Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(124,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.124");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.e (of order \(10\), degree \(4\), not 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: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 249.2 | ||
Root | \(0.951057 - 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.249 |
Dual form | 625.2.e.c.374.2 |
$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.951057 | − | 1.30902i | 0.672499 | − | 0.925615i | −0.327315 | − | 0.944915i | \(-0.606144\pi\) |
0.999814 | + | 0.0193004i | \(0.00614389\pi\) | |||||||
\(3\) | −0.951057 | + | 0.309017i | −0.549093 | + | 0.178411i | −0.570408 | − | 0.821362i | \(-0.693215\pi\) |
0.0213149 | + | 0.999773i | \(0.493215\pi\) | |||||||
\(4\) | −0.190983 | − | 0.587785i | −0.0954915 | − | 0.293893i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.500000 | + | 1.53884i | −0.204124 | + | 0.628230i | ||||
\(7\) | − | 0.618034i | − | 0.233595i | −0.993156 | − | 0.116797i | \(-0.962737\pi\) | ||
0.993156 | − | 0.116797i | \(-0.0372628\pi\) | |||||||
\(8\) | 2.12663 | + | 0.690983i | 0.751876 | + | 0.244299i | ||||
\(9\) | −1.61803 | + | 1.17557i | −0.539345 | + | 0.391857i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.23607 | + | 3.07768i | 1.27722 | + | 0.927957i | 0.999465 | − | 0.0326948i | \(-0.0104089\pi\) |
0.277757 | + | 0.960651i | \(0.410409\pi\) | |||||||
\(12\) | 0.363271 | + | 0.500000i | 0.104867 | + | 0.144338i | ||||
\(13\) | −1.08981 | − | 1.50000i | −0.302260 | − | 0.416025i | 0.630688 | − | 0.776037i | \(-0.282773\pi\) |
−0.932948 | + | 0.360011i | \(0.882773\pi\) | |||||||
\(14\) | −0.809017 | − | 0.587785i | −0.216219 | − | 0.157092i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.92705 | − | 2.85317i | 0.981763 | − | 0.713292i | ||||
\(17\) | 4.97980 | + | 1.61803i | 1.20778 | + | 0.392431i | 0.842617 | − | 0.538513i | \(-0.181014\pi\) |
0.365161 | + | 0.930944i | \(0.381014\pi\) | |||||||
\(18\) | 3.23607i | 0.762749i | ||||||||
\(19\) | −0.263932 | + | 0.812299i | −0.0605502 | + | 0.186354i | −0.976756 | − | 0.214353i | \(-0.931236\pi\) |
0.916206 | + | 0.400707i | \(0.131236\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.190983 | + | 0.587785i | 0.0416759 | + | 0.128265i | ||||
\(22\) | 8.05748 | − | 2.61803i | 1.71786 | − | 0.558167i | ||||
\(23\) | 2.21238 | − | 3.04508i | 0.461314 | − | 0.634944i | −0.513467 | − | 0.858110i | \(-0.671639\pi\) |
0.974781 | + | 0.223165i | \(0.0716390\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | 2.93893 | − | 4.04508i | 0.565597 | − | 0.778477i | ||||
\(28\) | −0.363271 | + | 0.118034i | −0.0686518 | + | 0.0223063i | ||||
\(29\) | 1.11803 | + | 3.44095i | 0.207614 | + | 0.638969i | 0.999596 | + | 0.0284251i | \(0.00904922\pi\) |
−0.791982 | + | 0.610544i | \(0.790951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.927051 | + | 2.85317i | −0.166503 | + | 0.512444i | −0.999144 | − | 0.0413693i | \(-0.986828\pi\) |
0.832641 | + | 0.553814i | \(0.186828\pi\) | |||||||
\(32\) | − | 3.38197i | − | 0.597853i | ||||||
\(33\) | −4.97980 | − | 1.61803i | −0.866871 | − | 0.281664i | ||||
\(34\) | 6.85410 | − | 4.97980i | 1.17547 | − | 0.854028i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | + | 0.726543i | 0.166667 | + | 0.121090i | ||||
\(37\) | −0.138757 | − | 0.190983i | −0.0228116 | − | 0.0313974i | 0.797459 | − | 0.603373i | \(-0.206177\pi\) |
−0.820270 | + | 0.571976i | \(0.806177\pi\) | |||||||
\(38\) | 0.812299 | + | 1.11803i | 0.131772 | + | 0.181369i | ||||
\(39\) | 1.50000 | + | 1.08981i | 0.240192 | + | 0.174510i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.618034 | − | 0.449028i | 0.0965207 | − | 0.0701264i | −0.538478 | − | 0.842639i | \(-0.681001\pi\) |
0.634999 | + | 0.772513i | \(0.281001\pi\) | |||||||
\(42\) | 0.951057 | + | 0.309017i | 0.146751 | + | 0.0476824i | ||||
\(43\) | − | 4.85410i | − | 0.740244i | −0.928983 | − | 0.370122i | \(-0.879316\pi\) | ||
0.928983 | − | 0.370122i | \(-0.120684\pi\) | |||||||
\(44\) | 1.00000 | − | 3.07768i | 0.150756 | − | 0.463978i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.88197 | − | 5.79210i | −0.277481 | − | 0.853998i | ||||
\(47\) | 0.587785 | − | 0.190983i | 0.0857373 | − | 0.0278577i | −0.265834 | − | 0.964019i | \(-0.585647\pi\) |
0.351572 | + | 0.936161i | \(0.385647\pi\) | |||||||
\(48\) | −2.85317 | + | 3.92705i | −0.411820 | + | 0.566821i | ||||
\(49\) | 6.61803 | 0.945433 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.23607 | −0.733196 | ||||||||
\(52\) | −0.673542 | + | 0.927051i | −0.0934035 | + | 0.128559i | ||||
\(53\) | 3.30220 | − | 1.07295i | 0.453592 | − | 0.147381i | −0.0733062 | − | 0.997309i | \(-0.523355\pi\) |
0.526898 | + | 0.849929i | \(0.323355\pi\) | |||||||
\(54\) | −2.50000 | − | 7.69421i | −0.340207 | − | 1.04705i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.427051 | − | 1.31433i | 0.0570671 | − | 0.175634i | ||||
\(57\) | − | 0.854102i | − | 0.113129i | ||||||
\(58\) | 5.56758 | + | 1.80902i | 0.731059 | + | 0.237536i | ||||
\(59\) | −8.78115 | + | 6.37988i | −1.14321 | + | 0.830590i | −0.987563 | − | 0.157223i | \(-0.949746\pi\) |
−0.155646 | + | 0.987813i | \(0.549746\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.04508 | − | 5.11855i | −0.902031 | − | 0.655364i | 0.0369561 | − | 0.999317i | \(-0.488234\pi\) |
−0.938987 | + | 0.343953i | \(0.888234\pi\) | |||||||
\(62\) | 2.85317 | + | 3.92705i | 0.362353 | + | 0.498736i | ||||
\(63\) | 0.726543 | + | 1.00000i | 0.0915358 | + | 0.125988i | ||||
\(64\) | 3.42705 | + | 2.48990i | 0.428381 | + | 0.311237i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.85410 | + | 4.97980i | −0.843682 | + | 0.612971i | ||||
\(67\) | −4.53077 | − | 1.47214i | −0.553521 | − | 0.179850i | 0.0188826 | − | 0.999822i | \(-0.493989\pi\) |
−0.572404 | + | 0.819972i | \(0.693989\pi\) | |||||||
\(68\) | − | 3.23607i | − | 0.392431i | ||||||
\(69\) | −1.16312 | + | 3.57971i | −0.140023 | + | 0.430947i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.04508 | − | 6.29412i | −0.242707 | − | 0.746975i | −0.996005 | − | 0.0892960i | \(-0.971538\pi\) |
0.753298 | − | 0.657679i | \(-0.228462\pi\) | |||||||
\(72\) | −4.25325 | + | 1.38197i | −0.501251 | + | 0.162866i | ||||
\(73\) | −5.29007 | + | 7.28115i | −0.619156 | + | 0.852194i | −0.997291 | − | 0.0735557i | \(-0.976565\pi\) |
0.378136 | + | 0.925750i | \(0.376565\pi\) | |||||||
\(74\) | −0.381966 | −0.0444026 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.527864 | 0.0605502 | ||||||||
\(77\) | 1.90211 | − | 2.61803i | 0.216766 | − | 0.298353i | ||||
\(78\) | 2.85317 | − | 0.927051i | 0.323058 | − | 0.104968i | ||||
\(79\) | 2.50000 | + | 7.69421i | 0.281272 | + | 0.865666i | 0.987491 | + | 0.157673i | \(0.0503992\pi\) |
−0.706219 | + | 0.707993i | \(0.749601\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | − | 1.23607i | − | 0.136501i | ||||||
\(83\) | −5.93085 | − | 1.92705i | −0.650996 | − | 0.211521i | −0.0351426 | − | 0.999382i | \(-0.511189\pi\) |
−0.615853 | + | 0.787861i | \(0.711189\pi\) | |||||||
\(84\) | 0.309017 | − | 0.224514i | 0.0337165 | − | 0.0244965i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.35410 | − | 4.61653i | −0.685180 | − | 0.497813i | ||||
\(87\) | −2.12663 | − | 2.92705i | −0.227998 | − | 0.313813i | ||||
\(88\) | 6.88191 | + | 9.47214i | 0.733614 | + | 1.00973i | ||||
\(89\) | −7.23607 | − | 5.25731i | −0.767022 | − | 0.557274i | 0.134034 | − | 0.990977i | \(-0.457207\pi\) |
−0.901056 | + | 0.433703i | \(0.857207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.927051 | + | 0.673542i | −0.0971813 | + | 0.0706064i | ||||
\(92\) | −2.21238 | − | 0.718847i | −0.230657 | − | 0.0749450i | ||||
\(93\) | − | 3.00000i | − | 0.311086i | ||||||
\(94\) | 0.309017 | − | 0.951057i | 0.0318727 | − | 0.0980940i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.04508 | + | 3.21644i | 0.106664 | + | 0.328277i | ||||
\(97\) | −3.66547 | + | 1.19098i | −0.372172 | + | 0.120926i | −0.489130 | − | 0.872211i | \(-0.662686\pi\) |
0.116958 | + | 0.993137i | \(0.462686\pi\) | |||||||
\(98\) | 6.29412 | − | 8.66312i | 0.635803 | − | 0.875107i | ||||
\(99\) | −10.4721 | −1.05249 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.47214 | 0.146483 | 0.0732415 | − | 0.997314i | \(-0.476666\pi\) | ||||
0.0732415 | + | 0.997314i | \(0.476666\pi\) | |||||||
\(102\) | −4.97980 | + | 6.85410i | −0.493073 | + | 0.678657i | ||||
\(103\) | −8.14324 | + | 2.64590i | −0.802377 | + | 0.260708i | −0.681366 | − | 0.731943i | \(-0.738614\pi\) |
−0.121011 | + | 0.992651i | \(0.538614\pi\) | |||||||
\(104\) | −1.28115 | − | 3.94298i | −0.125627 | − | 0.386641i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.73607 | − | 5.34307i | 0.168622 | − | 0.518965i | ||||
\(107\) | 16.4164i | 1.58703i | 0.608548 | + | 0.793517i | \(0.291752\pi\) | ||||
−0.608548 | + | 0.793517i | \(0.708248\pi\) | |||||||
\(108\) | −2.93893 | − | 0.954915i | −0.282798 | − | 0.0918867i | ||||
\(109\) | 8.09017 | − | 5.87785i | 0.774898 | − | 0.562996i | −0.128546 | − | 0.991704i | \(-0.541031\pi\) |
0.903443 | + | 0.428707i | \(0.141031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.190983 | + | 0.138757i | 0.0181273 | + | 0.0131703i | ||||
\(112\) | −1.76336 | − | 2.42705i | −0.166621 | − | 0.229335i | ||||
\(113\) | −9.90659 | − | 13.6353i | −0.931934 | − | 1.28270i | −0.959100 | − | 0.283066i | \(-0.908648\pi\) |
