Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(295,637)]
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([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.295");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.f (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 295.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.295 |
Dual form | 637.2.f.d.393.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 1.50000i | −0.612372 | + | 1.06066i | 0.378467 | + | 0.925615i | \(0.376451\pi\) |
−0.990839 | + | 0.135045i | \(0.956882\pi\) | |||||||
\(3\) | 1.36603 | − | 2.36603i | 0.788675 | − | 1.36603i | −0.138104 | − | 0.990418i | \(-0.544101\pi\) |
0.926779 | − | 0.375608i | \(-0.122566\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.73205 | −0.774597 | −0.387298 | − | 0.921954i | \(-0.626592\pi\) | ||||
−0.387298 | + | 0.921954i | \(0.626592\pi\) | |||||||
\(6\) | 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 | \(0.227889\pi\) | |||||||
\(12\) | −2.73205 | −0.788675 | ||||||||
\(13\) | −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 | −0.769841 | − | 0.638236i | \(-0.779664\pi\) |
−0.167808 | − | 0.985820i | \(-0.553669\pi\) | |||||||
\(18\) | 7.73205 | 1.82246 | ||||||||
\(19\) | 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 | ||||
\(23\) | −2.36603 | + | 4.09808i | −0.493350 | + | 0.854508i | −0.999971 | − | 0.00766135i | \(-0.997561\pi\) |
0.506620 | + | 0.862169i | \(0.330895\pi\) | |||||||
\(24\) | −2.36603 | + | 4.09808i | −0.482963 | + | 0.836516i | ||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | 2.76795 | − | 5.59808i | 0.542839 | − | 1.09787i | ||||
\(27\) | −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 | \(0.0768152\pi\) | |||||||
\(30\) | −4.09808 | − | 7.09808i | −0.748203 | − | 1.29593i | ||||
\(31\) | −4.19615 | −0.753651 | −0.376826 | − | 0.926284i | \(-0.622984\pi\) | ||||
−0.376826 | + | 0.926284i | \(0.622984\pi\) | |||||||
\(32\) | 2.59808 | + | 4.50000i | 0.459279 | + | 0.795495i | ||||
\(33\) | 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 | ||||
\(37\) | 3.50000 | − | 6.06218i | 0.575396 | − | 0.996616i | −0.420602 | − | 0.907245i | \(-0.638181\pi\) |
0.995998 | − | 0.0893706i | \(-0.0284856\pi\) | |||||||
\(38\) | −3.46410 | −0.561951 | ||||||||
\(39\) | −4.36603 | + | 8.83013i | −0.699124 | + | 1.41395i | ||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | −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 | \(0.828572\pi\) | |||||||
\(44\) | 1.26795 | 0.191151 | ||||||||
\(45\) | 3.86603 | + | 6.69615i | 0.576313 | + | 0.998203i | ||||
\(46\) | −4.09808 | − | 7.09808i | −0.604228 | − | 1.04655i | ||||
\(47\) | −12.9282 | −1.88577 | −0.942886 | − | 0.333115i | \(-0.891900\pi\) | ||||
−0.942886 | + | 0.333115i | \(0.891900\pi\) | |||||||
\(48\) | −6.83013 | − | 11.8301i | −0.985844 | − | 1.70753i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.73205 | − | 3.00000i | 0.244949 | − | 0.424264i | ||||
\(51\) | −21.1244 | −2.95800 | ||||||||
\(52\) | 2.00000 | + | 3.00000i | 0.277350 | + | 0.416025i | ||||
\(53\) | −9.92820 | −1.36374 | −0.681872 | − | 0.731472i | \(-0.738834\pi\) | ||||
−0.681872 | + | 0.731472i | \(0.738834\pi\) | |||||||
\(54\) | 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 | ||||||||
\(58\) | 2.59808 | + | 4.50000i | 0.341144 | + | 0.590879i | ||||
\(59\) | 3.63397 | + | 6.29423i | 0.473103 | + | 0.819439i | 0.999526 | − | 0.0307841i | \(-0.00980044\pi\) |
−0.526423 | + | 0.850223i | \(0.676467\pi\) | |||||||
\(60\) | 4.73205 | 0.610905 | ||||||||
\(61\) | −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 | ||||||||
\(65\) | 6.23205 | − | 0.401924i | 0.772991 | − | 0.0498525i | ||||
\(66\) | −6.00000 | −0.738549 | ||||||||
\(67\) | 3.09808 | − | 5.36603i | 0.378490 | − | 0.655564i | −0.612353 | − | 0.790585i | \(-0.709777\pi\) |
0.990843 | + | 0.135020i | \(0.0431100\pi\) | |||||||
\(68\) | −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 | \(0.949205\pi\) | |||||||
\(72\) | 3.86603 | + | 6.69615i | 0.455615 | + | 0.789149i | ||||
\(73\) | 3.19615 | 0.374081 | 0.187041 | − | 0.982352i | \(-0.440110\pi\) | ||||
0.187041 | + | 0.982352i | \(0.440110\pi\) | |||||||
\(74\) | 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 | ||||
\(79\) | 16.1962 | 1.82221 | 0.911105 | − | 0.412175i | \(-0.135231\pi\) | ||||
0.911105 | + | 0.412175i | \(0.135231\pi\) | |||||||
\(80\) | −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 | ||||
\(86\) | −0.339746 | −0.0366357 | ||||||||
\(87\) | −4.09808 | − | 7.09808i | −0.439360 | − | 0.760994i | ||||
\(88\) | 1.09808 | − | 1.90192i | 0.117055 | − | 0.202746i | ||||
\(89\) | 6.46410 | − | 11.1962i | 0.685193 | − | 1.18679i | −0.288183 | − | 0.957575i | \(-0.593051\pi\) |
0.973376 | − | 0.229214i | \(-0.0736157\pi\) | |||||||
\(90\) | −13.3923 | −1.41167 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.73205 | 0.493350 | ||||||||
\(93\) | −5.73205 | + | 9.92820i | −0.594386 | + | 1.02951i | ||||
\(94\) | 11.1962 | − | 19.3923i | 1.15479 | − | 2.00016i | ||||
\(95\) | −1.73205 | − | 3.00000i | −0.177705 | − | 0.307794i | ||||
\(96\) | 14.1962 | 1.44889 | ||||||||
\(97\) | 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 | ||||||||
\(100\) | 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 | ||||
\(103\) | 14.3923 | 1.41812 | 0.709058 | − | 0.705150i | \(-0.249120\pi\) | ||||
0.709058 | + | 0.705150i | \(0.249120\pi\) | |||||||
\(104\) | 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 | −0.611273 | − | 0.791420i | \(-0.709342\pi\) |
0.991026 | + | 0.133667i | \(0.0426754\pi\) | |||||||
\(108\) | 2.00000 | + | 3.46410i | 0.192450 | + | 0.333333i | ||||
