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 | 251.3 | ||
Root | \(-1.24098 + 0.678208i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.251 |
Dual form | 280.2.h.b.251.4 |
$q$-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 | \(-0.299152\pi\) | ||||
0.589939 | + | 0.807448i | \(0.299152\pi\) | |||||||
\(14\) | −1.58892 | − | 3.38753i | −0.424657 | − | 0.905354i | ||||
\(15\) | 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 | \(0.182341\pi\) | ||||
−0.840364 | + | 0.542022i | \(0.817659\pi\) | |||||||
\(24\) | 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 | ||||||||
\(28\) | −0.325625 | + | 5.28147i | −0.0615374 | + | 0.998105i | ||||
\(29\) | 0.376818i | 0.0699733i | 0.999388 | + | 0.0349866i | \(0.0111389\pi\) | ||||
−0.999388 | + | 0.0349866i | \(0.988861\pi\) | |||||||
\(30\) | 1.09238 | − | 1.99883i | 0.199440 | − | 0.364935i | ||||
\(31\) | 2.93636 | 0.527385 | 0.263693 | − | 0.964607i | \(-0.415060\pi\) | ||||
0.263693 | + | 0.964607i | \(0.415060\pi\) | |||||||
\(32\) | 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 | \(-0.990258\pi\) | ||
0.999532 | − | 0.0306000i | \(-0.00974181\pi\) | |||||||
\(38\) | −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 | \(-0.148375\pi\) | |||||||
\(42\) | 5.45624 | − | 2.55925i | 0.841916 | − | 0.394901i | ||||
\(43\) | −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 | \(-0.409088\pi\) | ||||
0.281741 | + | 0.959491i | \(0.409088\pi\) | |||||||
\(48\) | −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 | \(-0.752255\pi\) | ||
0.712099 | − | 0.702079i | \(-0.247745\pi\) | |||||||
\(54\) | 3.72031 | − | 6.80740i | 0.506270 | − | 0.926370i | ||||
\(55\) | −6.01679 | −0.811304 | ||||||||
\(56\) | 3.98603 | − | 6.33337i | 0.532656 | − | 0.846332i | ||||
\(57\) | 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 | \(-0.616277\pi\) | ||||
−0.357223 | + | 0.934019i | \(0.616277\pi\) | |||||||
\(62\) | −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 | ||||||||
\(70\) | −1.58892 | − | 3.38753i | −0.189912 | − | 0.404887i | ||||
\(71\) | − | 15.3803i | − | 1.82531i | −0.408735 | − | 0.912653i | \(-0.634030\pi\) | ||
0.408735 | − | 0.912653i | \(-0.365970\pi\) | |||||||
\(72\) | −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 | \(-0.836264\pi\) | ||
0.870592 | − | 0.492006i | \(-0.163736\pi\) | |||||||
\(80\) | −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 | \(-0.153053\pi\) | |||||||
\(84\) | −8.50679 | − | 0.524480i | −0.928167 | − | 0.0572254i | ||||
\(85\) | 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 | \(-0.0510206\pi\) | |||||||
\(98\) | 1.90334 | − | 9.71480i | 0.192266 | − | 0.981343i | ||||
\(99\) | −2.44098 | −0.245327 | ||||||||
\(100\) | 1.08007 | + | 1.68329i | 0.108007 | + | 0.168329i | ||||
\(101\) | 16.3016 | 1.62207 | 0.811037 | − | 0.584995i | \(-0.198904\pi\) | ||||
0.811037 | + | 0.584995i | \(0.198904\pi\) | |||||||
\(102\) | 10.8361 | + | 5.92205i | 1.07294 | + | 0.586370i | ||||
\(103\) | 11.8940 | 1.17195 | 0.585974 | − | 0.810330i | \(-0.300712\pi\) | ||||
0.585974 | + | 0.810330i | \(0.300712\pi\) | |||||||
