Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(43,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.w (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 267.6 | ||
Character | \(\chi\) | \(=\) | 280.267 |
Dual form | 280.2.w.a.43.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.25279 | − | 0.656136i | −0.885857 | − | 0.463958i | ||||
\(3\) | 0.683238 | − | 0.683238i | 0.394468 | − | 0.394468i | −0.481809 | − | 0.876276i | \(-0.660020\pi\) |
0.876276 | + | 0.481809i | \(0.160020\pi\) | |||||||
\(4\) | 1.13897 | + | 1.64400i | 0.569485 | + | 0.822001i | ||||
\(5\) | −2.03938 | + | 0.917023i | −0.912038 | + | 0.410105i | ||||
\(6\) | −1.30425 | + | 0.407657i | −0.532458 | + | 0.166425i | ||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.348203 | − | 2.80691i | −0.123108 | − | 0.992393i | ||||
\(9\) | 2.06637i | 0.688791i | ||||||||
\(10\) | 3.15661 | + | 0.189272i | 0.998207 | + | 0.0598530i | ||||
\(11\) | 5.41441 | 1.63251 | 0.816253 | − | 0.577694i | \(-0.196047\pi\) | ||||
0.816253 | + | 0.577694i | \(0.196047\pi\) | |||||||
\(12\) | 1.90143 | + | 0.345057i | 0.548896 | + | 0.0996094i | ||||
\(13\) | 3.15744 | + | 3.15744i | 0.875717 | + | 0.875717i | 0.993088 | − | 0.117371i | \(-0.0374466\pi\) |
−0.117371 | + | 0.993088i | \(0.537447\pi\) | |||||||
\(14\) | 1.34982 | − | 0.421899i | 0.360753 | − | 0.112757i | ||||
\(15\) | −0.766836 | + | 2.01993i | −0.197996 | + | 0.521543i | ||||
\(16\) | −1.40549 | + | 3.74494i | −0.351373 | + | 0.936236i | ||||
\(17\) | −2.46948 | − | 2.46948i | −0.598936 | − | 0.598936i | 0.341093 | − | 0.940029i | \(-0.389203\pi\) |
−0.940029 | + | 0.341093i | \(0.889203\pi\) | |||||||
\(18\) | 1.35582 | − | 2.58873i | 0.319570 | − | 0.610170i | ||||
\(19\) | 3.87964i | 0.890051i | 0.895518 | + | 0.445025i | \(0.146805\pi\) | ||||
−0.895518 | + | 0.445025i | \(0.853195\pi\) | |||||||
\(20\) | −3.83038 | − | 2.30828i | −0.856500 | − | 0.516148i | ||||
\(21\) | 0.966244i | 0.210852i | ||||||||
\(22\) | −6.78313 | − | 3.55259i | −1.44617 | − | 0.757415i | ||||
\(23\) | 0.659207 | + | 0.659207i | 0.137454 | + | 0.137454i | 0.772486 | − | 0.635032i | \(-0.219013\pi\) |
−0.635032 | + | 0.772486i | \(0.719013\pi\) | |||||||
\(24\) | −2.15569 | − | 1.67988i | −0.440029 | − | 0.342905i | ||||
\(25\) | 3.31814 | − | 3.74032i | 0.663627 | − | 0.748063i | ||||
\(26\) | −1.88390 | − | 6.02733i | −0.369464 | − | 1.18206i | ||||
\(27\) | 3.46154 | + | 3.46154i | 0.666173 | + | 0.666173i | ||||
\(28\) | −1.96786 | − | 0.357112i | −0.371891 | − | 0.0674877i | ||||
\(29\) | 5.76955 | 1.07138 | 0.535689 | − | 0.844415i | \(-0.320052\pi\) | ||||
0.535689 | + | 0.844415i | \(0.320052\pi\) | |||||||
\(30\) | 2.28603 | − | 2.02740i | 0.417370 | − | 0.370150i | ||||
\(31\) | 3.09841i | 0.556492i | 0.960510 | + | 0.278246i | \(0.0897530\pi\) | ||||
−0.960510 | + | 0.278246i | \(0.910247\pi\) | |||||||
\(32\) | 4.21798 | − | 3.76944i | 0.745640 | − | 0.666349i | ||||
\(33\) | 3.69933 | − | 3.69933i | 0.643971 | − | 0.643971i | ||||
\(34\) | 1.47343 | + | 4.71405i | 0.252690 | + | 0.808453i | ||||
\(35\) | 0.793626 | − | 2.09049i | 0.134147 | − | 0.353358i | ||||
\(36\) | −3.39712 | + | 2.35354i | −0.566187 | + | 0.392256i | ||||
\(37\) | −0.680801 | + | 0.680801i | −0.111923 | + | 0.111923i | −0.760850 | − | 0.648927i | \(-0.775218\pi\) |
0.648927 | + | 0.760850i | \(0.275218\pi\) | |||||||
\(38\) | 2.54557 | − | 4.86038i | 0.412946 | − | 0.788458i | ||||
\(39\) | 4.31457 | 0.690884 | ||||||||
\(40\) | 3.28412 | + | 5.40505i | 0.519265 | + | 0.854613i | ||||
\(41\) | −7.39465 | −1.15485 | −0.577425 | − | 0.816444i | \(-0.695942\pi\) | ||||
−0.577425 | + | 0.816444i | \(0.695942\pi\) | |||||||
\(42\) | 0.633988 | − | 1.21050i | 0.0978264 | − | 0.186785i | ||||
\(43\) | −0.0846505 | + | 0.0846505i | −0.0129091 | + | 0.0129091i | −0.713532 | − | 0.700623i | \(-0.752906\pi\) |
0.700623 | + | 0.713532i | \(0.252906\pi\) | |||||||
\(44\) | 6.16686 | + | 8.90131i | 0.929689 | + | 1.34192i | ||||
\(45\) | −1.89491 | − | 4.21412i | −0.282477 | − | 0.628203i | ||||
\(46\) | −0.393319 | − | 1.25838i | −0.0579917 | − | 0.185538i | ||||
\(47\) | 2.32683 | − | 2.32683i | 0.339403 | − | 0.339403i | −0.516740 | − | 0.856143i | \(-0.672854\pi\) |
0.856143 | + | 0.516740i | \(0.172854\pi\) | |||||||
\(48\) | 1.59840 | + | 3.51897i | 0.230709 | + | 0.507920i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −6.61109 | + | 2.50869i | −0.934949 | + | 0.354782i | ||||
\(51\) | −3.37448 | −0.472522 | ||||||||
\(52\) | −1.59461 | + | 8.78708i | −0.221133 | + | 1.21855i | ||||
\(53\) | −8.08545 | − | 8.08545i | −1.11062 | − | 1.11062i | −0.993066 | − | 0.117556i | \(-0.962494\pi\) |
−0.117556 | − | 0.993066i | \(-0.537506\pi\) | |||||||
\(54\) | −2.06534 | − | 6.60782i | −0.281058 | − | 0.899211i | ||||
\(55\) | −11.0420 | + | 4.96514i | −1.48891 | + | 0.669500i | ||||
\(56\) | 2.23100 | + | 1.73857i | 0.298130 | + | 0.232326i | ||||
\(57\) | 2.65072 | + | 2.65072i | 0.351096 | + | 0.351096i | ||||
\(58\) | −7.22804 | − | 3.78561i | −0.949088 | − | 0.497075i | ||||
\(59\) | 7.94305i | 1.03410i | 0.855956 | + | 0.517049i | \(0.172969\pi\) | ||||
−0.855956 | + | 0.517049i | \(0.827031\pi\) | |||||||
\(60\) | −4.19417 | + | 1.03996i | −0.541465 | + | 0.134258i | ||||
\(61\) | − | 4.20293i | − | 0.538130i | −0.963122 | − | 0.269065i | \(-0.913285\pi\) | ||
0.963122 | − | 0.269065i | \(-0.0867147\pi\) | |||||||
\(62\) | 2.03298 | − | 3.88167i | 0.258189 | − | 0.492972i | ||||
\(63\) | −1.46115 | − | 1.46115i | −0.184087 | − | 0.184087i | ||||
\(64\) | −7.75751 | + | 1.95475i | −0.969689 | + | 0.244344i | ||||
\(65\) | −9.33468 | − | 3.54378i | −1.15782 | − | 0.439551i | ||||
\(66\) | −7.06175 | + | 2.20722i | −0.869242 | + | 0.271690i | ||||
\(67\) | 7.82159 | + | 7.82159i | 0.955559 | + | 0.955559i | 0.999054 | − | 0.0434947i | \(-0.0138491\pi\) |
−0.0434947 | + | 0.999054i | \(0.513849\pi\) | |||||||
\(68\) | 1.24716 | − | 6.87249i | 0.151241 | − | 0.833412i | ||||
\(69\) | 0.900790 | 0.108442 | ||||||||
\(70\) | −2.36589 | + | 2.09822i | −0.282778 | + | 0.250786i | ||||
\(71\) | − | 2.85514i | − | 0.338842i | −0.985544 | − | 0.169421i | \(-0.945810\pi\) | ||
0.985544 | − | 0.169421i | \(-0.0541898\pi\) | |||||||
\(72\) | 5.80013 | − | 0.719517i | 0.683551 | − | 0.0847958i | ||||
\(73\) | 1.45516 | − | 1.45516i | 0.170314 | − | 0.170314i | −0.616803 | − | 0.787117i | \(-0.711573\pi\) |
0.787117 | + | 0.616803i | \(0.211573\pi\) | |||||||
\(74\) | 1.29960 | − | 0.406203i | 0.151075 | − | 0.0472202i | ||||
\(75\) | −0.288449 | − | 4.82260i | −0.0333073 | − | 0.556866i | ||||
\(76\) | −6.37814 | + | 4.41880i | −0.731623 | + | 0.506871i | ||||
\(77\) | −3.82857 | + | 3.82857i | −0.436306 | + | 0.436306i | ||||
\(78\) | −5.40525 | − | 2.83095i | −0.612025 | − | 0.320541i | ||||
\(79\) | −12.8568 | −1.44650 | −0.723249 | − | 0.690587i | \(-0.757352\pi\) | ||||
−0.723249 | + | 0.690587i | \(0.757352\pi\) | |||||||
\(80\) | −0.567870 | − | 8.92623i | −0.0634898 | − | 0.997982i | ||||
\(81\) | −1.46901 | −0.163223 | ||||||||
\(82\) | 9.26395 | + | 4.85190i | 1.02303 | + | 0.535802i | ||||
\(83\) | −3.88328 | + | 3.88328i | −0.426245 | + | 0.426245i | −0.887347 | − | 0.461102i | \(-0.847454\pi\) |
0.461102 | + | 0.887347i | \(0.347454\pi\) | |||||||
\(84\) | −1.58851 | + | 1.10052i | −0.173320 | + | 0.120077i | ||||
\(85\) | 7.30077 | + | 2.77163i | 0.791879 | + | 0.300626i | ||||
\(86\) | 0.161592 | − | 0.0505071i | 0.0174249 | − | 0.00544632i | ||||
\(87\) | 3.94197 | − | 3.94197i | 0.422624 | − | 0.422624i | ||||
\(88\) | −1.88531 | − | 15.1978i | −0.200975 | − | 1.62009i | ||||
\(89\) | − | 1.96589i | − | 0.208384i | −0.994557 | − | 0.104192i | \(-0.966774\pi\) | ||
0.994557 | − | 0.104192i | \(-0.0332256\pi\) | |||||||
\(90\) | −0.391106 | + | 6.52273i | −0.0412262 | + | 0.687556i | ||||
\(91\) | −4.46530 | −0.468091 | ||||||||
\(92\) | −0.332921 | + | 1.83455i | −0.0347094 | + | 0.191266i | ||||
\(93\) | 2.11695 | + | 2.11695i | 0.219518 | + | 0.219518i | ||||
\(94\) | −4.44175 | + | 1.38832i | −0.458132 | + | 0.143194i | ||||
\(95\) | −3.55772 | − | 7.91206i | −0.365015 | − | 0.811760i | ||||
\(96\) | 0.306460 | − | 5.45730i | 0.0312780 | − | 0.556984i | ||||
\(97\) | −13.2788 | − | 13.2788i | −1.34826 | − | 1.34826i | −0.887552 | − | 0.460707i | \(-0.847596\pi\) |
−0.460707 | − | 0.887552i | \(-0.652404\pi\) | |||||||
\(98\) | −0.656136 | + | 1.25279i | −0.0662798 | + | 0.126551i | ||||
\(99\) | 11.1882i | 1.12446i | ||||||||
\(100\) | 9.92835 | + | 1.19491i | 0.992835 | + | 0.119491i | ||||
\(101\) | − | 12.7251i | − | 1.26619i | −0.774073 | − | 0.633097i | \(-0.781784\pi\) | ||
0.774073 | − | 0.633097i | \(-0.218216\pi\) | |||||||
\(102\) | 4.22752 | + | 2.21412i | 0.418587 | + | 0.219230i | ||||
\(103\) | 8.27848 | + | 8.27848i | 0.815703 | + | 0.815703i | 0.985482 | − | 0.169779i | \(-0.0543054\pi\) |
−0.169779 | + | 0.985482i | \(0.554305\pi\) | |||||||
\(104\) | 7.76324 | − | 9.96210i | 0.761248 | − | 0.976864i | ||||
\(105\) | −0.886068 | − | 1.97054i | −0.0864714 | − | 0.192305i | ||||
\(106\) | 4.82422 | + | 15.4345i | 0.468570 | + | 1.49913i | ||||
\(107\) | −4.27215 | − | 4.27215i | −0.413004 | − | 0.413004i | 0.469780 | − | 0.882784i | \(-0.344333\pi\) |
−0.882784 | + | 0.469780i | \(0.844333\pi\) | |||||||
\(108\) | −1.74819 | + | 9.63337i | −0.168219 | + | 0.926971i | ||||
\(109\) | 18.5611 | 1.77783 | 0.888915 | − | 0.458073i | \(-0.151460\pi\) | ||||
0.888915 | + | 0.458073i | \(0.151460\pi\) | |||||||
\(110\) | 17.0912 | + | 1.02480i | 1.62958 | + | 0.0977105i | ||||
\(111\) | 0.930298i | 0.0883000i | ||||||||
\(112\) | −1.65424 | − | 3.64191i | −0.156311 | − | 0.344128i | ||||
\(113\) | −7.33321 | + | 7.33321i | −0.689851 | + | 0.689851i | −0.962199 | − | 0.272348i | \(-0.912200\pi\) |
0.272348 | + | 0.962199i | \(0.412200\pi\) | |||||||
\(114\) | −1.58156 | − | 5.06003i | −0.148127 | − | 0.473915i | ||||
\(115\) | −1.94888 | − | 0.739865i | −0.181734 | − | 0.0689927i | ||||
