Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,27,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 27, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 27);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 27 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\), degree \(1\), 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: | \(12.8487876219\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 2728193x^{6} + 2071419806976x^{4} + 503906274711956480x^{2} + 26754716118873014272000 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{33}\cdot 3^{38}\cdot 5^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.4 | ||
Root | \(-269.997i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.27.b.a.2.5 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3239.96i | − | 0.395503i | −0.980252 | − | 0.197752i | \(-0.936636\pi\) | ||
0.980252 | − | 0.197752i | \(-0.0633640\pi\) | |||||||
\(3\) | −1.06686e6 | − | 1.18477e6i | −0.669162 | − | 0.743117i | ||||
\(4\) | 5.66115e7 | 0.843577 | ||||||||
\(5\) | 1.50979e9i | 1.23682i | 0.785857 | + | 0.618409i | \(0.212222\pi\) | ||||
−0.785857 | + | 0.618409i | \(0.787778\pi\) | |||||||
\(6\) | −3.83861e9 | + | 3.45659e9i | −0.293905 | + | 0.264656i | ||||
\(7\) | 7.23448e10 | 0.746677 | 0.373338 | − | 0.927695i | \(-0.378213\pi\) | ||||
0.373338 | + | 0.927695i | \(0.378213\pi\) | |||||||
\(8\) | − | 4.00850e11i | − | 0.729141i | ||||||
\(9\) | −2.65486e11 | + | 2.52796e12i | −0.104445 | + | 0.994531i | ||||
\(10\) | 4.89166e12 | 0.489166 | ||||||||
\(11\) | − | 2.86233e13i | − | 0.829116i | −0.910023 | − | 0.414558i | \(-0.863936\pi\) | ||
0.910023 | − | 0.414558i | \(-0.136064\pi\) | |||||||
\(12\) | −6.03965e13 | − | 6.70715e13i | −0.564489 | − | 0.626876i | ||||
\(13\) | 4.12039e14 | 1.36043 | 0.680213 | − | 0.733015i | \(-0.261887\pi\) | ||||
0.680213 | + | 0.733015i | \(0.261887\pi\) | |||||||
\(14\) | − | 2.34394e14i | − | 0.295313i | ||||||
\(15\) | 1.78875e15 | − | 1.61073e15i | 0.919100 | − | 0.827631i | ||||
\(16\) | 2.50039e15 | 0.555199 | ||||||||
\(17\) | − | 1.55296e16i | − | 1.56792i | −0.620811 | − | 0.783960i | \(-0.713196\pi\) | ||
0.620811 | − | 0.783960i | \(-0.286804\pi\) | |||||||
\(18\) | 8.19051e15 | + | 8.60165e14i | 0.393340 | + | 0.0413085i | ||||
\(19\) | 2.79629e15 | 0.0664944 | 0.0332472 | − | 0.999447i | \(-0.489415\pi\) | ||||
0.0332472 | + | 0.999447i | \(0.489415\pi\) | |||||||
\(20\) | 8.54713e16i | 1.04335i | ||||||||
\(21\) | −7.71817e16 | − | 8.57118e16i | −0.499647 | − | 0.554868i | ||||
\(22\) | −9.27386e16 | −0.327918 | ||||||||
\(23\) | 6.09267e17i | 1.20878i | 0.796690 | + | 0.604388i | \(0.206582\pi\) | ||||
−0.796690 | + | 0.604388i | \(0.793418\pi\) | |||||||
\(24\) | −4.74914e17 | + | 4.27650e17i | −0.541837 | + | 0.487913i | ||||
\(25\) | −7.89340e17 | −0.529717 | ||||||||
\(26\) | − | 1.33499e18i | − | 0.538053i | ||||||
\(27\) | 3.27829e18 | − | 2.38244e18i | 0.808943 | − | 0.587887i | ||||
\(28\) | 4.09554e18 | 0.629879 | ||||||||
\(29\) | 1.18881e18i | 0.115861i | 0.998321 | + | 0.0579307i | \(0.0184502\pi\) | ||||
−0.998321 | + | 0.0579307i | \(0.981550\pi\) | |||||||
\(30\) | −5.21871e18 | − | 5.79548e18i | −0.327331 | − | 0.363507i | ||||
\(31\) | 2.23543e19 | 0.915502 | 0.457751 | − | 0.889080i | \(-0.348655\pi\) | ||||
0.457751 | + | 0.889080i | \(0.348655\pi\) | |||||||
\(32\) | − | 3.50017e19i | − | 0.948724i | ||||||
\(33\) | −3.39120e19 | + | 3.05371e19i | −0.616130 | + | 0.554813i | ||||
\(34\) | −5.03153e19 | −0.620118 | ||||||||
\(35\) | 1.09225e20i | 0.923503i | ||||||||
\(36\) | −1.50296e19 | + | 1.43112e20i | −0.0881076 | + | 0.838963i | ||||
\(37\) | 4.09546e19 | 0.168144 | 0.0840718 | − | 0.996460i | \(-0.473207\pi\) | ||||
0.0840718 | + | 0.996460i | \(0.473207\pi\) | |||||||
\(38\) | − | 9.05987e18i | − | 0.0262988i | ||||||
\(39\) | −4.39588e20 | − | 4.88171e20i | −0.910345 | − | 1.01096i | ||||
\(40\) | 6.05197e20 | 0.901814 | ||||||||
\(41\) | − | 2.65906e20i | − | 0.287434i | −0.989619 | − | 0.143717i | \(-0.954094\pi\) | ||
0.989619 | − | 0.143717i | \(-0.0459055\pi\) | |||||||
\(42\) | −2.77703e20 | + | 2.50066e20i | −0.219452 | + | 0.197612i | ||||
\(43\) | 2.85094e21 | 1.65920 | 0.829598 | − | 0.558361i | \(-0.188570\pi\) | ||||
0.829598 | + | 0.558361i | \(0.188570\pi\) | |||||||
\(44\) | − | 1.62041e21i | − | 0.699423i | ||||||
\(45\) | −3.81669e21 | − | 4.00827e20i | −1.23005 | − | 0.129180i | ||||
\(46\) | 1.97400e21 | 0.478075 | ||||||||
\(47\) | 6.83375e21i | 1.25137i | 0.780075 | + | 0.625687i | \(0.215181\pi\) | ||||
−0.780075 | + | 0.625687i | \(0.784819\pi\) | |||||||
\(48\) | −2.66757e21 | − | 2.96239e21i | −0.371518 | − | 0.412578i | ||||
\(49\) | −4.15372e21 | −0.442474 | ||||||||
\(50\) | 2.55743e21i | 0.209505i | ||||||||
\(51\) | −1.83990e22 | + | 1.65679e22i | −1.16515 | + | 1.04919i | ||||
\(52\) | 2.33261e22 | 1.14762 | ||||||||
\(53\) | − | 2.17521e22i | − | 0.835441i | −0.908576 | − | 0.417720i | \(-0.862829\pi\) | ||
0.908576 | − | 0.417720i | \(-0.137171\pi\) | |||||||
\(54\) | −7.71903e21 | − | 1.06215e22i | −0.232511 | − | 0.319940i | ||||
\(55\) | 4.32151e22 | 1.02547 | ||||||||
\(56\) | − | 2.89994e22i | − | 0.544433i | ||||||
\(57\) | −2.98325e21 | − | 3.31295e21i | −0.0444955 | − | 0.0494131i | ||||
\(58\) | 3.85171e21 | 0.0458236 | ||||||||
\(59\) | 6.38240e22i | 0.608006i | 0.952671 | + | 0.304003i | \(0.0983233\pi\) | ||||
−0.952671 | + | 0.304003i | \(0.901677\pi\) | |||||||
\(60\) | 1.01264e23 | − | 9.11859e22i | 0.775331 | − | 0.698170i | ||||
\(61\) | −2.23066e23 | −1.37767 | −0.688837 | − | 0.724916i | \(-0.741878\pi\) | ||||
−0.688837 | + | 0.724916i | \(0.741878\pi\) | |||||||
\(62\) | − | 7.24272e22i | − | 0.362084i | ||||||
\(63\) | −1.92065e22 | + | 1.82885e23i | −0.0779869 | + | 0.742593i | ||||
\(64\) | 5.43943e22 | 0.179975 | ||||||||
\(65\) | 6.22091e23i | 1.68260i | ||||||||
\(66\) | 9.89391e22 | + | 1.09874e23i | 0.219430 | + | 0.243682i | ||||
\(67\) | −7.65550e23 | −1.39637 | −0.698186 | − | 0.715917i | \(-0.746009\pi\) | ||||
−0.698186 | + | 0.715917i | \(0.746009\pi\) | |||||||
\(68\) | − | 8.79154e23i | − | 1.32266i | ||||||
\(69\) | 7.21840e23 | − | 6.50003e23i | 0.898262 | − | 0.808867i | ||||
\(70\) | 3.53886e23 | 0.365248 | ||||||||
\(71\) | − | 4.93143e22i | − | 0.0423267i | −0.999776 | − | 0.0211633i | \(-0.993263\pi\) | ||
0.999776 | − | 0.0211633i | \(-0.00673700\pi\) | |||||||
\(72\) | 1.01333e24 | + | 1.06420e23i | 0.725153 | + | 0.0761553i | ||||
\(73\) | −7.06916e23 | −0.422835 | −0.211417 | − | 0.977396i | \(-0.567808\pi\) | ||||
−0.211417 | + | 0.977396i | \(0.567808\pi\) | |||||||
\(74\) | − | 1.32691e23i | − | 0.0665014i | ||||||
\(75\) | 8.42115e23 | + | 9.35185e23i | 0.354466 | + | 0.393642i | ||||
\(76\) | 1.58302e23 | 0.0560931 | ||||||||
\(77\) | − | 2.07075e24i | − | 0.619082i | ||||||
\(78\) | −1.58166e24 | + | 1.42425e24i | −0.399836 | + | 0.360044i | ||||
\(79\) | −1.47639e24 | −0.316263 | −0.158132 | − | 0.987418i | \(-0.550547\pi\) | ||||
−0.158132 | + | 0.987418i | \(0.550547\pi\) | |||||||
\(80\) | 3.77506e24i | 0.686680i | ||||||||
\(81\) | −6.32012e24 | − | 1.34228e24i | −0.978182 | − | 0.207748i | ||||
\(82\) | −8.61527e23 | −0.113681 | ||||||||
\(83\) | 1.16553e25i | 1.31374i | 0.754006 | + | 0.656868i | \(0.228119\pi\) | ||||
−0.754006 | + | 0.656868i | \(0.771881\pi\) | |||||||
\(84\) | −4.36937e24 | − | 4.85227e24i | −0.421491 | − | 0.468074i | ||||
\(85\) | 2.34464e25 | 1.93923 | ||||||||
\(86\) | − | 9.23693e24i | − | 0.656218i | ||||||
\(87\) | 1.40847e24 | − | 1.26829e24i | 0.0860986 | − | 0.0775300i | ||||
\(88\) | −1.14737e25 | −0.604543 | ||||||||
\(89\) | − | 3.65050e25i | − | 1.66067i | −0.557266 | − | 0.830334i | \(-0.688150\pi\) | ||
0.557266 | − | 0.830334i | \(-0.311850\pi\) | |||||||
\(90\) | −1.29867e24 | + | 1.23659e25i | −0.0510910 | + | 0.486490i | ||||
\(91\) | 2.98089e25 | 1.01580 | ||||||||
\(92\) | 3.44915e25i | 1.01970i | ||||||||
\(93\) | −2.38489e25 | − | 2.64847e25i | −0.612619 | − | 0.680325i | ||||
\(94\) | 2.21411e25 | 0.494922 | ||||||||
\(95\) | 4.22180e24i | 0.0822414i | ||||||||
\(96\) | −4.14690e25 | + | 3.73420e25i | −0.705013 | + | 0.634850i | ||||
\(97\) | −6.39313e25 | −0.949907 | −0.474953 | − | 0.880011i | \(-0.657535\pi\) | ||||
−0.474953 | + | 0.880011i | \(0.657535\pi\) | |||||||
\(98\) | 1.34579e25i | 0.175000i | ||||||||
\(99\) | 7.23588e25 | + | 7.59909e24i | 0.824582 | + | 0.0865973i | ||||
\(100\) | −4.46857e25 | −0.446857 | ||||||||
\(101\) | 5.16061e25i | 0.453444i | 0.973960 | + | 0.226722i | \(0.0728009\pi\) | ||||
−0.973960 | + | 0.226722i | \(0.927199\pi\) | |||||||
\(102\) | 5.36794e25 | + | 5.96120e25i | 0.414959 | + | 0.460820i | ||||
\(103\) | −7.98999e25 | −0.544080 | −0.272040 | − | 0.962286i | \(-0.587698\pi\) | ||||
−0.272040 | + | 0.962286i | \(0.587698\pi\) | |||||||
\(104\) | − | 1.65166e26i | − | 0.991942i | ||||||
\(105\) | 1.29406e26 | − | 1.16528e26i | 0.686270 | − | 0.617973i | ||||
\(106\) | −7.04761e25 | −0.330420 | ||||||||
\(107\) | 4.87315e25i | 0.202218i | 0.994875 | + | 0.101109i | \(0.0322392\pi\) | ||||
