Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(107,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.l (of order \(20\), degree \(8\), 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: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 107.7 | ||
Character | \(\chi\) | \(=\) | 750.107 |
Dual form | 750.2.l.c.743.7 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{13}{20}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.891007 | + | 0.453990i | 0.630037 | + | 0.321020i | ||||
\(3\) | −0.646378 | − | 1.60692i | −0.373187 | − | 0.927756i | ||||
\(4\) | 0.587785 | + | 0.809017i | 0.293893 | + | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.153600 | − | 1.72523i | 0.0627067 | − | 0.704321i | ||||
\(7\) | 2.03922 | + | 2.03922i | 0.770754 | + | 0.770754i | 0.978238 | − | 0.207484i | \(-0.0665276\pi\) |
−0.207484 | + | 0.978238i | \(0.566528\pi\) | |||||||
\(8\) | 0.156434 | + | 0.987688i | 0.0553079 | + | 0.349201i | ||||
\(9\) | −2.16439 | + | 2.07736i | −0.721463 | + | 0.692453i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.60836 | − | 0.847507i | 0.786450 | − | 0.255533i | 0.111858 | − | 0.993724i | \(-0.464320\pi\) |
0.674592 | + | 0.738191i | \(0.264320\pi\) | |||||||
\(12\) | 0.920095 | − | 1.46746i | 0.265608 | − | 0.423618i | ||||
\(13\) | 2.68521 | + | 5.27002i | 0.744744 | + | 1.46164i | 0.882071 | + | 0.471116i | \(0.156149\pi\) |
−0.137328 | + | 0.990526i | \(0.543851\pi\) | |||||||
\(14\) | 0.891173 | + | 2.74275i | 0.238176 | + | 0.733031i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | −5.91053 | + | 0.936136i | −1.43351 | + | 0.227046i | −0.824387 | − | 0.566026i | \(-0.808480\pi\) |
−0.609127 | + | 0.793073i | \(0.708480\pi\) | |||||||
\(18\) | −2.87159 | + | 0.868327i | −0.676839 | + | 0.204667i | ||||
\(19\) | 3.04743 | − | 4.19443i | 0.699129 | − | 0.962269i | −0.300834 | − | 0.953677i | \(-0.597265\pi\) |
0.999963 | − | 0.00859233i | \(-0.00273506\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.95876 | − | 4.59498i | 0.427437 | − | 1.00271i | ||||
\(22\) | 2.70883 | + | 0.429036i | 0.577523 | + | 0.0914707i | ||||
\(23\) | −0.515607 | + | 1.01194i | −0.107512 | + | 0.211003i | −0.938494 | − | 0.345295i | \(-0.887779\pi\) |
0.830983 | + | 0.556298i | \(0.187779\pi\) | |||||||
\(24\) | 1.48602 | − | 0.889798i | 0.303333 | − | 0.181629i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.91469i | 1.15997i | ||||||||
\(27\) | 4.73716 | + | 2.13524i | 0.911668 | + | 0.410928i | ||||
\(28\) | −0.451141 | + | 2.84839i | −0.0852576 | + | 0.538296i | ||||
\(29\) | 2.34612 | − | 1.70456i | 0.435664 | − | 0.316528i | −0.348246 | − | 0.937403i | \(-0.613223\pi\) |
0.783910 | + | 0.620875i | \(0.213223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.56563 | + | 3.31712i | 0.820011 | + | 0.595773i | 0.916716 | − | 0.399540i | \(-0.130830\pi\) |
−0.0967046 | + | 0.995313i | \(0.530830\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −3.04786 | − | 3.64362i | −0.530565 | − | 0.634272i | ||||
\(34\) | −5.69132 | − | 1.84922i | −0.976053 | − | 0.317139i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.95281 | − | 0.529988i | −0.492136 | − | 0.0883313i | ||||
\(37\) | 7.18975 | − | 3.66336i | 1.18199 | − | 0.602253i | 0.251243 | − | 0.967924i | \(-0.419161\pi\) |
0.930744 | + | 0.365671i | \(0.119161\pi\) | |||||||
\(38\) | 4.61952 | − | 2.35376i | 0.749384 | − | 0.381830i | ||||
\(39\) | 6.73285 | − | 7.72135i | 1.07812 | − | 1.23641i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.02666 | + | 1.63326i | 0.785033 | + | 0.255073i | 0.673988 | − | 0.738743i | \(-0.264580\pi\) |
0.111045 | + | 0.993815i | \(0.464580\pi\) | |||||||
\(42\) | 3.83135 | − | 3.20490i | 0.591190 | − | 0.494527i | ||||
\(43\) | −3.10789 | + | 3.10789i | −0.473950 | + | 0.473950i | −0.903190 | − | 0.429241i | \(-0.858781\pi\) |
0.429241 | + | 0.903190i | \(0.358781\pi\) | |||||||
\(44\) | 2.21880 | + | 1.61205i | 0.334497 | + | 0.243026i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.918819 | + | 0.667561i | −0.135473 | + | 0.0984265i | ||||
\(47\) | 0.726167 | − | 4.58484i | 0.105922 | − | 0.668768i | −0.876402 | − | 0.481581i | \(-0.840063\pi\) |
0.982324 | − | 0.187187i | \(-0.0599371\pi\) | |||||||
\(48\) | 1.72801 | − | 0.118176i | 0.249417 | − | 0.0170573i | ||||
\(49\) | 1.31687i | 0.188124i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.32473 | + | 8.89266i | 0.745612 | + | 1.24522i | ||||
\(52\) | −2.68521 | + | 5.27002i | −0.372372 | + | 0.730821i | ||||
\(53\) | −5.29057 | − | 0.837944i | −0.726715 | − | 0.115100i | −0.217894 | − | 0.975972i | \(-0.569919\pi\) |
−0.508821 | + | 0.860872i | \(0.669919\pi\) | |||||||
\(54\) | 3.25146 | + | 4.05314i | 0.442468 | + | 0.551563i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.69511 | + | 2.33312i | −0.226519 | + | 0.311777i | ||||
\(57\) | −8.70992 | − | 2.18579i | −1.15366 | − | 0.289516i | ||||
\(58\) | 2.86426 | − | 0.453655i | 0.376096 | − | 0.0595678i | ||||
\(59\) | −0.912145 | + | 2.80729i | −0.118751 | + | 0.365478i | −0.992711 | − | 0.120520i | \(-0.961544\pi\) |
0.873960 | + | 0.485998i | \(0.161544\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.41844 | − | 4.36552i | −0.181613 | − | 0.558947i | 0.818261 | − | 0.574847i | \(-0.194939\pi\) |
−0.999874 | + | 0.0159002i | \(0.994939\pi\) | |||||||
\(62\) | 2.56206 | + | 5.02833i | 0.325382 | + | 0.638599i | ||||
\(63\) | −8.64987 | − | 0.177478i | −1.08978 | − | 0.0223601i | ||||
\(64\) | −0.951057 | + | 0.309017i | −0.118882 | + | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.06150 | − | 4.63019i | −0.130662 | − | 0.569937i | ||||
\(67\) | −0.0721944 | − | 0.455818i | −0.00881995 | − | 0.0556870i | 0.982886 | − | 0.184216i | \(-0.0589745\pi\) |
−0.991706 | + | 0.128529i | \(0.958975\pi\) | |||||||
\(68\) | −4.23147 | − | 4.23147i | −0.513141 | − | 0.513141i | ||||
\(69\) | 1.95938 | + | 0.174447i | 0.235882 | + | 0.0210009i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.36294 | − | 4.62869i | −0.399107 | − | 0.549324i | 0.561412 | − | 0.827536i | \(-0.310258\pi\) |
−0.960520 | + | 0.278212i | \(0.910258\pi\) | |||||||
\(72\) | −2.39037 | − | 1.81277i | −0.281707 | − | 0.213637i | ||||
\(73\) | −8.09812 | − | 4.12620i | −0.947814 | − | 0.482935i | −0.0894583 | − | 0.995991i | \(-0.528514\pi\) |
−0.858356 | + | 0.513055i | \(0.828514\pi\) | |||||||
\(74\) | 8.06924 | 0.938031 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.18460 | 0.594715 | ||||||||
\(77\) | 7.04728 | + | 3.59077i | 0.803113 | + | 0.409206i | ||||
\(78\) | 9.50443 | − | 3.82312i | 1.07617 | − | 0.432884i | ||||
\(79\) | −6.90557 | − | 9.50470i | −0.776937 | − | 1.06936i | −0.995613 | − | 0.0935650i | \(-0.970174\pi\) |
0.218676 | − | 0.975798i | \(-0.429826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.369168 | − | 8.99243i | 0.0410187 | − | 0.999158i | ||||
\(82\) | 3.73730 | + | 3.73730i | 0.412716 | + | 0.412716i | ||||
\(83\) | 1.88912 | + | 11.9275i | 0.207358 | + | 1.30921i | 0.843288 | + | 0.537462i | \(0.180617\pi\) |
−0.635930 | + | 0.771747i | \(0.719383\pi\) | |||||||
\(84\) | 4.86875 | − | 1.11619i | 0.531224 | − | 0.121786i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.18011 | + | 1.35820i | −0.450753 | + | 0.146458i | ||||
\(87\) | −4.25557 | − | 2.66824i | −0.456245 | − | 0.286066i | ||||
\(88\) | 1.24511 | + | 2.44367i | 0.132729 | + | 0.260496i | ||||
\(89\) | 0.402182 | + | 1.23779i | 0.0426312 | + | 0.131205i | 0.970107 | − | 0.242678i | \(-0.0780260\pi\) |
−0.927476 | + | 0.373884i | \(0.878026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.27101 | + | 16.2225i | −0.552552 | + | 1.70058i | ||||
\(92\) | −1.12174 | + | 0.177666i | −0.116950 | + | 0.0185230i | ||||
\(93\) | 2.37923 | − | 9.48072i | 0.246715 | − | 0.983105i | ||||
\(94\) | 2.72849 | − | 3.75545i | 0.281423 | − | 0.387345i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.59332 | + | 0.679206i | 0.162618 | + | 0.0693212i | ||||
\(97\) | 6.52722 | + | 1.03381i | 0.662738 | + | 0.104967i | 0.478737 | − | 0.877959i | \(-0.341095\pi\) |
0.184002 | + | 0.982926i | \(0.441095\pi\) | |||||||
\(98\) | −0.597845 | + | 1.17334i | −0.0603915 | + | 0.118525i | ||||
\(99\) | −3.88493 | + | 7.25283i | −0.390450 | + | 0.728937i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 3.52971i | − | 0.351219i | −0.984460 | − | 0.175610i | \(-0.943810\pi\) | ||
0.984460 | − | 0.175610i | \(-0.0561896\pi\) | |||||||
\(102\) | 0.707192 | + | 10.3408i | 0.0700225 | + | 1.02389i | ||||
\(103\) | −1.00941 | + | 6.37316i | −0.0994601 | + | 0.627966i | 0.886722 | + | 0.462303i | \(0.152977\pi\) |
−0.986182 | + | 0.165664i | \(0.947023\pi\) | |||||||
\(104\) | −4.78508 | + | 3.47657i | −0.469216 | + | 0.340905i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.33351 | − | 3.14848i | −0.420908 | − | 0.305807i | ||||
\(107\) | −8.76915 | + | 8.76915i | −0.847745 | + | 0.847745i | −0.989851 | − | 0.142106i | \(-0.954613\pi\) |
0.142106 | + | 0.989851i | \(0.454613\pi\) | |||||||
\(108\) | 1.05699 | + | 5.08751i | 0.101709 | + | 0.489546i | ||||
\(109\) | −2.65577 | − | 0.862912i | −0.254377 | − | 0.0826520i | 0.179053 | − | 0.983839i | \(-0.442697\pi\) |
−0.433430 | + | 0.901187i | \(0.642697\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.5340 | − | 9.18544i | −0.999846 | − | 0.871844i | ||||
\(112\) | −2.56957 | + | 1.30926i | −0.242802 | + | 0.123714i | ||||
\(113\) | −4.11863 | + | 2.09855i | −0.387449 | + | 0.197415i | −0.636854 | − | 0.770984i | \(-0.719765\pi\) |
0.249406 | + | 0.968399i | \(0.419765\pi\) | |||||||
\(114\) | −6.76826 | − | 5.90178i | −0.633906 | − | 0.552752i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.75803 | + | 0.896139i | 0.256077 | + | 0.0832044i | ||||