\(116\) | 6.57135 | + | 9.48516i | 0.610134 | + | 0.880675i | ||||
\(117\) | −6.52445 | + | 6.52445i | −0.603186 | + | 0.603186i | ||||
\(118\) | 5.21172 | − | 9.95099i | 0.479778 | − | 0.916063i | ||||
\(119\) | 3.49237 | 0.320145 | ||||||||
\(120\) | 5.93677 | + | 1.44910i | 0.541950 | + | 0.132284i | ||||
\(121\) | 18.3159 | 1.66508 | ||||||||
\(122\) | −2.75770 | + | 5.26540i | −0.249670 | + | 0.476707i | ||||
\(123\) | −5.05230 | + | 5.05230i | −0.455551 | + | 0.455551i | ||||
\(124\) | −5.09380 | + | 3.52900i | −0.457437 | + | 0.316914i | ||||
\(125\) | −3.33698 | + | 10.6707i | −0.298469 | + | 0.954419i | ||||
\(126\) | 0.871800 | + | 2.78922i | 0.0776661 | + | 0.248484i | ||||
\(127\) | 15.8188 | − | 15.8188i | 1.40369 | − | 1.40369i | 0.615754 | − | 0.787938i | \(-0.288851\pi\) |
0.787938 | − | 0.615754i | \(-0.211149\pi\) | |||||||
\(128\) | 11.0011 | + | 2.64109i | 0.972371 | + | 0.233442i | ||||
\(129\) | 0.115673i | 0.0101844i | ||||||||
\(130\) | 9.36920 | + | 10.5644i | 0.821733 | + | 0.926562i | ||||
\(131\) | 8.12773 | 0.710123 | 0.355062 | − | 0.934843i | \(-0.384460\pi\) | ||||
0.355062 | + | 0.934843i | \(0.384460\pi\) | |||||||
\(132\) | 10.2951 | + | 1.86828i | 0.896077 | + | 0.162613i | ||||
\(133\) | −2.74332 | − | 2.74332i | −0.237876 | − | 0.237876i | ||||
\(134\) | −4.66679 | − | 14.9308i | −0.403149 | − | 1.28983i | ||||
\(135\) | −10.2337 | − | 3.88508i | −0.880776 | − | 0.334374i | ||||
\(136\) | −6.07172 | + | 7.79148i | −0.520646 | + | 0.668114i | ||||
\(137\) | 4.20821 | + | 4.20821i | 0.359531 | + | 0.359531i | 0.863640 | − | 0.504109i | \(-0.168179\pi\) |
−0.504109 | + | 0.863640i | \(0.668179\pi\) | |||||||
\(138\) | −1.12850 | − | 0.591041i | −0.0960644 | − | 0.0503127i | ||||
\(139\) | − | 21.7350i | − | 1.84354i | −0.387741 | − | 0.921769i | \(-0.626744\pi\) | ||
0.387741 | − | 0.921769i | \(-0.373256\pi\) | |||||||
\(140\) | 4.34069 | − | 1.07629i | 0.366855 | − | 0.0909628i | ||||
\(141\) | − | 3.17956i | − | 0.267767i | ||||||
\(142\) | −1.87336 | + | 3.57689i | −0.157209 | + | 0.300166i | ||||
\(143\) | 17.0957 | + | 17.0957i | 1.42961 | + | 1.42961i | ||||
\(144\) | −7.73845 | − | 2.90427i | −0.644870 | − | 0.242022i | ||||
\(145\) | −11.7663 | + | 5.29081i | −0.977138 | + | 0.439378i | ||||
\(146\) | −2.77780 | + | 0.868230i | −0.229892 | + | 0.0718552i | ||||
\(147\) | −0.683238 | − | 0.683238i | −0.0563525 | − | 0.0563525i | ||||
\(148\) | −1.89465 | − | 0.343826i | −0.155739 | − | 0.0282623i | ||||
\(149\) | 13.2830 | 1.08818 | 0.544092 | − | 0.839025i | \(-0.316874\pi\) | ||||
0.544092 | + | 0.839025i | \(0.316874\pi\) | |||||||
\(150\) | −2.80292 | + | 6.23097i | −0.228857 | + | 0.508757i | ||||
\(151\) | − | 10.5109i | − | 0.855365i | −0.903929 | − | 0.427682i | \(-0.859330\pi\) | ||
0.903929 | − | 0.427682i | \(-0.140670\pi\) | |||||||
\(152\) | 10.8898 | − | 1.35090i | 0.883280 | − | 0.109573i | ||||
\(153\) | 5.10286 | − | 5.10286i | 0.412542 | − | 0.412542i | ||||
\(154\) | 7.30846 | − | 2.28433i | 0.588932 | − | 0.184077i | ||||
\(155\) | −2.84132 | − | 6.31884i | −0.228220 | − | 0.507542i | ||||
\(156\) | 4.91417 | + | 7.09317i | 0.393448 | + | 0.567908i | ||||
\(157\) | −14.7455 | + | 14.7455i | −1.17682 | + | 1.17682i | −0.196273 | + | 0.980549i | \(0.562884\pi\) |
−0.980549 | + | 0.196273i | \(0.937116\pi\) | |||||||
\(158\) | 16.1068 | + | 8.43578i | 1.28139 | + | 0.671115i | ||||
\(159\) | −11.0486 | −0.876209 | ||||||||
\(160\) | −5.14540 | + | 11.5553i | −0.406779 | + | 0.913526i | ||||
\(161\) | −0.932259 | −0.0734723 | ||||||||
\(162\) | 1.84036 | + | 0.963871i | 0.144593 | + | 0.0757289i | ||||
\(163\) | 6.86932 | − | 6.86932i | 0.538047 | − | 0.538047i | −0.384908 | − | 0.922955i | \(-0.625767\pi\) |
0.922955 | + | 0.384908i | \(0.125767\pi\) | |||||||
\(164\) | −8.42229 | − | 12.1568i | −0.657670 | − | 0.949289i | ||||
\(165\) | −4.15197 | + | 10.9367i | −0.323230 | + | 0.851422i | ||||
\(166\) | 7.41290 | − | 2.31698i | 0.575352 | − | 0.179832i | ||||
\(167\) | −3.08533 | + | 3.08533i | −0.238750 | + | 0.238750i | −0.816332 | − | 0.577583i | \(-0.803996\pi\) |
0.577583 | + | 0.816332i | \(0.303996\pi\) | |||||||
\(168\) | 2.71216 | − | 0.336449i | 0.209248 | − | 0.0259576i | ||||
\(169\) | 6.93890i | 0.533762i | ||||||||
\(170\) | −7.32777 | − | 8.26257i | −0.562014 | − | 0.633710i | ||||
\(171\) | −8.01678 | −0.613059 | ||||||||
\(172\) | −0.235580 | − | 0.0427512i | −0.0179628 | − | 0.00325975i | ||||
\(173\) | −6.45046 | − | 6.45046i | −0.490419 | − | 0.490419i | 0.418019 | − | 0.908438i | \(-0.362725\pi\) |
−0.908438 | + | 0.418019i | \(0.862725\pi\) | |||||||
\(174\) | −7.52494 | + | 2.35200i | −0.570464 | + | 0.178305i | ||||
\(175\) | 0.298526 | + | 4.99108i | 0.0225665 | + | 0.377290i | ||||
\(176\) | −7.60991 | + | 20.2767i | −0.573618 | + | 1.52841i | ||||
\(177\) | 5.42700 | + | 5.42700i | 0.407918 | + | 0.407918i | ||||
\(178\) | −1.28989 | + | 2.46285i | −0.0966814 | + | 0.184598i | ||||
\(179\) | − | 19.1642i | − | 1.43240i | −0.697895 | − | 0.716201i | \(-0.745880\pi\) | ||
0.697895 | − | 0.716201i | \(-0.254120\pi\) | |||||||
\(180\) | 4.76977 | − | 7.91500i | 0.355518 | − | 0.589949i | ||||
\(181\) | − | 13.4361i | − | 0.998700i | −0.866400 | − | 0.499350i | \(-0.833572\pi\) | ||
0.866400 | − | 0.499350i | \(-0.166428\pi\) | |||||||
\(182\) | 5.59409 | + | 2.92984i | 0.414661 | + | 0.217175i | ||||
\(183\) | −2.87160 | − | 2.87160i | −0.212275 | − | 0.212275i | ||||
\(184\) | 1.62080 | − | 2.07987i | 0.119487 | − | 0.153330i | ||||
\(185\) | 0.764101 | − | 2.01272i | 0.0561778 | − | 0.147978i | ||||
\(186\) | −1.26309 | − | 4.04111i | −0.0926143 | − | 0.296309i | ||||
\(187\) | −13.3708 | − | 13.3708i | −0.977767 | − | 0.977767i | ||||
\(188\) | 6.47551 | + | 1.17512i | 0.472275 | + | 0.0857047i | ||||
\(189\) | −4.89535 | −0.356084 | ||||||||
\(190\) | −0.734307 | + | 12.2465i | −0.0532723 | + | 0.888455i | ||||
\(191\) | − | 0.448780i | − | 0.0324726i | −0.999868 | − | 0.0162363i | \(-0.994832\pi\) | ||
0.999868 | − | 0.0162363i | \(-0.00516839\pi\) | |||||||
\(192\) | −3.96467 | + | 6.63578i | −0.286125 | + | 0.478896i | ||||
\(193\) | −2.00162 | + | 2.00162i | −0.144080 | + | 0.144080i | −0.775467 | − | 0.631388i | \(-0.782486\pi\) |
0.631388 | + | 0.775467i | \(0.282486\pi\) | |||||||
\(194\) | 7.92287 | + | 25.3483i | 0.568829 | + | 1.81990i | ||||
\(195\) | −8.79904 | + | 3.95656i | −0.630113 | + | 0.283335i | ||||
\(196\) | 1.64400 | − | 1.13897i | 0.117429 | − | 0.0813551i | ||||
\(197\) | 9.07212 | − | 9.07212i | 0.646362 | − | 0.646362i | −0.305750 | − | 0.952112i | \(-0.598907\pi\) |
0.952112 | + | 0.305750i | \(0.0989072\pi\) | |||||||
\(198\) | 7.34098 | − | 14.0165i | 0.521700 | − | 0.996107i | ||||
\(199\) | 18.1441 | 1.28620 | 0.643101 | − | 0.765781i | \(-0.277647\pi\) | ||||
0.643101 | + | 0.765781i | \(0.277647\pi\) | |||||||
\(200\) | −11.6541 | − | 8.01133i | −0.824071 | − | 0.566487i | ||||
\(201\) | 10.6880 | 0.753874 | ||||||||
\(202\) | −8.34939 | + | 15.9419i | −0.587461 | + | 1.12167i | ||||
\(203\) | −4.07969 | + | 4.07969i | −0.286338 | + | 0.286338i | ||||
\(204\) | −3.84343 | − | 5.54765i | −0.269094 | − | 0.388413i | ||||
\(205\) | 15.0805 | − | 6.78107i | 1.05327 | − | 0.473610i | ||||
\(206\) | −4.93940 | − | 15.8030i | −0.344144 | − | 1.10105i | ||||
\(207\) | −1.36217 | + | 1.36217i | −0.0946771 | + | 0.0946771i | ||||
\(208\) | −16.2622 | + | 7.38669i | −1.12758 | + | 0.512175i | ||||
\(209\) | 21.0060i | 1.45301i | ||||||||
\(210\) | −0.182883 | + | 3.05005i | −0.0126201 | + | 0.210474i | ||||
\(211\) | 13.0722 | 0.899929 | 0.449964 | − | 0.893046i | \(-0.351437\pi\) | ||||
0.449964 | + | 0.893046i | \(0.351437\pi\) | |||||||
\(212\) | 4.08341 | − | 22.5016i | 0.280450 | − | 1.54542i | ||||
\(213\) | −1.95074 | − | 1.95074i | −0.133662 | − | 0.133662i | ||||
\(214\) | 2.54900 | + | 8.15522i | 0.174246 | + | 0.557479i | ||||
\(215\) | 0.0950080 | − | 0.250261i | 0.00647949 | − | 0.0170677i | ||||
\(216\) | 8.51091 | − | 10.9215i | 0.579094 | − | 0.743117i | ||||
\(217\) | −2.19091 | − | 2.19091i | −0.148729 | − | 0.148729i | ||||
\(218\) | −23.2532 | − | 12.1786i | −1.57490 | − | 0.824839i | ||||
\(219\) | − | 1.98844i | − | 0.134367i | ||||||
\(220\) | −20.7393 | − | 12.4980i | −1.39824 | − | 0.842615i | ||||
\(221\) | − | 15.5945i | − | 1.04900i | ||||||
\(222\) | 0.610402 | − | 1.16547i | 0.0409675 | − | 0.0782211i | ||||
\(223\) | −6.46091 | − | 6.46091i | −0.432655 | − | 0.432655i | 0.456876 | − | 0.889531i | \(-0.348968\pi\) |
−0.889531 | + | 0.456876i | \(0.848968\pi\) | |||||||
\(224\) | −0.317167 | + | 5.64796i | −0.0211916 | + | 0.377370i | ||||
\(225\) | 7.72889 | + | 6.85651i | 0.515259 | + | 0.457100i | ||||
\(226\) | 13.9986 | − | 4.37540i | 0.931171 | − | 0.291047i | ||||
\(227\) | 6.74613 | + | 6.74613i | 0.447756 | + | 0.447756i | 0.894608 | − | 0.446852i | \(-0.147455\pi\) |
−0.446852 | + | 0.894608i | \(0.647455\pi\) | |||||||
\(228\) | −1.33870 | + | 7.37688i | −0.0886574 | + | 0.488546i | ||||
\(229\) | −20.4172 | −1.34921 | −0.674603 | − | 0.738181i | \(-0.735685\pi\) | ||||
−0.674603 | + | 0.738181i | \(0.735685\pi\) | |||||||
\(230\) | 1.95609 | + | 2.20563i | 0.128981 | + | 0.145435i | ||||
\(231\) | 5.23164i | 0.344217i | ||||||||
\(232\) | −2.00897 | − | 16.1946i | −0.131896 | − | 1.06323i | ||||
\(233\) | −9.85773 | + | 9.85773i | −0.645802 | + | 0.645802i | −0.951976 | − | 0.306174i | \(-0.900951\pi\) |
0.306174 | + | 0.951976i | \(0.400951\pi\) | |||||||
\(234\) | 12.4547 | − | 3.89285i | 0.814190 | − | 0.254483i | ||||
\(235\) | −2.61153 | + | 6.87905i | −0.170358 | + | 0.448740i | ||||
\(236\) | −13.0584 | + | 9.04691i | −0.850030 | + | 0.588904i | ||||
\(237\) | −8.78422 | + | 8.78422i | −0.570597 | + | 0.570597i | ||||
\(238\) | −4.37521 | − | 2.29147i | −0.283603 | − | 0.148534i | ||||
\(239\) | −4.45737 | −0.288324 | −0.144162 | − | 0.989554i | \(-0.546049\pi\) | ||||
−0.144162 | + | 0.989554i | \(0.546049\pi\) | |||||||
\(240\) | −6.48673 | − | 5.71075i | −0.418716 | − | 0.368627i | ||||
