Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(109,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.d (of order \(2\), degree \(1\), 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: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3x^{18} + 8x^{16} - 24x^{14} + 56x^{12} - 92x^{10} + 224x^{8} - 384x^{6} + 512x^{4} - 768x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 109.13 | ||
Root | \(-0.847166 - 1.13239i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.109 |
Dual form | 1080.2.d.i.109.14 |
$q$-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 \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.847166 | − | 1.13239i | 0.599037 | − | 0.800721i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.564618 | − | 1.91865i | −0.282309 | − | 0.959323i | ||||
\(5\) | −1.82935 | + | 1.28588i | −0.818109 | + | 0.575064i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.09701i | 0.414631i | 0.978274 | + | 0.207315i | \(0.0664726\pi\) | ||||
−0.978274 | + | 0.207315i | \(0.933527\pi\) | |||||||
\(8\) | −2.65098 | − | 0.986045i | −0.937264 | − | 0.348619i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.0936411 | + | 3.16089i | −0.0296119 | + | 0.999561i | ||||
\(11\) | 1.89459i | 0.571240i | 0.958343 | + | 0.285620i | \(0.0921996\pi\) | ||||
−0.958343 | + | 0.285620i | \(0.907800\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.10133 | 1.13750 | 0.568752 | − | 0.822509i | \(-0.307427\pi\) | ||||
0.568752 | + | 0.822509i | \(0.307427\pi\) | |||||||
\(14\) | 1.24224 | + | 0.929350i | 0.332004 | + | 0.248379i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.36241 | + | 2.16661i | −0.840603 | + | 0.541652i | ||||
\(17\) | 1.70100i | 0.412553i | 0.978494 | + | 0.206276i | \(0.0661346\pi\) | ||||
−0.978494 | + | 0.206276i | \(0.933865\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.95035i | 1.36510i | 0.730837 | + | 0.682552i | \(0.239130\pi\) | ||||
−0.730837 | + | 0.682552i | \(0.760870\pi\) | |||||||
\(20\) | 3.50003 | + | 2.78384i | 0.782632 | + | 0.622485i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.14542 | + | 1.60503i | 0.457404 | + | 0.342194i | ||||
\(23\) | − | 0.424153i | − | 0.0884420i | −0.999022 | − | 0.0442210i | \(-0.985919\pi\) | ||
0.999022 | − | 0.0442210i | \(-0.0140806\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.69302 | − | 4.70465i | 0.338604 | − | 0.940929i | ||||
\(26\) | 3.47451 | − | 4.64430i | 0.681407 | − | 0.910823i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.10477 | − | 0.619392i | 0.397765 | − | 0.117054i | ||||
\(29\) | 7.44798i | 1.38306i | 0.722350 | + | 0.691528i | \(0.243062\pi\) | ||||
−0.722350 | + | 0.691528i | \(0.756938\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.46635 | 0.442970 | 0.221485 | − | 0.975164i | \(-0.428910\pi\) | ||||
0.221485 | + | 0.975164i | \(0.428910\pi\) | |||||||
\(32\) | −0.395078 | + | 5.64304i | −0.0698405 | + | 0.997558i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.92620 | + | 1.44103i | 0.330340 | + | 0.247134i | ||||
\(35\) | −1.41062 | − | 2.00681i | −0.238439 | − | 0.339213i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00954 | −0.659164 | −0.329582 | − | 0.944127i | \(-0.606908\pi\) | ||||
−0.329582 | + | 0.944127i | \(0.606908\pi\) | |||||||
\(38\) | 6.73812 | + | 5.04094i | 1.09307 | + | 0.817748i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.11751 | − | 1.60503i | 0.967263 | − | 0.253778i | ||||
\(41\) | 8.17051 | 1.27602 | 0.638009 | − | 0.770029i | \(-0.279758\pi\) | ||||
0.638009 | + | 0.770029i | \(0.279758\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0436 | 1.68413 | 0.842064 | − | 0.539377i | \(-0.181340\pi\) | ||||
0.842064 | + | 0.539377i | \(0.181340\pi\) | |||||||
\(44\) | 3.63505 | − | 1.06972i | 0.548004 | − | 0.161266i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.480307 | − | 0.359328i | −0.0708174 | − | 0.0529801i | ||||
\(47\) | − | 2.28638i | − | 0.333503i | −0.985999 | − | 0.166752i | \(-0.946672\pi\) | ||
0.985999 | − | 0.166752i | \(-0.0533278\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.79657 | 0.828081 | ||||||||
\(50\) | −3.89323 | − | 5.90278i | −0.550586 | − | 0.834779i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.31568 | − | 7.86900i | −0.321128 | − | 1.09123i | ||||
\(53\) | −12.3020 | −1.68981 | −0.844907 | − | 0.534913i | \(-0.820345\pi\) | ||||
−0.844907 | + | 0.534913i | \(0.820345\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.43622 | − | 3.46586i | −0.328499 | − | 0.467337i | ||||
\(56\) | 1.08170 | − | 2.90816i | 0.144548 | − | 0.388619i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.43402 | + | 6.30968i | 1.10744 | + | 0.828501i | ||||
\(59\) | 12.4017i | 1.61456i | 0.590166 | + | 0.807282i | \(0.299062\pi\) | ||||
−0.590166 | + | 0.807282i | \(0.700938\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.83171i | 0.362564i | 0.983431 | + | 0.181282i | \(0.0580246\pi\) | ||||
−0.983431 | + | 0.181282i | \(0.941975\pi\) | |||||||
\(62\) | 2.08941 | − | 2.79287i | 0.265355 | − | 0.354695i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.05543 | + | 5.22798i | 0.756929 | + | 0.653497i | ||||
\(65\) | −7.50275 | + | 5.27382i | −0.930601 | + | 0.654137i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.91266 | 0.600177 | 0.300089 | − | 0.953911i | \(-0.402984\pi\) | ||||
0.300089 | + | 0.953911i | \(0.402984\pi\) | |||||||
\(68\) | 3.26362 | − | 0.960415i | 0.395772 | − | 0.116467i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.46753 | − | 0.102725i | −0.414449 | − | 0.0122780i | ||||
\(71\) | −1.69810 | −0.201528 | −0.100764 | − | 0.994910i | \(-0.532129\pi\) | ||||
−0.100764 | + | 0.994910i | \(0.532129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.69321i | − | 0.783381i | −0.920097 | − | 0.391691i | \(-0.871890\pi\) | ||
0.920097 | − | 0.391691i | \(-0.128110\pi\) | |||||||
\(74\) | −3.39675 | + | 4.54036i | −0.394864 | + | 0.527807i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.4166 | − | 3.35968i | 1.30958 | − | 0.385381i | ||||
\(77\) | −2.07838 | −0.236854 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.7388 | −1.43323 | −0.716614 | − | 0.697470i | \(-0.754309\pi\) | ||||
−0.716614 | + | 0.697470i | \(0.754309\pi\) | |||||||
\(80\) | 3.36502 | − | 8.28714i | 0.376221 | − | 0.926530i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.92178 | − | 9.25221i | 0.764383 | − | 1.02174i | ||||
\(83\) | 2.43343 | 0.267104 | 0.133552 | − | 0.991042i | \(-0.457362\pi\) | ||||
0.133552 | + | 0.991042i | \(0.457362\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.18728 | − | 3.11172i | −0.237244 | − | 0.337513i | ||||
\(86\) | 9.35574 | − | 12.5056i | 1.00886 | − | 1.34852i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.86815 | − | 5.02253i | 0.199145 | − | 0.535403i | ||||
\(89\) | −12.0320 | −1.27539 | −0.637695 | − | 0.770289i | \(-0.720112\pi\) | ||||
−0.637695 | + | 0.770289i | \(0.720112\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.49919i | 0.471644i | ||||||||
\(92\) | −0.813800 | + | 0.239485i | −0.0848445 | + | 0.0249680i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.58908 | − | 1.93695i | −0.267043 | − | 0.199781i | ||||
\(95\) | −7.65144 | − | 10.8853i | −0.785021 | − | 1.11680i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.20448i | − | 0.223831i | −0.993718 | − | 0.111916i | \(-0.964301\pi\) | ||
0.993718 | − | 0.111916i | \(-0.0356987\pi\) | |||||||
\(98\) | 4.91066 | − | 6.56398i | 0.496051 | − | 0.663062i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.98246 | − | 0.591978i | −0.998246 | − | 0.0591978i | ||||
\(101\) | 2.45373i | 0.244156i | 0.992521 | + | 0.122078i | \(0.0389558\pi\) | ||||
−0.992521 | + | 0.122078i | \(0.961044\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.7324i | 1.45163i | 0.687891 | + | 0.725814i | \(0.258537\pi\) | ||||
−0.687891 | + | 0.725814i | \(0.741463\pi\) | |||||||
\(104\) | −10.8725 | − | 4.04409i | −1.06614 | − | 0.396556i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.4219 | + | 13.9307i | −1.01226 | + | 1.35307i | ||||
\(107\) | −11.1789 | −1.08070 | −0.540352 | − | 0.841439i | \(-0.681709\pi\) | ||||
−0.540352 | + | 0.841439i | \(0.681709\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.23427i | − | 0.309787i | −0.987931 | − | 0.154894i | \(-0.950497\pi\) | ||
0.987931 | − | 0.154894i | \(-0.0495035\pi\) | |||||||
