Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,2,Mod(35,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.574922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 35.1 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.35 |
Dual form | 72.2.f.a.35.2 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.866025 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 2.44949 | 1.09545 | 0.547723 | − | 0.836660i | \(-0.315495\pi\) | ||||
0.547723 | + | 0.836660i | \(0.315495\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.46410i | − | 1.30931i | −0.755929 | − | 0.654654i | \(-0.772814\pi\) | ||
0.755929 | − | 0.654654i | \(-0.227186\pi\) | |||||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.00000 | − | 1.73205i | −0.948683 | − | 0.547723i | ||||
\(11\) | 2.82843i | 0.852803i | 0.904534 | + | 0.426401i | \(0.140219\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | −2.44949 | + | 4.24264i | −0.654654 | + | 1.13389i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | − | 1.41421i | − | 0.342997i | −0.985184 | − | 0.171499i | \(-0.945139\pi\) | ||
0.985184 | − | 0.171499i | \(-0.0548609\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 2.44949 | + | 4.24264i | 0.547723 | + | 0.948683i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | − | 3.46410i | 0.426401 | − | 0.738549i | ||||
\(23\) | −4.89898 | −1.02151 | −0.510754 | − | 0.859727i | \(-0.670634\pi\) | ||||
−0.510754 | + | 0.859727i | \(0.670634\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.44949 | − | 4.24264i | 0.480384 | − | 0.832050i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.00000 | − | 3.46410i | 1.13389 | − | 0.654654i | ||||
\(29\) | −2.44949 | −0.454859 | −0.227429 | − | 0.973795i | \(-0.573032\pi\) | ||||
−0.227429 | + | 0.973795i | \(0.573032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410i | 0.622171i | 0.950382 | + | 0.311086i | \(0.100693\pi\) | ||||
−0.950382 | + | 0.311086i | \(0.899307\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.866025 | − | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | + | 1.73205i | −0.171499 | + | 0.297044i | ||||
\(35\) | − | 8.48528i | − | 1.43427i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 4.89898 | + | 2.82843i | 0.794719 | + | 0.458831i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 6.92820i | − | 1.09545i | ||||||
\(41\) | − | 1.41421i | − | 0.220863i | −0.993884 | − | 0.110432i | \(-0.964777\pi\) | ||
0.993884 | − | 0.110432i | \(-0.0352233\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | −4.89898 | + | 2.82843i | −0.738549 | + | 0.426401i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | + | 3.46410i | 0.884652 | + | 0.510754i | ||||
\(47\) | 4.89898 | 0.714590 | 0.357295 | − | 0.933992i | \(-0.383699\pi\) | ||||
0.357295 | + | 0.933992i | \(0.383699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | −1.22474 | − | 0.707107i | −0.173205 | − | 0.100000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.00000 | + | 3.46410i | −0.832050 | + | 0.480384i | ||||
\(53\) | −7.34847 | −1.00939 | −0.504695 | − | 0.863298i | \(-0.668395\pi\) | ||||
−0.504695 | + | 0.863298i | \(0.668395\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.92820i | 0.934199i | ||||||||
\(56\) | −9.79796 | −1.30931 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | + | 1.73205i | 0.393919 | + | 0.227429i | ||||
\(59\) | 11.3137i | 1.47292i | 0.676481 | + | 0.736460i | \(0.263504\pi\) | ||||
−0.676481 | + | 0.736460i | \(0.736496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.8564i | − | 1.77413i | −0.461644 | − | 0.887066i | \(-0.652740\pi\) | ||
0.461644 | − | 0.887066i | \(-0.347260\pi\) | |||||||
\(62\) | 2.44949 | − | 4.24264i | 0.311086 | − | 0.538816i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 8.48528i | 1.05247i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 2.44949 | − | 1.41421i | 0.297044 | − | 0.171499i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.00000 | + | 10.3923i | −0.717137 | + | 1.24212i | ||||
\(71\) | 14.6969 | 1.74421 | 0.872103 | − | 0.489323i | \(-0.162756\pi\) | ||||
0.872103 | + | 0.489323i | \(0.162756\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | − | 6.92820i | −0.458831 | − | 0.794719i | ||||
\(77\) | 9.79796 | 1.11658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.46410i | − | 0.389742i | −0.980829 | − | 0.194871i | \(-0.937571\pi\) | ||
0.980829 | − | 0.194871i | \(-0.0624288\pi\) | |||||||
\(80\) | −4.89898 | + | 8.48528i | −0.547723 | + | 0.948683i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.00000 | + | 1.73205i | −0.110432 | + | 0.191273i | ||||
\(83\) | − | 14.1421i | − | 1.55230i | −0.630548 | − | 0.776151i | \(-0.717170\pi\) | ||
0.630548 | − | 0.776151i | \(-0.282830\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 3.46410i | − | 0.375735i | ||||||
\(86\) | −9.79796 | − | 5.65685i | −1.05654 | − | 0.609994i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.00000 | 0.852803 | ||||||||
\(89\) | 7.07107i | 0.749532i | 0.927119 | + | 0.374766i | \(0.122277\pi\) | ||||
−0.927119 | + | 0.374766i | \(0.877723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | 1.25794 | ||||||||
\(92\) | −4.89898 | − | 8.48528i | −0.510754 | − | 0.884652i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.00000 | − | 3.46410i | −0.618853 | − | 0.357295i | ||||
\(95\) | −9.79796 | −1.00525 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 6.12372 | + | 3.53553i | 0.618590 | + | 0.357143i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | + | 1.73205i | 0.100000 | + | 0.173205i | ||||
\(101\) | −2.44949 | −0.243733 | −0.121867 | − | 0.992546i | \(-0.538888\pi\) | ||||
−0.121867 | + | 0.992546i | \(0.538888\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.46410i | 0.341328i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) | ||||
−0.985329 | + | 0.170664i | \(0.945409\pi\) | |||||||
\(104\) | 9.79796 | 0.960769 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.00000 | + | 5.19615i | 0.874157 | + | 0.504695i | ||||
\(107\) | 11.3137i | 1.09374i | 0.837218 | + | 0.546869i | \(0.184180\pi\) | ||||
−0.837218 | + | 0.546869i | \(0.815820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.3923i | 0.995402i | 0.867349 | + | 0.497701i | \(0.165822\pi\) | ||||
−0.867349 | + | 0.497701i | \(0.834178\pi\) | |||||||
\(110\) | 4.89898 | − | 8.48528i | 0.467099 | − | 0.809040i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.0000 | + | 6.92820i | 1.13389 | + | 0.654654i | ||||
\(113\) | − | 18.3848i | − | 1.72949i | −0.502208 | − | 0.864747i | \(-0.667479\pi\) | ||
0.502208 | − | 0.864747i | \(-0.332521\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.0000 | −1.11901 | ||||||||
\(116\) | −2.44949 | − | 4.24264i | −0.227429 | − | 0.393919i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.00000 | − | 13.8564i | 0.736460 | − | 1.27559i | ||||
\(119\) | −4.89898 | −0.449089 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | −9.79796 | + | 16.9706i | −0.887066 | + | 1.53644i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.00000 | + | 3.46410i | −0.538816 | + | 0.311086i | ||||