\(117\) | −16.7596 | − | 5.82824i | −1.54942 | − | 0.538821i | ||||
\(118\) | −2.08721 | + | 2.08721i | −0.192143 | + | 0.192143i | ||||
\(119\) | −13.9619 | − | 10.1439i | −1.27988 | − | 0.929890i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.81392 | + | 2.04443i | −0.255811 | + | 0.185857i | ||||
\(122\) | 0.718062 | − | 4.53366i | 0.0650103 | − | 0.410459i | ||||
\(123\) | −0.624604 | − | 9.13316i | −0.0563186 | − | 0.823509i | ||||
\(124\) | 5.64343i | 0.506795i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.62652 | − | 4.08509i | −0.679424 | − | 0.363929i | ||||
\(127\) | −5.68850 | + | 11.1643i | −0.504773 | + | 0.990672i | 0.488245 | + | 0.872707i | \(0.337637\pi\) |
−0.993018 | + | 0.117966i | \(0.962363\pi\) | |||||||
\(128\) | −0.987688 | − | 0.156434i | −0.0873001 | − | 0.0138270i | ||||
\(129\) | 7.00302 | + | 2.98527i | 0.616581 | + | 0.262838i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.00579 | − | 9.64264i | 0.612099 | − | 0.842482i | −0.384649 | − | 0.923063i | \(-0.625678\pi\) |
0.996748 | + | 0.0805811i | \(0.0256776\pi\) | |||||||
\(132\) | 1.15626 | − | 4.60744i | 0.100639 | − | 0.401026i | ||||
\(133\) | 14.7678 | − | 2.33899i | 1.28053 | − | 0.202816i | ||||
\(134\) | 0.142611 | − | 0.438912i | 0.0123197 | − | 0.0379162i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.84922 | − | 5.69132i | −0.158569 | − | 0.488026i | ||||
\(137\) | −9.02083 | − | 17.7044i | −0.770702 | − | 1.51259i | −0.856427 | − | 0.516268i | \(-0.827321\pi\) |
0.0857255 | − | 0.996319i | \(-0.472679\pi\) | |||||||
\(138\) | 1.66662 | + | 1.04497i | 0.141872 | + | 0.0889540i | ||||
\(139\) | −9.07922 | + | 2.95002i | −0.770090 | + | 0.250217i | −0.667603 | − | 0.744517i | \(-0.732680\pi\) |
−0.102486 | + | 0.994734i | \(0.532680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.83686 | + | 1.79665i | −0.659982 | + | 0.151305i | ||||
\(142\) | −0.895020 | − | 5.65093i | −0.0751084 | − | 0.474216i | ||||
\(143\) | 11.4704 | + | 11.4704i | 0.959201 | + | 0.959201i | ||||
\(144\) | −1.30685 | − | 2.70040i | −0.108904 | − | 0.225033i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.34223 | − | 7.35294i | −0.442126 | − | 0.608534i | ||||
\(147\) | 2.11610 | − | 0.851194i | 0.174533 | − | 0.0702053i | ||||
\(148\) | 7.18975 | + | 3.66336i | 0.590994 | + | 0.301126i | ||||
\(149\) | −12.0089 | −0.983807 | −0.491903 | − | 0.870650i | \(-0.663699\pi\) | ||||
−0.491903 | + | 0.870650i | \(0.663699\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1277 | −0.905558 | −0.452779 | − | 0.891623i | \(-0.649567\pi\) | ||||
−0.452779 | + | 0.891623i | \(0.649567\pi\) | |||||||
\(152\) | 4.61952 | + | 2.35376i | 0.374692 | + | 0.190915i | ||||
\(153\) | 10.8480 | − | 14.3044i | 0.877009 | − | 1.15645i | ||||
\(154\) | 4.64900 | + | 6.39880i | 0.374627 | + | 0.515630i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.2042 | + | 0.908493i | 0.816988 | + | 0.0727376i | ||||
\(157\) | −11.6119 | − | 11.6119i | −0.926732 | − | 0.926732i | 0.0707617 | − | 0.997493i | \(-0.477457\pi\) |
−0.997493 | + | 0.0707617i | \(0.977457\pi\) | |||||||
\(158\) | −1.83786 | − | 11.6038i | −0.146213 | − | 0.923150i | ||||
\(159\) | 2.07320 | + | 9.04315i | 0.164415 | + | 0.717169i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.11500 | + | 1.01213i | −0.245497 | + | 0.0797667i | ||||
\(162\) | 4.41141 | − | 7.84471i | 0.346593 | − | 0.616339i | ||||
\(163\) | −2.97400 | − | 5.83680i | −0.232941 | − | 0.457173i | 0.744715 | − | 0.667383i | \(-0.232585\pi\) |
−0.977656 | + | 0.210209i | \(0.932585\pi\) | |||||||
\(164\) | 1.63326 | + | 5.02666i | 0.127536 | + | 0.392516i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.73173 | + | 11.4851i | −0.289639 | + | 0.891416i | ||||
\(167\) | 16.7884 | − | 2.65903i | 1.29913 | − | 0.205762i | 0.531720 | − | 0.846920i | \(-0.321546\pi\) |
0.767408 | + | 0.641159i | \(0.221546\pi\) | |||||||
\(168\) | 4.84483 | + | 1.21583i | 0.373787 | + | 0.0938035i | ||||
\(169\) | −12.9216 | + | 17.7850i | −0.993968 | + | 1.36808i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.11750 | + | 15.4090i | 0.161929 | + | 1.17836i | ||||
\(172\) | −4.34111 | − | 0.687565i | −0.331007 | − | 0.0524263i | ||||
\(173\) | 3.08240 | − | 6.04954i | 0.234350 | − | 0.459938i | −0.743642 | − | 0.668578i | \(-0.766903\pi\) |
0.977993 | + | 0.208639i | \(0.0669035\pi\) | |||||||
\(174\) | −2.58038 | − | 4.30941i | −0.195618 | − | 0.326696i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.74259i | 0.206731i | ||||||||
\(177\) | 5.10069 | − | 0.348829i | 0.383391 | − | 0.0262196i | ||||
\(178\) | −0.203597 | + | 1.28546i | −0.0152603 | + | 0.0963496i | ||||
\(179\) | 7.59016 | − | 5.51457i | 0.567315 | − | 0.412179i | −0.266814 | − | 0.963748i | \(-0.585971\pi\) |
0.834129 | + | 0.551569i | \(0.185971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.3025 | + | 8.93831i | 0.914440 | + | 0.664379i | 0.942134 | − | 0.335237i | \(-0.108816\pi\) |
−0.0276940 | + | 0.999616i | \(0.508816\pi\) | |||||||
\(182\) | −12.0614 | + | 12.0614i | −0.894048 | + | 0.894048i | ||||
\(183\) | −6.09819 | + | 5.10110i | −0.450791 | + | 0.377084i | ||||
\(184\) | −1.08014 | − | 0.350958i | −0.0796287 | − | 0.0258729i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.42407 | − | 7.36724i | 0.471036 | − | 0.540192i | ||||
\(187\) | −14.6234 | + | 7.45099i | −1.06937 | + | 0.544871i | ||||
\(188\) | 4.13604 | − | 2.10742i | 0.301652 | − | 0.153699i | ||||
\(189\) | 5.30590 | + | 14.0144i | 0.385947 | + | 1.01940i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.2756 | + | 3.98859i | 0.888232 | + | 0.288604i | 0.717371 | − | 0.696691i | \(-0.245345\pi\) |
0.170861 | + | 0.985295i | \(0.445345\pi\) | |||||||
\(192\) | 1.11131 | + | 1.32853i | 0.0802018 | + | 0.0958784i | ||||
\(193\) | 3.91447 | − | 3.91447i | 0.281770 | − | 0.281770i | −0.552045 | − | 0.833815i | \(-0.686152\pi\) |
0.833815 | + | 0.552045i | \(0.186152\pi\) | |||||||
\(194\) | 5.34645 | + | 3.88442i | 0.383853 | + | 0.278885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.06537 | + | 0.774035i | −0.0760977 | + | 0.0552882i | ||||
\(197\) | 4.00150 | − | 25.2645i | 0.285095 | − | 1.80002i | −0.264282 | − | 0.964445i | \(-0.585135\pi\) |
0.549378 | − | 0.835574i | \(-0.314865\pi\) | |||||||
\(198\) | −6.75421 | + | 4.69860i | −0.480001 | + | 0.333915i | ||||
\(199\) | 0.0768328i | 0.00544653i | 0.999996 | + | 0.00272327i | \(0.000866844\pi\) | ||||
−0.999996 | + | 0.00272327i | \(0.999133\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.685798 | + | 0.410641i | −0.0483725 | + | 0.0289644i | ||||
\(202\) | 1.60245 | − | 3.14499i | 0.112748 | − | 0.221281i | ||||
\(203\) | 8.26024 | + | 1.30829i | 0.579755 | + | 0.0918242i | ||||
\(204\) | −4.06451 | + | 9.53477i | −0.284573 | + | 0.667568i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.79275 | + | 5.22027i | −0.264253 | + | 0.363713i | ||||
\(207\) | −0.986179 | − | 3.26133i | −0.0685442 | − | 0.226678i | ||||
\(208\) | −5.84187 | + | 0.925261i | −0.405061 | + | 0.0641553i | ||||
\(209\) | 4.39399 | − | 13.5233i | 0.303939 | − | 0.935427i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.99342 | + | 6.13511i | 0.137232 | + | 0.422358i | 0.995931 | − | 0.0901236i | \(-0.0287262\pi\) |
−0.858698 | + | 0.512482i | \(0.828726\pi\) | |||||||
\(212\) | −2.43181 | − | 4.77269i | −0.167017 | − | 0.327790i | ||||
\(213\) | −5.26420 | + | 8.39586i | −0.360697 | + | 0.575275i | ||||
\(214\) | −11.7945 | + | 3.83226i | −0.806254 | + | 0.261968i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.36790 | + | 5.01287i | −0.0930738 | + | 0.341082i | ||||
\(217\) | 2.54598 | + | 16.0747i | 0.172832 | + | 1.09122i | ||||
\(218\) | −1.97456 | − | 1.97456i | −0.133734 | − | 0.133734i | ||||
\(219\) | −1.39603 | + | 15.6801i | −0.0943347 | + | 1.05957i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.8045 | − | 28.6349i | −1.39946 | − | 1.92619i | ||||
\(222\) | −5.21578 | − | 12.9666i | −0.350061 | − | 0.870264i | ||||
\(223\) | 4.84642 | + | 2.46937i | 0.324540 | + | 0.165362i | 0.608668 | − | 0.793425i | \(-0.291704\pi\) |
−0.284128 | + | 0.958786i | \(0.591704\pi\) | |||||||
\(224\) | −2.88390 | −0.192689 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.62245 | −0.307481 | ||||||||
\(227\) | 17.4834 | + | 8.90823i | 1.16041 | + | 0.591260i | 0.924750 | − | 0.380575i | \(-0.124274\pi\) |
0.235662 | + | 0.971835i | \(0.424274\pi\) | |||||||
\(228\) | −3.35122 | − | 8.33125i | −0.221940 | − | 0.551750i | ||||
\(229\) | −10.2833 | − | 14.1538i | −0.679543 | − | 0.935310i | 0.320385 | − | 0.947287i | \(-0.396188\pi\) |
−0.999928 | + | 0.0119768i | \(0.996188\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.21487 | − | 13.6454i | 0.0799327 | − | 0.897803i | ||||
\(232\) | 2.05059 | + | 2.05059i | 0.134628 | + | 0.134628i | ||||
\(233\) | −4.54007 | − | 28.6649i | −0.297430 | − | 1.87790i | −0.455148 | − | 0.890416i | \(-0.650414\pi\) |
0.157718 | − | 0.987484i | \(-0.449586\pi\) | |||||||
\(234\) | −12.2869 | − | 12.8017i | −0.803221 | − | 0.836872i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.80729 | + | 0.912145i | −0.182739 | + | 0.0593756i | ||||
\(237\) | −10.8097 | + | 17.2403i | −0.702165 | + | 1.11988i | ||||
\(238\) | −7.83489 | − | 15.3768i | −0.507861 | − | 0.996733i | ||||
\(239\) | −1.74681 | − | 5.37613i | −0.112992 | − | 0.347753i | 0.878531 | − | 0.477685i | \(-0.158524\pi\) |
−0.991523 | + | 0.129932i | \(0.958524\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.35617 | − | 13.4069i | 0.280605 | − | 0.863614i | −0.707076 | − | 0.707137i | \(-0.749986\pi\) |