\(110\) | −5.98859 | − | 0.177411i | −0.570990 | − | 0.0169155i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.37679 | − | 3.68860i | −0.224585 | − | 0.348540i | ||||
\(113\) | − | 14.2007i | − | 1.33589i | −0.744210 | − | 0.667945i | \(-0.767174\pi\) | ||
0.744210 | − | 0.667945i | \(-0.232826\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.545411 | + | 0.775923i | 0.0508598 | + | 0.0723552i | ||||
\(116\) | 14.2900 | − | 4.20527i | 1.32680 | − | 0.390449i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.0436 | + | 10.5063i | 1.29282 | + | 0.967183i | ||||
\(119\) | −1.86601 | −0.171057 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.41053 | 0.673685 | ||||||||
\(122\) | 3.20660 | + | 2.39893i | 0.290312 | + | 0.217189i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.39255 | − | 4.73206i | −0.125054 | − | 0.424951i | ||||
\(125\) | 2.95249 | + | 10.7834i | 0.264079 | + | 0.964501i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.3182i | 1.80294i | 0.432837 | + | 0.901472i | \(0.357513\pi\) | ||||
−0.432837 | + | 0.901472i | \(0.642487\pi\) | |||||||
\(128\) | 11.0501 | − | 2.42815i | 0.976698 | − | 0.214620i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.384053 | + | 12.9638i | −0.0336836 | + | 1.13700i | ||||
\(131\) | − | 1.49044i | − | 0.130221i | −0.997878 | − | 0.0651104i | \(-0.979260\pi\) | ||
0.997878 | − | 0.0651104i | \(-0.0207399\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.52759 | −0.566014 | ||||||||
\(134\) | 4.16184 | − | 5.56305i | 0.359528 | − | 0.480575i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.67726 | − | 4.50932i | 0.143824 | − | 0.386671i | ||||
\(137\) | − | 7.45176i | − | 0.636647i | −0.947982 | − | 0.318324i | \(-0.896880\pi\) | ||
0.947982 | − | 0.318324i | \(-0.103120\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.71608i | − | 0.230375i | −0.993344 | − | 0.115187i | \(-0.963253\pi\) | ||
0.993344 | − | 0.115187i | \(-0.0367468\pi\) | |||||||
\(140\) | −3.05390 | + | 3.83957i | −0.258102 | + | 0.324503i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.43857 | + | 1.92291i | −0.120722 | + | 0.161367i | ||||
\(143\) | 7.77033i | 0.649788i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.57722 | − | 13.6249i | −0.795344 | − | 1.13149i | ||||
\(146\) | −7.57933 | − | 5.67027i | −0.627270 | − | 0.469275i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.26386 | + | 7.69289i | 0.186088 | + | 0.632352i | ||||
\(149\) | − | 6.06321i | − | 0.496718i | −0.968668 | − | 0.248359i | \(-0.920109\pi\) | ||
0.968668 | − | 0.248359i | \(-0.0798912\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.8664 | −1.12843 | −0.564215 | − | 0.825628i | \(-0.690821\pi\) | ||||
−0.564215 | + | 0.825628i | \(0.690821\pi\) | |||||||
\(152\) | 5.86731 | − | 15.7743i | 0.475902 | − | 1.27946i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.76074 | + | 2.35354i | −0.141884 | + | 0.189654i | ||||
\(155\) | −4.51181 | + | 3.17144i | −0.362398 | + | 0.254736i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.6208 | −0.927439 | −0.463720 | − | 0.885982i | \(-0.653486\pi\) | ||||
−0.463720 | + | 0.885982i | \(0.653486\pi\) | |||||||
\(158\) | −10.7919 | + | 14.4253i | −0.858557 | + | 1.14762i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.53355 | − | 10.8311i | −0.516522 | − | 0.856274i | ||||
\(161\) | 0.465300 | 0.0366708 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.01908 | 0.393124 | 0.196562 | − | 0.980491i | \(-0.437022\pi\) | ||||
0.196562 | + | 0.980491i | \(0.437022\pi\) | |||||||
\(164\) | −4.61322 | − | 15.6763i | −0.360232 | − | 1.22411i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.06152 | − | 2.75559i | 0.160005 | − | 0.213876i | ||||
\(167\) | 3.74825i | 0.290048i | 0.989428 | + | 0.145024i | \(0.0463260\pi\) | ||||
−0.989428 | + | 0.145024i | \(0.953674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.82087 | 0.293913 | ||||||||
\(170\) | −5.37667 | − | 0.159283i | −0.412372 | − | 0.0122165i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.23540 | − | 21.1887i | −0.475445 | − | 1.61562i | ||||
\(173\) | 10.6039 | 0.806202 | 0.403101 | − | 0.915155i | \(-0.367932\pi\) | ||||
0.403101 | + | 0.915155i | \(0.367932\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.16104 | + | 1.85726i | 0.390138 | + | 0.140396i | ||||
\(176\) | −4.10483 | − | 6.37039i | −0.309413 | − | 0.480186i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.1931 | + | 13.6249i | −0.764006 | + | 1.02123i | ||||
\(179\) | 15.7506i | 1.17725i | 0.808405 | + | 0.588627i | \(0.200331\pi\) | ||||
−0.808405 | + | 0.588627i | \(0.799669\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.9558i | − | 1.55764i | −0.627250 | − | 0.778818i | \(-0.715820\pi\) | ||
0.627250 | − | 0.778818i | \(-0.284180\pi\) | |||||||
\(182\) | 5.09485 | + | 3.81157i | 0.377655 | + | 0.282532i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.418234 | + | 1.12442i | −0.0308326 | + | 0.0828936i | ||||
\(185\) | 7.33484 | − | 5.15579i | 0.539268 | − | 0.379061i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.22269 | −0.235667 | ||||||||
\(188\) | −4.38676 | + | 1.29093i | −0.319938 | + | 0.0941510i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.8084 | − | 0.557197i | −1.36451 | − | 0.0404233i | ||||
\(191\) | 18.2070 | 1.31741 | 0.658707 | − | 0.752400i | \(-0.271104\pi\) | ||||
0.658707 | + | 0.752400i | \(0.271104\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 8.88723i | − | 0.639717i | −0.947465 | − | 0.319859i | \(-0.896365\pi\) | ||
0.947465 | − | 0.319859i | \(-0.103635\pi\) | |||||||
\(194\) | −2.49634 | − | 1.86756i | −0.179227 | − | 0.134083i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.27285 | − | 11.1216i | −0.233775 | − | 0.794398i | ||||
\(197\) | 8.73792 | 0.622551 | 0.311276 | − | 0.950320i | \(-0.399244\pi\) | ||||
0.311276 | + | 0.950320i | \(0.399244\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.72289 | 0.689237 | 0.344619 | − | 0.938743i | \(-0.388008\pi\) | ||||
0.344619 | + | 0.938743i | \(0.388008\pi\) | |||||||
\(200\) | −9.12716 | + | 10.8025i | −0.645388 | + | 0.763855i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.77859 | + | 2.07872i | 0.195501 | + | 0.146258i | ||||
\(203\) | −8.17051 | −0.573457 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.9467 | + | 10.5063i | −1.04392 | + | 0.733792i | ||||
\(206\) | 16.6828 | + | 12.4808i | 1.16235 | + | 0.869579i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.7903 | + | 8.88596i | −0.956189 | + | 0.616130i | ||||
\(209\) | −11.2735 | −0.779802 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0843i | 0.969600i | 0.874625 | + | 0.484800i | \(0.161108\pi\) | ||||
−0.874625 | + | 0.484800i | \(0.838892\pi\) | |||||||
\(212\) | 6.94595 | + | 23.6033i | 0.477050 | + | 1.62108i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.47038 | + | 12.6589i | −0.647382 | + | 0.865343i | ||||
\(215\) | −20.2025 | + | 14.2007i | −1.37780 | + | 0.968481i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.70561i | 0.183669i | ||||||||
\(218\) | −3.66246 | − | 2.73997i | −0.248053 | − | 0.185574i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.27423 | + | 6.63113i | −0.355589 | + | 0.447071i | ||||
\(221\) | 6.97635i | 0.469280i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.23727i | − | 0.417679i | −0.977950 | − | 0.208839i | \(-0.933031\pi\) | ||
0.977950 | − | 0.208839i | \(-0.0669686\pi\) | |||||||
\(224\) | −6.19047 | − | 0.433404i | −0.413618 | − | 0.0289580i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.0808 | − | 12.0304i | −1.06968 | − | 0.800248i | ||||
\(227\) | −9.75082 | −0.647184 | −0.323592 | − | 0.946197i | \(-0.604891\pi\) | ||||
−0.323592 | + | 0.946197i | \(0.604891\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 26.7906i | − | 1.77037i | −0.465239 | − | 0.885185i | \(-0.654032\pi\) | ||
0.465239 | − | 0.885185i | \(-0.345968\pi\) | |||||||
\(230\) | 1.34070 | + | 0.0397182i | 0.0884033 | + | 0.00261894i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.34404 | − | 19.7445i | 0.482160 | − | 1.29629i | ||||
\(233\) | 27.7728i | 1.81946i | 0.415201 | + | 0.909730i | \(0.363711\pi\) | ||||
−0.415201 | + | 0.909730i | \(0.636289\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.94002 | + | 4.18259i | 0.191786 | + | 0.272842i | ||||
\(236\) | 23.7945 | − | 7.00222i | 1.54889 | − | 0.455806i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.58082 | + | 2.11306i | −0.102470 | + | 0.136969i | ||||
