Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(1549,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2125.1 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.2125 |
Dual form | 2646.2.e.l.1549.1 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.724745 | + | 1.25529i | −0.324116 | + | 0.561385i | −0.981333 | − | 0.192316i | \(-0.938400\pi\) |
0.657217 | + | 0.753701i | \(0.271733\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.724745 | − | 1.25529i | 0.229184 | − | 0.396959i | ||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44949 | − | 4.24264i | −0.679366 | − | 1.17670i | −0.975172 | − | 0.221449i | \(-0.928921\pi\) |
0.295806 | − | 0.955248i | \(-0.404412\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.27526 | − | 2.20881i | −0.292564 | − | 0.506735i | 0.681852 | − | 0.731491i | \(-0.261175\pi\) |
−0.974415 | + | 0.224756i | \(0.927842\pi\) | |||||||
\(20\) | −0.724745 | + | 1.25529i | −0.162058 | + | 0.280692i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | − | 1.73205i | −0.213201 | − | 0.369274i | ||||
\(23\) | −0.500000 | + | 0.866025i | −0.104257 | + | 0.180579i | −0.913434 | − | 0.406986i | \(-0.866580\pi\) |
0.809177 | + | 0.587565i | \(0.199913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.44949 | + | 2.51059i | 0.289898 | + | 0.502118i | ||||
\(26\) | 2.44949 | + | 4.24264i | 0.480384 | + | 0.832050i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.44949 | + | 5.97469i | −0.640554 | + | 1.10947i | 0.344755 | + | 0.938693i | \(0.387962\pi\) |
−0.985309 | + | 0.170780i | \(0.945371\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | + | 1.73205i | −0.171499 | + | 0.297044i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.89898 | − | 10.2173i | −0.969786 | − | 1.67972i | −0.696165 | − | 0.717881i | \(-0.745112\pi\) |
−0.273621 | − | 0.961838i | \(-0.588221\pi\) | |||||||
\(38\) | 1.27526 | + | 2.20881i | 0.206874 | + | 0.358316i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.724745 | − | 1.25529i | 0.114592 | − | 0.198480i | ||||
\(41\) | 4.89898 | + | 8.48528i | 0.765092 | + | 1.32518i | 0.940198 | + | 0.340629i | \(0.110640\pi\) |
−0.175106 | + | 0.984550i | \(0.556027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.44949 | + | 5.97469i | −0.526042 | + | 0.911132i | 0.473497 | + | 0.880795i | \(0.342991\pi\) |
−0.999540 | + | 0.0303367i | \(0.990342\pi\) | |||||||
\(44\) | 1.00000 | + | 1.73205i | 0.150756 | + | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.500000 | − | 0.866025i | 0.0737210 | − | 0.127688i | ||||
\(47\) | −9.79796 | −1.42918 | −0.714590 | − | 0.699544i | \(-0.753387\pi\) | ||||
−0.714590 | + | 0.699544i | \(0.753387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.44949 | − | 2.51059i | −0.204989 | − | 0.355051i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.44949 | − | 4.24264i | −0.339683 | − | 0.588348i | ||||
\(53\) | −5.44949 | + | 9.43879i | −0.748545 | + | 1.29652i | 0.199975 | + | 0.979801i | \(0.435914\pi\) |
−0.948520 | + | 0.316717i | \(0.897419\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.89898 | −0.390898 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.44949 | − | 5.97469i | 0.452940 | − | 0.784515i | ||||
\(59\) | 2.00000 | 0.260378 | 0.130189 | − | 0.991489i | \(-0.458442\pi\) | ||||
0.130189 | + | 0.991489i | \(0.458442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.55051 | 0.838707 | 0.419353 | − | 0.907823i | \(-0.362257\pi\) | ||||
0.419353 | + | 0.907823i | \(0.362257\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.10102 | 0.880773 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.8990 | −1.57586 | −0.787931 | − | 0.615764i | \(-0.788847\pi\) | ||||
−0.787931 | + | 0.615764i | \(0.788847\pi\) | |||||||
\(68\) | 1.00000 | − | 1.73205i | 0.121268 | − | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.101021 | −0.0119889 | −0.00599446 | − | 0.999982i | \(-0.501908\pi\) | ||||
−0.00599446 | + | 0.999982i | \(0.501908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.44949 | − | 5.97469i | 0.403732 | − | 0.699285i | −0.590441 | − | 0.807081i | \(-0.701046\pi\) |
0.994173 | + | 0.107796i | \(0.0343794\pi\) | |||||||
\(74\) | 5.89898 | + | 10.2173i | 0.685742 | + | 1.18774i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.27526 | − | 2.20881i | −0.146282 | − | 0.253368i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.89898 | −0.213652 | −0.106826 | − | 0.994278i | \(-0.534069\pi\) | ||||
−0.106826 | + | 0.994278i | \(0.534069\pi\) | |||||||
\(80\) | −0.724745 | + | 1.25529i | −0.0810289 | + | 0.140346i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.89898 | − | 8.48528i | −0.541002 | − | 0.937043i | ||||
\(83\) | 1.00000 | − | 1.73205i | 0.109764 | − | 0.190117i | −0.805910 | − | 0.592037i | \(-0.798324\pi\) |
0.915675 | + | 0.401920i | \(0.131657\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.44949 | + | 2.51059i | 0.157219 | + | 0.272312i | ||||
\(86\) | 3.44949 | − | 5.97469i | 0.371968 | − | 0.644268i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | − | 1.73205i | −0.106600 | − | 0.184637i | ||||
\(89\) | −8.44949 | − | 14.6349i | −0.895644 | − | 1.55130i | −0.833005 | − | 0.553265i | \(-0.813382\pi\) |
−0.0626387 | − | 0.998036i | \(-0.519952\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.500000 | + | 0.866025i | −0.0521286 | + | 0.0902894i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.79796 | 1.01058 | ||||||||
\(95\) | 3.69694 | 0.379298 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.44949 | + | 2.51059i | −0.147173 | + | 0.254912i | −0.930182 | − | 0.367099i | \(-0.880351\pi\) |
0.783008 | + | 0.622011i | \(0.213684\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.44949 | + | 2.51059i | 0.144949 | + | 0.251059i | ||||
\(101\) | −8.62372 | − | 14.9367i | −0.858093 | − | 1.48626i | −0.873746 | − | 0.486383i | \(-0.838316\pi\) |
0.0156533 | − | 0.999877i | \(-0.495017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.00000 | + | 12.1244i | −0.689730 | + | 1.19465i | 0.282194 | + | 0.959357i | \(0.408938\pi\) |
−0.971925 | + | 0.235291i | \(0.924396\pi\) | |||||||
\(104\) | 2.44949 | + | 4.24264i | 0.240192 | + | 0.416025i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.44949 | − | 9.43879i | 0.529301 | − | 0.916777i | ||||
\(107\) | −6.00000 | − | 10.3923i | −0.580042 | − | 1.00466i | −0.995474 | − | 0.0950377i | \(-0.969703\pi\) |
0.415432 | − | 0.909624i | \(-0.363630\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.34847 | + | 10.9959i | −0.608073 | + | 1.05321i | 0.383485 | + | 0.923547i | \(0.374724\pi\) |
−0.991558 | + | 0.129666i | \(0.958609\pi\) | |||||||
\(110\) | 2.89898 | 0.276407 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.05051 | − | 5.28364i | −0.286968 | − | 0.497043i | 0.686117 | − | 0.727492i | \(-0.259314\pi\) |
−0.973084 | + | 0.230449i | \(0.925981\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.724745 | − | 1.25529i | −0.0675828 | − | 0.117057i | ||||
\(116\) | −3.44949 | + | 5.97469i | −0.320277 | + | 0.554736i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.00000 | −0.184115 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | −6.55051 | −0.593055 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | −11.4495 | −1.02407 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.00000 | −0.266207 | −0.133103 | − | 0.991102i | \(-0.542494\pi\) | ||||