0.0271666 | − | 0.999631i | \(-0.491352\pi\) | |||||||
\(114\) | −1.11803 | − | 0.812299i | −0.104713 | − | 0.0760788i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.80902 | − | 1.31433i | 0.167963 | − | 0.122032i | ||||
\(117\) | 3.52671 | + | 1.14590i | 0.326045 | + | 0.105938i | ||||
\(118\) | 17.5623i | 1.61674i | ||||||||
\(119\) | 1.00000 | − | 3.07768i | 0.0916698 | − | 0.282131i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.07295 | + | 15.6129i | 0.461177 | + | 1.41936i | ||||
\(122\) | −13.4005 | + | 4.35410i | −1.21323 | + | 0.394202i | ||||
\(123\) | −0.449028 | + | 0.618034i | −0.0404875 | + | 0.0557262i | ||||
\(124\) | 1.85410 | 0.166503 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | −11.6902 | + | 16.0902i | −1.03734 | + | 1.42777i | −0.138043 | + | 0.990426i | \(0.544081\pi\) |
−0.899294 | + | 0.437346i | \(0.855919\pi\) | |||||||
\(128\) | 12.9515 | − | 4.20820i | 1.14476 | − | 0.371956i | ||||
\(129\) | 1.50000 | + | 4.61653i | 0.132068 | + | 0.406462i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.10081 | − | 6.46564i | 0.183549 | − | 0.564905i | −0.816371 | − | 0.577527i | \(-0.804018\pi\) |
0.999920 | + | 0.0126218i | \(0.00401775\pi\) | |||||||
\(132\) | 3.23607i | 0.281664i | ||||||||
\(133\) | 0.502029 | + | 0.163119i | 0.0435314 | + | 0.0141442i | ||||
\(134\) | −6.23607 | + | 4.53077i | −0.538714 | + | 0.391399i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.47214 | + | 6.88191i | 0.812229 | + | 0.590119i | ||||
\(137\) | −7.02067 | − | 9.66312i | −0.599816 | − | 0.825576i | 0.395875 | − | 0.918304i | \(-0.370441\pi\) |
−0.995691 | + | 0.0927283i | \(0.970441\pi\) | |||||||
\(138\) | 3.57971 | + | 4.92705i | 0.304725 | + | 0.419418i | ||||
\(139\) | 4.04508 | + | 2.93893i | 0.343100 | + | 0.249276i | 0.745968 | − | 0.665981i | \(-0.231987\pi\) |
−0.402869 | + | 0.915258i | \(0.631987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.500000 | + | 0.363271i | −0.0421076 | + | 0.0305930i | ||||
\(142\) | −10.1841 | − | 3.30902i | −0.854631 | − | 0.277687i | ||||
\(143\) | − | 9.70820i | − | 0.811841i | ||||||
\(144\) | −3.00000 | + | 9.23305i | −0.250000 | + | 0.769421i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.50000 | + | 13.8496i | 0.372423 | + | 1.14620i | ||||
\(147\) | −6.29412 | + | 2.04508i | −0.519131 | + | 0.168676i | ||||
\(148\) | −0.0857567 | + | 0.118034i | −0.00704916 | + | 0.00970233i | ||||
\(149\) | 3.94427 | 0.323127 | 0.161564 | − | 0.986862i | \(-0.448346\pi\) | ||||
0.161564 | + | 0.986862i | \(0.448346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5623 | 1.18506 | 0.592532 | − | 0.805547i | \(-0.298128\pi\) | ||||
0.592532 | + | 0.805547i | \(0.298128\pi\) | |||||||
\(152\) | −1.12257 | + | 1.54508i | −0.0910524 | + | 0.125323i | ||||
\(153\) | −9.95959 | + | 3.23607i | −0.805185 | + | 0.261621i | ||||
\(154\) | −1.61803 | − | 4.97980i | −0.130385 | − | 0.401283i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.354102 | − | 1.08981i | 0.0283508 | − | 0.0872549i | ||||
\(157\) | − | 13.1803i | − | 1.05191i | −0.850514 | − | 0.525953i | \(-0.823709\pi\) | ||
0.850514 | − | 0.525953i | \(-0.176291\pi\) | |||||||
\(158\) | 12.4495 | + | 4.04508i | 0.990428 | + | 0.321810i | ||||
\(159\) | −2.80902 | + | 2.04087i | −0.222770 | + | 0.161852i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.88197 | − | 1.36733i | −0.148320 | − | 0.107761i | ||||
\(162\) | −0.951057 | − | 1.30902i | −0.0747221 | − | 0.102846i | ||||
\(163\) | −6.46564 | − | 8.89919i | −0.506428 | − | 0.697038i | 0.476884 | − | 0.878966i | \(-0.341766\pi\) |
−0.983312 | + | 0.181928i | \(0.941766\pi\) | |||||||
\(164\) | −0.381966 | − | 0.277515i | −0.0298265 | − | 0.0216702i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.16312 | + | 5.93085i | −0.633581 | + | 0.460323i | ||||
\(167\) | −13.8496 | − | 4.50000i | −1.07171 | − | 0.348220i | −0.280558 | − | 0.959837i | \(-0.590520\pi\) |
−0.791154 | + | 0.611617i | \(0.790520\pi\) | |||||||
\(168\) | 1.38197i | 0.106621i | ||||||||
\(169\) | 2.95492 | − | 9.09429i | 0.227301 | − | 0.699561i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.527864 | − | 1.62460i | −0.0403668 | − | 0.124236i | ||||
\(172\) | −2.85317 | + | 0.927051i | −0.217552 | + | 0.0706870i | ||||
\(173\) | 11.1024 | − | 15.2812i | 0.844100 | − | 1.16180i | −0.141032 | − | 0.990005i | \(-0.545042\pi\) |
0.985132 | − | 0.171799i | \(-0.0549581\pi\) | |||||||
\(174\) | −5.85410 | −0.443798 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 25.4164 | 1.91583 | ||||||||
\(177\) | 6.37988 | − | 8.78115i | 0.479541 | − | 0.660032i | ||||
\(178\) | −13.7638 | + | 4.47214i | −1.03164 | + | 0.335201i | ||||
\(179\) | 0.163119 | + | 0.502029i | 0.0121921 | + | 0.0375234i | 0.956967 | − | 0.290195i | \(-0.0937202\pi\) |
−0.944775 | + | 0.327719i | \(0.893720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.0901699 | − | 0.277515i | 0.00670228 | − | 0.0206275i | −0.947649 | − | 0.319313i | \(-0.896548\pi\) |
0.954352 | + | 0.298685i | \(0.0965480\pi\) | |||||||
\(182\) | 1.85410i | 0.137435i | ||||||||
\(183\) | 8.28199 | + | 2.69098i | 0.612223 | + | 0.198923i | ||||
\(184\) | 6.80902 | − | 4.94704i | 0.501967 | − | 0.364701i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.92705 | − | 2.85317i | −0.287945 | − | 0.209205i | ||||
\(187\) | 16.1150 | + | 22.1803i | 1.17844 | + | 1.62199i | ||||
\(188\) | −0.224514 | − | 0.309017i | −0.0163744 | − | 0.0225374i | ||||
\(189\) | −2.50000 | − | 1.81636i | −0.181848 | − | 0.132120i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.47214 | − | 1.06957i | 0.106520 | − | 0.0773913i | −0.533250 | − | 0.845958i | \(-0.679030\pi\) |
0.639770 | + | 0.768566i | \(0.279030\pi\) | |||||||
\(192\) | −4.02874 | − | 1.30902i | −0.290749 | − | 0.0944702i | ||||
\(193\) | 7.70820i | 0.554849i | 0.960747 | + | 0.277424i | \(0.0894808\pi\) | ||||
−0.960747 | + | 0.277424i | \(0.910519\pi\) | |||||||
\(194\) | −1.92705 | + | 5.93085i | −0.138354 | + | 0.425810i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.26393 | − | 3.88998i | −0.0902809 | − | 0.277856i | ||||
\(197\) | 3.52671 | − | 1.14590i | 0.251268 | − | 0.0816419i | −0.180675 | − | 0.983543i | \(-0.557828\pi\) |
0.431943 | + | 0.901901i | \(0.357828\pi\) | |||||||
\(198\) | −9.95959 | + | 13.7082i | −0.707797 | + | 0.974200i | ||||
\(199\) | 17.5623 | 1.24496 | 0.622479 | − | 0.782636i | \(-0.286125\pi\) | ||||
0.622479 | + | 0.782636i | \(0.286125\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.76393 | 0.336022 | ||||||||
\(202\) | 1.40008 | − | 1.92705i | 0.0985096 | − | 0.135587i | ||||
\(203\) | 2.12663 | − | 0.690983i | 0.149260 | − | 0.0484975i | ||||
\(204\) | 1.00000 | + | 3.07768i | 0.0700140 | + | 0.215481i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.28115 | + | 13.1760i | −0.298282 | + | 0.918018i | ||||
\(207\) | 7.52786i | 0.523223i | ||||||||
\(208\) | −8.55951 | − | 2.78115i | −0.593495 | − | 0.192838i | ||||
\(209\) | −3.61803 | + | 2.62866i | −0.250265 | + | 0.181828i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.42705 | + | 5.39607i | 0.511299 | + | 0.371481i | 0.813316 | − | 0.581822i | \(-0.197660\pi\) |
−0.302017 | + | 0.953303i | \(0.597660\pi\) | |||||||
\(212\) | −1.26133 | − | 1.73607i | −0.0866283 | − | 0.119234i | ||||
\(213\) | 3.88998 | + | 5.35410i | 0.266537 | + | 0.366857i | ||||
\(214\) | 21.4894 | + | 15.6129i | 1.46898 | + | 1.06728i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.04508 | − | 6.57164i | 0.615440 | − | 0.447143i | ||||
\(217\) | 1.76336 | + | 0.572949i | 0.119704 | + | 0.0388943i | ||||
\(218\) | − | 16.1803i | − | 1.09587i | ||||||
\(219\) | 2.78115 | − | 8.55951i | 0.187933 | − | 0.578398i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | − | 9.23305i | −0.201802 | − | 0.621082i | ||||
\(222\) | 0.363271 | − | 0.118034i | 0.0243812 | − | 0.00792192i | ||||
\(223\) | −0.106001 | + | 0.145898i | −0.00709836 | + | 0.00977005i | −0.812551 | − | 0.582890i | \(-0.801922\pi\) |
0.805453 | + | 0.592660i | \(0.201922\pi\) | |||||||
\(224\) | −2.09017 | −0.139655 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.2705 | −1.81401 | ||||||||
\(227\) | −8.67802 | + | 11.9443i | −0.575981 | + | 0.792769i | −0.993247 | − | 0.116015i | \(-0.962988\pi\) |
0.417267 | + | 0.908784i | \(0.362988\pi\) | |||||||
\(228\) | −0.502029 | + | 0.163119i | −0.0332477 | + | 0.0108028i | ||||
\(229\) | −6.70820 | − | 20.6457i | −0.443291 | − | 1.36431i | −0.884348 | − | 0.466829i | \(-0.845396\pi\) |
0.441057 | − | 0.897479i | \(-0.354604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | + | 3.07768i | −0.0657952 | + | 0.202497i | ||||
\(232\) | 8.09017i | 0.531146i | ||||||||
\(233\) | −2.80017 | − | 0.909830i | −0.183445 | − | 0.0596049i | 0.215854 | − | 0.976426i | \(-0.430746\pi\) |
−0.399299 | + | 0.916821i | \(0.630746\pi\) | |||||||
\(234\) | 4.85410 | − | 3.52671i | 0.317323 | − | 0.230548i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.42705 | + | 3.94298i | 0.353271 | + | 0.256666i | ||||
\(237\) | −4.75528 | − | 6.54508i | −0.308889 | − | 0.425149i | ||||
\(238\) | −3.07768 | − | 4.23607i | −0.199497 | − | 0.274584i | ||||
\(239\) | −16.6074 | − | 12.0660i | −1.07424 | − | 0.780483i | −0.0975727 | − | 0.995228i | \(-0.531108\pi\) |
−0.976670 | + | 0.214745i | \(0.931108\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.04508 | + | 1.48584i | −0.131736 | + | 0.0957114i | −0.651702 | − | 0.758475i | \(-0.725945\pi\) |
0.519966 | + | 0.854187i | \(0.325945\pi\) | |||||||
