Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(263,637)]
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, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.263");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.g (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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.373 |
Dual form | 637.2.g.d.263.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 1.50000i | −0.612372 | − | 1.06066i | −0.990839 | − | 0.135045i | \(-0.956882\pi\) |
0.378467 | − | 0.925615i | \(-0.376451\pi\) | |||||||
\(3\) | −2.73205 | −1.57735 | −0.788675 | − | 0.614810i | \(-0.789233\pi\) | ||||
−0.788675 | + | 0.614810i | \(0.789233\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 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 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | −3.00000 | −0.948683 | ||||||||
\(11\) | 1.26795 | 0.382301 | 0.191151 | − | 0.981561i | \(-0.438778\pi\) | ||||
0.191151 | + | 0.981561i | \(0.438778\pi\) | |||||||
\(12\) | 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 | ||||
\(16\) | 2.50000 | + | 4.33013i | 0.625000 | + | 1.08253i | ||||
\(17\) | −3.86603 | + | 6.69615i | −0.937649 | + | 1.62406i | −0.167808 | + | 0.985820i | \(0.553669\pi\) |
−0.769841 | + | 0.638236i | \(0.779664\pi\) | |||||||
\(18\) | −3.86603 | − | 6.69615i | −0.911231 | − | 1.57830i | ||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0.866025 | + | 1.50000i | 0.193649 | + | 0.335410i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.09808 | − | 1.90192i | −0.234111 | − | 0.405492i | ||||
\(23\) | −2.36603 | − | 4.09808i | −0.493350 | − | 0.854508i | 0.506620 | − | 0.862169i | \(-0.330895\pi\) |
−0.999971 | + | 0.00766135i | \(0.997561\pi\) | |||||||
\(24\) | 4.73205 | 0.965926 | ||||||||
\(25\) | 1.00000 | + | 1.73205i | 0.200000 | + | 0.346410i | ||||
\(26\) | 3.46410 | + | 5.19615i | 0.679366 | + | 1.01905i | ||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.50000 | − | 2.59808i | 0.278543 | − | 0.482451i | −0.692480 | − | 0.721437i | \(-0.743482\pi\) |
0.971023 | + | 0.238987i | \(0.0768152\pi\) | |||||||
\(30\) | 8.19615 | 1.49641 | ||||||||
\(31\) | 2.09808 | + | 3.63397i | 0.376826 | + | 0.652681i | 0.990598 | − | 0.136802i | \(-0.0436823\pi\) |
−0.613773 | + | 0.789483i | \(0.710349\pi\) | |||||||
\(32\) | 2.59808 | − | 4.50000i | 0.459279 | − | 0.795495i | ||||
\(33\) | −3.46410 | −0.603023 | ||||||||
\(34\) | 13.3923 | 2.29676 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.23205 | + | 3.86603i | −0.372008 | + | 0.644338i | ||||
\(37\) | 3.50000 | + | 6.06218i | 0.575396 | + | 0.996616i | 0.995998 | + | 0.0893706i | \(0.0284856\pi\) |
−0.420602 | + | 0.907245i | \(0.638181\pi\) | |||||||
\(38\) | 1.73205 | + | 3.00000i | 0.280976 | + | 0.486664i | ||||
\(39\) | 9.83013 | − | 0.633975i | 1.57408 | − | 0.101517i | ||||
\(40\) | −1.50000 | + | 2.59808i | −0.237171 | + | 0.410792i | ||||
\(41\) | −2.59808 | + | 4.50000i | −0.405751 | + | 0.702782i | −0.994409 | − | 0.105601i | \(-0.966323\pi\) |
0.588657 | + | 0.808383i | \(0.299657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0980762 | + | 0.169873i | 0.0149565 | + | 0.0259054i | 0.873407 | − | 0.486991i | \(-0.161906\pi\) |
−0.858450 | + | 0.512897i | \(0.828572\pi\) | |||||||
\(44\) | −0.633975 | + | 1.09808i | −0.0955753 | + | 0.165541i | ||||
\(45\) | 3.86603 | − | 6.69615i | 0.576313 | − | 0.998203i | ||||
\(46\) | −4.09808 | + | 7.09808i | −0.604228 | + | 1.04655i | ||||
\(47\) | 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 | ||||
\(52\) | 1.59808 | − | 3.23205i | 0.221613 | − | 0.448205i | ||||
\(53\) | 4.96410 | + | 8.59808i | 0.681872 | + | 1.18104i | 0.974409 | + | 0.224782i | \(0.0721671\pi\) |
−0.292537 | + | 0.956254i | \(0.594500\pi\) | |||||||
\(54\) | 3.46410 | + | 6.00000i | 0.471405 | + | 0.816497i | ||||
\(55\) | 1.09808 | − | 1.90192i | 0.148065 | − | 0.256455i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.46410 | 0.723738 | ||||||||
\(58\) | −5.19615 | −0.682288 | ||||||||
\(59\) | 3.63397 | − | 6.29423i | 0.473103 | − | 0.819439i | −0.526423 | − | 0.850223i | \(-0.676467\pi\) |
0.999526 | + | 0.0307841i | \(0.00980044\pi\) | |||||||
\(60\) | −2.36603 | − | 4.09808i | −0.305453 | − | 0.529059i | ||||
\(61\) | 4.80385 | 0.615070 | 0.307535 | − | 0.951537i | \(-0.400496\pi\) | ||||
0.307535 | + | 0.951537i | \(0.400496\pi\) | |||||||
\(62\) | 3.63397 | − | 6.29423i | 0.461515 | − | 0.799368i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.76795 | + | 5.59808i | −0.343322 | + | 0.694356i | ||||
\(66\) | 3.00000 | + | 5.19615i | 0.369274 | + | 0.639602i | ||||
\(67\) | −6.19615 | −0.756980 | −0.378490 | − | 0.925605i | \(-0.623557\pi\) | ||||
−0.378490 | + | 0.925605i | \(0.623557\pi\) | |||||||
\(68\) | −3.86603 | − | 6.69615i | −0.468824 | − | 0.812028i | ||||
\(69\) | 6.46410 | + | 11.1962i | 0.778186 | + | 1.34786i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | − | 5.19615i | −0.356034 | − | 0.616670i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
−0.987294 | + | 0.158901i | \(0.949205\pi\) | |||||||
\(72\) | −7.73205 | −0.911231 | ||||||||
\(73\) | −1.59808 | − | 2.76795i | −0.187041 | − | 0.323964i | 0.757222 | − | 0.653158i | \(-0.226556\pi\) |
−0.944262 | + | 0.329194i | \(0.893223\pi\) | |||||||
\(74\) | 6.06218 | − | 10.5000i | 0.704714 | − | 1.22060i | ||||
\(75\) | −2.73205 | − | 4.73205i | −0.315470 | − | 0.546410i | ||||
\(76\) | 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 | \(0.801897\pi\) | |||||||
\(80\) | 8.66025 | 0.968246 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 9.00000 | 0.993884 | ||||||||
\(83\) | 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 | ||||
\(87\) | −4.09808 | + | 7.09808i | −0.439360 | + | 0.760994i | ||||
\(88\) | −2.19615 | −0.234111 | ||||||||
\(89\) | 6.46410 | + | 11.1962i | 0.685193 | + | 1.18679i | 0.973376 | + | 0.229214i | \(0.0736157\pi\) |
−0.288183 | + | 0.957575i | \(0.593051\pi\) | |||||||
\(90\) | −13.3923 | −1.41167 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.73205 | 0.493350 | ||||||||
\(93\) | −5.73205 | − | 9.92820i | −0.594386 | − | 1.02951i | ||||
\(94\) | −22.3923 | −2.30959 | ||||||||
\(95\) | −1.73205 | + | 3.00000i | −0.177705 | + | 0.307794i | ||||
\(96\) | −7.09808 | + | 12.2942i | −0.724444 | + | 1.25477i | ||||
\(97\) | 3.19615 | + | 5.53590i | 0.324520 | + | 0.562085i | 0.981415 | − | 0.191897i | \(-0.0614639\pi\) |
−0.656895 | + | 0.753982i | \(0.728131\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.66025 | 0.568877 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | 7.73205 | 0.769368 | 0.384684 | − | 0.923048i | \(-0.374310\pi\) | ||||
0.384684 | + | 0.923048i | \(0.374310\pi\) | |||||||
\(102\) | −36.5885 | −3.62280 | ||||||||
\(103\) | −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 | ||||
\(107\) | 3.92820 | + | 6.80385i | 0.379754 | + | 0.657753i | 0.991026 | − | 0.133667i | \(-0.0426754\pi\) |
−0.611273 | + | 0.791420i | \(0.709342\pi\) | |||||||
\(108\) | 2.00000 | − | 3.46410i | 0.192450 | − | 0.333333i | ||||
\(109\) | 4.19615 | + | 7.26795i | 0.401919 | + | 0.696143i | 0.993957 | − | 0.109766i | \(-0.0350102\pi\) |
−0.592039 | + | 0.805909i | \(0.701677\pi\) | |||||||
\(110\) | −3.80385 | −0.362683 | ||||||||
\(111\) | −9.56218 | − | 16.5622i | −0.907602 | − | 1.57201i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.69615 | − | 11.5981i | −0.629921 | − | 1.09106i | −0.987567 | − | 0.157198i | \(-0.949754\pi\) |
0.357646 | − | 0.933857i | \(-0.383579\pi\) | |||||||
\(114\) | −4.73205 | − | 8.19615i | −0.443197 | − | 0.767640i | ||||
