Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [270,2,Mod(109,270)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(270, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("270.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 270 = 2 \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 270.c (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: | \(2.15596085457\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(-2.17945 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 270.109 |
Dual form | 270.2.c.c.109.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/270\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(217\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.17945 | + | 0.500000i | −0.974679 | + | 0.223607i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.35890i | − | 1.64751i | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||
0.566947 | − | 0.823754i | \(-0.308125\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.500000 | + | 2.17945i | 0.158114 | + | 0.689202i | ||||
\(11\) | −4.35890 | −1.31426 | −0.657129 | − | 0.753778i | \(-0.728229\pi\) | ||||
−0.657129 | + | 0.753778i | \(0.728229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −4.35890 | −1.16496 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 4.00000i | − | 0.970143i | −0.874475 | − | 0.485071i | \(-0.838794\pi\) | ||
0.874475 | − | 0.485071i | \(-0.161206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 2.17945 | − | 0.500000i | 0.487340 | − | 0.111803i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.35890i | 0.929320i | ||||||||
\(23\) | − | 2.00000i | − | 0.417029i | −0.978019 | − | 0.208514i | \(-0.933137\pi\) | ||
0.978019 | − | 0.208514i | \(-0.0668628\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.50000 | − | 2.17945i | 0.900000 | − | 0.435890i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.35890i | 0.823754i | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.00000 | 1.25724 | 0.628619 | − | 0.777714i | \(-0.283621\pi\) | ||||
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 2.17945 | + | 9.50000i | 0.368394 | + | 1.60579i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.71780i | 1.43320i | 0.697486 | + | 0.716599i | \(0.254302\pi\) | ||||
−0.697486 | + | 0.716599i | \(0.745698\pi\) | |||||||
\(38\) | 6.00000i | 0.973329i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.500000 | − | 2.17945i | −0.0790569 | − | 0.344601i | ||||
\(41\) | 8.71780 | 1.36149 | 0.680746 | − | 0.732520i | \(-0.261656\pi\) | ||||
0.680746 | + | 0.732520i | \(0.261656\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.71780i | − | 1.32945i | −0.747087 | − | 0.664726i | \(-0.768548\pi\) | ||
0.747087 | − | 0.664726i | \(-0.231452\pi\) | |||||||
\(44\) | 4.35890 | 0.657129 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | − | 2.00000i | − | 0.291730i | −0.989305 | − | 0.145865i | \(-0.953403\pi\) | ||
0.989305 | − | 0.145865i | \(-0.0465965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12.0000 | −1.71429 | ||||||||
\(50\) | −2.17945 | − | 4.50000i | −0.308221 | − | 0.636396i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.00000i | − | 0.412082i | −0.978543 | − | 0.206041i | \(-0.933942\pi\) | ||
0.978543 | − | 0.206041i | \(-0.0660580\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.50000 | − | 2.17945i | 1.28098 | − | 0.293877i | ||||
\(56\) | 4.35890 | 0.582482 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.71780 | 1.13496 | 0.567480 | − | 0.823387i | \(-0.307918\pi\) | ||||
0.567480 | + | 0.823387i | \(0.307918\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | −0.512148 | −0.256074 | − | 0.966657i | \(-0.582429\pi\) | ||||
−0.256074 | + | 0.966657i | \(0.582429\pi\) | |||||||
\(62\) | − | 7.00000i | − | 0.889001i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.71780i | − | 1.06505i | −0.846415 | − | 0.532524i | \(-0.821244\pi\) | ||
0.846415 | − | 0.532524i | \(-0.178756\pi\) | |||||||
\(68\) | 4.00000i | 0.485071i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9.50000 | − | 2.17945i | 1.13547 | − | 0.260494i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.35890i | 0.510171i | 0.966919 | + | 0.255085i | \(0.0821035\pi\) | ||||
−0.966919 | + | 0.255085i | \(0.917896\pi\) | |||||||
\(74\) | 8.71780 | 1.01342 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | 19.0000i | 2.16525i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −2.17945 | + | 0.500000i | −0.243670 | + | 0.0559017i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 8.71780i | − | 0.962720i | ||||||
\(83\) | − | 5.00000i | − | 0.548821i | −0.961613 | − | 0.274411i | \(-0.911517\pi\) | ||
0.961613 | − | 0.274411i | \(-0.0884828\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | + | 8.71780i | 0.216930 | + | 0.945578i | ||||
\(86\) | −8.71780 | −0.940064 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 4.35890i | − | 0.464660i | ||||||
\(89\) | −8.71780 | −0.924085 | −0.462042 | − | 0.886858i | \(-0.652883\pi\) | ||||
