Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(251,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("280.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.h (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: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.4 | ||
Root | \(-1.24098 - 0.678208i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.251 |
Dual form | 280.2.h.a.251.3 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.24098 | + | 0.678208i | −0.877506 | + | 0.479565i | ||||
\(3\) | 1.61069i | 0.929929i | 0.885329 | + | 0.464965i | \(0.153933\pi\) | ||||
−0.885329 | + | 0.464965i | \(0.846067\pi\) | |||||||
\(4\) | 1.08007 | − | 1.68329i | 0.540034 | − | 0.841643i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.09238 | − | 1.99883i | −0.445962 | − | 0.816019i | ||||
\(7\) | −2.13463 | − | 1.56312i | −0.806816 | − | 0.590803i | ||||
\(8\) | −0.198727 | + | 2.82144i | −0.0702605 | + | 0.997529i | ||||
\(9\) | 0.405694 | 0.135231 | ||||||||
\(10\) | 1.24098 | − | 0.678208i | 0.392433 | − | 0.214468i | ||||
\(11\) | −6.01679 | −1.81413 | −0.907066 | − | 0.420989i | \(-0.861683\pi\) | ||||
−0.907066 | + | 0.420989i | \(0.861683\pi\) | |||||||
\(12\) | 2.71124 | + | 1.73965i | 0.782669 | + | 0.502194i | ||||
\(13\) | −4.25411 | −1.17988 | −0.589939 | − | 0.807448i | \(-0.700848\pi\) | ||||
−0.589939 | + | 0.807448i | \(0.700848\pi\) | |||||||
\(14\) | 3.70916 | + | 0.492075i | 0.991314 | + | 0.131513i | ||||
\(15\) | − | 1.61069i | − | 0.415877i | ||||||
\(16\) | −1.66690 | − | 3.63613i | −0.416726 | − | 0.909032i | ||||
\(17\) | 5.42124i | 1.31484i | 0.753523 | + | 0.657421i | \(0.228353\pi\) | ||||
−0.753523 | + | 0.657421i | \(0.771647\pi\) | |||||||
\(18\) | −0.503458 | + | 0.275145i | −0.118666 | + | 0.0648522i | ||||
\(19\) | − | 4.53588i | − | 1.04060i | −0.853983 | − | 0.520301i | \(-0.825820\pi\) | ||
0.853983 | − | 0.520301i | \(-0.174180\pi\) | |||||||
\(20\) | −1.08007 | + | 1.68329i | −0.241511 | + | 0.376394i | ||||
\(21\) | 2.51769 | − | 3.43822i | 0.549405 | − | 0.750282i | ||||
\(22\) | 7.46673 | − | 4.08064i | 1.59191 | − | 0.869995i | ||||
\(23\) | − | 5.19890i | − | 1.08404i | −0.840364 | − | 0.542022i | \(-0.817659\pi\) | ||
0.840364 | − | 0.542022i | \(-0.182341\pi\) | |||||||
\(24\) | −4.54445 | − | 0.320086i | −0.927631 | − | 0.0653373i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.27927 | − | 2.88517i | 1.03535 | − | 0.565829i | ||||
\(27\) | 5.48550i | 1.05568i | ||||||||
\(28\) | −4.93673 | + | 1.90492i | −0.932953 | + | 0.359997i | ||||
\(29\) | − | 0.376818i | − | 0.0699733i | −0.999388 | − | 0.0349866i | \(-0.988861\pi\) | ||
0.999388 | − | 0.0349866i | \(-0.0111389\pi\) | |||||||
\(30\) | 1.09238 | + | 1.99883i | 0.199440 | + | 0.364935i | ||||
\(31\) | −2.93636 | −0.527385 | −0.263693 | − | 0.964607i | \(-0.584940\pi\) | ||||
−0.263693 | + | 0.964607i | \(0.584940\pi\) | |||||||
\(32\) | 4.53465 | + | 3.38186i | 0.801620 | + | 0.597834i | ||||
\(33\) | − | 9.69116i | − | 1.68701i | ||||||
\(34\) | −3.67672 | − | 6.72765i | −0.630553 | − | 1.15378i | ||||
\(35\) | 2.13463 | + | 1.56312i | 0.360819 | + | 0.264215i | ||||
\(36\) | 0.438177 | − | 0.682898i | 0.0730295 | − | 0.113816i | ||||
\(37\) | 0.372265i | 0.0612000i | 0.999532 | + | 0.0306000i | \(0.00974181\pi\) | ||||
−0.999532 | + | 0.0306000i | \(0.990258\pi\) | |||||||
\(38\) | 3.07627 | + | 5.62894i | 0.499037 | + | 0.913135i | ||||
\(39\) | − | 6.85203i | − | 1.09720i | ||||||
\(40\) | 0.198727 | − | 2.82144i | 0.0314214 | − | 0.446108i | ||||
\(41\) | − | 5.75560i | − | 0.898874i | −0.893312 | − | 0.449437i | \(-0.851625\pi\) | ||
0.893312 | − | 0.449437i | \(-0.148375\pi\) | |||||||
\(42\) | −0.792578 | + | 5.97429i | −0.122297 | + | 0.921853i | ||||
\(43\) | −4.96515 | −0.757178 | −0.378589 | − | 0.925565i | \(-0.623591\pi\) | ||||
−0.378589 | + | 0.925565i | \(0.623591\pi\) | |||||||
\(44\) | −6.49855 | + | 10.1280i | −0.979693 | + | 1.52685i | ||||
\(45\) | −0.405694 | −0.0604772 | ||||||||
\(46\) | 3.52593 | + | 6.45173i | 0.519870 | + | 0.951256i | ||||
\(47\) | −3.86303 | −0.563481 | −0.281741 | − | 0.959491i | \(-0.590912\pi\) | ||||
−0.281741 | + | 0.959491i | \(0.590912\pi\) | |||||||
\(48\) | 5.85666 | − | 2.68486i | 0.845336 | − | 0.387526i | ||||
\(49\) | 2.11332 | + | 6.67337i | 0.301903 | + | 0.953339i | ||||
\(50\) | −1.24098 | + | 0.678208i | −0.175501 | + | 0.0959131i | ||||
\(51\) | −8.73190 | −1.22271 | ||||||||
\(52\) | −4.59473 | + | 7.16089i | −0.637174 | + | 0.993036i | ||||
\(53\) | 10.2224i | 1.40416i | 0.712099 | + | 0.702079i | \(0.247745\pi\) | ||||
−0.712099 | + | 0.702079i | \(0.752255\pi\) | |||||||
\(54\) | −3.72031 | − | 6.80740i | −0.506270 | − | 0.926370i | ||||
\(55\) | 6.01679 | 0.811304 | ||||||||
\(56\) | 4.83445 | − | 5.71210i | 0.646030 | − | 0.763312i | ||||
\(57\) | 7.30587 | 0.967686 | ||||||||
\(58\) | 0.255561 | + | 0.467624i | 0.0335568 | + | 0.0614020i | ||||
\(59\) | 10.5835i | 1.37786i | 0.724828 | + | 0.688930i | \(0.241919\pi\) | ||||
−0.724828 | + | 0.688930i | \(0.758081\pi\) | |||||||
\(60\) | −2.71124 | − | 1.73965i | −0.350020 | − | 0.224588i | ||||
\(61\) | 5.58001 | 0.714447 | 0.357223 | − | 0.934019i | \(-0.383723\pi\) | ||||
0.357223 | + | 0.934019i | \(0.383723\pi\) | |||||||
\(62\) | 3.64396 | − | 1.99146i | 0.462784 | − | 0.252916i | ||||
\(63\) | −0.866007 | − | 0.634147i | −0.109107 | − | 0.0798950i | ||||
\(64\) | −7.92102 | − | 1.12139i | −0.990127 | − | 0.140174i | ||||
\(65\) | 4.25411 | 0.527657 | ||||||||
\(66\) | 6.57262 | + | 12.0265i | 0.809034 | + | 1.48037i | ||||
\(67\) | −0.782596 | −0.0956093 | −0.0478047 | − | 0.998857i | \(-0.515223\pi\) | ||||
−0.0478047 | + | 0.998857i | \(0.515223\pi\) | |||||||
\(68\) | 9.12549 | + | 5.85531i | 1.10663 | + | 0.710060i | ||||
\(69\) | 8.37378 | 1.00809 | ||||||||
\(70\) | −3.70916 | − | 0.492075i | −0.443329 | − | 0.0588142i | ||||
\(71\) | 15.3803i | 1.82531i | 0.408735 | + | 0.912653i | \(0.365970\pi\) | ||||
−0.408735 | + | 0.912653i | \(0.634030\pi\) | |||||||
\(72\) | −0.0806221 | + | 1.14464i | −0.00950141 | + | 0.134897i | ||||
\(73\) | − | 8.77164i | − | 1.02664i | −0.858196 | − | 0.513321i | \(-0.828415\pi\) | ||
0.858196 | − | 0.513321i | \(-0.171585\pi\) | |||||||
\(74\) | −0.252473 | − | 0.461974i | −0.0293494 | − | 0.0537034i | ||||
\(75\) | 1.61069i | 0.185986i | ||||||||
\(76\) | −7.63518 | − | 4.89906i | −0.875816 | − | 0.561961i | ||||
\(77\) | 12.8437 | + | 9.40496i | 1.46367 | + | 1.07179i | ||||
\(78\) | 4.64710 | + | 8.50324i | 0.526181 | + | 0.962803i | ||||
\(79\) | 8.74609i | 0.984012i | 0.870592 | + | 0.492006i | \(0.163736\pi\) | ||||
−0.870592 | + | 0.492006i | \(0.836264\pi\) | |||||||
\(80\) | 1.66690 | + | 3.63613i | 0.186366 | + | 0.406531i | ||||
\(81\) | −7.61833 | −0.846481 | ||||||||
\(82\) | 3.90349 | + | 7.14259i | 0.431069 | + | 0.788767i | ||||
\(83\) | − | 8.42742i | − | 0.925029i | −0.886612 | − | 0.462515i | \(-0.846947\pi\) | ||
0.886612 | − | 0.462515i | \(-0.153053\pi\) | |||||||
\(84\) | −3.06823 | − | 7.95151i | −0.334772 | − | 0.867581i | ||||
\(85\) | − | 5.42124i | − | 0.588016i | ||||||
\(86\) | 6.16165 | − | 3.36740i | 0.664428 | − | 0.363116i | ||||
\(87\) | 0.606935 | 0.0650702 | ||||||||
\(88\) | 1.19570 | − | 16.9760i | 0.127462 | − | 1.80965i | ||||
\(89\) | − | 1.94765i | − | 0.206451i | −0.994658 | − | 0.103225i | \(-0.967084\pi\) | ||
0.994658 | − | 0.103225i | \(-0.0329163\pi\) | |||||||
\(90\) | 0.503458 | − | 0.275145i | 0.0530691 | − | 0.0290028i | ||||
\(91\) | 9.08097 | + | 6.64968i | 0.951944 | + | 0.697076i | ||||
\(92\) | −8.75123 | − | 5.61516i | −0.912379 | − | 0.585421i | ||||
\(93\) | − | 4.72954i | − | 0.490431i | ||||||
\(94\) | 4.79395 | − | 2.61994i | 0.494458 | − | 0.270226i | ||||
\(95\) | 4.53588i | 0.465371i | ||||||||
\(96\) | −5.44711 | + | 7.30389i | −0.555943 | + | 0.745450i | ||||
\(97\) | − | 3.14377i | − | 0.319201i | −0.987182 | − | 0.159601i | \(-0.948979\pi\) | ||
0.987182 | − | 0.159601i | \(-0.0510206\pi\) | |||||||
\(98\) | −7.14852 | − | 6.84826i | −0.722110 | − | 0.691778i | ||||
\(99\) | −2.44098 | −0.245327 | ||||||||
\(100\) | 1.08007 | − | 1.68329i | 0.108007 | − | 0.168329i | ||||
\(101\) | −16.3016 | −1.62207 | −0.811037 | − | 0.584995i | \(-0.801096\pi\) | ||||
−0.811037 | + | 0.584995i | \(0.801096\pi\) | |||||||
\(102\) | 10.8361 | − | 5.92205i | 1.07294 | − | 0.586370i | ||||
\(103\) | −11.8940 | −1.17195 | −0.585974 | − | 0.810330i | \(-0.699288\pi\) | ||||
−0.585974 | + | 0.810330i | \(0.699288\pi\) | |||||||
\(104\) | 0.845405 | − | 12.0027i | 0.0828988 | − | 1.17696i | ||||
\(105\) | −2.51769 | + | 3.43822i | −0.245702 | + | 0.335536i | ||||
\(106\) | −6.93293 | − | 12.6858i | −0.673385 | − | 1.23216i | ||||
\(107\) | 10.4794 | 1.01308 | 0.506542 | − | 0.862215i | \(-0.330923\pi\) | ||||
0.506542 | + | 0.862215i | \(0.330923\pi\) | |||||||
\(108\) | 9.23367 | + | 5.92471i | 0.888510 | + | 0.570106i | ||||
\(109\) | 0.676794i | 0.0648251i | 0.999475 | + | 0.0324126i | \(0.0103190\pi\) | ||||
−0.999475 | + | 0.0324126i | \(0.989681\pi\) | |||||||
\(110\) | −7.46673 | + | 4.08064i | −0.711925 | + | 0.389073i | ||||
\(111\) | −0.599602 | −0.0569117 | ||||||||
\(112\) | −2.12547 | + | 10.3674i | −0.200838 | + | 0.979624i | ||||
\(113\) | −9.10537 | −0.856562 | −0.428281 | − | 0.903646i | \(-0.640881\pi\) | ||||
