Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,2,Mod(25,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.q (of order \(9\), 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: | \(1.72476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 97.3 | ||
Character | \(\chi\) | \(=\) | 216.97 |
Dual form | 216.2.q.b.49.3 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.997080 | + | 1.41627i | 0.575664 | + | 0.817686i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.95510 | + | 0.711598i | 0.874347 | + | 0.318236i | 0.739926 | − | 0.672688i | \(-0.234860\pi\) |
0.134421 | + | 0.990924i | \(0.457083\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.739573 | − | 4.19433i | 0.279532 | − | 1.58531i | −0.444653 | − | 0.895703i | \(-0.646673\pi\) |
0.724186 | − | 0.689605i | \(-0.242216\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.01166 | + | 2.82428i | −0.337221 | + | 0.941426i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.33115 | − | 0.848468i | 0.702867 | − | 0.255823i | 0.0342324 | − | 0.999414i | \(-0.489101\pi\) |
0.668634 | + | 0.743591i | \(0.266879\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.38271 | + | 3.67753i | −1.21555 | + | 1.01996i | −0.216500 | + | 0.976283i | \(0.569464\pi\) |
−0.999046 | + | 0.0436808i | \(0.986092\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.941573 | + | 3.47847i | 0.243113 | + | 0.898138i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.340351 | + | 0.589505i | 0.0825473 | + | 0.142976i | 0.904343 | − | 0.426806i | \(-0.140361\pi\) |
−0.821796 | + | 0.569782i | \(0.807028\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.58368 | + | 4.47506i | −0.592736 | + | 1.02665i | 0.401126 | + | 0.916023i | \(0.368619\pi\) |
−0.993862 | + | 0.110626i | \(0.964714\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.67773 | − | 3.13464i | 1.45720 | − | 0.684035i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.23287 | − | 6.99197i | −0.257072 | − | 1.45793i | −0.790698 | − | 0.612206i | \(-0.790282\pi\) |
0.533627 | − | 0.845720i | \(-0.320829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.514184 | − | 0.431451i | −0.102837 | − | 0.0862903i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00866 | + | 1.38324i | −0.963917 | + | 0.266204i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.22836 | + | 3.54802i | 0.785187 | + | 0.658850i | 0.944549 | − | 0.328370i | \(-0.106499\pi\) |
−0.159362 | + | 0.987220i | \(0.550944\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.787375 | − | 4.46543i | −0.141417 | − | 0.802014i | −0.970175 | − | 0.242407i | \(-0.922063\pi\) |
0.828758 | − | 0.559607i | \(-0.189048\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.52600 | + | 2.45555i | 0.613798 | + | 0.427456i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.43061 | − | 7.67405i | 0.748910 | − | 1.29715i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.69778 | − | 6.40475i | −0.607912 | − | 1.05293i | −0.991584 | − | 0.129465i | \(-0.958674\pi\) |
0.383672 | − | 0.923469i | \(-0.374659\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.57830 | − | 2.54033i | −1.53376 | − | 0.406778i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.256172 | + | 0.214954i | −0.0400074 | + | 0.0335702i | −0.662572 | − | 0.748998i | \(-0.730535\pi\) |
0.622565 | + | 0.782568i | \(0.286091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.61090 | + | 0.586320i | −0.245660 | + | 0.0894130i | −0.461916 | − | 0.886924i | \(-0.652838\pi\) |
0.216256 | + | 0.976337i | \(0.430616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.98765 | + | 4.80184i | −0.594444 | + | 0.715816i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.889756 | + | 5.04606i | −0.129784 | + | 0.736043i | 0.848566 | + | 0.529089i | \(0.177466\pi\) |
−0.978351 | + | 0.206954i | \(0.933645\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.4676 | − | 3.80989i | −1.49537 | − | 0.544270i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.495544 | + | 1.06981i | −0.0693900 | + | 0.149804i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.45353 | 1.29854 | 0.649271 | − | 0.760557i | \(-0.275074\pi\) | ||||
0.649271 | + | 0.760557i | \(0.275074\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.16139 | 0.695961 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.91404 | + | 0.802799i | −1.18069 | + | 0.106333i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.52366 | − | 3.46633i | −1.23987 | − | 0.451277i | −0.362906 | − | 0.931826i | \(-0.618216\pi\) |
−0.876968 | + | 0.480548i | \(0.840438\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.36385 | − | 7.73479i | 0.174623 | − | 0.990338i | −0.763954 | − | 0.645270i | \(-0.776745\pi\) |
0.938578 | − | 0.345068i | \(-0.112144\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.0977 | + | 6.33201i | 1.39818 | + | 0.797758i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.1856 | + | 4.07121i | −1.38740 | + | 0.504971i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.13628 | − | 2.63165i | 0.383157 | − | 0.321507i | −0.430783 | − | 0.902455i | \(-0.641763\pi\) |
0.813940 | + | 0.580948i | \(0.197318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.67327 | − | 8.71764i | 1.04414 | − | 1.04948i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.77081 | + | 4.79919i | 0.328835 | + | 0.569559i | 0.982281 | − | 0.187414i | \(-0.0600106\pi\) |
−0.653446 | + | 0.756973i | \(0.726677\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.43331 | + | 7.67871i | −0.518879 | + | 0.898725i | 0.480880 | + | 0.876786i | \(0.340317\pi\) |
−0.999759 | + | 0.0219389i | \(0.993016\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0983709 | − | 1.15842i | 0.0113589 | − | 0.133762i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.83470 | − | 10.4051i | −0.209083 | − | 1.18577i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.53194 | + | 3.80275i | 0.509883 | + | 0.427842i | 0.861088 | − | 0.508456i | \(-0.169784\pi\) |
−0.351205 | + | 0.936299i | \(0.614228\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.95308 | − | 5.71443i | −0.772564 | − | 0.634937i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.90986 | − | 5.79806i | −0.758456 | − | 0.636420i | 0.179268 | − | 0.983800i | \(-0.442627\pi\) |
−0.937724 | + | 0.347380i | \(0.887071\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.245929 | + | 1.39473i | 0.0266748 | + | 0.151280i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.808948 | + | 9.52617i | −0.0867283 | + | 1.02131i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.983567 | − | 1.70359i | 0.104258 | − | 0.180580i | −0.809177 | − | 0.587565i | \(-0.800087\pi\) |
0.913435 | + | 0.406985i | \(0.133420\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.1834 | + | 21.1023i | 1.27717 | + | 2.21213i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.53919 | − | 5.56753i | 0.574387 | − | 0.577326i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.23578 | + | 6.91064i | −0.844974 | + | 0.709017i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.443556 | − | 0.161441i | 0.0450363 | − | 0.0163919i | −0.319404 | − | 0.947619i | \(-0.603483\pi\) |
0.364440 | + | 0.931227i | \(0.381260\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0379741 | + | 7.44216i | 0.00381654 | + | 0.747965i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.35090 | + | 13.3326i | −0.233923 | + | 1.32665i | 0.610946 | + | 0.791673i | \(0.290789\pi\) |
−0.844869 | + | 0.534973i | \(0.820322\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.63679 | − | 0.959715i | −0.259811 | − | 0.0945635i | 0.208831 | − | 0.977952i | \(-0.433034\pi\) |
−0.468642 | + | 0.883388i | \(0.655256\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 15.2862 | − | 1.37668i | 1.49178 | − | 0.134350i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.3455 | 1.67685 | 0.838426 | − | 0.545016i | \(-0.183476\pi\) | ||||
0.838426 | + | 0.545016i | \(0.183476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1417 | 0.971398 | 0.485699 | − | 0.874126i | \(-0.338565\pi\) | ||||