−0.462042 | + | 0.886858i | \(0.652883\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.00000i | 0.208514i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.00000 | −0.206284 | ||||||||
\(95\) | 13.0767 | − | 3.00000i | 1.34164 | − | 0.307794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.35890i | 0.442579i | 0.975208 | + | 0.221290i | \(0.0710266\pi\) | ||||
−0.975208 | + | 0.221290i | \(0.928973\pi\) | |||||||
\(98\) | 12.0000i | 1.21218i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.50000 | + | 2.17945i | −0.450000 | + | 0.217945i | ||||
\(101\) | 4.35890 | 0.433727 | 0.216863 | − | 0.976202i | \(-0.430417\pi\) | ||||
0.216863 | + | 0.976202i | \(0.430417\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.71780i | 0.858990i | 0.903069 | + | 0.429495i | \(0.141308\pi\) | ||||
−0.903069 | + | 0.429495i | \(0.858692\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.00000 | −0.291386 | ||||||||
\(107\) | − | 15.0000i | − | 1.45010i | −0.688694 | − | 0.725052i | \(-0.741816\pi\) | ||
0.688694 | − | 0.725052i | \(-0.258184\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | −2.17945 | − | 9.50000i | −0.207802 | − | 0.905789i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 4.35890i | − | 0.411877i | ||||||
\(113\) | − | 18.0000i | − | 1.69330i | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||
0.532152 | − | 0.846649i | \(-0.321383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | + | 4.35890i | 0.0932505 | + | 0.406469i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 8.71780i | − | 0.802538i | ||||||
\(119\) | −17.4356 | −1.59832 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.00000 | 0.727273 | ||||||||
\(122\) | 4.00000i | 0.362143i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.00000 | −0.628619 | ||||||||
\(125\) | −8.71780 | + | 7.00000i | −0.779744 | + | 0.626099i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.35890i | − | 0.386790i | −0.981121 | − | 0.193395i | \(-0.938050\pi\) | ||
0.981121 | − | 0.193395i | \(-0.0619498\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.0767 | −1.14252 | −0.571258 | − | 0.820770i | \(-0.693544\pi\) | ||||
−0.571258 | + | 0.820770i | \(0.693544\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.1534i | 2.26779i | ||||||||
\(134\) | −8.71780 | −0.753103 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | 18.0000i | 1.53784i | 0.639343 | + | 0.768922i | \(0.279207\pi\) | ||||
−0.639343 | + | 0.768922i | \(0.720793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −2.17945 | − | 9.50000i | −0.184197 | − | 0.802897i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.35890 | 0.360745 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 8.71780i | − | 0.716599i | ||||||
\(149\) | −4.35890 | −0.357095 | −0.178547 | − | 0.983931i | \(-0.557140\pi\) | ||||
−0.178547 | + | 0.983931i | \(0.557140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.0000 | −0.895167 | −0.447584 | − | 0.894242i | \(-0.647715\pi\) | ||||
−0.447584 | + | 0.894242i | \(0.647715\pi\) | |||||||
\(152\) | − | 6.00000i | − | 0.486664i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 19.0000 | 1.53106 | ||||||||
\(155\) | −15.2561 | + | 3.50000i | −1.22540 | + | 0.281127i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.4356i | 1.39151i | 0.718278 | + | 0.695756i | \(0.244931\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.500000 | + | 2.17945i | 0.0395285 | + | 0.172301i | ||||
\(161\) | −8.71780 | −0.687059 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.4356i | − | 1.36566i | −0.730577 | − | 0.682831i | \(-0.760749\pi\) | ||
0.730577 | − | 0.682831i | \(-0.239251\pi\) | |||||||
\(164\) | −8.71780 | −0.680746 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.00000 | −0.388075 | ||||||||
\(167\) | 18.0000i | 1.39288i | 0.717614 | + | 0.696441i | \(0.245234\pi\) | ||||
−0.717614 | + | 0.696441i | \(0.754766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 8.71780 | − | 2.00000i | 0.668625 | − | 0.153393i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.71780i | 0.664726i | ||||||||
\(173\) | − | 19.0000i | − | 1.44454i | −0.691609 | − | 0.722272i | \(-0.743098\pi\) | ||
0.691609 | − | 0.722272i | \(-0.256902\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.50000 | − | 19.6150i | −0.718132 | − | 1.48276i | ||||
\(176\) | −4.35890 | −0.328564 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.71780i | 0.653427i | ||||||||
\(179\) | 21.7945 | 1.62900 | 0.814499 | − | 0.580166i | \(-0.197012\pi\) | ||||
0.814499 | + | 0.580166i | \(0.197012\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.00000 | 0.147442 | ||||||||
\(185\) | −4.35890 | − | 19.0000i | −0.320473 | − | 1.39691i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.4356i | 1.27502i | ||||||||
\(188\) | 2.00000i | 0.145865i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.00000 | − | 13.0767i | −0.217643 | − | 0.948683i | ||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 21.7945i | − | 1.56880i | −0.620254 | − | 0.784401i | \(-0.712970\pi\) | ||
