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 | 249.1 | ||
Root | \(-0.951057 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.249 |
Dual form | 625.2.e.c.374.1 |
$q$-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 | −0.999814 | − | 0.0193004i | \(-0.993856\pi\) |
0.327315 | + | 0.944915i | \(0.393856\pi\) | |||||||
\(3\) | 0.951057 | − | 0.309017i | 0.549093 | − | 0.178411i | −0.0213149 | − | 0.999773i | \(-0.506785\pi\) |
0.570408 | + | 0.821362i | \(0.306785\pi\) | |||||||
\(4\) | −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 | \(0.0372628\pi\) | ||||
−0.993156 | + | 0.116797i | \(0.962737\pi\) | |||||||
\(8\) | −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 | 0.932948 | − | 0.360011i | \(-0.117227\pi\) |
−0.630688 | + | 0.776037i | \(0.717227\pi\) | |||||||
\(14\) | −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 | −0.365161 | − | 0.930944i | \(-0.618986\pi\) |
−0.842617 | + | 0.538513i | \(0.818986\pi\) | |||||||
\(18\) | − | 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 | −0.974781 | − | 0.223165i | \(-0.928361\pi\) |
0.513467 | + | 0.858110i | \(0.328361\pi\) | |||||||
\(24\) | −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 | 0.820270 | − | 0.571976i | \(-0.193823\pi\) |
−0.797459 | + | 0.603373i | \(0.793823\pi\) | |||||||
\(38\) | −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 | \(0.120684\pi\) | ||||
−0.928983 | + | 0.370122i | \(0.879316\pi\) | |||||||
\(44\) | 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 | −0.351572 | − | 0.936161i | \(-0.614353\pi\) |
0.265834 | + | 0.964019i | \(0.414353\pi\) | |||||||
\(48\) | 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 | −0.526898 | − | 0.849929i | \(-0.676645\pi\) |
0.0733062 | + | 0.997309i | \(0.476645\pi\) | |||||||
\(54\) | −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 | 0.572404 | − | 0.819972i | \(-0.306011\pi\) |
−0.0188826 | + | 0.999822i | \(0.506011\pi\) | |||||||
\(68\) | 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 | −0.378136 | − | 0.925750i | \(-0.623435\pi\) |
0.997291 | + | 0.0735557i | \(0.0234347\pi\) | |||||||
\(74\) | −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 | 0.615853 | − | 0.787861i | \(-0.288811\pi\) |
0.0351426 | + | 0.999382i | \(0.488811\pi\) | |||||||
\(84\) | 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 | −0.116958 | − | 0.993137i | \(-0.537314\pi\) |
0.489130 | + | 0.872211i | \(0.337314\pi\) | |||||||
\(98\) | −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 | 0.121011 | − | 0.992651i | \(-0.461386\pi\) |
0.681366 | + | 0.731943i | \(0.261386\pi\) | |||||||
\(104\) | −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 | \(-0.708248\pi\) | ||
0.608548 | − | 0.793517i | \(-0.291752\pi\) | |||||||
\(108\) | 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 | \(0.0913515\pi\) |
−0.0271666 | + | 0.999631i | \(0.508648\pi\) | |||||||
\(114\) | −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 | \(-0.455919\pi\) |
0.899294 | − | 0.437346i | \(-0.144081\pi\) | |||||||
\(128\) | −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 | 0.995691 | − | 0.0927283i | \(-0.0295588\pi\) |
−0.395875 | + | 0.918304i | \(0.629559\pi\) | |||||||
\(138\) | −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 | \(0.176291\pi\) | ||||
−0.850514 | + | 0.525953i | \(0.823709\pi\) | |||||||
\(158\) | −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 | 0.983312 | − | 0.181928i | \(-0.0582338\pi\) |
