Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,2,Mod(34,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.e (of order \(3\), degree \(2\), 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: | \(0.790518980011\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.67 |
Dual form | 99.2.e.b.34.1 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | 1.50000 | − | 2.59808i | 0.670820 | − | 1.16190i | −0.306851 | − | 0.951757i | \(-0.599275\pi\) |
0.977672 | − | 0.210138i | \(-0.0673912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 3.46410i | 0.755929 | + | 1.30931i | 0.944911 | + | 0.327327i | \(0.106148\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | 3.46410i | 1.00000i | ||||||||
\(13\) | −1.00000 | + | 1.73205i | −0.277350 | + | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.19615i | 1.34164i | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −3.00000 | − | 5.19615i | −0.670820 | − | 1.16190i | ||||
\(21\) | −6.00000 | − | 3.46410i | −1.30931 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.50000 | + | 2.59808i | −0.312772 | + | 0.541736i | −0.978961 | − | 0.204046i | \(-0.934591\pi\) |
0.666190 | + | 0.745782i | \(0.267924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 8.00000 | 1.51186 | ||||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.50000 | + | 0.866025i | 0.261116 | + | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.0000 | 2.02837 | ||||||||
\(36\) | −3.00000 | − | 5.19615i | −0.500000 | − | 0.866025i | ||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.46410i | − | 0.554700i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | − | 6.92820i | −0.609994 | − | 1.05654i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) |
0.381246 | − | 0.924473i | \(-0.375495\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | −4.50000 | − | 7.79423i | −0.670820 | − | 1.16190i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.50000 | − | 2.59808i | −0.218797 | − | 0.378968i | 0.735643 | − | 0.677369i | \(-0.236880\pi\) |
−0.954441 | + | 0.298401i | \(0.903547\pi\) | |||||||
\(48\) | 6.00000 | + | 3.46410i | 0.866025 | + | 0.500000i | ||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.00000 | − | 5.19615i | 1.26025 | − | 0.727607i | ||||
\(52\) | 2.00000 | + | 3.46410i | 0.277350 | + | 0.480384i | ||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.00000 | + | 1.73205i | −0.397360 | + | 0.229416i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 9.00000 | + | 5.19615i | 1.16190 | + | 0.670820i | ||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.0000 | 1.51186 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 3.00000 | + | 5.19615i | 0.372104 | + | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.50000 | − | 11.2583i | 0.794101 | − | 1.37542i | −0.129307 | − | 0.991605i | \(-0.541275\pi\) |
0.923408 | − | 0.383819i | \(-0.125391\pi\) | |||||||
\(68\) | −6.00000 | + | 10.3923i | −0.727607 | + | 1.26025i | ||||
\(69\) | − | 5.19615i | − | 0.625543i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.00000 | + | 3.46410i | 0.692820 | + | 0.400000i | ||||
\(76\) | 2.00000 | − | 3.46410i | 0.229416 | − | 0.397360i | ||||
\(77\) | 2.00000 | − | 3.46410i | 0.227921 | − | 0.394771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | − | 1.73205i | −0.112509 | − | 0.194871i | 0.804272 | − | 0.594261i | \(-0.202555\pi\) |
−0.916781 | + | 0.399390i | \(0.869222\pi\) | |||||||
\(80\) | −12.0000 | −1.34164 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.00000 | + | 15.5885i | 0.987878 | + | 1.71106i | 0.628372 | + | 0.777913i | \(0.283721\pi\) |
0.359506 | + | 0.933143i | \(0.382945\pi\) | |||||||
\(84\) | −12.0000 | + | 6.92820i | −1.30931 | + | 0.755929i | ||||
\(85\) | −9.00000 | + | 15.5885i | −0.976187 | + | 1.69081i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.00000 | − | 5.19615i | −0.964901 | − | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | −0.838628 | ||||||||
\(92\) | 3.00000 | + | 5.19615i | 0.312772 | + | 0.541736i | ||||
\(93\) | − | 13.8564i | − | 1.43684i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.00000 | − | 5.19615i | 0.307794 | − | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | − | 1.73205i | −0.101535 | − | 0.175863i | 0.810782 | − | 0.585348i | \(-0.199042\pi\) |
−0.912317 | + | 0.409484i | \(0.865709\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | −8.00000 | −0.800000 | ||||||||
\(101\) | −3.00000 | − | 5.19615i | −0.298511 | − | 0.517036i | 0.677284 | − | 0.735721i | \(-0.263157\pi\) |
−0.975796 | + | 0.218685i | \(0.929823\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.50000 | + | 4.33013i | −0.246332 | + | 0.426660i | −0.962505 | − | 0.271263i | \(-0.912559\pi\) |
0.716173 | + | 0.697923i | \(0.245892\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.0000 | + | 10.3923i | −1.75662 | + | 1.01419i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 9.00000 | + | 5.19615i | 0.866025 | + | 0.500000i | ||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | + | 1.73205i | −0.284747 | + | 0.164399i | ||||
\(112\) | 8.00000 | − | 13.8564i | 0.755929 | − | 1.30931i | ||||
\(113\) | 3.00000 | − | 5.19615i | 0.282216 | − | 0.488813i | −0.689714 | − | 0.724082i | \(-0.742264\pi\) |
0.971930 | + | 0.235269i | \(0.0755971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.50000 | + | 7.79423i | 0.419627 | + | 0.726816i | ||||
\(116\) | 12.0000 | 1.11417 | ||||||||
\(117\) | 3.00000 | + | 5.19615i | 0.277350 | + | 0.480384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.0000 | − | 20.7846i | −1.10004 | − | 1.90532i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.00000 | + | 13.8564i | 0.718421 | + | 1.24434i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.0000 | + | 6.92820i | 1.05654 | + | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.00000 | + | 15.5885i | −0.786334 | + | 1.36197i | 0.141865 | + | 0.989886i | \(0.454690\pi\) |
−0.928199 | + | 0.372084i | \(0.878643\pi\) | |||||||
\(132\) | 3.00000 | − | 1.73205i | 0.261116 | − | 0.150756i | ||||
\(133\) | 4.00000 | + | 6.92820i | 0.346844 | + | 0.600751i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.5000 | + | 7.79423i | 1.16190 | + | 0.670820i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.00000 | − | 15.5885i | −0.768922 | − | 1.33181i | −0.938148 | − | 0.346235i | \(-0.887460\pi\) |
0.169226 | − | 0.985577i | \(-0.445873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.00000 | − | 8.66025i | 0.424094 | − | 0.734553i | −0.572241 | − | 0.820086i | \(-0.693926\pi\) |
0.996335 | + | 0.0855324i | \(0.0272591\pi\) | |||||||
\(140\) | 12.0000 | − | 20.7846i | 1.01419 | − | 1.75662i | ||||
\(141\) | 4.50000 | + | 2.59808i | 0.378968 | + | 0.218797i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00000 | 0.167248 | ||||||||
\(144\) | −12.0000 | −1.00000 | ||||||||
\(145\) | 18.0000 | 1.49482 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 15.5885i | − | 1.28571i | ||||||
\(148\) | 2.00000 | − | 3.46410i | 0.164399 | − | 0.284747i | ||||
\(149\) | 6.00000 | − | 10.3923i | 0.491539 | − | 0.851371i | −0.508413 | − | 0.861113i | \(-0.669768\pi\) |