\(125\) | −9.79796 | −0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.3923i | − | 0.922168i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.866025 | + | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.00000 | − | 10.3923i | 0.526235 | − | 0.911465i | ||||
\(131\) | − | 5.65685i | − | 0.494242i | −0.968985 | − | 0.247121i | \(-0.920516\pi\) | ||
0.968985 | − | 0.247121i | \(-0.0794845\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.8564i | 1.20150i | ||||||||
\(134\) | 4.89898 | + | 2.82843i | 0.423207 | + | 0.244339i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | − | 9.89949i | − | 0.845771i | −0.906183 | − | 0.422885i | \(-0.861017\pi\) | ||
0.906183 | − | 0.422885i | \(-0.138983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 14.6969 | − | 8.48528i | 1.24212 | − | 0.717137i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −18.0000 | − | 10.3923i | −1.51053 | − | 0.872103i | ||||
\(143\) | −9.79796 | −0.819346 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | 4.89898 | + | 2.82843i | 0.405442 | + | 0.234082i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.1464 | 1.40469 | 0.702345 | − | 0.711837i | \(-0.252136\pi\) | ||||
0.702345 | + | 0.711837i | \(0.252136\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.46410i | − | 0.281905i | −0.990016 | − | 0.140952i | \(-0.954984\pi\) | ||
0.990016 | − | 0.140952i | \(-0.0450164\pi\) | |||||||
\(152\) | 11.3137i | 0.917663i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.0000 | − | 6.92820i | −0.966988 | − | 0.558291i | ||||
\(155\) | 8.48528i | 0.681554i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.8564i | 1.10586i | 0.833227 | + | 0.552931i | \(0.186491\pi\) | ||||
−0.833227 | + | 0.552931i | \(0.813509\pi\) | |||||||
\(158\) | −2.44949 | + | 4.24264i | −0.194871 | + | 0.337526i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.0000 | − | 6.92820i | 0.948683 | − | 0.547723i | ||||
\(161\) | 16.9706i | 1.33747i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0000 | −1.25322 | −0.626608 | − | 0.779334i | \(-0.715557\pi\) | ||||
−0.626608 | + | 0.779334i | \(0.715557\pi\) | |||||||
\(164\) | 2.44949 | − | 1.41421i | 0.191273 | − | 0.110432i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.0000 | + | 17.3205i | −0.776151 | + | 1.34433i | ||||
\(167\) | −19.5959 | −1.51638 | −0.758189 | − | 0.652035i | \(-0.773915\pi\) | ||||
−0.758189 | + | 0.652035i | \(0.773915\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.44949 | + | 4.24264i | −0.187867 | + | 0.325396i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000 | + | 13.8564i | 0.609994 | + | 1.05654i | ||||
\(173\) | −2.44949 | −0.186231 | −0.0931156 | − | 0.995655i | \(-0.529683\pi\) | ||||
−0.0931156 | + | 0.995655i | \(0.529683\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.46410i | − | 0.261861i | ||||||
\(176\) | −9.79796 | − | 5.65685i | −0.738549 | − | 0.426401i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.00000 | − | 8.66025i | 0.374766 | − | 0.649113i | ||||
\(179\) | − | 5.65685i | − | 0.422813i | −0.977398 | − | 0.211407i | \(-0.932196\pi\) | ||
0.977398 | − | 0.211407i | \(-0.0678044\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.3923i | − | 0.772454i | −0.922404 | − | 0.386227i | \(-0.873778\pi\) | ||
0.922404 | − | 0.386227i | \(-0.126222\pi\) | |||||||
\(182\) | −14.6969 | − | 8.48528i | −1.08941 | − | 0.628971i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.8564i | 1.02151i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | 0.292509 | ||||||||
\(188\) | 4.89898 | + | 8.48528i | 0.357295 | + | 0.618853i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.0000 | + | 6.92820i | 0.870572 | + | 0.502625i | ||||
\(191\) | 19.5959 | 1.41791 | 0.708955 | − | 0.705253i | \(-0.249167\pi\) | ||||
0.708955 | + | 0.705253i | \(0.249167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | −9.79796 | − | 5.65685i | −0.703452 | − | 0.406138i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.00000 | − | 8.66025i | −0.357143 | − | 0.618590i | ||||
\(197\) | 7.34847 | 0.523557 | 0.261778 | − | 0.965128i | \(-0.415691\pi\) | ||||
0.261778 | + | 0.965128i | \(0.415691\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.3923i | − | 0.736691i | −0.929689 | − | 0.368345i | \(-0.879924\pi\) | ||
0.929689 | − | 0.368345i | \(-0.120076\pi\) | |||||||
\(200\) | − | 2.82843i | − | 0.200000i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.00000 | + | 1.73205i | 0.211079 | + | 0.121867i | ||||
\(203\) | 8.48528i | 0.595550i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 3.46410i | − | 0.241943i | ||||||
\(206\) | 2.44949 | − | 4.24264i | 0.170664 | − | 0.295599i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.0000 | − | 6.92820i | −0.832050 | − | 0.480384i | ||||
\(209\) | − | 11.3137i | − | 0.782586i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | −7.34847 | − | 12.7279i | −0.504695 | − | 0.874157i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.00000 | − | 13.8564i | 0.546869 | − | 0.947204i | ||||
\(215\) | 19.5959 | 1.33643 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0000 | 0.814613 | ||||||||
\(218\) | 7.34847 | − | 12.7279i | 0.497701 | − | 0.862044i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.0000 | + | 6.92820i | −0.809040 | + | 0.467099i | ||||
\(221\) | 4.89898 | 0.329541 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.3205i | 1.15987i | 0.814664 | + | 0.579934i | \(0.196921\pi\) | ||||
−0.814664 | + | 0.579934i | \(0.803079\pi\) | |||||||
\(224\) | −9.79796 | − | 16.9706i | −0.654654 | − | 1.13389i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.0000 | + | 22.5167i | −0.864747 | + | 1.49779i | ||||
\(227\) | 2.82843i | 0.187729i | 0.995585 | + | 0.0938647i | \(0.0299221\pi\) | ||||
−0.995585 | + | 0.0938647i | \(0.970078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.3205i | − | 1.14457i | −0.820054 | − | 0.572286i | \(-0.806057\pi\) | ||
0.820054 | − | 0.572286i | \(-0.193943\pi\) | |||||||
\(230\) | 14.6969 | + | 8.48528i | 0.969087 | + | 0.559503i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.92820i | 0.454859i | ||||||||
\(233\) | − | 1.41421i | − | 0.0926482i | −0.998926 | − | 0.0463241i | \(-0.985249\pi\) | ||
0.998926 | − | 0.0463241i | \(-0.0147507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | 0.782794 | ||||||||
\(236\) | −19.5959 | + | 11.3137i | −1.27559 | + | 0.736460i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.00000 | + | 3.46410i | 0.388922 | + | 0.224544i | ||||
\(239\) | 9.79796 | 0.633777 | 0.316889 | − | 0.948463i | \(-0.397362\pi\) | ||||
0.316889 | + | 0.948463i | \(0.397362\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.0000 | −1.80364 | −0.901819 | − | 0.432113i | \(-0.857768\pi\) | ||||
−0.901819 | + | 0.432113i | \(0.857768\pi\) | |||||||
\(242\) | −3.67423 | − | 2.12132i | −0.236189 | − | 0.136364i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 24.0000 | − | 13.8564i | 1.53644 | − | 0.887066i | ||||
\(245\) | −12.2474 | −0.782461 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 13.8564i | − | 0.881662i | ||||||