−0.994875 | + | 0.101109i | \(0.967761\pi\) | |||||||
\(108\) | 1.85589e26 | − | 1.34874e26i | 0.682406 | − | 0.495928i | ||||
\(109\) | 9.21751e25 | 0.300655 | 0.150328 | − | 0.988636i | \(-0.451967\pi\) | ||||
0.150328 | + | 0.988636i | \(0.451967\pi\) | |||||||
\(110\) | − | 1.40016e26i | − | 0.405575i | ||||||
\(111\) | −4.36928e25 | − | 4.85217e25i | −0.112515 | − | 0.124950i | ||||
\(112\) | 1.80890e26 | 0.414554 | ||||||||
\(113\) | 5.50376e26i | 1.12367i | 0.827249 | + | 0.561836i | \(0.189905\pi\) | ||||
−0.827249 | + | 0.561836i | \(0.810095\pi\) | |||||||
\(114\) | −1.07338e25 | + | 9.66561e24i | −0.0195430 | + | 0.0175981i | ||||
\(115\) | −9.19864e26 | −1.49504 | ||||||||
\(116\) | 6.73004e25i | 0.0977380i | ||||||||
\(117\) | −1.09391e26 | + | 1.04162e27i | −0.142090 | + | 1.35298i | ||||
\(118\) | 2.06788e26 | 0.240469 | ||||||||
\(119\) | − | 1.12348e27i | − | 1.17073i | ||||||
\(120\) | −6.45661e26 | − | 7.17019e26i | −0.603460 | − | 0.670153i | ||||
\(121\) | 3.72522e26 | 0.312566 | ||||||||
\(122\) | 7.22727e26i | 0.544875i | ||||||||
\(123\) | −3.15037e26 | + | 2.83685e26i | −0.213597 | + | 0.192340i | ||||
\(124\) | 1.26551e27 | 0.772296 | ||||||||
\(125\) | 1.05802e27i | 0.581654i | ||||||||
\(126\) | 5.92541e26 | + | 6.22284e25i | 0.293698 | + | 0.0308441i | ||||
\(127\) | 2.20531e27 | 0.986326 | 0.493163 | − | 0.869937i | \(-0.335841\pi\) | ||||
0.493163 | + | 0.869937i | \(0.335841\pi\) | |||||||
\(128\) | − | 2.52516e27i | − | 1.01991i | ||||||
\(129\) | −3.04155e27 | − | 3.37770e27i | −1.11027 | − | 1.23298i | ||||
\(130\) | 2.01555e27 | 0.665473 | ||||||||
\(131\) | − | 1.52198e27i | − | 0.454865i | −0.973794 | − | 0.227432i | \(-0.926967\pi\) | ||
0.973794 | − | 0.227432i | \(-0.0730331\pi\) | |||||||
\(132\) | −1.91981e27 | + | 1.72875e27i | −0.519753 | + | 0.468027i | ||||
\(133\) | 2.02297e26 | 0.0496498 | ||||||||
\(134\) | 2.48035e27i | 0.552270i | ||||||||
\(135\) | 3.59698e27 | + | 4.94951e27i | 0.727108 | + | 1.00051i | ||||
\(136\) | −6.22503e27 | −1.14324 | ||||||||
\(137\) | 4.94120e27i | 0.825021i | 0.910953 | + | 0.412510i | \(0.135348\pi\) | ||||
−0.910953 | + | 0.412510i | \(0.864652\pi\) | |||||||
\(138\) | −2.10599e27 | − | 2.33874e27i | −0.319910 | − | 0.355266i | ||||
\(139\) | −4.32039e27 | −0.597490 | −0.298745 | − | 0.954333i | \(-0.596568\pi\) | ||||
−0.298745 | + | 0.954333i | \(0.596568\pi\) | |||||||
\(140\) | 6.18340e27i | 0.779046i | ||||||||
\(141\) | 8.09641e27 | − | 7.29065e27i | 0.929917 | − | 0.837371i | ||||
\(142\) | −1.59776e26 | −0.0167403 | ||||||||
\(143\) | − | 1.17939e28i | − | 1.12795i | ||||||
\(144\) | −6.63820e26 | + | 6.32091e27i | −0.0579879 | + | 0.552163i | ||||
\(145\) | −1.79485e27 | −0.143299 | ||||||||
\(146\) | 2.29038e27i | 0.167233i | ||||||||
\(147\) | 4.43143e27 | + | 4.92119e27i | 0.296087 | + | 0.328810i | ||||
\(148\) | 2.31850e27 | 0.141842 | ||||||||
\(149\) | − | 2.51496e28i | − | 1.40965i | −0.709383 | − | 0.704824i | \(-0.751026\pi\) | ||
0.709383 | − | 0.704824i | \(-0.248974\pi\) | |||||||
\(150\) | 3.02997e27 | − | 2.72842e27i | 0.155687 | − | 0.140193i | ||||
\(151\) | 2.08256e26 | 0.00981514 | 0.00490757 | − | 0.999988i | \(-0.498438\pi\) | ||||
0.00490757 | + | 0.999988i | \(0.498438\pi\) | |||||||
\(152\) | − | 1.12089e27i | − | 0.0484838i | ||||||
\(153\) | 3.92582e28 | + | 4.12289e27i | 1.55935 | + | 0.163762i | ||||
\(154\) | −6.70915e27 | −0.244849 | ||||||||
\(155\) | 3.37502e28i | 1.13231i | ||||||||
\(156\) | −2.48857e28 | − | 2.76361e28i | −0.767946 | − | 0.852818i | ||||
\(157\) | −5.10679e28 | −1.45028 | −0.725141 | − | 0.688600i | \(-0.758226\pi\) | ||||
−0.725141 | + | 0.688600i | \(0.758226\pi\) | |||||||
\(158\) | 4.78345e27i | 0.125083i | ||||||||
\(159\) | −2.57712e28 | + | 2.32065e28i | −0.620830 | + | 0.559045i | ||||
\(160\) | 5.28452e28 | 1.17340 | ||||||||
\(161\) | 4.40773e28i | 0.902565i | ||||||||
\(162\) | −4.34893e27 | + | 2.04770e28i | −0.0821651 | + | 0.386875i | ||||
\(163\) | −1.22193e28 | −0.213112 | −0.106556 | − | 0.994307i | \(-0.533982\pi\) | ||||
−0.106556 | + | 0.994307i | \(0.533982\pi\) | |||||||
\(164\) | − | 1.50534e28i | − | 0.242473i | ||||||
\(165\) | −4.61045e28 | − | 5.11999e28i | −0.686202 | − | 0.762041i | ||||
\(166\) | 3.77627e28 | 0.519587 | ||||||||
\(167\) | − | 5.19846e28i | − | 0.661547i | −0.943710 | − | 0.330774i | \(-0.892690\pi\) | ||
0.943710 | − | 0.330774i | \(-0.107310\pi\) | |||||||
\(168\) | −3.43575e28 | + | 3.09383e28i | −0.404577 | + | 0.364313i | ||||
\(169\) | 7.80428e28 | 0.850757 | ||||||||
\(170\) | − | 7.59654e28i | − | 0.766973i | ||||||
\(171\) | −7.42375e26 | + | 7.06891e27i | −0.00694502 | + | 0.0661307i | ||||
\(172\) | 1.61396e29 | 1.39966 | ||||||||
\(173\) | 6.26303e28i | 0.503716i | 0.967764 | + | 0.251858i | \(0.0810415\pi\) | ||||
−0.967764 | + | 0.251858i | \(0.918958\pi\) | |||||||
\(174\) | −4.10923e27 | − | 4.56338e27i | −0.0306634 | − | 0.0340523i | ||||
\(175\) | −5.71046e28 | −0.395527 | ||||||||
\(176\) | − | 7.15697e28i | − | 0.460325i | ||||||
\(177\) | 7.56167e28 | − | 6.80913e28i | 0.451820 | − | 0.406854i | ||||
\(178\) | −1.18275e29 | −0.656800 | ||||||||
\(179\) | 1.39021e29i | 0.717778i | 0.933380 | + | 0.358889i | \(0.116844\pi\) | ||||
−0.933380 | + | 0.358889i | \(0.883156\pi\) | |||||||
\(180\) | −2.16068e29 | − | 2.26914e28i | −1.03764 | − | 0.108973i | ||||
\(181\) | −2.06516e29 | −0.922854 | −0.461427 | − | 0.887178i | \(-0.652662\pi\) | ||||
−0.461427 | + | 0.887178i | \(0.652662\pi\) | |||||||
\(182\) | − | 9.65796e28i | − | 0.401752i | ||||||
\(183\) | 2.37981e29 | + | 2.64282e29i | 0.921887 | + | 1.02377i | ||||
\(184\) | 2.44224e29 | 0.881368 | ||||||||
\(185\) | 6.18327e28i | 0.207963i | ||||||||
\(186\) | −8.58094e28 | + | 7.72696e28i | −0.269071 | + | 0.242293i | ||||
\(187\) | −4.44509e29 | −1.29999 | ||||||||
\(188\) | 3.86869e29i | 1.05563i | ||||||||
\(189\) | 2.37167e29 | − | 1.72357e29i | 0.604019 | − | 0.438961i | ||||
\(190\) | 1.36785e28 | 0.0325268 | ||||||||
\(191\) | − | 3.87887e29i | − | 0.861533i | −0.902463 | − | 0.430766i | \(-0.858243\pi\) | ||
0.902463 | − | 0.430766i | \(-0.141757\pi\) | |||||||
\(192\) | −5.80310e28 | − | 6.44446e28i | −0.120433 | − | 0.133743i | ||||
\(193\) | 1.73735e29 | 0.337010 | 0.168505 | − | 0.985701i | \(-0.446106\pi\) | ||||
0.168505 | + | 0.985701i | \(0.446106\pi\) | |||||||
\(194\) | 2.07135e29i | 0.375691i | ||||||||
\(195\) | 7.37034e29 | − | 6.63684e29i | 1.25037 | − | 1.12593i | ||||
\(196\) | −2.35148e29 | −0.373261 | ||||||||
\(197\) | − | 7.64816e29i | − | 1.13631i | −0.822922 | − | 0.568154i | \(-0.807658\pi\) | ||
0.822922 | − | 0.568154i | \(-0.192342\pi\) | |||||||
\(198\) | 2.46208e28 | − | 2.34440e29i | 0.0342495 | − | 0.326125i | ||||
\(199\) | −5.16667e29 | −0.673164 | −0.336582 | − | 0.941654i | \(-0.609271\pi\) | ||||
−0.336582 | + | 0.941654i | \(0.609271\pi\) | |||||||
\(200\) | 3.16407e29i | 0.386238i | ||||||||
\(201\) | 8.16734e29 | + | 9.06999e29i | 0.934398 | + | 1.03767i | ||||
\(202\) | 1.67202e29 | 0.179339 | ||||||||
\(203\) | 8.60043e28i | 0.0865110i | ||||||||
\(204\) | −1.04159e30 | + | 9.37934e29i | −0.982892 | + | 0.885075i | ||||
\(205\) | 4.01462e29 | 0.355504 | ||||||||
\(206\) | 2.58873e29i | 0.215185i | ||||||||
\(207\) | −1.54021e30 | − | 1.61752e29i | −1.20217 | − | 0.126251i | ||||
\(208\) | 1.03026e30 | 0.755307 | ||||||||
\(209\) | − | 8.00391e28i | − | 0.0551316i | ||||||
\(210\) | −3.77546e29 | − | 4.19272e29i | −0.244410 | − | 0.271422i | ||||
\(211\) | −1.03117e30 | −0.627564 | −0.313782 | − | 0.949495i | \(-0.601596\pi\) | ||||
−0.313782 | + | 0.949495i | \(0.601596\pi\) | |||||||
\(212\) | − | 1.23142e30i | − | 0.704759i | ||||||
\(213\) | −5.84260e28 | + | 5.26114e28i | −0.0314537 | + | 0.0283234i | ||||
\(214\) | 1.57888e29 | 0.0799781 | ||||||||
\(215\) | 4.30431e30i | 2.05212i | ||||||||
\(216\) | −9.55001e29 | − | 1.31410e30i | −0.428652 | − | 0.589834i | ||||
\(217\) | 1.61722e30 | 0.683584 | ||||||||
\(218\) | − | 2.98644e29i | − | 0.118910i | ||||||
\(219\) | 7.54181e29 | + | 8.37532e29i | 0.282945 | + | 0.314216i | ||||
\(220\) | 2.44647e30 | 0.865059 | ||||||||
\(221\) | − | 6.39880e30i | − | 2.13304i | ||||||
\(222\) | −1.57209e29 | + | 1.41563e29i | −0.0494183 | + | 0.0445002i | ||||
\(223\) | 4.34086e29 | 0.128710 | 0.0643550 | − | 0.997927i | \(-0.479501\pi\) | ||||
0.0643550 | + | 0.997927i | \(0.479501\pi\) | |||||||
\(224\) | − | 2.53219e30i | − | 0.708390i | ||||||
\(225\) | 2.09559e29 | − | 1.99542e30i | 0.0553264 | − | 0.526820i | ||||
\(226\) | 1.78320e30 | 0.444416 | ||||||||
\(227\) | 6.97813e30i | 1.64211i | 0.570848 | + | 0.821056i | \(0.306615\pi\) | ||||
−0.570848 | + | 0.821056i | \(0.693385\pi\) | |||||||
\(228\) | −1.68886e29 | − | 1.87551e29i | −0.0375354 | − | 0.0416838i | ||||
\(229\) | −3.64200e30 | −0.764678 | −0.382339 | − | 0.924022i | \(-0.624881\pi\) | ||||
−0.382339 | + | 0.924022i | \(0.624881\pi\) | |||||||
\(230\) | 2.98033e30i | 0.591292i | ||||||||
\(231\) | −2.45336e30 | + | 2.20920e30i | −0.460050 | + | 0.414266i | ||||