0.620254 | − | 0.784401i | \(-0.287030\pi\) | |||||||
\(194\) | 4.35890 | 0.312951 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.0000 | 0.857143 | ||||||||
\(197\) | − | 5.00000i | − | 0.356235i | −0.984009 | − | 0.178118i | \(-0.942999\pi\) | ||
0.984009 | − | 0.178118i | \(-0.0570008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.00000 | 0.212664 | 0.106332 | − | 0.994331i | \(-0.466089\pi\) | ||||
0.106332 | + | 0.994331i | \(0.466089\pi\) | |||||||
\(200\) | 2.17945 | + | 4.50000i | 0.154110 | + | 0.318198i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 4.35890i | − | 0.306691i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.0000 | + | 4.35890i | −1.32702 | + | 0.304439i | ||||
\(206\) | 8.71780 | 0.607398 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.1534 | 1.80907 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.00000 | 0.413057 | 0.206529 | − | 0.978441i | \(-0.433783\pi\) | ||||
0.206529 | + | 0.978441i | \(0.433783\pi\) | |||||||
\(212\) | 3.00000i | 0.206041i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.0000 | −1.02538 | ||||||||
\(215\) | 4.35890 | + | 19.0000i | 0.297274 | + | 1.29579i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 30.5123i | − | 2.07131i | ||||||
\(218\) | 10.0000i | 0.677285i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.50000 | + | 2.17945i | −0.640490 | + | 0.146938i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.71780i | − | 0.583787i | −0.956451 | − | 0.291893i | \(-0.905715\pi\) | ||
0.956451 | − | 0.291893i | \(-0.0942853\pi\) | |||||||
\(224\) | −4.35890 | −0.291241 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.0000 | −1.19734 | ||||||||
\(227\) | − | 4.00000i | − | 0.265489i | −0.991150 | − | 0.132745i | \(-0.957621\pi\) | ||
0.991150 | − | 0.132745i | \(-0.0423790\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 4.35890 | − | 1.00000i | 0.287417 | − | 0.0659380i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.0000i | 0.917170i | 0.888650 | + | 0.458585i | \(0.151644\pi\) | ||||
−0.888650 | + | 0.458585i | \(0.848356\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.00000 | + | 4.35890i | 0.0652328 | + | 0.284343i | ||||
\(236\) | −8.71780 | −0.567480 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17.4356i | 1.13018i | ||||||||
\(239\) | −8.71780 | −0.563907 | −0.281954 | − | 0.959428i | \(-0.590982\pi\) | ||||
−0.281954 | + | 0.959428i | \(0.590982\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0000 | −0.901819 | −0.450910 | − | 0.892570i | \(-0.648900\pi\) | ||||
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | − | 8.00000i | − | 0.514259i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.00000 | 0.256074 | ||||||||
\(245\) | 26.1534 | − | 6.00000i | 1.67088 | − | 0.383326i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 7.00000i | 0.444500i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.00000 | + | 8.71780i | 0.442719 | + | 0.551362i | ||||
\(251\) | 26.1534 | 1.65079 | 0.825394 | − | 0.564557i | \(-0.190953\pi\) | ||||
0.825394 | + | 0.564557i | \(0.190953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.71780i | 0.548083i | ||||||||
\(254\) | −4.35890 | −0.273502 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.0000i | 0.748539i | 0.927320 | + | 0.374270i | \(0.122107\pi\) | ||||
−0.927320 | + | 0.374270i | \(0.877893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.0000 | 2.36121 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.0767i | 0.807881i | ||||||||
\(263\) | − | 2.00000i | − | 0.123325i | −0.998097 | − | 0.0616626i | \(-0.980360\pi\) | ||
0.998097 | − | 0.0616626i | \(-0.0196403\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.50000 | + | 6.53835i | 0.0921443 | + | 0.401648i | ||||
\(266\) | 26.1534 | 1.60357 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.71780i | 0.532524i | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.00000 | −0.303728 | −0.151864 | − | 0.988401i | \(-0.548528\pi\) | ||||
−0.151864 | + | 0.988401i | \(0.548528\pi\) | |||||||
\(272\) | − | 4.00000i | − | 0.242536i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | −19.6150 | + | 9.50000i | −1.18283 | + | 0.572872i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 17.4356i | − | 1.04760i | −0.851840 | − | 0.523802i | \(-0.824513\pi\) | ||
0.851840 | − | 0.523802i | \(-0.175487\pi\) | |||||||
\(278\) | 4.00000i | 0.239904i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.50000 | + | 2.17945i | −0.567734 | + | 0.130247i | ||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.71780i | 0.518219i | 0.965848 | + | 0.259110i | \(0.0834291\pi\) | ||||
−0.965848 | + | 0.259110i | \(0.916571\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 38.0000i | − | 2.24307i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 4.35890i | − | 0.255085i | ||||||
