Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 165.6 | ||
Character | \(\chi\) | \(=\) | 784.165 |
Dual form | 784.2.x.p.765.6 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.947436 | + | 1.04994i | −0.669939 | + | 0.742417i | ||||
\(3\) | 0.0278645 | + | 0.103992i | 0.0160876 | + | 0.0600397i | 0.973503 | − | 0.228674i | \(-0.0734390\pi\) |
−0.957415 | + | 0.288714i | \(0.906772\pi\) | |||||||
\(4\) | −0.204729 | − | 1.98949i | −0.102365 | − | 0.994747i | ||||
\(5\) | −1.01195 | + | 3.77665i | −0.452557 | + | 1.68897i | 0.242614 | + | 0.970123i | \(0.421995\pi\) |
−0.695171 | + | 0.718844i | \(0.744671\pi\) | |||||||
\(6\) | −0.135585 | − | 0.0692696i | −0.0553522 | − | 0.0282792i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.28281 | + | 1.66997i | 0.807095 | + | 0.590422i | ||||
\(9\) | 2.58804 | − | 1.49420i | 0.862679 | − | 0.498068i | ||||
\(10\) | −3.00648 | − | 4.64061i | −0.950732 | − | 1.46749i | ||||
\(11\) | 4.58934 | − | 1.22971i | 1.38374 | − | 0.370772i | 0.511261 | − | 0.859425i | \(-0.329178\pi\) |
0.872478 | + | 0.488654i | \(0.162512\pi\) | |||||||
\(12\) | 0.201186 | − | 0.0767265i | 0.0580775 | − | 0.0221490i | ||||
\(13\) | 1.87012 | − | 1.87012i | 0.518678 | − | 0.518678i | −0.398493 | − | 0.917171i | \(-0.630467\pi\) |
0.917171 | + | 0.398493i | \(0.130467\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.420938 | −0.108686 | ||||||||
\(16\) | −3.91617 | + | 0.814616i | −0.979043 | + | 0.203654i | ||||
\(17\) | 1.62511 | − | 2.81477i | 0.394147 | − | 0.682682i | −0.598845 | − | 0.800865i | \(-0.704374\pi\) |
0.992992 | + | 0.118183i | \(0.0377069\pi\) | |||||||
\(18\) | −0.883183 | + | 4.13294i | −0.208168 | + | 0.974143i | ||||
\(19\) | 2.09607 | + | 0.561641i | 0.480872 | + | 0.128849i | 0.491109 | − | 0.871098i | \(-0.336592\pi\) |
−0.0102365 | + | 0.999948i | \(0.503258\pi\) | |||||||
\(20\) | 7.72079 | + | 1.24008i | 1.72642 | + | 0.277289i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.05699 | + | 5.98359i | −0.651753 | + | 1.27571i | ||||
\(23\) | 6.23669 | − | 3.60076i | 1.30044 | − | 0.750810i | 0.319961 | − | 0.947431i | \(-0.396330\pi\) |
0.980480 | + | 0.196621i | \(0.0629969\pi\) | |||||||
\(24\) | −0.110053 | + | 0.283926i | −0.0224646 | + | 0.0579562i | ||||
\(25\) | −8.90888 | − | 5.14354i | −1.78178 | − | 1.02871i | ||||
\(26\) | 0.191686 | + | 3.73533i | 0.0375928 | + | 0.732558i | ||||
\(27\) | 0.455881 | + | 0.455881i | 0.0877344 | + | 0.0877344i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.46438 | + | 3.46438i | −0.643319 | + | 0.643319i | −0.951370 | − | 0.308051i | \(-0.900323\pi\) |
0.308051 | + | 0.951370i | \(0.400323\pi\) | |||||||
\(30\) | 0.398812 | − | 0.441957i | 0.0728127 | − | 0.0806900i | ||||
\(31\) | −4.80978 | + | 8.33078i | −0.863862 | + | 1.49625i | 0.00431170 | + | 0.999991i | \(0.498628\pi\) |
−0.868173 | + | 0.496261i | \(0.834706\pi\) | |||||||
\(32\) | 2.85503 | − | 4.88352i | 0.504703 | − | 0.863293i | ||||
\(33\) | 0.255760 | + | 0.442989i | 0.0445220 | + | 0.0771144i | ||||
\(34\) | 1.41564 | + | 4.37307i | 0.242780 | + | 0.749976i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.50256 | − | 4.84298i | −0.583760 | − | 0.807163i | ||||
\(37\) | 0.146341 | − | 0.546153i | 0.0240584 | − | 0.0897871i | −0.952853 | − | 0.303433i | \(-0.901867\pi\) |
0.976911 | + | 0.213646i | \(0.0685338\pi\) | |||||||
\(38\) | −2.57558 | + | 1.66862i | −0.417815 | + | 0.270686i | ||||
\(39\) | 0.246587 | + | 0.142367i | 0.0394856 | + | 0.0227970i | ||||
\(40\) | −8.61695 | + | 6.93144i | −1.36246 | + | 1.09596i | ||||
\(41\) | − | 0.425757i | − | 0.0664921i | −0.999447 | − | 0.0332460i | \(-0.989416\pi\) | ||
0.999447 | − | 0.0332460i | \(-0.0105845\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.63112 | + | 4.63112i | 0.706240 | + | 0.706240i | 0.965742 | − | 0.259503i | \(-0.0835586\pi\) |
−0.259503 | + | 0.965742i | \(0.583559\pi\) | |||||||
\(44\) | −3.38608 | − | 8.87871i | −0.510470 | − | 1.33852i | ||||
\(45\) | 3.02412 | + | 11.2862i | 0.450809 | + | 1.68244i | ||||
\(46\) | −2.12831 | + | 9.95961i | −0.313802 | + | 1.46846i | ||||
\(47\) | 0.163964 | + | 0.283994i | 0.0239166 | + | 0.0414247i | 0.877736 | − | 0.479145i | \(-0.159053\pi\) |
−0.853819 | + | 0.520569i | \(0.825720\pi\) | |||||||
\(48\) | −0.193836 | − | 0.384551i | −0.0279778 | − | 0.0555051i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.8410 | − | 4.48057i | 1.95741 | − | 0.633648i | ||||
\(51\) | 0.337996 | + | 0.0905657i | 0.0473289 | + | 0.0126817i | ||||
\(52\) | −4.10346 | − | 3.33773i | −0.569048 | − | 0.462859i | ||||
\(53\) | −4.64008 | + | 1.24331i | −0.637364 | + | 0.170781i | −0.563009 | − | 0.826451i | \(-0.690356\pi\) |
−0.0743548 | + | 0.997232i | \(0.523690\pi\) | |||||||
\(54\) | −0.910564 | + | 0.0467276i | −0.123912 | + | 0.00635882i | ||||
\(55\) | 18.5767i | 2.50489i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.233624i | 0.0309443i | ||||||||
\(58\) | −0.355097 | − | 6.91965i | −0.0466265 | − | 0.908595i | ||||
\(59\) | 11.9870 | − | 3.21190i | 1.56057 | − | 0.418154i | 0.627728 | − | 0.778433i | \(-0.283985\pi\) |
0.932845 | + | 0.360279i | \(0.117318\pi\) | |||||||
\(60\) | 0.0861783 | + | 0.837453i | 0.0111256 | + | 0.108115i | ||||
\(61\) | 8.05996 | + | 2.15966i | 1.03197 | + | 0.276516i | 0.734783 | − | 0.678303i | \(-0.237284\pi\) |
0.297189 | + | 0.954819i | \(0.403951\pi\) | |||||||
\(62\) | −4.18982 | − | 12.9428i | −0.532108 | − | 1.64374i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.42243 | + | 7.62442i | 0.302804 | + | 0.953053i | ||||
\(65\) | 5.17032 | + | 8.95525i | 0.641299 | + | 1.11076i | ||||
\(66\) | −0.707426 | − | 0.151172i | −0.0870781 | − | 0.0186080i | ||||
\(67\) | 0.527697 | + | 1.96939i | 0.0644685 | + | 0.240600i | 0.990640 | − | 0.136504i | \(-0.0435867\pi\) |
−0.926171 | + | 0.377104i | \(0.876920\pi\) | |||||||
\(68\) | −5.93268 | − | 2.65688i | −0.719443 | − | 0.322194i | ||||
\(69\) | 0.548232 | + | 0.548232i | 0.0659993 | + | 0.0659993i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.205828i | − | 0.0244273i | −0.999925 | − | 0.0122137i | \(-0.996112\pi\) | ||
0.999925 | − | 0.0122137i | \(-0.00388783\pi\) | |||||||
\(72\) | 8.40327 | + | 0.910952i | 0.990334 | + | 0.107357i | ||||
\(73\) | −5.86419 | − | 3.38569i | −0.686351 | − | 0.396265i | 0.115892 | − | 0.993262i | \(-0.463027\pi\) |
−0.802244 | + | 0.596997i | \(0.796361\pi\) | |||||||
\(74\) | 0.434777 | + | 0.671095i | 0.0505418 | + | 0.0780132i | ||||
\(75\) | 0.286645 | − | 1.06977i | 0.0330989 | − | 0.123527i | ||||
\(76\) | 0.688254 | − | 4.28511i | 0.0789481 | − | 0.491536i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.383102 | + | 0.124017i | −0.0433778 | + | 0.0140422i | ||||
\(79\) | −2.01751 | − | 3.49443i | −0.226987 | − | 0.393154i | 0.729926 | − | 0.683526i | \(-0.239554\pi\) |
−0.956914 | + | 0.290372i | \(0.906221\pi\) | |||||||
\(80\) | 0.886451 | − | 15.6143i | 0.0991082 | − | 1.74574i | ||||
\(81\) | 4.44791 | − | 7.70400i | 0.494212 | − | 0.856000i | ||||
\(82\) | 0.447017 | + | 0.403378i | 0.0493648 | + | 0.0445456i | ||||
\(83\) | −6.75185 | + | 6.75185i | −0.741112 | + | 0.741112i | −0.972792 | − | 0.231680i | \(-0.925578\pi\) |
0.231680 | + | 0.972792i | \(0.425578\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.98586 | + | 8.98586i | 0.974653 | + | 0.974653i | ||||
\(86\) | −9.25008 | + | 0.474688i | −0.997462 | + | 0.0511869i | ||||
\(87\) | −0.456800 | − | 0.263734i | −0.0489741 | − | 0.0282752i | ||||
\(88\) | 12.5302 | + | 4.85685i | 1.33572 | + | 0.517742i | ||||
\(89\) | 7.25247 | − | 4.18722i | 0.768761 | − | 0.443844i | −0.0636716 | − | 0.997971i | \(-0.520281\pi\) |
0.832432 | + | 0.554127i | \(0.186948\pi\) | |||||||
\(90\) | −14.7149 | − | 7.51779i | −1.55109 | − | 0.792444i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.44052 | − | 11.6707i | −0.879985 | − | 1.21675i | ||||
\(93\) | −1.00035 | − | 0.268044i | −0.103732 | − | 0.0277949i | ||||
\(94\) | −0.453520 | − | 0.0969145i | −0.0467771 | − | 0.00999596i | ||||
\(95\) | −4.24224 | + | 7.34777i | −0.435245 | + | 0.753866i | ||||
\(96\) | 0.587401 | + | 0.160822i | 0.0599513 | + | 0.0164139i | ||||
\(97\) | −12.6981 | −1.28929 | −0.644647 | − | 0.764480i | \(-0.722996\pi\) | ||||
−0.644647 | + | 0.764480i | \(0.722996\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.0400 | − | 10.0400i | 1.00905 | − | 1.00905i | ||||
\(100\) | −8.40914 | + | 18.7772i | −0.840914 | + | 1.87772i | ||||
\(101\) | −6.09459 | + | 1.63304i | −0.606435 | + | 0.162494i | −0.548953 | − | 0.835853i | \(-0.684974\pi\) |
−0.0574812 | + | 0.998347i | \(0.518307\pi\) | |||||||
\(102\) | −0.415318 | + | 0.269069i | −0.0411226 | + | 0.0266418i | ||||
\(103\) | −12.3083 | + | 7.10617i | −1.21277 | + | 0.700192i | −0.963361 | − | 0.268207i | \(-0.913569\pi\) |
−0.249407 | + | 0.968399i | \(0.580236\pi\) | |||||||
\(104\) | 7.39217 | − | 1.14609i | 0.724862 | − | 0.112383i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.09079 | − | 6.04974i | 0.300204 | − | 0.587602i | ||||
\(107\) | −3.19377 | + | 11.9193i | −0.308754 | + | 1.15228i | 0.620912 | + | 0.783880i | \(0.286762\pi\) |
−0.929666 | + | 0.368404i | \(0.879904\pi\) | |||||||
\(108\) | 0.813641 | − | 1.00031i | 0.0782926 | − | 0.0962544i | ||||
\(109\) | −1.74408 | − | 6.50900i | −0.167053 | − | 0.623450i | −0.997769 | − | 0.0667541i | \(-0.978736\pi\) |
0.830717 | − | 0.556695i | \(-0.187931\pi\) | |||||||
\(110\) | −19.5044 | − | 17.6003i | −1.85967 | − | 1.67812i | ||||
\(111\) | 0.0608732 | 0.00577783 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.68827 | −0.911396 | −0.455698 | − | 0.890134i | \(-0.650610\pi\) | ||||
−0.455698 | + | 0.890134i | \(0.650610\pi\) | |||||||
\(114\) | −0.245291 | − | 0.221344i | −0.0229736 | − | 0.0207308i | ||||
\(115\) | 7.28756 | + | 27.1976i | 0.679569 | + | 2.53619i | ||||