\(109\) | −8.39230 | −0.803837 | −0.401919 | − | 0.915675i | \(-0.631656\pi\) | ||||
−0.401919 | + | 0.915675i | \(0.631656\pi\) | |||||||
\(110\) | 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 | −0.987567 | − | 0.157198i | \(-0.949754\pi\) |
0.357646 | − | 0.933857i | \(-0.383579\pi\) | |||||||
\(114\) | −4.73205 | + | 8.19615i | −0.443197 | + | 0.767640i | ||||
\(115\) | 4.09808 | − | 7.09808i | 0.382148 | − | 0.661899i | ||||
\(116\) | −3.00000 | −0.278543 | ||||||||
\(117\) | 8.92820 | + | 13.3923i | 0.825413 | + | 1.23812i | ||||
\(118\) | −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 | ||||
\(122\) | 8.32051 | 0.753303 | ||||||||
\(123\) | 7.09808 | + | 12.2942i | 0.640012 | + | 1.10853i | ||||
\(124\) | 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 | 0.0925619 | + | 0.995707i | \(0.470494\pi\) |
−0.908588 | + | 0.417693i | \(0.862839\pi\) | |||||||
\(128\) | −6.06218 | + | 10.5000i | −0.535826 | + | 0.928078i | ||||
\(129\) | 0.535898 | 0.0471832 | ||||||||
\(130\) | −4.79423 | + | 9.69615i | −0.420482 | + | 0.850409i | ||||
\(131\) | 3.46410 | 0.302660 | 0.151330 | − | 0.988483i | \(-0.451644\pi\) | ||||
0.151330 | + | 0.988483i | \(0.451644\pi\) | |||||||
\(132\) | 1.73205 | − | 3.00000i | 0.150756 | − | 0.261116i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.36603 | + | 9.29423i | 0.463554 | + | 0.802899i | ||||
\(135\) | 6.92820 | 0.596285 | ||||||||
\(136\) | 6.69615 | + | 11.5981i | 0.574190 | + | 0.994527i | ||||
\(137\) | −4.03590 | − | 6.99038i | −0.344810 | − | 0.597229i | 0.640509 | − | 0.767951i | \(-0.278723\pi\) |
−0.985319 | + | 0.170722i | \(0.945390\pi\) | |||||||
\(138\) | −22.3923 | −1.90616 | ||||||||
\(139\) | −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 | ||||
\(142\) | 10.3923 | 0.872103 | ||||||||
\(143\) | 2.02628 | − | 4.09808i | 0.169446 | − | 0.342698i | ||||
\(144\) | −22.3205 | −1.86004 | ||||||||
\(145\) | −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 | ||||||||
\(149\) | 3.23205 | + | 5.59808i | 0.264780 | + | 0.458612i | 0.967506 | − | 0.252848i | \(-0.0813674\pi\) |
−0.702726 | + | 0.711461i | \(0.748034\pi\) | |||||||
\(150\) | −4.73205 | − | 8.19615i | −0.386370 | − | 0.669213i | ||||
\(151\) | 2.00000 | 0.162758 | 0.0813788 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813788 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(152\) | −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 | ||||||||
\(156\) | 9.83013 | − | 0.633975i | 0.787040 | − | 0.0507586i | ||||
\(157\) | −1.19615 | −0.0954634 | −0.0477317 | − | 0.998860i | \(-0.515199\pi\) | ||||
−0.0477317 | + | 0.998860i | \(0.515199\pi\) | |||||||
\(158\) | −14.0263 | + | 24.2942i | −1.11587 | + | 1.93275i | ||||
\(159\) | −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 | ||||
\(163\) | −8.09808 | − | 14.0263i | −0.634290 | − | 1.09862i | −0.986665 | − | 0.162764i | \(-0.947959\pi\) |
0.352375 | − | 0.935859i | \(-0.385374\pi\) | |||||||
\(164\) | 5.19615 | 0.405751 | ||||||||
\(165\) | −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 | ||||
\(170\) | −23.1962 | −1.77906 | ||||||||
\(171\) | 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 | ||||
\(177\) | 19.8564 | 1.49250 | ||||||||
\(178\) | 11.1962 | + | 19.3923i | 0.839187 | + | 1.45351i | ||||
\(179\) | 3.46410 | − | 6.00000i | 0.258919 | − | 0.448461i | −0.707034 | − | 0.707180i | \(-0.749967\pi\) |
0.965953 | + | 0.258719i | \(0.0833004\pi\) | |||||||
\(180\) | 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 | ||||
\(185\) | −6.06218 | + | 10.5000i | −0.445700 | + | 0.771975i | ||||
\(186\) | −9.92820 | − | 17.1962i | −0.727971 | − | 1.26088i | ||||
\(187\) | 9.80385 | 0.716928 | ||||||||
\(188\) | 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 | \(0.224262\pi\) | |||||||
\(194\) | −11.0718 | −0.794909 | ||||||||
\(195\) | 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 | 0.899291 | − | 0.437351i | \(-0.144083\pi\) |
−0.828403 | + | 0.560133i | \(0.810750\pi\) | |||||||
\(200\) | 3.46410 | 0.244949 | ||||||||
\(201\) | −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 | ||||
\(205\) | 4.50000 | − | 7.79423i | 0.314294 | − | 0.544373i | ||||
\(206\) | −12.4641 | + | 21.5885i | −0.868415 | + | 1.50414i | ||||
\(207\) | 21.1244 | 1.46824 | ||||||||
\(208\) | −7.99038 | + | 16.1603i | −0.554033 | + | 1.12051i | ||||
\(209\) | −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 | \(0.146890\pi\) | |||||||
\(212\) | 4.96410 | + | 8.59808i | 0.340936 | + | 0.590518i | ||||
\(213\) | −16.3923 | −1.12318 | ||||||||
\(214\) | 6.80385 | + | 11.7846i | 0.465101 | + | 0.805579i | ||||
\(215\) | −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 | ||||
\(219\) | 4.36603 | − | 7.56218i | 0.295029 | − | 0.511005i | ||||
\(220\) | −2.19615 | −0.148065 | ||||||||
\(221\) | 15.4641 | + | 23.1962i | 1.04023 | + | 1.56034i | ||||
\(222\) | 33.1244 | 2.22316 | ||||||||
\(223\) | −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 | ||||
\(226\) | 23.1962 | 1.54299 | ||||||||
\(227\) | 2.83013 | + | 4.90192i | 0.187842 | + | 0.325352i | 0.944531 | − | 0.328424i | \(-0.106517\pi\) |
−0.756688 | + | 0.653776i | \(0.773184\pi\) | |||||||
\(228\) | −2.73205 | − | 4.73205i | −0.180934 | − | 0.313388i | ||||
\(229\) | 14.3923 | 0.951070 | 0.475535 | − | 0.879697i | \(-0.342254\pi\) | ||||
0.475535 | + | 0.879697i | \(0.342254\pi\) | |||||||
\(230\) | 7.09808 | + | 12.2942i | 0.468033 | + | 0.810657i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.59808 | + | 4.50000i | −0.170572 | + | 0.295439i | ||||
\(233\) | −1.85641 | −0.121617 | −0.0608086 | − | 0.998149i | \(-0.519368\pi\) | ||||
−0.0608086 | + | 0.998149i | \(0.519368\pi\) | |||||||
\(234\) | −27.8205 | + | 1.79423i | −1.81868 | + | 0.117292i | ||||