\(241\) | 5.85350 | 0.377057 | 0.188529 | − | 0.982068i | \(-0.439628\pi\) | ||||
0.188529 | + | 0.982068i | \(0.439628\pi\) | |||||||
\(242\) | −22.9459 | − | 12.0177i | −1.47502 | − | 0.772527i | ||||
\(243\) | −11.3883 | + | 11.3883i | −0.730559 | + | 0.730559i | ||||
\(244\) | 6.90963 | − | 4.78702i | 0.442344 | − | 0.306457i | ||||
\(245\) | 0.917023 | + | 2.03938i | 0.0585865 | + | 0.130291i | ||||
\(246\) | 9.64448 | − | 3.01448i | 0.614910 | − | 0.192196i | ||||
\(247\) | −12.2498 | + | 12.2498i | −0.779433 | + | 0.779433i | ||||
\(248\) | 8.69698 | − | 1.07888i | 0.552259 | − | 0.0685087i | ||||
\(249\) | 5.30641i | 0.336280i | ||||||||
\(250\) | 11.1820 | − | 11.1787i | 0.707211 | − | 0.707002i | ||||
\(251\) | 4.36889 | 0.275762 | 0.137881 | − | 0.990449i | \(-0.455971\pi\) | ||||
0.137881 | + | 0.990449i | \(0.455971\pi\) | |||||||
\(252\) | 0.737926 | − | 4.06633i | 0.0464849 | − | 0.256155i | ||||
\(253\) | 3.56922 | + | 3.56922i | 0.224395 | + | 0.224395i | ||||
\(254\) | −30.1970 | + | 9.43837i | −1.89473 | + | 0.592216i | ||||
\(255\) | 6.88184 | − | 3.09448i | 0.430958 | − | 0.193784i | ||||
\(256\) | −12.0492 | − | 10.5270i | −0.753074 | − | 0.657935i | ||||
\(257\) | −6.53348 | − | 6.53348i | −0.407547 | − | 0.407547i | 0.473335 | − | 0.880882i | \(-0.343050\pi\) |
−0.880882 | + | 0.473335i | \(0.843050\pi\) | |||||||
\(258\) | 0.0758971 | − | 0.144914i | 0.00472515 | − | 0.00902194i | ||||
\(259\) | − | 0.962798i | − | 0.0598254i | ||||||
\(260\) | −4.80594 | − | 19.3825i | −0.298052 | − | 1.20205i | ||||
\(261\) | 11.9220i | 0.737956i | ||||||||
\(262\) | −10.1824 | − | 5.33290i | −0.629068 | − | 0.329468i | ||||
\(263\) | 11.5702 | + | 11.5702i | 0.713446 | + | 0.713446i | 0.967254 | − | 0.253808i | \(-0.0816833\pi\) |
−0.253808 | + | 0.967254i | \(0.581683\pi\) | |||||||
\(264\) | −11.6718 | − | 9.09558i | −0.718350 | − | 0.559794i | ||||
\(265\) | 23.9038 | + | 9.07476i | 1.46840 | + | 0.557458i | ||||
\(266\) | 1.63682 | + | 5.23680i | 0.100360 | + | 0.321089i | ||||
\(267\) | −1.34317 | − | 1.34317i | −0.0822006 | − | 0.0822006i | ||||
\(268\) | −3.95015 | + | 21.7673i | −0.241294 | + | 1.32965i | ||||
\(269\) | −15.9197 | −0.970644 | −0.485322 | − | 0.874336i | \(-0.661298\pi\) | ||||
−0.485322 | + | 0.874336i | \(0.661298\pi\) | |||||||
\(270\) | 10.2715 | + | 11.5819i | 0.625106 | + | 0.704851i | ||||
\(271\) | 20.8120i | 1.26424i | 0.774872 | + | 0.632119i | \(0.217814\pi\) | ||||
−0.774872 | + | 0.632119i | \(0.782186\pi\) | |||||||
\(272\) | 12.7189 | − | 5.77722i | 0.771195 | − | 0.350295i | ||||
\(273\) | −3.05086 | + | 3.05086i | −0.184647 | + | 0.184647i | ||||
\(274\) | −2.51085 | − | 8.03316i | −0.151686 | − | 0.485301i | ||||
\(275\) | 17.9658 | − | 20.2516i | 1.08338 | − | 1.22122i | ||||
\(276\) | 1.02597 | + | 1.48090i | 0.0617563 | + | 0.0891398i | ||||
\(277\) | −14.4770 | + | 14.4770i | −0.869840 | + | 0.869840i | −0.992454 | − | 0.122615i | \(-0.960872\pi\) |
0.122615 | + | 0.992454i | \(0.460872\pi\) | |||||||
\(278\) | −14.2611 | + | 27.2294i | −0.855324 | + | 1.63311i | ||||
\(279\) | −6.40248 | −0.383306 | ||||||||
\(280\) | −6.14417 | − | 1.49972i | −0.367184 | − | 0.0896255i | ||||
\(281\) | 22.0154 | 1.31333 | 0.656664 | − | 0.754184i | \(-0.271967\pi\) | ||||
0.656664 | + | 0.754184i | \(0.271967\pi\) | |||||||
\(282\) | −2.08622 | + | 3.98332i | −0.124233 | + | 0.237203i | ||||
\(283\) | 0.00141407 | − | 0.00141407i | 8.40579e−5 | − | 8.40579e-5i | −0.707065 | − | 0.707149i | \(-0.749981\pi\) |
0.707149 | + | 0.707065i | \(0.249981\pi\) | |||||||
\(284\) | 4.69385 | − | 3.25192i | 0.278529 | − | 0.192966i | ||||
\(285\) | −7.83659 | − | 2.97505i | −0.464199 | − | 0.176227i | ||||
\(286\) | −10.2002 | − | 32.6344i | −0.603152 | − | 1.92972i | ||||
\(287\) | 5.22881 | − | 5.22881i | 0.308647 | − | 0.308647i | ||||
\(288\) | 7.78906 | + | 8.71591i | 0.458975 | + | 0.513590i | ||||
\(289\) | − | 4.80337i | − | 0.282551i | ||||||
\(290\) | 18.2122 | + | 1.09201i | 1.06946 | + | 0.0641253i | ||||
\(291\) | −18.1452 | −1.06369 | ||||||||
\(292\) | 4.04968 | + | 0.734904i | 0.236990 | + | 0.0430070i | ||||
\(293\) | 13.2135 | + | 13.2135i | 0.771940 | + | 0.771940i | 0.978445 | − | 0.206505i | \(-0.0662091\pi\) |
−0.206505 | + | 0.978445i | \(0.566209\pi\) | |||||||
\(294\) | 0.407657 | + | 1.30425i | 0.0237751 | + | 0.0760655i | ||||
\(295\) | −7.28397 | − | 16.1989i | −0.424089 | − | 0.943137i | ||||
\(296\) | 2.14801 | + | 1.67389i | 0.124850 | + | 0.0972930i | ||||
\(297\) | 18.7422 | + | 18.7422i | 1.08753 | + | 1.08753i | ||||
\(298\) | −16.6408 | − | 8.71545i | −0.963976 | − | 0.504872i | ||||
\(299\) | 4.16282i | 0.240742i | ||||||||
\(300\) | 7.59984 | − | 5.96701i | 0.438777 | − | 0.344506i | ||||
\(301\) | − | 0.119714i | − | 0.00690019i | ||||||
\(302\) | −6.89658 | + | 13.1680i | −0.396854 | + | 0.757731i | ||||
\(303\) | −8.69426 | − | 8.69426i | −0.499472 | − | 0.499472i | ||||
\(304\) | −14.5290 | − | 5.45280i | −0.833297 | − | 0.312740i | ||||
\(305\) | 3.85419 | + | 8.57137i | 0.220690 | + | 0.490795i | ||||
\(306\) | −9.74098 | + | 3.04465i | −0.556855 | + | 0.174051i | ||||
\(307\) | −15.4316 | − | 15.4316i | −0.880731 | − | 0.880731i | 0.112878 | − | 0.993609i | \(-0.463993\pi\) |
−0.993609 | + | 0.112878i | \(0.963993\pi\) | |||||||
\(308\) | −10.6548 | − | 1.93355i | −0.607114 | − | 0.110174i | ||||
\(309\) | 11.3123 | 0.643537 | ||||||||
\(310\) | −0.586443 | + | 9.78048i | −0.0333077 | + | 0.555494i | ||||
\(311\) | − | 22.4892i | − | 1.27524i | −0.770349 | − | 0.637622i | \(-0.779918\pi\) | ||
0.770349 | − | 0.637622i | \(-0.220082\pi\) | |||||||
\(312\) | −1.50235 | − | 12.1106i | −0.0850536 | − | 0.685629i | ||||
\(313\) | 10.8617 | − | 10.8617i | 0.613942 | − | 0.613942i | −0.330029 | − | 0.943971i | \(-0.607058\pi\) |
0.943971 | + | 0.330029i | \(0.107058\pi\) | |||||||
\(314\) | 28.1482 | − | 8.79800i | 1.58849 | − | 0.496500i | ||||
\(315\) | 4.31974 | + | 1.63993i | 0.243390 | + | 0.0923994i | ||||
\(316\) | −14.6435 | − | 21.1365i | −0.823760 | − | 1.18902i | ||||
\(317\) | −5.29117 | + | 5.29117i | −0.297182 | + | 0.297182i | −0.839909 | − | 0.542727i | \(-0.817392\pi\) |
0.542727 | + | 0.839909i | \(0.317392\pi\) | |||||||
\(318\) | 13.8416 | + | 7.24937i | 0.776196 | + | 0.406524i | ||||
\(319\) | 31.2387 | 1.74903 | ||||||||
\(320\) | 14.0280 | − | 11.1003i | 0.784187 | − | 0.620525i | ||||
\(321\) | −5.83778 | −0.325833 | ||||||||
\(322\) | 1.16793 | + | 0.611689i | 0.0650860 | + | 0.0340881i | ||||
\(323\) | 9.58068 | − | 9.58068i | 0.533083 | − | 0.533083i | ||||
\(324\) | −1.67316 | − | 2.41506i | −0.0929534 | − | 0.134170i | ||||
\(325\) | 22.2867 | − | 1.33301i | 1.23624 | − | 0.0739421i | ||||
\(326\) | −13.1130 | + | 4.09861i | −0.726264 | + | 0.227001i | ||||
\(327\) | 12.6816 | − | 12.6816i | 0.701296 | − | 0.701296i | ||||
\(328\) | 2.57484 | + | 20.7561i | 0.142172 | + | 1.14607i | ||||
\(329\) | 3.29064i | 0.181419i | ||||||||
\(330\) | 12.3775 | − | 10.9772i | 0.681360 | − | 0.604273i | ||||
\(331\) | −6.80525 | −0.374050 | −0.187025 | − | 0.982355i | \(-0.559885\pi\) | ||||
−0.187025 | + | 0.982355i | \(0.559885\pi\) | |||||||
\(332\) | −10.8071 | − | 1.96118i | −0.593115 | − | 0.107634i | ||||
\(333\) | −1.40679 | − | 1.40679i | −0.0770915 | − | 0.0770915i | ||||
\(334\) | 5.88966 | − | 1.84088i | 0.322268 | − | 0.100728i | ||||
\(335\) | −23.1238 | − | 8.77861i | −1.26339 | − | 0.479627i | ||||
\(336\) | −3.61853 | − | 1.35805i | −0.197407 | − | 0.0740876i | ||||
\(337\) | −18.9299 | − | 18.9299i | −1.03118 | − | 1.03118i | −0.999498 | − | 0.0316788i | \(-0.989915\pi\) |
−0.0316788 | − | 0.999498i | \(-0.510085\pi\) | |||||||
\(338\) | 4.55286 | − | 8.69300i | 0.247643 | − | 0.472837i | ||||
\(339\) | 10.0207i | 0.544247i | ||||||||
\(340\) | 3.75879 | + | 15.1593i | 0.203849 | + | 0.822128i | ||||
\(341\) | 16.7761i | 0.908476i | ||||||||
\(342\) | 10.0434 | + | 5.26010i | 0.543082 | + | 0.284434i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 0.267082 | + | 0.208131i | 0.0144001 | + | 0.0112217i | ||||
\(345\) | −1.83705 | + | 0.826045i | −0.0989036 | + | 0.0444728i | ||||
\(346\) | 3.84870 | + | 12.3135i | 0.206907 | + | 0.661975i | ||||
\(347\) | 12.1708 | + | 12.1708i | 0.653362 | + | 0.653362i | 0.953801 | − | 0.300439i | \(-0.0971333\pi\) |
−0.300439 | + | 0.953801i | \(0.597133\pi\) | |||||||
\(348\) | 10.9704 | + | 1.99082i | 0.588076 | + | 0.106719i | ||||
\(349\) | 15.7645 | 0.843856 | 0.421928 | − | 0.906629i | \(-0.361353\pi\) | ||||
0.421928 | + | 0.906629i | \(0.361353\pi\) | |||||||
\(350\) | 2.90084 | − | 6.44865i | 0.155056 | − | 0.344695i | ||||
\(351\) | 21.8592i | 1.16676i | ||||||||
\(352\) | 22.8379 | − | 20.4093i | 1.21726 | − | 1.08782i | ||||
\(353\) | −12.5792 | + | 12.5792i | −0.669525 | + | 0.669525i | −0.957606 | − | 0.288081i | \(-0.906983\pi\) |
0.288081 | + | 0.957606i | \(0.406983\pi\) | |||||||
\(354\) | −3.23804 | − | 10.3597i | −0.172100 | − | 0.550614i | ||||
\(355\) | 2.61823 | + | 5.82271i | 0.138961 | + | 0.309037i | ||||
\(356\) | 3.23193 | − | 2.23909i | 0.171292 | − | 0.118672i | ||||
\(357\) | 2.38612 | − | 2.38612i | 0.126287 | − | 0.126287i | ||||
\(358\) | −12.5743 | + | 24.0088i | −0.664574 | + | 1.26890i | ||||
\(359\) | −33.7490 | −1.78120 | −0.890602 | − | 0.454784i | \(-0.849716\pi\) | ||||
−0.890602 | + | 0.454784i | \(0.849716\pi\) | |||||||
\(360\) | −11.1688 | + | 6.78622i | −0.588650 | + | 0.357665i | ||||
\(361\) | 3.94838 | 0.207810 | ||||||||
\(362\) | −8.81594 | + | 16.8327i | −0.463355 | + | 0.884706i | ||||
\(363\) | 12.5141 | − | 12.5141i | 0.656819 | − | 0.656819i | ||||
\(364\) | −5.08585 | − | 7.34097i | −0.266571 | − | 0.384771i | ||||
\(365\) | −1.63321 | + | 4.30205i | −0.0854861 | + | 0.225179i | ||||
\(366\) | 1.71336 | + | 5.48168i | 0.0895585 | + | 0.286532i | ||||
\(367\) | 2.19334 | − | 2.19334i | 0.114491 | − | 0.114491i | −0.647540 | − | 0.762031i | \(-0.724202\pi\) |