\(232\) | 4.76534e29 | 0.0844793 | ||||||||
\(233\) | − | 3.66681e30i | − | 0.614698i | −0.951597 | − | 0.307349i | \(-0.900558\pi\) | ||
0.951597 | − | 0.307349i | \(-0.0994419\pi\) | |||||||
\(234\) | 3.37481e30 | + | 3.54421e29i | 0.535110 | + | 0.0561971i | ||||
\(235\) | −1.03175e31 | −1.54772 | ||||||||
\(236\) | 3.61317e30i | 0.512900i | ||||||||
\(237\) | 1.57510e30 | + | 1.74918e30i | 0.211631 | + | 0.235020i | ||||
\(238\) | −3.64005e30 | −0.463028 | ||||||||
\(239\) | 5.55263e29i | 0.0668846i | 0.999441 | + | 0.0334423i | \(0.0106470\pi\) | ||||
−0.999441 | + | 0.0334423i | \(0.989353\pi\) | |||||||
\(240\) | 4.47258e30 | − | 4.02746e30i | 0.510283 | − | 0.459500i | ||||
\(241\) | 7.73779e30 | 0.836364 | 0.418182 | − | 0.908363i | \(-0.362667\pi\) | ||||
0.418182 | + | 0.908363i | \(0.362667\pi\) | |||||||
\(242\) | − | 1.20696e30i | − | 0.123621i | ||||||
\(243\) | 5.15239e30 | + | 8.91990e30i | 0.500181 | + | 0.865921i | ||||
\(244\) | −1.26281e31 | −1.16217 | ||||||||
\(245\) | − | 6.27123e30i | − | 0.547260i | ||||||
\(246\) | 9.19129e29 | + | 1.02071e30i | 0.0760711 | + | 0.0844784i | ||||
\(247\) | 1.15218e30 | 0.0904607 | ||||||||
\(248\) | − | 8.96071e30i | − | 0.667530i | ||||||
\(249\) | 1.38088e31 | − | 1.24346e31i | 0.976259 | − | 0.879102i | ||||
\(250\) | 3.42796e30 | 0.230046 | ||||||||
\(251\) | 2.05034e30i | 0.130638i | 0.997864 | + | 0.0653188i | \(0.0208064\pi\) | ||||
−0.997864 | + | 0.0653188i | \(0.979194\pi\) | |||||||
\(252\) | −1.08731e30 | + | 1.03534e31i | −0.0657879 | + | 0.626434i | ||||
\(253\) | 1.74393e31 | 1.00222 | ||||||||
\(254\) | − | 7.14511e30i | − | 0.390095i | ||||||
\(255\) | −2.50140e31 | − | 2.77785e31i | −1.29766 | − | 1.44108i | ||||
\(256\) | −4.53110e30 | −0.223401 | ||||||||
\(257\) | 1.47948e31i | 0.693390i | 0.937978 | + | 0.346695i | \(0.112696\pi\) | ||||
−0.937978 | + | 0.346695i | \(0.887304\pi\) | |||||||
\(258\) | −1.09436e31 | + | 9.85452e30i | −0.487647 | + | 0.439116i | ||||
\(259\) | 2.96285e30 | 0.125549 | ||||||||
\(260\) | 3.52175e31i | 1.41940i | ||||||||
\(261\) | −3.00527e30 | − | 3.15613e29i | −0.115228 | − | 0.0121012i | ||||
\(262\) | −4.93116e30 | −0.179901 | ||||||||
\(263\) | − | 4.00479e30i | − | 0.139045i | −0.997580 | − | 0.0695225i | \(-0.977852\pi\) | ||
0.997580 | − | 0.0695225i | \(-0.0221476\pi\) | |||||||
\(264\) | 1.22408e31 | + | 1.35936e31i | 0.404537 | + | 0.449246i | ||||
\(265\) | 3.28411e31 | 1.03329 | ||||||||
\(266\) | − | 6.55434e29i | − | 0.0196367i | ||||||
\(267\) | −4.32500e31 | + | 3.89458e31i | −1.23407 | + | 1.11126i | ||||
\(268\) | −4.33389e31 | −1.17795 | ||||||||
\(269\) | − | 2.96267e31i | − | 0.767190i | −0.923501 | − | 0.383595i | \(-0.874686\pi\) | ||
0.923501 | − | 0.383595i | \(-0.125314\pi\) | |||||||
\(270\) | 1.60362e31 | − | 1.16541e31i | 0.395707 | − | 0.287574i | ||||
\(271\) | 1.36862e31 | 0.321871 | 0.160936 | − | 0.986965i | \(-0.448549\pi\) | ||||
0.160936 | + | 0.986965i | \(0.448549\pi\) | |||||||
\(272\) | − | 3.88301e31i | − | 0.870508i | ||||||
\(273\) | −3.18019e31 | − | 3.53166e31i | −0.679733 | − | 0.754857i | ||||
\(274\) | 1.60093e31 | 0.326298 | ||||||||
\(275\) | 2.25935e31i | 0.439197i | ||||||||
\(276\) | 4.08645e31 | − | 3.67976e31i | 0.757753 | − | 0.682341i | ||||
\(277\) | 7.51885e31 | 1.33019 | 0.665096 | − | 0.746758i | \(-0.268391\pi\) | ||||
0.665096 | + | 0.746758i | \(0.268391\pi\) | |||||||
\(278\) | 1.39979e31i | 0.236309i | ||||||||
\(279\) | −5.93475e30 | + | 5.65109e31i | −0.0956198 | + | 0.910495i | ||||
\(280\) | 4.37829e31 | 0.673364 | ||||||||
\(281\) | − | 1.65770e31i | − | 0.243402i | −0.992567 | − | 0.121701i | \(-0.961165\pi\) | ||
0.992567 | − | 0.121701i | \(-0.0388350\pi\) | |||||||
\(282\) | −2.36215e31 | − | 2.62321e31i | −0.331183 | − | 0.367785i | ||||
\(283\) | −5.53803e31 | −0.741535 | −0.370768 | − | 0.928726i | \(-0.620905\pi\) | ||||
−0.370768 | + | 0.928726i | \(0.620905\pi\) | |||||||
\(284\) | − | 2.79175e30i | − | 0.0357058i | ||||||
\(285\) | 5.00185e30 | − | 4.50407e30i | 0.0611150 | − | 0.0550328i | ||||
\(286\) | −3.82119e31 | −0.446108 | ||||||||
\(287\) | − | 1.92369e31i | − | 0.214620i | ||||||
\(288\) | 8.84831e31 | + | 9.29247e30i | 0.943535 | + | 0.0990898i | ||||
\(289\) | −1.43068e32 | −1.45838 | ||||||||
\(290\) | 5.81525e30i | 0.0566754i | ||||||||
\(291\) | 6.82057e31 | + | 7.57438e31i | 0.635641 | + | 0.705892i | ||||
\(292\) | −4.00196e31 | −0.356694 | ||||||||
\(293\) | 7.12735e31i | 0.607644i | 0.952729 | + | 0.303822i | \(0.0982628\pi\) | ||||
−0.952729 | + | 0.303822i | \(0.901737\pi\) | |||||||
\(294\) | 1.59445e31 | − | 1.43577e31i | 0.130045 | − | 0.117103i | ||||
\(295\) | −9.63607e31 | −0.751993 | ||||||||
\(296\) | − | 1.64166e31i | − | 0.122600i | ||||||
\(297\) | −6.81935e31 | − | 9.38355e31i | −0.487426 | − | 0.670708i | ||||
\(298\) | −8.14840e31 | −0.557520 | ||||||||
\(299\) | 2.51042e32i | 1.64445i | ||||||||
\(300\) | 4.76734e31 | + | 5.29422e31i | 0.299020 | + | 0.332067i | ||||
\(301\) | 2.06250e32 | 1.23888 | ||||||||
\(302\) | − | 6.74741e29i | − | 0.00388192i | ||||||
\(303\) | 6.11413e31 | − | 5.50565e31i | 0.336962 | − | 0.303427i | ||||
\(304\) | 6.99182e30 | 0.0369176 | ||||||||
\(305\) | − | 3.36783e32i | − | 1.70393i | ||||||
\(306\) | 1.33580e31 | − | 1.27195e32i | 0.0647684 | − | 0.616726i | ||||
\(307\) | 3.23426e31 | 0.150306 | 0.0751529 | − | 0.997172i | \(-0.476056\pi\) | ||||
0.0751529 | + | 0.997172i | \(0.476056\pi\) | |||||||
\(308\) | − | 1.17228e32i | − | 0.522243i | ||||||
\(309\) | 8.52420e31 | + | 9.46629e31i | 0.364077 | + | 0.404315i | ||||
\(310\) | 1.09350e32 | 0.447832 | ||||||||
\(311\) | − | 2.14585e32i | − | 0.842782i | −0.906879 | − | 0.421391i | \(-0.861542\pi\) | ||
0.906879 | − | 0.421391i | \(-0.138458\pi\) | |||||||
\(312\) | −1.95683e32 | + | 1.76209e32i | −0.737129 | + | 0.663770i | ||||
\(313\) | 1.69832e32 | 0.613680 | 0.306840 | − | 0.951761i | \(-0.400728\pi\) | ||||
0.306840 | + | 0.951761i | \(0.400728\pi\) | |||||||
\(314\) | 1.65458e32i | 0.573592i | ||||||||
\(315\) | −2.76117e32 | − | 2.89977e31i | −0.918452 | − | 0.0964555i | ||||
\(316\) | −8.35806e31 | −0.266792 | ||||||||
\(317\) | 1.88890e32i | 0.578681i | 0.957226 | + | 0.289341i | \(0.0934360\pi\) | ||||
−0.957226 | + | 0.289341i | \(0.906564\pi\) | |||||||
\(318\) | 7.51882e31 | + | 8.34979e31i | 0.221104 | + | 0.245540i | ||||
\(319\) | 3.40277e31 | 0.0960626 | ||||||||
\(320\) | 8.21237e31i | 0.222597i | ||||||||
\(321\) | 5.77356e31 | − | 5.19897e31i | 0.150272 | − | 0.135317i | ||||
\(322\) | 1.42809e32 | 0.356968 | ||||||||
\(323\) | − | 4.34252e31i | − | 0.104258i | ||||||
\(324\) | −3.57791e32 | − | 7.59883e31i | −0.825172 | − | 0.175251i | ||||
\(325\) | −3.25239e32 | −0.720641 | ||||||||
\(326\) | 3.95901e31i | 0.0842865i | ||||||||
\(327\) | −9.83379e31 | − | 1.09206e32i | −0.201187 | − | 0.223422i | ||||
\(328\) | −1.06588e32 | −0.209580 | ||||||||
\(329\) | 4.94386e32i | 0.934371i | ||||||||
\(330\) | −1.65886e32 | + | 1.49377e32i | −0.301390 | + | 0.271395i | ||||
\(331\) | 9.85527e32 | 1.72149 | 0.860745 | − | 0.509036i | \(-0.169998\pi\) | ||||
0.860745 | + | 0.509036i | \(0.169998\pi\) | |||||||
\(332\) | 6.59824e32i | 1.10824i | ||||||||
\(333\) | −1.08729e31 | + | 1.03532e32i | −0.0175618 | + | 0.167224i | ||||
\(334\) | −1.68428e32 | −0.261644 | ||||||||
\(335\) | − | 1.15582e33i | − | 1.72706i | ||||||
\(336\) | −1.92985e32 | − | 2.14313e32i | −0.277404 | − | 0.308062i | ||||
\(337\) | −6.35654e32 | −0.879087 | −0.439543 | − | 0.898221i | \(-0.644860\pi\) | ||||
−0.439543 | + | 0.898221i | \(0.644860\pi\) | |||||||
\(338\) | − | 2.52856e32i | − | 0.336478i | ||||||
\(339\) | 6.52067e32 | − | 5.87174e32i | 0.835019 | − | 0.751918i | ||||
\(340\) | 1.32733e33 | 1.63589 | ||||||||
\(341\) | − | 6.39855e32i | − | 0.759057i | ||||||
\(342\) | 2.29030e31 | + | 2.40527e30i | 0.0261549 | + | 0.00274678i | ||||
\(343\) | −9.79635e32 | −1.07706 | ||||||||
\(344\) | − | 1.14280e33i | − | 1.20979i | ||||||
\(345\) | 9.81366e32 | + | 1.08983e33i | 1.00042 | + | 1.11099i | ||||
\(346\) | 2.02920e32 | 0.199221 | ||||||||
\(347\) | 2.07743e33i | 1.96446i | 0.187676 | + | 0.982231i | \(0.439904\pi\) | ||||
−0.187676 | + | 0.982231i | \(0.560096\pi\) | |||||||
\(348\) | 7.97353e31 | − | 7.18001e31i | 0.0726308 | − | 0.0654026i | ||||
\(349\) | −1.70165e33 | −1.49327 | −0.746637 | − | 0.665232i | \(-0.768333\pi\) | ||||
−0.746637 | + | 0.665232i | \(0.768333\pi\) | |||||||
\(350\) | 1.85017e32i | 0.156432i | ||||||||
\(351\) | 1.35078e33 | − | 9.81660e32i | 1.10051 | − | 0.799776i | ||||
\(352\) | −1.00187e33 | −0.786603 | ||||||||
\(353\) | 1.98122e33i | 1.49921i | 0.661885 | + | 0.749605i | \(0.269757\pi\) | ||||
−0.661885 | + | 0.749605i | \(0.730243\pi\) | |||||||
\(354\) | −2.20613e32 | − | 2.44995e32i | −0.160912 | − | 0.178696i | ||||
\(355\) | 7.44540e31 | 0.0523503 | ||||||||
\(356\) | − | 2.06660e33i | − | 1.40090i | ||||||
\(357\) | −1.33107e33 | + | 1.19860e33i | −0.869989 | + | 0.783408i | ||||
\(358\) | 4.50422e32 | 0.283884 | ||||||||
