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 | 257.7 | ||
Character | \(\chi\) | \(=\) | 750.257 |
Dual form | 750.2.l.b.143.7 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{17}{20}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.453990 | + | 0.891007i | 0.321020 | + | 0.630037i | ||||
\(3\) | −1.32853 | + | 1.11131i | −0.767028 | + | 0.641614i | ||||
\(4\) | −0.587785 | + | 0.809017i | −0.293893 | + | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.59332 | − | 0.679206i | −0.650471 | − | 0.277285i | ||||
\(7\) | −2.03922 | − | 2.03922i | −0.770754 | − | 0.770754i | 0.207484 | − | 0.978238i | \(-0.433472\pi\) |
−0.978238 | + | 0.207484i | \(0.933472\pi\) | |||||||
\(8\) | −0.987688 | − | 0.156434i | −0.349201 | − | 0.0553079i | ||||
\(9\) | 0.529988 | − | 2.95281i | 0.176663 | − | 0.984271i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.60836 | − | 0.847507i | −0.786450 | − | 0.255533i | −0.111858 | − | 0.993724i | \(-0.535680\pi\) |
−0.674592 | + | 0.738191i | \(0.735680\pi\) | |||||||
\(12\) | −0.118176 | − | 1.72801i | −0.0341146 | − | 0.498835i | ||||
\(13\) | 5.27002 | + | 2.68521i | 1.46164 | + | 0.744744i | 0.990526 | − | 0.137328i | \(-0.0438513\pi\) |
0.471116 | + | 0.882071i | \(0.343851\pi\) | |||||||
\(14\) | 0.891173 | − | 2.74275i | 0.238176 | − | 0.733031i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | − | 0.951057i | −0.0772542 | − | 0.237764i | ||||
\(17\) | 0.936136 | − | 5.91053i | 0.227046 | − | 1.43351i | −0.566026 | − | 0.824387i | \(-0.691520\pi\) |
0.793073 | − | 0.609127i | \(-0.208480\pi\) | |||||||
\(18\) | 2.87159 | − | 0.868327i | 0.676839 | − | 0.204667i | ||||
\(19\) | −3.04743 | − | 4.19443i | −0.699129 | − | 0.962269i | −0.999963 | − | 0.00859233i | \(-0.997265\pi\) |
0.300834 | − | 0.953677i | \(-0.402735\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.97538 | + | 0.442965i | 1.08572 | + | 0.0966630i | ||||
\(22\) | −0.429036 | − | 2.70883i | −0.0914707 | − | 0.577523i | ||||
\(23\) | −1.01194 | + | 0.515607i | −0.211003 | + | 0.107512i | −0.556298 | − | 0.830983i | \(-0.687779\pi\) |
0.345295 | + | 0.938494i | \(0.387779\pi\) | |||||||
\(24\) | 1.48602 | − | 0.889798i | 0.303333 | − | 0.181629i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.91469i | 1.15997i | ||||||||
\(27\) | 2.57738 | + | 4.51188i | 0.496017 | + | 0.868313i | ||||
\(28\) | 2.84839 | − | 0.451141i | 0.538296 | − | 0.0852576i | ||||
\(29\) | 2.34612 | + | 1.70456i | 0.435664 | + | 0.316528i | 0.783910 | − | 0.620875i | \(-0.213223\pi\) |
−0.348246 | + | 0.937403i | \(0.613223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.56563 | − | 3.31712i | 0.820011 | − | 0.595773i | −0.0967046 | − | 0.995313i | \(-0.530830\pi\) |
0.916716 | + | 0.399540i | \(0.130830\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 4.40713 | − | 1.77275i | 0.767182 | − | 0.308596i | ||||
\(34\) | 5.69132 | − | 1.84922i | 0.976053 | − | 0.317139i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.07736 | + | 2.16439i | 0.346226 | + | 0.360732i | ||||
\(37\) | 3.66336 | − | 7.18975i | 0.602253 | − | 1.18199i | −0.365671 | − | 0.930744i | \(-0.619161\pi\) |
0.967924 | − | 0.251243i | \(-0.0808395\pi\) | |||||||
\(38\) | 2.35376 | − | 4.61952i | 0.381830 | − | 0.749384i | ||||
\(39\) | −9.98549 | + | 2.28924i | −1.59896 | + | 0.366571i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.02666 | + | 1.63326i | −0.785033 | + | 0.255073i | −0.673988 | − | 0.738743i | \(-0.735420\pi\) |
−0.111045 | + | 0.993815i | \(0.535420\pi\) | |||||||
\(42\) | 1.86409 | + | 4.63420i | 0.287635 | + | 0.715072i | ||||
\(43\) | 3.10789 | − | 3.10789i | 0.473950 | − | 0.473950i | −0.429241 | − | 0.903190i | \(-0.641219\pi\) |
0.903190 | + | 0.429241i | \(0.141219\pi\) | |||||||
\(44\) | 2.21880 | − | 1.61205i | 0.334497 | − | 0.243026i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.918819 | − | 0.667561i | −0.135473 | − | 0.0984265i | ||||
\(47\) | −4.58484 | + | 0.726167i | −0.668768 | + | 0.105922i | −0.481581 | − | 0.876402i | \(-0.659937\pi\) |
−0.187187 | + | 0.982324i | \(0.559937\pi\) | |||||||
\(48\) | 1.46746 | + | 0.920095i | 0.211809 | + | 0.132804i | ||||
\(49\) | 1.31687i | 0.188124i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.32473 | + | 8.89266i | 0.745612 | + | 1.24522i | ||||
\(52\) | −5.27002 | + | 2.68521i | −0.730821 | + | 0.372372i | ||||
\(53\) | 0.837944 | + | 5.29057i | 0.115100 | + | 0.726715i | 0.975972 | + | 0.217894i | \(0.0699187\pi\) |
−0.860872 | + | 0.508821i | \(0.830081\pi\) | |||||||
\(54\) | −2.85001 | + | 4.34482i | −0.387837 | + | 0.591255i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.69511 | + | 2.33312i | 0.226519 | + | 0.311777i | ||||
\(57\) | 8.70992 | + | 2.18579i | 1.15366 | + | 0.289516i | ||||
\(58\) | −0.453655 | + | 2.86426i | −0.0595678 | + | 0.376096i | ||||
\(59\) | −0.912145 | − | 2.80729i | −0.118751 | − | 0.365478i | 0.873960 | − | 0.485998i | \(-0.161544\pi\) |
−0.992711 | + | 0.120520i | \(0.961544\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.41844 | + | 4.36552i | −0.181613 | + | 0.558947i | −0.999874 | − | 0.0159002i | \(-0.994939\pi\) |
0.818261 | + | 0.574847i | \(0.194939\pi\) | |||||||
\(62\) | 5.02833 | + | 2.56206i | 0.638599 | + | 0.325382i | ||||
\(63\) | −7.10221 | + | 4.94069i | −0.894795 | + | 0.622468i | ||||
\(64\) | 0.951057 | + | 0.309017i | 0.118882 | + | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.58033 | + | 3.12197i | 0.440708 | + | 0.384287i | ||||
\(67\) | 0.455818 | + | 0.0721944i | 0.0556870 | + | 0.00881995i | 0.184216 | − | 0.982886i | \(-0.441025\pi\) |
−0.128529 | + | 0.991706i | \(0.541025\pi\) | |||||||
\(68\) | 4.23147 | + | 4.23147i | 0.513141 | + | 0.513141i | ||||
\(69\) | 0.771390 | − | 1.80957i | 0.0928645 | − | 0.217847i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.36294 | − | 4.62869i | 0.399107 | − | 0.549324i | −0.561412 | − | 0.827536i | \(-0.689742\pi\) |
0.960520 | + | 0.278212i | \(0.0897418\pi\) | |||||||
\(72\) | −0.985385 | + | 2.83355i | −0.116129 | + | 0.333937i | ||||
\(73\) | −4.12620 | − | 8.09812i | −0.482935 | − | 0.947814i | −0.995991 | − | 0.0894583i | \(-0.971486\pi\) |
0.513055 | − | 0.858356i | \(-0.328514\pi\) | |||||||
\(74\) | 8.06924 | 0.938031 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.18460 | 0.594715 | ||||||||
\(77\) | 3.59077 | + | 7.04728i | 0.409206 | + | 0.803113i | ||||
\(78\) | −6.57304 | − | 7.85784i | −0.744250 | − | 0.889725i | ||||
\(79\) | 6.90557 | − | 9.50470i | 0.776937 | − | 1.06936i | −0.218676 | − | 0.975798i | \(-0.570174\pi\) |
0.995613 | − | 0.0935650i | \(-0.0298263\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.43823 | − | 3.12991i | −0.937581 | − | 0.347768i | ||||
\(82\) | −3.73730 | − | 3.73730i | −0.412716 | − | 0.412716i | ||||
\(83\) | −11.9275 | − | 1.88912i | −1.30921 | − | 0.207358i | −0.537462 | − | 0.843288i | \(-0.680617\pi\) |
−0.771747 | + | 0.635930i | \(0.780617\pi\) | |||||||
\(84\) | −3.28282 | + | 3.76480i | −0.358185 | + | 0.410773i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.18011 | + | 1.35820i | 0.450753 | + | 0.146458i | ||||
\(87\) | −5.01118 | + | 0.342708i | −0.537255 | + | 0.0367421i | ||||
\(88\) | 2.44367 | + | 1.24511i | 0.260496 | + | 0.132729i | ||||
\(89\) | 0.402182 | − | 1.23779i | 0.0426312 | − | 0.131205i | −0.927476 | − | 0.373884i | \(-0.878026\pi\) |
0.970107 | + | 0.242678i | \(0.0780260\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.27101 | − | 16.2225i | −0.552552 | − | 1.70058i | ||||
\(92\) | 0.177666 | − | 1.12174i | 0.0185230 | − | 0.116950i | ||||
\(93\) | −2.37923 | + | 9.48072i | −0.246715 | + | 0.983105i | ||||
\(94\) | −2.72849 | − | 3.75545i | −0.281423 | − | 0.387345i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.153600 | + | 1.72523i | −0.0156767 | + | 0.176080i | ||||
\(97\) | −1.03381 | − | 6.52722i | −0.104967 | − | 0.662738i | −0.982926 | − | 0.184002i | \(-0.941095\pi\) |
0.877959 | − | 0.478737i | \(-0.158905\pi\) | |||||||
\(98\) | −1.17334 | + | 0.597845i | −0.118525 | + | 0.0603915i | ||||
\(99\) | −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 | \(-0.0561896\pi\) | |||||||
\(102\) | −5.50604 | + | 8.78155i | −0.545179 | + | 0.869503i | ||||
\(103\) | 6.37316 | − | 1.00941i | 0.627966 | − | 0.0994601i | 0.165664 | − | 0.986182i | \(-0.447023\pi\) |
0.462303 | + | 0.886722i | \(0.347023\pi\) | |||||||
\(104\) | −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 | −0.142106 | − | 0.989851i | \(-0.545387\pi\) |
0.989851 | + | 0.142106i | \(0.0453874\pi\) | |||||||
\(108\) | −5.16514 | − | 0.566874i | −0.497016 | − | 0.0545474i | ||||
\(109\) | 2.65577 | − | 0.862912i | 0.254377 | − | 0.0826520i | −0.179053 | − | 0.983839i | \(-0.557303\pi\) |
0.433430 | + | 0.901187i | \(0.357303\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.12314 | + | 13.6229i | 0.296435 | + | 1.29303i | ||||
\(112\) | −1.30926 | + | 2.56957i | −0.123714 | + | 0.242802i | ||||
\(113\) | −2.09855 | + | 4.11863i | −0.197415 | + | 0.387449i | −0.968399 | − | 0.249406i | \(-0.919765\pi\) |
0.770984 | + | 0.636854i | \(0.219765\pi\) | |||||||