0.987682 | − | 0.156477i | \(-0.0500137\pi\) | |||||||
\(242\) | −3.43537 | + | 0.544110i | −0.220834 | + | 0.0349767i | ||||
\(243\) | −14.6887 | + | 5.21929i | −0.942283 | + | 0.334817i | ||||
\(244\) | 2.69804 | − | 3.71353i | 0.172724 | − | 0.237734i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.58984 | − | 8.42127i | 0.228880 | − | 0.536920i | ||||
\(247\) | 30.2878 | + | 4.79711i | 1.92716 | + | 0.305233i | ||||
\(248\) | −2.56206 | + | 5.02833i | −0.162691 | + | 0.319299i | ||||
\(249\) | 17.9454 | − | 10.7453i | 1.13724 | − | 0.680957i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.3182i | 1.09311i | 0.837422 | + | 0.546557i | \(0.184062\pi\) | ||||
−0.837422 | + | 0.546557i | \(0.815938\pi\) | |||||||
\(252\) | −4.94069 | − | 7.10221i | −0.311234 | − | 0.447397i | ||||
\(253\) | −0.487266 | + | 3.07648i | −0.0306341 | + | 0.193416i | ||||
\(254\) | −10.1370 | + | 7.36495i | −0.636051 | + | 0.462118i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 4.28914 | − | 4.28914i | 0.267549 | − | 0.267549i | −0.560563 | − | 0.828112i | \(-0.689415\pi\) |
0.828112 | + | 0.560563i | \(0.189415\pi\) | |||||||
\(258\) | 4.88445 | + | 5.83919i | 0.304093 | + | 0.363532i | ||||
\(259\) | 22.1319 | + | 7.19110i | 1.37521 | + | 0.446833i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.53695 | + | 8.56306i | −0.0951347 | + | 0.530040i | ||||
\(262\) | 10.6199 | − | 5.41110i | 0.656098 | − | 0.334299i | ||||
\(263\) | 21.2757 | − | 10.8405i | 1.31191 | − | 0.668454i | 0.348711 | − | 0.937230i | \(-0.386619\pi\) |
0.963203 | + | 0.268777i | \(0.0866193\pi\) | |||||||
\(264\) | 3.12197 | − | 3.58033i | 0.192144 | − | 0.220354i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.2201 | + | 4.62038i | 0.871889 | + | 0.283294i | ||||
\(267\) | 1.72907 | − | 1.44635i | 0.105817 | − | 0.0885154i | ||||
\(268\) | 0.326329 | − | 0.326329i | 0.0199337 | − | 0.0199337i | ||||
\(269\) | 11.2436 | + | 8.16896i | 0.685535 | + | 0.498070i | 0.875189 | − | 0.483781i | \(-0.160737\pi\) |
−0.189654 | + | 0.981851i | \(0.560737\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1633 | − | 8.83716i | 0.738868 | − | 0.536819i | −0.153488 | − | 0.988151i | \(-0.549051\pi\) |
0.892357 | + | 0.451331i | \(0.149051\pi\) | |||||||
\(272\) | 0.936136 | − | 5.91053i | 0.0567616 | − | 0.358378i | ||||
\(273\) | 29.4753 | − | 2.01578i | 1.78393 | − | 0.122000i | ||||
\(274\) | − | 19.8701i | − | 1.20040i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.01056 | + | 1.68771i | 0.0608288 | + | 0.101588i | ||||
\(277\) | 0.823495 | − | 1.61620i | 0.0494790 | − | 0.0971080i | −0.864943 | − | 0.501870i | \(-0.832646\pi\) |
0.914422 | + | 0.404762i | \(0.132646\pi\) | |||||||
\(278\) | −9.42893 | − | 1.49340i | −0.565509 | − | 0.0895679i | ||||
\(279\) | −16.7727 | + | 2.30490i | −1.00415 | + | 0.137991i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.4707 | + | 18.5409i | −0.803597 | + | 1.10606i | 0.188683 | + | 0.982038i | \(0.439578\pi\) |
−0.992280 | + | 0.124018i | \(0.960422\pi\) | |||||||
\(282\) | −7.79835 | − | 1.95703i | −0.464385 | − | 0.116540i | ||||
\(283\) | −2.81001 | + | 0.445062i | −0.167038 | + | 0.0264562i | −0.239393 | − | 0.970923i | \(-0.576948\pi\) |
0.0723553 | + | 0.997379i | \(0.476948\pi\) | |||||||
\(284\) | 1.76800 | − | 5.44135i | 0.104912 | − | 0.322885i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.01274 | + | 15.4276i | 0.296409 | + | 0.912255i | ||||
\(287\) | 6.91991 | + | 13.5811i | 0.408469 | + | 0.801666i | ||||
\(288\) | 0.0615410 | − | 2.99937i | 0.00362634 | − | 0.176739i | ||||
\(289\) | 17.8900 | − | 5.81283i | 1.05236 | − | 0.341931i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.55780 | − | 11.1570i | −0.149941 | − | 0.654032i | ||||
\(292\) | −1.42179 | − | 8.97684i | −0.0832041 | − | 0.525330i | ||||
\(293\) | 9.44461 | + | 9.44461i | 0.551760 | + | 0.551760i | 0.926948 | − | 0.375189i | \(-0.122422\pi\) |
−0.375189 | + | 0.926948i | \(0.622422\pi\) | |||||||
\(294\) | 2.27189 | + | 0.202270i | 0.132500 | + | 0.0117966i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.74298 | + | 6.52816i | 0.275680 | + | 0.379441i | ||||
\(297\) | 14.1659 | + | 1.55470i | 0.821987 | + | 0.0902130i | ||||
\(298\) | −10.7000 | − | 5.45192i | −0.619834 | − | 0.315821i | ||||
\(299\) | −6.71745 | −0.388480 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.6754 | −0.730597 | ||||||||
\(302\) | −9.91484 | − | 5.05186i | −0.570535 | − | 0.290702i | ||||
\(303\) | −5.67196 | + | 2.28153i | −0.325846 | + | 0.131070i | ||||
\(304\) | 3.04743 | + | 4.19443i | 0.174782 | + | 0.240567i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 16.1597 | − | 7.82047i | 0.923790 | − | 0.447066i | ||||
\(307\) | −23.1889 | − | 23.1889i | −1.32346 | − | 1.32346i | −0.910955 | − | 0.412506i | \(-0.864654\pi\) |
−0.412506 | − | 0.910955i | \(-0.635346\pi\) | |||||||
\(308\) | 1.23730 | + | 7.81197i | 0.0705014 | + | 0.445129i | ||||
\(309\) | 10.8936 | − | 2.49743i | 0.619717 | − | 0.142074i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.84506 | + | 3.19885i | −0.558262 | + | 0.181390i | −0.574539 | − | 0.818477i | \(-0.694819\pi\) |
0.0162770 | + | 0.999868i | \(0.494819\pi\) | |||||||
\(312\) | 8.67954 | + | 5.44207i | 0.491382 | + | 0.308097i | ||||
\(313\) | 6.22820 | + | 12.2235i | 0.352039 | + | 0.690915i | 0.997330 | − | 0.0730212i | \(-0.0232641\pi\) |
−0.645292 | + | 0.763936i | \(0.723264\pi\) | |||||||
\(314\) | −5.07459 | − | 15.6180i | −0.286376 | − | 0.881374i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.63047 | − | 11.1734i | 0.204230 | − | 0.628556i | ||||
\(317\) | −18.6415 | + | 2.95253i | −1.04701 | + | 0.165830i | −0.656159 | − | 0.754623i | \(-0.727820\pi\) |
−0.390853 | + | 0.920453i | \(0.627820\pi\) | |||||||
\(318\) | −2.25827 | + | 8.99872i | −0.126638 | + | 0.504623i | ||||
\(319\) | 4.67490 | − | 6.43445i | 0.261744 | − | 0.360260i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.7595 | + | 8.42314i | 1.10287 | + | 0.470134i | ||||
\(322\) | −3.23498 | − | 0.512371i | −0.180279 | − | 0.0285533i | ||||
\(323\) | −14.0854 | + | 27.6441i | −0.783732 | + | 1.53816i | ||||
\(324\) | 7.49202 | − | 4.98695i | 0.416223 | − | 0.277053i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 6.55079i | − | 0.362815i | ||||||
\(327\) | 0.330001 | + | 4.82538i | 0.0182491 | + | 0.266844i | ||||
\(328\) | −0.826810 | + | 5.22028i | −0.0456530 | + | 0.288241i | ||||
\(329\) | 10.8303 | − | 7.86870i | 0.597096 | − | 0.433815i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.6753 | − | 18.6542i | −1.41124 | − | 1.02533i | −0.993141 | − | 0.116926i | \(-0.962696\pi\) |
−0.418100 | − | 0.908401i | \(-0.637304\pi\) | |||||||
\(332\) | −8.53912 | + | 8.53912i | −0.468645 | + | 0.468645i | ||||
\(333\) | −7.95131 | + | 22.8646i | −0.435729 | + | 1.25297i | ||||
\(334\) | 16.1658 | + | 5.25258i | 0.884552 | + | 0.287408i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.76480 | + | 3.28282i | 0.205386 | + | 0.179093i | ||||
\(337\) | 14.3569 | − | 7.31518i | 0.782068 | − | 0.398483i | −0.0169001 | − | 0.999857i | \(-0.505380\pi\) |
0.798968 | + | 0.601374i | \(0.205380\pi\) | |||||||
\(338\) | −19.5874 | + | 9.98030i | −1.06542 | + | 0.542857i | ||||
\(339\) | 6.03440 | + | 5.26186i | 0.327744 | + | 0.285785i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.7201 | + | 4.78284i | 0.797137 | + | 0.259006i | ||||
\(342\) | −5.10883 | + | 14.6908i | −0.276254 | + | 0.794390i | ||||
\(343\) | 11.5892 | − | 11.5892i | 0.625757 | − | 0.625757i | ||||
\(344\) | −3.55581 | − | 2.58345i | −0.191717 | − | 0.139290i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.49287 | − | 3.99080i | 0.295299 | − | 0.214547i | ||||
\(347\) | −3.74283 | + | 23.6313i | −0.200925 | + | 1.26859i | 0.656634 | + | 0.754209i | \(0.271980\pi\) |
−0.857560 | + | 0.514384i | \(0.828020\pi\) | |||||||
\(348\) | −0.342708 | − | 5.01118i | −0.0183711 | − | 0.268628i | ||||
\(349\) | 24.8956i | 1.33263i | 0.745670 | + | 0.666315i | \(0.232129\pi\) | ||||
−0.745670 | + | 0.666315i | \(0.767871\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.46750 | + | 30.6986i | 0.0783293 | + | 1.63857i | ||||
\(352\) | −1.24511 | + | 2.44367i | −0.0663646 | + | 0.130248i | ||||
\(353\) | −16.7047 | − | 2.64576i | −0.889101 | − | 0.140820i | −0.304857 | − | 0.952398i | \(-0.598609\pi\) |
−0.584244 | + | 0.811578i | \(0.698609\pi\) | |||||||
\(354\) | 4.70311 | + | 2.00485i | 0.249968 | + | 0.106557i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.764995 | + | 1.05293i | −0.0405447 | + | 0.0558049i | ||||
\(357\) | −7.27579 | + | 28.9924i | −0.385076 | + | 1.53444i | ||||
\(358\) | 9.26645 | − | 1.46766i | 0.489747 | − | 0.0775683i | ||||
\(359\) | −1.67961 | + | 5.16932i | −0.0886466 | + | 0.272826i | −0.985546 | − | 0.169409i | \(-0.945814\pi\) |
0.896899 | + | 0.442235i | \(0.145814\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.43509 | − | 7.49444i | −0.128163 | − | 0.394444i | ||||
\(362\) | 6.90373 | + | 13.5493i | 0.362852 | + | 0.712137i | ||||
\(363\) | 5.10410 | + | 3.20027i | 0.267896 | + | 0.167971i | ||||
\(364\) | −16.2225 | + | 5.27101i | −0.850290 | + | 0.276276i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.74938 | + | 1.77659i | −0.405066 | + | 0.0928640i | ||||
\(367\) | 2.80465 | + | 17.7079i | 0.146401 | + | 0.924343i | 0.946084 | + | 0.323920i | \(0.105001\pi\) |
−0.799683 | + | 0.600422i | \(0.794999\pi\) | |||||||
\(368\) | −0.803077 | − | 0.803077i | −0.0418633 | − | 0.0418633i | ||||
\(369\) | −14.2725 | + | 6.90716i | −0.742998 | + | 0.359573i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.07990 | − | 12.4974i | −0.471405 | − | 0.648833i | ||||