\(104\) | −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 | \(-0.989681\pi\) | ||
0.999475 | − | 0.0324126i | \(-0.0103190\pi\) | |||||||
\(110\) | 7.46673 | + | 4.08064i | 0.711925 | + | 0.389073i | ||||
\(111\) | 0.599602 | 0.0569117 | ||||||||
\(112\) | −9.24193 | + | 5.15623i | −0.873280 | + | 0.487218i | ||||
\(113\) | −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 | ||||||||
\(126\) | −0.644615 | − | 1.37430i | −0.0574269 | − | 0.122432i | ||||
\(127\) | 3.74123i | 0.331980i | 0.986127 | + | 0.165990i | \(0.0530820\pi\) | ||||
−0.986127 | + | 0.165990i | \(0.946918\pi\) | |||||||
\(128\) | 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 | \(0.972718\pi\) | |||||||
\(140\) | −0.325625 | + | 5.28147i | −0.0275204 | + | 0.446366i | ||||
\(141\) | 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 | \(-0.944532\pi\) | ||
0.984856 | − | 0.173377i | \(-0.0554679\pi\) | |||||||
\(150\) | 1.09238 | − | 1.99883i | 0.0891924 | − | 0.163204i | ||||
\(151\) | 0.625768i | 0.0509243i | 0.999676 | + | 0.0254622i | \(0.00810573\pi\) | ||||
−0.999676 | + | 0.0254622i | \(0.991894\pi\) | |||||||
\(152\) | −12.7977 | + | 0.901400i | −1.03803 | + | 0.0731132i | ||||
\(153\) | 2.19936i | 0.177808i | ||||||||
\(154\) | 9.56021 | + | 20.3820i | 0.770384 | + | 1.64243i | ||||
\(155\) | 2.93636 | 0.235854 | ||||||||
\(156\) | −11.5339 | + | 7.40066i | −0.923454 | + | 0.592527i | ||||
\(157\) | −2.91713 | −0.232812 | −0.116406 | − | 0.993202i | \(-0.537137\pi\) | ||||
−0.116406 | + | 0.993202i | \(0.537137\pi\) | |||||||
\(158\) | −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 | \(-0.422028\pi\) | ||||
0.242515 | + | 0.970148i | \(0.422028\pi\) | |||||||
\(168\) | 10.2011 | + | 6.42024i | 0.787029 | + | 0.495332i | ||||
\(169\) | 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 | \(-0.387387\pi\) | ||||
0.346449 | + | 0.938069i | \(0.387387\pi\) | |||||||
\(174\) | 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 | \(-0.746195\pi\) | ||||
−0.698603 | + | 0.715509i | \(0.746195\pi\) | |||||||
\(182\) | −6.75945 | − | 14.4109i | −0.501043 | − | 1.06821i | ||||
\(183\) | − | 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 | \(0.0130190\pi\) | ||||
−0.999164 | + | 0.0408889i | \(0.986981\pi\) | |||||||
\(192\) | −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 | ||||||||
\(196\) | −8.95066 | + | 10.7650i | −0.639333 | + | 0.768930i | ||||
\(197\) | 21.2252i | 1.51223i | 0.654437 | + | 0.756116i | \(0.272906\pi\) | ||||
−0.654437 | + | 0.756116i | \(0.727094\pi\) | |||||||
\(198\) | 3.02920 | + | 1.65549i | 0.215276 | + | 0.117650i | ||||
\(199\) | −17.9614 | −1.27325 | −0.636626 | − | 0.771172i | \(-0.719671\pi\) | ||||
−0.636626 | + | 0.771172i | \(0.719671\pi\) | |||||||
\(200\) | −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 | ||||||||
\(210\) | 5.45624 | − | 2.55925i | 0.376516 | − | 0.176605i | ||||
\(211\) | −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 | \(-0.794653\pi\) | ||||
−0.799029 | + | 0.601293i | \(0.794653\pi\) | |||||||
\(224\) | 14.9661 | − | 0.130838i | 0.999962 | − | 0.00874200i | ||||