−0.476884 | + | 0.878966i | \(0.658234\pi\) | |||||||
\(164\) | −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 | 0.791154 | − | 0.611617i | \(-0.209480\pi\) |
0.280558 | + | 0.959837i | \(0.409480\pi\) | |||||||
\(168\) | − | 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 | \(0.454958\pi\) |
−0.985132 | + | 0.171799i | \(0.945042\pi\) | |||||||
\(174\) | −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 | \(-0.910519\pi\) | ||
0.960747 | − | 0.277424i | \(-0.0894808\pi\) | |||||||
\(194\) | −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 | −0.431943 | − | 0.901901i | \(-0.642172\pi\) |
0.180675 | + | 0.983543i | \(0.442172\pi\) | |||||||
\(198\) | 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 | −0.805453 | − | 0.592660i | \(-0.798078\pi\) |
0.812551 | + | 0.582890i | \(0.198078\pi\) | |||||||
\(224\) | −2.09017 | −0.139655 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.2705 | −1.81401 | ||||||||
\(227\) | 8.67802 | − | 11.9443i | 0.575981 | − | 0.792769i | −0.417267 | − | 0.908784i | \(-0.637012\pi\) |
0.993247 | + | 0.116015i | \(0.0370120\pi\) | |||||||
\(228\) | 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 | 0.399299 | − | 0.916821i | \(-0.369254\pi\) |
−0.215854 | + | 0.976426i | \(0.569254\pi\) | |||||||
\(234\) | 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 | \(0.252573\pi\) | ||||
−0.701367 | + | 0.712800i | \(0.747427\pi\) | |||||||
\(258\) | −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 | 0.564167 | − | 0.825661i | \(-0.309197\pi\) |
−0.959587 | + | 0.281412i | \(0.909197\pi\) | |||||||
\(264\) | −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 | \(0.466258\pi\) |
−0.978413 | + | 0.206657i | \(0.933742\pi\) | |||||||
\(278\) | −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 | 0.986396 | − | 0.164384i | \(-0.0525638\pi\) |
0.701389 | + | 0.712779i | \(0.252564\pi\) | |||||||
\(284\) | −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 | \(0.193218\pi\) | ||||
−0.821357 | + | 0.570415i | \(0.806782\pi\) | |||||||
\(294\) | −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 | \(0.0848984\pi\) | ||||
−0.964642 | + | 0.263565i | \(0.915102\pi\) | |||||||
\(308\) | 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 | 0.433978 | − | 0.900924i | \(-0.357110\pi\) |
−0.990936 | + | 0.134337i | \(0.957110\pi\) | |||||||
\(314\) | −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 | 0.506182 | − | 0.862427i | \(-0.331056\pi\) |
−0.0974121 | + | 0.995244i | \(0.531056\pi\) | |||||||
\(318\) | − | 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 | 0.664550 | − | 0.747244i | \(-0.268623\pi\) |
−0.916028 | + | 0.401114i | \(0.868623\pi\) | |||||||
\(338\) | 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 | 0.247063 | − | 0.969000i | \(-0.420535\pi\) |
0.769441 | + | 0.638717i | \(0.220535\pi\) | |||||||
\(348\) | 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 | 0.0365381 | − | 0.999332i | \(-0.488367\pi\) |
0.616953 | + | 0.787000i | \(0.288367\pi\) | |||||||
\(354\) | −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 | −0.404329 | − | 0.914614i | \(-0.632495\pi\) |
−0.864705 | + | 0.502279i | \(0.832495\pi\) | |||||||
\(368\) | 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 | \(-0.538636\pi\) |
0.981475 | − | 0.191589i | \(-0.0613642\pi\) | |||||||
\(374\) | 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 | −0.648990 | − | 0.760797i | \(-0.724808\pi\) |