\(372\) | 9.06854 | − | 3.64779i | 0.470182 | − | 0.189129i | ||||
\(373\) | −22.8020 | − | 11.6182i | −1.18064 | − | 0.601568i | −0.250269 | − | 0.968176i | \(-0.580519\pi\) |
−0.930376 | + | 0.366608i | \(0.880519\pi\) | |||||||
\(374\) | −16.4122 | −0.848656 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.64199 | 0.239392 | ||||||||
\(377\) | 15.2829 | + | 7.78702i | 0.787109 | + | 0.401052i | ||||
\(378\) | −1.63481 | + | 14.8957i | −0.0840853 | + | 0.766154i | ||||
\(379\) | −5.71732 | − | 7.86922i | −0.293679 | − | 0.404215i | 0.636526 | − | 0.771255i | \(-0.280371\pi\) |
−0.930205 | + | 0.367041i | \(0.880371\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.6171 | + | 1.92460i | 1.10748 | + | 0.0986003i | ||||
\(382\) | 9.12687 | + | 9.12687i | 0.466971 | + | 0.466971i | ||||
\(383\) | −3.81540 | − | 24.0895i | −0.194958 | − | 1.23092i | −0.869968 | − | 0.493108i | \(-0.835861\pi\) |
0.675010 | − | 0.737808i | \(-0.264139\pi\) | |||||||
\(384\) | 0.387043 | + | 1.68825i | 0.0197512 | + | 0.0861533i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.26495 | − | 1.71069i | 0.267979 | − | 0.0870717i | ||||
\(387\) | 0.270487 | − | 13.1829i | 0.0137496 | − | 0.670125i | ||||
\(388\) | 3.00023 | + | 5.88829i | 0.152314 | + | 0.298932i | ||||
\(389\) | 5.49358 | + | 16.9075i | 0.278536 | + | 0.857245i | 0.988262 | + | 0.152767i | \(0.0488186\pi\) |
−0.709726 | + | 0.704477i | \(0.751181\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.10020 | − | 6.46376i | 0.106212 | − | 0.326886i | ||||
\(392\) | −1.30065 | + | 0.206003i | −0.0656929 | + | 0.0104047i | ||||
\(393\) | −20.0234 | − | 5.02496i | −1.01004 | − | 0.253475i | ||||
\(394\) | 15.0352 | − | 20.6942i | 0.757462 | − | 1.04256i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.15117 | + | 1.12013i | −0.409612 | + | 0.0562888i | ||||
\(397\) | −19.0036 | − | 3.00987i | −0.953762 | − | 0.151061i | −0.339889 | − | 0.940466i | \(-0.610389\pi\) |
−0.613873 | + | 0.789405i | \(0.710389\pi\) | |||||||
\(398\) | −0.0348814 | + | 0.0684585i | −0.00174845 | + | 0.00343152i | ||||
\(399\) | −13.3041 | − | 22.2188i | −0.666040 | − | 1.11233i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 31.1439i | − | 1.55525i | −0.628726 | − | 0.777627i | \(-0.716423\pi\) | ||
0.628726 | − | 0.777627i | \(-0.283577\pi\) | |||||||
\(402\) | −0.797478 | + | 0.0545384i | −0.0397746 | + | 0.00272013i | ||||
\(403\) | −5.22164 | + | 32.9681i | −0.260108 | + | 1.64226i | ||||
\(404\) | 2.85559 | − | 2.07471i | 0.142071 | − | 0.103221i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.76598 | + | 4.91577i | 0.335790 | + | 0.243966i | ||||
\(407\) | 15.6487 | − | 15.6487i | 0.775678 | − | 0.775678i | ||||
\(408\) | −7.95020 | + | 6.65030i | −0.393594 | + | 0.329239i | ||||
\(409\) | 14.9223 | + | 4.84855i | 0.737860 | + | 0.239745i | 0.653749 | − | 0.756711i | \(-0.273195\pi\) |
0.0841106 | + | 0.996456i | \(0.473195\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.6187 | + | 25.9395i | −1.11570 | + | 1.27950i | ||||
\(412\) | −5.74931 | + | 2.92942i | −0.283248 | + | 0.144322i | ||||
\(413\) | −7.58476 | + | 3.86463i | −0.373222 | + | 0.190166i | ||||
\(414\) | 0.601920 | − | 3.35358i | 0.0295827 | − | 0.164819i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.62520 | − | 1.82774i | −0.275798 | − | 0.0896122i | ||||
\(417\) | 10.6091 | + | 12.6828i | 0.519528 | + | 0.621078i | ||||
\(418\) | 10.0545 | − | 10.0545i | 0.491783 | − | 0.491783i | ||||
\(419\) | 2.78733 | + | 2.02511i | 0.136170 | + | 0.0989333i | 0.653785 | − | 0.756680i | \(-0.273180\pi\) |
−0.517615 | + | 0.855614i | \(0.673180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.9206 | − | 7.93429i | 0.532238 | − | 0.386694i | −0.288956 | − | 0.957342i | \(-0.593308\pi\) |
0.821194 | + | 0.570649i | \(0.193308\pi\) | |||||||
\(422\) | −1.00913 | + | 6.37141i | −0.0491238 | + | 0.310156i | ||||
\(423\) | 7.95265 | + | 11.4319i | 0.386671 | + | 0.555838i | ||||
\(424\) | − | 5.35652i | − | 0.260135i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.50208 | + | 5.09087i | −0.411927 | + | 0.246653i | ||||
\(427\) | 6.00974 | − | 11.7948i | 0.290832 | − | 0.570790i | ||||
\(428\) | −12.2488 | − | 1.94001i | −0.592066 | − | 0.0937741i | ||||
\(429\) | 11.0178 | − | 25.8462i | 0.531944 | − | 1.24787i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.4092 | + | 22.5853i | −0.790401 | + | 1.08789i | 0.203657 | + | 0.979042i | \(0.434717\pi\) |
−0.994058 | + | 0.108852i | \(0.965283\pi\) | |||||||
\(432\) | −3.49460 | + | 3.84548i | −0.168134 | + | 0.185016i | ||||
\(433\) | −2.57946 | + | 0.408546i | −0.123961 | + | 0.0196335i | −0.218107 | − | 0.975925i | \(-0.569988\pi\) |
0.0941457 | + | 0.995558i | \(0.469988\pi\) | |||||||
\(434\) | −5.02927 | + | 15.4785i | −0.241413 | + | 0.742992i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.862912 | − | 2.65577i | −0.0413260 | − | 0.127188i | ||||
\(437\) | 2.67322 | + | 5.24649i | 0.127877 | + | 0.250974i | ||||
\(438\) | −8.36250 | + | 13.3373i | −0.399576 | + | 0.637282i | ||||
\(439\) | 10.4899 | − | 3.40836i | 0.500653 | − | 0.162672i | −0.0477940 | − | 0.998857i | \(-0.515219\pi\) |
0.548447 | + | 0.836185i | \(0.315219\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.73560 | − | 2.85021i | −0.130267 | − | 0.135724i | ||||
\(442\) | −5.53695 | − | 34.9589i | −0.263366 | − | 1.66283i | ||||
\(443\) | 1.32181 | + | 1.32181i | 0.0628009 | + | 0.0628009i | 0.737810 | − | 0.675009i | \(-0.235860\pi\) |
−0.675009 | + | 0.737810i | \(0.735860\pi\) | |||||||
\(444\) | 1.23943 | − | 13.9213i | 0.0588208 | − | 0.660675i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.19712 | + | 4.40046i | 0.151388 | + | 0.208368i | ||||
\(447\) | 7.76229 | + | 19.2973i | 0.367144 | + | 0.912733i | ||||
\(448\) | −2.56957 | − | 1.30926i | −0.121401 | − | 0.0618568i | ||||
\(449\) | 20.5238 | 0.968579 | 0.484289 | − | 0.874908i | \(-0.339078\pi\) | ||||
0.484289 | + | 0.874908i | \(0.339078\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.4955 | 0.682569 | ||||||||
\(452\) | −4.11863 | − | 2.09855i | −0.193724 | − | 0.0987075i | ||||
\(453\) | 7.19269 | + | 17.8813i | 0.337942 | + | 0.840137i | ||||
\(454\) | 11.5336 | + | 15.8746i | 0.541296 | + | 0.745031i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.796353 | − | 8.94462i | 0.0372926 | − | 0.418870i | ||||
\(457\) | 11.0498 | + | 11.0498i | 0.516886 | + | 0.516886i | 0.916628 | − | 0.399742i | \(-0.130900\pi\) |
−0.399742 | + | 0.916628i | \(0.630900\pi\) | |||||||
\(458\) | −2.73683 | − | 17.2797i | −0.127884 | − | 0.807427i | ||||
\(459\) | −29.9980 | − | 8.18580i | −1.40019 | − | 0.382080i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.2689 | − | 4.31131i | 0.617992 | − | 0.200798i | 0.0167435 | − | 0.999860i | \(-0.494670\pi\) |
0.601249 | + | 0.799062i | \(0.294670\pi\) | |||||||
\(462\) | 7.27735 | − | 11.6066i | 0.338573 | − | 0.539989i | ||||
\(463\) | −14.9657 | − | 29.3718i | −0.695515 | − | 1.36502i | −0.920531 | − | 0.390669i | \(-0.872244\pi\) |
0.225017 | − | 0.974355i | \(-0.427756\pi\) | |||||||
\(464\) | 0.896139 | + | 2.75803i | 0.0416022 | + | 0.128038i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.96836 | − | 27.6018i | 0.415451 | − | 1.27863i | ||||
\(467\) | −3.65255 | + | 0.578507i | −0.169020 | + | 0.0267701i | −0.240371 | − | 0.970681i | \(-0.577269\pi\) |
0.0713509 | + | 0.997451i | \(0.477269\pi\) | |||||||
\(468\) | −5.13588 | − | 16.9845i | −0.237406 | − | 0.785110i | ||||
\(469\) | 0.782294 | − | 1.07673i | 0.0361230 | − | 0.0497190i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.1537 | + | 26.1651i | −0.513937 | + | 1.20562i | ||||
\(472\) | −2.91542 | − | 0.461757i | −0.134193 | − | 0.0212541i | ||||
\(473\) | −5.47254 | + | 10.7405i | −0.251628 | + | 0.493847i | ||||
\(474\) | −17.4585 | + | 10.4538i | −0.801894 | + | 0.480157i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 17.2578i | − | 0.791012i | ||||||
\(477\) | 13.1916 | − | 9.17677i | 0.604000 | − | 0.420175i | ||||
\(478\) | 0.884293 | − | 5.58321i | 0.0404466 | − | 0.255370i | ||||
\(479\) | 4.35190 | − | 3.16184i | 0.198844 | − | 0.144468i | −0.483908 | − | 0.875119i | \(-0.660783\pi\) |
0.682752 | + | 0.730651i | \(0.260783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 38.6120 | + | 28.0533i | 1.76056 | + | 1.27912i | ||||
\(482\) | 9.96798 | − | 9.96798i | 0.454029 | − | 0.454029i | ||||
\(483\) | 3.63988 | + | 4.35135i | 0.165620 | + | 0.197993i | ||||
\(484\) | −3.30796 | − | 1.07482i | −0.150362 | − | 0.0488555i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −15.4573 | − | 2.01813i | −0.701156 | − | 0.0915443i | ||||
\(487\) | 3.73900 | − | 1.90512i | 0.169430 | − | 0.0863291i | −0.367219 | − | 0.930135i | \(-0.619690\pi\) |
0.536649 | + | 0.843806i | \(0.319690\pi\) | |||||||
\(488\) | 4.08988 | − | 2.08390i | 0.185140 | − | 0.0943336i | ||||
\(489\) | −7.45695 | + | 8.55176i | −0.337215 | + | 0.386724i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.0362 | + | 9.75934i | 1.35551 | + | 0.440433i | 0.894543 | − | 0.446983i | \(-0.147501\pi\) |
0.460970 | + | 0.887416i | \(0.347501\pi\) | |||||||
\(492\) | 7.02175 | − | 5.87365i | 0.316565 | − | 0.264805i | ||||
\(493\) | −12.2711 | + | 12.2711i | −0.552664 | + | 0.552664i | ||||
\(494\) | 24.8088 | + | 18.0246i | 1.11620 | + | 0.810966i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.56563 | + | 3.31712i | −0.205003 | + | 0.148943i | ||||
\(497\) | 2.58115 | − | 16.2967i | 0.115780 | − | 0.731007i | ||||
\(498\) | 20.8677 | − | 1.42712i | 0.935106 | − | 0.0639506i | ||||