\(225\) | 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 | \(-0.682285\pi\) | ||||
−0.541875 | + | 0.840459i | \(0.682285\pi\) | |||||||
\(230\) | 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 | ||||||||
\(238\) | 18.3646 | − | 8.61392i | 1.19040 | − | 0.558357i | ||||
\(239\) | − | 1.68909i | − | 0.109258i | −0.998507 | − | 0.0546292i | \(-0.982602\pi\) | ||
0.998507 | − | 0.0546292i | \(-0.0173977\pi\) | |||||||
\(240\) | −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 | \(-0.145328\pi\) | |||||||
\(252\) | −0.132104 | + | 2.14266i | −0.00832178 | + | 0.134975i | ||||
\(253\) | − | 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 | \(0.0581232\pi\) | ||||
−0.983375 | + | 0.181587i | \(0.941877\pi\) | |||||||
\(264\) | −27.3430 | + | 1.92589i | −1.68285 | + | 0.118530i | ||||
\(265\) | − | 10.2224i | − | 0.627958i | ||||||
\(266\) | −15.3654 | + | 7.20715i | −0.942114 | + | 0.441899i | ||||
\(267\) | 3.13706 | 0.191985 | ||||||||
\(268\) | −0.845257 | − | 1.31733i | −0.0516323 | − | 0.0804689i | ||||
\(269\) | 13.3475 | 0.813810 | 0.406905 | − | 0.913470i | \(-0.366608\pi\) | ||||
0.406905 | + | 0.913470i | \(0.366608\pi\) | |||||||
\(270\) | 3.72031 | − | 6.80740i | 0.226411 | − | 0.414285i | ||||
\(271\) | 24.7908 | 1.50593 | 0.752966 | − | 0.658059i | \(-0.228622\pi\) | ||||
0.752966 | + | 0.658059i | \(0.228622\pi\) | |||||||
\(272\) | −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 | \(-0.979994\pi\) | ||
0.998026 | − | 0.0628078i | \(-0.0200055\pi\) | |||||||
\(278\) | 1.36899 | − | 2.50497i | 0.0821065 | − | 0.150238i | ||||
\(279\) | 1.19126 | 0.0713189 | ||||||||
\(280\) | 3.98603 | − | 6.33337i | 0.238211 | − | 0.378491i | ||||
\(281\) | −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 | \(-0.411045\pi\) | ||||
0.275838 | + | 0.961204i | \(0.411045\pi\) | |||||||
\(294\) | 15.6475 | + | 3.06568i | 0.912580 | + | 0.178794i | ||||
\(295\) | 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 | \(0.758351\pi\) | |||||||
\(308\) | 1.95922 | − | 31.7775i | 0.111637 | − | 1.81069i | ||||
\(309\) | 19.1574i | 1.08983i | ||||||||
\(310\) | −3.64396 | − | 1.99146i | −0.206963 | − | 0.113107i | ||||
\(311\) | 16.5947 | 0.941001 | 0.470500 | − | 0.882400i | \(-0.344073\pi\) | ||||
0.470500 | + | 0.882400i | \(0.344073\pi\) | |||||||
\(312\) | 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 | \(0.269969\pi\) | ||||
−0.661386 | + | 0.750046i | \(0.730031\pi\) | |||||||
\(318\) | −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 | ||||||||
\(322\) | 17.6114 | − | 8.26064i | 0.981445 | − | 0.460347i | ||||
\(323\) | 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 | ||||||||
\(336\) | −8.30507 | − | 14.8858i | −0.453079 | − | 0.812089i | ||||
\(337\) | −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 | \(-0.119277\pi\) | ||||
0.930610 | + | 0.366012i | \(0.119277\pi\) | |||||||
\(350\) | −1.58892 | − | 3.38753i | −0.0849314 | − | 0.181071i | ||||
\(351\) | 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 | \(-0.693949\pi\) | ||
0.572301 | − | 0.820044i | \(-0.306051\pi\) | |||||||
