Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(117,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.117");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.h (of order \(4\), 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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.8 | ||
Root | \(1.29397 + 1.29397i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.253 |
Dual form | 370.2.h.e.117.8 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.29397 | − | 1.29397i | 0.747075 | − | 0.747075i | −0.226854 | − | 0.973929i | \(-0.572844\pi\) |
0.973929 | + | 0.226854i | \(0.0728439\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.20164 | + | 0.390851i | −0.984605 | + | 0.174794i | ||||
\(6\) | −1.29397 | + | 1.29397i | −0.528262 | + | 0.528262i | ||||
\(7\) | −2.67087 | + | 2.67087i | −1.00950 | + | 1.00950i | −0.00954076 | + | 0.999954i | \(0.503037\pi\) |
−0.999954 | + | 0.00954076i | \(0.996963\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 0.348729i | − | 0.116243i | ||||||
\(10\) | 2.20164 | − | 0.390851i | 0.696221 | − | 0.123598i | ||||
\(11\) | 1.29587i | 0.390719i | 0.980732 | + | 0.195359i | \(0.0625873\pi\) | ||||
−0.980732 | + | 0.195359i | \(0.937413\pi\) | |||||||
\(12\) | 1.29397 | − | 1.29397i | 0.373538 | − | 0.373538i | ||||
\(13\) | −6.92612 | −1.92096 | −0.960480 | − | 0.278349i | \(-0.910213\pi\) | ||||
−0.960480 | + | 0.278349i | \(0.910213\pi\) | |||||||
\(14\) | 2.67087 | − | 2.67087i | 0.713821 | − | 0.713821i | ||||
\(15\) | −2.34312 | + | 3.35462i | −0.604990 | + | 0.866158i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.85071i | 1.17647i | 0.808690 | + | 0.588235i | \(0.200177\pi\) | ||||
−0.808690 | + | 0.588235i | \(0.799823\pi\) | |||||||
\(18\) | 0.348729i | 0.0821963i | ||||||||
\(19\) | −4.69555 | − | 4.69555i | −1.07723 | − | 1.07723i | −0.996756 | − | 0.0804769i | \(-0.974356\pi\) |
−0.0804769 | − | 0.996756i | \(-0.525644\pi\) | |||||||
\(20\) | −2.20164 | + | 0.390851i | −0.492303 | + | 0.0873969i | ||||
\(21\) | 6.91207i | 1.50834i | ||||||||
\(22\) | − | 1.29587i | − | 0.276280i | ||||||
\(23\) | 3.33959 | 0.696352 | 0.348176 | − | 0.937429i | \(-0.386801\pi\) | ||||
0.348176 | + | 0.937429i | \(0.386801\pi\) | |||||||
\(24\) | −1.29397 | + | 1.29397i | −0.264131 | + | 0.264131i | ||||
\(25\) | 4.69447 | − | 1.72103i | 0.938894 | − | 0.344206i | ||||
\(26\) | 6.92612 | 1.35832 | ||||||||
\(27\) | 3.43067 | + | 3.43067i | 0.660233 | + | 0.660233i | ||||
\(28\) | −2.67087 | + | 2.67087i | −0.504748 | + | 0.504748i | ||||
\(29\) | 3.73955 | − | 3.73955i | 0.694417 | − | 0.694417i | −0.268783 | − | 0.963201i | \(-0.586622\pi\) |
0.963201 | + | 0.268783i | \(0.0866216\pi\) | |||||||
\(30\) | 2.34312 | − | 3.35462i | 0.427793 | − | 0.612466i | ||||
\(31\) | −0.146916 | − | 0.146916i | −0.0263869 | − | 0.0263869i | 0.693790 | − | 0.720177i | \(-0.255939\pi\) |
−0.720177 | + | 0.693790i | \(0.755939\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.67682 | + | 1.67682i | 0.291896 | + | 0.291896i | ||||
\(34\) | − | 4.85071i | − | 0.831890i | ||||||
\(35\) | 4.83640 | − | 6.92422i | 0.817501 | − | 1.17041i | ||||
\(36\) | − | 0.348729i | − | 0.0581216i | ||||||
\(37\) | −6.03371 | + | 0.770943i | −0.991936 | + | 0.126742i | ||||
\(38\) | 4.69555 | + | 4.69555i | 0.761719 | + | 0.761719i | ||||
\(39\) | −8.96221 | + | 8.96221i | −1.43510 | + | 1.43510i | ||||
\(40\) | 2.20164 | − | 0.390851i | 0.348110 | − | 0.0617989i | ||||
\(41\) | 6.38351i | 0.996937i | 0.866908 | + | 0.498469i | \(0.166104\pi\) | ||||
−0.866908 | + | 0.498469i | \(0.833896\pi\) | |||||||
\(42\) | − | 6.91207i | − | 1.06656i | ||||||
\(43\) | −2.51195 | −0.383069 | −0.191535 | − | 0.981486i | \(-0.561346\pi\) | ||||
−0.191535 | + | 0.981486i | \(0.561346\pi\) | |||||||
\(44\) | 1.29587i | 0.195359i | ||||||||
\(45\) | 0.136301 | + | 0.767778i | 0.0203186 | + | 0.114454i | ||||
\(46\) | −3.33959 | −0.492395 | ||||||||
\(47\) | −2.93686 | + | 2.93686i | −0.428385 | + | 0.428385i | −0.888078 | − | 0.459693i | \(-0.847960\pi\) |
0.459693 | + | 0.888078i | \(0.347960\pi\) | |||||||
\(48\) | 1.29397 | − | 1.29397i | 0.186769 | − | 0.186769i | ||||
\(49\) | − | 7.26713i | − | 1.03816i | ||||||
\(50\) | −4.69447 | + | 1.72103i | −0.663899 | + | 0.243390i | ||||
\(51\) | 6.27669 | + | 6.27669i | 0.878912 | + | 0.878912i | ||||
\(52\) | −6.92612 | −0.960480 | ||||||||
\(53\) | −1.30971 | − | 1.30971i | −0.179902 | − | 0.179902i | 0.611411 | − | 0.791313i | \(-0.290602\pi\) |
−0.791313 | + | 0.611411i | \(0.790602\pi\) | |||||||
\(54\) | −3.43067 | − | 3.43067i | −0.466855 | − | 0.466855i | ||||
\(55\) | −0.506490 | − | 2.85304i | −0.0682952 | − | 0.384704i | ||||
\(56\) | 2.67087 | − | 2.67087i | 0.356910 | − | 0.356910i | ||||
\(57\) | −12.1518 | −1.60955 | ||||||||
\(58\) | −3.73955 | + | 3.73955i | −0.491027 | + | 0.491027i | ||||
\(59\) | 4.70039 | + | 4.70039i | 0.611938 | + | 0.611938i | 0.943451 | − | 0.331512i | \(-0.107559\pi\) |
−0.331512 | + | 0.943451i | \(0.607559\pi\) | |||||||
\(60\) | −2.34312 | + | 3.35462i | −0.302495 | + | 0.433079i | ||||
\(61\) | −7.81965 | − | 7.81965i | −1.00120 | − | 1.00120i | −0.999999 | − | 0.00120494i | \(-0.999616\pi\) |
−0.00120494 | − | 0.999999i | \(-0.500384\pi\) | |||||||
\(62\) | 0.146916 | + | 0.146916i | 0.0186584 | + | 0.0186584i | ||||
\(63\) | 0.931412 | + | 0.931412i | 0.117347 | + | 0.117347i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 15.2488 | − | 2.70708i | 1.89139 | − | 0.335772i | ||||
\(66\) | −1.67682 | − | 1.67682i | −0.206402 | − | 0.206402i | ||||
\(67\) | 3.10789 | + | 3.10789i | 0.379690 | + | 0.379690i | 0.870990 | − | 0.491301i | \(-0.163478\pi\) |
−0.491301 | + | 0.870990i | \(0.663478\pi\) | |||||||
\(68\) | 4.85071i | 0.588235i | ||||||||
\(69\) | 4.32133 | − | 4.32133i | 0.520227 | − | 0.520227i | ||||
\(70\) | −4.83640 | + | 6.92422i | −0.578060 | + | 0.827603i | ||||
\(71\) | −5.59124 | −0.663558 | −0.331779 | − | 0.943357i | \(-0.607649\pi\) | ||||
−0.331779 | + | 0.943357i | \(0.607649\pi\) | |||||||
\(72\) | 0.348729i | 0.0410982i | ||||||||
\(73\) | 0.134980 | − | 0.134980i | 0.0157983 | − | 0.0157983i | −0.699164 | − | 0.714962i | \(-0.746444\pi\) |
0.714962 | + | 0.699164i | \(0.246444\pi\) | |||||||
\(74\) | 6.03371 | − | 0.770943i | 0.701404 | − | 0.0896204i | ||||
\(75\) | 3.84755 | − | 8.30148i | 0.444277 | − | 0.958572i | ||||
\(76\) | −4.69555 | − | 4.69555i | −0.538617 | − | 0.538617i | ||||
\(77\) | −3.46110 | − | 3.46110i | −0.394429 | − | 0.394429i | ||||
\(78\) | 8.96221 | − | 8.96221i | 1.01477 | − | 1.01477i | ||||
\(79\) | 10.8080 | + | 10.8080i | 1.21600 | + | 1.21600i | 0.969021 | + | 0.246978i | \(0.0794376\pi\) |
0.246978 | + | 0.969021i | \(0.420562\pi\) | |||||||
\(80\) | −2.20164 | + | 0.390851i | −0.246151 | + | 0.0436984i | ||||
\(81\) | 9.92458 | 1.10273 | ||||||||
\(82\) | − | 6.38351i | − | 0.704941i | ||||||
\(83\) | −8.74652 | − | 8.74652i | −0.960055 | − | 0.960055i | 0.0391772 | − | 0.999232i | \(-0.487526\pi\) |
−0.999232 | + | 0.0391772i | \(0.987526\pi\) | |||||||
\(84\) | 6.91207i | 0.754169i | ||||||||
\(85\) | −1.89590 | − | 10.6795i | −0.205640 | − | 1.15836i | ||||
\(86\) | 2.51195 | 0.270871 | ||||||||
\(87\) | − | 9.67775i | − | 1.03756i | ||||||
\(88\) | − | 1.29587i | − | 0.138140i | ||||||
\(89\) | 3.83829 | − | 3.83829i | 0.406858 | − | 0.406858i | −0.473783 | − | 0.880642i | \(-0.657112\pi\) |
0.880642 | + | 0.473783i | \(0.157112\pi\) | |||||||
\(90\) | −0.136301 | − | 0.767778i | −0.0143674 | − | 0.0809309i | ||||
\(91\) | 18.4988 | − | 18.4988i | 1.93920 | − | 1.93920i | ||||
\(92\) | 3.33959 | 0.348176 | ||||||||
\(93\) | −0.380211 | −0.0394261 | ||||||||
\(94\) | 2.93686 | − | 2.93686i | 0.302914 | − | 0.302914i | ||||
\(95\) | 12.1732 | + | 8.50267i | 1.24894 | + | 0.872356i | ||||
\(96\) | −1.29397 | + | 1.29397i | −0.132066 | + | 0.132066i | ||||
\(97\) | − | 13.2514i | − | 1.34547i | −0.739882 | − | 0.672737i | \(-0.765119\pi\) | ||
0.739882 | − | 0.672737i | \(-0.234881\pi\) | |||||||
\(98\) | 7.26713i | 0.734091i | ||||||||
\(99\) | 0.451907 | 0.0454184 | ||||||||
\(100\) | 4.69447 | − | 1.72103i | 0.469447 | − | 0.172103i | ||||
\(101\) | 13.7890i | 1.37205i | 0.727577 | + | 0.686026i | \(0.240646\pi\) | ||||
−0.727577 | + | 0.686026i | \(0.759354\pi\) | |||||||
\(102\) | −6.27669 | − | 6.27669i | −0.621485 | − | 0.621485i | ||||
\(103\) | 10.6833i | 1.05265i | 0.850283 | + | 0.526327i | \(0.176431\pi\) | ||||
−0.850283 | + | 0.526327i | \(0.823569\pi\) | |||||||
\(104\) | 6.92612 | 0.679162 | ||||||||
\(105\) | −2.70159 | − | 15.2179i | −0.263648 | − | 1.48512i | ||||
\(106\) | 1.30971 | + | 1.30971i | 0.127210 | + | 0.127210i | ||||
\(107\) | −7.62669 | + | 7.62669i | −0.737300 | + | 0.737300i | −0.972055 | − | 0.234755i | \(-0.924571\pi\) |
0.234755 | + | 0.972055i | \(0.424571\pi\) | |||||||
\(108\) | 3.43067 | + | 3.43067i | 0.330116 | + | 0.330116i | ||||
\(109\) | −3.39395 | − | 3.39395i | −0.325081 | − | 0.325081i | 0.525631 | − | 0.850713i | \(-0.323829\pi\) |
−0.850713 | + | 0.525631i | \(0.823829\pi\) | |||||||
\(110\) | 0.506490 | + | 2.85304i | 0.0482920 | + | 0.272027i | ||||
\(111\) | −6.80987 | + | 8.80503i | −0.646365 | + | 0.835737i | ||||
\(112\) | −2.67087 | + | 2.67087i | −0.252374 | + | 0.252374i | ||||
\(113\) | − | 4.28955i | − | 0.403527i | −0.979434 | − | 0.201764i | \(-0.935333\pi\) | ||