\(115\) | −8.19615 | −0.764295 | ||||||||
\(116\) | 1.50000 | + | 2.59808i | 0.139272 | + | 0.241225i | ||||
\(117\) | −16.0622 | + | 1.03590i | −1.48495 | + | 0.0957688i | ||||
\(118\) | −12.5885 | −1.15886 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.09808 | − | 7.09808i | 0.374101 | − | 0.647963i | ||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | −4.16025 | − | 7.20577i | −0.376652 | − | 0.652380i | ||||
\(123\) | 7.09808 | − | 12.2942i | 0.640012 | − | 1.10853i | ||||
\(124\) | −4.19615 | −0.376826 | ||||||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.19615 | + | 15.9282i | −0.816027 | + | 1.41340i | 0.0925619 | + | 0.995707i | \(0.470494\pi\) |
−0.908588 | + | 0.417693i | \(0.862839\pi\) | |||||||
\(128\) | −6.06218 | − | 10.5000i | −0.535826 | − | 0.928078i | ||||
\(129\) | −0.267949 | − | 0.464102i | −0.0235916 | − | 0.0408619i | ||||
\(130\) | 10.7942 | − | 0.696152i | 0.946716 | − | 0.0610566i | ||||
\(131\) | −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 | ||||
\(136\) | 6.69615 | − | 11.5981i | 0.574190 | − | 0.994527i | ||||
\(137\) | −4.03590 | + | 6.99038i | −0.344810 | + | 0.597229i | −0.985319 | − | 0.170722i | \(-0.945390\pi\) |
0.640509 | + | 0.767951i | \(0.278723\pi\) | |||||||
\(138\) | 11.1962 | − | 19.3923i | 0.953080 | − | 1.65078i | ||||
\(139\) | −5.29423 | − | 9.16987i | −0.449051 | − | 0.777778i | 0.549274 | − | 0.835642i | \(-0.314904\pi\) |
−0.998324 | + | 0.0578639i | \(0.981571\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.6603 | + | 30.5885i | −1.48726 | + | 2.57601i | ||||
\(142\) | −5.19615 | + | 9.00000i | −0.436051 | + | 0.755263i | ||||
\(143\) | −4.56218 | + | 0.294229i | −0.381508 | + | 0.0246046i | ||||
\(144\) | 11.1603 | + | 19.3301i | 0.930021 | + | 1.61084i | ||||
\(145\) | −2.59808 | − | 4.50000i | −0.215758 | − | 0.373705i | ||||
\(146\) | −2.76795 | + | 4.79423i | −0.229077 | + | 0.396773i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.00000 | −0.575396 | ||||||||
\(149\) | −6.46410 | −0.529560 | −0.264780 | − | 0.964309i | \(-0.585299\pi\) | ||||
−0.264780 | + | 0.964309i | \(0.585299\pi\) | |||||||
\(150\) | −4.73205 | + | 8.19615i | −0.386370 | + | 0.669213i | ||||
\(151\) | −1.00000 | − | 1.73205i | −0.0813788 | − | 0.140952i | 0.822464 | − | 0.568818i | \(-0.192599\pi\) |
−0.903842 | + | 0.427865i | \(0.859266\pi\) | |||||||
\(152\) | 3.46410 | 0.280976 | ||||||||
\(153\) | −17.2583 | + | 29.8923i | −1.39525 | + | 2.41665i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.26795 | 0.583776 | ||||||||
\(156\) | −4.36603 | + | 8.83013i | −0.349562 | + | 0.706976i | ||||
\(157\) | 0.598076 | + | 1.03590i | 0.0477317 | + | 0.0826737i | 0.888904 | − | 0.458093i | \(-0.151467\pi\) |
−0.841172 | + | 0.540767i | \(0.818134\pi\) | |||||||
\(158\) | 28.0526 | 2.23174 | ||||||||
\(159\) | −13.5622 | − | 23.4904i | −1.07555 | − | 1.86291i | ||||
\(160\) | −4.50000 | − | 7.79423i | −0.355756 | − | 0.616188i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.13397 | + | 3.69615i | 0.167661 | + | 0.290397i | ||||
\(163\) | 16.1962 | 1.26858 | 0.634290 | − | 0.773095i | \(-0.281292\pi\) | ||||
0.634290 | + | 0.773095i | \(0.281292\pi\) | |||||||
\(164\) | −2.59808 | − | 4.50000i | −0.202876 | − | 0.351391i | ||||
\(165\) | −3.00000 | + | 5.19615i | −0.233550 | + | 0.404520i | ||||
\(166\) | −1.90192 | − | 3.29423i | −0.147618 | − | 0.255682i | ||||
\(167\) | −3.29423 | + | 5.70577i | −0.254915 | + | 0.441526i | −0.964872 | − | 0.262719i | \(-0.915381\pi\) |
0.709957 | + | 0.704245i | \(0.248714\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8923 | − | 1.66987i | 0.991716 | − | 0.128452i | ||||
\(170\) | 11.5981 | − | 20.0885i | 0.889532 | − | 1.54071i | ||||
\(171\) | −8.92820 | −0.682757 | ||||||||
\(172\) | −0.196152 | −0.0149565 | ||||||||
\(173\) | −8.53590 | −0.648972 | −0.324486 | − | 0.945890i | \(-0.605191\pi\) | ||||
−0.324486 | + | 0.945890i | \(0.605191\pi\) | |||||||
\(174\) | 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 | ||||
\(178\) | 11.1962 | − | 19.3923i | 0.839187 | − | 1.45351i | ||||
\(179\) | −6.92820 | −0.517838 | −0.258919 | − | 0.965899i | \(-0.583366\pi\) | ||||
−0.258919 | + | 0.965899i | \(0.583366\pi\) | |||||||
\(180\) | 3.86603 | + | 6.69615i | 0.288157 | + | 0.499102i | ||||
\(181\) | −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 | ||||||||
\(184\) | 4.09808 | + | 7.09808i | 0.302114 | + | 0.523277i | ||||
\(185\) | 12.1244 | 0.891400 | ||||||||
\(186\) | −9.92820 | + | 17.1962i | −0.727971 | + | 1.26088i | ||||
\(187\) | −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 | ||||||||
\(191\) | 4.73205 | 0.342399 | 0.171200 | − | 0.985236i | \(-0.445236\pi\) | ||||
0.171200 | + | 0.985236i | \(0.445236\pi\) | |||||||
\(192\) | −2.73205 | −0.197169 | ||||||||
\(193\) | 5.00000 | 0.359908 | 0.179954 | − | 0.983675i | \(-0.442405\pi\) | ||||
0.179954 | + | 0.983675i | \(0.442405\pi\) | |||||||
\(194\) | 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 | −0.996649 | − | 0.0818013i | \(-0.973933\pi\) |
0.569166 | + | 0.822222i | \(0.307266\pi\) | |||||||
\(198\) | −4.90192 | − | 8.49038i | −0.348365 | − | 0.603385i | ||||
\(199\) | 1.00000 | − | 1.73205i | 0.0708881 | − | 0.122782i | −0.828403 | − | 0.560133i | \(-0.810750\pi\) |
0.899291 | + | 0.437351i | \(0.144083\pi\) | |||||||
\(200\) | −1.73205 | − | 3.00000i | −0.122474 | − | 0.212132i | ||||
\(201\) | 16.9282 | 1.19402 | ||||||||
\(202\) | −6.69615 | − | 11.5981i | −0.471140 | − | 0.816038i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 10.5622 | + | 18.2942i | 0.739500 | + | 1.28085i | ||||
\(205\) | 4.50000 | + | 7.79423i | 0.314294 | + | 0.544373i | ||||
\(206\) | 24.9282 | 1.73683 | ||||||||
\(207\) | −10.5622 | − | 18.2942i | −0.734122 | − | 1.27154i | ||||
\(208\) | −10.0000 | − | 15.0000i | −0.693375 | − | 1.04006i | ||||
\(209\) | −2.53590 | −0.175412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.901924 | − | 1.56218i | 0.0620910 | − | 0.107545i | −0.833309 | − | 0.552808i | \(-0.813556\pi\) |
0.895400 | + | 0.445263i | \(0.146890\pi\) | |||||||
\(212\) | −9.92820 | −0.681872 | ||||||||
\(213\) | 8.19615 | + | 14.1962i | 0.561591 | + | 0.972704i | ||||
\(214\) | 6.80385 | − | 11.7846i | 0.465101 | − | 0.805579i | ||||
\(215\) | 0.339746 | 0.0231705 | ||||||||
\(216\) | 6.92820 | 0.471405 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.26795 | − | 12.5885i | 0.492248 | − | 0.852598i | ||||
\(219\) | 4.36603 | + | 7.56218i | 0.295029 | + | 0.511005i | ||||
\(220\) | 1.09808 | + | 1.90192i | 0.0740323 | + | 0.128228i | ||||
\(221\) | 12.3564 | − | 24.9904i | 0.831182 | − | 1.68103i | ||||
\(222\) | −16.5622 | + | 28.6865i | −1.11158 | + | 1.92531i | ||||
\(223\) | −5.00000 | + | 8.66025i | −0.334825 | + | 0.579934i | −0.983451 | − | 0.181173i | \(-0.942010\pi\) |
0.648626 | + | 0.761107i | \(0.275344\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.46410 | + | 7.73205i | 0.297607 | + | 0.515470i | ||||
\(226\) | −11.5981 | + | 20.0885i | −0.771493 | + | 1.33626i | ||||
\(227\) | 2.83013 | − | 4.90192i | 0.187842 | − | 0.325352i | −0.756688 | − | 0.653776i | \(-0.773184\pi\) |
0.944531 | + | 0.328424i | \(0.106517\pi\) | |||||||
\(228\) | −2.73205 | + | 4.73205i | −0.180934 | + | 0.313388i | ||||
\(229\) | −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 | \(0.147299\pi\) | |||||||
\(234\) | 15.4641 | + | 23.1962i | 1.01092 | + | 1.51638i | ||||
\(235\) | −11.1962 | − | 19.3923i | −0.730356 | − | 1.26501i | ||||
\(236\) | 3.63397 | + | 6.29423i | 0.236552 | + | 0.409719i | ||||