\(114\) | 2.00666 | + | 8.75292i | 0.187941 | + | 0.819786i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.75803 | + | 0.896139i | −0.256077 | + | 0.0832044i | ||||
\(117\) | 10.7220 | − | 14.1383i | 0.991247 | − | 1.30708i | ||||
\(118\) | 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 | ||||
\(122\) | −4.53366 | + | 0.718062i | −0.410459 | + | 0.0650103i | ||||
\(123\) | 4.86302 | − | 7.75601i | 0.438484 | − | 0.699336i | ||||
\(124\) | 5.64343i | 0.506795i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.62652 | − | 4.08509i | −0.679424 | − | 0.363929i | ||||
\(127\) | −11.1643 | + | 5.68850i | −0.990672 | + | 0.504773i | −0.872707 | − | 0.488245i | \(-0.837637\pi\) |
−0.117966 | + | 0.993018i | \(0.537637\pi\) | |||||||
\(128\) | 0.156434 | + | 0.987688i | 0.0138270 | + | 0.0873001i | ||||
\(129\) | −0.675105 | + | 7.58276i | −0.0594397 | + | 0.667625i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.00579 | − | 9.64264i | −0.612099 | − | 0.842482i | 0.384649 | − | 0.923063i | \(-0.374322\pi\) |
−0.996748 | + | 0.0805811i | \(0.974322\pi\) | |||||||
\(132\) | −1.15626 | + | 4.60744i | −0.100639 | + | 0.401026i | ||||
\(133\) | −2.33899 | + | 14.7678i | −0.202816 | + | 1.28053i | ||||
\(134\) | 0.142611 | + | 0.438912i | 0.0123197 | + | 0.0379162i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.84922 | + | 5.69132i | −0.158569 | + | 0.488026i | ||||
\(137\) | −17.7044 | − | 9.02083i | −1.51259 | − | 0.770702i | −0.516268 | − | 0.856427i | \(-0.672679\pi\) |
−0.996319 | + | 0.0857255i | \(0.972679\pi\) | |||||||
\(138\) | 1.96255 | − | 0.134216i | 0.167063 | − | 0.0114252i | ||||
\(139\) | 9.07922 | + | 2.95002i | 0.770090 | + | 0.250217i | 0.667603 | − | 0.744517i | \(-0.267320\pi\) |
0.102486 | + | 0.994734i | \(0.467320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.28411 | − | 6.05991i | 0.445002 | − | 0.510336i | ||||
\(142\) | 5.65093 | + | 0.895020i | 0.474216 | + | 0.0751084i | ||||
\(143\) | −11.4704 | − | 11.4704i | −0.959201 | − | 0.959201i | ||||
\(144\) | −2.97207 | + | 0.408421i | −0.247672 | + | 0.0340351i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.34223 | − | 7.35294i | 0.442126 | − | 0.608534i | ||||
\(147\) | −1.46344 | − | 1.74950i | −0.120703 | − | 0.144296i | ||||
\(148\) | 3.66336 | + | 7.18975i | 0.301126 | + | 0.590994i | ||||
\(149\) | −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 | \(0.649567\pi\) | |||||||
\(152\) | 2.35376 | + | 4.61952i | 0.190915 | + | 0.374692i | ||||
\(153\) | −16.9566 | − | 5.89674i | −1.37086 | − | 0.476724i | ||||
\(154\) | −4.64900 | + | 6.39880i | −0.374627 | + | 0.515630i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.01729 | − | 9.42401i | 0.321641 | − | 0.754524i | ||||
\(157\) | 11.6119 | + | 11.6119i | 0.926732 | + | 0.926732i | 0.997493 | − | 0.0707617i | \(-0.0225430\pi\) |
−0.0707617 | + | 0.997493i | \(0.522543\pi\) | |||||||
\(158\) | 11.6038 | + | 1.83786i | 0.923150 | + | 0.146213i | ||||
\(159\) | −6.99269 | − | 6.09747i | −0.554556 | − | 0.483561i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.11500 | + | 1.01213i | 0.245497 | + | 0.0797667i | ||||
\(162\) | −1.04210 | − | 8.93946i | −0.0818753 | − | 0.702351i | ||||
\(163\) | −5.83680 | − | 2.97400i | −0.457173 | − | 0.232941i | 0.210209 | − | 0.977656i | \(-0.432585\pi\) |
−0.667383 | + | 0.744715i | \(0.732585\pi\) | |||||||
\(164\) | 1.63326 | − | 5.02666i | 0.127536 | − | 0.392516i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.73173 | − | 11.4851i | −0.289639 | − | 0.891416i | ||||
\(167\) | −2.65903 | + | 16.7884i | −0.205762 | + | 1.29913i | 0.641159 | + | 0.767408i | \(0.278454\pi\) |
−0.846920 | + | 0.531720i | \(0.821546\pi\) | |||||||
\(168\) | −4.84483 | − | 1.21583i | −0.373787 | − | 0.0938035i | ||||
\(169\) | 12.9216 | + | 17.7850i | 0.993968 | + | 1.36808i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.0005 | + | 6.77551i | −1.07064 | + | 0.518136i | ||||
\(172\) | 0.687565 | + | 4.34111i | 0.0524263 | + | 0.331007i | ||||
\(173\) | 6.04954 | − | 3.08240i | 0.459938 | − | 0.234350i | −0.208639 | − | 0.977993i | \(-0.566903\pi\) |
0.668578 | + | 0.743642i | \(0.266903\pi\) | |||||||
\(174\) | −2.58038 | − | 4.30941i | −0.195618 | − | 0.326696i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.74259i | 0.206731i | ||||||||
\(177\) | 4.33158 | + | 2.71590i | 0.325581 | + | 0.204140i | ||||
\(178\) | 1.28546 | − | 0.203597i | 0.0963496 | − | 0.0152603i | ||||
\(179\) | 7.59016 | + | 5.51457i | 0.567315 | + | 0.412179i | 0.834129 | − | 0.551569i | \(-0.185971\pi\) |
−0.266814 | + | 0.963748i | \(0.585971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.3025 | − | 8.93831i | 0.914440 | − | 0.664379i | −0.0276940 | − | 0.999616i | \(-0.508816\pi\) |
0.942134 | + | 0.335237i | \(0.108816\pi\) | |||||||
\(182\) | 12.0614 | − | 12.0614i | 0.894048 | − | 0.894048i | ||||
\(183\) | −2.96699 | − | 7.37605i | −0.219326 | − | 0.545253i | ||||
\(184\) | 1.08014 | − | 0.350958i | 0.0796287 | − | 0.0258729i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.52753 | + | 2.18425i | −0.698593 | + | 0.160157i | ||||
\(187\) | −7.45099 | + | 14.6234i | −0.544871 | + | 1.06937i | ||||
\(188\) | 2.10742 | − | 4.13604i | 0.153699 | − | 0.301652i | ||||
\(189\) | 3.94488 | − | 14.4566i | 0.286948 | − | 1.05156i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.2756 | + | 3.98859i | −0.888232 | + | 0.288604i | −0.717371 | − | 0.696691i | \(-0.754655\pi\) |
−0.170861 | + | 0.985295i | \(0.554655\pi\) | |||||||
\(192\) | −1.60692 | + | 0.646378i | −0.115970 | + | 0.0466483i | ||||
\(193\) | −3.91447 | + | 3.91447i | −0.281770 | + | 0.281770i | −0.833815 | − | 0.552045i | \(-0.813848\pi\) |
0.552045 | + | 0.833815i | \(0.313848\pi\) | |||||||
\(194\) | 5.34645 | − | 3.88442i | 0.383853 | − | 0.278885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.06537 | − | 0.774035i | −0.0760977 | − | 0.0552882i | ||||
\(197\) | −25.2645 | + | 4.00150i | −1.80002 | + | 0.285095i | −0.964445 | − | 0.264282i | \(-0.914865\pi\) |
−0.835574 | + | 0.549378i | \(0.814865\pi\) | |||||||
\(198\) | −8.22604 | − | 0.168782i | −0.584599 | − | 0.0119948i | ||||
\(199\) | 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 | ||||
\(202\) | 3.14499 | − | 1.60245i | 0.221281 | − | 0.112748i | ||||
\(203\) | −1.30829 | − | 8.26024i | −0.0918242 | − | 0.579755i | ||||
\(204\) | −10.3241 | − | 0.919171i | −0.722832 | − | 0.0643548i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.79275 | + | 5.22027i | 0.264253 | + | 0.363713i | ||||
\(207\) | 0.986179 | + | 3.26133i | 0.0685442 | + | 0.226678i | ||||
\(208\) | 0.925261 | − | 5.84187i | 0.0641553 | − | 0.405061i | ||||
\(209\) | 4.39399 | + | 13.5233i | 0.303939 | + | 0.935427i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.99342 | − | 6.13511i | 0.137232 | − | 0.422358i | −0.858698 | − | 0.512482i | \(-0.828726\pi\) |
0.995931 | + | 0.0901236i | \(0.0287262\pi\) | |||||||
\(212\) | −4.77269 | − | 2.43181i | −0.327790 | − | 0.167017i | ||||
\(213\) | 0.676131 | + | 9.88661i | 0.0463278 | + | 0.677420i | ||||
\(214\) | 11.7945 | + | 3.83226i | 0.806254 | + | 0.261968i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.83984 | − | 4.85953i | −0.125185 | − | 0.330649i | ||||
\(217\) | −16.0747 | − | 2.54598i | −1.09122 | − | 0.172832i | ||||
\(218\) | 1.97456 | + | 1.97456i | 0.133734 | + | 0.133734i | ||||
\(219\) | 14.4813 | + | 6.17313i | 0.978555 | + | 0.417141i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.8045 | − | 28.6349i | 1.39946 | − | 1.92619i | ||||
\(222\) | −10.7202 | + | 8.96742i | −0.719495 | + | 0.601854i | ||||
\(223\) | 2.46937 | + | 4.84642i | 0.165362 | + | 0.324540i | 0.958786 | − | 0.284128i | \(-0.0917040\pi\) |
−0.793425 | + | 0.608668i | \(0.791704\pi\) | |||||||
\(224\) | −2.88390 | −0.192689 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.62245 | −0.307481 | ||||||||
\(227\) | 8.90823 | + | 17.4834i | 0.591260 | + | 1.16041i | 0.971835 | + | 0.235662i | \(0.0757260\pi\) |
−0.380575 | + | 0.924750i | \(0.624274\pi\) | |||||||
\(228\) | −6.88791 | + | 5.76169i | −0.456163 | + | 0.381577i | ||||
\(229\) | 10.2833 | − | 14.1538i | 0.679543 | − | 0.935310i | −0.320385 | − | 0.947287i | \(-0.603812\pi\) |
0.999928 | + | 0.0119768i | \(0.00381244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.6022 | − | 5.37208i | −0.829161 | − | 0.353457i | ||||
\(232\) | −2.05059 | − | 2.05059i | −0.134628 | − | 0.134628i | ||||
\(233\) | 28.6649 | + | 4.54007i | 1.87790 | + | 0.297430i | 0.987484 | − | 0.157718i | \(-0.0504138\pi\) |
0.890416 | + | 0.455148i | \(0.150414\pi\) | |||||||
\(234\) | 17.4650 | + | 3.13471i | 1.14172 | + | 0.204923i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.80729 | + | 0.912145i | 0.182739 | + | 0.0593756i | ||||
\(237\) | 1.38839 | + | 20.3015i | 0.0901857 | + | 1.31872i | ||||
\(238\) | −15.3768 | − | 7.83489i | −0.996733 | − | 0.507861i | ||||
\(239\) | −1.74681 | + | 5.37613i | −0.112992 | + | 0.347753i | −0.991523 | − | 0.129932i | \(-0.958524\pi\) |
0.878531 | + | 0.477685i | \(0.158524\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.35617 | + | 13.4069i | 0.280605 | + | 0.863614i | 0.987682 | + | 0.156477i | \(0.0500137\pi\) |