0.762031 | + | 0.647540i | \(0.224202\pi\) | |||||||
\(368\) | −3.39520 | + | 1.54218i | −0.176987 | + | 0.0803918i | ||||
\(369\) | − | 15.2801i | − | 0.795450i | ||||||
\(370\) | −2.27788 | + | 2.02017i | −0.118421 | + | 0.105023i | ||||
\(371\) | 11.4346 | 0.593652 | ||||||||
\(372\) | −1.06913 | + | 5.89143i | −0.0554318 | + | 0.305456i | ||||
\(373\) | 5.66659 | + | 5.66659i | 0.293405 | + | 0.293405i | 0.838424 | − | 0.545019i | \(-0.183478\pi\) |
−0.545019 | + | 0.838424i | \(0.683478\pi\) | |||||||
\(374\) | 7.97773 | + | 25.5238i | 0.412519 | + | 1.31980i | ||||
\(375\) | 5.01070 | + | 9.57060i | 0.258751 | + | 0.494224i | ||||
\(376\) | −7.34142 | − | 5.72100i | −0.378605 | − | 0.295038i | ||||
\(377\) | 18.2170 | + | 18.2170i | 0.938225 | + | 0.938225i | ||||
\(378\) | 6.13285 | + | 3.21202i | 0.315440 | + | 0.165208i | ||||
\(379\) | 9.13563i | 0.469266i | 0.972084 | + | 0.234633i | \(0.0753888\pi\) | ||||
−0.972084 | + | 0.234633i | \(0.924611\pi\) | |||||||
\(380\) | 8.95531 | − | 14.8605i | 0.459398 | − | 0.762328i | ||||
\(381\) | − | 21.6160i | − | 1.10742i | ||||||
\(382\) | −0.294461 | + | 0.562227i | −0.0150659 | + | 0.0287660i | ||||
\(383\) | 7.64787 | + | 7.64787i | 0.390788 | + | 0.390788i | 0.874968 | − | 0.484180i | \(-0.160882\pi\) |
−0.484180 | + | 0.874968i | \(0.660882\pi\) | |||||||
\(384\) | 9.32087 | − | 5.71189i | 0.475654 | − | 0.291484i | ||||
\(385\) | 4.29702 | − | 11.3188i | 0.218996 | − | 0.576859i | ||||
\(386\) | 3.82095 | − | 1.19428i | 0.194481 | − | 0.0607871i | ||||
\(387\) | −0.174919 | − | 0.174919i | −0.00889165 | − | 0.00889165i | ||||
\(388\) | 6.70623 | − | 36.9546i | 0.340457 | − | 1.87609i | ||||
\(389\) | −27.8987 | −1.41452 | −0.707261 | − | 0.706952i | \(-0.750070\pi\) | ||||
−0.707261 | + | 0.706952i | \(0.750070\pi\) | |||||||
\(390\) | 13.6194 | + | 0.816627i | 0.689645 | + | 0.0413515i | ||||
\(391\) | − | 3.25579i | − | 0.164652i | ||||||
\(392\) | −2.80691 | + | 0.348203i | −0.141770 | + | 0.0175869i | ||||
\(393\) | 5.55317 | − | 5.55317i | 0.280121 | − | 0.280121i | ||||
\(394\) | −17.3180 | + | 5.41292i | −0.872469 | + | 0.272699i | ||||
\(395\) | 26.2198 | − | 11.7899i | 1.31926 | − | 0.593216i | ||||
\(396\) | −18.3934 | + | 12.7430i | −0.924304 | + | 0.640361i | ||||
\(397\) | −8.36699 | + | 8.36699i | −0.419927 | + | 0.419927i | −0.885179 | − | 0.465251i | \(-0.845964\pi\) |
0.465251 | + | 0.885179i | \(0.345964\pi\) | |||||||
\(398\) | −22.7308 | − | 11.9050i | −1.13939 | − | 0.596744i | ||||
\(399\) | −3.74868 | −0.187669 | ||||||||
\(400\) | 9.34366 | + | 17.6832i | 0.467183 | + | 0.884161i | ||||
\(401\) | −34.4862 | −1.72216 | −0.861080 | − | 0.508470i | \(-0.830211\pi\) | ||||
−0.861080 | + | 0.508470i | \(0.830211\pi\) | |||||||
\(402\) | −13.3898 | − | 7.01279i | −0.667825 | − | 0.349766i | ||||
\(403\) | −9.78307 | + | 9.78307i | −0.487329 | + | 0.487329i | ||||
\(404\) | 20.9201 | − | 14.4935i | 1.04081 | − | 0.721079i | ||||
\(405\) | 2.99587 | − | 1.34712i | 0.148866 | − | 0.0669388i | ||||
\(406\) | 7.78783 | − | 2.43417i | 0.386503 | − | 0.120806i | ||||
\(407\) | −3.68614 | + | 3.68614i | −0.182715 | + | 0.182715i | ||||
\(408\) | 1.17500 | + | 9.47187i | 0.0581713 | + | 0.468927i | ||||
\(409\) | − | 24.8534i | − | 1.22892i | −0.788947 | − | 0.614461i | \(-0.789374\pi\) | ||
0.788947 | − | 0.614461i | \(-0.210626\pi\) | |||||||
\(410\) | −23.3420 | − | 1.39960i | −1.15278 | − | 0.0691213i | ||||
\(411\) | 5.75041 | 0.283647 | ||||||||
\(412\) | −4.18090 | + | 23.0388i | −0.205978 | + | 1.13504i | ||||
\(413\) | −5.61659 | − | 5.61659i | −0.276374 | − | 0.276374i | ||||
\(414\) | 2.60028 | − | 0.812743i | 0.127797 | − | 0.0399442i | ||||
\(415\) | 4.35842 | − | 11.4805i | 0.213947 | − | 0.563557i | ||||
\(416\) | 25.2198 | + | 1.41624i | 1.23650 | + | 0.0694371i | ||||
\(417\) | −14.8502 | − | 14.8502i | −0.727216 | − | 0.727216i | ||||
\(418\) | 13.7828 | − | 26.3161i | 0.674138 | − | 1.28716i | ||||
\(419\) | 1.88796i | 0.0922330i | 0.998936 | + | 0.0461165i | \(0.0146845\pi\) | ||||
−0.998936 | + | 0.0461165i | \(0.985315\pi\) | |||||||
\(420\) | 2.23036 | − | 3.70108i | 0.108831 | − | 0.180594i | ||||
\(421\) | 1.78407i | 0.0869500i | 0.999055 | + | 0.0434750i | \(0.0138429\pi\) | ||||
−0.999055 | + | 0.0434750i | \(0.986157\pi\) | |||||||
\(422\) | −16.3768 | − | 8.57716i | −0.797208 | − | 0.417529i | ||||
\(423\) | 4.80810 | + | 4.80810i | 0.233778 | + | 0.233778i | ||||
\(424\) | −19.8798 | + | 25.5105i | −0.965447 | + | 1.23890i | ||||
\(425\) | −17.4307 | + | 1.04256i | −0.845512 | + | 0.0505718i | ||||
\(426\) | 1.16392 | + | 3.72382i | 0.0563920 | + | 0.180419i | ||||
\(427\) | 2.97192 | + | 2.97192i | 0.143821 | + | 0.143821i | ||||
\(428\) | 2.15757 | − | 11.8893i | 0.104290 | − | 0.574690i | ||||
\(429\) | 23.3609 | 1.12787 | ||||||||
\(430\) | −0.283230 | + | 0.251186i | −0.0136586 | + | 0.0121133i | ||||
\(431\) | 32.0625i | 1.54439i | 0.635383 | + | 0.772197i | \(0.280842\pi\) | ||||
−0.635383 | + | 0.772197i | \(0.719158\pi\) | |||||||
\(432\) | −17.8284 | + | 8.09810i | −0.857770 | + | 0.389620i | ||||
\(433\) | 22.4346 | − | 22.4346i | 1.07814 | − | 1.07814i | 0.0814590 | − | 0.996677i | \(-0.474042\pi\) |
0.996677 | − | 0.0814590i | \(-0.0259580\pi\) | |||||||
\(434\) | 1.30722 | + | 4.18229i | 0.0627484 | + | 0.200756i | ||||
\(435\) | −4.42430 | + | 11.6541i | −0.212129 | + | 0.558770i | ||||
\(436\) | 21.1405 | + | 30.5145i | 1.01245 | + | 1.46138i | ||||
\(437\) | −2.55749 | + | 2.55749i | −0.122341 | + | 0.122341i | ||||
\(438\) | −1.30469 | + | 2.49110i | −0.0623405 | + | 0.119030i | ||||
\(439\) | 15.5671 | 0.742977 | 0.371489 | − | 0.928438i | \(-0.378847\pi\) | ||||
0.371489 | + | 0.928438i | \(0.378847\pi\) | |||||||
\(440\) | 17.7816 | + | 29.2652i | 0.847704 | + | 1.39516i | ||||
\(441\) | 2.06637 | 0.0983987 | ||||||||
\(442\) | −10.2321 | + | 19.5366i | −0.486691 | + | 0.929262i | ||||
\(443\) | −22.7365 | + | 22.7365i | −1.08025 | + | 1.08025i | −0.0837592 | + | 0.996486i | \(0.526693\pi\) |
−0.996486 | + | 0.0837592i | \(0.973307\pi\) | |||||||
\(444\) | −1.52941 | + | 1.05958i | −0.0725827 | + | 0.0502855i | ||||
\(445\) | 1.80277 | + | 4.00919i | 0.0854593 | + | 0.190054i | ||||
\(446\) | 3.85494 | + | 12.3334i | 0.182537 | + | 0.584004i | ||||
\(447\) | 9.07544 | − | 9.07544i | 0.429254 | − | 0.429254i | ||||
\(448\) | 4.10317 | − | 6.86760i | 0.193857 | − | 0.324464i | ||||
\(449\) | 7.97082i | 0.376166i | 0.982153 | + | 0.188083i | \(0.0602274\pi\) | ||||
−0.982153 | + | 0.188083i | \(0.939773\pi\) | |||||||
\(450\) | −5.18388 | − | 13.6610i | −0.244370 | − | 0.643984i | ||||
\(451\) | −40.0377 | −1.88530 | ||||||||
\(452\) | −20.4081 | − | 3.70351i | −0.959918 | − | 0.174198i | ||||
\(453\) | −7.18144 | − | 7.18144i | −0.337414 | − | 0.337414i | ||||
\(454\) | −4.02511 | − | 12.8779i | −0.188908 | − | 0.604388i | ||||
\(455\) | 9.10644 | − | 4.09478i | 0.426917 | − | 0.191966i | ||||
\(456\) | 6.51734 | − | 8.36332i | 0.305203 | − | 0.391648i | ||||
\(457\) | 3.30838 | + | 3.30838i | 0.154759 | + | 0.154759i | 0.780240 | − | 0.625480i | \(-0.215097\pi\) |
−0.625480 | + | 0.780240i | \(0.715097\pi\) | |||||||
\(458\) | 25.5785 | + | 13.3965i | 1.19520 | + | 0.625975i | ||||
\(459\) | − | 17.0964i | − | 0.797990i | ||||||
\(460\) | −1.00338 | − | 4.04665i | −0.0467827 | − | 0.188676i | ||||
\(461\) | − | 12.0107i | − | 0.559393i | −0.960088 | − | 0.279697i | \(-0.909766\pi\) | ||
0.960088 | − | 0.279697i | \(-0.0902339\pi\) | |||||||
\(462\) | 3.43267 | − | 6.55416i | 0.159702 | − | 0.304927i | ||||
\(463\) | 2.07725 | + | 2.07725i | 0.0965380 | + | 0.0965380i | 0.753726 | − | 0.657188i | \(-0.228254\pi\) |
−0.657188 | + | 0.753726i | \(0.728254\pi\) | |||||||
\(464\) | −8.10905 | + | 21.6066i | −0.376453 | + | 1.00306i | ||||
\(465\) | −6.25857 | − | 2.37598i | −0.290234 | − | 0.110183i | ||||
\(466\) | 18.8177 | − | 5.88167i | 0.871713 | − | 0.272463i | ||||
\(467\) | −5.60472 | − | 5.60472i | −0.259356 | − | 0.259356i | 0.565436 | − | 0.824792i | \(-0.308708\pi\) |
−0.824792 | + | 0.565436i | \(0.808708\pi\) | |||||||
\(468\) | −18.1574 | − | 3.29506i | −0.839325 | − | 0.152314i | ||||
\(469\) | −11.0614 | −0.510768 | ||||||||
\(470\) | 7.78530 | − | 6.90449i | 0.359109 | − | 0.318480i | ||||
\(471\) | 20.1494i | 0.928437i | ||||||||
\(472\) | 22.2955 | − | 2.76579i | 1.02623 | − | 0.127306i | ||||
\(473\) | −0.458333 | + | 0.458333i | −0.0210742 | + | 0.0210742i | ||||
\(474\) | 16.7684 | − | 5.24115i | 0.770200 | − | 0.240734i | ||||
\(475\) | 14.5111 | + | 12.8732i | 0.665814 | + | 0.590662i | ||||
\(476\) | 3.97770 | + | 5.74146i | 0.182318 | + | 0.263159i | ||||
\(477\) | 16.7076 | − | 16.7076i | 0.764986 | − | 0.764986i | ||||
\(478\) | 5.58416 | + | 2.92464i | 0.255413 | + | 0.133770i | ||||
\(479\) | −30.2393 | −1.38167 | −0.690835 | − | 0.723013i | \(-0.742757\pi\) | ||||
−0.690835 | + | 0.723013i | \(0.742757\pi\) | |||||||
\(480\) | 4.37949 | + | 11.4105i | 0.199895 | + | 0.520818i | ||||
\(481\) | −4.29918 | −0.196026 | ||||||||
\(482\) | −7.33321 | − | 3.84069i | −0.334019 | − | 0.174939i | ||||
\(483\) | −0.636955 | + | 0.636955i | −0.0289824 | + | 0.0289824i | ||||
\(484\) | 20.8612 | + | 30.1113i | 0.948237 | + | 1.36870i | ||||
\(485\) | 39.2575 | + | 14.9036i | 1.78259 | + | 0.676736i | ||||
\(486\) | 21.7394 | − | 6.79488i | 0.986120 | − | 0.308222i | ||||
\(487\) | 5.59965 | − | 5.59965i | 0.253745 | − | 0.253745i | −0.568759 | − | 0.822504i | \(-0.692576\pi\) |
0.822504 | + | 0.568759i | \(0.192576\pi\) | |||||||
\(488\) | −11.7973 | + | 1.46347i | −0.534037 | + | 0.0662483i | ||||
\(489\) | − | 9.38676i | − | 0.424484i | ||||||
\(490\) | 0.189272 | − | 3.15661i | 0.00855044 | − | 0.142601i | ||||
\(491\) | 11.2713 | 0.508667 | 0.254333 | − | 0.967117i | \(-0.418144\pi\) | ||||
0.254333 | + | 0.967117i | \(0.418144\pi\) | |||||||
\(492\) | −14.0604 | − | 2.55158i | −0.633893 | − | 0.115034i | ||||
\(493\) | −14.2478 | − | 14.2478i | −0.641687 | − | 0.641687i | ||||
