Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,2,Mod(35,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.ce (of order \(18\), degree \(6\), 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: | \(5.46176749826\) |
Analytic rank: | \(0\) |
Dimension: | \(240\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 35.8 | ||
Character | \(\chi\) | \(=\) | 684.35 |
Dual form | 684.2.ce.a.215.8 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{2}{9}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.12762 | − | 0.853506i | −0.797348 | − | 0.603520i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.543054 | + | 1.92486i | 0.271527 | + | 0.962431i | ||||
\(5\) | 4.17116 | + | 0.735488i | 1.86540 | + | 0.328920i | 0.988436 | − | 0.151635i | \(-0.0484540\pi\) |
0.876964 | + | 0.480556i | \(0.159565\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.05168 | − | 1.18454i | 0.775461 | − | 0.447713i | −0.0593582 | − | 0.998237i | \(-0.518905\pi\) |
0.834819 | + | 0.550524i | \(0.185572\pi\) | |||||||
\(8\) | 1.03052 | − | 2.63401i | 0.364345 | − | 0.931264i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.07574 | − | 4.38947i | −1.28886 | − | 1.38807i | ||||
\(11\) | 2.46013 | − | 4.26108i | 0.741758 | − | 1.28476i | −0.209936 | − | 0.977715i | \(-0.567325\pi\) |
0.951694 | − | 0.307048i | \(-0.0993412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.96446 | − | 1.44294i | −1.09954 | − | 0.400201i | −0.272395 | − | 0.962186i | \(-0.587816\pi\) |
−0.827147 | + | 0.561985i | \(0.810038\pi\) | |||||||
\(14\) | −3.32452 | − | 0.415413i | −0.888516 | − | 0.111024i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.41019 | + | 2.09061i | −0.852546 | + | 0.522652i | ||||
\(17\) | 2.78144 | − | 3.31479i | 0.674598 | − | 0.803955i | −0.314804 | − | 0.949157i | \(-0.601939\pi\) |
0.989402 | + | 0.145202i | \(0.0463831\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.10988 | − | 1.45220i | −0.942871 | − | 0.333158i | ||||
\(20\) | 0.849452 | + | 8.42832i | 0.189943 | + | 1.88463i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.41095 | + | 2.70514i | −1.36682 | + | 0.576737i | ||||
\(23\) | 0.671956 | + | 3.81085i | 0.140112 | + | 0.794617i | 0.971162 | + | 0.238419i | \(0.0766292\pi\) |
−0.831050 | + | 0.556198i | \(0.812260\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.1592 | + | 4.42558i | 2.43184 | + | 0.885117i | ||||
\(26\) | 3.23884 | + | 5.01078i | 0.635188 | + | 0.982695i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.39424 | + | 3.30593i | 0.641451 | + | 0.624762i | ||||
\(29\) | −2.73073 | − | 3.25435i | −0.507083 | − | 0.604318i | 0.450393 | − | 0.892830i | \(-0.351284\pi\) |
−0.957476 | + | 0.288512i | \(0.906839\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.29690 | + | 2.48082i | −0.771747 | + | 0.445568i | −0.833497 | − | 0.552523i | \(-0.813665\pi\) |
0.0617507 | + | 0.998092i | \(0.480332\pi\) | |||||||
\(32\) | 5.62974 | + | 0.553205i | 0.995207 | + | 0.0977937i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.96560 | + | 1.36385i | −1.02309 | + | 0.233898i | ||||
\(35\) | 9.42909 | − | 3.43191i | 1.59381 | − | 0.580098i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.93259 | 0.810912 | 0.405456 | − | 0.914114i | \(-0.367113\pi\) | ||||
0.405456 | + | 0.914114i | \(0.367113\pi\) | |||||||
\(38\) | 3.39492 | + | 5.14534i | 0.550728 | + | 0.834685i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.23577 | − | 10.2290i | 0.985961 | − | 1.61734i | ||||
\(41\) | 0.564228 | + | 1.55020i | 0.0881175 | + | 0.242101i | 0.975922 | − | 0.218120i | \(-0.0699924\pi\) |
−0.887804 | + | 0.460221i | \(0.847770\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.22562 | − | 1.45040i | −1.25440 | − | 0.221184i | −0.493321 | − | 0.869848i | \(-0.664217\pi\) |
−0.761075 | + | 0.648664i | \(0.775328\pi\) | |||||||
\(44\) | 9.53797 | + | 2.42142i | 1.43790 | + | 0.365043i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.49487 | − | 4.87071i | 0.367849 | − | 0.718147i | ||||
\(47\) | −6.63122 | + | 5.56426i | −0.967263 | + | 0.811630i | −0.982119 | − | 0.188260i | \(-0.939715\pi\) |
0.0148563 | + | 0.999890i | \(0.495271\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.693747 | + | 1.20160i | −0.0991067 | + | 0.171658i | ||||
\(50\) | −9.93368 | − | 15.3683i | −1.40483 | − | 2.17341i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.624555 | − | 8.41462i | 0.0866102 | − | 1.16690i | ||||
\(53\) | −2.44391 | + | 0.430928i | −0.335697 | + | 0.0591925i | −0.338956 | − | 0.940802i | \(-0.610074\pi\) |
0.00325877 | + | 0.999995i | \(0.498963\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.3956 | − | 15.9642i | 1.80626 | − | 2.15262i | ||||
\(56\) | −1.00578 | − | 6.62484i | −0.134403 | − | 0.885281i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.301611 | + | 6.00037i | 0.0396034 | + | 0.787887i | ||||
\(59\) | 3.10160 | + | 2.60255i | 0.403794 | + | 0.338823i | 0.821958 | − | 0.569548i | \(-0.192882\pi\) |
−0.418164 | + | 0.908371i | \(0.637326\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.847176 | + | 4.80457i | 0.108470 | + | 0.615162i | 0.989778 | + | 0.142620i | \(0.0455526\pi\) |
−0.881308 | + | 0.472543i | \(0.843336\pi\) | |||||||
\(62\) | 6.96267 | + | 0.870014i | 0.884260 | + | 0.110492i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.87604 | − | 5.42882i | −0.734505 | − | 0.678603i | ||||
\(65\) | −15.4751 | − | 8.93456i | −1.91945 | − | 1.10820i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.57119 | + | 10.2147i | 1.04714 | + | 1.24793i | 0.967969 | + | 0.251068i | \(0.0807819\pi\) |
0.0791678 | + | 0.996861i | \(0.474774\pi\) | |||||||
\(68\) | 7.89099 | + | 3.55378i | 0.956923 | + | 0.430959i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −13.5616 | − | 4.17790i | −1.62092 | − | 0.499355i | ||||
\(71\) | 1.59125 | − | 9.02445i | 0.188847 | − | 1.07101i | −0.732065 | − | 0.681235i | \(-0.761443\pi\) |
0.920912 | − | 0.389770i | \(-0.127446\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.973188 | + | 0.354212i | −0.113903 | + | 0.0414573i | −0.398343 | − | 0.917237i | \(-0.630415\pi\) |
0.284440 | + | 0.958694i | \(0.408192\pi\) | |||||||
\(74\) | −5.56208 | − | 4.20999i | −0.646579 | − | 0.489402i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.563407 | − | 8.69957i | 0.0646272 | − | 0.997909i | ||||
\(77\) | − | 11.6565i | − | 1.32838i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.557573 | + | 1.53192i | 0.0627319 | + | 0.172355i | 0.967099 | − | 0.254402i | \(-0.0818785\pi\) |
−0.904367 | + | 0.426756i | \(0.859656\pi\) | |||||||
\(80\) | −15.7621 | + | 6.21211i | −1.76225 | + | 0.694535i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.686873 | − | 2.22961i | 0.0758525 | − | 0.246219i | ||||
\(83\) | −2.35877 | − | 4.08551i | −0.258909 | − | 0.448443i | 0.707041 | − | 0.707172i | \(-0.250030\pi\) |
−0.965950 | + | 0.258729i | \(0.916696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.0398 | − | 11.7808i | 1.52283 | − | 1.27781i | ||||
\(86\) | 8.03745 | + | 8.65612i | 0.866701 | + | 0.933413i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.68851 | − | 10.8712i | −0.926198 | − | 1.15887i | ||||
\(89\) | −0.0667092 | + | 0.183282i | −0.00707117 | + | 0.0194279i | −0.943178 | − | 0.332288i | \(-0.892179\pi\) |
0.936107 | + | 0.351716i | \(0.114402\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.84300 | + | 1.73559i | −1.03183 | + | 0.181939i | ||||
\(92\) | −6.97045 | + | 3.36292i | −0.726720 | + | 0.350608i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.2266 | − | 0.614576i | 1.26108 | − | 0.0633887i | ||||
\(95\) | −16.0749 | − | 9.08015i | −1.64925 | − | 0.931603i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.7227 | + | 12.3538i | 1.49487 | + | 1.25434i | 0.888259 | + | 0.459343i | \(0.151915\pi\) |
0.606609 | + | 0.795000i | \(0.292529\pi\) | |||||||
\(98\) | 1.80786 | − | 0.762836i | 0.182621 | − | 0.0770581i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.91554 | + | 25.8081i | −0.191554 | + | 2.58081i | ||||
\(101\) | −0.213461 | + | 0.586480i | −0.0212402 | + | 0.0583569i | −0.949860 | − | 0.312677i | \(-0.898774\pi\) |
0.928619 | + | 0.371034i | \(0.120997\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.867609 | + | 0.500914i | 0.0854881 | + | 0.0493566i | 0.542135 | − | 0.840292i | \(-0.317616\pi\) |
−0.456647 | + | 0.889648i | \(0.650950\pi\) | |||||||
\(104\) | −7.88620 | + | 8.95544i | −0.773305 | + | 0.878153i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.12361 | + | 1.59997i | 0.303391 | + | 0.155403i | ||||
\(107\) | 8.77073 | + | 15.1913i | 0.847898 | + | 1.46860i | 0.883080 | + | 0.469222i | \(0.155465\pi\) |
−0.0351824 | + | 0.999381i | \(0.511201\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.547450 | − | 3.10474i | 0.0524362 | − | 0.297381i | −0.947300 | − | 0.320348i | \(-0.896200\pi\) |
0.999736 | + | 0.0229672i | \(0.00731134\pi\) | |||||||
\(110\) | −28.7307 | + | 6.56838i | −2.73937 | + | 0.626270i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.52020 | + | 8.32874i | −0.427119 | + | 0.786992i | ||||