\(239\) | 6.89512 | 0.446008 | 0.223004 | − | 0.974817i | \(-0.428414\pi\) | ||||
0.223004 | + | 0.974817i | \(0.428414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7239 | 0.690784 | 0.345392 | − | 0.938458i | \(-0.387746\pi\) | ||||
0.345392 | + | 0.938458i | \(0.387746\pi\) | |||||||
\(242\) | 6.27795 | − | 8.39162i | 0.403562 | − | 0.539434i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.43306 | − | 1.59884i | 0.347816 | − | 0.102355i | ||||
\(245\) | −10.6039 | + | 7.45370i | −0.677461 | + | 0.476199i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.4043i | 1.55281i | ||||||||
\(248\) | −6.53826 | − | 2.43193i | −0.415180 | − | 0.154428i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.7123 | + | 5.79200i | 0.930490 | + | 0.366318i | ||||
\(251\) | − | 15.6506i | − | 0.987859i | −0.869502 | − | 0.493930i | \(-0.835560\pi\) | ||
0.869502 | − | 0.493930i | \(-0.164440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.803596 | 0.0505217 | ||||||||
\(254\) | 23.0081 | + | 17.2129i | 1.44366 | + | 1.08003i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.61163 | − | 14.5700i | 0.413227 | − | 0.910628i | ||||
\(257\) | − | 12.0836i | − | 0.753755i | −0.926263 | − | 0.376878i | \(-0.876998\pi\) | ||
0.926263 | − | 0.376878i | \(-0.123002\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 4.39850i | − | 0.273310i | ||||||
\(260\) | 14.3548 | + | 11.4174i | 0.890246 | + | 0.708079i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.68777 | − | 1.26265i | −0.104270 | − | 0.0780070i | ||||
\(263\) | − | 7.88836i | − | 0.486417i | −0.969974 | − | 0.243208i | \(-0.921800\pi\) | ||
0.969974 | − | 0.243208i | \(-0.0781999\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.5047 | − | 15.8190i | 1.38245 | − | 0.971751i | ||||
\(266\) | −5.52996 | + | 7.39179i | −0.339063 | + | 0.453219i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.77378 | − | 9.42566i | −0.169435 | − | 0.575764i | ||||
\(269\) | − | 27.9544i | − | 1.70441i | −0.523207 | − | 0.852206i | \(-0.675265\pi\) | ||
0.523207 | − | 0.852206i | \(-0.324735\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.19311 | −0.497696 | −0.248848 | − | 0.968543i | \(-0.580052\pi\) | ||||
−0.248848 | + | 0.968543i | \(0.580052\pi\) | |||||||
\(272\) | −3.68539 | − | 5.71946i | −0.223460 | − | 0.346793i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.43831 | − | 6.31288i | −0.509777 | − | 0.381375i | ||||
\(275\) | 8.91337 | + | 3.20758i | 0.537497 | + | 0.193424i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.7989 | −1.73036 | −0.865180 | − | 0.501461i | \(-0.832796\pi\) | ||||
−0.865180 | + | 0.501461i | \(0.832796\pi\) | |||||||
\(278\) | −3.07566 | − | 2.30097i | −0.184466 | − | 0.138003i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.76074 | + | 6.71096i | 0.105224 | + | 0.401057i | ||||
\(281\) | 26.2790 | 1.56767 | 0.783836 | − | 0.620968i | \(-0.213260\pi\) | ||||
0.783836 | + | 0.620968i | \(0.213260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.01908 | 0.476685 | 0.238342 | − | 0.971181i | \(-0.423396\pi\) | ||||
0.238342 | + | 0.971181i | \(0.423396\pi\) | |||||||
\(284\) | 0.958779 | + | 3.25806i | 0.0568931 | + | 0.193330i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.79905 | + | 6.58276i | 0.520299 | + | 0.389247i | ||||
\(287\) | 8.96313i | 0.529077i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.1066 | 0.829800 | ||||||||
\(290\) | −23.5423 | − | 0.697437i | −1.38245 | − | 0.0409549i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.8419 | + | 3.77911i | −0.751516 | + | 0.221156i | ||||
\(293\) | 10.3414 | 0.604154 | 0.302077 | − | 0.953284i | \(-0.402320\pi\) | ||||
0.302077 | + | 0.953284i | \(0.402320\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.9471 | − | 22.6870i | −0.928476 | − | 1.32089i | ||||
\(296\) | 10.6292 | + | 3.95358i | 0.617811 | + | 0.229797i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.86593 | − | 5.13655i | −0.397732 | − | 0.297552i | ||||
\(299\) | − | 1.73959i | − | 0.100603i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.1149i | 0.698291i | ||||||||
\(302\) | −11.7471 | + | 15.7022i | −0.675971 | + | 0.903558i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.8921 | − | 20.0075i | −0.739411 | − | 1.14751i | ||||
\(305\) | −3.64124 | − | 5.18018i | −0.208497 | − | 0.296616i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.5835 | −0.889395 | −0.444698 | − | 0.895681i | \(-0.646689\pi\) | ||||
−0.444698 | + | 0.895681i | \(0.646689\pi\) | |||||||
\(308\) | 1.17349 | + | 3.98768i | 0.0668660 | + | 0.227219i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.230952 | + | 7.79587i | −0.0131172 | + | 0.442776i | ||||
\(311\) | 28.1450 | 1.59596 | 0.797978 | − | 0.602687i | \(-0.205903\pi\) | ||||
0.797978 | + | 0.602687i | \(0.205903\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7.10412i | − | 0.401548i | −0.979638 | − | 0.200774i | \(-0.935654\pi\) | ||
0.979638 | − | 0.200774i | \(-0.0643457\pi\) | |||||||
\(314\) | −9.84474 | + | 13.1593i | −0.555571 | + | 0.742621i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.19257 | + | 24.4413i | 0.404613 | + | 1.37493i | ||||
\(317\) | −10.6039 | −0.595576 | −0.297788 | − | 0.954632i | \(-0.596249\pi\) | ||||
−0.297788 | + | 0.954632i | \(0.596249\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.1109 | −0.790057 | ||||||||
\(320\) | −17.8000 | − | 1.77722i | −0.995053 | − | 0.0993495i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.394187 | − | 0.526902i | 0.0219672 | − | 0.0293631i | ||||
\(323\) | −10.1215 | −0.563177 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.94362 | − | 19.2953i | 0.385163 | − | 1.07031i | ||||
\(326\) | 4.25199 | − | 5.68356i | 0.235496 | − | 0.314783i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −21.6599 | − | 8.05648i | −1.19597 | − | 0.444845i | ||||
\(329\) | 2.50819 | 0.138281 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 32.0939i | − | 1.76404i | −0.471214 | − | 0.882019i | \(-0.656184\pi\) | ||
0.471214 | − | 0.882019i | \(-0.343816\pi\) | |||||||
\(332\) | −1.37396 | − | 4.66889i | −0.0754058 | − | 0.256239i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.24449 | + | 3.17539i | 0.232248 | + | 0.173750i | ||||
\(335\) | −8.98696 | + | 6.31710i | −0.491010 | + | 0.345140i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.7507i | 1.23931i | 0.784875 | + | 0.619654i | \(0.212727\pi\) | ||||
−0.784875 | + | 0.619654i | \(0.787273\pi\) | |||||||
\(338\) | 3.23692 | − | 4.32672i | 0.176065 | − | 0.235343i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.73531 | + | 5.95355i | −0.256808 | + | 0.322877i | ||||
\(341\) | 4.67272i | 0.253042i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.0380i | 0.757979i | ||||||||
\(344\) | −29.2763 | − | 10.8895i | −1.57847 | − | 0.587120i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.98330 | − | 12.0078i | 0.482945 | − | 0.645543i | ||||
\(347\) | 23.2109 | 1.24603 | 0.623013 | − | 0.782211i | \(-0.285908\pi\) | ||||
0.623013 | + | 0.782211i | \(0.285908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.0786i | 1.44948i | 0.689021 | + | 0.724742i | \(0.258041\pi\) | ||||
−0.689021 | + | 0.724742i | \(0.741959\pi\) | |||||||
\(350\) | 6.47540 | − | 4.27091i | 0.346125 | − | 0.228290i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.6912 | − | 0.748510i | −0.569845 | − | 0.0398957i | ||||
\(353\) | − | 10.9128i | − | 0.580832i | −0.956900 | − | 0.290416i | \(-0.906206\pi\) | ||
0.956900 | − | 0.290416i | \(-0.0937937\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.10642 | − | 2.18356i | 0.164871 | − | 0.115891i | ||||
\(356\) | 6.79349 | + | 23.0852i | 0.360054 | + | 1.22351i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.8358 | + | 13.3434i | 0.942652 | + | 0.705219i | ||||
\(359\) | 4.15889 | 0.219498 | 0.109749 | − | 0.993959i | \(-0.464995\pi\) | ||||
0.109749 | + | 0.993959i | \(0.464995\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4067 | −0.863508 | ||||||||
\(362\) | −23.7302 | − | 17.7531i | −1.24723 | − | 0.933081i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.63237 | − | 2.54033i | 0.452459 | − | 0.133149i | ||||
\(365\) | 8.60668 | + | 12.2442i | 0.450494 | + | 0.640891i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.0413i | 1.51595i | 0.652286 | + | 0.757973i | \(0.273810\pi\) | ||||