−0.428281 | + | 0.903646i | \(0.640881\pi\) | |||||||
\(114\) | −9.06645 | + | 4.95490i | −0.849151 | + | 0.464069i | ||||
\(115\) | 5.19890i | 0.484800i | ||||||||
\(116\) | −0.634292 | − | 0.406989i | −0.0588925 | − | 0.0377880i | ||||
\(117\) | −1.72587 | −0.159556 | ||||||||
\(118\) | −7.17784 | − | 13.1340i | −0.660774 | − | 1.20908i | ||||
\(119\) | 8.47403 | − | 11.5724i | 0.776813 | − | 1.06084i | ||||
\(120\) | 4.54445 | + | 0.320086i | 0.414849 | + | 0.0292197i | ||||
\(121\) | 25.2018 | 2.29107 | ||||||||
\(122\) | −6.92468 | + | 3.78440i | −0.626931 | + | 0.342624i | ||||
\(123\) | 9.27046 | 0.835889 | ||||||||
\(124\) | −3.17147 | + | 4.94273i | −0.284806 | + | 0.443870i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.50478 | + | 0.199632i | 0.134057 | + | 0.0177846i | ||||
\(127\) | − | 3.74123i | − | 0.331980i | −0.986127 | − | 0.165990i | \(-0.946918\pi\) | ||
0.986127 | − | 0.165990i | \(-0.0530820\pi\) | |||||||
\(128\) | 10.5904 | − | 3.98047i | 0.936065 | − | 0.351827i | ||||
\(129\) | − | 7.99729i | − | 0.704122i | ||||||
\(130\) | −5.27927 | + | 2.88517i | −0.463023 | + | 0.253046i | ||||
\(131\) | − | 17.5774i | − | 1.53575i | −0.640601 | − | 0.767874i | \(-0.721315\pi\) | ||
0.640601 | − | 0.767874i | \(-0.278685\pi\) | |||||||
\(132\) | −16.3130 | − | 10.4671i | −1.41986 | − | 0.911045i | ||||
\(133\) | −7.09012 | + | 9.68244i | −0.614791 | + | 0.839574i | ||||
\(134\) | 0.971187 | − | 0.530763i | 0.0838978 | − | 0.0458509i | ||||
\(135\) | − | 5.48550i | − | 0.472117i | ||||||
\(136\) | −15.2957 | − | 1.07734i | −1.31159 | − | 0.0923815i | ||||
\(137\) | −0.767338 | −0.0655581 | −0.0327791 | − | 0.999463i | \(-0.510436\pi\) | ||||
−0.0327791 | + | 0.999463i | \(0.510436\pi\) | |||||||
\(138\) | −10.3917 | + | 5.67917i | −0.884601 | + | 0.483443i | ||||
\(139\) | 2.01854i | 0.171210i | 0.996329 | + | 0.0856052i | \(0.0272824\pi\) | ||||
−0.996329 | + | 0.0856052i | \(0.972718\pi\) | |||||||
\(140\) | 4.93673 | − | 1.90492i | 0.417229 | − | 0.160996i | ||||
\(141\) | − | 6.22213i | − | 0.523998i | ||||||
\(142\) | −10.4310 | − | 19.0867i | −0.875354 | − | 1.60172i | ||||
\(143\) | 25.5961 | 2.14045 | ||||||||
\(144\) | −0.676253 | − | 1.47515i | −0.0563544 | − | 0.122930i | ||||
\(145\) | 0.376818i | 0.0312930i | ||||||||
\(146\) | 5.94899 | + | 10.8854i | 0.492342 | + | 0.900885i | ||||
\(147\) | −10.7487 | + | 3.40390i | −0.886538 | + | 0.280749i | ||||
\(148\) | 0.626629 | + | 0.402072i | 0.0515086 | + | 0.0330501i | ||||
\(149\) | 4.23267i | 0.346754i | 0.984856 | + | 0.173377i | \(0.0554679\pi\) | ||||
−0.984856 | + | 0.173377i | \(0.944532\pi\) | |||||||
\(150\) | −1.09238 | − | 1.99883i | −0.0891924 | − | 0.163204i | ||||
\(151\) | − | 0.625768i | − | 0.0509243i | −0.999676 | − | 0.0254622i | \(-0.991894\pi\) | ||
0.999676 | − | 0.0254622i | \(-0.00810573\pi\) | |||||||
\(152\) | 12.7977 | + | 0.901400i | 1.03803 | + | 0.0731132i | ||||
\(153\) | 2.19936i | 0.177808i | ||||||||
\(154\) | −22.3172 | − | 2.96072i | −1.79838 | − | 0.238581i | ||||
\(155\) | 2.93636 | 0.235854 | ||||||||
\(156\) | −11.5339 | − | 7.40066i | −0.923454 | − | 0.592527i | ||||
\(157\) | 2.91713 | 0.232812 | 0.116406 | − | 0.993202i | \(-0.462863\pi\) | ||||
0.116406 | + | 0.993202i | \(0.462863\pi\) | |||||||
\(158\) | −5.93167 | − | 10.8537i | −0.471898 | − | 0.863477i | ||||
\(159\) | −16.4651 | −1.30577 | ||||||||
\(160\) | −4.53465 | − | 3.38186i | −0.358495 | − | 0.267359i | ||||
\(161\) | −8.12649 | + | 11.0977i | −0.640457 | + | 0.874624i | ||||
\(162\) | 9.45421 | − | 5.16681i | 0.742793 | − | 0.405943i | ||||
\(163\) | −7.14397 | −0.559559 | −0.279779 | − | 0.960064i | \(-0.590261\pi\) | ||||
−0.279779 | + | 0.960064i | \(0.590261\pi\) | |||||||
\(164\) | −9.68833 | − | 6.21644i | −0.756531 | − | 0.485423i | ||||
\(165\) | 9.69116i | 0.754456i | ||||||||
\(166\) | 5.71554 | + | 10.4583i | 0.443612 | + | 0.811719i | ||||
\(167\) | −6.26796 | −0.485029 | −0.242515 | − | 0.970148i | \(-0.577972\pi\) | ||||
−0.242515 | + | 0.970148i | \(0.577972\pi\) | |||||||
\(168\) | 9.20040 | + | 7.78677i | 0.709826 | + | 0.600763i | ||||
\(169\) | 5.09746 | 0.392112 | ||||||||
\(170\) | 3.67672 | + | 6.72765i | 0.281992 | + | 0.515987i | ||||
\(171\) | − | 1.84018i | − | 0.140722i | ||||||
\(172\) | −5.36270 | + | 8.35776i | −0.408902 | + | 0.637274i | ||||
\(173\) | −9.11366 | −0.692898 | −0.346449 | − | 0.938069i | \(-0.612613\pi\) | ||||
−0.346449 | + | 0.938069i | \(0.612613\pi\) | |||||||
\(174\) | −0.753195 | + | 0.411628i | −0.0570995 | + | 0.0312054i | ||||
\(175\) | −2.13463 | − | 1.56312i | −0.161363 | − | 0.118161i | ||||
\(176\) | 10.0294 | + | 21.8778i | 0.755996 | + | 1.64910i | ||||
\(177\) | −17.0468 | −1.28131 | ||||||||
\(178\) | 1.32091 | + | 2.41700i | 0.0990067 | + | 0.181162i | ||||
\(179\) | 10.9518 | 0.818579 | 0.409290 | − | 0.912405i | \(-0.365777\pi\) | ||||
0.409290 | + | 0.912405i | \(0.365777\pi\) | |||||||
\(180\) | −0.438177 | + | 0.682898i | −0.0326598 | + | 0.0509002i | ||||
\(181\) | 18.7975 | 1.39721 | 0.698603 | − | 0.715509i | \(-0.253805\pi\) | ||||
0.698603 | + | 0.715509i | \(0.253805\pi\) | |||||||
\(182\) | −15.7792 | − | 2.09334i | −1.16963 | − | 0.155169i | ||||
\(183\) | 8.98763i | 0.664385i | ||||||||
\(184\) | 14.6684 | + | 1.03316i | 1.08137 | + | 0.0761655i | ||||
\(185\) | − | 0.372265i | − | 0.0273695i | ||||||
\(186\) | 3.20761 | + | 5.86928i | 0.235194 | + | 0.430356i | ||||
\(187\) | − | 32.6185i | − | 2.38530i | ||||||
\(188\) | −4.17234 | + | 6.50259i | −0.304299 | + | 0.474250i | ||||
\(189\) | 8.57449 | − | 11.7095i | 0.623702 | − | 0.851743i | ||||
\(190\) | −3.07627 | − | 5.62894i | −0.223176 | − | 0.408366i | ||||
\(191\) | − | 1.13019i | − | 0.0817778i | −0.999164 | − | 0.0408889i | \(-0.986981\pi\) | ||
0.999164 | − | 0.0408889i | \(-0.0130190\pi\) | |||||||
\(192\) | 1.80621 | − | 12.7583i | 0.130352 | − | 0.920748i | ||||
\(193\) | −3.27357 | −0.235636 | −0.117818 | − | 0.993035i | \(-0.537590\pi\) | ||||
−0.117818 | + | 0.993035i | \(0.537590\pi\) | |||||||
\(194\) | 2.13213 | + | 3.90136i | 0.153078 | + | 0.280101i | ||||
\(195\) | 6.85203i | 0.490684i | ||||||||
\(196\) | 13.5157 | + | 3.65037i | 0.965409 | + | 0.260741i | ||||
\(197\) | − | 21.2252i | − | 1.51223i | −0.654437 | − | 0.756116i | \(-0.727094\pi\) | ||
0.654437 | − | 0.756116i | \(-0.272906\pi\) | |||||||
\(198\) | 3.02920 | − | 1.65549i | 0.215276 | − | 0.117650i | ||||
\(199\) | 17.9614 | 1.27325 | 0.636626 | − | 0.771172i | \(-0.280329\pi\) | ||||
0.636626 | + | 0.771172i | \(0.280329\pi\) | |||||||
\(200\) | −0.198727 | + | 2.82144i | −0.0140521 | + | 0.199506i | ||||
\(201\) | − | 1.26052i | − | 0.0889099i | ||||||
\(202\) | 20.2300 | − | 11.0559i | 1.42338 | − | 0.777890i | ||||
\(203\) | −0.589011 | + | 0.804368i | −0.0413404 | + | 0.0564556i | ||||
\(204\) | −9.43105 | + | 14.6983i | −0.660306 | + | 1.02909i | ||||
\(205\) | 5.75560i | 0.401989i | ||||||||
\(206\) | 14.7602 | − | 8.06659i | 1.02839 | − | 0.562026i | ||||
\(207\) | − | 2.10916i | − | 0.146597i | ||||||
\(208\) | 7.09120 | + | 15.4685i | 0.491686 | + | 1.07255i | ||||
\(209\) | 27.2915i | 1.88779i | ||||||||
\(210\) | 0.792578 | − | 5.97429i | 0.0546931 | − | 0.412265i | ||||
\(211\) | −7.43642 | −0.511944 | −0.255972 | − | 0.966684i | \(-0.582396\pi\) | ||||
−0.255972 | + | 0.966684i | \(0.582396\pi\) | |||||||
\(212\) | 17.2073 | + | 11.0409i | 1.18180 | + | 0.758293i | ||||
\(213\) | −24.7728 | −1.69741 | ||||||||
\(214\) | −13.0048 | + | 7.10723i | −0.888988 | + | 0.485840i | ||||
\(215\) | 4.96515 | 0.338620 | ||||||||
\(216\) | −15.4770 | − | 1.09011i | −1.05308 | − | 0.0741729i | ||||
\(217\) | 6.26804 | + | 4.58987i | 0.425503 | + | 0.311581i | ||||
\(218\) | −0.459007 | − | 0.839889i | −0.0310879 | − | 0.0568845i | ||||
\(219\) | 14.1283 | 0.954705 | ||||||||
\(220\) | 6.49855 | − | 10.1280i | 0.438132 | − | 0.682829i | ||||
\(221\) | − | 23.0625i | − | 1.55135i | ||||||
\(222\) | 0.744095 | − | 0.406655i | 0.0499404 | − | 0.0272929i | ||||
\(223\) | 23.8641 | 1.59806 | 0.799029 | − | 0.601293i | \(-0.205347\pi\) | ||||
0.799029 | + | 0.601293i | \(0.205347\pi\) | |||||||
\(224\) | −4.39357 | − | 14.3072i | −0.293558 | − | 0.955941i | ||||
\(225\) | 0.405694 | 0.0270462 | ||||||||
\(226\) | 11.2996 | − | 6.17534i | 0.751638 | − | 0.410777i | ||||
\(227\) | − | 12.1282i | − | 0.804974i | −0.915426 | − | 0.402487i | \(-0.868146\pi\) | ||
0.915426 | − | 0.402487i | \(-0.131854\pi\) | |||||||
\(228\) | 7.89084 | − | 12.2979i | 0.522584 | − | 0.814447i | ||||
\(229\) | 16.4001 | 1.08375 | 0.541875 | − | 0.840459i | \(-0.317715\pi\) | ||||
0.541875 | + | 0.840459i | \(0.317715\pi\) | |||||||
\(230\) | −3.52593 | − | 6.45173i | −0.232493 | − | 0.425415i | ||||
\(231\) | −15.1484 | + | 20.6871i | −0.996694 | + | 1.36111i | ||||
\(232\) | 1.06317 | + | 0.0748837i | 0.0698004 | + | 0.00491636i | ||||
\(233\) | −26.4108 | −1.73023 | −0.865114 | − | 0.501575i | \(-0.832754\pi\) | ||||
−0.865114 | + | 0.501575i | \(0.832754\pi\) | |||||||
\(234\) | 2.14177 | − | 1.17050i | 0.140012 | − | 0.0765177i | ||||
\(235\) | 3.86303 | 0.251997 | ||||||||
\(236\) | 17.8151 | + | 11.4310i | 1.15967 | + | 0.744092i | ||||
\(237\) | −14.0872 | −0.915062 | ||||||||
\(238\) | −2.66766 | + | 20.1082i | −0.172918 | + | 1.30342i | ||||