\(113\) | − | 2.93545i | − | 0.276144i | −0.990422 | − | 0.138072i | \(-0.955909\pi\) | ||
0.990422 | − | 0.138072i | \(-0.0440905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.3899i | 1.52836i | ||||||||
\(116\) | 4.78125 | − | 7.02356i | 0.443928 | − | 0.652121i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.27613 | − | 5.58192i | −0.117477 | − | 0.513858i | ||||
\(119\) | 1.78013 | − | 10.0956i | 0.163184 | − | 0.925462i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.60452 | − | 11.4394i | −0.600411 | − | 1.03994i | ||||
\(122\) | 3.14544 | − | 6.14080i | 0.284775 | − | 0.555962i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.10868 | − | 6.92373i | −0.638379 | − | 0.621769i | ||||
\(125\) | 29.1227 | + | 16.8140i | 2.60481 | + | 1.50389i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.70038 | + | 4.67176i | −0.150884 | + | 0.414551i | −0.991990 | − | 0.126320i | \(-0.959683\pi\) |
0.841105 | + | 0.540872i | \(0.181906\pi\) | |||||||
\(128\) | 1.99241 | + | 11.1369i | 0.176106 | + | 0.984371i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.82435 | + | 23.2829i | 0.861652 | + | 2.04205i | ||||
\(131\) | 7.62616 | + | 6.39911i | 0.666301 | + | 0.559093i | 0.911968 | − | 0.410262i | \(-0.134563\pi\) |
−0.245667 | + | 0.969354i | \(0.579007\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.1523 | + | 1.88885i | −0.880319 | + | 0.163784i | ||||
\(134\) | −0.946694 | − | 18.8339i | −0.0817819 | − | 1.62700i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.86486 | − | 10.7423i | −0.502908 | − | 0.921146i | ||||
\(137\) | 6.82117 | − | 1.20276i | 0.582772 | − | 0.102758i | 0.125513 | − | 0.992092i | \(-0.459942\pi\) |
0.457259 | + | 0.889334i | \(0.348831\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.85427 | + | 5.09456i | −0.157277 | + | 0.432115i | −0.993156 | − | 0.116799i | \(-0.962737\pi\) |
0.835878 | + | 0.548915i | \(0.184959\pi\) | |||||||
\(140\) | 11.7265 | + | 16.2860i | 0.991066 | + | 1.37642i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.49676 | + | 8.81801i | −0.796950 | + | 0.739991i | ||||
\(143\) | −15.9016 | + | 13.3430i | −1.32976 | + | 1.11580i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.99676 | − | 15.5829i | −0.747141 | − | 1.29409i | ||||
\(146\) | 1.39971 | + | 0.431206i | 0.115841 | + | 0.0356869i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.67866 | + | 9.49455i | 0.220184 | + | 0.780447i | ||||
\(149\) | −5.56930 | − | 15.3015i | −0.456255 | − | 1.25355i | −0.928252 | − | 0.371951i | \(-0.878689\pi\) |
0.471997 | − | 0.881600i | \(-0.343533\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 0.224746i | − | 0.0182896i | −0.999958 | − | 0.00914478i | \(-0.997089\pi\) | ||
0.999958 | − | 0.00914478i | \(-0.00291091\pi\) | |||||||
\(152\) | −8.06045 | + | 9.32894i | −0.653789 | + | 0.756677i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.94888 | + | 13.1441i | −0.801703 | + | 1.05918i | ||||
\(155\) | −19.7477 | + | 7.18757i | −1.58617 | + | 0.577320i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.09430 | + | 11.8774i | −0.167143 | + | 0.947917i | 0.779684 | + | 0.626174i | \(0.215380\pi\) |
−0.946827 | + | 0.321743i | \(0.895731\pi\) | |||||||
\(158\) | 0.678773 | − | 2.20332i | 0.0540003 | − | 0.175286i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 23.0757 | + | 6.44812i | 1.82429 | + | 0.509768i | ||||
\(161\) | 5.89273 | + | 7.02268i | 0.464412 | + | 0.553464i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.80807 | − | 2.19859i | −0.298271 | − | 0.172207i | 0.343395 | − | 0.939191i | \(-0.388423\pi\) |
−0.641666 | + | 0.766984i | \(0.721756\pi\) | |||||||
\(164\) | −2.67752 | + | 1.92790i | −0.209079 | + | 0.150544i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.827212 | + | 6.62013i | −0.0642041 | + | 0.513821i | ||||
\(167\) | 3.56050 | + | 20.1926i | 0.275520 | + | 1.56255i | 0.737306 | + | 0.675559i | \(0.236098\pi\) |
−0.461786 | + | 0.886991i | \(0.652791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.67624 | + | 3.08473i | 0.282788 | + | 0.237287i | ||||
\(170\) | −25.8866 | + | 1.30120i | −1.98541 | + | 0.0997975i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.67514 | − | 16.6208i | −0.127728 | − | 1.26733i | ||||
\(173\) | 2.73872 | − | 3.26387i | 0.208221 | − | 0.248148i | −0.651819 | − | 0.758374i | \(-0.725994\pi\) |
0.860040 | + | 0.510226i | \(0.170438\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30.1890 | − | 5.32314i | 2.28207 | − | 0.402391i | ||||
\(176\) | 0.518724 | + | 19.6742i | 0.0391003 | + | 1.48300i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.231655 | − | 0.149736i | 0.0173633 | − | 0.0112232i | ||||
\(179\) | 4.10247 | − | 7.10569i | 0.306633 | − | 0.531104i | −0.670991 | − | 0.741466i | \(-0.734131\pi\) |
0.977624 | + | 0.210362i | \(0.0674642\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.61966 | + | 3.03726i | −0.269047 | + | 0.225757i | −0.767322 | − | 0.641261i | \(-0.778411\pi\) |
0.498275 | + | 0.867019i | \(0.333967\pi\) | |||||||
\(182\) | 12.5805 | + | 6.44398i | 0.932529 | + | 0.477660i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.7303 | + | 2.15723i | 0.791047 | + | 0.159033i | ||||
\(185\) | 20.5746 | + | 3.62786i | 1.51268 | + | 0.266726i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.28187 | − | 20.0068i | −0.532503 | − | 1.46304i | ||||
\(188\) | −14.3115 | − | 9.74249i | −1.04378 | − | 0.710544i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.3764 | + | 23.9590i | 0.752784 | + | 1.73817i | ||||
\(191\) | 16.4905 | 1.19321 | 0.596604 | − | 0.802536i | \(-0.296516\pi\) | ||||
0.596604 | + | 0.802536i | \(0.296516\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.8738 | + | 5.04966i | −0.998660 | + | 0.363482i | −0.789068 | − | 0.614306i | \(-0.789436\pi\) |
−0.209592 | + | 0.977789i | \(0.567214\pi\) | |||||||
\(194\) | −6.05757 | − | 26.4964i | −0.434908 | − | 1.90233i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.68967 | − | 0.682831i | −0.192119 | − | 0.0487736i | ||||
\(197\) | −20.2363 | + | 11.6835i | −1.44178 | + | 0.832412i | −0.997969 | − | 0.0637088i | \(-0.979707\pi\) |
−0.443811 | + | 0.896120i | \(0.646374\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.86734 | + | 9.37593i | 0.557701 | + | 0.664642i | 0.969058 | − | 0.246832i | \(-0.0793897\pi\) |
−0.411358 | + | 0.911474i | \(0.634945\pi\) | |||||||
\(200\) | 24.1874 | − | 27.4668i | 1.71031 | − | 1.94220i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.741267 | − | 0.479136i | 0.0521554 | − | 0.0337119i | ||||
\(203\) | −9.45747 | − | 3.44224i | −0.663784 | − | 0.241598i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.21333 | + | 6.88113i | 0.0847426 | + | 0.480599i | ||||
\(206\) | −0.550800 | − | 1.30535i | −0.0383760 | − | 0.0909481i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 16.5362 | − | 3.36741i | 1.14658 | − | 0.233488i | ||||
\(209\) | −16.2988 | + | 13.9399i | −1.12741 | + | 0.964243i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.1716 | − | 13.3137i | 0.769082 | − | 0.916556i | −0.229304 | − | 0.973355i | \(-0.573645\pi\) |
0.998386 | + | 0.0567987i | \(0.0180893\pi\) | |||||||
\(212\) | −2.15665 | − | 4.47018i | −0.148120 | − | 0.307013i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.07586 | − | 24.6159i | 0.210262 | − | 1.68271i | ||||
\(215\) | −33.2437 | − | 12.0997i | −2.26720 | − | 0.825193i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.87724 | + | 10.1797i | −0.398973 | + | 0.691042i | ||||
\(218\) | −3.26723 | + | 3.03372i | −0.221285 | + | 0.205469i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 38.0035 | + | 17.1152i | 2.56220 | + | 1.15391i | ||||
\(221\) | −15.8100 | + | 9.12788i | −1.06349 | + | 0.614008i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.2507 | − | 3.04177i | −1.15519 | − | 0.203692i | −0.436951 | − | 0.899485i | \(-0.643942\pi\) |
−0.718242 | + | 0.695793i | \(0.755053\pi\) | |||||||
\(224\) | 12.2057 | − | 5.53363i | 0.815528 | − | 0.369731i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.50543 | + | 3.31007i | −0.166658 | + | 0.220183i | ||||
\(227\) | 14.1929 | 0.942018 | 0.471009 | − | 0.882128i | \(-0.343890\pi\) | ||||
0.471009 | + | 0.882128i | \(0.343890\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.146313 | 0.00966863 | 0.00483432 | − | 0.999988i | \(-0.498461\pi\) | ||||
0.00483432 | + | 0.999988i | \(0.498461\pi\) | |||||||
\(230\) | 13.9889 | − | 18.4816i | 0.922399 | − | 1.21864i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.3861 | + | 3.83908i | −0.747533 | + | 0.252048i | ||||
\(233\) | 6.57849 | + | 1.15996i | 0.430971 | + | 0.0759918i | 0.384926 | − | 0.922948i | \(-0.374227\pi\) |
0.0460453 | + | 0.998939i | \(0.485338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −31.7523 | + | 18.3322i | −2.07129 | + | 1.19586i | ||||
\(236\) | −3.32521 | + | 7.38347i | −0.216453 | + | 0.480623i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.6240 | + | 9.86465i | −0.688649 | + | 0.639430i | ||||