−0.707076 | + | 0.707137i | \(0.749986\pi\) | |||||||
\(242\) | 0.544110 | − | 3.43537i | 0.0349767 | − | 0.220834i | ||||
\(243\) | 14.6887 | − | 5.21929i | 0.942283 | − | 0.334817i | ||||
\(244\) | −2.69804 | − | 3.71353i | −0.172724 | − | 0.237734i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.11842 | + | 0.811827i | 0.581369 | + | 0.0517602i | ||||
\(247\) | −4.79711 | − | 30.2878i | −0.305233 | − | 1.92716i | ||||
\(248\) | −5.02833 | + | 2.56206i | −0.319299 | + | 0.162691i | ||||
\(249\) | 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 | \(0.815938\pi\) | |||||||
\(252\) | 0.177478 | − | 8.64987i | 0.0111801 | − | 0.544891i | ||||
\(253\) | 3.07648 | − | 0.487266i | 0.193416 | − | 0.0306341i | ||||
\(254\) | −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 | −0.828112 | − | 0.560563i | \(-0.810585\pi\) |
0.560563 | + | 0.828112i | \(0.310585\pi\) | |||||||
\(258\) | −7.06278 | + | 2.84098i | −0.439710 | + | 0.176872i | ||||
\(259\) | −22.1319 | + | 7.19110i | −1.37521 | + | 0.446833i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.27666 | − | 6.02427i | 0.388515 | − | 0.372893i | ||||
\(262\) | 5.41110 | − | 10.6199i | 0.334299 | − | 0.656098i | ||||
\(263\) | 10.8405 | − | 21.2757i | 0.668454 | − | 1.31191i | −0.268777 | − | 0.963203i | \(-0.586619\pi\) |
0.937230 | − | 0.348711i | \(-0.113381\pi\) | |||||||
\(264\) | −4.63019 | + | 1.06150i | −0.284968 | + | 0.0653308i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.2201 | + | 4.62038i | −0.871889 | + | 0.283294i | ||||
\(267\) | 0.841253 | + | 2.09139i | 0.0514839 | + | 0.127991i | ||||
\(268\) | −0.326329 | + | 0.326329i | −0.0199337 | + | 0.0199337i | ||||
\(269\) | 11.2436 | − | 8.16896i | 0.685535 | − | 0.498070i | −0.189654 | − | 0.981851i | \(-0.560737\pi\) |
0.875189 | + | 0.483781i | \(0.160737\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1633 | + | 8.83716i | 0.738868 | + | 0.536819i | 0.892357 | − | 0.451331i | \(-0.149051\pi\) |
−0.153488 | + | 0.988151i | \(0.549051\pi\) | |||||||
\(272\) | −5.91053 | + | 0.936136i | −0.358378 | + | 0.0567616i | ||||
\(273\) | 25.0309 | + | 15.6944i | 1.51494 | + | 0.949867i | ||||
\(274\) | − | 19.8701i | − | 1.20040i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.01056 | + | 1.68771i | 0.0608288 | + | 0.101588i | ||||
\(277\) | 1.61620 | − | 0.823495i | 0.0971080 | − | 0.0494790i | −0.404762 | − | 0.914422i | \(-0.632646\pi\) |
0.501870 | + | 0.864943i | \(0.332646\pi\) | |||||||
\(278\) | 1.49340 | + | 9.42893i | 0.0895679 | + | 0.565509i | ||||
\(279\) | −7.37512 | − | 15.2395i | −0.441537 | − | 0.912364i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.4707 | + | 18.5409i | 0.803597 | + | 1.10606i | 0.992280 | + | 0.124018i | \(0.0395782\pi\) |
−0.188683 | + | 0.982038i | \(0.560422\pi\) | |||||||
\(282\) | 7.79835 | + | 1.95703i | 0.464385 | + | 0.116540i | ||||
\(283\) | 0.445062 | − | 2.81001i | 0.0264562 | − | 0.167038i | −0.970923 | − | 0.239393i | \(-0.923052\pi\) |
0.997379 | + | 0.0723553i | \(0.0230516\pi\) | |||||||
\(284\) | 1.76800 | + | 5.44135i | 0.104912 | + | 0.322885i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.01274 | − | 15.4276i | 0.296409 | − | 0.912255i | ||||
\(287\) | 13.5811 | + | 6.91991i | 0.801666 | + | 0.408469i | ||||
\(288\) | −1.71320 | − | 2.46271i | −0.100951 | − | 0.145117i | ||||
\(289\) | −17.8900 | − | 5.81283i | −1.05236 | − | 0.341931i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.62720 | + | 7.52273i | 0.505735 | + | 0.440990i | ||||
\(292\) | 8.97684 | + | 1.42179i | 0.525330 | + | 0.0832041i | ||||
\(293\) | −9.44461 | − | 9.44461i | −0.551760 | − | 0.551760i | 0.375189 | − | 0.926948i | \(-0.377578\pi\) |
−0.926948 | + | 0.375189i | \(0.877578\pi\) | |||||||
\(294\) | 0.894424 | − | 2.09819i | 0.0521639 | − | 0.122369i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.74298 | + | 6.52816i | −0.275680 | + | 0.379441i | ||||
\(297\) | −2.89888 | − | 13.9530i | −0.168210 | − | 0.809633i | ||||
\(298\) | −5.45192 | − | 10.7000i | −0.315821 | − | 0.619834i | ||||
\(299\) | −6.71745 | −0.388480 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.6754 | −0.730597 | ||||||||
\(302\) | −5.05186 | − | 9.91484i | −0.290702 | − | 0.570535i | ||||
\(303\) | 3.92259 | + | 4.68933i | 0.225347 | + | 0.269395i | ||||
\(304\) | −3.04743 | + | 4.19443i | −0.174782 | + | 0.240567i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.44408 | − | 17.7855i | −0.139719 | − | 1.01673i | ||||
\(307\) | 23.1889 | + | 23.1889i | 1.32346 | + | 1.32346i | 0.910955 | + | 0.412506i | \(0.135346\pi\) |
0.412506 | + | 0.910955i | \(0.364654\pi\) | |||||||
\(308\) | −7.81197 | − | 1.23730i | −0.445129 | − | 0.0705014i | ||||
\(309\) | −7.34518 | + | 8.42358i | −0.417852 | + | 0.479201i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.84506 | + | 3.19885i | 0.558262 | + | 0.181390i | 0.574539 | − | 0.818477i | \(-0.305181\pi\) |
−0.0162770 | + | 0.999868i | \(0.505181\pi\) | |||||||
\(312\) | 10.2207 | − | 0.698977i | 0.578631 | − | 0.0395718i | ||||
\(313\) | 12.2235 | + | 6.22820i | 0.690915 | + | 0.352039i | 0.763936 | − | 0.645292i | \(-0.223264\pi\) |
−0.0730212 | + | 0.997330i | \(0.523264\pi\) | |||||||
\(314\) | −5.07459 | + | 15.6180i | −0.286376 | + | 0.881374i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.63047 | + | 11.1734i | 0.204230 | + | 0.628556i | ||||
\(317\) | 2.95253 | − | 18.6415i | 0.165830 | − | 1.04701i | −0.754623 | − | 0.656159i | \(-0.772180\pi\) |
0.920453 | − | 0.390853i | \(-0.127820\pi\) | |||||||
\(318\) | 2.25827 | − | 8.99872i | 0.126638 | − | 0.504623i | ||||
\(319\) | −4.67490 | − | 6.43445i | −0.261744 | − | 0.360260i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.90486 | + | 21.3953i | −0.106319 | + | 1.19417i | ||||
\(322\) | 0.512371 | + | 3.23498i | 0.0285533 | + | 0.180279i | ||||
\(323\) | −27.6441 | + | 14.0854i | −1.53816 | + | 0.783732i | ||||
\(324\) | 7.49202 | − | 4.98695i | 0.416223 | − | 0.277053i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 6.55079i | − | 0.362815i | ||||||
\(327\) | −2.56931 | + | 4.09779i | −0.142083 | + | 0.226608i | ||||
\(328\) | 5.22028 | − | 0.826810i | 0.288241 | − | 0.0456530i | ||||
\(329\) | 10.8303 | + | 7.86870i | 0.597096 | + | 0.433815i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.6753 | + | 18.6542i | −1.41124 | + | 1.02533i | −0.418100 | + | 0.908401i | \(0.637304\pi\) |
−0.993141 | + | 0.116926i | \(0.962696\pi\) | |||||||
\(332\) | 8.53912 | − | 8.53912i | 0.468645 | − | 0.468645i | ||||
\(333\) | −19.2885 | − | 14.6277i | −1.05700 | − | 0.801593i | ||||
\(334\) | −16.1658 | + | 5.25258i | −0.884552 | + | 0.287408i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.11619 | − | 4.86875i | −0.0608932 | − | 0.265612i | ||||
\(337\) | 7.31518 | − | 14.3569i | 0.398483 | − | 0.782068i | −0.601374 | − | 0.798968i | \(-0.705380\pi\) |
0.999857 | + | 0.0169001i | \(0.00537972\pi\) | |||||||
\(338\) | −9.98030 | + | 19.5874i | −0.542857 | + | 1.06542i | ||||
\(339\) | −1.78909 | − | 7.80387i | −0.0971698 | − | 0.423848i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.7201 | + | 4.78284i | −0.797137 | + | 0.259006i | ||||
\(342\) | −12.3931 | − | 9.39851i | −0.670143 | − | 0.508213i | ||||
\(343\) | −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 | ||||
\(347\) | 23.6313 | − | 3.74283i | 1.26859 | − | 0.200925i | 0.514384 | − | 0.857560i | \(-0.328020\pi\) |
0.754209 | + | 0.656634i | \(0.228020\pi\) | |||||||
\(348\) | 2.66824 | − | 4.25557i | 0.143033 | − | 0.228123i | ||||
\(349\) | 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 | ||||
\(352\) | −2.44367 | + | 1.24511i | −0.130248 | + | 0.0663646i | ||||
\(353\) | 2.64576 | + | 16.7047i | 0.140820 | + | 0.889101i | 0.952398 | + | 0.304857i | \(0.0986087\pi\) |
−0.811578 | + | 0.584244i | \(0.801391\pi\) | |||||||
\(354\) | −0.453389 | + | 5.09246i | −0.0240974 | + | 0.270661i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.764995 | + | 1.05293i | 0.0405447 | + | 0.0558049i | ||||
\(357\) | 7.27579 | − | 28.9924i | 0.385076 | − | 1.53444i | ||||
\(358\) | −1.46766 | + | 9.26645i | −0.0775683 | + | 0.489747i | ||||
\(359\) | −1.67961 | − | 5.16932i | −0.0886466 | − | 0.272826i | 0.896899 | − | 0.442235i | \(-0.145814\pi\) |
−0.985546 | + | 0.169409i | \(0.945814\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.43509 | + | 7.49444i | −0.128163 | + | 0.394444i | ||||
\(362\) | 13.5493 | + | 6.90373i | 0.712137 | + | 0.362852i | ||||
\(363\) | 6.01037 | − | 0.411041i | 0.315463 | − | 0.0215740i | ||||
\(364\) | 16.2225 | + | 5.27101i | 0.850290 | + | 0.276276i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.22512 | − | 5.99226i | 0.273122 | − | 0.313221i | ||||
\(367\) | −17.7079 | − | 2.80465i | −0.924343 | − | 0.146401i | −0.323920 | − | 0.946084i | \(-0.605001\pi\) |
−0.600422 | + | 0.799683i | \(0.705001\pi\) | |||||||
\(368\) | 0.803077 | + | 0.803077i | 0.0418633 | + | 0.0418633i | ||||
\(369\) | 2.15865 | + | 15.7084i | 0.112375 | + | 0.817747i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.07990 | − | 12.4974i | 0.471405 | − | 0.648833i | ||||
\(372\) | −6.27159 | − | 7.49747i | −0.325167 | − | 0.388726i | ||||