\(239\) | 1.68909i | 0.109258i | 0.998507 | + | 0.0546292i | \(0.0173977\pi\) | ||||
−0.998507 | + | 0.0546292i | \(0.982602\pi\) | |||||||
\(240\) | −5.85666 | + | 2.68486i | −0.378046 | + | 0.173307i | ||||
\(241\) | 5.25118i | 0.338258i | 0.985594 | + | 0.169129i | \(0.0540955\pi\) | ||||
−0.985594 | + | 0.169129i | \(0.945905\pi\) | |||||||
\(242\) | −31.2750 | + | 17.0921i | −2.01043 | + | 1.09872i | ||||
\(243\) | 4.18577i | 0.268517i | ||||||||
\(244\) | 6.02679 | − | 9.39275i | 0.385826 | − | 0.601309i | ||||
\(245\) | −2.11332 | − | 6.67337i | −0.135015 | − | 0.426346i | ||||
\(246\) | −11.5045 | + | 6.28730i | −0.733498 | + | 0.400864i | ||||
\(247\) | 19.2961i | 1.22778i | ||||||||
\(248\) | 0.583532 | − | 8.28474i | 0.0370543 | − | 0.526082i | ||||
\(249\) | 13.5739 | 0.860212 | ||||||||
\(250\) | 1.24098 | − | 0.678208i | 0.0784865 | − | 0.0428936i | ||||
\(251\) | − | 13.9692i | − | 0.881730i | −0.897574 | − | 0.440865i | \(-0.854672\pi\) | ||
0.897574 | − | 0.440865i | \(-0.145328\pi\) | |||||||
\(252\) | −2.00280 | + | 0.772816i | −0.126164 | + | 0.0486828i | ||||
\(253\) | 31.2807i | 1.96660i | ||||||||
\(254\) | 2.53733 | + | 4.64280i | 0.159206 | + | 0.291315i | ||||
\(255\) | 8.73190 | 0.546813 | ||||||||
\(256\) | −10.4429 | + | 12.1222i | −0.652679 | + | 0.757635i | ||||
\(257\) | 21.6938i | 1.35322i | 0.736341 | + | 0.676610i | \(0.236552\pi\) | ||||
−0.736341 | + | 0.676610i | \(0.763448\pi\) | |||||||
\(258\) | 5.42382 | + | 9.92448i | 0.337672 | + | 0.617871i | ||||
\(259\) | 0.581895 | − | 0.794650i | 0.0361572 | − | 0.0493771i | ||||
\(260\) | 4.59473 | − | 7.16089i | 0.284953 | − | 0.444099i | ||||
\(261\) | − | 0.152873i | − | 0.00946257i | ||||||
\(262\) | 11.9212 | + | 21.8133i | 0.736492 | + | 1.34763i | ||||
\(263\) | − | 5.88968i | − | 0.363173i | −0.983375 | − | 0.181587i | \(-0.941877\pi\) | ||
0.983375 | − | 0.181587i | \(-0.0581232\pi\) | |||||||
\(264\) | 27.3430 | + | 1.92589i | 1.68285 | + | 0.118530i | ||||
\(265\) | − | 10.2224i | − | 0.627958i | ||||||
\(266\) | 2.23199 | − | 16.8243i | 0.136852 | − | 1.03156i | ||||
\(267\) | 3.13706 | 0.191985 | ||||||||
\(268\) | −0.845257 | + | 1.31733i | −0.0516323 | + | 0.0804689i | ||||
\(269\) | −13.3475 | −0.813810 | −0.406905 | − | 0.913470i | \(-0.633392\pi\) | ||||
−0.406905 | + | 0.913470i | \(0.633392\pi\) | |||||||
\(270\) | 3.72031 | + | 6.80740i | 0.226411 | + | 0.414285i | ||||
\(271\) | −24.7908 | −1.50593 | −0.752966 | − | 0.658059i | \(-0.771378\pi\) | ||||
−0.752966 | + | 0.658059i | \(0.771378\pi\) | |||||||
\(272\) | 19.7123 | − | 9.03668i | 1.19523 | − | 0.547929i | ||||
\(273\) | −10.7105 | + | 14.6266i | −0.648231 | + | 0.885241i | ||||
\(274\) | 0.952252 | − | 0.520415i | 0.0575277 | − | 0.0314394i | ||||
\(275\) | −6.01679 | −0.362826 | ||||||||
\(276\) | 9.04426 | − | 14.0955i | 0.544400 | − | 0.848448i | ||||
\(277\) | 2.09066i | 0.125616i | 0.998026 | + | 0.0628078i | \(0.0200055\pi\) | ||||
−0.998026 | + | 0.0628078i | \(0.979994\pi\) | |||||||
\(278\) | −1.36899 | − | 2.50497i | −0.0821065 | − | 0.150238i | ||||
\(279\) | −1.19126 | −0.0713189 | ||||||||
\(280\) | −4.83445 | + | 5.71210i | −0.288914 | + | 0.341363i | ||||
\(281\) | −4.09181 | −0.244097 | −0.122048 | − | 0.992524i | \(-0.538946\pi\) | ||||
−0.122048 | + | 0.992524i | \(0.538946\pi\) | |||||||
\(282\) | 4.21990 | + | 7.72155i | 0.251291 | + | 0.459811i | ||||
\(283\) | 5.92294i | 0.352082i | 0.984383 | + | 0.176041i | \(0.0563291\pi\) | ||||
−0.984383 | + | 0.176041i | \(0.943671\pi\) | |||||||
\(284\) | 25.8895 | + | 16.6118i | 1.53626 | + | 0.985728i | ||||
\(285\) | −7.30587 | −0.432763 | ||||||||
\(286\) | −31.7643 | + | 17.3595i | −1.87826 | + | 1.02649i | ||||
\(287\) | −8.99669 | + | 12.2861i | −0.531058 | + | 0.725226i | ||||
\(288\) | 1.83968 | + | 1.37200i | 0.108404 | + | 0.0808458i | ||||
\(289\) | −12.3898 | −0.728812 | ||||||||
\(290\) | −0.255561 | − | 0.467624i | −0.0150070 | − | 0.0274598i | ||||
\(291\) | 5.06362 | 0.296835 | ||||||||
\(292\) | −14.7652 | − | 9.47397i | −0.864067 | − | 0.554422i | ||||
\(293\) | −9.44316 | −0.551675 | −0.275838 | − | 0.961204i | \(-0.588955\pi\) | ||||
−0.275838 | + | 0.961204i | \(0.588955\pi\) | |||||||
\(294\) | 11.0304 | − | 11.5140i | 0.643305 | − | 0.671511i | ||||
\(295\) | − | 10.5835i | − | 0.616198i | ||||||
\(296\) | −1.05032 | − | 0.0739790i | −0.0610488 | − | 0.00429994i | ||||
\(297\) | − | 33.0051i | − | 1.91515i | ||||||
\(298\) | −2.87063 | − | 5.25267i | −0.166291 | − | 0.304279i | ||||
\(299\) | 22.1167i | 1.27904i | ||||||||
\(300\) | 2.71124 | + | 1.73965i | 0.156534 | + | 0.100439i | ||||
\(301\) | 10.5988 | + | 7.76111i | 0.610903 | + | 0.447343i | ||||
\(302\) | 0.424401 | + | 0.776567i | 0.0244215 | + | 0.0446864i | ||||
\(303\) | − | 26.2568i | − | 1.50841i | ||||||
\(304\) | −16.4930 | + | 7.56088i | −0.945941 | + | 0.433646i | ||||
\(305\) | −5.58001 | −0.319510 | ||||||||
\(306\) | −1.49162 | − | 2.72937i | −0.0852704 | − | 0.156027i | ||||
\(307\) | 24.1204i | 1.37663i | 0.725414 | + | 0.688313i | \(0.241649\pi\) | ||||
−0.725414 | + | 0.688313i | \(0.758351\pi\) | |||||||
\(308\) | 29.7033 | − | 11.4615i | 1.69250 | − | 0.653082i | ||||
\(309\) | − | 19.1574i | − | 1.08983i | ||||||
\(310\) | −3.64396 | + | 1.99146i | −0.206963 | + | 0.113107i | ||||
\(311\) | −16.5947 | −0.941001 | −0.470500 | − | 0.882400i | \(-0.655927\pi\) | ||||
−0.470500 | + | 0.882400i | \(0.655927\pi\) | |||||||
\(312\) | 19.3326 | + | 1.36168i | 1.09449 | + | 0.0770900i | ||||
\(313\) | − | 11.3871i | − | 0.643637i | −0.946801 | − | 0.321819i | \(-0.895706\pi\) | ||
0.946801 | − | 0.321819i | \(-0.104294\pi\) | |||||||
\(314\) | −3.62010 | + | 1.97842i | −0.204294 | + | 0.111649i | ||||
\(315\) | 0.866007 | + | 0.634147i | 0.0487940 | + | 0.0357301i | ||||
\(316\) | 14.7222 | + | 9.44638i | 0.828187 | + | 0.531400i | ||||
\(317\) | − | 26.7084i | − | 1.50009i | −0.661386 | − | 0.750046i | \(-0.730031\pi\) | ||
0.661386 | − | 0.750046i | \(-0.269969\pi\) | |||||||
\(318\) | 20.4329 | − | 11.1668i | 1.14582 | − | 0.626201i | ||||
\(319\) | 2.26723i | 0.126941i | ||||||||
\(320\) | 7.92102 | + | 1.12139i | 0.442798 | + | 0.0626876i | ||||
\(321\) | 16.8791i | 0.942097i | ||||||||
\(322\) | 2.55825 | − | 19.2835i | 0.142566 | − | 1.07463i | ||||
\(323\) | 24.5901 | 1.36823 | ||||||||
\(324\) | −8.22832 | + | 12.8238i | −0.457129 | + | 0.712435i | ||||
\(325\) | −4.25411 | −0.235976 | ||||||||
\(326\) | 8.86553 | − | 4.84510i | 0.491016 | − | 0.268345i | ||||
\(327\) | −1.09010 | −0.0602828 | ||||||||
\(328\) | 16.2391 | + | 1.14379i | 0.896653 | + | 0.0631553i | ||||
\(329\) | 8.24616 | + | 6.03838i | 0.454626 | + | 0.332907i | ||||
\(330\) | −6.57262 | − | 12.0265i | −0.361811 | − | 0.662040i | ||||
\(331\) | −3.25364 | −0.178836 | −0.0894182 | − | 0.995994i | \(-0.528501\pi\) | ||||
−0.0894182 | + | 0.995994i | \(0.528501\pi\) | |||||||
\(332\) | −14.1858 | − | 9.10219i | −0.778545 | − | 0.499547i | ||||
\(333\) | 0.151026i | 0.00827615i | ||||||||
\(334\) | 7.77842 | − | 4.25098i | 0.425616 | − | 0.232603i | ||||
\(335\) | 0.782596 | 0.0427578 | ||||||||
\(336\) | −16.6986 | − | 3.42346i | −0.910982 | − | 0.186765i | ||||
\(337\) | −12.0157 | −0.654539 | −0.327270 | − | 0.944931i | \(-0.606129\pi\) | ||||
−0.327270 | + | 0.944931i | \(0.606129\pi\) | |||||||
\(338\) | −6.32585 | + | 3.45714i | −0.344081 | + | 0.188043i | ||||
\(339\) | − | 14.6659i | − | 0.796542i | ||||||
\(340\) | −9.12549 | − | 5.85531i | −0.494899 | − | 0.317549i | ||||
\(341\) | 17.6675 | 0.956746 | ||||||||
\(342\) | 1.24802 | + | 2.28363i | 0.0674853 | + | 0.123484i | ||||
\(343\) | 5.92010 | − | 17.5486i | 0.319655 | − | 0.947534i | ||||
\(344\) | 0.986707 | − | 14.0089i | 0.0531997 | − | 0.755307i | ||||
\(345\) | −8.37378 | −0.450829 | ||||||||
\(346\) | 11.3099 | − | 6.18095i | 0.608023 | − | 0.332290i | ||||
\(347\) | −15.5740 | −0.836057 | −0.418028 | − | 0.908434i | \(-0.637279\pi\) | ||||
−0.418028 | + | 0.908434i | \(0.637279\pi\) | |||||||
\(348\) | 0.655531 | − | 1.02164i | 0.0351401 | − | 0.0547659i | ||||
\(349\) | −34.7705 | −1.86122 | −0.930610 | − | 0.366012i | \(-0.880723\pi\) | ||||
−0.930610 | + | 0.366012i | \(0.880723\pi\) | |||||||
\(350\) | 3.70916 | + | 0.492075i | 0.198263 | + | 0.0263025i | ||||
\(351\) | − | 23.3359i | − | 1.24558i | ||||||
\(352\) | −27.2840 | − | 20.3479i | −1.45424 | − | 1.08455i | ||||
\(353\) | − | 12.5154i | − | 0.666126i | −0.942905 | − | 0.333063i | \(-0.891918\pi\) | ||
0.942905 | − | 0.333063i | \(-0.108082\pi\) | |||||||
\(354\) | 21.1547 | − | 11.5612i | 1.12436 | − | 0.614473i | ||||
\(355\) | − | 15.3803i | − | 0.816302i | ||||||
\(356\) | −3.27846 | − | 2.10360i | −0.173758 | − | 0.111491i | ||||
\(357\) | 18.6394 | + | 13.6490i | 0.986502 | + | 0.722382i | ||||
\(358\) | −13.5910 | + | 7.42763i | −0.718308 | + | 0.392562i | ||||
\(359\) | 31.0752i | 1.64009i | 0.572301 | + | 0.820044i | \(0.306051\pi\) | ||||
−0.572301 | + | 0.820044i | \(0.693949\pi\) | |||||||
\(360\) | 0.0806221 | − | 1.14464i | 0.00424916 | − | 0.0603278i | ||||
\(361\) | −1.57420 | −0.0828526 | ||||||||
\(362\) | −23.3273 | + | 12.7486i | −1.22606 | + | 0.670052i | ||||
\(363\) | 40.5922i | 2.13054i | ||||||||
\(364\) | 21.0014 | − | 8.10376i | 1.10077 | − | 0.424752i | ||||