\(237\) | 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 | \(0.670774\pi\) | |||||||
\(240\) | −23.6603 | −1.52726 | ||||||||
\(241\) | −10.5981 | + | 18.3564i | −0.682682 | + | 1.18244i | 0.291477 | + | 0.956578i | \(0.405853\pi\) |
−0.974159 | + | 0.225862i | \(0.927480\pi\) | |||||||
\(242\) | 8.13397 | + | 14.0885i | 0.522872 | + | 0.905640i | ||||
\(243\) | 18.7321 | 1.20166 | ||||||||
\(244\) | −2.40192 | + | 4.16025i | −0.153767 | + | 0.266333i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −24.5885 | −1.56770 | ||||||||
\(247\) | 7.19615 | − | 0.464102i | 0.457880 | − | 0.0295301i | ||||
\(248\) | −3.63397 | − | 6.29423i | −0.230758 | − | 0.399684i | ||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | −10.5000 | − | 18.1865i | −0.664078 | − | 1.15022i | ||||
\(251\) | −0.803848 | − | 1.39230i | −0.0507384 | − | 0.0878815i | 0.839541 | − | 0.543297i | \(-0.182824\pi\) |
−0.890279 | + | 0.455415i | \(0.849491\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.00000 | − | 5.19615i | −0.188608 | − | 0.326679i | ||||
\(254\) | 31.8564 | 1.99885 | ||||||||
\(255\) | −18.2942 | − | 31.6865i | −1.14563 | − | 1.98429i | ||||
\(256\) | −9.50000 | + | 16.4545i | −0.593750 | + | 1.02841i | ||||
\(257\) | 3.06218 | + | 5.30385i | 0.191013 | + | 0.330845i | 0.945586 | − | 0.325371i | \(-0.105489\pi\) |
−0.754573 | + | 0.656216i | \(0.772156\pi\) | |||||||
\(258\) | −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 | ||||
\(262\) | 6.00000 | 0.370681 | ||||||||
\(263\) | 1.26795 | 0.0781851 | 0.0390925 | − | 0.999236i | \(-0.487553\pi\) | ||||
0.0390925 | + | 0.999236i | \(0.487553\pi\) | |||||||
\(264\) | 6.00000 | 0.369274 | ||||||||
\(265\) | 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 | ||||
\(269\) | 2.53590 | − | 4.39230i | 0.154616 | − | 0.267804i | −0.778303 | − | 0.627889i | \(-0.783919\pi\) |
0.932919 | + | 0.360086i | \(0.117252\pi\) | |||||||
\(270\) | 12.0000 | 0.730297 | ||||||||
\(271\) | 2.90192 | + | 5.02628i | 0.176279 | + | 0.305325i | 0.940603 | − | 0.339508i | \(-0.110260\pi\) |
−0.764324 | + | 0.644832i | \(0.776927\pi\) | |||||||
\(272\) | −38.6603 | −2.34412 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.9808 | 0.844609 | ||||||||
\(275\) | 1.26795 | + | 2.19615i | 0.0764602 | + | 0.132433i | ||||
\(276\) | −12.9282 | −0.778186 | ||||||||
\(277\) | −8.50000 | + | 14.7224i | −0.510716 | + | 0.884585i | 0.489207 | + | 0.872167i | \(0.337286\pi\) |
−0.999923 | + | 0.0124177i | \(0.996047\pi\) | |||||||
\(278\) | −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 | \(0.369198\pi\) | |||||||
\(282\) | 61.1769 | 3.64303 | ||||||||
\(283\) | −10.1962 | −0.606098 | −0.303049 | − | 0.952975i | \(-0.598005\pi\) | ||||
−0.303049 | + | 0.952975i | \(0.598005\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 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 | ||||
\(289\) | −21.3923 | − | 37.0526i | −1.25837 | − | 2.17956i | ||||
\(290\) | −4.50000 | + | 7.79423i | −0.264249 | + | 0.457693i | ||||
\(291\) | −8.73205 | − | 15.1244i | −0.511882 | − | 0.886605i | ||||
\(292\) | 3.19615 | 0.187041 | ||||||||
\(293\) | −0.401924 | − | 0.696152i | −0.0234806 | − | 0.0406697i | 0.854046 | − | 0.520197i | \(-0.174141\pi\) |
−0.877527 | + | 0.479527i | \(0.840808\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.29423 | − | 10.9019i | −0.366464 | − | 0.634735i | ||||
\(296\) | −6.06218 | − | 10.5000i | −0.352357 | − | 0.610300i | ||||
\(297\) | −5.07180 | −0.294295 | ||||||||
\(298\) | 5.59808 | + | 9.69615i | 0.324288 | + | 0.561683i | ||||
\(299\) | 9.46410 | + | 14.1962i | 0.547323 | + | 0.820985i | ||||
\(300\) | 5.46410 | 0.315470 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.73205 | + | 3.00000i | −0.0996683 | + | 0.172631i | ||||
\(303\) | −21.1244 | −1.21356 | ||||||||
\(304\) | −5.00000 | − | 8.66025i | −0.286770 | − | 0.496700i | ||||
\(305\) | 4.16025 | − | 7.20577i | 0.238215 | − | 0.412601i | ||||
\(306\) | 59.7846 | 3.41766 | ||||||||
\(307\) | 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 | ||||
\(310\) | −6.29423 | − | 10.9019i | −0.357488 | − | 0.619188i | ||||
\(311\) | 0.633975 | + | 1.09808i | 0.0359494 | + | 0.0622662i | 0.883440 | − | 0.468544i | \(-0.155221\pi\) |
−0.847491 | + | 0.530810i | \(0.821888\pi\) | |||||||
\(312\) | −17.0263 | + | 1.09808i | −0.963923 | + | 0.0621663i | ||||
\(313\) | 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 | \(0.108562\pi\) | |||||||
\(318\) | −23.4904 | + | 40.6865i | −1.31728 | + | 2.28159i | ||||
\(319\) | 1.90192 | − | 3.29423i | 0.106487 | − | 0.184441i | ||||
\(320\) | 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 | ||||
\(325\) | −4.00000 | − | 6.00000i | −0.221880 | − | 0.332820i | ||||
\(326\) | −14.0263 | − | 24.2942i | −0.776844 | − | 1.34553i | ||||
\(327\) | −11.4641 | − | 19.8564i | −0.633966 | − | 1.09806i | ||||
\(328\) | 4.50000 | − | 7.79423i | 0.248471 | − | 0.430364i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 10.3923 | 0.572078 | ||||||||
\(331\) | 24.9808 | 1.37307 | 0.686533 | − | 0.727098i | \(-0.259132\pi\) | ||||
0.686533 | + | 0.727098i | \(0.259132\pi\) | |||||||
\(332\) | −1.09808 | + | 1.90192i | −0.0602648 | + | 0.104382i | ||||
\(333\) | 15.6244 | + | 27.0622i | 0.856209 | + | 1.48300i | ||||
\(334\) | 11.4115 | 0.624412 | ||||||||
\(335\) | −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 | \(0.403145\pi\) | |||||||
\(338\) | −13.6699 | − | 17.8923i | −0.743543 | − | 0.973213i | ||||
\(339\) | 18.2942 | + | 31.6865i | 0.993606 | + | 1.72098i | ||||
\(340\) | −13.3923 | −0.726300 | ||||||||
\(341\) | 2.66025 | + | 4.60770i | 0.144061 | + | 0.249521i | ||||
\(342\) | 7.73205 | + | 13.3923i | 0.418101 | + | 0.724173i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.169873 | − | 0.294229i | −0.00915894 | − | 0.0158637i | ||||
\(345\) | 22.3923 | 1.20556 | ||||||||
\(346\) | 7.39230 | + | 12.8038i | 0.397413 | + | 0.688339i | ||||
\(347\) | −3.63397 | + | 6.29423i | −0.195082 | + | 0.337892i | −0.946927 | − | 0.321448i | \(-0.895831\pi\) |
0.751845 | + | 0.659339i | \(0.229164\pi\) | |||||||
\(348\) | −4.09808 | − | 7.09808i | −0.219680 | − | 0.380497i | ||||
\(349\) | −12.3923 | + | 21.4641i | −0.663345 | + | 1.14895i | 0.316386 | + | 0.948630i | \(0.397530\pi\) |
−0.979731 | + | 0.200317i | \(0.935803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.3923 | − | 0.928203i | 0.768204 | − | 0.0495438i | ||||
\(352\) | 3.29423 | − | 5.70577i | 0.175583 | − | 0.304119i | ||||
\(353\) | −20.6603 | −1.09963 | −0.549817 | − | 0.835285i | \(-0.685303\pi\) | ||||
−0.549817 | + | 0.835285i | \(0.685303\pi\) | |||||||
\(354\) | 34.3923 | 1.82793 | ||||||||
\(355\) | −10.3923 | −0.551566 | ||||||||
\(356\) | −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 | \(0.333148\pi\) | |||||||
\(360\) | −6.69615 | + | 11.5981i | −0.352918 | + | 0.611272i | ||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 4.83975 | + | 8.38269i | 0.254371 | + | 0.440584i | ||||
\(363\) | 25.6603 | 1.34681 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.53590 | −0.289762 | ||||||||
\(366\) | 11.3660 | + | 19.6865i | 0.594112 | + | 1.02903i | ||||
\(367\) | −4.19615 | −0.219037 | −0.109519 | − | 0.993985i | \(-0.534931\pi\) | ||||
−0.109519 | + | 0.993985i | \(0.534931\pi\) | |||||||
\(368\) | 11.8301 | − | 20.4904i | 0.616688 | − | 1.06813i | ||||
\(369\) | −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 | ||||||||
\(373\) | −11.3923 | −0.589871 | −0.294936 | − | 0.955517i | \(-0.595298\pi\) | ||||
−0.294936 | + | 0.955517i | \(0.595298\pi\) | |||||||