\(373\) | −11.6182 | − | 22.8020i | −0.601568 | − | 1.18064i | −0.968176 | − | 0.250269i | \(-0.919481\pi\) |
0.366608 | − | 0.930376i | \(-0.380519\pi\) | |||||||
\(374\) | −16.4122 | −0.848656 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.64199 | 0.239392 | ||||||||
\(377\) | 7.78702 | + | 15.2829i | 0.401052 | + | 0.787109i | ||||
\(378\) | 14.6719 | − | 3.04824i | 0.754639 | − | 0.156785i | ||||
\(379\) | 5.71732 | − | 7.86922i | 0.293679 | − | 0.404215i | −0.636526 | − | 0.771255i | \(-0.719629\pi\) |
0.930205 | + | 0.367041i | \(0.119629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.51045 | − | 19.9643i | 0.436004 | − | 1.02280i | ||||
\(382\) | −9.12687 | − | 9.12687i | −0.466971 | − | 0.466971i | ||||
\(383\) | 24.0895 | + | 3.81540i | 1.23092 | + | 0.194958i | 0.737808 | − | 0.675010i | \(-0.235861\pi\) |
0.493108 | + | 0.869968i | \(0.335861\pi\) | |||||||
\(384\) | −1.30545 | − | 1.13833i | −0.0666187 | − | 0.0580900i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.26495 | − | 1.71069i | −0.267979 | − | 0.0870717i | ||||
\(387\) | −7.52989 | − | 10.8242i | −0.382766 | − | 0.550224i | ||||
\(388\) | 5.88829 | + | 3.00023i | 0.298932 | + | 0.152314i | ||||
\(389\) | 5.49358 | − | 16.9075i | 0.278536 | − | 0.857245i | −0.709726 | − | 0.704477i | \(-0.751181\pi\) |
0.988262 | − | 0.152767i | \(-0.0488186\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.10020 | + | 6.46376i | 0.106212 | + | 0.326886i | ||||
\(392\) | 0.206003 | − | 1.30065i | 0.0104047 | − | 0.0656929i | ||||
\(393\) | 20.0234 | + | 5.02496i | 1.01004 | + | 0.253475i | ||||
\(394\) | −15.0352 | − | 20.6942i | −0.757462 | − | 1.04256i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.58416 | − | 7.40608i | −0.180111 | − | 0.372170i | ||||
\(397\) | 3.00987 | + | 19.0036i | 0.151061 | + | 0.953762i | 0.940466 | + | 0.339889i | \(0.110389\pi\) |
−0.789405 | + | 0.613873i | \(0.789611\pi\) | |||||||
\(398\) | −0.0684585 | + | 0.0348814i | −0.00343152 | + | 0.00174845i | ||||
\(399\) | −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 | \(-0.283577\pi\) | |||||||
\(402\) | −0.677230 | − | 0.424623i | −0.0337772 | − | 0.0211783i | ||||
\(403\) | 32.9681 | − | 5.22164i | 1.64226 | − | 0.260108i | ||||
\(404\) | 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 | ||||
\(408\) | −3.86806 | − | 9.61614i | −0.191498 | − | 0.476070i | ||||
\(409\) | −14.9223 | + | 4.84855i | −0.737860 | + | 0.239745i | −0.653749 | − | 0.756711i | \(-0.726805\pi\) |
−0.0841106 | + | 0.996456i | \(0.526805\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 33.5457 | − | 7.69057i | 1.65469 | − | 0.379348i | ||||
\(412\) | −2.92942 | + | 5.74931i | −0.144322 | + | 0.283248i | ||||
\(413\) | −3.86463 | + | 7.58476i | −0.190166 | + | 0.373222i | ||||
\(414\) | −2.45815 | + | 2.35930i | −0.120811 | + | 0.115953i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.62520 | − | 1.82774i | 0.275798 | − | 0.0896122i | ||||
\(417\) | −15.3404 | + | 6.17063i | −0.751223 | + | 0.302177i | ||||
\(418\) | −10.0545 | + | 10.0545i | −0.491783 | + | 0.491783i | ||||
\(419\) | 2.78733 | − | 2.02511i | 0.136170 | − | 0.0989333i | −0.517615 | − | 0.855614i | \(-0.673180\pi\) |
0.653785 | + | 0.756680i | \(0.273180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.9206 | + | 7.93429i | 0.532238 | + | 0.386694i | 0.821194 | − | 0.570649i | \(-0.193308\pi\) |
−0.288956 | + | 0.957342i | \(0.593308\pi\) | |||||||
\(422\) | 6.37141 | − | 1.00913i | 0.310156 | − | 0.0491238i | ||||
\(423\) | −0.285673 | + | 13.9230i | −0.0138899 | + | 0.676962i | ||||
\(424\) | − | 5.35652i | − | 0.260135i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.50208 | + | 5.09087i | −0.411927 | + | 0.246653i | ||||
\(427\) | 11.7948 | − | 6.00974i | 0.570790 | − | 0.290832i | ||||
\(428\) | 1.94001 | + | 12.2488i | 0.0937741 | + | 0.592066i | ||||
\(429\) | 27.9859 | + | 2.49162i | 1.35117 | + | 0.120297i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.4092 | + | 22.5853i | 0.790401 | + | 1.08789i | 0.994058 | + | 0.108852i | \(0.0347173\pi\) |
−0.203657 | + | 0.979042i | \(0.565283\pi\) | |||||||
\(432\) | 3.49460 | − | 3.84548i | 0.168134 | − | 0.185016i | ||||
\(433\) | 0.408546 | − | 2.57946i | 0.0196335 | − | 0.123961i | −0.975925 | − | 0.218107i | \(-0.930012\pi\) |
0.995558 | + | 0.0941457i | \(0.0300119\pi\) | |||||||
\(434\) | −5.02927 | − | 15.4785i | −0.241413 | − | 0.742992i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.862912 | + | 2.65577i | −0.0413260 | + | 0.127188i | ||||
\(437\) | 5.24649 | + | 2.67322i | 0.250974 | + | 0.127877i | ||||
\(438\) | 1.07407 | + | 15.7055i | 0.0513213 | + | 0.750436i | ||||
\(439\) | −10.4899 | − | 3.40836i | −0.500653 | − | 0.162672i | 0.0477940 | − | 0.998857i | \(-0.484781\pi\) |
−0.548447 | + | 0.836185i | \(0.684781\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.88846 | + | 0.697923i | 0.185165 | + | 0.0332344i | ||||
\(442\) | 34.9589 | + | 5.53695i | 1.66283 | + | 0.263366i | ||||
\(443\) | −1.32181 | − | 1.32181i | −0.0628009 | − | 0.0628009i | 0.675009 | − | 0.737810i | \(-0.264140\pi\) |
−0.737810 | + | 0.675009i | \(0.764140\pi\) | |||||||
\(444\) | −12.8569 | − | 5.48068i | −0.610162 | − | 0.260102i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.19712 | + | 4.40046i | −0.151388 | + | 0.208368i | ||||
\(447\) | 15.9542 | − | 13.3456i | 0.754607 | − | 0.631224i | ||||
\(448\) | −1.30926 | − | 2.56957i | −0.0618568 | − | 0.121401i | ||||
\(449\) | 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 | ||||||||
\(452\) | −2.09855 | − | 4.11863i | −0.0987075 | − | 0.193724i | ||||
\(453\) | 14.7835 | − | 12.3663i | 0.694588 | − | 0.581019i | ||||
\(454\) | −11.5336 | + | 15.8746i | −0.541296 | + | 0.745031i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.26075 | − | 3.52142i | −0.386845 | − | 0.164905i | ||||
\(457\) | −11.0498 | − | 11.0498i | −0.516886 | − | 0.516886i | 0.399742 | − | 0.916628i | \(-0.369100\pi\) |
−0.916628 | + | 0.399742i | \(0.869100\pi\) | |||||||
\(458\) | 17.2797 | + | 2.73683i | 0.807427 | + | 0.127884i | ||||
\(459\) | 29.0804 | − | 11.0100i | 1.35736 | − | 0.513901i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.2689 | − | 4.31131i | −0.617992 | − | 0.200798i | −0.0167435 | − | 0.999860i | \(-0.505330\pi\) |
−0.601249 | + | 0.799062i | \(0.705330\pi\) | |||||||
\(462\) | −0.934699 | − | 13.6675i | −0.0434861 | − | 0.635868i | ||||
\(463\) | −29.3718 | − | 14.9657i | −1.36502 | − | 0.695515i | −0.390669 | − | 0.920531i | \(-0.627756\pi\) |
−0.974355 | + | 0.225017i | \(0.927756\pi\) | |||||||
\(464\) | 0.896139 | − | 2.75803i | 0.0416022 | − | 0.128038i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.96836 | + | 27.6018i | 0.415451 | + | 1.27863i | ||||
\(467\) | 0.578507 | − | 3.65255i | 0.0267701 | − | 0.169020i | −0.970681 | − | 0.240371i | \(-0.922731\pi\) |
0.997451 | + | 0.0713509i | \(0.0227310\pi\) | |||||||
\(468\) | 5.13588 | + | 16.9845i | 0.237406 | + | 0.785110i | ||||
\(469\) | −0.782294 | − | 1.07673i | −0.0361230 | − | 0.0497190i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.3312 | − | 2.52237i | −1.30543 | − | 0.116225i | ||||
\(472\) | 0.461757 | + | 2.91542i | 0.0212541 | + | 0.134193i | ||||
\(473\) | −10.7405 | + | 5.47254i | −0.493847 | + | 0.251628i | ||||
\(474\) | −17.4585 | + | 10.4538i | −0.801894 | + | 0.480157i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 17.2578i | − | 0.791012i | ||||||
\(477\) | 16.0662 | + | 0.329645i | 0.735619 | + | 0.0150934i | ||||
\(478\) | −5.58321 | + | 0.884293i | −0.255370 | + | 0.0404466i | ||||
\(479\) | 4.35190 | + | 3.16184i | 0.198844 | + | 0.144468i | 0.682752 | − | 0.730651i | \(-0.260783\pi\) |
−0.483908 | + | 0.875119i | \(0.660783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 38.6120 | − | 28.0533i | 1.76056 | − | 1.27912i | ||||
\(482\) | −9.96798 | + | 9.96798i | −0.454029 | + | 0.454029i | ||||
\(483\) | −5.26316 | + | 2.11709i | −0.239482 | + | 0.0963309i | ||||
\(484\) | 3.30796 | − | 1.07482i | 0.150362 | − | 0.0488555i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 11.3190 | + | 10.7183i | 0.513439 | + | 0.486190i | ||||
\(487\) | 1.90512 | − | 3.73900i | 0.0863291 | − | 0.169430i | −0.843806 | − | 0.536649i | \(-0.819690\pi\) |
0.930135 | + | 0.367219i | \(0.119690\pi\) | |||||||
\(488\) | 2.08390 | − | 4.08988i | 0.0943336 | − | 0.185140i | ||||
\(489\) | 11.0594 | − | 2.53544i | 0.500123 | − | 0.114656i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0362 | + | 9.75934i | −1.35551 | + | 0.440433i | −0.894543 | − | 0.446983i | \(-0.852499\pi\) |
−0.460970 | + | 0.887416i | \(0.652499\pi\) | |||||||
\(492\) | 3.41633 | + | 8.49313i | 0.154020 | + | 0.382900i | ||||
\(493\) | 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 | ||||
\(497\) | −16.2967 | + | 2.58115i | −0.731007 | + | 0.115780i | ||||
\(498\) | 17.7212 | + | 11.1112i | 0.794106 | + | 0.497904i | ||||
\(499\) | − | 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 | ||||
\(502\) | −15.4306 | + | 7.86229i | −0.688702 | + | 0.350911i | ||||
\(503\) | 0.104371 | + | 0.658974i | 0.00465369 | + | 0.0293822i | 0.989906 | − | 0.141726i | \(-0.0452652\pi\) |