\(360\) | −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 | ||||||||
\(364\) | −1.38525 | + | 22.4680i | −0.0726066 | + | 1.17764i | ||||
\(365\) | − | 8.77164i | − | 0.459129i | ||||||
\(366\) | −6.09548 | + | 11.1535i | −0.318616 | + | 0.583002i | ||||
\(367\) | −14.0542 | −0.733624 | −0.366812 | − | 0.930295i | \(-0.619551\pi\) | ||||
−0.366812 | + | 0.930295i | \(0.619551\pi\) | |||||||
\(368\) | −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 | \(0.170933\pi\) | ||||
−0.859247 | + | 0.511561i | \(0.829067\pi\) | |||||||
\(374\) | −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 | ||||||||
\(378\) | 18.5823 | − | 8.71603i | 0.955769 | − | 0.448304i | ||||
\(379\) | −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 | \(-0.508913\pi\) | ||||
−0.0279977 | + | 0.999608i | \(0.508913\pi\) | |||||||
\(384\) | −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 | \(0.153786\pi\) | ||||
−0.885543 | + | 0.464557i | \(0.846214\pi\) | |||||||
\(390\) | 4.64710 | − | 8.50324i | 0.235315 | − | 0.430578i | ||||
\(391\) | −28.1844 | −1.42535 | ||||||||
\(392\) | 18.4085 | − | 7.28878i | 0.929771 | − | 0.368139i | ||||
\(393\) | 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 | \(-0.494265\pi\) | ||||
0.0180164 | + | 0.999838i | \(0.494265\pi\) | |||||||
\(398\) | 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 | ||||||||
\(406\) | 1.27648 | − | 0.598734i | 0.0633506 | − | 0.0297147i | ||||
\(407\) | 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 | \(-0.00161808\pi\) | |||||||
\(420\) | −8.50679 | − | 0.524480i | −0.415089 | − | 0.0255920i | ||||
\(421\) | − | 9.48511i | − | 0.462276i | −0.972921 | − | 0.231138i | \(-0.925755\pi\) | ||
0.972921 | − | 0.231138i | \(-0.0742449\pi\) | |||||||
\(422\) | 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 | \(0.106951\pi\) | ||||
−0.944082 | + | 0.329711i | \(0.893049\pi\) | |||||||
\(432\) | −19.9460 | − | 9.14381i | −0.959651 | − | 0.439932i | ||||
\(433\) | − | 6.48406i | − | 0.311604i | −0.987788 | − | 0.155802i | \(-0.950204\pi\) | ||
0.987788 | − | 0.155802i | \(-0.0497962\pi\) | |||||||
\(434\) | −4.66564 | − | 9.94698i | −0.223958 | − | 0.477470i | ||||
\(435\) | −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 | \(-0.430756\pi\) | ||||
0.215826 | + | 0.976432i | \(0.430756\pi\) | |||||||
\(440\) | 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 | ||||||||
\(448\) | −18.6613 | − | 9.98773i | −0.881665 | − | 0.471876i | ||||
\(449\) | −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 | \(-0.572557\pi\) | ||||
−0.225977 | + | 0.974133i | \(0.572557\pi\) | |||||||
\(462\) | −32.8291 | + | 15.3985i | −1.52735 | + | 0.716403i | ||||
\(463\) | − | 28.6011i | − | 1.32921i | −0.747196 | − | 0.664604i | \(-0.768600\pi\) | ||
0.747196 | − | 0.664604i | \(-0.231400\pi\) | |||||||
\(464\) | −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 | ||||||
\(476\) | −28.6321 | − | 1.76529i | −1.31235 | − | 0.0809120i | ||||
\(477\) | − | 4.14717i | − | 0.189886i | ||||||
\(478\) | −1.14556 | + | 2.09613i | −0.0523965 | + | 0.0958749i | ||||