\(359\) | − | 7.03773e32i | − | 0.427764i | −0.976859 | − | 0.213882i | \(-0.931389\pi\) | ||
0.976859 | − | 0.213882i | \(-0.0686109\pi\) | |||||||
\(360\) | −1.60671e32 | + | 1.52992e33i | −0.0941902 | + | 0.896882i | ||||
\(361\) | −1.76063e33 | −0.995578 | ||||||||
\(362\) | 6.69106e32i | 0.364992i | ||||||||
\(363\) | −3.97429e32 | − | 4.41352e32i | −0.209157 | − | 0.232273i | ||||
\(364\) | 1.68752e33 | 0.856904 | ||||||||
\(365\) | − | 1.06729e33i | − | 0.522969i | ||||||
\(366\) | 8.56264e32 | − | 7.71049e32i | 0.404906 | − | 0.364609i | ||||
\(367\) | 2.59950e32 | 0.118640 | 0.0593200 | − | 0.998239i | \(-0.481107\pi\) | ||||
0.0593200 | + | 0.998239i | \(0.481107\pi\) | |||||||
\(368\) | 1.52341e33i | 0.671112i | ||||||||
\(369\) | 6.72201e32 | + | 7.05944e31i | 0.285862 | + | 0.0300212i | ||||
\(370\) | 2.00336e32 | 0.0822500 | ||||||||
\(371\) | − | 1.57365e33i | − | 0.623804i | ||||||
\(372\) | −1.35012e33 | − | 1.49934e33i | −0.516791 | − | 0.573906i | ||||
\(373\) | 2.97352e33 | 1.09915 | 0.549573 | − | 0.835446i | \(-0.314790\pi\) | ||||
0.549573 | + | 0.835446i | \(0.314790\pi\) | |||||||
\(374\) | 1.44019e33i | 0.514150i | ||||||||
\(375\) | 1.25351e33 | − | 1.12876e33i | 0.432237 | − | 0.389221i | ||||
\(376\) | 2.73931e33 | 0.912428 | ||||||||
\(377\) | 4.89837e32i | 0.157621i | ||||||||
\(378\) | −5.58431e32 | − | 7.68412e32i | −0.173611 | − | 0.238892i | ||||
\(379\) | −2.17945e33 | −0.654692 | −0.327346 | − | 0.944905i | \(-0.606154\pi\) | ||||
−0.327346 | + | 0.944905i | \(0.606154\pi\) | |||||||
\(380\) | 2.39002e32i | 0.0693770i | ||||||||
\(381\) | −2.35275e33 | − | 2.61278e33i | −0.660011 | − | 0.732955i | ||||
\(382\) | −1.25674e33 | −0.340739 | ||||||||
\(383\) | − | 4.63588e33i | − | 1.21492i | −0.794350 | − | 0.607460i | \(-0.792188\pi\) | ||
0.794350 | − | 0.607460i | \(-0.207812\pi\) | |||||||
\(384\) | −2.99173e33 | + | 2.69400e33i | −0.757909 | + | 0.682481i | ||||
\(385\) | 3.12639e33 | 0.765691 | ||||||||
\(386\) | − | 5.62896e32i | − | 0.133289i | ||||||
\(387\) | −7.56884e32 | + | 7.20707e33i | −0.173295 | + | 1.65012i | ||||
\(388\) | −3.61925e33 | −0.801320 | ||||||||
\(389\) | 6.97643e33i | 1.49379i | 0.664944 | + | 0.746893i | \(0.268455\pi\) | ||||
−0.664944 | + | 0.746893i | \(0.731545\pi\) | |||||||
\(390\) | −2.15031e33 | − | 2.38796e33i | −0.445309 | − | 0.494524i | ||||
\(391\) | 9.46167e33 | 1.89527 | ||||||||
\(392\) | 1.66502e33i | 0.322626i | ||||||||
\(393\) | −1.80319e33 | + | 1.62374e33i | −0.338018 | + | 0.304378i | ||||
\(394\) | −2.47798e33 | −0.449414 | ||||||||
\(395\) | − | 2.22903e33i | − | 0.391160i | ||||||
\(396\) | 4.09634e33 | + | 4.30196e32i | 0.695598 | + | 0.0730515i | ||||
\(397\) | −1.07984e34 | −1.77453 | −0.887267 | − | 0.461257i | \(-0.847399\pi\) | ||||
−0.887267 | + | 0.461257i | \(0.847399\pi\) | |||||||
\(398\) | 1.67398e33i | 0.266239i | ||||||||
\(399\) | −2.15822e32 | − | 2.39675e32i | −0.0332237 | − | 0.0368956i | ||||
\(400\) | −1.97366e33 | −0.294098 | ||||||||
\(401\) | − | 8.32622e33i | − | 1.20108i | −0.799596 | − | 0.600538i | \(-0.794953\pi\) | ||
0.799596 | − | 0.600538i | \(-0.205047\pi\) | |||||||
\(402\) | 2.93864e33 | − | 2.64619e33i | 0.410401 | − | 0.369558i | ||||
\(403\) | 9.21085e33 | 1.24547 | ||||||||
\(404\) | 2.92150e33i | 0.382515i | ||||||||
\(405\) | 2.02655e33 | − | 9.54203e33i | 0.256946 | − | 1.20983i | ||||
\(406\) | 2.78651e32 | 0.0342154 | ||||||||
\(407\) | − | 1.17226e33i | − | 0.139411i | ||||||
\(408\) | 6.64124e33 | + | 7.37522e33i | 0.765009 | + | 0.849558i | ||||
\(409\) | −1.60150e33 | −0.178700 | −0.0893501 | − | 0.996000i | \(-0.528479\pi\) | ||||
−0.0893501 | + | 0.996000i | \(0.528479\pi\) | |||||||
\(410\) | − | 1.30072e33i | − | 0.140603i | ||||||
\(411\) | 5.85417e33 | − | 5.27156e33i | 0.613087 | − | 0.552072i | ||||
\(412\) | −4.52325e33 | −0.458973 | ||||||||
\(413\) | 4.61733e33i | 0.453984i | ||||||||
\(414\) | −5.24070e32 | + | 4.99021e33i | −0.0499327 | + | 0.475460i | ||||
\(415\) | −1.75970e34 | −1.62485 | ||||||||
\(416\) | − | 1.44221e34i | − | 1.29067i | ||||||
\(417\) | 4.60925e33 | + | 5.11866e33i | 0.399817 | + | 0.444005i | ||||
\(418\) | −2.59324e32 | −0.0218047 | ||||||||
\(419\) | 9.70810e33i | 0.791320i | 0.918397 | + | 0.395660i | \(0.129484\pi\) | ||||
−0.918397 | + | 0.395660i | \(0.870516\pi\) | |||||||
\(420\) | 7.32590e33 | − | 6.59682e33i | 0.578922 | − | 0.521307i | ||||
\(421\) | 2.25116e34 | 1.72480 | 0.862400 | − | 0.506227i | \(-0.168960\pi\) | ||||
0.862400 | + | 0.506227i | \(0.168960\pi\) | |||||||
\(422\) | 3.34095e33i | 0.248204i | ||||||||
\(423\) | −1.72755e34 | − | 1.81426e33i | −1.24453 | − | 0.130700i | ||||
\(424\) | −8.71933e33 | −0.609154 | ||||||||
\(425\) | 1.22581e34i | 0.830554i | ||||||||
\(426\) | 1.70459e32 | + | 1.89298e32i | 0.0112020 | + | 0.0124400i | ||||
\(427\) | −1.61377e34 | −1.02868 | ||||||||
\(428\) | 2.75876e33i | 0.170587i | ||||||||
\(429\) | −1.39731e34 | + | 1.25825e34i | −0.838199 | + | 0.754782i | ||||
\(430\) | 1.39458e34 | 0.811622 | ||||||||
\(431\) | 4.70060e33i | 0.265429i | 0.991154 | + | 0.132715i | \(0.0423694\pi\) | ||||
−0.991154 | + | 0.132715i | \(0.957631\pi\) | |||||||
\(432\) | 8.19701e33 | − | 5.95705e33i | 0.449125 | − | 0.326394i | ||||
\(433\) | −2.36737e34 | −1.25871 | −0.629353 | − | 0.777120i | \(-0.716680\pi\) | ||||
−0.629353 | + | 0.777120i | \(0.716680\pi\) | |||||||
\(434\) | − | 5.23973e33i | − | 0.270360i | ||||||
\(435\) | 1.91485e33 | + | 2.12648e33i | 0.0958905 | + | 0.106488i | ||||
\(436\) | 5.21817e33 | 0.253626 | ||||||||
\(437\) | 1.70369e33i | 0.0803768i | ||||||||
\(438\) | 2.71357e33 | − | 2.44352e33i | 0.124273 | − | 0.111906i | ||||
\(439\) | 3.98133e34 | 1.77006 | 0.885032 | − | 0.465530i | \(-0.154136\pi\) | ||||
0.885032 | + | 0.465530i | \(0.154136\pi\) | |||||||
\(440\) | − | 1.73228e34i | − | 0.747709i | ||||||
\(441\) | 1.10275e33 | − | 1.05004e34i | 0.0462143 | − | 0.440054i | ||||
\(442\) | −2.07319e34 | −0.843624 | ||||||||
\(443\) | − | 3.14794e34i | − | 1.24388i | −0.783065 | − | 0.621940i | \(-0.786345\pi\) | ||
0.783065 | − | 0.621940i | \(-0.213655\pi\) | |||||||
\(444\) | −2.47352e33 | − | 2.74689e33i | −0.0949153 | − | 0.105405i | ||||
\(445\) | 5.51148e34 | 2.05394 | ||||||||
\(446\) | − | 1.40642e33i | − | 0.0509053i | ||||||
\(447\) | −2.97965e34 | + | 2.68312e34i | −1.04753 | + | 0.943282i | ||||
\(448\) | 3.93514e33 | 0.134383 | ||||||||
\(449\) | − | 1.99275e34i | − | 0.661073i | −0.943793 | − | 0.330536i | \(-0.892770\pi\) | ||
0.943793 | − | 0.330536i | \(-0.107230\pi\) | |||||||
\(450\) | −6.46510e33 | − | 6.78962e32i | −0.208359 | − | 0.0218818i | ||||
\(451\) | −7.61113e33 | −0.238316 | ||||||||
\(452\) | 3.11576e34i | 0.947903i | ||||||||
\(453\) | −2.22180e32 | − | 2.46735e32i | −0.00656791 | − | 0.00729379i | ||||
\(454\) | 2.26089e34 | 0.649461 | ||||||||
\(455\) | 4.50050e34i | 1.25636i | ||||||||
\(456\) | −1.32800e33 | + | 1.19583e33i | −0.0360291 | + | 0.0324435i | ||||
\(457\) | 1.23188e34 | 0.324831 | 0.162415 | − | 0.986722i | \(-0.448072\pi\) | ||||
0.162415 | + | 0.986722i | \(0.448072\pi\) | |||||||
\(458\) | 1.18000e34i | 0.302433i | ||||||||
\(459\) | −3.69984e34 | − | 5.09105e34i | −0.921760 | − | 1.26836i | ||||
\(460\) | −5.20749e34 | −1.26118 | ||||||||
\(461\) | − | 3.82432e34i | − | 0.900413i | −0.892924 | − | 0.450207i | \(-0.851350\pi\) | ||
0.892924 | − | 0.450207i | \(-0.148650\pi\) | |||||||
\(462\) | 7.15772e33 | + | 7.94879e33i | 0.163844 | + | 0.181951i | ||||
\(463\) | −2.50099e34 | −0.556619 | −0.278310 | − | 0.960491i | \(-0.589774\pi\) | ||||
−0.278310 | + | 0.960491i | \(0.589774\pi\) | |||||||
\(464\) | 2.97250e33i | 0.0643262i | ||||||||
\(465\) | 3.99862e34 | − | 3.60068e34i | 0.841437 | − | 0.757697i | ||||
\(466\) | −1.18803e34 | −0.243115 | ||||||||
\(467\) | 7.58886e34i | 1.51028i | 0.655564 | + | 0.755140i | \(0.272431\pi\) | ||||
−0.655564 | + | 0.755140i | \(0.727569\pi\) | |||||||
\(468\) | −6.19276e33 | + | 5.89676e34i | −0.119864 | + | 1.14135i | ||||
\(469\) | −5.53835e34 | −1.04264 | ||||||||
\(470\) | 3.34283e34i | 0.612129i | ||||||||
\(471\) | 5.44823e34 | + | 6.05037e34i | 0.970474 | + | 1.07773i | ||||
\(472\) | 2.55838e34 | 0.443322 | ||||||||
\(473\) | − | 8.16034e34i | − | 1.37567i | ||||||
\(474\) | 5.66727e33 | − | 5.10327e33i | 0.0929514 | − | 0.0837008i | ||||
\(475\) | −2.20722e33 | −0.0352232 | ||||||||
\(476\) | − | 6.36022e34i | − | 0.987601i | ||||||
\(477\) | 5.49886e34 | + | 5.77489e33i | 0.830871 | + | 0.0872578i | ||||
\(478\) | 1.79903e33 | 0.0264531 | ||||||||
\(479\) | 1.96148e34i | 0.280686i | 0.990103 | + | 0.140343i | \(0.0448206\pi\) | ||||
−0.990103 | + | 0.140343i | \(0.955179\pi\) | |||||||
\(480\) | −5.63784e34 | − | 6.26093e34i | −0.785193 | − | 0.871972i | ||||
\(481\) | 1.68749e34 | 0.228747 | ||||||||
\(482\) | − | 2.50702e34i | − | 0.330785i | ||||||
\(483\) | 5.22214e34 | − | 4.70243e34i | 0.670711 | − | 0.603962i | ||||
\(484\) | 2.10890e34 | 0.263674 | ||||||||
\(485\) | − | 9.65226e34i | − | 1.17486i | ||||||