\(235\) | 22.3923 | 1.46071 | ||||||||
\(236\) | 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 | \(0.670774\pi\) | |||||||
\(240\) | 11.8301 | + | 20.4904i | 0.763631 | + | 1.32265i | ||||
\(241\) | −10.5981 | − | 18.3564i | −0.682682 | − | 1.18244i | −0.974159 | − | 0.225862i | \(-0.927480\pi\) |
0.291477 | − | 0.956578i | \(-0.405853\pi\) | |||||||
\(242\) | −16.2679 | −1.04574 | ||||||||
\(243\) | −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 | ||||||||
\(247\) | −4.00000 | − | 6.00000i | −0.254514 | − | 0.381771i | ||||
\(248\) | 7.26795 | 0.461515 | ||||||||
\(249\) | 3.00000 | − | 5.19615i | 0.190117 | − | 0.329293i | ||||
\(250\) | −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 | ||||
\(254\) | −15.9282 | − | 27.5885i | −0.999424 | − | 1.73105i | ||||
\(255\) | 36.5885 | 2.29126 | ||||||||
\(256\) | −9.50000 | − | 16.4545i | −0.593750 | − | 1.02841i | ||||
\(257\) | 3.06218 | − | 5.30385i | 0.191013 | − | 0.330845i | −0.754573 | − | 0.656216i | \(-0.772156\pi\) |
0.945586 | + | 0.325371i | \(0.105489\pi\) | |||||||
\(258\) | −0.464102 | + | 0.803848i | −0.0288937 | + | 0.0500454i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.46410 | − | 5.19615i | −0.214834 | − | 0.322252i | ||||
\(261\) | −13.3923 | −0.828963 | ||||||||
\(262\) | −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 | ||||
\(268\) | −6.19615 | −0.378490 | ||||||||
\(269\) | 2.53590 | + | 4.39230i | 0.154616 | + | 0.267804i | 0.932919 | − | 0.360086i | \(-0.117252\pi\) |
−0.778303 | + | 0.627889i | \(0.783919\pi\) | |||||||
\(270\) | −6.00000 | + | 10.3923i | −0.365148 | + | 0.632456i | ||||
\(271\) | 2.90192 | − | 5.02628i | 0.176279 | − | 0.305325i | −0.764324 | − | 0.644832i | \(-0.776927\pi\) |
0.940603 | + | 0.339508i | \(0.110260\pi\) | |||||||
\(272\) | −38.6603 | −2.34412 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.9808 | 0.844609 | ||||||||
\(275\) | 1.26795 | − | 2.19615i | 0.0764602 | − | 0.132433i | ||||
\(276\) | 6.46410 | − | 11.1962i | 0.389093 | − | 0.673929i | ||||
\(277\) | −8.50000 | − | 14.7224i | −0.510716 | − | 0.884585i | −0.999923 | − | 0.0124177i | \(-0.996047\pi\) |
0.489207 | − | 0.872167i | \(-0.337286\pi\) | |||||||
\(278\) | 18.3397 | 1.09994 | ||||||||
\(279\) | 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 | ||||
\(285\) | −9.46410 | −0.560605 | ||||||||
\(286\) | 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 | ||||
\(291\) | 17.4641 | 1.02376 | ||||||||
\(292\) | −1.59808 | − | 2.76795i | −0.0935203 | − | 0.161982i | ||||
\(293\) | −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 | ||||
\(297\) | 2.53590 | − | 4.39230i | 0.147148 | − | 0.254867i | ||||
\(298\) | −11.1962 | −0.648576 | ||||||||
\(299\) | 7.56218 | − | 15.2942i | 0.437332 | − | 0.884488i | ||||
\(300\) | 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 | ||||
\(304\) | 10.0000 | 0.573539 | ||||||||
\(305\) | 4.16025 | + | 7.20577i | 0.238215 | + | 0.412601i | ||||
\(306\) | −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 | ||||
\(310\) | −6.29423 | + | 10.9019i | −0.357488 | + | 0.619188i | ||||
\(311\) | −1.26795 | −0.0718988 | −0.0359494 | − | 0.999354i | \(-0.511446\pi\) | ||||
−0.0359494 | + | 0.999354i | \(0.511446\pi\) | |||||||
\(312\) | 7.56218 | − | 15.2942i | 0.428124 | − | 0.865865i | ||||
\(313\) | −28.7846 | −1.62700 | −0.813501 | − | 0.581563i | \(-0.802441\pi\) | ||||
−0.813501 | + | 0.581563i | \(0.802441\pi\) | |||||||
\(314\) | 1.03590 | − | 1.79423i | 0.0584591 | − | 0.101254i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.09808 | − | 14.0263i | −0.455552 | − | 0.789040i | ||||
\(317\) | −6.46410 | −0.363060 | −0.181530 | − | 0.983385i | \(-0.558105\pi\) | ||||
−0.181530 | + | 0.983385i | \(0.558105\pi\) | |||||||
\(318\) | −23.4904 | − | 40.6865i | −1.31728 | − | 2.28159i | ||||
\(319\) | 1.90192 | + | 3.29423i | 0.106487 | + | 0.184441i | ||||
\(320\) | −1.73205 | −0.0968246 | ||||||||
\(321\) | −10.7321 | − | 18.5885i | −0.599005 | − | 1.03751i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.73205 | − | 13.3923i | 0.430223 | − | 0.745168i | ||||
\(324\) | −2.46410 | −0.136895 | ||||||||
\(325\) | 7.19615 | − | 0.464102i | 0.399171 | − | 0.0257437i | ||||
\(326\) | 28.0526 | 1.55369 | ||||||||
\(327\) | −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 | ||||||||
\(331\) | −12.4904 | − | 21.6340i | −0.686533 | − | 1.18911i | −0.972952 | − | 0.231006i | \(-0.925798\pi\) |
0.286419 | − | 0.958105i | \(-0.407535\pi\) | |||||||
\(332\) | −1.09808 | − | 1.90192i | −0.0602648 | − | 0.104382i | ||||
\(333\) | −31.2487 | −1.71242 | ||||||||
\(334\) | −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 | \(0.403145\pi\) | |||||||
\(338\) | −8.66025 | + | 20.7846i | −0.471056 | + | 1.13053i | ||||
\(339\) | −36.5885 | −1.98721 | ||||||||
\(340\) | 6.69615 | − | 11.5981i | 0.363150 | − | 0.628994i | ||||
\(341\) | 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 | ||||
\(345\) | −11.1962 | − | 19.3923i | −0.602781 | − | 1.04405i | ||||
\(346\) | −14.7846 | −0.794826 | ||||||||
\(347\) | −3.63397 | − | 6.29423i | −0.195082 | − | 0.337892i | 0.751845 | − | 0.659339i | \(-0.229164\pi\) |
−0.946927 | + | 0.321448i | \(0.895831\pi\) | |||||||
\(348\) | −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 | ||||
\(352\) | −6.58846 | −0.351166 | ||||||||
\(353\) | 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 | ||||
\(359\) | 18.9282 | 0.998992 | 0.499496 | − | 0.866316i | \(-0.333518\pi\) | ||||
0.499496 | + | 0.866316i | \(0.333518\pi\) | |||||||
\(360\) | −6.69615 | − | 11.5981i | −0.352918 | − | 0.611272i | ||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 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 | ||||