\(116\) | 7.60162 | + | 6.18310i | 0.705792 | + | 0.574086i | ||||
\(117\) | 2.04560 | − | 7.63429i | 0.189116 | − | 0.705790i | ||||
\(118\) | −7.98461 | + | 15.6286i | −0.735043 | + | 1.43873i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.960920 | − | 0.702951i | −0.0877196 | − | 0.0641704i | ||||
\(121\) | 10.0236 | − | 5.78713i | 0.911237 | − | 0.526103i | ||||
\(122\) | −9.90380 | + | 6.41630i | −0.896648 | + | 0.580904i | ||||
\(123\) | 0.0442752 | − | 0.0118635i | 0.00399216 | − | 0.00106970i | ||||
\(124\) | 17.5587 | + | 7.86347i | 1.57682 | + | 0.706160i | ||||
\(125\) | 14.6172 | − | 14.6172i | 1.30740 | − | 1.30740i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.53241 | −0.845865 | −0.422932 | − | 0.906161i | \(-0.638999\pi\) | ||||
−0.422932 | + | 0.906161i | \(0.638999\pi\) | |||||||
\(128\) | −10.3003 | − | 4.68026i | −0.910422 | − | 0.413681i | ||||
\(129\) | −0.352555 | + | 0.610643i | −0.0310407 | + | 0.0537641i | ||||
\(130\) | −14.3010 | − | 3.05603i | −1.25428 | − | 0.268032i | ||||
\(131\) | 6.07909 | + | 1.62889i | 0.531133 | + | 0.142317i | 0.514411 | − | 0.857544i | \(-0.328010\pi\) |
0.0167215 | + | 0.999860i | \(0.494677\pi\) | |||||||
\(132\) | 0.828962 | − | 0.599525i | 0.0721519 | − | 0.0521820i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.56769 | − | 1.31183i | −0.221815 | − | 0.113324i | ||||
\(135\) | −2.18303 | + | 1.26037i | −0.187885 | + | 0.108476i | ||||
\(136\) | 8.41038 | − | 3.71171i | 0.721184 | − | 0.318276i | ||||
\(137\) | 2.73070 | + | 1.57657i | 0.233300 | + | 0.134696i | 0.612093 | − | 0.790785i | \(-0.290328\pi\) |
−0.378794 | + | 0.925481i | \(0.623661\pi\) | |||||||
\(138\) | −1.09502 | + | 0.0561934i | −0.0932145 | + | 0.00478350i | ||||
\(139\) | −7.44059 | − | 7.44059i | −0.631103 | − | 0.631103i | 0.317242 | − | 0.948345i | \(-0.397243\pi\) |
−0.948345 | + | 0.317242i | \(0.897243\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0249642 | + | 0.0249642i | −0.00210237 | + | 0.00210237i | ||||
\(142\) | 0.216107 | + | 0.195009i | 0.0181353 | + | 0.0163648i | ||||
\(143\) | 6.28292 | − | 10.8823i | 0.525404 | − | 0.910027i | ||||
\(144\) | −8.91800 | + | 7.95982i | −0.743167 | + | 0.663318i | ||||
\(145\) | −9.57795 | − | 16.5895i | −0.795406 | − | 1.37768i | ||||
\(146\) | 9.11070 | − | 2.94929i | 0.754007 | − | 0.244085i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.11653 | − | 0.179332i | −0.0917782 | − | 0.0147410i | ||||
\(149\) | 4.82515 | − | 18.0077i | 0.395292 | − | 1.47525i | −0.425992 | − | 0.904727i | \(-0.640075\pi\) |
0.821283 | − | 0.570521i | \(-0.193259\pi\) | |||||||
\(150\) | 0.851615 | + | 1.31450i | 0.0695341 | + | 0.107328i | ||||
\(151\) | 1.40354 | + | 0.810335i | 0.114219 | + | 0.0659441i | 0.556021 | − | 0.831168i | \(-0.312327\pi\) |
−0.441802 | + | 0.897112i | \(0.645661\pi\) | |||||||
\(152\) | 3.84701 | + | 4.78249i | 0.312034 | + | 0.387911i | ||||
\(153\) | − | 9.71298i | − | 0.785248i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −26.5951 | − | 26.5951i | −2.13617 | − | 2.13617i | ||||
\(156\) | 0.232755 | − | 0.519731i | 0.0186353 | − | 0.0416118i | ||||
\(157\) | −3.42633 | − | 12.7873i | −0.273451 | − | 1.02053i | −0.956872 | − | 0.290509i | \(-0.906175\pi\) |
0.683421 | − | 0.730025i | \(-0.260491\pi\) | |||||||
\(158\) | 5.58038 | + | 1.19249i | 0.443951 | + | 0.0948696i | ||||
\(159\) | −0.258587 | − | 0.447886i | −0.0205073 | − | 0.0355197i | ||||
\(160\) | 15.5542 | + | 15.7243i | 1.22967 | + | 1.24312i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.87460 | + | 11.9691i | 0.304417 | + | 0.940379i | ||||
\(163\) | 4.19272 | + | 1.12344i | 0.328400 | + | 0.0879944i | 0.419252 | − | 0.907870i | \(-0.362292\pi\) |
−0.0908523 | + | 0.995864i | \(0.528959\pi\) | |||||||
\(164\) | −0.847041 | + | 0.0871650i | −0.0661428 | + | 0.00680644i | ||||
\(165\) | −1.93183 | + | 0.517632i | −0.150393 | + | 0.0402976i | ||||
\(166\) | −0.692061 | − | 13.4860i | −0.0537144 | − | 1.04671i | ||||
\(167\) | − | 3.61974i | − | 0.280104i | −0.990144 | − | 0.140052i | \(-0.955273\pi\) | ||
0.990144 | − | 0.140052i | \(-0.0447270\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00529i | 0.461945i | ||||||||
\(170\) | −17.9481 | + | 0.921045i | −1.37656 | + | 0.0706410i | ||||
\(171\) | 6.26393 | − | 1.67841i | 0.479014 | − | 0.128352i | ||||
\(172\) | 8.26547 | − | 10.1617i | 0.630236 | − | 0.774824i | ||||
\(173\) | 22.5452 | + | 6.04096i | 1.71408 | + | 0.459286i | 0.976418 | − | 0.215888i | \(-0.0692646\pi\) |
0.737659 | + | 0.675173i | \(0.235931\pi\) | |||||||
\(174\) | 0.709692 | − | 0.229740i | 0.0538016 | − | 0.0174165i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.9709 | + | 8.55431i | −1.27923 | + | 0.644805i | ||||
\(177\) | 0.668023 | + | 1.15705i | 0.0502117 | + | 0.0869692i | ||||
\(178\) | −2.47495 | + | 11.5818i | −0.185505 | + | 0.868089i | ||||
\(179\) | 3.89515 | + | 14.5369i | 0.291137 | + | 1.08654i | 0.944237 | + | 0.329267i | \(0.106802\pi\) |
−0.653099 | + | 0.757272i | \(0.726532\pi\) | |||||||
\(180\) | 21.8346 | − | 8.32707i | 1.62746 | − | 0.620663i | ||||
\(181\) | −3.54568 | − | 3.54568i | −0.263548 | − | 0.263548i | 0.562946 | − | 0.826494i | \(-0.309668\pi\) |
−0.826494 | + | 0.562946i | \(0.809668\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.898347i | 0.0664077i | ||||||||
\(184\) | 20.2503 | + | 2.19523i | 1.49287 | + | 0.161834i | ||||
\(185\) | 1.91454 | + | 1.10536i | 0.140760 | + | 0.0812676i | ||||
\(186\) | 1.22920 | − | 0.796353i | 0.0901294 | − | 0.0583915i | ||||
\(187\) | 3.99683 | − | 14.9164i | 0.292277 | − | 1.09079i | ||||
\(188\) | 0.531436 | − | 0.384347i | 0.0387589 | − | 0.0280314i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.69544 | − | 11.4156i | −0.268095 | − | 0.828177i | ||||
\(191\) | 5.83672 | + | 10.1095i | 0.422331 | + | 0.731498i | 0.996167 | − | 0.0874720i | \(-0.0278788\pi\) |
−0.573836 | + | 0.818970i | \(0.694545\pi\) | |||||||
\(192\) | −0.725378 | + | 0.464364i | −0.0523496 | + | 0.0335126i | ||||
\(193\) | 4.34510 | − | 7.52593i | 0.312767 | − | 0.541728i | −0.666193 | − | 0.745779i | \(-0.732077\pi\) |
0.978960 | + | 0.204051i | \(0.0654108\pi\) | |||||||
\(194\) | 12.0306 | − | 13.3322i | 0.863748 | − | 0.957194i | ||||
\(195\) | −0.787205 | + | 0.787205i | −0.0563729 | + | 0.0563729i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.77420 | + | 2.77420i | 0.197654 | + | 0.197654i | 0.798993 | − | 0.601340i | \(-0.205366\pi\) |
−0.601340 | + | 0.798993i | \(0.705366\pi\) | |||||||
\(198\) | 1.02909 | + | 20.0535i | 0.0731342 | + | 1.42514i | ||||
\(199\) | 11.0757 | + | 6.39455i | 0.785135 | + | 0.453298i | 0.838247 | − | 0.545291i | \(-0.183581\pi\) |
−0.0531124 | + | 0.998589i | \(0.516914\pi\) | |||||||
\(200\) | −11.7477 | − | 26.6193i | −0.830690 | − | 1.88227i | ||||
\(201\) | −0.190097 | + | 0.109752i | −0.0134084 | + | 0.00774133i | ||||
\(202\) | 4.05965 | − | 7.94613i | 0.285636 | − | 0.559088i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.110982 | − | 0.690982i | 0.00777031 | − | 0.0483784i | ||||
\(205\) | 1.60793 | + | 0.430844i | 0.112303 | + | 0.0300915i | ||||
\(206\) | 4.20026 | − | 19.6555i | 0.292646 | − | 1.36946i | ||||
\(207\) | 10.7605 | − | 18.6378i | 0.747909 | − | 1.29542i | ||||
\(208\) | −5.80029 | + | 8.84715i | −0.402178 | + | 0.613439i | ||||
\(209\) | 10.3103 | 0.713175 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.71453 | − | 5.71453i | 0.393405 | − | 0.393405i | −0.482494 | − | 0.875899i | \(-0.660269\pi\) |
0.875899 | + | 0.482494i | \(0.160269\pi\) | |||||||
\(212\) | 3.42351 | + | 8.97687i | 0.235128 | + | 0.616534i | ||||
\(213\) | 0.0214045 | − | 0.00573531i | 0.00146661 | − | 0.000392977i | ||||
\(214\) | −9.48862 | − | 14.6461i | −0.648629 | − | 1.00118i | ||||
\(215\) | −22.1766 | + | 12.8037i | −1.51243 | + | 0.873202i | ||||
\(216\) | 0.279384 | + | 1.80200i | 0.0190096 | + | 0.122610i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.48644 | + | 4.33569i | 0.574774 | + | 0.293650i | ||||
\(219\) | 0.188681 | − | 0.704168i | 0.0127499 | − | 0.0475833i | ||||
\(220\) | 36.9583 | − | 3.80320i | 2.49173 | − | 0.256412i | ||||
\(221\) | −2.22481 | − | 8.30311i | −0.149657 | − | 0.558528i | ||||
\(222\) | −0.0576735 | + | 0.0639130i | −0.00387079 | + | 0.00428956i | ||||
\(223\) | −3.63378 | −0.243336 | −0.121668 | − | 0.992571i | \(-0.538824\pi\) | ||||
−0.121668 | + | 0.992571i | \(0.538824\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −30.7420 | −2.04947 | ||||||||
\(226\) | 9.17902 | − | 10.1721i | 0.610579 | − | 0.676636i | ||||
\(227\) | −6.16616 | − | 23.0124i | −0.409262 | − | 1.52739i | −0.796057 | − | 0.605222i | \(-0.793084\pi\) |
0.386794 | − | 0.922166i | \(-0.373582\pi\) | |||||||
\(228\) | 0.464794 | − | 0.0478298i | 0.0307817 | − | 0.00316760i | ||||
\(229\) | −2.53448 | + | 9.45881i | −0.167483 | + | 0.625056i | 0.830227 | + | 0.557425i | \(0.188211\pi\) |
−0.997710 | + | 0.0676308i | \(0.978456\pi\) | |||||||
\(230\) | −35.4602 | − | 18.1165i | −2.33818 | − | 1.19457i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.6939 | + | 2.12312i | −0.899049 | + | 0.139390i | ||||
\(233\) | −22.7274 | + | 13.1217i | −1.48892 | + | 0.859629i | −0.999920 | − | 0.0126550i | \(-0.995972\pi\) |
−0.489000 | + | 0.872284i | \(0.662638\pi\) | |||||||
\(234\) | 6.07744 | + | 9.38075i | 0.397294 | + | 0.613239i | ||||
\(235\) | −1.23847 | + | 0.331846i | −0.0807887 | + | 0.0216473i | ||||
\(236\) | −8.84415 | − | 23.1905i | −0.575705 | − | 1.50957i | ||||
\(237\) | 0.307175 | − | 0.307175i | 0.0199531 | − | 0.0199531i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.5711 | 1.84811 | 0.924055 | − | 0.382259i | \(-0.124854\pi\) | ||||
0.924055 | + | 0.382259i | \(0.124854\pi\) | |||||||
\(240\) | 1.64846 | − | 0.342902i | 0.106408 | − | 0.0221343i | ||||
\(241\) | 8.25667 | − | 14.3010i | 0.531859 | − | 0.921207i | −0.467449 | − | 0.884020i | \(-0.654827\pi\) |