\(248\) | 9.79796 | 0.622171 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.0000 | + | 6.92820i | 0.758947 | + | 0.438178i | ||||
\(251\) | − | 14.1421i | − | 0.892644i | −0.894873 | − | 0.446322i | \(-0.852734\pi\) | ||
0.894873 | − | 0.446322i | \(-0.147266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 13.8564i | − | 0.871145i | ||||||
\(254\) | −7.34847 | + | 12.7279i | −0.461084 | + | 0.798621i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 24.0416i | 1.49968i | 0.661622 | + | 0.749838i | \(0.269869\pi\) | ||||
−0.661622 | + | 0.749838i | \(0.730131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −14.6969 | + | 8.48528i | −0.911465 | + | 0.526235i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.00000 | + | 6.92820i | −0.247121 | + | 0.428026i | ||||
\(263\) | −9.79796 | −0.604168 | −0.302084 | − | 0.953281i | \(-0.597682\pi\) | ||||
−0.302084 | + | 0.953281i | \(0.597682\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.0000 | −1.10573 | ||||||||
\(266\) | 9.79796 | − | 16.9706i | 0.600751 | − | 1.04053i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.00000 | − | 6.92820i | −0.244339 | − | 0.423207i | ||||
\(269\) | −7.34847 | −0.448044 | −0.224022 | − | 0.974584i | \(-0.571919\pi\) | ||||
−0.224022 | + | 0.974584i | \(0.571919\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.1769i | 1.89386i | 0.321436 | + | 0.946931i | \(0.395835\pi\) | ||||
−0.321436 | + | 0.946931i | \(0.604165\pi\) | |||||||
\(272\) | 4.89898 | + | 2.82843i | 0.297044 | + | 0.171499i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.00000 | + | 12.1244i | −0.422885 | + | 0.732459i | ||||
\(275\) | 2.82843i | 0.170561i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.3205i | 1.04069i | 0.853957 | + | 0.520344i | \(0.174196\pi\) | ||||
−0.853957 | + | 0.520344i | \(0.825804\pi\) | |||||||
\(278\) | 4.89898 | + | 2.82843i | 0.293821 | + | 0.169638i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −24.0000 | −1.43427 | ||||||||
\(281\) | 24.0416i | 1.43420i | 0.696969 | + | 0.717102i | \(0.254532\pi\) | ||||
−0.696969 | + | 0.717102i | \(0.745468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.0000 | −0.951101 | −0.475551 | − | 0.879688i | \(-0.657751\pi\) | ||||
−0.475551 | + | 0.879688i | \(0.657751\pi\) | |||||||
\(284\) | 14.6969 | + | 25.4558i | 0.872103 | + | 1.51053i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.0000 | + | 6.92820i | 0.709575 | + | 0.409673i | ||||
\(287\) | −4.89898 | −0.289178 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000 | 0.882353 | ||||||||
\(290\) | 7.34847 | + | 4.24264i | 0.431517 | + | 0.249136i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.00000 | − | 6.92820i | −0.234082 | − | 0.405442i | ||||
\(293\) | −26.9444 | −1.57411 | −0.787054 | − | 0.616884i | \(-0.788395\pi\) | ||||
−0.787054 | + | 0.616884i | \(0.788395\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.7128i | 1.61350i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.0000 | − | 12.1244i | −1.21650 | − | 0.702345i | ||||
\(299\) | − | 16.9706i | − | 0.981433i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 27.7128i | − | 1.59734i | ||||||
\(302\) | −2.44949 | + | 4.24264i | −0.140952 | + | 0.244137i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.00000 | − | 13.8564i | 0.458831 | − | 0.794719i | ||||
\(305\) | − | 33.9411i | − | 1.94346i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.00000 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | 9.79796 | + | 16.9706i | 0.558291 | + | 0.966988i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.00000 | − | 10.3923i | 0.340777 | − | 0.590243i | ||||
\(311\) | 9.79796 | 0.555591 | 0.277796 | − | 0.960640i | \(-0.410396\pi\) | ||||
0.277796 | + | 0.960640i | \(0.410396\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | 9.79796 | − | 16.9706i | 0.552931 | − | 0.957704i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.00000 | − | 3.46410i | 0.337526 | − | 0.194871i | ||||
\(317\) | 12.2474 | 0.687885 | 0.343943 | − | 0.938991i | \(-0.388237\pi\) | ||||
0.343943 | + | 0.938991i | \(0.388237\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.92820i | − | 0.387905i | ||||||
\(320\) | −19.5959 | −1.09545 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.0000 | − | 20.7846i | 0.668734 | − | 1.15828i | ||||
\(323\) | 5.65685i | 0.314756i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.46410i | 0.192154i | ||||||||
\(326\) | 19.5959 | + | 11.3137i | 1.08532 | + | 0.626608i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.00000 | −0.220863 | ||||||||
\(329\) | − | 16.9706i | − | 0.935617i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 24.4949 | − | 14.1421i | 1.34433 | − | 0.776151i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.0000 | + | 13.8564i | 1.31322 | + | 0.758189i | ||||
\(335\) | −9.79796 | −0.535320 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.00000 | −0.217894 | −0.108947 | − | 0.994048i | \(-0.534748\pi\) | ||||
−0.108947 | + | 0.994048i | \(0.534748\pi\) | |||||||
\(338\) | −1.22474 | − | 0.707107i | −0.0666173 | − | 0.0384615i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00000 | − | 3.46410i | 0.325396 | − | 0.187867i | ||||
\(341\) | −9.79796 | −0.530589 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.92820i | − | 0.374088i | ||||||
\(344\) | − | 22.6274i | − | 1.21999i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | + | 1.73205i | 0.161281 | + | 0.0931156i | ||||
\(347\) | − | 14.1421i | − | 0.759190i | −0.925153 | − | 0.379595i | \(-0.876063\pi\) | ||
0.925153 | − | 0.379595i | \(-0.123937\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.7128i | 1.48343i | 0.670714 | + | 0.741716i | \(0.265988\pi\) | ||||
−0.670714 | + | 0.741716i | \(0.734012\pi\) | |||||||
\(350\) | −2.44949 | + | 4.24264i | −0.130931 | + | 0.226779i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.00000 | + | 13.8564i | 0.426401 | + | 0.738549i | ||||
\(353\) | 15.5563i | 0.827981i | 0.910281 | + | 0.413990i | \(0.135865\pi\) | ||||
−0.910281 | + | 0.413990i | \(0.864135\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.0000 | 1.91068 | ||||||||
\(356\) | −12.2474 | + | 7.07107i | −0.649113 | + | 0.374766i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.00000 | + | 6.92820i | −0.211407 | + | 0.366167i | ||||
\(359\) | −14.6969 | −0.775675 | −0.387837 | − | 0.921728i | \(-0.626778\pi\) | ||||
−0.387837 | + | 0.921728i | \(0.626778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | −7.34847 | + | 12.7279i | −0.386227 | + | 0.668965i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.0000 | + | 20.7846i | 0.628971 | + | 1.08941i | ||||
\(365\) | −9.79796 | −0.512849 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 24.2487i | − | 1.26577i | −0.774245 | − | 0.632886i | \(-0.781870\pi\) | ||
0.774245 | − | 0.632886i | \(-0.218130\pi\) | |||||||
\(368\) | 9.79796 | − | 16.9706i | 0.510754 | − | 0.884652i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.4558i | 1.32160i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.8564i | 0.717458i | 0.933442 | + | 0.358729i | \(0.116790\pi\) | ||||