0.979434 | − | 0.201764i | \(-0.0646673\pi\) | |||||||
\(114\) | 12.1518 | 1.13812 | ||||||||
\(115\) | −7.35258 | + | 1.30528i | −0.685632 | + | 0.121718i | ||||
\(116\) | 3.73955 | − | 3.73955i | 0.347209 | − | 0.347209i | ||||
\(117\) | 2.41534i | 0.223298i | ||||||||
\(118\) | −4.70039 | − | 4.70039i | −0.432706 | − | 0.432706i | ||||
\(119\) | −12.9556 | − | 12.9556i | −1.18764 | − | 1.18764i | ||||
\(120\) | 2.34312 | − | 3.35462i | 0.213896 | − | 0.306233i | ||||
\(121\) | 9.32073 | 0.847339 | ||||||||
\(122\) | 7.81965 | + | 7.81965i | 0.707958 | + | 0.707958i | ||||
\(123\) | 8.26009 | + | 8.26009i | 0.744787 | + | 0.744787i | ||||
\(124\) | −0.146916 | − | 0.146916i | −0.0131935 | − | 0.0131935i | ||||
\(125\) | −9.66289 | + | 5.62393i | −0.864275 | + | 0.503019i | ||||
\(126\) | −0.931412 | − | 0.931412i | −0.0829768 | − | 0.0829768i | ||||
\(127\) | 0.938326 | − | 0.938326i | 0.0832629 | − | 0.0832629i | −0.664249 | − | 0.747512i | \(-0.731248\pi\) |
0.747512 | + | 0.664249i | \(0.231248\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.25040 | + | 3.25040i | −0.286182 | + | 0.286182i | ||||
\(130\) | −15.2488 | + | 2.70708i | −1.33741 | + | 0.237426i | ||||
\(131\) | 2.47395 | + | 2.47395i | 0.216150 | + | 0.216150i | 0.806874 | − | 0.590724i | \(-0.201158\pi\) |
−0.590724 | + | 0.806874i | \(0.701158\pi\) | |||||||
\(132\) | 1.67682 | + | 1.67682i | 0.145948 | + | 0.145948i | ||||
\(133\) | 25.0824 | 2.17492 | ||||||||
\(134\) | −3.10789 | − | 3.10789i | −0.268481 | − | 0.268481i | ||||
\(135\) | −8.89400 | − | 6.21224i | −0.765473 | − | 0.534664i | ||||
\(136\) | − | 4.85071i | − | 0.415945i | ||||||
\(137\) | 14.6348 | − | 14.6348i | 1.25034 | − | 1.25034i | 0.294767 | − | 0.955569i | \(-0.404758\pi\) |
0.955569 | − | 0.294767i | \(-0.0952420\pi\) | |||||||
\(138\) | −4.32133 | + | 4.32133i | −0.367856 | + | 0.367856i | ||||
\(139\) | −14.2080 | −1.20511 | −0.602554 | − | 0.798078i | \(-0.705850\pi\) | ||||
−0.602554 | + | 0.798078i | \(0.705850\pi\) | |||||||
\(140\) | 4.83640 | − | 6.92422i | 0.408750 | − | 0.585204i | ||||
\(141\) | 7.60043i | 0.640072i | ||||||||
\(142\) | 5.59124 | 0.469207 | ||||||||
\(143\) | − | 8.97533i | − | 0.750555i | ||||||
\(144\) | − | 0.348729i | − | 0.0290608i | ||||||
\(145\) | −6.77155 | + | 9.69476i | −0.562347 | + | 0.805106i | ||||
\(146\) | −0.134980 | + | 0.134980i | −0.0111711 | + | 0.0111711i | ||||
\(147\) | −9.40346 | − | 9.40346i | −0.775585 | − | 0.775585i | ||||
\(148\) | −6.03371 | + | 0.770943i | −0.495968 | + | 0.0633712i | ||||
\(149\) | 7.52248i | 0.616266i | 0.951343 | + | 0.308133i | \(0.0997041\pi\) | ||||
−0.951343 | + | 0.308133i | \(0.900296\pi\) | |||||||
\(150\) | −3.84755 | + | 8.30148i | −0.314152 | + | 0.677813i | ||||
\(151\) | 4.35018i | 0.354012i | 0.984210 | + | 0.177006i | \(0.0566412\pi\) | ||||
−0.984210 | + | 0.177006i | \(0.943359\pi\) | |||||||
\(152\) | 4.69555 | + | 4.69555i | 0.380860 | + | 0.380860i | ||||
\(153\) | 1.69159 | 0.136757 | ||||||||
\(154\) | 3.46110 | + | 3.46110i | 0.278903 | + | 0.278903i | ||||
\(155\) | 0.380880 | + | 0.266035i | 0.0305930 | + | 0.0213684i | ||||
\(156\) | −8.96221 | + | 8.96221i | −0.717551 | + | 0.717551i | ||||
\(157\) | −13.0961 | + | 13.0961i | −1.04518 | + | 1.04518i | −0.0462518 | + | 0.998930i | \(0.514728\pi\) |
−0.998930 | + | 0.0462518i | \(0.985272\pi\) | |||||||
\(158\) | −10.8080 | − | 10.8080i | −0.859841 | − | 0.859841i | ||||
\(159\) | −3.38945 | −0.268801 | ||||||||
\(160\) | 2.20164 | − | 0.390851i | 0.174055 | − | 0.0308995i | ||||
\(161\) | −8.91961 | + | 8.91961i | −0.702964 | + | 0.702964i | ||||
\(162\) | −9.92458 | −0.779748 | ||||||||
\(163\) | 14.8033i | 1.15948i | 0.814801 | + | 0.579741i | \(0.196846\pi\) | ||||
−0.814801 | + | 0.579741i | \(0.803154\pi\) | |||||||
\(164\) | 6.38351i | 0.498469i | ||||||||
\(165\) | −4.34714 | − | 3.03637i | −0.338424 | − | 0.236381i | ||||
\(166\) | 8.74652 | + | 8.74652i | 0.678861 | + | 0.678861i | ||||
\(167\) | 1.13442i | 0.0877842i | 0.999036 | + | 0.0438921i | \(0.0139758\pi\) | ||||
−0.999036 | + | 0.0438921i | \(0.986024\pi\) | |||||||
\(168\) | − | 6.91207i | − | 0.533278i | ||||||
\(169\) | 34.9711 | 2.69009 | ||||||||
\(170\) | 1.89590 | + | 10.6795i | 0.145409 | + | 0.819083i | ||||
\(171\) | −1.63748 | + | 1.63748i | −0.125221 | + | 0.125221i | ||||
\(172\) | −2.51195 | −0.191535 | ||||||||
\(173\) | 7.57033 | − | 7.57033i | 0.575562 | − | 0.575562i | −0.358116 | − | 0.933677i | \(-0.616581\pi\) |
0.933677 | + | 0.358116i | \(0.116581\pi\) | |||||||
\(174\) | 9.67775i | 0.733668i | ||||||||
\(175\) | −7.94169 | + | 17.1350i | −0.600335 | + | 1.29528i | ||||
\(176\) | 1.29587i | 0.0976797i | ||||||||
\(177\) | 12.1643 | 0.914328 | ||||||||
\(178\) | −3.83829 | + | 3.83829i | −0.287692 | + | 0.287692i | ||||
\(179\) | −5.64137 | + | 5.64137i | −0.421656 | + | 0.421656i | −0.885773 | − | 0.464118i | \(-0.846371\pi\) |
0.464118 | + | 0.885773i | \(0.346371\pi\) | |||||||
\(180\) | 0.136301 | + | 0.767778i | 0.0101593 | + | 0.0572268i | ||||
\(181\) | −5.21779 | −0.387835 | −0.193918 | − | 0.981018i | \(-0.562119\pi\) | ||||
−0.193918 | + | 0.981018i | \(0.562119\pi\) | |||||||
\(182\) | −18.4988 | + | 18.4988i | −1.37122 | + | 1.37122i | ||||
\(183\) | −20.2368 | −1.49595 | ||||||||
\(184\) | −3.33959 | −0.246198 | ||||||||
\(185\) | 12.9828 | − | 4.05562i | 0.954511 | − | 0.298175i | ||||
\(186\) | 0.380211 | 0.0278784 | ||||||||
\(187\) | −6.28588 | −0.459669 | ||||||||
\(188\) | −2.93686 | + | 2.93686i | −0.214193 | + | 0.214193i | ||||
\(189\) | −18.3258 | −1.33300 | ||||||||
\(190\) | −12.1732 | − | 8.50267i | −0.883136 | − | 0.616849i | ||||
\(191\) | −6.11582 | + | 6.11582i | −0.442525 | + | 0.442525i | −0.892860 | − | 0.450335i | \(-0.851305\pi\) |
0.450335 | + | 0.892860i | \(0.351305\pi\) | |||||||
\(192\) | 1.29397 | − | 1.29397i | 0.0933844 | − | 0.0933844i | ||||
\(193\) | −15.9965 | −1.15145 | −0.575725 | − | 0.817643i | \(-0.695280\pi\) | ||||
−0.575725 | + | 0.817643i | \(0.695280\pi\) | |||||||
\(194\) | 13.2514i | 0.951394i | ||||||||
\(195\) | 16.2287 | − | 23.2345i | 1.16216 | − | 1.66386i | ||||
\(196\) | − | 7.26713i | − | 0.519081i | ||||||
\(197\) | 17.7621 | − | 17.7621i | 1.26550 | − | 1.26550i | 0.317109 | − | 0.948389i | \(-0.397288\pi\) |
0.948389 | − | 0.317109i | \(-0.102712\pi\) | |||||||
\(198\) | −0.451907 | −0.0321156 | ||||||||
\(199\) | −15.7905 | + | 15.7905i | −1.11936 | + | 1.11936i | −0.127524 | + | 0.991835i | \(0.540703\pi\) |
−0.991835 | + | 0.127524i | \(0.959297\pi\) | |||||||
\(200\) | −4.69447 | + | 1.72103i | −0.331949 | + | 0.121695i | ||||
\(201\) | 8.04306 | 0.567314 | ||||||||
\(202\) | − | 13.7890i | − | 0.970188i | ||||||
\(203\) | 19.9757i | 1.40202i | ||||||||
\(204\) | 6.27669 | + | 6.27669i | 0.439456 | + | 0.439456i | ||||
\(205\) | −2.49500 | − | 14.0542i | −0.174258 | − | 0.981590i | ||||
\(206\) | − | 10.6833i | − | 0.744338i | ||||||
\(207\) | − | 1.16461i | − | 0.0809462i | ||||||
\(208\) | −6.92612 | −0.480240 | ||||||||
\(209\) | 6.08481 | − | 6.08481i | 0.420895 | − | 0.420895i | ||||
\(210\) | 2.70159 | + | 15.2179i | 0.186427 | + | 1.05014i | ||||
\(211\) | −24.3785 | −1.67829 | −0.839144 | − | 0.543909i | \(-0.816944\pi\) | ||||
−0.839144 | + | 0.543909i | \(0.816944\pi\) | |||||||
\(212\) | −1.30971 | − | 1.30971i | −0.0899510 | − | 0.0899510i | ||||
\(213\) | −7.23491 | + | 7.23491i | −0.495728 | + | 0.495728i | ||||
\(214\) | 7.62669 | − | 7.62669i | 0.521350 | − | 0.521350i | ||||
\(215\) | 5.53043 | − | 0.981798i | 0.377172 | − | 0.0669581i | ||||
\(216\) | −3.43067 | − | 3.43067i | −0.233428 | − | 0.233428i | ||||
\(217\) | 0.784789 | 0.0532750 | ||||||||
\(218\) | 3.39395 | + | 3.39395i | 0.229867 | + | 0.229867i | ||||
\(219\) | − | 0.349322i | − | 0.0236050i | ||||||
\(220\) | −0.506490 | − | 2.85304i | −0.0341476 | − | 0.192352i | ||||
\(221\) | − | 33.5966i | − | 2.25995i | ||||||
\(222\) | 6.80987 | − | 8.80503i | 0.457049 | − | 0.590955i | ||||
\(223\) | 11.0916 | + | 11.0916i | 0.742750 | + | 0.742750i | 0.973106 | − | 0.230356i | \(-0.0739892\pi\) |
−0.230356 | + | 0.973106i | \(0.573989\pi\) | |||||||
\(224\) | 2.67087 | − | 2.67087i | 0.178455 | − | 0.178455i | ||||
\(225\) | −0.600173 | − | 1.63710i | −0.0400115 | − | 0.109140i | ||||
\(226\) | 4.28955i | 0.285337i | ||||||||
\(227\) | 13.1902i | 0.875463i | 0.899106 | + | 0.437732i | \(0.144218\pi\) | ||||
−0.899106 | + | 0.437732i | \(0.855782\pi\) | |||||||
\(228\) | −12.1518 | −0.804775 | ||||||||
\(229\) | − | 6.06268i | − | 0.400633i | −0.979731 | − | 0.200317i | \(-0.935803\pi\) | ||
0.979731 | − | 0.200317i | \(-0.0641971\pi\) | |||||||
\(230\) | 7.35258 | − | 1.30528i | 0.484815 | − | 0.0860676i | ||||
\(231\) | −8.95713 | −0.589336 | ||||||||
\(232\) | −3.73955 | + | 3.73955i | −0.245514 | + | 0.245514i | ||||
\(233\) | −11.6145 | + | 11.6145i | −0.760893 | + | 0.760893i | −0.976484 | − | 0.215590i | \(-0.930832\pi\) |
0.215590 | + | 0.976484i | \(0.430832\pi\) | |||||||
\(234\) | − | 2.41534i | − | 0.157896i | ||||||
\(235\) | 5.31805 | − | 7.61379i | 0.346911 | − | 0.496669i | ||||
\(236\) | 4.70039 | + | 4.70039i | 0.305969 | + | 0.305969i | ||||
\(237\) | 27.9706 | 1.81689 | ||||||||
\(238\) | 12.9556 | + | 12.9556i | 0.839789 | + | 0.839789i | ||||
\(239\) | −0.628920 | − | 0.628920i | −0.0406815 | − | 0.0406815i | 0.686473 | − | 0.727155i | \(-0.259158\pi\) |