0.999953 | + | 0.00974235i | \(0.00310113\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | − | 6.92820i | −0.325515 | − | 0.563809i | 0.656101 | − | 0.754673i | \(-0.272204\pi\) |
−0.981617 | + | 0.190864i | \(0.938871\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.00000 | + | 15.5885i | −0.727607 | + | 1.26025i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0000 | + | 20.7846i | 0.963863 | + | 1.66946i | ||||
\(156\) | −6.00000 | − | 3.46410i | −0.480384 | − | 0.277350i | ||||
\(157\) | 3.50000 | − | 6.06218i | 0.279330 | − | 0.483814i | −0.691888 | − | 0.722005i | \(-0.743221\pi\) |
0.971219 | + | 0.238190i | \(0.0765542\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.50000 | + | 2.59808i | −0.356873 | + | 0.206041i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0000 | −0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | −0.0783260 | −0.0391630 | − | 0.999233i | \(-0.512469\pi\) | ||||
−0.0391630 | + | 0.999233i | \(0.512469\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.50000 | − | 2.59808i | 0.350325 | − | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.00000 | + | 15.5885i | −0.696441 | + | 1.20627i | 0.273252 | + | 0.961943i | \(0.411901\pi\) |
−0.969693 | + | 0.244328i | \(0.921432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | − | 5.19615i | 0.229416 | − | 0.397360i | ||||
\(172\) | −16.0000 | −1.21999 | ||||||||
\(173\) | −9.00000 | − | 15.5885i | −0.684257 | − | 1.18517i | −0.973670 | − | 0.227964i | \(-0.926793\pi\) |
0.289412 | − | 0.957205i | \(-0.406540\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.00000 | − | 13.8564i | 0.604743 | − | 1.04745i | ||||
\(176\) | −2.00000 | + | 3.46410i | −0.150756 | + | 0.261116i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.0000 | 1.12115 | 0.560576 | − | 0.828103i | \(-0.310580\pi\) | ||||
0.560576 | + | 0.828103i | \(0.310580\pi\) | |||||||
\(180\) | −18.0000 | −1.34164 | ||||||||
\(181\) | −1.00000 | −0.0743294 | −0.0371647 | − | 0.999309i | \(-0.511833\pi\) | ||||
−0.0371647 | + | 0.999309i | \(0.511833\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.0000 | + | 6.92820i | 0.887066 | + | 0.512148i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | − | 5.19615i | 0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000 | + | 5.19615i | 0.219382 | + | 0.379980i | ||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | −18.0000 | + | 10.3923i | −1.30931 | + | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.50000 | − | 2.59808i | −0.108536 | − | 0.187990i | 0.806641 | − | 0.591041i | \(-0.201283\pi\) |
−0.915177 | + | 0.403051i | \(0.867950\pi\) | |||||||
\(192\) | 12.0000 | − | 6.92820i | 0.866025 | − | 0.500000i | ||||
\(193\) | 2.00000 | − | 3.46410i | 0.143963 | − | 0.249351i | −0.785022 | − | 0.619467i | \(-0.787349\pi\) |
0.928986 | + | 0.370116i | \(0.120682\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.00000 | − | 5.19615i | −0.644503 | − | 0.372104i | ||||
\(196\) | 9.00000 | + | 15.5885i | 0.642857 | + | 1.11346i | ||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0000 | 0.779769 | 0.389885 | − | 0.920864i | \(-0.372515\pi\) | ||||
0.389885 | + | 0.920864i | \(0.372515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.5167i | 1.58820i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.0000 | + | 20.7846i | −0.842235 | + | 1.45879i | ||||
\(204\) | − | 20.7846i | − | 1.45521i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.50000 | + | 7.79423i | 0.312772 | + | 0.541736i | ||||
\(208\) | 8.00000 | 0.554700 | ||||||||
\(209\) | −1.00000 | − | 1.73205i | −0.0691714 | − | 0.119808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | − | 3.46410i | 0.137686 | − | 0.238479i | −0.788935 | − | 0.614477i | \(-0.789367\pi\) |
0.926620 | + | 0.375999i | \(0.122700\pi\) | |||||||
\(212\) | 3.00000 | − | 5.19615i | 0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −24.0000 | −1.63679 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −32.0000 | −2.17230 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.00000 | + | 1.73205i | −0.202721 | + | 0.117041i | ||||
\(220\) | −3.00000 | + | 5.19615i | −0.202260 | + | 0.350325i | ||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.50000 | − | 9.52628i | −0.368307 | − | 0.637927i | 0.620994 | − | 0.783815i | \(-0.286729\pi\) |
−0.989301 | + | 0.145889i | \(0.953396\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.0000 | −0.800000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.00000 | − | 15.5885i | −0.597351 | − | 1.03464i | −0.993210 | − | 0.116331i | \(-0.962887\pi\) |
0.395860 | − | 0.918311i | \(-0.370447\pi\) | |||||||
\(228\) | 6.92820i | 0.458831i | ||||||||
\(229\) | −11.5000 | + | 19.9186i | −0.759941 | + | 1.31626i | 0.182939 | + | 0.983124i | \(0.441439\pi\) |
−0.942880 | + | 0.333133i | \(0.891894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.92820i | 0.455842i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00000 | −0.587095 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.00000 | + | 1.73205i | 0.194871 | + | 0.112509i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | − | 10.3923i | 0.388108 | − | 0.672222i | −0.604087 | − | 0.796918i | \(-0.706462\pi\) |
0.992195 | + | 0.124696i | \(0.0397955\pi\) | |||||||
\(240\) | 18.0000 | − | 10.3923i | 1.16190 | − | 0.670820i | ||||
\(241\) | −1.00000 | − | 1.73205i | −0.0644157 | − | 0.111571i | 0.832019 | − | 0.554747i | \(-0.187185\pi\) |
−0.896435 | + | 0.443176i | \(0.853852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | −16.0000 | −1.02430 | ||||||||
\(245\) | 13.5000 | + | 23.3827i | 0.862483 | + | 1.49387i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | + | 3.46410i | −0.127257 | + | 0.220416i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27.0000 | − | 15.5885i | −1.71106 | − | 0.987878i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0000 | −0.946792 | −0.473396 | − | 0.880850i | \(-0.656972\pi\) | ||||
−0.473396 | + | 0.880850i | \(0.656972\pi\) | |||||||
\(252\) | 12.0000 | − | 20.7846i | 0.755929 | − | 1.30931i | ||||
\(253\) | 3.00000 | 0.188608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 31.1769i | − | 1.95237i | ||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −3.00000 | + | 5.19615i | −0.187135 | + | 0.324127i | −0.944294 | − | 0.329104i | \(-0.893253\pi\) |
0.757159 | + | 0.653231i | \(0.226587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | + | 6.92820i | 0.248548 | + | 0.430498i | ||||
\(260\) | 12.0000 | 0.744208 | ||||||||
\(261\) | 18.0000 | 1.11417 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0000 | + | 20.7846i | 0.739952 | + | 1.28163i | 0.952517 | + | 0.304487i | \(0.0984850\pi\) |
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.50000 | − | 7.79423i | 0.276433 | − | 0.478796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.50000 | + | 2.59808i | −0.275396 | + | 0.159000i | ||||
\(268\) | −13.0000 | − | 22.5167i | −0.794101 | − | 1.37542i | ||||
\(269\) | 27.0000 | 1.64622 | 0.823110 | − | 0.567883i | \(-0.192237\pi\) | ||||
0.823110 | + | 0.567883i | \(0.192237\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.00000 | 0.121491 | 0.0607457 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607457 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(272\) | 12.0000 | + | 20.7846i | 0.727607 | + | 1.26025i | ||||