\(499\) | − | 10.2536i | − | 0.459015i | −0.973307 | − | 0.229508i | \(-0.926288\pi\) | ||
0.973307 | − | 0.229508i | \(-0.0737116\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.1245 | − | 25.2590i | −0.675714 | − | 1.12849i | ||||
\(502\) | −7.86229 | + | 15.4306i | −0.350911 | + | 0.688702i | ||||
\(503\) | −0.658974 | − | 0.104371i | −0.0293822 | − | 0.00465369i | 0.141726 | − | 0.989906i | \(-0.454735\pi\) |
−0.171108 | + | 0.985252i | \(0.554735\pi\) | |||||||
\(504\) | −1.17785 | − | 8.57114i | −0.0524654 | − | 0.381789i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.83085 | + | 2.51995i | −0.0813911 | + | 0.112025i | ||||
\(507\) | 36.9314 | + | 9.26810i | 1.64018 | + | 0.411611i | ||||
\(508\) | −12.3757 | + | 1.96012i | −0.549084 | + | 0.0869664i | ||||
\(509\) | −8.01814 | + | 24.6773i | −0.355398 | + | 1.09380i | 0.600381 | + | 0.799714i | \(0.295016\pi\) |
−0.955779 | + | 0.294087i | \(0.904984\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.09964 | − | 24.9281i | −0.358307 | − | 1.10276i | ||||
\(512\) | −0.453990 | − | 0.891007i | −0.0200637 | − | 0.0393773i | ||||
\(513\) | 23.3923 | − | 13.3627i | 1.03280 | − | 0.589978i | ||||
\(514\) | 5.76888 | − | 1.87442i | 0.254454 | − | 0.0826772i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.70114 | + | 7.42026i | 0.0748885 | + | 0.326659i | ||||
\(517\) | −1.99158 | − | 12.5743i | −0.0875896 | − | 0.553019i | ||||
\(518\) | 16.4550 | + | 16.4550i | 0.722991 | + | 0.722991i | ||||
\(519\) | −11.7135 | − | 1.04287i | −0.514167 | − | 0.0457771i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.0053 | + | 33.0404i | 1.05169 | + | 1.44753i | 0.887334 | + | 0.461127i | \(0.152555\pi\) |
0.164357 | + | 0.986401i | \(0.447445\pi\) | |||||||
\(522\) | −5.25698 | + | 6.93199i | −0.230092 | + | 0.303405i | ||||
\(523\) | 24.2703 | + | 12.3663i | 1.06126 | + | 0.540741i | 0.895334 | − | 0.445396i | \(-0.146937\pi\) |
0.165931 | + | 0.986137i | \(0.446937\pi\) | |||||||
\(524\) | 11.9190 | 0.520682 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.8782 | 1.04114 | ||||||||
\(527\) | −30.0906 | − | 15.3319i | −1.31077 | − | 0.667868i | ||||
\(528\) | 4.40713 | − | 1.77275i | 0.191796 | − | 0.0771491i | ||||
\(529\) | 12.7609 | + | 17.5639i | 0.554822 | + | 0.763646i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.85751 | − | 7.97093i | −0.167402 | − | 0.345909i | ||||
\(532\) | 10.5726 | + | 10.5726i | 0.458379 | + | 0.458379i | ||||
\(533\) | 4.89032 | + | 30.8763i | 0.211823 | + | 1.33740i | ||||
\(534\) | 2.19724 | − | 0.503731i | 0.0950839 | − | 0.0217986i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.438912 | − | 0.142611i | 0.0189581 | − | 0.00615987i | ||||
\(537\) | −13.7676 | − | 8.63229i | −0.594116 | − | 0.372511i | ||||
\(538\) | 6.30950 | + | 12.3831i | 0.272022 | + | 0.533873i | ||||
\(539\) | 1.11605 | + | 3.43486i | 0.0480718 | + | 0.147950i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.75771 | − | 14.6427i | 0.204550 | − | 0.629540i | −0.795182 | − | 0.606371i | \(-0.792625\pi\) |
0.999732 | − | 0.0231685i | \(-0.00737544\pi\) | |||||||
\(542\) | 14.8496 | − | 2.35194i | 0.637844 | − | 0.101025i | ||||
\(543\) | 6.41107 | − | 25.5467i | 0.275125 | − | 1.09631i | ||||
\(544\) | 3.51743 | − | 4.84132i | 0.150808 | − | 0.207570i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 27.1779 | + | 11.5855i | 1.16311 | + | 0.495812i | ||||
\(547\) | −22.1803 | − | 3.51301i | −0.948360 | − | 0.150205i | −0.336953 | − | 0.941522i | \(-0.609396\pi\) |
−0.611407 | + | 0.791316i | \(0.709396\pi\) | |||||||
\(548\) | 9.02083 | − | 17.7044i | 0.385351 | − | 0.756293i | ||||
\(549\) | 12.1388 | + | 6.50207i | 0.518072 | + | 0.277502i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 15.0352i | − | 0.640520i | ||||||
\(552\) | 0.134216 | + | 1.96255i | 0.00571260 | + | 0.0835315i | ||||
\(553\) | 5.30021 | − | 33.4642i | 0.225388 | − | 1.42304i | ||||
\(554\) | 1.46748 | − | 1.06619i | 0.0623472 | − | 0.0452979i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.72325 | − | 5.61127i | −0.327539 | − | 0.237971i | ||||
\(557\) | −1.66485 | + | 1.66485i | −0.0705420 | + | 0.0705420i | −0.741498 | − | 0.670956i | \(-0.765884\pi\) |
0.670956 | + | 0.741498i | \(0.265884\pi\) | |||||||
\(558\) | −15.9909 | − | 5.56095i | −0.676951 | − | 0.235414i | ||||
\(559\) | −24.7240 | − | 8.03333i | −1.04572 | − | 0.339773i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.4254 | + | 18.6825i | 0.904581 | + | 0.788775i | ||||
\(562\) | −20.4199 | + | 10.4045i | −0.861362 | + | 0.438886i | ||||
\(563\) | 42.1004 | − | 21.4512i | 1.77432 | − | 0.904062i | 0.845023 | − | 0.534729i | \(-0.179586\pi\) |
0.929297 | − | 0.369332i | \(-0.120414\pi\) | |||||||
\(564\) | −6.05991 | − | 5.28411i | −0.255168 | − | 0.222501i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.70579 | − | 0.879165i | −0.113733 | − | 0.0369541i | ||||
\(567\) | 19.0904 | − | 17.5848i | 0.801721 | − | 0.738490i | ||||
\(568\) | 4.04562 | − | 4.04562i | 0.169750 | − | 0.169750i | ||||
\(569\) | −19.9798 | − | 14.5162i | −0.837599 | − | 0.608551i | 0.0841003 | − | 0.996457i | \(-0.473198\pi\) |
−0.921699 | + | 0.387906i | \(0.873198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.83866 | − | 3.51549i | 0.202491 | − | 0.147119i | −0.481919 | − | 0.876216i | \(-0.660060\pi\) |
0.684410 | + | 0.729097i | \(0.260060\pi\) | |||||||
\(572\) | −2.53761 | + | 16.0218i | −0.106103 | + | 0.669907i | ||||
\(573\) | −1.52534 | − | 22.3041i | −0.0637221 | − | 0.931766i | ||||
\(574\) | 15.2424i | 0.636206i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.41652 | − | 2.64452i | 0.0590216 | − | 0.110188i | ||||
\(577\) | 14.3066 | − | 28.0783i | 0.595591 | − | 1.16891i | −0.374739 | − | 0.927130i | \(-0.622268\pi\) |
0.970330 | − | 0.241783i | \(-0.0777324\pi\) | |||||||
\(578\) | 18.5791 | + | 2.94264i | 0.772789 | + | 0.122398i | ||||
\(579\) | −8.82048 | − | 3.76002i | −0.366567 | − | 0.156261i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.4704 | + | 28.1751i | −0.849256 | + | 1.16890i | ||||
\(582\) | 2.78613 | − | 11.1021i | 0.115489 | − | 0.460198i | ||||
\(583\) | −14.5099 | + | 2.29814i | −0.600937 | + | 0.0951791i | ||||
\(584\) | 2.80857 | − | 8.64390i | 0.116220 | − | 0.357687i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.12744 | + | 12.7030i | 0.170503 | + | 0.524755i | ||||
\(587\) | −5.11433 | − | 10.0374i | −0.211091 | − | 0.414289i | 0.761048 | − | 0.648696i | \(-0.224685\pi\) |
−0.972139 | + | 0.234407i | \(0.924685\pi\) | |||||||
\(588\) | 1.93244 | + | 1.21164i | 0.0796926 | + | 0.0499673i | ||||
\(589\) | 27.8269 | − | 9.04151i | 1.14659 | − | 0.372549i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −43.1845 | + | 9.90032i | −1.77637 | + | 0.407245i | ||||
\(592\) | 1.26231 | + | 7.96990i | 0.0518805 | + | 0.327561i | ||||
\(593\) | −17.4049 | − | 17.4049i | −0.714734 | − | 0.714734i | 0.252788 | − | 0.967522i | \(-0.418653\pi\) |
−0.967522 | + | 0.252788i | \(0.918653\pi\) | |||||||
\(594\) | 11.9161 | + | 7.81642i | 0.488922 | + | 0.320711i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.05865 | − | 9.71540i | −0.289134 | − | 0.397958i | ||||
\(597\) | 0.123464 | − | 0.0496631i | 0.00505306 | − | 0.00203257i | ||||
\(598\) | −5.98529 | − | 3.04966i | −0.244757 | − | 0.124710i | ||||
\(599\) | 25.8531 | 1.05633 | 0.528165 | − | 0.849142i | \(-0.322880\pi\) | ||||
0.528165 | + | 0.849142i | \(0.322880\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.7027 | −1.49714 | −0.748568 | − | 0.663058i | \(-0.769258\pi\) | ||||
−0.748568 | + | 0.663058i | \(0.769258\pi\) | |||||||
\(602\) | −11.2939 | − | 5.75450i | −0.460303 | − | 0.234536i | ||||
\(603\) | 1.10315 | + | 0.836594i | 0.0449239 | + | 0.0340687i | ||||
\(604\) | −6.54069 | − | 9.00249i | −0.266137 | − | 0.366306i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.08955 | − | 0.542162i | −0.247371 | − | 0.0220238i | ||||
\(607\) | −23.2173 | − | 23.2173i | −0.942362 | − | 0.942362i | 0.0560654 | − | 0.998427i | \(-0.482144\pi\) |
−0.998427 | + | 0.0560654i | \(0.982144\pi\) | |||||||
\(608\) | 0.811051 | + | 5.12077i | 0.0328925 | + | 0.207675i | ||||
\(609\) | −3.23692 | − | 14.1192i | −0.131166 | − | 0.572139i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.1121 | − | 8.48435i | 1.05638 | − | 0.343240i | ||||
\(612\) | 17.9488 | + | 0.368274i | 0.725539 | + | 0.0148866i | ||||
\(613\) | −9.97216 | − | 19.5715i | −0.402772 | − | 0.790484i | 0.597161 | − | 0.802122i | \(-0.296295\pi\) |
−0.999932 | + | 0.0116379i | \(0.996295\pi\) | |||||||
\(614\) | −10.1339 | − | 31.1890i | −0.408972 | − | 1.25869i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.44412 | + | 7.52224i | −0.0984766 | + | 0.303080i | ||||
\(617\) | −6.32162 | + | 1.00125i | −0.254499 | + | 0.0403086i | −0.282380 | − | 0.959303i | \(-0.591124\pi\) |
0.0278814 | + | 0.999611i | \(0.491124\pi\) | |||||||
\(618\) | 10.8401 | + | 2.72038i | 0.436053 | + | 0.109430i | ||||
\(619\) | −14.0949 | + | 19.4000i | −0.566524 | + | 0.779753i | −0.992138 | − | 0.125152i | \(-0.960058\pi\) |
0.425614 | + | 0.904905i | \(0.360058\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.60325 | + | 3.69276i | −0.184722 | + | 0.148185i | ||||
\(622\) | −10.2243 | − | 1.61936i | −0.409956 | − | 0.0649306i | ||||
\(623\) | −1.70399 | + | 3.34426i | −0.0682688 | + | 0.133985i | ||||
\(624\) | 5.26288 | + | 8.78935i | 0.210684 | + | 0.351856i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.7188i | 0.548313i | ||||||||
\(627\) | −24.5711 | + | 1.68038i | −0.981274 | + | 0.0671079i | ||||
\(628\) | 2.56892 | − | 16.2195i | 0.102511 | − | 0.647230i | ||||