−0.133103 | + | 0.991102i | \(0.542494\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.10102 | −0.622801 | ||||||||
\(131\) | −4.27526 | + | 7.40496i | −0.373531 | + | 0.646974i | −0.990106 | − | 0.140322i | \(-0.955186\pi\) |
0.616575 | + | 0.787296i | \(0.288520\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.8990 | 1.11430 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | + | 1.73205i | −0.0857493 | + | 0.148522i | ||||
\(137\) | 3.89898 | + | 6.75323i | 0.333112 | + | 0.576967i | 0.983120 | − | 0.182960i | \(-0.0585678\pi\) |
−0.650008 | + | 0.759927i | \(0.725235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.27526 | − | 3.94086i | −0.192985 | − | 0.334259i | 0.753253 | − | 0.657730i | \(-0.228483\pi\) |
−0.946238 | + | 0.323471i | \(0.895150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.101021 | 0.00847745 | ||||||||
\(143\) | 4.89898 | − | 8.48528i | 0.409673 | − | 0.709575i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.00000 | − | 8.66025i | −0.415227 | − | 0.719195i | ||||
\(146\) | −3.44949 | + | 5.97469i | −0.285482 | + | 0.494469i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.89898 | − | 10.2173i | −0.484893 | − | 0.839860i | ||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.50000 | + | 4.33013i | 0.203447 | + | 0.352381i | 0.949637 | − | 0.313353i | \(-0.101452\pi\) |
−0.746190 | + | 0.665733i | \(0.768119\pi\) | |||||||
\(152\) | 1.27526 | + | 2.20881i | 0.103437 | + | 0.179158i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.34847 | + | 7.53177i | −0.349277 | + | 0.604966i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.34847 | −0.666280 | −0.333140 | − | 0.942877i | \(-0.608108\pi\) | ||||
−0.333140 | + | 0.942877i | \(0.608108\pi\) | |||||||
\(158\) | 1.89898 | 0.151075 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.724745 | − | 1.25529i | 0.0572961 | − | 0.0992398i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.89898 | + | 17.1455i | 0.775348 | + | 1.34294i | 0.934599 | + | 0.355704i | \(0.115759\pi\) |
−0.159251 | + | 0.987238i | \(0.550908\pi\) | |||||||
\(164\) | 4.89898 | + | 8.48528i | 0.382546 | + | 0.662589i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.00000 | + | 1.73205i | −0.0776151 | + | 0.134433i | ||||
\(167\) | −5.34847 | − | 9.26382i | −0.413877 | − | 0.716856i | 0.581433 | − | 0.813594i | \(-0.302492\pi\) |
−0.995310 | + | 0.0967384i | \(0.969159\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.50000 | + | 9.52628i | −0.423077 | + | 0.732791i | ||||
\(170\) | −1.44949 | − | 2.51059i | −0.111171 | − | 0.192553i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.44949 | + | 5.97469i | −0.263021 | + | 0.455566i | ||||
\(173\) | 3.10102 | 0.235766 | 0.117883 | − | 0.993027i | \(-0.462389\pi\) | ||||
0.117883 | + | 0.993027i | \(0.462389\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | + | 1.73205i | 0.0753778 | + | 0.130558i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.44949 | + | 14.6349i | 0.633316 | + | 1.09694i | ||||
\(179\) | 10.3485 | − | 17.9241i | 0.773481 | − | 1.33971i | −0.162163 | − | 0.986764i | \(-0.551847\pi\) |
0.935644 | − | 0.352944i | \(-0.114819\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3485 | −0.769196 | −0.384598 | − | 0.923084i | \(-0.625660\pi\) | ||||
−0.384598 | + | 0.923084i | \(0.625660\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.500000 | − | 0.866025i | 0.0368605 | − | 0.0638442i | ||||
\(185\) | 17.1010 | 1.25729 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | 0.292509 | ||||||||
\(188\) | −9.79796 | −0.714590 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.69694 | −0.268204 | ||||||||
\(191\) | −4.10102 | −0.296739 | −0.148370 | − | 0.988932i | \(-0.547403\pi\) | ||||
−0.148370 | + | 0.988932i | \(0.547403\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.8990 | −1.28840 | −0.644198 | − | 0.764858i | \(-0.722809\pi\) | ||||
−0.644198 | + | 0.764858i | \(0.722809\pi\) | |||||||
\(194\) | 1.44949 | − | 2.51059i | 0.104067 | − | 0.180250i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.6969 | −1.18961 | −0.594804 | − | 0.803871i | \(-0.702770\pi\) | ||||
−0.594804 | + | 0.803871i | \(0.702770\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.44949 | − | 2.51059i | 0.102752 | − | 0.177971i | −0.810066 | − | 0.586339i | \(-0.800569\pi\) |
0.912817 | + | 0.408368i | \(0.133902\pi\) | |||||||
\(200\) | −1.44949 | − | 2.51059i | −0.102494 | − | 0.177526i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.62372 | + | 14.9367i | 0.606763 | + | 1.05094i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.2020 | −0.991914 | ||||||||
\(206\) | 7.00000 | − | 12.1244i | 0.487713 | − | 0.844744i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.44949 | − | 4.24264i | −0.169842 | − | 0.294174i | ||||
\(209\) | 2.55051 | − | 4.41761i | 0.176422 | − | 0.305573i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.44949 | − | 11.1708i | −0.444001 | − | 0.769033i | 0.553981 | − | 0.832529i | \(-0.313108\pi\) |
−0.997982 | + | 0.0634968i | \(0.979775\pi\) | |||||||
\(212\) | −5.44949 | + | 9.43879i | −0.374272 | + | 0.648259i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | + | 10.3923i | 0.410152 | + | 0.710403i | ||||
\(215\) | −5.00000 | − | 8.66025i | −0.340997 | − | 0.590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.34847 | − | 10.9959i | 0.429973 | − | 0.744734i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.89898 | −0.195449 | ||||||||
\(221\) | −9.79796 | −0.659082 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.55051 | − | 9.61377i | 0.371690 | − | 0.643785i | −0.618136 | − | 0.786071i | \(-0.712112\pi\) |
0.989826 | + | 0.142286i | \(0.0454452\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.05051 | + | 5.28364i | 0.202917 | + | 0.351462i | ||||
\(227\) | −2.72474 | − | 4.71940i | −0.180848 | − | 0.313237i | 0.761322 | − | 0.648374i | \(-0.224551\pi\) |
−0.942169 | + | 0.335137i | \(0.891217\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.623724 | + | 1.08032i | −0.0412169 | + | 0.0713897i | −0.885898 | − | 0.463880i | \(-0.846457\pi\) |
0.844681 | + | 0.535270i | \(0.179790\pi\) | |||||||
\(230\) | 0.724745 | + | 1.25529i | 0.0477883 | + | 0.0827717i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.44949 | − | 5.97469i | 0.226470 | − | 0.392258i | ||||
\(233\) | −3.50000 | − | 6.06218i | −0.229293 | − | 0.397146i | 0.728306 | − | 0.685252i | \(-0.240308\pi\) |
−0.957599 | + | 0.288106i | \(0.906975\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.10102 | − | 12.2993i | 0.463220 | − | 0.802320i | ||||
\(236\) | 2.00000 | 0.130189 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.39898 | + | 5.88721i | 0.219862 | + | 0.380812i | 0.954766 | − | 0.297360i | \(-0.0961061\pi\) |
−0.734904 | + | 0.678171i | \(0.762773\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.449490 | − | 0.778539i | −0.0289542 | − | 0.0501501i | 0.851185 | − | 0.524865i | \(-0.175884\pi\) |
−0.880139 | + | 0.474715i | \(0.842551\pi\) | |||||||