−0.933442 | + | 0.358729i | \(0.883210\pi\) | |||||||
\(374\) | −4.89898 | − | 2.82843i | −0.253320 | − | 0.146254i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 13.8564i | − | 0.714590i | ||||||
\(377\) | − | 8.48528i | − | 0.437014i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | −9.79796 | − | 16.9706i | −0.502625 | − | 0.870572i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −24.0000 | − | 13.8564i | −1.22795 | − | 0.708955i | ||||
\(383\) | 9.79796 | 0.500652 | 0.250326 | − | 0.968162i | \(-0.419462\pi\) | ||||
0.250326 | + | 0.968162i | \(0.419462\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 24.0000 | 1.22315 | ||||||||
\(386\) | −17.1464 | − | 9.89949i | −0.872730 | − | 0.503871i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.00000 | + | 13.8564i | 0.406138 | + | 0.703452i | ||||
\(389\) | 26.9444 | 1.36613 | 0.683067 | − | 0.730355i | \(-0.260646\pi\) | ||||
0.683067 | + | 0.730355i | \(0.260646\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.92820i | 0.350374i | ||||||||
\(392\) | 14.1421i | 0.714286i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.00000 | − | 5.19615i | −0.453413 | − | 0.261778i | ||||
\(395\) | − | 8.48528i | − | 0.426941i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | −7.34847 | + | 12.7279i | −0.368345 | + | 0.637993i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | − | 1.41421i | − | 0.0706225i | −0.999376 | − | 0.0353112i | \(-0.988758\pi\) | ||
0.999376 | − | 0.0353112i | \(-0.0112422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0000 | −0.597763 | ||||||||
\(404\) | −2.44949 | − | 4.24264i | −0.121867 | − | 0.211079i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | − | 10.3923i | 0.297775 | − | 0.515761i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.0000 | 1.58230 | 0.791149 | − | 0.611623i | \(-0.209483\pi\) | ||||
0.791149 | + | 0.611623i | \(0.209483\pi\) | |||||||
\(410\) | −2.44949 | + | 4.24264i | −0.120972 | + | 0.209529i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.00000 | + | 3.46410i | −0.295599 | + | 0.170664i | ||||
\(413\) | 39.1918 | 1.92850 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 34.6410i | − | 1.70046i | ||||||
\(416\) | 9.79796 | + | 16.9706i | 0.480384 | + | 0.832050i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.00000 | + | 13.8564i | −0.391293 | + | 0.677739i | ||||
\(419\) | 19.7990i | 0.967244i | 0.875277 | + | 0.483622i | \(0.160679\pi\) | ||||
−0.875277 | + | 0.483622i | \(0.839321\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 24.2487i | − | 1.18181i | −0.806741 | − | 0.590905i | \(-0.798771\pi\) | ||
0.806741 | − | 0.590905i | \(-0.201229\pi\) | |||||||
\(422\) | −24.4949 | − | 14.1421i | −1.19239 | − | 0.688428i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 20.7846i | 1.00939i | ||||||||
\(425\) | − | 1.41421i | − | 0.0685994i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −48.0000 | −2.32288 | ||||||||
\(428\) | −19.5959 | + | 11.3137i | −0.947204 | + | 0.546869i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.0000 | − | 13.8564i | −1.15738 | − | 0.668215i | ||||
\(431\) | −14.6969 | −0.707927 | −0.353963 | − | 0.935259i | \(-0.615166\pi\) | ||||
−0.353963 | + | 0.935259i | \(0.615166\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.0000 | −1.05725 | −0.528626 | − | 0.848855i | \(-0.677293\pi\) | ||||
−0.528626 | + | 0.848855i | \(0.677293\pi\) | |||||||
\(434\) | −14.6969 | − | 8.48528i | −0.705476 | − | 0.407307i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.0000 | + | 10.3923i | −0.862044 | + | 0.497701i | ||||
\(437\) | 19.5959 | 0.937400 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.46410i | − | 0.165333i | −0.996577 | − | 0.0826663i | \(-0.973656\pi\) | ||
0.996577 | − | 0.0826663i | \(-0.0263436\pi\) | |||||||
\(440\) | 19.5959 | 0.934199 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.00000 | − | 3.46410i | −0.285391 | − | 0.164771i | ||||
\(443\) | 2.82843i | 0.134383i | 0.997740 | + | 0.0671913i | \(0.0214038\pi\) | ||||
−0.997740 | + | 0.0671913i | \(0.978596\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.3205i | 0.821071i | ||||||||
\(446\) | 12.2474 | − | 21.2132i | 0.579934 | − | 1.00447i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 27.7128i | 1.30931i | ||||||||
\(449\) | 24.0416i | 1.13459i | 0.823513 | + | 0.567297i | \(0.192011\pi\) | ||||
−0.823513 | + | 0.567297i | \(0.807989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | 31.8434 | − | 18.3848i | 1.49779 | − | 0.864747i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.00000 | − | 3.46410i | 0.0938647 | − | 0.162578i | ||||
\(455\) | 29.3939 | 1.37801 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.00000 | 0.374224 | 0.187112 | − | 0.982339i | \(-0.440087\pi\) | ||||
0.187112 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(458\) | −12.2474 | + | 21.2132i | −0.572286 | + | 0.991228i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.0000 | − | 20.7846i | −0.559503 | − | 0.969087i | ||||
\(461\) | −17.1464 | −0.798589 | −0.399294 | − | 0.916823i | \(-0.630745\pi\) | ||||
−0.399294 | + | 0.916823i | \(0.630745\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.3205i | − | 0.804952i | −0.915430 | − | 0.402476i | \(-0.868150\pi\) | ||
0.915430 | − | 0.402476i | \(-0.131850\pi\) | |||||||
\(464\) | 4.89898 | − | 8.48528i | 0.227429 | − | 0.393919i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.00000 | + | 1.73205i | −0.0463241 | + | 0.0802357i | ||||
\(467\) | 36.7696i | 1.70149i | 0.525577 | + | 0.850746i | \(0.323849\pi\) | ||||
−0.525577 | + | 0.850746i | \(0.676151\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.8564i | 0.639829i | ||||||||
\(470\) | −14.6969 | − | 8.48528i | −0.677919 | − | 0.391397i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 32.0000 | 1.47292 | ||||||||
\(473\) | 22.6274i | 1.04041i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | −4.89898 | − | 8.48528i | −0.224544 | − | 0.388922i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.0000 | − | 6.92820i | −0.548867 | − | 0.316889i | ||||
\(479\) | −24.4949 | −1.11920 | −0.559600 | − | 0.828763i | \(-0.689045\pi\) | ||||
−0.559600 | + | 0.828763i | \(0.689045\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 34.2929 | + | 19.7990i | 1.56200 | + | 0.901819i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.00000 | + | 5.19615i | 0.136364 | + | 0.236189i | ||||
\(485\) | 19.5959 | 0.889805 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.3923i | − | 0.470920i | −0.971884 | − | 0.235460i | \(-0.924340\pi\) | ||
0.971884 | − | 0.235460i | \(-0.0756597\pi\) | |||||||
\(488\) | −39.1918 | −1.77413 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15.0000 | + | 8.66025i | 0.677631 | + | 0.391230i | ||||
\(491\) | − | 39.5980i | − | 1.78703i | −0.449032 | − | 0.893516i | \(-0.648231\pi\) | ||
0.449032 | − | 0.893516i | \(-0.351769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.46410i | 0.156015i | ||||||||
\(494\) | −9.79796 | + | 16.9706i | −0.440831 | + | 0.763542i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.0000 | − | 6.92820i | −0.538816 | − | 0.311086i | ||||