\(486\) | 2.89001e34 | − | 1.66936e34i | 0.342475 | − | 0.197823i | ||||
\(487\) | −6.39772e34 | −0.738157 | −0.369079 | − | 0.929398i | \(-0.620327\pi\) | ||||
−0.369079 | + | 0.929398i | \(0.620327\pi\) | |||||||
\(488\) | 8.94161e34i | 1.00452i | ||||||||
\(489\) | 1.30363e34 | + | 1.44770e34i | 0.142606 | + | 0.158367i | ||||
\(490\) | −2.03185e34 | −0.216443 | ||||||||
\(491\) | 3.95052e34i | 0.409822i | 0.978781 | + | 0.204911i | \(0.0656905\pi\) | ||||
−0.978781 | + | 0.204911i | \(0.934309\pi\) | |||||||
\(492\) | −1.78347e34 | + | 1.60598e34i | −0.180186 | + | 0.162254i | ||||
\(493\) | 1.84618e34 | 0.181662 | ||||||||
\(494\) | − | 3.73302e33i | − | 0.0357775i | ||||||
\(495\) | −1.14730e34 | + | 1.09246e35i | −0.107105 | + | 1.01986i | ||||
\(496\) | 5.58946e34 | 0.508286 | ||||||||
\(497\) | − | 3.56763e33i | − | 0.0316043i | ||||||
\(498\) | −4.02875e34 | − | 4.47401e34i | −0.347688 | − | 0.386114i | ||||
\(499\) | −6.99361e34 | −0.588023 | −0.294011 | − | 0.955802i | \(-0.594990\pi\) | ||||
−0.294011 | + | 0.955802i | \(0.594990\pi\) | |||||||
\(500\) | 5.98962e34i | 0.490670i | ||||||||
\(501\) | −6.15897e34 | + | 5.54603e34i | −0.491607 | + | 0.442682i | ||||
\(502\) | 6.64304e33 | 0.0516676 | ||||||||
\(503\) | 2.74354e34i | 0.207935i | 0.994581 | + | 0.103967i | \(0.0331538\pi\) | ||||
−0.994581 | + | 0.103967i | \(0.966846\pi\) | |||||||
\(504\) | 7.33093e34 | + | 7.69892e33i | 0.541455 | + | 0.0568634i | ||||
\(505\) | −7.79143e34 | −0.560827 | ||||||||
\(506\) | − | 5.65026e34i | − | 0.396380i | ||||||
\(507\) | −8.32607e34 | − | 9.24627e34i | −0.569294 | − | 0.632212i | ||||
\(508\) | 1.24846e35 | 0.832042 | ||||||||
\(509\) | 1.87923e35i | 1.22081i | 0.792089 | + | 0.610406i | \(0.208994\pi\) | ||||
−0.792089 | + | 0.610406i | \(0.791006\pi\) | |||||||
\(510\) | −9.00014e34 | + | 8.10445e34i | −0.569950 | + | 0.513229i | ||||
\(511\) | −5.11417e34 | −0.315721 | ||||||||
\(512\) | − | 1.54780e35i | − | 0.931550i | ||||||
\(513\) | 9.16703e33 | − | 6.66200e33i | 0.0537902 | − | 0.0390912i | ||||
\(514\) | 4.79345e34 | 0.274238 | ||||||||
\(515\) | − | 1.20632e35i | − | 0.672927i | ||||||
\(516\) | −1.72187e35 | − | 1.91217e35i | −0.936599 | − | 1.04011i | ||||
\(517\) | 1.95605e35 | 1.03753 | ||||||||
\(518\) | − | 9.59953e33i | − | 0.0496550i | ||||||
\(519\) | 7.42024e34 | − | 6.68178e34i | 0.374320 | − | 0.337067i | ||||
\(520\) | 2.49365e35 | 1.22685 | ||||||||
\(521\) | 3.32580e35i | 1.59590i | 0.602725 | + | 0.797949i | \(0.294082\pi\) | ||||
−0.602725 | + | 0.797949i | \(0.705918\pi\) | |||||||
\(522\) | −1.02257e33 | + | 9.73697e33i | −0.00478606 | + | 0.0455730i | ||||
\(523\) | 9.57976e34 | 0.437354 | 0.218677 | − | 0.975797i | \(-0.429826\pi\) | ||||
0.218677 | + | 0.975797i | \(0.429826\pi\) | |||||||
\(524\) | − | 8.61616e34i | − | 0.383713i | ||||||
\(525\) | 6.09226e34 | + | 6.76557e34i | 0.264672 | + | 0.293923i | ||||
\(526\) | −1.29754e34 | −0.0549927 | ||||||||
\(527\) | − | 3.47153e35i | − | 1.43543i | ||||||
\(528\) | −8.47935e34 | + | 7.63548e34i | −0.342075 | + | 0.308032i | ||||
\(529\) | −1.17154e35 | −0.461140 | ||||||||
\(530\) | − | 1.06404e35i | − | 0.408669i | ||||||
\(531\) | −1.61345e35 | − | 1.69444e34i | −0.604681 | − | 0.0635034i | ||||
\(532\) | 1.14523e34 | 0.0418834 | ||||||||
\(533\) | − | 1.09564e35i | − | 0.391033i | ||||||
\(534\) | 1.26183e35 | + | 1.40128e35i | 0.439505 | + | 0.488079i | ||||
\(535\) | −7.35742e34 | −0.250107 | ||||||||
\(536\) | 3.06870e35i | 1.01815i | ||||||||
\(537\) | 1.64707e35 | − | 1.48316e35i | 0.533393 | − | 0.480310i | ||||
\(538\) | −9.59893e34 | −0.303426 | ||||||||
\(539\) | 1.18893e35i | 0.366862i | ||||||||
\(540\) | 2.03631e35 | + | 2.80199e35i | 0.613372 | + | 0.844011i | ||||
\(541\) | −6.65949e35 | −1.95829 | −0.979144 | − | 0.203168i | \(-0.934876\pi\) | ||||
−0.979144 | + | 0.203168i | \(0.934876\pi\) | |||||||
\(542\) | − | 4.43428e34i | − | 0.127301i | ||||||
\(543\) | 2.20324e35 | + | 2.44674e35i | 0.617538 | + | 0.685788i | ||||
\(544\) | −5.43563e35 | −1.48752 | ||||||||
\(545\) | 1.39165e35i | 0.371856i | ||||||||
\(546\) | −1.14425e35 | + | 1.03037e35i | −0.298548 | + | 0.268837i | ||||
\(547\) | 4.84906e35 | 1.23544 | 0.617720 | − | 0.786398i | \(-0.288056\pi\) | ||||
0.617720 | + | 0.786398i | \(0.288056\pi\) | |||||||
\(548\) | 2.79729e35i | 0.695968i | ||||||||
\(549\) | 5.92210e34 | − | 5.63904e35i | 0.143892 | − | 1.37014i | ||||
\(550\) | 7.32023e34 | 0.173704 | ||||||||
\(551\) | 3.32426e33i | 0.00770413i | ||||||||
\(552\) | −2.60553e35 | − | 2.89349e35i | −0.589778 | − | 0.654960i | ||||
\(553\) | −1.06809e35 | −0.236146 | ||||||||
\(554\) | − | 2.43608e35i | − | 0.526095i | ||||||
\(555\) | 7.32574e34 | − | 6.59668e34i | 0.154541 | − | 0.139161i | ||||
\(556\) | −2.44584e35 | −0.504029 | ||||||||
\(557\) | − | 1.95574e35i | − | 0.393726i | −0.980431 | − | 0.196863i | \(-0.936925\pi\) | ||
0.980431 | − | 0.196863i | \(-0.0630754\pi\) | |||||||
\(558\) | 1.83093e35 | + | 1.92284e34i | 0.360104 | + | 0.0378180i | ||||
\(559\) | 1.17470e36 | 2.25721 | ||||||||
\(560\) | 2.73106e35i | 0.512728i | ||||||||
\(561\) | 4.74229e35 | + | 5.26640e35i | 0.869903 | + | 0.966043i | ||||
\(562\) | −5.37090e34 | −0.0962665 | ||||||||
\(563\) | − | 6.33217e35i | − | 1.10903i | −0.832173 | − | 0.554515i | \(-0.812904\pi\) | ||
0.832173 | − | 0.554515i | \(-0.187096\pi\) | |||||||
\(564\) | 4.58350e35 | − | 4.12735e35i | 0.784456 | − | 0.706387i | ||||
\(565\) | −8.30950e35 | −1.38978 | ||||||||
\(566\) | 1.79430e35i | 0.293280i | ||||||||
\(567\) | −4.57227e35 | − | 9.71067e34i | −0.730386 | − | 0.155121i | ||||
\(568\) | −1.97676e34 | −0.0308621 | ||||||||
\(569\) | 3.30032e35i | 0.503612i | 0.967778 | + | 0.251806i | \(0.0810245\pi\) | ||||
−0.967778 | + | 0.251806i | \(0.918976\pi\) | |||||||
\(570\) | −1.45930e34 | − | 1.62058e34i | −0.0217657 | − | 0.0241712i | ||||
\(571\) | −1.69115e35 | −0.246554 | −0.123277 | − | 0.992372i | \(-0.539340\pi\) | ||||
−0.123277 | + | 0.992372i | \(0.539340\pi\) | |||||||
\(572\) | − | 6.67672e35i | − | 0.951513i | ||||||
\(573\) | −4.59557e35 | + | 4.13821e35i | −0.640220 | + | 0.576505i | ||||
\(574\) | −6.23270e34 | −0.0848831 | ||||||||
\(575\) | − | 4.80919e35i | − | 0.640309i | ||||||
\(576\) | −1.44409e34 | + | 1.37507e35i | −0.0187976 | + | 0.178991i | ||||
\(577\) | 1.26120e36 | 1.60509 | 0.802544 | − | 0.596592i | \(-0.203479\pi\) | ||||
0.802544 | + | 0.596592i | \(0.203479\pi\) | |||||||
\(578\) | 4.63534e35i | 0.576793i | ||||||||
\(579\) | −1.85351e35 | − | 2.05836e35i | −0.225514 | − | 0.250438i | ||||
\(580\) | −1.01609e35 | −0.120884 | ||||||||
\(581\) | 8.43199e35i | 0.980936i | ||||||||
\(582\) | 2.45407e35 | − | 2.20984e35i | 0.279183 | − | 0.251398i | ||||
\(583\) | −6.22619e35 | −0.692677 | ||||||||
\(584\) | 2.83367e35i | 0.308306i | ||||||||
\(585\) | −1.57262e36 | − | 1.65156e35i | −1.67340 | − | 0.175739i | ||||
\(586\) | 2.30924e35 | 0.240325 | ||||||||
\(587\) | 1.21848e36i | 1.24029i | 0.784487 | + | 0.620146i | \(0.212927\pi\) | ||||
−0.784487 | + | 0.620146i | \(0.787073\pi\) | |||||||
\(588\) | 2.50870e35 | + | 2.78596e35i | 0.249772 | + | 0.277376i | ||||
\(589\) | 6.25091e34 | 0.0608757 | ||||||||
\(590\) | 3.12205e35i | 0.297416i | ||||||||
\(591\) | −9.06130e35 | + | 8.15952e35i | −0.844410 | + | 0.760374i | ||||
\(592\) | 1.02403e35 | 0.0933532 | ||||||||
\(593\) | − | 1.08175e36i | − | 0.964756i | −0.875963 | − | 0.482378i | \(-0.839773\pi\) | ||
0.875963 | − | 0.482378i | \(-0.160227\pi\) | |||||||
\(594\) | −3.04024e35 | + | 2.20944e35i | −0.265267 | + | 0.192779i | ||||
\(595\) | 1.69622e36 | 1.44798 | ||||||||
\(596\) | − | 1.42376e36i | − | 1.18915i | ||||||
\(597\) | 5.51211e35 | + | 6.12131e35i | 0.450456 | + | 0.500239i | ||||
\(598\) | 8.13367e35 | 0.650386 | ||||||||
\(599\) | − | 1.32797e36i | − | 1.03906i | −0.854454 | − | 0.519528i | \(-0.826108\pi\) | ||
0.854454 | − | 0.519528i | \(-0.173892\pi\) | |||||||
\(600\) | 3.74868e35 | − | 3.37561e35i | 0.287020 | − | 0.258456i | ||||
\(601\) | −1.28827e36 | −0.965248 | −0.482624 | − | 0.875828i | \(-0.660316\pi\) | ||||
−0.482624 | + | 0.875828i | \(0.660316\pi\) | |||||||
\(602\) | − | 6.68244e35i | − | 0.489982i | ||||||
\(603\) | 2.03243e35 | − | 1.93528e36i | 0.145844 | − | 1.38873i | ||||
\(604\) | 1.17897e34 | 0.00827982 | ||||||||
\(605\) | 5.62429e35i | 0.386587i | ||||||||
\(606\) | −1.78381e35 | − | 1.98096e35i | −0.120007 | − | 0.133270i | ||||
\(607\) | 3.53784e35 | 0.232962 | 0.116481 | − | 0.993193i | \(-0.462839\pi\) | ||||
0.116481 | + | 0.993193i | \(0.462839\pi\) | |||||||
\(608\) | − | 9.78749e34i | − | 0.0630848i | ||||||
\(609\) | 1.01895e35 | − | 9.17545e34i | 0.0642878 | − | 0.0578899i | ||||
\(610\) | −1.09116e36 | −0.673911 | ||||||||
\(611\) | 2.81577e36i | 1.70240i | ||||||||
\(612\) | 2.22247e36 | + | 2.33403e35i | 1.31543 | + | 0.138146i | ||||
\(613\) | 1.14461e36 | 0.663242 | 0.331621 | − | 0.943413i | \(-0.392405\pi\) | ||||
0.331621 | + | 0.943413i | \(0.392405\pi\) | |||||||
\(614\) | − | 1.04789e35i | − | 0.0594465i | ||||||