\(374\) | 16.9808 | 0.878054 | ||||||||
\(375\) | −33.1244 | −1.71053 | ||||||||
\(376\) | −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 | 0.291220 | + | 0.956656i | \(0.405939\pi\) |
−0.974098 | + | 0.226124i | \(0.927394\pi\) | |||||||
\(380\) | −1.73205 | − | 3.00000i | −0.0888523 | − | 0.153897i | ||||
\(381\) | 25.1244 | − | 43.5167i | 1.28716 | − | 2.22943i | ||||
\(382\) | −4.09808 | − | 7.09808i | −0.209676 | − | 0.363169i | ||||
\(383\) | 11.6603 | 0.595811 | 0.297906 | − | 0.954595i | \(-0.403712\pi\) | ||||
0.297906 | + | 0.954595i | \(0.403712\pi\) | |||||||
\(384\) | 16.5622 | + | 28.6865i | 0.845185 | + | 1.46390i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.33013 | − | 7.50000i | −0.220398 | − | 0.381740i | ||||
\(387\) | 0.437822 | + | 0.758330i | 0.0222558 | + | 0.0385481i | ||||
\(388\) | −6.39230 | −0.324520 | ||||||||
\(389\) | 11.7679 | + | 20.3827i | 0.596659 | + | 1.03344i | 0.993310 | + | 0.115474i | \(0.0368387\pi\) |
−0.396652 | + | 0.917969i | \(0.629828\pi\) | |||||||
\(390\) | −29.4904 | + | 1.90192i | −1.49330 | + | 0.0963077i | ||||
\(391\) | 36.5885 | 1.85036 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.73205 | − | 8.19615i | 0.238700 | − | 0.413441i | ||||
\(394\) | 20.7846 | 1.04711 | ||||||||
\(395\) | 14.0263 | + | 24.2942i | 0.705739 | + | 1.22238i | ||||
\(396\) | −2.83013 | + | 4.90192i | −0.142219 | + | 0.246331i | ||||
\(397\) | 18.7846 | 0.942773 | 0.471386 | − | 0.881927i | \(-0.343754\pi\) | ||||
0.471386 | + | 0.881927i | \(0.343754\pi\) | |||||||
\(398\) | −3.46410 | −0.173640 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | + | 8.66025i | −0.250000 | + | 0.433013i | ||||
\(401\) | 5.42820 | + | 9.40192i | 0.271072 | + | 0.469510i | 0.969136 | − | 0.246525i | \(-0.0792887\pi\) |
−0.698065 | + | 0.716034i | \(0.745955\pi\) | |||||||
\(402\) | −14.6603 | − | 25.3923i | −0.731187 | − | 1.26645i | ||||
\(403\) | −8.39230 | − | 12.5885i | −0.418050 | − | 0.627076i | ||||
\(404\) | −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 | ||||
\(409\) | −8.40192 | + | 14.5526i | −0.415448 | + | 0.719578i | −0.995475 | − | 0.0950195i | \(-0.969709\pi\) |
0.580027 | + | 0.814597i | \(0.303042\pi\) | |||||||
\(410\) | 7.79423 | − | 13.5000i | 0.384930 | − | 0.666717i | ||||
\(411\) | 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 | ||||
\(416\) | −8.30385 | + | 16.7942i | −0.407130 | + | 0.823405i | ||||
\(417\) | 14.4641 | + | 25.0526i | 0.708310 | + | 1.22683i | ||||
\(418\) | 2.19615 | + | 3.80385i | 0.107417 | + | 0.186052i | ||||
\(419\) | −16.0981 | + | 27.8827i | −0.786442 | + | 1.36216i | 0.141691 | + | 0.989911i | \(0.454746\pi\) |
−0.928134 | + | 0.372247i | \(0.878587\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.1769 | −1.56821 | −0.784103 | − | 0.620630i | \(-0.786877\pi\) | ||||
−0.784103 | + | 0.620630i | \(0.786877\pi\) | |||||||
\(422\) | −3.12436 | −0.152091 | ||||||||
\(423\) | 28.8564 | − | 49.9808i | 1.40305 | − | 2.43015i | ||||
\(424\) | −8.59808 | − | 14.8923i | −0.417559 | − | 0.723234i | ||||
\(425\) | −15.4641 | −0.750119 | ||||||||
\(426\) | 14.1962 | − | 24.5885i | 0.687806 | − | 1.19131i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.85641 | −0.379754 | ||||||||
\(429\) | 12.4641 | − | 0.803848i | 0.601772 | − | 0.0388101i | ||||
\(430\) | −0.294229 | − | 0.509619i | −0.0141890 | − | 0.0245760i | ||||
\(431\) | 0.679492 | 0.0327300 | 0.0163650 | − | 0.999866i | \(-0.494791\pi\) | ||||
0.0163650 | + | 0.999866i | \(0.494791\pi\) | |||||||
\(432\) | −10.0000 | − | 17.3205i | −0.481125 | − | 0.833333i | ||||
\(433\) | −6.79423 | − | 11.7679i | −0.326510 | − | 0.565532i | 0.655307 | − | 0.755363i | \(-0.272539\pi\) |
−0.981817 | + | 0.189831i | \(0.939206\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.09808 | + | 12.2942i | 0.340327 | + | 0.589463i | ||||
\(436\) | −8.39230 | −0.401919 | ||||||||
\(437\) | 4.73205 | + | 8.19615i | 0.226365 | + | 0.392075i | ||||
\(438\) | 7.56218 | − | 13.0981i | 0.361335 | − | 0.625850i | ||||
\(439\) | 7.29423 | + | 12.6340i | 0.348135 | + | 0.602987i | 0.985918 | − | 0.167229i | \(-0.0534819\pi\) |
−0.637784 | + | 0.770216i | \(0.720149\pi\) | |||||||
\(440\) | −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 | \(0.979769\pi\) | |||||||
\(444\) | 19.1244 | 0.907602 | ||||||||
\(445\) | 22.3923 | 1.06150 | ||||||||
\(446\) | 17.3205 | 0.820150 | ||||||||
\(447\) | 17.6603 | 0.835301 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | + | 10.3923i | 0.283158 | + | 0.490443i | 0.972161 | − | 0.234315i | \(-0.0752847\pi\) |
−0.689003 | + | 0.724758i | \(0.741951\pi\) | |||||||
\(450\) | 7.73205 | − | 13.3923i | 0.364492 | − | 0.631319i | ||||
\(451\) | −3.29423 | + | 5.70577i | −0.155119 | + | 0.268674i | ||||
\(452\) | 13.3923 | 0.629921 | ||||||||
\(453\) | 2.73205 | + | 4.73205i | 0.128363 | + | 0.222331i | ||||
\(454\) | −9.80385 | −0.460117 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.46410 | −0.443197 | ||||||||
\(457\) | −5.50000 | − | 9.52628i | −0.257279 | − | 0.445621i | 0.708233 | − | 0.705979i | \(-0.249493\pi\) |
−0.965512 | + | 0.260358i | \(0.916159\pi\) | |||||||
\(458\) | 24.9282 | 1.16482 | ||||||||
\(459\) | 15.4641 | − | 26.7846i | 0.721802 | − | 1.25020i | ||||
\(460\) | 4.09808 | − | 7.09808i | 0.191074 | − | 0.330950i | ||||
\(461\) | −7.79423 | − | 13.5000i | −0.363013 | − | 0.628758i | 0.625442 | − | 0.780271i | \(-0.284919\pi\) |
−0.988455 | + | 0.151513i | \(0.951585\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.58846 | −0.213244 | −0.106622 | − | 0.994300i | \(-0.534003\pi\) | ||||
−0.106622 | + | 0.994300i | \(0.534003\pi\) | |||||||
\(464\) | 15.0000 | 0.696358 | ||||||||
\(465\) | −19.8564 | −0.920819 | ||||||||
\(466\) | −3.21539 | −0.148950 | ||||||||
\(467\) | 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 | ||||
\(471\) | −1.63397 | − | 2.83013i | −0.0752896 | − | 0.130405i | ||||
\(472\) | −6.29423 | + | 10.9019i | −0.289715 | + | 0.501802i | ||||
\(473\) | 0.124356 | + | 0.215390i | 0.00571788 | + | 0.00990366i | ||||
\(474\) | −76.6410 | −3.52024 | ||||||||
\(475\) | −2.00000 | − | 3.46410i | −0.0917663 | − | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.1603 | + | 38.3827i | 1.01465 | + | 1.75742i | ||||
\(478\) | 13.6865 | + | 23.7058i | 0.626007 | + | 1.08428i | ||||
\(479\) | −1.26795 | −0.0579341 | −0.0289670 | − | 0.999580i | \(-0.509222\pi\) | ||||
−0.0289670 | + | 0.999580i | \(0.509222\pi\) | |||||||
\(480\) | 12.2942 | + | 21.2942i | 0.561152 | + | 0.971944i | ||||
\(481\) | −14.0000 | − | 21.0000i | −0.638345 | − | 0.957518i | ||||
\(482\) | 36.7128 | 1.67222 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.69615 | − | 8.13397i | 0.213461 | − | 0.369726i | ||||
\(485\) | 11.0718 | 0.502744 | ||||||||
\(486\) | −16.2224 | − | 28.0981i | −0.735864 | − | 1.27455i | ||||
\(487\) | −20.3923 | + | 35.3205i | −0.924064 | + | 1.60052i | −0.131003 | + | 0.991382i | \(0.541820\pi\) |
−0.793060 | + | 0.609143i | \(0.791514\pi\) | |||||||
\(488\) | −8.32051 | −0.376652 | ||||||||
\(489\) | −44.2487 | −2.00100 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.80385 | + | 6.58846i | −0.171665 | + | 0.297333i | −0.939002 | − | 0.343911i | \(-0.888248\pi\) |
0.767337 | + | 0.641244i | \(0.221581\pi\) | |||||||
\(492\) | 7.09808 | + | 12.2942i | 0.320006 | + | 0.554267i | ||||
\(493\) | 11.5981 | + | 20.0885i | 0.522351 | + | 0.904739i | ||||
\(494\) | −6.92820 | − | 10.3923i | −0.311715 | − | 0.467572i | ||||
\(495\) | 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 | \(-0.170842\pi\) | |||||||