\(273\) | 12.0000 | − | 6.92820i | 0.726273 | − | 0.419314i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | + | 3.46410i | −0.120605 | + | 0.208893i | ||||
\(276\) | −9.00000 | − | 5.19615i | −0.541736 | − | 0.312772i | ||||
\(277\) | −1.00000 | − | 1.73205i | −0.0600842 | − | 0.104069i | 0.834419 | − | 0.551131i | \(-0.185804\pi\) |
−0.894503 | + | 0.447062i | \(0.852470\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.0000 | + | 20.7846i | 0.718421 | + | 1.24434i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | + | 10.3923i | 0.357930 | + | 0.619953i | 0.987615 | − | 0.156898i | \(-0.0501493\pi\) |
−0.629685 | + | 0.776851i | \(0.716816\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.00000 | − | 8.66025i | 0.297219 | − | 0.514799i | −0.678280 | − | 0.734804i | \(-0.737274\pi\) |
0.975499 | + | 0.220005i | \(0.0706075\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.3923i | 0.615587i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.00000 | + | 1.73205i | 0.175863 | + | 0.101535i | ||||
\(292\) | 2.00000 | − | 3.46410i | 0.117041 | − | 0.202721i | ||||
\(293\) | −3.00000 | + | 5.19615i | −0.175262 | + | 0.303562i | −0.940252 | − | 0.340480i | \(-0.889411\pi\) |
0.764990 | + | 0.644042i | \(0.222744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.50000 | − | 2.59808i | 0.261116 | − | 0.150756i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | − | 5.19615i | −0.173494 | − | 0.300501i | ||||
\(300\) | 12.0000 | − | 6.92820i | 0.692820 | − | 0.400000i | ||||
\(301\) | 16.0000 | − | 27.7128i | 0.922225 | − | 1.59734i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00000 | + | 5.19615i | 0.517036 | + | 0.298511i | ||||
\(304\) | −4.00000 | − | 6.92820i | −0.229416 | − | 0.397360i | ||||
\(305\) | −24.0000 | −1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | −4.00000 | − | 6.92820i | −0.227921 | − | 0.394771i | ||||
\(309\) | − | 8.66025i | − | 0.492665i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.50000 | − | 2.59808i | 0.0850572 | − | 0.147323i | −0.820358 | − | 0.571850i | \(-0.806226\pi\) |
0.905416 | + | 0.424526i | \(0.139559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.50000 | − | 9.52628i | −0.310878 | − | 0.538457i | 0.667674 | − | 0.744453i | \(-0.267290\pi\) |
−0.978553 | + | 0.205996i | \(0.933957\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.0000 | − | 31.1769i | 1.01419 | − | 1.75662i | ||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | 13.5000 | + | 23.3827i | 0.758236 | + | 1.31330i | 0.943750 | + | 0.330661i | \(0.107272\pi\) |
−0.185514 | + | 0.982642i | \(0.559395\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000 | − | 5.19615i | 0.167968 | − | 0.290929i | ||||
\(320\) | −12.0000 | + | 20.7846i | −0.670820 | + | 1.16190i | ||||
\(321\) | 18.0000 | − | 10.3923i | 1.00466 | − | 0.580042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | −18.0000 | −1.00000 | ||||||||
\(325\) | 8.00000 | 0.443760 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.0000 | + | 12.1244i | −1.16130 | + | 0.670478i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.00000 | − | 10.3923i | 0.330791 | − | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5000 | − | 25.1147i | −0.796992 | − | 1.38043i | −0.921567 | − | 0.388221i | \(-0.873090\pi\) |
0.124574 | − | 0.992210i | \(-0.460243\pi\) | |||||||
\(332\) | 36.0000 | 1.97576 | ||||||||
\(333\) | 3.00000 | − | 5.19615i | 0.164399 | − | 0.284747i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.5000 | − | 33.7750i | −1.06540 | − | 1.84532i | ||||
\(336\) | 27.7128i | 1.51186i | ||||||||
\(337\) | −16.0000 | + | 27.7128i | −0.871576 | + | 1.50961i | −0.0112091 | + | 0.999937i | \(0.503568\pi\) |
−0.860366 | + | 0.509676i | \(0.829765\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.3923i | 0.564433i | ||||||||
\(340\) | 18.0000 | + | 31.1769i | 0.976187 | + | 1.69081i | ||||
\(341\) | 8.00000 | 0.433224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.5000 | − | 7.79423i | −0.726816 | − | 0.419627i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.00000 | + | 10.3923i | −0.322097 | + | 0.557888i | −0.980921 | − | 0.194409i | \(-0.937721\pi\) |
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(348\) | −18.0000 | + | 10.3923i | −0.964901 | + | 0.557086i | ||||
\(349\) | 14.0000 | + | 24.2487i | 0.749403 | + | 1.29800i | 0.948109 | + | 0.317945i | \(0.102993\pi\) |
−0.198706 | + | 0.980059i | \(0.563674\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.00000 | − | 5.19615i | −0.480384 | − | 0.277350i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.50000 | − | 12.9904i | −0.399185 | − | 0.691408i | 0.594441 | − | 0.804139i | \(-0.297373\pi\) |
−0.993626 | + | 0.112731i | \(0.964040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.00000 | − | 5.19615i | 0.159000 | − | 0.275396i | ||||
\(357\) | 36.0000 | + | 20.7846i | 1.90532 | + | 1.10004i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.00000 | −0.316668 | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 1.73205i | − | 0.0909091i | ||||||
\(364\) | −8.00000 | + | 13.8564i | −0.419314 | + | 0.726273i | ||||
\(365\) | 3.00000 | − | 5.19615i | 0.157027 | − | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.50000 | + | 16.4545i | 0.495896 | + | 0.858917i | 0.999989 | − | 0.00473247i | \(-0.00150640\pi\) |
−0.504093 | + | 0.863649i | \(0.668173\pi\) | |||||||
\(368\) | 12.0000 | 0.625543 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | + | 10.3923i | 0.311504 | + | 0.539542i | ||||
\(372\) | −24.0000 | − | 13.8564i | −1.24434 | − | 0.718421i | ||||
\(373\) | −4.00000 | + | 6.92820i | −0.207112 | + | 0.358729i | −0.950804 | − | 0.309794i | \(-0.899740\pi\) |
0.743691 | + | 0.668523i | \(0.233073\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.50000 | + | 2.59808i | −0.232379 | + | 0.134164i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.0000 | −0.667765 | −0.333883 | − | 0.942615i | \(-0.608359\pi\) | ||||
−0.333883 | + | 0.942615i | \(0.608359\pi\) | |||||||
\(380\) | −6.00000 | − | 10.3923i | −0.307794 | − | 0.533114i | ||||
\(381\) | 6.00000 | − | 3.46410i | 0.307389 | − | 0.177471i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.5000 | − | 23.3827i | 0.689818 | − | 1.19480i | −0.282079 | − | 0.959391i | \(-0.591024\pi\) |
0.971897 | − | 0.235408i | \(-0.0756427\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | − | 10.3923i | −0.305788 | − | 0.529641i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.0000 | −1.21999 | ||||||||
\(388\) | −4.00000 | −0.203069 | ||||||||
\(389\) | −15.0000 | − | 25.9808i | −0.760530 | − | 1.31728i | −0.942578 | − | 0.333987i | \(-0.891606\pi\) |
0.182047 | − | 0.983290i | \(-0.441728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | − | 15.5885i | 0.455150 | − | 0.788342i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 31.1769i | − | 1.57267i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.00000 | −0.301893 | ||||||||
\(396\) | −3.00000 | + | 5.19615i | −0.150756 | + | 0.261116i | ||||
\(397\) | 17.0000 | 0.853206 | 0.426603 | − | 0.904439i | \(-0.359710\pi\) | ||||