\(365\) | 8.77164i | 0.459129i | ||||||||
\(366\) | −6.09548 | − | 11.1535i | −0.318616 | − | 0.583002i | ||||
\(367\) | 14.0542 | 0.733624 | 0.366812 | − | 0.930295i | \(-0.380449\pi\) | ||||
0.366812 | + | 0.930295i | \(0.380449\pi\) | |||||||
\(368\) | −18.9039 | + | 8.66606i | −0.985431 | + | 0.451750i | ||||
\(369\) | − | 2.33501i | − | 0.121556i | ||||||
\(370\) | 0.252473 | + | 0.461974i | 0.0131255 | + | 0.0240169i | ||||
\(371\) | 15.9789 | − | 21.8211i | 0.829581 | − | 1.13290i | ||||
\(372\) | −7.96118 | − | 5.10823i | −0.412768 | − | 0.264849i | ||||
\(373\) | − | 19.7598i | − | 1.02312i | −0.859247 | − | 0.511561i | \(-0.829067\pi\) | ||
0.859247 | − | 0.511561i | \(-0.170933\pi\) | |||||||
\(374\) | 22.1221 | + | 40.4789i | 1.14391 | + | 2.09311i | ||||
\(375\) | − | 1.61069i | − | 0.0831754i | ||||||
\(376\) | 0.767688 | − | 10.8993i | 0.0395905 | − | 0.562089i | ||||
\(377\) | 1.60302i | 0.0825600i | ||||||||
\(378\) | −2.69928 | + | 20.3466i | −0.138836 | + | 1.04652i | ||||
\(379\) | −0.483016 | −0.0248108 | −0.0124054 | − | 0.999923i | \(-0.503949\pi\) | ||||
−0.0124054 | + | 0.999923i | \(0.503949\pi\) | |||||||
\(380\) | 7.63518 | + | 4.89906i | 0.391677 | + | 0.251316i | ||||
\(381\) | 6.02594 | 0.308718 | ||||||||
\(382\) | 0.766505 | + | 1.40255i | 0.0392178 | + | 0.0717605i | ||||
\(383\) | 1.09585 | 0.0559953 | 0.0279977 | − | 0.999608i | \(-0.491087\pi\) | ||||
0.0279977 | + | 0.999608i | \(0.491087\pi\) | |||||||
\(384\) | 6.41129 | + | 17.0577i | 0.327175 | + | 0.870474i | ||||
\(385\) | −12.8437 | − | 9.40496i | −0.654573 | − | 0.479321i | ||||
\(386\) | 4.06243 | − | 2.22016i | 0.206772 | − | 0.113003i | ||||
\(387\) | −2.01433 | −0.102394 | ||||||||
\(388\) | −5.29186 | − | 3.39548i | −0.268654 | − | 0.172380i | ||||
\(389\) | − | 18.3250i | − | 0.929114i | −0.885543 | − | 0.464557i | \(-0.846214\pi\) | ||
0.885543 | − | 0.464557i | \(-0.153786\pi\) | |||||||
\(390\) | −4.64710 | − | 8.50324i | −0.235315 | − | 0.430578i | ||||
\(391\) | 28.1844 | 1.42535 | ||||||||
\(392\) | −19.2485 | + | 4.63643i | −0.972194 | + | 0.234175i | ||||
\(393\) | 28.3117 | 1.42814 | ||||||||
\(394\) | 14.3951 | + | 26.3401i | 0.725214 | + | 1.32699i | ||||
\(395\) | − | 8.74609i | − | 0.440064i | ||||||
\(396\) | −2.63642 | + | 4.10886i | −0.132485 | + | 0.206478i | ||||
\(397\) | −0.717950 | −0.0360329 | −0.0180164 | − | 0.999838i | \(-0.505735\pi\) | ||||
−0.0180164 | + | 0.999838i | \(0.505735\pi\) | |||||||
\(398\) | −22.2898 | + | 12.1816i | −1.11729 | + | 0.610608i | ||||
\(399\) | −15.5954 | − | 11.4199i | −0.780745 | − | 0.571712i | ||||
\(400\) | −1.66690 | − | 3.63613i | −0.0833452 | − | 0.181806i | ||||
\(401\) | −21.1139 | −1.05438 | −0.527189 | − | 0.849748i | \(-0.676754\pi\) | ||||
−0.527189 | + | 0.849748i | \(0.676754\pi\) | |||||||
\(402\) | 0.854892 | + | 1.56428i | 0.0426381 | + | 0.0780190i | ||||
\(403\) | 12.4916 | 0.622250 | ||||||||
\(404\) | −17.6069 | + | 27.4403i | −0.875975 | + | 1.36521i | ||||
\(405\) | 7.61833 | 0.378558 | ||||||||
\(406\) | 0.185423 | − | 1.39768i | 0.00920237 | − | 0.0693655i | ||||
\(407\) | − | 2.23984i | − | 0.111025i | ||||||
\(408\) | 1.73526 | − | 24.6365i | 0.0859083 | − | 1.21969i | ||||
\(409\) | 1.08609i | 0.0537038i | 0.999639 | + | 0.0268519i | \(0.00854825\pi\) | ||||
−0.999639 | + | 0.0268519i | \(0.991452\pi\) | |||||||
\(410\) | −3.90349 | − | 7.14259i | −0.192780 | − | 0.352748i | ||||
\(411\) | − | 1.23594i | − | 0.0609644i | ||||||
\(412\) | −12.8463 | + | 20.0210i | −0.632892 | + | 0.986362i | ||||
\(413\) | 16.5433 | − | 22.5920i | 0.814044 | − | 1.11168i | ||||
\(414\) | 1.43045 | + | 2.61743i | 0.0703027 | + | 0.128639i | ||||
\(415\) | 8.42742i | 0.413686i | ||||||||
\(416\) | −19.2909 | − | 14.3868i | −0.945814 | − | 0.705371i | ||||
\(417\) | −3.25123 | −0.159214 | ||||||||
\(418\) | −18.5093 | − | 33.8682i | −0.905318 | − | 1.65655i | ||||
\(419\) | − | 0.208107i | − | 0.0101667i | −0.999987 | − | 0.00508334i | \(-0.998382\pi\) | ||
0.999987 | − | 0.00508334i | \(-0.00161808\pi\) | |||||||
\(420\) | 3.06823 | + | 7.95151i | 0.149714 | + | 0.387994i | ||||
\(421\) | 9.48511i | 0.462276i | 0.972921 | + | 0.231138i | \(0.0742449\pi\) | ||||
−0.972921 | + | 0.231138i | \(0.925755\pi\) | |||||||
\(422\) | 9.22846 | − | 5.04344i | 0.449234 | − | 0.245511i | ||||
\(423\) | −1.56721 | −0.0762003 | ||||||||
\(424\) | −28.8419 | − | 2.03147i | −1.40069 | − | 0.0986568i | ||||
\(425\) | 5.42124i | 0.262969i | ||||||||
\(426\) | 30.7426 | − | 16.8011i | 1.48948 | − | 0.814017i | ||||
\(427\) | −11.9113 | − | 8.72221i | −0.576427 | − | 0.422097i | ||||
\(428\) | 11.3185 | − | 17.6399i | 0.547100 | − | 0.852656i | ||||
\(429\) | 41.2273i | 1.99047i | ||||||||
\(430\) | −6.16165 | + | 3.36740i | −0.297141 | + | 0.162391i | ||||
\(431\) | − | 13.6900i | − | 0.659423i | −0.944082 | − | 0.329711i | \(-0.893049\pi\) | ||
0.944082 | − | 0.329711i | \(-0.106951\pi\) | |||||||
\(432\) | 19.9460 | − | 9.14381i | 0.959651 | − | 0.439932i | ||||
\(433\) | − | 6.48406i | − | 0.311604i | −0.987788 | − | 0.155802i | \(-0.950204\pi\) | ||
0.987788 | − | 0.155802i | \(-0.0497962\pi\) | |||||||
\(434\) | −10.8914 | − | 1.44491i | −0.522805 | − | 0.0693578i | ||||
\(435\) | −0.606935 | −0.0291003 | ||||||||
\(436\) | 1.13924 | + | 0.730984i | 0.0545596 | + | 0.0350078i | ||||
\(437\) | −23.5816 | −1.12806 | ||||||||
\(438\) | −17.5330 | + | 9.58196i | −0.837760 | + | 0.457844i | ||||
\(439\) | −9.04411 | −0.431652 | −0.215826 | − | 0.976432i | \(-0.569244\pi\) | ||||
−0.215826 | + | 0.976432i | \(0.569244\pi\) | |||||||
\(440\) | −1.19570 | + | 16.9760i | −0.0570026 | + | 0.809299i | ||||
\(441\) | 0.857361 | + | 2.70734i | 0.0408267 | + | 0.128921i | ||||
\(442\) | 15.6412 | + | 28.6202i | 0.743976 | + | 1.36132i | ||||
\(443\) | 8.66264 | 0.411574 | 0.205787 | − | 0.978597i | \(-0.434025\pi\) | ||||
0.205787 | + | 0.978597i | \(0.434025\pi\) | |||||||
\(444\) | −0.647611 | + | 1.00930i | −0.0307343 | + | 0.0478993i | ||||
\(445\) | 1.94765i | 0.0923277i | ||||||||
\(446\) | −29.6149 | + | 16.1848i | −1.40231 | + | 0.766373i | ||||
\(447\) | −6.81750 | −0.322457 | ||||||||
\(448\) | 15.1556 | + | 14.7752i | 0.716035 | + | 0.698064i | ||||
\(449\) | −26.5808 | −1.25443 | −0.627213 | − | 0.778848i | \(-0.715804\pi\) | ||||
−0.627213 | + | 0.778848i | \(0.715804\pi\) | |||||||
\(450\) | −0.503458 | + | 0.275145i | −0.0237332 | + | 0.0129704i | ||||
\(451\) | 34.6303i | 1.63068i | ||||||||
\(452\) | −9.83443 | + | 15.3270i | −0.462573 | + | 0.720919i | ||||
\(453\) | 1.00792 | 0.0473560 | ||||||||
\(454\) | 8.22541 | + | 15.0508i | 0.386037 | + | 0.706369i | ||||
\(455\) | −9.08097 | − | 6.64968i | −0.425722 | − | 0.311742i | ||||
\(456\) | −1.45187 | + | 20.6131i | −0.0679901 | + | 0.965295i | ||||
\(457\) | 33.4034 | 1.56254 | 0.781272 | − | 0.624191i | \(-0.214571\pi\) | ||||
0.781272 | + | 0.624191i | \(0.214571\pi\) | |||||||
\(458\) | −20.3522 | + | 11.1227i | −0.950998 | + | 0.519729i | ||||
\(459\) | −29.7382 | −1.38806 | ||||||||
\(460\) | 8.75123 | + | 5.61516i | 0.408028 | + | 0.261808i | ||||
\(461\) | 9.70385 | 0.451954 | 0.225977 | − | 0.974133i | \(-0.427443\pi\) | ||||
0.225977 | + | 0.974133i | \(0.427443\pi\) | |||||||
\(462\) | 4.76878 | − | 35.9461i | 0.221864 | − | 1.67236i | ||||
\(463\) | 28.6011i | 1.32921i | 0.747196 | + | 0.664604i | \(0.231400\pi\) | ||||
−0.747196 | + | 0.664604i | \(0.768600\pi\) | |||||||
\(464\) | −1.37016 | + | 0.628119i | −0.0636080 | + | 0.0291597i | ||||
\(465\) | 4.72954i | 0.219327i | ||||||||
\(466\) | 32.7753 | − | 17.9120i | 1.51829 | − | 0.829758i | ||||
\(467\) | 8.61107i | 0.398473i | 0.979951 | + | 0.199236i | \(0.0638462\pi\) | ||||
−0.979951 | + | 0.199236i | \(0.936154\pi\) | |||||||
\(468\) | −1.86405 | + | 2.90513i | −0.0861659 | + | 0.134289i | ||||
\(469\) | 1.67056 | + | 1.22329i | 0.0771391 | + | 0.0564863i | ||||
\(470\) | −4.79395 | + | 2.61994i | −0.221129 | + | 0.120849i | ||||
\(471\) | 4.69857i | 0.216499i | ||||||||
\(472\) | −29.8608 | − | 2.10323i | −1.37445 | − | 0.0968091i | ||||
\(473\) | 29.8743 | 1.37362 | ||||||||
\(474\) | 17.4819 | − | 9.55405i | 0.802973 | − | 0.438832i | ||||
\(475\) | − | 4.53588i | − | 0.208120i | ||||||
\(476\) | −10.3270 | − | 26.7632i | −0.473339 | − | 1.22669i | ||||
\(477\) | 4.14717i | 0.189886i | ||||||||
\(478\) | −1.14556 | − | 2.09613i | −0.0523965 | − | 0.0958749i | ||||
\(479\) | 6.75741 | 0.308754 | 0.154377 | − | 0.988012i | \(-0.450663\pi\) | ||||
0.154377 | + | 0.988012i | \(0.450663\pi\) | |||||||
\(480\) | 5.44711 | − | 7.30389i | 0.248625 | − | 0.333375i | ||||
\(481\) | − | 1.58366i | − | 0.0722086i | ||||||
\(482\) | −3.56139 | − | 6.51661i | −0.162217 | − | 0.296824i | ||||
\(483\) | −17.8750 | − | 13.0892i | −0.813339 | − | 0.595580i | ||||
\(484\) | 27.2197 | − | 42.4219i | 1.23726 | − | 1.92827i | ||||
\(485\) | 3.14377i | 0.142751i | ||||||||
\(486\) | −2.83882 | − | 5.19446i | −0.128771 | − | 0.235625i | ||||
\(487\) | 7.72534i | 0.350069i | 0.984562 | + | 0.175034i | \(0.0560036\pi\) | ||||
−0.984562 | + | 0.175034i | \(0.943996\pi\) | |||||||
\(488\) | −1.10890 | + | 15.7436i | −0.0501974 | + | 0.712681i | ||||
\(489\) | − | 11.5067i | − | 0.520350i | ||||||
\(490\) | 7.14852 | + | 6.84826i | 0.322937 | + | 0.309373i | ||||