−0.727155 | + | 0.686473i | \(0.759158\pi\) | |||||||
\(240\) | −2.34312 | + | 3.35462i | −0.151248 | + | 0.216540i | ||||
\(241\) | 14.1376 | − | 14.1376i | 0.910686 | − | 0.910686i | −0.0856405 | − | 0.996326i | \(-0.527294\pi\) |
0.996326 | + | 0.0856405i | \(0.0272937\pi\) | |||||||
\(242\) | −9.32073 | −0.599159 | ||||||||
\(243\) | 2.55012 | − | 2.55012i | 0.163590 | − | 0.163590i | ||||
\(244\) | −7.81965 | − | 7.81965i | −0.500602 | − | 0.500602i | ||||
\(245\) | 2.84036 | + | 15.9996i | 0.181464 | + | 1.02218i | ||||
\(246\) | −8.26009 | − | 8.26009i | −0.526644 | − | 0.526644i | ||||
\(247\) | 32.5219 | + | 32.5219i | 2.06932 | + | 2.06932i | ||||
\(248\) | 0.146916 | + | 0.146916i | 0.00932919 | + | 0.00932919i | ||||
\(249\) | −22.6355 | −1.43447 | ||||||||
\(250\) | 9.66289 | − | 5.62393i | 0.611135 | − | 0.355688i | ||||
\(251\) | 14.7200 | + | 14.7200i | 0.929119 | + | 0.929119i | 0.997649 | − | 0.0685304i | \(-0.0218310\pi\) |
−0.0685304 | + | 0.997649i | \(0.521831\pi\) | |||||||
\(252\) | 0.931412 | + | 0.931412i | 0.0586735 | + | 0.0586735i | ||||
\(253\) | 4.32766i | 0.272078i | ||||||||
\(254\) | −0.938326 | + | 0.938326i | −0.0588758 | + | 0.0588758i | ||||
\(255\) | −16.2723 | − | 11.3658i | −1.01901 | − | 0.711753i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.6607i | 1.47591i | 0.674848 | + | 0.737957i | \(0.264209\pi\) | ||||
−0.674848 | + | 0.737957i | \(0.735791\pi\) | |||||||
\(258\) | 3.25040 | − | 3.25040i | 0.202361 | − | 0.202361i | ||||
\(259\) | 14.0562 | − | 18.1744i | 0.873409 | − | 1.12930i | ||||
\(260\) | 15.2488 | − | 2.70708i | 0.945693 | − | 0.167886i | ||||
\(261\) | −1.30409 | − | 1.30409i | −0.0807212 | − | 0.0807212i | ||||
\(262\) | −2.47395 | − | 2.47395i | −0.152841 | − | 0.152841i | ||||
\(263\) | 17.6417 | − | 17.6417i | 1.08783 | − | 1.08783i | 0.0920831 | − | 0.995751i | \(-0.470647\pi\) |
0.995751 | − | 0.0920831i | \(-0.0293525\pi\) | |||||||
\(264\) | −1.67682 | − | 1.67682i | −0.103201 | − | 0.103201i | ||||
\(265\) | 3.39541 | + | 2.37161i | 0.208578 | + | 0.145687i | ||||
\(266\) | −25.0824 | −1.53790 | ||||||||
\(267\) | − | 9.93329i | − | 0.607908i | ||||||
\(268\) | 3.10789 | + | 3.10789i | 0.189845 | + | 0.189845i | ||||
\(269\) | − | 2.23989i | − | 0.136568i | −0.997666 | − | 0.0682841i | \(-0.978248\pi\) | ||
0.997666 | − | 0.0682841i | \(-0.0217524\pi\) | |||||||
\(270\) | 8.89400 | + | 6.21224i | 0.541271 | + | 0.378065i | ||||
\(271\) | 0.860850 | 0.0522929 | 0.0261465 | − | 0.999658i | \(-0.491676\pi\) | ||||
0.0261465 | + | 0.999658i | \(0.491676\pi\) | |||||||
\(272\) | 4.85071i | 0.294118i | ||||||||
\(273\) | − | 47.8738i | − | 2.89746i | ||||||
\(274\) | −14.6348 | + | 14.6348i | −0.884121 | + | 0.884121i | ||||
\(275\) | 2.23022 | + | 6.08341i | 0.134488 | + | 0.366844i | ||||
\(276\) | 4.32133 | − | 4.32133i | 0.260114 | − | 0.260114i | ||||
\(277\) | 1.08776 | 0.0653573 | 0.0326787 | − | 0.999466i | \(-0.489596\pi\) | ||||
0.0326787 | + | 0.999466i | \(0.489596\pi\) | |||||||
\(278\) | 14.2080 | 0.852140 | ||||||||
\(279\) | −0.0512340 | + | 0.0512340i | −0.00306730 | + | 0.00306730i | ||||
\(280\) | −4.83640 | + | 6.92422i | −0.289030 | + | 0.413802i | ||||
\(281\) | −12.3965 | + | 12.3965i | −0.739516 | + | 0.739516i | −0.972484 | − | 0.232969i | \(-0.925156\pi\) |
0.232969 | + | 0.972484i | \(0.425156\pi\) | |||||||
\(282\) | − | 7.60043i | − | 0.452599i | ||||||
\(283\) | − | 2.50115i | − | 0.148678i | −0.997233 | − | 0.0743390i | \(-0.976315\pi\) | ||
0.997233 | − | 0.0743390i | \(-0.0236847\pi\) | |||||||
\(284\) | −5.59124 | −0.331779 | ||||||||
\(285\) | 26.7540 | − | 4.74955i | 1.58477 | − | 0.281339i | ||||
\(286\) | 8.97533i | 0.530722i | ||||||||
\(287\) | −17.0496 | − | 17.0496i | −1.00640 | − | 1.00640i | ||||
\(288\) | 0.348729i | 0.0205491i | ||||||||
\(289\) | −6.52939 | −0.384082 | ||||||||
\(290\) | 6.77155 | − | 9.69476i | 0.397639 | − | 0.569296i | ||||
\(291\) | −17.1469 | − | 17.1469i | −1.00517 | − | 1.00517i | ||||
\(292\) | 0.134980 | − | 0.134980i | 0.00789913 | − | 0.00789913i | ||||
\(293\) | 7.08204 | + | 7.08204i | 0.413737 | + | 0.413737i | 0.883038 | − | 0.469301i | \(-0.155494\pi\) |
−0.469301 | + | 0.883038i | \(0.655494\pi\) | |||||||
\(294\) | 9.40346 | + | 9.40346i | 0.548421 | + | 0.548421i | ||||
\(295\) | −12.1857 | − | 8.51143i | −0.709481 | − | 0.495555i | ||||
\(296\) | 6.03371 | − | 0.770943i | 0.350702 | − | 0.0448102i | ||||
\(297\) | −4.44569 | + | 4.44569i | −0.257965 | + | 0.257965i | ||||
\(298\) | − | 7.52248i | − | 0.435766i | ||||||
\(299\) | −23.1304 | −1.33766 | ||||||||
\(300\) | 3.84755 | − | 8.30148i | 0.222139 | − | 0.479286i | ||||
\(301\) | 6.70911 | − | 6.70911i | 0.386707 | − | 0.386707i | ||||
\(302\) | − | 4.35018i | − | 0.250324i | ||||||
\(303\) | 17.8425 | + | 17.8425i | 1.02503 | + | 1.02503i | ||||
\(304\) | −4.69555 | − | 4.69555i | −0.269308 | − | 0.269308i | ||||
\(305\) | 20.2724 | + | 14.1598i | 1.16079 | + | 0.810787i | ||||
\(306\) | −1.69159 | −0.0967015 | ||||||||
\(307\) | 18.8346 | + | 18.8346i | 1.07495 | + | 1.07495i | 0.996954 | + | 0.0779923i | \(0.0248510\pi\) |
0.0779923 | + | 0.996954i | \(0.475149\pi\) | |||||||
\(308\) | −3.46110 | − | 3.46110i | −0.197214 | − | 0.197214i | ||||
\(309\) | 13.8238 | + | 13.8238i | 0.786411 | + | 0.786411i | ||||
\(310\) | −0.380880 | − | 0.266035i | −0.0216325 | − | 0.0151098i | ||||
\(311\) | −15.1202 | − | 15.1202i | −0.857389 | − | 0.857389i | 0.133641 | − | 0.991030i | \(-0.457333\pi\) |
−0.991030 | + | 0.133641i | \(0.957333\pi\) | |||||||
\(312\) | 8.96221 | − | 8.96221i | 0.507385 | − | 0.507385i | ||||
\(313\) | −8.77570 | −0.496032 | −0.248016 | − | 0.968756i | \(-0.579779\pi\) | ||||
−0.248016 | + | 0.968756i | \(0.579779\pi\) | |||||||
\(314\) | 13.0961 | − | 13.0961i | 0.739055 | − | 0.739055i | ||||
\(315\) | −2.41468 | − | 1.68660i | −0.136052 | − | 0.0950289i | ||||
\(316\) | 10.8080 | + | 10.8080i | 0.608000 | + | 0.608000i | ||||
\(317\) | 13.7979 | + | 13.7979i | 0.774970 | + | 0.774970i | 0.978971 | − | 0.204001i | \(-0.0653946\pi\) |
−0.204001 | + | 0.978971i | \(0.565395\pi\) | |||||||
\(318\) | 3.38945 | 0.190071 | ||||||||
\(319\) | 4.84596 | + | 4.84596i | 0.271322 | + | 0.271322i | ||||
\(320\) | −2.20164 | + | 0.390851i | −0.123076 | + | 0.0218492i | ||||
\(321\) | 19.7374i | 1.10164i | ||||||||
\(322\) | 8.91961 | − | 8.91961i | 0.497071 | − | 0.497071i | ||||
\(323\) | 22.7768 | − | 22.7768i | 1.26733 | − | 1.26733i | ||||
\(324\) | 9.92458 | 0.551365 | ||||||||
\(325\) | −32.5145 | + | 11.9200i | −1.80358 | + | 0.661205i | ||||
\(326\) | − | 14.8033i | − | 0.819877i | ||||||
\(327\) | −8.78335 | −0.485721 | ||||||||
\(328\) | − | 6.38351i | − | 0.352471i | ||||||
\(329\) | − | 15.6880i | − | 0.864905i | ||||||
\(330\) | 4.34714 | + | 3.03637i | 0.239302 | + | 0.167147i | ||||
\(331\) | 0.223075 | − | 0.223075i | 0.0122613 | − | 0.0122613i | −0.700950 | − | 0.713211i | \(-0.747240\pi\) |
0.713211 | + | 0.700950i | \(0.247240\pi\) | |||||||
\(332\) | −8.74652 | − | 8.74652i | −0.480028 | − | 0.480028i | ||||
\(333\) | 0.268851 | + | 2.10413i | 0.0147329 | + | 0.115306i | ||||
\(334\) | − | 1.13442i | − | 0.0620728i | ||||||
\(335\) | −8.05720 | − | 5.62775i | −0.440212 | − | 0.307477i | ||||
\(336\) | 6.91207i | 0.377085i | ||||||||
\(337\) | −12.6737 | − | 12.6737i | −0.690381 | − | 0.690381i | 0.271935 | − | 0.962316i | \(-0.412336\pi\) |
−0.962316 | + | 0.271935i | \(0.912336\pi\) | |||||||
\(338\) | −34.9711 | −1.90218 | ||||||||
\(339\) | −5.55057 | − | 5.55057i | −0.301465 | − | 0.301465i | ||||
\(340\) | −1.89590 | − | 10.6795i | −0.102820 | − | 0.579179i | ||||
\(341\) | 0.190384 | − | 0.190384i | 0.0103099 | − | 0.0103099i | ||||
\(342\) | 1.63748 | − | 1.63748i | 0.0885446 | − | 0.0885446i | ||||
\(343\) | 0.713468 | + | 0.713468i | 0.0385236 | + | 0.0385236i | ||||
\(344\) | 2.51195 | 0.135435 | ||||||||
\(345\) | −7.82504 | + | 11.2030i | −0.421286 | + | 0.603151i | ||||
\(346\) | −7.57033 | + | 7.57033i | −0.406983 | + | 0.406983i | ||||
\(347\) | 9.68557 | 0.519948 | 0.259974 | − | 0.965616i | \(-0.416286\pi\) | ||||
0.259974 | + | 0.965616i | \(0.416286\pi\) | |||||||
\(348\) | − | 9.67775i | − | 0.518782i | ||||||
\(349\) | − | 9.40675i | − | 0.503532i | −0.967788 | − | 0.251766i | \(-0.918989\pi\) | ||
0.967788 | − | 0.251766i | \(-0.0810113\pi\) | |||||||
\(350\) | 7.94169 | − | 17.1350i | 0.424501 | − | 0.915904i | ||||
\(351\) | −23.7612 | − | 23.7612i | −1.26828 | − | 1.26828i | ||||
\(352\) | − | 1.29587i | − | 0.0690700i | ||||||
\(353\) | 8.93094i | 0.475346i | 0.971345 | + | 0.237673i | \(0.0763846\pi\) | ||||
−0.971345 | + | 0.237673i | \(0.923615\pi\) | |||||||
\(354\) | −12.1643 | −0.646528 | ||||||||
\(355\) | 12.3099 | − | 2.18534i | 0.653343 | − | 0.115986i | ||||
\(356\) | 3.83829 | − | 3.83829i | 0.203429 | − | 0.203429i | ||||
\(357\) | −33.5285 | −1.77451 | ||||||||
\(358\) | 5.64137 | − | 5.64137i | 0.298156 | − | 0.298156i | ||||
\(359\) | 14.7945i | 0.780823i | 0.920640 | + | 0.390412i | \(0.127667\pi\) | ||||
−0.920640 | + | 0.390412i | \(0.872333\pi\) | |||||||
\(360\) | −0.136301 | − | 0.767778i | −0.00718370 | − | 0.0404655i | ||||
\(361\) | 25.0964i | 1.32086i | ||||||||
\(362\) | 5.21779 | 0.274241 | ||||||||
\(363\) | 12.0608 | − | 12.0608i | 0.633026 | − | 0.633026i | ||||