0.999308 | − | 0.0371872i | \(-0.0118398\pi\) | |||||||
\(242\) | −3.42061 | + | 16.0071i | −0.219885 | + | 1.02897i | ||||
\(243\) | 2.79333 | + | 0.748470i | 0.179192 | + | 0.0480144i | ||||
\(244\) | 2.64652 | − | 16.4774i | 0.169426 | − | 1.05486i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0294920 | + | 0.0577261i | −0.00188034 | + | 0.00368048i | ||||
\(247\) | 4.97025 | − | 2.86958i | 0.316249 | − | 0.182587i | ||||
\(248\) | −24.8919 | + | 10.9854i | −1.58064 | + | 0.697574i | ||||
\(249\) | −0.890275 | − | 0.514000i | −0.0564189 | − | 0.0325734i | ||||
\(250\) | 1.49825 | + | 29.1960i | 0.0947579 | + | 1.84652i | ||||
\(251\) | 11.5207 | + | 11.5207i | 0.727183 | + | 0.727183i | 0.970058 | − | 0.242875i | \(-0.0780904\pi\) |
−0.242875 | + | 0.970058i | \(0.578090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.1944 | − | 24.1944i | 1.52109 | − | 1.52109i | ||||
\(254\) | 9.03135 | − | 10.0084i | 0.566678 | − | 0.627984i | ||||
\(255\) | −0.684069 | + | 1.18484i | −0.0428381 | + | 0.0741977i | ||||
\(256\) | 14.6728 | − | 6.38035i | 0.917050 | − | 0.398772i | ||||
\(257\) | −10.3014 | − | 17.8425i | −0.642583 | − | 1.11299i | −0.984854 | − | 0.173385i | \(-0.944530\pi\) |
0.342272 | − | 0.939601i | \(-0.388804\pi\) | |||||||
\(258\) | −0.307113 | − | 0.948705i | −0.0191200 | − | 0.0590638i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.7579 | − | 12.1197i | 1.03928 | − | 0.751633i | ||||
\(261\) | −3.78945 | + | 14.1424i | −0.234561 | + | 0.875394i | ||||
\(262\) | −7.46978 | + | 4.83939i | −0.461485 | + | 0.298978i | ||||
\(263\) | 17.6675 | + | 10.2003i | 1.08942 | + | 0.628979i | 0.933423 | − | 0.358778i | \(-0.116806\pi\) |
0.156001 | + | 0.987757i | \(0.450140\pi\) | |||||||
\(264\) | −0.155926 | + | 1.43837i | −0.00959656 | + | 0.0885255i | ||||
\(265\) | − | 18.7821i | − | 1.15377i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.637523 | + | 0.637523i | 0.0390158 | + | 0.0390158i | ||||
\(268\) | 3.81006 | − | 1.45304i | 0.232736 | − | 0.0887587i | ||||
\(269\) | −3.47959 | − | 12.9860i | −0.212154 | − | 0.791770i | −0.987149 | − | 0.159803i | \(-0.948914\pi\) |
0.774995 | − | 0.631968i | \(-0.217752\pi\) | |||||||
\(270\) | 0.744971 | − | 3.48616i | 0.0453375 | − | 0.212161i | ||||
\(271\) | 4.74944 | + | 8.22627i | 0.288508 | + | 0.499710i | 0.973454 | − | 0.228884i | \(-0.0735075\pi\) |
−0.684946 | + | 0.728594i | \(0.740174\pi\) | |||||||
\(272\) | −4.07125 | + | 12.3470i | −0.246856 | + | 0.748645i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.24247 | + | 1.37336i | −0.256297 | + | 0.0829678i | ||||
\(275\) | −47.2110 | − | 12.6501i | −2.84693 | − | 0.762832i | ||||
\(276\) | 0.978464 | − | 1.20294i | 0.0588966 | − | 0.0724086i | ||||
\(277\) | −10.5732 | + | 2.83307i | −0.635279 | + | 0.170223i | −0.562064 | − | 0.827094i | \(-0.689993\pi\) |
−0.0732151 | + | 0.997316i | \(0.523326\pi\) | |||||||
\(278\) | 14.8616 | − | 0.762656i | 0.891341 | − | 0.0457411i | ||||
\(279\) | 28.7472i | 1.72105i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.2210i | 1.20628i | 0.797634 | + | 0.603142i | \(0.206085\pi\) | ||||
−0.797634 | + | 0.603142i | \(0.793915\pi\) | |||||||
\(282\) | −0.00255882 | − | 0.0498629i | −0.000152376 | − | 0.00296929i | ||||
\(283\) | −29.4881 | + | 7.90130i | −1.75288 | + | 0.469684i | −0.985238 | − | 0.171191i | \(-0.945238\pi\) |
−0.767645 | + | 0.640875i | \(0.778572\pi\) | |||||||
\(284\) | −0.409494 | + | 0.0421391i | −0.0242990 | + | 0.00250050i | ||||
\(285\) | −0.882316 | − | 0.236416i | −0.0522639 | − | 0.0140041i | ||||
\(286\) | 5.47309 | + | 16.9070i | 0.323630 | + | 0.999731i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.0919384 | − | 16.9047i | 0.00541752 | − | 0.996122i | ||||
\(289\) | 3.21805 | + | 5.57382i | 0.189297 | + | 0.327872i | ||||
\(290\) | 26.4924 | + | 5.66126i | 1.55569 | + | 0.332441i | ||||
\(291\) | −0.353826 | − | 1.32050i | −0.0207416 | − | 0.0774089i | ||||
\(292\) | −5.53524 | + | 12.3599i | −0.323925 | + | 0.723310i | ||||
\(293\) | −1.36393 | − | 1.36393i | −0.0796814 | − | 0.0796814i | 0.666143 | − | 0.745824i | \(-0.267944\pi\) |
−0.745824 | + | 0.666143i | \(0.767944\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 48.5209i | 2.82499i | ||||||||
\(296\) | 1.24613 | − | 1.00238i | 0.0724297 | − | 0.0582621i | ||||
\(297\) | 2.65280 | + | 1.53159i | 0.153931 | + | 0.0888721i | ||||
\(298\) | 14.3354 | + | 22.1272i | 0.830428 | + | 1.28180i | ||||
\(299\) | 4.92952 | − | 18.3972i | 0.285082 | − | 1.06394i | ||||
\(300\) | −2.18699 | − | 0.351264i | −0.126266 | − | 0.0202802i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.18057 | + | 0.705887i | −0.125477 | + | 0.0406193i | ||||
\(303\) | −0.339646 | − | 0.588284i | −0.0195121 | − | 0.0337960i | ||||
\(304\) | −8.66611 | − | 0.491989i | −0.497035 | − | 0.0282175i | ||||
\(305\) | −16.3125 | + | 28.2541i | −0.934053 | + | 1.61783i | ||||
\(306\) | 10.1980 | + | 9.20243i | 0.582981 | + | 0.526068i | ||||
\(307\) | 17.6399 | − | 17.6399i | 1.00676 | − | 1.00676i | 0.00678402 | − | 0.999977i | \(-0.497841\pi\) |
0.999977 | − | 0.00678402i | \(-0.00215944\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.08195 | − | 1.08195i | −0.0615498 | − | 0.0615498i | ||||
\(310\) | 53.1204 | − | 2.72599i | 3.01704 | − | 0.154826i | ||||
\(311\) | −23.9867 | − | 13.8487i | −1.36016 | − | 0.785289i | −0.370516 | − | 0.928826i | \(-0.620819\pi\) |
−0.989645 | + | 0.143537i | \(0.954152\pi\) | |||||||
\(312\) | 0.325163 | + | 0.736790i | 0.0184087 | + | 0.0417125i | ||||
\(313\) | −4.27477 | + | 2.46804i | −0.241624 | + | 0.139502i | −0.615923 | − | 0.787806i | \(-0.711217\pi\) |
0.374299 | + | 0.927308i | \(0.377883\pi\) | |||||||
\(314\) | 16.6720 | + | 8.51768i | 0.940857 | + | 0.480680i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.53910 | + | 4.72923i | −0.367853 | + | 0.266040i | ||||
\(317\) | −25.3204 | − | 6.78457i | −1.42213 | − | 0.381060i | −0.535894 | − | 0.844285i | \(-0.680025\pi\) |
−0.886240 | + | 0.463226i | \(0.846692\pi\) | |||||||
\(318\) | 0.715246 | + | 0.152844i | 0.0401090 | + | 0.00857104i | ||||
\(319\) | −11.6390 | + | 20.1594i | −0.651661 | + | 1.12871i | ||||
\(320\) | −31.2461 | + | 1.43313i | −1.74671 | + | 0.0801142i | ||||
\(321\) | −1.32850 | −0.0741499 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.98724 | − | 4.98724i | 0.277497 | − | 0.277497i | ||||
\(324\) | −16.2377 | − | 7.27185i | −0.902094 | − | 0.403992i | ||||
\(325\) | −26.2797 | + | 7.04164i | −1.45774 | + | 0.390600i | ||||
\(326\) | −5.15188 | + | 3.33771i | −0.285336 | + | 0.184858i | ||||
\(327\) | 0.628285 | − | 0.362741i | 0.0347442 | − | 0.0200596i | ||||
\(328\) | 0.711000 | − | 0.971922i | 0.0392584 | − | 0.0536654i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.28680 | − | 2.51872i | 0.0708362 | − | 0.138651i | ||||
\(331\) | 0.808626 | − | 3.01783i | 0.0444461 | − | 0.165875i | −0.940136 | − | 0.340801i | \(-0.889302\pi\) |
0.984582 | + | 0.174926i | \(0.0559685\pi\) | |||||||
\(332\) | 14.8151 | + | 12.0505i | 0.813083 | + | 0.661355i | ||||
\(333\) | −0.437328 | − | 1.63213i | −0.0239654 | − | 0.0894402i | ||||
\(334\) | 3.80050 | + | 3.42947i | 0.207954 | + | 0.187652i | ||||
\(335\) | −7.97170 | −0.435541 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.1602 | −0.716881 | −0.358441 | − | 0.933553i | \(-0.616691\pi\) | ||||
−0.358441 | + | 0.933553i | \(0.616691\pi\) | |||||||
\(338\) | −6.30517 | − | 5.68963i | −0.342956 | − | 0.309475i | ||||
\(339\) | −0.269959 | − | 1.00750i | −0.0146622 | − | 0.0547199i | ||||
\(340\) | 16.0376 | − | 19.7170i | 0.869763 | − | 1.06930i | ||||
\(341\) | −11.8293 | + | 44.1474i | −0.640591 | + | 2.39072i | ||||
\(342\) | −4.17244 | + | 8.16691i | −0.225620 | + | 0.441616i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.83815 | + | 18.3058i | 0.153023 | + | 0.986982i | ||||
\(345\) | −2.62526 | + | 1.51569i | −0.141339 | + | 0.0816022i | ||||
\(346\) | −27.7027 | + | 17.9475i | −1.48931 | + | 0.964866i | ||||
\(347\) | 11.5508 | − | 3.09502i | 0.620079 | − | 0.166150i | 0.0649151 | − | 0.997891i | \(-0.479322\pi\) |
0.555164 | + | 0.831741i | \(0.312656\pi\) | |||||||
\(348\) | −0.431176 | + | 0.962795i | −0.0231135 | + | 0.0516112i | ||||
\(349\) | −9.54687 | + | 9.54687i | −0.511032 | + | 0.511032i | −0.914843 | − | 0.403810i | \(-0.867686\pi\) |
0.403810 | + | 0.914843i | \(0.367686\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.70511 | 0.0910119 | ||||||||
\(352\) | 7.09738 | − | 25.9230i | 0.378292 | − | 1.38170i | ||||
\(353\) | −0.707195 | + | 1.22490i | −0.0376402 | + | 0.0651947i | −0.884232 | − | 0.467048i | \(-0.845317\pi\) |
0.846592 | + | 0.532243i | \(0.178651\pi\) | |||||||
\(354\) | −1.84774 | − | 0.394850i | −0.0982061 | − | 0.0209860i | ||||
\(355\) | 0.777341 | + | 0.208288i | 0.0412570 | + | 0.0110548i | ||||
\(356\) | −9.81524 | − | 13.5715i | −0.520207 | − | 0.719288i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.9532 | − | 9.68313i | −1.00171 | − | 0.511769i | ||||
\(359\) | 8.19593 | − | 4.73192i | 0.432565 | − | 0.249741i | −0.267874 | − | 0.963454i | \(-0.586321\pi\) |
0.700439 | + | 0.713713i | \(0.252988\pi\) | |||||||
\(360\) | −11.9440 | + | 30.8143i | −0.629505 | + | 1.62406i | ||||
\(361\) | −12.3764 | − | 7.14552i | −0.651389 | − | 0.376080i | ||||
\(362\) | 7.08203 | − | 0.363430i | 0.372223 | − | 0.0191014i | ||||
\(363\) | 0.881117 | + | 0.881117i | 0.0462466 | + | 0.0462466i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.7208 | − | 18.7208i | 0.979892 | − | 0.979892i | ||||
\(366\) | −0.943207 | − | 0.851127i | −0.0493022 | − | 0.0444891i | ||||
\(367\) | 4.93145 | − | 8.54151i | 0.257419 | − | 0.445863i | −0.708130 | − | 0.706082i | \(-0.750461\pi\) |
0.965550 | + | 0.260218i | \(0.0837945\pi\) | |||||||
\(368\) | −21.4907 | + | 19.1817i | −1.12028 | + | 0.999915i | ||||