0.485699 | + | 0.874126i | \(0.338565\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.38389 | − | 11.6231i | 0.511016 | − | 1.10322i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.18308 | + | 3.34237i | 0.863871 | + | 0.314423i | 0.735683 | − | 0.677326i | \(-0.236862\pi\) |
0.128189 | + | 0.991750i | \(0.459084\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.56508 | − | 14.5473i | 0.239195 | − | 1.35654i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.95254 | − | 16.0984i | −0.550312 | − | 1.48830i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.72429 | − | 0.991562i | 0.249736 | − | 0.0908964i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.71215 | + | 3.11486i | −0.337468 | + | 0.283169i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.559858 | − | 0.148484i | −0.0504807 | − | 0.0133883i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.89969 | − | 10.2186i | −0.527684 | − | 0.913976i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.20346 | − | 9.01266i | 0.461733 | − | 0.799744i | −0.537315 | − | 0.843382i | \(-0.680561\pi\) |
0.999047 | + | 0.0436375i | \(0.0138947\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.43659 | − | 1.69687i | −0.214529 | − | 0.149401i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.62938 | + | 14.9120i | 0.229730 | + | 1.30286i | 0.853433 | + | 0.521202i | \(0.174516\pi\) |
−0.623703 | + | 0.781661i | \(0.714373\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.8591 | + | 14.1464i | 1.46187 | + | 1.22665i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.7767 | − | 0.859782i | −0.927513 | − | 0.0739982i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.5223 | + | 12.1857i | 1.24073 | + | 1.04109i | 0.997467 | + | 0.0711323i | \(0.0226613\pi\) |
0.243260 | + | 0.969961i | \(0.421783\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.98835 | + | 11.2765i | 0.168650 | + | 0.956460i | 0.945221 | + | 0.326431i | \(0.105846\pi\) |
−0.776571 | + | 0.630029i | \(0.783043\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.03376 | + | 3.77118i | −0.676564 | + | 0.317591i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.09647 | + | 12.2914i | −0.593437 | + | 1.02786i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.74210 | + | 9.94561i | 0.476856 | + | 0.825938i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.04117 | − | 18.6237i | −0.415789 | − | 1.53606i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.47668 | + | 6.27368i | −0.612514 | + | 0.513960i | −0.895440 | − | 0.445182i | \(-0.853139\pi\) |
0.282927 | + | 0.959142i | \(0.408695\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.61982 | + | 3.13736i | −0.701471 | + | 0.255314i | −0.668039 | − | 0.744127i | \(-0.732866\pi\) |
−0.0334320 | + | 0.999441i | \(0.510644\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00925 | + | 0.364865i | −0.162438 | + | 0.0294976i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.63819 | − | 9.29064i | 0.131583 | − | 0.746242i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.470052 | − | 0.171085i | −0.0375142 | − | 0.0136541i | 0.323195 | − | 0.946332i | \(-0.395243\pi\) |
−0.360709 | + | 0.932678i | \(0.617465\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.42592 | + | 13.3888i | 0.747524 | + | 1.06180i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −30.2384 | −2.38312 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.75047 | −0.607064 | −0.303532 | − | 0.952821i | \(-0.598166\pi\) | ||||
−0.303532 | + | 0.952821i | \(0.598166\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.14632 | + | 7.30994i | 0.400640 | + | 0.569078i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.9210 | − | 7.97859i | −1.69630 | − | 0.617402i | −0.700902 | − | 0.713257i | \(-0.747219\pi\) |
−0.995395 | + | 0.0958557i | \(0.969441\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.42649 | − | 19.4326i | 0.263576 | − | 1.49482i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.0250 | − | 11.8243i | −0.766631 | − | 0.904225i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.74869 | + | 2.09235i | −0.437065 | + | 0.159079i | −0.551175 | − | 0.834389i | \(-0.685820\pi\) |
0.114110 | + | 0.993468i | \(0.463598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.18993 | + | 1.83757i | −0.165543 | + | 0.138907i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.58658 | − | 16.9443i | −0.344748 | − | 1.27361i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.87922 | + | 4.98696i | 0.215203 | + | 0.372743i | 0.953335 | − | 0.301913i | \(-0.0976252\pi\) |
−0.738132 | + | 0.674656i | \(0.764292\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.87176 | − | 11.9022i | 0.510774 | − | 0.884687i | −0.489148 | − | 0.872201i | \(-0.662692\pi\) |
0.999922 | − | 0.0124858i | \(-0.00397445\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.3145 | − | 5.78062i | 0.910310 | − | 0.427316i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.67193 | − | 15.1532i | −0.196444 | − | 1.11409i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.29358 | + | 1.08545i | 0.0945962 | + | 0.0793757i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.09749 | + | 22.0310i | 0.152570 | + | 1.60252i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.96488 | − | 5.00513i | −0.431604 | − | 0.362159i | 0.400953 | − | 0.916099i | \(-0.368679\pi\) |
−0.832556 | + | 0.553940i | \(0.813124\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.234364 | + | 1.32915i | 0.0168699 | + | 0.0956741i | 0.992080 | − | 0.125606i | \(-0.0400876\pi\) |
−0.975210 | + | 0.221280i | \(0.928976\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.9188 | − | 11.7825i | −1.21158 | − | 0.843761i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.52195 | − | 7.83225i | 0.322176 | − | 0.558024i | −0.658761 | − | 0.752352i | \(-0.728919\pi\) |
0.980937 | + | 0.194328i | \(0.0622525\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.80907 | + | 4.86545i | 0.199130 | + | 0.344903i | 0.948246 | − | 0.317535i | \(-0.102855\pi\) |
−0.749117 | + | 0.662438i | \(0.769522\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.85426 | + | 1.81786i | 0.483462 | + | 0.128222i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.0087 | − | 15.1111i | 1.26397 | − | 1.06059i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.653803 | + | 0.237965i | −0.0456636 | + | 0.0166202i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.9945 | + | 3.59154i | 1.45922 | + | 0.249629i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.22598 | + | 12.6242i | −0.153975 | + | 0.873233i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.64659 | + | 2.41916i | 0.457570 | + | 0.166542i | 0.560513 | − | 0.828145i | \(-0.310604\pi\) |
−0.102943 | + | 0.994687i | \(0.532826\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.03424 | + | 8.70941i | −0.276422 | + | 0.596759i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.56669 | −0.243246 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.3118 | −1.31097 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.2955 | + | 1.37752i | −1.03358 | + | 0.0930838i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.65958 | − | 1.33198i | −0.246170 | − | 0.0895987i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.77934 | − | 15.7624i | 0.186118 | − | 1.05553i | −0.738392 | − | 0.674372i | \(-0.764414\pi\) |
0.924510 | − | 0.381157i | \(-0.124474\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.73872 | − | 1.01571i | 0.115915 | − | 0.0677142i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.95630 | + | 1.43997i | −0.262589 | + | 0.0955744i | −0.469960 | − | 0.882688i | \(-0.655732\pi\) |
0.207371 | + | 0.978262i | \(0.433509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.9610 | + | 9.19738i | −0.724324 | + | 0.607780i | −0.928578 | − | 0.371138i | \(-0.878968\pi\) |
0.204253 | + | 0.978918i | \(0.434523\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.9071 | − | 12.9732i | 0.849226 | − | 0.853571i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.52385 | + | 6.10349i | 0.230855 | + | 0.399853i | 0.958060 | − | 0.286568i | \(-0.0925143\pi\) |