\(364\) | 18.4988 | − | 18.4988i | 0.969600 | − | 0.969600i | ||||
\(365\) | −0.244421 | + | 0.349936i | −0.0127936 | + | 0.0183165i | ||||
\(366\) | 20.2368 | 1.05780 | ||||||||
\(367\) | 19.5831 | − | 19.5831i | 1.02223 | − | 1.02223i | 0.0224808 | − | 0.999747i | \(-0.492844\pi\) |
0.999747 | − | 0.0224808i | \(-0.00715646\pi\) | |||||||
\(368\) | 3.33959 | 0.174088 | ||||||||
\(369\) | 2.22612 | 0.115887 | ||||||||
\(370\) | −12.9828 | + | 4.05562i | −0.674941 | + | 0.210842i | ||||
\(371\) | 6.99612 | 0.363221 | ||||||||
\(372\) | −0.380211 | −0.0197130 | ||||||||
\(373\) | 7.70109 | − | 7.70109i | 0.398747 | − | 0.398747i | −0.479044 | − | 0.877791i | \(-0.659016\pi\) |
0.877791 | + | 0.479044i | \(0.159016\pi\) | |||||||
\(374\) | 6.28588 | 0.325035 | ||||||||
\(375\) | −5.22631 | + | 19.7807i | −0.269885 | + | 1.02147i | ||||
\(376\) | 2.93686 | − | 2.93686i | 0.151457 | − | 0.151457i | ||||
\(377\) | −25.9006 | + | 25.9006i | −1.33395 | + | 1.33395i | ||||
\(378\) | 18.3258 | 0.942576 | ||||||||
\(379\) | 19.2451i | 0.988556i | 0.869304 | + | 0.494278i | \(0.164567\pi\) | ||||
−0.869304 | + | 0.494278i | \(0.835433\pi\) | |||||||
\(380\) | 12.1732 | + | 8.50267i | 0.624472 | + | 0.436178i | ||||
\(381\) | − | 2.42834i | − | 0.124407i | ||||||
\(382\) | 6.11582 | − | 6.11582i | 0.312913 | − | 0.312913i | ||||
\(383\) | −8.69427 | −0.444257 | −0.222128 | − | 0.975017i | \(-0.571300\pi\) | ||||
−0.222128 | + | 0.975017i | \(0.571300\pi\) | |||||||
\(384\) | −1.29397 | + | 1.29397i | −0.0660328 | + | 0.0660328i | ||||
\(385\) | 8.97288 | + | 6.26733i | 0.457300 | + | 0.319413i | ||||
\(386\) | 15.9965 | 0.814198 | ||||||||
\(387\) | 0.875992i | 0.0445292i | ||||||||
\(388\) | − | 13.2514i | − | 0.672737i | ||||||
\(389\) | −14.2389 | − | 14.2389i | −0.721941 | − | 0.721941i | 0.247059 | − | 0.969000i | \(-0.420536\pi\) |
−0.969000 | + | 0.247059i | \(0.920536\pi\) | |||||||
\(390\) | −16.2287 | + | 23.2345i | −0.821772 | + | 1.17652i | ||||
\(391\) | 16.1994i | 0.819237i | ||||||||
\(392\) | 7.26713i | 0.367045i | ||||||||
\(393\) | 6.40246 | 0.322961 | ||||||||
\(394\) | −17.7621 | + | 17.7621i | −0.894842 | + | 0.894842i | ||||
\(395\) | −28.0198 | − | 19.5711i | −1.40983 | − | 0.984730i | ||||
\(396\) | 0.451907 | 0.0227092 | ||||||||
\(397\) | 10.2910 | + | 10.2910i | 0.516489 | + | 0.516489i | 0.916507 | − | 0.400018i | \(-0.130996\pi\) |
−0.400018 | + | 0.916507i | \(0.630996\pi\) | |||||||
\(398\) | 15.7905 | − | 15.7905i | 0.791507 | − | 0.791507i | ||||
\(399\) | 32.4560 | − | 32.4560i | 1.62483 | − | 1.62483i | ||||
\(400\) | 4.69447 | − | 1.72103i | 0.234724 | − | 0.0860514i | ||||
\(401\) | −13.7676 | − | 13.7676i | −0.687523 | − | 0.687523i | 0.274161 | − | 0.961684i | \(-0.411600\pi\) |
−0.961684 | + | 0.274161i | \(0.911600\pi\) | |||||||
\(402\) | −8.04306 | −0.401151 | ||||||||
\(403\) | 1.01756 | + | 1.01756i | 0.0506883 | + | 0.0506883i | ||||
\(404\) | 13.7890i | 0.686026i | ||||||||
\(405\) | −21.8504 | + | 3.87903i | −1.08575 | + | 0.192750i | ||||
\(406\) | − | 19.9757i | − | 0.991379i | ||||||
\(407\) | −0.999040 | − | 7.81889i | −0.0495206 | − | 0.387568i | ||||
\(408\) | −6.27669 | − | 6.27669i | −0.310742 | − | 0.310742i | ||||
\(409\) | −14.5393 | + | 14.5393i | −0.718920 | + | 0.718920i | −0.968384 | − | 0.249464i | \(-0.919745\pi\) |
0.249464 | + | 0.968384i | \(0.419745\pi\) | |||||||
\(410\) | 2.49500 | + | 14.0542i | 0.123219 | + | 0.694089i | ||||
\(411\) | − | 37.8741i | − | 1.86819i | ||||||
\(412\) | 10.6833i | 0.526327i | ||||||||
\(413\) | −25.1083 | −1.23550 | ||||||||
\(414\) | 1.16461i | 0.0572376i | ||||||||
\(415\) | 22.6753 | + | 15.8381i | 1.11309 | + | 0.777463i | ||||
\(416\) | 6.92612 | 0.339581 | ||||||||
\(417\) | −18.3848 | + | 18.3848i | −0.900307 | + | 0.900307i | ||||
\(418\) | −6.08481 | + | 6.08481i | −0.297618 | + | 0.297618i | ||||
\(419\) | − | 8.30494i | − | 0.405723i | −0.979207 | − | 0.202861i | \(-0.934976\pi\) | ||
0.979207 | − | 0.202861i | \(-0.0650241\pi\) | |||||||
\(420\) | −2.70159 | − | 15.2179i | −0.131824 | − | 0.742559i | ||||
\(421\) | −5.43095 | − | 5.43095i | −0.264688 | − | 0.264688i | 0.562267 | − | 0.826956i | \(-0.309929\pi\) |
−0.826956 | + | 0.562267i | \(0.809929\pi\) | |||||||
\(422\) | 24.3785 | 1.18673 | ||||||||
\(423\) | 1.02417 | + | 1.02417i | 0.0497968 | + | 0.0497968i | ||||
\(424\) | 1.30971 | + | 1.30971i | 0.0636050 | + | 0.0636050i | ||||
\(425\) | 8.34821 | + | 22.7715i | 0.404948 | + | 1.10458i | ||||
\(426\) | 7.23491 | − | 7.23491i | 0.350533 | − | 0.350533i | ||||
\(427\) | 41.7706 | 2.02142 | ||||||||
\(428\) | −7.62669 | + | 7.62669i | −0.368650 | + | 0.368650i | ||||
\(429\) | −11.6138 | − | 11.6138i | −0.560721 | − | 0.560721i | ||||
\(430\) | −5.53043 | + | 0.981798i | −0.266701 | + | 0.0473465i | ||||
\(431\) | 16.0000 | + | 16.0000i | 0.770693 | + | 0.770693i | 0.978228 | − | 0.207535i | \(-0.0665439\pi\) |
−0.207535 | + | 0.978228i | \(0.566544\pi\) | |||||||
\(432\) | 3.43067 | + | 3.43067i | 0.165058 | + | 0.165058i | ||||
\(433\) | −21.6988 | − | 21.6988i | −1.04278 | − | 1.04278i | −0.999043 | − | 0.0437350i | \(-0.986074\pi\) |
−0.0437350 | − | 0.999043i | \(-0.513926\pi\) | |||||||
\(434\) | −0.784789 | −0.0376711 | ||||||||
\(435\) | 3.78256 | + | 21.3070i | 0.181360 | + | 1.02159i | ||||
\(436\) | −3.39395 | − | 3.39395i | −0.162541 | − | 0.162541i | ||||
\(437\) | −15.6812 | − | 15.6812i | −0.750134 | − | 0.750134i | ||||
\(438\) | 0.349322i | 0.0166912i | ||||||||
\(439\) | 5.60815 | − | 5.60815i | 0.267662 | − | 0.267662i | −0.560495 | − | 0.828158i | \(-0.689389\pi\) |
0.828158 | + | 0.560495i | \(0.189389\pi\) | |||||||
\(440\) | 0.506490 | + | 2.85304i | 0.0241460 | + | 0.136013i | ||||
\(441\) | −2.53426 | −0.120679 | ||||||||
\(442\) | 33.5966i | 1.59803i | ||||||||
\(443\) | 17.9895 | − | 17.9895i | 0.854708 | − | 0.854708i | −0.136001 | − | 0.990709i | \(-0.543425\pi\) |
0.990709 | + | 0.136001i | \(0.0434250\pi\) | |||||||
\(444\) | −6.80987 | + | 8.80503i | −0.323182 | + | 0.417868i | ||||
\(445\) | −6.95036 | + | 9.95076i | −0.329479 | + | 0.471711i | ||||
\(446\) | −11.0916 | − | 11.0916i | −0.525203 | − | 0.525203i | ||||
\(447\) | 9.73388 | + | 9.73388i | 0.460397 | + | 0.460397i | ||||
\(448\) | −2.67087 | + | 2.67087i | −0.126187 | + | 0.126187i | ||||
\(449\) | 6.18967 | + | 6.18967i | 0.292109 | + | 0.292109i | 0.837913 | − | 0.545804i | \(-0.183776\pi\) |
−0.545804 | + | 0.837913i | \(0.683776\pi\) | |||||||
\(450\) | 0.600173 | + | 1.63710i | 0.0282924 | + | 0.0771737i | ||||
\(451\) | −8.27219 | −0.389522 | ||||||||
\(452\) | − | 4.28955i | − | 0.201764i | ||||||
\(453\) | 5.62901 | + | 5.62901i | 0.264474 | + | 0.264474i | ||||
\(454\) | − | 13.1902i | − | 0.619046i | ||||||
\(455\) | −33.4975 | + | 47.9580i | −1.57039 | + | 2.24831i | ||||
\(456\) | 12.1518 | 0.569062 | ||||||||
\(457\) | − | 31.9423i | − | 1.49420i | −0.664712 | − | 0.747100i | \(-0.731446\pi\) | ||
0.664712 | − | 0.747100i | \(-0.268554\pi\) | |||||||
\(458\) | 6.06268i | 0.283291i | ||||||||
\(459\) | −16.6412 | + | 16.6412i | −0.776744 | + | 0.776744i | ||||
\(460\) | −7.35258 | + | 1.30528i | −0.342816 | + | 0.0608590i | ||||
\(461\) | 2.73403 | − | 2.73403i | 0.127336 | − | 0.127336i | −0.640566 | − | 0.767903i | \(-0.721300\pi\) |
0.767903 | + | 0.640566i | \(0.221300\pi\) | |||||||
\(462\) | 8.95713 | 0.416723 | ||||||||
\(463\) | −4.32970 | −0.201218 | −0.100609 | − | 0.994926i | \(-0.532079\pi\) | ||||
−0.100609 | + | 0.994926i | \(0.532079\pi\) | |||||||
\(464\) | 3.73955 | − | 3.73955i | 0.173604 | − | 0.173604i | ||||
\(465\) | 0.837090 | − | 0.148606i | 0.0388191 | − | 0.00689143i | ||||
\(466\) | 11.6145 | − | 11.6145i | 0.538033 | − | 0.538033i | ||||
\(467\) | − | 0.826696i | − | 0.0382549i | −0.999817 | − | 0.0191275i | \(-0.993911\pi\) | ||
0.999817 | − | 0.0191275i | \(-0.00608884\pi\) | |||||||
\(468\) | 2.41534i | 0.111649i | ||||||||
\(469\) | −16.6016 | −0.766590 | ||||||||
\(470\) | −5.31805 | + | 7.61379i | −0.245303 | + | 0.351198i | ||||
\(471\) | 33.8920i | 1.56166i | ||||||||
\(472\) | −4.70039 | − | 4.70039i | −0.216353 | − | 0.216353i | ||||
\(473\) | − | 3.25516i | − | 0.149672i | ||||||
\(474\) | −27.9706 | −1.28473 | ||||||||
\(475\) | −30.1243 | − | 13.9620i | −1.38220 | − | 0.640619i | ||||
\(476\) | −12.9556 | − | 12.9556i | −0.593821 | − | 0.593821i | ||||
\(477\) | −0.456733 | + | 0.456733i | −0.0209124 | + | 0.0209124i | ||||
\(478\) | 0.628920 | + | 0.628920i | 0.0287661 | + | 0.0287661i | ||||
\(479\) | 19.7849 | + | 19.7849i | 0.903997 | + | 0.903997i | 0.995779 | − | 0.0917818i | \(-0.0292562\pi\) |
−0.0917818 | + | 0.995779i | \(0.529256\pi\) | |||||||
\(480\) | 2.34312 | − | 3.35462i | 0.106948 | − | 0.153117i | ||||
\(481\) | 41.7902 | − | 5.33965i | 1.90547 | − | 0.243467i | ||||
\(482\) | −14.1376 | + | 14.1376i | −0.643952 | + | 0.643952i | ||||
\(483\) | 23.0835i | 1.05033i | ||||||||
\(484\) | 9.32073 | 0.423669 | ||||||||
\(485\) | 5.17931 | + | 29.1748i | 0.235180 | + | 1.32476i | ||||
\(486\) | −2.55012 | + | 2.55012i | −0.115676 | + | 0.115676i | ||||
\(487\) | 28.2154i | 1.27856i | 0.768973 | + | 0.639282i | \(0.220768\pi\) | ||||
−0.768973 | + | 0.639282i | \(0.779232\pi\) | |||||||
\(488\) | 7.81965 | + | 7.81965i | 0.353979 | + | 0.353979i | ||||
\(489\) | 19.1550 | + | 19.1550i | 0.866220 | + | 0.866220i | ||||