0.426603 | + | 0.904439i | \(0.359710\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.0000 | − | 6.92820i | −0.600751 | − | 0.346844i | ||||
\(400\) | −8.00000 | + | 13.8564i | −0.400000 | + | 0.692820i | ||||
\(401\) | −10.5000 | + | 18.1865i | −0.524345 | + | 0.908192i | 0.475253 | + | 0.879849i | \(0.342356\pi\) |
−0.999598 | + | 0.0283431i | \(0.990977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | − | 13.8564i | −0.398508 | − | 0.690237i | ||||
\(404\) | −12.0000 | −0.597022 | ||||||||
\(405\) | −27.0000 | −1.34164 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.00000 | − | 1.73205i | −0.0495682 | − | 0.0858546i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0000 | + | 27.7128i | −0.791149 | + | 1.37031i | 0.134107 | + | 0.990967i | \(0.457183\pi\) |
−0.925256 | + | 0.379344i | \(0.876150\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.0000 | + | 15.5885i | 1.33181 | + | 0.768922i | ||||
\(412\) | 5.00000 | + | 8.66025i | 0.246332 | + | 0.426660i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 54.0000 | 2.65076 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.3205i | 0.848189i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.5000 | − | 18.1865i | 0.512959 | − | 0.888470i | −0.486928 | − | 0.873442i | \(-0.661883\pi\) |
0.999887 | − | 0.0150285i | \(-0.00478389\pi\) | |||||||
\(420\) | 41.5692i | 2.02837i | ||||||||
\(421\) | 3.50000 | + | 6.06218i | 0.170580 | + | 0.295452i | 0.938623 | − | 0.344946i | \(-0.112103\pi\) |
−0.768043 | + | 0.640398i | \(0.778769\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.00000 | −0.437595 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000 | + | 20.7846i | 0.582086 | + | 1.00820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.0000 | − | 27.7128i | 0.774294 | − | 1.34112i | ||||
\(428\) | −12.0000 | + | 20.7846i | −0.580042 | + | 1.00466i | ||||
\(429\) | −3.00000 | + | 1.73205i | −0.144841 | + | 0.0836242i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | 18.0000 | − | 10.3923i | 0.866025 | − | 0.500000i | ||||
\(433\) | 17.0000 | 0.816968 | 0.408484 | − | 0.912766i | \(-0.366058\pi\) | ||||
0.408484 | + | 0.912766i | \(0.366058\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −27.0000 | + | 15.5885i | −1.29455 | + | 0.747409i | ||||
\(436\) | 14.0000 | − | 24.2487i | 0.670478 | − | 1.16130i | ||||
\(437\) | −3.00000 | + | 5.19615i | −0.143509 | + | 0.248566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.0000 | − | 22.5167i | −0.620456 | − | 1.07466i | −0.989401 | − | 0.145210i | \(-0.953614\pi\) |
0.368945 | − | 0.929451i | \(-0.379719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.5000 | + | 23.3827i | 0.642857 | + | 1.11346i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.00000 | − | 10.3923i | −0.285069 | − | 0.493753i | 0.687557 | − | 0.726130i | \(-0.258683\pi\) |
−0.972626 | + | 0.232377i | \(0.925350\pi\) | |||||||
\(444\) | 6.92820i | 0.328798i | ||||||||
\(445\) | 4.50000 | − | 7.79423i | 0.213320 | − | 0.369482i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.7846i | 0.983078i | ||||||||
\(448\) | −16.0000 | − | 27.7128i | −0.755929 | − | 1.30931i | ||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.00000 | − | 10.3923i | −0.282216 | − | 0.488813i | ||||
\(453\) | 12.0000 | + | 6.92820i | 0.563809 | + | 0.325515i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0000 | + | 20.7846i | −0.562569 | + | 0.974398i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.00000 | + | 8.66025i | 0.233890 | + | 0.405110i | 0.958950 | − | 0.283577i | \(-0.0915211\pi\) |
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 31.1769i | − | 1.45521i | ||||||
\(460\) | 18.0000 | 0.839254 | ||||||||
\(461\) | −15.0000 | − | 25.9808i | −0.698620 | − | 1.21004i | −0.968945 | − | 0.247276i | \(-0.920465\pi\) |
0.270326 | − | 0.962769i | \(-0.412869\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.5000 | + | 25.1147i | −0.673872 | + | 1.16718i | 0.302925 | + | 0.953014i | \(0.402037\pi\) |
−0.976797 | + | 0.214166i | \(0.931297\pi\) | |||||||
\(464\) | 12.0000 | − | 20.7846i | 0.557086 | − | 0.964901i | ||||
\(465\) | −36.0000 | − | 20.7846i | −1.66946 | − | 0.963863i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.0000 | 0.694117 | 0.347059 | − | 0.937843i | \(-0.387180\pi\) | ||||
0.347059 | + | 0.937843i | \(0.387180\pi\) | |||||||
\(468\) | 12.0000 | 0.554700 | ||||||||
\(469\) | 52.0000 | 2.40114 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.1244i | 0.558661i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.00000 | + | 6.92820i | −0.183920 | + | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | − | 6.92820i | −0.183533 | − | 0.317888i | ||||
\(476\) | −48.0000 | −2.20008 | ||||||||
\(477\) | 4.50000 | − | 7.79423i | 0.206041 | − | 0.356873i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.00000 | + | 5.19615i | 0.137073 | + | 0.237418i | 0.926388 | − | 0.376571i | \(-0.122897\pi\) |
−0.789314 | + | 0.613990i | \(0.789564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | + | 3.46410i | −0.0911922 | + | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.0000 | − | 10.3923i | 0.819028 | − | 0.472866i | ||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | −6.00000 | −0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000 | 0.362515 | 0.181257 | − | 0.983436i | \(-0.441983\pi\) | ||||
0.181257 | + | 0.983436i | \(0.441983\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.50000 | − | 0.866025i | 0.0678323 | − | 0.0391630i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.0000 | − | 25.9808i | 0.676941 | − | 1.17250i | −0.298957 | − | 0.954267i | \(-0.596639\pi\) |
0.975898 | − | 0.218229i | \(-0.0700279\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0000 | − | 31.1769i | −0.810679 | − | 1.40414i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.50000 | + | 7.79423i | −0.202260 | + | 0.350325i | ||||
\(496\) | 32.0000 | 1.43684 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.5000 | + | 35.5070i | −0.917706 | + | 1.58951i | −0.114816 | + | 0.993387i | \(0.536628\pi\) |
−0.802890 | + | 0.596127i | \(0.796706\pi\) | |||||||
\(500\) | 3.00000 | − | 5.19615i | 0.134164 | − | 0.232379i | ||||
\(501\) | − | 31.1769i | − | 1.39288i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.5000 | − | 7.79423i | −0.599556 | − | 0.346154i | ||||
\(508\) | −4.00000 | + | 6.92820i | −0.177471 | + | 0.307389i | ||||
\(509\) | 4.50000 | − | 7.79423i | 0.199459 | − | 0.345473i | −0.748894 | − | 0.662690i | \(-0.769415\pi\) |
0.948353 | + | 0.317217i | \(0.102748\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000 | + | 6.92820i | 0.176950 | + | 0.306486i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.3923i | 0.458831i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.50000 | + | 12.9904i | 0.330489 | + | 0.572425i | ||||
\(516\) | 24.0000 | − | 13.8564i | 1.05654 | − | 0.609994i | ||||
\(517\) | −1.50000 | + | 2.59808i | −0.0659699 | + | 0.114263i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.0000 | + | 15.5885i | 1.18517 | + | 0.684257i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.0000 | 1.84005 | 0.920027 | − | 0.391856i | \(-0.128167\pi\) | ||||