\(491\) | −33.1648 | −1.49671 | −0.748354 | − | 0.663300i | \(-0.769156\pi\) | ||||
−0.748354 | + | 0.663300i | \(0.769156\pi\) | |||||||
\(492\) | 10.0127 | − | 15.6048i | 0.451409 | − | 0.703521i | ||||
\(493\) | 2.04282 | 0.0920039 | ||||||||
\(494\) | −13.0868 | − | 23.9461i | −0.588802 | − | 1.07739i | ||||
\(495\) | 2.44098 | 0.109714 | ||||||||
\(496\) | 4.89463 | + | 10.6770i | 0.219775 | + | 0.479410i | ||||
\(497\) | 24.0412 | − | 32.8313i | 1.07840 | − | 1.47269i | ||||
\(498\) | −16.8450 | + | 9.20594i | −0.754841 | + | 0.412528i | ||||
\(499\) | −9.13507 | −0.408942 | −0.204471 | − | 0.978873i | \(-0.565547\pi\) | ||||
−0.204471 | + | 0.978873i | \(0.565547\pi\) | |||||||
\(500\) | −1.08007 | + | 1.68329i | −0.0483021 | + | 0.0752788i | ||||
\(501\) | − | 10.0957i | − | 0.451043i | ||||||
\(502\) | 9.47404 | + | 17.3355i | 0.422847 | + | 0.773723i | ||||
\(503\) | −13.9338 | −0.621277 | −0.310639 | − | 0.950528i | \(-0.600543\pi\) | ||||
−0.310639 | + | 0.950528i | \(0.600543\pi\) | |||||||
\(504\) | 1.96131 | − | 2.31736i | 0.0873635 | − | 0.103224i | ||||
\(505\) | 16.3016 | 0.725413 | ||||||||
\(506\) | −21.2148 | − | 38.8187i | −0.943113 | − | 1.72570i | ||||
\(507\) | 8.21040i | 0.364637i | ||||||||
\(508\) | −6.29756 | − | 4.04078i | −0.279409 | − | 0.179281i | ||||
\(509\) | 11.4366 | 0.506918 | 0.253459 | − | 0.967346i | \(-0.418432\pi\) | ||||
0.253459 | + | 0.967346i | \(0.418432\pi\) | |||||||
\(510\) | −10.8361 | + | 5.92205i | −0.479832 | + | 0.262233i | ||||
\(511\) | −13.7111 | + | 18.7242i | −0.606544 | + | 0.828311i | ||||
\(512\) | 4.73805 | − | 22.1258i | 0.209394 | − | 0.977831i | ||||
\(513\) | 24.8816 | 1.09855 | ||||||||
\(514\) | −14.7129 | − | 26.9216i | −0.648958 | − | 1.18746i | ||||
\(515\) | 11.8940 | 0.524111 | ||||||||
\(516\) | −13.4617 | − | 8.63762i | −0.592619 | − | 0.380250i | ||||
\(517\) | 23.2431 | 1.02223 | ||||||||
\(518\) | −0.183182 | + | 1.38079i | −0.00804858 | + | 0.0606685i | ||||
\(519\) | − | 14.6792i | − | 0.644347i | ||||||
\(520\) | −0.845405 | + | 12.0027i | −0.0370735 | + | 0.526353i | ||||
\(521\) | − | 13.5526i | − | 0.593751i | −0.954916 | − | 0.296875i | \(-0.904055\pi\) | ||
0.954916 | − | 0.296875i | \(-0.0959446\pi\) | |||||||
\(522\) | 0.103679 | + | 0.189712i | 0.00453792 | + | 0.00830347i | ||||
\(523\) | − | 16.3634i | − | 0.715522i | −0.933813 | − | 0.357761i | \(-0.883540\pi\) | ||
0.933813 | − | 0.357761i | \(-0.116460\pi\) | |||||||
\(524\) | −29.5879 | − | 18.9848i | −1.29255 | − | 0.829357i | ||||
\(525\) | 2.51769 | − | 3.43822i | 0.109881 | − | 0.150056i | ||||
\(526\) | 3.99443 | + | 7.30898i | 0.174165 | + | 0.318687i | ||||
\(527\) | − | 15.9187i | − | 0.693429i | ||||||
\(528\) | −35.2383 | + | 16.1542i | −1.53355 | + | 0.703023i | ||||
\(529\) | −4.02852 | −0.175153 | ||||||||
\(530\) | 6.93293 | + | 12.6858i | 0.301147 | + | 0.551037i | ||||
\(531\) | 4.29368i | 0.186330i | ||||||||
\(532\) | 8.64051 | + | 22.3924i | 0.374614 | + | 0.970833i | ||||
\(533\) | 24.4850i | 1.06056i | ||||||||
\(534\) | −3.89303 | + | 2.12758i | −0.168468 | + | 0.0920693i | ||||
\(535\) | −10.4794 | −0.453065 | ||||||||
\(536\) | 0.155523 | − | 2.20805i | 0.00671756 | − | 0.0953731i | ||||
\(537\) | 17.6400i | 0.761221i | ||||||||
\(538\) | 16.5640 | − | 9.05236i | 0.714123 | − | 0.390275i | ||||
\(539\) | −12.7154 | − | 40.1523i | −0.547692 | − | 1.72948i | ||||
\(540\) | −9.23367 | − | 5.92471i | −0.397354 | − | 0.254959i | ||||
\(541\) | 23.4050i | 1.00626i | 0.864211 | + | 0.503129i | \(0.167818\pi\) | ||||
−0.864211 | + | 0.503129i | \(0.832182\pi\) | |||||||
\(542\) | 30.7649 | − | 16.8133i | 1.32146 | − | 0.722193i | ||||
\(543\) | 30.2768i | 1.29930i | ||||||||
\(544\) | −18.3339 | + | 24.5834i | −0.786058 | + | 1.05400i | ||||
\(545\) | − | 0.676794i | − | 0.0289907i | ||||||
\(546\) | 3.37172 | − | 25.4153i | 0.144296 | − | 1.08767i | ||||
\(547\) | 21.2928 | 0.910416 | 0.455208 | − | 0.890385i | \(-0.349565\pi\) | ||||
0.455208 | + | 0.890385i | \(0.349565\pi\) | |||||||
\(548\) | −0.828778 | + | 1.29165i | −0.0354036 | + | 0.0551765i | ||||
\(549\) | 2.26377 | 0.0966155 | ||||||||
\(550\) | 7.46673 | − | 4.08064i | 0.318382 | − | 0.173999i | ||||
\(551\) | −1.70920 | −0.0728144 | ||||||||
\(552\) | −1.66409 | + | 23.6261i | −0.0708285 | + | 1.00559i | ||||
\(553\) | 13.6712 | − | 18.6697i | 0.581358 | − | 0.793917i | ||||
\(554\) | −1.41790 | − | 2.59447i | −0.0602409 | − | 0.110228i | ||||
\(555\) | 0.599602 | 0.0254517 | ||||||||
\(556\) | 3.39778 | + | 2.18016i | 0.144098 | + | 0.0924594i | ||||
\(557\) | 2.06871i | 0.0876541i | 0.999039 | + | 0.0438270i | \(0.0139551\pi\) | ||||
−0.999039 | + | 0.0438270i | \(0.986045\pi\) | |||||||
\(558\) | 1.47833 | − | 0.807922i | 0.0625828 | − | 0.0342021i | ||||
\(559\) | 21.1223 | 0.893378 | ||||||||
\(560\) | 2.12547 | − | 10.3674i | 0.0898174 | − | 0.438101i | ||||
\(561\) | 52.5381 | 2.21816 | ||||||||
\(562\) | 5.07785 | − | 2.77509i | 0.214196 | − | 0.117060i | ||||
\(563\) | 25.5312i | 1.07601i | 0.842941 | + | 0.538006i | \(0.180822\pi\) | ||||
−0.842941 | + | 0.538006i | \(0.819178\pi\) | |||||||
\(564\) | −10.4736 | − | 6.72033i | −0.441019 | − | 0.282977i | ||||
\(565\) | 9.10537 | 0.383066 | ||||||||
\(566\) | −4.01698 | − | 7.35025i | −0.168846 | − | 0.308954i | ||||
\(567\) | 16.2623 | + | 11.9084i | 0.682954 | + | 0.500104i | ||||
\(568\) | −43.3946 | − | 3.05648i | −1.82080 | − | 0.128247i | ||||
\(569\) | 26.3859 | 1.10616 | 0.553078 | − | 0.833130i | \(-0.313453\pi\) | ||||
0.553078 | + | 0.833130i | \(0.313453\pi\) | |||||||
\(570\) | 9.06645 | − | 4.95490i | 0.379752 | − | 0.207538i | ||||
\(571\) | 17.6202 | 0.737384 | 0.368692 | − | 0.929552i | \(-0.379806\pi\) | ||||
0.368692 | + | 0.929552i | \(0.379806\pi\) | |||||||
\(572\) | 27.6455 | − | 43.0856i | 1.15592 | − | 1.80150i | ||||
\(573\) | 1.82038 | 0.0760476 | ||||||||
\(574\) | 2.83219 | − | 21.3484i | 0.118213 | − | 0.891067i | ||||
\(575\) | − | 5.19890i | − | 0.216809i | ||||||
\(576\) | −3.21351 | − | 0.454941i | −0.133896 | − | 0.0189559i | ||||
\(577\) | 29.5306i | 1.22938i | 0.788770 | + | 0.614688i | \(0.210718\pi\) | ||||
−0.788770 | + | 0.614688i | \(0.789282\pi\) | |||||||
\(578\) | 15.3755 | − | 8.40286i | 0.639537 | − | 0.349513i | ||||
\(579\) | − | 5.27268i | − | 0.219125i | ||||||
\(580\) | 0.634292 | + | 0.406989i | 0.0263375 | + | 0.0168993i | ||||
\(581\) | −13.1731 | + | 17.9895i | −0.546510 | + | 0.746328i | ||||
\(582\) | −6.28386 | + | 3.43419i | −0.260474 | + | 0.142352i | ||||
\(583\) | − | 61.5062i | − | 2.54733i | ||||||
\(584\) | 24.7486 | + | 1.74316i | 1.02411 | + | 0.0721324i | ||||
\(585\) | 1.72587 | 0.0713558 | ||||||||
\(586\) | 11.7188 | − | 6.40442i | 0.484098 | − | 0.264564i | ||||
\(587\) | 5.32153i | 0.219643i | 0.993951 | + | 0.109822i | \(0.0350279\pi\) | ||||
−0.993951 | + | 0.109822i | \(0.964972\pi\) | |||||||
\(588\) | −5.87960 | + | 21.7696i | −0.242471 | + | 0.897762i | ||||
\(589\) | 13.3190i | 0.548798i | ||||||||
\(590\) | 7.17784 | + | 13.1340i | 0.295507 | + | 0.540717i | ||||
\(591\) | 34.1871 | 1.40627 | ||||||||
\(592\) | 1.35360 | − | 0.620531i | 0.0556328 | − | 0.0255037i | ||||
\(593\) | 45.6864i | 1.87611i | 0.346481 | + | 0.938057i | \(0.387377\pi\) | ||||
−0.346481 | + | 0.938057i | \(0.612623\pi\) | |||||||
\(594\) | 22.3843 | + | 40.9587i | 0.918440 | + | 1.68056i | ||||
\(595\) | −8.47403 | + | 11.5724i | −0.347401 | + | 0.474420i | ||||
\(596\) | 7.12480 | + | 4.57158i | 0.291843 | + | 0.187259i | ||||
\(597\) | 28.9302i | 1.18404i | ||||||||
\(598\) | −14.9997 | − | 27.4464i | −0.613384 | − | 1.12237i | ||||
\(599\) | 22.5049i | 0.919525i | 0.888042 | + | 0.459762i | \(0.152065\pi\) | ||||
−0.888042 | + | 0.459762i | \(0.847935\pi\) | |||||||
\(600\) | −4.54445 | − | 0.320086i | −0.185526 | − | 0.0130675i | ||||
\(601\) | 4.49699i | 0.183436i | 0.995785 | + | 0.0917181i | \(0.0292359\pi\) | ||||
−0.995785 | + | 0.0917181i | \(0.970764\pi\) | |||||||
\(602\) | −18.4165 | − | 2.44323i | −0.750601 | − | 0.0995784i | ||||
\(603\) | −0.317494 | −0.0129294 | ||||||||
\(604\) | −1.05335 | − | 0.675873i | −0.0428601 | − | 0.0275009i | ||||
\(605\) | −25.2018 | −1.02460 | ||||||||
\(606\) | 17.8076 | + | 32.5842i | 0.723383 | + | 1.32364i | ||||
\(607\) | −10.8910 | −0.442051 | −0.221025 | − | 0.975268i | \(-0.570940\pi\) | ||||
−0.221025 | + | 0.975268i | \(0.570940\pi\) | |||||||
\(608\) | 15.3397 | − | 20.5686i | 0.622107 | − | 0.834167i | ||||
\(609\) | −1.29558 | − | 0.948711i | −0.0524997 | − | 0.0384437i | ||||
\(610\) | 6.92468 | − | 3.78440i | 0.280372 | − | 0.153226i | ||||
\(611\) | 16.4338 | 0.664839 | ||||||||
\(612\) | 3.70215 | + | 2.37546i | 0.149651 | + | 0.0960223i | ||||
\(613\) | 30.5045i | 1.23206i | 0.787721 | + | 0.616032i | \(0.211261\pi\) | ||||
−0.787721 | + | 0.616032i | \(0.788739\pi\) | |||||||
\(614\) | −16.3587 | − | 29.9330i | −0.660182 | − | 1.20800i | ||||
\(615\) | −9.27046 | −0.373821 | ||||||||
\(616\) | −29.0879 | + | 34.3685i | −1.17198 | + | 1.38475i | ||||
\(617\) | −39.6859 | −1.59769 | −0.798847 | − | 0.601534i | \(-0.794557\pi\) | ||||
−0.798847 | + | 0.601534i | \(0.794557\pi\) | |||||||
\(618\) | 12.9927 | + | 23.7740i | 0.522644 | + | 0.956332i | ||||
\(619\) | 13.7231i | 0.551579i | 0.961218 | + | 0.275789i | \(0.0889392\pi\) | ||||