−0.727205 | + | 0.686421i | \(0.759181\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.33032 | + | 9.23239i | −0.347712 | + | 0.602255i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.867026 | + | 10.2101i | −0.0563194 | + | 0.663218i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.17975 | + | 12.3620i | 0.140997 | + | 0.799631i | 0.970495 | + | 0.241122i | \(0.0775153\pi\) |
−0.829498 | + | 0.558509i | \(0.811374\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.3747 | + | 18.7746i | 1.44128 | + | 1.20938i | 0.938649 | + | 0.344874i | \(0.112078\pi\) |
0.502629 | + | 0.864502i | \(0.332366\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.16042 | − | 15.5452i | 0.0744412 | − | 0.997225i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.7540 | − | 14.8974i | −1.13426 | − | 0.951761i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.13366 | − | 29.1144i | −0.326647 | − | 1.85251i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.32196 | − | 15.5674i | 0.0837757 | − | 0.986543i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.31998 | + | 5.75038i | −0.209556 | + | 0.362961i | −0.951575 | − | 0.307418i | \(-0.900535\pi\) |
0.742019 | + | 0.670379i | \(0.233868\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.80646 | − | 15.2532i | −0.553658 | − | 0.958963i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.73011 | + | 1.73896i | −0.108344 | + | 0.108898i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.0707 | − | 13.4849i | 1.00246 | − | 0.841165i | 0.0151383 | − | 0.999885i | \(-0.495181\pi\) |
0.987324 | + | 0.158720i | \(0.0507367\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.5984 | + | 10.7729i | −1.83916 | + | 0.669398i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.2983 | + | 8.35266i | −0.885040 | + | 0.517017i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.306469 | + | 1.73807i | −0.0188977 | + | 0.107174i | −0.992798 | − | 0.119804i | \(-0.961773\pi\) |
0.973900 | + | 0.226978i | \(0.0728845\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.4826 | + | 6.72711i | 1.13538 | + | 0.413243i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.39344 | − | 0.305613i | 0.207675 | − | 0.0187032i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.8211 | 1.51337 | 0.756684 | − | 0.653781i | \(-0.226818\pi\) | ||||
0.756684 | + | 0.653781i | \(0.226818\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.9629 | −0.848188 | −0.424094 | − | 0.905618i | \(-0.639407\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639407\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.7388 | + | 38.2958i | −1.07360 | + | 2.31777i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.56471 | − | 0.569508i | −0.0943555 | − | 0.0343426i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.70629 | + | 15.3481i | −0.162605 | + | 0.922178i | 0.788895 | + | 0.614528i | \(0.210654\pi\) |
−0.951500 | + | 0.307650i | \(0.900457\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.4082 | + | 2.29374i | 0.802725 | + | 0.137323i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.9646 | − | 6.90254i | 1.13133 | − | 0.411771i | 0.292556 | − | 0.956248i | \(-0.405494\pi\) |
0.838775 | + | 0.544478i | \(0.183272\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.8757 | − | 9.96486i | 0.705935 | − | 0.592350i | −0.217520 | − | 0.976056i | \(-0.569797\pi\) |
0.923455 | + | 0.383706i | \(0.125352\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.9991 | − | 4.77366i | −1.06617 | − | 0.282767i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.712130 | + | 1.23344i | 0.0420357 | + | 0.0728079i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.26832 | − | 14.3212i | 0.486372 | − | 0.842421i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.670906 | + | 0.467227i | 0.0393292 | + | 0.0273893i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.79392 | + | 21.5164i | 0.221643 | + | 1.25700i | 0.868999 | + | 0.494814i | \(0.164764\pi\) |
−0.647356 | + | 0.762188i | \(0.724125\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.1531 | − | 13.5540i | −0.940467 | − | 0.789146i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.5023 | + | 7.47421i | −0.609404 | + | 0.433698i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31.1165 | + | 26.1098i | 1.79951 | + | 1.50997i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.26784 | + | 7.19028i | 0.0730771 | + | 0.414441i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.2267 | + | 9.96417i | −1.21944 | + | 0.572427i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.17052 | − | 14.1518i | 0.467843 | − | 0.810328i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.4443 | − | 21.5541i | −0.710232 | − | 1.23016i | −0.964770 | − | 0.263094i | \(-0.915257\pi\) |
0.254539 | − | 0.967063i | \(-0.418076\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.26988 | − | 4.69134i | −0.0722407 | − | 0.266881i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.69907 | − | 1.42569i | 0.0963455 | − | 0.0808435i | −0.593343 | − | 0.804950i | \(-0.702192\pi\) |
0.689688 | + | 0.724107i | \(0.257748\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.6348 | + | 4.59869i | −0.714161 | + | 0.259933i | −0.673445 | − | 0.739237i | \(-0.735186\pi\) |
−0.0407162 | + | 0.999171i | \(0.512964\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17.1913 | + | 20.2768i | 0.968623 | + | 1.14247i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.76942 | − | 27.0487i | 0.267877 | − | 1.51921i | −0.492838 | − | 0.870121i | \(-0.664040\pi\) |
0.760715 | − | 0.649086i | \(-0.224849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.8673 | + | 4.68331i | 0.720430 | + | 0.262215i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.2948 | + | 24.5660i | 0.965304 | + | 1.37114i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.51743 | −0.195715 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.84019 | 0.213016 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.1121 | + | 14.3634i | 0.559199 | + | 0.794299i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.5068 | + | 7.46386i | 1.13058 | + | 0.411496i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.12868 | + | 23.4149i | −0.226933 | + | 1.28700i | 0.632023 | + | 0.774950i | \(0.282225\pi\) |
−0.858956 | + | 0.512050i | \(0.828886\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.8297 | − | 3.96412i | 1.19626 | − | 0.217232i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.00441 | − | 2.91337i | 0.437327 | − | 0.159174i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.9915 | − | 13.4184i | 0.871110 | − | 0.730948i | −0.0932216 | − | 0.995645i | \(-0.529717\pi\) |
0.964332 | + | 0.264697i | \(0.0852721\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.42256 | + | 16.3384i | 0.240200 | + | 0.887378i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.62426 | − | 9.74150i | −0.304571 | − | 0.527532i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.81486 | + | 15.2678i | −0.475958 | + | 0.824383i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 23.1605 | − | 10.8720i | 1.24692 | − | 0.585327i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.31831 | + | 13.1478i | 0.124454 | + | 0.705811i | 0.981631 | + | 0.190790i | \(0.0611049\pi\) |
−0.857177 | + | 0.515021i | \(0.827784\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.77715 | + | 7.36491i | 0.469830 | + | 0.394234i | 0.846733 | − | 0.532019i | \(-0.178566\pi\) |
−0.376902 | + | 0.926253i | \(0.623011\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.8646 | − | 24.4818i | 0.900165 | − | 1.30674i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.1875 | − | 14.4220i | −0.914799 | − | 0.767607i | 0.0582273 | − | 0.998303i | \(-0.481455\pi\) |
−0.973026 | + | 0.230696i | \(0.925900\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.00212 | + | 11.3546i | 0.106262 | + | 0.602639i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.12066 | + | 2.86968i | 0.218089 | + | 0.151880i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.41502 | − | 7.64704i | 0.233016 | − | 0.403595i | −0.725678 | − | 0.688034i | \(-0.758474\pi\) |
0.958694 | + | 0.284439i | \(0.0918073\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.85077 | − | 6.66974i | −0.202672 | − | 0.351039i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.11280 | − | 2.15165i | −0.425812 | − | 0.112932i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.1317 | + | 11.8579i | −0.739687 | + | 0.620671i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.3876 | + | 7.42050i | −1.06423 | + | 0.387347i | −0.814015 | − | 0.580844i | \(-0.802723\pi\) |