−0.972229 | + | 0.234031i | \(0.924808\pi\) | |||||||
\(384\) | −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 | −0.904597 | − | 0.426268i | \(-0.859828\pi\) |
−0.481280 | + | 0.876567i | \(0.659828\pi\) | |||||||
\(398\) | −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 | −0.377605 | − | 0.925967i | \(-0.623252\pi\) |
−0.849758 | + | 0.527173i | \(0.823252\pi\) | |||||||
\(434\) | 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 | \(-0.748085\pi\) | ||
0.702840 | − | 0.711348i | \(-0.251915\pi\) | |||||||
\(444\) | 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 | \(-0.832999\pi\) | ||
0.865500 | − | 0.500909i | \(-0.167001\pi\) | |||||||
\(458\) | 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 | 0.340443 | − | 0.940265i | \(-0.389423\pi\) |
−0.999448 | + | 0.0332229i | \(0.989423\pi\) | |||||||
\(464\) | 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 | 0.842736 | − | 0.538328i | \(-0.180944\pi\) |
0.365367 | + | 0.930864i | \(0.380944\pi\) | |||||||
\(468\) | 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 | \(0.108877\pi\) |
0.0278844 | + | 0.999611i | \(0.491123\pi\) | |||||||
\(488\) | 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 | −0.963762 | − | 0.266764i | \(-0.914046\pi\) |
−0.622900 | + | 0.782301i | \(0.714046\pi\) | |||||||
\(504\) | 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 | −0.605943 | − | 0.795508i | \(-0.707204\pi\) |
0.943820 | + | 0.330461i | \(0.107204\pi\) | |||||||
\(524\) | −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 | 0.157760 | − | 0.987478i | \(-0.449573\pi\) |
0.708055 | + | 0.706157i | \(0.249573\pi\) | |||||||
\(548\) | 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 | \(0.0321809\pi\) | ||||
−0.994894 | + | 0.100927i | \(0.967819\pi\) | |||||||
\(558\) | 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 | 0.890603 | − | 0.454782i | \(-0.150283\pi\) |
−0.707735 | + | 0.706478i | \(0.750283\pi\) | |||||||
\(564\) | 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 | \(0.448192\pi\) |
−0.988561 | + | 0.150822i | \(0.951808\pi\) | |||||||
\(578\) | −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 | 0.739987 | − | 0.672621i | \(-0.234831\pi\) |
−0.868369 | + | 0.495919i | \(0.834831\pi\) | |||||||
\(588\) | −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 | \(0.0719137\pi\) | ||||
−0.974588 | + | 0.224007i | \(0.928086\pi\) | |||||||
\(594\) | 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 | \(-0.743354\pi\) | ||
0.692191 | − | 0.721715i | \(-0.256646\pi\) | |||||||
\(608\) | −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 | 0.593316 | − | 0.804970i | \(-0.297819\pi\) |
−0.948917 | + | 0.315527i | \(0.897819\pi\) | |||||||
\(614\) | −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 | 0.568593 | − | 0.822619i | \(-0.307488\pi\) |
−0.0235215 | + | 0.999723i | \(0.507488\pi\) | |||||||
\(618\) | 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 | \(0.208013\pi\) | ||||
−0.793965 | + | 0.607964i | \(0.791987\pi\) | |||||||
\(644\) | −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 | 0.468135 | − | 0.883657i | \(-0.344926\pi\) |
0.898130 | + | 0.439731i | \(0.144926\pi\) | |||||||
\(648\) | −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 | 0.0685963 | − | 0.997645i | \(-0.478148\pi\) |
0.641896 | + | 0.766791i | \(0.278148\pi\) | |||||||
\(654\) | 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 | −0.924396 | − | 0.381435i | \(-0.875430\pi\) |