\(615\) | −4.28304e35 | − | 4.75639e35i | −0.237889 | − | 0.264181i | ||||
\(616\) | −8.30059e35 | −0.451398 | ||||||||
\(617\) | 3.77998e35i | 0.201271i | 0.994923 | + | 0.100636i | \(0.0320876\pi\) | ||||
−0.994923 | + | 0.100636i | \(0.967912\pi\) | |||||||
\(618\) | 3.06704e35 | − | 2.76181e35i | 0.159908 | − | 0.143994i | ||||
\(619\) | −8.13578e35 | −0.415356 | −0.207678 | − | 0.978197i | \(-0.566591\pi\) | ||||
−0.207678 | + | 0.978197i | \(0.566591\pi\) | |||||||
\(620\) | 1.91065e36i | 0.955189i | ||||||||
\(621\) | 1.45154e36 | + | 1.99735e36i | 0.710624 | + | 0.977831i | ||||
\(622\) | −6.95249e35 | −0.333323 | ||||||||
\(623\) | − | 2.64095e36i | − | 1.23998i | ||||||
\(624\) | −1.09914e36 | − | 1.22062e36i | −0.505423 | − | 0.561281i | ||||
\(625\) | −2.77360e36 | −1.24912 | ||||||||
\(626\) | − | 5.50248e35i | − | 0.242713i | ||||||
\(627\) | −9.48278e34 | + | 8.53905e34i | −0.0409692 | + | 0.0368919i | ||||
\(628\) | −2.89103e36 | −1.22343 | ||||||||
\(629\) | − | 6.36008e35i | − | 0.263636i | ||||||
\(630\) | −9.39516e34 | + | 8.94610e35i | −0.0381485 | + | 0.363251i | ||||
\(631\) | 2.20267e36 | 0.876130 | 0.438065 | − | 0.898943i | \(-0.355664\pi\) | ||||
0.438065 | + | 0.898943i | \(0.355664\pi\) | |||||||
\(632\) | 5.91810e35i | 0.230600i | ||||||||
\(633\) | 1.10011e36 | + | 1.22170e36i | 0.419942 | + | 0.466354i | ||||
\(634\) | 6.11998e35 | 0.228870 | ||||||||
\(635\) | 3.32954e36i | 1.21990i | ||||||||
\(636\) | −1.45895e36 | + | 1.31375e36i | −0.523718 | + | 0.471597i | ||||
\(637\) | −1.71149e36 | −0.601953 | ||||||||
\(638\) | − | 1.10249e35i | − | 0.0379931i | ||||||
\(639\) | 1.24665e35 | + | 1.30922e34i | 0.0420952 | + | 0.00442082i | ||||
\(640\) | 3.81246e36 | 1.26144 | ||||||||
\(641\) | − | 4.59533e36i | − | 1.48992i | −0.667110 | − | 0.744959i | \(-0.732469\pi\) | ||
0.667110 | − | 0.744959i | \(-0.267531\pi\) | |||||||
\(642\) | −1.68445e35 | − | 1.87061e35i | −0.0535183 | − | 0.0594331i | ||||
\(643\) | −9.02499e35 | −0.280998 | −0.140499 | − | 0.990081i | \(-0.544871\pi\) | ||||
−0.140499 | + | 0.990081i | \(0.544871\pi\) | |||||||
\(644\) | 2.49528e36i | 0.761383i | ||||||||
\(645\) | 5.09961e36 | − | 4.59209e36i | 1.52497 | − | 1.37320i | ||||
\(646\) | −1.40696e35 | −0.0412344 | ||||||||
\(647\) | − | 5.93690e36i | − | 1.70531i | −0.522473 | − | 0.852656i | \(-0.674990\pi\) | ||
0.522473 | − | 0.852656i | \(-0.325010\pi\) | |||||||
\(648\) | −5.38051e35 | + | 2.53342e36i | −0.151478 | + | 0.713233i | ||||
\(649\) | 1.82686e36 | 0.504108 | ||||||||
\(650\) | 1.05376e36i | 0.285016i | ||||||||
\(651\) | −1.72534e36 | − | 1.91603e36i | −0.457428 | − | 0.507983i | ||||
\(652\) | −6.91753e35 | −0.179776 | ||||||||
\(653\) | 1.77971e36i | 0.453396i | 0.973965 | + | 0.226698i | \(0.0727930\pi\) | ||||
−0.973965 | + | 0.226698i | \(0.927207\pi\) | |||||||
\(654\) | −3.53824e35 | + | 3.18611e35i | −0.0883642 | + | 0.0795702i | ||||
\(655\) | 2.29787e36 | 0.562585 | ||||||||
\(656\) | − | 6.64871e35i | − | 0.159583i | ||||||
\(657\) | 1.87676e35 | − | 1.78706e36i | 0.0441631 | − | 0.420522i | ||||
\(658\) | 1.60179e36 | 0.369547 | ||||||||
\(659\) | 5.05032e36i | 1.14238i | 0.820819 | + | 0.571188i | \(0.193517\pi\) | ||||
−0.820819 | + | 0.571188i | \(0.806483\pi\) | |||||||
\(660\) | −2.61004e36 | − | 2.89850e36i | −0.578864 | − | 0.642840i | ||||
\(661\) | −7.89441e35 | −0.171672 | −0.0858362 | − | 0.996309i | \(-0.527356\pi\) | ||||
−0.0858362 | + | 0.996309i | \(0.527356\pi\) | |||||||
\(662\) | − | 3.19307e36i | − | 0.680855i | ||||||
\(663\) | −7.58109e36 | + | 6.82662e36i | −1.58510 | + | 1.42735i | ||||
\(664\) | 4.67202e36 | 0.957899 | ||||||||
\(665\) | 3.05425e35i | 0.0614077i | ||||||||
\(666\) | 3.35439e35 | + | 3.52277e34i | 0.0661377 | + | 0.00694575i | ||||
\(667\) | −7.24304e35 | −0.140051 | ||||||||
\(668\) | − | 2.94293e36i | − | 0.558066i | ||||||
\(669\) | −4.63109e35 | − | 5.14291e35i | −0.0861279 | − | 0.0956466i | ||||
\(670\) | −3.74480e36 | −0.683057 | ||||||||
\(671\) | 6.38491e36i | 1.14225i | ||||||||
\(672\) | −3.00006e36 | + | 2.70150e36i | −0.526417 | + | 0.474028i | ||||
\(673\) | 3.68376e36 | 0.634008 | 0.317004 | − | 0.948424i | \(-0.397323\pi\) | ||||
0.317004 | + | 0.948424i | \(0.397323\pi\) | |||||||
\(674\) | 2.05950e36i | 0.347682i | ||||||||
\(675\) | −2.58768e36 | + | 1.88056e36i | −0.428511 | + | 0.311414i | ||||
\(676\) | 4.41812e36 | 0.717679 | ||||||||
\(677\) | 6.57244e36i | 1.04731i | 0.851931 | + | 0.523653i | \(0.175431\pi\) | ||||
−0.851931 | + | 0.523653i | \(0.824569\pi\) | |||||||
\(678\) | −1.90242e36 | − | 2.11268e36i | −0.297386 | − | 0.330253i | ||||
\(679\) | −4.62509e36 | −0.709273 | ||||||||
\(680\) | − | 9.39847e36i | − | 1.41397i | ||||||
\(681\) | 8.26747e36 | − | 7.44469e36i | 1.22028 | − | 1.09884i | ||||
\(682\) | −2.07311e36 | −0.300210 | ||||||||
\(683\) | 1.77368e36i | 0.252003i | 0.992030 | + | 0.126001i | \(0.0402144\pi\) | ||||
−0.992030 | + | 0.126001i | \(0.959786\pi\) | |||||||
\(684\) | −4.20269e34 | + | 4.00182e35i | −0.00585866 | + | 0.0557863i | ||||
\(685\) | −7.46015e36 | −1.02040 | ||||||||
\(686\) | 3.17398e36i | 0.425982i | ||||||||
\(687\) | 3.88550e36 | + | 4.31493e36i | 0.511693 | + | 0.568245i | ||||
\(688\) | 7.12847e36 | 0.921184 | ||||||||
\(689\) | − | 8.96273e36i | − | 1.13655i | ||||||
\(690\) | 3.53099e36 | − | 3.17959e36i | 0.439399 | − | 0.395670i | ||||
\(691\) | −2.55446e36 | −0.311949 | −0.155975 | − | 0.987761i | \(-0.549852\pi\) | ||||
−0.155975 | + | 0.987761i | \(0.549852\pi\) | |||||||
\(692\) | 3.54560e36i | 0.424923i | ||||||||
\(693\) | 5.23478e36 | + | 5.49755e35i | 0.615696 | + | 0.0646602i | ||||
\(694\) | 6.73080e36 | 0.776951 | ||||||||
\(695\) | − | 6.52287e36i | − | 0.738986i | ||||||
\(696\) | −5.08395e35 | − | 5.64583e35i | −0.0565303 | − | 0.0627780i | ||||
\(697\) | −4.12942e36 | −0.450674 | ||||||||
\(698\) | 5.51328e36i | 0.590595i | ||||||||
\(699\) | −4.34432e36 | + | 3.91197e36i | −0.456792 | + | 0.411332i | ||||
\(700\) | −3.23278e36 | −0.333658 | ||||||||
\(701\) | − | 1.82234e37i | − | 1.84627i | −0.384481 | − | 0.923133i | \(-0.625620\pi\) | ||
0.384481 | − | 0.923133i | \(-0.374380\pi\) | |||||||
\(702\) | −3.18054e36 | − | 4.37649e36i | −0.316314 | − | 0.435254i | ||||
\(703\) | 1.14521e35 | 0.0111806 | ||||||||
\(704\) | − | 1.55695e36i | − | 0.149221i | ||||||
\(705\) | 1.10073e37 | + | 1.22239e37i | 1.03567 | + | 1.15014i | ||||
\(706\) | 6.41910e36 | 0.592943 | ||||||||
\(707\) | 3.73343e36i | 0.338576i | ||||||||
\(708\) | 4.28077e36 | − | 3.85475e36i | 0.381145 | − | 0.343213i | ||||
\(709\) | −1.90577e37 | −1.66598 | −0.832990 | − | 0.553288i | \(-0.813373\pi\) | ||||
−0.832990 | + | 0.553288i | \(0.813373\pi\) | |||||||
\(710\) | − | 2.41228e35i | − | 0.0207047i | ||||||
\(711\) | 3.91960e35 | − | 3.73226e36i | 0.0330322 | − | 0.314533i | ||||
\(712\) | −1.46330e37 | −1.21086 | ||||||||
\(713\) | 1.36197e37i | 1.10664i | ||||||||
\(714\) | 3.88342e36 | + | 4.31262e36i | 0.309840 | + | 0.344084i | ||||
\(715\) | 1.78063e37 | 1.39507 | ||||||||
\(716\) | 7.87017e36i | 0.605501i | ||||||||
\(717\) | 6.57858e35 | − | 5.92388e35i | 0.0497031 | − | 0.0447566i | ||||
\(718\) | −2.28020e36 | −0.169182 | ||||||||
\(719\) | 2.36064e37i | 1.72010i | 0.510207 | + | 0.860052i | \(0.329569\pi\) | ||||
−0.510207 | + | 0.860052i | \(0.670431\pi\) | |||||||
\(720\) | −9.54322e36 | − | 1.00223e36i | −0.682924 | − | 0.0717205i | ||||
\(721\) | −5.78034e36 | −0.406252 | ||||||||
\(722\) | 5.70439e36i | 0.393755i | ||||||||
\(723\) | −8.25514e36 | − | 9.16749e36i | −0.559663 | − | 0.621516i | ||||
\(724\) | −1.16912e37 | −0.778498 | ||||||||
\(725\) | − | 9.38376e35i | − | 0.0613738i | ||||||
\(726\) | −1.42997e36 | + | 1.28765e36i | −0.0918649 | + | 0.0827224i | ||||
\(727\) | 1.46646e36 | 0.0925385 | 0.0462692 | − | 0.998929i | \(-0.485267\pi\) | ||||
0.0462692 | + | 0.998929i | \(0.485267\pi\) | |||||||
\(728\) | − | 1.19489e37i | − | 0.740660i | ||||||
\(729\) | 5.07113e36 | − | 1.56207e37i | 0.308778 | − | 0.951134i | ||||
\(730\) | −3.45799e36 | −0.206836 | ||||||||
\(731\) | − | 4.42739e37i | − | 2.60149i | ||||||
\(732\) | 1.34724e37 | + | 1.49614e37i | 0.777682 | + | 0.863631i | ||||
\(733\) | 8.03765e36 | 0.455803 | 0.227901 | − | 0.973684i | \(-0.426814\pi\) | ||||
0.227901 | + | 0.973684i | \(0.426814\pi\) | |||||||
\(734\) | − | 8.42230e35i | − | 0.0469226i | ||||||
\(735\) | −7.42995e36 | + | 6.69052e36i | −0.406678 | + | 0.366205i | ||||
\(736\) | 2.13254e37 | 1.14680 | ||||||||
\(737\) | 2.19126e37i | 1.15775i | ||||||||
\(738\) | 2.28723e35 | − | 2.17791e36i | 0.0118735 | − | 0.113059i | ||||
\(739\) | 1.99427e37 | 1.01720 | 0.508600 | − | 0.861003i | \(-0.330163\pi\) | ||||
0.508600 | + | 0.861003i | \(0.330163\pi\) | |||||||
\(740\) | 3.50044e36i | 0.175433i | ||||||||
\(741\) | −1.22921e36 | − | 1.36507e36i | −0.0605328 | − | 0.0672228i | ||||
\(742\) | −5.09858e36 | −0.246717 | ||||||||
\(743\) | − | 1.63133e37i | − | 0.775689i | −0.921725 | − | 0.387845i | \(-0.873220\pi\) | ||
0.921725 | − | 0.387845i | \(-0.126780\pi\) | |||||||