\(239\) | −9.01958 | + | 15.6224i | −0.583428 | + | 1.01053i | 0.411641 | + | 0.911346i | \(0.364956\pi\) |
−0.995069 | + | 0.0991812i | \(0.968378\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.2234 | − | 8.81659i | −1.56037 | − | 0.567927i | −0.589545 | − | 0.807735i | \(-0.700693\pi\) |
−0.970820 | + | 0.239809i | \(0.922915\pi\) | |||||||
\(242\) | −2.31618 | + | 18.5363i | −0.148890 | + | 1.19156i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.78807 | + | 4.23984i | −0.562599 | + | 0.271428i | ||||
\(245\) | −3.77750 | + | 4.50185i | −0.241335 | + | 0.287612i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.1980 | + | 11.6875i | 0.903396 | + | 0.743659i | ||||
\(248\) | 2.10645 | + | 13.8746i | 0.133759 | + | 0.881040i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −18.4885 | − | 43.8162i | −1.16931 | − | 2.77118i | ||||
\(251\) | −2.36645 | − | 13.4208i | −0.149369 | − | 0.847115i | −0.963755 | − | 0.266790i | \(-0.914037\pi\) |
0.814385 | − | 0.580324i | \(-0.197074\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.8914 | + | 6.51195i | 1.12482 | + | 0.409403i | ||||
\(254\) | 5.90476 | − | 3.81668i | 0.370497 | − | 0.239480i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.25873 | − | 14.2587i | 0.453670 | − | 0.891170i | ||||
\(257\) | −7.01354 | − | 8.35841i | −0.437493 | − | 0.521384i | 0.501576 | − | 0.865114i | \(-0.332754\pi\) |
−0.939068 | + | 0.343730i | \(0.888309\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.1201 | − | 5.84283i | 0.628831 | − | 0.363056i | ||||
\(260\) | 8.79398 | − | 34.6394i | 0.545379 | − | 2.14825i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.13773 | − | 13.7247i | −0.193850 | − | 0.847917i | ||||
\(263\) | 0.651063 | − | 0.236968i | 0.0401463 | − | 0.0146120i | −0.321869 | − | 0.946784i | \(-0.604311\pi\) |
0.362015 | + | 0.932172i | \(0.382089\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5109 | −0.645680 | ||||||||
\(266\) | 13.0601 | + | 6.53518i | 0.800767 | + | 0.400698i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15.0074 | + | 22.0455i | −0.916720 | + | 1.34664i | ||||
\(269\) | −7.26990 | − | 19.9739i | −0.443253 | − | 1.21783i | −0.937340 | − | 0.348416i | \(-0.886720\pi\) |
0.494086 | − | 0.869413i | \(-0.335503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.5639 | − | 3.44964i | −1.18842 | − | 0.209551i | −0.455734 | − | 0.890116i | \(-0.650623\pi\) |
−0.732688 | + | 0.680565i | \(0.761734\pi\) | |||||||
\(272\) | −2.55530 | + | 17.1190i | −0.154938 | + | 1.03799i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.71825 | − | 4.46566i | −0.526689 | − | 0.269780i | ||||
\(275\) | 48.7710 | − | 40.9237i | 2.94100 | − | 2.46779i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.11262 | − | 14.0515i | 0.487440 | − | 0.844271i | −0.512456 | − | 0.858714i | \(-0.671264\pi\) |
0.999896 | + | 0.0144429i | \(0.00459749\pi\) | |||||||
\(278\) | 6.43915 | − | 4.16210i | 0.386195 | − | 0.249626i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.677210 | − | 28.3730i | 0.0404711 | − | 1.69561i | ||||
\(281\) | −21.1699 | + | 3.73283i | −1.26289 | + | 0.222682i | −0.764701 | − | 0.644385i | \(-0.777113\pi\) |
−0.498191 | + | 0.867067i | \(0.666002\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.89394 | − | 2.25711i | 0.112583 | − | 0.134171i | −0.706810 | − | 0.707404i | \(-0.749866\pi\) |
0.819393 | + | 0.573232i | \(0.194311\pi\) | |||||||
\(284\) | 18.2350 | − | 1.83782i | 1.08205 | − | 0.109054i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 29.3193 | − | 1.47375i | 1.73369 | − | 0.0871444i | ||||
\(287\) | 2.99388 | + | 2.51217i | 0.176723 | + | 0.148289i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.299414 | − | 1.69806i | −0.0176126 | − | 0.0998858i | ||||
\(290\) | −3.15513 | + | 25.2503i | −0.185276 | + | 1.48275i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.21030 | − | 1.68090i | −0.0708275 | − | 0.0983670i | ||||
\(293\) | 9.55476 | + | 5.51644i | 0.558195 | + | 0.322274i | 0.752421 | − | 0.658683i | \(-0.228886\pi\) |
−0.194226 | + | 0.980957i | \(0.562219\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.0231 | + | 13.1368i | 0.641791 | + | 0.764857i | ||||
\(296\) | 5.08315 | − | 12.9925i | 0.295452 | − | 0.755173i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.77990 | + | 22.0078i | −0.392749 | + | 1.27488i | ||||
\(299\) | 2.83490 | − | 16.0775i | 0.163947 | − | 0.929788i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.5944 | + | 6.76780i | −1.07176 | + | 0.390089i | ||||
\(302\) | −0.191822 | + | 0.253428i | −0.0110381 | + | 0.0145831i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.0514 | − | 3.63986i | 0.977967 | − | 0.208760i | ||||
\(305\) | 20.6637i | 1.18320i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.92839 | − | 10.7932i | −0.224205 | − | 0.615999i | 0.775680 | − | 0.631126i | \(-0.217407\pi\) |
−0.999886 | + | 0.0151271i | \(0.995185\pi\) | |||||||
\(308\) | 22.4371 | − | 6.33009i | 1.27847 | − | 0.360690i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 28.4025 | + | 8.74993i | 1.61316 | + | 0.496963i | ||||
\(311\) | −3.18725 | − | 5.52048i | −0.180732 | − | 0.313038i | 0.761398 | − | 0.648285i | \(-0.224513\pi\) |
−0.942130 | + | 0.335247i | \(0.891180\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.60754 | + | 8.06168i | −0.543050 | + | 0.455673i | −0.872580 | − | 0.488472i | \(-0.837554\pi\) |
0.329529 | + | 0.944145i | \(0.393110\pi\) | |||||||
\(314\) | 12.4990 | − | 11.6057i | 0.705358 | − | 0.654945i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.64594 | + | 1.90517i | −0.148846 | + | 0.107174i | ||||
\(317\) | 1.37807 | − | 3.78621i | 0.0774000 | − | 0.212655i | −0.894958 | − | 0.446151i | \(-0.852794\pi\) |
0.972358 | + | 0.233496i | \(0.0750167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.5850 | + | 3.62969i | −1.15254 | + | 0.203224i | ||||
\(320\) | −20.5171 | − | 26.9663i | −1.14694 | − | 1.50746i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.650856 | − | 12.9484i | −0.0362708 | − | 0.721586i | ||||
\(323\) | −16.2451 | + | 9.58417i | −0.903904 | + | 0.533278i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −41.8187 | − | 35.0901i | −2.31968 | − | 1.94645i | ||||
\(326\) | 2.41754 | + | 5.72938i | 0.133895 | + | 0.317321i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.66470 | + | 0.111338i | 0.257565 | + | 0.00614759i | ||||
\(329\) | −7.01406 | + | 19.2710i | −0.386698 | + | 1.06244i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.202955 | − | 0.117176i | −0.0111554 | − | 0.00644059i | 0.494412 | − | 0.869228i | \(-0.335383\pi\) |
−0.505567 | + | 0.862787i | \(0.668717\pi\) | |||||||
\(332\) | 6.58310 | − | 6.75896i | 0.361295 | − | 0.370946i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.2196 | − | 25.8085i | 0.723345 | − | 1.41218i | ||||
\(335\) | 28.2390 | + | 48.9114i | 1.54286 | + | 2.67231i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.32528 | − | 7.51605i | 0.0721927 | − | 0.409425i | −0.927200 | − | 0.374568i | \(-0.877791\pi\) |
0.999392 | − | 0.0348576i | \(-0.0110978\pi\) | |||||||
\(338\) | −1.51256 | − | 6.61610i | −0.0822726 | − | 0.359868i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 30.3008 | + | 20.6271i | 1.64329 | + | 1.11866i | ||||
\(341\) | 24.4126i | 1.32202i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8706i | 1.07291i | ||||||||
\(344\) | −12.2971 | + | 20.1717i | −0.663013 | + | 1.08759i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.87397 | + | 1.34290i | −0.315786 | + | 0.0721947i | ||||
\(347\) | 3.09850 | − | 17.5725i | 0.166336 | − | 0.943339i | −0.781340 | − | 0.624106i | \(-0.785463\pi\) |
0.947676 | − | 0.319234i | \(-0.103425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.25938 | − | 5.64541i | −0.174471 | − | 0.302192i | 0.765507 | − | 0.643427i | \(-0.222488\pi\) |
−0.939978 | + | 0.341235i | \(0.889155\pi\) | |||||||
\(350\) | −38.5850 | − | 19.7640i | −2.06246 | − | 1.05643i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.2072 | − | 22.6278i | 0.863845 | − | 1.20607i | ||||
\(353\) | −4.43020 | − | 2.55777i | −0.235796 | − | 0.136137i | 0.377447 | − | 0.926031i | \(-0.376802\pi\) |
−0.613243 | + | 0.789894i | \(0.710135\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.2748 | − | 36.4721i | 0.704551 | − | 1.93574i | ||||
\(356\) | −0.389019 | − | 0.0288740i | −0.0206180 | − | 0.00153032i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.6908 | + | 4.51103i | −0.565025 | + | 0.238415i | ||||
\(359\) | 11.7130 | + | 9.82840i | 0.618190 | + | 0.518723i | 0.897234 | − | 0.441555i | \(-0.145573\pi\) |
−0.279044 | + | 0.960278i | \(0.590018\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.7822 | + | 11.9368i | 0.778011 | + | 0.628251i | ||||
\(362\) | 6.67392 | − | 0.335467i | 0.350773 | − | 0.0176318i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.68604 | − | 18.0039i | −0.455272 | − | 0.943661i | ||||