\(497\) | − | 50.9117i | − | 2.28370i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0000 | 1.43252 | 0.716258 | − | 0.697835i | \(-0.245853\pi\) | ||||
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | −9.79796 | − | 16.9706i | −0.438178 | − | 0.758947i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.0000 | + | 17.3205i | −0.446322 | + | 0.773052i | ||||
\(503\) | −14.6969 | −0.655304 | −0.327652 | − | 0.944798i | \(-0.606257\pi\) | ||||
−0.327652 | + | 0.944798i | \(0.606257\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | −9.79796 | + | 16.9706i | −0.435572 | + | 0.754434i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.0000 | − | 10.3923i | 0.798621 | − | 0.461084i | ||||
\(509\) | −41.6413 | −1.84572 | −0.922860 | − | 0.385136i | \(-0.874154\pi\) | ||||
−0.922860 | + | 0.385136i | \(0.874154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.8564i | 0.612971i | ||||||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.0000 | − | 29.4449i | 0.749838 | − | 1.29876i | ||||
\(515\) | 8.48528i | 0.373906i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.8564i | 0.609404i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 24.0000 | 1.05247 | ||||||||
\(521\) | − | 26.8701i | − | 1.17720i | −0.808425 | − | 0.588599i | \(-0.799680\pi\) | ||
0.808425 | − | 0.588599i | \(-0.200320\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | 9.79796 | − | 5.65685i | 0.428026 | − | 0.247121i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0000 | + | 6.92820i | 0.523225 | + | 0.302084i | ||||
\(527\) | 4.89898 | 0.213403 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 22.0454 | + | 12.7279i | 0.957591 | + | 0.552866i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −24.0000 | + | 13.8564i | −1.04053 | + | 0.600751i | ||||
\(533\) | 4.89898 | 0.212198 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.7128i | 1.19813i | ||||||||
\(536\) | 11.3137i | 0.488678i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.00000 | + | 5.19615i | 0.388018 | + | 0.224022i | ||||
\(539\) | − | 14.1421i | − | 0.609145i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.3923i | 0.446800i | 0.974727 | + | 0.223400i | \(0.0717156\pi\) | ||||
−0.974727 | + | 0.223400i | \(0.928284\pi\) | |||||||
\(542\) | 22.0454 | − | 38.1838i | 0.946931 | − | 1.64013i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.00000 | − | 6.92820i | −0.171499 | − | 0.297044i | ||||
\(545\) | 25.4558i | 1.09041i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 17.1464 | − | 9.89949i | 0.732459 | − | 0.422885i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.00000 | − | 3.46410i | 0.0852803 | − | 0.147710i | ||||
\(551\) | 9.79796 | 0.417407 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.0000 | −0.510292 | ||||||||
\(554\) | 12.2474 | − | 21.2132i | 0.520344 | − | 0.901263i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.00000 | − | 6.92820i | −0.169638 | − | 0.293821i | ||||
\(557\) | −7.34847 | −0.311365 | −0.155682 | − | 0.987807i | \(-0.549758\pi\) | ||||
−0.155682 | + | 0.987807i | \(0.549758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.7128i | 1.17213i | ||||||||
\(560\) | 29.3939 | + | 16.9706i | 1.24212 | + | 0.717137i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.0000 | − | 29.4449i | 0.717102 | − | 1.24206i | ||||
\(563\) | − | 14.1421i | − | 0.596020i | −0.954563 | − | 0.298010i | \(-0.903677\pi\) | ||
0.954563 | − | 0.298010i | \(-0.0963229\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 45.0333i | − | 1.89457i | ||||||
\(566\) | 19.5959 | + | 11.3137i | 0.823678 | + | 0.475551i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 41.5692i | − | 1.74421i | ||||||
\(569\) | − | 9.89949i | − | 0.415008i | −0.978234 | − | 0.207504i | \(-0.933466\pi\) | ||
0.978234 | − | 0.207504i | \(-0.0665341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.0000 | −1.67395 | −0.836974 | − | 0.547243i | \(-0.815677\pi\) | ||||
−0.836974 | + | 0.547243i | \(0.815677\pi\) | |||||||
\(572\) | −9.79796 | − | 16.9706i | −0.409673 | − | 0.709575i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.00000 | + | 3.46410i | 0.250435 | + | 0.144589i | ||||
\(575\) | −4.89898 | −0.204302 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | −18.3712 | − | 10.6066i | −0.764140 | − | 0.441176i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.00000 | − | 10.3923i | −0.249136 | − | 0.431517i | ||||
\(581\) | −48.9898 | −2.03244 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 20.7846i | − | 0.860811i | ||||||
\(584\) | 11.3137i | 0.468165i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.0000 | + | 19.0526i | 1.36322 | + | 0.787054i | ||||
\(587\) | − | 22.6274i | − | 0.933933i | −0.884275 | − | 0.466967i | \(-0.845347\pi\) | ||
0.884275 | − | 0.466967i | \(-0.154653\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 13.8564i | − | 0.570943i | ||||||
\(590\) | 19.5959 | − | 33.9411i | 0.806751 | − | 1.39733i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.07107i | 0.290374i | 0.989404 | + | 0.145187i | \(0.0463784\pi\) | ||||
−0.989404 | + | 0.145187i | \(0.953622\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | −0.491952 | ||||||||
\(596\) | 17.1464 | + | 29.6985i | 0.702345 | + | 1.21650i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.0000 | + | 20.7846i | −0.490716 | + | 0.849946i | ||||
\(599\) | −4.89898 | −0.200167 | −0.100083 | − | 0.994979i | \(-0.531911\pi\) | ||||
−0.100083 | + | 0.994979i | \(0.531911\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | −19.5959 | + | 33.9411i | −0.798670 | + | 1.38334i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.00000 | − | 3.46410i | 0.244137 | − | 0.140952i | ||||
\(605\) | 7.34847 | 0.298758 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.0333i | 1.82785i | 0.405887 | + | 0.913923i | \(0.366962\pi\) | ||||
−0.405887 | + | 0.913923i | \(0.633038\pi\) | |||||||
\(608\) | −19.5959 | + | 11.3137i | −0.794719 | + | 0.458831i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.0000 | + | 41.5692i | −0.971732 | + | 1.68309i | ||||
\(611\) | 16.9706i | 0.686555i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 4.89898 | + | 2.82843i | 0.197707 | + | 0.114146i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 27.7128i | − | 1.11658i | ||||||
\(617\) | 24.0416i | 0.967880i | 0.875101 | + | 0.483940i | \(0.160795\pi\) | ||||
−0.875101 | + | 0.483940i | \(0.839205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.00000 | 0.321547 | 0.160774 | − | 0.986991i | \(-0.448601\pi\) | ||||
0.160774 | + | 0.986991i | \(0.448601\pi\) | |||||||
\(620\) | −14.6969 | + | 8.48528i | −0.590243 | + | 0.340777i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.0000 | − | 6.92820i | −0.481156 | − | 0.277796i | ||||
\(623\) | 24.4949 | 0.981367 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 12.2474 | + | 7.07107i | 0.489506 | + | 0.282617i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −24.0000 | + | 13.8564i | −0.957704 | + | 0.552931i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.1769i | 1.24113i | 0.784154 | + | 0.620567i | \(0.213097\pi\) | ||||