\(367\) | 2.09808 | − | 3.63397i | 0.109519 | − | 0.189692i | −0.806057 | − | 0.591838i | \(-0.798402\pi\) |
0.915575 | + | 0.402146i | \(0.131736\pi\) | |||||||
\(368\) | 11.8301 | + | 20.4904i | 0.616688 | + | 1.06813i | ||||
\(369\) | 23.1962 | 1.20754 | ||||||||
\(370\) | −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 | ||||
\(376\) | 22.3923 | 1.15479 | ||||||||
\(377\) | −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 | ||||
\(382\) | 8.19615 | 0.419352 | ||||||||
\(383\) | −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 | ||||
\(387\) | 0.437822 | − | 0.758330i | 0.0222558 | − | 0.0385481i | ||||
\(388\) | 3.19615 | − | 5.53590i | 0.162260 | − | 0.281043i | ||||
\(389\) | −23.5359 | −1.19332 | −0.596659 | − | 0.802495i | \(-0.703505\pi\) | ||||
−0.596659 | + | 0.802495i | \(0.703505\pi\) | |||||||
\(390\) | 16.3923 | + | 24.5885i | 0.830057 | + | 1.24508i | ||||
\(391\) | 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 | ||||
\(395\) | −28.0526 | −1.41148 | ||||||||
\(396\) | −2.83013 | − | 4.90192i | −0.142219 | − | 0.246331i | ||||
\(397\) | −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 | ||||
\(401\) | 5.42820 | − | 9.40192i | 0.271072 | − | 0.469510i | −0.698065 | − | 0.716034i | \(-0.745955\pi\) |
0.969136 | + | 0.246525i | \(0.0792887\pi\) | |||||||
\(402\) | 29.3205 | 1.46237 | ||||||||
\(403\) | 15.0981 | − | 0.973721i | 0.752089 | − | 0.0485045i | ||||
\(404\) | 7.73205 | 0.384684 | ||||||||
\(405\) | −2.13397 | + | 3.69615i | −0.106038 | + | 0.183663i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.43782 | + | 7.68653i | 0.219975 | + | 0.381007i | ||||
\(408\) | 36.5885 | 1.81140 | ||||||||
\(409\) | −8.40192 | − | 14.5526i | −0.415448 | − | 0.719578i | 0.580027 | − | 0.814597i | \(-0.303042\pi\) |
−0.995475 | + | 0.0950195i | \(0.969709\pi\) | |||||||
\(410\) | 7.79423 | + | 13.5000i | 0.384930 | + | 0.666717i | ||||
\(411\) | −22.0526 | −1.08777 | ||||||||
\(412\) | −7.19615 | − | 12.4641i | −0.354529 | − | 0.614062i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −18.2942 | + | 31.6865i | −0.899112 | + | 1.55731i | ||||
\(415\) | −3.80385 | −0.186724 | ||||||||
\(416\) | −10.3923 | − | 15.5885i | −0.509525 | − | 0.764287i | ||||
\(417\) | −28.9282 | −1.41662 | ||||||||
\(418\) | 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 | \(0.786877\pi\) | |||||||
\(422\) | 1.56218 | + | 2.70577i | 0.0760456 | + | 0.131715i | ||||
\(423\) | 28.8564 | + | 49.9808i | 1.40305 | + | 2.43015i | ||||
\(424\) | 17.1962 | 0.835119 | ||||||||
\(425\) | 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 | ||||||||
\(429\) | −6.92820 | − | 10.3923i | −0.334497 | − | 0.501745i | ||||
\(430\) | 0.588457 | 0.0283779 | ||||||||
\(431\) | −0.339746 | + | 0.588457i | −0.0163650 | + | 0.0283450i | −0.874092 | − | 0.485761i | \(-0.838543\pi\) |
0.857727 | + | 0.514106i | \(0.171876\pi\) | |||||||
\(432\) | −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 | ||||
\(436\) | 4.19615 | + | 7.26795i | 0.200959 | + | 0.348072i | ||||
\(437\) | −9.46410 | −0.452729 | ||||||||
\(438\) | 7.56218 | + | 13.0981i | 0.361335 | + | 0.625850i | ||||
\(439\) | 7.29423 | − | 12.6340i | 0.348135 | − | 0.602987i | −0.637784 | − | 0.770216i | \(-0.720149\pi\) |
0.985918 | + | 0.167229i | \(0.0534819\pi\) | |||||||
\(440\) | −1.90192 | + | 3.29423i | −0.0906707 | + | 0.157046i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −48.1865 | + | 3.10770i | −2.29200 | + | 0.147818i | ||||
\(443\) | 23.3205 | 1.10799 | 0.553995 | − | 0.832520i | \(-0.313103\pi\) | ||||
0.553995 | + | 0.832520i | \(0.313103\pi\) | |||||||
\(444\) | −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 | 0.972161 | − | 0.234315i | \(-0.0752847\pi\) |
−0.689003 | + | 0.724758i | \(0.741951\pi\) | |||||||
\(450\) | −15.4641 | −0.728985 | ||||||||
\(451\) | −3.29423 | − | 5.70577i | −0.155119 | − | 0.268674i | ||||
\(452\) | −6.69615 | + | 11.5981i | −0.314961 | + | 0.545528i | ||||
\(453\) | 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 | −0.965512 | − | 0.260358i | \(-0.916159\pi\) |
0.708233 | + | 0.705979i | \(0.249493\pi\) | |||||||
\(458\) | −12.4641 | + | 21.5885i | −0.582409 | + | 1.00876i | ||||
\(459\) | 15.4641 | + | 26.7846i | 0.721802 | + | 1.25020i | ||||
\(460\) | −8.19615 | −0.382148 | ||||||||
\(461\) | −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 | \(0.534003\pi\) | |||||||
\(464\) | −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 | ||||
\(467\) | −25.5167 | −1.18077 | −0.590385 | − | 0.807122i | \(-0.701024\pi\) | ||||
−0.590385 | + | 0.807122i | \(0.701024\pi\) | |||||||
\(468\) | 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 | ||||
\(473\) | −0.248711 | −0.0114358 | ||||||||
\(474\) | 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 | ||||
\(478\) | 13.6865 | − | 23.7058i | 0.626007 | − | 1.08428i | ||||
\(479\) | 0.633975 | − | 1.09808i | 0.0289670 | − | 0.0501724i | −0.851178 | − | 0.524876i | \(-0.824112\pi\) |
0.880146 | + | 0.474704i | \(0.157445\pi\) | |||||||
\(480\) | −24.5885 | −1.12230 | ||||||||
\(481\) | −11.1865 | + | 22.6244i | −0.510062 | + | 1.03158i | ||||
\(482\) | 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 | ||||
\(486\) | 32.4449 | 1.47173 | ||||||||
\(487\) | −20.3923 | − | 35.3205i | −0.924064 | − | 1.60052i | −0.793060 | − | 0.609143i | \(-0.791514\pi\) |
−0.131003 | − | 0.991382i | \(-0.541820\pi\) | |||||||
\(488\) | 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 | −0.939002 | − | 0.343911i | \(-0.888248\pi\) |
0.767337 | + | 0.641244i | \(0.221581\pi\) | |||||||
\(492\) | 7.09808 | − | 12.2942i | 0.320006 | − | 0.554267i | ||||
\(493\) | −23.1962 | −1.04470 | ||||||||