\(365\) | −4.31984 | + | 0.761705i | −0.226111 | + | 0.0398695i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.55658 | − | 12.5191i | 0.237851 | − | 0.653491i | −0.762130 | − | 0.647424i | \(-0.775846\pi\) |
0.999982 | − | 0.00606742i | \(-0.00193133\pi\) | |||||||
\(368\) | −10.2585 | − | 11.5909i | −0.534760 | − | 0.604218i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −20.1040 | − | 21.6514i | −1.04515 | − | 1.12560i | ||||
\(371\) | −4.50367 | + | 3.77903i | −0.233819 | + | 0.196197i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.1873 | + | 21.1090i | 0.631035 | + | 1.09298i | 0.987341 | + | 0.158615i | \(0.0507028\pi\) |
−0.356306 | + | 0.934369i | \(0.615964\pi\) | |||||||
\(374\) | −8.86472 | + | 28.7751i | −0.458384 | + | 1.48793i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.82269 | + | 23.2008i | 0.403424 | + | 1.19649i | ||||
\(377\) | 6.12999 | + | 16.8420i | 0.315711 | + | 0.867408i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 30.0944i | − | 1.54585i | −0.634499 | − | 0.772924i | \(-0.718794\pi\) | ||
0.634499 | − | 0.772924i | \(-0.281206\pi\) | |||||||
\(380\) | 8.74850 | − | 35.8730i | 0.448788 | − | 1.84024i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.5950 | − | 14.0747i | −0.951402 | − | 0.720125i | ||||
\(383\) | −3.41839 | + | 1.24419i | −0.174671 | + | 0.0635752i | −0.427875 | − | 0.903838i | \(-0.640738\pi\) |
0.253204 | + | 0.967413i | \(0.418516\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.57320 | − | 48.6211i | 0.436931 | − | 2.47796i | ||||
\(386\) | 19.9543 | + | 6.14730i | 1.01565 | + | 0.312889i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.7842 | + | 35.0481i | −0.801322 | + | 1.77930i | ||||
\(389\) | −4.00467 | − | 4.77258i | −0.203045 | − | 0.241980i | 0.654907 | − | 0.755709i | \(-0.272708\pi\) |
−0.857952 | + | 0.513730i | \(0.828263\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.5012 | + | 8.37226i | 0.733356 | + | 0.423403i | ||||
\(392\) | 2.45012 | + | 3.06562i | 0.123750 | + | 0.154837i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 32.7908 | + | 4.09735i | 1.65198 | + | 0.206421i | ||||
\(395\) | 1.19902 | + | 6.79998i | 0.0603292 | + | 0.342144i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.93552 | − | 8.33689i | −0.498649 | − | 0.418416i | 0.358465 | − | 0.933543i | \(-0.383300\pi\) |
−0.857114 | + | 0.515127i | \(0.827745\pi\) | |||||||
\(398\) | −0.868953 | − | 17.2873i | −0.0435567 | − | 0.866534i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −50.7172 | + | 10.3280i | −2.53586 | + | 0.516401i | ||||
\(401\) | 16.6333 | − | 19.8227i | 0.830625 | − | 0.989901i | −0.169365 | − | 0.985553i | \(-0.554172\pi\) |
0.999991 | − | 0.00434722i | \(-0.00138377\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.6146 | − | 3.63490i | 1.02688 | − | 0.181067i | ||||
\(404\) | −1.24481 | − | 0.0923932i | −0.0619318 | − | 0.00459673i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.72646 | + | 11.9535i | 0.383458 | + | 0.593244i | ||||
\(407\) | 12.1348 | − | 21.0181i | 0.601501 | − | 1.04183i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.8428 | − | 19.1674i | 1.12951 | − | 0.947768i | 0.130460 | − | 0.991454i | \(-0.458355\pi\) |
0.999045 | + | 0.0436860i | \(0.0139101\pi\) | |||||||
\(410\) | 4.50491 | − | 8.79488i | 0.222482 | − | 0.434348i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.493033 | + | 1.94205i | −0.0242900 | + | 0.0956780i | ||||
\(413\) | 9.44629 | + | 1.66564i | 0.464822 | + | 0.0819606i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.83397 | − | 18.7762i | −0.335466 | − | 0.921686i | ||||
\(416\) | −21.5206 | − | 10.3166i | −1.05513 | − | 0.505811i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 30.2767 | − | 1.80777i | 1.48088 | − | 0.0884209i | ||||
\(419\) | 6.12219 | 0.299089 | 0.149544 | − | 0.988755i | \(-0.452219\pi\) | ||||
0.149544 | + | 0.988755i | \(0.452219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.83129 | + | 2.48639i | −0.332937 | + | 0.121179i | −0.503079 | − | 0.864240i | \(-0.667800\pi\) |
0.170142 | + | 0.985420i | \(0.445577\pi\) | |||||||
\(422\) | −23.9606 | + | 5.47785i | −1.16639 | + | 0.266658i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.38344 | + | 6.88138i | −0.0671858 | + | 0.334189i | ||||
\(425\) | 48.4900 | − | 27.9957i | 2.35211 | − | 1.35799i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.42932 | + | 8.85392i | 0.359530 | + | 0.428471i | ||||
\(428\) | −24.4783 | + | 25.1322i | −1.18320 | + | 1.21481i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 27.1590 | + | 42.0175i | 1.30973 | + | 2.02627i | ||||
\(431\) | 13.8715 | + | 5.04883i | 0.668168 | + | 0.243193i | 0.653759 | − | 0.756703i | \(-0.273191\pi\) |
0.0144094 | + | 0.999896i | \(0.495413\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.63194 | + | 26.2691i | 0.222597 | + | 1.26241i | 0.867226 | + | 0.497915i | \(0.165901\pi\) |
−0.644629 | + | 0.764495i | \(0.722988\pi\) | |||||||
\(434\) | 15.3157 | − | 6.46255i | 0.735178 | − | 0.310212i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.27350 | − | 0.632277i | 0.300446 | − | 0.0302806i | ||||
\(437\) | 2.77247 | − | 16.6379i | 0.132625 | − | 0.795901i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.2411 | + | 13.3966i | −0.536508 | + | 0.639385i | −0.964401 | − | 0.264444i | \(-0.914811\pi\) |
0.427893 | + | 0.903829i | \(0.359256\pi\) | |||||||
\(440\) | −28.2456 | − | 51.7357i | −1.34655 | − | 2.46640i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 25.6183 | + | 3.20111i | 1.21854 | + | 0.152262i | ||||
\(443\) | −31.0821 | − | 11.3129i | −1.47675 | − | 0.537494i | −0.526828 | − | 0.849972i | \(-0.676619\pi\) |
−0.949925 | + | 0.312477i | \(0.898841\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.413057 | + | 0.715436i | −0.0195808 | + | 0.0339149i | ||||
\(446\) | 16.8561 | + | 18.1535i | 0.798159 | + | 0.859595i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −18.4864 | − | 4.17781i | −0.873399 | − | 0.197383i | ||||
\(449\) | 25.3686 | − | 14.6466i | 1.19722 | − | 0.691215i | 0.237286 | − | 0.971440i | \(-0.423742\pi\) |
0.959934 | + | 0.280225i | \(0.0904090\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.99361 | + | 1.40949i | 0.376404 | + | 0.0663702i | ||||
\(452\) | 5.65034 | − | 1.59411i | 0.265769 | − | 0.0749805i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16.0042 | − | 12.1138i | −0.751116 | − | 0.568527i | ||||
\(455\) | −42.3333 | −1.98461 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.9763 | −1.12157 | −0.560783 | − | 0.827963i | \(-0.689500\pi\) | ||||
−0.560783 | + | 0.827963i | \(0.689500\pi\) | |||||||
\(458\) | −0.164985 | − | 0.124879i | −0.00770926 | − | 0.00583522i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −31.5483 | + | 8.90059i | −1.47095 | + | 0.414992i | ||||
\(461\) | −19.2838 | − | 3.40025i | −0.898134 | − | 0.158365i | −0.294523 | − | 0.955644i | \(-0.595161\pi\) |
−0.603611 | + | 0.797279i | \(0.706272\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.803683 | + | 0.464006i | −0.0373503 | + | 0.0215642i | −0.518559 | − | 0.855042i | \(-0.673531\pi\) |
0.481209 | + | 0.876606i | \(0.340198\pi\) | |||||||
\(464\) | 16.1159 | + | 5.38907i | 0.748160 | + | 0.250181i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.42800 | − | 6.92278i | −0.297771 | − | 0.320692i | ||||
\(467\) | 15.9239 | − | 27.5810i | 0.736869 | − | 1.27630i | −0.217029 | − | 0.976165i | \(-0.569637\pi\) |
0.953898 | − | 0.300130i | \(-0.0970301\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.6850 | + | 10.8045i | 1.37073 | + | 0.498904i | ||||
\(470\) | 51.4513 | + | 6.42905i | 2.37327 | + | 0.296550i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.0514 | − | 5.48766i | 0.462654 | − | 0.252590i | ||||
\(473\) | −26.4164 | + | 31.4818i | −1.21463 | + | 1.44754i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −43.5460 | − | 35.8462i | −1.99803 | − | 1.64474i | ||||
\(476\) | 20.3993 | − | 2.05596i | 0.935002 | − | 0.0942346i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 23.5045 | − | 9.91783i | 1.07507 | − | 0.453631i | ||||
\(479\) | −0.747358 | − | 4.23848i | −0.0341476 | − | 0.193661i | 0.962962 | − | 0.269637i | \(-0.0869038\pi\) |
−0.997110 | + | 0.0759763i | \(0.975793\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.5550 | − | 7.11745i | −0.891632 | − | 0.324528i | ||||
\(482\) | 19.7898 | + | 30.6166i | 0.901399 | + | 1.39455i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.4326 | − | 18.9250i | 0.837845 | − | 0.860226i | ||||
\(485\) | 52.3248 | + | 62.3583i | 2.37595 | + | 2.83155i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.4925 | + | 18.1822i | −1.42706 | + | 0.823915i | −0.996888 | − | 0.0788302i | \(-0.974882\pi\) |
−0.430175 | + | 0.902745i | \(0.641548\pi\) | |||||||
\(488\) | 13.5283 | + | 2.71975i | 0.612399 | + | 0.123117i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.10194 | − | 1.85225i | 0.366008 | − | 0.0836763i | ||||
\(491\) | 12.1750 | − | 4.43132i | 0.549448 | − | 0.199983i | −0.0523531 | − | 0.998629i | \(-0.516672\pi\) |
