.382267 | + | 0.924052i | \(0.375143\pi\) |
−0.991386 | + | 0.130973i | \(0.958190\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 49.9808 | − | 86.5692i | 1.76819 | − | 3.06260i | ||||
\(800\) | −5.19615 | − | 9.00000i | −0.183712 | − | 0.318198i | ||||
\(801\) | 28.8564 | + | 49.9808i | 1.01959 | + | 1.76598i | ||||
\(802\) | −18.8038 | −0.663987 | ||||||||
\(803\) | 4.05256 | 0.143012 | ||||||||
\(804\) | −8.46410 | − | 14.6603i | −0.298506 | − | 0.517027i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.6147 | − | 23.4904i | −0.409112 | − | 0.827413i | ||||
\(807\) | −6.92820 | + | 12.0000i | −0.243884 | + | 0.422420i | ||||
\(808\) | 6.69615 | − | 11.5981i | 0.235570 | − | 0.408019i | ||||
\(809\) | −1.03590 | + | 1.79423i | −0.0364202 | + | 0.0630817i | −0.883661 | − | 0.468127i | \(-0.844929\pi\) |
0.847241 | + | 0.531209i | \(0.178262\pi\) | |||||||
\(810\) | −3.69615 | − | 6.40192i | −0.129870 | − | 0.224941i | ||||
\(811\) | 16.5885 | 0.582500 | 0.291250 | − | 0.956647i | \(-0.405929\pi\) | ||||
0.291250 | + | 0.956647i | \(0.405929\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.92820 | + | 13.7321i | −0.278054 | + | 0.481604i | ||||
\(814\) | 7.68653 | − | 13.3135i | 0.269413 | − | 0.466637i | ||||
\(815\) | −28.0526 | −0.982638 | ||||||||
\(816\) | −52.8109 | + | 91.4711i | −1.84875 | + | 3.20213i | ||||
\(817\) | 0.392305 | 0.0137250 | ||||||||
\(818\) | 29.1051 | 1.01764 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | 4.14359 | 0.144612 | 0.0723062 | − | 0.997382i | \(-0.476964\pi\) | ||||
0.0723062 | + | 0.997382i | \(0.476964\pi\) | |||||||
\(822\) | 19.0981 | − | 33.0788i | 0.666122 | − | 1.15376i | ||||
\(823\) | −41.1769 | −1.43534 | −0.717669 | − | 0.696385i | \(-0.754791\pi\) | ||||
−0.717669 | + | 0.696385i | \(0.754791\pi\) | |||||||
\(824\) | 12.4641 | − | 21.5885i | 0.434208 | − | 0.752070i | ||||
\(825\) | −3.46410 | + | 6.00000i | −0.120605 | + | 0.208893i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.9808 | −0.590479 | −0.295239 | − | 0.955423i | \(-0.595399\pi\) | ||||
−0.295239 | + | 0.955423i | \(0.595399\pi\) | |||||||
\(828\) | −10.5622 | − | 18.2942i | −0.367061 | − | 0.635768i | ||||
\(829\) | −0.205771 | + | 0.356406i | −0.00714673 | + | 0.0123785i | −0.869577 | − | 0.493798i | \(-0.835608\pi\) |
0.862430 | + | 0.506176i | \(0.168942\pi\) | |||||||
\(830\) | 3.29423 | − | 5.70577i | 0.114344 | − | 0.198050i | ||||
\(831\) | 23.2224 | − | 40.2224i | 0.805577 | − | 1.39530i | ||||
\(832\) | −3.59808 | − | 0.232051i | −0.124741 | − | 0.00804491i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 25.0526 | + | 43.3923i | 0.867499 | + | 1.50255i | ||||
\(835\) | −11.4115 | −0.394913 | ||||||||
\(836\) | −2.53590 | −0.0877059 | ||||||||
\(837\) | −8.39230 | − | 14.5359i | −0.290080 | − | 0.502434i | ||||
\(838\) | −27.8827 | − | 48.2942i | −0.963191 | − | 1.66830i | ||||
\(839\) | −9.00000 | + | 15.5885i | −0.310715 | + | 0.538173i | −0.978517 | − | 0.206165i | \(-0.933902\pi\) |
0.667803 | + | 0.744338i | \(0.267235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | −55.7321 | −1.92065 | ||||||||
\(843\) | 18.2942 | − | 31.6865i | 0.630087 | − | 1.09134i | ||||