\(629\) | −39.0658 | + | 28.3830i | −1.55766 | + | 1.13170i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.7895 | − | 17.2841i | −0.947046 | − | 0.688069i | 0.00306072 | − | 0.999995i | \(-0.499026\pi\) |
−0.950106 | + | 0.311926i | \(0.899026\pi\) | |||||||
\(632\) | 8.30741 | − | 8.30741i | 0.330451 | − | 0.330451i | ||||
\(633\) | 8.57013 | − | 7.16886i | 0.340632 | − | 0.284937i | ||||
\(634\) | −17.9501 | − | 5.83235i | −0.712891 | − | 0.231632i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.09747 | + | 6.99269i | −0.241780 | + | 0.277278i | ||||
\(637\) | −6.93992 | + | 3.53606i | −0.274970 | + | 0.140104i | ||||
\(638\) | 7.08655 | − | 3.61078i | 0.280559 | − | 0.142952i | ||||
\(639\) | 16.8941 | + | 3.03226i | 0.668322 | + | 0.119954i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.3395 | − | 5.95888i | −0.724368 | − | 0.235362i | −0.0764522 | − | 0.997073i | \(-0.524359\pi\) |
−0.647916 | + | 0.761712i | \(0.724359\pi\) | |||||||
\(642\) | 13.7818 | + | 16.4757i | 0.543925 | + | 0.650244i | ||||
\(643\) | −2.50826 | + | 2.50826i | −0.0989163 | + | 0.0989163i | −0.754833 | − | 0.655917i | \(-0.772282\pi\) |
0.655917 | + | 0.754833i | \(0.272282\pi\) | |||||||
\(644\) | −2.64978 | − | 1.92518i | −0.104416 | − | 0.0758627i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25.1003 | + | 18.2365i | −0.987560 | + | 0.717504i | ||||
\(647\) | −5.85671 | + | 36.9778i | −0.230251 | + | 1.45375i | 0.553591 | + | 0.832789i | \(0.313257\pi\) |
−0.783842 | + | 0.620960i | \(0.786743\pi\) | |||||||
\(648\) | 8.93946 | − | 1.04210i | 0.351175 | − | 0.0409376i | ||||
\(649\) | 8.09547i | 0.317775i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.1851 | − | 14.4815i | 0.947889 | − | 0.567576i | ||||
\(652\) | 2.97400 | − | 5.83680i | 0.116471 | − | 0.228587i | ||||
\(653\) | 2.19851 | + | 0.348209i | 0.0860342 | + | 0.0136265i | 0.199303 | − | 0.979938i | \(-0.436132\pi\) |
−0.113269 | + | 0.993564i | \(0.536132\pi\) | |||||||
\(654\) | −1.89664 | + | 4.44926i | −0.0741647 | + | 0.173980i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.10665 | + | 4.27594i | −0.121294 | + | 0.166947i | ||||
\(657\) | 26.0991 | − | 7.89200i | 1.01822 | − | 0.307896i | ||||
\(658\) | 13.2222 | − | 2.09419i | 0.515456 | − | 0.0816401i | ||||
\(659\) | 4.81311 | − | 14.8132i | 0.187492 | − | 0.577041i | −0.812490 | − | 0.582975i | \(-0.801889\pi\) |
0.999982 | + | 0.00593344i | \(0.00188868\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.225919 | − | 0.695307i | −0.00878723 | − | 0.0270443i | 0.946567 | − | 0.322508i | \(-0.104526\pi\) |
−0.955354 | + | 0.295464i | \(0.904526\pi\) | |||||||
\(662\) | −14.4080 | − | 28.2773i | −0.559984 | − | 1.09903i | ||||
\(663\) | −32.5665 | + | 51.9401i | −1.26478 | + | 2.01719i | ||||
\(664\) | −11.4851 | + | 3.73173i | −0.445708 | + | 0.144819i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −17.4650 | + | 16.7627i | −0.676755 | + | 0.649542i | ||||
\(667\) | 0.515226 | + | 3.25301i | 0.0199496 | + | 0.125957i | ||||
\(668\) | 12.0192 | + | 12.0192i | 0.465037 | + | 0.465037i | ||||
\(669\) | 0.835468 | − | 9.38397i | 0.0323011 | − | 0.362805i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.39961 | − | 10.1847i | −0.285659 | − | 0.393176i | ||||
\(672\) | 1.86409 | + | 4.63420i | 0.0719088 | + | 0.178768i | ||||
\(673\) | 13.4197 | + | 6.83769i | 0.517292 | + | 0.263574i | 0.693088 | − | 0.720853i | \(-0.256250\pi\) |
−0.175796 | + | 0.984427i | \(0.556250\pi\) | |||||||
\(674\) | 16.1131 | 0.620652 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21.9835 | −0.845520 | ||||||||
\(677\) | −20.6424 | − | 10.5178i | −0.793351 | − | 0.404233i | 0.00984177 | − | 0.999952i | \(-0.496867\pi\) |
−0.803193 | + | 0.595719i | \(0.796867\pi\) | |||||||
\(678\) | 2.98785 | + | 7.42791i | 0.114748 | + | 0.285267i | ||||
\(679\) | 11.2023 | + | 15.4186i | 0.429904 | + | 0.591712i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.01394 | − | 33.8525i | 0.115494 | − | 1.29723i | ||||
\(682\) | 10.9443 | + | 10.9443i | 0.419080 | + | 0.419080i | ||||
\(683\) | 0.679239 | + | 4.28854i | 0.0259903 | + | 0.164097i | 0.997270 | − | 0.0738455i | \(-0.0235272\pi\) |
−0.971279 | + | 0.237942i | \(0.923527\pi\) | |||||||
\(684\) | −11.2215 | + | 10.7703i | −0.429065 | + | 0.411812i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.5874 | − | 5.06466i | 0.595130 | − | 0.193370i | ||||
\(687\) | −16.0971 | + | 25.6732i | −0.614144 | + | 0.979495i | ||||
\(688\) | −1.99539 | − | 3.91618i | −0.0760736 | − | 0.149303i | ||||
\(689\) | −9.79031 | − | 30.1315i | −0.372981 | − | 1.14792i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.14266 | + | 28.1382i | −0.347803 | + | 1.07043i | 0.612263 | + | 0.790654i | \(0.290259\pi\) |
−0.960066 | + | 0.279774i | \(0.909741\pi\) | |||||||
\(692\) | 6.70597 | − | 1.06212i | 0.254923 | − | 0.0403758i | ||||
\(693\) | −22.7124 | + | 6.86790i | −0.862772 | + | 0.260890i | ||||
\(694\) | −14.0633 | + | 19.3564i | −0.533834 | + | 0.734759i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.96968 | − | 4.62058i | 0.0746603 | − | 0.175143i | ||||
\(697\) | −31.2392 | − | 4.94780i | −1.18327 | − | 0.187411i | ||||
\(698\) | −11.3024 | + | 22.1821i | −0.427801 | + | 0.839606i | ||||
\(699\) | −43.1276 | + | 25.8239i | −1.63124 | + | 0.976750i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19.5558i | − | 0.738612i | −0.929308 | − | 0.369306i | \(-0.879595\pi\) | ||
0.929308 | − | 0.369306i | \(-0.120405\pi\) | |||||||
\(702\) | −12.6293 | + | 28.0188i | −0.476662 | + | 1.05750i | ||||
\(703\) | 6.54457 | − | 41.3208i | 0.246833 | − | 1.55844i | ||||
\(704\) | −2.21880 | + | 1.61205i | −0.0836243 | + | 0.0607566i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.6828 | − | 9.94116i | −0.514960 | − | 0.374140i | ||||
\(707\) | 7.19787 | − | 7.19787i | 0.270704 | − | 0.270704i | ||||
\(708\) | 3.28032 | + | 3.92151i | 0.123282 | + | 0.147379i | ||||
\(709\) | −21.2009 | − | 6.88858i | −0.796216 | − | 0.258706i | −0.117467 | − | 0.993077i | \(-0.537477\pi\) |
−0.678749 | + | 0.734371i | \(0.737477\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34.6910 | + | 6.22654i | 1.30101 | + | 0.233514i | ||||
\(712\) | −1.15963 | + | 0.590863i | −0.0434591 | + | 0.0221435i | ||||
\(713\) | −5.71079 | + | 2.90979i | −0.213871 | + | 0.108973i | ||||
\(714\) | −19.6451 | + | 22.5293i | −0.735198 | + | 0.843138i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.92277 | + | 2.89918i | 0.333460 | + | 0.108348i | ||||
\(717\) | −7.50992 | + | 6.28201i | −0.280463 | + | 0.234606i | ||||
\(718\) | −3.84337 | + | 3.84337i | −0.143433 | + | 0.143433i | ||||
\(719\) | −2.20624 | − | 1.60292i | −0.0822787 | − | 0.0597790i | 0.545885 | − | 0.837860i | \(-0.316193\pi\) |
−0.628164 | + | 0.778081i | \(0.716193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.0547 | + | 10.9379i | −0.560667 | + | 0.407348i | ||||
\(722\) | 1.23272 | − | 7.78310i | 0.0458772 | − | 0.289657i | ||||
\(723\) | −24.3596 | + | 1.66592i | −0.905942 | + | 0.0619561i | ||||
\(724\) | 15.2068i | 0.565155i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.09489 | + | 5.16867i | 0.114862 | + | 0.191827i | ||||
\(727\) | −8.81556 | + | 17.3015i | −0.326951 | + | 0.641677i | −0.994713 | − | 0.102698i | \(-0.967253\pi\) |
0.667762 | + | 0.744375i | \(0.267253\pi\) | |||||||
\(728\) | −16.8473 | − | 2.66836i | −0.624404 | − | 0.0988959i | ||||
\(729\) | 17.8815 | + | 20.2300i | 0.662276 | + | 0.749260i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.4599 | − | 21.2787i | 0.571805 | − | 0.787022i | ||||
\(732\) | −7.71130 | − | 1.93519i | −0.285018 | − | 0.0715266i | ||||
\(733\) | 23.9728 | − | 3.79691i | 0.885454 | − | 0.140242i | 0.302889 | − | 0.953026i | \(-0.402049\pi\) |
0.582566 | + | 0.812784i | \(0.302049\pi\) | |||||||
\(734\) | −5.54024 | + | 17.0511i | −0.204494 | + | 0.629368i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.350958 | − | 1.08014i | −0.0129365 | − | 0.0398144i | ||||
\(737\) | −0.574618 | − | 1.12775i | −0.0211663 | − | 0.0415412i | ||||
\(738\) | −15.8527 | − | 0.325265i | −0.583546 | − | 0.0119732i | ||||
\(739\) | −6.13821 | + | 1.99443i | −0.225798 | + | 0.0733662i | −0.419731 | − | 0.907649i | \(-0.637876\pi\) |
0.193933 | + | 0.981015i | \(0.437876\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.8688 | − | 51.7708i | −0.436010 | − | 1.90185i | ||||
\(742\) | −2.41654 | − | 15.2575i | −0.0887141 | − | 0.560119i | ||||
\(743\) | 23.0403 | + | 23.0403i | 0.845265 | + | 0.845265i | 0.989538 | − | 0.144273i | \(-0.0460842\pi\) |
−0.144273 | + | 0.989538i | \(0.546084\pi\) | |||||||
\(744\) | 9.73619 | + | 0.866828i | 0.356946 | + | 0.0317794i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.0422 | − | 20.7038i | −0.550734 | − | 0.758020i | ||||
\(747\) | −28.8664 | − | 21.8913i | −1.05617 | − | 0.800961i | ||||
\(748\) | −14.6234 | − | 7.45099i | −0.534684 | − | 0.272435i | ||||
\(749\) | −35.7645 | −1.30681 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.4069 | 1.14606 | 0.573028 | − | 0.819536i | \(-0.305769\pi\) | ||||
0.573028 | + | 0.819536i | \(0.305769\pi\) | |||||||
\(752\) | 4.13604 | + | 2.10742i | 0.150826 | + | 0.0768497i | ||||
\(753\) | 27.8290 | − | 11.1941i | 1.01414 | − | 0.407936i | ||||
\(754\) | 10.0819 | + | 13.8766i | 0.367162 | + | 0.505355i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.21914 | + | 12.5300i | −0.298927 | + | 0.455712i | ||||
\(757\) | 6.35882 | + | 6.35882i | 0.231115 | + | 0.231115i | 0.813158 | − | 0.582043i | \(-0.197746\pi\) |
−0.582043 | + | 0.813158i | \(0.697746\pi\) | |||||||
\(758\) | −1.52162 | − | 9.60713i | −0.0552678 | − | 0.348947i | ||||