−0.652286 | + | 0.757973i | \(0.726190\pi\) | |||||||
\(368\) | 0.918973 | + | 1.42618i | 0.0479048 | + | 0.0743447i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.375457 | − | 12.6737i | 0.0195191 | − | 0.658875i | ||||
\(371\) | − | 13.4955i | − | 0.700649i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.47589 | −0.438865 | −0.219432 | − | 0.975628i | \(-0.570421\pi\) | ||||
−0.219432 | + | 0.975628i | \(0.570421\pi\) | |||||||
\(374\) | −2.73016 | + | 3.64935i | −0.141173 | + | 0.188703i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.25448 | + | 6.06117i | −0.116266 | + | 0.312581i | ||||
\(377\) | 30.5466i | 1.57323i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.9629i | 1.38499i | 0.721421 | + | 0.692497i | \(0.243489\pi\) | ||||
−0.721421 | + | 0.692497i | \(0.756511\pi\) | |||||||
\(380\) | −16.5648 | + | 20.8264i | −0.849757 | + | 1.06837i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.4244 | − | 20.6175i | 0.789180 | − | 1.05488i | ||||
\(383\) | − | 28.1503i | − | 1.43842i | −0.694795 | − | 0.719208i | \(-0.744505\pi\) | ||
0.694795 | − | 0.719208i | \(-0.255495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.80208 | − | 2.67255i | 0.193772 | − | 0.136206i | ||||
\(386\) | −10.0638 | − | 7.52897i | −0.512235 | − | 0.383214i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.22963 | + | 1.24469i | −0.214727 | + | 0.0631896i | ||||
\(389\) | − | 28.4441i | − | 1.44217i | −0.692844 | − | 0.721087i | \(-0.743643\pi\) | ||
0.692844 | − | 0.721087i | \(-0.256357\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.721484 | 0.0364870 | ||||||||
\(392\) | −15.3666 | − | 5.71568i | −0.776131 | − | 0.288685i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.40248 | − | 9.89475i | 0.372931 | − | 0.498490i | ||||
\(395\) | 23.3037 | − | 16.3806i | 1.17254 | − | 0.824197i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.9844 | 0.952800 | 0.476400 | − | 0.879229i | \(-0.341941\pi\) | ||||
0.476400 | + | 0.879229i | \(0.341941\pi\) | |||||||
\(398\) | 8.23690 | − | 11.0101i | 0.412879 | − | 0.551887i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.50048 | + | 19.4871i | 0.225024 | + | 0.974353i | ||||
\(401\) | 5.95556 | 0.297406 | 0.148703 | − | 0.988882i | \(-0.452490\pi\) | ||||
0.148703 | + | 0.988882i | \(0.452490\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.1153 | 0.503880 | ||||||||
\(404\) | 4.70785 | − | 1.38542i | 0.234224 | − | 0.0689274i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.92178 | + | 9.25221i | −0.343522 | + | 0.459179i | ||||
\(407\) | − | 7.59643i | − | 0.376541i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.3615 | −1.50128 | −0.750641 | − | 0.660711i | \(-0.770255\pi\) | ||||
−0.750641 | + | 0.660711i | \(0.770255\pi\) | |||||||
\(410\) | −0.765095 | + | 25.8261i | −0.0377853 | + | 1.27546i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 28.2663 | − | 8.31819i | 1.39258 | − | 0.409808i | ||||
\(413\) | −13.6048 | −0.669448 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.45159 | + | 3.12910i | −0.218520 | + | 0.153602i | ||||
\(416\) | −1.62034 | + | 23.1440i | −0.0794438 | + | 1.13473i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.55050 | + | 12.7660i | −0.467130 | + | 0.624404i | ||||
\(419\) | − | 2.72901i | − | 0.133321i | −0.997776 | − | 0.0666604i | \(-0.978766\pi\) | ||
0.997776 | − | 0.0666604i | \(-0.0212344\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 9.28319i | − | 0.452435i | −0.974077 | − | 0.226218i | \(-0.927364\pi\) | ||
0.974077 | − | 0.226218i | \(-0.0726360\pi\) | |||||||
\(422\) | 15.9489 | + | 11.9317i | 0.776379 | + | 0.580826i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 32.6125 | + | 12.1304i | 1.58380 | + | 0.589102i | ||||
\(425\) | 8.00260 | + | 2.87982i | 0.388183 | + | 0.139692i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.10642 | −0.150330 | ||||||||
\(428\) | 6.31181 | + | 21.4483i | 0.305093 | + | 1.03674i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.03413 | + | 34.9075i | −0.0498702 | + | 1.68339i | ||||
\(431\) | −16.1731 | −0.779031 | −0.389515 | − | 0.921020i | \(-0.627358\pi\) | ||||
−0.389515 | + | 0.921020i | \(0.627358\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.0559i | − | 1.20411i | −0.798456 | − | 0.602054i | \(-0.794349\pi\) | ||
0.798456 | − | 0.602054i | \(-0.205651\pi\) | |||||||
\(434\) | 3.06381 | + | 2.29210i | 0.147068 | + | 0.110024i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.20543 | + | 1.82613i | −0.297186 | + | 0.0874558i | ||||
\(437\) | 2.52386 | 0.120733 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.83550 | −0.469423 | −0.234711 | − | 0.972065i | \(-0.575415\pi\) | ||||
−0.234711 | + | 0.972065i | \(0.575415\pi\) | |||||||
\(440\) | 3.04088 | + | 11.5902i | 0.144968 | + | 0.552539i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.89996 | + | 5.91013i | 0.375763 | + | 0.281116i | ||||
\(443\) | 34.2623 | 1.62785 | 0.813926 | − | 0.580968i | \(-0.197326\pi\) | ||||
0.813926 | + | 0.580968i | \(0.197326\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.0107 | − | 15.4717i | 1.04341 | − | 0.733430i | ||||
\(446\) | −7.06303 | − | 5.28401i | −0.334444 | − | 0.250205i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.73514 | + | 6.64287i | −0.270960 | + | 0.313846i | ||||
\(449\) | −39.1812 | −1.84907 | −0.924537 | − | 0.381091i | \(-0.875548\pi\) | ||||
−0.924537 | + | 0.381091i | \(0.875548\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.4798i | 0.728913i | ||||||||
\(452\) | −27.2462 | + | 8.01798i | −1.28155 | + | 0.377134i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.26056 | + | 11.0417i | −0.387687 | + | 0.518214i | ||||
\(455\) | −5.78543 | − | 8.23059i | −0.271225 | − | 0.385856i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.7386i | 1.48467i | 0.670029 | + | 0.742335i | \(0.266282\pi\) | ||||
−0.670029 | + | 0.742335i | \(0.733718\pi\) | |||||||
\(458\) | −30.3374 | − | 22.6961i | −1.41757 | − | 1.06052i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.18077 | − | 1.48455i | 0.0550539 | − | 0.0692175i | ||||
\(461\) | − | 25.3865i | − | 1.18237i | −0.806537 | − | 0.591184i | \(-0.798661\pi\) | ||
0.806537 | − | 0.591184i | \(-0.201339\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 40.4827i | − | 1.88139i | −0.339252 | − | 0.940696i | \(-0.610174\pi\) | ||
0.339252 | − | 0.940696i | \(-0.389826\pi\) | |||||||
\(464\) | −16.1368 | − | 25.0432i | −0.749134 | − | 1.16260i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 31.4497 | + | 23.5282i | 1.45688 | + | 1.08992i | ||||
\(467\) | 23.7161 | 1.09745 | 0.548724 | − | 0.836003i | \(-0.315114\pi\) | ||||
0.548724 | + | 0.836003i | \(0.315114\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.38924i | 0.248852i | ||||||||
\(470\) | 7.22701 | + | 0.214099i | 0.333357 | + | 0.00987567i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.2286 | − | 32.8767i | 0.562868 | − | 1.51327i | ||||
\(473\) | 20.9230i | 0.962042i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.9943 | + | 10.0741i | 1.28447 | + | 0.462229i | ||||
\(476\) | 1.05358 | + | 3.58022i | 0.0482910 | + | 0.164099i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.84132 | − | 7.80797i | 0.267176 | − | 0.357128i | ||||
\(479\) | 16.8331 | 0.769123 | 0.384561 | − | 0.923099i | \(-0.374353\pi\) | ||||
0.384561 | + | 0.923099i | \(0.374353\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4444 | −0.749801 | ||||||||
\(482\) | 9.08489 | − | 12.1436i | 0.413806 | − | 0.553126i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.18412 | − | 14.2182i | −0.190187 | − | 0.646281i | ||||
\(485\) | 2.83470 | + | 4.03276i | 0.128717 | + | 0.183118i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.5175i | 0.567220i | 0.958940 | + | 0.283610i | \(0.0915322\pi\) | ||||
−0.958940 | + | 0.283610i | \(0.908468\pi\) | |||||||
\(488\) | 2.79219 | − | 7.50682i | 0.126397 | − | 0.339818i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.542797 | + | 18.3223i | −0.0245211 | + | 0.827718i | ||||
\(491\) | − | 28.1884i | − | 1.27213i | −0.771637 | − | 0.636063i | \(-0.780562\pi\) | ||
0.771637 | − | 0.636063i | \(-0.219438\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.6690 | −0.570583 | ||||||||
\(494\) | 27.6352 | + | 20.6745i | 1.24337 | + | 0.930191i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.29289 | + | 5.34361i | −0.372362 | + | 0.239935i | ||||