\(242\) | −3.50000 | + | 6.06218i | −0.224989 | + | 0.389692i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.55051 | 0.419353 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.24745 | + | 10.8209i | −0.397516 | + | 0.688517i | ||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.4495 | 0.724129 | ||||||||
\(251\) | −17.4495 | −1.10140 | −0.550701 | − | 0.834703i | \(-0.685640\pi\) | ||||
−0.550701 | + | 0.834703i | \(0.685640\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 3.00000 | 0.188237 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.10102 | − | 7.10318i | 0.255815 | − | 0.443084i | −0.709302 | − | 0.704905i | \(-0.750990\pi\) |
0.965116 | + | 0.261821i | \(0.0843230\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.10102 | 0.440387 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.27526 | − | 7.40496i | 0.264126 | − | 0.457480i | ||||
\(263\) | 12.9495 | + | 22.4292i | 0.798500 | + | 1.38304i | 0.920593 | + | 0.390523i | \(0.127706\pi\) |
−0.122093 | + | 0.992519i | \(0.538961\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.89898 | − | 13.6814i | −0.485230 | − | 0.840444i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.8990 | −0.787931 | ||||||||
\(269\) | −9.17423 | + | 15.8902i | −0.559363 | + | 0.968845i | 0.438187 | + | 0.898884i | \(0.355621\pi\) |
−0.997550 | + | 0.0699611i | \(0.977712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.55051 | − | 6.14966i | −0.215678 | − | 0.373565i | 0.737804 | − | 0.675015i | \(-0.235863\pi\) |
−0.953482 | + | 0.301450i | \(0.902530\pi\) | |||||||
\(272\) | 1.00000 | − | 1.73205i | 0.0606339 | − | 0.105021i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.89898 | − | 6.75323i | −0.235546 | − | 0.407978i | ||||
\(275\) | −2.89898 | + | 5.02118i | −0.174815 | + | 0.302789i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.34847 | + | 16.1920i | 0.561695 | + | 0.972884i | 0.997349 | + | 0.0727700i | \(0.0231839\pi\) |
−0.435654 | + | 0.900114i | \(0.643483\pi\) | |||||||
\(278\) | 2.27526 | + | 3.94086i | 0.136461 | + | 0.236357i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.50000 | + | 16.4545i | −0.566722 | + | 0.981592i | 0.430165 | + | 0.902750i | \(0.358455\pi\) |
−0.996887 | + | 0.0788417i | \(0.974878\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.4495 | −1.51282 | −0.756408 | − | 0.654101i | \(-0.773047\pi\) | ||||
−0.756408 | + | 0.654101i | \(0.773047\pi\) | |||||||
\(284\) | −0.101021 | −0.00599446 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.89898 | + | 8.48528i | −0.289683 | + | 0.501745i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 5.00000 | + | 8.66025i | 0.293610 | + | 0.508548i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.44949 | − | 5.97469i | 0.201866 | − | 0.349642i | ||||
\(293\) | 1.37628 | + | 2.38378i | 0.0804029 | + | 0.139262i | 0.903423 | − | 0.428750i | \(-0.141046\pi\) |
−0.823020 | + | 0.568012i | \(0.807713\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.44949 | + | 2.51059i | −0.0843926 | + | 0.146172i | ||||
\(296\) | 5.89898 | + | 10.2173i | 0.342871 | + | 0.593870i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | − | 5.19615i | 0.173785 | − | 0.301005i | ||||
\(299\) | 4.89898 | 0.283315 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.50000 | − | 4.33013i | −0.143859 | − | 0.249171i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.27526 | − | 2.20881i | −0.0731409 | − | 0.126684i | ||||
\(305\) | −4.74745 | + | 8.22282i | −0.271838 | + | 0.470837i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.2474 | 1.44095 | 0.720474 | − | 0.693482i | \(-0.243924\pi\) | ||||
0.720474 | + | 0.693482i | \(0.243924\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.34847 | − | 7.53177i | 0.246976 | − | 0.427776i | ||||
\(311\) | −30.6969 | −1.74066 | −0.870332 | − | 0.492466i | \(-0.836096\pi\) | ||||
−0.870332 | + | 0.492466i | \(0.836096\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.69694 | −0.265487 | −0.132743 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132743 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(314\) | 8.34847 | 0.471131 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.89898 | −0.106826 | ||||||||
\(317\) | −20.6969 | −1.16246 | −0.581228 | − | 0.813741i | \(-0.697428\pi\) | ||||
−0.581228 | + | 0.813741i | \(0.697428\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.7980 | −0.772537 | ||||||||
\(320\) | −0.724745 | + | 1.25529i | −0.0405145 | + | 0.0701731i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.10102 | −0.283828 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.10102 | − | 12.2993i | 0.393894 | − | 0.682244i | ||||
\(326\) | −9.89898 | − | 17.1455i | −0.548254 | − | 0.949603i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.89898 | − | 8.48528i | −0.270501 | − | 0.468521i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.69694 | 0.258167 | 0.129084 | − | 0.991634i | \(-0.458796\pi\) | ||||
0.129084 | + | 0.991634i | \(0.458796\pi\) | |||||||
\(332\) | 1.00000 | − | 1.73205i | 0.0548821 | − | 0.0950586i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.34847 | + | 9.26382i | 0.292655 | + | 0.506894i | ||||
\(335\) | 9.34847 | − | 16.1920i | 0.510761 | − | 0.884665i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.6969 | + | 20.2597i | 0.637173 | + | 1.10362i | 0.986050 | + | 0.166447i | \(0.0532296\pi\) |
−0.348877 | + | 0.937168i | \(0.613437\pi\) | |||||||
\(338\) | 5.50000 | − | 9.52628i | 0.299161 | − | 0.518161i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.44949 | + | 2.51059i | 0.0786096 | + | 0.136156i | ||||
\(341\) | 6.00000 | + | 10.3923i | 0.324918 | + | 0.562775i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.44949 | − | 5.97469i | 0.185984 | − | 0.322134i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.10102 | −0.166712 | ||||||||
\(347\) | −19.5959 | −1.05196 | −0.525982 | − | 0.850496i | \(-0.676302\pi\) | ||||
−0.525982 | + | 0.850496i | \(0.676302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.55051 | + | 9.61377i | −0.297112 | + | 0.514613i | −0.975474 | − | 0.220115i | \(-0.929357\pi\) |
0.678362 | + | 0.734728i | \(0.262690\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | − | 1.73205i | −0.0533002 | − | 0.0923186i | ||||
\(353\) | −3.00000 | − | 5.19615i | −0.159674 | − | 0.276563i | 0.775077 | − | 0.631867i | \(-0.217711\pi\) |
−0.934751 | + | 0.355303i | \(0.884378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0732141 | − | 0.126811i | 0.00388580 | − | 0.00673040i | ||||
\(356\) | −8.44949 | − | 14.6349i | −0.447822 | − | 0.775651i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.3485 | + | 17.9241i | −0.546934 | + | 0.947317i | ||||
\(359\) | −4.39898 | − | 7.61926i | −0.232169 | − | 0.402129i | 0.726277 | − | 0.687402i | \(-0.241249\pi\) |
−0.958446 | + | 0.285273i | \(0.907916\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.24745 | − | 10.8209i | 0.328813 | − | 0.569521i | ||||
\(362\) | 10.3485 | 0.543903 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.00000 | + | 8.66025i | 0.261712 | + | 0.453298i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.89898 | + | 11.9494i | 0.360124 | + | 0.623753i | 0.987981 | − | 0.154576i | \(-0.0494011\pi\) |
−0.627857 | + | 0.778329i | \(0.716068\pi\) | |||||||