0.601801 | + | 0.798646i | \(0.294450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.3829 | −0.827922 | ||||||||
\(494\) | −6.03455 | − | 25.2972i | −0.271507 | − | 1.13817i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.46682 | − | 17.4432i | 0.425073 | − | 0.783222i | ||||
\(497\) | −7.42505 | − | 20.4002i | −0.333059 | − | 0.915072i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.5963 | − | 5.92393i | −1.50398 | − | 0.265192i | −0.639863 | − | 0.768489i | \(-0.721009\pi\) |
−0.864113 | + | 0.503297i | \(0.832120\pi\) | |||||||
\(500\) | −16.5494 | + | 65.1881i | −0.740113 | + | 2.91530i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.78630 | + | 17.1534i | −0.392152 | + | 0.765592i | ||||
\(503\) | −1.18149 | + | 0.991387i | −0.0526800 | + | 0.0442037i | −0.668748 | − | 0.743490i | \(-0.733169\pi\) |
0.616068 | + | 0.787693i | \(0.288725\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.32173 | + | 2.28930i | −0.0588162 | + | 0.101873i | ||||
\(506\) | −14.6167 | − | 22.6134i | −0.649793 | − | 1.00529i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.91588 | − | 0.735982i | −0.439946 | − | 0.0326539i | ||||
\(509\) | −31.1834 | + | 5.49847i | −1.38218 | + | 0.243716i | −0.814801 | − | 0.579741i | \(-0.803154\pi\) |
−0.567379 | + | 0.823457i | \(0.692042\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.57709 | + | 1.87950i | −0.0697664 | + | 0.0831444i | ||||
\(512\) | −20.3550 | + | 9.88304i | −0.899572 | + | 0.436773i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.774651 | + | 15.4112i | 0.0341684 | + | 0.679760i | ||||
\(515\) | 3.25052 | + | 2.72751i | 0.143235 | + | 0.120189i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.39603 | + | 41.9450i | 0.325277 | + | 1.84474i | ||||
\(518\) | −16.3985 | − | 2.04906i | −0.720508 | − | 0.0900305i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −39.4812 | + | 31.5544i | −1.73137 | + | 1.38375i | ||||
\(521\) | −6.05147 | − | 3.49382i | −0.265120 | − | 0.153067i | 0.361548 | − | 0.932353i | \(-0.382248\pi\) |
−0.626668 | + | 0.779287i | \(0.715582\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.2320 | + | 22.9198i | 0.840957 | + | 1.00221i | 0.999889 | + | 0.0149239i | \(0.00475060\pi\) |
−0.158932 | + | 0.987290i | \(0.550805\pi\) | |||||||
\(524\) | −8.17598 | + | 18.1544i | −0.357169 | + | 0.793077i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.936405 | − | 0.288477i | −0.0408292 | − | 0.0125782i | ||||
\(527\) | −3.72819 | + | 21.1436i | −0.162402 | + | 0.921029i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.54188 | − | 2.74502i | 0.327908 | − | 0.119349i | ||||
\(530\) | 11.8523 | + | 8.97112i | 0.514831 | + | 0.389681i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.14903 | − | 18.5161i | −0.396661 | − | 0.802774i | ||||
\(533\) | − | 6.95986i | − | 0.301465i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.4111 | + | 69.8163i | 1.09862 | + | 3.01842i | ||||
\(536\) | 35.7386 | − | 12.0501i | 1.54367 | − | 0.520484i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.85015 | + | 28.7279i | −0.381557 | + | 1.23855i | ||||
\(539\) | 3.41342 | + | 5.91222i | 0.147026 | + | 0.254657i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0748 | + | 14.3275i | −0.734103 | + | 0.615985i | −0.931247 | − | 0.364389i | \(-0.881278\pi\) |
0.197144 | + | 0.980375i | \(0.436833\pi\) | |||||||
\(542\) | 19.1163 | + | 20.5878i | 0.821117 | + | 0.884322i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 17.4925 | − | 17.1227i | 0.749987 | − | 0.734130i | ||||
\(545\) | 4.56701 | − | 12.5477i | 0.195629 | − | 0.537487i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.39427 | + | 0.951155i | −0.230642 | + | 0.0406684i | −0.287775 | − | 0.957698i | \(-0.592915\pi\) |
0.0571324 | + | 0.998367i | \(0.481804\pi\) | |||||||
\(548\) | 6.01940 | + | 12.4767i | 0.257136 | + | 0.532976i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −89.9238 | + | 4.52005i | −3.83436 | + | 0.192736i | ||||
\(551\) | 6.49697 | + | 17.3406i | 0.276780 | + | 0.738733i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.95858 | + | 2.48254i | 0.125811 | + | 0.105568i | ||||
\(554\) | −21.1410 | + | 8.92054i | −0.898193 | + | 0.378998i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.8133 | − | 0.802591i | −0.458586 | − | 0.0340374i | ||||
\(557\) | −10.2490 | + | 28.1589i | −0.434263 | + | 1.19313i | 0.508908 | + | 0.860821i | \(0.330049\pi\) |
−0.943171 | + | 0.332308i | \(0.892173\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.5173 | + | 17.6192i | 1.29074 | + | 0.745211i | ||||
\(560\) | −24.9802 | + | 31.4160i | −1.05561 | + | 1.32757i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.0576 | + | 13.8595i | 1.14136 | + | 0.584626i | ||||
\(563\) | −8.98365 | − | 15.5601i | −0.378616 | − | 0.655782i | 0.612245 | − | 0.790668i | \(-0.290267\pi\) |
−0.990861 | + | 0.134886i | \(0.956933\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.15899 | − | 12.2442i | 0.0908294 | − | 0.515119i | ||||
\(566\) | −4.06211 | + | 0.928674i | −0.170743 | + | 0.0390351i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.1307 | − | 13.4913i | −0.928583 | − | 0.566082i | ||||
\(569\) | − | 41.6349i | − | 1.74543i | −0.488233 | − | 0.872713i | \(-0.662358\pi\) | ||
0.488233 | − | 0.872713i | \(-0.337642\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.68623i | 0.0705664i | 0.999377 | + | 0.0352832i | \(0.0112333\pi\) | ||||
−0.999377 | + | 0.0352832i | \(0.988767\pi\) | |||||||
\(572\) | −34.3189 | − | 23.3624i | −1.43494 | − | 0.976830i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.23181 | − | 5.38807i | −0.0514149 | − | 0.224894i | ||||
\(575\) | −8.69480 | + | 49.3106i | −0.362598 | + | 2.05640i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.96096 | + | 10.3247i | 0.248158 | + | 0.429822i | 0.963015 | − | 0.269449i | \(-0.0868414\pi\) |
−0.714857 | + | 0.699271i | \(0.753508\pi\) | |||||||
\(578\) | −1.11168 | + | 2.17032i | −0.0462398 | + | 0.0902733i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 25.1091 | − | 25.7799i | 1.04260 | − | 1.07045i | ||||
\(581\) | −9.67887 | − | 5.58810i | −0.401547 | − | 0.231833i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.17614 | + | 11.4738i | −0.172958 | + | 0.475198i | ||||
\(584\) | −0.0698957 | + | 2.92841i | −0.00289230 | + | 0.121179i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.06582 | − | 14.3755i | −0.250577 | − | 0.593846i | ||||
\(587\) | −26.5994 | − | 22.3195i | −1.09787 | − | 0.921226i | −0.100594 | − | 0.994928i | \(-0.532074\pi\) |
−0.997280 | + | 0.0737013i | \(0.976519\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.2624 | − | 3.95588i | 0.876102 | − | 0.162999i | ||||
\(590\) | −1.21751 | − | 24.2217i | −0.0501242 | − | 0.997191i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.8210 | + | 10.3121i | −0.691340 | + | 0.423825i | ||||
\(593\) | −37.9041 | + | 6.68351i | −1.55653 | + | 0.274459i | −0.884671 | − | 0.466217i | \(-0.845617\pi\) |
−0.671863 | + | 0.740676i | \(0.734506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.8504 | − | 40.8011i | 0.608807 | − | 1.67268i | ||||
\(596\) | 26.4289 | − | 19.0297i | 1.08257 | − | 0.779487i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.9190 | + | 15.7097i | −0.691868 | + | 0.642419i | ||||
\(599\) | −2.51107 | + | 2.10703i | −0.102599 | + | 0.0860911i | −0.692644 | − | 0.721279i | \(-0.743554\pi\) |
0.590045 | + | 0.807370i | \(0.299110\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.2155 | + | 26.3540i | 0.620652 | + | 1.07500i | 0.989365 | + | 0.145457i | \(0.0464653\pi\) |
−0.368713 | + | 0.929543i | \(0.620201\pi\) | |||||||
\(602\) | 26.7437 | + | 8.23891i | 1.08999 | + | 0.335793i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.432605 | − | 0.122049i | 0.0176024 | − | 0.00496611i | ||||
\(605\) | −19.1350 | − | 52.5730i | −0.777949 | − | 2.13740i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 22.1799i | − | 0.900254i | −0.892965 | − | 0.450127i | \(-0.851379\pi\) | ||
0.892965 | − | 0.450127i | \(-0.148621\pi\) | |||||||
\(608\) | −22.3342 | − | 10.4491i | −0.905771 | − | 0.423768i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17.6366 | − | 23.3008i | 0.714086 | − | 0.943423i | ||||
\(611\) | 34.3181 | − | 12.4908i | 1.38836 | − | 0.505322i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.903611 | + | 5.12463i | −0.0364965 | + | 0.206982i | −0.997603 | − | 0.0691957i | \(-0.977957\pi\) |
0.961107 | + | 0.276178i | \(0.0890678\pi\) | |||||||
\(614\) | −4.78231 | + | 15.5235i | −0.192998 | + | 0.626478i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30.7033 | − | 12.0123i | −1.23707 | − | 0.483988i | ||||
\(617\) | −5.84795 | − | 6.96932i | −0.235430 | − | 0.280574i | 0.635375 | − | 0.772204i | \(-0.280846\pi\) |
−0.870804 | + | 0.491630i | \(0.836401\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.0116 | − | 11.5537i | −0.804335 | − | 0.464383i | 0.0406494 | − | 0.999173i | \(-0.487057\pi\) |
−0.844985 | + | 0.534790i | \(0.820391\pi\) | |||||||