\(369\) | −0.636168 | − | 1.10188i | −0.0331176 | − | 0.0573613i | ||||
\(370\) | −2.97446 | + | 0.962884i | −0.154635 | + | 0.0500580i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.328470 | + | 2.04508i | −0.0170304 | + | 0.106032i | ||||
\(373\) | −3.14248 | + | 11.7279i | −0.162711 | + | 0.607248i | 0.835610 | + | 0.549324i | \(0.185115\pi\) |
−0.998321 | + | 0.0579237i | \(0.981552\pi\) | |||||||
\(374\) | 11.8745 | + | 18.3287i | 0.614015 | + | 0.947755i | ||||
\(375\) | 1.92737 | + | 1.11277i | 0.0995289 | + | 0.0574631i | ||||
\(376\) | −0.0999617 | + | 0.922117i | −0.00515513 | + | 0.0475546i | ||||
\(377\) | 12.9576i | 0.667351i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.8501 | − | 20.8501i | −1.07100 | − | 1.07100i | −0.997279 | − | 0.0737177i | \(-0.976514\pi\) |
−0.0737177 | − | 0.997279i | \(-0.523486\pi\) | |||||||
\(380\) | 15.4869 | + | 6.93560i | 0.794459 | + | 0.355789i | ||||
\(381\) | −0.265616 | − | 0.991293i | −0.0136079 | − | 0.0507855i | ||||
\(382\) | −16.1443 | − | 3.44992i | −0.826012 | − | 0.176513i | ||||
\(383\) | −18.6593 | − | 32.3189i | −0.953447 | − | 1.65142i | −0.737883 | − | 0.674929i | \(-0.764174\pi\) |
−0.215564 | − | 0.976490i | \(-0.569159\pi\) | |||||||
\(384\) | 0.199697 | − | 1.20155i | 0.0101908 | − | 0.0613166i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.78504 | + | 11.6924i | 0.192653 | + | 0.595128i | ||||
\(387\) | 18.9054 | + | 5.06568i | 0.961014 | + | 0.257503i | ||||
\(388\) | 2.59967 | + | 25.2628i | 0.131978 | + | 1.28252i | ||||
\(389\) | 13.4587 | − | 3.60626i | 0.682385 | − | 0.182845i | 0.0990579 | − | 0.995082i | \(-0.468417\pi\) |
0.583327 | + | 0.812237i | \(0.301750\pi\) | |||||||
\(390\) | −0.0806880 | − | 1.57234i | −0.00408580 | − | 0.0796185i | ||||
\(391\) | − | 23.4065i | − | 1.18372i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.677564i | 0.0341786i | ||||||||
\(394\) | −5.54111 | + | 0.284354i | −0.279157 | + | 0.0143255i | ||||
\(395\) | 15.2388 | − | 4.08323i | 0.766748 | − | 0.205450i | ||||
\(396\) | −22.0299 | − | 17.9190i | −1.10704 | − | 0.900462i | ||||
\(397\) | −4.97204 | − | 1.33225i | −0.249539 | − | 0.0668639i | 0.131881 | − | 0.991266i | \(-0.457898\pi\) |
−0.381420 | + | 0.924402i | \(0.624565\pi\) | |||||||
\(398\) | −17.2074 | + | 5.57033i | −0.862528 | + | 0.279215i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 39.0787 | + | 12.8857i | 1.95394 | + | 0.644284i | ||||
\(401\) | −4.13740 | − | 7.16619i | −0.206612 | − | 0.357862i | 0.744033 | − | 0.668143i | \(-0.232910\pi\) |
−0.950645 | + | 0.310280i | \(0.899577\pi\) | |||||||
\(402\) | 0.0648715 | − | 0.303573i | 0.00323550 | − | 0.0151408i | ||||
\(403\) | 6.58470 | + | 24.5744i | 0.328007 | + | 1.22414i | ||||
\(404\) | 4.49667 | + | 11.7908i | 0.223718 | + | 0.586615i | ||||
\(405\) | 24.5942 | + | 24.5942i | 1.22210 | + | 1.22210i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.68644i | − | 0.133162i | ||||||
\(408\) | 0.620338 | + | 0.771186i | 0.0307113 | + | 0.0381794i | ||||
\(409\) | 3.87211 | + | 2.23557i | 0.191464 | + | 0.110542i | 0.592668 | − | 0.805447i | \(-0.298075\pi\) |
−0.401204 | + | 0.915989i | \(0.631408\pi\) | |||||||
\(410\) | −1.97577 | + | 1.28003i | −0.0975765 | + | 0.0632161i | ||||
\(411\) | −0.0878609 | + | 0.327901i | −0.00433386 | + | 0.0161742i | ||||
\(412\) | 16.6575 | + | 23.0323i | 0.820658 | + | 1.13472i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.37356 | + | 28.9560i | 0.460685 | + | 1.42311i | ||||
\(415\) | −18.6668 | − | 32.3319i | −0.916318 | − | 1.58711i | ||||
\(416\) | −3.79353 | − | 14.4720i | −0.185993 | − | 0.709550i | ||||
\(417\) | 0.566432 | − | 0.981089i | 0.0277383 | − | 0.0480442i | ||||
\(418\) | −9.76831 | + | 10.8251i | −0.477784 | + | 0.529473i | ||||
\(419\) | −1.21304 | + | 1.21304i | −0.0592610 | + | 0.0592610i | −0.736116 | − | 0.676855i | \(-0.763342\pi\) |
0.676855 | + | 0.736116i | \(0.263342\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.4374 | + | 14.4374i | 0.703638 | + | 0.703638i | 0.965190 | − | 0.261552i | \(-0.0842341\pi\) |
−0.261552 | + | 0.965190i | \(0.584234\pi\) | |||||||
\(422\) | 0.585736 | + | 11.4141i | 0.0285132 | + | 0.555627i | ||||
\(423\) | 0.848690 | + | 0.489991i | 0.0412647 | + | 0.0238242i | ||||
\(424\) | −12.6687 | − | 4.91054i | −0.615246 | − | 0.238477i | ||||
\(425\) | −28.9558 | + | 16.7176i | −1.40456 | + | 0.810924i | ||||
\(426\) | −0.0142577 | + | 0.0279071i | −0.000690786 | + | 0.00135211i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 24.3673 | + | 3.91376i | 1.17784 | + | 0.189179i | ||||
\(429\) | 1.30674 | + | 0.350141i | 0.0630902 | + | 0.0169050i | ||||
\(430\) | 7.56788 | − | 35.4146i | 0.364956 | − | 1.70784i | ||||
\(431\) | 4.70748 | − | 8.15360i | 0.226751 | − | 0.392745i | −0.730092 | − | 0.683349i | \(-0.760523\pi\) |
0.956843 | + | 0.290604i | \(0.0938562\pi\) | |||||||
\(432\) | −2.15668 | − | 1.41394i | −0.103763 | − | 0.0680283i | ||||
\(433\) | −34.1850 | −1.64283 | −0.821413 | − | 0.570333i | \(-0.806814\pi\) | ||||
−0.821413 | + | 0.570333i | \(0.806814\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.45829 | − | 1.45829i | 0.0699195 | − | 0.0699195i | ||||
\(436\) | −12.5926 | + | 4.80243i | −0.603074 | + | 0.229995i | ||||
\(437\) | 15.0949 | − | 4.04467i | 0.722087 | − | 0.193483i | ||||
\(438\) | 0.560568 | + | 0.865258i | 0.0267850 | + | 0.0413436i | ||||
\(439\) | −17.9923 | + | 10.3879i | −0.858727 | + | 0.495786i | −0.863586 | − | 0.504202i | \(-0.831787\pi\) |
0.00485902 | + | 0.999988i | \(0.498453\pi\) | |||||||
\(440\) | −31.0225 | + | 42.4071i | −1.47894 | + | 2.02168i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.8256 | + | 5.53076i | 0.514921 | + | 0.263071i | ||||
\(443\) | −1.27873 | + | 4.77227i | −0.0607542 | + | 0.226738i | −0.989627 | − | 0.143661i | \(-0.954112\pi\) |
0.928873 | + | 0.370399i | \(0.120779\pi\) | |||||||
\(444\) | −0.0124625 | − | 0.121107i | −0.000591446 | − | 0.00574748i | ||||
\(445\) | 8.47450 | + | 31.6273i | 0.401730 | + | 1.49928i | ||||
\(446\) | 3.44277 | − | 3.81523i | 0.163020 | − | 0.180657i | ||||
\(447\) | 2.00710 | 0.0949327 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.2811 | 0.768355 | 0.384177 | − | 0.923259i | \(-0.374485\pi\) | ||||
0.384177 | + | 0.923259i | \(0.374485\pi\) | |||||||
\(450\) | 29.1261 | − | 32.2772i | 1.37302 | − | 1.52156i | ||||
\(451\) | −0.523558 | − | 1.95395i | −0.0246534 | − | 0.0920077i | ||||
\(452\) | 1.98347 | + | 19.2748i | 0.0932948 | + | 0.906608i | ||||
\(453\) | −0.0451592 | + | 0.168536i | −0.00212176 | + | 0.00791853i | ||||
\(454\) | 30.0036 | + | 15.3287i | 1.40814 | + | 0.719413i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.390145 | + | 0.533320i | −0.0182702 | + | 0.0249750i | ||||
\(457\) | 21.1023 | − | 12.1834i | 0.987126 | − | 0.569917i | 0.0827117 | − | 0.996574i | \(-0.473642\pi\) |
0.904414 | + | 0.426656i | \(0.140309\pi\) | |||||||
\(458\) | −7.52989 | − | 11.6227i | −0.351848 | − | 0.543091i | ||||
\(459\) | 2.02406 | − | 0.542345i | 0.0944749 | − | 0.0253145i | ||||
\(460\) | 52.6174 | − | 20.0667i | 2.45330 | − | 0.935615i | ||||
\(461\) | 12.6919 | − | 12.6919i | 0.591119 | − | 0.591119i | −0.346815 | − | 0.937934i | \(-0.612737\pi\) |
0.937934 | + | 0.346815i | \(0.112737\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.8710 | 0.923485 | 0.461742 | − | 0.887014i | \(-0.347224\pi\) | ||||
0.461742 | + | 0.887014i | \(0.347224\pi\) | |||||||
\(464\) | 10.7450 | − | 16.3892i | 0.498822 | − | 0.760851i | ||||
\(465\) | 2.02462 | − | 3.50674i | 0.0938893 | − | 0.162621i | ||||
\(466\) | 7.75585 | − | 36.2942i | 0.359283 | − | 1.68130i | ||||
\(467\) | 15.6773 | + | 4.20072i | 0.725459 | + | 0.194386i | 0.602606 | − | 0.798039i | \(-0.294129\pi\) |
0.122853 | + | 0.992425i | \(0.460796\pi\) | |||||||
\(468\) | −15.6072 | − | 2.50675i | −0.721442 | − | 0.115875i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.824951 | − | 1.61471i | 0.0380522 | − | 0.0744812i | ||||
\(471\) | 1.23430 | − | 0.712621i | 0.0568734 | − | 0.0328359i | ||||
\(472\) | 32.7278 | + | 12.6857i | 1.50642 | + | 0.583906i | ||||
\(473\) | 26.9488 | + | 15.5589i | 1.23911 | + | 0.715398i | ||||
\(474\) | 0.0314852 | + | 0.613542i | 0.00144616 | + | 0.0281809i | ||||
\(475\) | −15.7848 | − | 15.7848i | −0.724258 | − | 0.724258i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.1509 | + | 10.1509i | −0.464780 | + | 0.464780i | ||||
\(478\) | −27.0693 | + | 29.9978i | −1.23812 | + | 1.37207i | ||||
\(479\) | −4.32709 | + | 7.49474i | −0.197710 | + | 0.342443i | −0.947785 | − | 0.318909i | \(-0.896684\pi\) |
0.750076 | + | 0.661352i | \(0.230017\pi\) | |||||||
\(480\) | −1.20179 | + | 2.05566i | −0.0548539 | + | 0.0938276i | ||||
\(481\) | −0.747697 | − | 1.29505i | −0.0340921 | − | 0.0590492i | ||||
\(482\) | 7.19244 | + | 22.2182i | 0.327606 | + | 1.01201i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.5656 | − | 18.7571i | −0.616618 | − | 0.852596i | ||||
\(485\) | 12.8498 | − | 47.9561i | 0.583480 | − | 2.17758i | ||||
\(486\) | −3.43235 | + | 2.22369i | −0.155694 | + | 0.100869i | ||||
\(487\) | −22.2974 | − | 12.8734i | −1.01039 | − | 0.583350i | −0.0990854 | − | 0.995079i | \(-0.531592\pi\) |
−0.911306 | + | 0.411729i | \(0.864925\pi\) | |||||||
\(488\) | 14.7928 | + | 18.3899i | 0.669638 | + | 0.832473i | ||||
\(489\) | 0.467313i | 0.0211326i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.0762 | + | 24.0762i | 1.08654 | + | 1.08654i | 0.995882 | + | 0.0906632i | \(0.0288987\pi\) |
0.0906632 | + | 0.995882i | \(0.471101\pi\) | |||||||
\(492\) | −0.0326668 | − | 0.0856565i | −0.00147273 | − | 0.00386169i | ||||
\(493\) | 4.12144 | + | 15.3814i | 0.185620 | + | 0.692744i | ||||
\(494\) | −1.69613 | + | 7.93718i | −0.0763123 | + | 0.357111i | ||||
\(495\) | 27.7574 | + | 48.0773i | 1.24760 | + | 2.16091i | ||||