−0.961218 | + | 0.275789i | \(0.911061\pi\) | |||||||
\(620\) | 3.17147 | − | 4.94273i | 0.127369 | − | 0.198505i | ||||
\(621\) | 28.5185 | 1.14441 | ||||||||
\(622\) | 20.5937 | − | 11.2547i | 0.825734 | − | 0.451271i | ||||
\(623\) | −3.04441 | + | 4.15753i | −0.121972 | + | 0.166568i | ||||
\(624\) | −24.9149 | + | 11.4217i | −0.997393 | + | 0.457233i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.72283 | + | 14.1312i | 0.308666 | + | 0.564796i | ||||
\(627\) | −43.9579 | −1.75551 | ||||||||
\(628\) | 3.15070 | − | 4.91036i | 0.125726 | − | 0.195945i | ||||
\(629\) | −2.01814 | −0.0804684 | ||||||||
\(630\) | −1.50478 | − | 0.199632i | −0.0599520 | − | 0.00795352i | ||||
\(631\) | − | 36.7721i | − | 1.46387i | −0.681373 | − | 0.731936i | \(-0.738617\pi\) | ||
0.681373 | − | 0.731936i | \(-0.261383\pi\) | |||||||
\(632\) | −24.6766 | − | 1.73808i | −0.981580 | − | 0.0691372i | ||||
\(633\) | − | 11.9777i | − | 0.476072i | ||||||
\(634\) | 18.1138 | + | 33.1446i | 0.719392 | + | 1.31634i | ||||
\(635\) | 3.74123i | 0.148466i | ||||||||
\(636\) | −17.7834 | + | 27.7155i | −0.705159 | + | 1.09899i | ||||
\(637\) | −8.99031 | − | 28.3893i | −0.356209 | − | 1.12482i | ||||
\(638\) | −1.53766 | − | 2.81360i | −0.0608764 | − | 0.111391i | ||||
\(639\) | 6.23969i | 0.246838i | ||||||||
\(640\) | −10.5904 | + | 3.98047i | −0.418621 | + | 0.157342i | ||||
\(641\) | −40.2483 | −1.58971 | −0.794855 | − | 0.606799i | \(-0.792453\pi\) | ||||
−0.794855 | + | 0.606799i | \(0.792453\pi\) | |||||||
\(642\) | −11.4475 | − | 20.9466i | −0.451797 | − | 0.826696i | ||||
\(643\) | − | 12.3361i | − | 0.486487i | −0.969965 | − | 0.243243i | \(-0.921789\pi\) | ||
0.969965 | − | 0.243243i | \(-0.0782114\pi\) | |||||||
\(644\) | 9.90351 | + | 25.6655i | 0.390253 | + | 1.01136i | ||||
\(645\) | 7.99729i | 0.314893i | ||||||||
\(646\) | −30.5158 | + | 16.6772i | −1.20063 | + | 0.656155i | ||||
\(647\) | 47.9622 | 1.88559 | 0.942794 | − | 0.333376i | \(-0.108188\pi\) | ||||
0.942794 | + | 0.333376i | \(0.108188\pi\) | |||||||
\(648\) | 1.51397 | − | 21.4946i | 0.0594742 | − | 0.844389i | ||||
\(649\) | − | 63.6790i | − | 2.49962i | ||||||
\(650\) | 5.27927 | − | 2.88517i | 0.207070 | − | 0.113166i | ||||
\(651\) | −7.39284 | + | 10.0958i | −0.289748 | + | 0.395687i | ||||
\(652\) | −7.71598 | + | 12.0253i | −0.302181 | + | 0.470949i | ||||
\(653\) | − | 36.7504i | − | 1.43815i | −0.694930 | − | 0.719077i | \(-0.744565\pi\) | ||
0.694930 | − | 0.719077i | \(-0.255435\pi\) | |||||||
\(654\) | 1.35280 | − | 0.739316i | 0.0528985 | − | 0.0289095i | ||||
\(655\) | 17.5774i | 0.686808i | ||||||||
\(656\) | −20.9281 | + | 9.59404i | −0.817105 | + | 0.374584i | ||||
\(657\) | − | 3.55860i | − | 0.138834i | ||||||
\(658\) | −14.3286 | − | 1.90090i | −0.558587 | − | 0.0741049i | ||||
\(659\) | 15.4039 | 0.600050 | 0.300025 | − | 0.953931i | \(-0.403005\pi\) | ||||
0.300025 | + | 0.953931i | \(0.403005\pi\) | |||||||
\(660\) | 16.3130 | + | 10.4671i | 0.634983 | + | 0.407432i | ||||
\(661\) | 6.20639 | 0.241400 | 0.120700 | − | 0.992689i | \(-0.461486\pi\) | ||||
0.120700 | + | 0.992689i | \(0.461486\pi\) | |||||||
\(662\) | 4.03771 | − | 2.20665i | 0.156930 | − | 0.0857638i | ||||
\(663\) | 37.1465 | 1.44265 | ||||||||
\(664\) | 23.7774 | + | 1.67475i | 0.922743 | + | 0.0649930i | ||||
\(665\) | 7.09012 | − | 9.68244i | 0.274943 | − | 0.375469i | ||||
\(666\) | −0.102427 | − | 0.187420i | −0.00396896 | − | 0.00726238i | ||||
\(667\) | −1.95904 | −0.0758542 | ||||||||
\(668\) | −6.76983 | + | 10.5508i | −0.261932 | + | 0.408222i | ||||
\(669\) | 38.4375i | 1.48608i | ||||||||
\(670\) | −0.971187 | + | 0.530763i | −0.0375202 | + | 0.0205052i | ||||
\(671\) | −33.5738 | −1.29610 | ||||||||
\(672\) | 23.0444 | − | 7.07665i | 0.888958 | − | 0.272988i | ||||
\(673\) | −46.2742 | −1.78374 | −0.891870 | − | 0.452291i | \(-0.850607\pi\) | ||||
−0.891870 | + | 0.452291i | \(0.850607\pi\) | |||||||
\(674\) | 14.9113 | − | 8.14917i | 0.574362 | − | 0.313894i | ||||
\(675\) | 5.48550i | 0.211137i | ||||||||
\(676\) | 5.50560 | − | 8.58048i | 0.211754 | − | 0.330019i | ||||
\(677\) | 0.112071 | 0.00430726 | 0.00215363 | − | 0.999998i | \(-0.499314\pi\) | ||||
0.00215363 | + | 0.999998i | \(0.499314\pi\) | |||||||
\(678\) | 9.94652 | + | 18.2001i | 0.381994 | + | 0.698970i | ||||
\(679\) | −4.91408 | + | 6.71079i | −0.188585 | + | 0.257537i | ||||
\(680\) | 15.2957 | + | 1.07734i | 0.586562 | + | 0.0413143i | ||||
\(681\) | 19.5346 | 0.748569 | ||||||||
\(682\) | −21.9250 | + | 11.9822i | −0.839551 | + | 0.458822i | ||||
\(683\) | 0.561153 | 0.0214719 | 0.0107360 | − | 0.999942i | \(-0.496583\pi\) | ||||
0.0107360 | + | 0.999942i | \(0.496583\pi\) | |||||||
\(684\) | −3.09754 | − | 1.98752i | −0.118438 | − | 0.0759946i | ||||
\(685\) | 0.767338 | 0.0293185 | ||||||||
\(686\) | 4.55485 | + | 25.7925i | 0.173905 | + | 0.984762i | ||||
\(687\) | 26.4154i | 1.00781i | ||||||||
\(688\) | 8.27643 | + | 18.0539i | 0.315536 | + | 0.688299i | ||||
\(689\) | − | 43.4873i | − | 1.65673i | ||||||
\(690\) | 10.3917 | − | 5.67917i | 0.395606 | − | 0.216202i | ||||
\(691\) | 39.1762i | 1.49033i | 0.666879 | + | 0.745166i | \(0.267630\pi\) | ||||
−0.666879 | + | 0.745166i | \(0.732370\pi\) | |||||||
\(692\) | −9.84337 | + | 15.3409i | −0.374189 | + | 0.583173i | ||||
\(693\) | 5.21059 | + | 3.81553i | 0.197934 | + | 0.144940i | ||||
\(694\) | 19.3271 | − | 10.5624i | 0.733645 | − | 0.400944i | ||||
\(695\) | − | 2.01854i | − | 0.0765676i | ||||||
\(696\) | −0.120614 | + | 1.71243i | −0.00457187 | + | 0.0649094i | ||||
\(697\) | 31.2025 | 1.18188 | ||||||||
\(698\) | 43.1495 | − | 23.5816i | 1.63323 | − | 0.892577i | ||||
\(699\) | − | 42.5395i | − | 1.60899i | ||||||
\(700\) | −4.93673 | + | 1.90492i | −0.186591 | + | 0.0719994i | ||||
\(701\) | 49.6478i | 1.87517i | 0.347753 | + | 0.937586i | \(0.386945\pi\) | ||||
−0.347753 | + | 0.937586i | \(0.613055\pi\) | |||||||
\(702\) | 15.8266 | + | 28.9594i | 0.597337 | + | 1.09300i | ||||
\(703\) | 1.68855 | 0.0636849 | ||||||||
\(704\) | 47.6591 | + | 6.74717i | 1.79622 | + | 0.254294i | ||||
\(705\) | 6.22213i | 0.234339i | ||||||||
\(706\) | 8.48803 | + | 15.5313i | 0.319451 | + | 0.584530i | ||||
\(707\) | 34.7980 | + | 25.4814i | 1.30871 | + | 0.958326i | ||||
\(708\) | −18.4117 | + | 28.6946i | −0.691953 | + | 1.07841i | ||||
\(709\) | − | 13.0064i | − | 0.488465i | −0.969717 | − | 0.244233i | \(-0.921464\pi\) | ||
0.969717 | − | 0.244233i | \(-0.0785360\pi\) | |||||||
\(710\) | 10.4310 | + | 19.0867i | 0.391470 | + | 0.716310i | ||||
\(711\) | 3.54823i | 0.133069i | ||||||||
\(712\) | 5.49518 | + | 0.387051i | 0.205941 | + | 0.0145053i | ||||
\(713\) | 15.2658i | 0.571709i | ||||||||
\(714\) | −32.3880 | − | 4.29675i | −1.21209 | − | 0.160802i | ||||
\(715\) | −25.5961 | −0.957240 | ||||||||
\(716\) | 11.8287 | − | 18.4351i | 0.442061 | − | 0.688952i | ||||
\(717\) | −2.72060 | −0.101603 | ||||||||
\(718\) | −21.0755 | − | 38.5638i | −0.786529 | − | 1.43919i | ||||
\(719\) | −12.4976 | −0.466081 | −0.233041 | − | 0.972467i | \(-0.574868\pi\) | ||||
−0.233041 | + | 0.972467i | \(0.574868\pi\) | |||||||
\(720\) | 0.676253 | + | 1.47515i | 0.0252024 | + | 0.0549757i | ||||
\(721\) | 25.3893 | + | 18.5917i | 0.945546 | + | 0.692391i | ||||
\(722\) | 1.95355 | − | 1.06763i | 0.0727037 | − | 0.0397332i | ||||
\(723\) | −8.45800 | −0.314556 | ||||||||
\(724\) | 20.3026 | − | 31.6415i | 0.754539 | − | 1.17595i | ||||
\(725\) | − | 0.376818i | − | 0.0139947i | ||||||
\(726\) | −27.5299 | − | 50.3741i | −1.02173 | − | 1.86956i | ||||
\(727\) | −49.8167 | −1.84760 | −0.923800 | − | 0.382875i | \(-0.874934\pi\) | ||||
−0.923800 | + | 0.382875i | \(0.874934\pi\) | |||||||
\(728\) | −20.5663 | + | 24.2999i | −0.762237 | + | 0.900615i | ||||
\(729\) | −29.5969 | −1.09618 | ||||||||
\(730\) | −5.94899 | − | 10.8854i | −0.220182 | − | 0.402888i | ||||
\(731\) | − | 26.9172i | − | 0.995570i | ||||||
\(732\) | 15.1288 | + | 9.70726i | 0.559175 | + | 0.358791i | ||||
\(733\) | 48.8875 | 1.80570 | 0.902850 | − | 0.429955i | \(-0.141471\pi\) | ||||
0.902850 | + | 0.429955i | \(0.141471\pi\) | |||||||
\(734\) | −17.4410 | + | 9.53168i | −0.643760 | + | 0.351821i | ||||
\(735\) | 10.7487 | − | 3.40390i | 0.396472 | − | 0.125555i | ||||
\(736\) | 17.5819 | − | 23.5752i | 0.648079 | − | 0.868992i | ||||
\(737\) | 4.70872 | 0.173448 | ||||||||
\(738\) | 1.58362 | + | 2.89770i | 0.0582940 | + | 0.106666i | ||||
\(739\) | −39.3743 | −1.44841 | −0.724204 | − | 0.689585i | \(-0.757793\pi\) | ||||
−0.724204 | + | 0.689585i | \(0.757793\pi\) | |||||||
\(740\) | −0.626629 | − | 0.402072i | −0.0230353 | − | 0.0147805i | ||||
\(741\) | −31.0800 | −1.14175 | ||||||||
\(742\) | −5.03020 | + | 37.9166i | −0.184664 | + | 1.39196i | ||||
\(743\) | − | 35.6179i | − | 1.30669i | −0.757059 | − | 0.653346i | \(-0.773365\pi\) | ||
0.757059 | − | 0.653346i | \(-0.226635\pi\) | |||||||
\(744\) | 13.3441 | + | 0.939887i | 0.489219 | + | 0.0344579i | ||||
\(745\) | − | 4.23267i | − | 0.155073i | ||||||
\(746\) | 13.4012 | + | 24.5215i | 0.490654 | + | 0.897797i | ||||
\(747\) | − | 3.41895i | − | 0.125093i | ||||||
\(748\) | −54.9062 | − | 35.2302i | −2.00757 | − | 1.28814i | ||||
\(749\) | −22.3697 | − | 16.3806i | −0.817373 | − | 0.598534i | ||||
\(750\) | 1.09238 | + | 1.99883i | 0.0398880 | + | 0.0729869i | ||||