0.648420 | + | 0.761283i | \(0.275430\pi\) | |||||||
\(674\) | 12.7082 | 0.489502 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.90983 | −0.227301 | ||||||||
\(677\) | 6.24112 | − | 8.59017i | 0.239866 | − | 0.330147i | −0.672064 | − | 0.740493i | \(-0.734592\pi\) |
0.911930 | + | 0.410346i | \(0.134592\pi\) | |||||||
\(678\) | −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 | 0.543709 | − | 0.839274i | \(-0.317019\pi\) |
−0.0534426 | + | 0.998571i | \(0.517019\pi\) | |||||||
\(684\) | −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 | −0.452497 | − | 0.891766i | \(-0.649467\pi\) |
0.987949 | + | 0.154779i | \(0.0494667\pi\) | |||||||
\(728\) | 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 | 0.638121 | − | 0.769936i | \(-0.279712\pi\) |
0.0636931 | + | 0.997970i | \(0.479712\pi\) | |||||||
\(734\) | 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 | \(-0.825848\pi\) | ||
0.854029 | − | 0.520226i | \(-0.174152\pi\) | |||||||
\(744\) | 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 | \(0.186422\pi\) | ||||
−0.833346 | + | 0.552752i | \(0.813578\pi\) | |||||||
\(758\) | 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 | \(-0.574654\pi\) |
0.996831 | − | 0.0795442i | \(-0.0253465\pi\) | |||||||
\(774\) | 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 | 0.914686 | − | 0.404165i | \(-0.132438\pi\) |
−0.667037 | + | 0.745024i | \(0.732438\pi\) | |||||||
\(788\) | 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 | −0.468826 | − | 0.883291i | \(-0.655323\pi\) |
0.139897 | + | 0.990166i | \(0.455323\pi\) | |||||||
\(798\) | 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 | \(0.512518\pi\) |
−0.938171 | + | 0.346171i | \(0.887482\pi\) | |||||||
\(824\) | −19.1459 | −0.666979 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.8541 | 0.377663 | ||||||||
\(827\) | −0.567541 | + | 0.781153i | −0.0197353 | + | 0.0271633i | −0.818771 | − | 0.574121i | \(-0.805344\pi\) |
0.799035 | + | 0.601284i | \(0.205344\pi\) | |||||||
\(828\) | −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 | −0.547413 | − | 0.836863i | \(-0.684387\pi\) |
0.0490292 | + | 0.998797i | \(0.484387\pi\) | |||||||
\(854\) | 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 | \(0.109157\pi\) | ||||
−0.941774 | + | 0.336246i | \(0.890843\pi\) | |||||||
\(858\) | −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 | 0.538773 | − | 0.842451i | \(-0.318888\pi\) |
−0.967708 | + | 0.252072i | \(0.918888\pi\) | |||||||
\(864\) | −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 | \(0.411632\pi\) |
−0.999332 | + | 0.0365363i | \(0.988368\pi\) | |||||||
\(878\) | 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 | 0.619286 | − | 0.785165i | \(-0.287422\pi\) |
0.0395042 | + | 0.999219i | \(0.487422\pi\) | |||||||
\(884\) | −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 | 0.404857 | − | 0.914380i | \(-0.367321\pi\) |
−0.994735 | + | 0.102483i | \(0.967321\pi\) | |||||||
\(888\) | −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 | \(-0.813861\pi\) | ||
0.833837 | − | 0.552011i | \(-0.186139\pi\) | |||||||
\(908\) | −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 | 0.604127 | − | 0.796888i | \(-0.293522\pi\) |
−0.944571 | + | 0.328307i | \(0.893522\pi\) | |||||||
\(938\) | −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 | −0.349718 | − | 0.936855i | \(-0.613722\pi\) |
0.267742 | + | 0.963491i | \(0.413722\pi\) | |||||||