\(844\) | 0.901924 | + | 1.56218i | 0.0310455 | + | 0.0537724i | ||||
\(845\) | 13.6699 | − | 17.8923i | 0.470258 | − | 0.615514i | ||||
\(846\) | −99.9615 | −3.43675 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −24.8205 | − | 42.9904i | −0.852340 | − | 1.47630i | ||||
\(849\) | −13.9282 | − | 24.1244i | −0.478015 | − | 0.827946i | ||||
\(850\) | 13.3923 | + | 23.1962i | 0.459352 | + | 0.795621i | ||||
\(851\) | −33.1244 | −1.13549 | ||||||||
\(852\) | 8.19615 | + | 14.1962i | 0.280796 | + | 0.486352i | ||||
\(853\) | −5.58846 | −0.191345 | −0.0956726 | − | 0.995413i | \(-0.530500\pi\) | ||||
−0.0956726 | + | 0.995413i | \(0.530500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.73205 | − | 13.3923i | −0.264431 | − | 0.458007i | ||||
\(856\) | 13.6077 | 0.465101 | ||||||||
\(857\) | −15.0622 | − | 26.0885i | −0.514514 | − | 0.891165i | −0.999858 | − | 0.0168414i | \(-0.994639\pi\) |
0.485344 | − | 0.874323i | \(-0.338694\pi\) | |||||||
\(858\) | −9.58846 | − | 19.3923i | −0.327345 | − | 0.662042i | ||||
\(859\) | −3.90192 | + | 6.75833i | −0.133132 | + | 0.230591i | −0.924882 | − | 0.380254i | \(-0.875837\pi\) |
0.791750 | + | 0.610845i | \(0.209170\pi\) | |||||||
\(860\) | −0.169873 | − | 0.294229i | −0.00579262 | − | 0.0100331i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.588457 | + | 1.01924i | −0.0200429 | + | 0.0347154i | ||||
\(863\) | −3.75833 | + | 6.50962i | −0.127935 | + | 0.221590i | −0.922876 | − | 0.385096i | \(-0.874168\pi\) |
0.794941 | + | 0.606686i | \(0.207502\pi\) | |||||||
\(864\) | 20.7846 | 0.707107 | ||||||||
\(865\) | 14.7846 | 0.502692 | ||||||||
\(866\) | −11.7679 | + | 20.3827i | −0.399891 | + | 0.692632i | ||||
\(867\) | 58.4449 | − | 101.229i | 1.98489 | − | 3.43793i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.2679 | − | 17.7846i | −0.348316 | − | 0.603302i | ||||
\(870\) | 12.2942 | − | 21.2942i | 0.416813 | − | 0.721942i | ||||
\(871\) | −12.3923 | + | 18.5885i | −0.419897 | + | 0.629846i | ||||
\(872\) | −7.26795 | − | 12.5885i | −0.246124 | − | 0.426299i | ||||
\(873\) | −28.5359 | −0.965794 | ||||||||
\(874\) | 8.19615 | + | 14.1962i | 0.277239 | + | 0.480192i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.73205 | −0.295029 | ||||||||
\(877\) | −9.89230 | − | 17.1340i | −0.334039 | − | 0.578573i | 0.649260 | − | 0.760566i | \(-0.275079\pi\) |
−0.983300 | + | 0.181993i | \(0.941745\pi\) | |||||||
\(878\) | −25.2679 | −0.852752 | ||||||||
\(879\) | 1.09808 | + | 1.90192i | 0.0370372 | + | 0.0641503i | ||||
\(880\) | −5.49038 | − | 9.50962i | −0.185081 | − | 0.320569i | ||||
\(881\) | −4.20577 | − | 7.28461i | −0.141696 | − | 0.245425i | 0.786439 | − | 0.617667i | \(-0.211922\pi\) |
−0.928135 | + | 0.372243i | \(0.878589\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.7654 | −1.60743 | −0.803716 | − | 0.595013i | \(-0.797147\pi\) | ||||
−0.803716 | + | 0.595013i | \(0.797147\pi\) | |||||||
\(884\) | −27.8205 | − | 1.79423i | −0.935705 | − | 0.0603464i | ||||
\(885\) | 17.1962 | + | 29.7846i | 0.578042 | + | 1.00120i | ||||
\(886\) | −20.1962 | + | 34.9808i | −0.678503 | + | 1.17520i | ||||
\(887\) | −11.3205 | −0.380105 | −0.190053 | − | 0.981774i | \(-0.560866\pi\) | ||||