−0.250212 | + | 0.968191i | \(0.580500\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.347930 | − | 0.940962i | −0.0181125 | − | 0.0489845i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.99158 | − | 39.6512i | 0.362985 | − | 2.05859i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.1587 | − | 10.9769i | −1.56156 | − | 0.568361i | −0.590465 | − | 0.807063i | \(-0.701056\pi\) |
−0.971093 | + | 0.238702i | \(0.923278\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.58982 | − | 18.5443i | 0.443576 | − | 0.957624i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −31.5796 | −1.62643 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.3500 | 0.993942 | 0.496971 | − | 0.867767i | \(-0.334445\pi\) | ||||
0.496971 | + | 0.867767i | \(0.334445\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.9527 | − | 1.61682i | 0.919743 | − | 0.0828320i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.2072 | + | 8.08276i | 1.13474 | + | 0.413010i | 0.840009 | − | 0.542572i | \(-0.182549\pi\) |
0.294726 | + | 0.955582i | \(0.404772\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.81722 | − | 21.6486i | 0.194544 | − | 1.10331i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.0262414 | − | 5.14279i | −0.00133392 | − | 0.261423i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.25949 | − | 1.91430i | 0.266667 | − | 0.0970587i | −0.205226 | − | 0.978715i | \(-0.565793\pi\) |
0.471893 | + | 0.881656i | \(0.343571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.70219 | − | 3.10651i | 0.187228 | − | 0.157103i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.4977 | + | 18.5923i | −0.933086 | + | 0.937859i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.15436 | + | 10.6597i | 0.309659 | + | 0.536346i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.32648 | − | 7.49368i | 0.217140 | − | 0.376097i | −0.736793 | − | 0.676119i | \(-0.763661\pi\) |
0.953932 | + | 0.300022i | \(0.0969940\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.22539 | + | 37.9822i | −0.161471 | + | 1.90149i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.00348 | − | 28.3761i | −0.249862 | − | 1.41704i | −0.808925 | − | 0.587912i | \(-0.799950\pi\) |
0.559063 | − | 0.829125i | \(-0.311161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.8726 | + | 16.6751i | 0.989924 | + | 0.830645i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.52757 | − | 16.1201i | −0.473429 | − | 0.801013i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.0543 | − | 11.7930i | −0.696645 | − | 0.584555i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.223219 | − | 1.26594i | −0.0110375 | − | 0.0625966i | 0.978792 | − | 0.204859i | \(-0.0656735\pi\) |
−0.989829 | + | 0.142262i | \(0.954562\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.77834 | + | 32.7177i | −0.137045 | + | 1.61385i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.5824 | + | 37.3818i | −1.06200 | + | 1.83944i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.38357 | − | 16.2528i | −0.460622 | − | 0.797820i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.9881 | + | 14.0596i | −0.684999 | + | 0.688503i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.32223 | − | 6.14408i | 0.357714 | − | 0.300158i | −0.446165 | − | 0.894951i | \(-0.647210\pi\) |
0.803879 | + | 0.594793i | \(0.202766\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.9095 | + | 10.5222i | −1.40896 | + | 0.512820i | −0.930825 | − | 0.365465i | \(-0.880910\pi\) |
−0.478137 | + | 0.878285i | \(0.658688\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.3513 | − | 7.61782i | −0.649164 | − | 0.370391i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0793399 | − | 0.449959i | 0.00384855 | − | 0.0218262i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.4336 | − | 11.4409i | −1.52118 | − | 0.553664i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.4838 | + | 2.20501i | −1.18209 | + | 0.106459i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.17147 | −0.249101 | −0.124551 | − | 0.992213i | \(-0.539749\pi\) | ||||
−0.124551 | + | 0.992213i | \(0.539749\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.7835 | 1.23907 | 0.619537 | − | 0.784968i | \(-0.287320\pi\) | ||||
0.619537 | + | 0.784968i | \(0.287320\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.36037 | + | 18.0490i | −0.400849 | + | 0.865381i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.4748 | + | 12.5478i | 1.64915 | + | 0.600243i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.28234 | − | 24.2864i | 0.204385 | − | 1.15913i | −0.694019 | − | 0.719956i | \(-0.744162\pi\) |
0.898404 | − | 0.439169i | \(-0.144727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.3498 | − | 25.7090i | 1.01666 | − | 1.22424i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.76116 | − | 1.36895i | 0.178698 | − | 0.0650409i | −0.251121 | − | 0.967956i | \(-0.580799\pi\) |
0.429820 | + | 0.902915i | \(0.358577\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.13524 | − | 2.63078i | 0.148625 | − | 0.124711i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.3401 | − | 4.33367i | −0.772860 | − | 0.204975i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.9152 | − | 20.6377i | −0.562312 | − | 0.973952i | −0.997294 | − | 0.0735135i | \(-0.976579\pi\) |
0.434983 | − | 0.900439i | \(-0.356755\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.414793 | + | 0.718443i | −0.0195318 | + | 0.0338301i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.0380 | − | 9.07982i | −0.612579 | − | 0.426607i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.80345 | + | 49.9268i | 0.412712 | + | 2.34061i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.6052 | − | 24.8417i | −1.38487 | − | 1.16205i | −0.967370 | − | 0.253369i | \(-0.918461\pi\) |
−0.417502 | − | 0.908676i | \(-0.637094\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.52013 | − | 2.48184i | −0.117630 | − | 0.115843i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.4218 | − | 10.4232i | −0.578542 | − | 0.485455i | 0.305926 | − | 0.952055i | \(-0.401034\pi\) |
−0.884468 | + | 0.466601i | \(0.845479\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.21589 | + | 12.5670i | 0.102981 | + | 0.584036i | 0.992007 | + | 0.126180i | \(0.0402716\pi\) |
−0.889026 | + | 0.457857i | \(0.848617\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.7915 | − | 6.94339i | 0.685939 | − | 0.321992i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.29669 | − | 2.24593i | 0.0600035 | − | 0.103929i | −0.834463 | − | 0.551064i | \(-0.814222\pi\) |
0.894467 | + | 0.447134i | \(0.147555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.71850 | − | 15.1009i | −0.402583 | − | 0.697294i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.226376 | − | 0.836308i | −0.0104309 | − | 0.0385350i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.25777 | + | 2.73359i | −0.149792 | + | 0.125691i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.25925 | − | 1.18627i | 0.149545 | − | 0.0544299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.56378 | + | 26.6994i | −0.437895 | + | 1.22248i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.531048 | + | 3.01172i | −0.0242642 | + | 0.137609i | −0.994533 | − | 0.104419i | \(-0.966702\pi\) |
0.970269 | + | 0.242028i | \(0.0778127\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 39.7600 | + | 14.4714i | 1.81290 | + | 0.659841i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −30.1501 | − | 42.8259i | −1.37188 | − | 1.94865i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.982077 | 0.0445938 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.46808 | −0.202468 | −0.101234 | − | 0.994863i | \(-0.532279\pi\) | ||||
−0.101234 | + | 0.994863i | \(0.532279\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.72784 | − | 10.9768i | −0.349465 | − | 0.496387i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.3262 | − | 10.3099i | −1.27834 | − | 0.465278i | −0.388458 | − | 0.921466i | \(-0.626992\pi\) |