\(479\) | −6.75741 | −0.308754 | −0.154377 | − | 0.988012i | \(-0.549337\pi\) | ||||
−0.154377 | + | 0.988012i | \(0.549337\pi\) | |||||||
\(480\) | 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 | \(-0.943996\pi\) | ||
0.984562 | − | 0.175034i | \(-0.0560036\pi\) | |||||||
\(488\) | 1.10890 | + | 15.7436i | 0.0501974 | + | 0.712681i | ||||
\(489\) | − | 11.5067i | − | 0.520350i | ||||||
\(490\) | 1.90334 | − | 9.71480i | 0.0859841 | − | 0.438870i | ||||
\(491\) | −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 | \(-0.399457\pi\) | ||||
0.310639 | + | 0.950528i | \(0.399457\pi\) | |||||||
\(504\) | 1.61711 | − | 2.56941i | 0.0720317 | − | 0.114450i | ||||
\(505\) | 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 | \(-0.581568\pi\) | ||||
−0.253459 | + | 0.967346i | \(0.581568\pi\) | |||||||
\(510\) | 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 | ||||||||
\(518\) | −1.26106 | + | 0.591500i | −0.0554077 | + | 0.0259890i | ||||
\(519\) | 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 | ||||||||
\(532\) | 23.9561 | + | 1.47700i | 1.03863 | + | 0.0640359i | ||||
\(533\) | − | 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 | \(-0.832182\pi\) | ||
0.864211 | − | 0.503129i | \(-0.167818\pi\) | |||||||
\(542\) | −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 | ||||||
\(546\) | 23.2114 | − | 10.8873i | 0.993358 | − | 0.465935i | ||||
\(547\) | 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 | \(-0.986045\pi\) | ||
0.999039 | − | 0.0438270i | \(-0.0139551\pi\) | |||||||
\(558\) | −1.47833 | − | 0.807922i | −0.0625828 | − | 0.0342021i | ||||
\(559\) | −21.1223 | −0.893378 | ||||||||
\(560\) | −9.24193 | + | 5.15623i | −0.390543 | + | 0.217891i | ||||
\(561\) | 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 | ||||||||
\(574\) | −19.4972 | + | 9.14520i | −0.813799 | + | 0.381713i | ||||
\(575\) | 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 | \(0.964972\pi\) | |||||||
\(588\) | −17.3391 | − | 14.4167i | −0.715051 | − | 0.594534i | ||||
\(589\) | − | 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 | \(-0.847935\pi\) | ||
0.888042 | − | 0.459762i | \(-0.152065\pi\) | |||||||
\(600\) | 4.54445 | − | 0.320086i | 0.185526 | − | 0.0130675i | ||||
\(601\) | 4.49699i | 0.183436i | 0.995785 | + | 0.0917181i | \(0.0292359\pi\) | ||||
−0.995785 | + | 0.0917181i | \(0.970764\pi\) | |||||||
\(602\) | 7.88923 | + | 16.8196i | 0.321541 | + | 0.685514i | ||||
\(603\) | −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 | \(-0.429060\pi\) | ||||
0.221025 | + | 0.975268i | \(0.429060\pi\) | |||||||
\(608\) | −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 | \(-0.788739\pi\) | ||
0.787721 | − | 0.616032i | \(-0.211261\pi\) | |||||||
\(614\) | 16.3587 | − | 29.9330i | 0.660182 | − | 1.20800i | ||||
\(615\) | 9.27046 | 0.373821 | ||||||||
\(616\) | −23.9831 | + | 38.1066i | −0.966308 | + | 1.53536i | ||||
\(617\) | −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 | ||||||||
\(630\) | −0.644615 | − | 1.37430i | −0.0256821 | − | 0.0547533i | ||||