\(497\) | − | 1.86283i | − | 0.0835595i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.8003i | − | 0.752086i | −0.926602 | − | 0.376043i | \(-0.877284\pi\) | ||
0.926602 | − | 0.376043i | \(-0.122716\pi\) | |||||||
\(500\) | 19.0226 | − | 11.7533i | 0.850717 | − | 0.525625i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.7226 | − | 13.2587i | −0.791000 | − | 0.591764i | ||||
\(503\) | 30.4521i | 1.35779i | 0.734234 | + | 0.678897i | \(0.237542\pi\) | ||||
−0.734234 | + | 0.678897i | \(0.762458\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.15521 | − | 4.48873i | −0.140405 | − | 0.199746i | ||||
\(506\) | 0.680780 | − | 0.909985i | 0.0302643 | − | 0.0404538i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 38.9834 | − | 11.4720i | 1.72961 | − | 0.508988i | ||||
\(509\) | − | 21.7030i | − | 0.961968i | −0.876729 | − | 0.480984i | \(-0.840279\pi\) | ||
0.876729 | − | 0.480984i | \(-0.159721\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.34252 | 0.324814 | ||||||||
\(512\) | −10.8978 | − | 19.8302i | −0.481621 | − | 0.876380i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.6834 | − | 10.2368i | −0.603548 | − | 0.451527i | ||||
\(515\) | −18.9441 | − | 26.9507i | −0.834778 | − | 1.18759i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.33176 | 0.190511 | ||||||||
\(518\) | −4.98082 | − | 3.72626i | −0.218845 | − | 0.163723i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 25.0899 | − | 6.58276i | 1.10026 | − | 0.288673i | ||||
\(521\) | 25.8137 | 1.13092 | 0.565459 | − | 0.824777i | \(-0.308699\pi\) | ||||
0.565459 | + | 0.824777i | \(0.308699\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.2453 | −1.54117 | −0.770584 | − | 0.637339i | \(-0.780035\pi\) | ||||
−0.770584 | + | 0.637339i | \(0.780035\pi\) | |||||||
\(524\) | −2.85964 | + | 0.841532i | −0.124924 | + | 0.0367625i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.93270 | − | 6.68275i | −0.389484 | − | 0.291382i | ||||
\(527\) | 4.19526i | 0.182748i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.8201 | 0.992178 | ||||||||
\(530\) | 1.15198 | − | 38.8854i | 0.0500386 | − | 1.68907i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.68560 | + | 12.5241i | 0.159791 | + | 0.542991i | ||||
\(533\) | 33.5099 | 1.45148 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.4501 | − | 14.3747i | 0.884133 | − | 0.621473i | ||||
\(536\) | −13.0234 | − | 4.84410i | −0.562525 | − | 0.209233i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −31.6553 | − | 23.6820i | −1.36476 | − | 1.02101i | ||||
\(539\) | 10.9821i | 0.473033i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 3.29103i | − | 0.141492i | −0.997494 | − | 0.0707462i | \(-0.977462\pi\) | ||
0.997494 | − | 0.0707462i | \(-0.0225380\pi\) | |||||||
\(542\) | −6.94093 | + | 9.27781i | −0.298138 | + | 0.398516i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.59881 | − | 0.672026i | −0.411545 | − | 0.0288129i | ||||
\(545\) | 4.15889 | + | 5.91661i | 0.178147 | + | 0.253440i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.4815 | 1.38881 | 0.694404 | − | 0.719585i | \(-0.255668\pi\) | ||||
0.694404 | + | 0.719585i | \(0.255668\pi\) | |||||||
\(548\) | −14.2973 | + | 4.20740i | −0.610750 | + | 0.179731i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.1833 | − | 7.37607i | 0.476859 | − | 0.314517i | ||||
\(551\) | −44.3181 | −1.88801 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 13.9746i | − | 0.594260i | ||||||
\(554\) | −24.3975 | + | 32.6117i | −1.03655 | + | 1.38554i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.21119 | + | 1.53355i | −0.221004 | + | 0.0650368i | ||||
\(557\) | 19.5774 | 0.829523 | 0.414761 | − | 0.909930i | \(-0.363865\pi\) | ||||
0.414761 | + | 0.909930i | \(0.363865\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.2933 | 1.91570 | ||||||||
\(560\) | 9.09107 | + | 3.69146i | 0.384168 | + | 0.155993i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.2627 | − | 29.7581i | 0.939093 | − | 1.25527i | ||||
\(563\) | 7.22281 | 0.304405 | 0.152203 | − | 0.988349i | \(-0.451363\pi\) | ||||
0.152203 | + | 0.988349i | \(0.451363\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.2604 | + | 25.9780i | 0.768222 | + | 1.09290i | ||||
\(566\) | 6.79349 | − | 9.08073i | 0.285552 | − | 0.381692i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.50164 | + | 1.67440i | 0.188885 | + | 0.0702564i | ||||
\(569\) | 13.6522 | 0.572329 | 0.286165 | − | 0.958180i | \(-0.407620\pi\) | ||||
0.286165 | + | 0.958180i | \(0.407620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.9453i | 1.79721i | 0.438762 | + | 0.898603i | \(0.355417\pi\) | ||||
−0.438762 | + | 0.898603i | \(0.644583\pi\) | |||||||
\(572\) | 14.9085 | − | 4.38727i | 0.623356 | − | 0.183441i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.1498 | + | 7.59326i | 0.423643 | + | 0.316937i | ||||
\(575\) | −1.99549 | − | 0.718100i | −0.0832177 | − | 0.0299468i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.16155i | 0.131617i | 0.997832 | + | 0.0658086i | \(0.0209627\pi\) | ||||
−0.997832 | + | 0.0658086i | \(0.979037\pi\) | |||||||
\(578\) | 11.9506 | − | 15.9742i | 0.497081 | − | 0.664439i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20.7340 | + | 26.0682i | −0.860931 | + | 1.08242i | ||||
\(581\) | 2.66950i | 0.110749i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 23.3073i | − | 0.965290i | ||||||
\(584\) | −6.59981 | + | 17.7436i | −0.273102 | + | 0.734236i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.76092 | − | 11.7106i | 0.361910 | − | 0.483759i | ||||
\(587\) | 15.2097 | 0.627773 | 0.313886 | − | 0.949461i | \(-0.398369\pi\) | ||||
0.313886 | + | 0.949461i | \(0.398369\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.6757i | 0.604700i | ||||||||
\(590\) | −39.2004 | − | 1.16131i | −1.61386 | − | 0.0478103i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.4817 | − | 8.68709i | 0.554095 | − | 0.357037i | ||||
\(593\) | − | 20.6555i | − | 0.848219i | −0.905611 | − | 0.424110i | \(-0.860587\pi\) | ||
0.905611 | − | 0.424110i | \(-0.139413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.41358 | − | 2.39947i | 0.139943 | − | 0.0983687i | ||||
\(596\) | −11.6332 | + | 3.42340i | −0.476513 | + | 0.140228i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.96990 | − | 1.47372i | −0.0805550 | − | 0.0602650i | ||||
\(599\) | 33.1741 | 1.35546 | 0.677728 | − | 0.735313i | \(-0.262965\pi\) | ||||
0.677728 | + | 0.735313i | \(0.262965\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 48.2851 | 1.96959 | 0.984796 | − | 0.173716i | \(-0.0555774\pi\) | ||||
0.984796 | + | 0.173716i | \(0.0555774\pi\) | |||||||
\(602\) | 13.7188 | + | 10.2633i | 0.559137 | + | 0.418302i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.82921 | + | 26.6047i | 0.318566 | + | 1.08253i | ||||
\(605\) | −13.5564 | + | 9.52906i | −0.551147 | + | 0.387411i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.630607i | 0.0255955i | 0.999918 | + | 0.0127978i | \(0.00407377\pi\) | ||||
−0.999918 | + | 0.0127978i | \(0.995926\pi\) | |||||||
\(608\) | −33.5781 | − | 2.35085i | −1.36177 | − | 0.0953395i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.95073 | − | 0.265165i | −0.362405 | − | 0.0107362i | ||||
\(611\) | − | 9.37720i | − | 0.379361i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.1293 | 0.893794 | 0.446897 | − | 0.894585i | \(-0.352529\pi\) | ||||
0.446897 | + | 0.894585i | \(0.352529\pi\) | |||||||
\(614\) | −13.2018 | + | 17.6466i | −0.532781 | + | 0.712158i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.50976 | + | 2.04938i | 0.221995 | + | 0.0825718i | ||||
\(617\) | − | 20.2904i | − | 0.816860i | −0.912790 | − | 0.408430i | \(-0.866076\pi\) | ||
0.912790 | − | 0.408430i | \(-0.133924\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 20.6122i | − | 0.828473i | −0.910169 | − | 0.414236i | \(-0.864049\pi\) | ||
0.910169 | − | 0.414236i | \(-0.135951\pi\) | |||||||
\(620\) | 8.63232 | + | 6.86593i | 0.346682 | + | 0.275742i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23.8435 | − | 31.8711i | 0.956036 | − | 1.27792i | ||||
\(623\) | − | 13.1992i | − | 0.528816i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.2674 | − | 15.9301i | −0.770695 | − | 0.637204i | ||||