\(368\) | −0.500000 | + | 0.866025i | −0.0260643 | + | 0.0451447i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −17.1010 | −0.889040 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.44949 | − | 5.97469i | 0.178608 | − | 0.309358i | −0.762796 | − | 0.646639i | \(-0.776174\pi\) |
0.941404 | + | 0.337281i | \(0.109507\pi\) | |||||||
\(374\) | −4.00000 | −0.206835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.79796 | 0.505291 | ||||||||
\(377\) | 33.7980 | 1.74068 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.4949 | 1.15549 | 0.577743 | − | 0.816219i | \(-0.303934\pi\) | ||||
0.577743 | + | 0.816219i | \(0.303934\pi\) | |||||||
\(380\) | 3.69694 | 0.189649 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.10102 | 0.209826 | ||||||||
\(383\) | −1.44949 | + | 2.51059i | −0.0740655 | + | 0.128285i | −0.900679 | − | 0.434484i | \(-0.856931\pi\) |
0.826614 | + | 0.562769i | \(0.190264\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.8990 | 0.911034 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.44949 | + | 2.51059i | −0.0735867 | + | 0.127456i | ||||
\(389\) | −12.4495 | − | 21.5631i | −0.631214 | − | 1.09330i | −0.987304 | − | 0.158843i | \(-0.949224\pi\) |
0.356090 | − | 0.934452i | \(-0.384110\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.00000 | + | 1.73205i | 0.0505722 | + | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.6969 | 0.841180 | ||||||||
\(395\) | 1.37628 | − | 2.38378i | 0.0692479 | − | 0.119941i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.3485 | − | 33.5125i | −0.971072 | − | 1.68195i | −0.692332 | − | 0.721579i | \(-0.743417\pi\) |
−0.278740 | − | 0.960367i | \(-0.589917\pi\) | |||||||
\(398\) | −1.44949 | + | 2.51059i | −0.0726564 | + | 0.125844i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.44949 | + | 2.51059i | 0.0724745 | + | 0.125529i | ||||
\(401\) | −9.94949 | + | 17.2330i | −0.496854 | + | 0.860576i | −0.999993 | − | 0.00362911i | \(-0.998845\pi\) |
0.503140 | + | 0.864205i | \(0.332178\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.6969 | − | 25.4558i | −0.732107 | − | 1.26805i | ||||
\(404\) | −8.62372 | − | 14.9367i | −0.429046 | − | 0.743130i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.7980 | − | 20.4347i | 0.584803 | − | 1.01291i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.7980 | −0.682265 | −0.341133 | − | 0.940015i | \(-0.610811\pi\) | ||||
−0.341133 | + | 0.940015i | \(0.610811\pi\) | |||||||
\(410\) | 14.2020 | 0.701389 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.00000 | + | 12.1244i | −0.344865 | + | 0.597324i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.44949 | + | 2.51059i | 0.0711527 | + | 0.123240i | ||||
\(416\) | 2.44949 | + | 4.24264i | 0.120096 | + | 0.208013i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.55051 | + | 4.41761i | −0.124750 | + | 0.216073i | ||||
\(419\) | 14.7247 | + | 25.5040i | 0.719351 | + | 1.24595i | 0.961257 | + | 0.275653i | \(0.0888940\pi\) |
−0.241906 | + | 0.970300i | \(0.577773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.4495 | + | 19.8311i | −0.558014 | + | 0.966509i | 0.439648 | + | 0.898170i | \(0.355103\pi\) |
−0.997662 | + | 0.0683385i | \(0.978230\pi\) | |||||||
\(422\) | 6.44949 | + | 11.1708i | 0.313956 | + | 0.543788i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.44949 | − | 9.43879i | 0.264651 | − | 0.458388i | ||||
\(425\) | 5.79796 | 0.281242 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.00000 | − | 10.3923i | −0.290021 | − | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.00000 | + | 8.66025i | 0.241121 | + | 0.417635i | ||||
\(431\) | 15.7980 | − | 27.3629i | 0.760961 | − | 1.31802i | −0.181395 | − | 0.983410i | \(-0.558061\pi\) |
0.942356 | − | 0.334613i | \(-0.108605\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.79796 | −0.374746 | −0.187373 | − | 0.982289i | \(-0.559997\pi\) | ||||
−0.187373 | + | 0.982289i | \(0.559997\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.34847 | + | 10.9959i | −0.304037 | + | 0.526607i | ||||
\(437\) | 2.55051 | 0.122007 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.20204 | 0.105098 | 0.0525488 | − | 0.998618i | \(-0.483265\pi\) | ||||
0.0525488 | + | 0.998618i | \(0.483265\pi\) | |||||||
\(440\) | 2.89898 | 0.138203 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.79796 | 0.466041 | ||||||||
\(443\) | 14.8990 | 0.707872 | 0.353936 | − | 0.935270i | \(-0.384843\pi\) | ||||
0.353936 | + | 0.935270i | \(0.384843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.4949 | 1.16117 | ||||||||
\(446\) | −5.55051 | + | 9.61377i | −0.262824 | + | 0.455225i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.5959 | −0.971981 | −0.485991 | − | 0.873964i | \(-0.661541\pi\) | ||||
−0.485991 | + | 0.873964i | \(0.661541\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.79796 | + | 16.9706i | −0.461368 | + | 0.799113i | ||||
\(452\) | −3.05051 | − | 5.28364i | −0.143484 | − | 0.248521i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.72474 | + | 4.71940i | 0.127879 | + | 0.221492i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.4949 | −0.818377 | −0.409188 | − | 0.912450i | \(-0.634188\pi\) | ||||
−0.409188 | + | 0.912450i | \(0.634188\pi\) | |||||||
\(458\) | 0.623724 | − | 1.08032i | 0.0291447 | − | 0.0504801i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.724745 | − | 1.25529i | −0.0337914 | − | 0.0585284i | ||||
\(461\) | 2.82577 | − | 4.89437i | 0.131609 | − | 0.227954i | −0.792688 | − | 0.609628i | \(-0.791319\pi\) |
0.924297 | + | 0.381674i | \(0.124652\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.84847 | − | 3.20164i | −0.0859057 | − | 0.148793i | 0.819871 | − | 0.572548i | \(-0.194045\pi\) |
−0.905777 | + | 0.423755i | \(0.860712\pi\) | |||||||
\(464\) | −3.44949 | + | 5.97469i | −0.160139 | + | 0.277368i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.50000 | + | 6.06218i | 0.162134 | + | 0.280825i | ||||
\(467\) | 5.00000 | + | 8.66025i | 0.231372 | + | 0.400749i | 0.958212 | − | 0.286058i | \(-0.0923451\pi\) |
−0.726840 | + | 0.686807i | \(0.759012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.10102 | + | 12.2993i | −0.327546 | + | 0.567326i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.00000 | −0.0920575 | ||||||||
\(473\) | −13.7980 | −0.634431 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.69694 | − | 6.40329i | 0.169627 | − | 0.293803i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.39898 | − | 5.88721i | −0.155466 | − | 0.269274i | ||||
\(479\) | 4.79796 | + | 8.31031i | 0.219224 | + | 0.379708i | 0.954571 | − | 0.297983i | \(-0.0963140\pi\) |
−0.735347 | + | 0.677691i | \(0.762981\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.8990 | + | 50.0545i | −1.31768 | + | 2.28229i | ||||
\(482\) | 0.449490 | + | 0.778539i | 0.0204737 | + | 0.0354615i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.50000 | − | 6.06218i | 0.159091 | − | 0.275554i | ||||
\(485\) | −2.10102 | − | 3.63907i | −0.0954024 | − | 0.165242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.1969 | − | 31.5180i | 0.824582 | − | 1.42822i | −0.0776564 | − | 0.996980i | \(-0.524744\pi\) |
0.902238 | − | 0.431238i | \(-0.141923\pi\) | |||||||
\(488\) | −6.55051 | −0.296528 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.89898 | + | 13.6814i | 0.356476 | + | 0.617434i | 0.987369 | − | 0.158435i | \(-0.0506448\pi\) |