\(948\) | 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 | −0.425844 | − | 0.904796i | \(-0.640023\pi\) |
0.187311 | + | 0.982301i | \(0.440023\pi\) | |||||||
\(954\) | 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 | 0.371213 | − | 0.928548i | \(-0.378942\pi\) |
−0.245469 | + | 0.969404i | \(0.578942\pi\) | |||||||
\(968\) | − | 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 | −0.830519 | − | 0.556990i | \(-0.811956\pi\) |
0.786374 | + | 0.617751i | \(0.211956\pi\) | |||||||
\(978\) | −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 | 0.159484 | − | 0.987201i | \(-0.449017\pi\) |
−0.451237 | + | 0.892404i | \(0.649017\pi\) | |||||||
\(984\) | −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 | −0.658830 | − | 0.752292i | \(-0.728949\pi\) |
−0.0908191 | + | 0.995867i | \(0.528949\pi\) | |||||||
\(998\) | 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.249.1 | 8 | ||
5.2 | odd | 4 | 625.2.d.b.376.1 | 4 | |||
5.3 | odd | 4 | 625.2.d.h.376.1 | 4 | |||
5.4 | even | 2 | inner | 625.2.e.c.249.2 | 8 | ||
25.2 | odd | 20 | 625.2.d.b.251.1 | 4 | |||
25.3 | odd | 20 | 25.2.d.a.6.1 | ✓ | 4 | ||
25.4 | even | 10 | 125.2.e.a.99.1 | 8 | |||
25.6 | even | 5 | 625.2.b.a.624.1 | 4 | |||
25.8 | odd | 20 | 625.2.a.b.1.1 | 2 | |||
25.9 | even | 10 | 125.2.e.a.24.2 | 8 | |||
25.11 | even | 5 | inner | 625.2.e.c.374.2 | 8 | ||
25.12 | odd | 20 | 125.2.d.a.101.1 | 4 | |||
25.13 | odd | 20 | 25.2.d.a.21.1 | yes | 4 | ||
25.14 | even | 10 | inner | 625.2.e.c.374.1 | 8 | ||
25.16 | even | 5 | 125.2.e.a.24.1 | 8 | |||
25.17 | odd | 20 | 625.2.a.c.1.2 | 2 | |||
25.19 | even | 10 | 625.2.b.a.624.4 | 4 | |||
25.21 | even | 5 | 125.2.e.a.99.2 | 8 | |||
25.22 | odd | 20 | 125.2.d.a.26.1 | 4 | |||
25.23 | odd | 20 | 625.2.d.h.251.1 | 4 | |||
75.8 | even | 20 | 5625.2.a.f.1.2 | 2 | |||
75.17 | even | 20 | 5625.2.a.d.1.1 | 2 | |||
75.38 | even | 20 | 225.2.h.b.46.1 | 4 | |||
75.53 | even | 20 | 225.2.h.b.181.1 | 4 | |||
100.3 | even | 20 | 400.2.u.b.81.1 | 4 | |||
100.63 | even | 20 | 400.2.u.b.321.1 | 4 | |||
100.67 | even | 20 | 10000.2.a.l.1.2 | 2 | |||
100.83 | even | 20 | 10000.2.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.d.a.6.1 | ✓ | 4 | 25.3 | odd | 20 | ||
25.2.d.a.21.1 | yes | 4 | 25.13 | odd | 20 | ||
125.2.d.a.26.1 | 4 | 25.22 | odd | 20 | |||
125.2.d.a.101.1 | 4 | 25.12 | odd | 20 | |||
125.2.e.a.24.1 | 8 | 25.16 | even | 5 | |||
125.2.e.a.24.2 | 8 | 25.9 | even | 10 | |||
125.2.e.a.99.1 | 8 | 25.4 | even | 10 | |||
125.2.e.a.99.2 | 8 | 25.21 | even | 5 | |||
225.2.h.b.46.1 | 4 | 75.38 | even | 20 | |||
225.2.h.b.181.1 | 4 | 75.53 | even | 20 | |||
400.2.u.b.81.1 | 4 | 100.3 | even | 20 | |||
400.2.u.b.321.1 | 4 | 100.63 | even | 20 | |||
625.2.a.b.1.1 | 2 | 25.8 | odd | 20 | |||
625.2.a.c.1.2 | 2 | 25.17 | odd | 20 | |||
625.2.b.a.624.1 | 4 | 25.6 | even | 5 | |||
625.2.b.a.624.4 | 4 | 25.19 | even | 10 | |||
625.2.d.b.251.1 | 4 | 25.2 | odd | 20 | |||
625.2.d.b.376.1 | 4 | 5.2 | odd | 4 | |||
625.2.d.h.251.1 | 4 | 25.23 | odd | 20 | |||
625.2.d.h.376.1 | 4 | 5.3 | odd | 4 | |||
625.2.e.c.249.1 | 8 | 1.1 | even | 1 | trivial | ||
625.2.e.c.249.2 | 8 | 5.4 | even | 2 | inner | ||
625.2.e.c.374.1 | 8 | 25.14 | even | 10 | inner | ||
625.2.e.c.374.2 | 8 | 25.11 | even | 5 | inner | ||
5625.2.a.d.1.1 | 2 | 75.17 | even | 20 | |||
5625.2.a.f.1.2 | 2 | 75.8 | even | 20 | |||
10000.2.a.c.1.1 | 2 | 100.83 | even | 20 | |||
10000.2.a.l.1.2 | 2 | 100.67 | even | 20 |