\(494\) | 23.3839 | − | 7.30887i | 1.05209 | − | 0.328842i | ||||
\(495\) | −10.2598 | − | 22.8170i | −0.461145 | − | 1.02555i | ||||
\(496\) | −11.6034 | − | 4.35479i | −0.521007 | − | 0.195536i | ||||
\(497\) | 2.01889 | + | 2.01889i | 0.0905594 | + | 0.0905594i | ||||
\(498\) | 3.48172 | − | 6.64782i | 0.156020 | − | 0.297896i | ||||
\(499\) | 7.04115i | 0.315205i | 0.987503 | + | 0.157603i | \(0.0503765\pi\) | ||||
−0.987503 | + | 0.157603i | \(0.949623\pi\) | |||||||
\(500\) | −21.3434 | + | 6.66765i | −0.954508 | + | 0.298186i | ||||
\(501\) | 4.21602i | 0.188358i | ||||||||
\(502\) | −5.47331 | − | 2.86659i | −0.244286 | − | 0.127942i | ||||
\(503\) | 13.7302 | + | 13.7302i | 0.612199 | + | 0.612199i | 0.943518 | − | 0.331320i | \(-0.107494\pi\) |
−0.331320 | + | 0.943518i | \(0.607494\pi\) | |||||||
\(504\) | −3.59253 | + | 4.61008i | −0.160024 | + | 0.205349i | ||||
\(505\) | 11.6692 | + | 25.9513i | 0.519273 | + | 1.15482i | ||||
\(506\) | −2.12959 | − | 6.81337i | −0.0946718 | − | 0.302891i | ||||
\(507\) | 4.74092 | + | 4.74092i | 0.210552 | + | 0.210552i | ||||
\(508\) | 44.0233 | + | 7.98901i | 1.95322 | + | 0.354455i | ||||
\(509\) | −4.91505 | −0.217856 | −0.108928 | − | 0.994050i | \(-0.534742\pi\) | ||||
−0.108928 | + | 0.994050i | \(0.534742\pi\) | |||||||
\(510\) | −10.6519 | − | 0.638694i | −0.471674 | − | 0.0282819i | ||||
\(511\) | 2.05791i | 0.0910366i | ||||||||
\(512\) | 8.18800 | + | 21.0940i | 0.361862 | + | 0.932232i | ||||
\(513\) | −13.4295 | + | 13.4295i | −0.592928 | + | 0.592928i | ||||
\(514\) | 3.89823 | + | 12.4719i | 0.171944 | + | 0.550114i | ||||
\(515\) | −24.4745 | − | 9.29140i | −1.07848 | − | 0.409428i | ||||
\(516\) | −0.190166 | + | 0.131748i | −0.00837161 | + | 0.00579988i | ||||
\(517\) | 12.5984 | − | 12.5984i | 0.554078 | − | 0.554078i | ||||
\(518\) | −0.631726 | + | 1.20618i | −0.0277565 | + | 0.0529967i | ||||
\(519\) | −8.81439 | −0.386909 | ||||||||
\(520\) | −6.69671 | + | 27.4356i | −0.293670 | + | 1.20313i | ||||
\(521\) | 6.55084 | 0.286998 | 0.143499 | − | 0.989650i | \(-0.454165\pi\) | ||||
0.143499 | + | 0.989650i | \(0.454165\pi\) | |||||||
\(522\) | 7.82248 | − | 14.9358i | 0.342381 | − | 0.653723i | ||||
\(523\) | 18.1480 | − | 18.1480i | 0.793556 | − | 0.793556i | −0.188514 | − | 0.982070i | \(-0.560367\pi\) |
0.982070 | + | 0.188514i | \(0.0603671\pi\) | |||||||
\(524\) | 9.25725 | + | 13.3620i | 0.404405 | + | 0.583722i | ||||
\(525\) | 3.61406 | + | 3.20613i | 0.157730 | + | 0.139927i | ||||
\(526\) | −6.90339 | − | 22.0866i | −0.301002 | − | 0.963020i | ||||
\(527\) | 7.65146 | − | 7.65146i | 0.333303 | − | 0.333303i | ||||
\(528\) | 8.65441 | + | 19.0532i | 0.376635 | + | 0.829182i | ||||
\(529\) | − | 22.1309i | − | 0.962213i | ||||||
\(530\) | −23.9923 | − | 27.0530i | −1.04216 | − | 1.17511i | ||||
\(531\) | −16.4133 | −0.712277 | ||||||||
\(532\) | 1.38546 | − | 7.63459i | 0.0600675 | − | 0.331001i | ||||
\(533\) | −23.3482 | − | 23.3482i | −1.01132 | − | 1.01132i | ||||
\(534\) | 0.801409 | + | 2.56401i | 0.0346803 | + | 0.110956i | ||||
\(535\) | 12.6302 | + | 4.79487i | 0.546051 | + | 0.207300i | ||||
\(536\) | 19.2310 | − | 24.6780i | 0.830653 | − | 1.06593i | ||||
\(537\) | −13.0937 | − | 13.0937i | −0.565036 | − | 0.565036i | ||||
\(538\) | 19.9441 | + | 10.4455i | 0.859851 | + | 0.450338i | ||||
\(539\) | − | 5.41441i | − | 0.233215i | ||||||
\(540\) | −5.26880 | − | 21.2492i | −0.226733 | − | 0.914421i | ||||
\(541\) | − | 7.99669i | − | 0.343805i | −0.985114 | − | 0.171902i | \(-0.945009\pi\) | ||
0.985114 | − | 0.171902i | \(-0.0549913\pi\) | |||||||
\(542\) | 13.6555 | − | 26.0730i | 0.586553 | − | 1.11993i | ||||
\(543\) | −9.18008 | − | 9.18008i | −0.393955 | − | 0.393955i | ||||
\(544\) | −19.7247 | − | 1.10766i | −0.845691 | − | 0.0474906i | ||||
\(545\) | −37.8531 | + | 17.0209i | −1.62145 | + | 0.729097i | ||||
\(546\) | 5.82387 | − | 1.82031i | 0.249239 | − | 0.0779021i | ||||
\(547\) | 11.2540 | + | 11.2540i | 0.481186 | + | 0.481186i | 0.905510 | − | 0.424324i | \(-0.139488\pi\) |
−0.424324 | + | 0.905510i | \(0.639488\pi\) | |||||||
\(548\) | −2.12528 | + | 11.7113i | −0.0907875 | + | 0.500283i | ||||
\(549\) | 8.68482 | 0.370659 | ||||||||
\(550\) | −35.7952 | + | 13.5831i | −1.52631 | + | 0.579184i | ||||
\(551\) | 22.3838i | 0.953581i | ||||||||
\(552\) | −0.313658 | − | 2.52844i | −0.0133502 | − | 0.107617i | ||||
\(553\) | 9.09110 | − | 9.09110i | 0.386593 | − | 0.386593i | ||||
\(554\) | 27.6356 | − | 8.63778i | 1.17412 | − | 0.366984i | ||||
\(555\) | −0.853105 | − | 1.89723i | −0.0362123 | − | 0.0805329i | ||||
\(556\) | 35.7324 | − | 24.7555i | 1.51539 | − | 1.04987i | ||||
\(557\) | 1.87320 | − | 1.87320i | 0.0793700 | − | 0.0793700i | −0.666307 | − | 0.745677i | \(-0.732126\pi\) |
0.745677 | + | 0.666307i | \(0.232126\pi\) | |||||||
\(558\) | 8.02097 | + | 4.20090i | 0.339555 | + | 0.177838i | ||||
\(559\) | −0.534558 | −0.0226094 | ||||||||
\(560\) | 6.71334 | + | 5.91025i | 0.283690 | + | 0.249754i | ||||
\(561\) | −18.2708 | −0.771395 | ||||||||
\(562\) | −27.5807 | − | 14.4451i | −1.16342 | − | 0.609329i | ||||
\(563\) | 18.2779 | − | 18.2779i | 0.770322 | − | 0.770322i | −0.207840 | − | 0.978163i | \(-0.566643\pi\) |
0.978163 | + | 0.207840i | \(0.0666434\pi\) | |||||||
\(564\) | 5.22720 | − | 3.62142i | 0.220105 | − | 0.152489i | ||||
\(565\) | 8.23048 | − | 21.6799i | 0.346259 | − | 0.912082i | ||||
\(566\) | −0.00269936 | 0.000843713i | −0.000113463 | 3.54639e-5i | ||||||
\(567\) | 1.03875 | − | 1.03875i | 0.0436233 | − | 0.0436233i | ||||
\(568\) | −8.01412 | + | 0.994167i | −0.336265 | + | 0.0417143i | ||||
\(569\) | − | 0.0832566i | − | 0.00349030i | −0.999998 | − | 0.00174515i | \(-0.999445\pi\) | ||
0.999998 | − | 0.00174515i | \(-0.000555499\pi\) | |||||||
\(570\) | 7.86557 | + | 8.86898i | 0.329453 | + | 0.371481i | ||||
\(571\) | −7.17301 | −0.300181 | −0.150091 | − | 0.988672i | \(-0.547957\pi\) | ||||
−0.150091 | + | 0.988672i | \(0.547957\pi\) | |||||||
\(572\) | −8.63388 | + | 47.5769i | −0.361001 | + | 1.98929i | ||||
\(573\) | −0.306623 | − | 0.306623i | −0.0128094 | − | 0.0128094i | ||||
\(574\) | −9.98141 | + | 3.11979i | −0.416616 | + | 0.130218i | ||||
\(575\) | 4.65298 | − | 0.278304i | 0.194043 | − | 0.0116061i | ||||
\(576\) | −4.03924 | − | 16.0299i | −0.168302 | − | 0.667913i | ||||
\(577\) | −3.54999 | − | 3.54999i | −0.147788 | − | 0.147788i | 0.629341 | − | 0.777129i | \(-0.283325\pi\) |
−0.777129 | + | 0.629341i | \(0.783325\pi\) | |||||||
\(578\) | −3.15167 | + | 6.01762i | −0.131092 | + | 0.250300i | ||||
\(579\) | 2.73517i | 0.113670i | ||||||||
\(580\) | −22.0996 | − | 13.3178i | −0.917635 | − | 0.552990i | ||||
\(581\) | − | 5.49179i | − | 0.227838i | ||||||
\(582\) | 22.7321 | + | 11.9057i | 0.942276 | + | 0.493507i | ||||
\(583\) | −43.7780 | − | 43.7780i | −1.81310 | − | 1.81310i | ||||
\(584\) | −4.59120 | − | 3.57782i | −0.189985 | − | 0.148051i | ||||
\(585\) | 7.32276 | − | 19.2889i | 0.302759 | − | 0.797498i | ||||
\(586\) | −7.88389 | − | 25.2236i | −0.325681 | − | 1.04198i | ||||
\(587\) | 18.7905 | + | 18.7905i | 0.775568 | + | 0.775568i | 0.979074 | − | 0.203505i | \(-0.0652334\pi\) |
−0.203505 | + | 0.979074i | \(0.565233\pi\) | |||||||
\(588\) | 0.345057 | − | 1.90143i | 0.0142299 | − | 0.0784138i | ||||
\(589\) | −12.0207 | −0.495306 | ||||||||
\(590\) | −1.50340 | + | 25.0731i | −0.0618939 | + | 1.03224i | ||||
\(591\) | − | 12.3968i | − | 0.509937i | ||||||
\(592\) | −1.59270 | − | 3.50642i | −0.0654596 | − | 0.144113i | ||||
\(593\) | −7.24799 | + | 7.24799i | −0.297639 | + | 0.297639i | −0.840088 | − | 0.542449i | \(-0.817497\pi\) |
0.542449 | + | 0.840088i | \(0.317497\pi\) | |||||||
\(594\) | −11.1826 | − | 35.7775i | −0.458828 | − | 1.46797i | ||||
\(595\) | −7.12226 | + | 3.20258i | −0.291984 | + | 0.131293i | ||||
\(596\) | 15.1289 | + | 21.8373i | 0.619705 | + | 0.894490i | ||||
\(597\) | 12.3967 | − | 12.3967i | 0.507365 | − | 0.507365i | ||||
\(598\) | 2.73137 | − | 5.21514i | 0.111694 | − | 0.213263i | ||||
\(599\) | −20.5332 | −0.838963 | −0.419482 | − | 0.907764i | \(-0.637788\pi\) | ||||
−0.419482 | + | 0.907764i | \(0.637788\pi\) | |||||||
\(600\) | −13.4362 | + | 2.48890i | −0.548530 | + | 0.101609i | ||||
\(601\) | −27.1276 | −1.10656 | −0.553280 | − | 0.832995i | \(-0.686624\pi\) | ||||
−0.553280 | + | 0.832995i | \(0.686624\pi\) | |||||||
\(602\) | −0.0785486 | + | 0.149976i | −0.00320140 | + | 0.00611258i | ||||
\(603\) | −16.1623 | + | 16.1623i | −0.658180 | + | 0.658180i | ||||
\(604\) | 17.2800 | − | 11.9716i | 0.703111 | − | 0.487118i | ||||
\(605\) | −37.3530 | + | 16.7961i | −1.51861 | + | 0.682857i | ||||
\(606\) | 5.18747 | + | 16.5967i | 0.210727 | + | 0.674195i | ||||
\(607\) | 12.6435 | − | 12.6435i | 0.513185 | − | 0.513185i | −0.402316 | − | 0.915501i | \(-0.631795\pi\) |
0.915501 | + | 0.402316i | \(0.131795\pi\) | |||||||
\(608\) | 14.6241 | + | 16.3642i | 0.593084 | + | 0.663658i | ||||
\(609\) | 5.57479i | 0.225902i | ||||||||
\(610\) | 0.795497 | − | 13.2670i | 0.0322087 | − | 0.537166i | ||||
\(611\) | 14.6937 | 0.594442 | ||||||||
\(612\) | 14.2011 | + | 2.57711i | 0.574046 | + | 0.104173i | ||||
\(613\) | −0.474128 | − | 0.474128i | −0.0191498 | − | 0.0191498i | 0.697467 | − | 0.716617i | \(-0.254310\pi\) |
−0.716617 | + | 0.697467i | \(0.754310\pi\) | |||||||
\(614\) | 9.20737 | + | 29.4579i | 0.371579 | + | 1.18882i | ||||
\(615\) | 5.67048 | − | 14.9366i | 0.228656 | − | 0.602304i | ||||
\(616\) | 12.0796 | + | 9.41333i | 0.486700 | + | 0.379274i | ||||
\(617\) | −34.0848 | − | 34.0848i | −1.37220 | − | 1.37220i | −0.857171 | − | 0.515032i | \(-0.827780\pi\) |
−0.515032 | − | 0.857171i | \(-0.672220\pi\) | |||||||
\(618\) | −14.1720 | − | 7.42244i | −0.570081 | − | 0.298574i | ||||
\(619\) | 29.0177i | 1.16632i | 0.812357 | + | 0.583161i | \(0.198184\pi\) | ||||
−0.812357 | + | 0.583161i | \(0.801816\pi\) | |||||||
\(620\) | 7.15202 | − | 11.8681i | 0.287232 | − | 0.476635i | ||||
\(621\) | 4.56374i | 0.183136i | ||||||||