\(494\) | 12.4641 | − | 0.803848i | 0.560786 | − | 0.0361668i | ||||
\(495\) | −9.80385 | −0.440650 | ||||||||
\(496\) | −10.4904 | + | 18.1699i | −0.471032 | + | 0.815851i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.19615 | + | 9.00000i | 0.232845 | + | 0.403300i | ||||
\(499\) | −38.9808 | −1.74502 | −0.872509 | − | 0.488598i | \(-0.837509\pi\) | ||||
−0.872509 | + | 0.488598i | \(0.837509\pi\) | |||||||
\(500\) | −6.06218 | − | 10.5000i | −0.271109 | − | 0.469574i | ||||
\(501\) | 9.00000 | + | 15.5885i | 0.402090 | + | 0.696441i | ||||
\(502\) | 2.78461 | 0.124283 | ||||||||
\(503\) | −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 | ||||
\(506\) | 10.3923 | 0.461994 | ||||||||
\(507\) | 13.6603 | − | 32.7846i | 0.606673 | − | 1.45602i | ||||
\(508\) | 18.3923 | 0.816027 | ||||||||
\(509\) | 6.86603 | − | 11.8923i | 0.304331 | − | 0.527117i | −0.672781 | − | 0.739842i | \(-0.734900\pi\) |
0.977112 | + | 0.212725i | \(0.0682337\pi\) | |||||||
\(510\) | −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 | ||||
\(514\) | 5.30385 | + | 9.18653i | 0.233943 | + | 0.405201i | ||||
\(515\) | −24.9282 | −1.09847 | ||||||||
\(516\) | −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 | ||||||||
\(520\) | −10.7942 | + | 0.696152i | −0.473358 | + | 0.0305283i | ||||
\(521\) | 24.1244 | 1.05691 | 0.528454 | − | 0.848962i | \(-0.322772\pi\) | ||||
0.528454 | + | 0.848962i | \(0.322772\pi\) | |||||||
\(522\) | 11.5981 | − | 20.0885i | 0.507634 | − | 0.879248i | ||||
\(523\) | −14.5885 | + | 25.2679i | −0.637909 | + | 1.10489i | 0.347982 | + | 0.937501i | \(0.386867\pi\) |
−0.985891 | + | 0.167389i | \(0.946466\pi\) | |||||||
\(524\) | −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 | ||||
\(528\) | 17.3205 | 0.753778 | ||||||||
\(529\) | 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 | ||||
\(534\) | 61.1769 | 2.64738 | ||||||||
\(535\) | −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 | ||||
\(541\) | −14.6077 | −0.628034 | −0.314017 | − | 0.949417i | \(-0.601675\pi\) | ||||
−0.314017 | + | 0.949417i | \(0.601675\pi\) | |||||||
\(542\) | 5.02628 | + | 8.70577i | 0.215897 | + | 0.373945i | ||||
\(543\) | −7.63397 | + | 13.2224i | −0.327605 | + | 0.567429i | ||||
\(544\) | 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 | ||||
\(549\) | −10.7224 | + | 18.5718i | −0.457622 | + | 0.792625i | ||||
\(550\) | 2.19615 | + | 3.80385i | 0.0936443 | + | 0.162197i | ||||
\(551\) | 6.00000 | 0.255609 | ||||||||
\(552\) | −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 | \(0.791096\pi\) | |||||||
\(558\) | −32.4449 | −1.37350 | ||||||||
\(559\) | −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 | 0.994080 | + | 0.108654i | \(0.0346542\pi\) |
−0.402942 | + | 0.915225i | \(0.632013\pi\) | |||||||
\(564\) | 35.3205 | 1.48726 | ||||||||
\(565\) | 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 | ||||
\(569\) | −21.4641 | + | 37.1769i | −0.899822 | + | 1.55854i | −0.0721010 | + | 0.997397i | \(0.522970\pi\) |
−0.827721 | + | 0.561140i | \(0.810363\pi\) | |||||||
\(570\) | 8.19615 | − | 14.1962i | 0.343299 | − | 0.594611i | ||||
\(571\) | 16.7846 | 0.702414 | 0.351207 | − | 0.936298i | \(-0.385771\pi\) | ||||
0.351207 | + | 0.936298i | \(0.385771\pi\) | |||||||
\(572\) | −4.56218 | + | 0.294229i | −0.190754 | + | 0.0123023i | ||||
\(573\) | −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 | ||||
\(577\) | −43.1962 | −1.79828 | −0.899140 | − | 0.437662i | \(-0.855807\pi\) | ||||
−0.899140 | + | 0.437662i | \(0.855807\pi\) | |||||||
\(578\) | −37.0526 | − | 64.1769i | −1.54118 | − | 2.66941i | ||||
\(579\) | 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 | ||||
\(583\) | 6.29423 | − | 10.9019i | 0.260680 | − | 0.451512i | ||||
\(584\) | −5.53590 | −0.229077 | ||||||||
\(585\) | −15.4641 | − | 23.1962i | −0.639362 | − | 0.959043i | ||||
\(586\) | 1.39230 | 0.0575156 | ||||||||
\(587\) | 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 | ||||
\(590\) | 21.8038 | 0.897650 | ||||||||
\(591\) | 16.3923 | + | 28.3923i | 0.674289 | + | 1.16790i | ||||
\(592\) | −17.5000 | − | 30.3109i | −0.719246 | − | 1.24577i | ||||
\(593\) | 17.4449 | 0.716375 | 0.358187 | − | 0.933650i | \(-0.383395\pi\) | ||||
0.358187 | + | 0.933650i | \(0.383395\pi\) | |||||||
\(594\) | 4.39230 | + | 7.60770i | 0.180218 | + | 0.312148i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.23205 | − | 5.59808i | 0.132390 | − | 0.229306i | ||||
\(597\) | 5.46410 | 0.223631 | ||||||||
\(598\) | 16.3923 | + | 24.5885i | 0.670331 | + | 1.00550i | ||||
\(599\) | 43.8564 | 1.79192 | 0.895962 | − | 0.444131i | \(-0.146487\pi\) | ||||
0.895962 | + | 0.444131i | \(0.146487\pi\) | |||||||
\(600\) | 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 | ||||||||
\(604\) | −1.00000 | − | 1.73205i | −0.0406894 | − | 0.0704761i | ||||
\(605\) | −8.13397 | − | 14.0885i | −0.330693 | − | 0.572777i | ||||
\(606\) | −36.5885 | −1.48630 | ||||||||
\(607\) | −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 | ||||||||
\(611\) | 46.5167 | − | 3.00000i | 1.88186 | − | 0.121367i | ||||
\(612\) | 34.5167 | 1.39525 | ||||||||
\(613\) | −1.69615 | + | 2.93782i | −0.0685070 | + | 0.118658i | −0.898244 | − | 0.439497i | \(-0.855157\pi\) |
0.829737 | + | 0.558154i | \(0.188490\pi\) | |||||||
\(614\) | −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 | \(-0.632455\pi\) | |||||||
\(618\) | 34.0526 | + | 58.9808i | 1.36979 | + | 2.37255i | ||||
\(619\) | −35.3731 | −1.42176 | −0.710882 | − | 0.703311i | \(-0.751704\pi\) | ||||
−0.710882 | + | 0.703311i | \(0.751704\pi\) | |||||||