\(490\) | −2.84036 | − | 15.9996i | −0.128314 | − | 0.722790i | ||||
\(491\) | 2.48442 | 0.112121 | 0.0560603 | − | 0.998427i | \(-0.482146\pi\) | ||||
0.0560603 | + | 0.998427i | \(0.482146\pi\) | |||||||
\(492\) | 8.26009 | + | 8.26009i | 0.372394 | + | 0.372394i | ||||
\(493\) | 18.1395 | + | 18.1395i | 0.816961 | + | 0.816961i | ||||
\(494\) | −32.5219 | − | 32.5219i | −1.46323 | − | 1.46323i | ||||
\(495\) | −0.994939 | + | 0.176628i | −0.0447192 | + | 0.00793885i | ||||
\(496\) | −0.146916 | − | 0.146916i | −0.00659674 | − | 0.00659674i | ||||
\(497\) | 14.9335 | − | 14.9335i | 0.669859 | − | 0.669859i | ||||
\(498\) | 22.6355 | 1.01432 | ||||||||
\(499\) | 1.49326 | − | 1.49326i | 0.0668473 | − | 0.0668473i | −0.672893 | − | 0.739740i | \(-0.734948\pi\) |
0.739740 | + | 0.672893i | \(0.234948\pi\) | |||||||
\(500\) | −9.66289 | + | 5.62393i | −0.432138 | + | 0.251510i | ||||
\(501\) | 1.46791 | + | 1.46791i | 0.0655814 | + | 0.0655814i | ||||
\(502\) | −14.7200 | − | 14.7200i | −0.656986 | − | 0.656986i | ||||
\(503\) | 3.35307 | 0.149506 | 0.0747531 | − | 0.997202i | \(-0.476183\pi\) | ||||
0.0747531 | + | 0.997202i | \(0.476183\pi\) | |||||||
\(504\) | −0.931412 | − | 0.931412i | −0.0414884 | − | 0.0414884i | ||||
\(505\) | −5.38942 | − | 30.3584i | −0.239826 | − | 1.35093i | ||||
\(506\) | − | 4.32766i | − | 0.192388i | ||||||
\(507\) | 45.2517 | − | 45.2517i | 2.00970 | − | 2.00970i | ||||
\(508\) | 0.938326 | − | 0.938326i | 0.0416315 | − | 0.0416315i | ||||
\(509\) | 9.46119 | 0.419360 | 0.209680 | − | 0.977770i | \(-0.432758\pi\) | ||||
0.209680 | + | 0.977770i | \(0.432758\pi\) | |||||||
\(510\) | 16.2723 | + | 11.3658i | 0.720548 | + | 0.503285i | ||||
\(511\) | 0.721031i | 0.0318965i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | − | 32.2178i | − | 1.42245i | ||||||
\(514\) | − | 23.6607i | − | 1.04363i | ||||||
\(515\) | −4.17556 | − | 23.5207i | −0.183997 | − | 1.03645i | ||||
\(516\) | −3.25040 | + | 3.25040i | −0.143091 | + | 0.143091i | ||||
\(517\) | −3.80578 | − | 3.80578i | −0.167378 | − | 0.167378i | ||||
\(518\) | −14.0562 | + | 18.1744i | −0.617593 | + | 0.798536i | ||||
\(519\) | − | 19.5916i | − | 0.859976i | ||||||
\(520\) | −15.2488 | + | 2.70708i | −0.668706 | + | 0.118713i | ||||
\(521\) | 28.0496i | 1.22887i | 0.788966 | + | 0.614437i | \(0.210617\pi\) | ||||
−0.788966 | + | 0.614437i | \(0.789383\pi\) | |||||||
\(522\) | 1.30409 | + | 1.30409i | 0.0570785 | + | 0.0570785i | ||||
\(523\) | −10.2294 | −0.447300 | −0.223650 | − | 0.974669i | \(-0.571797\pi\) | ||||
−0.223650 | + | 0.974669i | \(0.571797\pi\) | |||||||
\(524\) | 2.47395 | + | 2.47395i | 0.108075 | + | 0.108075i | ||||
\(525\) | 11.8959 | + | 32.4485i | 0.519178 | + | 1.41617i | ||||
\(526\) | −17.6417 | + | 17.6417i | −0.769215 | + | 0.769215i | ||||
\(527\) | 0.712648 | − | 0.712648i | 0.0310434 | − | 0.0310434i | ||||
\(528\) | 1.67682 | + | 1.67682i | 0.0729741 | + | 0.0729741i | ||||
\(529\) | −11.8472 | −0.515094 | ||||||||
\(530\) | −3.39541 | − | 2.37161i | −0.147487 | − | 0.103016i | ||||
\(531\) | 1.63916 | − | 1.63916i | 0.0711337 | − | 0.0711337i | ||||
\(532\) | 25.0824 | 1.08746 | ||||||||
\(533\) | − | 44.2130i | − | 1.91508i | ||||||
\(534\) | 9.93329i | 0.429856i | ||||||||
\(535\) | 13.8104 | − | 19.7721i | 0.597074 | − | 0.854824i | ||||
\(536\) | −3.10789 | − | 3.10789i | −0.134241 | − | 0.134241i | ||||
\(537\) | 14.5995i | 0.630017i | ||||||||
\(538\) | 2.23989i | 0.0965683i | ||||||||
\(539\) | 9.41723 | 0.405629 | ||||||||
\(540\) | −8.89400 | − | 6.21224i | −0.382737 | − | 0.267332i | ||||
\(541\) | 11.2603 | − | 11.2603i | 0.484116 | − | 0.484116i | −0.422327 | − | 0.906443i | \(-0.638787\pi\) |
0.906443 | + | 0.422327i | \(0.138787\pi\) | |||||||
\(542\) | −0.860850 | −0.0369767 | ||||||||
\(543\) | −6.75168 | + | 6.75168i | −0.289742 | + | 0.289742i | ||||
\(544\) | − | 4.85071i | − | 0.207973i | ||||||
\(545\) | 8.79879 | + | 6.14574i | 0.376899 | + | 0.263255i | ||||
\(546\) | 47.8738i | 2.04881i | ||||||||
\(547\) | 25.5984 | 1.09451 | 0.547254 | − | 0.836966i | \(-0.315673\pi\) | ||||
0.547254 | + | 0.836966i | \(0.315673\pi\) | |||||||
\(548\) | 14.6348 | − | 14.6348i | 0.625168 | − | 0.625168i | ||||
\(549\) | −2.72694 | + | 2.72694i | −0.116383 | + | 0.116383i | ||||
\(550\) | −2.23022 | − | 6.08341i | −0.0950970 | − | 0.259398i | ||||
\(551\) | −35.1185 | −1.49610 | ||||||||
\(552\) | −4.32133 | + | 4.32133i | −0.183928 | + | 0.183928i | ||||
\(553\) | −57.7338 | −2.45509 | ||||||||
\(554\) | −1.08776 | −0.0462146 | ||||||||
\(555\) | 11.5515 | − | 22.0472i | 0.490332 | − | 0.935851i | ||||
\(556\) | −14.2080 | −0.602554 | ||||||||
\(557\) | 14.7290 | 0.624089 | 0.312045 | − | 0.950067i | \(-0.398986\pi\) | ||||
0.312045 | + | 0.950067i | \(0.398986\pi\) | |||||||
\(558\) | 0.0512340 | − | 0.0512340i | 0.00216891 | − | 0.00216891i | ||||
\(559\) | 17.3981 | 0.735861 | ||||||||
\(560\) | 4.83640 | − | 6.92422i | 0.204375 | − | 0.292602i | ||||
\(561\) | −8.13375 | + | 8.13375i | −0.343407 | + | 0.343407i | ||||
\(562\) | 12.3965 | − | 12.3965i | 0.522917 | − | 0.522917i | ||||
\(563\) | −30.0223 | −1.26529 | −0.632645 | − | 0.774442i | \(-0.718031\pi\) | ||||
−0.632645 | + | 0.774442i | \(0.718031\pi\) | |||||||
\(564\) | 7.60043i | 0.320036i | ||||||||
\(565\) | 1.67658 | + | 9.44407i | 0.0705341 | + | 0.397315i | ||||
\(566\) | 2.50115i | 0.105131i | ||||||||
\(567\) | −26.5073 | + | 26.5073i | −1.11320 | + | 1.11320i | ||||
\(568\) | 5.59124 | 0.234603 | ||||||||
\(569\) | −5.23109 | + | 5.23109i | −0.219298 | + | 0.219298i | −0.808203 | − | 0.588904i | \(-0.799559\pi\) |
0.588904 | + | 0.808203i | \(0.299559\pi\) | |||||||
\(570\) | −26.7540 | + | 4.74955i | −1.12060 | + | 0.198937i | ||||
\(571\) | −13.0995 | −0.548196 | −0.274098 | − | 0.961702i | \(-0.588379\pi\) | ||||
−0.274098 | + | 0.961702i | \(0.588379\pi\) | |||||||
\(572\) | − | 8.97533i | − | 0.375277i | ||||||
\(573\) | 15.8274i | 0.661199i | ||||||||
\(574\) | 17.0496 | + | 17.0496i | 0.711635 | + | 0.711635i | ||||
\(575\) | 15.6776 | − | 5.74752i | 0.653801 | − | 0.239688i | ||||
\(576\) | − | 0.348729i | − | 0.0145304i | ||||||
\(577\) | − | 21.6061i | − | 0.899475i | −0.893161 | − | 0.449737i | \(-0.851518\pi\) | ||
0.893161 | − | 0.449737i | \(-0.148482\pi\) | |||||||
\(578\) | 6.52939 | 0.271587 | ||||||||
\(579\) | −20.6990 | + | 20.6990i | −0.860220 | + | 0.860220i | ||||
\(580\) | −6.77155 | + | 9.69476i | −0.281173 | + | 0.402553i | ||||
\(581\) | 46.7217 | 1.93834 | ||||||||
\(582\) | 17.1469 | + | 17.1469i | 0.710763 | + | 0.710763i | ||||
\(583\) | 1.69721 | − | 1.69721i | 0.0702911 | − | 0.0702911i | ||||
\(584\) | −0.134980 | + | 0.134980i | −0.00558553 | + | 0.00558553i | ||||
\(585\) | −0.944038 | − | 5.31772i | −0.0390312 | − | 0.219861i | ||||
\(586\) | −7.08204 | − | 7.08204i | −0.292556 | − | 0.292556i | ||||
\(587\) | −37.7655 | −1.55875 | −0.779375 | − | 0.626557i | \(-0.784463\pi\) | ||||
−0.779375 | + | 0.626557i | \(0.784463\pi\) | |||||||
\(588\) | −9.40346 | − | 9.40346i | −0.387792 | − | 0.387792i | ||||
\(589\) | 1.37971i | 0.0568498i | ||||||||
\(590\) | 12.1857 | + | 8.51143i | 0.501679 | + | 0.350410i | ||||
\(591\) | − | 45.9674i | − | 1.89084i | ||||||
\(592\) | −6.03371 | + | 0.770943i | −0.247984 | + | 0.0316856i | ||||
\(593\) | −5.60150 | − | 5.60150i | −0.230026 | − | 0.230026i | 0.582678 | − | 0.812703i | \(-0.302005\pi\) |
−0.812703 | + | 0.582678i | \(0.802005\pi\) | |||||||
\(594\) | 4.44569 | − | 4.44569i | 0.182409 | − | 0.182409i | ||||
\(595\) | 33.5874 | + | 23.4600i | 1.37695 | + | 0.961765i | ||||
\(596\) | 7.52248i | 0.308133i | ||||||||
\(597\) | 40.8650i | 1.67249i | ||||||||
\(598\) | 23.1304 | 0.945871 | ||||||||
\(599\) | 3.81331i | 0.155808i | 0.996961 | + | 0.0779039i | \(0.0248227\pi\) | ||||
−0.996961 | + | 0.0779039i | \(0.975177\pi\) | |||||||
\(600\) | −3.84755 | + | 8.30148i | −0.157076 | + | 0.338906i | ||||
\(601\) | 15.0394 | 0.613469 | 0.306734 | − | 0.951795i | \(-0.400764\pi\) | ||||
0.306734 | + | 0.951795i | \(0.400764\pi\) | |||||||
\(602\) | −6.70911 | + | 6.70911i | −0.273443 | + | 0.273443i | ||||
\(603\) | 1.08381 | − | 1.08381i | 0.0441363 | − | 0.0441363i | ||||
\(604\) | 4.35018i | 0.177006i | ||||||||
\(605\) | −20.5209 | + | 3.64301i | −0.834294 | + | 0.148110i | ||||
\(606\) | −17.8425 | − | 17.8425i | −0.724803 | − | 0.724803i | ||||
\(607\) | 28.5167 | 1.15746 | 0.578729 | − | 0.815520i | \(-0.303549\pi\) | ||||
0.578729 | + | 0.815520i | \(0.303549\pi\) | |||||||
\(608\) | 4.69555 | + | 4.69555i | 0.190430 | + | 0.190430i | ||||
\(609\) | 25.8480 | + | 25.8480i | 1.04742 | + | 1.04742i | ||||
\(610\) | −20.2724 | − | 14.1598i | −0.820806 | − | 0.573313i | ||||
\(611\) | 20.3410 | − | 20.3410i | 0.822911 | − | 0.822911i | ||||
\(612\) | 1.69159 | 0.0683783 | ||||||||
\(613\) | −11.7097 | + | 11.7097i | −0.472948 | + | 0.472948i | −0.902867 | − | 0.429919i | \(-0.858542\pi\) |
0.429919 | + | 0.902867i | \(0.358542\pi\) | |||||||
\(614\) | −18.8346 | − | 18.8346i | −0.760102 | − | 0.760102i | ||||
\(615\) | −21.4142 | − | 14.9573i | −0.863506 | − | 0.603137i | ||||
\(616\) | 3.46110 | + | 3.46110i | 0.139452 | + | 0.139452i | ||||
\(617\) | −31.2569 | − | 31.2569i | −1.25836 | − | 1.25836i | −0.951878 | − | 0.306477i | \(-0.900850\pi\) |
−0.306477 | − | 0.951878i | \(-0.599150\pi\) | |||||||
\(618\) | −13.8238 | − | 13.8238i | −0.556077 | − | 0.556077i | ||||