−0.190053 | + | 0.981774i | \(0.560866\pi\) | |||||||
\(888\) | 16.5622 | − | 28.6865i | 0.555790 | − | 0.962657i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −19.3923 | + | 33.5885i | −0.650032 | + | 1.12589i | ||||
\(891\) | 1.56218 | + | 2.70577i | 0.0523349 | + | 0.0906468i | ||||
\(892\) | −5.00000 | − | 8.66025i | −0.167412 | − | 0.289967i | ||||
\(893\) | 25.8564 | 0.865252 | ||||||||
\(894\) | 30.5885 | 1.02303 | ||||||||
\(895\) | −6.00000 | − | 10.3923i | −0.200558 | − | 0.347376i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25.8564 | + | 38.7846i | −0.863320 | + | 1.29498i | ||||
\(898\) | 10.3923 | − | 18.0000i | 0.346796 | − | 0.600668i | ||||
\(899\) | −6.29423 | + | 10.9019i | −0.209924 | + | 0.363600i | ||||
\(900\) | 4.46410 | − | 7.73205i | 0.148803 | − | 0.257735i | ||||
\(901\) | 38.3827 | + | 66.4808i | 1.27871 | + | 2.21480i | ||||
\(902\) | 11.4115 | 0.379963 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.5981 | − | 20.0885i | 0.385746 | − | 0.668132i | ||||
\(905\) | −4.83975 | + | 8.38269i | −0.160879 | + | 0.278650i | ||||
\(906\) | −9.46410 | −0.314424 | ||||||||
\(907\) | 8.29423 | − | 14.3660i | 0.275405 | − | 0.477016i | −0.694832 | − | 0.719172i | \(-0.744521\pi\) |
0.970237 | + | 0.242156i | \(0.0778546\pi\) | |||||||
\(908\) | −5.66025 | −0.187842 | ||||||||
\(909\) | 34.5167 | 1.14485 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | −27.3205 | −0.904672 | ||||||||
\(913\) | −1.39230 | + | 2.41154i | −0.0460786 | + | 0.0798104i | ||||
\(914\) | 19.0526 | 0.630203 | ||||||||
\(915\) | −11.3660 | + | 19.6865i | −0.375749 | + | 0.650817i | ||||
\(916\) | −7.19615 | + | 12.4641i | −0.237768 | + | 0.411826i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −53.5692 | −1.76805 | ||||||||
\(919\) | 19.7846 | + | 34.2679i | 0.652634 | + | 1.13040i | 0.982481 | + | 0.186361i | \(0.0596694\pi\) |
−0.329847 | + | 0.944034i | \(0.606997\pi\) | |||||||
\(920\) | −7.09808 | + | 12.2942i | −0.234017 | + | 0.405329i | ||||
\(921\) | 6.26795 | − | 10.8564i | 0.206536 | − | 0.357731i | ||||
\(922\) | −13.5000 | + | 23.3827i | −0.444599 | + | 0.770068i | ||||
\(923\) | 12.0000 | − | 18.0000i | 0.394985 | − | 0.592477i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.00000 | − | 12.1244i | −0.230159 | − | 0.398646i | ||||
\(926\) | −7.94744 | −0.261169 | ||||||||
\(927\) | 64.2487 | 2.11020 | ||||||||
\(928\) | −7.79423 | − | 13.5000i | −0.255858 | − | 0.443159i | ||||
\(929\) | 26.2583 | + | 45.4808i | 0.861508 | + | 1.49218i | 0.870473 | + | 0.492216i | \(0.163813\pi\) |
−0.00896546 | + | 0.999960i | \(0.502854\pi\) | |||||||
\(930\) | 17.1962 | − | 29.7846i | 0.563884 | − | 0.976676i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.928203 | − | 1.60770i | 0.0304043 | − | 0.0526618i | ||||
\(933\) | 3.46410 | 0.113410 | ||||||||
\(934\) | 22.0981 | − | 38.2750i | 0.723071 | − | 1.25240i | ||||
\(935\) | 8.49038 | + | 14.7058i | 0.277665 | + | 0.480930i | ||||
\(936\) | −12.3564 | − | 24.9904i | −0.403882 | − | 0.816836i | ||||
\(937\) | 51.1962 | 1.67251 | 0.836253 | − | 0.548344i | \(-0.184742\pi\) | ||||