\(759\) | 5.25861 | − | 1.20557i | 0.190875 | − | 0.0437594i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.94031 | + | 2.90488i | −0.324086 | + | 0.105302i | −0.466541 | − | 0.884499i | \(-0.654500\pi\) |
0.142456 | + | 0.989801i | \(0.454500\pi\) | |||||||
\(762\) | 18.3872 | + | 11.5288i | 0.666098 | + | 0.417644i | ||||
\(763\) | −3.65604 | − | 7.17538i | −0.132358 | − | 0.259766i | ||||
\(764\) | 3.98859 | + | 12.2756i | 0.144302 | + | 0.444116i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.53686 | − | 23.1961i | 0.272318 | − | 0.838108i | ||||
\(767\) | −17.2438 | + | 2.73115i | −0.622637 | + | 0.0986161i | ||||
\(768\) | −0.421593 | + | 1.67996i | −0.0152129 | + | 0.0606203i | ||||
\(769\) | 15.8011 | − | 21.7484i | 0.569803 | − | 0.784266i | −0.422728 | − | 0.906256i | \(-0.638928\pi\) |
0.992531 | + | 0.121990i | \(0.0389276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.66471 | − | 4.11990i | −0.348066 | − | 0.148375i | ||||
\(772\) | 5.46774 | + | 0.866006i | 0.196788 | + | 0.0311682i | ||||
\(773\) | −9.86911 | + | 19.3692i | −0.354967 | + | 0.696662i | −0.997580 | − | 0.0695289i | \(-0.977850\pi\) |
0.642613 | + | 0.766191i | \(0.277850\pi\) | |||||||
\(774\) | 6.22592 | − | 11.6233i | 0.223786 | − | 0.417789i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.60858i | 0.237234i | ||||||||
\(777\) | −2.75007 | − | 40.2124i | −0.0986582 | − | 1.44261i | ||||
\(778\) | −2.78103 | + | 17.5587i | −0.0997048 | + | 0.629511i | ||||
\(779\) | 22.1690 | − | 16.1067i | 0.794288 | − | 0.577084i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.6946 | − | 9.22316i | −0.454248 | − | 0.330031i | ||||
\(782\) | 4.80578 | − | 4.80578i | 0.171854 | − | 0.171854i | ||||
\(783\) | 14.7536 | − | 3.06523i | 0.527251 | − | 0.109542i | ||||
\(784\) | −1.25241 | − | 0.406934i | −0.0447291 | − | 0.0145334i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15.5597 | − | 13.5677i | −0.554995 | − | 0.483943i | ||||
\(787\) | 16.6973 | − | 8.50770i | 0.595194 | − | 0.303267i | −0.130322 | − | 0.991472i | \(-0.541601\pi\) |
0.725516 | + | 0.688205i | \(0.241601\pi\) | |||||||
\(788\) | 22.7914 | − | 11.6128i | 0.811911 | − | 0.413689i | ||||
\(789\) | −31.1720 | − | 27.1813i | −1.10975 | − | 0.967678i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.6782 | − | 4.11941i | −0.450786 | − | 0.146469i | ||||
\(792\) | −7.77127 | − | 2.70251i | −0.276140 | − | 0.0960294i | ||||
\(793\) | 19.1976 | − | 19.1976i | 0.681725 | − | 0.681725i | ||||
\(794\) | −15.5659 | − | 11.3093i | −0.552412 | − | 0.401351i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.0621591 | + | 0.0451612i | −0.00220317 | + | 0.00160070i | ||||
\(797\) | −7.52391 | + | 47.5041i | −0.266511 | + | 1.68268i | 0.384116 | + | 0.923285i | \(0.374506\pi\) |
−0.650627 | + | 0.759398i | \(0.725494\pi\) | |||||||
\(798\) | −1.76696 | − | 25.8370i | −0.0625497 | − | 0.914622i | ||||
\(799\) | 27.7786i | 0.982737i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.44181 | − | 1.84358i | −0.121610 | − | 0.0651397i | ||||
\(802\) | 14.1390 | − | 27.7494i | 0.499267 | − | 0.979867i | ||||
\(803\) | −24.6198 | − | 3.89939i | −0.868814 | − | 0.137607i | ||||
\(804\) | −0.735318 | − | 0.313453i | −0.0259327 | − | 0.0110546i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19.6197 | + | 27.0043i | −0.691076 | + | 0.951184i | ||||
\(807\) | 5.85925 | − | 23.3478i | 0.206255 | − | 0.821883i | ||||
\(808\) | 3.48625 | − | 0.552168i | 0.122646 | − | 0.0194252i | ||||
\(809\) | −5.14657 | + | 15.8395i | −0.180944 | + | 0.556887i | −0.999855 | − | 0.0170329i | \(-0.994578\pi\) |
0.818911 | + | 0.573920i | \(0.194578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.03759 | + | 18.5818i | 0.212008 | + | 0.652495i | 0.999352 | + | 0.0359809i | \(0.0114556\pi\) |
−0.787344 | + | 0.616514i | \(0.788544\pi\) | |||||||
\(812\) | 3.79682 | + | 7.45167i | 0.133242 | + | 0.261502i | ||||
\(813\) | −22.0627 | − | 13.8333i | −0.773773 | − | 0.485156i | ||||
\(814\) | 21.0475 | − | 6.83874i | 0.737714 | − | 0.239698i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −10.1029 | + | 2.31614i | −0.353671 | + | 0.0810812i | ||||
\(817\) | 3.56475 | + | 22.5070i | 0.124715 | + | 0.787419i | ||||
\(818\) | 11.0947 | + | 11.0947i | 0.387916 | + | 0.387916i | ||||
\(819\) | −22.2914 | − | 46.0616i | −0.778925 | − | 1.60952i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.95552 | − | 10.9498i | −0.277650 | − | 0.382152i | 0.647304 | − | 0.762232i | \(-0.275896\pi\) |
−0.924954 | + | 0.380080i | \(0.875896\pi\) | |||||||
\(822\) | −31.9297 | + | 12.8436i | −1.11367 | + | 0.447972i | ||||
\(823\) | −9.34343 | − | 4.76071i | −0.325691 | − | 0.165948i | 0.283498 | − | 0.958973i | \(-0.408505\pi\) |
−0.609189 | + | 0.793025i | \(0.708505\pi\) | |||||||
\(824\) | −6.45260 | −0.224787 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.51258 | −0.296191 | ||||||||
\(827\) | −17.1630 | − | 8.74498i | −0.596815 | − | 0.304093i | 0.129365 | − | 0.991597i | \(-0.458706\pi\) |
−0.726180 | + | 0.687504i | \(0.758706\pi\) | |||||||
\(828\) | 2.05881 | − | 2.71480i | 0.0715485 | − | 0.0943457i | ||||
\(829\) | −18.5685 | − | 25.5573i | −0.644909 | − | 0.887641i | 0.353956 | − | 0.935262i | \(-0.384836\pi\) |
−0.998865 | + | 0.0476205i | \(0.984836\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.12939 | − | 0.278615i | −0.108557 | − | 0.00966503i | ||||
\(832\) | −4.18231 | − | 4.18231i | −0.144996 | − | 0.144996i | ||||
\(833\) | −1.23277 | − | 7.78338i | −0.0427128 | − | 0.269678i | ||||
\(834\) | 3.69489 | + | 16.1168i | 0.127943 | + | 0.558080i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13.5233 | − | 4.39399i | 0.467713 | − | 0.151969i | ||||
\(837\) | 14.5453 | + | 25.4625i | 0.502758 | + | 0.880112i | ||||
\(838\) | 1.56415 | + | 3.06981i | 0.0540325 | + | 0.106045i | ||||
\(839\) | 12.7405 | + | 39.2113i | 0.439852 | + | 1.35373i | 0.888032 | + | 0.459782i | \(0.152073\pi\) |
−0.448179 | + | 0.893944i | \(0.647927\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.36272 | + | 19.5824i | −0.219404 | + | 0.675256i | ||||
\(842\) | 13.3324 | − | 2.11165i | 0.459466 | − | 0.0727722i | ||||
\(843\) | 38.5009 | + | 9.66199i | 1.32604 | + | 0.332777i | ||||
\(844\) | −3.79170 | + | 5.21883i | −0.130516 | + | 0.179640i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.89589 | + | 13.7963i | 0.0651820 | + | 0.474327i | ||||
\(847\) | −9.90726 | − | 1.56916i | −0.340418 | − | 0.0539169i | ||||
\(848\) | 2.43181 | − | 4.77269i | 0.0835086 | − | 0.163895i | ||||
\(849\) | 2.53151 | + | 4.22779i | 0.0868812 | + | 0.145097i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.16443i | 0.314153i | ||||||||
\(852\) | −9.88661 | + | 0.676131i | −0.338710 | + | 0.0231639i | ||||
\(853\) | −2.92787 | + | 18.4859i | −0.100248 | + | 0.632944i | 0.885490 | + | 0.464659i | \(0.153823\pi\) |
−0.985738 | + | 0.168285i | \(0.946177\pi\) | |||||||
\(854\) | 10.7094 | − | 7.78087i | 0.366470 | − | 0.266256i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.0330 | − | 7.28939i | −0.342920 | − | 0.249146i | ||||
\(857\) | 19.8211 | − | 19.8211i | 0.677078 | − | 0.677078i | −0.282260 | − | 0.959338i | \(-0.591084\pi\) |
0.959338 | + | 0.282260i | \(0.0910842\pi\) | |||||||
\(858\) | 21.5508 | − | 18.0272i | 0.735734 | − | 0.615437i | ||||
\(859\) | 35.8942 | + | 11.6627i | 1.22469 | + | 0.397927i | 0.848789 | − | 0.528732i | \(-0.177332\pi\) |
0.375904 | + | 0.926659i | \(0.377332\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.3508 | − | 19.8983i | 0.591315 | − | 0.678131i | ||||
\(862\) | −24.8742 | + | 12.6740i | −0.847217 | + | 0.431679i | ||||
\(863\) | −22.6754 | + | 11.5537i | −0.771879 | + | 0.393292i | −0.795131 | − | 0.606438i | \(-0.792598\pi\) |
0.0232522 | + | 0.999730i | \(0.492598\pi\) | |||||||
\(864\) | −4.85953 | + | 1.83984i | −0.165324 | + | 0.0625925i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.48379 | − | 0.807033i | −0.0844027 | − | 0.0274241i | ||||
\(867\) | −20.9045 | − | 24.9906i | −0.709954 | − | 0.848725i | ||||
\(868\) | −11.5082 | + | 11.5082i | −0.390614 | + | 0.390614i | ||||
\(869\) | −26.0675 | − | 18.9392i | −0.884280 | − | 0.642467i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.20831 | − | 1.60443i | 0.0748258 | − | 0.0543641i | ||||
\(872\) | 0.436834 | − | 2.75806i | 0.0147931 | − | 0.0933998i | ||||
\(873\) | −16.2750 | + | 11.3218i | −0.550826 | + | 0.383185i | ||||
\(874\) | 5.88827i | 0.199174i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.5061 | + | 8.08714i | −0.456327 | + | 0.273239i | ||||
\(877\) | −15.4427 | + | 30.3080i | −0.521463 | + | 1.02343i | 0.468679 | + | 0.883368i | \(0.344730\pi\) |
−0.990143 | + | 0.140061i | \(0.955270\pi\) | |||||||
\(878\) | 10.8939 | + | 1.72542i | 0.367651 | + | 0.0582302i | ||||
\(879\) | 9.07195 | − | 21.2815i | 0.305989 | − | 0.717808i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.1879 | + | 37.4210i | −0.915985 | + | 1.26074i | 0.0490965 | + | 0.998794i | \(0.484366\pi\) |
−0.965081 | + | 0.261951i | \(0.915634\pi\) | |||||||
\(882\) | −1.14347 | − | 3.78150i | −0.0385027 | − | 0.127330i | ||||
\(883\) | −28.9570 | + | 4.58634i | −0.974480 | + | 0.154343i | −0.623315 | − | 0.781971i | \(-0.714215\pi\) |
−0.351165 | + | 0.936313i | \(0.614215\pi\) | |||||||
\(884\) | 10.9376 | − | 33.6624i | 0.367870 | − | 1.13219i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.577651 | + | 1.77783i | 0.0194065 | + | 0.0597272i | ||||
\(887\) | −11.4107 | − | 22.3947i | −0.383133 | − | 0.751940i | 0.616233 | − | 0.787564i | \(-0.288658\pi\) |
−0.999365 | + | 0.0356241i | \(0.988658\pi\) | |||||||