\(631\) | 36.7721i | 1.46387i | 0.681373 | + | 0.731936i | \(0.261383\pi\) | ||||
−0.681373 | + | 0.731936i | \(0.738617\pi\) | |||||||
\(632\) | −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 | \(-0.0782114\pi\) | |||||||
\(644\) | −27.4578 | − | 1.69289i | −1.08199 | − | 0.0667093i | ||||
\(645\) | − | 7.99729i | − | 0.314893i | ||||||
\(646\) | −30.5158 | − | 16.6772i | −1.20063 | − | 0.656155i | ||||
\(647\) | −47.9622 | −1.88559 | −0.942794 | − | 0.333376i | \(-0.891812\pi\) | ||||
−0.942794 | + | 0.333376i | \(0.891812\pi\) | |||||||
\(648\) | 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 | \(0.255435\pi\) | ||||
−0.694930 | + | 0.719077i | \(0.744565\pi\) | |||||||
\(654\) | −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 | ||||||
\(658\) | −6.13806 | − | 13.0861i | −0.239286 | − | 0.510150i | ||||
\(659\) | 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 | \(-0.538514\pi\) | ||||
−0.120700 | + | 0.992689i | \(0.538514\pi\) | |||||||
\(662\) | 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 | ||||||||
\(672\) | 0.210739 | + | 24.1056i | 0.00812945 | + | 0.929894i | ||||
\(673\) | −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 | \(-0.500686\pi\) | ||||
−0.00215363 | + | 0.999998i | \(0.500686\pi\) | |||||||
\(678\) | −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 | ||||||||
\(686\) | 19.2483 | − | 17.7624i | 0.734904 | − | 0.678171i | ||||
\(687\) | − | 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 | ||||||
\(700\) | −0.325625 | + | 5.28147i | −0.0123075 | + | 0.199621i | ||||
\(701\) | − | 49.6478i | − | 1.87517i | −0.347753 | − | 0.937586i | \(-0.613055\pi\) | ||
0.347753 | − | 0.937586i | \(-0.386945\pi\) | |||||||
\(702\) | 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 | \(0.0785360\pi\) | ||||
−0.969717 | + | 0.244233i | \(0.921464\pi\) | |||||||
\(710\) | −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 | ||||||||
\(714\) | 13.8743 | + | 29.5795i | 0.519233 | + | 1.10699i | ||||
\(715\) | −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 | \(-0.425132\pi\) | ||||
0.233041 | + | 0.972467i | \(0.425132\pi\) | |||||||
\(720\) | −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 | \(-0.125066\pi\) | ||||
0.923800 | + | 0.382875i | \(0.125066\pi\) | |||||||
\(728\) | 16.9570 | − | 26.9428i | 0.628469 | − | 0.998568i | ||||
\(729\) | −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 | \(-0.858529\pi\) | ||||
−0.902850 | + | 0.429955i | \(0.858529\pi\) | |||||||
\(734\) | 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 | ||||||||
\(742\) | −34.6287 | + | 16.2426i | −1.27126 | + | 0.596285i | ||||
\(743\) | 35.6179i | 1.30669i | 0.757059 | + | 0.653346i | \(0.226635\pi\) | ||||
−0.757059 | + | 0.653346i | \(0.773365\pi\) | |||||||
\(744\) | 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 | \(-0.922076\pi\) | ||
0.970184 | − | 0.242369i | \(-0.0779245\pi\) | |||||||
\(752\) | −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 | ||||||||
\(756\) | −28.9715 | − | 1.78622i | −1.05368 | − | 0.0649641i | ||||
\(757\) | 20.0483i | 0.728666i | 0.931269 | + | 0.364333i | \(0.118703\pi\) | ||||