\(626\) | −8.04464 | − | 6.01837i | −0.321528 | − | 0.240542i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.56131 | + | 22.2962i | 0.261825 | + | 0.889714i | ||||
\(629\) | − | 6.82022i | − | 0.271940i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.4121 | 0.971829 | 0.485915 | − | 0.874006i | \(-0.338487\pi\) | ||||
0.485915 | + | 0.874006i | \(0.338487\pi\) | |||||||
\(632\) | 33.7704 | + | 12.5610i | 1.34331 | + | 0.499651i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.98330 | + | 12.0078i | −0.356772 | + | 0.476891i | ||||
\(635\) | −26.1267 | − | 37.1689i | −1.03681 | − | 1.47500i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.7736 | 0.941945 | ||||||||
\(638\) | −11.9542 | + | 15.9790i | −0.473273 | + | 0.632615i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −17.0921 | + | 18.6510i | −0.675625 | + | 0.737246i | ||||
\(641\) | −6.81719 | −0.269263 | −0.134631 | − | 0.990896i | \(-0.542985\pi\) | ||||
−0.134631 | + | 0.990896i | \(0.542985\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.9317 | −0.628286 | −0.314143 | − | 0.949376i | \(-0.601717\pi\) | ||||
−0.314143 | + | 0.949376i | \(0.601717\pi\) | |||||||
\(644\) | −0.262717 | − | 0.892747i | −0.0103525 | − | 0.0351792i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.57463 | + | 11.4615i | −0.337364 | + | 0.450948i | ||||
\(647\) | − | 32.9746i | − | 1.29636i | −0.761485 | − | 0.648182i | \(-0.775530\pi\) | ||
0.761485 | − | 0.648182i | \(-0.224470\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.4961 | −0.922304 | ||||||||
\(650\) | −15.9674 | − | 24.2092i | −0.626293 | − | 0.949563i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.83386 | − | 9.62984i | −0.110983 | − | 0.377133i | ||||
\(653\) | −9.46910 | −0.370555 | −0.185277 | − | 0.982686i | \(-0.559318\pi\) | ||||
−0.185277 | + | 0.982686i | \(0.559318\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.91653 | + | 2.72654i | 0.0748852 | + | 0.106535i | ||||
\(656\) | −27.4726 | + | 17.7023i | −1.07263 | + | 0.691158i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.12485 | − | 2.84025i | 0.0828353 | − | 0.110724i | ||||
\(659\) | 41.5026i | 1.61671i | 0.588695 | + | 0.808356i | \(0.299642\pi\) | ||||
−0.588695 | + | 0.808356i | \(0.700358\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.7673i | 1.54677i | 0.633937 | + | 0.773385i | \(0.281438\pi\) | ||||
−0.633937 | + | 0.773385i | \(0.718562\pi\) | |||||||
\(662\) | −36.3428 | − | 27.1888i | −1.41250 | − | 1.05672i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.45098 | − | 2.39947i | −0.250347 | − | 0.0931175i | ||||
\(665\) | 11.9412 | − | 8.39371i | 0.463061 | − | 0.325494i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.15908 | 0.122320 | ||||||||
\(668\) | 7.19157 | − | 2.11633i | 0.278250 | − | 0.0818833i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.460027 | + | 15.5284i | −0.0177724 | + | 0.599914i | ||||
\(671\) | −5.36493 | −0.207111 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.8069i | 0.647860i | 0.946081 | + | 0.323930i | \(0.105004\pi\) | ||||
−0.946081 | + | 0.323930i | \(0.894996\pi\) | |||||||
\(674\) | 25.7627 | + | 19.2736i | 0.992341 | + | 0.742392i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.15733 | − | 7.33091i | −0.0829744 | − | 0.281958i | ||||
\(677\) | −8.73792 | −0.335826 | −0.167913 | − | 0.985802i | \(-0.553703\pi\) | ||||
−0.167913 | + | 0.985802i | \(0.553703\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.41834 | 0.0928074 | ||||||||
\(680\) | 2.73016 | + | 10.4059i | 0.104697 | + | 0.399047i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.29135 | + | 3.95858i | 0.202616 | + | 0.151582i | ||||
\(683\) | −37.2358 | −1.42479 | −0.712395 | − | 0.701779i | \(-0.752389\pi\) | ||||
−0.712395 | + | 0.701779i | \(0.752389\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.58208 | + | 13.6319i | 0.366112 | + | 0.520847i | ||||
\(686\) | 15.8965 | + | 11.8925i | 0.606930 | + | 0.454057i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −37.1330 | + | 23.9271i | −1.41568 | + | 0.912211i | ||||
\(689\) | −50.4547 | −1.92217 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 46.4665i | − | 1.76767i | −0.467798 | − | 0.883835i | \(-0.654953\pi\) | ||
0.467798 | − | 0.883835i | \(-0.345047\pi\) | |||||||
\(692\) | −5.98718 | − | 20.3452i | −0.227598 | − | 0.773409i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.6635 | − | 26.2838i | 0.746416 | − | 0.997720i | ||||
\(695\) | 3.49255 | + | 4.96864i | 0.132480 | + | 0.188471i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.8980i | 0.526425i | ||||||||
\(698\) | 30.6635 | + | 22.9401i | 1.16063 | + | 0.868294i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.649406 | − | 10.9509i | 0.0245452 | − | 0.413904i | ||||
\(701\) | − | 12.8977i | − | 0.487141i | −0.969883 | − | 0.243571i | \(-0.921681\pi\) | ||
0.969883 | − | 0.243571i | \(-0.0783187\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 23.8582i | − | 0.899827i | ||||||
\(704\) | −9.90487 | + | 11.4726i | −0.373304 | + | 0.432388i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.3576 | − | 9.24500i | −0.465085 | − | 0.347940i | ||||
\(707\) | −2.69177 | −0.101234 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.8715i | 0.708733i | 0.935107 | + | 0.354367i | \(0.115304\pi\) | ||||
−0.935107 | + | 0.354367i | \(0.884696\pi\) | |||||||
\(710\) | 0.159012 | − | 5.36751i | 0.00596761 | − | 0.201439i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 31.8967 | + | 11.8641i | 1.19538 | + | 0.444626i | ||||
\(713\) | − | 1.04611i | − | 0.0391772i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.99172 | − | 14.2146i | −0.373669 | − | 0.531597i | ||||
\(716\) | 30.2198 | − | 8.89307i | 1.12937 | − | 0.332350i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.52327 | − | 4.70949i | 0.131487 | − | 0.175757i | ||||
\(719\) | 18.6339 | 0.694927 | 0.347463 | − | 0.937694i | \(-0.387043\pi\) | ||||
0.347463 | + | 0.937694i | \(0.387043\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.1616 | −0.601889 | ||||||||
\(722\) | −13.8992 | + | 18.5787i | −0.517273 | + | 0.691429i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −40.2069 | + | 11.8321i | −1.49428 | + | 0.439735i | ||||
\(725\) | 35.0401 | + | 12.6096i | 1.30136 | + | 0.468308i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 24.8278i | − | 0.920812i | −0.887708 | − | 0.460406i | \(-0.847704\pi\) | ||
0.887708 | − | 0.460406i | \(-0.152296\pi\) | |||||||
\(728\) | 4.43641 | − | 11.9273i | 0.164424 | − | 0.442055i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21.1565 | + | 0.626760i | 0.783038 | + | 0.0231974i | ||||
\(731\) | 18.7851i | 0.694792i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.393641 | 0.0145395 | 0.00726973 | − | 0.999974i | \(-0.497686\pi\) | ||||
0.00726973 | + | 0.999974i | \(0.497686\pi\) | |||||||
\(734\) | 32.8861 | + | 24.6028i | 1.21385 | + | 0.908107i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.39351 | + | 0.167573i | 0.0882261 | + | 0.00617684i | ||||
\(737\) | 9.30748i | 0.342845i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.8787i | 0.473750i | 0.971540 | + | 0.236875i | \(0.0761233\pi\) | ||||
−0.971540 | + | 0.236875i | \(0.923877\pi\) | |||||||
\(740\) | −14.0335 | − | 11.1619i | −0.515883 | − | 0.410320i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.2821 | − | 11.4329i | −0.561025 | − | 0.419715i | ||||
\(743\) | 17.7082i | 0.649650i | 0.945774 | + | 0.324825i | \(0.105305\pi\) | ||||
−0.945774 | + | 0.324825i | \(0.894695\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.79657 | + | 11.0917i | 0.285644 | + | 0.406369i | ||||
\(746\) | −7.18049 | + | 9.59802i | −0.262896 | + | 0.351409i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.81959 | + | 6.18321i | 0.0665309 | + | 0.226081i | ||||
\(749\) | − | 12.2634i | − | 0.448093i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.8147 | −0.941993 | −0.470996 | − | 0.882135i | \(-0.656106\pi\) | ||||
−0.470996 | + | 0.882135i | \(0.656106\pi\) | |||||||
\(752\) | 4.95369 | + | 7.68777i | 0.180643 | + | 0.280344i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 34.5907 | + | 25.8780i | 1.25972 | + | 0.942423i | ||||
\(755\) | 25.3664 | − | 17.8305i | 0.923178 | − | 0.648919i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.20871 | −0.334696 | −0.167348 | − | 0.985898i | \(-0.553520\pi\) | ||||
−0.167348 | + | 0.985898i | \(0.553520\pi\) | |||||||