0.920027 | + | 0.391856i | \(0.128167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.0000 | −1.48672 | −0.743358 | − | 0.668894i | \(-0.766768\pi\) | ||||
−0.743358 | + | 0.668894i | \(0.766768\pi\) | |||||||
\(524\) | 18.0000 | + | 31.1769i | 0.786334 | + | 1.36197i | ||||
\(525\) | 27.7128i | 1.20949i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.0000 | − | 41.5692i | 1.04546 | − | 1.81078i | ||||
\(528\) | − | 6.92820i | − | 0.301511i | ||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.0000 | 0.693688 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0000 | + | 31.1769i | −0.778208 | + | 1.34790i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.5000 | + | 12.9904i | −0.970947 | + | 0.560576i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.00000 | 0.387657 | ||||||||
\(540\) | 27.0000 | − | 15.5885i | 1.16190 | − | 0.670820i | ||||
\(541\) | 14.0000 | 0.601907 | 0.300954 | − | 0.953639i | \(-0.402695\pi\) | ||||
0.300954 | + | 0.953639i | \(0.402695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.50000 | − | 0.866025i | 0.0643712 | − | 0.0371647i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.0000 | − | 36.3731i | 0.899541 | − | 1.55805i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000 | + | 24.2487i | 0.598597 | + | 1.03680i | 0.993028 | + | 0.117875i | \(0.0376081\pi\) |
−0.394432 | + | 0.918925i | \(0.629059\pi\) | |||||||
\(548\) | −36.0000 | −1.53784 | ||||||||
\(549\) | −24.0000 | −1.02430 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | + | 10.3923i | 0.255609 | + | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | − | 6.92820i | 0.170097 | − | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.3923i | 0.441129i | ||||||||
\(556\) | −10.0000 | − | 17.3205i | −0.424094 | − | 0.734553i | ||||
\(557\) | −30.0000 | −1.27114 | −0.635570 | − | 0.772043i | \(-0.719235\pi\) | ||||
−0.635570 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | −24.0000 | − | 41.5692i | −1.01419 | − | 1.75662i | ||||
\(561\) | −9.00000 | − | 5.19615i | −0.379980 | − | 0.219382i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.0000 | + | 20.7846i | −0.505740 | + | 0.875967i | 0.494238 | + | 0.869326i | \(0.335447\pi\) |
−0.999978 | + | 0.00664037i | \(0.997886\pi\) | |||||||
\(564\) | 9.00000 | − | 5.19615i | 0.378968 | − | 0.218797i | ||||
\(565\) | −9.00000 | − | 15.5885i | −0.378633 | − | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.0000 | − | 31.1769i | 0.755929 | − | 1.30931i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.0000 | + | 36.3731i | 0.880366 | + | 1.52484i | 0.850935 | + | 0.525271i | \(0.176036\pi\) |
0.0294311 | + | 0.999567i | \(0.490630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 2.00000 | − | 3.46410i | 0.0836242 | − | 0.144841i | ||||
\(573\) | 4.50000 | + | 2.59808i | 0.187990 | + | 0.108536i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | −12.0000 | + | 20.7846i | −0.500000 | + | 0.866025i | ||||
\(577\) | −7.00000 | −0.291414 | −0.145707 | − | 0.989328i | \(-0.546546\pi\) | ||||
−0.145707 | + | 0.989328i | \(0.546546\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.92820i | 0.287926i | ||||||||
\(580\) | 18.0000 | − | 31.1769i | 0.747409 | − | 1.29455i | ||||
\(581\) | −36.0000 | + | 62.3538i | −1.49353 | + | 2.58687i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.50000 | − | 2.59808i | −0.0621237 | − | 0.107601i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.0000 | 0.744208 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.50000 | + | 2.59808i | 0.0619116 | + | 0.107234i | 0.895320 | − | 0.445424i | \(-0.146947\pi\) |
−0.833408 | + | 0.552658i | \(0.813614\pi\) | |||||||
\(588\) | −27.0000 | − | 15.5885i | −1.11346 | − | 0.642857i | ||||
\(589\) | −8.00000 | + | 13.8564i | −0.329634 | + | 0.570943i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.0000 | + | 15.5885i | −1.11063 | + | 0.641223i | ||||
\(592\) | −4.00000 | − | 6.92820i | −0.164399 | − | 0.284747i | ||||
\(593\) | −36.0000 | −1.47834 | −0.739171 | − | 0.673517i | \(-0.764783\pi\) | ||||
−0.739171 | + | 0.673517i | \(0.764783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −72.0000 | −2.95171 | ||||||||
\(596\) | −12.0000 | − | 20.7846i | −0.491539 | − | 0.851371i | ||||
\(597\) | −16.5000 | + | 9.52628i | −0.675300 | + | 0.389885i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0000 | + | 20.7846i | −0.490307 | + | 0.849236i | −0.999938 | − | 0.0111569i | \(-0.996449\pi\) |
0.509631 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.0000 | + | 34.6410i | 0.815817 | + | 1.41304i | 0.908740 | + | 0.417363i | \(0.137046\pi\) |
−0.0929227 | + | 0.995673i | \(0.529621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.5000 | − | 33.7750i | −0.794101 | − | 1.37542i | ||||
\(604\) | −16.0000 | −0.651031 | ||||||||
\(605\) | 1.50000 | + | 2.59808i | 0.0609837 | + | 0.105627i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0000 | − | 24.2487i | 0.568242 | − | 0.984225i | −0.428497 | − | 0.903543i | \(-0.640957\pi\) |
0.996740 | − | 0.0806818i | \(-0.0257098\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 41.5692i | − | 1.68447i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.00000 | 0.242734 | ||||||||
\(612\) | 18.0000 | + | 31.1769i | 0.727607 | + | 1.26025i | ||||
\(613\) | −16.0000 | −0.646234 | −0.323117 | − | 0.946359i | \(-0.604731\pi\) | ||||
−0.323117 | + | 0.946359i | \(0.604731\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.50000 | + | 7.79423i | −0.181163 | + | 0.313784i | −0.942277 | − | 0.334835i | \(-0.891320\pi\) |
0.761114 | + | 0.648618i | \(0.224653\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.0000 | − | 38.1051i | −0.884255 | − | 1.53157i | −0.846566 | − | 0.532284i | \(-0.821334\pi\) |
−0.0376891 | − | 0.999290i | \(-0.512000\pi\) | |||||||
\(620\) | 48.0000 | 1.92773 | ||||||||
\(621\) | −13.5000 | − | 7.79423i | −0.541736 | − | 0.312772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.00000 | + | 10.3923i | 0.240385 | + | 0.416359i | ||||
\(624\) | −12.0000 | + | 6.92820i | −0.480384 | + | 0.277350i | ||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.00000 | + | 1.73205i | 0.119808 | + | 0.0691714i | ||||
\(628\) | −7.00000 | − | 12.1244i | −0.279330 | − | 0.483814i | ||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0000 | −1.23409 | −0.617045 | − | 0.786928i | \(-0.711670\pi\) | ||||
−0.617045 | + | 0.786928i | \(0.711670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.92820i | 0.275371i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.00000 | + | 10.3923i | −0.238103 | + | 0.412406i | ||||
\(636\) | 10.3923i | 0.412082i | ||||||||
\(637\) | −9.00000 | − | 15.5885i | −0.356593 | − | 0.617637i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5000 | + | 28.5788i | 0.651711 | + | 1.12880i | 0.982708 | + | 0.185164i | \(0.0592817\pi\) |
−0.330997 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.5000 | − | 26.8468i | 0.611260 | − | 1.05873i | −0.379768 | − | 0.925082i | \(-0.623996\pi\) |
0.991028 | − | 0.133652i | \(-0.0426705\pi\) | |||||||
\(644\) | −12.0000 | + | 20.7846i | −0.472866 | + | 0.819028i | ||||