−0.784154 | + | 0.620567i | \(0.786903\pi\) | |||||||
\(632\) | −9.79796 | −0.389742 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.0000 | − | 8.66025i | −0.595726 | − | 0.343943i | ||||
\(635\) | − | 25.4558i | − | 1.01018i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 17.3205i | − | 0.686264i | ||||||
\(638\) | −4.89898 | + | 8.48528i | −0.193952 | + | 0.335936i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.0000 | + | 13.8564i | 0.948683 | + | 0.547723i | ||||
\(641\) | 15.5563i | 0.614439i | 0.951639 | + | 0.307219i | \(0.0993986\pi\) | ||||
−0.951639 | + | 0.307219i | \(0.900601\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.0000 | 1.26196 | 0.630978 | − | 0.775800i | \(-0.282654\pi\) | ||||
0.630978 | + | 0.775800i | \(0.282654\pi\) | |||||||
\(644\) | −29.3939 | + | 16.9706i | −1.15828 | + | 0.668734i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.00000 | − | 6.92820i | 0.157378 | − | 0.272587i | ||||
\(647\) | −14.6969 | −0.577796 | −0.288898 | − | 0.957360i | \(-0.593289\pi\) | ||||
−0.288898 | + | 0.957360i | \(0.593289\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.0000 | −1.25611 | ||||||||
\(650\) | 2.44949 | − | 4.24264i | 0.0960769 | − | 0.166410i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.0000 | − | 27.7128i | −0.626608 | − | 1.08532i | ||||
\(653\) | 17.1464 | 0.670992 | 0.335496 | − | 0.942042i | \(-0.391096\pi\) | ||||
0.335496 | + | 0.942042i | \(0.391096\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 13.8564i | − | 0.541415i | ||||||
\(656\) | 4.89898 | + | 2.82843i | 0.191273 | + | 0.110432i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.0000 | + | 20.7846i | −0.467809 | + | 0.810268i | ||||
\(659\) | 11.3137i | 0.440720i | 0.975419 | + | 0.220360i | \(0.0707231\pi\) | ||||
−0.975419 | + | 0.220360i | \(0.929277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.8564i | 0.538952i | 0.963007 | + | 0.269476i | \(0.0868504\pi\) | ||||
−0.963007 | + | 0.269476i | \(0.913150\pi\) | |||||||
\(662\) | 4.89898 | + | 2.82843i | 0.190404 | + | 0.109930i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −40.0000 | −1.55230 | ||||||||
\(665\) | 33.9411i | 1.31618i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | 0.464642 | ||||||||
\(668\) | −19.5959 | − | 33.9411i | −0.758189 | − | 1.31322i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.0000 | + | 6.92820i | 0.463600 | + | 0.267660i | ||||
\(671\) | 39.1918 | 1.51298 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0000 | 0.539660 | 0.269830 | − | 0.962908i | \(-0.413032\pi\) | ||||
0.269830 | + | 0.962908i | \(0.413032\pi\) | |||||||
\(674\) | 4.89898 | + | 2.82843i | 0.188702 | + | 0.108947i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | + | 1.73205i | 0.0384615 | + | 0.0666173i | ||||
\(677\) | −17.1464 | −0.658991 | −0.329495 | − | 0.944157i | \(-0.606879\pi\) | ||||
−0.329495 | + | 0.944157i | \(0.606879\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 27.7128i | − | 1.06352i | ||||||
\(680\) | −9.79796 | −0.375735 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.0000 | + | 6.92820i | 0.459504 | + | 0.265295i | ||||
\(683\) | 36.7696i | 1.40695i | 0.710721 | + | 0.703474i | \(0.248369\pi\) | ||||
−0.710721 | + | 0.703474i | \(0.751631\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 24.2487i | − | 0.926496i | ||||||
\(686\) | −4.89898 | + | 8.48528i | −0.187044 | + | 0.323970i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −16.0000 | + | 27.7128i | −0.609994 | + | 1.05654i | ||||
\(689\) | − | 25.4558i | − | 0.969790i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.0000 | 1.21734 | 0.608669 | − | 0.793424i | \(-0.291704\pi\) | ||||
0.608669 | + | 0.793424i | \(0.291704\pi\) | |||||||
\(692\) | −2.44949 | − | 4.24264i | −0.0931156 | − | 0.161281i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.0000 | + | 17.3205i | −0.379595 | + | 0.657477i | ||||
\(695\) | −9.79796 | −0.371658 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.00000 | −0.0757554 | ||||||||
\(698\) | 19.5959 | − | 33.9411i | 0.741716 | − | 1.28469i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.00000 | − | 3.46410i | 0.226779 | − | 0.130931i | ||||
\(701\) | 7.34847 | 0.277548 | 0.138774 | − | 0.990324i | \(-0.455684\pi\) | ||||
0.138774 | + | 0.990324i | \(0.455684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | − | 22.6274i | − | 0.852803i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.0000 | − | 19.0526i | 0.413990 | − | 0.717053i | ||||
\(707\) | 8.48528i | 0.319122i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3.46410i | − | 0.130097i | −0.997882 | − | 0.0650485i | \(-0.979280\pi\) | ||
0.997882 | − | 0.0650485i | \(-0.0207202\pi\) | |||||||
\(710\) | −44.0908 | − | 25.4558i | −1.65470 | − | 0.955341i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20.0000 | 0.749532 | ||||||||
\(713\) | − | 16.9706i | − | 0.635553i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0000 | −0.897549 | ||||||||
\(716\) | 9.79796 | − | 5.65685i | 0.366167 | − | 0.211407i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.0000 | + | 10.3923i | 0.671754 | + | 0.387837i | ||||
\(719\) | 44.0908 | 1.64431 | 0.822155 | − | 0.569264i | \(-0.192772\pi\) | ||||
0.822155 | + | 0.569264i | \(0.192772\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 3.67423 | + | 2.12132i | 0.136741 | + | 0.0789474i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.0000 | − | 10.3923i | 0.668965 | − | 0.386227i | ||||
\(725\) | −2.44949 | −0.0909718 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 24.2487i | − | 0.899335i | −0.893196 | − | 0.449667i | \(-0.851542\pi\) | ||
0.893196 | − | 0.449667i | \(-0.148458\pi\) | |||||||
\(728\) | − | 33.9411i | − | 1.25794i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.0000 | + | 6.92820i | 0.444140 | + | 0.256424i | ||||
\(731\) | − | 11.3137i | − | 0.418453i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 38.1051i | − | 1.40744i | −0.710475 | − | 0.703722i | \(-0.751520\pi\) | ||
0.710475 | − | 0.703722i | \(-0.248480\pi\) | |||||||
\(734\) | −17.1464 | + | 29.6985i | −0.632886 | + | 1.09619i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.0000 | + | 13.8564i | −0.884652 | + | 0.510754i | ||||
\(737\) | − | 11.3137i | − | 0.416746i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.0000 | −1.47142 | −0.735712 | − | 0.677295i | \(-0.763152\pi\) | ||||
−0.735712 | + | 0.677295i | \(0.763152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.0000 | − | 31.1769i | 0.660801 | − | 1.14454i | ||||
\(743\) | 39.1918 | 1.43781 | 0.718905 | − | 0.695109i | \(-0.244644\pi\) | ||||
0.718905 | + | 0.695109i | \(0.244644\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42.0000 | 1.53876 | ||||||||
\(746\) | 9.79796 | − | 16.9706i | 0.358729 | − | 0.621336i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.00000 | + | 6.92820i | 0.146254 | + | 0.253320i | ||||
\(749\) | 39.1918 | 1.43204 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.46410i | 0.126407i | 0.998001 | + | 0.0632034i | \(0.0201317\pi\) | ||||