\(744\) | −1.06164e37 | + | 9.55983e36i | −0.496053 | + | 0.446685i | ||||
\(745\) | 3.79706e37 | 1.74348 | ||||||||
\(746\) | − | 9.63409e36i | − | 0.434716i | ||||||
\(747\) | −2.94642e37 | − | 3.09432e36i | −1.30655 | − | 0.137214i | ||||
\(748\) | −2.51643e37 | −1.09664 | ||||||||
\(749\) | 3.52547e36i | 0.150992i | ||||||||
\(750\) | −3.65715e36 | − | 4.06133e36i | −0.153938 | − | 0.170951i | ||||
\(751\) | 2.87515e37 | 1.18944 | 0.594718 | − | 0.803934i | \(-0.297264\pi\) | ||||
0.594718 | + | 0.803934i | \(0.297264\pi\) | |||||||
\(752\) | 1.70871e37i | 0.694761i | ||||||||
\(753\) | 2.42918e36 | − | 2.18743e36i | 0.0970790 | − | 0.0874177i | ||||
\(754\) | 1.58705e36 | 0.0623396 | ||||||||
\(755\) | 3.14421e35i | 0.0121395i | ||||||||
\(756\) | 1.34264e37 | − | 9.75740e36i | 0.509537 | − | 0.370298i | ||||
\(757\) | −2.47242e37 | −0.922308 | −0.461154 | − | 0.887320i | \(-0.652564\pi\) | ||||
−0.461154 | + | 0.887320i | \(0.652564\pi\) | |||||||
\(758\) | 7.06134e36i | 0.258933i | ||||||||
\(759\) | −1.86053e37 | − | 2.06615e37i | −0.670645 | − | 0.744764i | ||||
\(760\) | 1.69231e36 | 0.0599656 | ||||||||
\(761\) | − | 3.81096e36i | − | 0.132750i | −0.997795 | − | 0.0663749i | \(-0.978857\pi\) | ||
0.997795 | − | 0.0663749i | \(-0.0211433\pi\) | |||||||
\(762\) | −8.46530e36 | + | 7.62283e36i | −0.289886 | + | 0.261037i | ||||
\(763\) | 6.66839e36 | 0.224492 | ||||||||
\(764\) | − | 2.19589e37i | − | 0.726769i | ||||||
\(765\) | −6.22468e36 | + | 5.92716e37i | −0.202544 | + | 1.92863i | ||||
\(766\) | −1.50201e37 | −0.480505 | ||||||||
\(767\) | 2.62980e37i | 0.827147i | ||||||||
\(768\) | 4.83405e36 | + | 5.36831e36i | 0.149491 | + | 0.166013i | ||||
\(769\) | −5.50932e37 | −1.67516 | −0.837579 | − | 0.546317i | \(-0.816030\pi\) | ||||
−0.837579 | + | 0.546317i | \(0.816030\pi\) | |||||||
\(770\) | − | 1.01294e37i | − | 0.302833i | ||||||
\(771\) | 1.75284e37 | − | 1.57840e37i | 0.515270 | − | 0.463990i | ||||
\(772\) | 9.83541e36 | 0.284294 | ||||||||
\(773\) | 4.07752e37i | 1.15895i | 0.814991 | + | 0.579473i | \(0.196742\pi\) | ||||
−0.814991 | + | 0.579473i | \(0.803258\pi\) | |||||||
\(774\) | 2.33506e37 | + | 2.45228e36i | 0.652629 | + | 0.0685389i | ||||
\(775\) | −1.76451e37 | −0.484957 | ||||||||
\(776\) | 2.56268e37i | 0.692616i | ||||||||
\(777\) | −3.16095e36 | − | 3.51029e36i | −0.0840125 | − | 0.0932975i | ||||
\(778\) | 2.26034e37 | 0.590797 | ||||||||
\(779\) | − | 7.43550e35i | − | 0.0191128i | ||||||
\(780\) | 4.17246e37 | − | 3.75721e37i | 1.05478 | − | 0.949809i | ||||
\(781\) | −1.41154e36 | −0.0350937 | ||||||||
\(782\) | − | 3.06555e37i | − | 0.749584i | ||||||
\(783\) | 2.83228e36 | + | 3.89726e36i | 0.0681134 | + | 0.0937253i | ||||
\(784\) | −1.03859e37 | −0.245661 | ||||||||
\(785\) | − | 7.71017e37i | − | 1.79373i | ||||||
\(786\) | 5.26086e36 | + | 5.84228e36i | 0.120383 | + | 0.133687i | ||||
\(787\) | 7.37959e37 | 1.66097 | 0.830483 | − | 0.557044i | \(-0.188065\pi\) | ||||
0.830483 | + | 0.557044i | \(0.188065\pi\) | |||||||
\(788\) | − | 4.32974e37i | − | 0.958564i | ||||||
\(789\) | −4.74475e36 | + | 4.27255e36i | −0.103327 | + | 0.0930435i | ||||
\(790\) | −7.22198e36 | −0.154705 | ||||||||
\(791\) | 3.98168e37i | 0.839019i | ||||||||
\(792\) | 3.04609e36 | − | 2.90050e37i | 0.0631416 | − | 0.601236i | ||||
\(793\) | −9.19121e37 | −1.87422 | ||||||||
\(794\) | 3.49865e37i | 0.701834i | ||||||||
\(795\) | −3.50368e37 | − | 3.89091e37i | −0.691436 | − | 0.767853i | ||||
\(796\) | −2.92493e37 | −0.567866 | ||||||||
\(797\) | 1.96755e37i | 0.375809i | 0.982187 | + | 0.187905i | \(0.0601696\pi\) | ||||
−0.982187 | + | 0.187905i | \(0.939830\pi\) | |||||||
\(798\) | −7.76538e35 | + | 6.99256e35i | −0.0145923 | + | 0.0131401i | ||||
\(799\) | 1.06125e38 | 1.96205 | ||||||||
\(800\) | 2.76283e37i | 0.502555i | ||||||||
\(801\) | 9.22834e37 | + | 9.69157e36i | 1.65158 | + | 0.173449i | ||||
\(802\) | −2.69766e37 | −0.475030 | ||||||||
\(803\) | 2.02343e37i | 0.350579i | ||||||||
\(804\) | 4.62365e37 | + | 5.13466e37i | 0.788237 | + | 0.875352i | ||||
\(805\) | −6.65473e37 | −1.11631 | ||||||||
\(806\) | − | 2.98428e37i | − | 0.492588i | ||||||
\(807\) | −3.51007e37 | + | 3.16075e37i | −0.570112 | + | 0.513374i | ||||
\(808\) | 2.06863e37 | 0.330625 | ||||||||
\(809\) | − | 4.85719e37i | − | 0.763931i | −0.924177 | − | 0.381966i | \(-0.875247\pi\) | ||
0.924177 | − | 0.381966i | \(-0.124753\pi\) | |||||||
\(810\) | −3.09158e37 | − | 6.56596e36i | −0.478493 | − | 0.101623i | ||||
\(811\) | −8.26891e37 | −1.25944 | −0.629719 | − | 0.776823i | \(-0.716830\pi\) | ||||
−0.629719 | + | 0.776823i | \(0.716830\pi\) | |||||||
\(812\) | 4.86883e36i | 0.0729787i | ||||||||
\(813\) | −1.46013e37 | − | 1.62150e37i | −0.215384 | − | 0.239188i | ||||
\(814\) | −3.79807e36 | −0.0551374 | ||||||||
\(815\) | − | 1.84485e37i | − | 0.263581i | ||||||
\(816\) | −4.60047e37 | + | 4.14263e37i | −0.646889 | + | 0.582511i | ||||
\(817\) | 7.97204e36 | 0.110327 | ||||||||
\(818\) | 5.18882e36i | 0.0706765i | ||||||||
\(819\) | −7.91383e36 | + | 7.53557e37i | −0.106095 | + | 1.01024i | ||||
\(820\) | 2.27274e37 | 0.299895 | ||||||||
\(821\) | 8.74647e37i | 1.13598i | 0.823035 | + | 0.567991i | \(0.192279\pi\) | ||||
−0.823035 | + | 0.567991i | \(0.807721\pi\) | |||||||
\(822\) | −1.70797e37 | − | 1.89673e37i | −0.218346 | − | 0.242478i | ||||
\(823\) | 1.11665e38 | 1.40514 | 0.702568 | − | 0.711616i | \(-0.252037\pi\) | ||||
0.702568 | + | 0.711616i | \(0.252037\pi\) | |||||||
\(824\) | 3.20279e37i | 0.396711i | ||||||||
\(825\) | 2.67681e37 | − | 2.41041e37i | 0.326375 | − | 0.293894i | ||||
\(826\) | 1.49600e37 | 0.179552 | ||||||||
\(827\) | − | 1.30092e38i | − | 1.53702i | −0.639840 | − | 0.768508i | \(-0.720999\pi\) | ||
0.639840 | − | 0.768508i | \(-0.279001\pi\) | |||||||
\(828\) | −8.71933e37 | − | 9.15701e36i | −1.01412 | − | 0.106502i | ||||
\(829\) | −3.22666e36 | −0.0369440 | −0.0184720 | − | 0.999829i | \(-0.505880\pi\) | ||||
−0.0184720 | + | 0.999829i | \(0.505880\pi\) | |||||||
\(830\) | 5.70137e37i | 0.642634i | ||||||||
\(831\) | −8.02156e37 | − | 8.90809e37i | −0.890113 | − | 0.988488i | ||||
\(832\) | 2.24126e37 | 0.244843 | ||||||||
\(833\) | 6.45055e37i | 0.693764i | ||||||||
\(834\) | 1.65843e37 | − | 1.49338e37i | 0.175605 | − | 0.158129i | ||||
\(835\) | 7.84857e37 | 0.818213 | ||||||||
\(836\) | − | 4.53113e36i | − | 0.0465077i | ||||||
\(837\) | 7.32838e37 | − | 5.32579e37i | 0.740589 | − | 0.538211i | ||||
\(838\) | 3.14539e37 | 0.312970 | ||||||||
\(839\) | − | 1.31088e38i | − | 1.28427i | −0.766592 | − | 0.642135i | \(-0.778049\pi\) | ||
0.766592 | − | 0.642135i | \(-0.221951\pi\) | |||||||
\(840\) | −4.67102e37 | − | 5.18725e37i | −0.450589 | − | 0.500388i | ||||
\(841\) | 1.03867e38 | 0.986576 | ||||||||
\(842\) | − | 7.29368e37i | − | 0.682165i | ||||||
\(843\) | −1.96400e37 | + | 1.76854e37i | −0.180876 | + | 0.162876i | ||||
\(844\) | −5.83761e37 | −0.529399 | ||||||||
\(845\) | 1.17828e38i | 1.05223i | ||||||||
\(846\) | −5.87815e36 | + | 5.59719e37i | −0.0516923 | + | 0.492216i | ||||
\(847\) | 2.69500e37 | 0.233386 | ||||||||
\(848\) | − | 5.43889e37i | − | 0.463836i | ||||||
\(849\) | 5.90830e37 | + | 6.56129e37i | 0.496207 | + | 0.551047i | ||||
\(850\) | 3.97159e37 | 0.328487 | ||||||||
\(851\) | 2.49523e37i | 0.203248i | ||||||||
\(852\) | −3.30758e36 | + | 2.97841e36i | −0.0265336 | + | 0.0238930i | ||||
\(853\) | −8.59530e37 | −0.679084 | −0.339542 | − | 0.940591i | \(-0.610272\pi\) | ||||
−0.339542 | + | 0.940591i | \(0.610272\pi\) | |||||||
\(854\) | 5.22855e37i | 0.406845i | ||||||||
\(855\) | −1.06725e37 | − | 1.12083e36i | −0.0817916 | − | 0.00858973i | ||||
\(856\) | 1.95340e37 | 0.147446 | ||||||||
\(857\) | − | 1.69202e38i | − | 1.25793i | −0.777434 | − | 0.628964i | \(-0.783479\pi\) | ||
0.777434 | − | 0.628964i | \(-0.216521\pi\) | |||||||
\(858\) | 4.07668e37 | + | 4.52723e37i | 0.298519 | + | 0.331511i | ||||
\(859\) | −2.10542e38 | −1.51854 | −0.759272 | − | 0.650773i | \(-0.774445\pi\) | ||||
−0.759272 | + | 0.650773i | \(0.774445\pi\) | |||||||
\(860\) | 2.43673e38i | 1.73112i | ||||||||
\(861\) | −2.27913e37 | + | 2.05231e37i | −0.159488 | + | 0.143616i | ||||
\(862\) | 1.52298e37 | 0.104978 | ||||||||
\(863\) | − | 3.73003e37i | − | 0.253263i | −0.991950 | − | 0.126632i | \(-0.959583\pi\) | ||
0.991950 | − | 0.126632i | \(-0.0404166\pi\) | |||||||
\(864\) | −8.33897e37 | − | 1.14746e38i | −0.557742 | − | 0.767464i | ||||
\(865\) | −9.45584e37 | −0.623004 | ||||||||
\(866\) | 7.67021e37i | 0.497822i | ||||||||
\(867\) | 1.52633e38 | + | 1.69502e38i | 0.975889 | + | 1.08374i | ||||
\(868\) | 9.15531e37 | 0.576656 | ||||||||
\(869\) | 4.22592e37i | 0.262219i | ||||||||
\(870\) | 6.88973e36 | − | 6.20406e36i | 0.0421165 | − | 0.0379250i | ||||
\(871\) | −3.15436e38 | −1.89966 | ||||||||
\(872\) | − | 3.69483e37i | − | 0.219220i | ||||||
\(873\) | 1.69729e37 | − | 1.61616e38i | 0.0992133 | − | 0.944711i | ||||
\(874\) | 5.51988e36 | 0.0317893 | ||||||||
\(875\) | 7.65424e37i | 0.434308i | ||||||||