\(500\) | −6.06218 | + | 10.5000i | −0.271109 | + | 0.469574i | ||||
\(501\) | 9.00000 | − | 15.5885i | 0.402090 | − | 0.696441i | ||||
\(502\) | −1.39230 | + | 2.41154i | −0.0621416 | + | 0.107632i | ||||
\(503\) | −9.29423 | − | 16.0981i | −0.414409 | − | 0.717778i | 0.580957 | − | 0.813934i | \(-0.302678\pi\) |
−0.995366 | + | 0.0961565i | \(0.969345\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.69615 | − | 11.5981i | 0.297975 | − | 0.516108i | ||||
\(506\) | −5.19615 | + | 9.00000i | −0.230997 | + | 0.400099i | ||||
\(507\) | −35.2224 | + | 4.56218i | −1.56428 | + | 0.202613i | ||||
\(508\) | −9.19615 | − | 15.9282i | −0.408013 | − | 0.706700i | ||||
\(509\) | 6.86603 | + | 11.8923i | 0.304331 | + | 0.527117i | 0.977112 | − | 0.212725i | \(-0.0682337\pi\) |
−0.672781 | + | 0.739842i | \(0.734900\pi\) | |||||||
\(510\) | −31.6865 | + | 54.8827i | −1.40310 | + | 2.43025i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8.66025 | 0.382733 | ||||||||
\(513\) | 8.00000 | 0.353209 | ||||||||
\(514\) | 5.30385 | − | 9.18653i | 0.233943 | − | 0.405201i | ||||
\(515\) | 12.4641 | + | 21.5885i | 0.549234 | + | 0.951301i | ||||
\(516\) | 0.535898 | 0.0235916 | ||||||||
\(517\) | 8.19615 | − | 14.1962i | 0.360466 | − | 0.624346i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.3205 | 1.02366 | ||||||||
\(520\) | 4.79423 | − | 9.69615i | 0.210241 | − | 0.425204i | ||||
\(521\) | −12.0622 | − | 20.8923i | −0.528454 | − | 0.915308i | −0.999450 | − | 0.0331732i | \(-0.989439\pi\) |
0.470996 | − | 0.882135i | \(-0.343895\pi\) | |||||||
\(522\) | −23.1962 | −1.01527 | ||||||||
\(523\) | −14.5885 | − | 25.2679i | −0.637909 | − | 1.10489i | −0.985891 | − | 0.167389i | \(-0.946466\pi\) |
0.347982 | − | 0.937501i | \(-0.386867\pi\) | |||||||
\(524\) | −1.73205 | − | 3.00000i | −0.0756650 | − | 0.131056i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.09808 | − | 1.90192i | −0.0478784 | − | 0.0829278i | ||||
\(527\) | −32.4449 | −1.41332 | ||||||||
\(528\) | −8.66025 | − | 15.0000i | −0.376889 | − | 0.652791i | ||||
\(529\) | 0.303848 | − | 0.526279i | 0.0132108 | − | 0.0228817i | ||||
\(530\) | −14.8923 | − | 25.7942i | −0.646880 | − | 1.12043i | ||||
\(531\) | 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 | ||||
\(535\) | 13.6077 | 0.588312 | ||||||||
\(536\) | 10.7321 | 0.463554 | ||||||||
\(537\) | 18.9282 | 0.816812 | ||||||||
\(538\) | −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 | \(0.0649918\pi\) | |||||||
\(542\) | 5.02628 | − | 8.70577i | 0.215897 | − | 0.373945i | ||||
\(543\) | 15.2679 | 0.655210 | ||||||||
\(544\) | 20.0885 | + | 34.7942i | 0.861285 | + | 1.49179i | ||||
\(545\) | 14.5359 | 0.622649 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.8038 | 0.761238 | 0.380619 | − | 0.924732i | \(-0.375711\pi\) | ||||
0.380619 | + | 0.924732i | \(0.375711\pi\) | |||||||
\(548\) | −4.03590 | − | 6.99038i | −0.172405 | − | 0.298614i | ||||
\(549\) | 21.4449 | 0.915244 | ||||||||
\(550\) | 2.19615 | − | 3.80385i | 0.0936443 | − | 0.162197i | ||||
\(551\) | −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 | ||||||||
\(555\) | −33.1244 | −1.40605 | ||||||||
\(556\) | 10.5885 | 0.449051 | ||||||||
\(557\) | 43.6410 | 1.84913 | 0.924565 | − | 0.381025i | \(-0.124429\pi\) | ||||
0.924565 | + | 0.381025i | \(0.124429\pi\) | |||||||
\(558\) | 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 | ||||
\(562\) | −11.5981 | − | 20.0885i | −0.489235 | − | 0.847380i | ||||
\(563\) | 14.0263 | − | 24.2942i | 0.591137 | − | 1.02388i | −0.402942 | − | 0.915225i | \(-0.632013\pi\) |
0.994080 | − | 0.108654i | \(-0.0346542\pi\) | |||||||
\(564\) | −17.6603 | − | 30.5885i | −0.743631 | − | 1.28801i | ||||
\(565\) | −23.1962 | −0.975869 | ||||||||
\(566\) | 8.83013 | + | 15.2942i | 0.371158 | + | 0.642864i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.19615 | + | 9.00000i | 0.218026 | + | 0.377632i | ||||
\(569\) | −21.4641 | − | 37.1769i | −0.899822 | − | 1.55854i | −0.827721 | − | 0.561140i | \(-0.810363\pi\) |
−0.0721010 | − | 0.997397i | \(-0.522970\pi\) | |||||||
\(570\) | −16.3923 | −0.686598 | ||||||||
\(571\) | −8.39230 | − | 14.5359i | −0.351207 | − | 0.608308i | 0.635254 | − | 0.772303i | \(-0.280895\pi\) |
−0.986461 | + | 0.163995i | \(0.947562\pi\) | |||||||
\(572\) | 2.02628 | − | 4.09808i | 0.0847230 | − | 0.171349i | ||||
\(573\) | −12.9282 | −0.540083 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.73205 | − | 8.19615i | 0.197340 | − | 0.341803i | ||||
\(576\) | 4.46410 | 0.186004 | ||||||||
\(577\) | 21.5981 | + | 37.4090i | 0.899140 | + | 1.55736i | 0.828596 | + | 0.559847i | \(0.189140\pi\) |
0.0705436 | + | 0.997509i | \(0.477527\pi\) | |||||||
\(578\) | −37.0526 | + | 64.1769i | −1.54118 | + | 2.66941i | ||||
\(579\) | −13.6603 | −0.567701 | ||||||||
\(580\) | 5.19615 | 0.215758 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −15.1244 | + | 26.1962i | −0.626925 | + | 1.08587i | ||||
\(583\) | 6.29423 | + | 10.9019i | 0.260680 | + | 0.451512i | ||||
\(584\) | 2.76795 | + | 4.79423i | 0.114539 | + | 0.198387i | ||||
\(585\) | −12.3564 | + | 24.9904i | −0.510875 | + | 1.03323i | ||||
\(586\) | −0.696152 | + | 1.20577i | −0.0287578 | + | 0.0498100i | ||||
\(587\) | 8.19615 | − | 14.1962i | 0.338291 | − | 0.585938i | −0.645820 | − | 0.763490i | \(-0.723484\pi\) |
0.984111 | + | 0.177552i | \(0.0568177\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.19615 | − | 7.26795i | −0.172899 | − | 0.299471i | ||||
\(590\) | −10.9019 | + | 18.8827i | −0.448825 | + | 0.777388i | ||||
\(591\) | 16.3923 | − | 28.3923i | 0.674289 | − | 1.16790i | ||||
\(592\) | −17.5000 | + | 30.3109i | −0.719246 | + | 1.24577i | ||||
\(593\) | −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 | ||||
\(598\) | 13.0981 | − | 26.4904i | 0.535620 | − | 1.08327i | ||||
\(599\) | −21.9282 | − | 37.9808i | −0.895962 | − | 1.55185i | −0.832609 | − | 0.553861i | \(-0.813154\pi\) |
−0.0633527 | − | 0.997991i | \(-0.520179\pi\) | |||||||
\(600\) | 4.73205 | + | 8.19615i | 0.193185 | + | 0.334607i | ||||
\(601\) | −14.9904 | + | 25.9641i | −0.611470 | + | 1.05910i | 0.379522 | + | 0.925183i | \(0.376088\pi\) |
−0.990993 | + | 0.133915i | \(0.957245\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.6603 | −1.12641 | ||||||||
\(604\) | 2.00000 | 0.0813788 | ||||||||
\(605\) | −8.13397 | + | 14.0885i | −0.330693 | + | 0.572777i | ||||
\(606\) | 18.2942 | + | 31.6865i | 0.743152 | + | 1.28718i | ||||
\(607\) | 14.3923 | 0.584166 | 0.292083 | − | 0.956393i | \(-0.405652\pi\) | ||||
0.292083 | + | 0.956393i | \(0.405652\pi\) | |||||||
\(608\) | −5.19615 | + | 9.00000i | −0.210732 | + | 0.364998i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.4115 | −0.583506 | ||||||||
\(611\) | −20.6603 | + | 41.7846i | −0.835824 | + | 1.69042i | ||||
\(612\) | −17.2583 | − | 29.8923i | −0.697627 | − | 1.20832i | ||||
\(613\) | 3.39230 | 0.137014 | 0.0685070 | − | 0.997651i | \(-0.478176\pi\) | ||||
0.0685070 | + | 0.997651i | \(0.478176\pi\) | |||||||
\(614\) | −3.97372 | − | 6.88269i | −0.160366 | − | 0.277763i | ||||
\(615\) | −12.2942 | − | 21.2942i | −0.495751 | − | 0.858666i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.6962 | − | 42.7750i | −0.994230 | − | 1.72206i | −0.590016 | − | 0.807392i | \(-0.700878\pi\) |
−0.404214 | − | 0.914664i | \(-0.632455\pi\) | |||||||
\(618\) | −68.1051 | −2.73959 | ||||||||
\(619\) | 17.6865 | + | 30.6340i | 0.710882 | + | 1.23128i | 0.964527 | + | 0.263986i | \(0.0850373\pi\) |
−0.253645 | + | 0.967297i | \(0.581629\pi\) | |||||||
\(620\) | −3.63397 | + | 6.29423i | −0.145944 | + | 0.252782i | ||||