\(758\) | 30.5326 | + | 22.8421i | 1.10899 | + | 0.829663i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.55050 | + | 36.4013i | 0.346433 | + | 1.32041i | ||||
\(761\) | 6.94667 | 0.251816 | 0.125908 | − | 0.992042i | \(-0.459816\pi\) | ||||
0.125908 | + | 0.992042i | \(0.459816\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.54803 | 0.128447 | ||||||||
\(764\) | −10.2800 | − | 34.9329i | −0.371918 | − | 1.26383i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −31.8772 | − | 23.8480i | −1.15177 | − | 0.861664i | ||||
\(767\) | 50.8634i | 1.83657i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.468151 | 0.0168820 | 0.00844098 | − | 0.999964i | \(-0.497313\pi\) | ||||
0.00844098 | + | 0.999964i | \(0.497313\pi\) | |||||||
\(770\) | 0.194622 | − | 6.56954i | 0.00701369 | − | 0.236750i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.0515 | + | 5.01789i | −0.613696 | + | 0.180598i | ||||
\(773\) | −14.0083 | −0.503843 | −0.251921 | − | 0.967748i | \(-0.581062\pi\) | ||||
−0.251921 | + | 0.967748i | \(0.581062\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.17558 | − | 11.6033i | 0.149991 | − | 0.416803i | ||||
\(776\) | −2.17372 | + | 5.84405i | −0.0780320 | + | 0.209789i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −32.2099 | − | 24.0969i | −1.15478 | − | 0.863916i | ||||
\(779\) | 48.6174i | 1.74190i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 3.21720i | − | 0.115121i | ||||||
\(782\) | 0.611217 | − | 0.817002i | 0.0218571 | − | 0.0292159i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −19.4905 | + | 12.5589i | −0.696088 | + | 0.448532i | ||||
\(785\) | 21.2584 | − | 14.9429i | 0.758746 | − | 0.533337i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.3214 | −1.08084 | −0.540421 | − | 0.841395i | \(-0.681735\pi\) | ||||
−0.540421 | + | 0.841395i | \(0.681735\pi\) | |||||||
\(788\) | −4.93359 | − | 16.7650i | −0.175752 | − | 0.597228i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.19288 | − | 40.2660i | 0.0424406 | − | 1.43260i | ||||
\(791\) | 15.5783 | 0.553901 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.6138i | 0.412417i | ||||||||
\(794\) | 16.0829 | − | 21.4978i | 0.570763 | − | 0.762927i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.48972 | − | 18.6548i | −0.194578 | − | 0.661202i | ||||
\(797\) | −12.7941 | −0.453190 | −0.226595 | − | 0.973989i | \(-0.572759\pi\) | ||||
−0.226595 | + | 0.973989i | \(0.572759\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.88914 | 0.137588 | ||||||||
\(800\) | 25.8796 | + | 11.4125i | 0.914983 | + | 0.403492i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.04535 | − | 6.74402i | 0.178157 | − | 0.238140i | ||||
\(803\) | 12.6809 | 0.447499 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.851195 | + | 0.598321i | −0.0300007 | + | 0.0210880i | ||||
\(806\) | 8.56935 | − | 11.4545i | 0.301843 | − | 0.403467i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.41949 | − | 6.50481i | 0.0851174 | − | 0.228838i | ||||
\(809\) | 36.8282 | 1.29481 | 0.647405 | − | 0.762146i | \(-0.275854\pi\) | ||||
0.647405 | + | 0.762146i | \(0.275854\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 20.4801i | − | 0.719153i | −0.933116 | − | 0.359576i | \(-0.882921\pi\) | ||
0.933116 | − | 0.359576i | \(-0.117079\pi\) | |||||||
\(812\) | 4.61322 | + | 15.6763i | 0.161892 | + | 0.550131i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.60213 | − | 6.43544i | −0.301504 | − | 0.225562i | ||||
\(815\) | −9.18163 | + | 6.45394i | −0.321619 | + | 0.226072i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 65.7131i | 2.29901i | ||||||||
\(818\) | −25.7213 | + | 34.3811i | −0.899323 | + | 1.20211i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.5971 | + | 22.7454i | 0.998652 | + | 0.794303i | ||||
\(821\) | 37.8925i | 1.32246i | 0.750184 | + | 0.661229i | \(0.229965\pi\) | ||||
−0.750184 | + | 0.661229i | \(0.770035\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.89215i | 0.0659562i | 0.999456 | + | 0.0329781i | \(0.0104992\pi\) | ||||
−0.999456 | + | 0.0329781i | \(0.989501\pi\) | |||||||
\(824\) | 14.5268 | − | 39.0554i | 0.506066 | − | 1.36056i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.5255 | + | 15.4059i | −0.401024 | + | 0.536041i | ||||
\(827\) | −45.9585 | −1.59813 | −0.799067 | − | 0.601242i | \(-0.794673\pi\) | ||||
−0.799067 | + | 0.601242i | \(0.794673\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 44.1972i | − | 1.53503i | −0.641029 | − | 0.767517i | \(-0.721492\pi\) | ||
0.641029 | − | 0.767517i | \(-0.278508\pi\) | |||||||
\(830\) | −0.227869 | + | 7.69180i | −0.00790945 | + | 0.266986i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24.8353 | + | 21.4416i | 0.861009 | + | 0.743355i | ||||
\(833\) | 9.85996i | 0.341627i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.81981 | − | 6.85685i | −0.166796 | − | 0.237291i | ||||
\(836\) | 6.36521 | + | 21.6298i | 0.220145 | + | 0.748083i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.09030 | − | 2.31192i | −0.106753 | − | 0.0798640i | ||||
\(839\) | 29.2610 | 1.01020 | 0.505102 | − | 0.863060i | \(-0.331455\pi\) | ||||
0.505102 | + | 0.863060i | \(0.331455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4724 | −0.912841 | ||||||||
\(842\) | −10.5122 | − | 7.86441i | −0.362274 | − | 0.271025i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 27.0227 | − | 7.95223i | 0.930160 | − | 0.273727i | ||||
\(845\) | −6.98970 | + | 4.91319i | −0.240453 | + | 0.169019i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.12942i | 0.279330i | ||||||||
\(848\) | 41.3645 | − | 26.6537i | 1.42046 | − | 0.915291i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.0406 | − | 6.62238i | 0.344390 | − | 0.227146i | ||||
\(851\) | 1.70066i | 0.0582978i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.0803 | 0.345143 | 0.172572 | − | 0.984997i | \(-0.444792\pi\) | ||||
0.172572 | + | 0.984997i | \(0.444792\pi\) | |||||||
\(854\) | −2.63165 | + | 3.51768i | −0.0900532 | + | 0.120372i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.6351 | + | 11.0229i | 1.01291 | + | 0.376754i | ||||
\(857\) | 43.9269i | 1.50052i | 0.661145 | + | 0.750258i | \(0.270071\pi\) | ||||
−0.661145 | + | 0.750258i | \(0.729929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 9.28531i | − | 0.316811i | −0.987374 | − | 0.158405i | \(-0.949365\pi\) | ||
0.987374 | − | 0.158405i | \(-0.0506353\pi\) | |||||||
\(860\) | 38.6529 | + | 30.7435i | 1.31805 | + | 1.04835i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.7013 | + | 18.3143i | −0.466668 | + | 0.623787i | ||||
\(863\) | 33.4004i | 1.13696i | 0.822696 | + | 0.568481i | \(0.192469\pi\) | ||||
−0.822696 | + | 0.568481i | \(0.807531\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.3983 | + | 13.6354i | −0.659561 | + | 0.463618i | ||||
\(866\) | −28.3730 | − | 21.2265i | −0.964155 | − | 0.721305i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.19111 | − | 1.52764i | 0.176198 | − | 0.0518514i | ||||
\(869\) | − | 24.1348i | − | 0.818718i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.1484 | 0.682703 | ||||||||
\(872\) | −3.18914 | + | 8.57401i | −0.107998 | + | 0.290353i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.13813 | − | 2.85800i | 0.0723233 | − | 0.0966731i | ||||
\(875\) | −11.8295 | + | 3.23892i | −0.399912 | + | 0.109495i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.85859 | 0.197830 | 0.0989152 | − | 0.995096i | \(-0.468463\pi\) | ||||
0.0989152 | + | 0.995096i | \(0.468463\pi\) | |||||||
\(878\) | −8.33231 | + | 11.1376i | −0.281202 | + | 0.375877i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 15.7007 | + | 6.37533i | 0.529271 | + | 0.214912i | ||||
\(881\) | −33.5615 | −1.13071 | −0.565357 | − | 0.824846i | \(-0.691262\pi\) | ||||
−0.565357 | + | 0.824846i | \(0.691262\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.194722 | 0.00655291 | 0.00327645 | − | 0.999995i | \(-0.498957\pi\) | ||||
0.00327645 | + | 0.999995i | \(0.498957\pi\) | |||||||
\(884\) | 13.3852 | − | 3.93897i | 0.450191 | − | 0.132482i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29.0259 | − | 38.7984i | 0.975144 | − | 1.30346i | ||||
\(887\) | − | 7.68201i | − | 0.257937i | −0.991649 | − | 0.128968i | \(-0.958833\pi\) | ||
0.991649 | − | 0.128968i | \(-0.0411665\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.2892 | −0.747556 | ||||||||