\(876\) | 4.26953e37 | + | 4.74139e37i | 0.238686 | + | 0.265065i | ||||
\(877\) | −6.36707e37 | −0.350708 | −0.175354 | − | 0.984505i | \(-0.556107\pi\) | ||||
−0.175354 | + | 0.984505i | \(0.556107\pi\) | |||||||
\(878\) | − | 1.28994e38i | − | 0.700066i | ||||||
\(879\) | 8.44426e37 | − | 7.60389e37i | 0.451551 | − | 0.406612i | ||||
\(880\) | 1.08055e38 | 0.569338 | ||||||||
\(881\) | − | 1.20838e37i | − | 0.0627359i | −0.999508 | − | 0.0313679i | \(-0.990014\pi\) | ||
0.999508 | − | 0.0313679i | \(-0.00998636\pi\) | |||||||
\(882\) | −3.40211e37 | − | 3.57288e36i | −0.174043 | − | 0.0182779i | ||||
\(883\) | 2.84990e38 | 1.43662 | 0.718308 | − | 0.695726i | \(-0.244917\pi\) | ||||
0.718308 | + | 0.695726i | \(0.244917\pi\) | |||||||
\(884\) | − | 3.62246e38i | − | 1.79938i | ||||||
\(885\) | 1.02803e38 | + | 1.14165e38i | 0.503205 | + | 0.558818i | ||||
\(886\) | −1.01992e38 | −0.491959 | ||||||||
\(887\) | 3.48761e38i | 1.65776i | 0.559429 | + | 0.828878i | \(0.311020\pi\) | ||||
−0.559429 | + | 0.828878i | \(0.688980\pi\) | |||||||
\(888\) | −1.94499e37 | + | 1.75142e37i | −0.0911064 | + | 0.0820395i | ||||
\(889\) | 1.59542e38 | 0.736466 | ||||||||
\(890\) | − | 1.78570e38i | − | 0.812341i | ||||||
\(891\) | −3.84205e37 | + | 1.80903e38i | −0.172247 | + | 0.811027i | ||||
\(892\) | 2.45743e37 | 0.108577 | ||||||||
\(893\) | 1.91091e37i | 0.0832093i | ||||||||
\(894\) | 8.69320e37 | + | 9.65396e37i | 0.373071 | + | 0.414303i | ||||
\(895\) | −2.09892e38 | −0.887760 | ||||||||
\(896\) | − | 1.82682e38i | − | 0.761539i | ||||||
\(897\) | 2.97426e38 | − | 2.67826e38i | 1.22202 | − | 1.10040i | ||||
\(898\) | −6.45642e37 | −0.261457 | ||||||||
\(899\) | 2.65750e37i | 0.106071i | ||||||||
\(900\) | 1.18634e37 | − | 1.12964e38i | 0.0466721 | − | 0.444413i | ||||
\(901\) | −3.37802e38 | −1.30990 | ||||||||
\(902\) | 2.46598e37i | 0.0942550i | ||||||||
\(903\) | −2.20040e38 | − | 2.44359e38i | −0.829013 | − | 0.920635i | ||||
\(904\) | 2.20618e38 | 0.819315 | ||||||||
\(905\) | − | 3.11796e38i | − | 1.14140i | ||||||
\(906\) | −7.99411e35 | + | 7.19854e35i | −0.00288472 | + | 0.00259763i | ||||
\(907\) | −8.23661e37 | −0.292991 | −0.146495 | − | 0.989211i | \(-0.546799\pi\) | ||||
−0.146495 | + | 0.989211i | \(0.546799\pi\) | |||||||
\(908\) | 3.95042e38i | 1.38525i | ||||||||
\(909\) | −1.30458e38 | − | 1.37007e37i | −0.450964 | − | 0.0473601i | ||||
\(910\) | 1.45815e38 | 0.496893 | ||||||||
\(911\) | 5.93021e38i | 1.99219i | 0.0882755 | + | 0.996096i | \(0.471864\pi\) | ||||
−0.0882755 | + | 0.996096i | \(0.528136\pi\) | |||||||
\(912\) | −7.45929e36 | − | 8.28369e36i | −0.0247039 | − | 0.0274341i | ||||
\(913\) | 3.33613e38 | 1.08924 | ||||||||
\(914\) | − | 3.99124e37i | − | 0.128472i | ||||||
\(915\) | −3.99010e38 | + | 3.59300e38i | −1.26622 | + | 1.14021i | ||||
\(916\) | −2.06179e38 | −0.645065 | ||||||||
\(917\) | − | 1.10107e38i | − | 0.339637i | ||||||
\(918\) | −1.64948e38 | + | 1.19873e38i | −0.501640 | + | 0.364559i | ||||
\(919\) | 3.88502e38 | 1.16491 | 0.582453 | − | 0.812864i | \(-0.302093\pi\) | ||||
0.582453 | + | 0.812864i | \(0.302093\pi\) | |||||||
\(920\) | 3.68727e38i | 1.09009i | ||||||||
\(921\) | −3.45050e37 | − | 3.83185e37i | −0.100579 | − | 0.111695i | ||||
\(922\) | −1.23906e38 | −0.356116 | ||||||||
\(923\) | − | 2.03194e37i | − | 0.0575823i | ||||||
\(924\) | −1.38888e38 | + | 1.25066e38i | −0.388088 | + | 0.349465i | ||||
\(925\) | −3.23271e37 | −0.0890685 | ||||||||
\(926\) | 8.10311e37i | 0.220145i | ||||||||
\(927\) | 2.12123e37 | − | 2.01984e38i | 0.0568266 | − | 0.541104i | ||||
\(928\) | 4.16105e37 | 0.109921 | ||||||||
\(929\) | − | 4.97643e38i | − | 1.29632i | −0.761502 | − | 0.648162i | \(-0.775538\pi\) | ||
0.761502 | − | 0.648162i | \(-0.224462\pi\) | |||||||
\(930\) | −1.16661e38 | − | 1.29554e38i | −0.299672 | − | 0.332791i | ||||
\(931\) | −1.16150e37 | −0.0294220 | ||||||||
\(932\) | − | 2.07584e38i | − | 0.518545i | ||||||
\(933\) | −2.54234e38 | + | 2.28933e38i | −0.626285 | + | 0.563957i | ||||
\(934\) | 2.45876e38 | 0.597321 | ||||||||
\(935\) | − | 6.71114e38i | − | 1.60785i | ||||||
\(936\) | 4.17533e38 | + | 4.38492e37i | 0.986517 | + | 0.103604i | ||||
\(937\) | 8.43272e38 | 1.96496 | 0.982478 | − | 0.186378i | \(-0.0596750\pi\) | ||||
0.982478 | + | 0.186378i | \(0.0596750\pi\) | |||||||
\(938\) | 1.79441e38i | 0.412367i | ||||||||
\(939\) | −1.81187e38 | − | 2.01211e38i | −0.410651 | − | 0.456036i | ||||
\(940\) | −5.84089e38 | −1.30562 | ||||||||
\(941\) | − | 8.27185e37i | − | 0.182363i | −0.995834 | − | 0.0911817i | \(-0.970936\pi\) | ||
0.995834 | − | 0.0911817i | \(-0.0290644\pi\) | |||||||
\(942\) | 1.96030e38 | − | 1.76521e38i | 0.426246 | − | 0.383826i | ||||
\(943\) | 1.62008e38 | 0.347444 | ||||||||
\(944\) | 1.59585e38i | 0.337565i | ||||||||
\(945\) | 2.60223e38 | + | 3.58071e38i | 0.542915 | + | 0.747061i | ||||
\(946\) | −2.64392e38 | −0.544081 | ||||||||
\(947\) | 9.84098e36i | 0.0199751i | 0.999950 | + | 0.00998754i | \(0.00317919\pi\) | ||||
−0.999950 | + | 0.00998754i | \(0.996821\pi\) | |||||||
\(948\) | 8.91687e37 | + | 9.90236e37i | 0.178527 | + | 0.198258i | ||||
\(949\) | −2.91277e38 | −0.575235 | ||||||||
\(950\) | 7.15132e36i | 0.0139309i | ||||||||
\(951\) | 2.23791e38 | − | 2.01520e38i | 0.430028 | − | 0.387231i | ||||
\(952\) | −4.50348e38 | −0.853627 | ||||||||
\(953\) | 4.90868e37i | 0.0917820i | 0.998946 | + | 0.0458910i | \(0.0146127\pi\) | ||||
−0.998946 | + | 0.0458910i | \(0.985387\pi\) | |||||||
\(954\) | 1.87104e37 | − | 1.78161e38i | 0.0345108 | − | 0.328612i | ||||
\(955\) | 5.85627e38 | 1.06556 | ||||||||
\(956\) | 3.14343e37i | 0.0564223i | ||||||||
\(957\) | −3.63028e37 | − | 4.03150e37i | −0.0642814 | − | 0.0713857i | ||||
\(958\) | 6.35511e37 | 0.111012 | ||||||||
\(959\) | 3.57470e38i | 0.616024i | ||||||||
\(960\) | 9.72976e37 | − | 8.76145e37i | 0.165415 | − | 0.148953i | ||||
\(961\) | −9.65015e37 | −0.161856 | ||||||||
\(962\) | − | 5.46741e37i | − | 0.0904702i | ||||||
\(963\) | −1.23192e38 | − | 1.29375e37i | −0.201112 | − | 0.0211208i | ||||
\(964\) | 4.38048e38 | 0.705538 | ||||||||
\(965\) | 2.62303e38i | 0.416820i | ||||||||
\(966\) | −1.52357e38 | − | 1.69195e38i | −0.238869 | − | 0.265269i | ||||
\(967\) | −1.06101e39 | −1.64126 | −0.820629 | − | 0.571462i | \(-0.806377\pi\) | ||||
−0.820629 | + | 0.571462i | \(0.806377\pi\) | |||||||
\(968\) | − | 1.49325e38i | − | 0.227905i | ||||||
\(969\) | −5.14488e37 | + | 4.63286e37i | −0.0774758 | + | 0.0697654i | ||||
\(970\) | −3.12730e38 | −0.464662 | ||||||||
\(971\) | 4.24410e38i | 0.622207i | 0.950376 | + | 0.311104i | \(0.100699\pi\) | ||||
−0.950376 | + | 0.311104i | \(0.899301\pi\) | |||||||
\(972\) | 2.91685e38 | + | 5.04969e38i | 0.421941 | + | 0.730471i | ||||
\(973\) | −3.12557e38 | −0.446132 | ||||||||
\(974\) | 2.07284e38i | 0.291944i | ||||||||
\(975\) | 3.46984e38 | + | 3.85333e38i | 0.482225 | + | 0.535520i | ||||
\(976\) | −5.57754e38 | −0.764883 | ||||||||
\(977\) | 1.44920e38i | 0.196109i | 0.995181 | + | 0.0980547i | \(0.0312620\pi\) | ||||
−0.995181 | + | 0.0980547i | \(0.968738\pi\) | |||||||
\(978\) | 4.69051e37 | − | 4.22371e37i | 0.0626347 | − | 0.0564013i | ||||
\(979\) | −1.04490e39 | −1.37689 | ||||||||
\(980\) | − | 3.55023e38i | − | 0.461656i | ||||||
\(981\) | −2.44712e37 | + | 2.33015e38i | −0.0314020 | + | 0.299011i | ||||
\(982\) | 1.27996e38 | 0.162086 | ||||||||
\(983\) | − | 8.89643e38i | − | 1.11178i | −0.831255 | − | 0.555891i | \(-0.812377\pi\) | ||
0.831255 | − | 0.555891i | \(-0.187623\pi\) | |||||||
\(984\) | 1.13715e38 | + | 1.26283e38i | 0.140243 | + | 0.155743i | ||||
\(985\) | 1.15471e39 | 1.40541 | ||||||||
\(986\) | − | 5.98154e37i | − | 0.0718478i | ||||||
\(987\) | 5.85733e38 | − | 5.27440e38i | 0.694347 | − | 0.625245i | ||||
\(988\) | 6.52266e37 | 0.0763105 | ||||||||
\(989\) | 1.73698e39i | 2.00560i | ||||||||
\(990\) | 3.53954e38 | + | 3.71721e37i | 0.403357 | + | 0.0423604i | ||||
\(991\) | 1.20951e39 | 1.36035 | 0.680176 | − | 0.733048i | \(-0.261903\pi\) | ||||
0.680176 | + | 0.733048i | \(0.261903\pi\) | |||||||
\(992\) | − | 7.82440e38i | − | 0.868559i | ||||||
\(993\) | −1.05142e39 | − | 1.16762e39i | −1.15196 | − | 1.27927i | ||||
\(994\) | −1.15590e37 | −0.0124996 | ||||||||
\(995\) | − | 7.80057e38i | − | 0.832581i | ||||||
\(996\) | 7.81738e38 | − | 7.03939e38i | 0.823550 | − | 0.741590i | ||||
\(997\) | −1.34485e39 | −1.39842 | −0.699211 | − | 0.714915i | \(-0.746465\pi\) | ||||
−0.699211 | + | 0.714915i | \(0.746465\pi\) | |||||||
\(998\) | 2.26590e38i | 0.232565i | ||||||||
\(999\) | 1.34261e38 | − | 9.75720e37i | 0.136019 | − | 0.0988494i |
(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 | 3.27.b.a.2.4 | ✓ | 8 | |
3.2 | odd | 2 | inner | 3.27.b.a.2.5 | yes | 8 | |
4.3 | odd | 2 | 48.27.e.d.17.6 | 8 | |||
12.11 | even | 2 | 48.27.e.d.17.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.27.b.a.2.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
3.27.b.a.2.5 | yes | 8 | 3.2 | odd | 2 | inner | |
48.27.e.d.17.5 | 8 | 12.11 | even | 2 | |||
48.27.e.d.17.6 | 8 | 4.3 | odd | 2 |