\(621\) | 9.46410 | + | 16.3923i | 0.379781 | + | 0.657801i | ||||
\(622\) | 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 | ||||
\(626\) | −49.8564 | −1.99266 | ||||||||
\(627\) | 6.92820 | 0.276686 | ||||||||
\(628\) | −1.19615 | −0.0477317 | ||||||||
\(629\) | −54.1244 | −2.15808 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.39230 | + | 11.0718i | 0.254474 | + | 0.440761i | 0.964752 | − | 0.263159i | \(-0.0847645\pi\) |
−0.710279 | + | 0.703920i | \(0.751431\pi\) | |||||||
\(632\) | 14.0263 | − | 24.2942i | 0.557935 | − | 0.966373i | ||||
\(633\) | −2.46410 | + | 4.26795i | −0.0979392 | + | 0.169636i | ||||
\(634\) | −11.1962 | −0.444656 | ||||||||
\(635\) | 15.9282 | + | 27.5885i | 0.632091 | + | 1.09481i | ||||
\(636\) | 27.1244 | 1.07555 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.58846 | −0.260840 | ||||||||
\(639\) | −13.3923 | − | 23.1962i | −0.529791 | − | 0.917626i | ||||
\(640\) | −21.0000 | −0.830098 | ||||||||
\(641\) | −14.4282 | + | 24.9904i | −0.569880 | + | 0.987061i | 0.426698 | + | 0.904394i | \(0.359677\pi\) |
−0.996577 | + | 0.0826663i | \(0.973656\pi\) | |||||||
\(642\) | −18.5885 | + | 32.1962i | −0.733628 | + | 1.27068i | ||||
\(643\) | −0.392305 | − | 0.679492i | −0.0154710 | − | 0.0267965i | 0.858186 | − | 0.513338i | \(-0.171591\pi\) |
−0.873657 | + | 0.486542i | \(0.838258\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.928203 | −0.0365480 | ||||||||
\(646\) | −26.7846 | −1.05383 | ||||||||
\(647\) | −45.0333 | −1.77044 | −0.885221 | − | 0.465170i | \(-0.845993\pi\) | ||||
−0.885221 | + | 0.465170i | \(0.845993\pi\) | |||||||
\(648\) | 4.26795 | 0.167661 | ||||||||
\(649\) | 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 | ||||
\(653\) | 18.9282 | + | 32.7846i | 0.740718 | + | 1.28296i | 0.952169 | + | 0.305572i | \(0.0988478\pi\) |
−0.211451 | + | 0.977389i | \(0.567819\pi\) | |||||||
\(654\) | −19.8564 | + | 34.3923i | −0.776447 | + | 1.34485i | ||||
\(655\) | 3.00000 | + | 5.19615i | 0.117220 | + | 0.203030i | ||||
\(656\) | −25.9808 | −1.01438 | ||||||||
\(657\) | −7.13397 | − | 12.3564i | −0.278323 | − | 0.482069i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.1962 | − | 24.5885i | −0.553004 | − | 0.957830i | −0.998056 | − | 0.0623257i | \(-0.980148\pi\) |
0.445052 | − | 0.895505i | \(-0.353185\pi\) | |||||||
\(660\) | −3.00000 | − | 5.19615i | −0.116775 | − | 0.202260i | ||||
\(661\) | 33.1962 | 1.29118 | 0.645590 | − | 0.763684i | \(-0.276611\pi\) | ||||
0.645590 | + | 0.763684i | \(0.276611\pi\) | |||||||
\(662\) | −21.6340 | − | 37.4711i | −0.840828 | − | 1.45636i | ||||
\(663\) | −33.7583 | + | 68.2750i | −1.31106 | + | 2.65158i | ||||
\(664\) | −3.80385 | −0.147618 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 27.0622 | − | 46.8731i | 1.04864 | − | 1.81629i | ||||
\(667\) | −14.1962 | −0.549677 | ||||||||
\(668\) | −3.29423 | − | 5.70577i | −0.127458 | − | 0.220763i | ||||
\(669\) | 13.6603 | − | 23.6603i | 0.528136 | − | 0.914758i | ||||
\(670\) | 18.5885 | 0.718135 | ||||||||
\(671\) | 6.09103 | 0.235142 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0885 | − | 38.2583i | 0.851447 | − | 1.47475i | −0.0284546 | − | 0.999595i | \(-0.509059\pi\) |
0.879902 | − | 0.475155i | \(-0.157608\pi\) | |||||||
\(674\) | −9.52628 | − | 16.5000i | −0.366939 | − | 0.635556i | ||||
\(675\) | −4.00000 | − | 6.92820i | −0.153960 | − | 0.266667i | ||||
\(676\) | −5.00000 | + | 12.0000i | −0.192308 | + | 0.461538i | ||||
\(677\) | −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 | ||||
\(682\) | 4.60770 | − | 7.98076i | 0.176438 | − | 0.305599i | ||||
\(683\) | −7.73205 | + | 13.3923i | −0.295859 | + | 0.512442i | −0.975184 | − | 0.221395i | \(-0.928939\pi\) |
0.679326 | + | 0.733837i | \(0.262272\pi\) | |||||||
\(684\) | 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 | ||||
\(689\) | −19.8564 | − | 29.7846i | −0.756469 | − | 1.13470i | ||||
\(690\) | −19.3923 | − | 33.5885i | −0.738252 | − | 1.27869i | ||||
\(691\) | 0.196152 | + | 0.339746i | 0.00746199 | + | 0.0129245i | 0.869732 | − | 0.493524i | \(-0.164291\pi\) |
−0.862270 | + | 0.506448i | \(0.830958\pi\) | |||||||
\(692\) | 4.26795 | − | 7.39230i | 0.162243 | − | 0.281013i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.5885 | 0.477851 | ||||||||
\(695\) | −18.3397 | −0.695666 | ||||||||
\(696\) | 7.09808 | − | 12.2942i | 0.269052 | − | 0.466012i | ||||
\(697\) | −20.0885 | − | 34.7942i | −0.760905 | − | 1.31793i | ||||
\(698\) | 42.9282 | 1.62486 | ||||||||
\(699\) | −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 | \(0.371606\pi\) | |||||||
\(702\) | −13.8564 | − | 20.7846i | −0.522976 | − | 0.784465i | ||||
\(703\) | −7.00000 | − | 12.1244i | −0.264010 | − | 0.457279i | ||||
\(704\) | 1.26795 | 0.0477876 | ||||||||
\(705\) | 30.5885 | + | 52.9808i | 1.15203 | + | 1.99537i | ||||
\(706\) | 17.8923 | + | 30.9904i | 0.673386 | + | 1.16634i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.92820 | − | 17.1962i | −0.373125 | − | 0.646271i | ||||
\(709\) | 30.1769 | 1.13332 | 0.566659 | − | 0.823952i | \(-0.308236\pi\) | ||||
0.566659 | + | 0.823952i | \(0.308236\pi\) | |||||||
\(710\) | 9.00000 | + | 15.5885i | 0.337764 | + | 0.585024i | ||||
\(711\) | −36.1506 | + | 62.6147i | −1.35575 | + | 2.34824i | ||||
\(712\) | −11.1962 | − | 19.3923i | −0.419594 | − | 0.726757i | ||||
\(713\) | 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 | ||||
\(717\) | 43.1769 | 1.61247 | ||||||||
\(718\) | 32.7846 | 1.22351 | ||||||||
\(719\) | 7.26795 | 0.271049 | 0.135524 | − | 0.990774i | \(-0.456728\pi\) | ||||
0.135524 | + | 0.990774i | \(0.456728\pi\) | |||||||
\(720\) | 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 | ||||
\(724\) | 2.79423 | − | 4.83975i | 0.103847 | − | 0.179868i | ||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | −22.2224 | − | 38.4904i | −0.824752 | − | 1.42851i | ||||
\(727\) | 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 | ||||||||
\(730\) | 4.79423 | + | 8.30385i | 0.177442 | + | 0.307339i | ||||
\(731\) | −1.51666 | −0.0560957 | ||||||||
\(732\) | 6.56218 | − | 11.3660i | 0.242545 | − | 0.420100i | ||||
\(733\) | 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 | ||||||||
\(737\) | −7.85641 | −0.289394 | ||||||||
\(738\) | 40.1769 | 1.47893 | ||||||||
\(739\) | 40.7846 | 1.50029 | 0.750143 | − | 0.661276i | \(-0.229985\pi\) | ||||
0.750143 | + | 0.661276i | \(0.229985\pi\) | |||||||
\(740\) | −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 | −0.787777 | − | 0.615961i | \(-0.788768\pi\) |
0.927326 | + | 0.374254i | \(0.122101\pi\) | |||||||
\(744\) | 9.92820 | + | 17.1962i | 0.363986 | + | 0.630442i | ||||
\(745\) | −5.59808 | + | 9.69615i | −0.205098 | + | 0.355240i | ||||
\(746\) | 9.86603 | + | 17.0885i | 0.361221 | + | 0.625653i | ||||
\(747\) | 9.80385 | 0.358704 | ||||||||
\(748\) | −4.90192 | − | 8.49038i | −0.179232 | − | 0.310439i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 28.6865 | + | 49.6865i | 1.04748 | + | 1.81430i | ||||
\(751\) | −17.9019 | − | 31.0070i | −0.653250 | − | 1.13146i | −0.982329 | − | 0.187161i | \(-0.940072\pi\) |
0.329079 | − | 0.944302i | \(-0.393262\pi\) | |||||||
\(752\) | 64.6410 | 2.35722 | ||||||||
\(753\) | 2.19615 | + | 3.80385i | 0.0800322 | + | 0.138620i | ||||
\(754\) | 18.6962 | − | 1.20577i | 0.680874 | − | 0.0439116i | ||||
\(755\) | −3.46410 | −0.126072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.00000 | − | 13.8564i | 0.290765 | − | 0.503620i | −0.683226 | − | 0.730207i | \(-0.739424\pi\) |
0.973991 | + | 0.226587i | \(0.0727569\pi\) | |||||||