\(496\) | 12.0495 | − | 36.5429i | 0.541040 | − | 1.64082i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.38315 | − | 0.447749i | 0.0619802 | − | 0.0200641i | ||||
\(499\) | 9.09443 | + | 2.43684i | 0.407123 | + | 0.109088i | 0.456568 | − | 0.889689i | \(-0.349079\pi\) |
−0.0494451 | + | 0.998777i | \(0.515745\pi\) | |||||||
\(500\) | −32.0734 | − | 26.0883i | −1.43437 | − | 1.16670i | ||||
\(501\) | 0.376423 | − | 0.100862i | 0.0168174 | − | 0.00450620i | ||||
\(502\) | −23.0112 | + | 1.18087i | −1.02704 | + | 0.0527048i | ||||
\(503\) | − | 5.56169i | − | 0.247983i | −0.992283 | − | 0.123992i | \(-0.960430\pi\) | ||
0.992283 | − | 0.123992i | \(-0.0395696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 24.6697i | − | 1.09779i | ||||||
\(506\) | 2.47992 | + | 48.3253i | 0.110246 | + | 2.14832i | ||||
\(507\) | −0.624501 | + | 0.167335i | −0.0277351 | + | 0.00743159i | ||||
\(508\) | 1.95157 | + | 18.9647i | 0.0865867 | + | 0.841422i | ||||
\(509\) | −0.130579 | − | 0.0349885i | −0.00578781 | − | 0.00155084i | 0.255924 | − | 0.966697i | \(-0.417620\pi\) |
−0.261712 | + | 0.965146i | \(0.584287\pi\) | |||||||
\(510\) | −0.595896 | − | 1.84079i | −0.0263867 | − | 0.0815116i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −7.20259 | + | 21.4505i | −0.318312 | + | 0.947986i | ||||
\(513\) | 0.699519 | + | 1.21160i | 0.0308845 | + | 0.0534936i | ||||
\(514\) | 28.4934 | + | 6.08886i | 1.25679 | + | 0.268568i | ||||
\(515\) | −14.3822 | − | 53.6750i | −0.633754 | − | 2.36520i | ||||
\(516\) | 1.28705 | + | 0.576389i | 0.0566592 | + | 0.0253741i | ||||
\(517\) | 1.10172 | + | 1.10172i | 0.0484534 | + | 0.0484534i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.51284i | 0.110301i | ||||||||
\(520\) | −3.15212 | + | 29.0774i | −0.138230 | + | 1.27513i | ||||
\(521\) | −32.3309 | − | 18.6663i | −1.41644 | − | 0.817784i | −0.420458 | − | 0.907312i | \(-0.638131\pi\) |
−0.995984 | + | 0.0895282i | \(0.971464\pi\) | |||||||
\(522\) | −11.2584 | − | 17.3777i | −0.492766 | − | 0.760603i | ||||
\(523\) | −5.88406 | + | 21.9596i | −0.257292 | + | 0.960228i | 0.709509 | + | 0.704697i | \(0.248917\pi\) |
−0.966801 | + | 0.255531i | \(0.917750\pi\) | |||||||
\(524\) | 1.99609 | − | 12.4278i | 0.0871998 | − | 0.542911i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.4485 | + | 8.88557i | −1.19681 | + | 0.387429i | ||||
\(527\) | 15.6328 | + | 27.0768i | 0.680976 | + | 1.17949i | ||||
\(528\) | −1.36246 | − | 1.52647i | −0.0592937 | − | 0.0664313i | ||||
\(529\) | 14.4309 | − | 24.9950i | 0.627430 | − | 1.08674i | ||||
\(530\) | 19.7200 | + | 17.7948i | 0.856581 | + | 0.772958i | ||||
\(531\) | 26.2235 | − | 26.2235i | 1.13800 | − | 1.13800i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.796217 | − | 0.796217i | −0.0344880 | − | 0.0344880i | ||||
\(534\) | −1.27337 | + | 0.0653457i | −0.0551041 | + | 0.00282779i | ||||
\(535\) | −41.7831 | − | 24.1235i | −1.80644 | − | 1.04295i | ||||
\(536\) | −2.08419 | + | 5.37698i | −0.0900232 | + | 0.232250i | ||||
\(537\) | −1.40318 | + | 0.810128i | −0.0605518 | + | 0.0349596i | ||||
\(538\) | 16.9311 | + | 8.65006i | 0.729954 | + | 0.372931i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.95444 | + | 4.08509i | 0.127139 | + | 0.175794i | ||||
\(541\) | −5.77189 | − | 1.54657i | −0.248153 | − | 0.0664924i | 0.132598 | − | 0.991170i | \(-0.457668\pi\) |
−0.380751 | + | 0.924677i | \(0.624335\pi\) | |||||||
\(542\) | −13.1368 | − | 2.80726i | −0.564276 | − | 0.120582i | ||||
\(543\) | 0.269923 | − | 0.467520i | 0.0115835 | − | 0.0200632i | ||||
\(544\) | −9.10627 | − | 15.9725i | −0.390428 | − | 0.684815i | ||||
\(545\) | 26.3471 | 1.12859 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.794101 | − | 0.794101i | 0.0339533 | − | 0.0339533i | −0.689926 | − | 0.723880i | \(-0.742357\pi\) |
0.723880 | + | 0.689926i | \(0.242357\pi\) | |||||||
\(548\) | 2.57753 | − | 5.75549i | 0.110106 | − | 0.245862i | ||||
\(549\) | 24.0865 | − | 6.45394i | 1.02798 | − | 0.275448i | ||||
\(550\) | 58.0112 | − | 37.5833i | 2.47361 | − | 1.60256i | ||||
\(551\) | −9.20733 | + | 5.31585i | −0.392245 | + | 0.226463i | ||||
\(552\) | 0.335980 | + | 2.16704i | 0.0143002 | + | 0.0922352i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.04285 | − | 13.7853i | 0.299222 | − | 0.585681i | ||||
\(555\) | −0.0616006 | + | 0.229897i | −0.00261480 | + | 0.00975856i | ||||
\(556\) | −13.2797 | + | 16.3263i | −0.563185 | + | 0.692390i | ||||
\(557\) | 4.47037 | + | 16.6837i | 0.189416 | + | 0.706909i | 0.993642 | + | 0.112586i | \(0.0359134\pi\) |
−0.804226 | + | 0.594323i | \(0.797420\pi\) | |||||||
\(558\) | −30.1827 | − | 27.2361i | −1.27773 | − | 1.15300i | ||||
\(559\) | 17.3215 | 0.732623 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.66255 | 0.0701929 | ||||||||
\(562\) | −21.2308 | − | 19.1581i | −0.895565 | − | 0.808136i | ||||
\(563\) | 1.86914 | + | 6.97572i | 0.0787748 | + | 0.293992i | 0.994063 | − | 0.108809i | \(-0.0347036\pi\) |
−0.915288 | + | 0.402800i | \(0.868037\pi\) | |||||||
\(564\) | 0.0547771 | + | 0.0445553i | 0.00230653 | + | 0.00187612i | ||||
\(565\) | 9.80404 | − | 36.5892i | 0.412459 | − | 1.53932i | ||||
\(566\) | 19.6422 | − | 38.4465i | 0.825623 | − | 1.61603i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.343726 | − | 0.469867i | 0.0144224 | − | 0.0197152i | ||||
\(569\) | −14.9666 | + | 8.64097i | −0.627433 | + | 0.362248i | −0.779757 | − | 0.626082i | \(-0.784657\pi\) |
0.152324 | + | 0.988331i | \(0.451324\pi\) | |||||||
\(570\) | 1.08416 | − | 0.702386i | 0.0454105 | − | 0.0294197i | ||||
\(571\) | −24.6235 | + | 6.59784i | −1.03046 | + | 0.276111i | −0.734155 | − | 0.678982i | \(-0.762421\pi\) |
−0.296305 | + | 0.955093i | \(0.595755\pi\) | |||||||
\(572\) | −22.9366 | − | 10.2719i | −0.959029 | − | 0.429490i | ||||
\(573\) | −0.888668 | + | 0.888668i | −0.0371246 | + | 0.0371246i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −74.0826 | −3.08946 | ||||||||
\(576\) | 17.6618 | + | 16.1127i | 0.735908 | + | 0.671362i | ||||
\(577\) | 3.22470 | − | 5.58535i | 0.134246 | − | 0.232521i | −0.791063 | − | 0.611735i | \(-0.790472\pi\) |
0.925309 | + | 0.379213i | \(0.123805\pi\) | |||||||
\(578\) | −8.90105 | − | 1.90210i | −0.370235 | − | 0.0791168i | ||||
\(579\) | 0.903709 | + | 0.242148i | 0.0375569 | + | 0.0100633i | ||||
\(580\) | −31.0438 | + | 22.4516i | −1.28902 | + | 0.932253i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.72166 | + | 0.879592i | 0.0713653 | + | 0.0364602i | ||||
\(583\) | −19.7660 | + | 11.4119i | −0.818624 | + | 0.472633i | ||||
\(584\) | −7.73283 | − | 17.5219i | −0.319987 | − | 0.725061i | ||||
\(585\) | 26.7620 | + | 15.4510i | 1.10647 | + | 0.638821i | ||||
\(586\) | 2.72427 | − | 0.139802i | 0.112538 | − | 0.00577515i | ||||
\(587\) | −23.4107 | − | 23.4107i | −0.966264 | − | 0.966264i | 0.0331855 | − | 0.999449i | \(-0.489435\pi\) |
−0.999449 | + | 0.0331855i | \(0.989435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.7606 | + | 14.7606i | −0.608198 | + | 0.608198i | ||||
\(590\) | −50.9438 | − | 45.9704i | −2.09732 | − | 1.89257i | ||||
\(591\) | −0.211192 | + | 0.365796i | −0.00868729 | + | 0.0150468i | ||||
\(592\) | −0.128193 | + | 2.25804i | −0.00526869 | + | 0.0928050i | ||||
\(593\) | −6.99803 | − | 12.1209i | −0.287375 | − | 0.497748i | 0.685808 | − | 0.727783i | \(-0.259449\pi\) |
−0.973182 | + | 0.230035i | \(0.926116\pi\) | |||||||
\(594\) | −4.12143 | + | 1.33418i | −0.169104 | + | 0.0547421i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −36.8141 | − | 5.91290i | −1.50796 | − | 0.242202i | ||||
\(597\) | −0.356362 | + | 1.32996i | −0.0145849 | + | 0.0544317i | ||||
\(598\) | 14.6455 | + | 22.6059i | 0.598899 | + | 0.924423i | ||||
\(599\) | −38.2425 | − | 22.0793i | −1.56255 | − | 0.902136i | −0.996998 | − | 0.0774209i | \(-0.975331\pi\) |
−0.565548 | − | 0.824716i | \(-0.691335\pi\) | |||||||
\(600\) | 2.44084 | − | 1.96340i | 0.0996468 | − | 0.0801555i | ||||
\(601\) | 31.1376i | 1.27013i | 0.772459 | + | 0.635065i | \(0.219027\pi\) | ||||
−0.772459 | + | 0.635065i | \(0.780973\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.30838 | + | 4.30838i | 0.175451 | + | 0.175451i | ||||
\(604\) | 1.32481 | − | 2.95824i | 0.0539058 | − | 0.120369i | ||||
\(605\) | 11.7126 | + | 43.7119i | 0.476183 | + | 1.77714i | ||||
\(606\) | 0.939453 | + | 0.200755i | 0.0381627 | + | 0.00815512i | ||||
\(607\) | −4.40831 | − | 7.63542i | −0.178928 | − | 0.309912i | 0.762586 | − | 0.646887i | \(-0.223930\pi\) |
−0.941514 | + | 0.336975i | \(0.890596\pi\) | |||||||
\(608\) | 8.72714 | − | 8.63273i | 0.353932 | − | 0.350103i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.2099 | − | 43.8961i | −0.575344 | − | 1.77730i | ||||
\(611\) | 0.837735 | + | 0.224470i | 0.0338911 | + | 0.00908110i | ||||
\(612\) | −19.3239 | + | 1.98853i | −0.781123 | + | 0.0803816i | ||||
\(613\) | −9.24353 | + | 2.47680i | −0.373343 | + | 0.100037i | −0.440611 | − | 0.897698i | \(-0.645238\pi\) |
0.0672686 | + | 0.997735i | \(0.478572\pi\) | |||||||
\(614\) | 1.80808 | + | 35.2334i | 0.0729681 | + | 1.42190i | ||||
\(615\) | 0.179217i | 0.00722673i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 25.9915i | − | 1.04638i | −0.852216 | − | 0.523189i | \(-0.824742\pi\) | ||
0.852216 | − | 0.523189i | \(-0.175258\pi\) | |||||||
\(618\) | 2.16105 | − | 0.110899i | 0.0869302 | − | 0.00446101i | ||||
\(619\) | 23.3633 | − | 6.26017i | 0.939049 | − | 0.251617i | 0.243340 | − | 0.969941i | \(-0.421757\pi\) |
0.695709 | + | 0.718324i | \(0.255090\pi\) | |||||||
\(620\) | −47.4661 | + | 58.3557i | −1.90628 | + | 2.34362i | ||||
\(621\) | 4.48471 | + | 1.20167i | 0.179965 | + | 0.0482215i | ||||
\(622\) | 37.2661 | − | 12.0637i | 1.49424 | − | 0.483711i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.08165 | − | 0.356661i | −0.0433008 | − | 0.0142779i | ||||
\(625\) | 14.6944 | + | 25.4514i | 0.587775 | + | 1.01806i | ||||