\(620\) | −24.5591 | − | 34.1083i | −0.986319 | − | 1.36982i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.11776 | + | 8.94534i | −0.0448180 | + | 0.358675i | ||||
\(623\) | 0.0802385 | + | 0.455055i | 0.00321469 | + | 0.0182314i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 59.5477 | + | 49.9665i | 2.38191 | + | 1.99866i | ||||
\(626\) | 17.7144 | − | 0.890419i | 0.708008 | − | 0.0355883i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −23.9996 | + | 2.41881i | −0.957688 | + | 0.0965210i | ||||
\(629\) | 13.7197 | − | 16.3505i | 0.547040 | − | 0.651937i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.1908 | − | 3.38385i | 0.763972 | − | 0.134709i | 0.221933 | − | 0.975062i | \(-0.428763\pi\) |
0.542039 | + | 0.840353i | \(0.317652\pi\) | |||||||
\(632\) | 4.60969 | + | 0.110025i | 0.183364 | + | 0.00437654i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.78549 | + | 3.09322i | −0.190056 | + | 0.122847i | ||||
\(635\) | −10.5286 | + | 18.2360i | −0.417814 | + | 0.723675i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.48418 | − | 3.76267i | 0.177670 | − | 0.149082i | ||||
\(638\) | 26.3100 | + | 13.4765i | 1.04162 | + | 0.533541i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.119604 | + | 47.9192i | 0.00472776 | + | 1.89417i | ||||
\(641\) | 21.0061 | + | 3.70394i | 0.829691 | + | 0.146297i | 0.572335 | − | 0.820020i | \(-0.306038\pi\) |
0.257356 | + | 0.966317i | \(0.417149\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.01221 | + | 24.7608i | 0.355407 | + | 0.976472i | 0.980603 | + | 0.196005i | \(0.0627968\pi\) |
−0.625196 | + | 0.780468i | \(0.714981\pi\) | |||||||
\(644\) | −10.3176 | + | 15.1564i | −0.406571 | + | 0.597245i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.4985 | + | 3.05802i | 1.04257 | + | 0.120316i | ||||
\(647\) | −24.9968 | −0.982727 | −0.491363 | − | 0.870955i | \(-0.663501\pi\) | ||||
−0.491363 | + | 0.870955i | \(0.663501\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.7200 | − | 6.81353i | 0.734825 | − | 0.267454i | ||||
\(650\) | 17.2060 | + | 75.2608i | 0.674875 | + | 2.95197i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.16399 | − | 8.52395i | 0.0847485 | − | 0.333824i | ||||
\(653\) | 21.3431 | − | 12.3224i | 0.835220 | − | 0.482214i | −0.0204168 | − | 0.999792i | \(-0.506499\pi\) |
0.855636 | + | 0.517577i | \(0.173166\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.1035 | + | 32.3007i | 1.05902 | + | 1.26209i | ||||
\(656\) | −5.16498 | − | 4.10690i | −0.201659 | − | 0.160347i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.3571 | − | 15.7438i | 0.949539 | − | 0.613757i | ||||
\(659\) | −32.4811 | − | 11.8221i | −1.26528 | − | 0.460525i | −0.379744 | − | 0.925092i | \(-0.623988\pi\) |
−0.885538 | + | 0.464566i | \(0.846210\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.61468 | − | 26.1712i | −0.179490 | − | 1.01794i | −0.932832 | − | 0.360311i | \(-0.882670\pi\) |
0.753342 | − | 0.657629i | \(-0.228441\pi\) | |||||||
\(662\) | 0.128846 | + | 0.305354i | 0.00500773 | + | 0.0118679i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.1920 | + | 2.00282i | −0.511951 | + | 0.0777243i | ||||
\(665\) | −43.7363 | + | 0.411765i | −1.69602 | + | 0.0159676i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.5669 | − | 12.5932i | 0.409153 | − | 0.487609i | ||||
\(668\) | −36.9344 | + | 17.8191i | −1.42904 | + | 0.689443i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.90331 | − | 79.2556i | 0.382598 | − | 3.06191i | ||||
\(671\) | 22.5568 | + | 8.21001i | 0.870796 | + | 0.316944i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0909 | + | 17.4780i | −0.388977 | + | 0.673727i | −0.992312 | − | 0.123760i | \(-0.960505\pi\) |
0.603336 | + | 0.797487i | \(0.293838\pi\) | |||||||
\(674\) | −7.90941 | + | 7.34411i | −0.304659 | + | 0.282885i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.94129 | + | 8.75143i | −0.151588 | + | 0.336593i | ||||
\(677\) | −7.97495 | + | 4.60434i | −0.306502 | + | 0.176959i | −0.645360 | − | 0.763878i | \(-0.723293\pi\) |
0.338858 | + | 0.940838i | \(0.389959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 44.8399 | + | 7.90648i | 1.72080 | + | 0.303423i | ||||
\(680\) | −16.5624 | − | 49.1215i | −0.635141 | − | 1.88372i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 20.8363 | − | 27.5281i | 0.797863 | − | 1.05411i | ||||
\(683\) | 26.2485 | 1.00437 | 0.502186 | − | 0.864760i | \(-0.332529\pi\) | ||||
0.502186 | + | 0.864760i | \(0.332529\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.3368 | 1.12090 | ||||||||
\(686\) | 16.9597 | − | 22.4065i | 0.647523 | − | 0.855483i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 31.0831 | − | 12.2504i | 1.18503 | − | 0.467043i | ||||
\(689\) | 10.3106 | + | 1.81804i | 0.392802 | + | 0.0692616i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.4628 | − | 25.0933i | 1.65340 | − | 0.954593i | 0.677745 | − | 0.735297i | \(-0.262957\pi\) |
0.975658 | − | 0.219296i | \(-0.0703760\pi\) | |||||||
\(692\) | 7.76978 | + | 3.49919i | 0.295363 | + | 0.133019i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.4921 | + | 17.1705i | −0.701952 | + | 0.651782i | ||||
\(695\) | −11.4815 | + | 19.8865i | −0.435516 | + | 0.754336i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.70796 | + | 2.44150i | 0.254082 | + | 0.0924784i | ||||
\(698\) | −1.14305 | + | 9.14778i | −0.0432652 | + | 0.346249i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 26.6405 | + | 55.2189i | 1.00692 | + | 2.08708i | ||||
\(701\) | −20.3775 | + | 24.2850i | −0.769649 | + | 0.917231i | −0.998417 | − | 0.0562494i | \(-0.982086\pi\) |
0.228768 | + | 0.973481i | \(0.426530\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.2723 | − | 7.16312i | −0.764586 | − | 0.270162i | ||||
\(704\) | −37.5885 | + | 11.6826i | −1.41667 | + | 0.440306i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.81250 | + | 6.66540i | 0.105850 | + | 0.250856i | ||||
\(707\) | 0.256753 | + | 1.45612i | 0.00965620 | + | 0.0547630i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.480967 | − | 0.175058i | −0.0180631 | − | 0.00657443i | 0.332973 | − | 0.942936i | \(-0.391948\pi\) |
−0.351036 | + | 0.936362i | \(0.614170\pi\) | |||||||
\(710\) | −46.0981 | + | 29.7966i | −1.73003 | + | 1.11825i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.414022 | + | 0.364590i | 0.0155161 | + | 0.0136636i | ||||
\(713\) | −12.3414 | − | 14.7079i | −0.462187 | − | 0.550813i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −76.1417 | + | 43.9605i | −2.84754 | + | 1.64403i | ||||
\(716\) | 15.9053 | + | 4.03792i | 0.594410 | + | 0.150904i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.81924 | − | 21.0798i | −0.179853 | − | 0.786693i | ||||
\(719\) | −17.6720 | + | 6.43209i | −0.659055 | + | 0.239876i | −0.649828 | − | 0.760081i | \(-0.725159\pi\) |
−0.00922653 | + | 0.999957i | \(0.502937\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.37341 | 0.0883902 | ||||||||
\(722\) | −6.48061 | − | 26.0768i | −0.241183 | − | 0.970480i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.81197 | − | 5.31795i | −0.290330 | − | 0.197640i | ||||
\(725\) | −18.8010 | − | 51.6554i | −0.698252 | − | 1.91843i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.2376 | + | 6.74232i | 1.41815 | + | 0.250059i | 0.829582 | − | 0.558385i | \(-0.188579\pi\) |
0.588573 | + | 0.808444i | \(0.299690\pi\) | |||||||
\(728\) | −5.57189 | + | 27.7152i | −0.206508 | + | 1.02719i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.52126 | + | 2.82810i | 0.204351 | + | 0.104673i | ||||
\(731\) | −27.6868 | + | 23.2320i | −1.02404 | + | 0.859268i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.0421 | − | 41.6422i | 0.888017 | − | 1.53809i | 0.0458003 | − | 0.998951i | \(-0.485416\pi\) |
0.842216 | − | 0.539140i | \(-0.181250\pi\) | |||||||
\(734\) | −15.8232 | + | 10.2277i | −0.584045 | + | 0.377512i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.67475 | + | 21.8258i | 0.0617323 | + | 0.804510i | ||||
\(737\) | 64.6121 | − | 11.3929i | 2.38002 | − | 0.419661i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.1794 | − | 19.2819i | 0.595170 | − | 0.709297i | −0.381420 | − | 0.924402i | \(-0.624565\pi\) |
0.976591 | + | 0.215105i | \(0.0690094\pi\) | |||||||
\(740\) | 4.18999 | + | 41.5734i | 0.154027 | + | 1.52827i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.30386 | − | 0.417397i | 0.304844 | − | 0.0153231i | ||||
\(743\) | −20.5179 | − | 17.2165i | −0.752727 | − | 0.631613i | 0.183496 | − | 0.983021i | \(-0.441259\pi\) |
−0.936223 | + | 0.351408i | \(0.885703\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.9764 | − | 67.9214i | −0.438780 | − | 2.48845i | ||||
\(746\) | 4.27404 | − | 34.2049i | 0.156484 | − | 1.25233i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 34.5558 | − | 24.8813i | 1.26349 | − | 0.909752i | ||||
\(749\) | 35.9894 | + | 20.7785i | 1.31502 | + | 0.759229i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.5600 | − | 32.8447i | −1.00568 | − | 1.19852i | −0.980030 | − | 0.198849i | \(-0.936280\pi\) |