−0.985252 | + | 0.171108i | \(0.945265\pi\) | |||||||
\(504\) | 7.78767 | − | 3.76883i | 0.346890 | − | 0.167877i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.83085 | + | 2.51995i | 0.0813911 | + | 0.112025i | ||||
\(507\) | −36.9314 | − | 9.26810i | −1.64018 | − | 0.411611i | ||||
\(508\) | 1.96012 | − | 12.3757i | 0.0869664 | − | 0.549084i | ||||
\(509\) | −8.01814 | − | 24.6773i | −0.355398 | − | 1.09380i | −0.955779 | − | 0.294087i | \(-0.904984\pi\) |
0.600381 | − | 0.799714i | \(-0.295016\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.09964 | + | 24.9281i | −0.358307 | + | 1.10276i | ||||
\(512\) | −0.891007 | − | 0.453990i | −0.0393773 | − | 0.0200637i | ||||
\(513\) | 11.0704 | − | 24.5603i | 0.488770 | − | 1.08436i | ||||
\(514\) | −5.76888 | − | 1.87442i | −0.254454 | − | 0.0826772i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.73777 | − | 5.00321i | −0.252591 | − | 0.220254i | ||||
\(517\) | 12.5743 | + | 1.99158i | 0.553019 | + | 0.0875896i | ||||
\(518\) | −16.4550 | − | 16.4550i | −0.722991 | − | 0.722991i | ||||
\(519\) | −4.61151 | + | 10.8180i | −0.202423 | + | 0.474856i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.0053 | + | 33.0404i | −1.05169 | + | 1.44753i | −0.164357 | + | 0.986401i | \(0.552555\pi\) |
−0.887334 | + | 0.461127i | \(0.847445\pi\) | |||||||
\(522\) | 8.21721 | + | 2.85758i | 0.359657 | + | 0.125073i | ||||
\(523\) | 12.3663 | + | 24.2703i | 0.540741 | + | 1.06126i | 0.986137 | + | 0.165931i | \(0.0530628\pi\) |
−0.445396 | + | 0.895334i | \(0.646937\pi\) | |||||||
\(524\) | 11.9190 | 0.520682 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.8782 | 1.04114 | ||||||||
\(527\) | −15.3319 | − | 30.0906i | −0.667868 | − | 1.31077i | ||||
\(528\) | −3.04786 | − | 3.64362i | −0.132641 | − | 0.158568i | ||||
\(529\) | −12.7609 | + | 17.5639i | −0.554822 | + | 0.763646i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.77284 | + | 1.20556i | −0.380709 | + | 0.0523170i | ||||
\(532\) | −10.5726 | − | 10.5726i | −0.458379 | − | 0.458379i | ||||
\(533\) | −30.8763 | − | 4.89032i | −1.33740 | − | 0.211823i | ||||
\(534\) | −1.48152 | + | 1.69903i | −0.0641116 | + | 0.0735243i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.438912 | − | 0.142611i | −0.0189581 | − | 0.00615987i | ||||
\(537\) | −16.2122 | + | 1.10873i | −0.699606 | + | 0.0478451i | ||||
\(538\) | 12.3831 | + | 6.30950i | 0.533873 | + | 0.272022i | ||||
\(539\) | 1.11605 | − | 3.43486i | 0.0480718 | − | 0.147950i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.75771 | + | 14.6427i | 0.204550 | + | 0.629540i | 0.999732 | + | 0.0231685i | \(0.00737544\pi\) |
−0.795182 | + | 0.606371i | \(0.792625\pi\) | |||||||
\(542\) | −2.35194 | + | 14.8496i | −0.101025 | + | 0.637844i | ||||
\(543\) | −6.41107 | + | 25.5467i | −0.275125 | + | 1.09631i | ||||
\(544\) | −3.51743 | − | 4.84132i | −0.150808 | − | 0.207570i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.62000 | + | 29.4278i | −0.112126 | + | 1.25939i | ||||
\(547\) | 3.51301 | + | 22.1803i | 0.150205 | + | 0.948360i | 0.941522 | + | 0.336953i | \(0.109396\pi\) |
−0.791316 | + | 0.611407i | \(0.790604\pi\) | |||||||
\(548\) | 17.7044 | − | 9.02083i | 0.756293 | − | 0.385351i | ||||
\(549\) | 12.1388 | + | 6.50207i | 0.518072 | + | 0.277502i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 15.0352i | − | 0.640520i | ||||||
\(552\) | −1.04497 | + | 1.66662i | −0.0444770 | + | 0.0709362i | ||||
\(553\) | −33.4642 | + | 5.30021i | −1.42304 | + | 0.225388i | ||||
\(554\) | 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 | −0.670956 | − | 0.741498i | \(-0.734116\pi\) |
0.741498 | + | 0.670956i | \(0.234116\pi\) | |||||||
\(558\) | 10.2302 | − | 13.4899i | 0.433081 | − | 0.571071i | ||||
\(559\) | 24.7240 | − | 8.03333i | 1.04572 | − | 0.339773i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.35223 | − | 27.7080i | −0.268191 | − | 1.16983i | ||||
\(562\) | −10.4045 | + | 20.4199i | −0.438886 | + | 0.861362i | ||||
\(563\) | 21.4512 | − | 42.1004i | 0.904062 | − | 1.77432i | 0.369332 | − | 0.929297i | \(-0.379586\pi\) |
0.534729 | − | 0.845023i | \(-0.320414\pi\) | |||||||
\(564\) | 1.79665 | + | 7.83686i | 0.0756525 | + | 0.329991i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.70579 | − | 0.879165i | 0.113733 | − | 0.0369541i | ||||
\(567\) | 10.8248 | + | 23.5900i | 0.454600 | + | 0.990688i | ||||
\(568\) | −4.04562 | + | 4.04562i | −0.169750 | + | 0.169750i | ||||
\(569\) | −19.9798 | + | 14.5162i | −0.837599 | + | 0.608551i | −0.921699 | − | 0.387906i | \(-0.873198\pi\) |
0.0841003 | + | 0.996457i | \(0.473198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.83866 | + | 3.51549i | 0.202491 | + | 0.147119i | 0.684410 | − | 0.729097i | \(-0.260060\pi\) |
−0.481919 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(572\) | 16.0218 | − | 2.53761i | 0.669907 | − | 0.106103i | ||||
\(573\) | 11.8760 | − | 18.9409i | 0.496126 | − | 0.791269i | ||||
\(574\) | 15.2424i | 0.636206i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.41652 | − | 2.64452i | 0.0590216 | − | 0.110188i | ||||
\(577\) | 28.0783 | − | 14.3066i | 1.16891 | − | 0.595591i | 0.241783 | − | 0.970330i | \(-0.422268\pi\) |
0.927130 | + | 0.374739i | \(0.122268\pi\) | |||||||
\(578\) | −2.94264 | − | 18.5791i | −0.122398 | − | 0.772789i | ||||
\(579\) | 0.850312 | − | 9.55068i | 0.0353377 | − | 0.396913i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.4704 | + | 28.1751i | 0.849256 | + | 1.16890i | ||||
\(582\) | −2.78613 | + | 11.1021i | −0.115489 | + | 0.460198i | ||||
\(583\) | 2.29814 | − | 14.5099i | 0.0951791 | − | 0.600937i | ||||
\(584\) | 2.80857 | + | 8.64390i | 0.116220 | + | 0.357687i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.12744 | − | 12.7030i | 0.170503 | − | 0.524755i | ||||
\(587\) | −10.0374 | − | 5.11433i | −0.414289 | − | 0.211091i | 0.234407 | − | 0.972139i | \(-0.424685\pi\) |
−0.648696 | + | 0.761048i | \(0.724685\pi\) | |||||||
\(588\) | 2.27556 | − | 0.155623i | 0.0938427 | − | 0.00641777i | ||||
\(589\) | −27.8269 | − | 9.04151i | −1.14659 | − | 0.372549i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.1177 | − | 33.3927i | 1.19774 | − | 1.37359i | ||||
\(592\) | −7.96990 | − | 1.26231i | −0.327561 | − | 0.0518805i | ||||
\(593\) | 17.4049 | + | 17.4049i | 0.714734 | + | 0.714734i | 0.967522 | − | 0.252788i | \(-0.0813475\pi\) |
−0.252788 | + | 0.967522i | \(0.581347\pi\) | |||||||
\(594\) | 11.1161 | − | 8.91744i | 0.456100 | − | 0.365887i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.05865 | − | 9.71540i | 0.289134 | − | 0.397958i | ||||
\(597\) | −0.0853849 | − | 0.102075i | −0.00349457 | − | 0.00417764i | ||||
\(598\) | −3.04966 | − | 5.98529i | −0.124710 | − | 0.244757i | ||||
\(599\) | 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 | \(0.769258\pi\) | |||||||
\(602\) | −5.75450 | − | 11.2939i | −0.234536 | − | 0.460303i | ||||
\(603\) | 0.454755 | − | 1.30768i | 0.0185190 | − | 0.0532530i | ||||
\(604\) | 6.54069 | − | 9.00249i | 0.266137 | − | 0.366306i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.39740 | + | 5.62397i | −0.0973877 | + | 0.228458i | ||||
\(607\) | 23.2173 | + | 23.2173i | 0.942362 | + | 0.942362i | 0.998427 | − | 0.0560654i | \(-0.0178555\pi\) |
−0.0560654 | + | 0.998427i | \(0.517856\pi\) | |||||||
\(608\) | −5.12077 | − | 0.811051i | −0.207675 | − | 0.0328925i | ||||
\(609\) | 10.9178 | + | 9.52007i | 0.442411 | + | 0.385773i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.1121 | − | 8.48435i | −1.05638 | − | 0.343240i | ||||
\(612\) | 14.7374 | − | 10.2521i | 0.595723 | − | 0.414417i | ||||
\(613\) | −19.5715 | − | 9.97216i | −0.790484 | − | 0.402772i | 0.0116379 | − | 0.999932i | \(-0.496295\pi\) |
−0.802122 | + | 0.597161i | \(0.796295\pi\) | |||||||
\(614\) | −10.1339 | + | 31.1890i | −0.408972 | + | 1.25869i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.44412 | − | 7.52224i | −0.0984766 | − | 0.303080i | ||||
\(617\) | 1.00125 | − | 6.32162i | 0.0403086 | − | 0.254499i | −0.959303 | − | 0.282380i | \(-0.908876\pi\) |
0.999611 | + | 0.0278814i | \(0.00887607\pi\) | |||||||
\(618\) | −10.8401 | − | 2.72038i | −0.436053 | − | 0.109430i | ||||
\(619\) | 14.0949 | + | 19.4000i | 0.566524 | + | 0.779753i | 0.992138 | − | 0.125152i | \(-0.0399418\pi\) |
−0.425614 | + | 0.904905i | \(0.639942\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.93451 | − | 3.23682i | −0.198015 | − | 0.129889i | ||||
\(622\) | 1.61936 | + | 10.2243i | 0.0649306 | + | 0.409956i | ||||
\(623\) | −3.34426 | + | 1.70399i | −0.133985 | + | 0.0682688i | ||||
\(624\) | 5.26288 | + | 8.78935i | 0.210684 | + | 0.351856i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.7188i | 0.548313i | ||||||||
\(627\) | −20.8661 | − | 13.0831i | −0.833312 | − | 0.522487i | ||||
\(628\) | −16.2195 | + | 2.56892i | −0.647230 | + | 0.102511i | ||||
\(629\) | −39.0658 | − | 28.3830i | −1.55766 | − | 1.13170i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.7895 | + | 17.2841i | −0.947046 | + | 0.688069i | −0.950106 | − | 0.311926i | \(-0.899026\pi\) |
0.00306072 | + | 0.999995i | \(0.499026\pi\) | |||||||