\(751\) | 13.2839i | 0.484738i | 0.970184 | + | 0.242369i | \(0.0779245\pi\) | ||||
−0.970184 | + | 0.242369i | \(0.922076\pi\) | |||||||
\(752\) | 6.43931 | + | 14.0465i | 0.234817 | + | 0.512223i | ||||
\(753\) | 22.5000 | 0.819946 | ||||||||
\(754\) | −1.08718 | − | 1.98932i | −0.0395929 | − | 0.0724469i | ||||
\(755\) | 0.625768i | 0.0227740i | ||||||||
\(756\) | −10.4495 | − | 27.0804i | −0.380043 | − | 0.984905i | ||||
\(757\) | − | 20.0483i | − | 0.728666i | −0.931269 | − | 0.364333i | \(-0.881297\pi\) | ||
0.931269 | − | 0.364333i | \(-0.118703\pi\) | |||||||
\(758\) | 0.599413 | − | 0.327585i | 0.0217717 | − | 0.0118984i | ||||
\(759\) | −50.3833 | −1.82880 | ||||||||
\(760\) | −12.7977 | − | 0.901400i | −0.464221 | − | 0.0326972i | ||||
\(761\) | 28.5860i | 1.03624i | 0.855307 | + | 0.518121i | \(0.173368\pi\) | ||||
−0.855307 | + | 0.518121i | \(0.826632\pi\) | |||||||
\(762\) | −7.47808 | + | 4.08684i | −0.270902 | + | 0.148051i | ||||
\(763\) | 1.05791 | − | 1.44471i | 0.0382989 | − | 0.0523019i | ||||
\(764\) | −1.90244 | − | 1.22068i | −0.0688277 | − | 0.0441628i | ||||
\(765\) | − | 2.19936i | − | 0.0795181i | ||||||
\(766\) | −1.35993 | + | 0.743214i | −0.0491363 | + | 0.0268534i | ||||
\(767\) | − | 45.0236i | − | 1.62571i | ||||||
\(768\) | −19.5250 | − | 16.8202i | −0.704547 | − | 0.606945i | ||||
\(769\) | − | 26.3204i | − | 0.949137i | −0.880219 | − | 0.474569i | \(-0.842604\pi\) | ||
0.880219 | − | 0.474569i | \(-0.157396\pi\) | |||||||
\(770\) | 22.3172 | + | 2.96072i | 0.804258 | + | 0.106697i | ||||
\(771\) | −34.9418 | −1.25840 | ||||||||
\(772\) | −3.53568 | + | 5.51035i | −0.127252 | + | 0.198322i | ||||
\(773\) | −0.586223 | −0.0210850 | −0.0105425 | − | 0.999944i | \(-0.503356\pi\) | ||||
−0.0105425 | + | 0.999944i | \(0.503356\pi\) | |||||||
\(774\) | 2.49974 | − | 1.36613i | 0.0898514 | − | 0.0491046i | ||||
\(775\) | −2.93636 | −0.105477 | ||||||||
\(776\) | 8.86994 | + | 0.624750i | 0.318412 | + | 0.0224272i | ||||
\(777\) | 1.27993 | + | 0.937249i | 0.0459173 | + | 0.0336236i | ||||
\(778\) | 12.4282 | + | 22.7410i | 0.445571 | + | 0.815303i | ||||
\(779\) | −26.1067 | −0.935370 | ||||||||
\(780\) | 11.5339 | + | 7.40066i | 0.412981 | + | 0.264986i | ||||
\(781\) | − | 92.5401i | − | 3.31135i | ||||||
\(782\) | −34.9764 | + | 19.1149i | −1.25075 | + | 0.683548i | ||||
\(783\) | 2.06703 | 0.0738698 | ||||||||
\(784\) | 20.7425 | − | 18.8082i | 0.740804 | − | 0.671721i | ||||
\(785\) | −2.91713 | −0.104117 | ||||||||
\(786\) | −35.1343 | + | 19.2012i | −1.25320 | + | 0.684885i | ||||
\(787\) | 12.7886i | 0.455864i | 0.973677 | + | 0.227932i | \(0.0731964\pi\) | ||||
−0.973677 | + | 0.227932i | \(0.926804\pi\) | |||||||
\(788\) | −35.7281 | − | 22.9247i | −1.27276 | − | 0.816657i | ||||
\(789\) | 9.48642 | 0.337725 | ||||||||
\(790\) | 5.93167 | + | 10.8537i | 0.211039 | + | 0.386159i | ||||
\(791\) | 19.4366 | + | 14.2328i | 0.691087 | + | 0.506059i | ||||
\(792\) | 0.485087 | − | 6.88706i | 0.0172368 | − | 0.244721i | ||||
\(793\) | −23.7380 | −0.842960 | ||||||||
\(794\) | 0.890962 | − | 0.486919i | 0.0316191 | − | 0.0172801i | ||||
\(795\) | 16.4651 | 0.583957 | ||||||||
\(796\) | 19.3996 | − | 30.2342i | 0.687600 | − | 1.07162i | ||||
\(797\) | 27.5991 | 0.977609 | 0.488805 | − | 0.872393i | \(-0.337433\pi\) | ||||
0.488805 | + | 0.872393i | \(0.337433\pi\) | |||||||
\(798\) | 27.0986 | + | 3.59504i | 0.959282 | + | 0.127263i | ||||
\(799\) | − | 20.9424i | − | 0.740890i | ||||||
\(800\) | 4.53465 | + | 3.38186i | 0.160324 | + | 0.119567i | ||||
\(801\) | − | 0.790151i | − | 0.0279186i | ||||||
\(802\) | 26.2020 | − | 14.3196i | 0.925223 | − | 0.505643i | ||||
\(803\) | 52.7771i | 1.86247i | ||||||||
\(804\) | −2.12181 | − | 1.36144i | −0.0748304 | − | 0.0480144i | ||||
\(805\) | 8.12649 | − | 11.0977i | 0.286421 | − | 0.391144i | ||||
\(806\) | −15.5018 | + | 8.47189i | −0.546028 | + | 0.298410i | ||||
\(807\) | − | 21.4986i | − | 0.756786i | ||||||
\(808\) | 3.23957 | − | 45.9940i | 0.113968 | − | 1.61806i | ||||
\(809\) | −19.2283 | −0.676030 | −0.338015 | − | 0.941141i | \(-0.609755\pi\) | ||||
−0.338015 | + | 0.941141i | \(0.609755\pi\) | |||||||
\(810\) | −9.45421 | + | 5.16681i | −0.332187 | + | 0.181543i | ||||
\(811\) | 7.93942i | 0.278791i | 0.990237 | + | 0.139395i | \(0.0445159\pi\) | ||||
−0.990237 | + | 0.139395i | \(0.955484\pi\) | |||||||
\(812\) | 0.717809 | + | 1.86025i | 0.0251902 | + | 0.0652818i | ||||
\(813\) | − | 39.9301i | − | 1.40041i | ||||||
\(814\) | 1.51908 | + | 2.77960i | 0.0532437 | + | 0.0974250i | ||||
\(815\) | 7.14397 | 0.250242 | ||||||||
\(816\) | 14.5553 | + | 31.7503i | 0.509536 | + | 1.11148i | ||||
\(817\) | 22.5213i | 0.787921i | ||||||||
\(818\) | −0.736596 | − | 1.34782i | −0.0257545 | − | 0.0471254i | ||||
\(819\) | 3.68409 | + | 2.69773i | 0.128733 | + | 0.0942664i | ||||
\(820\) | 9.68833 | + | 6.21644i | 0.338331 | + | 0.217088i | ||||
\(821\) | − | 26.3775i | − | 0.920582i | −0.887768 | − | 0.460291i | \(-0.847745\pi\) | ||
0.887768 | − | 0.460291i | \(-0.152255\pi\) | |||||||
\(822\) | 0.838224 | + | 1.53378i | 0.0292364 | + | 0.0534967i | ||||
\(823\) | 21.7419i | 0.757875i | 0.925422 | + | 0.378938i | \(0.123711\pi\) | ||||
−0.925422 | + | 0.378938i | \(0.876289\pi\) | |||||||
\(824\) | 2.36365 | − | 33.5581i | 0.0823416 | − | 1.16905i | ||||
\(825\) | − | 9.69116i | − | 0.337403i | ||||||
\(826\) | −5.20790 | + | 39.2560i | −0.181206 | + | 1.36589i | ||||
\(827\) | 57.4711 | 1.99846 | 0.999232 | − | 0.0391762i | \(-0.0124734\pi\) | ||||
0.999232 | + | 0.0391762i | \(0.0124734\pi\) | |||||||
\(828\) | −3.55032 | − | 2.27804i | −0.123382 | − | 0.0791672i | ||||
\(829\) | −7.16668 | −0.248909 | −0.124455 | − | 0.992225i | \(-0.539718\pi\) | ||||
−0.124455 | + | 0.992225i | \(0.539718\pi\) | |||||||
\(830\) | −5.71554 | − | 10.4583i | −0.198389 | − | 0.363012i | ||||
\(831\) | −3.36740 | −0.116814 | ||||||||
\(832\) | 33.6969 | + | 4.77051i | 1.16823 | + | 0.165388i | ||||
\(833\) | −36.1779 | + | 11.4568i | −1.25349 | + | 0.396955i | ||||
\(834\) | 4.03472 | − | 2.20501i | 0.139711 | − | 0.0763533i | ||||
\(835\) | 6.26796 | 0.216912 | ||||||||
\(836\) | 45.9393 | + | 29.4766i | 1.58884 | + | 1.01947i | ||||
\(837\) | − | 16.1074i | − | 0.556753i | ||||||
\(838\) | 0.141140 | + | 0.258257i | 0.00487559 | + | 0.00892133i | ||||
\(839\) | −12.0764 | −0.416922 | −0.208461 | − | 0.978031i | \(-0.566845\pi\) | ||||
−0.208461 | + | 0.978031i | \(0.566845\pi\) | |||||||
\(840\) | −9.20040 | − | 7.78677i | −0.317444 | − | 0.268669i | ||||
\(841\) | 28.8580 | 0.995104 | ||||||||
\(842\) | −6.43288 | − | 11.7708i | −0.221692 | − | 0.405650i | ||||
\(843\) | − | 6.59061i | − | 0.226993i | ||||||
\(844\) | −8.03184 | + | 12.5176i | −0.276467 | + | 0.430874i | ||||
\(845\) | −5.09746 | −0.175358 | ||||||||
\(846\) | 1.94488 | − | 1.06289i | 0.0668662 | − | 0.0365430i | ||||
\(847\) | −53.7966 | − | 39.3934i | −1.84847 | − | 1.35357i | ||||
\(848\) | 37.1700 | − | 17.0398i | 1.27642 | − | 0.585149i | ||||
\(849\) | −9.53998 | −0.327411 | ||||||||
\(850\) | −3.67672 | − | 6.72765i | −0.126111 | − | 0.230757i | ||||
\(851\) | 1.93537 | 0.0663436 | ||||||||
\(852\) | −26.7563 | + | 41.6998i | −0.916657 | + | 1.42861i | ||||
\(853\) | −40.3302 | −1.38088 | −0.690440 | − | 0.723390i | \(-0.742583\pi\) | ||||
−0.690440 | + | 0.723390i | \(0.742583\pi\) | |||||||
\(854\) | 20.6971 | + | 2.74578i | 0.708241 | + | 0.0939588i | ||||
\(855\) | 1.84018i | 0.0629327i | ||||||||
\(856\) | −2.08254 | + | 29.5671i | −0.0711798 | + | 1.01058i | ||||
\(857\) | 13.5485i | 0.462810i | 0.972858 | + | 0.231405i | \(0.0743322\pi\) | ||||
−0.972858 | + | 0.231405i | \(0.925668\pi\) | |||||||
\(858\) | −27.9607 | − | 51.1623i | −0.954561 | − | 1.74665i | ||||
\(859\) | 24.4181i | 0.833136i | 0.909105 | + | 0.416568i | \(0.136767\pi\) | ||||
−0.909105 | + | 0.416568i | \(0.863233\pi\) | |||||||
\(860\) | 5.36270 | − | 8.35776i | 0.182866 | − | 0.284997i | ||||
\(861\) | −19.7890 | − | 14.4908i | −0.674409 | − | 0.493846i | ||||
\(862\) | 9.28465 | + | 16.9890i | 0.316236 | + | 0.578648i | ||||
\(863\) | 33.4276i | 1.13789i | 0.822376 | + | 0.568945i | \(0.192648\pi\) | ||||
−0.822376 | + | 0.568945i | \(0.807352\pi\) | |||||||
\(864\) | −18.5512 | + | 24.8748i | −0.631124 | + | 0.846258i | ||||
\(865\) | 9.11366 | 0.309874 | ||||||||
\(866\) | 4.39754 | + | 8.04659i | 0.149434 | + | 0.273434i | ||||
\(867\) | − | 19.9561i | − | 0.677743i | ||||||
\(868\) | 14.4960 | − | 5.59354i | 0.492026 | − | 0.189857i | ||||
\(869\) | − | 52.6234i | − | 1.78513i | ||||||
\(870\) | 0.753195 | − | 0.411628i | 0.0255357 | − | 0.0139555i | ||||
\(871\) | 3.32925 | 0.112807 | ||||||||
\(872\) | −1.90953 | − | 0.134497i | −0.0646649 | − | 0.00455464i | ||||
\(873\) | − | 1.27541i | − | 0.0431660i | ||||||
\(874\) | 29.2643 | − | 15.9932i | 0.989879 | − | 0.540978i | ||||
\(875\) | 2.13463 | + | 1.56312i | 0.0721638 | + | 0.0528430i | ||||
\(876\) | 15.2596 | − | 23.7821i | 0.515573 | − | 0.803521i | ||||
\(877\) | 33.1528i | 1.11949i | 0.828664 | + | 0.559746i | \(0.189101\pi\) | ||||
−0.828664 | + | 0.559746i | \(0.810899\pi\) | |||||||
\(878\) | 11.2236 | − | 6.13378i | 0.378777 | − | 0.207005i | ||||
\(879\) | − | 15.2100i | − | 0.513019i | ||||||