−0.931269 | + | 0.364333i | \(0.881297\pi\) | |||||||
\(758\) | 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 | \(-0.157396\pi\) | |||||||
\(770\) | 9.56021 | + | 20.3820i | 0.344526 | + | 0.734518i | ||||
\(771\) | −34.9418 | −1.25840 | ||||||||
\(772\) | −3.53568 | − | 5.51035i | −0.127252 | − | 0.198322i | ||||
\(773\) | 0.586223 | 0.0210850 | 0.0105425 | − | 0.999944i | \(-0.496644\pi\) | ||||
0.0105425 | + | 0.999944i | \(0.496644\pi\) | |||||||
\(774\) | 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 | ||||||||
\(784\) | −27.7879 | − | 3.43956i | −0.992426 | − | 0.122842i | ||||
\(785\) | −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 | \(-0.662567\pi\) | ||||
−0.488805 | + | 0.872393i | \(0.662567\pi\) | |||||||
\(798\) | −11.6085 | − | 24.7488i | −0.410935 | − | 0.876099i | ||||
\(799\) | 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 | \(0.955484\pi\) | |||||||
\(812\) | −1.99015 | − | 0.122701i | −0.0698407 | − | 0.00430597i | ||||
\(813\) | 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 | \(0.152255\pi\) | ||||
−0.887768 | + | 0.460291i | \(0.847745\pi\) | |||||||
\(822\) | −0.838224 | + | 1.53378i | −0.0292364 | + | 0.0534967i | ||||
\(823\) | − | 21.7419i | − | 0.757875i | −0.925422 | − | 0.378938i | \(-0.876289\pi\) | ||
0.925422 | − | 0.378938i | \(-0.123711\pi\) | |||||||
\(824\) | −2.36365 | − | 33.5581i | −0.0823416 | − | 1.16905i | ||||
\(825\) | − | 9.69116i | − | 0.337403i | ||||||
\(826\) | 35.8520 | − | 16.8164i | 1.24745 | − | 0.585118i | ||||
\(827\) | 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 | \(-0.460282\pi\) | ||||
0.124455 | + | 0.992225i | \(0.460282\pi\) | |||||||
\(830\) | −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 | \(-0.433155\pi\) | ||||
0.208461 | + | 0.978031i | \(0.433155\pi\) | |||||||
\(840\) | 10.2011 | + | 6.42024i | 0.351970 | + | 0.221519i | ||||
\(841\) | 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 | \(-0.257417\pi\) | ||||
0.690440 | + | 0.723390i | \(0.257417\pi\) | |||||||
\(854\) | 8.86619 | + | 18.9024i | 0.303395 | + | 0.646827i | ||||
\(855\) | − | 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 | \(-0.807352\pi\) | ||
0.822376 | − | 0.568945i | \(-0.192648\pi\) | |||||||
\(864\) | 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 | ||||||
\(868\) | −0.956152 | + | 15.5083i | −0.0324539 | + | 0.526386i | ||||
\(869\) | 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 | \(-0.810899\pi\) | ||
0.828664 | − | 0.559746i | \(-0.189101\pi\) | |||||||
\(878\) | −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 | \(-0.343946\pi\) | |||||||
\(882\) | 0.772173 | − | 3.94123i | 0.0260004 | − | 0.132708i | ||||
\(883\) | 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 | \(-0.709084\pi\) | ||||
−0.610632 | + | 0.791915i | \(0.709084\pi\) | |||||||
\(888\) | −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 | ||||||||
\(896\) | 16.3846 | + | 25.0508i | 0.547371 | + | 0.836890i | ||||
\(897\) | −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 | ||||||||
\(910\) | −6.75945 | − | 14.4109i | −0.224073 | − | 0.477717i | ||||