\(888\) | 7.42447 | − | 11.8413i | 0.249149 | − | 0.397367i | ||||
\(889\) | −34.3666 | + | 11.1664i | −1.15262 | + | 0.374509i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.65822 | − | 23.7683i | −0.223059 | − | 0.796270i | ||||
\(892\) | 0.850889 | + | 5.37230i | 0.0284899 | + | 0.179878i | ||||
\(893\) | −17.0179 | − | 17.0179i | −0.569481 | − | 0.569481i | ||||
\(894\) | −1.84456 | + | 20.7181i | −0.0616913 | + | 0.692916i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.69511 | − | 2.33312i | −0.0566297 | − | 0.0779441i | ||||
\(897\) | 4.34201 | + | 10.7944i | 0.144976 | + | 0.360415i | ||||
\(898\) | 18.2869 | + | 9.31762i | 0.610240 | + | 0.310933i | ||||
\(899\) | 16.3657 | 0.545828 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0545 | 1.06789 | ||||||||
\(902\) | 12.9156 | + | 6.58084i | 0.430043 | + | 0.219118i | ||||
\(903\) | 8.19310 | + | 20.3683i | 0.272649 | + | 0.677816i | ||||
\(904\) | −2.71701 | − | 3.73964i | −0.0903664 | − | 0.124379i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.70921 | + | 19.1978i | −0.0567846 | + | 0.637803i | ||||
\(907\) | 38.3276 | + | 38.3276i | 1.27265 | + | 1.27265i | 0.944694 | + | 0.327952i | \(0.106358\pi\) |
0.327952 | + | 0.944694i | \(0.393642\pi\) | |||||||
\(908\) | 3.06957 | + | 19.3805i | 0.101867 | + | 0.643164i | ||||
\(909\) | 7.33247 | + | 7.63967i | 0.243203 | + | 0.253392i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.3746 | − | 9.21947i | 0.940093 | − | 0.305455i | 0.201409 | − | 0.979507i | \(-0.435448\pi\) |
0.738683 | + | 0.674053i | \(0.235448\pi\) | |||||||
\(912\) | 4.77033 | − | 7.60818i | 0.157961 | − | 0.251932i | ||||
\(913\) | 15.0361 | + | 29.5101i | 0.497623 | + | 0.976640i | ||||
\(914\) | 4.82892 | + | 14.8619i | 0.159727 | + | 0.491588i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.40628 | − | 16.6388i | 0.178628 | − | 0.549762i | ||||
\(917\) | 33.9499 | − | 5.37713i | 1.12112 | − | 0.177569i | ||||
\(918\) | −23.0122 | − | 20.9124i | −0.759515 | − | 0.690213i | ||||
\(919\) | 8.11678 | − | 11.1718i | 0.267748 | − | 0.368523i | −0.653880 | − | 0.756598i | \(-0.726860\pi\) |
0.921628 | + | 0.388075i | \(0.126860\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.2739 | + | 52.2515i | −0.733951 | + | 1.72175i | ||||
\(922\) | 13.7799 | + | 2.18253i | 0.453818 | + | 0.0718777i | ||||
\(923\) | 15.3631 | − | 30.1518i | 0.505682 | − | 0.992457i | ||||
\(924\) | 11.7535 | − | 7.03773i | 0.386661 | − | 0.231524i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 32.9648i | − | 1.08329i | ||||||
\(927\) | −11.0546 | − | 15.8909i | −0.363080 | − | 0.521926i | ||||
\(928\) | −0.453655 | + | 2.86426i | −0.0148919 | + | 0.0940240i | ||||
\(929\) | −0.637117 | + | 0.462892i | −0.0209031 | + | 0.0151870i | −0.598188 | − | 0.801356i | \(-0.704112\pi\) |
0.577285 | + | 0.816543i | \(0.304112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.52351 | + | 4.01306i | 0.181026 | + | 0.131523i | ||||
\(932\) | 20.5218 | − | 20.5218i | 0.672214 | − | 0.672214i | ||||
\(933\) | 11.5039 | + | 13.7526i | 0.376622 | + | 0.450239i | ||||
\(934\) | −3.51708 | − | 1.14277i | −0.115082 | − | 0.0373925i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.13471 | − | 17.4650i | 0.102461 | − | 0.570860i | ||||
\(937\) | −3.72797 | + | 1.89949i | −0.121787 | + | 0.0620538i | −0.513823 | − | 0.857896i | \(-0.671771\pi\) |
0.392035 | + | 0.919950i | \(0.371771\pi\) | |||||||
\(938\) | 1.18586 | − | 0.604224i | 0.0387196 | − | 0.0197286i | ||||
\(939\) | 15.6165 | − | 17.9093i | 0.509625 | − | 0.584447i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.1196 | + | 3.93788i | 0.395086 | + | 0.128371i | 0.499821 | − | 0.866129i | \(-0.333399\pi\) |
−0.104734 | + | 0.994500i | \(0.533399\pi\) | |||||||
\(942\) | −21.8168 | + | 18.2496i | −0.710829 | + | 0.594604i | ||||
\(943\) | −4.24454 | + | 4.24454i | −0.138221 | + | 0.138221i | ||||
\(944\) | −2.38803 | − | 1.73500i | −0.0777236 | − | 0.0564695i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.75214 | + | 7.08535i | −0.317069 | + | 0.230364i | ||||
\(947\) | −6.23127 | + | 39.3427i | −0.202489 | + | 1.27847i | 0.651690 | + | 0.758486i | \(0.274060\pi\) |
−0.854179 | + | 0.519980i | \(0.825940\pi\) | |||||||
\(948\) | −20.3015 | + | 1.38839i | −0.659362 | + | 0.0450929i | ||||
\(949\) | − | 53.7570i | − | 1.74503i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.7940 | + | 28.0470i | 0.544581 | + | 0.909486i | ||||
\(952\) | 7.83489 | − | 15.3768i | 0.253930 | − | 0.498366i | ||||
\(953\) | −25.3183 | − | 4.01002i | −0.820139 | − | 0.129897i | −0.267755 | − | 0.963487i | \(-0.586282\pi\) |
−0.552384 | + | 0.833590i | \(0.686282\pi\) | |||||||
\(954\) | 15.9199 | − | 2.18771i | 0.515427 | − | 0.0708299i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.32263 | − | 4.57321i | 0.107462 | − | 0.147908i | ||||
\(957\) | −13.3614 | − | 3.35311i | −0.431913 | − | 0.108391i | ||||
\(958\) | 5.31302 | − | 0.841500i | 0.171656 | − | 0.0271876i | ||||
\(959\) | 17.7077 | − | 54.4987i | 0.571811 | − | 1.75985i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.262130 | + | 0.806752i | 0.00845579 | + | 0.0260243i | ||||
\(962\) | 21.6676 | + | 42.5251i | 0.698592 | + | 1.37106i | ||||
\(963\) | 0.763197 | − | 37.1965i | 0.0245937 | − | 1.19864i | ||||
\(964\) | 13.4069 | − | 4.35617i | 0.431807 | − | 0.140303i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.26768 | + | 5.52955i | 0.0407871 | + | 0.177910i | ||||
\(967\) | 0.593924 | + | 3.74989i | 0.0190993 | + | 0.120588i | 0.995396 | − | 0.0958486i | \(-0.0305565\pi\) |
−0.976297 | + | 0.216437i | \(0.930556\pi\) | |||||||
\(968\) | −2.45946 | − | 2.45946i | −0.0790499 | − | 0.0790499i | ||||
\(969\) | 53.5264 | + | 4.76554i | 1.71952 | + | 0.153091i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.56008 | − | 2.14727i | −0.0500655 | − | 0.0689092i | 0.783250 | − | 0.621707i | \(-0.213560\pi\) |
−0.833316 | + | 0.552797i | \(0.813560\pi\) | |||||||
\(972\) | −12.8563 | − | 8.81562i | −0.412366 | − | 0.282761i | ||||
\(973\) | −24.5303 | − | 12.4988i | −0.786406 | − | 0.400694i | ||||
\(974\) | 4.19638 | 0.134461 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.59018 | 0.146928 | ||||||||
\(977\) | −15.9953 | − | 8.15001i | −0.511735 | − | 0.260742i | 0.179001 | − | 0.983849i | \(-0.442713\pi\) |
−0.690736 | + | 0.723107i | \(0.742713\pi\) | |||||||
\(978\) | −10.5266 | + | 4.23429i | −0.336604 | + | 0.135398i | ||||
\(979\) | 2.09807 | + | 2.88774i | 0.0670546 | + | 0.0922927i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.54070 | − | 3.64931i | 0.240756 | − | 0.116513i | ||||
\(982\) | 22.3318 | + | 22.3318i | 0.712635 | + | 0.712635i | ||||
\(983\) | −6.25433 | − | 39.4883i | −0.199482 | − | 1.25948i | −0.860632 | − | 0.509227i | \(-0.829931\pi\) |
0.661150 | − | 0.750254i | \(-0.270069\pi\) | |||||||
\(984\) | 8.92300 | − | 2.04565i | 0.284455 | − | 0.0652131i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.5046 | + | 5.36268i | −0.525614 | + | 0.170782i | ||||
\(987\) | −19.6449 | − | 12.3173i | −0.625303 | − | 0.392065i | ||||
\(988\) | 13.9218 | + | 27.3230i | 0.442910 | + | 0.869260i | ||||
\(989\) | −1.54254 | − | 4.74745i | −0.0490499 | − | 0.150960i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.5601 | + | 38.6560i | −0.398984 | + | 1.22795i | 0.526831 | + | 0.849970i | \(0.323380\pi\) |
−0.925815 | + | 0.377977i | \(0.876620\pi\) | |||||||
\(992\) | −5.57395 | + | 0.882826i | −0.176973 | + | 0.0280298i | ||||
\(993\) | −13.3799 | + | 53.3158i | −0.424597 | + | 1.69193i | ||||
\(994\) | 9.69837 | − | 13.3487i | 0.307614 | − | 0.423394i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 19.2412 | + | 8.20219i | 0.609681 | + | 0.259896i | ||||
\(997\) | −11.2375 | − | 1.77985i | −0.355896 | − | 0.0563684i | −0.0240735 | − | 0.999710i | \(-0.507664\pi\) |
−0.331823 | + | 0.943342i | \(0.607664\pi\) | |||||||
\(998\) | 4.65505 | − | 9.13605i | 0.147353 | − | 0.289197i | ||||
\(999\) | 41.8812 | − | 2.00207i | 1.32506 | − | 0.0633427i |
(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 | 750.2.l.c.107.7 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.c.107.4 | 80 | ||
5.2 | odd | 4 | 750.2.l.b.143.2 | 80 | |||
5.3 | odd | 4 | 150.2.l.a.83.9 | yes | 80 | ||
5.4 | even | 2 | 750.2.l.a.107.4 | 80 | |||
15.2 | even | 4 | 750.2.l.b.143.7 | 80 | |||
15.8 | even | 4 | 150.2.l.a.83.4 | yes | 80 | ||
15.14 | odd | 2 | 750.2.l.a.107.7 | 80 | |||
25.3 | odd | 20 | inner | 750.2.l.c.743.4 | 80 | ||
25.4 | even | 10 | 750.2.l.b.257.7 | 80 | |||
25.21 | even | 5 | 150.2.l.a.47.4 | ✓ | 80 | ||
25.22 | odd | 20 | 750.2.l.a.743.7 | 80 | |||
75.29 | odd | 10 | 750.2.l.b.257.2 | 80 | |||
75.47 | even | 20 | 750.2.l.a.743.4 | 80 | |||
75.53 | even | 20 | inner | 750.2.l.c.743.7 | 80 | ||
75.71 | odd | 10 | 150.2.l.a.47.9 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.47.4 | ✓ | 80 | 25.21 | even | 5 | ||
150.2.l.a.47.9 | yes | 80 | 75.71 | odd | 10 | ||
150.2.l.a.83.4 | yes | 80 | 15.8 | even | 4 | ||
150.2.l.a.83.9 | yes | 80 | 5.3 | odd | 4 | ||
750.2.l.a.107.4 | 80 | 5.4 | even | 2 | |||
750.2.l.a.107.7 | 80 | 15.14 | odd | 2 | |||
750.2.l.a.743.4 | 80 | 75.47 | even | 20 | |||
750.2.l.a.743.7 | 80 | 25.22 | odd | 20 | |||
750.2.l.b.143.2 | 80 | 5.2 | odd | 4 | |||
750.2.l.b.143.7 | 80 | 15.2 | even | 4 | |||
750.2.l.b.257.2 | 80 | 75.29 | odd | 10 | |||
750.2.l.b.257.7 | 80 | 25.4 | even | 10 | |||
750.2.l.c.107.4 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.c.107.7 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.c.743.4 | 80 | 25.3 | odd | 20 | inner | ||
750.2.l.c.743.7 | 80 | 75.53 | even | 20 | inner |