−0.889883 | + | 0.456188i | \(0.849214\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.652447 | + | 3.70021i | −0.0293847 | + | 0.166649i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.22158 | + | 14.5772i | −0.234693 | + | 0.655196i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.1786 | − | 8.07235i | 0.994847 | − | 0.362095i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.92557 | + | 3.29394i | −0.175732 | + | 0.147457i | −0.726411 | − | 0.687260i | \(-0.758813\pi\) |
0.550679 | + | 0.834717i | \(0.314369\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.5571 | − | 39.0014i | −0.471657 | − | 1.74245i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.32680 | − | 5.76219i | −0.148335 | − | 0.256923i | 0.782277 | − | 0.622930i | \(-0.214058\pi\) |
−0.930612 | + | 0.366007i | \(0.880725\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.0837 | + | 24.3937i | −0.626717 | + | 1.08551i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30.9384 | − | 14.5230i | 1.37402 | − | 0.644989i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.89801 | − | 10.7641i | −0.0841278 | − | 0.477112i | −0.997541 | − | 0.0700798i | \(-0.977675\pi\) |
0.913414 | − | 0.407033i | \(-0.133436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.9283 | + | 24.2737i | 1.27971 | + | 1.07381i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.75068 | − | 25.9879i | 0.298050 | − | 1.14739i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.47226 | − | 3.75267i | −0.197071 | − | 0.165363i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.20726 | + | 12.5180i | 0.0970754 | + | 0.550542i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.69525 | − | 6.05548i | −0.381679 | − | 0.265806i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.1465 | + | 19.3062i | −0.488335 | + | 0.845822i | −0.999910 | − | 0.0134171i | \(-0.995729\pi\) |
0.511575 | + | 0.859239i | \(0.329062\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.2501 | − | 19.4858i | −0.491933 | − | 0.852053i | 0.508024 | − | 0.861343i | \(-0.330376\pi\) |
−0.999957 | + | 0.00928981i | \(0.997043\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.78603 | − | 1.26933i | −0.208879 | − | 0.0553983i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.36441 | − | 1.98397i | 0.102995 | − | 0.0864233i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −25.7547 | + | 9.37395i | −1.11977 | + | 0.407563i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.4246 | − | 23.3907i | 0.842956 | − | 1.01507i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.332229 | − | 1.88416i | 0.0143904 | − | 0.0816121i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.9121 | + | 12.3430i | 1.46615 | + | 0.533635i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.19209 | + | 9.05017i | −0.180902 | + | 0.390544i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.6340 | −1.19028 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.6333 | −1.36002 | −0.680012 | − | 0.733201i | \(-0.738025\pi\) | ||||
−0.680012 | + | 0.733201i | \(0.738025\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.7085 | − | 2.13519i | 1.01743 | − | 0.0916298i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.8280 | + | 7.21681i | 0.849339 | + | 0.309134i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.00203 | + | 11.3541i | −0.0856006 | + | 0.485465i | 0.911625 | + | 0.411024i | \(0.134829\pi\) |
−0.997225 | + | 0.0744418i | \(0.976282\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.4654 | + | 11.6769i | 0.873443 | + | 0.498358i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.8023 | + | 9.75524i | −1.14182 | + | 0.415587i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.3017 | − | 16.1960i | 0.820790 | − | 0.688725i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.7970 | − | 18.8932i | 0.797889 | − | 0.801971i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.96708 | + | 8.60324i | 0.210462 | + | 0.364531i | 0.951859 | − | 0.306535i | \(-0.0991698\pi\) |
−0.741397 | + | 0.671067i | \(0.765836\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.90390 | − | 8.49381i | 0.207413 | − | 0.359250i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.247482 | + | 2.91435i | −0.0104487 | + | 0.123044i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.60555 | − | 26.1193i | −0.194101 | − | 1.10080i | −0.913694 | − | 0.406403i | \(-0.866783\pi\) |
0.719593 | − | 0.694396i | \(-0.244328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.5754 | + | 13.0693i | 0.655262 | + | 0.549830i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −29.1105 | + | 24.9373i | −1.22253 | + | 1.04727i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.5862 | + | 23.1476i | 1.15647 | + | 0.970397i | 0.999851 | − | 0.0172614i | \(-0.00549475\pi\) |
0.156623 | + | 0.987658i | \(0.449939\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.24236 | + | 7.04575i | 0.0519910 | + | 0.294855i | 0.999706 | − | 0.0242636i | \(-0.00772411\pi\) |
−0.947715 | + | 0.319119i | \(0.896613\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.14117 | − | 13.4384i | 0.0476731 | − | 0.561398i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.38277 | + | 4.12708i | −0.0993684 | + | 0.172111i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.83173 | + | 13.5650i | 0.326039 | + | 0.564717i | 0.981722 | − | 0.190320i | \(-0.0609525\pi\) |
−0.655683 | + | 0.755036i | \(0.727619\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.64876 | + | 1.65719i | −0.0685200 | + | 0.0688705i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.4293 | + | 24.6941i | −1.22093 | + | 1.02449i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.0375 | − | 8.02101i | 0.912702 | − | 0.332196i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.182211 | − | 35.7098i | −0.00753351 | − | 1.47642i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.59747 | + | 9.05971i | −0.0659347 | + | 0.373934i | 0.933930 | + | 0.357457i | \(0.116356\pi\) |
−0.999864 | + | 0.0164772i | \(0.994755\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.0174 | + | 8.01367i | 0.907210 | + | 0.330197i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.6014 | − | 1.40506i | 0.641754 | − | 0.0577964i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.8285 | 0.814259 | 0.407129 | − | 0.913370i | \(-0.366530\pi\) | ||||
0.407129 | + | 0.913370i | \(0.366530\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.03186 | 0.247282 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.08994 | + | 8.82965i | −0.167390 | + | 0.361374i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.6087 | − | 9.68479i | −1.08720 | − | 0.395710i | −0.264619 | − | 0.964353i | \(-0.585246\pi\) |
−0.822584 | + | 0.568643i | \(0.807469\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.14558 | + | 40.5246i | −0.291474 | + | 1.65303i | 0.389723 | + | 0.920932i | \(0.372571\pi\) |
−0.681197 | + | 0.732100i | \(0.738540\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.25965 | + | 11.5201i | 0.173466 | + | 0.469133i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.47414 | + | 3.44831i | −0.385179 | + | 0.140194i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.62083 | − | 8.07283i | 0.390497 | − | 0.327666i | −0.426310 | − | 0.904577i | \(-0.640187\pi\) |
0.816807 | + | 0.576911i | \(0.195742\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 39.3576 | + | 10.4383i | 1.59485 | + | 0.422981i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.6575 | − | 25.3875i | −0.592978 | − | 1.02707i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.01692 | − | 6.95752i | 0.162242 | − | 0.281011i | −0.773430 | − | 0.633881i | \(-0.781461\pi\) |
0.935672 | + | 0.352870i | \(0.114794\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.988917 | − | 0.688694i | −0.0398770 | − | 0.0277708i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.677179 | − | 3.84047i | −0.0272622 | − | 0.154612i | 0.968138 | − | 0.250418i | \(-0.0805681\pi\) |
−0.995400 | + | 0.0958065i | \(0.969457\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.1733 | + | 17.7665i | 0.851026 | + | 0.714095i | 0.960015 | − | 0.279948i | \(-0.0903171\pi\) |