−0.998001 | + | 0.0632034i | \(0.979868\pi\) | |||||||
\(752\) | −9.79796 | + | 16.9706i | −0.357295 | + | 0.618853i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.00000 | + | 10.3923i | −0.218507 | + | 0.378465i | ||||
\(755\) | − | 8.48528i | − | 0.308811i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.3923i | 0.377715i | 0.982005 | + | 0.188857i | \(0.0604784\pi\) | ||||
−0.982005 | + | 0.188857i | \(0.939522\pi\) | |||||||
\(758\) | 4.89898 | + | 2.82843i | 0.177939 | + | 0.102733i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27.7128i | 1.00525i | ||||||||
\(761\) | − | 18.3848i | − | 0.666448i | −0.942848 | − | 0.333224i | \(-0.891864\pi\) | ||
0.942848 | − | 0.333224i | \(-0.108136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.0000 | 1.30329 | ||||||||
\(764\) | 19.5959 | + | 33.9411i | 0.708955 | + | 1.22795i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.0000 | − | 6.92820i | −0.433578 | − | 0.250326i | ||||
\(767\) | −39.1918 | −1.41514 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.00000 | 0.0721218 | 0.0360609 | − | 0.999350i | \(-0.488519\pi\) | ||||
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | −29.3939 | − | 16.9706i | −1.05928 | − | 0.611577i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.0000 | + | 24.2487i | 0.503871 | + | 0.872730i | ||||
\(773\) | 22.0454 | 0.792918 | 0.396459 | − | 0.918052i | \(-0.370239\pi\) | ||||
0.396459 | + | 0.918052i | \(0.370239\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.46410i | 0.124434i | ||||||||
\(776\) | − | 22.6274i | − | 0.812277i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −33.0000 | − | 19.0526i | −1.18311 | − | 0.683067i | ||||
\(779\) | 5.65685i | 0.202678i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.5692i | 1.48746i | ||||||||
\(782\) | 4.89898 | − | 8.48528i | 0.175187 | − | 0.303433i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.0000 | − | 17.3205i | 0.357143 | − | 0.618590i | ||||
\(785\) | 33.9411i | 1.21141i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | 0.712923 | 0.356462 | − | 0.934310i | \(-0.383983\pi\) | ||||
0.356462 | + | 0.934310i | \(0.383983\pi\) | |||||||
\(788\) | 7.34847 | + | 12.7279i | 0.261778 | + | 0.453413i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.00000 | + | 10.3923i | −0.213470 | + | 0.369742i | ||||
\(791\) | −63.6867 | −2.26444 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.0000 | 1.70453 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.0000 | − | 10.3923i | 0.637993 | − | 0.368345i | ||||
\(797\) | −12.2474 | −0.433827 | −0.216913 | − | 0.976191i | \(-0.569599\pi\) | ||||
−0.216913 | + | 0.976191i | \(0.569599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.92820i | − | 0.245102i | ||||||
\(800\) | 4.89898 | − | 2.82843i | 0.173205 | − | 0.100000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.00000 | + | 1.73205i | −0.0353112 | + | 0.0611608i | ||||
\(803\) | − | 11.3137i | − | 0.399252i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 41.5692i | 1.46512i | ||||||||
\(806\) | 14.6969 | + | 8.48528i | 0.517678 | + | 0.298881i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.92820i | 0.243733i | ||||||||
\(809\) | − | 1.41421i | − | 0.0497211i | −0.999691 | − | 0.0248606i | \(-0.992086\pi\) | ||
0.999691 | − | 0.0248606i | \(-0.00791417\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.00000 | −0.140459 | −0.0702295 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702295 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(812\) | −14.6969 | + | 8.48528i | −0.515761 | + | 0.297775i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −39.1918 | −1.37283 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | −1.11954 | ||||||||
\(818\) | −39.1918 | − | 22.6274i | −1.37031 | − | 0.791149i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | − | 3.46410i | 0.209529 | − | 0.120972i | ||||
\(821\) | −2.44949 | −0.0854878 | −0.0427439 | − | 0.999086i | \(-0.513610\pi\) | ||||
−0.0427439 | + | 0.999086i | \(0.513610\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 17.3205i | − | 0.603755i | −0.953347 | − | 0.301877i | \(-0.902387\pi\) | ||
0.953347 | − | 0.301877i | \(-0.0976134\pi\) | |||||||
\(824\) | 9.79796 | 0.341328 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −48.0000 | − | 27.7128i | −1.67013 | − | 0.964252i | ||||
\(827\) | − | 5.65685i | − | 0.196708i | −0.995151 | − | 0.0983540i | \(-0.968642\pi\) | ||
0.995151 | − | 0.0983540i | \(-0.0313578\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.3923i | 0.360940i | 0.983581 | + | 0.180470i | \(0.0577618\pi\) | ||||
−0.983581 | + | 0.180470i | \(0.942238\pi\) | |||||||
\(830\) | −24.4949 | + | 42.4264i | −0.850230 | + | 1.47264i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 27.7128i | − | 0.960769i | ||||||
\(833\) | 7.07107i | 0.244998i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48.0000 | −1.66111 | ||||||||
\(836\) | 19.5959 | − | 11.3137i | 0.677739 | − | 0.391293i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.0000 | − | 24.2487i | 0.483622 | − | 0.837658i | ||||
\(839\) | 4.89898 | 0.169132 | 0.0845658 | − | 0.996418i | \(-0.473050\pi\) | ||||
0.0845658 | + | 0.996418i | \(0.473050\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0000 | −0.793103 | ||||||||
\(842\) | −17.1464 | + | 29.6985i | −0.590905 | + | 1.02348i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.0000 | + | 34.6410i | 0.688428 | + | 1.19239i | ||||
\(845\) | 2.44949 | 0.0842650 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.3923i | − | 0.357084i | ||||||
\(848\) | 14.6969 | − | 25.4558i | 0.504695 | − | 0.874157i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.00000 | + | 1.73205i | −0.0342997 | + | 0.0594089i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 13.8564i | − | 0.474434i | −0.971457 | − | 0.237217i | \(-0.923765\pi\) | ||
0.971457 | − | 0.237217i | \(-0.0762353\pi\) | |||||||
\(854\) | 58.7878 | + | 33.9411i | 2.01168 | + | 1.16144i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 32.0000 | 1.09374 | ||||||||
\(857\) | − | 1.41421i | − | 0.0483086i | −0.999708 | − | 0.0241543i | \(-0.992311\pi\) | ||
0.999708 | − | 0.0241543i | \(-0.00768930\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.0000 | −1.36478 | −0.682391 | − | 0.730987i | \(-0.739060\pi\) | ||||
−0.682391 | + | 0.730987i | \(0.739060\pi\) | |||||||
\(860\) | 19.5959 | + | 33.9411i | 0.668215 | + | 1.15738i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0000 | + | 10.3923i | 0.613082 | + | 0.353963i | ||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 26.9444 | + | 15.5563i | 0.915608 | + | 0.528626i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.0000 | + | 20.7846i | 0.407307 | + | 0.705476i | ||||
\(869\) | 9.79796 | 0.332373 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 13.8564i | − | 0.469506i | ||||||
\(872\) | 29.3939 | 0.995402 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.0000 | − | 13.8564i | −0.811812 | − | 0.468700i | ||||
\(875\) | 33.9411i | 1.14742i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.4256i | 1.87159i | 0.352544 | + | 0.935795i | \(0.385317\pi\) | ||||