0.836253 | + | 0.548344i | \(0.184742\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −39.3205 | − | 68.1051i | −1.28318 | − | 2.22253i | ||||
\(940\) | −11.1962 | − | 19.3923i | −0.365178 | − | 0.632507i | ||||
\(941\) | −14.0718 | − | 24.3731i | −0.458727 | − | 0.794539i | 0.540167 | − | 0.841558i | \(-0.318361\pi\) |
−0.998894 | + | 0.0470189i | \(0.985028\pi\) | |||||||
\(942\) | 5.66025 | 0.184421 | ||||||||
\(943\) | −12.2942 | − | 21.2942i | −0.400355 | − | 0.693435i | ||||
\(944\) | 36.3397 | 1.18276 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.215390 | + | 0.373067i | 0.00700294 | + | 0.0121295i | ||||
\(947\) | −7.26795 | −0.236177 | −0.118088 | − | 0.993003i | \(-0.537677\pi\) | ||||
−0.118088 | + | 0.993003i | \(0.537677\pi\) | |||||||
\(948\) | 22.1244 | + | 38.3205i | 0.718566 | + | 1.24459i | ||||
\(949\) | 5.10770 | + | 10.3301i | 0.165803 | + | 0.335330i | ||||
\(950\) | −3.46410 | + | 6.00000i | −0.112390 | + | 0.194666i | ||||
\(951\) | −8.83013 | − | 15.2942i | −0.286336 | − | 0.495949i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.5885 | − | 21.8038i | 0.407780 | − | 0.706296i | −0.586861 | − | 0.809688i | \(-0.699636\pi\) |
0.994641 | + | 0.103392i | \(0.0329697\pi\) | |||||||
\(954\) | 38.3827 | − | 66.4808i | 1.24269 | − | 2.15239i | ||||
\(955\) | −8.19615 | −0.265221 | ||||||||
\(956\) | −15.8038 | −0.511133 | ||||||||
\(957\) | −5.19615 | + | 9.00000i | −0.167968 | + | 0.290929i | ||||
\(958\) | 1.09808 | − | 1.90192i | 0.0354772 | − | 0.0614484i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.36603 | − | 4.09808i | −0.0763631 | − | 0.132265i | ||||
\(961\) | 6.69615 | − | 11.5981i | 0.216005 | − | 0.374131i | ||||
\(962\) | 43.6244 | + | 2.81347i | 1.40651 | + | 0.0907098i | ||||
\(963\) | 17.5359 | + | 30.3731i | 0.565086 | + | 0.978758i | ||||
\(964\) | 21.1962 | 0.682682 | ||||||||
\(965\) | 4.33013 | + | 7.50000i | 0.139392 | + | 0.241434i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.9808 | 1.76806 | 0.884031 | − | 0.467428i | \(-0.154819\pi\) | ||||
0.884031 | + | 0.467428i | \(0.154819\pi\) | |||||||
\(968\) | −8.13397 | − | 14.0885i | −0.261436 | − | 0.452820i | ||||
\(969\) | 42.2487 | 1.35722 | ||||||||
\(970\) | −9.58846 | − | 16.6077i | −0.307867 | − | 0.533241i | ||||
\(971\) | −26.3205 | − | 45.5885i | −0.844665 | − | 1.46300i | −0.885912 | − | 0.463854i | \(-0.846466\pi\) |
0.0412463 | − | 0.999149i | \(-0.486867\pi\) | |||||||
\(972\) | −9.36603 | − | 16.2224i | −0.300415 | − | 0.520335i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 70.6410 | 2.26348 | ||||||||
\(975\) | −19.6603 | − | 1.26795i | −0.629632 | − | 0.0406069i | ||||
\(976\) | 12.0096 | + | 20.8013i | 0.384419 | + | 0.665832i | ||||
\(977\) | −15.8205 | + | 27.4019i | −0.506143 | + | 0.876665i | 0.493832 | + | 0.869557i | \(0.335596\pi\) |
−0.999975 | + | 0.00710779i | \(0.997738\pi\) | |||||||
\(978\) | −76.6410 | −2.45071 | ||||||||
\(979\) | 8.19615 | − | 14.1962i | 0.261950 | − | 0.453711i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.7321 | − | 32.4449i | 0.598068 | − | 1.03588i | ||||
\(982\) | −6.58846 | − | 11.4115i | −0.210246 | − | 0.364157i | ||||
\(983\) | −8.66025 | − | 15.0000i | −0.276219 | − | 0.478426i | 0.694223 | − | 0.719760i | \(-0.255748\pi\) |