\(758\) | 46.0526 | 1.67270 | ||||||||
\(759\) | 8.19615 | + | 14.1962i | 0.297501 | + | 0.515288i | ||||
\(760\) | 3.00000 | − | 5.19615i | 0.108821 | − | 0.188484i | ||||
\(761\) | −41.3205 | −1.49787 | −0.748934 | − | 0.662645i | \(-0.769434\pi\) | ||||
−0.748934 | + | 0.662645i | \(0.769434\pi\) | |||||||
\(762\) | −87.0333 | −3.15288 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.36603 | + | 4.09808i | −0.0855998 | + | 0.148263i | ||||
\(765\) | 29.8923 | + | 51.7750i | 1.08076 | + | 1.87193i | ||||
\(766\) | −10.0981 | − | 17.4904i | −0.364858 | − | 0.631953i | ||||
\(767\) | −11.6147 | + | 23.4904i | −0.419384 | + | 0.848189i | ||||
\(768\) | 25.9545 | − | 44.9545i | 0.936552 | − | 1.62216i | ||||
\(769\) | 7.58846 | − | 13.1436i | 0.273647 | − | 0.473970i | −0.696146 | − | 0.717900i | \(-0.745103\pi\) |
0.969793 | + | 0.243930i | \(0.0784367\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.36603 | − | 14.4904i | −0.301295 | − | 0.521858i | ||||
\(772\) | −2.50000 | + | 4.33013i | −0.0899770 | + | 0.155845i | ||||
\(773\) | −6.46410 | + | 11.1962i | −0.232498 | + | 0.402698i | −0.958542 | − | 0.284950i | \(-0.908023\pi\) |
0.726045 | + | 0.687647i | \(0.241356\pi\) | |||||||
\(774\) | 0.758330 | − | 1.31347i | 0.0272576 | − | 0.0472116i | ||||
\(775\) | −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 | ||||
\(780\) | 9.46410 | + | 14.1962i | 0.338869 | + | 0.508304i | ||||
\(781\) | −3.80385 | − | 6.58846i | −0.136112 | − | 0.235754i | ||||
\(782\) | −31.6865 | − | 54.8827i | −1.13311 | − | 1.96260i | ||||
\(783\) | −6.00000 | + | 10.3923i | −0.214423 | + | 0.371391i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.07180 | 0.0739456 | ||||||||
\(786\) | −16.3923 | −0.584694 | ||||||||
\(787\) | 6.49038 | − | 11.2417i | 0.231357 | − | 0.400722i | −0.726851 | − | 0.686796i | \(-0.759017\pi\) |
0.958208 | + | 0.286073i | \(0.0923501\pi\) | |||||||
\(788\) | −6.00000 | − | 10.3923i | −0.213741 | − | 0.370211i | ||||
\(789\) | −3.46410 | −0.123325 | ||||||||
\(790\) | 24.2942 | − | 42.0788i | 0.864350 | − | 1.49710i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −9.80385 | −0.348365 | ||||||||
\(793\) | −17.2846 | + | 1.11474i | −0.613794 | + | 0.0395855i | ||||
\(794\) | −16.2679 | − | 28.1769i | −0.577328 | − | 0.999961i | ||||
\(795\) | −46.9808 | −1.66624 | ||||||||
\(796\) | 1.00000 | + | 1.73205i | 0.0354441 | + | 0.0613909i | ||||
\(797\) | −17.1962 | − | 29.7846i | −0.609119 | − | 1.05503i | −0.991386 | − | 0.130973i | \(-0.958190\pi\) |
0.382267 | − | 0.924052i | \(-0.375143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 49.9808 | + | 86.5692i | 1.76819 | + | 3.06260i | ||||
\(800\) | 10.3923 | 0.367423 | ||||||||
\(801\) | 28.8564 | + | 49.9808i | 1.01959 | + | 1.76598i | ||||
\(802\) | 9.40192 | − | 16.2846i | 0.331993 | − | 0.575030i | ||||
\(803\) | −2.02628 | − | 3.50962i | −0.0715058 | − | 0.123852i | ||||
\(804\) | −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 | ||||
\(808\) | −13.3923 | −0.471140 | ||||||||
\(809\) | 2.07180 | 0.0728405 | 0.0364202 | − | 0.999337i | \(-0.488405\pi\) | ||||
0.0364202 | + | 0.999337i | \(0.488405\pi\) | |||||||
\(810\) | 7.39230 | 0.259739 | ||||||||
\(811\) | 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 | ||||
\(815\) | 14.0263 | − | 24.2942i | 0.491319 | − | 0.850990i | ||||
\(816\) | 105.622 | 3.69750 | ||||||||
\(817\) | −0.196152 | − | 0.339746i | −0.00686250 | − | 0.0118862i | ||||
\(818\) | 29.1051 | 1.01764 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | −2.07180 | − | 3.58846i | −0.0723062 | − | 0.125238i | 0.827605 | − | 0.561310i | \(-0.189703\pi\) |
−0.899912 | + | 0.436072i | \(0.856369\pi\) | |||||||
\(822\) | −38.1962 | −1.33224 | ||||||||
\(823\) | 20.5885 | − | 35.6603i | 0.717669 | − | 1.24304i | −0.244253 | − | 0.969712i | \(-0.578543\pi\) |
0.961921 | − | 0.273327i | \(-0.0881240\pi\) | |||||||
\(824\) | 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 | \(0.595399\pi\) | |||||||
\(828\) | 21.1244 | 0.734122 | ||||||||
\(829\) | 0.411543 | 0.0142935 | 0.00714673 | − | 0.999974i | \(-0.497725\pi\) | ||||
0.00714673 | + | 0.999974i | \(0.497725\pi\) | |||||||
\(830\) | −6.58846 | −0.228689 | ||||||||
\(831\) | 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 | ||||
\(835\) | 5.70577 | + | 9.88269i | 0.197456 | + | 0.342004i | ||||
\(836\) | 1.26795 | − | 2.19615i | 0.0438529 | − | 0.0759555i | ||||
\(837\) | −8.39230 | − | 14.5359i | −0.290080 | − | 0.502434i | ||||
\(838\) | 55.7654 | 1.92638 | ||||||||
\(839\) | −9.00000 | − | 15.5885i | −0.310715 | − | 0.538173i | 0.667803 | − | 0.744338i | \(-0.267235\pi\) |
−0.978517 | + | 0.206165i | \(0.933902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 27.8660 | + | 48.2654i | 0.960327 | + | 1.66333i | ||||
\(843\) | −36.5885 | −1.26017 | ||||||||
\(844\) | 0.901924 | + | 1.56218i | 0.0310455 | + | 0.0537724i | ||||
\(845\) | 8.66025 | − | 20.7846i | 0.297922 | − | 0.715012i | ||||
\(846\) | −99.9615 | −3.43675 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −24.8205 | + | 42.9904i | −0.852340 | + | 1.47630i | ||||
\(849\) | 27.8564 | 0.956029 | ||||||||
\(850\) | 13.3923 | + | 23.1962i | 0.459352 | + | 0.795621i | ||||
\(851\) | 16.5622 | − | 28.6865i | 0.567744 | − | 0.983362i | ||||
\(852\) | −16.3923 | −0.561591 | ||||||||
\(853\) | −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 | ||||
\(856\) | −6.80385 | − | 11.7846i | −0.232551 | − | 0.402790i | ||||
\(857\) | −15.0622 | − | 26.0885i | −0.514514 | − | 0.891165i | −0.999858 | − | 0.0168414i | \(-0.994639\pi\) |
0.485344 | − | 0.874323i | \(-0.338694\pi\) | |||||||
\(858\) | −12.0000 | − | 18.0000i | −0.409673 | − | 0.614510i | ||||
\(859\) | −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 | \(0.207502\pi\) | |||||||
\(864\) | −10.3923 | + | 18.0000i | −0.353553 | + | 0.612372i | ||||
\(865\) | −7.39230 | + | 12.8038i | −0.251346 | + | 0.435344i | ||||
\(866\) | −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 | ||||
\(871\) | 22.2942 | − | 1.43782i | 0.755411 | − | 0.0487187i | ||||
\(872\) | −7.26795 | − | 12.5885i | −0.246124 | − | 0.426299i | ||||
\(873\) | 14.2679 | + | 24.7128i | 0.482897 | + | 0.836402i | ||||
\(874\) | 8.19615 | − | 14.1962i | 0.277239 | − | 0.480192i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.73205 | −0.295029 | ||||||||
\(877\) | 19.7846 | 0.668079 | 0.334039 | − | 0.942559i | \(-0.391588\pi\) | ||||
0.334039 | + | 0.942559i | \(0.391588\pi\) | |||||||
\(878\) | 12.6340 | − | 21.8827i | 0.426376 | − | 0.738505i | ||||
\(879\) | 1.09808 | + | 1.90192i | 0.0370372 | + | 0.0641503i | ||||
\(880\) | 10.9808 | 0.370161 | ||||||||
\(881\) | −4.20577 | + | 7.28461i | −0.141696 | + | 0.245425i | −0.928135 | − | 0.372243i | \(-0.878589\pi\) |
0.786439 | + | 0.617667i | \(0.211922\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.7654 | −1.60743 | −0.803716 | − | 0.595013i | \(-0.797147\pi\) | ||||
−0.803716 | + | 0.595013i | \(0.797147\pi\) | |||||||
\(884\) | 15.4641 | + | 23.1962i | 0.520114 | + | 0.780171i | ||||
\(885\) | 17.1962 | + | 29.7846i | 0.578042 | + | 1.00120i | ||||
\(886\) | 40.3923 | 1.35701 | ||||||||
\(887\) | 5.66025 | + | 9.80385i | 0.190053 | + | 0.329181i | 0.945267 | − | 0.326296i | \(-0.105801\pi\) |
−0.755215 | + | 0.655477i | \(0.772467\pi\) | |||||||
\(888\) | 16.5622 | + | 28.6865i | 0.555790 | + | 0.962657i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −19.3923 | − | 33.5885i | −0.650032 | − | 1.12589i | ||||
\(891\) | −3.12436 | −0.104670 | ||||||||
\(892\) | −5.00000 | − | 8.66025i | −0.167412 | − | 0.289967i | ||||