\(620\) | −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 | ||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 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 | 0.964752 | − | 0.263159i | \(-0.0847645\pi\) |
−0.710279 | + | 0.703920i | \(0.751431\pi\) | |||||||
\(632\) | −28.0526 | −1.11587 | ||||||||
\(633\) | −2.46410 | − | 4.26795i | −0.0979392 | − | 0.169636i | ||||
\(634\) | 5.59808 | − | 9.69615i | 0.222328 | − | 0.385083i | ||||
\(635\) | 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 | ||||
\(640\) | 10.5000 | − | 18.1865i | 0.415049 | − | 0.718886i | ||||
\(641\) | −14.4282 | − | 24.9904i | −0.569880 | − | 0.987061i | −0.996577 | − | 0.0826663i | \(-0.973656\pi\) |
0.426698 | − | 0.904394i | \(-0.359677\pi\) | |||||||
\(642\) | 37.1769 | 1.46726 | ||||||||
\(643\) | −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 | ||||||||
\(646\) | 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 | ||||
\(649\) | −9.21539 | −0.361736 | ||||||||
\(650\) | −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 | −0.211451 | − | 0.977389i | \(-0.567819\pi\) |
0.952169 | − | 0.305572i | \(-0.0988478\pi\) | |||||||
\(654\) | −19.8564 | − | 34.3923i | −0.776447 | − | 1.34485i | ||||
\(655\) | −6.00000 | −0.234439 | ||||||||
\(656\) | 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 | −0.998056 | − | 0.0623257i | \(-0.980148\pi\) |
0.445052 | − | 0.895505i | \(-0.353185\pi\) | |||||||
\(660\) | −3.00000 | + | 5.19615i | −0.116775 | + | 0.202260i | ||||
\(661\) | −16.5981 | + | 28.7487i | −0.645590 | + | 1.11820i | 0.338574 | + | 0.940940i | \(0.390055\pi\) |
−0.984165 | + | 0.177256i | \(0.943278\pi\) | |||||||
\(662\) | 43.2679 | 1.68166 | ||||||||
\(663\) | 76.0070 | − | 4.90192i | 2.95187 | − | 0.190375i | ||||
\(664\) | −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 | ||||
\(668\) | 6.58846 | 0.254915 | ||||||||
\(669\) | 13.6603 | + | 23.6603i | 0.528136 | + | 0.914758i | ||||
\(670\) | −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 | −0.0284546 | − | 0.999595i | \(-0.509059\pi\) |
0.879902 | − | 0.475155i | \(-0.157608\pi\) | |||||||
\(674\) | −9.52628 | + | 16.5000i | −0.366939 | + | 0.635556i | ||||
\(675\) | 8.00000 | 0.307920 | ||||||||
\(676\) | −7.89230 | − | 10.3301i | −0.303550 | − | 0.397313i | ||||
\(677\) | 23.0718 | 0.886721 | 0.443361 | − | 0.896343i | \(-0.353786\pi\) | ||||
0.443361 | + | 0.896343i | \(0.353786\pi\) | |||||||
\(678\) | 31.6865 | − | 54.8827i | 1.21691 | − | 2.10776i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −11.5981 | − | 20.0885i | −0.444766 | − | 0.770357i | ||||
\(681\) | 15.4641 | 0.592586 | ||||||||
\(682\) | 4.60770 | + | 7.98076i | 0.176438 | + | 0.305599i | ||||
\(683\) | −7.73205 | − | 13.3923i | −0.295859 | − | 0.512442i | 0.679326 | − | 0.733837i | \(-0.262272\pi\) |
−0.975184 | + | 0.221395i | \(0.928939\pi\) | |||||||
\(684\) | −8.92820 | −0.341378 | ||||||||
\(685\) | 6.99038 | + | 12.1077i | 0.267089 | + | 0.462611i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.6603 | − | 34.0526i | 0.750085 | − | 1.29919i | ||||
\(688\) | 0.980762 | 0.0373912 | ||||||||
\(689\) | 35.7224 | − | 2.30385i | 1.36092 | − | 0.0877696i | ||||
\(690\) | 38.7846 | 1.47650 | ||||||||
\(691\) | 0.196152 | − | 0.339746i | 0.00746199 | − | 0.0129245i | −0.862270 | − | 0.506448i | \(-0.830958\pi\) |
0.869732 | + | 0.493524i | \(0.164291\pi\) | |||||||
\(692\) | 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 | ||||
\(696\) | 7.09808 | + | 12.2942i | 0.269052 | + | 0.466012i | ||||
\(697\) | 40.1769 | 1.52181 | ||||||||
\(698\) | −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 | \(0.371606\pi\) | |||||||
\(702\) | −11.0718 | + | 22.3923i | −0.417878 | + | 0.845143i | ||||
\(703\) | 14.0000 | 0.528020 | ||||||||
\(704\) | −0.633975 | + | 1.09808i | −0.0238938 | + | 0.0413853i | ||||
\(705\) | 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 | ||||
\(709\) | −15.0885 | − | 26.1340i | −0.566659 | − | 0.981482i | −0.996893 | − | 0.0787648i | \(-0.974902\pi\) |
0.430234 | − | 0.902717i | \(-0.358431\pi\) | |||||||
\(710\) | −18.0000 | −0.675528 | ||||||||
\(711\) | −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 | ||||
\(716\) | −6.92820 | −0.258919 | ||||||||
\(717\) | −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 | ||||
\(723\) | −57.9090 | −2.15366 | ||||||||
\(724\) | 2.79423 | + | 4.83975i | 0.103847 | + | 0.179868i | ||||
\(725\) | −3.00000 | + | 5.19615i | −0.111417 | + | 0.192980i | ||||
\(726\) | −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 | ||||
\(731\) | 0.758330 | − | 1.31347i | 0.0280479 | − | 0.0485803i | ||||
\(732\) | 6.56218 | + | 11.3660i | 0.242545 | + | 0.420100i | ||||
\(733\) | −23.5885 | −0.871260 | −0.435630 | − | 0.900126i | \(-0.643474\pi\) | ||||
−0.435630 | + | 0.900126i | \(0.643474\pi\) | |||||||
\(734\) | 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 | \(0.896651\pi\) | |||||||
\(740\) | 12.1244 | 0.445700 | ||||||||
\(741\) | −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 | ||||
\(746\) | −19.7321 | −0.722442 | ||||||||
\(747\) | −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 | ||||
\(751\) | −17.9019 | + | 31.0070i | −0.653250 | + | 1.13146i | 0.329079 | + | 0.944302i | \(0.393262\pi\) |
−0.982329 | + | 0.187161i | \(0.940072\pi\) | |||||||
\(752\) | −32.3205 | + | 55.9808i | −1.17861 | + | 2.04141i | ||||
\(753\) | −4.39230 | −0.160064 | ||||||||
\(754\) | −10.3923 | − | 15.5885i | −0.378465 | − | 0.567698i | ||||
\(755\) | −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 | \(0.0727569\pi\) | |||||||
\(758\) | −23.0263 | − | 39.8827i | −0.836352 | − | 1.44860i | ||||
\(759\) | −16.3923 | −0.595003 | ||||||||
\(760\) | 3.00000 | + | 5.19615i | 0.108821 | + | 0.188484i | ||||