\(632\) | −8.30741 | + | 8.30741i | −0.330451 | + | 0.330451i | ||||
\(633\) | 4.16968 | + | 10.3660i | 0.165730 | + | 0.412011i | ||||
\(634\) | 17.9501 | − | 5.83235i | 0.712891 | − | 0.231632i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.04315 | − | 2.07320i | 0.358584 | − | 0.0822077i | ||||
\(637\) | −3.53606 | + | 6.93992i | −0.140104 | + | 0.274970i | ||||
\(638\) | 3.61078 | − | 7.08655i | 0.142952 | − | 0.280559i | ||||
\(639\) | −11.8853 | − | 12.3833i | −0.470177 | − | 0.489875i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.3395 | − | 5.95888i | 0.724368 | − | 0.235362i | 0.0764522 | − | 0.997073i | \(-0.475641\pi\) |
0.647916 | + | 0.761712i | \(0.275641\pi\) | |||||||
\(642\) | −19.9281 | + | 8.01603i | −0.786501 | + | 0.316367i | ||||
\(643\) | 2.50826 | − | 2.50826i | 0.0989163 | − | 0.0989163i | −0.655917 | − | 0.754833i | \(-0.727718\pi\) |
0.754833 | + | 0.655917i | \(0.227718\pi\) | |||||||
\(644\) | −2.64978 | + | 1.92518i | −0.104416 | + | 0.0758627i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25.1003 | − | 18.2365i | −0.987560 | − | 0.717504i | ||||
\(647\) | 36.9778 | − | 5.85671i | 1.45375 | − | 0.230251i | 0.620960 | − | 0.783842i | \(-0.286743\pi\) |
0.832789 | + | 0.553591i | \(0.186743\pi\) | |||||||
\(648\) | 7.84471 | + | 4.41141i | 0.308169 | + | 0.173296i | ||||
\(649\) | 8.09547i | 0.317775i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.1851 | − | 14.4815i | 0.947889 | − | 0.567576i | ||||
\(652\) | 5.83680 | − | 2.97400i | 0.228587 | − | 0.116471i | ||||
\(653\) | −0.348209 | − | 2.19851i | −0.0136265 | − | 0.0860342i | 0.979938 | − | 0.199303i | \(-0.0638678\pi\) |
−0.993564 | + | 0.113269i | \(0.963868\pi\) | |||||||
\(654\) | −4.81760 | − | 0.428918i | −0.188383 | − | 0.0167720i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.10665 | + | 4.27594i | 0.121294 | + | 0.166947i | ||||
\(657\) | −26.0991 | + | 7.89200i | −1.01822 | + | 0.307896i | ||||
\(658\) | −2.09419 | + | 13.2222i | −0.0816401 | + | 0.515456i | ||||
\(659\) | 4.81311 | + | 14.8132i | 0.187492 | + | 0.577041i | 0.999982 | − | 0.00593344i | \(-0.00188868\pi\) |
−0.812490 | + | 0.582975i | \(0.801889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.225919 | + | 0.695307i | −0.00878723 | + | 0.0270443i | −0.955354 | − | 0.295464i | \(-0.904526\pi\) |
0.946567 | + | 0.322508i | \(0.104526\pi\) | |||||||
\(662\) | −28.2773 | − | 14.4080i | −1.09903 | − | 0.559984i | ||||
\(663\) | 4.18282 | + | 61.1625i | 0.162447 | + | 2.37536i | ||||
\(664\) | 11.4851 | + | 3.73173i | 0.445708 | + | 0.144819i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.27660 | − | 23.8270i | 0.165715 | − | 0.923277i | ||||
\(667\) | −3.25301 | − | 0.515226i | −0.125957 | − | 0.0199496i | ||||
\(668\) | −12.0192 | − | 12.0192i | −0.465037 | − | 0.465037i | ||||
\(669\) | −8.66651 | − | 3.69438i | −0.335067 | − | 0.142833i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.39961 | − | 10.1847i | 0.285659 | − | 0.393176i | ||||
\(672\) | 3.83135 | − | 3.20490i | 0.147797 | − | 0.123632i | ||||
\(673\) | 6.83769 | + | 13.4197i | 0.263574 | + | 0.517292i | 0.984427 | − | 0.175796i | \(-0.0562498\pi\) |
−0.720853 | + | 0.693088i | \(0.756250\pi\) | |||||||
\(674\) | 16.1131 | 0.620652 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21.9835 | −0.845520 | ||||||||
\(677\) | −10.5178 | − | 20.6424i | −0.404233 | − | 0.793351i | 0.595719 | − | 0.803193i | \(-0.296867\pi\) |
−0.999952 | + | 0.00984177i | \(0.996867\pi\) | |||||||
\(678\) | 6.14107 | − | 5.13697i | 0.235846 | − | 0.197284i | ||||
\(679\) | −11.2023 | + | 15.4186i | −0.429904 | + | 0.591712i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31.2643 | − | 13.3274i | −1.19805 | − | 0.510708i | ||||
\(682\) | −10.9443 | − | 10.9443i | −0.419080 | − | 0.419080i | ||||
\(683\) | −4.28854 | − | 0.679239i | −0.164097 | − | 0.0259903i | 0.0738455 | − | 0.997270i | \(-0.476473\pi\) |
−0.237942 | + | 0.971279i | \(0.576473\pi\) | |||||||
\(684\) | 2.74778 | − | 15.3092i | 0.105064 | − | 0.585361i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.5874 | − | 5.06466i | −0.595130 | − | 0.193370i | ||||
\(687\) | 2.06751 | + | 30.2317i | 0.0788803 | + | 1.15341i | ||||
\(688\) | −3.91618 | − | 1.99539i | −0.149303 | − | 0.0760736i | ||||
\(689\) | −9.79031 | + | 30.1315i | −0.372981 | + | 1.14792i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.14266 | − | 28.1382i | −0.347803 | − | 1.07043i | −0.960066 | − | 0.279774i | \(-0.909741\pi\) |
0.612263 | − | 0.790654i | \(-0.290259\pi\) | |||||||
\(692\) | −1.06212 | + | 6.70597i | −0.0403758 | + | 0.254923i | ||||
\(693\) | 22.7124 | − | 6.86790i | 0.862772 | − | 0.260890i | ||||
\(694\) | 14.0633 | + | 19.3564i | 0.533834 | + | 0.734759i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.00310 | + | 0.445433i | 0.189642 | + | 0.0168841i | ||||
\(697\) | 4.94780 | + | 31.2392i | 0.187411 | + | 1.18327i | ||||
\(698\) | −22.1821 | + | 11.3024i | −0.839606 | + | 0.427801i | ||||
\(699\) | −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 | \(-0.120405\pi\) | |||||||
\(702\) | −26.6864 | + | 15.2444i | −1.00721 | + | 0.575363i | ||||
\(703\) | −41.3208 | + | 6.54457i | −1.55844 | + | 0.246833i | ||||
\(704\) | −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 | ||||
\(708\) | −4.74325 | + | 1.90795i | −0.178262 | + | 0.0717053i | ||||
\(709\) | 21.2009 | − | 6.88858i | 0.796216 | − | 0.258706i | 0.117467 | − | 0.993077i | \(-0.462523\pi\) |
0.678749 | + | 0.734371i | \(0.262523\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.4058 | − | 25.4282i | −0.915287 | − | 0.953634i | ||||
\(712\) | −0.590863 | + | 1.15963i | −0.0221435 | + | 0.0434591i | ||||
\(713\) | −2.90979 | + | 5.71079i | −0.108973 | + | 0.213871i | ||||
\(714\) | 29.1356 | − | 6.67952i | 1.09037 | − | 0.249975i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.92277 | + | 2.89918i | −0.333460 | + | 0.108348i | ||||
\(717\) | −3.65385 | − | 9.08361i | −0.136455 | − | 0.339233i | ||||
\(718\) | 3.84337 | − | 3.84337i | 0.143433 | − | 0.143433i | ||||
\(719\) | −2.20624 | + | 1.60292i | −0.0822787 | + | 0.0597790i | −0.628164 | − | 0.778081i | \(-0.716193\pi\) |
0.545885 | + | 0.837860i | \(0.316193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.0547 | − | 10.9379i | −0.560667 | − | 0.407348i | ||||
\(722\) | −7.78310 | + | 1.23272i | −0.289657 | + | 0.0458772i | ||||
\(723\) | −20.6865 | − | 12.9704i | −0.769339 | − | 0.482376i | ||||
\(724\) | 15.2068i | 0.565155i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.09489 | + | 5.16867i | 0.114862 | + | 0.191827i | ||||
\(727\) | −17.3015 | + | 8.81556i | −0.641677 | + | 0.326951i | −0.744375 | − | 0.667762i | \(-0.767253\pi\) |
0.102698 | + | 0.994713i | \(0.467253\pi\) | |||||||
\(728\) | 2.66836 | + | 16.8473i | 0.0988959 | + | 0.624404i | ||||
\(729\) | −13.7142 | + | 23.2577i | −0.507934 | + | 0.861396i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.4599 | − | 21.2787i | −0.571805 | − | 0.787022i | ||||
\(732\) | 7.71130 | + | 1.93519i | 0.285018 | + | 0.0715266i | ||||
\(733\) | −3.79691 | + | 23.9728i | −0.140242 | + | 0.885454i | 0.812784 | + | 0.582566i | \(0.197951\pi\) |
−0.953026 | + | 0.302889i | \(0.902049\pi\) | |||||||
\(734\) | −5.54024 | − | 17.0511i | −0.204494 | − | 0.629368i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.350958 | + | 1.08014i | −0.0129365 | + | 0.0398144i | ||||
\(737\) | −1.12775 | − | 0.574618i | −0.0415412 | − | 0.0211663i | ||||
\(738\) | −13.0163 | + | 9.05484i | −0.479136 | + | 0.333313i | ||||
\(739\) | 6.13821 | + | 1.99443i | 0.225798 | + | 0.0733662i | 0.419731 | − | 0.907649i | \(-0.362124\pi\) |
−0.193933 | + | 0.981015i | \(0.562124\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 40.0322 | + | 34.9072i | 1.47062 | + | 1.28235i | ||||
\(742\) | 15.2575 | + | 2.41654i | 0.560119 | + | 0.0887141i | ||||
\(743\) | −23.0403 | − | 23.0403i | −0.845265 | − | 0.845265i | 0.144273 | − | 0.989538i | \(-0.453916\pi\) |
−0.989538 | + | 0.144273i | \(0.953916\pi\) | |||||||
\(744\) | 3.83305 | − | 8.99180i | 0.140526 | − | 0.329656i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.0422 | − | 20.7038i | 0.550734 | − | 0.758020i | ||||
\(747\) | −11.8996 | + | 34.2184i | −0.435385 | + | 1.25198i | ||||
\(748\) | −7.45099 | − | 14.6234i | −0.272435 | − | 0.534684i | ||||
\(749\) | −35.7645 | −1.30681 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.4069 | 1.14606 | 0.573028 | − | 0.819536i | \(-0.305769\pi\) | ||||
0.573028 | + | 0.819536i | \(0.305769\pi\) | |||||||
\(752\) | 2.10742 | + | 4.13604i | 0.0768497 | + | 0.150826i | ||||
\(753\) | −19.2458 | − | 23.0077i | −0.701357 | − | 0.838449i | ||||
\(754\) | −10.0819 | + | 13.8766i | −0.367162 | + | 0.505355i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 9.37689 | + | 11.6889i | 0.341034 | + | 0.425120i | ||||
\(757\) | −6.35882 | − | 6.35882i | −0.231115 | − | 0.231115i | 0.582043 | − | 0.813158i | \(-0.302254\pi\) |
−0.813158 | + | 0.582043i | \(0.802254\pi\) | |||||||
\(758\) | 9.60713 | + | 1.52162i | 0.348947 | + | 0.0552678i | ||||