\(242\) | 25.2623 | + | 8.20820i | 1.62392 | + | 0.527643i | ||||
\(243\) | 16.0000i | 1.02640i | ||||||||
\(244\) | −1.66312 | + | 5.11855i | −0.106470 | + | 0.327682i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.381966 | + | 1.17557i | 0.0243533 | + | 0.0749516i | ||||
\(247\) | 1.50609 | − | 0.489357i | 0.0958299 | − | 0.0311370i | ||||
\(248\) | −3.94298 | + | 5.42705i | −0.250380 | + | 0.344618i | ||||
\(249\) | 6.23607 | 0.395195 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.1803 | −1.84185 | −0.920923 | − | 0.389744i | \(-0.872564\pi\) | ||||
−0.920923 | + | 0.389744i | \(0.872564\pi\) | |||||||
\(252\) | 0.449028 | − | 0.618034i | 0.0282861 | − | 0.0389325i | ||||
\(253\) | 18.7436 | − | 6.09017i | 1.17840 | − | 0.382886i | ||||
\(254\) | 9.94427 | + | 30.6053i | 0.623959 | + | 1.92035i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.19098 | − | 12.8985i | 0.261936 | − | 0.806157i | ||||
\(257\) | − | 22.8541i | − | 1.42560i | −0.701367 | − | 0.712800i | \(-0.747427\pi\) | ||
0.701367 | − | 0.712800i | \(-0.252573\pi\) | |||||||
\(258\) | 7.46969 | + | 2.42705i | 0.465043 | + | 0.151102i | ||||
\(259\) | −0.118034 | + | 0.0857567i | −0.00733428 | + | 0.00532866i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.85410 | − | 4.25325i | −0.362360 | − | 0.263270i | ||||
\(262\) | −6.46564 | − | 8.89919i | −0.399448 | − | 0.549794i | ||||
\(263\) | 6.41264 | + | 8.82624i | 0.395420 | + | 0.544249i | 0.959587 | − | 0.281412i | \(-0.0908026\pi\) |
−0.564167 | + | 0.825661i | \(0.690803\pi\) | |||||||
\(264\) | −9.47214 | − | 6.88191i | −0.582970 | − | 0.423552i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.690983 | − | 0.502029i | 0.0423669 | − | 0.0307813i | ||||
\(267\) | 8.50651 | + | 2.76393i | 0.520590 | + | 0.169150i | ||||
\(268\) | 2.94427i | 0.179850i | ||||||||
\(269\) | 3.94427 | − | 12.1392i | 0.240487 | − | 0.740141i | −0.755860 | − | 0.654734i | \(-0.772781\pi\) |
0.996346 | − | 0.0854076i | \(-0.0272192\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.47214 | − | 7.60845i | −0.150172 | − | 0.462181i | 0.847468 | − | 0.530846i | \(-0.178126\pi\) |
−0.997640 | + | 0.0686657i | \(0.978126\pi\) | |||||||
\(272\) | 24.1724 | − | 7.85410i | 1.46567 | − | 0.476225i | ||||
\(273\) | 0.673542 | − | 0.927051i | 0.0407646 | − | 0.0561077i | ||||
\(274\) | −19.3262 | −1.16754 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.32624 | 0.140023 | ||||||||
\(277\) | 14.5231 | − | 19.9894i | 0.872610 | − | 1.20104i | −0.105804 | − | 0.994387i | \(-0.533742\pi\) |
0.978413 | − | 0.206657i | \(-0.0662584\pi\) | |||||||
\(278\) | 7.69421 | − | 2.50000i | 0.461468 | − | 0.149940i | ||||
\(279\) | −1.85410 | − | 5.70634i | −0.111002 | − | 0.341630i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.11803 | − | 9.59632i | 0.186006 | − | 0.572469i | −0.813958 | − | 0.580924i | \(-0.802691\pi\) |
0.999964 | + | 0.00845524i | \(0.00269142\pi\) | |||||||
\(282\) | 1.00000i | 0.0595491i | ||||||||
\(283\) | −28.3929 | − | 9.22542i | −1.68778 | − | 0.548395i | −0.701389 | − | 0.712779i | \(-0.747436\pi\) |
−0.986396 | + | 0.164384i | \(0.947436\pi\) | |||||||
\(284\) | −3.30902 | + | 2.40414i | −0.196354 | + | 0.142660i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.7082 | − | 9.23305i | −0.751452 | − | 0.545962i | ||||
\(287\) | −0.277515 | − | 0.381966i | −0.0163812 | − | 0.0225467i | ||||
\(288\) | 3.97574 | + | 5.47214i | 0.234273 | + | 0.322449i | ||||
\(289\) | 8.42705 | + | 6.12261i | 0.495709 | + | 0.360154i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.11803 | − | 2.26538i | 0.182782 | − | 0.132799i | ||||
\(292\) | 5.29007 | + | 1.71885i | 0.309578 | + | 0.100588i | ||||
\(293\) | − | 19.5279i | − | 1.14083i | −0.821357 | − | 0.570415i | \(-0.806782\pi\) | ||
0.821357 | − | 0.570415i | \(-0.193218\pi\) | |||||||
\(294\) | −3.30902 | + | 10.1841i | −0.192986 | + | 0.593949i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.163119 | − | 0.502029i | −0.00948110 | − | 0.0291798i | ||||
\(297\) | 24.8990 | − | 8.09017i | 1.44479 | − | 0.469439i | ||||
\(298\) | 3.75123 | − | 5.16312i | 0.217303 | − | 0.299091i | ||||
\(299\) | −6.97871 | −0.403589 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | −0.172917 | ||||||||
\(302\) | 13.8496 | − | 19.0623i | 0.796954 | − | 1.09691i | ||||
\(303\) | −1.40008 | + | 0.454915i | −0.0804328 | + | 0.0261342i | ||||
\(304\) | 1.28115 | + | 3.94298i | 0.0734792 | + | 0.226146i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.23607 | + | 16.1150i | −0.299326 | + | 0.921231i | ||||
\(307\) | − | 9.23607i | − | 0.527130i | −0.964642 | − | 0.263565i | \(-0.915102\pi\) | ||
0.964642 | − | 0.263565i | \(-0.0848984\pi\) | |||||||
\(308\) | −1.90211 | − | 0.618034i | −0.108383 | − | 0.0352158i | ||||
\(309\) | 6.92705 | − | 5.03280i | 0.394066 | − | 0.286306i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.88197 | − | 5.00004i | −0.390240 | − | 0.283526i | 0.375314 | − | 0.926898i | \(-0.377535\pi\) |
−0.765554 | + | 0.643372i | \(0.777535\pi\) | |||||||
\(312\) | 2.43690 | + | 3.35410i | 0.137962 | + | 0.189889i | ||||
\(313\) | 9.85359 | + | 13.5623i | 0.556958 | + | 0.766587i | 0.990936 | − | 0.134337i | \(-0.0428904\pi\) |
−0.433978 | + | 0.900924i | \(0.642890\pi\) | |||||||
\(314\) | −17.2533 | − | 12.5352i | −0.973659 | − | 0.707405i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.04508 | − | 2.93893i | 0.227554 | − | 0.165328i | ||||
\(317\) | −7.27794 | − | 2.36475i | −0.408770 | − | 0.132817i | 0.0974121 | − | 0.995244i | \(-0.468944\pi\) |
−0.506182 | + | 0.862427i | \(0.668944\pi\) | |||||||
\(318\) | 5.61803i | 0.315044i | ||||||||
\(319\) | −5.85410 | + | 18.0171i | −0.327767 | + | 1.00876i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.07295 | − | 15.6129i | −0.283144 | − | 0.871429i | ||||
\(322\) | −3.57971 | + | 1.16312i | −0.199490 | + | 0.0648181i | ||||
\(323\) | −2.62866 | + | 3.61803i | −0.146262 | + | 0.201313i | ||||
\(324\) | −0.618034 | −0.0343352 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −17.7984 | −0.985761 | ||||||||
\(327\) | −5.87785 | + | 8.09017i | −0.325046 | + | 0.447387i | ||||
\(328\) | 1.62460 | − | 0.527864i | 0.0897034 | − | 0.0291464i | ||||
\(329\) | −0.118034 | − | 0.363271i | −0.00650742 | − | 0.0200278i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.14590 | + | 21.9928i | −0.392774 | + | 1.20883i | 0.537907 | + | 0.843004i | \(0.319215\pi\) |
−0.930682 | + | 0.365830i | \(0.880785\pi\) | |||||||
\(332\) | 3.85410i | 0.211521i | ||||||||
\(333\) | 0.449028 | + | 0.145898i | 0.0246066 | + | 0.00799516i | ||||
\(334\) | −19.0623 | + | 13.8496i | −1.04304 | + | 0.757815i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.42705 | + | 1.76336i | 0.132406 | + | 0.0961989i | ||||
\(337\) | 4.61653 | + | 6.35410i | 0.251478 | + | 0.346130i | 0.916028 | − | 0.401114i | \(-0.131377\pi\) |
−0.664550 | + | 0.747244i | \(0.731377\pi\) | |||||||
\(338\) | −9.09429 | − | 12.5172i | −0.494664 | − | 0.680847i | ||||
\(339\) | 13.6353 | + | 9.90659i | 0.740565 | + | 0.538052i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.7082 | + | 9.23305i | −0.688188 | + | 0.499998i | ||||
\(342\) | −2.62866 | − | 0.854102i | −0.142141 | − | 0.0461845i | ||||
\(343\) | − | 8.41641i | − | 0.454443i | ||||||
\(344\) | 3.35410 | − | 10.3229i | 0.180841 | − | 0.556572i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.44427 | − | 29.0665i | −0.507727 | − | 1.56262i | ||||
\(347\) | −18.9354 | + | 6.15248i | −1.01650 | + | 0.330282i | −0.769441 | − | 0.638717i | \(-0.779465\pi\) |
−0.247063 | + | 0.969000i | \(0.579465\pi\) | |||||||
\(348\) | −1.31433 | + | 1.80902i | −0.0704554 | + | 0.0969735i | ||||
\(349\) | −21.7082 | −1.16201 | −0.581007 | − | 0.813899i | \(-0.697341\pi\) | ||||
−0.581007 | + | 0.813899i | \(0.697341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.27051 | −0.494823 | ||||||||
\(352\) | 10.4086 | − | 14.3262i | 0.554781 | − | 0.763591i | ||||
\(353\) | −12.2780 | + | 3.98936i | −0.653491 | + | 0.212332i | −0.616953 | − | 0.787000i | \(-0.711633\pi\) |
−0.0365381 | + | 0.999332i | \(0.511633\pi\) | |||||||
\(354\) | −5.42705 | − | 16.7027i | −0.288445 | − | 0.887741i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.70820 | + | 5.25731i | −0.0905346 | + | 0.278637i | ||||
\(357\) | 3.23607i | 0.171271i | ||||||||
\(358\) | 0.812299 | + | 0.263932i | 0.0429313 | + | 0.0139492i | ||||
\(359\) | 11.1180 | − | 8.07772i | 0.586787 | − | 0.426326i | −0.254377 | − | 0.967105i | \(-0.581870\pi\) |
0.841165 | + | 0.540779i | \(0.181870\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.7812 | + | 10.7391i | 0.777955 | + | 0.565218i | ||||
\(362\) | −0.277515 | − | 0.381966i | −0.0145858 | − | 0.0200757i | ||||
\(363\) | −9.64932 | − | 13.2812i | −0.506458 | − | 0.697080i | ||||
\(364\) | 0.572949 | + | 0.416272i | 0.0300307 | + | 0.0218186i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.3992 | − | 8.28199i | 0.595845 | − | 0.432907i | ||||
\(367\) | 24.3112 | + | 7.89919i | 1.26903 | + | 0.412334i | 0.864705 | − | 0.502279i | \(-0.167505\pi\) |
0.404329 | + | 0.914614i | \(0.367505\pi\) | |||||||
\(368\) | − | 18.2705i | − | 0.952416i | ||||||
\(369\) | −0.472136 | + | 1.45309i | −0.0245784 | + | 0.0756446i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.663119 | − | 2.04087i | −0.0344274 | − | 0.105957i | ||||
\(372\) | −1.76336 | + | 0.572949i | −0.0914257 | + | 0.0297060i | ||||