\(626\) | 1.45879 | − | 6.82655i | 0.0583050 | − | 0.272844i | ||||
\(627\) | 0.287290 | + | 1.07218i | 0.0114733 | + | 0.0428188i | ||||
\(628\) | −24.7387 | + | 9.43460i | −0.987181 | + | 0.376482i | ||||
\(629\) | −1.29948 | − | 1.29948i | −0.0518135 | − | 0.0518135i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 13.2008i | − | 0.525514i | −0.964862 | − | 0.262757i | \(-0.915368\pi\) | ||
0.964862 | − | 0.262757i | \(-0.0846318\pi\) | |||||||
\(632\) | 1.22999 | − | 11.3463i | 0.0489263 | − | 0.451331i | ||||
\(633\) | 0.753498 | + | 0.435032i | 0.0299488 | + | 0.0172910i | ||||
\(634\) | 31.1128 | − | 20.1568i | 1.23565 | − | 0.800529i | ||||
\(635\) | 9.64632 | − | 36.0005i | 0.382802 | − | 1.42864i | ||||
\(636\) | −0.838126 | + | 0.606153i | −0.0332339 | + | 0.0240355i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.1388 | − | 31.3200i | −0.401400 | − | 1.23997i | ||||
\(639\) | −0.307550 | − | 0.532692i | −0.0121665 | − | 0.0210730i | ||||
\(640\) | 28.0990 | − | 34.1642i | 1.11071 | − | 1.35046i | ||||
\(641\) | 12.0211 | − | 20.8211i | 0.474805 | − | 0.822386i | −0.524779 | − | 0.851239i | \(-0.675852\pi\) |
0.999584 | + | 0.0288526i | \(0.00918535\pi\) | |||||||
\(642\) | 1.25867 | − | 1.39484i | 0.0496759 | − | 0.0550501i | ||||
\(643\) | −17.9930 | + | 17.9930i | −0.709573 | + | 0.709573i | −0.966445 | − | 0.256872i | \(-0.917308\pi\) |
0.256872 | + | 0.966445i | \(0.417308\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.94941 | − | 1.94941i | −0.0767581 | − | 0.0767581i | ||||
\(646\) | 0.511189 | + | 9.96137i | 0.0201125 | + | 0.391925i | ||||
\(647\) | 21.3332 | + | 12.3167i | 0.838695 | + | 0.484221i | 0.856821 | − | 0.515615i | \(-0.172436\pi\) |
−0.0181252 | + | 0.999836i | \(0.505770\pi\) | |||||||
\(648\) | 23.0191 | − | 10.1589i | 0.904278 | − | 0.399080i | ||||
\(649\) | 51.0627 | − | 29.4810i | 2.00439 | − | 1.15723i | ||||
\(650\) | 17.5051 | − | 34.2635i | 0.686607 | − | 1.34393i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.37670 | − | 8.57140i | 0.0539156 | − | 0.335682i | ||||
\(653\) | −16.8853 | − | 4.52441i | −0.660774 | − | 0.177054i | −0.0871785 | − | 0.996193i | \(-0.527785\pi\) |
−0.573595 | + | 0.819139i | \(0.694452\pi\) | |||||||
\(654\) | −0.214406 | + | 1.00333i | −0.00838393 | + | 0.0392334i | ||||
\(655\) | −12.3035 | + | 21.3102i | −0.480736 | + | 0.832659i | ||||
\(656\) | 0.346828 | + | 1.66734i | 0.0135414 | + | 0.0650986i | ||||
\(657\) | −20.2357 | −0.789468 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.2113 | + | 22.2113i | −0.865229 | + | 0.865229i | −0.991940 | − | 0.126711i | \(-0.959558\pi\) |
0.126711 | + | 0.991940i | \(0.459558\pi\) | |||||||
\(660\) | 1.42533 | + | 3.73738i | 0.0554808 | + | 0.145477i | ||||
\(661\) | −21.7330 | + | 5.82333i | −0.845314 | + | 0.226501i | −0.655384 | − | 0.755296i | \(-0.727493\pi\) |
−0.189931 | + | 0.981798i | \(0.560826\pi\) | |||||||
\(662\) | 2.40241 | + | 3.70821i | 0.0933723 | + | 0.144124i | ||||
\(663\) | 0.801462 | − | 0.462724i | 0.0311262 | − | 0.0179707i | ||||
\(664\) | −26.6886 | + | 4.13782i | −1.03572 | + | 0.160579i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.12797 | + | 1.08717i | 0.0824572 | + | 0.0421271i | ||||
\(667\) | −9.13188 | + | 34.0806i | −0.353588 | + | 1.31961i | ||||
\(668\) | −7.20145 | + | 0.741068i | −0.278633 | + | 0.0286728i | ||||
\(669\) | −0.101253 | − | 0.377883i | −0.00391469 | − | 0.0146098i | ||||
\(670\) | 7.55268 | − | 8.36977i | 0.291785 | − | 0.323352i | ||||
\(671\) | 39.6457 | 1.53050 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.76133 | −0.183536 | −0.0917679 | − | 0.995780i | \(-0.529252\pi\) | ||||
−0.0917679 | + | 0.995780i | \(0.529252\pi\) | |||||||
\(674\) | 12.4684 | − | 13.8174i | 0.480266 | − | 0.532225i | ||||
\(675\) | −1.71655 | − | 6.40624i | −0.0660699 | − | 0.246576i | ||||
\(676\) | 11.9475 | − | 1.22946i | 0.459519 | − | 0.0472869i | ||||
\(677\) | 0.936462 | − | 3.49493i | 0.0359912 | − | 0.134321i | −0.945593 | − | 0.325353i | \(-0.894517\pi\) |
0.981584 | + | 0.191032i | \(0.0611835\pi\) | |||||||
\(678\) | 1.31358 | + | 0.671103i | 0.0504477 | + | 0.0257736i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.50692 | + | 35.5191i | 0.211181 | + | 1.36209i | ||||
\(681\) | 2.22129 | − | 1.28246i | 0.0851199 | − | 0.0491440i | ||||
\(682\) | −35.1445 | − | 54.2469i | −1.34575 | − | 2.07722i | ||||
\(683\) | −3.94113 | + | 1.05602i | −0.150803 | + | 0.0404076i | −0.333431 | − | 0.942775i | \(-0.608206\pi\) |
0.182628 | + | 0.983182i | \(0.441540\pi\) | |||||||
\(684\) | −4.62160 | − | 12.1184i | −0.176711 | − | 0.463359i | ||||
\(685\) | −8.71749 | + | 8.71749i | −0.333078 | + | 0.333078i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.05426 | −0.0402226 | ||||||||
\(688\) | −21.9089 | − | 14.3637i | −0.835268 | − | 0.547611i | ||||
\(689\) | −6.35238 | + | 11.0026i | −0.242006 | + | 0.419167i | ||||
\(690\) | 0.895884 | − | 4.19238i | 0.0341057 | − | 0.159601i | ||||
\(691\) | 32.6372 | + | 8.74512i | 1.24158 | + | 0.332680i | 0.819078 | − | 0.573683i | \(-0.194486\pi\) |
0.422501 | + | 0.906363i | \(0.361152\pi\) | |||||||
\(692\) | 7.40279 | − | 46.0902i | 0.281412 | − | 1.75209i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.69406 | + | 15.0599i | −0.292062 | + | 0.571667i | ||||
\(695\) | 35.6300 | − | 20.5710i | 1.35152 | − | 0.780302i | ||||
\(696\) | −0.602361 | − | 1.36489i | −0.0228324 | − | 0.0517362i | ||||
\(697\) | −1.19841 | − | 0.691901i | −0.0453929 | − | 0.0262076i | ||||
\(698\) | −0.978548 | − | 19.0686i | −0.0370386 | − | 0.721759i | ||||
\(699\) | −1.99783 | − | 1.99783i | −0.0755650 | − | 0.0755650i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.85253 | + | 8.85253i | −0.334355 | + | 0.334355i | −0.854238 | − | 0.519882i | \(-0.825976\pi\) |
0.519882 | + | 0.854238i | \(0.325976\pi\) | |||||||
\(702\) | −1.61548 | + | 1.79025i | −0.0609724 | + | 0.0675687i | ||||
\(703\) | 0.613485 | − | 1.06259i | 0.0231380 | − | 0.0400762i | ||||
\(704\) | 20.4932 | + | 32.0122i | 0.772366 | + | 1.20651i | ||||
\(705\) | −0.0690186 | − | 0.119544i | −0.00259939 | − | 0.00450227i | ||||
\(706\) | −0.616042 | − | 1.90302i | −0.0231850 | − | 0.0716212i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.16518 | − | 1.56591i | 0.0813724 | − | 0.0588505i | ||||
\(709\) | −12.1752 | + | 45.4386i | −0.457250 | + | 1.70648i | 0.224137 | + | 0.974558i | \(0.428044\pi\) |
−0.681387 | + | 0.731923i | \(0.738623\pi\) | |||||||
\(710\) | −0.955169 | + | 0.618818i | −0.0358469 | + | 0.0232238i | ||||
\(711\) | −10.4428 | − | 6.02914i | −0.391635 | − | 0.226110i | ||||
\(712\) | 23.5485 | + | 2.55277i | 0.882518 | + | 0.0956690i | ||||
\(713\) | 69.2753i | 2.59438i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.7407 | + | 34.7407i | 1.29923 | + | 1.29923i | ||||
\(716\) | 28.1236 | − | 10.7255i | 1.05103 | − | 0.400831i | ||||
\(717\) | 0.796120 | + | 2.97116i | 0.0297316 | + | 0.110960i | ||||
\(718\) | −2.79691 | + | 13.0884i | −0.104380 | + | 0.488454i | ||||
\(719\) | −11.2893 | − | 19.5536i | −0.421020 | − | 0.729228i | 0.575020 | − | 0.818140i | \(-0.304994\pi\) |
−0.996040 | + | 0.0889118i | \(0.971661\pi\) | |||||||
\(720\) | −21.0369 | − | 41.7351i | −0.783997 | − | 1.55537i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 19.2282 | − | 6.22450i | 0.715599 | − | 0.231652i | ||||
\(723\) | 1.71725 | + | 0.460137i | 0.0638653 | + | 0.0171127i | ||||
\(724\) | −6.32820 | + | 7.78000i | −0.235186 | + | 0.289142i | ||||
\(725\) | 48.6829 | − | 13.0445i | 1.80804 | − | 0.484462i | ||||
\(726\) | −1.75992 | + | 0.0903140i | −0.0653167 | + | 0.00335187i | ||||
\(727\) | − | 8.36564i | − | 0.310265i | −0.987894 | − | 0.155132i | \(-0.950420\pi\) | ||
0.987894 | − | 0.155132i | \(-0.0495804\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 26.3761i | − | 0.976893i | ||||||
\(730\) | 1.91887 | + | 37.3924i | 0.0710207 | + | 1.38396i | ||||
\(731\) | 20.5616 | − | 5.50947i | 0.760499 | − | 0.203775i | ||||
\(732\) | 1.78726 | − | 0.183918i | 0.0660589 | − | 0.00679781i | ||||
\(733\) | −1.22544 | − | 0.328355i | −0.0452625 | − | 0.0121281i | 0.236117 | − | 0.971725i | \(-0.424125\pi\) |
−0.281379 | + | 0.959597i | \(0.590792\pi\) | |||||||
\(734\) | 4.29581 | + | 13.2702i | 0.158561 | + | 0.489814i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.221555 | − | 40.7373i | 0.00816661 | − | 1.50160i | ||||
\(737\) | 4.84357 | + | 8.38930i | 0.178415 | + | 0.309024i | ||||
\(738\) | 1.75963 | + | 0.376021i | 0.0647728 | + | 0.0138415i | ||||
\(739\) | −5.21579 | − | 19.4656i | −0.191866 | − | 0.716053i | −0.993056 | − | 0.117643i | \(-0.962466\pi\) |
0.801190 | − | 0.598410i | \(-0.204201\pi\) | |||||||
\(740\) | 1.80714 | − | 4.03526i | 0.0664319 | − | 0.148339i | ||||
\(741\) | 0.436906 | + | 0.436906i | 0.0160501 | + | 0.0160501i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 22.0688i | − | 0.809625i | −0.914400 | − | 0.404813i | \(-0.867337\pi\) | ||
0.914400 | − | 0.404813i | \(-0.132663\pi\) | |||||||
\(744\) | −1.83599 | − | 2.28245i | −0.0673108 | − | 0.0836787i | ||||
\(745\) | 63.1259 | + | 36.4457i | 2.31275 | + | 1.33527i | ||||
\(746\) | −9.33624 | − | 14.4108i | −0.341824 | − | 0.527618i | ||||
\(747\) | −7.38541 | + | 27.5627i | −0.270218 | + | 1.00847i | ||||
\(748\) | −30.4943 | − | 4.89784i | −1.11498 | − | 0.179083i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.99439 | + | 0.969338i | −0.109340 | + | 0.0353952i | ||||
\(751\) | −10.2941 | − | 17.8298i | −0.375636 | − | 0.650620i | 0.614786 | − | 0.788694i | \(-0.289242\pi\) |
−0.990422 | + | 0.138074i | \(0.955909\pi\) | |||||||
\(752\) | −0.873457 | − | 0.978601i | −0.0318517 | − | 0.0356859i | ||||
\(753\) | −0.877043 | + | 1.51908i | −0.0319612 | + | 0.0553585i | ||||
\(754\) | −13.6047 | − | 12.2765i | −0.495453 | − | 0.447084i | ||||