\(622\) | −14.7560 | + | 28.1742i | −0.591660 | + | 1.12968i | ||||
\(623\) | 1.39009 | + | 1.39009i | 0.0556929 | + | 0.0556929i | ||||
\(624\) | −6.06409 | + | 16.1578i | −0.242758 | + | 0.646830i | ||||
\(625\) | −2.97994 | − | 24.8218i | −0.119197 | − | 0.992871i | ||||
\(626\) | −20.7343 | + | 6.48071i | −0.828708 | + | 0.259021i | ||||
\(627\) | 14.3521 | + | 14.3521i | 0.573167 | + | 0.573167i | ||||
\(628\) | −41.0365 | − | 7.44697i | −1.63753 | − | 0.297167i | ||||
\(629\) | 3.36244 | 0.134069 | ||||||||
\(630\) | −4.33571 | − | 4.88882i | −0.172739 | − | 0.194775i | ||||
\(631\) | 24.5158i | 0.975960i | 0.872855 | + | 0.487980i | \(0.162266\pi\) | ||||
−0.872855 | + | 0.487980i | \(0.837734\pi\) | |||||||
\(632\) | 4.47676 | + | 36.0878i | 0.178076 | + | 1.43549i | ||||
\(633\) | 8.93144 | − | 8.93144i | 0.354993 | − | 0.354993i | ||||
\(634\) | 10.1005 | − | 3.15700i | 0.401141 | − | 0.125381i | ||||
\(635\) | −17.7543 | + | 46.7668i | −0.704559 | + | 1.85588i | ||||
\(636\) | −12.5840 | − | 18.1639i | −0.498988 | − | 0.720245i | ||||
\(637\) | 3.15744 | − | 3.15744i | 0.125102 | − | 0.125102i | ||||
\(638\) | −39.1356 | − | 20.4969i | −1.54939 | − | 0.811478i | ||||
\(639\) | 5.89978 | 0.233392 | ||||||||
\(640\) | −24.8574 | + | 4.70210i | −0.982575 | + | 0.185867i | ||||
\(641\) | −42.5065 | −1.67891 | −0.839453 | − | 0.543432i | \(-0.817125\pi\) | ||||
−0.839453 | + | 0.543432i | \(0.817125\pi\) | |||||||
\(642\) | 7.31352 | + | 3.83038i | 0.288642 | + | 0.151173i | ||||
\(643\) | −3.14215 | + | 3.14215i | −0.123914 | + | 0.123914i | −0.766344 | − | 0.642430i | \(-0.777926\pi\) |
0.642430 | + | 0.766344i | \(0.277926\pi\) | |||||||
\(644\) | −1.06182 | − | 1.53264i | −0.0418414 | − | 0.0603943i | ||||
\(645\) | −0.106075 | − | 0.235901i | −0.00417669 | − | 0.00928858i | ||||
\(646\) | −18.2888 | + | 5.71636i | −0.719564 | + | 0.224907i | ||||
\(647\) | 10.1457 | − | 10.1457i | 0.398867 | − | 0.398867i | −0.478966 | − | 0.877833i | \(-0.658988\pi\) |
0.877833 | + | 0.478966i | \(0.158988\pi\) | |||||||
\(648\) | 0.511514 | + | 4.12338i | 0.0200942 | + | 0.161982i | ||||
\(649\) | 43.0070i | 1.68817i | ||||||||
\(650\) | −28.7952 | − | 12.9531i | −1.12944 | − | 0.508063i | ||||
\(651\) | −2.99382 | −0.117337 | ||||||||
\(652\) | 19.1171 | + | 3.46923i | 0.748685 | + | 0.135865i | ||||
\(653\) | 5.20264 | + | 5.20264i | 0.203595 | + | 0.203595i | 0.801538 | − | 0.597943i | \(-0.204015\pi\) |
−0.597943 | + | 0.801538i | \(0.704015\pi\) | |||||||
\(654\) | −24.2083 | + | 7.56656i | −0.946620 | + | 0.295876i | ||||
\(655\) | −16.5755 | + | 7.45332i | −0.647660 | + | 0.291225i | ||||
\(656\) | 10.3931 | − | 27.6925i | 0.405783 | − | 1.08121i | ||||
\(657\) | 3.00691 | + | 3.00691i | 0.117311 | + | 0.117311i | ||||
\(658\) | 2.15910 | − | 4.12248i | 0.0841707 | − | 0.160711i | ||||
\(659\) | − | 45.6133i | − | 1.77684i | −0.459032 | − | 0.888420i | \(-0.651804\pi\) | ||
0.459032 | − | 0.888420i | \(-0.348196\pi\) | |||||||
\(660\) | −22.7090 | + | 5.63075i | −0.883945 | + | 0.219177i | ||||
\(661\) | 45.1240i | 1.75512i | 0.479465 | + | 0.877561i | \(0.340831\pi\) | ||||
−0.479465 | + | 0.877561i | \(0.659169\pi\) | |||||||
\(662\) | 8.52556 | + | 4.46517i | 0.331355 | + | 0.173544i | ||||
\(663\) | −10.6547 | − | 10.6547i | −0.413795 | − | 0.413795i | ||||
\(664\) | 12.2522 | + | 9.54785i | 0.475477 | + | 0.370529i | ||||
\(665\) | 8.11036 | + | 3.07898i | 0.314506 | + | 0.119398i | ||||
\(666\) | 0.839367 | + | 2.68546i | 0.0325248 | + | 0.104059i | ||||
\(667\) | 3.80333 | + | 3.80333i | 0.147265 | + | 0.147265i | ||||
\(668\) | −8.58638 | − | 1.55819i | −0.332217 | − | 0.0602881i | ||||
\(669\) | −8.82868 | −0.341337 | ||||||||
\(670\) | 23.2093 | + | 26.1701i | 0.896653 | + | 1.01104i | ||||
\(671\) | − | 22.7564i | − | 0.878501i | ||||||
\(672\) | 3.64220 | + | 4.07560i | 0.140501 | + | 0.157220i | ||||
\(673\) | 5.25412 | − | 5.25412i | 0.202532 | − | 0.202532i | −0.598552 | − | 0.801084i | \(-0.704257\pi\) |
0.801084 | + | 0.598552i | \(0.204257\pi\) | |||||||
\(674\) | 11.2946 | + | 36.1358i | 0.435052 | + | 1.39190i | ||||
\(675\) | 24.4331 | − | 1.46139i | 0.940430 | − | 0.0562490i | ||||
\(676\) | −11.4076 | + | 7.90321i | −0.438753 | + | 0.303970i | ||||
\(677\) | 26.8547 | − | 26.8547i | 1.03211 | − | 1.03211i | 0.0326441 | − | 0.999467i | \(-0.489607\pi\) |
0.999467 | − | 0.0326441i | \(-0.0103928\pi\) | |||||||
\(678\) | 6.57492 | − | 12.5538i | 0.252508 | − | 0.482125i | ||||
\(679\) | 18.7791 | 0.720675 | ||||||||
\(680\) | 5.23758 | − | 21.4577i | 0.200852 | − | 0.822865i | ||||
\(681\) | 9.21842 | 0.353251 | ||||||||
\(682\) | 11.0074 | − | 21.0169i | 0.421495 | − | 0.804780i | ||||
\(683\) | 11.7713 | − | 11.7713i | 0.450416 | − | 0.450416i | −0.445077 | − | 0.895492i | \(-0.646824\pi\) |
0.895492 | + | 0.445077i | \(0.146824\pi\) | |||||||
\(684\) | −9.13088 | − | 13.1796i | −0.349128 | − | 0.503935i | ||||
\(685\) | −12.4412 | − | 4.72311i | −0.475352 | − | 0.180461i | ||||
\(686\) | −0.421899 | − | 1.34982i | −0.0161082 | − | 0.0515362i | ||||
\(687\) | −13.9498 | + | 13.9498i | −0.532218 | + | 0.532218i | ||||
\(688\) | −0.198036 | − | 0.435987i | −0.00755004 | − | 0.0166218i | ||||
\(689\) | − | 51.0587i | − | 1.94518i | ||||||
\(690\) | 2.84344 | + | 0.170494i | 0.108248 | + | 0.00649061i | ||||
\(691\) | 32.1658 | 1.22364 | 0.611822 | − | 0.790995i | \(-0.290437\pi\) | ||||
0.611822 | + | 0.790995i | \(0.290437\pi\) | |||||||
\(692\) | 3.25769 | − | 17.9515i | 0.123839 | − | 0.682412i | ||||
\(693\) | −7.91125 | − | 7.91125i | −0.300523 | − | 0.300523i | ||||
\(694\) | −7.26175 | − | 23.2331i | −0.275652 | − | 0.881917i | ||||
\(695\) | 19.9315 | + | 44.3259i | 0.756044 | + | 1.68138i | ||||
\(696\) | −12.4374 | − | 9.69217i | −0.471438 | − | 0.367381i | ||||
\(697\) | 18.2609 | + | 18.2609i | 0.691681 | + | 0.691681i | ||||
\(698\) | −19.7497 | − | 10.3437i | −0.747536 | − | 0.391514i | ||||
\(699\) | 13.4704i | 0.509496i | ||||||||
\(700\) | −7.86534 | + | 6.17547i | −0.297282 | + | 0.233411i | ||||
\(701\) | 36.5604i | 1.38087i | 0.723396 | + | 0.690433i | \(0.242580\pi\) | ||||
−0.723396 | + | 0.690433i | \(0.757420\pi\) | |||||||
\(702\) | 14.3426 | − | 27.3850i | 0.541327 | − | 1.03358i | ||||
\(703\) | −2.64126 | − | 2.64126i | −0.0996171 | − | 0.0996171i | ||||
\(704\) | −42.0024 | + | 10.5838i | −1.58302 | + | 0.398893i | ||||
\(705\) | 2.91573 | + | 6.48432i | 0.109813 | + | 0.244214i | ||||
\(706\) | 24.0128 | − | 7.50546i | 0.903734 | − | 0.282472i | ||||
\(707\) | 8.99799 | + | 8.99799i | 0.338404 | + | 0.338404i | ||||
\(708\) | −2.74081 | + | 15.1032i | −0.103006 | + | 0.567612i | ||||
\(709\) | −13.0843 | −0.491390 | −0.245695 | − | 0.969347i | \(-0.579016\pi\) | ||||
−0.245695 | + | 0.969347i | \(0.579016\pi\) | |||||||
\(710\) | 0.540397 | − | 9.01255i | 0.0202808 | − | 0.338235i | ||||
\(711\) | − | 26.5668i | − | 0.996335i | ||||||
\(712\) | −5.51808 | + | 0.684528i | −0.206799 | + | 0.0256538i | ||||
\(713\) | −2.04250 | + | 2.04250i | −0.0764921 | + | 0.0764921i | ||||
\(714\) | −4.55492 | + | 1.42369i | −0.170464 | + | 0.0532802i | ||||
\(715\) | −50.5418 | − | 19.1875i | −1.89016 | − | 0.717571i | ||||
\(716\) | 31.5060 | − | 21.8275i | 1.17744 | − | 0.815732i | ||||
\(717\) | −3.04545 | + | 3.04545i | −0.113734 | + | 0.113734i | ||||
\(718\) | 42.2804 | + | 22.1439i | 1.57789 | + | 0.826404i | ||||
\(719\) | 18.4708 | 0.688843 | 0.344422 | − | 0.938815i | \(-0.388075\pi\) | ||||
0.344422 | + | 0.938815i | \(0.388075\pi\) | |||||||
\(720\) | 18.4449 | − | 1.17343i | 0.687401 | − | 0.0437312i | ||||
\(721\) | −11.7075 | −0.436012 | ||||||||
\(722\) | −4.94650 | − | 2.59068i | −0.184090 | − | 0.0964150i | ||||
\(723\) | 3.99933 | − | 3.99933i | 0.148737 | − | 0.148737i | ||||
\(724\) | 22.0890 | − | 15.3034i | 0.820933 | − | 0.568745i | ||||
\(725\) | 19.1442 | − | 21.5799i | 0.710996 | − | 0.801459i | ||||
\(726\) | −23.8885 | + | 7.46659i | −0.886584 | + | 0.277111i | ||||
\(727\) | −25.3587 | + | 25.3587i | −0.940503 | + | 0.940503i | −0.998327 | − | 0.0578241i | \(-0.981584\pi\) |
0.0578241 | + | 0.998327i | \(0.481584\pi\) | |||||||
\(728\) | 1.55483 | + | 12.5337i | 0.0576258 | + | 0.464530i | ||||
\(729\) | 11.1548i | 0.413140i | ||||||||
\(730\) | 4.86880 | − | 4.31796i | 0.180202 | − | 0.159815i | ||||
\(731\) | 0.418085 | 0.0154634 | ||||||||
\(732\) | 1.45025 | − | 7.99159i | 0.0536028 | − | 0.295378i | ||||
\(733\) | 24.6327 | + | 24.6327i | 0.909830 | + | 0.909830i | 0.996258 | − | 0.0864280i | \(-0.0275453\pi\) |
−0.0864280 | + | 0.996258i | \(0.527545\pi\) | |||||||
\(734\) | −4.18693 | + | 1.30867i | −0.154542 | + | 0.0483038i | ||||
\(735\) | 2.01993 | + | 0.766836i | 0.0745061 | + | 0.0282852i | ||||
\(736\) | 5.26536 | + | 0.295681i | 0.194084 | + | 0.0108990i | ||||
\(737\) | 42.3493 | + | 42.3493i | 1.55996 | + | 1.55996i | ||||
\(738\) | −10.0258 | + | 19.1428i | −0.369056 | + | 0.704655i | ||||
\(739\) | 23.4559i | 0.862838i | 0.902152 | + | 0.431419i | \(0.141987\pi\) | ||||
−0.902152 | + | 0.431419i | \(0.858013\pi\) | |||||||
\(740\) | 4.17921 | − | 1.03625i | 0.153631 | − | 0.0380932i | ||||
\(741\) | 16.7390i | 0.614922i | ||||||||
\(742\) | −14.3251 | − | 7.50262i | −0.525891 | − | 0.275430i | ||||
\(743\) | −9.17537 | − | 9.17537i | −0.336612 | − | 0.336612i | 0.518479 | − | 0.855090i | \(-0.326498\pi\) |
−0.855090 | + | 0.518479i | \(0.826498\pi\) | |||||||
\(744\) | 5.20497 | − | 6.67923i | 0.190824 | − | 0.244873i | ||||
\(745\) | −27.0891 | + | 12.1808i | −0.992466 | + | 0.446270i | ||||
\(746\) | −3.38100 | − | 10.8171i | −0.123787 | − | 0.396042i | ||||
\(747\) | −8.02430 | − | 8.02430i | −0.293594 | − | 0.293594i | ||||
\(748\) | 6.75266 | − | 37.2105i | 0.246902 | − | 1.36055i | ||||
\(749\) | 6.04173 | 0.220760 | ||||||||
\(750\) | 0.00226196 | − | 15.2777i | 8.25952e−5 | − | 0.557861i | ||||
\(751\) | − | 34.6985i | − | 1.26617i | −0.774084 | − | 0.633083i | \(-0.781789\pi\) | ||