−0.108990 | + | 0.994043i | \(0.534762\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.8466 | + | 33.3150i | 0.635902 | + | 1.33689i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.41799 | − | 5.38533i | −0.257131 | − | 0.215759i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.68019 | − | 20.8714i | −0.147208 | − | 0.834856i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.0988 | + | 9.43472i | −0.802668 | + | 0.376786i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.51709 | − | 4.35973i | 0.100363 | − | 0.173834i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.29226 | − | 10.8985i | −0.250491 | − | 0.433863i | 0.713170 | − | 0.700991i | \(-0.247259\pi\) |
−0.963661 | + | 0.267128i | \(0.913925\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.20099 | + | 11.8255i | 0.127228 | + | 0.470021i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.5867 | − | 13.9179i | 0.658222 | − | 0.552314i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 59.8874 | − | 21.7972i | 2.37282 | − | 0.863637i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.3574 | + | 2.97038i | −0.647088 | + | 0.117507i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.12752 | + | 40.4222i | −0.281520 | + | 1.59658i | 0.435936 | + | 0.899977i | \(0.356417\pi\) |
−0.717457 | + | 0.696603i | \(0.754694\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.0607 | + | 6.20958i | 0.672808 | + | 0.244882i | 0.655756 | − | 0.754973i | \(-0.272350\pi\) |
0.0170514 | + | 0.999855i | \(0.494572\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.55628 | − | 5.05141i | −0.140028 | − | 0.198899i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.286590 | 0.0112670 | 0.00563350 | − | 0.999984i | \(-0.498207\pi\) | ||||
0.00563350 | + | 0.999984i | \(0.498207\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.1421 | −0.986914 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.2554 | − | 27.3508i | −0.754679 | − | 1.07196i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.82970 | − | 2.48581i | −0.267267 | − | 0.0972771i | 0.204911 | − | 0.978781i | \(-0.434310\pi\) |
−0.472177 | + | 0.881504i | \(0.656532\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.47061 | + | 31.0254i | −0.213755 | + | 1.21226i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17.2018 | − | 20.2892i | −0.671106 | − | 0.791555i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3014 | + | 3.74940i | −0.401285 | + | 0.146056i | −0.534775 | − | 0.844994i | \(-0.679604\pi\) |
0.133490 | + | 0.991050i | \(0.457381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.9108 | + | 10.8334i | −0.502171 | + | 0.421372i | −0.858364 | − | 0.513041i | \(-0.828519\pi\) |
0.356193 | + | 0.934412i | \(0.384075\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.76245 | − | 6.51106i | −0.0684479 | − | 0.252869i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.8946 | + | 39.6545i | 0.887813 | + | 1.53774i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.5946 | − | 33.9388i | 0.758705 | − | 1.31412i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.0951 | − | 11.7801i | 0.970233 | − | 0.455444i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.38338 | − | 19.1881i | −0.130614 | − | 0.740749i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.7906 | − | 24.9973i | −1.14834 | − | 0.963574i | −0.148663 | − | 0.988888i | \(-0.547497\pi\) |
−0.999680 | + | 0.0253140i | \(0.991941\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.17217 | + | 1.44975i | 0.122097 | + | 0.0558010i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.3174 | + | 8.65735i | 0.396531 | + | 0.332729i | 0.819151 | − | 0.573578i | \(-0.194445\pi\) |
−0.422620 | + | 0.906307i | \(0.638889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.349095 | − | 1.97982i | −0.0133971 | − | 0.0759785i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.98414 | − | 4.16743i | −0.229313 | − | 0.159696i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.8061 | + | 23.9128i | −0.528275 | + | 0.914998i | 0.471182 | + | 0.882036i | \(0.343827\pi\) |
−0.999457 | + | 0.0329623i | \(0.989506\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.7213 | + | 34.1583i | 0.753512 | + | 1.30512i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.9550 | − | 6.35327i | −0.913941 | − | 0.242392i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.4321 | + | 34.7656i | −1.57844 | + | 1.32446i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.5307 | − | 7.10858i | 0.742982 | − | 0.270423i | 0.0573322 | − | 0.998355i | \(-0.481741\pi\) |
0.685649 | + | 0.727932i | \(0.259518\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 31.2430 | + | 5.34475i | 1.18682 | + | 0.203030i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.13691 | + | 23.4616i | −0.156922 | + | 0.889948i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.213905 | − | 0.0778551i | −0.00810223 | − | 0.00294897i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.13065 | + | 11.0764i | −0.194059 | + | 0.418948i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.227676 | 0.00859920 | 0.00429960 | − | 0.999991i | \(-0.498631\pi\) | ||||
0.00429960 | + | 0.999991i | \(0.498631\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.2155 | 1.44133 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.3903 | + | 1.65624i | −0.692621 | + | 0.0623774i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 54.1828 | + | 19.7209i | 2.03775 | + | 0.741681i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.26873 | − | 18.5379i | 0.122760 | − | 0.696205i | −0.859854 | − | 0.510541i | \(-0.829445\pi\) |
0.982613 | − | 0.185664i | \(-0.0594436\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.3248 | + | 8.95234i | −0.574725 | + | 0.335739i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.2514 | + | 11.0106i | −1.13292 | + | 0.412350i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.6209 | + | 18.9812i | −0.845972 | + | 0.709855i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.3346 | + | 15.4130i | −0.572680 | + | 0.575610i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.87179 | − | 8.43819i | −0.181687 | − | 0.314692i | 0.760768 | − | 0.649024i | \(-0.224823\pi\) |
−0.942455 | + | 0.334332i | \(0.891489\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.97546 | + | 10.3498i | −0.222538 | + | 0.385447i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.28060 | + | 50.4084i | −0.159197 | + | 1.87471i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.643358 | − | 3.64866i | −0.0238937 | − | 0.135508i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.6693 | − | 15.6654i | −0.692405 | − | 0.580997i | 0.227197 | − | 0.973849i | \(-0.427044\pi\) |
−0.919602 | + | 0.392852i | \(0.871488\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.1733 | − | 13.8563i | 0.858270 | − | 0.513198i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.893911 | − | 0.750080i | −0.0330625 | − | 0.0277427i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.27026 | − | 12.8753i | −0.0838541 | − | 0.475560i | −0.997598 | − | 0.0692695i | \(-0.977933\pi\) |
0.913744 | − | 0.406291i | \(-0.133178\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.39661 | − | 39.9985i | 0.125286 | − | 1.47537i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.07825 | − | 8.79579i | 0.187060 | − | 0.323997i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.9397 | + | 31.0725i | 0.659922 | + | 1.14302i | 0.980635 | + | 0.195842i | \(0.0627441\pi\) |
−0.320713 | + | 0.947176i | \(0.603923\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.1153 | − | 36.3001i | 1.32673 | − | 1.33352i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.7781 | − | 33.3778i | 1.45932 | − | 1.22451i | 0.533910 | − | 0.845541i | \(-0.320722\pi\) |
0.925408 | − | 0.378972i | \(-0.123722\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.0820 | + | 6.94527i | −0.699110 | + | 0.254455i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.3658 | − | 13.6497i | 0.854909 | − | 0.499416i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.8283 | − | 72.7527i | 0.468734 | − | 2.65832i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.08467 | − | 1.12273i | −0.112561 | − | 0.0409690i | 0.285125 | − | 0.958490i | \(-0.407965\pi\) |