\(755\) | −4.48066 | + | 4.48066i | −0.163068 | + | 0.163068i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.3679 | − | 15.3679i | −0.558556 | − | 0.558556i | 0.370340 | − | 0.928896i | \(-0.379241\pi\) |
−0.928896 | + | 0.370340i | \(0.879241\pi\) | |||||||
\(758\) | 41.6454 | − | 2.13712i | 1.51263 | − | 0.0776237i | ||||
\(759\) | 3.19019 | + | 1.84186i | 0.115797 | + | 0.0668552i | ||||
\(760\) | −21.9548 | + | 9.68917i | −0.796383 | + | 0.351463i | ||||
\(761\) | −9.59011 | + | 5.53685i | −0.347641 | + | 0.200711i | −0.663646 | − | 0.748047i | \(-0.730992\pi\) |
0.316005 | + | 0.948758i | \(0.397658\pi\) | |||||||
\(762\) | 1.29245 | + | 0.660307i | 0.0468204 | + | 0.0239204i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.9178 | − | 13.6818i | 0.684424 | − | 0.494992i | ||||
\(765\) | 36.6825 | + | 9.82904i | 1.32626 | + | 0.355370i | ||||
\(766\) | 51.6113 | + | 11.0290i | 1.86479 | + | 0.398494i | ||||
\(767\) | 16.4105 | − | 28.4238i | 0.592548 | − | 1.02632i | ||||
\(768\) | 1.07235 | + | 1.34807i | 0.0386953 | + | 0.0486441i | ||||
\(769\) | −36.7776 | −1.32623 | −0.663117 | − | 0.748515i | \(-0.730767\pi\) | ||||
−0.663117 | + | 0.748515i | \(0.730767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.56843 | − | 1.56843i | 0.0564857 | − | 0.0564857i | ||||
\(772\) | −15.8624 | − | 7.10376i | −0.570899 | − | 0.255670i | ||||
\(773\) | 12.7966 | − | 3.42883i | 0.460261 | − | 0.123326i | −0.0212359 | − | 0.999774i | \(-0.506760\pi\) |
0.481496 | + | 0.876448i | \(0.340093\pi\) | |||||||
\(774\) | −23.2303 | + | 15.0500i | −0.834995 | + | 0.540962i | ||||
\(775\) | 85.6995 | − | 49.4786i | 3.07842 | − | 1.77732i | ||||
\(776\) | −28.9873 | − | 21.2054i | −1.04058 | − | 0.761228i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.96496 | + | 17.5475i | −0.321409 | + | 0.629109i | ||||
\(779\) | 0.239123 | − | 0.892418i | 0.00856746 | − | 0.0319742i | ||||
\(780\) | 1.72730 | + | 1.40497i | 0.0618473 | + | 0.0503062i | ||||
\(781\) | −0.253109 | − | 0.944617i | −0.00905696 | − | 0.0338011i | ||||
\(782\) | 24.5753 | + | 22.1761i | 0.878811 | + | 0.793017i | ||||
\(783\) | −3.15869 | −0.112882 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 51.7602 | 1.84740 | ||||||||
\(786\) | −0.711399 | − | 0.641949i | −0.0253747 | − | 0.0228975i | ||||
\(787\) | 6.76707 | + | 25.2550i | 0.241220 | + | 0.900245i | 0.975246 | + | 0.221123i | \(0.0709724\pi\) |
−0.734026 | + | 0.679121i | \(0.762361\pi\) | |||||||
\(788\) | 4.95130 | − | 6.08722i | 0.176383 | − | 0.216848i | ||||
\(789\) | −0.568455 | + | 2.12150i | −0.0202375 | + | 0.0755275i | ||||
\(790\) | −10.1507 | + | 19.8684i | −0.361145 | + | 0.706885i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 39.6857 | − | 6.15291i | 1.41017 | − | 0.218634i | ||||
\(793\) | 19.1119 | − | 11.0343i | 0.678684 | − | 0.391839i | ||||
\(794\) | 6.10947 | − | 3.95810i | 0.216817 | − | 0.140468i | ||||
\(795\) | 1.95318 | − | 0.523354i | 0.0692723 | − | 0.0185615i | ||||
\(796\) | 10.4544 | − | 23.3442i | 0.370546 | − | 0.827412i | ||||
\(797\) | −19.5355 | + | 19.5355i | −0.691984 | + | 0.691984i | −0.962668 | − | 0.270684i | \(-0.912750\pi\) |
0.270684 | + | 0.962668i | \(0.412750\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.06584 | 0.0377066 | ||||||||
\(800\) | −50.5537 | + | 28.8218i | −1.78734 | + | 1.01900i | ||||
\(801\) | 12.5131 | − | 21.6734i | 0.442129 | − | 0.765791i | ||||
\(802\) | 11.4440 | + | 2.44550i | 0.404100 | + | 0.0863536i | ||||
\(803\) | −31.0762 | − | 8.32684i | −1.09666 | − | 0.293848i | ||||
\(804\) | 0.257270 | + | 0.355727i | 0.00907321 | + | 0.0125455i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −32.0402 | − | 16.3692i | −1.12857 | − | 0.576580i | ||||
\(807\) | 1.25348 | − | 0.723697i | 0.0441246 | − | 0.0254753i | ||||
\(808\) | −16.6399 | − | 6.44984i | −0.585390 | − | 0.226905i | ||||
\(809\) | −35.1150 | − | 20.2736i | −1.23458 | − | 0.712783i | −0.266596 | − | 0.963808i | \(-0.585899\pi\) |
−0.967980 | + | 0.251026i | \(0.919232\pi\) | |||||||
\(810\) | −49.1238 | + | 2.52089i | −1.72604 | + | 0.0885752i | ||||
\(811\) | −11.3534 | − | 11.3534i | −0.398672 | − | 0.398672i | 0.479092 | − | 0.877764i | \(-0.340966\pi\) |
−0.877764 | + | 0.479092i | \(0.840966\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.723124 | + | 0.723124i | −0.0253611 | + | 0.0253611i | ||||
\(814\) | 2.82059 | + | 2.54523i | 0.0988617 | + | 0.0892104i | ||||
\(815\) | −8.48565 | + | 14.6976i | −0.297239 | + | 0.514834i | ||||
\(816\) | −1.39743 | − | 0.0793341i | −0.0489197 | − | 0.00277725i | ||||
\(817\) | 7.10615 | + | 12.3082i | 0.248613 | + | 0.430610i | ||||
\(818\) | −6.01578 | + | 1.94741i | −0.210337 | + | 0.0680898i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.527971 | − | 3.28718i | 0.0184375 | − | 0.114793i | ||||
\(821\) | 1.89736 | − | 7.08103i | 0.0662182 | − | 0.247130i | −0.924881 | − | 0.380257i | \(-0.875835\pi\) |
0.991099 | + | 0.133128i | \(0.0425021\pi\) | |||||||
\(822\) | −0.261033 | − | 0.402914i | −0.00910456 | − | 0.0140532i | ||||
\(823\) | −22.2136 | − | 12.8250i | −0.774318 | − | 0.447053i | 0.0600947 | − | 0.998193i | \(-0.480860\pi\) |
−0.834413 | + | 0.551140i | \(0.814193\pi\) | |||||||
\(824\) | −39.9644 | − | 4.33233i | −1.39223 | − | 0.150924i | ||||
\(825\) | − | 5.26205i | − | 0.183201i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.0664 | − | 17.0664i | −0.593456 | − | 0.593456i | 0.345108 | − | 0.938563i | \(-0.387842\pi\) |
−0.938563 | + | 0.345108i | \(0.887842\pi\) | |||||||
\(828\) | −39.2828 | − | 17.5923i | −1.36517 | − | 0.611375i | ||||
\(829\) | 5.17304 | + | 19.3060i | 0.179667 | + | 0.670526i | 0.995709 | + | 0.0925344i | \(0.0294968\pi\) |
−0.816043 | + | 0.577992i | \(0.803837\pi\) | |||||||
\(830\) | 51.6320 | + | 11.0334i | 1.79217 | + | 0.382976i | ||||
\(831\) | −0.589232 | − | 1.02058i | −0.0204402 | − | 0.0354035i | ||||
\(832\) | 18.7888 | + | 9.72836i | 0.651386 | + | 0.337270i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.493422 | + | 1.52424i | 0.0170858 | + | 0.0527800i | ||||
\(835\) | 13.6705 | + | 3.66299i | 0.473086 | + | 0.126763i | ||||
\(836\) | −2.11081 | − | 20.5122i | −0.0730040 | − | 0.709429i | ||||
\(837\) | −5.99053 | + | 1.60516i | −0.207063 | + | 0.0554824i | ||||
\(838\) | −0.124336 | − | 2.42290i | −0.00429512 | − | 0.0836975i | ||||
\(839\) | − | 33.7897i | − | 1.16655i | −0.812275 | − | 0.583275i | \(-0.801771\pi\) | ||
0.812275 | − | 0.583275i | \(-0.198229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.99618i | 0.172282i | ||||||||
\(842\) | −28.8369 | + | 1.47983i | −0.993787 | + | 0.0509983i | ||||
\(843\) | −2.10282 | + | 0.563449i | −0.0724249 | + | 0.0194062i | ||||
\(844\) | −12.5390 | − | 10.1991i | −0.431609 | − | 0.351067i | ||||
\(845\) | −22.6798 | − | 6.07705i | −0.780211 | − | 0.209057i | ||||
\(846\) | −1.31854 | + | 0.426834i | −0.0453323 | + | 0.0146749i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 17.1585 | − | 8.64888i | 0.589226 | − | 0.297004i | ||||
\(849\) | −1.64334 | − | 2.84635i | −0.0563993 | − | 0.0976865i | ||||
\(850\) | 9.88132 | − | 46.2406i | 0.338927 | − | 1.58604i | ||||
\(851\) | −1.05388 | − | 3.93313i | −0.0361265 | − | 0.134826i | ||||
\(852\) | −0.0157925 | − | 0.0414099i | −0.000541042 | − | 0.00141868i | ||||
\(853\) | −27.3617 | − | 27.3617i | −0.936845 | − | 0.936845i | 0.0612756 | − | 0.998121i | \(-0.480483\pi\) |
−0.998121 | + | 0.0612756i | \(0.980483\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.3551i | 0.867126i | ||||||||
\(856\) | −27.1956 | + | 21.8760i | −0.929528 | + | 0.747708i | ||||
\(857\) | 2.43604 | + | 1.40645i | 0.0832136 | + | 0.0480434i | 0.541029 | − | 0.841004i | \(-0.318035\pi\) |
−0.457816 | + | 0.889047i | \(0.651368\pi\) | |||||||
\(858\) | −1.60568 | + | 1.04026i | −0.0548171 | + | 0.0355139i | ||||
\(859\) | 9.66838 | − | 36.0829i | 0.329881 | − | 1.23113i | −0.579432 | − | 0.815020i | \(-0.696726\pi\) |
0.909313 | − | 0.416112i | \(-0.136608\pi\) | |||||||
\(860\) | 30.0130 | + | 41.4989i | 1.02343 | + | 1.41510i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.10071 | + | 12.6676i | 0.139671 | + | 0.431459i | ||||
\(863\) | 21.6095 | + | 37.4288i | 0.735597 | + | 1.27409i | 0.954461 | + | 0.298336i | \(0.0964317\pi\) |
−0.218864 | + | 0.975755i | \(0.570235\pi\) | |||||||
\(864\) | 3.52786 | − | 0.924753i | 0.120020 | − | 0.0314607i | ||||
\(865\) | −45.6291 | + | 79.0319i | −1.55144 | + | 2.68717i | ||||
\(866\) | 32.3881 | − | 35.8921i | 1.10059 | − | 1.21966i | ||||
\(867\) | −0.489962 | + | 0.489962i | −0.0166400 | + | 0.0166400i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.5562 | − | 13.5562i | −0.459862 | − | 0.459862i | ||||
\(870\) | 0.149474 | + | 2.91274i | 0.00506763 | + | 0.0987512i | ||||
\(871\) | 4.66986 | + | 2.69615i | 0.158232 | + | 0.0913554i | ||||
\(872\) | 6.88841 | − | 17.7714i | 0.233271 | − | 0.601814i | ||||
\(873\) | −32.8631 | + | 18.9735i | −1.11225 | + | 0.642157i | ||||
\(874\) | −10.0548 | + | 19.6807i | −0.340109 | + | 0.665711i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.43957 | − | 0.231216i | −0.0486385 | − | 0.00781208i | ||||
\(877\) | −9.87251 | − | 2.64533i | −0.333371 | − | 0.0893265i | 0.0882507 | − | 0.996098i | \(-0.471872\pi\) |
−0.421622 | + | 0.906772i | \(0.638539\pi\) | |||||||
\(878\) | 6.13998 | − | 28.7326i | 0.207214 | − | 0.969679i | ||||
\(879\) | 0.103832 | − | 0.179842i | 0.00350217 | − | 0.00606593i | ||||
\(880\) | −15.1329 | − | 72.7496i | −0.510130 | − | 2.45239i | ||||
\(881\) | 38.6974 | 1.30375 | 0.651875 | − | 0.758327i | \(-0.273983\pi\) | ||||
0.651875 | + | 0.758327i | \(0.273983\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.08807 | − | 9.08807i | 0.305838 | − | 0.305838i | −0.537455 | − | 0.843293i | \(-0.680614\pi\) |
0.843293 | + | 0.537455i | \(0.180614\pi\) | |||||||
\(884\) | −16.0635 | + | 6.12614i | −0.540274 | + | 0.206044i | ||||