\(645\) | 36.0000 | − | 20.7846i | 1.41750 | − | 0.818393i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.0000 | 0.825595 | 0.412798 | − | 0.910823i | \(-0.364552\pi\) | ||||
0.412798 | + | 0.910823i | \(0.364552\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 48.0000 | − | 27.7128i | 1.88127 | − | 1.08615i | ||||
\(652\) | −1.00000 | + | 1.73205i | −0.0391630 | + | 0.0678323i | ||||
\(653\) | −9.00000 | + | 15.5885i | −0.352197 | + | 0.610023i | −0.986634 | − | 0.162951i | \(-0.947899\pi\) |
0.634437 | + | 0.772975i | \(0.281232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.0000 | + | 46.7654i | 1.05498 | + | 1.82727i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.00000 | − | 5.19615i | 0.117041 | − | 0.202721i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000 | + | 20.7846i | 0.467454 | + | 0.809653i | 0.999309 | − | 0.0371821i | \(-0.0118382\pi\) |
−0.531855 | + | 0.846836i | \(0.678505\pi\) | |||||||
\(660\) | − | 10.3923i | − | 0.404520i | ||||||
\(661\) | −7.00000 | + | 12.1244i | −0.272268 | + | 0.471583i | −0.969442 | − | 0.245319i | \(-0.921107\pi\) |
0.697174 | + | 0.716902i | \(0.254441\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.7846i | 0.807207i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.0000 | 0.930680 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.0000 | −0.696963 | ||||||||
\(668\) | 18.0000 | + | 31.1769i | 0.696441 | + | 1.20627i | ||||
\(669\) | 16.5000 | + | 9.52628i | 0.637927 | + | 0.368307i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00000 | + | 6.92820i | −0.154418 | + | 0.267460i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0000 | + | 29.4449i | 0.655302 | + | 1.13502i | 0.981818 | + | 0.189824i | \(0.0607919\pi\) |
−0.326516 | + | 0.945192i | \(0.605875\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.0000 | − | 10.3923i | 0.692820 | − | 0.400000i | ||||
\(676\) | 18.0000 | 0.692308 | ||||||||
\(677\) | −18.0000 | − | 31.1769i | −0.691796 | − | 1.19823i | −0.971249 | − | 0.238067i | \(-0.923486\pi\) |
0.279453 | − | 0.960159i | \(-0.409847\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.00000 | − | 6.92820i | 0.153506 | − | 0.265880i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.0000 | + | 15.5885i | 1.03464 | + | 0.597351i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.0000 | 0.573959 | 0.286980 | − | 0.957937i | \(-0.407349\pi\) | ||||
0.286980 | + | 0.957937i | \(0.407349\pi\) | |||||||
\(684\) | −6.00000 | − | 10.3923i | −0.229416 | − | 0.397360i | ||||
\(685\) | −54.0000 | −2.06323 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 39.8372i | − | 1.51988i | ||||||
\(688\) | −16.0000 | + | 27.7128i | −0.609994 | + | 1.05654i | ||||
\(689\) | −3.00000 | + | 5.19615i | −0.114291 | + | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.5000 | + | 21.6506i | 0.475522 | + | 0.823629i | 0.999607 | − | 0.0280373i | \(-0.00892572\pi\) |
−0.524084 | + | 0.851666i | \(0.675592\pi\) | |||||||
\(692\) | −36.0000 | −1.36851 | ||||||||
\(693\) | −6.00000 | − | 10.3923i | −0.227921 | − | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.0000 | − | 25.9808i | −0.568982 | − | 0.985506i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.00000 | − | 5.19615i | 0.340411 | − | 0.196537i | ||||
\(700\) | −16.0000 | − | 27.7128i | −0.604743 | − | 1.04745i | ||||
\(701\) | 36.0000 | 1.35970 | 0.679851 | − | 0.733351i | \(-0.262045\pi\) | ||||
0.679851 | + | 0.733351i | \(0.262045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | 4.00000 | + | 6.92820i | 0.150756 | + | 0.261116i | ||||
\(705\) | 13.5000 | − | 7.79423i | 0.508439 | − | 0.293548i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.0000 | − | 20.7846i | 0.451306 | − | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5000 | − | 19.9186i | −0.431892 | − | 0.748058i | 0.565145 | − | 0.824992i | \(-0.308820\pi\) |
−0.997036 | + | 0.0769337i | \(0.975487\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.00000 | −0.225018 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.0000 | − | 20.7846i | −0.449404 | − | 0.778390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.00000 | − | 5.19615i | 0.112194 | − | 0.194325i | ||||
\(716\) | 15.0000 | − | 25.9808i | 0.560576 | − | 0.970947i | ||||
\(717\) | 20.7846i | 0.776215i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00000 | −0.111881 | −0.0559406 | − | 0.998434i | \(-0.517816\pi\) | ||||
−0.0559406 | + | 0.998434i | \(0.517816\pi\) | |||||||
\(720\) | −18.0000 | + | 31.1769i | −0.670820 | + | 1.16190i | ||||
\(721\) | −20.0000 | −0.744839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.00000 | + | 1.73205i | 0.111571 | + | 0.0644157i | ||||
\(724\) | −1.00000 | + | 1.73205i | −0.0371647 | + | 0.0643712i | ||||
\(725\) | 12.0000 | − | 20.7846i | 0.445669 | − | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0000 | + | 24.2487i | 0.519231 | + | 0.899335i | 0.999750 | + | 0.0223506i | \(0.00711500\pi\) |
−0.480519 | + | 0.876984i | \(0.659552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000 | + | 41.5692i | 0.887672 | + | 1.53749i | ||||
\(732\) | 24.0000 | − | 13.8564i | 0.887066 | − | 0.512148i | ||||
\(733\) | 20.0000 | − | 34.6410i | 0.738717 | − | 1.27950i | −0.214356 | − | 0.976756i | \(-0.568765\pi\) |
0.953073 | − | 0.302740i | \(-0.0979013\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −40.5000 | − | 23.3827i | −1.49387 | − | 0.862483i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.0000 | −0.478861 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.0000 | −0.367856 | −0.183928 | − | 0.982940i | \(-0.558881\pi\) | ||||
−0.183928 | + | 0.982940i | \(0.558881\pi\) | |||||||
\(740\) | −6.00000 | − | 10.3923i | −0.220564 | − | 0.382029i | ||||
\(741\) | − | 6.92820i | − | 0.254514i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.00000 | − | 5.19615i | 0.110059 | − | 0.190628i | −0.805735 | − | 0.592277i | \(-0.798229\pi\) |
0.915794 | + | 0.401648i | \(0.131563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | − | 31.1769i | −0.659469 | − | 1.14223i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 54.0000 | 1.97576 | ||||||||
\(748\) | 12.0000 | 0.438763 | ||||||||
\(749\) | −24.0000 | − | 41.5692i | −0.876941 | − | 1.51891i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | − | 13.8564i | 0.291924 | − | 0.505627i | −0.682341 | − | 0.731034i | \(-0.739038\pi\) |
0.974265 | + | 0.225407i | \(0.0723712\pi\) | |||||||
\(752\) | −6.00000 | + | 10.3923i | −0.218797 | + | 0.378968i | ||||
\(753\) | 22.5000 | − | 12.9904i | 0.819946 | − | 0.473396i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.0000 | −0.873449 | ||||||||
\(756\) | 41.5692i | 1.51186i | ||||||||
\(757\) | 29.0000 | 1.05402 | 0.527011 | − | 0.849858i | \(-0.323312\pi\) | ||||
0.527011 | + | 0.849858i | \(0.323312\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.50000 | + | 2.59808i | −0.163340 | + | 0.0943042i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | + | 10.3923i | −0.217500 | + | 0.376721i | −0.954043 | − | 0.299670i | \(-0.903123\pi\) |