\(890\) | 1.12669 | − | 38.0319i | 0.0377667 | − | 1.27483i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.9671 | + | 3.52168i | −0.400689 | + | 0.117915i | ||||
\(893\) | 13.6048 | 0.455267 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.2534 | − | 28.8133i | −0.676996 | − | 0.963122i | ||||
\(896\) | 2.66370 | + | 12.1220i | 0.0889881 | + | 0.404969i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.1930 | + | 44.3684i | −1.10766 | + | 1.48059i | ||||
\(899\) | 18.3693i | 0.612652i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 20.9257i | − | 0.697138i | ||||||
\(902\) | 17.5291 | + | 13.1139i | 0.583656 | + | 0.436646i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.0025 | + | 37.6459i | −0.465718 | + | 1.25208i | ||||
\(905\) | 26.9467 | + | 38.3355i | 0.895739 | + | 1.27432i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.7134 | −1.15264 | −0.576320 | − | 0.817224i | \(-0.695512\pi\) | ||||
−0.576320 | + | 0.817224i | \(0.695512\pi\) | |||||||
\(908\) | 5.50549 | + | 18.7084i | 0.182706 | + | 0.620859i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −14.2215 | − | 0.421309i | −0.471437 | − | 0.0139663i | ||||
\(911\) | −18.8670 | −0.625091 | −0.312546 | − | 0.949903i | \(-0.601182\pi\) | ||||
−0.312546 | + | 0.949903i | \(0.601182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.61035i | 0.152580i | ||||||||
\(914\) | 35.9405 | + | 26.8879i | 1.18881 | + | 0.889372i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −51.4016 | + | 15.1264i | −1.69836 | + | 0.499792i | ||||
\(917\) | 1.63503 | 0.0539935 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.4932 | −0.873931 | −0.436965 | − | 0.899478i | \(-0.643947\pi\) | ||||
−0.436965 | + | 0.899478i | \(0.643947\pi\) | |||||||
\(920\) | −0.680780 | − | 2.59476i | −0.0224446 | − | 0.0855467i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.7474 | − | 21.5066i | −0.946747 | − | 0.708282i | ||||
\(923\) | −6.96447 | −0.229238 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.78823 | + | 18.8635i | −0.223196 | + | 0.620227i | ||||
\(926\) | −45.8423 | − | 34.2956i | −1.50647 | − | 1.12702i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −42.0293 | − | 2.94253i | −1.37968 | − | 0.0965933i | ||||
\(929\) | −57.5829 | −1.88923 | −0.944617 | − | 0.328176i | \(-0.893566\pi\) | ||||
−0.944617 | + | 0.328176i | \(0.893566\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.4916i | 1.13042i | ||||||||
\(932\) | 53.2863 | − | 15.6811i | 1.74545 | − | 0.513650i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.0914 | − | 26.8558i | 0.657412 | − | 0.878750i | ||||
\(935\) | 5.89543 | − | 4.14400i | 0.192801 | − | 0.135523i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.1596i | 0.887267i | 0.896208 | + | 0.443633i | \(0.146311\pi\) | ||||
−0.896208 | + | 0.443633i | \(0.853689\pi\) | |||||||
\(938\) | 6.10272 | + | 4.56558i | 0.199261 | + | 0.149071i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.36492 | − | 8.00242i | 0.207601 | − | 0.261010i | ||||
\(941\) | 47.4407i | 1.54652i | 0.634088 | + | 0.773261i | \(0.281375\pi\) | ||||
−0.634088 | + | 0.773261i | \(0.718625\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.46555i | − | 0.112854i | ||||||
\(944\) | −26.8696 | − | 41.6996i | −0.874531 | − | 1.35721i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.6930 | + | 17.7253i | 0.770327 | + | 0.576299i | ||||
\(947\) | −24.5863 | −0.798947 | −0.399473 | − | 0.916745i | \(-0.630807\pi\) | ||||
−0.399473 | + | 0.916745i | \(0.630807\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 27.4511i | − | 0.891099i | ||||||
\(950\) | 35.1236 | − | 23.1661i | 1.13956 | − | 0.751606i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.94677 | + | 1.83997i | 0.160326 | + | 0.0596338i | ||||
\(953\) | − | 50.0020i | − | 1.61973i | −0.586620 | − | 0.809863i | \(-0.699542\pi\) | ||
0.586620 | − | 0.809863i | \(-0.300458\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.3070 | + | 23.4121i | −1.07779 | + | 0.757597i | ||||
\(956\) | −3.89311 | − | 13.2293i | −0.125912 | − | 0.427866i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.2604 | − | 19.0616i | 0.460733 | − | 0.615853i | ||||
\(959\) | 8.17466 | 0.263973 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.9171 | −0.803778 | ||||||||
\(962\) | −13.9312 | + | 18.6215i | −0.449159 | + | 0.600382i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.05489 | − | 20.5753i | −0.195015 | − | 0.662686i | ||||
\(965\) | 11.4279 | + | 16.2578i | 0.367878 | + | 0.523358i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.52916i | 0.209964i | 0.994474 | + | 0.104982i | \(0.0334784\pi\) | ||||
−0.994474 | + | 0.104982i | \(0.966522\pi\) | |||||||
\(968\) | −19.6452 | − | 7.30711i | −0.631421 | − | 0.234860i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.96813 | + | 0.206430i | 0.223733 | + | 0.00662807i | ||||
\(971\) | 22.2092i | 0.712726i | 0.934348 | + | 0.356363i | \(0.115983\pi\) | ||||
−0.934348 | + | 0.356363i | \(0.884017\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.97956 | 0.0955204 | ||||||||
\(974\) | 14.1747 | + | 10.6044i | 0.454185 | + | 0.339786i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.13520 | − | 9.52138i | −0.196383 | − | 0.304772i | ||||
\(977\) | − | 48.6812i | − | 1.55745i | −0.627366 | − | 0.778725i | \(-0.715867\pi\) | ||
0.627366 | − | 0.778725i | \(-0.284133\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 22.7957i | − | 0.728554i | ||||||
\(980\) | 20.2882 | + | 16.1367i | 0.648083 | + | 0.515468i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −31.9203 | − | 23.8803i | −1.01862 | − | 0.762051i | ||||
\(983\) | 1.13847i | 0.0363115i | 0.999835 | + | 0.0181558i | \(0.00577948\pi\) | ||||
−0.999835 | + | 0.0181558i | \(0.994221\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.9847 | + | 11.2359i | −0.509315 | + | 0.358007i | ||||
\(986\) | −10.7328 | + | 14.3463i | −0.341801 | + | 0.456878i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 46.8233 | − | 13.7791i | 1.48965 | − | 0.438372i | ||||
\(989\) | − | 4.68416i | − | 0.148948i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.1309 | 1.37010 | 0.685049 | − | 0.728497i | \(-0.259781\pi\) | ||||
0.685049 | + | 0.728497i | \(0.259781\pi\) | |||||||
\(992\) | −0.974400 | + | 13.9177i | −0.0309372 | + | 0.441888i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.10946 | − | 1.57813i | −0.0669079 | − | 0.0500552i | ||||
\(995\) | −17.7865 | + | 12.5025i | −0.563871 | + | 0.396355i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.7853 | −0.879969 | −0.439984 | − | 0.898005i | \(-0.645016\pi\) | ||||
−0.439984 | + | 0.898005i | \(0.645016\pi\) | |||||||
\(998\) | −19.0245 | − | 14.2327i | −0.602211 | − | 0.450527i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.2.d.i.109.13 | yes | 20 | |
3.2 | odd | 2 | inner | 1080.2.d.i.109.8 | yes | 20 | |
4.3 | odd | 2 | 4320.2.d.i.3889.6 | 20 | |||
5.4 | even | 2 | 1080.2.d.j.109.8 | yes | 20 | ||
8.3 | odd | 2 | 4320.2.d.j.3889.15 | 20 | |||
8.5 | even | 2 | 1080.2.d.j.109.7 | yes | 20 | ||
12.11 | even | 2 | 4320.2.d.i.3889.15 | 20 | |||
15.14 | odd | 2 | 1080.2.d.j.109.13 | yes | 20 | ||
20.19 | odd | 2 | 4320.2.d.j.3889.16 | 20 | |||
24.5 | odd | 2 | 1080.2.d.j.109.14 | yes | 20 | ||
24.11 | even | 2 | 4320.2.d.j.3889.6 | 20 | |||
40.19 | odd | 2 | 4320.2.d.i.3889.5 | 20 | |||
40.29 | even | 2 | inner | 1080.2.d.i.109.14 | yes | 20 | |
60.59 | even | 2 | 4320.2.d.j.3889.5 | 20 | |||
120.29 | odd | 2 | inner | 1080.2.d.i.109.7 | ✓ | 20 | |
120.59 | even | 2 | 4320.2.d.i.3889.16 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.d.i.109.7 | ✓ | 20 | 120.29 | odd | 2 | inner | |
1080.2.d.i.109.8 | yes | 20 | 3.2 | odd | 2 | inner | |
1080.2.d.i.109.13 | yes | 20 | 1.1 | even | 1 | trivial | |
1080.2.d.i.109.14 | yes | 20 | 40.29 | even | 2 | inner | |
1080.2.d.j.109.7 | yes | 20 | 8.5 | even | 2 | ||
1080.2.d.j.109.8 | yes | 20 | 5.4 | even | 2 | ||
1080.2.d.j.109.13 | yes | 20 | 15.14 | odd | 2 | ||
1080.2.d.j.109.14 | yes | 20 | 24.5 | odd | 2 | ||
4320.2.d.i.3889.5 | 20 | 40.19 | odd | 2 | |||
4320.2.d.i.3889.6 | 20 | 4.3 | odd | 2 | |||
4320.2.d.i.3889.15 | 20 | 12.11 | even | 2 | |||
4320.2.d.i.3889.16 | 20 | 120.59 | even | 2 | |||
4320.2.d.j.3889.5 | 20 | 60.59 | even | 2 | |||
4320.2.d.j.3889.6 | 20 | 24.11 | even | 2 | |||
4320.2.d.j.3889.15 | 20 | 8.3 | odd | 2 | |||
4320.2.d.j.3889.16 | 20 | 20.19 | odd | 2 |