\(293\) | − | 6.00000i | − | 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.0000 | + | 4.35890i | −1.10622 | + | 0.253785i | ||||
\(296\) | −8.71780 | −0.506712 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.35890i | 0.252504i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −38.0000 | −2.19028 | ||||||||
\(302\) | 11.0000i | 0.632979i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.00000 | −0.344124 | ||||||||
\(305\) | 8.71780 | − | 2.00000i | 0.499180 | − | 0.114520i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | − | 19.0000i | − | 1.08263i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.50000 | + | 15.2561i | 0.198787 | + | 0.866491i | ||||
\(311\) | 26.1534 | 1.48302 | 0.741511 | − | 0.670940i | \(-0.234109\pi\) | ||||
0.741511 | + | 0.670940i | \(0.234109\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 21.7945i | − | 1.23190i | −0.787786 | − | 0.615949i | \(-0.788773\pi\) | ||
0.787786 | − | 0.615949i | \(-0.211227\pi\) | |||||||
\(314\) | 17.4356 | 0.983948 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.0000i | 0.954815i | 0.878682 | + | 0.477408i | \(0.158423\pi\) | ||||
−0.878682 | + | 0.477408i | \(0.841577\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.17945 | − | 0.500000i | 0.121835 | − | 0.0279508i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.71780i | 0.485824i | ||||||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −17.4356 | −0.965668 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.71780i | 0.481360i | ||||||||
\(329\) | −8.71780 | −0.480628 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | 0.549650 | 0.274825 | − | 0.961494i | \(-0.411380\pi\) | ||||
0.274825 | + | 0.961494i | \(0.411380\pi\) | |||||||
\(332\) | 5.00000i | 0.274411i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.0000 | 0.984916 | ||||||||
\(335\) | 4.35890 | + | 19.0000i | 0.238152 | + | 1.03808i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.4356i | − | 0.949777i | −0.880046 | − | 0.474889i | \(-0.842488\pi\) | ||
0.880046 | − | 0.474889i | \(-0.157512\pi\) | |||||||
\(338\) | − | 13.0000i | − | 0.707107i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.00000 | − | 8.71780i | −0.108465 | − | 0.472789i | ||||
\(341\) | −30.5123 | −1.65233 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 21.7945i | 1.17679i | ||||||||
\(344\) | 8.71780 | 0.470032 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.0000 | −1.02145 | ||||||||
\(347\) | − | 27.0000i | − | 1.44944i | −0.689046 | − | 0.724718i | \(-0.741970\pi\) | ||
0.689046 | − | 0.724718i | \(-0.258030\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | −19.6150 | + | 9.50000i | −1.04847 | + | 0.507796i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.35890i | 0.232330i | ||||||||
\(353\) | 26.0000i | 1.38384i | 0.721974 | + | 0.691920i | \(0.243235\pi\) | ||||
−0.721974 | + | 0.691920i | \(0.756765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.71780 | 0.462042 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 21.7945i | − | 1.15187i | ||||||
\(359\) | −26.1534 | −1.38032 | −0.690162 | − | 0.723655i | \(-0.742461\pi\) | ||||
−0.690162 | + | 0.723655i | \(0.742461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | − | 8.00000i | − | 0.420471i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.17945 | − | 9.50000i | −0.114078 | − | 0.497253i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.35890i | − | 0.227533i | −0.993508 | − | 0.113766i | \(-0.963708\pi\) | ||
0.993508 | − | 0.113766i | \(-0.0362915\pi\) | |||||||
\(368\) | − | 2.00000i | − | 0.104257i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19.0000 | + | 4.35890i | −0.987763 | + | 0.226608i | ||||
\(371\) | −13.0767 | −0.678908 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 17.4356 | 0.901573 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.00000 | 0.103142 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(380\) | −13.0767 | + | 3.00000i | −0.670820 | + | 0.153897i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 4.00000i | − | 0.204390i | −0.994764 | − | 0.102195i | \(-0.967413\pi\) | ||
0.994764 | − | 0.102195i | \(-0.0325866\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.50000 | − | 41.4095i | −0.484165 | − | 2.11043i | ||||
\(386\) | −21.7945 | −1.10931 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 4.35890i | − | 0.221290i | ||||||
\(389\) | 4.35890 | 0.221005 | 0.110502 | − | 0.993876i | \(-0.464754\pi\) | ||||
0.110502 | + | 0.993876i | \(0.464754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | − | 12.0000i | − | 0.606092i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.00000 | −0.251896 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.8712i | 1.75013i | 0.484001 | + | 0.875067i | \(0.339183\pi\) | ||||
−0.484001 | + | 0.875067i | \(0.660817\pi\) | |||||||
\(398\) | − | 3.00000i | − | 0.150376i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.50000 | − | 2.17945i | 0.225000 | − | 0.108972i | ||||
\(401\) | −34.8712 | −1.74138 | −0.870692 | − | 0.491828i | \(-0.836329\pi\) | ||||