\(893\) | −12.9282 | + | 22.3923i | −0.432626 | + | 0.749330i | ||||
\(894\) | −15.2942 | − | 26.4904i | −0.511516 | − | 0.885971i | ||||
\(895\) | −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 | ||||
\(899\) | 12.5885 | 0.419849 | ||||||||
\(900\) | −8.92820 | −0.297607 | ||||||||
\(901\) | −76.7654 | −2.55743 | ||||||||
\(902\) | 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 | ||||
\(906\) | 4.73205 | − | 8.19615i | 0.157212 | − | 0.272299i | ||||
\(907\) | −16.5885 | −0.550811 | −0.275405 | − | 0.961328i | \(-0.588812\pi\) | ||||
−0.275405 | + | 0.961328i | \(0.588812\pi\) | |||||||
\(908\) | 2.83013 | + | 4.90192i | 0.0939211 | + | 0.162676i | ||||
\(909\) | 34.5167 | 1.14485 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 13.6603 | + | 23.6603i | 0.452336 | + | 0.783469i | ||||
\(913\) | 2.78461 | 0.0921571 | ||||||||
\(914\) | −9.52628 | + | 16.5000i | −0.315101 | + | 0.545771i | ||||
\(915\) | −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 | ||||||||
\(919\) | −39.5692 | −1.30527 | −0.652634 | − | 0.757673i | \(-0.726336\pi\) | ||||
−0.652634 | + | 0.757673i | \(0.726336\pi\) | |||||||
\(920\) | 14.1962 | 0.468033 | ||||||||
\(921\) | −12.5359 | −0.413072 | ||||||||
\(922\) | −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 | ||||
\(926\) | 3.97372 | + | 6.88269i | 0.130585 | + | 0.226179i | ||||
\(927\) | −32.1244 | + | 55.6410i | −1.05510 | + | 1.82749i | ||||
\(928\) | −7.79423 | − | 13.5000i | −0.255858 | − | 0.443159i | ||||
\(929\) | −52.5167 | −1.72302 | −0.861508 | − | 0.507744i | \(-0.830480\pi\) | ||||
−0.861508 | + | 0.507744i | \(0.830480\pi\) | |||||||
\(930\) | 17.1962 | + | 29.7846i | 0.563884 | + | 0.976676i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.928203 | + | 1.60770i | 0.0304043 | + | 0.0526618i | ||||
\(933\) | −1.73205 | − | 3.00000i | −0.0567048 | − | 0.0982156i | ||||
\(934\) | −44.1962 | −1.44614 | ||||||||
\(935\) | 8.49038 | + | 14.7058i | 0.277665 | + | 0.480930i | ||||
\(936\) | 27.8205 | − | 1.79423i | 0.909342 | − | 0.0586462i | ||||
\(937\) | 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 | ||||
\(940\) | 22.3923 | 0.730356 | ||||||||
\(941\) | −14.0718 | − | 24.3731i | −0.458727 | − | 0.794539i | 0.540167 | − | 0.841558i | \(-0.318361\pi\) |
−0.998894 | + | 0.0470189i | \(0.985028\pi\) | |||||||
\(942\) | −2.83013 | + | 4.90192i | −0.0922105 | + | 0.159713i | ||||
\(943\) | 24.5885 | 0.800710 | ||||||||
\(944\) | 36.3397 | 1.18276 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.215390 | − | 0.373067i | 0.00700294 | − | 0.0121295i | ||||
\(947\) | 3.63397 | + | 6.29423i | 0.118088 | + | 0.204535i | 0.919010 | − | 0.394234i | \(-0.128990\pi\) |
−0.800922 | + | 0.598769i | \(0.795657\pi\) | |||||||
\(948\) | 22.1244 | + | 38.3205i | 0.718566 | + | 1.24459i | ||||
\(949\) | 6.39230 | + | 9.58846i | 0.207503 | + | 0.311254i | ||||
\(950\) | −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 | 0.994641 | − | 0.103392i | \(-0.0329697\pi\) |
−0.586861 | + | 0.809688i | \(0.699636\pi\) | |||||||
\(954\) | 38.3827 | − | 66.4808i | 1.24269 | − | 2.15239i | ||||
\(955\) | 4.09808 | − | 7.09808i | 0.132611 | − | 0.229688i | ||||
\(956\) | 7.90192 | − | 13.6865i | 0.255566 | − | 0.442654i | ||||
\(957\) | −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 | ||||
\(962\) | −19.3756 | + | 39.1865i | −0.624696 | + | 1.26342i | ||||
\(963\) | 17.5359 | + | 30.3731i | 0.565086 | + | 0.978758i | ||||
\(964\) | −10.5981 | − | 18.3564i | −0.341341 | − | 0.591220i | ||||
\(965\) | 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 | \(0.154819\pi\) | |||||||
\(968\) | 16.2679 | 0.522872 | ||||||||
\(969\) | −21.1244 | + | 36.5885i | −0.678612 | + | 1.17539i | ||||
\(970\) | −9.58846 | − | 16.6077i | −0.307867 | − | 0.533241i | ||||
\(971\) | 52.6410 | 1.68933 | 0.844665 | − | 0.535295i | \(-0.179799\pi\) | ||||
0.844665 | + | 0.535295i | \(0.179799\pi\) | |||||||
\(972\) | −9.36603 | + | 16.2224i | −0.300415 | + | 0.520335i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 70.6410 | 2.26348 | ||||||||
\(975\) | 10.9282 | + | 16.3923i | 0.349983 | + | 0.524974i | ||||
\(976\) | 12.0096 | + | 20.8013i | 0.384419 | + | 0.665832i | ||||
\(977\) | 31.6410 | 1.01229 | 0.506143 | − | 0.862450i | \(-0.331071\pi\) | ||||
0.506143 | + | 0.862450i | \(0.331071\pi\) | |||||||
\(978\) | 38.3205 | + | 66.3731i | 1.22535 | + | 2.12238i | ||||
\(979\) | 8.19615 | + | 14.1962i | 0.261950 | + | 0.453711i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.7321 | + | 32.4449i | 0.598068 | + | 1.03588i | ||||
\(982\) | 13.1769 | 0.420492 | ||||||||
\(983\) | −8.66025 | − | 15.0000i | −0.276219 | − | 0.478426i | 0.694223 | − | 0.719760i | \(-0.255748\pi\) |
−0.970442 | + | 0.241334i | \(0.922415\pi\) | |||||||
\(984\) | −12.2942 | + | 21.2942i | −0.391926 | + | 0.678835i | ||||
\(985\) | 10.3923 | + | 18.0000i | 0.331126 | + | 0.573528i | ||||
\(986\) | 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 | ||||
\(990\) | −16.9808 | −0.539684 | ||||||||
\(991\) | 18.9808 | 0.602944 | 0.301472 | − | 0.953475i | \(-0.402522\pi\) | ||||
0.301472 | + | 0.953475i | \(0.402522\pi\) | |||||||
\(992\) | 21.8038 | 0.692273 | ||||||||
\(993\) | −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 | ||||
\(997\) | −2.40192 | + | 4.16025i | −0.0760697 | + | 0.131757i | −0.901551 | − | 0.432673i | \(-0.857570\pi\) |
0.825481 | + | 0.564430i | \(0.190904\pi\) | |||||||
\(998\) | −67.5167 | −2.13720 | ||||||||
\(999\) | −14.0000 | − | 24.2487i | −0.442940 | − | 0.767195i |
(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.g.d.373.1 | 4 | ||
7.2 | even | 3 | 637.2.f.d.295.1 | 4 | |||
7.3 | odd | 6 | 637.2.h.d.165.2 | 4 | |||
7.4 | even | 3 | 637.2.h.e.165.2 | 4 | |||
7.5 | odd | 6 | 91.2.f.b.22.1 | ✓ | 4 | ||
7.6 | odd | 2 | 637.2.g.e.373.1 | 4 | |||
13.3 | even | 3 | 637.2.h.e.471.2 | 4 | |||
21.5 | even | 6 | 819.2.o.b.568.2 | 4 | |||
28.19 | even | 6 | 1456.2.s.o.113.2 | 4 | |||
91.3 | odd | 6 | 637.2.g.e.263.1 | 4 | |||
91.9 | even | 3 | 8281.2.a.r.1.2 | 2 | |||
91.16 | even | 3 | 637.2.f.d.393.1 | 4 | |||
91.19 | even | 12 | 1183.2.c.e.337.2 | 4 | |||
91.30 | even | 6 | 8281.2.a.t.1.1 | 2 | |||
91.33 | even | 12 | 1183.2.c.e.337.4 | 4 | |||
91.55 | odd | 6 | 637.2.h.d.471.2 | 4 | |||
91.61 | odd | 6 | 1183.2.a.f.1.2 | 2 | |||
91.68 | odd | 6 | 91.2.f.b.29.1 | yes | 4 | ||
91.81 | even | 3 | inner | 637.2.g.d.263.1 | 4 | ||
91.82 | odd | 6 | 1183.2.a.e.1.1 | 2 | |||
273.68 | even | 6 | 819.2.o.b.757.2 | 4 | |||
364.159 | even | 6 | 1456.2.s.o.1121.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.b.22.1 | ✓ | 4 | 7.5 | odd | 6 | ||
91.2.f.b.29.1 | yes | 4 | 91.68 | odd | 6 | ||
637.2.f.d.295.1 | 4 | 7.2 | even | 3 | |||
637.2.f.d.393.1 | 4 | 91.16 | even | 3 | |||
637.2.g.d.263.1 | 4 | 91.81 | even | 3 | inner | ||
637.2.g.d.373.1 | 4 | 1.1 | even | 1 | trivial | ||
637.2.g.e.263.1 | 4 | 91.3 | odd | 6 | |||
637.2.g.e.373.1 | 4 | 7.6 | odd | 2 | |||
637.2.h.d.165.2 | 4 | 7.3 | odd | 6 | |||
637.2.h.d.471.2 | 4 | 91.55 | odd | 6 | |||
637.2.h.e.165.2 | 4 | 7.4 | even | 3 | |||
637.2.h.e.471.2 | 4 | 13.3 | even | 3 | |||
819.2.o.b.568.2 | 4 | 21.5 | even | 6 | |||
819.2.o.b.757.2 | 4 | 273.68 | even | 6 | |||
1183.2.a.e.1.1 | 2 | 91.82 | odd | 6 | |||
1183.2.a.f.1.2 | 2 | 91.61 | odd | 6 | |||
1183.2.c.e.337.2 | 4 | 91.19 | even | 12 | |||
1183.2.c.e.337.4 | 4 | 91.33 | even | 12 | |||
1456.2.s.o.113.2 | 4 | 28.19 | even | 6 | |||
1456.2.s.o.1121.2 | 4 | 364.159 | even | 6 | |||
8281.2.a.r.1.2 | 2 | 91.9 | even | 3 | |||
8281.2.a.t.1.1 | 2 | 91.30 | even | 6 |