−0.0256472 | − | 0.999671i | \(-0.508165\pi\) | |||||||
\(752\) | 10.9810 | − | 32.8384i | 0.400437 | − | 1.19749i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.46247 | − | 24.2234i | 0.271767 | − | 0.882164i | ||||
\(755\) | 0.165298 | − | 0.937452i | 0.00601581 | − | 0.0341174i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6260 | − | 10.0550i | 1.00408 | − | 0.365456i | 0.212925 | − | 0.977068i | \(-0.431701\pi\) |
0.791158 | + | 0.611612i | \(0.209479\pi\) | |||||||
\(758\) | −25.6858 | + | 33.9351i | −0.932950 | + | 1.23258i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −40.4828 | + | 32.9842i | −1.46846 | + | 1.19646i | ||||
\(761\) | 12.6138i | 0.457251i | 0.973514 | + | 0.228625i | \(0.0734231\pi\) | ||||
−0.973514 | + | 0.228625i | \(0.926577\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.55449 | − | 7.01841i | −0.0924788 | − | 0.254083i | ||||
\(764\) | 8.95521 | + | 31.7419i | 0.323988 | + | 1.14838i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.91656 | + | 1.51464i | 0.177643 | + | 0.0547262i | ||||
\(767\) | −8.54081 | − | 14.7931i | −0.308391 | − | 0.534149i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4964 | + | 11.3248i | −0.486693 | + | 0.408384i | −0.852839 | − | 0.522173i | \(-0.825121\pi\) |
0.366147 | + | 0.930557i | \(0.380677\pi\) | |||||||
\(770\) | −51.1657 | + | 47.5088i | −1.84388 | + | 1.71210i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.2541 | − | 23.9630i | −0.620990 | − | 0.862446i | ||||
\(773\) | 15.9489 | − | 43.8192i | 0.573642 | − | 1.57607i | −0.225063 | − | 0.974344i | \(-0.572259\pi\) |
0.798704 | − | 0.601723i | \(-0.205519\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −63.2259 | + | 11.1484i | −2.27114 | + | 0.400464i | ||||
\(776\) | 47.7123 | − | 26.0490i | 1.71277 | − | 0.935103i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.442319 | + | 8.79967i | 0.0158579 | + | 0.315484i | ||||
\(779\) | −0.0676968 | − | 7.19052i | −0.00242549 | − | 0.257627i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.5392 | − | 28.9818i | −1.23591 | − | 1.03705i | ||||
\(782\) | −9.20604 | − | 21.8176i | −0.329207 | − | 0.780195i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.146278 | − | 5.54805i | −0.00522421 | − | 0.198145i | ||||
\(785\) | −17.4713 | + | 48.0021i | −0.623578 | + | 1.71327i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.8761 | − | 14.9395i | −0.922382 | − | 0.532537i | −0.0379877 | − | 0.999278i | \(-0.512095\pi\) |
−0.884394 | + | 0.466741i | \(0.845428\pi\) | |||||||
\(788\) | −33.4785 | − | 32.6074i | −1.19262 | − | 1.16159i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.45179 | − | 8.69116i | 0.158387 | − | 0.309218i | ||||
\(791\) | −3.47715 | − | 6.02260i | −0.123633 | − | 0.214139i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.57414 | − | 20.2699i | 0.126921 | − | 0.719806i | ||||
\(794\) | 4.08790 | + | 17.8809i | 0.145074 | + | 0.634568i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.7750 | + | 20.2352i | −0.488241 | + | 0.717216i | ||||
\(797\) | − | 20.4097i | − | 0.722950i | −0.932382 | − | 0.361475i | \(-0.882273\pi\) | ||
0.932382 | − | 0.361475i | \(-0.117727\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.4578i | 1.32516i | ||||||||
\(800\) | 66.0048 | + | 31.6414i | 2.33362 | + | 1.11869i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −35.6748 | + | 8.15593i | −1.25972 | + | 0.287996i | ||||
\(803\) | −0.884851 | + | 5.01824i | −0.0312257 | + | 0.177090i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.4144 | + | 33.6268i | 0.684268 | + | 1.18519i | ||||
\(806\) | −26.3478 | − | 13.4959i | −0.928062 | − | 0.475372i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.32482 | + | 1.16664i | 0.0466069 | + | 0.0410423i | ||||
\(809\) | −18.5251 | − | 10.6955i | −0.651309 | − | 0.376033i | 0.137649 | − | 0.990481i | \(-0.456046\pi\) |
−0.788957 | + | 0.614448i | \(0.789379\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.15199 | − | 5.91254i | 0.0755665 | − | 0.207617i | −0.896158 | − | 0.443735i | \(-0.853653\pi\) |
0.971724 | + | 0.236118i | \(0.0758752\pi\) | |||||||
\(812\) | 1.48992 | − | 20.0736i | 0.0522858 | − | 0.704447i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −31.6226 | + | 13.3433i | −1.10837 | + | 0.467683i | ||||
\(815\) | −14.2670 | − | 11.9715i | −0.499752 | − | 0.419342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.7000 | + | 17.9062i | 1.10904 | + | 0.626460i | ||||
\(818\) | −42.1175 | + | 2.11705i | −1.47261 | + | 0.0740211i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.5863 | + | 6.07231i | −0.439533 | + | 0.212054i | ||||
\(821\) | 42.5399 | − | 7.50093i | 1.48465 | − | 0.261784i | 0.628216 | − | 0.778039i | \(-0.283785\pi\) |
0.856435 | + | 0.516255i | \(0.172674\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.72283 | − | 18.4708i | 0.234343 | − | 0.643852i | −0.765657 | − | 0.643249i | \(-0.777586\pi\) |
1.00000 | 0.000602960i | \(-0.000191928\pi\) | ||||||||
\(824\) | 2.21351 | − | 1.76909i | 0.0771112 | − | 0.0616292i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.23020 | − | 9.94068i | −0.321160 | − | 0.345880i | ||||
\(827\) | 34.7622 | − | 29.1689i | 1.20880 | − | 1.01430i | 0.209466 | − | 0.977816i | \(-0.432828\pi\) |
0.999334 | − | 0.0364873i | \(-0.0116168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.49047 | − | 14.7059i | −0.294886 | − | 0.510758i | 0.680072 | − | 0.733145i | \(-0.261948\pi\) |
−0.974958 | + | 0.222387i | \(0.928615\pi\) | |||||||
\(830\) | −8.31946 | + | 27.0052i | −0.288773 | + | 0.937365i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15.4618 | + | 30.0011i | 0.536042 | + | 1.04010i | ||||
\(833\) | 2.05345 | + | 5.64182i | 0.0711480 | + | 0.195477i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 86.8453i | 3.00541i | ||||||||
\(836\) | −35.6835 | − | 23.8028i | −1.23414 | − | 0.823238i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.90351 | − | 5.22533i | −0.238478 | − | 0.180506i | ||||
\(839\) | 31.7940 | − | 11.5721i | 1.09765 | − | 0.399512i | 0.271201 | − | 0.962523i | \(-0.412579\pi\) |
0.826450 | + | 0.563010i | \(0.190357\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.90185 | − | 10.7859i | 0.0655811 | − | 0.371929i | ||||
\(842\) | 9.82525 | + | 3.02685i | 0.338600 | + | 0.104312i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 31.6939 | + | 14.2736i | 1.09095 | + | 0.491319i | ||||
\(845\) | 13.0654 | + | 15.5708i | 0.449464 | + | 0.535650i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.1007 | − | 15.6466i | −0.931191 | − | 0.537623i | ||||
\(848\) | 7.43330 | − | 6.57881i | 0.255260 | − | 0.225917i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −78.5727 | − | 9.81799i | −2.69502 | − | 0.336754i | ||||
\(851\) | 3.31448 | + | 18.7973i | 0.113619 | + | 0.644365i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.214013 | + | 0.179578i | 0.00732767 | + | 0.00614864i | 0.646444 | − | 0.762961i | \(-0.276255\pi\) |
−0.639116 | + | 0.769110i | \(0.720700\pi\) | |||||||
\(854\) | −0.820574 | − | 16.3248i | −0.0280795 | − | 0.558624i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 49.0526 | − | 7.44717i | 1.67658 | − | 0.254539i | ||||
\(857\) | 25.5799 | − | 30.4849i | 0.873792 | − | 1.04135i | −0.124997 | − | 0.992157i | \(-0.539892\pi\) |
0.998790 | − | 0.0491882i | \(-0.0156634\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.77072 | + | 0.841208i | −0.162775 | + | 0.0287016i | −0.254442 | − | 0.967088i | \(-0.581892\pi\) |
0.0916666 | + | 0.995790i | \(0.470781\pi\) | |||||||
\(860\) | 5.23716 | − | 70.5602i | 0.178586 | − | 2.40608i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.3326 | − | 17.5326i | −0.385990 | − | 0.597163i | ||||
\(863\) | −17.4697 | + | 30.2584i | −0.594675 | + | 1.03001i | 0.398918 | + | 0.916987i | \(0.369386\pi\) |
−0.993593 | + | 0.113020i | \(0.963947\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.8242 | − | 11.5999i | 0.470036 | − | 0.394407i | ||||
\(866\) | 17.1977 | − | 33.5749i | 0.584403 | − | 1.14092i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −22.7861 | − | 5.78476i | −0.773412 | − | 0.196348i | ||||
\(869\) | 7.89934 | + | 1.39287i | 0.267967 | + | 0.0472498i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.2408 | − | 52.8636i | −0.651949 | − | 1.79122i | ||||
\(872\) | −7.61377 | − | 4.64150i | −0.257835 | − | 0.157181i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.3269 | + | 16.3950i | −0.586091 | + | 0.554568i | ||||
\(875\) | 79.6672 | 2.69324 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.6231 | + | 6.05032i | −0.561322 | + | 0.204305i | −0.607070 | − | 0.794648i | \(-0.707655\pi\) |
0.0457475 | + | 0.998953i | \(0.485433\pi\) | |||||||
\(878\) | 24.1098 | − | 5.51194i | 0.813665 | − | 0.186019i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.3065 | + | 82.4460i | −0.414852 | + | 2.77925i | ||||
\(881\) | −32.5283 | + | 18.7802i | −1.09591 | + | 0.632721i | −0.935143 | − | 0.354272i | \(-0.884729\pi\) |