\(619\) | −3.97357 | −0.159711 | −0.0798556 | − | 0.996806i | \(-0.525446\pi\) | ||||
−0.0798556 | + | 0.996806i | \(0.525446\pi\) | |||||||
\(620\) | 0.380880 | + | 0.266035i | 0.0152965 | + | 0.0106842i | ||||
\(621\) | 11.4570 | + | 11.4570i | 0.459755 | + | 0.459755i | ||||
\(622\) | 15.1202 | + | 15.1202i | 0.606265 | + | 0.606265i | ||||
\(623\) | 20.5032i | 0.821443i | ||||||||
\(624\) | −8.96221 | + | 8.96221i | −0.358775 | + | 0.358775i | ||||
\(625\) | 19.0761 | − | 16.1586i | 0.763045 | − | 0.646345i | ||||
\(626\) | 8.77570 | 0.350748 | ||||||||
\(627\) | − | 15.7472i | − | 0.628881i | ||||||
\(628\) | −13.0961 | + | 13.0961i | −0.522591 | + | 0.522591i | ||||
\(629\) | −3.73962 | − | 29.2678i | −0.149109 | − | 1.16698i | ||||
\(630\) | 2.41468 | + | 1.68660i | 0.0962032 | + | 0.0671956i | ||||
\(631\) | −31.7078 | − | 31.7078i | −1.26227 | − | 1.26227i | −0.949991 | − | 0.312278i | \(-0.898908\pi\) |
−0.312278 | − | 0.949991i | \(-0.601092\pi\) | |||||||
\(632\) | −10.8080 | − | 10.8080i | −0.429921 | − | 0.429921i | ||||
\(633\) | −31.5452 | + | 31.5452i | −1.25381 | + | 1.25381i | ||||
\(634\) | −13.7979 | − | 13.7979i | −0.547986 | − | 0.547986i | ||||
\(635\) | −1.69911 | + | 2.43260i | −0.0674273 | + | 0.0965350i | ||||
\(636\) | −3.38945 | −0.134400 | ||||||||
\(637\) | 50.3330i | 1.99427i | ||||||||
\(638\) | −4.84596 | − | 4.84596i | −0.191853 | − | 0.191853i | ||||
\(639\) | 1.94983i | 0.0771341i | ||||||||
\(640\) | 2.20164 | − | 0.390851i | 0.0870276 | − | 0.0154497i | ||||
\(641\) | −3.77934 | −0.149275 | −0.0746374 | − | 0.997211i | \(-0.523780\pi\) | ||||
−0.0746374 | + | 0.997211i | \(0.523780\pi\) | |||||||
\(642\) | − | 19.7374i | − | 0.778975i | ||||||
\(643\) | 28.5420i | 1.12558i | 0.826598 | + | 0.562792i | \(0.190273\pi\) | ||||
−0.826598 | + | 0.562792i | \(0.809727\pi\) | |||||||
\(644\) | −8.91961 | + | 8.91961i | −0.351482 | + | 0.351482i | ||||
\(645\) | 5.88580 | − | 8.42664i | 0.231753 | − | 0.331799i | ||||
\(646\) | −22.7768 | + | 22.7768i | −0.896140 | + | 0.896140i | ||||
\(647\) | −22.3386 | −0.878222 | −0.439111 | − | 0.898433i | \(-0.644707\pi\) | ||||
−0.439111 | + | 0.898433i | \(0.644707\pi\) | |||||||
\(648\) | −9.92458 | −0.389874 | ||||||||
\(649\) | −6.09108 | + | 6.09108i | −0.239096 | + | 0.239096i | ||||
\(650\) | 32.5145 | − | 11.9200i | 1.27532 | − | 0.467543i | ||||
\(651\) | 1.01550 | − | 1.01550i | 0.0398004 | − | 0.0398004i | ||||
\(652\) | 14.8033i | 0.579741i | ||||||||
\(653\) | − | 19.9863i | − | 0.782125i | −0.920364 | − | 0.391063i | \(-0.872108\pi\) | ||
0.920364 | − | 0.391063i | \(-0.127892\pi\) | |||||||
\(654\) | 8.78335 | 0.343456 | ||||||||
\(655\) | −6.41371 | − | 4.47982i | −0.250605 | − | 0.175041i | ||||
\(656\) | 6.38351i | 0.249234i | ||||||||
\(657\) | −0.0470716 | − | 0.0470716i | −0.00183644 | − | 0.00183644i | ||||
\(658\) | 15.6880i | 0.611581i | ||||||||
\(659\) | −30.3524 | −1.18236 | −0.591182 | − | 0.806538i | \(-0.701338\pi\) | ||||
−0.591182 | + | 0.806538i | \(0.701338\pi\) | |||||||
\(660\) | −4.34714 | − | 3.03637i | −0.169212 | − | 0.118190i | ||||
\(661\) | 10.1177 | + | 10.1177i | 0.393535 | + | 0.393535i | 0.875945 | − | 0.482411i | \(-0.160239\pi\) |
−0.482411 | + | 0.875945i | \(0.660239\pi\) | |||||||
\(662\) | −0.223075 | + | 0.223075i | −0.00867004 | + | 0.00867004i | ||||
\(663\) | −43.4731 | − | 43.4731i | −1.68835 | − | 1.68835i | ||||
\(664\) | 8.74652 | + | 8.74652i | 0.339431 | + | 0.339431i | ||||
\(665\) | −55.2226 | + | 9.80349i | −2.14144 | + | 0.380163i | ||||
\(666\) | −0.268851 | − | 2.10413i | −0.0104178 | − | 0.0815335i | ||||
\(667\) | 12.4886 | − | 12.4886i | 0.483559 | − | 0.483559i | ||||
\(668\) | 1.13442i | 0.0438921i | ||||||||
\(669\) | 28.7045 | 1.10978 | ||||||||
\(670\) | 8.05720 | + | 5.62775i | 0.311277 | + | 0.217419i | ||||
\(671\) | 10.1332 | − | 10.1332i | 0.391189 | − | 0.391189i | ||||
\(672\) | − | 6.91207i | − | 0.266639i | ||||||
\(673\) | −13.7492 | − | 13.7492i | −0.529992 | − | 0.529992i | 0.390578 | − | 0.920570i | \(-0.372275\pi\) |
−0.920570 | + | 0.390578i | \(0.872275\pi\) | |||||||
\(674\) | 12.6737 | + | 12.6737i | 0.488173 | + | 0.488173i | ||||
\(675\) | 22.0095 | + | 10.2009i | 0.847145 | + | 0.392633i | ||||
\(676\) | 34.9711 | 1.34504 | ||||||||
\(677\) | −24.9315 | − | 24.9315i | −0.958197 | − | 0.958197i | 0.0409634 | − | 0.999161i | \(-0.486957\pi\) |
−0.999161 | + | 0.0409634i | \(0.986957\pi\) | |||||||
\(678\) | 5.55057 | + | 5.55057i | 0.213168 | + | 0.213168i | ||||
\(679\) | 35.3928 | + | 35.3928i | 1.35825 | + | 1.35825i | ||||
\(680\) | 1.89590 | + | 10.6795i | 0.0727046 | + | 0.409542i | ||||
\(681\) | 17.0677 | + | 17.0677i | 0.654037 | + | 0.654037i | ||||
\(682\) | −0.190384 | + | 0.190384i | −0.00729018 | + | 0.00729018i | ||||
\(683\) | 37.2952 | 1.42706 | 0.713531 | − | 0.700624i | \(-0.247095\pi\) | ||||
0.713531 | + | 0.700624i | \(0.247095\pi\) | |||||||
\(684\) | −1.63748 | + | 1.63748i | −0.0626105 | + | 0.0626105i | ||||
\(685\) | −26.5006 | + | 37.9407i | −1.01254 | + | 1.44964i | ||||
\(686\) | −0.713468 | − | 0.713468i | −0.0272403 | − | 0.0272403i | ||||
\(687\) | −7.84495 | − | 7.84495i | −0.299303 | − | 0.299303i | ||||
\(688\) | −2.51195 | −0.0957673 | ||||||||
\(689\) | 9.07118 | + | 9.07118i | 0.345585 | + | 0.345585i | ||||
\(690\) | 7.82504 | − | 11.2030i | 0.297894 | − | 0.426492i | ||||
\(691\) | − | 5.06456i | − | 0.192665i | −0.995349 | − | 0.0963324i | \(-0.969289\pi\) | ||
0.995349 | − | 0.0963324i | \(-0.0307112\pi\) | |||||||
\(692\) | 7.57033 | − | 7.57033i | 0.287781 | − | 0.287781i | ||||
\(693\) | −1.20699 | + | 1.20699i | −0.0458496 | + | 0.0458496i | ||||
\(694\) | −9.68557 | −0.367659 | ||||||||
\(695\) | 31.2810 | − | 5.55321i | 1.18656 | − | 0.210645i | ||||
\(696\) | 9.67775i | 0.366834i | ||||||||
\(697\) | −30.9646 | −1.17287 | ||||||||
\(698\) | 9.40675i | 0.356051i | ||||||||
\(699\) | 30.0578i | 1.13689i | ||||||||
\(700\) | −7.94169 | + | 17.1350i | −0.300168 | + | 0.647642i | ||||
\(701\) | −18.0567 | + | 18.0567i | −0.681993 | + | 0.681993i | −0.960449 | − | 0.278456i | \(-0.910177\pi\) |
0.278456 | + | 0.960449i | \(0.410177\pi\) | |||||||
\(702\) | 23.7612 | + | 23.7612i | 0.896810 | + | 0.896810i | ||||
\(703\) | 31.9516 | + | 24.7116i | 1.20508 | + | 0.932015i | ||||
\(704\) | 1.29587i | 0.0488398i | ||||||||
\(705\) | −2.97063 | − | 16.7334i | −0.111881 | − | 0.630218i | ||||
\(706\) | − | 8.93094i | − | 0.336120i | ||||||
\(707\) | −36.8286 | − | 36.8286i | −1.38508 | − | 1.38508i | ||||
\(708\) | 12.1643 | 0.457164 | ||||||||
\(709\) | 20.2886 | + | 20.2886i | 0.761953 | + | 0.761953i | 0.976675 | − | 0.214722i | \(-0.0688845\pi\) |
−0.214722 | + | 0.976675i | \(0.568885\pi\) | |||||||
\(710\) | −12.3099 | + | 2.18534i | −0.461983 | + | 0.0820144i | ||||
\(711\) | 3.76908 | − | 3.76908i | 0.141352 | − | 0.141352i | ||||
\(712\) | −3.83829 | + | 3.83829i | −0.143846 | + | 0.143846i | ||||
\(713\) | −0.490640 | − | 0.490640i | −0.0183746 | − | 0.0183746i | ||||
\(714\) | 33.5285 | 1.25477 | ||||||||
\(715\) | 3.50801 | + | 19.7605i | 0.131192 | + | 0.739000i | ||||
\(716\) | −5.64137 | + | 5.64137i | −0.210828 | + | 0.210828i | ||||
\(717\) | −1.62761 | −0.0607842 | ||||||||
\(718\) | − | 14.7945i | − | 0.552125i | ||||||
\(719\) | − | 37.3366i | − | 1.39242i | −0.717838 | − | 0.696210i | \(-0.754868\pi\) | ||
0.717838 | − | 0.696210i | \(-0.245132\pi\) | |||||||
\(720\) | 0.136301 | + | 0.767778i | 0.00507964 | + | 0.0286134i | ||||
\(721\) | −28.5336 | − | 28.5336i | −1.06265 | − | 1.06265i | ||||
\(722\) | − | 25.0964i | − | 0.933992i | ||||||
\(723\) | − | 36.5874i | − | 1.36070i | ||||||
\(724\) | −5.21779 | −0.193918 | ||||||||
\(725\) | 11.1193 | − | 23.9911i | 0.412962 | − | 0.891007i | ||||
\(726\) | −12.0608 | + | 12.0608i | −0.447617 | + | 0.447617i | ||||
\(727\) | 6.83943 | 0.253660 | 0.126830 | − | 0.991924i | \(-0.459520\pi\) | ||||
0.126830 | + | 0.991924i | \(0.459520\pi\) | |||||||
\(728\) | −18.4988 | + | 18.4988i | −0.685611 | + | 0.685611i | ||||
\(729\) | 23.1742i | 0.858303i | ||||||||
\(730\) | 0.244421 | − | 0.349936i | 0.00904644 | − | 0.0129517i | ||||
\(731\) | − | 12.1848i | − | 0.450669i | ||||||
\(732\) | −20.2368 | −0.747975 | ||||||||
\(733\) | −10.1492 | + | 10.1492i | −0.374870 | + | 0.374870i | −0.869247 | − | 0.494378i | \(-0.835396\pi\) |
0.494378 | + | 0.869247i | \(0.335396\pi\) | |||||||
\(734\) | −19.5831 | + | 19.5831i | −0.722824 | + | 0.722824i | ||||
\(735\) | 24.3784 | + | 17.0277i | 0.899212 | + | 0.628077i | ||||
\(736\) | −3.33959 | −0.123099 | ||||||||
\(737\) | −4.02742 | + | 4.02742i | −0.148352 | + | 0.148352i | ||||
\(738\) | −2.22612 | −0.0819446 | ||||||||
\(739\) | 32.3194 | 1.18889 | 0.594445 | − | 0.804136i | \(-0.297372\pi\) | ||||
0.594445 | + | 0.804136i | \(0.297372\pi\) | |||||||
\(740\) | 12.9828 | − | 4.05562i | 0.477256 | − | 0.149088i | ||||
\(741\) | 84.1650 | 3.09188 | ||||||||
\(742\) | −6.99612 | −0.256836 | ||||||||
\(743\) | −17.4266 | + | 17.4266i | −0.639319 | + | 0.639319i | −0.950387 | − | 0.311069i | \(-0.899313\pi\) |
0.311069 | + | 0.950387i | \(0.399313\pi\) | |||||||
\(744\) | 0.380211 | 0.0139392 | ||||||||
\(745\) | −2.94017 | − | 16.5618i | −0.107719 | − | 0.606778i | ||||
\(746\) | −7.70109 | + | 7.70109i | −0.281957 | + | 0.281957i | ||||