−0.970442 | + | 0.241334i | \(0.922415\pi\) | |||||||
\(984\) | 24.5885 | 0.783851 | ||||||||
\(985\) | −20.7846 | −0.662253 | ||||||||
\(986\) | 20.0885 | + | 34.7942i | 0.639747 | + | 1.10807i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.19615 | − | 6.46410i | −0.101683 | − | 0.205650i | ||||
\(989\) | 0.464102 | − | 0.803848i | 0.0147576 | − | 0.0255609i | ||||
\(990\) | 8.49038 | − | 14.7058i | 0.269842 | − | 0.467380i | ||||
\(991\) | −9.49038 | + | 16.4378i | −0.301472 | + | 0.522165i | −0.976470 | − | 0.215655i | \(-0.930811\pi\) |
0.674998 | + | 0.737820i | \(0.264145\pi\) | |||||||
\(992\) | −10.9019 | − | 18.8827i | −0.346136 | − | 0.599526i | ||||
\(993\) | −68.2487 | −2.16581 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.73205 | + | 3.00000i | −0.0549097 | + | 0.0951064i | ||||
\(996\) | 3.00000 | − | 5.19615i | 0.0950586 | − | 0.164646i | ||||
\(997\) | 4.80385 | 0.152139 | 0.0760697 | − | 0.997103i | \(-0.475763\pi\) | ||||
0.0760697 | + | 0.997103i | \(0.475763\pi\) | |||||||
\(998\) | 33.7583 | − | 58.4711i | 1.06860 | − | 1.85087i | ||||
\(999\) | 28.0000 | 0.885881 |
(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 | 637.2.h.e.471.2 | 4 | ||
7.2 | even | 3 | 637.2.f.d.393.1 | 4 | |||
7.3 | odd | 6 | 637.2.g.e.263.1 | 4 | |||
7.4 | even | 3 | 637.2.g.d.263.1 | 4 | |||
7.5 | odd | 6 | 91.2.f.b.29.1 | yes | 4 | ||
7.6 | odd | 2 | 637.2.h.d.471.2 | 4 | |||
13.9 | even | 3 | 637.2.g.d.373.1 | 4 | |||
21.5 | even | 6 | 819.2.o.b.757.2 | 4 | |||
28.19 | even | 6 | 1456.2.s.o.1121.2 | 4 | |||
91.9 | even | 3 | 637.2.f.d.295.1 | 4 | |||
91.16 | even | 3 | 8281.2.a.r.1.2 | 2 | |||
91.23 | even | 6 | 8281.2.a.t.1.1 | 2 | |||
91.48 | odd | 6 | 637.2.g.e.373.1 | 4 | |||
91.54 | even | 12 | 1183.2.c.e.337.2 | 4 | |||
91.61 | odd | 6 | 91.2.f.b.22.1 | ✓ | 4 | ||
91.68 | odd | 6 | 1183.2.a.f.1.2 | 2 | |||
91.74 | even | 3 | inner | 637.2.h.e.165.2 | 4 | ||
91.75 | odd | 6 | 1183.2.a.e.1.1 | 2 | |||
91.87 | odd | 6 | 637.2.h.d.165.2 | 4 | |||
91.89 | even | 12 | 1183.2.c.e.337.4 | 4 | |||
273.152 | even | 6 | 819.2.o.b.568.2 | 4 | |||
364.243 | even | 6 | 1456.2.s.o.113.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.b.22.1 | ✓ | 4 | 91.61 | odd | 6 | ||
91.2.f.b.29.1 | yes | 4 | 7.5 | odd | 6 | ||
637.2.f.d.295.1 | 4 | 91.9 | even | 3 | |||
637.2.f.d.393.1 | 4 | 7.2 | even | 3 | |||
637.2.g.d.263.1 | 4 | 7.4 | even | 3 | |||
637.2.g.d.373.1 | 4 | 13.9 | even | 3 | |||
637.2.g.e.263.1 | 4 | 7.3 | odd | 6 | |||
637.2.g.e.373.1 | 4 | 91.48 | odd | 6 | |||
637.2.h.d.165.2 | 4 | 91.87 | odd | 6 | |||
637.2.h.d.471.2 | 4 | 7.6 | odd | 2 | |||
637.2.h.e.165.2 | 4 | 91.74 | even | 3 | inner | ||
637.2.h.e.471.2 | 4 | 1.1 | even | 1 | trivial | ||
819.2.o.b.568.2 | 4 | 273.152 | even | 6 | |||
819.2.o.b.757.2 | 4 | 21.5 | even | 6 | |||
1183.2.a.e.1.1 | 2 | 91.75 | odd | 6 | |||
1183.2.a.f.1.2 | 2 | 91.68 | odd | 6 | |||
1183.2.c.e.337.2 | 4 | 91.54 | even | 12 | |||
1183.2.c.e.337.4 | 4 | 91.89 | even | 12 | |||
1456.2.s.o.113.2 | 4 | 364.243 | even | 6 | |||
1456.2.s.o.1121.2 | 4 | 28.19 | even | 6 | |||
8281.2.a.r.1.2 | 2 | 91.16 | even | 3 | |||
8281.2.a.t.1.1 | 2 | 91.23 | even | 6 |