−0.870692 | + | 0.491828i | \(0.836329\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4.35890 | −0.216863 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 38.0000i | − | 1.88359i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.0000 | 1.53285 | 0.766426 | − | 0.642333i | \(-0.222033\pi\) | ||||
0.766426 | + | 0.642333i | \(0.222033\pi\) | |||||||
\(410\) | 4.35890 | + | 19.0000i | 0.215271 | + | 0.938343i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 8.71780i | − | 0.429495i | ||||||
\(413\) | − | 38.0000i | − | 1.86986i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.50000 | + | 10.8972i | 0.122720 | + | 0.534925i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 26.1534i | − | 1.27920i | ||||||
\(419\) | −8.71780 | −0.425892 | −0.212946 | − | 0.977064i | \(-0.568306\pi\) | ||||
−0.212946 | + | 0.977064i | \(0.568306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0000 | 0.779792 | 0.389896 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389896 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(422\) | − | 6.00000i | − | 0.292075i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.00000 | 0.145693 | ||||||||
\(425\) | −8.71780 | − | 18.0000i | −0.422875 | − | 0.873128i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.4356i | 0.843768i | ||||||||
\(428\) | 15.0000i | 0.725052i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.0000 | − | 4.35890i | 0.916261 | − | 0.210205i | ||||
\(431\) | 8.71780 | 0.419922 | 0.209961 | − | 0.977710i | \(-0.432666\pi\) | ||||
0.209961 | + | 0.977710i | \(0.432666\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 21.7945i | − | 1.04738i | −0.851910 | − | 0.523688i | \(-0.824556\pi\) | ||
0.851910 | − | 0.523688i | \(-0.175444\pi\) | |||||||
\(434\) | −30.5123 | −1.46464 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.0000 | 0.478913 | ||||||||
\(437\) | 12.0000i | 0.574038i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.00000 | −0.429547 | −0.214773 | − | 0.976664i | \(-0.568901\pi\) | ||||
−0.214773 | + | 0.976664i | \(0.568901\pi\) | |||||||
\(440\) | 2.17945 | + | 9.50000i | 0.103901 | + | 0.452895i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000i | 0.570137i | 0.958507 | + | 0.285069i | \(0.0920164\pi\) | ||||
−0.958507 | + | 0.285069i | \(0.907984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.0000 | − | 4.35890i | 0.900686 | − | 0.206632i | ||||
\(446\) | −8.71780 | −0.412800 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.35890i | 0.205939i | ||||||||
\(449\) | −26.1534 | −1.23425 | −0.617127 | − | 0.786863i | \(-0.711704\pi\) | ||||
−0.617127 | + | 0.786863i | \(0.711704\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −38.0000 | −1.78935 | ||||||||
\(452\) | 18.0000i | 0.846649i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.00000 | −0.187729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.35890i | − | 0.203901i | −0.994789 | − | 0.101950i | \(-0.967492\pi\) | ||
0.994789 | − | 0.101950i | \(-0.0325083\pi\) | |||||||
\(458\) | − | 22.0000i | − | 1.02799i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.00000 | − | 4.35890i | −0.0466252 | − | 0.203235i | ||||
\(461\) | 39.2301 | 1.82713 | 0.913564 | − | 0.406696i | \(-0.133319\pi\) | ||||
0.913564 | + | 0.406696i | \(0.133319\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.0767i | 0.607726i | 0.952716 | + | 0.303863i | \(0.0982765\pi\) | ||||
−0.952716 | + | 0.303863i | \(0.901724\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.0000 | 0.648537 | ||||||||
\(467\) | 21.0000i | 0.971764i | 0.874024 | + | 0.485882i | \(0.161502\pi\) | ||||
−0.874024 | + | 0.485882i | \(0.838498\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −38.0000 | −1.75468 | ||||||||
\(470\) | 4.35890 | − | 1.00000i | 0.201061 | − | 0.0461266i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.71780i | 0.401269i | ||||||||
\(473\) | 38.0000i | 1.74724i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.0000 | + | 13.0767i | −1.23884 | + | 0.600000i | ||||
\(476\) | 17.4356 | 0.799159 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.71780i | 0.398743i | ||||||||
\(479\) | −8.71780 | −0.398326 | −0.199163 | − | 0.979966i | \(-0.563822\pi\) | ||||
−0.199163 | + | 0.979966i | \(0.563822\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 14.0000i | 0.637683i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.00000 | −0.363636 | ||||||||
\(485\) | −2.17945 | − | 9.50000i | −0.0989637 | − | 0.431373i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.1534i | 1.18512i | 0.805525 | + | 0.592562i | \(0.201883\pi\) | ||||
−0.805525 | + | 0.592562i | \(0.798117\pi\) | |||||||
\(488\) | − | 4.00000i | − | 0.181071i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.00000 | − | 26.1534i | −0.271052 | − | 1.18149i | ||||
\(491\) | −13.0767 | −0.590143 | −0.295072 | − | 0.955475i | \(-0.595343\pi\) | ||||