\(747\) | −3.05017 | + | 3.05017i | −0.111600 | + | 0.111600i | ||||
\(748\) | −6.28588 | −0.229834 | ||||||||
\(749\) | − | 40.7398i | − | 1.48860i | ||||||
\(750\) | 5.22631 | − | 19.7807i | 0.190838 | − | 0.722290i | ||||
\(751\) | − | 9.29027i | − | 0.339007i | −0.985530 | − | 0.169503i | \(-0.945784\pi\) | ||
0.985530 | − | 0.169503i | \(-0.0542164\pi\) | |||||||
\(752\) | −2.93686 | + | 2.93686i | −0.107096 | + | 0.107096i | ||||
\(753\) | 38.0946 | 1.38824 | ||||||||
\(754\) | 25.9006 | − | 25.9006i | 0.943243 | − | 0.943243i | ||||
\(755\) | −1.70027 | − | 9.57754i | −0.0618791 | − | 0.348562i | ||||
\(756\) | −18.3258 | −0.666502 | ||||||||
\(757\) | − | 27.5608i | − | 1.00171i | −0.865530 | − | 0.500857i | \(-0.833018\pi\) | ||
0.865530 | − | 0.500857i | \(-0.166982\pi\) | |||||||
\(758\) | − | 19.2451i | − | 0.699015i | ||||||
\(759\) | 5.59987 | + | 5.59987i | 0.203263 | + | 0.203263i | ||||
\(760\) | −12.1732 | − | 8.50267i | −0.441568 | − | 0.308424i | ||||
\(761\) | − | 14.9003i | − | 0.540137i | −0.962841 | − | 0.270069i | \(-0.912954\pi\) | ||
0.962841 | − | 0.270069i | \(-0.0870464\pi\) | |||||||
\(762\) | 2.42834i | 0.0879693i | ||||||||
\(763\) | 18.1296 | 0.656336 | ||||||||
\(764\) | −6.11582 | + | 6.11582i | −0.221263 | + | 0.221263i | ||||
\(765\) | −3.72427 | + | 0.661157i | −0.134651 | + | 0.0239042i | ||||
\(766\) | 8.69427 | 0.314137 | ||||||||
\(767\) | −32.5554 | − | 32.5554i | −1.17551 | − | 1.17551i | ||||
\(768\) | 1.29397 | − | 1.29397i | 0.0466922 | − | 0.0466922i | ||||
\(769\) | −19.2793 | + | 19.2793i | −0.695229 | + | 0.695229i | −0.963378 | − | 0.268148i | \(-0.913588\pi\) |
0.268148 | + | 0.963378i | \(0.413588\pi\) | |||||||
\(770\) | −8.97288 | − | 6.26733i | −0.323360 | − | 0.225859i | ||||
\(771\) | 30.6163 | + | 30.6163i | 1.10262 | + | 1.10262i | ||||
\(772\) | −15.9965 | −0.575725 | ||||||||
\(773\) | 12.1435 | + | 12.1435i | 0.436770 | + | 0.436770i | 0.890923 | − | 0.454153i | \(-0.150058\pi\) |
−0.454153 | + | 0.890923i | \(0.650058\pi\) | |||||||
\(774\) | − | 0.875992i | − | 0.0314869i | ||||||
\(775\) | −0.942541 | − | 0.436847i | −0.0338571 | − | 0.0156920i | ||||
\(776\) | 13.2514i | 0.475697i | ||||||||
\(777\) | −5.32882 | − | 41.7054i | −0.191170 | − | 1.49617i | ||||
\(778\) | 14.2389 | + | 14.2389i | 0.510490 | + | 0.510490i | ||||
\(779\) | 29.9741 | − | 29.9741i | 1.07393 | − | 1.07393i | ||||
\(780\) | 16.2287 | − | 23.2345i | 0.581081 | − | 0.831928i | ||||
\(781\) | − | 7.24551i | − | 0.259265i | ||||||
\(782\) | − | 16.1994i | − | 0.579288i | ||||||
\(783\) | 25.6583 | 0.916954 | ||||||||
\(784\) | − | 7.26713i | − | 0.259540i | ||||||
\(785\) | 23.7143 | − | 33.9515i | 0.846400 | − | 1.21178i | ||||
\(786\) | −6.40246 | −0.228368 | ||||||||
\(787\) | 26.4221 | − | 26.4221i | 0.941846 | − | 0.941846i | −0.0565540 | − | 0.998400i | \(-0.518011\pi\) |
0.998400 | + | 0.0565540i | \(0.0180113\pi\) | |||||||
\(788\) | 17.7621 | − | 17.7621i | 0.632749 | − | 0.632749i | ||||
\(789\) | − | 45.6558i | − | 1.62539i | ||||||
\(790\) | 28.0198 | + | 19.5711i | 0.996899 | + | 0.696309i | ||||
\(791\) | 11.4569 | + | 11.4569i | 0.407359 | + | 0.407359i | ||||
\(792\) | −0.451907 | −0.0160578 | ||||||||
\(793\) | 54.1599 | + | 54.1599i | 1.92327 | + | 1.92327i | ||||
\(794\) | −10.2910 | − | 10.2910i | −0.365213 | − | 0.365213i | ||||
\(795\) | 7.46236 | − | 1.32477i | 0.264663 | − | 0.0469847i | ||||
\(796\) | −15.7905 | + | 15.7905i | −0.559680 | + | 0.559680i | ||||
\(797\) | 48.7252 | 1.72593 | 0.862967 | − | 0.505261i | \(-0.168604\pi\) | ||||
0.862967 | + | 0.505261i | \(0.168604\pi\) | |||||||
\(798\) | −32.4560 | + | 32.4560i | −1.14893 | + | 1.14893i | ||||
\(799\) | −14.2459 | − | 14.2459i | −0.503982 | − | 0.503982i | ||||
\(800\) | −4.69447 | + | 1.72103i | −0.165975 | + | 0.0608475i | ||||
\(801\) | −1.33853 | − | 1.33853i | −0.0472945 | − | 0.0472945i | ||||
\(802\) | 13.7676 | + | 13.7676i | 0.486152 | + | 0.486152i | ||||
\(803\) | 0.174917 | + | 0.174917i | 0.00617267 | + | 0.00617267i | ||||
\(804\) | 8.04306 | 0.283657 | ||||||||
\(805\) | 16.1516 | − | 23.1240i | 0.569268 | − | 0.815016i | ||||
\(806\) | −1.01756 | − | 1.01756i | −0.0358420 | − | 0.0358420i | ||||
\(807\) | −2.89835 | − | 2.89835i | −0.102027 | − | 0.102027i | ||||
\(808\) | − | 13.7890i | − | 0.485094i | ||||||
\(809\) | −31.4838 | + | 31.4838i | −1.10691 | + | 1.10691i | −0.113356 | + | 0.993554i | \(0.536160\pi\) |
−0.993554 | + | 0.113356i | \(0.963840\pi\) | |||||||
\(810\) | 21.8504 | − | 3.87903i | 0.767744 | − | 0.136295i | ||||
\(811\) | −17.7803 | −0.624352 | −0.312176 | − | 0.950024i | \(-0.601058\pi\) | ||||
−0.312176 | + | 0.950024i | \(0.601058\pi\) | |||||||
\(812\) | 19.9757i | 0.701011i | ||||||||
\(813\) | 1.11392 | − | 1.11392i | 0.0390667 | − | 0.0390667i | ||||
\(814\) | 0.999040 | + | 7.81889i | 0.0350163 | + | 0.274052i | ||||
\(815\) | −5.78587 | − | 32.5915i | −0.202670 | − | 1.14163i | ||||
\(816\) | 6.27669 | + | 6.27669i | 0.219728 | + | 0.219728i | ||||
\(817\) | 11.7950 | + | 11.7950i | 0.412655 | + | 0.412655i | ||||
\(818\) | 14.5393 | − | 14.5393i | 0.508353 | − | 0.508353i | ||||
\(819\) | −6.45107 | − | 6.45107i | −0.225419 | − | 0.225419i | ||||
\(820\) | −2.49500 | − | 14.0542i | −0.0871292 | − | 0.490795i | ||||
\(821\) | −23.5885 | −0.823243 | −0.411622 | − | 0.911355i | \(-0.635038\pi\) | ||||
−0.411622 | + | 0.911355i | \(0.635038\pi\) | |||||||
\(822\) | 37.8741i | 1.32101i | ||||||||
\(823\) | −34.7320 | − | 34.7320i | −1.21068 | − | 1.21068i | −0.970803 | − | 0.239878i | \(-0.922892\pi\) |
−0.239878 | − | 0.970803i | \(-0.577108\pi\) | |||||||
\(824\) | − | 10.6833i | − | 0.372169i | ||||||
\(825\) | 10.7576 | + | 4.98592i | 0.374532 | + | 0.173587i | ||||
\(826\) | 25.1083 | 0.873629 | ||||||||
\(827\) | 33.9081i | 1.17910i | 0.807732 | + | 0.589549i | \(0.200695\pi\) | ||||
−0.807732 | + | 0.589549i | \(0.799305\pi\) | |||||||
\(828\) | − | 1.16461i | − | 0.0404731i | ||||||
\(829\) | 16.2123 | − | 16.2123i | 0.563075 | − | 0.563075i | −0.367105 | − | 0.930180i | \(-0.619651\pi\) |
0.930180 | + | 0.367105i | \(0.119651\pi\) | |||||||
\(830\) | −22.6753 | − | 15.8381i | −0.787071 | − | 0.549750i | ||||
\(831\) | 1.40753 | − | 1.40753i | 0.0488268 | − | 0.0488268i | ||||
\(832\) | −6.92612 | −0.240120 | ||||||||
\(833\) | 35.2507 | 1.22137 | ||||||||
\(834\) | 18.3848 | − | 18.3848i | 0.636613 | − | 0.636613i | ||||
\(835\) | −0.443390 | − | 2.49759i | −0.0153441 | − | 0.0864328i | ||||
\(836\) | 6.08481 | − | 6.08481i | 0.210448 | − | 0.210448i | ||||
\(837\) | − | 1.00804i | − | 0.0348431i | ||||||
\(838\) | 8.30494i | 0.286889i | ||||||||
\(839\) | 11.5043 | 0.397174 | 0.198587 | − | 0.980083i | \(-0.436365\pi\) | ||||
0.198587 | + | 0.980083i | \(0.436365\pi\) | |||||||
\(840\) | 2.70159 | + | 15.2179i | 0.0932136 | + | 0.525068i | ||||
\(841\) | 1.03152i | 0.0355697i | ||||||||
\(842\) | 5.43095 | + | 5.43095i | 0.187163 | + | 0.187163i | ||||
\(843\) | 32.0816i | 1.10495i | ||||||||
\(844\) | −24.3785 | −0.839144 | ||||||||
\(845\) | −76.9940 | + | 13.6685i | −2.64867 | + | 0.470210i | ||||
\(846\) | −1.02417 | − | 1.02417i | −0.0352117 | − | 0.0352117i | ||||
\(847\) | −24.8945 | + | 24.8945i | −0.855385 | + | 0.855385i | ||||
\(848\) | −1.30971 | − | 1.30971i | −0.0449755 | − | 0.0449755i | ||||
\(849\) | −3.23642 | − | 3.23642i | −0.111074 | − | 0.111074i | ||||
\(850\) | −8.34821 | − | 22.7715i | −0.286341 | − | 0.781057i | ||||
\(851\) | −20.1501 | + | 2.57463i | −0.690736 | + | 0.0882573i | ||||
\(852\) | −7.23491 | + | 7.23491i | −0.247864 | + | 0.247864i | ||||
\(853\) | − | 9.19244i | − | 0.314743i | −0.987539 | − | 0.157372i | \(-0.949698\pi\) | ||
0.987539 | − | 0.157372i | \(-0.0503021\pi\) | |||||||
\(854\) | −41.7706 | −1.42936 | ||||||||
\(855\) | 2.96513 | − | 4.24515i | 0.101405 | − | 0.145181i | ||||
\(856\) | 7.62669 | − | 7.62669i | 0.260675 | − | 0.260675i | ||||
\(857\) | 22.7340i | 0.776579i | 0.921538 | + | 0.388289i | \(0.126934\pi\) | ||||
−0.921538 | + | 0.388289i | \(0.873066\pi\) | |||||||
\(858\) | 11.6138 | + | 11.6138i | 0.396490 | + | 0.396490i | ||||
\(859\) | −8.40939 | − | 8.40939i | −0.286925 | − | 0.286925i | 0.548938 | − | 0.835863i | \(-0.315032\pi\) |
−0.835863 | + | 0.548938i | \(0.815032\pi\) | |||||||
\(860\) | 5.53043 | − | 0.981798i | 0.188586 | − | 0.0334790i | ||||
\(861\) | −44.1233 | −1.50372 | ||||||||
\(862\) | −16.0000 | − | 16.0000i | −0.544962 | − | 0.544962i | ||||
\(863\) | −12.6007 | − | 12.6007i | −0.428932 | − | 0.428932i | 0.459333 | − | 0.888264i | \(-0.348089\pi\) |
−0.888264 | + | 0.459333i | \(0.848089\pi\) | |||||||
\(864\) | −3.43067 | − | 3.43067i | −0.116714 | − | 0.116714i | ||||
\(865\) | −13.7083 | + | 19.6260i | −0.466096 | + | 0.667305i | ||||
\(866\) | 21.6988 | + | 21.6988i | 0.737356 | + | 0.737356i | ||||
\(867\) | −8.44886 | + | 8.44886i | −0.286938 | + | 0.286938i | ||||
\(868\) | 0.784789 | 0.0266375 | ||||||||
\(869\) | −14.0058 | + | 14.0058i | −0.475114 | + | 0.475114i | ||||
\(870\) | −3.78256 | − | 21.3070i | −0.128241 | − | 0.722374i | ||||
\(871\) | −21.5256 | − | 21.5256i | −0.729369 | − | 0.729369i | ||||
\(872\) | 3.39395 | + | 3.39395i | 0.114934 | + | 0.114934i | ||||
\(873\) | −4.62115 | −0.156402 | ||||||||
\(874\) | 15.6812 | + | 15.6812i | 0.530425 | + | 0.530425i | ||||
\(875\) | 10.7876 | − | 40.8292i | 0.364686 | − | 1.38028i | ||||