0.774084 | − | 0.633083i | \(-0.218211\pi\) | |||||||
\(752\) | 5.44351 | + | 11.9842i | 0.198504 | + | 0.437018i | ||||
\(753\) | 2.98499 | − | 2.98499i | 0.108779 | − | 0.108779i | ||||
\(754\) | −10.8693 | − | 34.7750i | −0.395836 | − | 1.26643i | ||||
\(755\) | 9.63874 | + | 21.4357i | 0.350790 | + | 0.780126i | ||||
\(756\) | −5.57566 | − | 8.04797i | −0.202785 | − | 0.292702i | ||||
\(757\) | −11.2942 | + | 11.2942i | −0.410495 | + | 0.410495i | −0.881911 | − | 0.471416i | \(-0.843743\pi\) |
0.471416 | + | 0.881911i | \(0.343743\pi\) | |||||||
\(758\) | 5.99421 | − | 11.4450i | 0.217720 | − | 0.415702i | ||||
\(759\) | 4.87725 | 0.177033 | ||||||||
\(760\) | −20.9697 | + | 12.7412i | −0.760649 | + | 0.462172i | ||||
\(761\) | 51.7952 | 1.87757 | 0.938787 | − | 0.344499i | \(-0.111951\pi\) | ||||
0.938787 | + | 0.344499i | \(0.111951\pi\) | |||||||
\(762\) | −14.1831 | + | 27.0804i | −0.513798 | + | 0.981018i | ||||
\(763\) | −13.1247 | + | 13.1247i | −0.475145 | + | 0.475145i | ||||
\(764\) | 0.737795 | − | 0.511147i | 0.0266925 | − | 0.0184926i | ||||
\(765\) | −5.72722 | + | 15.0861i | −0.207068 | + | 0.545439i | ||||
\(766\) | −4.56314 | − | 14.5992i | −0.164873 | − | 0.527492i | ||||
\(767\) | −25.0797 | + | 25.0797i | −0.905577 | + | 0.905577i | ||||
\(768\) | −15.4249 | + | 1.04004i | −0.556598 | + | 0.0375293i | ||||
\(769\) | − | 7.52971i | − | 0.271528i | −0.990741 | − | 0.135764i | \(-0.956651\pi\) | ||
0.990741 | − | 0.135764i | \(-0.0433490\pi\) | |||||||
\(770\) | −12.8099 | + | 11.3606i | −0.461638 | + | 0.409409i | ||||
\(771\) | −8.92784 | −0.321528 | ||||||||
\(772\) | −5.57046 | − | 1.01088i | −0.200485 | − | 0.0363825i | ||||
\(773\) | −6.95427 | − | 6.95427i | −0.250128 | − | 0.250128i | 0.570895 | − | 0.821023i | \(-0.306596\pi\) |
−0.821023 | + | 0.570895i | \(0.806596\pi\) | |||||||
\(774\) | 0.104367 | + | 0.333908i | 0.00375138 | + | 0.0120021i | ||||
\(775\) | 11.5891 | + | 10.2810i | 0.416291 | + | 0.369303i | ||||
\(776\) | −32.6487 | + | 41.8962i | −1.17202 | + | 1.50399i | ||||
\(777\) | −0.657820 | − | 0.657820i | −0.0235992 | − | 0.0235992i | ||||
\(778\) | 34.9513 | + | 18.3054i | 1.25306 | + | 0.656279i | ||||
\(779\) | − | 28.6886i | − | 1.02788i | ||||||
\(780\) | −16.5265 | − | 9.95925i | −0.591742 | − | 0.356598i | ||||
\(781\) | − | 15.4589i | − | 0.553162i | ||||||
\(782\) | −2.13624 | + | 4.07883i | −0.0763919 | + | 0.145858i | ||||
\(783\) | 19.9715 | + | 19.9715i | 0.713724 | + | 0.713724i | ||||
\(784\) | 3.74494 | + | 1.40549i | 0.133748 | + | 0.0501961i | ||||
\(785\) | 16.5498 | − | 43.5938i | 0.590686 | − | 1.55593i | ||||
\(786\) | −10.6006 | + | 3.31333i | −0.378111 | + | 0.118183i | ||||
\(787\) | −12.5412 | − | 12.5412i | −0.447047 | − | 0.447047i | 0.447325 | − | 0.894372i | \(-0.352377\pi\) |
−0.894372 | + | 0.447325i | \(0.852377\pi\) | |||||||
\(788\) | 25.2475 | + | 4.58171i | 0.899404 | + | 0.163217i | ||||
\(789\) | 15.8103 | 0.562863 | ||||||||
\(790\) | −40.5837 | − | 2.43342i | −1.44390 | − | 0.0865773i | ||||
\(791\) | − | 10.3707i | − | 0.368741i | ||||||
\(792\) | 31.4043 | − | 3.89576i | 1.11590 | − | 0.138430i | ||||
\(793\) | 13.2705 | − | 13.2705i | 0.471250 | − | 0.471250i | ||||
\(794\) | 15.9720 | − | 4.99220i | 0.566824 | − | 0.177167i | ||||
\(795\) | 22.5322 | − | 10.1318i | 0.799136 | − | 0.359338i | ||||
\(796\) | 20.6656 | + | 29.8290i | 0.732474 | + | 1.05726i | ||||
\(797\) | 21.9527 | − | 21.9527i | 0.777606 | − | 0.777606i | −0.201817 | − | 0.979423i | \(-0.564685\pi\) |
0.979423 | + | 0.201817i | \(0.0646846\pi\) | |||||||
\(798\) | 4.69631 | + | 2.45964i | 0.166248 | + | 0.0870705i | ||||
\(799\) | −11.4921 | −0.406562 | ||||||||
\(800\) | −0.103059 | − | 28.2841i | −0.00364369 | − | 0.999993i | ||||
\(801\) | 4.06226 | 0.143533 | ||||||||
\(802\) | 43.2040 | + | 22.6277i | 1.52559 | + | 0.799010i | ||||
\(803\) | 7.87885 | − | 7.87885i | 0.278039 | − | 0.278039i | ||||
\(804\) | 12.1733 | + | 17.5711i | 0.429320 | + | 0.619686i | ||||
\(805\) | 1.90123 | − | 0.854903i | 0.0670095 | − | 0.0301314i | ||||
\(806\) | 18.6752 | − | 5.83712i | 0.657805 | − | 0.205604i | ||||
\(807\) | −10.8770 | + | 10.8770i | −0.382887 | + | 0.382887i | ||||
\(808\) | −35.7182 | + | 4.43091i | −1.25656 | + | 0.155879i | ||||
\(809\) | − | 15.6233i | − | 0.549285i | −0.961546 | − | 0.274642i | \(-0.911441\pi\) | ||
0.961546 | − | 0.274642i | \(-0.0885595\pi\) | |||||||
\(810\) | −4.63709 | − | 0.278043i | −0.162931 | − | 0.00976942i | ||||
\(811\) | 12.8151 | 0.450000 | 0.225000 | − | 0.974359i | \(-0.427762\pi\) | ||||
0.225000 | + | 0.974359i | \(0.427762\pi\) | |||||||
\(812\) | −11.3537 | − | 2.06037i | −0.398435 | − | 0.0723049i | ||||
\(813\) | 14.2195 | + | 14.2195i | 0.498700 | + | 0.498700i | ||||
\(814\) | 7.03657 | − | 2.19935i | 0.246632 | − | 0.0770872i | ||||
\(815\) | −7.70982 | + | 20.3085i | −0.270063 | + | 0.711375i | ||||
\(816\) | 4.74280 | − | 12.6372i | 0.166031 | − | 0.442392i | ||||
\(817\) | −0.328414 | − | 0.328414i | −0.0114897 | − | 0.0114897i | ||||
\(818\) | −16.3072 | + | 31.1361i | −0.570168 | + | 1.08865i | ||||
\(819\) | − | 9.22697i | − | 0.322416i | ||||||
\(820\) | 28.3243 | + | 17.0689i | 0.989129 | + | 0.596073i | ||||
\(821\) | − | 1.83369i | − | 0.0639962i | −0.999488 | − | 0.0319981i | \(-0.989813\pi\) | ||
0.999488 | − | 0.0319981i | \(-0.0101871\pi\) | |||||||
\(822\) | −7.20407 | − | 3.77305i | −0.251271 | − | 0.131600i | ||||
\(823\) | −9.77602 | − | 9.77602i | −0.340770 | − | 0.340770i | 0.515886 | − | 0.856657i | \(-0.327463\pi\) |
−0.856657 | + | 0.515886i | \(0.827463\pi\) | |||||||
\(824\) | 20.3544 | − | 26.1196i | 0.709078 | − | 0.909918i | ||||
\(825\) | −1.56178 | − | 26.1116i | −0.0543743 | − | 0.909088i | ||||
\(826\) | 3.35116 | + | 10.7217i | 0.116602 | + | 0.373054i | ||||
\(827\) | 9.46776 | + | 9.46776i | 0.329226 | + | 0.329226i | 0.852292 | − | 0.523066i | \(-0.175212\pi\) |
−0.523066 | + | 0.852292i | \(0.675212\pi\) | |||||||
\(828\) | −3.79087 | − | 0.687938i | −0.131742 | − | 0.0239075i | ||||
\(829\) | 29.4393 | 1.02247 | 0.511234 | − | 0.859442i | \(-0.329189\pi\) | ||||
0.511234 | + | 0.859442i | \(0.329189\pi\) | |||||||
\(830\) | −12.9930 | + | 11.5230i | −0.450993 | + | 0.399969i | ||||
\(831\) | 19.7825i | 0.686247i | ||||||||
\(832\) | −30.6659 | − | 18.3219i | −1.06315 | − | 0.635197i | ||||
\(833\) | −2.46948 | + | 2.46948i | −0.0855623 | + | 0.0855623i | ||||
\(834\) | 8.86042 | + | 28.3479i | 0.306811 | + | 0.981607i | ||||
\(835\) | 3.46284 | − | 9.12147i | 0.119836 | − | 0.315661i | ||||
\(836\) | −34.5339 | + | 23.9252i | −1.19438 | + | 0.827470i | ||||
\(837\) | −10.7253 | + | 10.7253i | −0.370720 | + | 0.370720i | ||||
\(838\) | 1.23876 | − | 2.36522i | 0.0427923 | − | 0.0817052i | ||||
\(839\) | 8.19787 | 0.283022 | 0.141511 | − | 0.989937i | \(-0.454804\pi\) | ||||
0.141511 | + | 0.989937i | \(0.454804\pi\) | |||||||
\(840\) | −5.22260 | + | 3.17326i | −0.180197 | + | 0.109488i | ||||
\(841\) | 4.28771 | 0.147852 | ||||||||
\(842\) | 1.17059 | − | 2.23506i | 0.0403412 | − | 0.0770253i | ||||
\(843\) | 15.0417 | − | 15.0417i | 0.518065 | − | 0.518065i | ||||
\(844\) | 14.8889 | + | 21.4908i | 0.512496 | + | 0.739743i | ||||
\(845\) | −6.36314 | − | 14.1511i | −0.218899 | − | 0.486811i | ||||
\(846\) | −2.86878 | − | 9.17831i | −0.0986305 | − | 0.315557i | ||||
\(847\) | −12.9513 | + | 12.9513i | −0.445011 | + | 0.445011i | ||||
\(848\) | 41.6436 | − | 18.9155i | 1.43005 | − | 0.649562i | ||||
\(849\) | − | 0.00193230i | − | 6.63162e-5i | ||||||
\(850\) | 22.5211 | + | 10.1308i | 0.772466 | + | 0.347483i | ||||
\(851\) | −0.897577 | −0.0307685 | ||||||||
\(852\) | 0.985185 | − | 5.42885i | 0.0337519 | − | 0.185989i | ||||
\(853\) | −12.0948 | − | 12.0948i | −0.414118 | − | 0.414118i | 0.469053 | − | 0.883170i | \(-0.344595\pi\) |
−0.883170 | + | 0.469053i | \(0.844595\pi\) | |||||||
\(854\) | −1.77321 | − | 5.67318i | −0.0606781 | − | 0.194132i | ||||
\(855\) | 16.3493 | − | 7.35158i | 0.559133 | − | 0.251419i | ||||
\(856\) | −10.5040 | + | 13.4791i | −0.359018 | + | 0.460707i | ||||
\(857\) | 13.0039 | + | 13.0039i | 0.444205 | + | 0.444205i | 0.893422 | − | 0.449218i | \(-0.148297\pi\) |
−0.449218 | + | 0.893422i | \(0.648297\pi\) | |||||||
\(858\) | −29.2663 | − | 15.3279i | −0.999134 | − | 0.523286i | ||||
\(859\) | 46.0549i | 1.57137i | 0.618624 | + | 0.785687i | \(0.287690\pi\) | ||||
−0.618624 | + | 0.785687i | \(0.712310\pi\) | |||||||
\(860\) | 0.519641 | − | 0.128846i | 0.0177196 | − | 0.00439363i | ||||
\(861\) | − | 7.14504i | − | 0.243502i | ||||||
\(862\) | 21.0373 | − | 40.1676i | 0.716535 | − | 1.36811i | ||||
\(863\) | 8.93749 | + | 8.93749i | 0.304236 | + | 0.304236i | 0.842669 | − | 0.538433i | \(-0.180983\pi\) |
−0.538433 | + | 0.842669i | \(0.680983\pi\) | |||||||
\(864\) | 27.6487 | + | 1.55264i | 0.940629 | + | 0.0528220i | ||||
\(865\) | 19.0701 | + | 7.23971i | 0.648405 | + | 0.246158i | ||||
\(866\) | −42.8259 | + | 13.3857i | −1.45528 | + | 0.454864i | ||||
\(867\) | −3.28185 | − | 3.28185i | −0.111457 | − | 0.111457i | ||||
\(868\) | 1.10648 | − | 6.09724i | 0.0375564 | − | 0.206954i | ||||
\(869\) | −69.6118 | −2.36142 | ||||||||
\(870\) | 13.1894 | − | 11.6972i | 0.447162 | − | 0.396571i | ||||
\(871\) | 49.3924i | 1.67360i | ||||||||
\(872\) | −6.46302 | − | 52.0993i | −0.218866 | − | 1.76431i | ||||
\(873\) | 27.4390 | − | 27.4390i | 0.928669 | − | 0.928669i | ||||
\(874\) | 4.88205 | − | 1.52594i | 0.165138 | − | 0.0516156i | ||||
\(875\) | −5.18574 | − | 9.90495i | −0.175310 | − | 0.334848i | ||||
\(876\) | 3.26901 | − | 2.26478i | 0.110450 | − | 0.0765198i | ||||
\(877\) | −5.94628 | + | 5.94628i | −0.200792 | + | 0.200792i | −0.800339 | − | 0.599547i | \(-0.795347\pi\) |
0.599547 | + | 0.800339i | \(0.295347\pi\) | |||||||
\(878\) | −19.5023 | − | 10.2141i | −0.658172 | − | 0.344710i | ||||
\(879\) | 18.0559 | 0.609011 | ||||||||
\(880\) | −3.07468 | − | 48.3303i | −0.103648 | − | 1.62921i | ||||