0.736543 | + | 0.676391i | \(0.236457\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.0000 | + | 48.4974i | 1.01367 | + | 1.75572i | ||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 27.0000 | + | 46.7654i | 0.976187 | + | 1.69081i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | − | 27.7128i | − | 1.00000i | ||||||
\(769\) | −4.00000 | + | 6.92820i | −0.144244 | + | 0.249837i | −0.929091 | − | 0.369852i | \(-0.879408\pi\) |
0.784847 | + | 0.619690i | \(0.212742\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 10.3923i | − | 0.374270i | ||||||
\(772\) | −4.00000 | − | 6.92820i | −0.143963 | − | 0.249351i | ||||
\(773\) | 18.0000 | 0.647415 | 0.323708 | − | 0.946157i | \(-0.395071\pi\) | ||||
0.323708 | + | 0.946157i | \(0.395071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.0000 | 1.14947 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.0000 | − | 6.92820i | −0.430498 | − | 0.248548i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −18.0000 | + | 10.3923i | −0.644503 | + | 0.372104i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27.0000 | + | 15.5885i | −0.964901 | + | 0.557086i | ||||
\(784\) | 36.0000 | 1.28571 | ||||||||
\(785\) | −10.5000 | − | 18.1865i | −0.374761 | − | 0.649105i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.0000 | + | 27.7128i | −0.570338 | + | 0.987855i | 0.426193 | + | 0.904632i | \(0.359855\pi\) |
−0.996531 | + | 0.0832226i | \(0.973479\pi\) | |||||||
\(788\) | 18.0000 | − | 31.1769i | 0.641223 | − | 1.11063i | ||||
\(789\) | −36.0000 | − | 20.7846i | −1.28163 | − | 0.739952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.0000 | 0.853342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0000 | 0.568177 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.5885i | 0.552866i | ||||||||
\(796\) | 11.0000 | − | 19.0526i | 0.389885 | − | 0.675300i | ||||
\(797\) | −15.0000 | + | 25.9808i | −0.531327 | + | 0.920286i | 0.468004 | + | 0.883726i | \(0.344973\pi\) |
−0.999331 | + | 0.0365596i | \(0.988360\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.00000 | + | 15.5885i | 0.318397 | + | 0.551480i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.50000 | − | 7.79423i | 0.159000 | − | 0.275396i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.00000 | − | 1.73205i | −0.0352892 | − | 0.0611227i | ||||
\(804\) | 39.0000 | + | 22.5167i | 1.37542 | + | 0.794101i | ||||
\(805\) | −18.0000 | + | 31.1769i | −0.634417 | + | 1.09884i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −40.5000 | + | 23.3827i | −1.42567 | + | 0.823110i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00000 | −0.210949 | −0.105474 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.00000 | 0.280918 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(812\) | 24.0000 | + | 41.5692i | 0.842235 | + | 1.45879i | ||||
\(813\) | −3.00000 | + | 1.73205i | −0.105215 | + | 0.0607457i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.50000 | + | 2.59808i | −0.0525427 | + | 0.0910066i | ||||
\(816\) | −36.0000 | − | 20.7846i | −1.26025 | − | 0.727607i | ||||
\(817\) | −8.00000 | − | 13.8564i | −0.279885 | − | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.0000 | + | 20.7846i | −0.419314 | + | 0.726273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.00000 | − | 10.3923i | −0.209401 | − | 0.362694i | 0.742125 | − | 0.670262i | \(-0.233818\pi\) |
−0.951526 | + | 0.307568i | \(0.900485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.5000 | − | 42.4352i | 0.854016 | − | 1.47920i | −0.0235383 | − | 0.999723i | \(-0.507493\pi\) |
0.877555 | − | 0.479477i | \(-0.159174\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6.92820i | − | 0.241209i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.0000 | 0.625921 | 0.312961 | − | 0.949766i | \(-0.398679\pi\) | ||||
0.312961 | + | 0.949766i | \(0.398679\pi\) | |||||||
\(828\) | 18.0000 | 0.625543 | ||||||||
\(829\) | −7.00000 | −0.243120 | −0.121560 | − | 0.992584i | \(-0.538790\pi\) | ||||
−0.121560 | + | 0.992584i | \(0.538790\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.00000 | + | 1.73205i | 0.104069 | + | 0.0600842i | ||||
\(832\) | 8.00000 | − | 13.8564i | 0.277350 | − | 0.480384i | ||||
\(833\) | 27.0000 | − | 46.7654i | 0.935495 | − | 1.62032i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.0000 | + | 46.7654i | 0.934374 | + | 1.61838i | ||||
\(836\) | −4.00000 | −0.138343 | ||||||||
\(837\) | −36.0000 | − | 20.7846i | −1.24434 | − | 0.718421i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.50000 | − | 12.9904i | −0.258929 | − | 0.448478i | 0.707026 | − | 0.707187i | \(-0.250036\pi\) |
−0.965955 | + | 0.258709i | \(0.916703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.0000 | − | 10.3923i | −0.619953 | − | 0.357930i | ||||
\(844\) | −4.00000 | − | 6.92820i | −0.137686 | − | 0.238479i | ||||
\(845\) | 27.0000 | 0.928828 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.00000 | −0.137442 | ||||||||
\(848\) | −6.00000 | − | 10.3923i | −0.206041 | − | 0.356873i | ||||
\(849\) | 17.3205i | 0.594438i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.00000 | + | 5.19615i | −0.102839 | + | 0.178122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | − | 38.1051i | −0.753266 | − | 1.30469i | −0.946232 | − | 0.323489i | \(-0.895144\pi\) |
0.192966 | − | 0.981205i | \(-0.438189\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.00000 | − | 15.5885i | −0.307794 | − | 0.533114i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.00000 | + | 10.3923i | 0.204956 | + | 0.354994i | 0.950119 | − | 0.311888i | \(-0.100962\pi\) |
−0.745163 | + | 0.666883i | \(0.767628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.50000 | − | 11.2583i | 0.221777 | − | 0.384129i | −0.733571 | − | 0.679613i | \(-0.762148\pi\) |
0.955348 | + | 0.295484i | \(0.0954809\pi\) | |||||||
\(860\) | −24.0000 | + | 41.5692i | −0.818393 | + | 1.41750i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.0000 | −1.22545 | −0.612727 | − | 0.790295i | \(-0.709928\pi\) | ||||
−0.612727 | + | 0.790295i | \(0.709928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −54.0000 | −1.83606 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −28.5000 | + | 16.4545i | −0.967911 | + | 0.558824i | ||||
\(868\) | −32.0000 | + | 55.4256i | −1.08615 | + | 1.88127i | ||||
\(869\) | −1.00000 | + | 1.73205i | −0.0339227 | + | 0.0587558i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.0000 | + | 22.5167i | 0.440488 | + | 0.762948i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.00000 | −0.203069 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.00000 | + | 10.3923i | 0.202837 | + | 0.351324i | ||||
\(876\) | 6.92820i | 0.234082i | ||||||||
\(877\) | 20.0000 | − | 34.6410i | 0.675352 | − | 1.16974i | −0.301014 | − | 0.953620i | \(-0.597325\pi\) |
0.976366 | − | 0.216124i | \(-0.0693416\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 10.3923i | − | 0.350524i | ||||||
\(880\) | 6.00000 | + | 10.3923i | 0.202260 | + | 0.350325i | ||||
\(881\) | −39.0000 | −1.31394 | −0.656972 | − | 0.753915i | \(-0.728163\pi\) | ||||
−0.656972 | + | 0.753915i | \(0.728163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.00000 | 0.168263 | 0.0841317 | − | 0.996455i | \(-0.473188\pi\) | ||||
0.0841317 | + | 0.996455i | \(0.473188\pi\) | |||||||