−0.295072 | + | 0.955475i | \(0.595343\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.00000 | 0.314309 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.0000 | −1.34298 | −0.671492 | − | 0.741012i | \(-0.734346\pi\) | ||||
−0.671492 | + | 0.741012i | \(0.734346\pi\) | |||||||
\(500\) | 8.71780 | − | 7.00000i | 0.389872 | − | 0.313050i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 26.1534i | − | 1.16728i | ||||||
\(503\) | 30.0000i | 1.33763i | 0.743427 | + | 0.668817i | \(0.233199\pi\) | ||||
−0.743427 | + | 0.668817i | \(0.766801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.50000 | + | 2.17945i | −0.422744 | + | 0.0969842i | ||||
\(506\) | 8.71780 | 0.387553 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.35890i | 0.193395i | ||||||||
\(509\) | 13.0767 | 0.579614 | 0.289807 | − | 0.957085i | \(-0.406409\pi\) | ||||
0.289807 | + | 0.957085i | \(0.406409\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.0000 | 0.840511 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.0000 | 0.529297 | ||||||||
\(515\) | −4.35890 | − | 19.0000i | −0.192076 | − | 0.837240i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.71780i | 0.383408i | ||||||||
\(518\) | − | 38.0000i | − | 1.66962i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.4356 | 0.763867 | 0.381934 | − | 0.924190i | \(-0.375258\pi\) | ||||
0.381934 | + | 0.924190i | \(0.375258\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.8712i | 1.52481i | 0.647100 | + | 0.762405i | \(0.275982\pi\) | ||||
−0.647100 | + | 0.762405i | \(0.724018\pi\) | |||||||
\(524\) | 13.0767 | 0.571258 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.00000 | −0.0872041 | ||||||||
\(527\) | − | 28.0000i | − | 1.21970i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0000 | 0.826087 | ||||||||
\(530\) | 6.53835 | − | 1.50000i | 0.284008 | − | 0.0651558i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 26.1534i | − | 1.13389i | ||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.50000 | + | 32.6917i | 0.324253 | + | 1.41339i | ||||
\(536\) | 8.71780 | 0.376552 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 52.3068 | 2.25301 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.0000 | 1.71973 | 0.859867 | − | 0.510518i | \(-0.170546\pi\) | ||||
0.859867 | + | 0.510518i | \(0.170546\pi\) | |||||||
\(542\) | 5.00000i | 0.214768i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | 21.7945 | − | 5.00000i | 0.933574 | − | 0.214176i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 17.4356i | − | 0.745492i | −0.927933 | − | 0.372746i | \(-0.878416\pi\) | ||
0.927933 | − | 0.372746i | \(-0.121584\pi\) | |||||||
\(548\) | − | 18.0000i | − | 0.768922i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.50000 | + | 19.6150i | 0.405081 | + | 0.836388i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −17.4356 | −0.740767 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | 33.0000i | 1.39825i | 0.714997 | + | 0.699127i | \(0.246428\pi\) | ||||
−0.714997 | + | 0.699127i | \(0.753572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.17945 | + | 9.50000i | 0.0920985 | + | 0.401448i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.0000i | 0.463595i | 0.972764 | + | 0.231797i | \(0.0744606\pi\) | ||||
−0.972764 | + | 0.231797i | \(0.925539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00000 | + | 39.2301i | 0.378633 | + | 1.65042i | ||||
\(566\) | 8.71780 | 0.366436 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.4356 | 0.730938 | 0.365469 | − | 0.930823i | \(-0.380909\pi\) | ||||
0.365469 | + | 0.930823i | \(0.380909\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0000 | 0.669579 | 0.334790 | − | 0.942293i | \(-0.391335\pi\) | ||||
0.334790 | + | 0.942293i | \(0.391335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −38.0000 | −1.58609 | ||||||||
\(575\) | −4.35890 | − | 9.00000i | −0.181779 | − | 0.375326i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 17.4356i | − | 0.725853i | −0.931818 | − | 0.362927i | \(-0.881778\pi\) | ||
0.931818 | − | 0.362927i | \(-0.118222\pi\) | |||||||
\(578\) | − | 1.00000i | − | 0.0415945i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.7945 | −0.904188 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.0767i | 0.541581i | ||||||||
\(584\) | −4.35890 | −0.180373 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | − | 3.00000i | − | 0.123823i | −0.998082 | − | 0.0619116i | \(-0.980280\pi\) | ||
0.998082 | − | 0.0619116i | \(-0.0197197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.0000 | −1.73058 | ||||||||
\(590\) | 4.35890 | + | 19.0000i | 0.179453 | + | 0.782218i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.71780i | 0.358299i | ||||||||
\(593\) | − | 6.00000i | − | 0.246390i | −0.992382 | − | 0.123195i | \(-0.960686\pi\) | ||
0.992382 | − | 0.123195i | \(-0.0393141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 38.0000 | − | 8.71780i | 1.55785 | − | 0.357395i | ||||
\(596\) | 4.35890 | 0.178547 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.1534 | 1.06860 | 0.534299 | − | 0.845295i | \(-0.320576\pi\) | ||||