\(885\) | −5.04577 | + | 1.35201i | −0.169612 | + | 0.0454473i | ||||
\(886\) | −3.79907 | − | 5.86401i | −0.127632 | − | 0.197005i | ||||
\(887\) | 20.3494 | − | 11.7487i | 0.683265 | − | 0.394483i | −0.117819 | − | 0.993035i | \(-0.537590\pi\) |
0.801084 | + | 0.598552i | \(0.204257\pi\) | |||||||
\(888\) | 0.138962 | + | 0.101656i | 0.00466326 | + | 0.00341136i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −41.2357 | − | 21.0671i | −1.38222 | − | 0.706172i | ||||
\(891\) | 10.9393 | − | 40.8260i | 0.366480 | − | 1.36772i | ||||
\(892\) | 0.743941 | + | 7.22938i | 0.0249090 | + | 0.242058i | ||||
\(893\) | 0.184178 | + | 0.687361i | 0.00616327 | + | 0.0230017i | ||||
\(894\) | −1.90160 | + | 2.10733i | −0.0635991 | + | 0.0704796i | ||||
\(895\) | −58.8424 | −1.96689 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.05052 | 0.0684648 | ||||||||
\(898\) | −15.4253 | + | 17.0942i | −0.514750 | + | 0.570439i | ||||
\(899\) | −12.1981 | − | 45.5238i | −0.406829 | − | 1.51831i | ||||
\(900\) | 6.29380 | + | 61.1611i | 0.209793 | + | 2.03870i | ||||
\(901\) | −4.04101 | + | 15.0813i | −0.134626 | + | 0.502430i | ||||
\(902\) | 2.54755 | + | 1.30154i | 0.0848243 | + | 0.0433364i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.1165 | − | 16.1791i | −0.735583 | − | 0.538108i | ||||
\(905\) | 16.9788 | − | 9.80272i | 0.564394 | − | 0.325853i | ||||
\(906\) | −0.134167 | − | 0.207092i | −0.00445740 | − | 0.00688016i | ||||
\(907\) | 18.5581 | − | 4.97263i | 0.616211 | − | 0.165113i | 0.0628064 | − | 0.998026i | \(-0.479995\pi\) |
0.553405 | + | 0.832912i | \(0.313328\pi\) | |||||||
\(908\) | −44.5207 | + | 16.9789i | −1.47747 | + | 0.563463i | ||||
\(909\) | −13.3329 | + | 13.3329i | −0.442226 | + | 0.442226i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.6476 | 0.352770 | 0.176385 | − | 0.984321i | \(-0.443560\pi\) | ||||
0.176385 | + | 0.984321i | \(0.443560\pi\) | |||||||
\(912\) | −0.190314 | − | 0.914913i | −0.00630193 | − | 0.0302958i | ||||
\(913\) | −22.6837 | + | 39.2894i | −0.750723 | + | 1.30029i | ||||
\(914\) | −7.20129 | + | 33.6991i | −0.238197 | + | 1.11467i | ||||
\(915\) | −3.39274 | − | 0.909082i | −0.112160 | − | 0.0300533i | ||||
\(916\) | 19.3371 | + | 3.10584i | 0.638917 | + | 0.102620i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.34824 | + | 2.63897i | −0.0444985 | + | 0.0870989i | ||||
\(919\) | 33.9084 | − | 19.5770i | 1.11854 | − | 0.645787i | 0.177509 | − | 0.984119i | \(-0.443196\pi\) |
0.941027 | + | 0.338332i | \(0.109863\pi\) | |||||||
\(920\) | −28.7829 | + | 74.2568i | −0.948943 | + | 2.44817i | ||||
\(921\) | 2.32593 | + | 1.34288i | 0.0766420 | + | 0.0442493i | ||||
\(922\) | 1.30091 | + | 25.3504i | 0.0428431 | + | 0.834869i | ||||
\(923\) | −0.384924 | − | 0.384924i | −0.0126699 | − | 0.0126699i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.11290 | + | 4.11290i | −0.135231 | + | 0.135231i | ||||
\(926\) | −18.8265 | + | 20.8633i | −0.618678 | + | 0.685611i | ||||
\(927\) | −21.2362 | + | 36.7821i | −0.697487 | + | 1.20808i | ||||
\(928\) | 7.02748 | + | 26.8093i | 0.230688 | + | 0.880057i | ||||
\(929\) | 28.6023 | + | 49.5406i | 0.938411 | + | 1.62538i | 0.768435 | + | 0.639927i | \(0.221036\pi\) |
0.169976 | + | 0.985448i | \(0.445631\pi\) | |||||||
\(930\) | 1.76365 | + | 5.44813i | 0.0578325 | + | 0.178651i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 30.7584 | + | 42.5296i | 1.00753 | + | 1.39310i | ||||
\(933\) | 0.771776 | − | 2.88031i | 0.0252668 | − | 0.0942971i | ||||
\(934\) | −19.2637 | + | 12.4802i | −0.630328 | + | 0.408366i | ||||
\(935\) | 52.2892 | + | 30.1892i | 1.71004 | + | 0.987292i | ||||
\(936\) | 17.4187 | − | 14.0115i | 0.569349 | − | 0.457981i | ||||
\(937\) | − | 23.0753i | − | 0.753837i | −0.926246 | − | 0.376919i | \(-0.876984\pi\) | ||
0.926246 | − | 0.376919i | \(-0.123016\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.375770 | − | 0.375770i | −0.0122628 | − | 0.0122628i | ||||
\(940\) | 0.913757 | + | 2.39598i | 0.0298035 | + | 0.0781484i | ||||
\(941\) | 6.29666 | + | 23.4995i | 0.205265 | + | 0.766060i | 0.989369 | + | 0.145430i | \(0.0464565\pi\) |
−0.784103 | + | 0.620630i | \(0.786877\pi\) | |||||||
\(942\) | −0.421211 | + | 1.97110i | −0.0137238 | + | 0.0642218i | ||||
\(943\) | −1.53305 | − | 2.65532i | −0.0499229 | − | 0.0864690i | ||||
\(944\) | −44.3266 | + | 22.3432i | −1.44271 | + | 0.727208i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −41.8681 | + | 13.5534i | −1.36125 | + | 0.440660i | ||||
\(947\) | 15.7694 | + | 4.22540i | 0.512436 | + | 0.137307i | 0.505766 | − | 0.862671i | \(-0.331210\pi\) |
0.00667058 | + | 0.999978i | \(0.497877\pi\) | |||||||
\(948\) | −0.674010 | − | 0.548235i | −0.0218908 | − | 0.0178058i | ||||
\(949\) | −17.2984 | + | 4.63509i | −0.561530 | + | 0.150461i | ||||
\(950\) | 31.5282 | − | 1.61794i | 1.02291 | − | 0.0524928i | ||||
\(951\) | − | 2.82216i | − | 0.0915148i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.30572i | 0.236656i | 0.992975 | + | 0.118328i | \(0.0377534\pi\) | ||||
−0.992975 | + | 0.118328i | \(0.962247\pi\) | |||||||
\(954\) | −1.04047 | − | 20.2752i | −0.0336863 | − | 0.656434i | ||||
\(955\) | −44.0865 | + | 11.8129i | −1.42660 | + | 0.382258i | ||||
\(956\) | −5.84934 | − | 56.8420i | −0.189181 | − | 1.83840i | ||||
\(957\) | −2.42073 | − | 0.648632i | −0.0782510 | − | 0.0209673i | ||||
\(958\) | −3.76935 | − | 11.6440i | −0.121782 | − | 0.376199i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.01969 | − | 3.20941i | −0.0329104 | − | 0.103583i | ||||
\(961\) | −30.7679 | − | 53.2916i | −0.992513 | − | 1.71908i | ||||
\(962\) | 2.06811 | + | 0.441943i | 0.0666787 | + | 0.0142488i | ||||
\(963\) | 9.54430 | + | 35.6198i | 0.307561 | + | 1.14783i | ||||
\(964\) | −30.1421 | − | 13.4988i | −0.970812 | − | 0.434766i | ||||
\(965\) | 24.0257 | + | 24.0257i | 0.773416 | + | 0.773416i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 32.6337i | − | 1.04943i | −0.851279 | − | 0.524714i | \(-0.824172\pi\) | ||
0.851279 | − | 0.524714i | \(-0.175828\pi\) | |||||||
\(968\) | 32.5463 | + | 3.52816i | 1.04608 | + | 0.113400i | ||||
\(969\) | 0.657599 | + | 0.379665i | 0.0211251 | + | 0.0121966i | ||||
\(970\) | 38.1765 | + | 58.9269i | 1.22577 | + | 1.89203i | ||||
\(971\) | −6.78495 | + | 25.3218i | −0.217740 | + | 0.812615i | 0.767445 | + | 0.641115i | \(0.221528\pi\) |
−0.985184 | + | 0.171500i | \(0.945139\pi\) | |||||||
\(972\) | 0.917200 | − | 5.71054i | 0.0294192 | − | 0.183166i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 34.6416 | − | 11.2141i | 1.10999 | − | 0.359323i | ||||
\(975\) | −1.46454 | − | 2.53667i | −0.0469030 | − | 0.0812383i | ||||
\(976\) | −33.3235 | − | 1.89183i | −1.06666 | − | 0.0605559i | ||||
\(977\) | 21.1362 | − | 36.6090i | 0.676207 | − | 1.17123i | −0.299907 | − | 0.953968i | \(-0.596956\pi\) |
0.976114 | − | 0.217257i | \(-0.0697109\pi\) | |||||||
\(978\) | −0.490649 | − | 0.442749i | −0.0156892 | − | 0.0141576i | ||||
\(979\) | 28.1350 | − | 28.1350i | 0.899199 | − | 0.899199i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.2395 | − | 14.2395i | −0.454633 | − | 0.454633i | ||||
\(982\) | −48.0892 | + | 2.46780i | −1.53459 | + | 0.0787506i | ||||
\(983\) | 34.0579 | + | 19.6634i | 1.08628 | + | 0.627164i | 0.932583 | − | 0.360954i | \(-0.117549\pi\) |
0.153696 | + | 0.988118i | \(0.450882\pi\) | |||||||
\(984\) | 0.120884 | + | 0.0468560i | 0.00385363 | + | 0.00149371i | ||||
\(985\) | −13.2845 | + | 7.66982i | −0.423280 | + | 0.244381i | ||||
\(986\) | −20.0543 | − | 10.2457i | −0.638659 | − | 0.326288i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.72656 | − | 9.30080i | −0.214000 | − | 0.295898i | ||||
\(989\) | 45.5585 | + | 12.2074i | 1.44867 | + | 0.388171i | ||||
\(990\) | −76.7764 | − | 16.4066i | −2.44012 | − | 0.521437i | ||||
\(991\) | 11.6473 | − | 20.1737i | 0.369988 | − | 0.640838i | −0.619575 | − | 0.784937i | \(-0.712695\pi\) |
0.989563 | + | 0.144099i | \(0.0460285\pi\) | |||||||
\(992\) | 26.9515 | + | 47.2733i | 0.855711 | + | 1.50093i | ||||
\(993\) | 0.336362 | 0.0106741 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35.3580 | + | 35.3580i | −1.12092 | + | 1.12092i | ||||
\(996\) | −0.840335 | + | 1.87643i | −0.0266270 | + | 0.0594569i | ||||
\(997\) | 44.4973 | − | 11.9230i | 1.40924 | − | 0.377606i | 0.527589 | − | 0.849500i | \(-0.323096\pi\) |
0.881656 | + | 0.471893i | \(0.156429\pi\) | |||||||
\(998\) | −11.1749 | + | 7.23981i | −0.353736 | + | 0.229172i | ||||
\(999\) | 0.315695 | − | 0.182267i | 0.00998816 | − | 0.00576667i |
(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 | 784.2.x.p.165.6 | 96 | ||
7.2 | even | 3 | inner | 784.2.x.p.373.23 | 96 | ||
7.3 | odd | 6 | 784.2.m.l.197.9 | ✓ | 48 | ||
7.4 | even | 3 | 784.2.m.l.197.10 | yes | 48 | ||
7.5 | odd | 6 | inner | 784.2.x.p.373.24 | 96 | ||
7.6 | odd | 2 | inner | 784.2.x.p.165.5 | 96 | ||
16.13 | even | 4 | inner | 784.2.x.p.557.23 | 96 | ||
112.13 | odd | 4 | inner | 784.2.x.p.557.24 | 96 | ||
112.45 | odd | 12 | 784.2.m.l.589.9 | yes | 48 | ||
112.61 | odd | 12 | inner | 784.2.x.p.765.5 | 96 | ||
112.93 | even | 12 | inner | 784.2.x.p.765.6 | 96 | ||
112.109 | even | 12 | 784.2.m.l.589.10 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.2.m.l.197.9 | ✓ | 48 | 7.3 | odd | 6 | ||
784.2.m.l.197.10 | yes | 48 | 7.4 | even | 3 | ||
784.2.m.l.589.9 | yes | 48 | 112.45 | odd | 12 | ||
784.2.m.l.589.10 | yes | 48 | 112.109 | even | 12 | ||
784.2.x.p.165.5 | 96 | 7.6 | odd | 2 | inner | ||
784.2.x.p.165.6 | 96 | 1.1 | even | 1 | trivial | ||
784.2.x.p.373.23 | 96 | 7.2 | even | 3 | inner | ||
784.2.x.p.373.24 | 96 | 7.5 | odd | 6 | inner | ||
784.2.x.p.557.23 | 96 | 16.13 | even | 4 | inner | ||
784.2.x.p.557.24 | 96 | 112.13 | odd | 4 | inner | ||
784.2.x.p.765.5 | 96 | 112.61 | odd | 12 | inner | ||
784.2.x.p.765.6 | 96 | 112.93 | even | 12 | inner |