−0.630893 | + | 0.775869i | \(0.717312\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.89898 | + | 11.9494i | 0.310714 | + | 0.538173i | ||||
\(494\) | 6.24745 | − | 10.8209i | 0.281086 | − | 0.486855i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.6969 | − | 21.9917i | 0.568393 | − | 0.984486i | −0.428332 | − | 0.903621i | \(-0.640899\pi\) |
0.996725 | − | 0.0808642i | \(-0.0257680\pi\) | |||||||
\(500\) | −11.4495 | −0.512037 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.4495 | 0.778809 | ||||||||
\(503\) | 24.4949 | 1.09217 | 0.546087 | − | 0.837729i | \(-0.316117\pi\) | ||||
0.546087 | + | 0.837729i | \(0.316117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.0000 | 1.11249 | ||||||||
\(506\) | 2.00000 | 0.0889108 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.00000 | −0.133103 | ||||||||
\(509\) | −3.55051 | + | 6.14966i | −0.157374 | + | 0.272579i | −0.933921 | − | 0.357480i | \(-0.883636\pi\) |
0.776547 | + | 0.630059i | \(0.216969\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.10102 | + | 7.10318i | −0.180888 | + | 0.313308i | ||||
\(515\) | −10.1464 | − | 17.5741i | −0.447105 | − | 0.774409i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.79796 | − | 16.9706i | −0.430914 | − | 0.746364i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.10102 | −0.311400 | ||||||||
\(521\) | −4.65153 | + | 8.05669i | −0.203787 | + | 0.352970i | −0.949746 | − | 0.313023i | \(-0.898658\pi\) |
0.745958 | + | 0.665993i | \(0.231992\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.17423 | + | 12.4261i | 0.313707 | + | 0.543357i | 0.979162 | − | 0.203081i | \(-0.0650956\pi\) |
−0.665455 | + | 0.746438i | \(0.731762\pi\) | |||||||
\(524\) | −4.27526 | + | 7.40496i | −0.186765 | + | 0.323487i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.9495 | − | 22.4292i | −0.564625 | − | 0.977958i | ||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | 7.89898 | + | 13.6814i | 0.343110 | + | 0.594284i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0000 | − | 41.5692i | 1.03956 | − | 1.80056i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.3939 | 0.752003 | ||||||||
\(536\) | 12.8990 | 0.557151 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.17423 | − | 15.8902i | 0.395529 | − | 0.685077i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.24745 | + | 16.0171i | 0.397579 | + | 0.688627i | 0.993427 | − | 0.114471i | \(-0.0365172\pi\) |
−0.595848 | + | 0.803097i | \(0.703184\pi\) | |||||||
\(542\) | 3.55051 | + | 6.14966i | 0.152507 | + | 0.264151i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.00000 | + | 1.73205i | −0.0428746 | + | 0.0742611i | ||||
\(545\) | −9.20204 | − | 15.9384i | −0.394172 | − | 0.682726i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.79796 | − | 6.57826i | 0.162389 | − | 0.281266i | −0.773336 | − | 0.633996i | \(-0.781413\pi\) |
0.935725 | + | 0.352730i | \(0.114747\pi\) | |||||||
\(548\) | 3.89898 | + | 6.75323i | 0.166556 | + | 0.288484i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.89898 | − | 5.02118i | 0.123613 | − | 0.214104i | ||||
\(551\) | 17.5959 | 0.749611 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.34847 | − | 16.1920i | −0.397178 | − | 0.687933i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.27526 | − | 3.94086i | −0.0964923 | − | 0.167130i | ||||
\(557\) | −6.44949 | + | 11.1708i | −0.273274 | + | 0.473324i | −0.969698 | − | 0.244306i | \(-0.921440\pi\) |
0.696424 | + | 0.717630i | \(0.254773\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.7980 | 1.42950 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.50000 | − | 16.4545i | 0.400733 | − | 0.694090i | ||||
\(563\) | 39.9444 | 1.68346 | 0.841728 | − | 0.539902i | \(-0.181539\pi\) | ||||
0.841728 | + | 0.539902i | \(0.181539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.84337 | 0.372043 | ||||||||
\(566\) | 25.4495 | 1.06972 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.101021 | 0.00423873 | ||||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.7980 | 1.41440 | 0.707200 | − | 0.707013i | \(-0.249958\pi\) | ||||
0.707200 | + | 0.707013i | \(0.249958\pi\) | |||||||
\(572\) | 4.89898 | − | 8.48528i | 0.204837 | − | 0.354787i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.89898 | −0.120896 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.79796 | − | 13.5065i | 0.324633 | − | 0.562281i | −0.656805 | − | 0.754061i | \(-0.728092\pi\) |
0.981438 | + | 0.191779i | \(0.0614258\pi\) | |||||||
\(578\) | −6.50000 | − | 11.2583i | −0.270364 | − | 0.468285i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.00000 | − | 8.66025i | −0.207614 | − | 0.359597i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.7980 | −0.902779 | ||||||||
\(584\) | −3.44949 | + | 5.97469i | −0.142741 | + | 0.247234i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.37628 | − | 2.38378i | −0.0568534 | − | 0.0984730i | ||||
\(587\) | 8.07321 | − | 13.9832i | 0.333217 | − | 0.577149i | −0.649924 | − | 0.760000i | \(-0.725199\pi\) |
0.983141 | + | 0.182850i | \(0.0585324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.65153 | − | 13.2528i | −0.315276 | − | 0.546074i | ||||
\(590\) | 1.44949 | − | 2.51059i | 0.0596745 | − | 0.103359i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.89898 | − | 10.2173i | −0.242447 | − | 0.419930i | ||||
\(593\) | 7.34847 | + | 12.7279i | 0.301765 | + | 0.522673i | 0.976536 | − | 0.215355i | \(-0.0690907\pi\) |
−0.674770 | + | 0.738028i | \(0.735757\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.00000 | + | 5.19615i | −0.122885 | + | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.89898 | −0.200334 | ||||||||
\(599\) | 33.7980 | 1.38095 | 0.690474 | − | 0.723358i | \(-0.257402\pi\) | ||||
0.690474 | + | 0.723358i | \(0.257402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.34847 | + | 14.4600i | −0.340541 | + | 0.589835i | −0.984533 | − | 0.175198i | \(-0.943944\pi\) |
0.643992 | + | 0.765032i | \(0.277277\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.50000 | + | 4.33013i | 0.101724 | + | 0.176190i | ||||
\(605\) | 5.07321 | + | 8.78706i | 0.206255 | + | 0.357245i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.3485 | + | 17.9241i | −0.420031 | + | 0.727516i | −0.995942 | − | 0.0899969i | \(-0.971314\pi\) |
0.575911 | + | 0.817513i | \(0.304648\pi\) | |||||||
\(608\) | 1.27526 | + | 2.20881i | 0.0517184 | + | 0.0895789i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.74745 | − | 8.22282i | 0.192219 | − | 0.332932i | ||||
\(611\) | 24.0000 | + | 41.5692i | 0.970936 | + | 1.68171i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.34847 | − | 12.7279i | 0.296802 | − | 0.514076i | −0.678601 | − | 0.734508i | \(-0.737413\pi\) |
0.975402 | + | 0.220432i | \(0.0707466\pi\) | |||||||
\(614\) | −25.2474 | −1.01890 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.69694 | − | 13.3315i | −0.309867 | − | 0.536706i | 0.668466 | − | 0.743743i | \(-0.266951\pi\) |
−0.978333 | + | 0.207037i | \(0.933618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.0732 | − | 26.1076i | −0.605844 | − | 1.04935i | −0.991918 | − | 0.126884i | \(-0.959502\pi\) |
0.386074 | − | 0.922468i | \(-0.373831\pi\) | |||||||