\(373\) | −16.6170 | + | 22.8713i | −0.860395 | + | 1.18423i | 0.121080 | + | 0.992643i | \(0.461364\pi\) |
−0.981475 | + | 0.191589i | \(0.938636\pi\) | |||||||
\(374\) | 44.3607 | 2.29384 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.38197 | 0.0712695 | ||||||||
\(377\) | 3.94298 | − | 5.42705i | 0.203074 | − | 0.279507i | ||||
\(378\) | −4.75528 | + | 1.54508i | −0.244585 | + | 0.0794706i | ||||
\(379\) | −4.51064 | − | 13.8823i | −0.231696 | − | 0.713087i | −0.997543 | − | 0.0700639i | \(-0.977680\pi\) |
0.765846 | − | 0.643024i | \(-0.222320\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.14590 | − | 18.9151i | 0.314864 | − | 0.969051i | ||||
\(382\) | − | 2.94427i | − | 0.150642i | ||||||
\(383\) | 31.7279 | + | 10.3090i | 1.62122 | + | 0.526766i | 0.972229 | − | 0.234031i | \(-0.0751916\pi\) |
0.648990 | + | 0.760797i | \(0.275192\pi\) | |||||||
\(384\) | −11.0172 | + | 8.00448i | −0.562220 | + | 0.408477i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.0902 | + | 7.33094i | 0.513576 | + | 0.373135i | ||||
\(387\) | 5.70634 | + | 7.85410i | 0.290070 | + | 0.399246i | ||||
\(388\) | 1.40008 | + | 1.92705i | 0.0710785 | + | 0.0978312i | ||||
\(389\) | 12.1353 | + | 8.81678i | 0.615282 | + | 0.447028i | 0.851270 | − | 0.524727i | \(-0.175833\pi\) |
−0.235988 | + | 0.971756i | \(0.575833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.9443 | − | 11.5842i | 0.806336 | − | 0.585838i | ||||
\(392\) | 14.0741 | + | 4.57295i | 0.710849 | + | 0.230969i | ||||
\(393\) | 6.79837i | 0.342933i | ||||||||
\(394\) | 1.85410 | − | 5.70634i | 0.0934083 | − | 0.287481i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.00000 | + | 6.15537i | 0.100504 | + | 0.309319i | ||||
\(397\) | 27.6134 | − | 8.97214i | 1.38588 | − | 0.450299i | 0.481280 | − | 0.876567i | \(-0.340172\pi\) |
0.904597 | + | 0.426268i | \(0.140172\pi\) | |||||||
\(398\) | 16.7027 | − | 22.9894i | 0.837233 | − | 1.15235i | ||||
\(399\) | −0.527864 | −0.0264263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.5967 | 1.32818 | 0.664089 | − | 0.747653i | \(-0.268820\pi\) | ||||
0.664089 | + | 0.747653i | \(0.268820\pi\) | |||||||
\(402\) | 4.53077 | − | 6.23607i | 0.225974 | − | 0.311027i | ||||
\(403\) | 5.29007 | − | 1.71885i | 0.263517 | − | 0.0856219i | ||||
\(404\) | −0.281153 | − | 0.865300i | −0.0139879 | − | 0.0430503i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.11803 | − | 3.44095i | 0.0554871 | − | 0.170772i | ||||
\(407\) | − | 1.23607i | − | 0.0612696i | ||||||
\(408\) | −11.1352 | − | 3.61803i | −0.551273 | − | 0.179119i | ||||
\(409\) | 1.28115 | − | 0.930812i | 0.0633489 | − | 0.0460257i | −0.555660 | − | 0.831410i | \(-0.687534\pi\) |
0.619009 | + | 0.785384i | \(0.287534\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.66312 | + | 7.02067i | 0.476647 | + | 0.346304i | ||||
\(412\) | 3.11044 | + | 4.28115i | 0.153240 | + | 0.210917i | ||||
\(413\) | 3.94298 | + | 5.42705i | 0.194022 | + | 0.267048i | ||||
\(414\) | 9.85410 | + | 7.15942i | 0.484303 | + | 0.351867i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.07295 | + | 3.68571i | −0.248722 | + | 0.180707i | ||||
\(417\) | −4.75528 | − | 1.54508i | −0.232867 | − | 0.0756631i | ||||
\(418\) | 7.23607i | 0.353928i | ||||||||
\(419\) | 2.92705 | − | 9.00854i | 0.142996 | − | 0.440096i | −0.853752 | − | 0.520680i | \(-0.825679\pi\) |
0.996748 | + | 0.0805840i | \(0.0256785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.88854 | + | 30.4338i | 0.481938 | + | 1.48325i | 0.836367 | + | 0.548170i | \(0.184675\pi\) |
−0.354429 | + | 0.935083i | \(0.615325\pi\) | |||||||
\(422\) | 14.1271 | − | 4.59017i | 0.687696 | − | 0.223446i | ||||
\(423\) | −0.726543 | + | 1.00000i | −0.0353257 | + | 0.0486217i | ||||
\(424\) | 7.76393 | 0.377050 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.7082 | 0.518814 | ||||||||
\(427\) | −3.16344 | + | 4.35410i | −0.153090 | + | 0.210710i | ||||
\(428\) | 9.64932 | − | 3.13525i | 0.466418 | − | 0.151548i | ||||
\(429\) | 3.00000 | + | 9.23305i | 0.144841 | + | 0.445776i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.21885 | + | 28.3727i | −0.444056 | + | 1.36666i | 0.439459 | + | 0.898263i | \(0.355170\pi\) |
−0.883515 | + | 0.468402i | \(0.844830\pi\) | |||||||
\(432\) | − | 24.2705i | − | 1.16772i | ||||||
\(433\) | 25.5398 | + | 8.29837i | 1.22736 | + | 0.398794i | 0.849758 | − | 0.527173i | \(-0.176748\pi\) |
0.377605 | + | 0.925967i | \(0.376748\pi\) | |||||||
\(434\) | 2.42705 | − | 1.76336i | 0.116502 | − | 0.0846438i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.00000 | − | 3.63271i | −0.239457 | − | 0.173975i | ||||
\(437\) | 1.88960 | + | 2.60081i | 0.0903919 | + | 0.124414i | ||||
\(438\) | −8.55951 | − | 11.7812i | −0.408989 | − | 0.562925i | ||||
\(439\) | −33.1525 | − | 24.0867i | −1.58228 | − | 1.14959i | −0.914021 | − | 0.405667i | \(-0.867039\pi\) |
−0.668261 | − | 0.743927i | \(-0.732961\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.7082 | + | 7.77997i | −0.509914 | + | 0.370475i | ||||
\(442\) | −14.9394 | − | 4.85410i | −0.710594 | − | 0.230886i | ||||
\(443\) | 29.9443i | 1.42270i | 0.702840 | + | 0.711348i | \(0.251915\pi\) | ||||
−0.702840 | + | 0.711348i | \(0.748085\pi\) | |||||||
\(444\) | 0.0450850 | − | 0.138757i | 0.00213964 | − | 0.00658513i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.0901699 | + | 0.277515i | 0.00426967 | + | 0.0131407i | ||||
\(447\) | −3.75123 | + | 1.21885i | −0.177427 | + | 0.0576495i | ||||
\(448\) | 1.53884 | − | 2.11803i | 0.0727034 | − | 0.100068i | ||||
\(449\) | −4.67376 | −0.220568 | −0.110284 | − | 0.993900i | \(-0.535176\pi\) | ||||
−0.110284 | + | 0.993900i | \(0.535176\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | −6.12261 | + | 8.42705i | −0.287983 | + | 0.396375i | ||||
\(453\) | −13.8496 | + | 4.50000i | −0.650710 | + | 0.211428i | ||||
\(454\) | 7.38197 | + | 22.7194i | 0.346453 | + | 1.06627i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.590170 | − | 1.81636i | 0.0276372 | − | 0.0850587i | ||||
\(457\) | 21.4164i | 1.00182i | 0.865500 | + | 0.500909i | \(0.167001\pi\) | ||||
−0.865500 | + | 0.500909i | \(0.832999\pi\) | |||||||
\(458\) | −33.4055 | − | 10.8541i | −1.56094 | − | 0.507179i | ||||
\(459\) | 21.1803 | − | 15.3884i | 0.988614 | − | 0.718270i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.663119 | − | 0.481784i | −0.0308845 | − | 0.0224389i | 0.572236 | − | 0.820089i | \(-0.306076\pi\) |
−0.603120 | + | 0.797650i | \(0.706076\pi\) | |||||||
\(462\) | 3.07768 | + | 4.23607i | 0.143187 | + | 0.197080i | ||||
\(463\) | 14.1801 | + | 19.5172i | 0.659005 | + | 0.907042i | 0.999448 | − | 0.0332229i | \(-0.0105771\pi\) |
−0.340443 | + | 0.940265i | \(0.610577\pi\) | |||||||
\(464\) | 14.2082 | + | 10.3229i | 0.659599 | + | 0.479227i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.85410 | + | 2.80017i | −0.178538 | + | 0.129715i | ||||
\(467\) | −26.1073 | − | 8.48278i | −1.20810 | − | 0.392536i | −0.365367 | − | 0.930864i | \(-0.619056\pi\) |
−0.842736 | + | 0.538328i | \(0.819056\pi\) | |||||||
\(468\) | − | 2.29180i | − | 0.105938i | ||||||
\(469\) | −0.909830 | + | 2.80017i | −0.0420120 | + | 0.129300i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.07295 | + | 12.5352i | 0.187672 | + | 0.577594i | ||||
\(472\) | −23.0826 | + | 7.50000i | −1.06246 | + | 0.345215i | ||||
\(473\) | 14.9394 | − | 20.5623i | 0.686914 | − | 0.945456i | ||||
\(474\) | −13.0902 | −0.601251 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | −4.08174 | + | 5.61803i | −0.186890 | + | 0.257232i | ||||
\(478\) | −31.5891 | + | 10.2639i | −1.44485 | + | 0.469461i | ||||
\(479\) | 3.35410 | + | 10.3229i | 0.153253 | + | 0.471664i | 0.997980 | − | 0.0635340i | \(-0.0202371\pi\) |
−0.844727 | + | 0.535198i | \(0.820237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.135255 | + | 0.416272i | −0.00616709 | + | 0.0189804i | ||||
\(482\) | 4.09017i | 0.186302i | ||||||||
\(483\) | 2.21238 | + | 0.718847i | 0.100667 | + | 0.0327087i | ||||
\(484\) | 8.20820 | − | 5.96361i | 0.373100 | − | 0.271073i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 20.9443 | + | 15.2169i | 0.950051 | + | 0.690253i | ||||
\(487\) | −21.4050 | − | 29.4615i | −0.969954 | − | 1.33503i | −0.942070 | − | 0.335417i | \(-0.891123\pi\) |
−0.0278844 | − | 0.999611i | \(-0.508877\pi\) | |||||||
\(488\) | −11.4454 | − | 15.7533i | −0.518110 | − | 0.713118i | ||||
\(489\) | 8.89919 | + | 6.46564i | 0.402435 | + | 0.292386i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.9894 | − | 25.4213i | 1.57905 | − | 1.14725i | 0.661272 | − | 0.750147i | \(-0.270017\pi\) |
0.917776 | − | 0.397099i | \(-0.129983\pi\) | |||||||
\(492\) | 0.449028 | + | 0.145898i | 0.0202437 | + | 0.00657759i | ||||
\(493\) | 18.9443i | 0.853207i | ||||||||
\(494\) | 0.791796 | − | 2.43690i | 0.0356246 | − | 0.109641i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.50000 | + | 13.8496i | 0.202056 | + | 0.621864i | ||||
\(497\) | −3.88998 | + | 1.26393i | −0.174490 | + | 0.0566951i | ||||
\(498\) | 5.93085 | − | 8.16312i | 0.265768 | − | 0.365798i | ||||
\(499\) | −7.56231 | −0.338535 | −0.169268 | − | 0.985570i | \(-0.554140\pi\) | ||||
−0.169268 | + | 0.985570i | \(0.554140\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.5623 | 0.650596 | ||||||||
\(502\) | −27.7522 | + | 38.1976i | −1.23864 | + | 1.70484i | ||||
\(503\) | 35.5851 | − | 11.5623i | 1.58666 | − | 0.515538i | 0.622900 | − | 0.782301i | \(-0.285954\pi\) |