−0.397687 | + | 0.917521i | \(0.630187\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.4544 | + | 1.03158i | −0.417422 | + | 0.0375930i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.0851 | −0.694579 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.70968 | −0.134831 | −0.0674153 | − | 0.997725i | \(-0.521475\pi\) | ||||
−0.0674153 | + | 0.997725i | \(0.521475\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.8220 | − | 27.6811i | 0.465410 | − | 1.00476i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.5395 | − | 7.47578i | −0.744557 | − | 0.270997i | −0.0582436 | − | 0.998302i | \(-0.518550\pi\) |
−0.686314 | + | 0.727306i | \(0.740772\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.50053 | − | 42.5376i | 0.271537 | − | 1.53996i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.18791 | − | 0.716428i | −0.151414 | − | 0.0259025i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 54.4870 | − | 19.8316i | 1.96741 | − | 0.716079i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.44362 | + | 2.05044i | −0.0881193 | + | 0.0739409i | −0.685783 | − | 0.727806i | \(-0.740540\pi\) |
0.597664 | + | 0.801747i | \(0.296096\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.1221 | + | 9.31496i | 1.26489 | + | 0.335470i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.7097 | + | 39.3344i | 0.816812 | + | 1.41476i | 0.908020 | + | 0.418927i | \(0.137594\pi\) |
−0.0912081 | + | 0.995832i | \(0.529073\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.52176 | + | 2.63576i | −0.0546632 | + | 0.0946794i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −44.7694 | − | 31.1780i | −1.60609 | − | 1.11850i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.300066 | − | 1.70176i | −0.0107510 | − | 0.0609718i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5311 | + | 8.83667i | 0.376833 | + | 0.316201i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26.0862 | − | 11.9220i | −0.932243 | − | 0.426056i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.797255 | − | 0.668976i | −0.0284552 | − | 0.0238768i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.633058 | + | 3.59025i | 0.0225661 | + | 0.127979i | 0.994010 | − | 0.109292i | \(-0.0348583\pi\) |
−0.971444 | + | 0.237271i | \(0.923747\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.76716 | + | 1.29895i | −0.0985135 | + | 0.0462439i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.8105 | − | 36.0449i | 0.739938 | − | 1.28161i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.4676 | + | 38.9150i | 0.797846 | + | 1.38191i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.90118 | + | 32.8838i | 0.315692 | + | 1.16627i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.2489 | + | 18.6691i | −0.788097 | + | 0.661292i | −0.945274 | − | 0.326279i | \(-0.894205\pi\) |
0.157177 | + | 0.987571i | \(0.449761\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.27751 | + | 1.19292i | −0.115950 | + | 0.0422023i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.81636 | + | 4.50132i | 0.134845 | + | 0.159046i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.81954 | + | 21.6617i | −0.134789 | + | 0.764425i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −59.1191 | − | 21.5176i | −2.08367 | − | 0.758395i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.7486 | + | 35.1534i | 0.871192 | + | 1.23746i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.22527 | 0.0782362 | 0.0391181 | − | 0.999235i | \(-0.487545\pi\) | ||||
0.0391181 | + | 0.999235i | \(0.487545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.6813 | −0.550647 | −0.275323 | − | 0.961352i | \(-0.588785\pi\) | ||||
−0.275323 | + | 0.961352i | \(0.588785\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.9222 | − | 19.7753i | −0.488272 | − | 0.693552i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.1529 | − | 5.51522i | −0.530784 | − | 0.193190i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.53823 | − | 8.72374i | 0.0538159 | − | 0.305205i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −71.9244 | + | 13.0610i | −2.51324 | + | 0.456387i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.22581 | − | 0.810127i | 0.0776812 | − | 0.0282736i | −0.302887 | − | 0.953026i | \(-0.597951\pi\) |
0.380568 | + | 0.924753i | \(0.375728\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.5031 | + | 34.8252i | −1.44671 | + | 1.21393i | −0.511767 | + | 0.859124i | \(0.671009\pi\) |
−0.934940 | + | 0.354807i | \(0.884547\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.753562 | − | 2.78390i | −0.0262356 | − | 0.0969230i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.1687 | − | 28.0050i | −0.562241 | − | 0.973829i | −0.997301 | − | 0.0734277i | \(-0.976606\pi\) |
0.435060 | − | 0.900401i | \(-0.356727\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0283 | − | 22.5658i | 0.452493 | − | 0.783741i | −0.546047 | − | 0.837754i | \(-0.683868\pi\) |
0.998540 | + | 0.0540134i | \(0.0172014\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.4355 | + | 11.4705i | −0.847658 | + | 0.397906i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.31670 | − | 7.46740i | −0.0456211 | − | 0.258730i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37.1802 | − | 31.1979i | −1.28667 | − | 1.07965i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.1204 | + | 21.2767i | 0.349814 | + | 0.735429i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.6070 | − | 22.3259i | −0.918576 | − | 0.770777i | 0.0551551 | − | 0.998478i | \(-0.482435\pi\) |
−0.973731 | + | 0.227701i | \(0.926879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.254819 | + | 1.44515i | 0.00878686 | + | 0.0498328i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.6851 | + | 19.9766i | 0.987966 | + | 0.688032i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.5273 | − | 35.5544i | 0.706161 | − | 1.22311i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.3193 | + | 17.8736i | 0.354577 | + | 0.614145i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.9540 | + | 6.88342i | 0.890738 | + | 0.236238i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40.2229 | + | 33.7510i | −1.37882 | + | 1.15697i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.4815 | + | 5.99877i | −0.564315 | + | 0.205394i | −0.608396 | − | 0.793634i | \(-0.708187\pi\) |
0.0440801 | + | 0.999028i | \(0.485964\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.1857 | − | 30.2514i | −0.382544 | − | 1.03458i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.0600734 | − | 0.340693i | 0.00205207 | − | 0.0116379i | −0.983765 | − | 0.179464i | \(-0.942564\pi\) |
0.985817 | + | 0.167826i | \(0.0536747\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.3253 | − | 14.3132i | −1.34176 | − | 0.488361i | −0.431394 | − | 0.902163i | \(-0.641978\pi\) |
−0.910367 | + | 0.413802i | \(0.864200\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.03685 | + | 2.23841i | −0.0353356 | + | 0.0762849i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.65260 | 0.0562552 | 0.0281276 | − | 0.999604i | \(-0.491046\pi\) | ||||
0.0281276 | + | 0.999604i | \(0.491046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.7282 | −0.432771 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.5269 | − | 2.56913i | 0.968823 | − | 0.0872522i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.7911 | + | 5.01955i | 0.467831 | + | 0.170277i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.06743 | + | 23.0675i | −0.137819 | + | 0.781613i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.00722548 | + | 1.41605i | 0.000244545 | + | 0.0479260i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −47.2233 | + | 17.1879i | −1.59644 | + | 0.581056i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.57937 | − | 3.84255i | 0.154634 | − | 0.129754i | −0.562188 | − | 0.827009i | \(-0.690040\pi\) |
0.716822 | + | 0.697256i | \(0.245596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.6903 | + | 26.8268i | −0.900241 | + | 0.904846i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.0661 | − | 20.8992i | −0.406519 | − | 0.704111i | 0.587978 | − | 0.808877i | \(-0.299924\pi\) |