\(876\) | − | 0.349322i | − | 0.0118025i | ||||||
\(877\) | 7.77308 | − | 7.77308i | 0.262478 | − | 0.262478i | −0.563582 | − | 0.826060i | \(-0.690577\pi\) |
0.826060 | + | 0.563582i | \(0.190577\pi\) | |||||||
\(878\) | −5.60815 | + | 5.60815i | −0.189266 | + | 0.189266i | ||||
\(879\) | 18.3279 | 0.618186 | ||||||||
\(880\) | −0.506490 | − | 2.85304i | −0.0170738 | − | 0.0961759i | ||||
\(881\) | − | 17.5111i | − | 0.589963i | −0.955503 | − | 0.294982i | \(-0.904686\pi\) | ||
0.955503 | − | 0.294982i | \(-0.0953136\pi\) | |||||||
\(882\) | 2.53426 | 0.0853330 | ||||||||
\(883\) | − | 13.3235i | − | 0.448372i | −0.974546 | − | 0.224186i | \(-0.928028\pi\) | ||
0.974546 | − | 0.224186i | \(-0.0719723\pi\) | |||||||
\(884\) | − | 33.5966i | − | 1.12998i | ||||||
\(885\) | −26.7816 | + | 4.75444i | −0.900252 | + | 0.159819i | ||||
\(886\) | −17.9895 | + | 17.9895i | −0.604370 | + | 0.604370i | ||||
\(887\) | 11.6899 | + | 11.6899i | 0.392508 | + | 0.392508i | 0.875580 | − | 0.483072i | \(-0.160479\pi\) |
−0.483072 | + | 0.875580i | \(0.660479\pi\) | |||||||
\(888\) | 6.80987 | − | 8.80503i | 0.228524 | − | 0.295478i | ||||
\(889\) | 5.01230i | 0.168107i | ||||||||
\(890\) | 6.95036 | − | 9.95076i | 0.232977 | − | 0.333550i | ||||
\(891\) | 12.8609i | 0.430857i | ||||||||
\(892\) | 11.0916 | + | 11.0916i | 0.371375 | + | 0.371375i | ||||
\(893\) | 27.5804 | 0.922942 | ||||||||
\(894\) | −9.73388 | − | 9.73388i | −0.325550 | − | 0.325550i | ||||
\(895\) | 10.2154 | − | 14.6252i | 0.341462 | − | 0.488867i | ||||
\(896\) | 2.67087 | − | 2.67087i | 0.0892276 | − | 0.0892276i | ||||
\(897\) | −29.9301 | + | 29.9301i | −0.999336 | + | 0.999336i | ||||
\(898\) | −6.18967 | − | 6.18967i | −0.206552 | − | 0.206552i | ||||
\(899\) | −1.09880 | −0.0366471 | ||||||||
\(900\) | −0.600173 | − | 1.63710i | −0.0200058 | − | 0.0545700i | ||||
\(901\) | 6.35301 | − | 6.35301i | 0.211649 | − | 0.211649i | ||||
\(902\) | 8.27219 | 0.275434 | ||||||||
\(903\) | − | 17.3628i | − | 0.577798i | ||||||
\(904\) | 4.28955i | 0.142668i | ||||||||
\(905\) | 11.4877 | − | 2.03938i | 0.381865 | − | 0.0677912i | ||||
\(906\) | −5.62901 | − | 5.62901i | −0.187011 | − | 0.187011i | ||||
\(907\) | − | 32.4447i | − | 1.07731i | −0.842527 | − | 0.538654i | \(-0.818933\pi\) | ||
0.842527 | − | 0.538654i | \(-0.181067\pi\) | |||||||
\(908\) | 13.1902i | 0.437732i | ||||||||
\(909\) | 4.80862 | 0.159492 | ||||||||
\(910\) | 33.4975 | − | 47.9580i | 1.11043 | − | 1.58979i | ||||
\(911\) | −30.7018 | + | 30.7018i | −1.01719 | + | 1.01719i | −0.0173451 | + | 0.999850i | \(0.505521\pi\) |
−0.999850 | + | 0.0173451i | \(0.994479\pi\) | |||||||
\(912\) | −12.1518 | −0.402387 | ||||||||
\(913\) | 11.3343 | − | 11.3343i | 0.375111 | − | 0.375111i | ||||
\(914\) | 31.9423i | 1.05656i | ||||||||
\(915\) | 44.5543 | − | 7.90958i | 1.47292 | − | 0.261483i | ||||
\(916\) | − | 6.06268i | − | 0.200317i | ||||||
\(917\) | −13.2152 | −0.436406 | ||||||||
\(918\) | 16.6412 | − | 16.6412i | 0.549241 | − | 0.549241i | ||||
\(919\) | 31.2648 | − | 31.2648i | 1.03133 | − | 1.03133i | 0.0318365 | − | 0.999493i | \(-0.489864\pi\) |
0.999493 | − | 0.0318365i | \(-0.0101356\pi\) | |||||||
\(920\) | 7.35258 | − | 1.30528i | 0.242407 | − | 0.0430338i | ||||
\(921\) | 48.7429 | 1.60613 | ||||||||
\(922\) | −2.73403 | + | 2.73403i | −0.0900405 | + | 0.0900405i | ||||
\(923\) | 38.7256 | 1.27467 | ||||||||
\(924\) | −8.95713 | −0.294668 | ||||||||
\(925\) | −26.9983 | + | 14.0034i | −0.887697 | + | 0.460427i | ||||
\(926\) | 4.32970 | 0.142283 | ||||||||
\(927\) | 3.72557 | 0.122364 | ||||||||
\(928\) | −3.73955 | + | 3.73955i | −0.122757 | + | 0.122757i | ||||
\(929\) | −6.27539 | −0.205889 | −0.102944 | − | 0.994687i | \(-0.532826\pi\) | ||||
−0.102944 | + | 0.994687i | \(0.532826\pi\) | |||||||
\(930\) | −0.837090 | + | 0.148606i | −0.0274493 | + | 0.00487298i | ||||
\(931\) | −34.1232 | + | 34.1232i | −1.11834 | + | 1.11834i | ||||
\(932\) | −11.6145 | + | 11.6145i | −0.380447 | + | 0.380447i | ||||
\(933\) | −39.1303 | −1.28107 | ||||||||
\(934\) | 0.826696i | 0.0270503i | ||||||||
\(935\) | 13.8393 | − | 2.45684i | 0.452592 | − | 0.0803472i | ||||
\(936\) | − | 2.41534i | − | 0.0789479i | ||||||
\(937\) | −37.4173 | + | 37.4173i | −1.22237 | + | 1.22237i | −0.255585 | + | 0.966787i | \(0.582268\pi\) |
−0.966787 | + | 0.255585i | \(0.917732\pi\) | |||||||
\(938\) | 16.6016 | 0.542061 | ||||||||
\(939\) | −11.3555 | + | 11.3555i | −0.370573 | + | 0.370573i | ||||
\(940\) | 5.31805 | − | 7.61379i | 0.173456 | − | 0.248335i | ||||
\(941\) | −17.9677 | −0.585730 | −0.292865 | − | 0.956154i | \(-0.594609\pi\) | ||||
−0.292865 | + | 0.956154i | \(0.594609\pi\) | |||||||
\(942\) | − | 33.8920i | − | 1.10426i | ||||||
\(943\) | 21.3183i | 0.694219i | ||||||||
\(944\) | 4.70039 | + | 4.70039i | 0.152985 | + | 0.152985i | ||||
\(945\) | 40.3468 | − | 7.16264i | 1.31248 | − | 0.233001i | ||||
\(946\) | 3.25516i | 0.105834i | ||||||||
\(947\) | 36.1480i | 1.17465i | 0.809351 | + | 0.587326i | \(0.199819\pi\) | ||||
−0.809351 | + | 0.587326i | \(0.800181\pi\) | |||||||
\(948\) | 27.9706 | 0.908443 | ||||||||
\(949\) | −0.934890 | + | 0.934890i | −0.0303478 | + | 0.0303478i | ||||
\(950\) | 30.1243 | + | 13.9620i | 0.977362 | + | 0.452986i | ||||
\(951\) | 35.7083 | 1.15792 | ||||||||
\(952\) | 12.9556 | + | 12.9556i | 0.419895 | + | 0.419895i | ||||
\(953\) | −25.3431 | + | 25.3431i | −0.820945 | + | 0.820945i | −0.986244 | − | 0.165299i | \(-0.947141\pi\) |
0.165299 | + | 0.986244i | \(0.447141\pi\) | |||||||
\(954\) | 0.456733 | − | 0.456733i | 0.0147873 | − | 0.0147873i | ||||
\(955\) | 11.0745 | − | 15.8552i | 0.358362 | − | 0.513063i | ||||
\(956\) | −0.628920 | − | 0.628920i | −0.0203407 | − | 0.0203407i | ||||
\(957\) | 12.5411 | 0.405396 | ||||||||
\(958\) | −19.7849 | − | 19.7849i | −0.639223 | − | 0.639223i | ||||
\(959\) | 78.1754i | 2.52442i | ||||||||
\(960\) | −2.34312 | + | 3.35462i | −0.0756238 | + | 0.108270i | ||||
\(961\) | − | 30.9568i | − | 0.998607i | ||||||
\(962\) | −41.7902 | + | 5.33965i | −1.34737 | + | 0.172157i | ||||
\(963\) | 2.65965 | + | 2.65965i | 0.0857061 | + | 0.0857061i | ||||
\(964\) | 14.1376 | − | 14.1376i | 0.455343 | − | 0.455343i | ||||
\(965\) | 35.2185 | − | 6.25223i | 1.13372 | − | 0.201266i | ||||
\(966\) | − | 23.0835i | − | 0.742698i | ||||||
\(967\) | 20.8936i | 0.671892i | 0.941881 | + | 0.335946i | \(0.109056\pi\) | ||||
−0.941881 | + | 0.335946i | \(0.890944\pi\) | |||||||
\(968\) | −9.32073 | −0.299580 | ||||||||
\(969\) | − | 58.9450i | − | 1.89359i | ||||||
\(970\) | −5.17931 | − | 29.1748i | −0.166298 | − | 0.936747i | ||||
\(971\) | −28.1995 | −0.904966 | −0.452483 | − | 0.891773i | \(-0.649462\pi\) | ||||
−0.452483 | + | 0.891773i | \(0.649462\pi\) | |||||||
\(972\) | 2.55012 | − | 2.55012i | 0.0817950 | − | 0.0817950i | ||||
\(973\) | 37.9478 | − | 37.9478i | 1.21655 | − | 1.21655i | ||||
\(974\) | − | 28.2154i | − | 0.904081i | ||||||
\(975\) | −26.6486 | + | 57.4970i | −0.853439 | + | 1.84138i | ||||
\(976\) | −7.81965 | − | 7.81965i | −0.250301 | − | 0.250301i | ||||
\(977\) | 21.6547 | 0.692796 | 0.346398 | − | 0.938088i | \(-0.387405\pi\) | ||||
0.346398 | + | 0.938088i | \(0.387405\pi\) | |||||||
\(978\) | −19.1550 | − | 19.1550i | −0.612510 | − | 0.612510i | ||||
\(979\) | 4.97392 | + | 4.97392i | 0.158967 | + | 0.158967i | ||||
\(980\) | 2.84036 | + | 15.9996i | 0.0907320 | + | 0.511089i | ||||
\(981\) | −1.18357 | + | 1.18357i | −0.0377885 | + | 0.0377885i | ||||
\(982\) | −2.48442 | −0.0792812 | ||||||||
\(983\) | −30.3949 | + | 30.3949i | −0.969448 | + | 0.969448i | −0.999547 | − | 0.0300989i | \(-0.990418\pi\) |
0.0300989 | + | 0.999547i | \(0.490418\pi\) | |||||||
\(984\) | −8.26009 | − | 8.26009i | −0.263322 | − | 0.263322i | ||||
\(985\) | −32.1635 | + | 46.0482i | −1.02481 | + | 1.46722i | ||||
\(986\) | −18.1395 | − | 18.1395i | −0.577679 | − | 0.577679i | ||||
\(987\) | −20.2998 | − | 20.2998i | −0.646150 | − | 0.646150i | ||||
\(988\) | 32.5219 | + | 32.5219i | 1.03466 | + | 1.03466i | ||||
\(989\) | −8.38888 | −0.266751 | ||||||||
\(990\) | 0.994939 | − | 0.176628i | 0.0316212 | − | 0.00561361i | ||||
\(991\) | −9.25603 | − | 9.25603i | −0.294027 | − | 0.294027i | 0.544642 | − | 0.838669i | \(-0.316666\pi\) |
−0.838669 | + | 0.544642i | \(0.816666\pi\) | |||||||
\(992\) | 0.146916 | + | 0.146916i | 0.00466460 | + | 0.00466460i | ||||
\(993\) | − | 0.577305i | − | 0.0183202i | ||||||
\(994\) | −14.9335 | + | 14.9335i | −0.473662 | + | 0.473662i | ||||
\(995\) | 28.5934 | − | 40.9368i | 0.906470 | − | 1.29778i | ||||
\(996\) | −22.6355 | −0.717233 | ||||||||
\(997\) | 4.98797i | 0.157971i | 0.996876 | + | 0.0789854i | \(0.0251680\pi\) | ||||
−0.996876 | + | 0.0789854i | \(0.974832\pi\) | |||||||
\(998\) | −1.49326 | + | 1.49326i | −0.0472682 | + | 0.0472682i | ||||
\(999\) | −23.3445 | − | 18.0548i | −0.738588 | − | 0.571229i |
(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 | 370.2.h.e.253.8 | yes | 20 | |
5.2 | odd | 4 | 370.2.g.e.327.3 | yes | 20 | ||
37.6 | odd | 4 | 370.2.g.e.43.3 | ✓ | 20 | ||
185.117 | even | 4 | inner | 370.2.h.e.117.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.e.43.3 | ✓ | 20 | 37.6 | odd | 4 | ||
370.2.g.e.327.3 | yes | 20 | 5.2 | odd | 4 | ||
370.2.h.e.117.8 | yes | 20 | 185.117 | even | 4 | inner | |
370.2.h.e.253.8 | yes | 20 | 1.1 | even | 1 | trivial |