0.534299 | + | 0.845295i | \(0.320576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0000 | −0.530281 | −0.265141 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265141 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(602\) | 38.0000i | 1.54876i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.0000 | 0.447584 | ||||||||
\(605\) | −17.4356 | + | 4.00000i | −0.708858 | + | 0.162623i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 8.71780i | − | 0.353845i | −0.984225 | − | 0.176922i | \(-0.943386\pi\) | ||
0.984225 | − | 0.176922i | \(-0.0566141\pi\) | |||||||
\(608\) | 6.00000i | 0.243332i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.00000 | − | 8.71780i | −0.0809776 | − | 0.352973i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.71780i | − | 0.352109i | −0.984380 | − | 0.176054i | \(-0.943667\pi\) | ||
0.984380 | − | 0.176054i | \(-0.0563334\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −19.0000 | −0.765532 | ||||||||
\(617\) | 2.00000i | 0.0805170i | 0.999189 | + | 0.0402585i | \(0.0128181\pi\) | ||||
−0.999189 | + | 0.0402585i | \(0.987182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.0000 | −1.28619 | −0.643094 | − | 0.765787i | \(-0.722350\pi\) | ||||
−0.643094 | + | 0.765787i | \(0.722350\pi\) | |||||||
\(620\) | 15.2561 | − | 3.50000i | 0.612702 | − | 0.140563i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 26.1534i | − | 1.04866i | ||||||
\(623\) | 38.0000i | 1.52244i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | − | 19.6150i | 0.620000 | − | 0.784602i | ||||
\(626\) | −21.7945 | −0.871083 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 17.4356i | − | 0.695756i | ||||||
\(629\) | 34.8712 | 1.39041 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.00000 | 0.199047 | 0.0995234 | − | 0.995035i | \(-0.468268\pi\) | ||||
0.0995234 | + | 0.995035i | \(0.468268\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.0000 | 0.675156 | ||||||||
\(635\) | 2.17945 | + | 9.50000i | 0.0864888 | + | 0.376996i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | − | 2.17945i | −0.0197642 | − | 0.0861503i | ||||
\(641\) | 8.71780 | 0.344332 | 0.172166 | − | 0.985068i | \(-0.444923\pi\) | ||||
0.172166 | + | 0.985068i | \(0.444923\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 8.71780 | 0.343529 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.0000 | 0.944267 | ||||||||
\(647\) | 12.0000i | 0.471769i | 0.971781 | + | 0.235884i | \(0.0757987\pi\) | ||||
−0.971781 | + | 0.235884i | \(0.924201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −38.0000 | −1.49163 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.4356i | 0.682831i | ||||||||
\(653\) | − | 35.0000i | − | 1.36966i | −0.728705 | − | 0.684828i | \(-0.759877\pi\) | ||
0.728705 | − | 0.684828i | \(-0.240123\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.5000 | − | 6.53835i | 1.11359 | − | 0.255474i | ||||
\(656\) | 8.71780 | 0.340373 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.71780i | 0.339855i | ||||||||
\(659\) | −4.35890 | −0.169799 | −0.0848993 | − | 0.996390i | \(-0.527057\pi\) | ||||
−0.0848993 | + | 0.996390i | \(0.527057\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0000 | −0.855701 | −0.427850 | − | 0.903850i | \(-0.640729\pi\) | ||||
−0.427850 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(662\) | − | 10.0000i | − | 0.388661i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.00000 | 0.194038 | ||||||||
\(665\) | −13.0767 | − | 57.0000i | −0.507093 | − | 2.21037i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − | 18.0000i | − | 0.696441i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 19.0000 | − | 4.35890i | 0.734034 | − | 0.168399i | ||||
\(671\) | 17.4356 | 0.673094 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 13.0767i | − | 0.504070i | −0.967718 | − | 0.252035i | \(-0.918900\pi\) | ||
0.967718 | − | 0.252035i | \(-0.0810997\pi\) | |||||||
\(674\) | −17.4356 | −0.671594 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | 26.0000i | 0.999261i | 0.866239 | + | 0.499631i | \(0.166531\pi\) | ||||
−0.866239 | + | 0.499631i | \(0.833469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.0000 | 0.729153 | ||||||||
\(680\) | −8.71780 | + | 2.00000i | −0.334312 | + | 0.0766965i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 30.5123i | 1.16838i | ||||||||
\(683\) | − | 20.0000i | − | 0.765279i | −0.923898 | − | 0.382639i | \(-0.875015\pi\) | ||
0.923898 | − | 0.382639i | \(-0.124985\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.00000 | − | 39.2301i | −0.343872 | − | 1.49890i | ||||
\(686\) | 21.7945 | 0.832118 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 8.71780i | − | 0.332363i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0000 | −0.760836 | −0.380418 | − | 0.924815i | \(-0.624220\pi\) | ||||
−0.380418 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(692\) | 19.0000i | 0.722272i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.0000 | −1.02491 | ||||||||