\(911\) | 6.93039i | 0.229614i | 0.993388 | + | 0.114807i | \(0.0366250\pi\) | ||||
−0.993388 | + | 0.114807i | \(0.963375\pi\) | |||||||
\(912\) | −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 | \(0.101364\pi\) | ||||
−0.949724 | + | 0.313089i | \(0.898636\pi\) | |||||||
\(920\) | 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 | ||||||
\(924\) | 51.1836 | + | 3.15569i | 1.68382 | + | 0.103814i | ||||
\(925\) | − | 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 | \(-0.168221\pi\) | |||||||
\(938\) | 1.24348 | + | 2.65106i | 0.0406012 | + | 0.0865603i | ||||
\(939\) | 18.3410 | 0.598537 | ||||||||
\(940\) | 4.17234 | + | 6.50259i | 0.136087 | + | 0.212091i | ||||
\(941\) | 14.1430 | 0.461048 | 0.230524 | − | 0.973067i | \(-0.425956\pi\) | ||||
0.230524 | + | 0.973067i | \(0.425956\pi\) | |||||||
\(942\) | −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 | ||||||||
\(952\) | 34.3347 | + | 21.6092i | 1.11279 | + | 0.700359i | ||||
\(953\) | 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 | ||||||||
\(966\) | 13.3053 | + | 28.3664i | 0.428090 | + | 0.912674i | ||||
\(967\) | − | 48.0941i | − | 1.54660i | −0.634040 | − | 0.773301i | \(-0.718604\pi\) | ||
0.634040 | − | 0.773301i | \(-0.281396\pi\) | |||||||
\(968\) | −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 | ||||||||
\(980\) | −8.95066 | + | 10.7650i | −0.285918 | + | 0.343876i | ||||
\(981\) | − | 0.274571i | − | 0.00876638i | ||||||
\(982\) | 41.1569 | + | 22.4926i | 1.31337 | + | 0.717769i | ||||
\(983\) | 50.8845 | 1.62296 | 0.811482 | − | 0.584377i | \(-0.198661\pi\) | ||||
0.811482 | + | 0.584377i | \(0.198661\pi\) | |||||||
\(984\) | −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 | \(0.225891\pi\) | ||||
−0.758585 | + | 0.651574i | \(0.774109\pi\) | |||||||
\(992\) | 13.3153 | − | 9.93034i | 0.422763 | − | 0.315289i | ||||
\(993\) | − | 5.24060i | − | 0.166305i | ||||||
\(994\) | −52.1012 | + | 24.4381i | −1.65255 | + | 0.775129i | ||||
\(995\) | −17.9614 | −0.569416 | ||||||||
\(996\) | 14.6608 | + | 22.8488i | 0.464544 | + | 0.723992i | ||||
\(997\) | −29.5605 | −0.936189 | −0.468095 | − | 0.883678i | \(-0.655059\pi\) | ||||
−0.468095 | + | 0.883678i | \(0.655059\pi\) | |||||||
\(998\) | 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.b.251.3 | yes | 16 | |
4.3 | odd | 2 | 1120.2.h.b.111.5 | 16 | |||
7.6 | odd | 2 | 280.2.h.a.251.3 | ✓ | 16 | ||
8.3 | odd | 2 | 280.2.h.a.251.4 | yes | 16 | ||
8.5 | even | 2 | 1120.2.h.a.111.5 | 16 | |||
28.27 | even | 2 | 1120.2.h.a.111.12 | 16 | |||
56.13 | odd | 2 | 1120.2.h.b.111.12 | 16 | |||
56.27 | even | 2 | inner | 280.2.h.b.251.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.h.a.251.3 | ✓ | 16 | 7.6 | odd | 2 | ||
280.2.h.a.251.4 | yes | 16 | 8.3 | odd | 2 | ||
280.2.h.b.251.3 | yes | 16 | 1.1 | even | 1 | trivial | |
280.2.h.b.251.4 | yes | 16 | 56.27 | even | 2 | inner | |
1120.2.h.a.111.5 | 16 | 8.5 | even | 2 | |||
1120.2.h.a.111.12 | 16 | 28.27 | even | 2 | |||
1120.2.h.b.111.5 | 16 | 4.3 | odd | 2 | |||
1120.2.h.b.111.12 | 16 | 56.13 | odd | 2 |