0.963762 | + | 0.266764i | \(0.0859543\pi\) | |||||||
\(504\) | 0.854102 | + | 2.62866i | 0.0380447 | + | 0.117090i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.85410 | − | 30.3278i | 0.438068 | − | 1.34824i | ||||
\(507\) | 9.56231i | 0.424677i | ||||||||
\(508\) | 11.6902 | + | 3.79837i | 0.518668 | + | 0.168526i | ||||
\(509\) | −16.4443 | + | 11.9475i | −0.728880 | + | 0.529562i | −0.889209 | − | 0.457502i | \(-0.848744\pi\) |
0.160329 | + | 0.987064i | \(0.448744\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.50000 | + | 3.26944i | 0.199068 | + | 0.144632i | ||||
\(512\) | 3.11044 | + | 4.28115i | 0.137463 | + | 0.189202i | ||||
\(513\) | 2.51014 | + | 3.45492i | 0.110826 | + | 0.152538i | ||||
\(514\) | −29.9164 | − | 21.7355i | −1.31956 | − | 0.958714i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.42705 | − | 1.76336i | 0.106845 | − | 0.0776274i | ||||
\(517\) | 3.07768 | + | 1.00000i | 0.135356 | + | 0.0439799i | ||||
\(518\) | 0.236068i | 0.0103722i | ||||||||
\(519\) | −5.83688 | + | 17.9641i | −0.256211 | + | 0.788535i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.07295 | + | 27.9237i | 0.397493 | + | 1.22336i | 0.927003 | + | 0.375054i | \(0.122376\pi\) |
−0.529510 | + | 0.848304i | \(0.677624\pi\) | |||||||
\(522\) | −11.1352 | + | 3.61803i | −0.487373 | + | 0.158357i | ||||
\(523\) | −7.72696 | + | 10.6353i | −0.337877 | + | 0.465047i | −0.943820 | − | 0.330461i | \(-0.892796\pi\) |
0.605943 | + | 0.795508i | \(0.292796\pi\) | |||||||
\(524\) | −4.20163 | −0.183549 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.6525 | 0.769685 | ||||||||
\(527\) | −9.23305 | + | 12.7082i | −0.402198 | + | 0.553578i | ||||
\(528\) | −24.1724 | + | 7.85410i | −1.05197 | + | 0.341806i | ||||
\(529\) | 2.72949 | + | 8.40051i | 0.118673 | + | 0.365239i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.70820 | − | 20.6457i | 0.291111 | − | 0.895948i | ||||
\(532\) | − | 0.326238i | − | 0.0141442i | ||||||
\(533\) | −1.34708 | − | 0.437694i | −0.0583487 | − | 0.0189586i | ||||
\(534\) | 11.7082 | − | 8.50651i | 0.506664 | − | 0.368113i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.61803 | − | 6.26137i | −0.372242 | − | 0.270450i | ||||
\(537\) | −0.310271 | − | 0.427051i | −0.0133892 | − | 0.0184286i | ||||
\(538\) | −12.1392 | − | 16.7082i | −0.523359 | − | 0.720342i | ||||
\(539\) | 28.0344 | + | 20.3682i | 1.20753 | + | 0.877321i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.9443 | + | 15.9434i | −0.943458 | + | 0.685462i | −0.949251 | − | 0.314521i | \(-0.898156\pi\) |
0.00579261 | + | 0.999983i | \(0.498156\pi\) | |||||||
\(542\) | −12.3107 | − | 4.00000i | −0.528791 | − | 0.171815i | ||||
\(543\) | 0.291796i | 0.0125222i | ||||||||
\(544\) | 5.47214 | − | 16.8415i | 0.234616 | − | 0.722073i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.572949 | − | 1.76336i | −0.0245200 | − | 0.0754647i | ||||
\(547\) | −20.2497 | + | 6.57953i | −0.865815 | + | 0.281320i | −0.708055 | − | 0.706157i | \(-0.750427\pi\) |
−0.157760 | + | 0.987478i | \(0.550427\pi\) | |||||||
\(548\) | −4.33901 | + | 5.97214i | −0.185353 | + | 0.255117i | ||||
\(549\) | 17.4164 | 0.743314 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.09017 | −0.131646 | ||||||||
\(552\) | −4.94704 | + | 6.80902i | −0.210560 | + | 0.289811i | ||||
\(553\) | 4.75528 | − | 1.54508i | 0.202215 | − | 0.0657037i | ||||
\(554\) | −12.3541 | − | 38.0220i | −0.524875 | − | 1.61540i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.954915 | − | 2.93893i | 0.0404974 | − | 0.124638i | ||||
\(557\) | − | 4.76393i | − | 0.201854i | −0.994894 | − | 0.100927i | \(-0.967819\pi\) | ||
0.994894 | − | 0.100927i | \(-0.0321809\pi\) | |||||||
\(558\) | −9.23305 | − | 3.00000i | −0.390866 | − | 0.127000i | ||||
\(559\) | −7.28115 | + | 5.29007i | −0.307960 | + | 0.223746i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.1803 | − | 16.1150i | −0.936455 | − | 0.680374i | ||||
\(562\) | −9.59632 | − | 13.2082i | −0.404796 | − | 0.557154i | ||||
\(563\) | −4.33901 | − | 5.97214i | −0.182868 | − | 0.251696i | 0.707735 | − | 0.706478i | \(-0.249717\pi\) |
−0.890603 | + | 0.454782i | \(0.849717\pi\) | |||||||
\(564\) | 0.309017 | + | 0.224514i | 0.0130120 | + | 0.00945374i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −39.0795 | + | 28.3929i | −1.64264 | + | 1.19344i | ||||
\(567\) | −0.587785 | − | 0.190983i | −0.0246847 | − | 0.00802053i | ||||
\(568\) | − | 14.7984i | − | 0.620926i | ||||||
\(569\) | −6.34346 | + | 19.5232i | −0.265932 | + | 0.818453i | 0.725546 | + | 0.688174i | \(0.241587\pi\) |
−0.991477 | + | 0.130279i | \(0.958413\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.51064 | − | 7.72696i | −0.105067 | − | 0.323363i | 0.884679 | − | 0.466201i | \(-0.154377\pi\) |
−0.989746 | + | 0.142837i | \(0.954377\pi\) | |||||||
\(572\) | −5.70634 | + | 1.85410i | −0.238594 | + | 0.0775239i | ||||
\(573\) | −1.06957 | + | 1.47214i | −0.0446819 | + | 0.0614994i | ||||
\(574\) | −0.763932 | −0.0318859 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.47214 | −0.353006 | ||||||||
\(577\) | 19.8537 | − | 27.3262i | 0.826519 | − | 1.13761i | −0.162042 | − | 0.986784i | \(-0.551808\pi\) |
0.988561 | − | 0.150822i | \(-0.0481921\pi\) | |||||||
\(578\) | 16.0292 | − | 5.20820i | 0.666727 | − | 0.216633i | ||||
\(579\) | −2.38197 | − | 7.33094i | −0.0989911 | − | 0.304663i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.19098 | + | 3.66547i | −0.0494103 | + | 0.152069i | ||||
\(582\) | − | 6.23607i | − | 0.258493i | ||||||
\(583\) | 17.2905 | + | 5.61803i | 0.716101 | + | 0.232675i | ||||
\(584\) | −16.2812 | + | 11.8290i | −0.673719 | + | 0.489485i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.5623 | − | 18.5721i | −1.05597 | − | 0.767206i | ||||
\(587\) | 3.11044 | + | 4.28115i | 0.128382 | + | 0.176702i | 0.868369 | − | 0.495919i | \(-0.165169\pi\) |
−0.739987 | + | 0.672621i | \(0.765169\pi\) | |||||||
\(588\) | 2.40414 | + | 3.30902i | 0.0991451 | + | 0.136462i | ||||
\(589\) | −2.07295 | − | 1.50609i | −0.0854144 | − | 0.0620572i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00000 | + | 2.17963i | −0.123404 | + | 0.0896579i | ||||
\(592\) | −1.08981 | − | 0.354102i | −0.0447911 | − | 0.0145535i | ||||
\(593\) | − | 10.9098i | − | 0.448013i | −0.974588 | − | 0.224007i | \(-0.928086\pi\) | ||
0.974588 | − | 0.224007i | \(-0.0719137\pi\) | |||||||
\(594\) | 13.0902 | − | 40.2874i | 0.537096 | − | 1.65301i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.753289 | − | 2.31838i | −0.0308559 | − | 0.0949647i | ||||
\(597\) | −16.7027 | + | 5.42705i | −0.683598 | + | 0.222114i | ||||
\(598\) | −6.63715 | + | 9.13525i | −0.271413 | + | 0.373568i | ||||
\(599\) | 9.47214 | 0.387021 | 0.193510 | − | 0.981098i | \(-0.438013\pi\) | ||||
0.193510 | + | 0.981098i | \(0.438013\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.72949 | 0.111338 | 0.0556691 | − | 0.998449i | \(-0.482271\pi\) | ||||
0.0556691 | + | 0.998449i | \(0.482271\pi\) | |||||||
\(602\) | −2.85317 | + | 3.92705i | −0.116287 | + | 0.160055i | ||||
\(603\) | 9.06154 | − | 2.94427i | 0.369014 | − | 0.119900i | ||||
\(604\) | −2.78115 | − | 8.55951i | −0.113164 | − | 0.348281i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.736068 | + | 2.26538i | −0.0299007 | + | 0.0920249i | ||||
\(607\) | 35.5623i | 1.44343i | 0.692191 | + | 0.721715i | \(0.256646\pi\) | ||||
−0.692191 | + | 0.721715i | \(0.743354\pi\) | |||||||
\(608\) | 2.74717 | + | 0.892609i | 0.111412 | + | 0.0362001i | ||||
\(609\) | −1.80902 | + | 1.31433i | −0.0733051 | + | 0.0532592i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.927051 | − | 0.673542i | −0.0375045 | − | 0.0272486i | ||||
\(612\) | 3.80423 | + | 5.23607i | 0.153777 | + | 0.211656i | ||||
\(613\) | 8.80427 | + | 12.1180i | 0.355601 | + | 0.489443i | 0.948917 | − | 0.315527i | \(-0.102181\pi\) |
−0.593316 | + | 0.804970i | \(0.702181\pi\) | |||||||
\(614\) | −12.0902 | − | 8.78402i | −0.487920 | − | 0.354494i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.85410 | − | 4.25325i | 0.235868 | − | 0.171368i | ||||
\(617\) | −13.5393 | − | 4.39919i | −0.545072 | − | 0.177105i | 0.0235215 | − | 0.999723i | \(-0.492512\pi\) |
−0.568593 | + | 0.822619i | \(0.692512\pi\) | |||||||
\(618\) | − | 13.8541i | − | 0.557294i | ||||||
\(619\) | −9.43363 | + | 29.0337i | −0.379170 | + | 1.16696i | 0.561453 | + | 0.827509i | \(0.310243\pi\) |
−0.940622 | + | 0.339455i | \(0.889757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.81559 | − | 17.8986i | −0.233372 | − | 0.718244i | ||||
\(622\) | −13.0903 | + | 4.25329i | −0.524872 | + | 0.170541i | ||||
\(623\) | −3.24920 | + | 4.47214i | −0.130176 | + | 0.179172i | ||||
\(624\) | 9.00000 | 0.360288 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 27.1246 | 1.08412 | ||||||||
\(627\) | 2.62866 | − | 3.61803i | 0.104978 | − | 0.144490i | ||||
\(628\) | −7.74721 | + | 2.51722i | −0.309147 | + | 0.100448i | ||||
\(629\) | −0.381966 | − | 1.17557i | −0.0152300 | − | 0.0468731i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.16312 | + | 9.73508i | −0.125922 | + | 0.387547i | −0.994068 | − | 0.108761i | \(-0.965312\pi\) |
0.868146 | + | 0.496309i | \(0.165312\pi\) | |||||||
\(632\) | 18.0902i | 0.719588i | ||||||||
\(633\) | −8.73102 | − | 2.83688i | −0.347027 | − | 0.112756i | ||||
\(634\) | −10.0172 | + | 7.27794i | −0.397835 | + | 0.289044i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.73607 | + | 1.26133i | 0.0688396 | + | 0.0500149i | ||||