\(759\) | −3.54569 | + | 4.06626i | −0.128700 | + | 0.147596i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.94031 | + | 2.90488i | 0.324086 | + | 0.105302i | 0.466541 | − | 0.884499i | \(-0.345500\pi\) |
−0.142456 | + | 0.989801i | \(0.545500\pi\) | |||||||
\(762\) | 21.6520 | − | 1.48075i | 0.784370 | − | 0.0536419i | ||||
\(763\) | −7.17538 | − | 3.65604i | −0.259766 | − | 0.132358i | ||||
\(764\) | 3.98859 | − | 12.2756i | 0.144302 | − | 0.444116i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.53686 | + | 23.1961i | 0.272318 | + | 0.838108i | ||||
\(767\) | 2.73115 | − | 17.2438i | 0.0986161 | − | 0.622637i | ||||
\(768\) | 0.421593 | − | 1.67996i | 0.0152129 | − | 0.0606203i | ||||
\(769\) | −15.8011 | − | 21.7484i | −0.569803 | − | 0.784266i | 0.422728 | − | 0.906256i | \(-0.361072\pi\) |
−0.992531 | + | 0.121990i | \(0.961072\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.931697 | − | 10.4648i | 0.0335543 | − | 0.376881i | ||||
\(772\) | −0.866006 | − | 5.46774i | −0.0311682 | − | 0.196788i | ||||
\(773\) | −19.3692 | + | 9.86911i | −0.696662 | + | 0.354967i | −0.766191 | − | 0.642613i | \(-0.777850\pi\) |
0.0695289 | + | 0.997580i | \(0.477850\pi\) | |||||||
\(774\) | 6.22592 | − | 11.6233i | 0.223786 | − | 0.417789i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.60858i | 0.237234i | ||||||||
\(777\) | 21.4114 | − | 34.1490i | 0.768130 | − | 1.22509i | ||||
\(778\) | 17.5587 | − | 2.78103i | 0.629511 | − | 0.0997048i | ||||
\(779\) | 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 | ||||
\(783\) | −1.64391 | + | 14.9787i | −0.0587487 | + | 0.535296i | ||||
\(784\) | 1.25241 | − | 0.406934i | 0.0447291 | − | 0.0145334i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.61315 | + | 20.1222i | 0.164545 | + | 0.717736i | ||||
\(787\) | 8.50770 | − | 16.6973i | 0.303267 | − | 0.595194i | −0.688205 | − | 0.725516i | \(-0.741601\pi\) |
0.991472 | + | 0.130322i | \(0.0416010\pi\) | |||||||
\(788\) | 11.6128 | − | 22.7914i | 0.413689 | − | 0.811911i | ||||
\(789\) | 9.24190 | + | 40.3125i | 0.329020 | + | 1.43516i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.6782 | − | 4.11941i | 0.450786 | − | 0.146469i | ||||
\(792\) | 4.97169 | − | 6.55580i | 0.176661 | − | 0.232950i | ||||
\(793\) | −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 | ||||
\(797\) | 47.5041 | − | 7.52391i | 1.68268 | − | 0.266511i | 0.759398 | − | 0.650627i | \(-0.225494\pi\) |
0.923285 | + | 0.384116i | \(0.125494\pi\) | |||||||
\(798\) | 13.7571 | − | 21.9412i | 0.486997 | − | 0.776710i | ||||
\(799\) | 27.7786i | 0.982737i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.44181 | − | 1.84358i | −0.121610 | − | 0.0651397i | ||||
\(802\) | 27.7494 | − | 14.1390i | 0.979867 | − | 0.499267i | ||||
\(803\) | 3.89939 | + | 24.6198i | 0.137607 | + | 0.868814i | ||||
\(804\) | 0.0708861 | − | 0.796191i | 0.00249996 | − | 0.0280795i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19.6197 | + | 27.0043i | 0.691076 | + | 0.951184i | ||||
\(807\) | −5.85925 | + | 23.3478i | −0.206255 | + | 0.821883i | ||||
\(808\) | −0.552168 | + | 3.48625i | −0.0194252 | + | 0.122646i | ||||
\(809\) | −5.14657 | − | 15.8395i | −0.180944 | − | 0.556887i | 0.818911 | − | 0.573920i | \(-0.194578\pi\) |
−0.999855 | + | 0.0170329i | \(0.994578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.03759 | − | 18.5818i | 0.212008 | − | 0.652495i | −0.787344 | − | 0.616514i | \(-0.788544\pi\) |
0.999352 | − | 0.0359809i | \(-0.0114556\pi\) | |||||||
\(812\) | 7.45167 | + | 3.79682i | 0.261502 | + | 0.133242i | ||||
\(813\) | −25.9801 | + | 1.77675i | −0.911163 | + | 0.0623132i | ||||
\(814\) | −21.0475 | − | 6.83874i | −0.737714 | − | 0.239698i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.81198 | − | 7.81211i | 0.238467 | − | 0.273478i | ||||
\(817\) | −22.5070 | − | 3.56475i | −0.787419 | − | 0.124715i | ||||
\(818\) | −11.0947 | − | 11.0947i | −0.387916 | − | 0.387916i | ||||
\(819\) | −50.6956 | + | 6.96659i | −1.77145 | + | 0.243432i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.95552 | − | 10.9498i | 0.277650 | − | 0.382152i | −0.647304 | − | 0.762232i | \(-0.724104\pi\) |
0.924954 | + | 0.380080i | \(0.124104\pi\) | |||||||
\(822\) | 22.0818 | + | 26.3980i | 0.770191 | + | 0.920737i | ||||
\(823\) | −4.76071 | − | 9.34343i | −0.165948 | − | 0.325691i | 0.793025 | − | 0.609189i | \(-0.208505\pi\) |
−0.958973 | + | 0.283498i | \(0.908505\pi\) | |||||||
\(824\) | −6.45260 | −0.224787 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.51258 | −0.296191 | ||||||||
\(827\) | −8.74498 | − | 17.1630i | −0.304093 | − | 0.596815i | 0.687504 | − | 0.726180i | \(-0.258706\pi\) |
−0.991597 | + | 0.129365i | \(0.958706\pi\) | |||||||
\(828\) | −3.21813 | − | 1.11912i | −0.111838 | − | 0.0388923i | ||||
\(829\) | 18.5685 | − | 25.5573i | 0.644909 | − | 0.887641i | −0.353956 | − | 0.935262i | \(-0.615164\pi\) |
0.998865 | + | 0.0476205i | \(0.0151638\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.23201 | + | 2.89013i | −0.0427381 | + | 0.100258i | ||||
\(832\) | 4.18231 | + | 4.18231i | 0.144996 | + | 0.144996i | ||||
\(833\) | 7.78338 | + | 1.23277i | 0.269678 | + | 0.0427128i | ||||
\(834\) | −12.4625 | − | 10.8670i | −0.431540 | − | 0.376293i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −13.5233 | − | 4.39399i | −0.467713 | − | 0.151969i | ||||
\(837\) | 26.7338 | + | 12.0501i | 0.924057 | + | 0.416512i | ||||
\(838\) | 3.06981 | + | 1.56415i | 0.106045 | + | 0.0540325i | ||||
\(839\) | 12.7405 | − | 39.2113i | 0.439852 | − | 1.35373i | −0.448179 | − | 0.893944i | \(-0.647927\pi\) |
0.888032 | − | 0.459782i | \(-0.152073\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.36272 | − | 19.5824i | −0.219404 | − | 0.675256i | ||||
\(842\) | −2.11165 | + | 13.3324i | −0.0727722 | + | 0.459466i | ||||
\(843\) | −38.5009 | − | 9.66199i | −1.32604 | − | 0.332777i | ||||
\(844\) | 3.79170 | + | 5.21883i | 0.130516 | + | 0.179640i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.5352 | + | 6.06639i | −0.430970 | + | 0.208567i | ||||
\(847\) | 1.56916 | + | 9.90726i | 0.0539169 | + | 0.340418i | ||||
\(848\) | 4.77269 | − | 2.43181i | 0.163895 | − | 0.0835086i | ||||
\(849\) | 2.53151 | + | 4.22779i | 0.0868812 | + | 0.145097i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.16443i | 0.314153i | ||||||||
\(852\) | −8.39586 | − | 5.26420i | −0.287637 | − | 0.180349i | ||||
\(853\) | 18.4859 | − | 2.92787i | 0.632944 | − | 0.100248i | 0.168285 | − | 0.985738i | \(-0.446177\pi\) |
0.464659 | + | 0.885490i | \(0.346177\pi\) | |||||||
\(854\) | 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 | −0.959338 | − | 0.282260i | \(-0.908916\pi\) |
0.282260 | + | 0.959338i | \(0.408916\pi\) | |||||||
\(858\) | 10.4853 | + | 26.0668i | 0.357961 | + | 0.889905i | ||||
\(859\) | −35.8942 | + | 11.6627i | −1.22469 | + | 0.397927i | −0.848789 | − | 0.528732i | \(-0.822668\pi\) |
−0.375904 | + | 0.926659i | \(0.622668\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.7330 | + | 5.89946i | −0.876979 | + | 0.201053i | ||||
\(862\) | −12.6740 | + | 24.8742i | −0.431679 | + | 0.847217i | ||||
\(863\) | −11.5537 | + | 22.6754i | −0.393292 | + | 0.771879i | −0.999730 | − | 0.0232522i | \(-0.992598\pi\) |
0.606438 | + | 0.795131i | \(0.292598\pi\) | |||||||
\(864\) | 5.01287 | + | 1.36790i | 0.170541 | + | 0.0465369i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.48379 | − | 0.807033i | 0.0844027 | − | 0.0274241i | ||||
\(867\) | 30.2273 | − | 12.1588i | 1.02657 | − | 0.412936i | ||||
\(868\) | 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 | ||||
\(872\) | −2.75806 | + | 0.436834i | −0.0933998 | + | 0.0147931i | ||||
\(873\) | −19.8216 | − | 0.406698i | −0.670858 | − | 0.0137647i | ||||
\(874\) | 5.88827i | 0.199174i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.5061 | + | 8.08714i | −0.456327 | + | 0.273239i | ||||
\(877\) | −30.3080 | + | 15.4427i | −1.02343 | + | 0.521463i | −0.883368 | − | 0.468679i | \(-0.844730\pi\) |
−0.140061 | + | 0.990143i | \(0.544730\pi\) | |||||||
\(878\) | −1.72542 | − | 10.8939i | −0.0582302 | − | 0.367651i | ||||
\(879\) | 23.0433 | + | 2.05158i | 0.777232 | + | 0.0691981i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.1879 | + | 37.4210i | 0.915985 | + | 1.26074i | 0.965081 | + | 0.261951i | \(0.0843658\pi\) |
−0.0490965 | + | 0.998794i | \(0.515634\pi\) | |||||||
\(882\) | 1.14347 | + | 3.78150i | 0.0385027 | + | 0.127330i | ||||
\(883\) | 4.58634 | − | 28.9570i | 0.154343 | − | 0.974480i | −0.781971 | − | 0.623315i | \(-0.785785\pi\) |
0.936313 | − | 0.351165i | \(-0.114215\pi\) | |||||||
\(884\) | 10.9376 | + | 33.6624i | 0.367870 | + | 1.13219i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.577651 | − | 1.77783i | 0.0194065 | − | 0.0597272i | ||||
\(887\) | −22.3947 | − | 11.4107i | −0.751940 | − | 0.383133i | 0.0356241 | − | 0.999365i | \(-0.488658\pi\) |
−0.787564 | + | 0.616233i | \(0.788658\pi\) | |||||||
\(888\) | −0.953595 | − | 13.9438i | −0.0320005 | − | 0.467922i | ||||
\(889\) | 34.3666 | + | 11.1664i | 1.15262 | + | 0.374509i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.3573 | + | 15.3154i | 0.648494 | + | 0.513085i | ||||