\(880\) | −10.0294 | − | 21.8778i | −0.338092 | − | 0.737502i | ||||
\(881\) | − | 52.3710i | − | 1.76442i | −0.470853 | − | 0.882212i | \(-0.656054\pi\) | ||
0.470853 | − | 0.882212i | \(-0.343946\pi\) | |||||||
\(882\) | −2.90011 | − | 2.77829i | −0.0976518 | − | 0.0935500i | ||||
\(883\) | 3.17165 | 0.106735 | 0.0533673 | − | 0.998575i | \(-0.483005\pi\) | ||||
0.0533673 | + | 0.998575i | \(0.483005\pi\) | |||||||
\(884\) | −38.8209 | − | 24.9091i | −1.30569 | − | 0.837784i | ||||
\(885\) | 17.0468 | 0.573020 | ||||||||
\(886\) | −10.7502 | + | 5.87507i | −0.361159 | + | 0.197377i | ||||
\(887\) | 36.3723 | 1.22126 | 0.610632 | − | 0.791915i | \(-0.290916\pi\) | ||||
0.610632 | + | 0.791915i | \(0.290916\pi\) | |||||||
\(888\) | 0.119157 | − | 1.69174i | 0.00399864 | − | 0.0567711i | ||||
\(889\) | −5.84798 | + | 7.98615i | −0.196135 | + | 0.267847i | ||||
\(890\) | −1.32091 | − | 2.41700i | −0.0442771 | − | 0.0810181i | ||||
\(891\) | 45.8379 | 1.53563 | ||||||||
\(892\) | 25.7749 | − | 40.1701i | 0.863006 | − | 1.34499i | ||||
\(893\) | 17.5223i | 0.586360i | ||||||||
\(894\) | 8.46039 | − | 4.62368i | 0.282958 | − | 0.154639i | ||||
\(895\) | −10.9518 | −0.366080 | ||||||||
\(896\) | −28.8285 | − | 8.05715i | −0.963093 | − | 0.269170i | ||||
\(897\) | −35.6230 | −1.18942 | ||||||||
\(898\) | 32.9863 | − | 18.0273i | 1.10077 | − | 0.601579i | ||||
\(899\) | 1.10647i | 0.0369029i | ||||||||
\(900\) | 0.438177 | − | 0.682898i | 0.0146059 | − | 0.0227633i | ||||
\(901\) | −55.4182 | −1.84625 | ||||||||
\(902\) | −23.4865 | − | 42.9755i | −0.782016 | − | 1.43093i | ||||
\(903\) | −12.5007 | + | 17.0713i | −0.415998 | + | 0.568097i | ||||
\(904\) | 1.80948 | − | 25.6902i | 0.0601824 | − | 0.854445i | ||||
\(905\) | −18.7975 | −0.624850 | ||||||||
\(906\) | −1.25080 | + | 0.683576i | −0.0415552 | + | 0.0227103i | ||||
\(907\) | −13.5038 | −0.448388 | −0.224194 | − | 0.974545i | \(-0.571975\pi\) | ||||
−0.224194 | + | 0.974545i | \(0.571975\pi\) | |||||||
\(908\) | −20.4152 | − | 13.0992i | −0.677501 | − | 0.434713i | ||||
\(909\) | −6.61347 | −0.219355 | ||||||||
\(910\) | 15.7792 | + | 2.09334i | 0.523075 | + | 0.0693936i | ||||
\(911\) | − | 6.93039i | − | 0.229614i | −0.993388 | − | 0.114807i | \(-0.963375\pi\) | ||
0.993388 | − | 0.114807i | \(-0.0366250\pi\) | |||||||
\(912\) | −12.1782 | − | 26.5651i | −0.403260 | − | 0.879658i | ||||
\(913\) | 50.7060i | 1.67813i | ||||||||
\(914\) | −41.4529 | + | 22.6544i | −1.37114 | + | 0.749342i | ||||
\(915\) | − | 8.98763i | − | 0.297122i | ||||||
\(916\) | 17.7133 | − | 27.6061i | 0.585262 | − | 0.912131i | ||||
\(917\) | −27.4756 | + | 37.5214i | −0.907325 | + | 1.23907i | ||||
\(918\) | 36.9045 | − | 20.1687i | 1.21803 | − | 0.665665i | ||||
\(919\) | − | 18.9826i | − | 0.626178i | −0.949724 | − | 0.313089i | \(-0.898636\pi\) | ||
0.949724 | − | 0.313089i | \(-0.101364\pi\) | |||||||
\(920\) | −14.6684 | − | 1.03316i | −0.483601 | − | 0.0340622i | ||||
\(921\) | −38.8504 | −1.28017 | ||||||||
\(922\) | −12.0423 | + | 6.58123i | −0.396592 | + | 0.216741i | ||||
\(923\) | − | 65.4295i | − | 2.15364i | ||||||
\(924\) | 18.4609 | + | 47.8426i | 0.607320 | + | 1.57391i | ||||
\(925\) | 0.372265i | 0.0122400i | ||||||||
\(926\) | −19.3975 | − | 35.4935i | −0.637442 | − | 1.16639i | ||||
\(927\) | −4.82531 | −0.158484 | ||||||||
\(928\) | 1.27434 | − | 1.70874i | 0.0418324 | − | 0.0560920i | ||||
\(929\) | 55.6476i | 1.82574i | 0.408250 | + | 0.912870i | \(0.366139\pi\) | ||||
−0.408250 | + | 0.912870i | \(0.633861\pi\) | |||||||
\(930\) | −3.20761 | − | 5.86928i | −0.105182 | − | 0.192461i | ||||
\(931\) | 30.2696 | − | 9.58577i | 0.992046 | − | 0.314161i | ||||
\(932\) | −28.5255 | + | 44.4569i | −0.934383 | + | 1.45624i | ||||
\(933\) | − | 26.7289i | − | 0.875064i | ||||||
\(934\) | −5.84009 | − | 10.6862i | −0.191094 | − | 0.349662i | ||||
\(935\) | 32.6185i | 1.06674i | ||||||||
\(936\) | 0.342975 | − | 4.86942i | 0.0112105 | − | 0.159162i | ||||
\(937\) | − | 30.8690i | − | 1.00845i | −0.863574 | − | 0.504223i | \(-0.831779\pi\) | ||
0.863574 | − | 0.504223i | \(-0.168221\pi\) | |||||||
\(938\) | −2.90277 | − | 0.385096i | −0.0947789 | − | 0.0125738i | ||||
\(939\) | 18.3410 | 0.598537 | ||||||||
\(940\) | 4.17234 | − | 6.50259i | 0.136087 | − | 0.212091i | ||||
\(941\) | −14.1430 | −0.461048 | −0.230524 | − | 0.973067i | \(-0.574044\pi\) | ||||
−0.230524 | + | 0.973067i | \(0.574044\pi\) | |||||||
\(942\) | −3.18661 | − | 5.83084i | −0.103825 | − | 0.189979i | ||||
\(943\) | −29.9228 | −0.974420 | ||||||||
\(944\) | 38.4831 | − | 17.6418i | 1.25252 | − | 0.574190i | ||||
\(945\) | −8.57449 | + | 11.7095i | −0.278928 | + | 0.380911i | ||||
\(946\) | −37.0734 | + | 20.2610i | −1.20536 | + | 0.658741i | ||||
\(947\) | 10.5002 | 0.341212 | 0.170606 | − | 0.985339i | \(-0.445428\pi\) | ||||
0.170606 | + | 0.985339i | \(0.445428\pi\) | |||||||
\(948\) | −15.2151 | + | 23.7128i | −0.494165 | + | 0.770156i | ||||
\(949\) | 37.3155i | 1.21131i | ||||||||
\(950\) | 3.07627 | + | 5.62894i | 0.0998073 | + | 0.182627i | ||||
\(951\) | 43.0188 | 1.39498 | ||||||||
\(952\) | 30.9666 | + | 26.2087i | 1.00363 | + | 0.849428i | ||||
\(953\) | 36.8415 | 1.19341 | 0.596706 | − | 0.802460i | \(-0.296476\pi\) | ||||
0.596706 | + | 0.802460i | \(0.296476\pi\) | |||||||
\(954\) | −2.81264 | − | 5.14656i | −0.0910627 | − | 0.166626i | ||||
\(955\) | 1.13019i | 0.0365721i | ||||||||
\(956\) | 2.84323 | + | 1.82434i | 0.0919566 | + | 0.0590033i | ||||
\(957\) | −3.65180 | −0.118046 | ||||||||
\(958\) | −8.38581 | + | 4.58293i | −0.270933 | + | 0.148068i | ||||
\(959\) | 1.63799 | + | 1.19944i | 0.0528933 | + | 0.0387319i | ||||
\(960\) | −1.80621 | + | 12.7583i | −0.0582950 | + | 0.411771i | ||||
\(961\) | −22.3778 | −0.721865 | ||||||||
\(962\) | 1.07405 | + | 1.96529i | 0.0346287 | + | 0.0633635i | ||||
\(963\) | 4.25144 | 0.137001 | ||||||||
\(964\) | 8.83924 | + | 5.67163i | 0.284693 | + | 0.182671i | ||||
\(965\) | 3.27357 | 0.105380 | ||||||||
\(966\) | 31.0597 | + | 4.12053i | 0.999329 | + | 0.132576i | ||||
\(967\) | 48.0941i | 1.54660i | 0.634040 | + | 0.773301i | \(0.281396\pi\) | ||||
−0.634040 | + | 0.773301i | \(0.718604\pi\) | |||||||
\(968\) | −5.00827 | + | 71.1053i | −0.160972 | + | 2.28541i | ||||
\(969\) | 39.6069i | 1.27236i | ||||||||
\(970\) | −2.13213 | − | 3.90136i | −0.0684585 | − | 0.125265i | ||||
\(971\) | 13.7904i | 0.442555i | 0.975211 | + | 0.221277i | \(0.0710226\pi\) | ||||
−0.975211 | + | 0.221277i | \(0.928977\pi\) | |||||||
\(972\) | 7.04584 | + | 4.52091i | 0.225996 | + | 0.145008i | ||||
\(973\) | 3.15522 | − | 4.30884i | 0.101152 | − | 0.138135i | ||||
\(974\) | −5.23939 | − | 9.58700i | −0.167881 | − | 0.307187i | ||||
\(975\) | − | 6.85203i | − | 0.219441i | ||||||
\(976\) | −9.30134 | − | 20.2896i | −0.297729 | − | 0.649455i | ||||
\(977\) | 19.9730 | 0.638992 | 0.319496 | − | 0.947588i | \(-0.396486\pi\) | ||||
0.319496 | + | 0.947588i | \(0.396486\pi\) | |||||||
\(978\) | 7.80393 | + | 14.2796i | 0.249542 | + | 0.456611i | ||||
\(979\) | 11.7186i | 0.374529i | ||||||||
\(980\) | −13.5157 | − | 3.65037i | −0.431744 | − | 0.116607i | ||||
\(981\) | 0.274571i | 0.00876638i | ||||||||
\(982\) | 41.1569 | − | 22.4926i | 1.31337 | − | 0.717769i | ||||
\(983\) | −50.8845 | −1.62296 | −0.811482 | − | 0.584377i | \(-0.801339\pi\) | ||||
−0.811482 | + | 0.584377i | \(0.801339\pi\) | |||||||
\(984\) | −1.84229 | + | 26.1560i | −0.0587300 | + | 0.833824i | ||||
\(985\) | 21.2252i | 0.676291i | ||||||||
\(986\) | −2.53510 | + | 1.38546i | −0.0807340 | + | 0.0441219i | ||||
\(987\) | −9.72593 | + | 13.2820i | −0.309580 | + | 0.422770i | ||||
\(988\) | 32.4809 | + | 20.8411i | 1.03336 | + | 0.663045i | ||||
\(989\) | 25.8133i | 0.820815i | ||||||||
\(990\) | −3.02920 | + | 1.65549i | −0.0962744 | + | 0.0526149i | ||||
\(991\) | − | 41.0233i | − | 1.30315i | −0.758585 | − | 0.651574i | \(-0.774109\pi\) | ||
0.758585 | − | 0.651574i | \(-0.225891\pi\) | |||||||
\(992\) | −13.3153 | − | 9.93034i | −0.422763 | − | 0.315289i | ||||
\(993\) | − | 5.24060i | − | 0.166305i | ||||||
\(994\) | −7.56827 | + | 57.0480i | −0.240051 | + | 1.80945i | ||||
\(995\) | −17.9614 | −0.569416 | ||||||||
\(996\) | 14.6608 | − | 22.8488i | 0.464544 | − | 0.723992i | ||||
\(997\) | 29.5605 | 0.936189 | 0.468095 | − | 0.883678i | \(-0.344941\pi\) | ||||
0.468095 | + | 0.883678i | \(0.344941\pi\) | |||||||
\(998\) | 11.3365 | − | 6.19548i | 0.358849 | − | 0.196114i | ||||
\(999\) | −2.04206 | −0.0646079 |
(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 | 280.2.h.a.251.4 | yes | 16 | |
4.3 | odd | 2 | 1120.2.h.a.111.5 | 16 | |||
7.6 | odd | 2 | 280.2.h.b.251.4 | yes | 16 | ||
8.3 | odd | 2 | 280.2.h.b.251.3 | yes | 16 | ||
8.5 | even | 2 | 1120.2.h.b.111.5 | 16 | |||
28.27 | even | 2 | 1120.2.h.b.111.12 | 16 | |||
56.13 | odd | 2 | 1120.2.h.a.111.12 | 16 | |||
56.27 | even | 2 | inner | 280.2.h.a.251.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.h.a.251.3 | ✓ | 16 | 56.27 | even | 2 | inner | |
280.2.h.a.251.4 | yes | 16 | 1.1 | even | 1 | trivial | |
280.2.h.b.251.3 | yes | 16 | 8.3 | odd | 2 | ||
280.2.h.b.251.4 | yes | 16 | 7.6 | odd | 2 | ||
1120.2.h.a.111.5 | 16 | 4.3 | odd | 2 | |||
1120.2.h.a.111.12 | 16 | 56.13 | odd | 2 | |||
1120.2.h.b.111.5 | 16 | 8.5 | even | 2 | |||
1120.2.h.b.111.12 | 16 | 28.27 | even | 2 |