\(620\) | −4.34847 | + | 7.53177i | −0.174639 | + | 0.302483i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.6969 | 1.23084 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.05051 | − | 1.81954i | 0.0420204 | − | 0.0727815i | ||||
\(626\) | 4.69694 | 0.187727 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.34847 | −0.333140 | ||||||||
\(629\) | −23.5959 | −0.940831 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.8990 | 1.11064 | 0.555320 | − | 0.831636i | \(-0.312596\pi\) | ||||
0.555320 | + | 0.831636i | \(0.312596\pi\) | |||||||
\(632\) | 1.89898 | 0.0755373 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.6969 | 0.821980 | ||||||||
\(635\) | 2.17423 | − | 3.76588i | 0.0862819 | − | 0.149445i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.7980 | 0.546266 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.724745 | − | 1.25529i | 0.0286481 | − | 0.0496199i | ||||
\(641\) | −3.74745 | − | 6.49077i | −0.148015 | − | 0.256370i | 0.782479 | − | 0.622678i | \(-0.213955\pi\) |
−0.930494 | + | 0.366308i | \(0.880622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.6969 | + | 34.1161i | 0.776771 | + | 1.34541i | 0.933793 | + | 0.357812i | \(0.116477\pi\) |
−0.157022 | + | 0.987595i | \(0.550189\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.10102 | 0.200697 | ||||||||
\(647\) | −25.3485 | + | 43.9048i | −0.996551 | + | 1.72608i | −0.426412 | + | 0.904529i | \(0.640223\pi\) |
−0.570139 | + | 0.821548i | \(0.693111\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.00000 | + | 3.46410i | 0.0785069 | + | 0.135978i | ||||
\(650\) | −7.10102 | + | 12.2993i | −0.278525 | + | 0.482419i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.89898 | + | 17.1455i | 0.387674 | + | 0.671471i | ||||
\(653\) | 4.89898 | − | 8.48528i | 0.191712 | − | 0.332055i | −0.754106 | − | 0.656753i | \(-0.771929\pi\) |
0.945818 | + | 0.324698i | \(0.105263\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.19694 | − | 10.7334i | −0.242134 | − | 0.419389i | ||||
\(656\) | 4.89898 | + | 8.48528i | 0.191273 | + | 0.331295i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.3485 | + | 21.3882i | −0.481028 | + | 0.833165i | −0.999763 | − | 0.0217701i | \(-0.993070\pi\) |
0.518735 | + | 0.854935i | \(0.326403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.55051 | 0.176994 | 0.0884972 | − | 0.996076i | \(-0.471794\pi\) | ||||
0.0884972 | + | 0.996076i | \(0.471794\pi\) | |||||||
\(662\) | −4.69694 | −0.182552 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.00000 | + | 1.73205i | −0.0388075 | + | 0.0672166i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.44949 | − | 5.97469i | −0.133565 | − | 0.231341i | ||||
\(668\) | −5.34847 | − | 9.26382i | −0.206938 | − | 0.358428i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.34847 | + | 16.1920i | −0.361163 | + | 0.625552i | ||||
\(671\) | 6.55051 | + | 11.3458i | 0.252880 | + | 0.438000i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.29796 | − | 7.44428i | 0.165674 | − | 0.286956i | −0.771220 | − | 0.636568i | \(-0.780353\pi\) |
0.936894 | + | 0.349612i | \(0.113687\pi\) | |||||||
\(674\) | −11.6969 | − | 20.2597i | −0.450549 | − | 0.780374i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.50000 | + | 9.52628i | −0.211538 | + | 0.366395i | ||||
\(677\) | −14.6969 | −0.564849 | −0.282425 | − | 0.959289i | \(-0.591139\pi\) | ||||
−0.282425 | + | 0.959289i | \(0.591139\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.44949 | − | 2.51059i | −0.0555854 | − | 0.0962767i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.00000 | − | 10.3923i | −0.229752 | − | 0.397942i | ||||
\(683\) | 25.8990 | − | 44.8583i | 0.990997 | − | 1.71646i | 0.379551 | − | 0.925171i | \(-0.376079\pi\) |
0.611446 | − | 0.791286i | \(-0.290588\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.3031 | −0.431868 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.44949 | + | 5.97469i | −0.131511 | + | 0.227783i | ||||
\(689\) | 53.3939 | 2.03414 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 51.0454 | 1.94186 | 0.970929 | − | 0.239366i | \(-0.0769396\pi\) | ||||
0.970929 | + | 0.239366i | \(0.0769396\pi\) | |||||||
\(692\) | 3.10102 | 0.117883 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.5959 | 0.743851 | ||||||||
\(695\) | 6.59592 | 0.250197 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.5959 | 0.742248 | ||||||||
\(698\) | 5.55051 | − | 9.61377i | 0.210090 | − | 0.363886i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.39388 | 0.279263 | 0.139631 | − | 0.990204i | \(-0.455408\pi\) | ||||
0.139631 | + | 0.990204i | \(0.455408\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.0454 | + | 26.0594i | −0.567448 | + | 0.982849i | ||||
\(704\) | 1.00000 | + | 1.73205i | 0.0376889 | + | 0.0652791i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.00000 | + | 5.19615i | 0.112906 | + | 0.195560i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.5959 | 1.03639 | 0.518193 | − | 0.855264i | \(-0.326605\pi\) | ||||
0.518193 | + | 0.855264i | \(0.326605\pi\) | |||||||
\(710\) | −0.0732141 | + | 0.126811i | −0.00274768 | + | 0.00475911i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.44949 | + | 14.6349i | 0.316658 | + | 0.548468i | ||||
\(713\) | −3.00000 | + | 5.19615i | −0.112351 | + | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.10102 | + | 12.2993i | 0.265563 | + | 0.459969i | ||||
\(716\) | 10.3485 | − | 17.9241i | 0.386740 | − | 0.669854i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.39898 | + | 7.61926i | 0.164168 | + | 0.284348i | ||||
\(719\) | 4.89898 | + | 8.48528i | 0.182701 | + | 0.316448i | 0.942799 | − | 0.333360i | \(-0.108183\pi\) |
−0.760098 | + | 0.649808i | \(0.774849\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.24745 | + | 10.8209i | −0.232506 | + | 0.402712i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.3485 | −0.384598 | ||||||||
\(725\) | −20.0000 | −0.742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.24745 | − | 7.35680i | 0.157529 | − | 0.272848i | −0.776448 | − | 0.630181i | \(-0.782981\pi\) |
0.933977 | + | 0.357333i | \(0.116314\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.00000 | − | 8.66025i | −0.185058 | − | 0.320530i | ||||
\(731\) | 6.89898 | + | 11.9494i | 0.255168 | + | 0.441964i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.72474 | − | 15.1117i | 0.322256 | − | 0.558163i | −0.658697 | − | 0.752408i | \(-0.728892\pi\) |
0.980953 | + | 0.194245i | \(0.0622255\pi\) | |||||||
\(734\) | −6.89898 | − | 11.9494i | −0.254646 | − | 0.441060i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.500000 | − | 0.866025i | 0.0184302 | − | 0.0319221i | ||||
\(737\) | −12.8990 | − | 22.3417i | −0.475140 | − | 0.822967i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.79796 | + | 11.7744i | −0.250067 | + | 0.433129i | −0.963544 | − | 0.267550i | \(-0.913786\pi\) |
0.713477 | + | 0.700679i | \(0.247119\pi\) | |||||||
\(740\) | 17.1010 | 0.628646 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0000 | + | 31.1769i | 0.660356 | + | 1.14377i | 0.980522 | + | 0.196409i | \(0.0629279\pi\) |
−0.320166 | + | 0.947361i | \(0.603739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.34847 | − | 7.53177i | −0.159316 | − | 0.275943i | ||||