\(637\) | −7.21242 | − | 9.92705i | −0.285767 | − | 0.393324i | ||||
\(638\) | 18.0171 | + | 24.7984i | 0.713303 | + | 0.981777i | ||||
\(639\) | 10.7082 | + | 7.77997i | 0.423610 | + | 0.307771i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.881966 | − | 0.640786i | 0.0348356 | − | 0.0253095i | −0.570231 | − | 0.821484i | \(-0.693146\pi\) |
0.605067 | + | 0.796175i | \(0.293146\pi\) | |||||||
\(642\) | −25.2623 | − | 8.20820i | −0.997022 | − | 0.323952i | ||||
\(643\) | − | 30.8328i | − | 1.21593i | −0.793965 | − | 0.607964i | \(-0.791987\pi\) | ||
0.793965 | − | 0.607964i | \(-0.208013\pi\) | |||||||
\(644\) | −0.444272 | + | 1.36733i | −0.0175068 | + | 0.0538803i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.23607 | + | 6.88191i | 0.0879769 | + | 0.270765i | ||||
\(647\) | −34.7526 | + | 11.2918i | −1.36626 | + | 0.443926i | −0.898130 | − | 0.439731i | \(-0.855074\pi\) |
−0.468135 | + | 0.883657i | \(0.655074\pi\) | |||||||
\(648\) | 1.31433 | − | 1.80902i | 0.0516317 | − | 0.0710649i | ||||
\(649\) | −56.8328 | −2.23088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.85410 | −0.0726680 | ||||||||
\(652\) | −3.99598 | + | 5.50000i | −0.156495 | + | 0.215397i | ||||
\(653\) | −18.1558 | + | 5.89919i | −0.710493 | + | 0.230853i | −0.641896 | − | 0.766791i | \(-0.721852\pi\) |
−0.0685963 | + | 0.997645i | \(0.521852\pi\) | |||||||
\(654\) | 5.00000 | + | 15.3884i | 0.195515 | + | 0.601735i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.14590 | − | 3.52671i | 0.0447398 | − | 0.137695i | ||||
\(657\) | − | 18.0000i | − | 0.702247i | ||||||
\(658\) | −0.587785 | − | 0.190983i | −0.0229143 | − | 0.00744529i | ||||
\(659\) | 12.5623 | − | 9.12705i | 0.489358 | − | 0.355539i | −0.315579 | − | 0.948899i | \(-0.602199\pi\) |
0.804937 | + | 0.593360i | \(0.202199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.9271 | − | 11.5717i | −0.619490 | − | 0.450086i | 0.233253 | − | 0.972416i | \(-0.425063\pi\) |
−0.852744 | + | 0.522330i | \(0.825063\pi\) | |||||||
\(662\) | 21.9928 | + | 30.2705i | 0.854775 | + | 1.17650i | ||||
\(663\) | 5.70634 | + | 7.85410i | 0.221616 | + | 0.305028i | ||||
\(664\) | −11.2812 | − | 8.19624i | −0.437794 | − | 0.318076i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.618034 | − | 0.449028i | 0.0239483 | − | 0.0173995i | ||||
\(667\) | 12.9515 | + | 4.20820i | 0.501485 | + | 0.162942i | ||||
\(668\) | 9.00000i | 0.348220i | ||||||||
\(669\) | 0.0557281 | − | 0.171513i | 0.00215457 | − | 0.00663109i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.0902 | − | 43.3651i | −0.543945 | − | 1.67409i | ||||
\(672\) | 1.98787 | − | 0.645898i | 0.0766837 | − | 0.0249161i | ||||
\(673\) | 7.15942 | − | 9.85410i | 0.275976 | − | 0.379848i | −0.648420 | − | 0.761283i | \(-0.724570\pi\) |
0.924396 | + | 0.381435i | \(0.124570\pi\) | |||||||
\(674\) | 12.7082 | 0.489502 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.90983 | −0.227301 | ||||||||
\(677\) | −6.24112 | + | 8.59017i | −0.239866 | + | 0.330147i | −0.911930 | − | 0.410346i | \(-0.865408\pi\) |
0.672064 | + | 0.740493i | \(0.265408\pi\) | |||||||
\(678\) | 25.9358 | − | 8.42705i | 0.996058 | − | 0.323639i | ||||
\(679\) | 0.736068 | + | 2.26538i | 0.0282477 | + | 0.0869375i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.56231 | − | 14.0413i | 0.174828 | − | 0.538065i | ||||
\(682\) | 25.4164i | 0.973245i | ||||||||
\(683\) | −12.8128 | − | 4.16312i | −0.490267 | − | 0.159297i | 0.0534426 | − | 0.998571i | \(-0.482981\pi\) |
−0.543709 | + | 0.839274i | \(0.682981\pi\) | |||||||
\(684\) | −0.854102 | + | 0.620541i | −0.0326574 | + | 0.0237270i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.0172 | − | 8.00448i | −0.420639 | − | 0.305612i | ||||
\(687\) | 12.7598 | + | 17.5623i | 0.486815 | + | 0.670044i | ||||
\(688\) | −13.8496 | − | 19.0623i | −0.528010 | − | 0.726744i | ||||
\(689\) | −5.20820 | − | 3.78398i | −0.198417 | − | 0.144158i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.3435 | + | 21.3193i | −1.11628 | + | 0.811023i | −0.983641 | − | 0.180141i | \(-0.942344\pi\) |
−0.132637 | + | 0.991165i | \(0.542344\pi\) | |||||||
\(692\) | −11.1024 | − | 3.60739i | −0.422050 | − | 0.137132i | ||||
\(693\) | 6.47214i | 0.245856i | ||||||||
\(694\) | −9.95492 | + | 30.6381i | −0.377883 | + | 1.16301i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.50000 | − | 7.69421i | −0.0947623 | − | 0.291648i | ||||
\(697\) | 3.80423 | − | 1.23607i | 0.144095 | − | 0.0468194i | ||||
\(698\) | −20.6457 | + | 28.4164i | −0.781452 | + | 1.07558i | ||||
\(699\) | 2.94427 | 0.111363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.0132 | −1.54905 | −0.774523 | − | 0.632546i | \(-0.782010\pi\) | ||||
−0.774523 | + | 0.632546i | \(0.782010\pi\) | |||||||
\(702\) | −8.81678 | + | 12.1353i | −0.332768 | + | 0.458016i | ||||
\(703\) | 0.191758 | − | 0.0623059i | 0.00723228 | − | 0.00234991i | ||||
\(704\) | 6.85410 | + | 21.0948i | 0.258324 | + | 0.795039i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.45492 | + | 19.8662i | −0.242934 | + | 0.747674i | ||||
\(707\) | − | 0.909830i | − | 0.0342177i | ||||||
\(708\) | −6.37988 | − | 2.07295i | −0.239771 | − | 0.0779062i | ||||
\(709\) | −27.1353 | + | 19.7149i | −1.01909 | + | 0.740409i | −0.966095 | − | 0.258186i | \(-0.916875\pi\) |
−0.0529906 | + | 0.998595i | \(0.516875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.0902 | − | 9.51057i | −0.490920 | − | 0.356674i | ||||
\(712\) | −11.7557 | − | 16.1803i | −0.440564 | − | 0.606384i | ||||
\(713\) | 6.63715 | + | 9.13525i | 0.248563 | + | 0.342118i | ||||
\(714\) | 4.23607 | + | 3.07768i | 0.158531 | + | 0.115179i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.263932 | − | 0.191758i | 0.00986360 | − | 0.00716633i | ||||
\(717\) | 19.5232 | + | 6.34346i | 0.729106 | + | 0.236901i | ||||
\(718\) | − | 22.2361i | − | 0.829843i | ||||||
\(719\) | 7.19756 | − | 22.1518i | 0.268424 | − | 0.826123i | −0.722461 | − | 0.691412i | \(-0.756989\pi\) |
0.990885 | − | 0.134712i | \(-0.0430108\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.63525 | + | 5.03280i | 0.0609001 | + | 0.187431i | ||||
\(722\) | 28.1154 | − | 9.13525i | 1.04635 | − | 0.339979i | ||||
\(723\) | 1.48584 | − | 2.04508i | 0.0552590 | − | 0.0760575i | ||||
\(724\) | −0.180340 | −0.00670228 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −26.5623 | −0.985820 | ||||||||
\(727\) | −14.4374 | + | 19.8713i | −0.535452 | + | 0.736987i | −0.987949 | − | 0.154779i | \(-0.950533\pi\) |
0.452497 | + | 0.891766i | \(0.350533\pi\) | |||||||
\(728\) | −2.43690 | + | 0.791796i | −0.0903174 | + | 0.0293459i | ||||
\(729\) | −4.01722 | − | 12.3637i | −0.148786 | − | 0.457916i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.85410 | − | 24.1724i | 0.290494 | − | 0.894050i | ||||
\(732\) | − | 5.38197i | − | 0.198923i | ||||||
\(733\) | −19.0009 | − | 6.17376i | −0.701814 | − | 0.228033i | −0.0636931 | − | 0.997970i | \(-0.520288\pi\) |
−0.638121 | + | 0.769936i | \(0.720288\pi\) | |||||||
\(734\) | 33.4615 | − | 24.3112i | 1.23509 | − | 0.897343i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.2984 | − | 7.48221i | −0.379603 | − | 0.275798i | ||||
\(737\) | −14.6619 | − | 20.1803i | −0.540077 | − | 0.743352i | ||||
\(738\) | 1.45309 | + | 2.00000i | 0.0534888 | + | 0.0736210i | ||||
\(739\) | 12.9271 | + | 9.39205i | 0.475529 | + | 0.345492i | 0.799592 | − | 0.600543i | \(-0.205049\pi\) |
−0.324063 | + | 0.946036i | \(0.605049\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.28115 | + | 0.930812i | −0.0470643 | + | 0.0341942i | ||||
\(742\) | −3.30220 | − | 1.07295i | −0.121227 | − | 0.0393892i | ||||
\(743\) | 28.3607i | 1.04045i | 0.854029 | + | 0.520226i | \(0.174152\pi\) | ||||
−0.854029 | + | 0.520226i | \(0.825848\pi\) | |||||||
\(744\) | 2.07295 | − | 6.37988i | 0.0759980 | − | 0.233898i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 14.1353 | + | 43.5038i | 0.517528 | + | 1.59279i | ||||
\(747\) | 11.8617 | − | 3.85410i | 0.433997 | − | 0.141014i | ||||
\(748\) | 9.95959 | − | 13.7082i | 0.364159 | − | 0.501222i | ||||
\(749\) | 10.1459 | 0.370723 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.11146 | −0.186520 | −0.0932598 | − | 0.995642i | \(-0.529729\pi\) | ||||
−0.0932598 | + | 0.995642i | \(0.529729\pi\) | |||||||
\(752\) | 1.76336 | − | 2.42705i | 0.0643030 | − | 0.0885054i | ||||
\(753\) | 27.7522 | − | 9.01722i | 1.01134 | − | 0.328606i | ||||
\(754\) | −3.35410 | − | 10.3229i | −0.122149 | − | 0.375937i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.590170 | + | 1.81636i | −0.0214643 | + | 0.0660602i | ||||
\(757\) | − | 30.4164i | − | 1.10550i | −0.833346 | − | 0.552752i | \(-0.813578\pi\) | ||
0.833346 | − | 0.552752i | \(-0.186422\pi\) | |||||||
\(758\) | −22.4621 | − | 7.29837i | −0.815860 | − | 0.265089i | ||||
\(759\) | −15.9443 | + | 11.5842i | −0.578740 | + | 0.420480i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9271 | + | 10.8451i | 0.541105 | + | 0.393136i | 0.824495 | − | 0.565869i | \(-0.191459\pi\) |
−0.283390 | + | 0.959005i | \(0.591459\pi\) | |||||||
\(762\) | −18.9151 | − | 26.0344i | −0.685223 | − | 0.943128i | ||||
\(763\) | −3.63271 | − | 5.00000i | −0.131513 | − | 0.181012i | ||||
\(764\) | −0.909830 | − | 0.661030i | −0.0329165 | − | 0.0239152i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43.6697 | − | 31.7279i | 1.57785 | − | 1.14638i | ||||
\(767\) | 19.1396 | + | 6.21885i | 0.691092 | + | 0.224550i | ||||