−0.994497 | + | 0.104765i | \(0.966591\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.53478 | + | 2.65832i | −0.0516495 | + | 0.0894595i | −0.890694 | − | 0.454603i | \(-0.849781\pi\) |
0.839045 | + | 0.544062i | \(0.183115\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.09032 | − | 36.3916i | 0.103880 | − | 1.22329i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.67707 | + | 20.8537i | 0.123464 | + | 0.700198i | 0.982208 | + | 0.187794i | \(0.0601338\pi\) |
−0.858745 | + | 0.512404i | \(0.828755\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.9537 | − | 28.4906i | −1.13877 | − | 0.955543i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.0571 | − | 7.42171i | −0.705441 | − | 0.248637i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.2826 | − | 17.0191i | −0.678730 | − | 0.569522i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.08046 | + | 11.7989i | 0.0695420 | + | 0.394392i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.95305 | + | 70.1031i | −0.198766 | + | 2.34067i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.5141 | − | 21.6751i | 0.417368 | − | 0.722903i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.21752 | + | 5.57290i | 0.107191 | + | 0.185660i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.91926 | + | 8.96489i | −0.296814 | + | 0.298333i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.9046 | − | 18.3801i | 0.728133 | − | 0.610976i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.6493 | − | 15.8870i | 1.44935 | − | 0.527521i | 0.506941 | − | 0.861981i | \(-0.330776\pi\) |
0.942410 | + | 0.334460i | \(0.108554\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −35.2767 | − | 20.1277i | −1.17005 | − | 0.667594i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.44322 | + | 25.1988i | −0.147210 | + | 0.834872i | 0.818355 | + | 0.574713i | \(0.194886\pi\) |
−0.965566 | + | 0.260159i | \(0.916225\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.0274 | − | 7.65333i | −0.695904 | − | 0.253288i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 28.1894 | − | 2.53874i | 0.931914 | − | 0.0839282i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 64.4903 | 2.12966 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.2063 | −0.765505 | −0.382752 | − | 0.923851i | \(-0.625024\pi\) | ||||
−0.382752 | + | 0.923851i | \(0.625024\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.1186 | − | 39.1156i | 0.597027 | − | 1.28890i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.7928 | − | 10.8437i | −0.980644 | − | 0.356925i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.861997 | + | 4.88863i | −0.0283423 | + | 0.160737i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.37805 | − | 6.47613i | 0.176638 | − | 0.212704i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.37628 | − | 1.95680i | 0.176390 | − | 0.0642007i | −0.252315 | − | 0.967645i | \(-0.581192\pi\) |
0.428705 | + | 0.903444i | \(0.358970\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 44.0943 | − | 36.9995i | 1.44513 | − | 1.21261i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.71328 | + | 0.984823i | 0.121567 | + | 0.0322417i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.75668 | + | 3.04267i | 0.0574497 | + | 0.0995058i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.6584 | + | 21.9249i | −0.413531 | + | 0.716256i | −0.995273 | − | 0.0971171i | \(-0.969038\pi\) |
0.581742 | + | 0.813373i | \(0.302371\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.1109 | − | 13.3091i | −0.623661 | − | 0.434325i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.64780 | + | 9.34516i | 0.0537169 | + | 0.304644i | 0.999815 | − | 0.0192367i | \(-0.00612361\pi\) |
−0.946098 | + | 0.323880i | \(0.895012\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.81878 | + | 1.52614i | 0.0592276 | + | 0.0496979i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.5764 | + | 44.5653i | −0.376580 | + | 1.44971i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.8676 | + | 30.9356i | 1.19804 | + | 1.00527i | 0.999684 | + | 0.0251400i | \(0.00800316\pi\) |
0.198351 | + | 0.980131i | \(0.436441\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.80880 | − | 49.9572i | −0.285946 | − | 1.62168i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.0639 | − | 20.2149i | 1.39644 | − | 0.655514i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.0133 | − | 19.0757i | 0.356757 | − | 0.617922i | −0.630660 | − | 0.776059i | \(-0.717216\pi\) |
0.987417 | + | 0.158138i | \(0.0505490\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.10029 | − | 14.0301i | −0.262119 | − | 0.454004i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.19687 | + | 22.8933i | 0.200316 | + | 0.740034i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 61.8511 | − | 51.8992i | 1.99728 | − | 1.67591i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.81040 | − | 3.57069i | 0.316464 | − | 0.115184i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.5478 | + | 48.9884i | −0.565469 | + | 1.57863i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.487612 | + | 2.76539i | −0.0156968 | + | 0.0890209i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.8898 | − | 11.6069i | −1.02551 | − | 0.373254i | −0.226138 | − | 0.974095i | \(-0.572610\pi\) |
−0.799368 | + | 0.600841i | \(0.794832\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.50716 | − | 4.98164i | −0.112666 | − | 0.160033i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.1756 | 1.16093 | 0.580465 | − | 0.814286i | \(-0.302871\pi\) | ||||
0.580465 | + | 0.814286i | \(0.302871\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.7679 | 1.56343 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.82898 | + | 5.43876i | 0.122625 | + | 0.174180i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53.2406 | − | 19.3780i | −1.70332 | − | 0.619956i | −0.707120 | − | 0.707094i | \(-0.750006\pi\) |
−0.996196 | + | 0.0871372i | \(0.972228\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.847398 | − | 4.80584i | 0.0270830 | − | 0.153595i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.2600 | + | 28.6430i | −0.327576 | + | 0.914499i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.5948 | − | 13.6834i | 1.19909 | − | 0.436432i | 0.336181 | − | 0.941797i | \(-0.390865\pi\) |
0.862905 | + | 0.505366i | \(0.168642\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.4143 | − | 12.0950i | 0.459277 | − | 0.385379i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.87604 | + | 36.4853i | 0.314358 | + | 1.16134i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.08557 | + | 10.5405i | 0.193510 | + | 0.335169i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.34039 | − | 4.05368i | 0.0743450 | − | 0.128769i | −0.826456 | − | 0.563001i | \(-0.809647\pi\) |
0.900801 | + | 0.434232i | \(0.142980\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −37.2785 | + | 17.4992i | −1.18300 | + | 0.555320i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.02976 | + | 11.5114i | 0.0643478 | + | 0.364935i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.0879 | − | 15.1775i | −0.572849 | − | 0.480677i | 0.309741 | − | 0.950821i | \(-0.399758\pi\) |
−0.882590 | + | 0.470144i | \(0.844202\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 27.3802 | + | 26.9643i | 0.866272 | + | 0.853112i |
(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 | 216.2.q.b.97.3 | yes | 30 | |
3.2 | odd | 2 | 648.2.q.b.289.2 | 30 | |||
4.3 | odd | 2 | 432.2.u.f.97.3 | 30 | |||
27.5 | odd | 18 | 648.2.q.b.361.2 | 30 | |||
27.7 | even | 9 | 5832.2.a.k.1.4 | 15 | |||
27.20 | odd | 18 | 5832.2.a.l.1.12 | 15 | |||
27.22 | even | 9 | inner | 216.2.q.b.49.3 | ✓ | 30 | |
108.103 | odd | 18 | 432.2.u.f.49.3 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.q.b.49.3 | ✓ | 30 | 27.22 | even | 9 | inner | |
216.2.q.b.97.3 | yes | 30 | 1.1 | even | 1 | trivial | |
432.2.u.f.49.3 | 30 | 108.103 | odd | 18 | |||
432.2.u.f.97.3 | 30 | 4.3 | odd | 2 | |||
648.2.q.b.289.2 | 30 | 3.2 | odd | 2 | |||
648.2.q.b.361.2 | 30 | 27.5 | odd | 18 | |||
5832.2.a.k.1.4 | 15 | 27.7 | even | 9 | |||
5832.2.a.l.1.12 | 15 | 27.20 | odd | 18 |