\(746\) | −3.44949 | + | 5.97469i | −0.126295 | + | 0.218749i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.00000 | 0.146254 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.702041 | + | 1.21597i | −0.0256178 | + | 0.0443714i | −0.878550 | − | 0.477650i | \(-0.841489\pi\) |
0.852932 | + | 0.522022i | \(0.174822\pi\) | |||||||
\(752\) | −9.79796 | −0.357295 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −33.7980 | −1.23085 | ||||||||
\(755\) | −7.24745 | −0.263762 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.3939 | −1.28641 | −0.643206 | − | 0.765693i | \(-0.722396\pi\) | ||||
−0.643206 | + | 0.765693i | \(0.722396\pi\) | |||||||
\(758\) | −22.4949 | −0.817051 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.69694 | −0.134102 | ||||||||
\(761\) | 1.00000 | − | 1.73205i | 0.0362500 | − | 0.0627868i | −0.847331 | − | 0.531065i | \(-0.821792\pi\) |
0.883581 | + | 0.468278i | \(0.155125\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.10102 | −0.148370 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.44949 | − | 2.51059i | 0.0523722 | − | 0.0907113i | ||||
\(767\) | −4.89898 | − | 8.48528i | −0.176892 | − | 0.306386i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.0454 | + | 29.5235i | 0.614673 | + | 1.06465i | 0.990442 | + | 0.137932i | \(0.0440454\pi\) |
−0.375769 | + | 0.926714i | \(0.622621\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.8990 | −0.644198 | ||||||||
\(773\) | 16.9722 | − | 29.3967i | 0.610447 | − | 1.05733i | −0.380718 | − | 0.924691i | \(-0.624323\pi\) |
0.991165 | − | 0.132635i | \(-0.0423437\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.69694 | + | 15.0635i | 0.312403 | + | 0.541098i | ||||
\(776\) | 1.44949 | − | 2.51059i | 0.0520336 | − | 0.0901249i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.4495 | + | 21.5631i | 0.446336 | + | 0.773076i | ||||
\(779\) | 12.4949 | − | 21.6418i | 0.447676 | − | 0.775398i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.101021 | − | 0.174973i | −0.00361480 | − | 0.00626101i | ||||
\(782\) | −1.00000 | − | 1.73205i | −0.0357599 | − | 0.0619380i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.05051 | − | 10.4798i | 0.215952 | − | 0.374040i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.3939 | −0.406148 | −0.203074 | − | 0.979163i | \(-0.565093\pi\) | ||||
−0.203074 | + | 0.979163i | \(0.565093\pi\) | |||||||
\(788\) | −16.6969 | −0.594804 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.37628 | + | 2.38378i | −0.0489657 | + | 0.0848111i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.0454 | − | 27.7915i | −0.569789 | − | 0.986904i | ||||
\(794\) | 19.3485 | + | 33.5125i | 0.686651 | + | 1.18932i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.44949 | − | 2.51059i | 0.0513758 | − | 0.0889855i | ||||
\(797\) | −8.97219 | − | 15.5403i | −0.317811 | − | 0.550465i | 0.662220 | − | 0.749310i | \(-0.269615\pi\) |
−0.980031 | + | 0.198844i | \(0.936281\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.79796 | + | 16.9706i | −0.346627 | + | 0.600375i | ||||
\(800\) | −1.44949 | − | 2.51059i | −0.0512472 | − | 0.0887628i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.94949 | − | 17.2330i | 0.351329 | − | 0.608519i | ||||
\(803\) | 13.7980 | 0.486919 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.6969 | + | 25.4558i | 0.517678 | + | 0.896644i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.62372 | + | 14.9367i | 0.303382 | + | 0.525472i | ||||
\(809\) | −8.10102 | + | 14.0314i | −0.284817 | + | 0.493317i | −0.972565 | − | 0.232632i | \(-0.925266\pi\) |
0.687748 | + | 0.725950i | \(0.258599\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.00000 | −0.0702295 | −0.0351147 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351147 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.7980 | + | 20.4347i | −0.413518 | + | 0.716235i | ||||
\(815\) | −28.6969 | −1.00521 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.5959 | 0.615603 | ||||||||
\(818\) | 13.7980 | 0.482434 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.2020 | −0.495957 | ||||||||
\(821\) | −0.404082 | −0.0141026 | −0.00705128 | − | 0.999975i | \(-0.502245\pi\) | ||||
−0.00705128 | + | 0.999975i | \(0.502245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.3939 | −0.466881 | −0.233441 | − | 0.972371i | \(-0.574998\pi\) | ||||
−0.233441 | + | 0.972371i | \(0.574998\pi\) | |||||||
\(824\) | 7.00000 | − | 12.1244i | 0.243857 | − | 0.422372i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.4949 | 1.26905 | 0.634526 | − | 0.772902i | \(-0.281195\pi\) | ||||
0.634526 | + | 0.772902i | \(0.281195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.651531 | + | 1.12848i | −0.0226286 | + | 0.0391939i | −0.877118 | − | 0.480275i | \(-0.840537\pi\) |
0.854489 | + | 0.519469i | \(0.173870\pi\) | |||||||
\(830\) | −1.44949 | − | 2.51059i | −0.0503125 | − | 0.0871438i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.44949 | − | 4.24264i | −0.0849208 | − | 0.147087i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.5051 | 0.536576 | ||||||||
\(836\) | 2.55051 | − | 4.41761i | 0.0882112 | − | 0.152786i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.7247 | − | 25.5040i | −0.508658 | − | 0.881021i | ||||
\(839\) | −17.5505 | + | 30.3984i | −0.605911 | + | 1.04947i | 0.385996 | + | 0.922500i | \(0.373858\pi\) |
−0.991907 | + | 0.126968i | \(0.959475\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.29796 | − | 16.1045i | −0.320619 | − | 0.555329i | ||||
\(842\) | 11.4495 | − | 19.8311i | 0.394575 | − | 0.683425i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.44949 | − | 11.1708i | −0.222001 | − | 0.384516i | ||||
\(845\) | −7.97219 | − | 13.8082i | −0.274252 | − | 0.475018i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.44949 | + | 9.43879i | −0.187136 | + | 0.324129i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.79796 | −0.198868 | ||||||||
\(851\) | 11.7980 | 0.404429 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.4217 | + | 21.5150i | −0.425310 | + | 0.736659i | −0.996449 | − | 0.0841942i | \(-0.973168\pi\) |
0.571139 | + | 0.820853i | \(0.306502\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | + | 10.3923i | 0.205076 | + | 0.355202i | ||||
\(857\) | −17.4495 | − | 30.2234i | −0.596063 | − | 1.03241i | −0.993396 | − | 0.114737i | \(-0.963397\pi\) |
0.397333 | − | 0.917675i | \(-0.369936\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.00000 | − | 8.66025i | 0.170598 | − | 0.295484i | −0.768031 | − | 0.640412i | \(-0.778763\pi\) |
0.938629 | + | 0.344928i | \(0.112097\pi\) | |||||||
\(860\) | −5.00000 | − | 8.66025i | −0.170499 | − | 0.295312i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.7980 | + | 27.3629i | −0.538081 | + | 0.931983i | ||||
\(863\) | 5.94949 | + | 10.3048i | 0.202523 | + | 0.350780i | 0.949341 | − | 0.314249i | \(-0.101753\pi\) |
−0.746818 | + | 0.665029i | \(0.768419\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.24745 | + | 3.89270i | −0.0764155 | + | 0.132356i | ||||
\(866\) | 7.79796 | 0.264985 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.89898 | − | 3.28913i | −0.0644185 | − | 0.111576i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.5959 | + | 54.7257i | 1.07059 | + | 1.85431i | ||||