\(761\) | 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 | ||||
\(765\) | 29.8923 | − | 51.7750i | 1.08076 | − | 1.87193i | ||||
\(766\) | 20.1962 | 0.729717 | ||||||||
\(767\) | −14.5359 | − | 21.8038i | −0.524861 | − | 0.787291i | ||||
\(768\) | −51.9090 | −1.87310 | ||||||||
\(769\) | 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 | ||||
\(772\) | 5.00000 | 0.179954 | ||||||||
\(773\) | −6.46410 | − | 11.1962i | −0.232498 | − | 0.402698i | 0.726045 | − | 0.687647i | \(-0.241356\pi\) |
−0.958542 | + | 0.284950i | \(0.908023\pi\) | |||||||
\(774\) | 0.758330 | + | 1.31347i | 0.0272576 | + | 0.0472116i | ||||
\(775\) | 8.39230 | 0.301460 | ||||||||
\(776\) | −5.53590 | − | 9.58846i | −0.198727 | − | 0.344206i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.3827 | − | 35.3038i | 0.730755 | − | 1.26570i | ||||
\(779\) | −10.3923 | −0.372343 | ||||||||
\(780\) | −17.0263 | + | 1.09808i | −0.609639 | + | 0.0393174i | ||||
\(781\) | 7.60770 | 0.272225 | ||||||||
\(782\) | −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 | ||||||||
\(786\) | 8.19615 | + | 14.1962i | 0.292347 | + | 0.506360i | ||||
\(787\) | 6.49038 | + | 11.2417i | 0.231357 | + | 0.400722i | 0.958208 | − | 0.286073i | \(-0.0923501\pi\) |
−0.726851 | + | 0.686796i | \(0.759017\pi\) | |||||||
\(788\) | 12.0000 | 0.427482 | ||||||||
\(789\) | 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 | ||||||||
\(793\) | 9.60770 | + | 14.4115i | 0.341179 | + | 0.511769i | ||||
\(794\) | 32.5359 | 1.15466 | ||||||||
\(795\) | 23.4904 | − | 40.6865i | 0.833118 | − | 1.44300i | ||||
\(796\) | 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 | ||||
\(800\) | −5.19615 | − | 9.00000i | −0.183712 | − | 0.318198i | ||||
\(801\) | −57.7128 | −2.03918 | ||||||||
\(802\) | 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 | ||||
\(807\) | 13.8564 | 0.487769 | ||||||||
\(808\) | 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 | ||||
\(814\) | −15.3731 | −0.538826 | ||||||||
\(815\) | 14.0263 | + | 24.2942i | 0.491319 | + | 0.850990i | ||||
\(816\) | −52.8109 | + | 91.4711i | −1.84875 | + | 3.20213i | ||||
\(817\) | −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 | −0.899912 | − | 0.436072i | \(-0.856369\pi\) |
0.827605 | + | 0.561310i | \(0.189703\pi\) | |||||||
\(822\) | 19.0981 | − | 33.0788i | 0.666122 | − | 1.15376i | ||||
\(823\) | 20.5885 | + | 35.6603i | 0.717669 | + | 1.24304i | 0.961921 | + | 0.273327i | \(0.0881240\pi\) |
−0.244253 | + | 0.969712i | \(0.578543\pi\) | |||||||
\(824\) | −24.9282 | −0.868415 | ||||||||
\(825\) | −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 | ||||
\(831\) | −46.4449 | −1.61115 | ||||||||
\(832\) | −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 | ||||
\(837\) | 16.7846 | 0.580161 | ||||||||
\(838\) | −27.8827 | − | 48.2942i | −0.963191 | − | 1.66830i | ||||
\(839\) | −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 | ||||
\(843\) | 18.2942 | − | 31.6865i | 0.630087 | − | 1.09134i | ||||
\(844\) | −1.80385 | −0.0620910 | ||||||||
\(845\) | −22.3301 | + | 2.89230i | −0.768180 | + | 0.0994983i | ||||
\(846\) | −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 | ||||
\(850\) | −26.7846 | −0.918705 | ||||||||
\(851\) | 16.5622 | + | 28.6865i | 0.567744 | + | 0.983362i | ||||
\(852\) | 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 | ||||
\(856\) | −6.80385 | + | 11.7846i | −0.232551 | + | 0.402790i | ||||
\(857\) | 30.1244 | 1.02903 | 0.514514 | − | 0.857482i | \(-0.327972\pi\) | ||||
0.514514 | + | 0.857482i | \(0.327972\pi\) | |||||||
\(858\) | 21.5885 | − | 1.39230i | 0.737018 | − | 0.0475325i | ||||
\(859\) | 7.80385 | 0.266264 | 0.133132 | − | 0.991098i | \(-0.457497\pi\) | ||||
0.133132 | + | 0.991098i | \(0.457497\pi\) | |||||||
\(860\) | −0.169873 | + | 0.294229i | −0.00579262 | + | 0.0100331i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.588457 | − | 1.01924i | −0.0200429 | − | 0.0347154i | ||||
\(863\) | 7.51666 | 0.255870 | 0.127935 | − | 0.991783i | \(-0.459165\pi\) | ||||
0.127935 | + | 0.991783i | \(0.459165\pi\) | |||||||
\(864\) | −10.3923 | − | 18.0000i | −0.353553 | − | 0.612372i | ||||
\(865\) | −7.39230 | − | 12.8038i | −0.251346 | − | 0.435344i | ||||
\(866\) | 23.5359 | 0.799782 | ||||||||
\(867\) | 58.4449 | + | 101.229i | 1.98489 | + | 3.43793i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.2679 | + | 17.7846i | −0.348316 | + | 0.603302i | ||||
\(870\) | −24.5885 | −0.833627 | ||||||||
\(871\) | −9.90192 | + | 20.0263i | −0.335514 | + | 0.678565i | ||||
\(872\) | 14.5359 | 0.492248 | ||||||||
\(873\) | 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 | ||||||||
\(877\) | −9.89230 | − | 17.1340i | −0.334039 | − | 0.578573i | 0.649260 | − | 0.760566i | \(-0.275079\pi\) |
−0.983300 | + | 0.181993i | \(0.941745\pi\) | |||||||
\(878\) | 12.6340 | + | 21.8827i | 0.426376 | + | 0.738505i | ||||
\(879\) | −2.19615 | −0.0740744 | ||||||||
\(880\) | −5.49038 | − | 9.50962i | −0.185081 | − | 0.320569i | ||||
\(881\) | −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 | \(0.797147\pi\) | |||||||
\(884\) | 12.3564 | − | 24.9904i | 0.415591 | − | 0.840517i | ||||
\(885\) | −34.3923 | −1.15608 | ||||||||
\(886\) | −20.1962 | + | 34.9808i | −0.678503 | + | 1.17520i | ||||
\(887\) | 5.66025 | − | 9.80385i | 0.190053 | − | 0.329181i | −0.755215 | − | 0.655477i | \(-0.772467\pi\) |
0.945267 | + | 0.326296i | \(0.105801\pi\) | |||||||
\(888\) | 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 | ||||
\(892\) | 10.0000 | 0.334825 | ||||||||
\(893\) | −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 | ||||
\(898\) | −20.7846 | −0.693591 | ||||||||
\(899\) | −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 | ||||