\(884\) | −12.0000 | − | 20.7846i | −0.403604 | − | 0.699062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.0000 | − | 25.9808i | 0.503651 | − | 0.872349i | −0.496340 | − | 0.868128i | \(-0.665323\pi\) |
0.999991 | − | 0.00422062i | \(-0.00134347\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00000 | − | 13.8564i | −0.268311 | − | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.50000 | + | 7.79423i | −0.150756 | + | 0.261116i | ||||
\(892\) | −22.0000 | −0.736614 | ||||||||
\(893\) | −3.00000 | − | 5.19615i | −0.100391 | − | 0.173883i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.5000 | − | 38.9711i | 0.752092 | − | 1.30266i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.00000 | + | 5.19615i | 0.300501 | + | 0.173494i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −48.0000 | −1.60089 | ||||||||
\(900\) | −12.0000 | + | 20.7846i | −0.400000 | + | 0.692820i | ||||
\(901\) | −18.0000 | −0.599667 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 55.4256i | 1.84445i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.50000 | + | 2.59808i | −0.0498617 | + | 0.0863630i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0000 | + | 24.2487i | 0.464862 | + | 0.805165i | 0.999195 | − | 0.0401089i | \(-0.0127705\pi\) |
−0.534333 | + | 0.845274i | \(0.679437\pi\) | |||||||
\(908\) | −36.0000 | −1.19470 | ||||||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.50000 | + | 12.9904i | 0.248486 | + | 0.430391i | 0.963106 | − | 0.269122i | \(-0.0867336\pi\) |
−0.714620 | + | 0.699513i | \(0.753400\pi\) | |||||||
\(912\) | 12.0000 | + | 6.92820i | 0.397360 | + | 0.229416i | ||||
\(913\) | 9.00000 | − | 15.5885i | 0.297857 | − | 0.515903i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.0000 | − | 20.7846i | 1.19012 | − | 0.687118i | ||||
\(916\) | 23.0000 | + | 39.8372i | 0.759941 | + | 1.31626i | ||||
\(917\) | −72.0000 | −2.37765 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.0000 | 1.84727 | 0.923635 | − | 0.383274i | \(-0.125203\pi\) | ||||
0.923635 | + | 0.383274i | \(0.125203\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.0000 | − | 13.8564i | 0.790827 | − | 0.456584i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 12.0000 | + | 6.92820i | 0.394771 | + | 0.227921i | ||||
\(925\) | −4.00000 | − | 6.92820i | −0.131519 | − | 0.227798i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.50000 | + | 12.9904i | 0.246332 | + | 0.426660i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.5000 | − | 18.1865i | −0.344494 | − | 0.596681i | 0.640768 | − | 0.767735i | \(-0.278616\pi\) |
−0.985262 | + | 0.171054i | \(0.945283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.00000 | + | 15.5885i | −0.294963 | + | 0.510891i | ||||
\(932\) | −6.00000 | + | 10.3923i | −0.196537 | + | 0.340411i | ||||
\(933\) | 5.19615i | 0.170114i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.0000 | 0.588663 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.0000 | −0.914720 | −0.457360 | − | 0.889282i | \(-0.651205\pi\) | ||||
−0.457360 | + | 0.889282i | \(0.651205\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.5000 | + | 9.52628i | 0.538457 | + | 0.310878i | ||||
\(940\) | −9.00000 | + | 15.5885i | −0.293548 | + | 0.508439i | ||||
\(941\) | 27.0000 | − | 46.7654i | 0.880175 | − | 1.52451i | 0.0290288 | − | 0.999579i | \(-0.490759\pi\) |
0.851146 | − | 0.524929i | \(-0.175908\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 62.3538i | 2.02837i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.50000 | − | 2.59808i | −0.0487435 | − | 0.0844261i | 0.840624 | − | 0.541619i | \(-0.182188\pi\) |
−0.889368 | + | 0.457193i | \(0.848855\pi\) | |||||||
\(948\) | 6.00000 | − | 3.46410i | 0.194871 | − | 0.112509i | ||||
\(949\) | −2.00000 | + | 3.46410i | −0.0649227 | + | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.5000 | − | 23.3827i | −1.31330 | − | 0.758236i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.00000 | −0.291233 | ||||||||
\(956\) | −12.0000 | − | 20.7846i | −0.388108 | − | 0.672222i | ||||
\(957\) | 10.3923i | 0.335936i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36.0000 | − | 62.3538i | 1.16250 | − | 2.01351i | ||||
\(960\) | − | 41.5692i | − | 1.34164i | ||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.0000 | + | 31.1769i | −0.580042 | + | 1.00466i | ||||
\(964\) | −4.00000 | −0.128831 | ||||||||
\(965\) | −6.00000 | − | 10.3923i | −0.193147 | − | 0.334540i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0000 | − | 34.6410i | 0.643157 | − | 1.11398i | −0.341567 | − | 0.939857i | \(-0.610958\pi\) |
0.984724 | − | 0.174123i | \(-0.0557089\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.0000 | − | 10.3923i | 0.578243 | − | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.0000 | 0.866471 | 0.433236 | − | 0.901281i | \(-0.357372\pi\) | ||||
0.433236 | + | 0.901281i | \(0.357372\pi\) | |||||||
\(972\) | 27.0000 | − | 15.5885i | 0.866025 | − | 0.500000i | ||||
\(973\) | 40.0000 | 1.28234 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.0000 | + | 6.92820i | −0.384308 | + | 0.221880i | ||||
\(976\) | −16.0000 | + | 27.7128i | −0.512148 | + | 0.887066i | ||||
\(977\) | −22.5000 | + | 38.9711i | −0.719839 | + | 1.24680i | 0.241225 | + | 0.970469i | \(0.422451\pi\) |
−0.961063 | + | 0.276328i | \(0.910882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.50000 | − | 2.59808i | −0.0479402 | − | 0.0830349i | ||||
\(980\) | 54.0000 | 1.72497 | ||||||||
\(981\) | 21.0000 | − | 36.3731i | 0.670478 | − | 1.16130i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.0000 | − | 46.7654i | 0.860292 | − | 1.49007i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.7846i | 0.661581i | ||||||||
\(988\) | 4.00000 | + | 6.92820i | 0.127257 | + | 0.220416i | ||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.5000 | + | 25.1147i | 1.38043 | + | 0.796992i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.5000 | − | 28.5788i | 0.523085 | − | 0.906010i | ||||
\(996\) | −54.0000 | + | 31.1769i | −1.71106 | + | 0.987878i | ||||
\(997\) | 5.00000 | + | 8.66025i | 0.158352 | + | 0.274273i | 0.934274 | − | 0.356555i | \(-0.116049\pi\) |
−0.775923 | + | 0.630828i | \(0.782715\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.3923i | 0.328798i |
(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 | 99.2.e.b.67.1 | yes | 2 | |
3.2 | odd | 2 | 297.2.e.b.199.1 | 2 | |||
9.2 | odd | 6 | 297.2.e.b.100.1 | 2 | |||
9.4 | even | 3 | 891.2.a.d.1.1 | 1 | |||
9.5 | odd | 6 | 891.2.a.e.1.1 | 1 | |||
9.7 | even | 3 | inner | 99.2.e.b.34.1 | ✓ | 2 | |
11.10 | odd | 2 | 1089.2.e.b.364.1 | 2 | |||
99.32 | even | 6 | 9801.2.a.g.1.1 | 1 | |||
99.43 | odd | 6 | 1089.2.e.b.727.1 | 2 | |||
99.76 | odd | 6 | 9801.2.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.e.b.34.1 | ✓ | 2 | 9.7 | even | 3 | inner | |
99.2.e.b.67.1 | yes | 2 | 1.1 | even | 1 | trivial | |
297.2.e.b.100.1 | 2 | 9.2 | odd | 6 | |||
297.2.e.b.199.1 | 2 | 3.2 | odd | 2 | |||
891.2.a.d.1.1 | 1 | 9.4 | even | 3 | |||
891.2.a.e.1.1 | 1 | 9.5 | odd | 6 | |||
1089.2.e.b.364.1 | 2 | 11.10 | odd | 2 | |||
1089.2.e.b.727.1 | 2 | 99.43 | odd | 6 | |||
9801.2.a.f.1.1 | 1 | 99.76 | odd | 6 | |||
9801.2.a.g.1.1 | 1 | 99.32 | even | 6 |