−0.160763 | + | 0.986993i | \(0.551396\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.4909 | + | 32.7623i | 0.925141 | + | 1.10254i | 0.994478 | + | 0.104947i | \(0.0334672\pi\) |
−0.0693368 | + | 0.997593i | \(0.522088\pi\) | |||||||
\(884\) | −26.1556 | − | 25.4750i | −0.879707 | − | 0.856818i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.3931 | + | 39.2854i | 0.853098 | + | 1.31982i | ||||
\(887\) | 2.31077 | + | 0.841050i | 0.0775879 | + | 0.0282397i | 0.380523 | − | 0.924772i | \(-0.375744\pi\) |
−0.302935 | + | 0.953011i | \(0.597966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.04523 | + | 11.5991i | 0.0685950 | + | 0.389021i | ||||
\(890\) | 1.07640 | − | 0.454193i | 0.0360810 | − | 0.0152246i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.51309 | − | 34.8571i | −0.117627 | − | 1.16710i | ||||
\(893\) | 35.3339 | − | 13.2385i | 1.18241 | − | 0.443010i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.3382 | − | 26.6217i | 0.746684 | − | 0.889864i | ||||
\(896\) | 17.2798 | + | 20.4892i | 0.577279 | + | 0.684497i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −41.1071 | − | 5.13651i | −1.37176 | − | 0.171407i | ||||
\(899\) | 19.8071 | + | 7.20920i | 0.660605 | + | 0.240440i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.36916 | + | 9.29966i | −0.178873 | + | 0.309817i | ||||
\(902\) | −7.81075 | − | 8.41196i | −0.260069 | − | 0.280088i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.73201 | − | 3.02505i | −0.257163 | − | 0.100612i | ||||
\(905\) | −17.3321 | + | 10.0067i | −0.576137 | + | 0.332633i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.9369 | − | 4.39705i | −0.828016 | − | 0.146002i | −0.256450 | − | 0.966558i | \(-0.582553\pi\) |
−0.571566 | + | 0.820556i | \(0.693664\pi\) | |||||||
\(908\) | 7.70752 | + | 27.3194i | 0.255783 | + | 0.906627i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 47.7358 | + | 36.1317i | 1.58243 | + | 1.19775i | ||||
\(911\) | 19.4697 | 0.645058 | 0.322529 | − | 0.946560i | \(-0.395467\pi\) | ||||
0.322529 | + | 0.946560i | \(0.395467\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.2116 | −0.768190 | ||||||||
\(914\) | 27.0362 | + | 20.4639i | 0.894277 | + | 0.676887i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.0794558 | + | 0.281632i | 0.00262529 | + | 0.00930539i | ||||
\(917\) | 23.2264 | + | 4.09544i | 0.767003 | + | 0.135243i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.6842 | − | 15.9835i | 0.913219 | − | 0.527247i | 0.0317534 | − | 0.999496i | \(-0.489891\pi\) |
0.881465 | + | 0.472249i | \(0.156558\pi\) | |||||||
\(920\) | 43.1712 | + | 16.8902i | 1.42331 | + | 0.556852i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.8426 | + | 20.2930i | 0.620549 | + | 0.668314i | ||||
\(923\) | −19.3302 | + | 33.4809i | −0.636262 | + | 1.10204i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 59.9763 | + | 21.8296i | 1.97201 | + | 0.717752i | ||||
\(926\) | 1.30228 | + | 0.162725i | 0.0427956 | + | 0.00534749i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.5730 | − | 19.8318i | −0.445554 | − | 0.651011i | ||||
\(929\) | 17.3537 | − | 20.6813i | 0.569357 | − | 0.678533i | −0.402142 | − | 0.915577i | \(-0.631734\pi\) |
0.971499 | + | 0.237044i | \(0.0761787\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.59619 | − | 3.93099i | 0.150634 | − | 0.128833i | ||||
\(932\) | 1.33970 | + | 13.2926i | 0.0438833 | + | 0.435414i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −41.4966 | + | 17.5097i | −1.35781 | + | 0.572936i | ||||
\(935\) | −15.6591 | − | 88.8072i | −0.512108 | − | 2.90431i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.7346 | + | 10.4586i | 0.938720 | + | 0.341666i | 0.765660 | − | 0.643245i | \(-0.222412\pi\) |
0.173060 | + | 0.984911i | \(0.444635\pi\) | |||||||
\(938\) | −24.2518 | − | 37.5197i | −0.791848 | − | 1.22506i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −52.5302 | − | 51.1635i | −1.71335 | − | 1.66877i | ||||
\(941\) | −10.6636 | − | 12.7084i | −0.347624 | − | 0.414282i | 0.563695 | − | 0.825983i | \(-0.309379\pi\) |
−0.911319 | + | 0.411701i | \(0.864935\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.52845 | + | 3.19185i | −0.180031 | + | 0.103941i | ||||
\(944\) | −16.0179 | − | 2.39096i | −0.521339 | − | 0.0778190i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 56.6576 | − | 12.9530i | 1.84210 | − | 0.421138i | ||||
\(947\) | −44.4089 | + | 16.1635i | −1.44309 | + | 0.525244i | −0.940654 | − | 0.339368i | \(-0.889787\pi\) |
−0.502441 | + | 0.864611i | \(0.667565\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.36927 | 0.141832 | ||||||||
\(950\) | 18.5083 | + | 77.5877i | 0.600488 | + | 2.51728i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −24.7575 | − | 15.0926i | −0.802394 | − | 0.489155i | ||||
\(953\) | 13.8733 | + | 38.1165i | 0.449399 | + | 1.23471i | 0.933143 | + | 0.359504i | \(0.117054\pi\) |
−0.483744 | + | 0.875209i | \(0.660724\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 68.7844 | + | 12.1285i | 2.22581 | + | 0.392471i | ||||
\(956\) | −34.9690 | − | 8.87766i | −1.13098 | − | 0.287124i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.77483 | + | 5.41726i | −0.0896507 | + | 0.175024i | ||||
\(959\) | 12.5701 | − | 10.5476i | 0.405911 | − | 0.340600i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.19108 | + | 5.52711i | −0.102938 | + | 0.178294i | ||||
\(962\) | 15.9758 | + | 24.7161i | 0.515082 | + | 0.796879i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.81612 | − | 51.4145i | 0.122909 | − | 1.65595i | ||||
\(965\) | −61.5840 | + | 10.8589i | −1.98246 | + | 0.349561i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.64232 | + | 10.2995i | −0.277918 | + | 0.331210i | −0.886889 | − | 0.461983i | \(-0.847138\pi\) |
0.608971 | + | 0.793193i | \(0.291583\pi\) | |||||||
\(968\) | −36.9375 | + | 5.60786i | −1.18722 | + | 0.180243i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.77932 | − | 114.976i | −0.185563 | − | 3.69166i | ||||
\(971\) | −1.57017 | − | 1.31753i | −0.0503890 | − | 0.0422814i | 0.617245 | − | 0.786771i | \(-0.288249\pi\) |
−0.667634 | + | 0.744489i | \(0.732693\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.23033 | + | 12.6489i | 0.0715012 | + | 0.405504i | ||||
\(974\) | 51.0303 | + | 6.37644i | 1.63512 | + | 0.204314i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.9335 | − | 14.6134i | −0.413991 | − | 0.467762i | ||||
\(977\) | −38.4227 | − | 22.1834i | −1.22925 | − | 0.709709i | −0.262379 | − | 0.964965i | \(-0.584507\pi\) |
−0.966874 | + | 0.255256i | \(0.917840\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.616866 | + | 0.735152i | 0.0197151 | + | 0.0234956i | ||||
\(980\) | −10.7168 | − | 4.82642i | −0.342336 | − | 0.154174i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.5109 | − | 5.39456i | −0.558795 | − | 0.172147i | ||||
\(983\) | −2.37730 | + | 13.4823i | −0.0758241 | + | 0.430020i | 0.923138 | + | 0.384469i | \(0.125615\pi\) |
−0.998962 | + | 0.0455508i | \(0.985496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −93.0021 | + | 33.8500i | −2.96329 | + | 1.07855i | ||||
\(986\) | 20.7289 | + | 15.6899i | 0.660142 | + | 0.499668i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.7866 | + | 33.6761i | −0.470424 | + | 1.07138i | ||||
\(989\) | − | 32.3212i | − | 1.02775i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.62582 | − | 9.96186i | −0.115178 | − | 0.316449i | 0.868687 | − | 0.495361i | \(-0.164964\pi\) |
−0.983865 | + | 0.178912i | \(0.942742\pi\) | |||||||
\(992\) | −25.5628 | + | 11.5893i | −0.811621 | + | 0.367960i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.03903 | + | 29.3410i | −0.286701 | + | 0.930639i | ||||
\(995\) | 25.9201 | + | 44.8948i | 0.821721 | + | 1.42326i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.5916 | − | 16.4393i | 0.620473 | − | 0.520639i | −0.277479 | − | 0.960732i | \(-0.589499\pi\) |
0.897952 | + | 0.440093i | \(0.145054\pi\) | |||||||
\(998\) | 32.8277 | + | 35.3546i | 1.03914 | + | 1.11913i | ||||
\(999\) | 0 | 0 |
(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 | 684.2.ce.a.35.8 | ✓ | 240 | |
3.2 | odd | 2 | inner | 684.2.ce.a.35.33 | yes | 240 | |
4.3 | odd | 2 | inner | 684.2.ce.a.35.29 | yes | 240 | |
12.11 | even | 2 | inner | 684.2.ce.a.35.12 | yes | 240 | |
19.6 | even | 9 | inner | 684.2.ce.a.215.12 | yes | 240 | |
57.44 | odd | 18 | inner | 684.2.ce.a.215.29 | yes | 240 | |
76.63 | odd | 18 | inner | 684.2.ce.a.215.33 | yes | 240 | |
228.215 | even | 18 | inner | 684.2.ce.a.215.8 | yes | 240 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.2.ce.a.35.8 | ✓ | 240 | 1.1 | even | 1 | trivial | |
684.2.ce.a.35.12 | yes | 240 | 12.11 | even | 2 | inner | |
684.2.ce.a.35.29 | yes | 240 | 4.3 | odd | 2 | inner | |
684.2.ce.a.35.33 | yes | 240 | 3.2 | odd | 2 | inner | |
684.2.ce.a.215.8 | yes | 240 | 228.215 | even | 18 | inner | |
684.2.ce.a.215.12 | yes | 240 | 19.6 | even | 9 | inner | |
684.2.ce.a.215.29 | yes | 240 | 57.44 | odd | 18 | inner | |
684.2.ce.a.215.33 | yes | 240 | 76.63 | odd | 18 | inner |