\(905\) | 9.67949 | 0.321757 | ||||||||
\(906\) | 4.73205 | + | 8.19615i | 0.157212 | + | 0.272299i | ||||
\(907\) | 8.29423 | − | 14.3660i | 0.275405 | − | 0.477016i | −0.694832 | − | 0.719172i | \(-0.744521\pi\) |
0.970237 | + | 0.242156i | \(0.0778546\pi\) | |||||||
\(908\) | 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 | ||||
\(913\) | −1.39230 | + | 2.41154i | −0.0460786 | + | 0.0798104i | ||||
\(914\) | −9.52628 | − | 16.5000i | −0.315101 | − | 0.545771i | ||||
\(915\) | 22.7321 | 0.751498 | ||||||||
\(916\) | −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 | ||||
\(922\) | 27.0000 | 0.889198 | ||||||||
\(923\) | 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 | ||||
\(928\) | 15.5885 | 0.511716 | ||||||||
\(929\) | 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 | ||||
\(933\) | −1.73205 | + | 3.00000i | −0.0567048 | + | 0.0982156i | ||||
\(934\) | 22.0981 | − | 38.2750i | 0.723071 | − | 1.25240i | ||||
\(935\) | −16.9808 | −0.555330 | ||||||||
\(936\) | −15.4641 | − | 23.1962i | −0.505460 | − | 0.758190i | ||||
\(937\) | 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 | ||||
\(941\) | 28.1436 | 0.917455 | 0.458727 | − | 0.888577i | \(-0.348305\pi\) | ||||
0.458727 | + | 0.888577i | \(0.348305\pi\) | |||||||
\(942\) | −2.83013 | − | 4.90192i | −0.0922105 | − | 0.159713i | ||||
\(943\) | −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 | ||||
\(947\) | 3.63397 | − | 6.29423i | 0.118088 | − | 0.204535i | −0.800922 | − | 0.598769i | \(-0.795657\pi\) |
0.919010 | + | 0.394234i | \(0.128990\pi\) | |||||||
\(948\) | −44.2487 | −1.43713 | ||||||||
\(949\) | −11.5000 | + | 0.741670i | −0.373306 | + | 0.0240756i | ||||
\(950\) | 6.92820 | 0.224781 | ||||||||
\(951\) | −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 | \(0.699636\pi\) | |||||||
\(954\) | −76.7654 | −2.48537 | ||||||||
\(955\) | 4.09808 | + | 7.09808i | 0.132611 | + | 0.229688i | ||||
\(956\) | 7.90192 | + | 13.6865i | 0.255566 | + | 0.442654i | ||||
\(957\) | 10.3923 | 0.335936 | ||||||||
\(958\) | 1.09808 | + | 1.90192i | 0.0354772 | + | 0.0614484i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.36603 | + | 4.09808i | −0.0763631 | + | 0.132265i | ||||
\(961\) | −13.3923 | −0.432010 | ||||||||
\(962\) | −24.2487 | − | 36.3731i | −0.781810 | − | 1.17271i | ||||
\(963\) | −35.0718 | −1.13017 | ||||||||
\(964\) | −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 | \(0.154819\pi\) | |||||||
\(968\) | −8.13397 | − | 14.0885i | −0.261436 | − | 0.452820i | ||||
\(969\) | −21.1244 | − | 36.5885i | −0.678612 | − | 1.17539i | ||||
\(970\) | 19.1769 | 0.615734 | ||||||||
\(971\) | −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 | ||||||||
\(975\) | 8.73205 | − | 17.6603i | 0.279649 | − | 0.565581i | ||||
\(976\) | −24.0192 | −0.768837 | ||||||||
\(977\) | −15.8205 | + | 27.4019i | −0.506143 | + | 0.876665i | 0.493832 | + | 0.869557i | \(0.335596\pi\) |
−0.999975 | + | 0.00710779i | \(0.997738\pi\) | |||||||
\(978\) | 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 | ||||
\(982\) | −6.58846 | − | 11.4115i | −0.210246 | − | 0.364157i | ||||
\(983\) | 17.3205 | 0.552438 | 0.276219 | − | 0.961095i | \(-0.410918\pi\) | ||||
0.276219 | + | 0.961095i | \(0.410918\pi\) | |||||||
\(984\) | −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 | ||||
\(989\) | −0.928203 | −0.0295151 | ||||||||
\(990\) | 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 | ||||
\(996\) | −6.00000 | −0.190117 | ||||||||
\(997\) | −2.40192 | − | 4.16025i | −0.0760697 | − | 0.131757i | 0.825481 | − | 0.564430i | \(-0.190904\pi\) |
−0.901551 | + | 0.432673i | \(0.857570\pi\) | |||||||
\(998\) | 33.7583 | − | 58.4711i | 1.06860 | − | 1.85087i | ||||
\(999\) | −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.f.d.295.1 | 4 | ||
7.2 | even | 3 | 637.2.h.e.165.2 | 4 | |||
7.3 | odd | 6 | 637.2.g.e.373.1 | 4 | |||
7.4 | even | 3 | 637.2.g.d.373.1 | 4 | |||
7.5 | odd | 6 | 637.2.h.d.165.2 | 4 | |||
7.6 | odd | 2 | 91.2.f.b.22.1 | ✓ | 4 | ||
13.3 | even | 3 | inner | 637.2.f.d.393.1 | 4 | ||
13.4 | even | 6 | 8281.2.a.t.1.1 | 2 | |||
13.9 | even | 3 | 8281.2.a.r.1.2 | 2 | |||
21.20 | even | 2 | 819.2.o.b.568.2 | 4 | |||
28.27 | even | 2 | 1456.2.s.o.113.2 | 4 | |||
91.3 | odd | 6 | 637.2.h.d.471.2 | 4 | |||
91.6 | even | 12 | 1183.2.c.e.337.2 | 4 | |||
91.16 | even | 3 | 637.2.g.d.263.1 | 4 | |||
91.20 | even | 12 | 1183.2.c.e.337.4 | 4 | |||
91.48 | odd | 6 | 1183.2.a.f.1.2 | 2 | |||
91.55 | odd | 6 | 91.2.f.b.29.1 | yes | 4 | ||
91.68 | odd | 6 | 637.2.g.e.263.1 | 4 | |||
91.69 | odd | 6 | 1183.2.a.e.1.1 | 2 | |||
91.81 | even | 3 | 637.2.h.e.471.2 | 4 | |||
273.146 | even | 6 | 819.2.o.b.757.2 | 4 | |||
364.55 | 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 | 7.6 | odd | 2 | ||
91.2.f.b.29.1 | yes | 4 | 91.55 | odd | 6 | ||
637.2.f.d.295.1 | 4 | 1.1 | even | 1 | trivial | ||
637.2.f.d.393.1 | 4 | 13.3 | even | 3 | inner | ||
637.2.g.d.263.1 | 4 | 91.16 | even | 3 | |||
637.2.g.d.373.1 | 4 | 7.4 | even | 3 | |||
637.2.g.e.263.1 | 4 | 91.68 | odd | 6 | |||
637.2.g.e.373.1 | 4 | 7.3 | odd | 6 | |||
637.2.h.d.165.2 | 4 | 7.5 | odd | 6 | |||
637.2.h.d.471.2 | 4 | 91.3 | odd | 6 | |||
637.2.h.e.165.2 | 4 | 7.2 | even | 3 | |||
637.2.h.e.471.2 | 4 | 91.81 | even | 3 | |||
819.2.o.b.568.2 | 4 | 21.20 | even | 2 | |||
819.2.o.b.757.2 | 4 | 273.146 | even | 6 | |||
1183.2.a.e.1.1 | 2 | 91.69 | odd | 6 | |||
1183.2.a.f.1.2 | 2 | 91.48 | odd | 6 | |||
1183.2.c.e.337.2 | 4 | 91.6 | even | 12 | |||
1183.2.c.e.337.4 | 4 | 91.20 | even | 12 | |||
1456.2.s.o.113.2 | 4 | 28.27 | even | 2 | |||
1456.2.s.o.1121.2 | 4 | 364.55 | even | 6 | |||
8281.2.a.r.1.2 | 2 | 13.9 | even | 3 | |||
8281.2.a.t.1.1 | 2 | 13.4 | even | 6 |