\(892\) | −5.37230 | − | 0.850889i | −0.179878 | − | 0.0284899i | ||||
\(893\) | 17.0179 | + | 17.0179i | 0.569481 | + | 0.569481i | ||||
\(894\) | 19.1340 | + | 8.15651i | 0.639938 | + | 0.272795i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.69511 | − | 2.33312i | 0.0566297 | − | 0.0779441i | ||||
\(897\) | 8.92433 | − | 7.46515i | 0.297975 | − | 0.249254i | ||||
\(898\) | 9.31762 | + | 18.2869i | 0.310933 | + | 0.610240i | ||||
\(899\) | 16.3657 | 0.545828 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0545 | 1.06789 | ||||||||
\(902\) | 6.58084 | + | 12.9156i | 0.219118 | + | 0.430043i | ||||
\(903\) | 16.8396 | − | 14.0863i | 0.560388 | − | 0.468761i | ||||
\(904\) | 2.71701 | − | 3.73964i | 0.0903664 | − | 0.124379i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17.7300 | + | 7.55799i | 0.589040 | + | 0.251097i | ||||
\(907\) | −38.3276 | − | 38.3276i | −1.27265 | − | 1.27265i | −0.944694 | − | 0.327952i | \(-0.893642\pi\) |
−0.327952 | − | 0.944694i | \(-0.606358\pi\) | |||||||
\(908\) | −19.3805 | − | 3.06957i | −0.643164 | − | 0.101867i | ||||
\(909\) | −10.4226 | − | 1.87070i | −0.345695 | − | 0.0620473i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.3746 | − | 9.21947i | −0.940093 | − | 0.305455i | −0.201409 | − | 0.979507i | \(-0.564552\pi\) |
−0.738683 | + | 0.674053i | \(0.764552\pi\) | |||||||
\(912\) | −0.612698 | − | 8.95907i | −0.0202885 | − | 0.296665i | ||||
\(913\) | 29.5101 | + | 15.0361i | 0.976640 | + | 0.497623i | ||||
\(914\) | 4.82892 | − | 14.8619i | 0.159727 | − | 0.491588i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.40628 | + | 16.6388i | 0.178628 | + | 0.549762i | ||||
\(917\) | −5.37713 | + | 33.9499i | −0.177569 | + | 1.12112i | ||||
\(918\) | 23.0122 | + | 20.9124i | 0.759515 | + | 0.690213i | ||||
\(919\) | −8.11678 | − | 11.1718i | −0.267748 | − | 0.368523i | 0.653880 | − | 0.756598i | \(-0.273140\pi\) |
−0.921628 | + | 0.388075i | \(0.873140\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −56.5772 | − | 5.03715i | −1.86428 | − | 0.165980i | ||||
\(922\) | −2.18253 | − | 13.7799i | −0.0718777 | − | 0.453818i | ||||
\(923\) | 30.1518 | − | 15.3631i | 0.992457 | − | 0.505682i | ||||
\(924\) | 11.7535 | − | 7.03773i | 0.386661 | − | 0.231524i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 32.9648i | − | 1.08329i | ||||||
\(927\) | 0.397100 | − | 19.3537i | 0.0130425 | − | 0.635660i | ||||
\(928\) | 2.86426 | − | 0.453655i | 0.0940240 | − | 0.0148919i | ||||
\(929\) | −0.637117 | − | 0.462892i | −0.0209031 | − | 0.0151870i | 0.577285 | − | 0.816543i | \(-0.304112\pi\) |
−0.598188 | + | 0.801356i | \(0.704112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.52351 | − | 4.01306i | 0.181026 | − | 0.131523i | ||||
\(932\) | −20.5218 | + | 20.5218i | −0.672214 | + | 0.672214i | ||||
\(933\) | −16.6344 | + | 6.69112i | −0.544585 | + | 0.219057i | ||||
\(934\) | 3.51708 | − | 1.14277i | 0.115082 | − | 0.0373925i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.8017 | + | 12.2869i | −0.418436 | + | 0.401611i | ||||
\(937\) | −1.89949 | + | 3.72797i | −0.0620538 | + | 0.121787i | −0.919950 | − | 0.392035i | \(-0.871771\pi\) |
0.857896 | + | 0.513823i | \(0.171771\pi\) | |||||||
\(938\) | 0.604224 | − | 1.18586i | 0.0197286 | − | 0.0387196i | ||||
\(939\) | −23.1608 | + | 5.30976i | −0.755824 | + | 0.173277i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.1196 | + | 3.93788i | −0.395086 | + | 0.128371i | −0.499821 | − | 0.866129i | \(-0.666601\pi\) |
0.104734 | + | 0.994500i | \(0.466601\pi\) | |||||||
\(942\) | −10.6146 | − | 26.3884i | −0.345844 | − | 0.859781i | ||||
\(943\) | 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 | ||||
\(947\) | 39.3427 | − | 6.23127i | 1.27847 | − | 0.202489i | 0.519980 | − | 0.854179i | \(-0.325940\pi\) |
0.758486 | + | 0.651690i | \(0.225940\pi\) | |||||||
\(948\) | −17.2403 | − | 10.8097i | −0.559940 | − | 0.351083i | ||||
\(949\) | − | 53.7570i | − | 1.74503i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.7940 | + | 28.0470i | 0.544581 | + | 0.909486i | ||||
\(952\) | 15.3768 | − | 7.83489i | 0.498366 | − | 0.253930i | ||||
\(953\) | 4.01002 | + | 25.3183i | 0.129897 | + | 0.820139i | 0.963487 | + | 0.267755i | \(0.0862819\pi\) |
−0.833590 | + | 0.552384i | \(0.813718\pi\) | |||||||
\(954\) | 7.00017 | + | 14.4647i | 0.226639 | + | 0.468312i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.32263 | − | 4.57321i | −0.107462 | − | 0.147908i | ||||
\(957\) | 13.3614 | + | 3.35311i | 0.431913 | + | 0.108391i | ||||
\(958\) | −0.841500 | + | 5.31302i | −0.0271876 | + | 0.171656i | ||||
\(959\) | 17.7077 | + | 54.4987i | 0.571811 | + | 1.75985i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.262130 | − | 0.806752i | 0.00845579 | − | 0.0260243i | ||||
\(962\) | 42.5251 | + | 21.6676i | 1.37106 | + | 0.698592i | ||||
\(963\) | −21.2461 | − | 30.5412i | −0.684647 | − | 0.984177i | ||||
\(964\) | −13.4069 | − | 4.35617i | −0.431807 | − | 0.140303i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.27577 | − | 3.72837i | −0.137571 | − | 0.119958i | ||||
\(967\) | −3.74989 | − | 0.593924i | −0.120588 | − | 0.0190993i | 0.0958486 | − | 0.995396i | \(-0.469444\pi\) |
−0.216437 | + | 0.976297i | \(0.569444\pi\) | |||||||
\(968\) | 2.45946 | + | 2.45946i | 0.0790499 | + | 0.0790499i | ||||
\(969\) | 21.0729 | − | 49.4340i | 0.676958 | − | 1.58805i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.56008 | − | 2.14727i | 0.0500655 | − | 0.0689092i | −0.783250 | − | 0.621707i | \(-0.786440\pi\) |
0.833316 | + | 0.552797i | \(0.186440\pi\) | |||||||
\(972\) | −4.41133 | + | 14.9513i | −0.141494 | + | 0.479562i | ||||
\(973\) | −12.4988 | − | 24.5303i | −0.400694 | − | 0.786406i | ||||
\(974\) | 4.19638 | 0.134461 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.59018 | 0.146928 | ||||||||
\(977\) | −8.15001 | − | 15.9953i | −0.260742 | − | 0.511735i | 0.723107 | − | 0.690736i | \(-0.242713\pi\) |
−0.983849 | + | 0.179001i | \(0.942713\pi\) | |||||||
\(978\) | 7.27995 | + | 8.70293i | 0.232787 | + | 0.278289i | ||||
\(979\) | −2.09807 | + | 2.88774i | −0.0670546 | + | 0.0922927i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.14049 | − | 8.29933i | −0.0364131 | − | 0.264977i | ||||
\(982\) | −22.3318 | − | 22.3318i | −0.712635 | − | 0.712635i | ||||
\(983\) | 39.4883 | + | 6.25433i | 1.25948 | + | 0.199482i | 0.750254 | − | 0.661150i | \(-0.229931\pi\) |
0.509227 | + | 0.860632i | \(0.329931\pi\) | |||||||
\(984\) | −6.01646 | + | 6.89978i | −0.191798 | + | 0.219957i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 16.5046 | + | 5.36268i | 0.525614 | + | 0.170782i | ||||
\(987\) | −23.1330 | + | 1.58203i | −0.736331 | + | 0.0503566i | ||||
\(988\) | 27.3230 | + | 13.9218i | 0.869260 | + | 0.442910i | ||||
\(989\) | −1.54254 | + | 4.74745i | −0.0490499 | + | 0.150960i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.5601 | − | 38.6560i | −0.398984 | − | 1.22795i | −0.925815 | − | 0.377977i | \(-0.876620\pi\) |
0.526831 | − | 0.849970i | \(-0.323380\pi\) | |||||||
\(992\) | 0.882826 | − | 5.57395i | 0.0280298 | − | 0.176973i | ||||
\(993\) | 13.3799 | − | 53.3158i | 0.424597 | − | 1.69193i | ||||
\(994\) | −9.69837 | − | 13.3487i | −0.307614 | − | 0.423394i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.85489 | + | 20.8341i | −0.0587744 | + | 0.660153i | ||||
\(997\) | 1.77985 | + | 11.2375i | 0.0563684 | + | 0.355896i | 0.999710 | + | 0.0240735i | \(0.00766359\pi\) |
−0.943342 | + | 0.331823i | \(0.892336\pi\) | |||||||
\(998\) | 9.13605 | − | 4.65505i | 0.289197 | − | 0.147353i | ||||
\(999\) | 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.b.257.7 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.b.257.2 | 80 | ||
5.2 | odd | 4 | 750.2.l.c.743.4 | 80 | |||
5.3 | odd | 4 | 750.2.l.a.743.7 | 80 | |||
5.4 | even | 2 | 150.2.l.a.47.4 | ✓ | 80 | ||
15.2 | even | 4 | 750.2.l.c.743.7 | 80 | |||
15.8 | even | 4 | 750.2.l.a.743.4 | 80 | |||
15.14 | odd | 2 | 150.2.l.a.47.9 | yes | 80 | ||
25.6 | even | 5 | 750.2.l.a.107.4 | 80 | |||
25.8 | odd | 20 | inner | 750.2.l.b.143.2 | 80 | ||
25.17 | odd | 20 | 150.2.l.a.83.9 | yes | 80 | ||
25.19 | even | 10 | 750.2.l.c.107.7 | 80 | |||
75.8 | even | 20 | inner | 750.2.l.b.143.7 | 80 | ||
75.17 | even | 20 | 150.2.l.a.83.4 | yes | 80 | ||
75.44 | odd | 10 | 750.2.l.c.107.4 | 80 | |||
75.56 | odd | 10 | 750.2.l.a.107.7 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.47.4 | ✓ | 80 | 5.4 | even | 2 | ||
150.2.l.a.47.9 | yes | 80 | 15.14 | odd | 2 | ||
150.2.l.a.83.4 | yes | 80 | 75.17 | even | 20 | ||
150.2.l.a.83.9 | yes | 80 | 25.17 | odd | 20 | ||
750.2.l.a.107.4 | 80 | 25.6 | even | 5 | |||
750.2.l.a.107.7 | 80 | 75.56 | odd | 10 | |||
750.2.l.a.743.4 | 80 | 15.8 | even | 4 | |||
750.2.l.a.743.7 | 80 | 5.3 | odd | 4 | |||
750.2.l.b.143.2 | 80 | 25.8 | odd | 20 | inner | ||
750.2.l.b.143.7 | 80 | 75.8 | even | 20 | inner | ||
750.2.l.b.257.2 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.b.257.7 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.c.107.4 | 80 | 75.44 | odd | 10 | |||
750.2.l.c.107.7 | 80 | 25.19 | even | 10 | |||
750.2.l.c.743.4 | 80 | 5.2 | odd | 4 | |||
750.2.l.c.743.7 | 80 | 15.2 | even | 4 |