\(768\) | 13.5623i | 0.489388i | ||||||||
\(769\) | −4.14590 | + | 12.7598i | −0.149505 | + | 0.460129i | −0.997563 | − | 0.0697749i | \(-0.977772\pi\) |
0.848058 | + | 0.529904i | \(0.177772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.06231 | + | 21.7355i | 0.254343 | + | 0.782786i | ||||
\(772\) | 4.53077 | − | 1.47214i | 0.163066 | − | 0.0529833i | ||||
\(773\) | −21.2538 | + | 29.2533i | −0.764445 | + | 1.05217i | 0.232387 | + | 0.972623i | \(0.425346\pi\) |
−0.996831 | + | 0.0795442i | \(0.974654\pi\) | |||||||
\(774\) | 15.7082 | 0.564620 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.61803 | −0.309369 | ||||||||
\(777\) | 0.0857567 | − | 0.118034i | 0.00307650 | − | 0.00423445i | ||||
\(778\) | 23.0826 | − | 7.50000i | 0.827552 | − | 0.268888i | ||||
\(779\) | 0.201626 | + | 0.620541i | 0.00722401 | + | 0.0222332i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7082 | − | 32.9565i | 0.383170 | − | 1.17927i | ||||
\(782\) | − | 31.8885i | − | 1.14033i | ||||||
\(783\) | 17.2048 | + | 5.59017i | 0.614848 | + | 0.199776i | ||||
\(784\) | 25.9894 | − | 18.8824i | 0.928191 | − | 0.674370i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.89919 | + | 6.46564i | 0.317423 | + | 0.230622i | ||||
\(787\) | −6.94742 | − | 9.56231i | −0.247649 | − | 0.340859i | 0.667037 | − | 0.745024i | \(-0.267562\pi\) |
−0.914686 | + | 0.404165i | \(0.867562\pi\) | |||||||
\(788\) | −1.34708 | − | 1.85410i | −0.0479879 | − | 0.0660496i | ||||
\(789\) | −8.82624 | − | 6.41264i | −0.314222 | − | 0.228296i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.42705 | + | 6.12261i | −0.299631 | + | 0.217695i | ||||
\(792\) | −22.2703 | − | 7.23607i | −0.791342 | − | 0.257122i | ||||
\(793\) | 16.1459i | 0.573358i | ||||||||
\(794\) | 14.5172 | − | 44.6794i | 0.515197 | − | 1.58561i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.35410 | − | 10.3229i | −0.118883 | − | 0.365884i | ||||
\(797\) | 9.28605 | − | 3.01722i | 0.328929 | − | 0.106875i | −0.139897 | − | 0.990166i | \(-0.544677\pi\) |
0.468826 | + | 0.883291i | \(0.344677\pi\) | |||||||
\(798\) | −0.502029 | + | 0.690983i | −0.0177716 | + | 0.0244605i | ||||
\(799\) | 3.23607 | 0.114484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.8885 | 0.632061 | ||||||||
\(802\) | 25.2950 | − | 34.8156i | 0.893198 | − | 1.22938i | ||||
\(803\) | −44.8182 | + | 14.5623i | −1.58160 | + | 0.513893i | ||||
\(804\) | −0.909830 | − | 2.80017i | −0.0320872 | − | 0.0987543i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.78115 | − | 8.55951i | 0.0979619 | − | 0.301496i | ||||
\(807\) | 12.7639i | 0.449312i | ||||||||
\(808\) | 3.13068 | + | 1.01722i | 0.110137 | + | 0.0357857i | ||||
\(809\) | 25.0623 | − | 18.2088i | 0.881144 | − | 0.640188i | −0.0524101 | − | 0.998626i | \(-0.516690\pi\) |
0.933554 | + | 0.358437i | \(0.116690\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.8992 | + | 8.64527i | 0.417837 | + | 0.303576i | 0.776767 | − | 0.629788i | \(-0.216858\pi\) |
−0.358930 | + | 0.933364i | \(0.616858\pi\) | |||||||
\(812\) | −0.812299 | − | 1.11803i | −0.0285061 | − | 0.0392353i | ||||
\(813\) | 4.70228 | + | 6.47214i | 0.164916 | + | 0.226988i | ||||
\(814\) | −1.61803 | − | 1.17557i | −0.0567121 | − | 0.0412037i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −20.5623 | + | 14.9394i | −0.719825 | + | 0.522983i | ||||
\(817\) | 3.94298 | + | 1.28115i | 0.137948 | + | 0.0448219i | ||||
\(818\) | − | 2.56231i | − | 0.0895889i | ||||||
\(819\) | 0.708204 | − | 2.17963i | 0.0247466 | − | 0.0761624i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.5729 | − | 38.6956i | −0.438799 | − | 1.35048i | −0.889143 | − | 0.457629i | \(-0.848699\pi\) |
0.450344 | − | 0.892855i | \(-0.351301\pi\) | |||||||
\(822\) | 18.3803 | − | 5.97214i | 0.641088 | − | 0.208302i | ||||
\(823\) | 28.0422 | − | 38.5967i | 0.977489 | − | 1.34540i | 0.0393176 | − | 0.999227i | \(-0.487482\pi\) |
0.938171 | − | 0.346171i | \(-0.112518\pi\) | |||||||
\(824\) | −19.1459 | −0.666979 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.8541 | 0.377663 | ||||||||
\(827\) | 0.567541 | − | 0.781153i | 0.0197353 | − | 0.0271633i | −0.799035 | − | 0.601284i | \(-0.794656\pi\) |
0.818771 | + | 0.574121i | \(0.194656\pi\) | |||||||
\(828\) | 4.42477 | − | 1.43769i | 0.153771 | − | 0.0499633i | ||||
\(829\) | 11.0795 | + | 34.0993i | 0.384808 | + | 1.18432i | 0.936620 | + | 0.350348i | \(0.113937\pi\) |
−0.551812 | + | 0.833969i | \(0.686063\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.63525 | + | 23.4989i | −0.264864 | + | 0.815168i | ||||
\(832\) | − | 7.85410i | − | 0.272292i | ||||||
\(833\) | 32.9565 | + | 10.7082i | 1.14187 | + | 0.371017i | ||||
\(834\) | −6.54508 | + | 4.75528i | −0.226638 | + | 0.164662i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.23607 | + | 1.62460i | 0.0773360 | + | 0.0561879i | ||||
\(837\) | 8.81678 | + | 12.1353i | 0.304752 | + | 0.419456i | ||||
\(838\) | −9.00854 | − | 12.3992i | −0.311195 | − | 0.428323i | ||||
\(839\) | 8.78115 | + | 6.37988i | 0.303159 | + | 0.220258i | 0.728956 | − | 0.684561i | \(-0.240006\pi\) |
−0.425797 | + | 0.904819i | \(0.640006\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8713 | − | 9.35156i | 0.443839 | − | 0.322468i | ||||
\(842\) | 49.2429 | + | 16.0000i | 1.69702 | + | 0.551396i | ||||
\(843\) | 10.0902i | 0.347524i | ||||||||
\(844\) | 1.75329 | − | 5.39607i | 0.0603507 | − | 0.185740i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.618034 | + | 1.90211i | 0.0212484 | + | 0.0653960i | ||||
\(847\) | 9.64932 | − | 3.13525i | 0.331555 | − | 0.107729i | ||||
\(848\) | 9.90659 | − | 13.6353i | 0.340194 | − | 0.468237i | ||||
\(849\) | 29.8541 | 1.02459 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.888544 | −0.0304589 | ||||||||
\(852\) | 2.40414 | − | 3.30902i | 0.0823645 | − | 0.113365i | ||||
\(853\) | 14.5559 | − | 4.72949i | 0.498384 | − | 0.161935i | −0.0490292 | − | 0.998797i | \(-0.515613\pi\) |
0.547413 | + | 0.836863i | \(0.315613\pi\) | |||||||
\(854\) | 2.69098 | + | 8.28199i | 0.0920835 | + | 0.283404i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.3435 | + | 34.9116i | −0.387711 | + | 1.19325i | ||||
\(857\) | − | 19.6869i | − | 0.672492i | −0.941774 | − | 0.336246i | \(-0.890843\pi\) | ||
0.941774 | − | 0.336246i | \(-0.109157\pi\) | |||||||
\(858\) | 14.9394 | + | 4.85410i | 0.510022 | + | 0.165716i | ||||
\(859\) | −1.28115 | + | 0.930812i | −0.0437124 | + | 0.0317589i | −0.609427 | − | 0.792842i | \(-0.708600\pi\) |
0.565715 | + | 0.824601i | \(0.308600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.381966 | + | 0.277515i | 0.0130174 | + | 0.00945767i | ||||
\(862\) | 28.3727 | + | 39.0517i | 0.966378 | + | 1.33010i | ||||
\(863\) | 12.6008 | + | 17.3435i | 0.428935 | + | 0.590378i | 0.967708 | − | 0.252072i | \(-0.0811121\pi\) |
−0.538773 | + | 0.842451i | \(0.681112\pi\) | |||||||
\(864\) | −13.6803 | − | 9.93935i | −0.465415 | − | 0.338144i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 35.1525 | − | 25.5398i | 1.19453 | − | 0.867877i | ||||
\(867\) | −9.90659 | − | 3.21885i | −0.336446 | − | 0.109318i | ||||
\(868\) | − | 1.14590i | − | 0.0388943i | ||||||
\(869\) | −13.0902 | + | 40.2874i | −0.444054 | + | 1.36666i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.72949 | + | 8.40051i | 0.0924852 | + | 0.284640i | ||||
\(872\) | 21.2663 | − | 6.90983i | 0.720167 | − | 0.233996i | ||||
\(873\) | 4.53077 | − | 6.23607i | 0.153343 | − | 0.211059i | ||||
\(874\) | 5.20163 | 0.175948 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.56231 | −0.187933 | ||||||||
\(877\) | 21.4783 | − | 29.5623i | 0.725270 | − | 0.998248i | −0.274063 | − | 0.961712i | \(-0.588368\pi\) |
0.999332 | − | 0.0365363i | \(-0.0116324\pi\) | |||||||
\(878\) | −63.0598 | + | 20.4894i | −2.12816 | + | 0.691482i | ||||
\(879\) | 6.03444 | + | 18.5721i | 0.203537 | + | 0.626421i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.4721 | + | 38.3853i | −0.420197 | + | 1.29323i | 0.487322 | + | 0.873222i | \(0.337974\pi\) |
−0.907519 | + | 0.420011i | \(0.862026\pi\) | |||||||
\(882\) | 21.4164i | 0.721128i | ||||||||
\(883\) | −19.5762 | − | 6.36068i | −0.658790 | − | 0.214054i | −0.0395042 | − | 0.999219i | \(-0.512578\pi\) |
−0.619286 | + | 0.785165i | \(0.712578\pi\) | |||||||
\(884\) | −4.85410 | + | 3.52671i | −0.163261 | + | 0.118616i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.1976 | + | 28.4787i | 1.31687 | + | 0.956760i | ||||
\(887\) | 17.5680 | + | 24.1803i | 0.589877 | + | 0.811896i | 0.994735 | − | 0.102483i | \(-0.0326789\pi\) |
−0.404857 | + | 0.914380i | \(0.632679\pi\) | |||||||
\(888\) | 0.310271 | + | 0.427051i | 0.0104120 | + | 0.0143309i | ||||
\(889\) | 9.94427 | + | 7.22494i | 0.333520 | + | 0.242317i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.23607 | − | 3.07768i | 0.141914 | − | 0.103106i | ||||
\(892\) | 0.106001 | + | 0.0344419i | 0.00354918 | + | 0.00115320i | ||||
\(893\) | 0.527864i | 0.0176643i | ||||||||
\(894\) | −1.97214 | + | 6.06961i | −0.0659581 | + | 0.202998i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.60081 | − | 8.00448i | −0.0868871 | − | 0.267411i | ||||
\(897\) | 6.63715 | − | 2.15654i | 0.221608 | − | 0.0720048i | ||||
\(898\) | −4.44501 | + | 6.11803i | −0.148332 | + | 0.204161i | ||||
\(899\) | −10.8541 | −0.362005 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.1803 | 0.605675 | ||||||||
\(902\) | 3.80423 | − | 5.23607i | 0.126667 | − | 0.174342i | ||||