\(881\) | 23.6599 | 0.797122 | 0.398561 | − | 0.917142i | \(-0.369510\pi\) | ||||
0.398561 | + | 0.917142i | \(0.369510\pi\) | |||||||
\(882\) | −2.58873 | − | 1.35582i | −0.0871672 | − | 0.0456529i | ||||
\(883\) | 21.7857 | − | 21.7857i | 0.733148 | − | 0.733148i | −0.238094 | − | 0.971242i | \(-0.576523\pi\) |
0.971242 | + | 0.238094i | \(0.0765227\pi\) | |||||||
\(884\) | 25.6373 | − | 17.7616i | 0.862277 | − | 0.597389i | ||||
\(885\) | −16.0444 | − | 6.09102i | −0.539326 | − | 0.204747i | ||||
\(886\) | 43.4024 | − | 13.5659i | 1.45813 | − | 0.455754i | ||||
\(887\) | 34.7838 | − | 34.7838i | 1.16793 | − | 1.16793i | 0.185230 | − | 0.982695i | \(-0.440697\pi\) |
0.982695 | − | 0.185230i | \(-0.0593030\pi\) | |||||||
\(888\) | 2.61126 | − | 0.323932i | 0.0876283 | − | 0.0108705i | ||||
\(889\) | 22.3712i | 0.750305i | ||||||||
\(890\) | 0.372088 | − | 6.20554i | 0.0124724 | − | 0.208010i | ||||
\(891\) | −7.95383 | −0.266463 | ||||||||
\(892\) | 3.26297 | − | 17.9806i | 0.109252 | − | 0.602033i | ||||
\(893\) | 9.02727 | + | 9.02727i | 0.302086 | + | 0.302086i | ||||
\(894\) | −17.3244 | + | 5.41491i | −0.579413 | + | 0.181102i | ||||
\(895\) | 17.5740 | + | 39.0831i | 0.587435 | + | 1.30640i | ||||
\(896\) | −9.64650 | + | 5.91143i | −0.322267 | + | 0.197487i | ||||
\(897\) | 2.84419 | + | 2.84419i | 0.0949648 | + | 0.0949648i | ||||
\(898\) | 5.22994 | − | 9.98577i | 0.174525 | − | 0.333229i | ||||
\(899\) | 17.8765i | 0.596213i | ||||||||
\(900\) | −2.46914 | + | 20.5157i | −0.0823046 | + | 0.683856i | ||||
\(901\) | 39.9337i | 1.33038i | ||||||||
\(902\) | 50.1588 | + | 26.2702i | 1.67011 | + | 0.874701i | ||||
\(903\) | −0.0817930 | − | 0.0817930i | −0.00272190 | − | 0.00272190i | ||||
\(904\) | 23.1371 | + | 18.0302i | 0.769530 | + | 0.599677i | ||||
\(905\) | 12.3213 | + | 27.4014i | 0.409572 | + | 0.910853i | ||||
\(906\) | 4.28484 | + | 13.7089i | 0.142354 | + | 0.455446i | ||||
\(907\) | 6.75591 | + | 6.75591i | 0.224326 | + | 0.224326i | 0.810317 | − | 0.585991i | \(-0.199295\pi\) |
−0.585991 | + | 0.810317i | \(0.699295\pi\) | |||||||
\(908\) | −3.40701 | + | 18.7743i | −0.113066 | + | 0.623047i | ||||
\(909\) | 26.2948 | 0.872142 | ||||||||
\(910\) | −14.0952 | − | 0.845156i | −0.467251 | − | 0.0280167i | ||||
\(911\) | − | 24.7078i | − | 0.818605i | −0.912399 | − | 0.409302i | \(-0.865772\pi\) | ||
0.912399 | − | 0.409302i | \(-0.134228\pi\) | |||||||
\(912\) | −13.6523 | + | 6.20123i | −0.452074 | + | 0.205343i | ||||
\(913\) | −21.0257 | + | 21.0257i | −0.695848 | + | 0.695848i | ||||
\(914\) | −1.97396 | − | 6.31545i | −0.0652928 | − | 0.208897i | ||||
\(915\) | 8.48961 | + | 3.22296i | 0.280658 | + | 0.106548i | ||||
\(916\) | −23.2546 | − | 33.5659i | −0.768353 | − | 1.10905i | ||||
\(917\) | −5.74717 | + | 5.74717i | −0.189788 | + | 0.189788i | ||||
\(918\) | −11.2175 | + | 21.4182i | −0.370234 | + | 0.706905i | ||||
\(919\) | −1.05781 | −0.0348938 | −0.0174469 | − | 0.999848i | \(-0.505554\pi\) | ||||
−0.0174469 | + | 0.999848i | \(0.505554\pi\) | |||||||
\(920\) | −1.39813 | + | 5.72796i | −0.0460950 | + | 0.188845i | ||||
\(921\) | −21.0870 | −0.694839 | ||||||||
\(922\) | −7.88064 | + | 15.0469i | −0.259535 | + | 0.495543i | ||||
\(923\) | 9.01493 | − | 9.01493i | 0.296730 | − | 0.296730i | ||||
\(924\) | −8.60084 | + | 5.95869i | −0.282947 | + | 0.196026i | ||||
\(925\) | 0.287420 | + | 4.80540i | 0.00945033 | + | 0.158001i | ||||
\(926\) | −1.23940 | − | 3.96532i | −0.0407292 | − | 0.130308i | ||||
\(927\) | −17.1064 | + | 17.1064i | −0.561849 | + | 0.561849i | ||||
\(928\) | 24.3358 | − | 21.7480i | 0.798863 | − | 0.713912i | ||||
\(929\) | 17.9400i | 0.588591i | 0.955714 | + | 0.294296i | \(0.0950850\pi\) | ||||
−0.955714 | + | 0.294296i | \(0.904915\pi\) | |||||||
\(930\) | 6.28171 | + | 7.08307i | 0.205986 | + | 0.232263i | ||||
\(931\) | 3.87964 | 0.127150 | ||||||||
\(932\) | −27.4338 | − | 4.97847i | −0.898624 | − | 0.163075i | ||||
\(933\) | −15.3655 | − | 15.3655i | −0.503043 | − | 0.503043i | ||||
\(934\) | 3.34409 | + | 10.6990i | 0.109422 | + | 0.350082i | ||||
\(935\) | 39.5294 | + | 15.0068i | 1.29275 | + | 0.490773i | ||||
\(936\) | 20.5854 | + | 16.0417i | 0.672855 | + | 0.524341i | ||||
\(937\) | 7.24822 | + | 7.24822i | 0.236789 | + | 0.236789i | 0.815519 | − | 0.578730i | \(-0.196452\pi\) |
−0.578730 | + | 0.815519i | \(0.696452\pi\) | |||||||
\(938\) | 13.8576 | + | 7.25778i | 0.452467 | + | 0.236975i | ||||
\(939\) | − | 14.8423i | − | 0.484360i | ||||||
\(940\) | −14.2836 | + | 3.54167i | −0.465881 | + | 0.115516i | ||||
\(941\) | 31.3685i | 1.02259i | 0.859407 | + | 0.511293i | \(0.170833\pi\) | ||||
−0.859407 | + | 0.511293i | \(0.829167\pi\) | |||||||
\(942\) | 13.2208 | − | 25.2430i | 0.430756 | − | 0.822462i | ||||
\(943\) | −4.87460 | − | 4.87460i | −0.158739 | − | 0.158739i | ||||
\(944\) | −29.7463 | − | 11.1639i | −0.968159 | − | 0.363354i | ||||
\(945\) | 9.98348 | − | 4.48915i | 0.324763 | − | 0.146032i | ||||
\(946\) | 0.874923 | − | 0.273466i | 0.0284462 | − | 0.00889116i | ||||
\(947\) | 10.5999 | + | 10.5999i | 0.344450 | + | 0.344450i | 0.858037 | − | 0.513587i | \(-0.171684\pi\) |
−0.513587 | + | 0.858037i | \(0.671684\pi\) | |||||||
\(948\) | −24.4463 | − | 4.43631i | −0.793978 | − | 0.144085i | ||||
\(949\) | 9.18919 | 0.298294 | ||||||||
\(950\) | −9.73280 | − | 25.6487i | −0.315774 | − | 0.832152i | ||||
\(951\) | 7.23026i | 0.234457i | ||||||||
\(952\) | −1.21605 | − | 9.80277i | −0.0394125 | − | 0.317710i | ||||
\(953\) | 6.64018 | − | 6.64018i | 0.215097 | − | 0.215097i | −0.591332 | − | 0.806428i | \(-0.701398\pi\) |
0.806428 | + | 0.591332i | \(0.201398\pi\) | |||||||
\(954\) | −31.8935 | + | 9.96864i | −1.03259 | + | 0.322747i | ||||
\(955\) | 0.411541 | + | 0.915232i | 0.0133172 | + | 0.0296162i | ||||
\(956\) | −5.07682 | − | 7.32794i | −0.164196 | − | 0.237002i | ||||
\(957\) | 21.3435 | − | 21.3435i | 0.689936 | − | 0.689936i | ||||
\(958\) | 37.8835 | + | 19.8411i | 1.22396 | + | 0.641037i | ||||
\(959\) | −5.95131 | −0.192178 | ||||||||
\(960\) | 2.00029 | − | 17.1686i | 0.0645591 | − | 0.554113i | ||||
\(961\) | 21.3998 | 0.690317 | ||||||||
\(962\) | 5.38598 | + | 2.82085i | 0.173651 | + | 0.0909478i | ||||
\(963\) | 8.82784 | − | 8.82784i | 0.284473 | − | 0.284473i | ||||
\(964\) | 6.66697 | + | 9.62317i | 0.214729 | + | 0.309941i | ||||
\(965\) | 2.24653 | − | 5.91760i | 0.0723184 | − | 0.190494i | ||||
\(966\) | 1.21590 | − | 0.380042i | 0.0391209 | − | 0.0122277i | ||||
\(967\) | −29.9303 | + | 29.9303i | −0.962495 | + | 0.962495i | −0.999322 | − | 0.0368270i | \(-0.988275\pi\) |
0.0368270 | + | 0.999322i | \(0.488275\pi\) | |||||||
\(968\) | −6.37763 | − | 51.4110i | −0.204985 | − | 1.65241i | ||||
\(969\) | − | 13.0918i | − | 0.420568i | ||||||
\(970\) | −39.4027 | − | 44.4293i | −1.26514 | − | 1.42654i | ||||
\(971\) | −27.5224 | −0.883237 | −0.441618 | − | 0.897203i | \(-0.645595\pi\) | ||||
−0.441618 | + | 0.897203i | \(0.645595\pi\) | |||||||
\(972\) | −31.6933 | − | 5.75145i | −1.01656 | − | 0.184478i | ||||
\(973\) | 15.3690 | + | 15.3690i | 0.492706 | + | 0.492706i | ||||
\(974\) | −10.6893 | + | 3.34106i | −0.342508 | + | 0.107055i | ||||
\(975\) | 14.3163 | − | 16.1379i | 0.458490 | − | 0.516825i | ||||
\(976\) | 15.7397 | + | 5.90718i | 0.503817 | + | 0.189084i | ||||
\(977\) | 16.9569 | + | 16.9569i | 0.542499 | + | 0.542499i | 0.924261 | − | 0.381762i | \(-0.124682\pi\) |
−0.381762 | + | 0.924261i | \(0.624682\pi\) | |||||||
\(978\) | −6.15899 | + | 11.7596i | −0.196943 | + | 0.376032i | ||||
\(979\) | − | 10.6441i | − | 0.340188i | ||||||
\(980\) | −2.30828 | + | 3.83038i | −0.0737354 | + | 0.122357i | ||||
\(981\) | 38.3541i | 1.22455i | ||||||||
\(982\) | −14.1206 | − | 7.39551i | −0.450606 | − | 0.236000i | ||||
\(983\) | −29.2243 | − | 29.2243i | −0.932109 | − | 0.932109i | 0.0657283 | − | 0.997838i | \(-0.479063\pi\) |
−0.997838 | + | 0.0657283i | \(0.979063\pi\) | |||||||
\(984\) | 15.9406 | + | 12.4221i | 0.508168 | + | 0.396004i | ||||
\(985\) | −10.1821 | + | 26.8208i | −0.324430 | + | 0.854583i | ||||
\(986\) | 8.50100 | + | 27.1980i | 0.270727 | + | 0.866159i | ||||
\(987\) | 2.24829 | + | 2.24829i | 0.0715638 | + | 0.0715638i | ||||
\(988\) | −34.0907 | − | 6.18652i | −1.08457 | − | 0.196819i | ||||
\(989\) | −0.111604 | −0.00354881 | ||||||||
\(990\) | −2.11761 | + | 35.3167i | −0.0673021 | + | 1.12244i | ||||
\(991\) | − | 17.2817i | − | 0.548972i | −0.961591 | − | 0.274486i | \(-0.911492\pi\) | ||
0.961591 | − | 0.274486i | \(-0.0885077\pi\) | |||||||
\(992\) | 11.6793 | + | 13.0690i | 0.370817 | + | 0.414943i | ||||
\(993\) | −4.64961 | + | 4.64961i | −0.147551 | + | 0.147551i | ||||
\(994\) | −1.20458 | − | 3.85391i | −0.0382069 | − | 0.122239i | ||||
\(995\) | −37.0027 | + | 16.6386i | −1.17307 | + | 0.527478i | ||||
\(996\) | −8.72375 | + | 6.04384i | −0.276422 | + | 0.191506i | ||||
\(997\) | 1.00560 | − | 1.00560i | 0.0318476 | − | 0.0318476i | −0.691004 | − | 0.722851i | \(-0.742831\pi\) |
0.722851 | + | 0.691004i | \(0.242831\pi\) | |||||||
\(998\) | 4.61995 | − | 8.82109i | 0.146242 | − | 0.279227i | ||||
\(999\) | −4.71324 | −0.149120 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 280.2.w.a.267.6 | yes | 72 | |
4.3 | odd | 2 | 1120.2.bi.a.687.11 | 72 | |||
5.3 | odd | 4 | inner | 280.2.w.a.43.14 | yes | 72 | |
8.3 | odd | 2 | inner | 280.2.w.a.267.14 | yes | 72 | |
8.5 | even | 2 | 1120.2.bi.a.687.12 | 72 | |||
20.3 | even | 4 | 1120.2.bi.a.463.12 | 72 | |||
40.3 | even | 4 | inner | 280.2.w.a.43.6 | ✓ | 72 | |
40.13 | odd | 4 | 1120.2.bi.a.463.11 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.w.a.43.6 | ✓ | 72 | 40.3 | even | 4 | inner | |
280.2.w.a.43.14 | yes | 72 | 5.3 | odd | 4 | inner | |
280.2.w.a.267.6 | yes | 72 | 1.1 | even | 1 | trivial | |
280.2.w.a.267.14 | yes | 72 | 8.3 | odd | 2 | inner | |
1120.2.bi.a.463.11 | 72 | 40.13 | odd | 4 | |||
1120.2.bi.a.463.12 | 72 | 20.3 | even | 4 | |||
1120.2.bi.a.687.11 | 72 | 4.3 | odd | 2 | |||
1120.2.bi.a.687.12 | 72 | 8.5 | even | 2 |