\(695\) | 8.71780 | − | 2.00000i | 0.330685 | − | 0.0758643i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 34.8712i | − | 1.32084i | ||||||
\(698\) | − | 14.0000i | − | 0.529908i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.50000 | + | 19.6150i | 0.359066 | + | 0.741379i | ||||
\(701\) | 21.7945 | 0.823167 | 0.411583 | − | 0.911372i | \(-0.364976\pi\) | ||||
0.411583 | + | 0.911372i | \(0.364976\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 52.3068i | − | 1.97279i | ||||||
\(704\) | 4.35890 | 0.164282 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.0000 | 0.978523 | ||||||||
\(707\) | − | 19.0000i | − | 0.714569i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.0000 | −0.450669 | −0.225335 | − | 0.974281i | \(-0.572348\pi\) | ||||
−0.225335 | + | 0.974281i | \(0.572348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 8.71780i | − | 0.326713i | ||||||
\(713\) | − | 14.0000i | − | 0.524304i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.7945 | −0.814499 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.1534i | 0.976036i | ||||||||
\(719\) | −34.8712 | −1.30048 | −0.650238 | − | 0.759731i | \(-0.725331\pi\) | ||||
−0.650238 | + | 0.759731i | \(0.725331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.0000 | 1.41519 | ||||||||
\(722\) | − | 17.0000i | − | 0.632674i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.00000 | −0.297318 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.2301i | 1.45496i | 0.686127 | + | 0.727482i | \(0.259309\pi\) | ||||
−0.686127 | + | 0.727482i | \(0.740691\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.50000 | + | 2.17945i | −0.351611 | + | 0.0806650i | ||||
\(731\) | −34.8712 | −1.28976 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.71780i | 0.321999i | 0.986954 | + | 0.161000i | \(0.0514718\pi\) | ||||
−0.986954 | + | 0.161000i | \(0.948528\pi\) | |||||||
\(734\) | −4.35890 | −0.160890 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.00000 | −0.0737210 | ||||||||
\(737\) | 38.0000i | 1.39975i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0000 | −0.588570 | −0.294285 | − | 0.955718i | \(-0.595081\pi\) | ||||
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 4.35890 | + | 19.0000i | 0.160236 | + | 0.698454i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.0767i | 0.480061i | ||||||||
\(743\) | 48.0000i | 1.76095i | 0.474093 | + | 0.880475i | \(0.342776\pi\) | ||||
−0.474093 | + | 0.880475i | \(0.657224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.50000 | − | 2.17945i | 0.348053 | − | 0.0798489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 17.4356i | − | 0.637509i | ||||||
\(749\) | −65.3835 | −2.38906 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.0000 | 1.27717 | 0.638584 | − | 0.769552i | \(-0.279520\pi\) | ||||
0.638584 | + | 0.769552i | \(0.279520\pi\) | |||||||
\(752\) | − | 2.00000i | − | 0.0729325i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.9739 | − | 5.50000i | 0.872501 | − | 0.200165i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.71780i | 0.316854i | 0.987371 | + | 0.158427i | \(0.0506422\pi\) | ||||
−0.987371 | + | 0.158427i | \(0.949358\pi\) | |||||||
\(758\) | − | 4.00000i | − | 0.145287i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.00000 | + | 13.0767i | 0.108821 | + | 0.474342i | ||||
\(761\) | 52.3068 | 1.89612 | 0.948060 | − | 0.318092i | \(-0.103042\pi\) | ||||
0.948060 | + | 0.318092i | \(0.103042\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.5890i | 1.57803i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.00000 | −0.144526 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.00000 | −0.324548 | −0.162274 | − | 0.986746i | \(-0.551883\pi\) | ||||
−0.162274 | + | 0.986746i | \(0.551883\pi\) | |||||||
\(770\) | −41.4095 | + | 9.50000i | −1.49230 | + | 0.342356i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.7945i | 0.784401i | ||||||||
\(773\) | 18.0000i | 0.647415i | 0.946157 | + | 0.323708i | \(0.104929\pi\) | ||||
−0.946157 | + | 0.323708i | \(0.895071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.5000 | − | 15.2561i | 1.13151 | − | 0.548017i | ||||
\(776\) | −4.35890 | −0.156475 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 4.35890i | − | 0.156274i | ||||||
\(779\) | −52.3068 | −1.87409 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 8.00000i | 0.286079i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.0000 | −0.428571 | ||||||||
\(785\) | −8.71780 | − | 38.0000i | −0.311152 | − | 1.35628i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 17.4356i | − | 0.621512i | −0.950490 | − | 0.310756i | \(-0.899418\pi\) | ||
0.950490 | − | 0.310756i | \(-0.100582\pi\) | |||||||
\(788\) | 5.00000i | 0.178118i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −78.4602 | −2.78972 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 34.8712 | 1.23753 | ||||||||
\(795\) | 0 |