−0.352544 | + | 0.935795i | \(0.614683\pi\) | |||||||
\(878\) | −2.44949 | + | 4.24264i | −0.0826663 | + | 0.143182i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −24.0000 | − | 13.8564i | −0.809040 | − | 0.467099i | ||||
\(881\) | − | 43.8406i | − | 1.47703i | −0.674238 | − | 0.738514i | \(-0.735528\pi\) | ||
0.674238 | − | 0.738514i | \(-0.264472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.0000 | −1.34611 | −0.673054 | − | 0.739594i | \(-0.735018\pi\) | ||||
−0.673054 | + | 0.739594i | \(0.735018\pi\) | |||||||
\(884\) | 4.89898 | + | 8.48528i | 0.164771 | + | 0.285391i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.00000 | − | 3.46410i | 0.0671913 | − | 0.116379i | ||||
\(887\) | 9.79796 | 0.328983 | 0.164492 | − | 0.986378i | \(-0.447402\pi\) | ||||
0.164492 | + | 0.986378i | \(0.447402\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.0000 | −1.20740 | ||||||||
\(890\) | 12.2474 | − | 21.2132i | 0.410535 | − | 0.711068i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30.0000 | + | 17.3205i | −1.00447 | + | 0.579934i | ||||
\(893\) | −19.5959 | −0.655752 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 13.8564i | − | 0.463169i | ||||||
\(896\) | 19.5959 | − | 33.9411i | 0.654654 | − | 1.13389i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.0000 | − | 29.4449i | 0.567297 | − | 0.982588i | ||||
\(899\) | − | 8.48528i | − | 0.283000i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.3923i | 0.346218i | ||||||||
\(902\) | −4.89898 | − | 2.82843i | −0.163118 | − | 0.0941763i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −52.0000 | −1.72949 | ||||||||
\(905\) | − | 25.4558i | − | 0.846181i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.00000 | 0.265636 | 0.132818 | − | 0.991140i | \(-0.457597\pi\) | ||||
0.132818 | + | 0.991140i | \(0.457597\pi\) | |||||||
\(908\) | −4.89898 | + | 2.82843i | −0.162578 | + | 0.0938647i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −36.0000 | − | 20.7846i | −1.19339 | − | 0.689003i | ||||
\(911\) | −39.1918 | −1.29848 | −0.649242 | − | 0.760582i | \(-0.724914\pi\) | ||||
−0.649242 | + | 0.760582i | \(0.724914\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.0000 | 1.32381 | ||||||||
\(914\) | −9.79796 | − | 5.65685i | −0.324088 | − | 0.187112i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 30.0000 | − | 17.3205i | 0.991228 | − | 0.572286i | ||||
\(917\) | −19.5959 | −0.647114 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.3923i | 0.342811i | 0.985201 | + | 0.171405i | \(0.0548307\pi\) | ||||
−0.985201 | + | 0.171405i | \(0.945169\pi\) | |||||||
\(920\) | 33.9411i | 1.11901i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 21.0000 | + | 12.1244i | 0.691598 | + | 0.399294i | ||||
\(923\) | 50.9117i | 1.67578i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.2474 | + | 21.2132i | −0.402476 | + | 0.697109i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12.0000 | + | 6.92820i | −0.393919 | + | 0.227429i | ||||
\(929\) | − | 1.41421i | − | 0.0463988i | −0.999731 | − | 0.0231994i | \(-0.992615\pi\) | ||
0.999731 | − | 0.0231994i | \(-0.00738527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.0000 | 0.655474 | ||||||||
\(932\) | 2.44949 | − | 1.41421i | 0.0802357 | − | 0.0463241i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26.0000 | − | 45.0333i | 0.850746 | − | 1.47354i | ||||
\(935\) | 9.79796 | 0.320428 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 9.79796 | − | 16.9706i | 0.319915 | − | 0.554109i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.0000 | + | 20.7846i | 0.391397 | + | 0.677919i | ||||
\(941\) | 2.44949 | 0.0798511 | 0.0399255 | − | 0.999203i | \(-0.487288\pi\) | ||||
0.0399255 | + | 0.999203i | \(0.487288\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.92820i | 0.225613i | ||||||||
\(944\) | −39.1918 | − | 22.6274i | −1.27559 | − | 0.736460i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.0000 | − | 27.7128i | 0.520205 | − | 0.901021i | ||||
\(947\) | − | 22.6274i | − | 0.735292i | −0.929966 | − | 0.367646i | \(-0.880164\pi\) | ||
0.929966 | − | 0.367646i | \(-0.119836\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 13.8564i | − | 0.449798i | ||||||
\(950\) | 4.89898 | + | 2.82843i | 0.158944 | + | 0.0917663i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.8564i | 0.449089i | ||||||||
\(953\) | − | 26.8701i | − | 0.870407i | −0.900332 | − | 0.435203i | \(-0.856677\pi\) | ||
0.900332 | − | 0.435203i | \(-0.143323\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.0000 | 1.55324 | ||||||||
\(956\) | 9.79796 | + | 16.9706i | 0.316889 | + | 0.548867i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.0000 | + | 17.3205i | 0.969256 | + | 0.559600i | ||||
\(959\) | −34.2929 | −1.10737 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −28.0000 | − | 48.4974i | −0.901819 | − | 1.56200i | ||||
\(965\) | 34.2929 | 1.10393 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.0333i | 1.44817i | 0.689709 | + | 0.724087i | \(0.257739\pi\) | ||||
−0.689709 | + | 0.724087i | \(0.742261\pi\) | |||||||
\(968\) | − | 8.48528i | − | 0.272727i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24.0000 | − | 13.8564i | −0.770594 | − | 0.444902i | ||||
\(971\) | − | 31.1127i | − | 0.998454i | −0.866471 | − | 0.499227i | \(-0.833617\pi\) | ||
0.866471 | − | 0.499227i | \(-0.166383\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.8564i | 0.444216i | ||||||||
\(974\) | −7.34847 | + | 12.7279i | −0.235460 | + | 0.407829i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 48.0000 | + | 27.7128i | 1.53644 | + | 0.887066i | ||||
\(977\) | 24.0416i | 0.769160i | 0.923092 | + | 0.384580i | \(0.125654\pi\) | ||||
−0.923092 | + | 0.384580i | \(0.874346\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.0000 | −0.639203 | ||||||||
\(980\) | −12.2474 | − | 21.2132i | −0.391230 | − | 0.677631i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28.0000 | + | 48.4974i | −0.893516 | + | 1.54761i | ||||
\(983\) | 48.9898 | 1.56253 | 0.781266 | − | 0.624198i | \(-0.214574\pi\) | ||||
0.781266 | + | 0.624198i | \(0.214574\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.0000 | 0.573528 | ||||||||
\(986\) | 2.44949 | − | 4.24264i | 0.0780076 | − | 0.135113i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.0000 | − | 13.8564i | 0.763542 | − | 0.440831i | ||||
\(989\) | −39.1918 | −1.24623 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 51.9615i | − | 1.65061i | −0.564686 | − | 0.825306i | \(-0.691003\pi\) | ||
0.564686 | − | 0.825306i | \(-0.308997\pi\) | |||||||
\(992\) | 9.79796 | + | 16.9706i | 0.311086 | + | 0.538816i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −36.0000 | + | 62.3538i | −1.14185 | + | 1.97774i | ||||
\(995\) | − | 25.4558i | − | 0.807005i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 13.8564i | − | 0.438837i | −0.975631 | − | 0.219418i | \(-0.929584\pi\) | ||
0.975631 | − | 0.219418i | \(-0.0704160\pi\) | |||||||
\(998\) | −39.1918 | − | 22.6274i | −1.24060 | − | 0.716258i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))