\(903\) | 2.85317 | − | 0.927051i | 0.0949475 | − | 0.0308503i | ||||
\(904\) | −11.6459 | − | 35.8424i | −0.387337 | − | 1.19210i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.28115 | + | 22.4091i | −0.241900 | + | 0.744492i | ||||
\(907\) | 33.2492i | 1.10402i | 0.833837 | + | 0.552011i | \(0.186139\pi\) | ||||
−0.833837 | + | 0.552011i | \(0.813861\pi\) | |||||||
\(908\) | 8.67802 | + | 2.81966i | 0.287990 | + | 0.0935737i | ||||
\(909\) | −2.38197 | + | 1.73060i | −0.0790048 | + | 0.0574004i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.5517 | + | 23.6502i | 1.07848 | + | 0.783565i | 0.977418 | − | 0.211315i | \(-0.0677745\pi\) |
0.101067 | + | 0.994880i | \(0.467774\pi\) | |||||||
\(912\) | −2.43690 | − | 3.35410i | −0.0806937 | − | 0.111065i | ||||
\(913\) | −19.1926 | − | 26.4164i | −0.635184 | − | 0.874255i | ||||
\(914\) | 28.0344 | + | 20.3682i | 0.927297 | + | 0.673721i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.8541 | + | 7.88597i | −0.358630 | + | 0.260560i | ||||
\(917\) | −3.99598 | − | 1.29837i | −0.131959 | − | 0.0428761i | ||||
\(918\) | − | 42.3607i | − | 1.39811i | ||||||
\(919\) | 16.4443 | − | 50.6103i | 0.542446 | − | 1.66948i | −0.184539 | − | 0.982825i | \(-0.559079\pi\) |
0.726985 | − | 0.686653i | \(-0.240921\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.85410 | + | 8.78402i | 0.0940459 | + | 0.289443i | ||||
\(922\) | −1.26133 | + | 0.409830i | −0.0415396 | + | 0.0134970i | ||||
\(923\) | −7.21242 | + | 9.92705i | −0.237400 | + | 0.326753i | ||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 39.0344 | 1.28275 | ||||||||
\(927\) | 10.0656 | − | 13.8541i | 0.330597 | − | 0.455028i | ||||
\(928\) | 11.6372 | − | 3.78115i | 0.382010 | − | 0.124122i | ||||
\(929\) | −12.8647 | − | 39.5936i | −0.422079 | − | 1.29902i | −0.905764 | − | 0.423782i | \(-0.860702\pi\) |
0.483685 | − | 0.875242i | \(-0.339298\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.74671 | + | 5.37582i | −0.0572461 | + | 0.176186i | ||||
\(932\) | 1.81966i | 0.0596049i | ||||||||
\(933\) | 8.09024 | + | 2.62868i | 0.264862 | + | 0.0860590i | ||||
\(934\) | −35.9336 | + | 26.1073i | −1.17578 | + | 0.854257i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.70820 | + | 4.87380i | 0.219265 | + | 0.159305i | ||||
\(937\) | 10.4211 | + | 14.3435i | 0.340444 | + | 0.468580i | 0.944571 | − | 0.328307i | \(-0.106478\pi\) |
−0.604127 | + | 0.796888i | \(0.706478\pi\) | |||||||
\(938\) | 2.80017 | + | 3.85410i | 0.0914288 | + | 0.125841i | ||||
\(939\) | −13.5623 | − | 9.85359i | −0.442589 | − | 0.321560i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.5517 | − | 27.2829i | 1.22415 | − | 0.889396i | 0.227712 | − | 0.973729i | \(-0.426876\pi\) |
0.996438 | + | 0.0843322i | \(0.0268757\pi\) | |||||||
\(942\) | 20.2825 | + | 6.59017i | 0.660838 | + | 0.214719i | ||||
\(943\) | − | 2.87539i | − | 0.0936355i | ||||||
\(944\) | −16.2812 | + | 50.1082i | −0.529906 | + | 1.63088i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.7082 | − | 39.1118i | −0.413179 | − | 1.27164i | ||||
\(947\) | 2.52265 | − | 0.819660i | 0.0819753 | − | 0.0266354i | −0.267742 | − | 0.963491i | \(-0.586278\pi\) |
0.349718 | + | 0.936855i | \(0.386278\pi\) | |||||||
\(948\) | −2.93893 | + | 4.04508i | −0.0954519 | + | 0.131378i | ||||
\(949\) | 16.6869 | 0.541680 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.65248 | 0.248149 | ||||||||
\(952\) | 4.25325 | − | 5.85410i | 0.137849 | − | 0.189733i | ||||
\(953\) | 7.36369 | − | 2.39261i | 0.238533 | − | 0.0775042i | −0.187311 | − | 0.982301i | \(-0.559977\pi\) |
0.425844 | + | 0.904796i | \(0.359977\pi\) | |||||||
\(954\) | 3.47214 | + | 10.6861i | 0.112415 | + | 0.345976i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.92047 | + | 12.0660i | −0.126797 | + | 0.390242i | ||||
\(957\) | − | 18.9443i | − | 0.612381i | ||||||
\(958\) | 16.7027 | + | 5.42705i | 0.539641 | + | 0.175340i | ||||
\(959\) | −5.97214 | + | 4.33901i | −0.192850 | + | 0.140114i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.7984 | + | 12.9313i | 0.574141 | + | 0.417138i | ||||
\(962\) | 0.416272 | + | 0.572949i | 0.0134211 | + | 0.0184726i | ||||
\(963\) | −19.2986 | − | 26.5623i | −0.621890 | − | 0.855958i | ||||
\(964\) | 1.26393 | + | 0.918300i | 0.0407085 | + | 0.0295765i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.04508 | − | 2.21238i | 0.0979740 | − | 0.0711823i | ||||
\(967\) | −3.91023 | − | 1.27051i | −0.125744 | − | 0.0408568i | 0.245469 | − | 0.969404i | \(-0.421058\pi\) |
−0.371213 | + | 0.928548i | \(0.621058\pi\) | |||||||
\(968\) | 36.7082i | 1.17985i | ||||||||
\(969\) | 1.38197 | − | 4.25325i | 0.0443951 | − | 0.136634i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.73607 | + | 5.34307i | 0.0557131 | + | 0.171467i | 0.975041 | − | 0.222025i | \(-0.0712667\pi\) |
−0.919328 | + | 0.393492i | \(0.871267\pi\) | |||||||
\(972\) | 9.40456 | − | 3.05573i | 0.301652 | − | 0.0980125i | ||||
\(973\) | 1.81636 | − | 2.50000i | 0.0582297 | − | 0.0801463i | ||||
\(974\) | −58.9230 | −1.88801 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42.2705 | −1.35305 | ||||||||
\(977\) | 1.37984 | − | 1.89919i | 0.0441450 | − | 0.0607604i | −0.786374 | − | 0.617751i | \(-0.788044\pi\) |
0.830519 | + | 0.556990i | \(0.188044\pi\) | |||||||
\(978\) | 16.9273 | − | 5.50000i | 0.541274 | − | 0.175871i | ||||
\(979\) | −14.4721 | − | 44.5407i | −0.462531 | − | 1.42353i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.18034 | + | 19.0211i | −0.197323 | + | 0.607298i | ||||
\(982\) | − | 69.9787i | − | 2.23311i | ||||||
\(983\) | 9.14729 | + | 2.97214i | 0.291753 | + | 0.0947964i | 0.451237 | − | 0.892404i | \(-0.350983\pi\) |
−0.159484 | + | 0.987201i | \(0.550983\pi\) | |||||||
\(984\) | −1.38197 | + | 1.00406i | −0.0440555 | + | 0.0320082i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 24.7984 | + | 18.0171i | 0.789741 | + | 0.573781i | ||||
\(987\) | 0.224514 | + | 0.309017i | 0.00714636 | + | 0.00983612i | ||||
\(988\) | −0.575274 | − | 0.791796i | −0.0183019 | − | 0.0251904i | ||||
\(989\) | −14.7812 | − | 10.7391i | −0.470013 | − | 0.341485i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.4271 | − | 9.02878i | 0.394758 | − | 0.286809i | −0.372644 | − | 0.927974i | \(-0.621549\pi\) |
0.767403 | + | 0.641166i | \(0.221549\pi\) | |||||||
\(992\) | 9.64932 | + | 3.13525i | 0.306366 | + | 0.0995444i | ||||
\(993\) | − | 23.1246i | − | 0.733837i | ||||||
\(994\) | −2.04508 | + | 6.29412i | −0.0648662 | + | 0.199638i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.19098 | − | 3.66547i | −0.0377377 | − | 0.116145i | ||||
\(997\) | 23.6704 | − | 7.69098i | 0.749649 | − | 0.243576i | 0.0908191 | − | 0.995867i | \(-0.471051\pi\) |
0.658830 | + | 0.752292i | \(0.271051\pi\) | |||||||
\(998\) | −7.19218 | + | 9.89919i | −0.227664 | + | 0.313353i | ||||
\(999\) | −1.18034 | −0.0373443 |
(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 | 625.2.e.c.249.2 | 8 | ||
5.2 | odd | 4 | 625.2.d.h.376.1 | 4 | |||
5.3 | odd | 4 | 625.2.d.b.376.1 | 4 | |||
5.4 | even | 2 | inner | 625.2.e.c.249.1 | 8 | ||
25.2 | odd | 20 | 625.2.d.h.251.1 | 4 | |||
25.3 | odd | 20 | 125.2.d.a.26.1 | 4 | |||
25.4 | even | 10 | 125.2.e.a.99.2 | 8 | |||
25.6 | even | 5 | 625.2.b.a.624.4 | 4 | |||
25.8 | odd | 20 | 625.2.a.c.1.2 | 2 | |||
25.9 | even | 10 | 125.2.e.a.24.1 | 8 | |||
25.11 | even | 5 | inner | 625.2.e.c.374.1 | 8 | ||
25.12 | odd | 20 | 25.2.d.a.21.1 | yes | 4 | ||
25.13 | odd | 20 | 125.2.d.a.101.1 | 4 | |||
25.14 | even | 10 | inner | 625.2.e.c.374.2 | 8 | ||
25.16 | even | 5 | 125.2.e.a.24.2 | 8 | |||
25.17 | odd | 20 | 625.2.a.b.1.1 | 2 | |||
25.19 | even | 10 | 625.2.b.a.624.1 | 4 | |||
25.21 | even | 5 | 125.2.e.a.99.1 | 8 | |||
25.22 | odd | 20 | 25.2.d.a.6.1 | ✓ | 4 | ||
25.23 | odd | 20 | 625.2.d.b.251.1 | 4 | |||
75.8 | even | 20 | 5625.2.a.d.1.1 | 2 | |||
75.17 | even | 20 | 5625.2.a.f.1.2 | 2 | |||
75.47 | even | 20 | 225.2.h.b.181.1 | 4 | |||
75.62 | even | 20 | 225.2.h.b.46.1 | 4 | |||
100.47 | even | 20 | 400.2.u.b.81.1 | 4 | |||
100.67 | even | 20 | 10000.2.a.c.1.1 | 2 | |||
100.83 | even | 20 | 10000.2.a.l.1.2 | 2 | |||
100.87 | even | 20 | 400.2.u.b.321.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.d.a.6.1 | ✓ | 4 | 25.22 | odd | 20 | ||
25.2.d.a.21.1 | yes | 4 | 25.12 | odd | 20 | ||
125.2.d.a.26.1 | 4 | 25.3 | odd | 20 | |||
125.2.d.a.101.1 | 4 | 25.13 | odd | 20 | |||
125.2.e.a.24.1 | 8 | 25.9 | even | 10 | |||
125.2.e.a.24.2 | 8 | 25.16 | even | 5 | |||
125.2.e.a.99.1 | 8 | 25.21 | even | 5 | |||
125.2.e.a.99.2 | 8 | 25.4 | even | 10 | |||
225.2.h.b.46.1 | 4 | 75.62 | even | 20 | |||
225.2.h.b.181.1 | 4 | 75.47 | even | 20 | |||
400.2.u.b.81.1 | 4 | 100.47 | even | 20 | |||
400.2.u.b.321.1 | 4 | 100.87 | even | 20 | |||
625.2.a.b.1.1 | 2 | 25.17 | odd | 20 | |||
625.2.a.c.1.2 | 2 | 25.8 | odd | 20 | |||
625.2.b.a.624.1 | 4 | 25.19 | even | 10 | |||
625.2.b.a.624.4 | 4 | 25.6 | even | 5 | |||
625.2.d.b.251.1 | 4 | 25.23 | odd | 20 | |||
625.2.d.b.376.1 | 4 | 5.3 | odd | 4 | |||
625.2.d.h.251.1 | 4 | 25.2 | odd | 20 | |||
625.2.d.h.376.1 | 4 | 5.2 | odd | 4 | |||
625.2.e.c.249.1 | 8 | 5.4 | even | 2 | inner | ||
625.2.e.c.249.2 | 8 | 1.1 | even | 1 | trivial | ||
625.2.e.c.374.1 | 8 | 25.11 | even | 5 | inner | ||
625.2.e.c.374.2 | 8 | 25.14 | even | 10 | inner | ||
5625.2.a.d.1.1 | 2 | 75.8 | even | 20 | |||
5625.2.a.f.1.2 | 2 | 75.17 | even | 20 | |||
10000.2.a.c.1.1 | 2 | 100.67 | even | 20 | |||
10000.2.a.l.1.2 | 2 | 100.83 | even | 20 |