\(872\) | 6.34847 | − | 10.9959i | 0.214986 | − | 0.372367i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.55051 | −0.0862723 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.2474 | + | 19.4812i | −0.379799 | + | 0.657832i | −0.991033 | − | 0.133619i | \(-0.957340\pi\) |
0.611233 | + | 0.791450i | \(0.290674\pi\) | |||||||
\(878\) | −2.20204 | −0.0743153 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.89898 | −0.0977246 | ||||||||
\(881\) | −19.5959 | −0.660203 | −0.330102 | − | 0.943945i | \(-0.607083\pi\) | ||||
−0.330102 | + | 0.943945i | \(0.607083\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.7980 | −0.666254 | −0.333127 | − | 0.942882i | \(-0.608104\pi\) | ||||
−0.333127 | + | 0.942882i | \(0.608104\pi\) | |||||||
\(884\) | −9.79796 | −0.329541 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.8990 | −0.500541 | ||||||||
\(887\) | −7.10102 | + | 12.2993i | −0.238429 | + | 0.412971i | −0.960264 | − | 0.279094i | \(-0.909966\pi\) |
0.721835 | + | 0.692065i | \(0.243299\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −24.4949 | −0.821071 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.55051 | − | 9.61377i | 0.185845 | − | 0.321893i | ||||
\(893\) | 12.4949 | + | 21.6418i | 0.418126 | + | 0.724215i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.0000 | + | 25.9808i | 0.501395 | + | 0.868441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.5959 | 0.687295 | ||||||||
\(899\) | −20.6969 | + | 35.8481i | −0.690282 | + | 1.19560i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.8990 | + | 18.8776i | 0.363098 | + | 0.628904i | ||||
\(902\) | 9.79796 | − | 16.9706i | 0.326236 | − | 0.565058i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.05051 | + | 5.28364i | 0.101458 | + | 0.175731i | ||||
\(905\) | 7.50000 | − | 12.9904i | 0.249308 | − | 0.431815i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.34847 | − | 2.33562i | −0.0447752 | − | 0.0775529i | 0.842769 | − | 0.538275i | \(-0.180924\pi\) |
−0.887544 | + | 0.460722i | \(0.847590\pi\) | |||||||
\(908\) | −2.72474 | − | 4.71940i | −0.0904238 | − | 0.156619i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.9949 | − | 45.0245i | 0.861249 | − | 1.49173i | −0.00947432 | − | 0.999955i | \(-0.503016\pi\) |
0.870724 | − | 0.491773i | \(-0.163651\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.00000 | 0.132381 | ||||||||
\(914\) | 17.4949 | 0.578680 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.623724 | + | 1.08032i | −0.0206084 | + | 0.0356949i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.8485 | + | 22.2542i | 0.423832 | + | 0.734098i | 0.996311 | − | 0.0858213i | \(-0.0273514\pi\) |
−0.572479 | + | 0.819920i | \(0.694018\pi\) | |||||||
\(920\) | 0.724745 | + | 1.25529i | 0.0238941 | + | 0.0413858i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.82577 | + | 4.89437i | −0.0930616 | + | 0.161187i | ||||
\(923\) | 0.247449 | + | 0.428594i | 0.00814487 | + | 0.0141073i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.1010 | − | 29.6198i | 0.562278 | − | 0.973894i | ||||
\(926\) | 1.84847 | + | 3.20164i | 0.0607445 | + | 0.105213i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.44949 | − | 5.97469i | 0.113235 | − | 0.196129i | ||||
\(929\) | −34.2929 | −1.12511 | −0.562556 | − | 0.826759i | \(-0.690182\pi\) | ||||
−0.562556 | + | 0.826759i | \(0.690182\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.50000 | − | 6.06218i | −0.114646 | − | 0.198573i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.00000 | − | 8.66025i | −0.163605 | − | 0.283372i | ||||
\(935\) | −2.89898 | + | 5.02118i | −0.0948068 | + | 0.164210i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.5959 | 1.48955 | 0.744777 | − | 0.667314i | \(-0.232556\pi\) | ||||
0.744777 | + | 0.667314i | \(0.232556\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.10102 | − | 12.2993i | 0.231610 | − | 0.401160i | ||||
\(941\) | 1.44949 | 0.0472520 | 0.0236260 | − | 0.999721i | \(-0.492479\pi\) | ||||
0.0236260 | + | 0.999721i | \(0.492479\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.79796 | −0.319065 | ||||||||
\(944\) | 2.00000 | 0.0650945 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.7980 | 0.448610 | ||||||||
\(947\) | −52.4949 | −1.70585 | −0.852927 | − | 0.522029i | \(-0.825175\pi\) | ||||
−0.852927 | + | 0.522029i | \(0.825175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.7980 | −1.09713 | ||||||||
\(950\) | −3.69694 | + | 6.40329i | −0.119945 | + | 0.207750i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.39388 | 0.109938 | 0.0549692 | − | 0.998488i | \(-0.482494\pi\) | ||||
0.0549692 | + | 0.998488i | \(0.482494\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.97219 | − | 5.14799i | 0.0961779 | − | 0.166585i | ||||
\(956\) | 3.39898 | + | 5.88721i | 0.109931 | + | 0.190406i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.79796 | − | 8.31031i | −0.155015 | − | 0.268494i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 28.8990 | − | 50.0545i | 0.931740 | − | 1.61382i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.449490 | − | 0.778539i | −0.0144771 | − | 0.0250751i | ||||
\(965\) | 12.9722 | − | 22.4685i | 0.417590 | − | 0.723287i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.2980 | − | 21.3007i | −0.395476 | − | 0.684984i | 0.597686 | − | 0.801730i | \(-0.296087\pi\) |
−0.993162 | + | 0.116746i | \(0.962754\pi\) | |||||||
\(968\) | −3.50000 | + | 6.06218i | −0.112494 | + | 0.194846i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.10102 | + | 3.63907i | 0.0674597 | + | 0.116844i | ||||
\(971\) | −0.0278064 | − | 0.0481621i | −0.000892350 | − | 0.00154560i | 0.865579 | − | 0.500773i | \(-0.166951\pi\) |
−0.866471 | + | 0.499227i | \(0.833617\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18.1969 | + | 31.5180i | −0.583068 | + | 1.00990i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.55051 | 0.209677 | ||||||||
\(977\) | 37.5959 | 1.20280 | 0.601400 | − | 0.798948i | \(-0.294610\pi\) | ||||
0.601400 | + | 0.798948i | \(0.294610\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.8990 | − | 29.2699i | 0.540094 | − | 0.935470i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.89898 | − | 13.6814i | −0.252067 | − | 0.436592i | ||||
\(983\) | −16.5959 | − | 28.7450i | −0.529328 | − | 0.916822i | −0.999415 | − | 0.0342024i | \(-0.989111\pi\) |
0.470087 | − | 0.882620i | \(-0.344222\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.1010 | − | 20.9596i | 0.385571 | − | 0.667828i | ||||
\(986\) | −6.89898 | − | 11.9494i | −0.219708 | − | 0.380546i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.24745 | + | 10.8209i | −0.198758 | + | 0.344259i | ||||
\(989\) | −3.44949 | − | 5.97469i | −0.109687 | − | 0.189984i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.898979 | − | 1.55708i | 0.0285570 | − | 0.0494622i | −0.851394 | − | 0.524527i | \(-0.824242\pi\) |
0.879951 | + | 0.475065i | \(0.157575\pi\) | |||||||
\(992\) | −6.00000 | −0.190500 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.10102 | + | 3.63907i | 0.0666068 | + | 0.115366i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.0732 | − | 45.1601i | −0.825747 | − | 1.43024i | −0.901347 | − | 0.433097i | \(-0.857421\pi\) |
0.0756001 | − | 0.997138i | \(-0.475913\pi\) | |||||||
\(998\) | −12.6969 | + | 21.9917i | −0.401915 | + | 0.696136i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))