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 | 109.2 | ||
Root | \(2.17945 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 270.109 |
Dual form | 270.2.c.c.109.4 |
$q$-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 | \(0.308125\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | 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 | \(-0.271771\pi\) | ||||
0.657129 | + | 0.753778i | \(0.271771\pi\) | |||||||
\(12\) | 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 | \(-0.745698\pi\) | ||
0.697486 | − | 0.716599i | \(-0.254302\pi\) | |||||||
\(38\) | 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 | \(-0.738344\pi\) | ||||
−0.680746 | + | 0.732520i | \(0.738344\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.71780i | 1.32945i | 0.747087 | + | 0.664726i | \(0.231452\pi\) | ||||
−0.747087 | + | 0.664726i | \(0.768548\pi\) | |||||||
\(44\) | −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 | \(-0.692082\pi\) | ||||
−0.567480 | + | 0.823387i | \(0.692082\pi\) | |||||||
\(60\) | 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 | \(0.178756\pi\) | ||||
−0.846415 | + | 0.532524i | \(0.821244\pi\) | |||||||
\(68\) | 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 | \(-0.917896\pi\) | ||
0.966919 | − | 0.255085i | \(-0.0821035\pi\) | |||||||
\(74\) | −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 | \(-0.347117\pi\) | ||||
0.462042 | + | 0.886858i | \(0.347117\pi\) | |||||||
\(90\) | 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 | \(-0.928973\pi\) | ||
0.975208 | − | 0.221290i | \(-0.0710266\pi\) | |||||||
\(98\) | 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 | \(-0.569583\pi\) | ||||
−0.216863 | + | 0.976202i | \(0.569583\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.71780i | − | 0.858990i | −0.903069 | − | 0.429495i | \(-0.858692\pi\) | ||
0.903069 | − | 0.429495i | \(-0.141308\pi\) | |||||||
\(104\) | 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 | \(0.0619498\pi\) | ||||
−0.981121 | + | 0.193395i | \(0.938050\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.0767 | 1.14252 | 0.571258 | − | 0.820770i | \(-0.306456\pi\) | ||||
0.571258 | + | 0.820770i | \(0.306456\pi\) | |||||||
\(132\) | 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 | \(-0.442860\pi\) | ||||
0.178547 | + | 0.983931i | \(0.442860\pi\) | |||||||
\(150\) | 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 | \(-0.755069\pi\) | ||
0.718278 | − | 0.695756i | \(-0.244931\pi\) | |||||||
\(158\) | 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 | \(0.239251\pi\) | ||||
−0.730577 | + | 0.682831i | \(0.760749\pi\) | |||||||
\(164\) | 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 | \(-0.802988\pi\) | ||||
−0.814499 | + | 0.580166i | \(0.802988\pi\) | |||||||
\(180\) | 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 | \(0.287030\pi\) | ||||
−0.620254 | + | 0.784401i | \(0.712970\pi\) | |||||||
\(194\) | −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 | \(0.0942853\pi\) | ||||
−0.956451 | + | 0.291893i | \(0.905715\pi\) | |||||||
\(224\) | 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 | \(-0.409018\pi\) | ||||
0.281954 | + | 0.959428i | \(0.409018\pi\) | |||||||
\(240\) | 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 | \(-0.809047\pi\) | ||||
−0.825394 | + | 0.564557i | \(0.809047\pi\) | |||||||
\(252\) | 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 | \(0.175487\pi\) | ||||
−0.851840 | + | 0.523802i | \(0.824513\pi\) | |||||||
\(278\) | 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 | \(-0.916571\pi\) | ||
0.965848 | − | 0.259110i | \(-0.0834291\pi\) | |||||||
\(284\) | 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 | \(-0.765891\pi\) | ||||
−0.741511 | + | 0.670940i | \(0.765891\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.7945i | 1.23190i | 0.787786 | + | 0.615949i | \(0.211227\pi\) | ||||
−0.787786 | + | 0.615949i | \(0.788773\pi\) | |||||||
\(314\) | −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 | \(0.157512\pi\) | ||||
−0.880046 | + | 0.474889i | \(0.842488\pi\) | |||||||
\(338\) | − | 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 | \(-0.257539\pi\) | ||||
0.690162 | + | 0.723655i | \(0.257539\pi\) | |||||||
\(360\) | 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 | \(0.0362915\pi\) | ||||
−0.993508 | + | 0.113766i | \(0.963708\pi\) | |||||||
\(368\) | − | 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 | \(-0.535246\pi\) | ||||
−0.110502 | + | 0.993876i | \(0.535246\pi\) | |||||||
\(390\) | 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 | \(-0.660817\pi\) | ||
0.484001 | − | 0.875067i | \(-0.339183\pi\) | |||||||
\(398\) | − | 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 | \(-0.163671\pi\) | ||||
0.870692 | + | 0.491828i | \(0.163671\pi\) | |||||||
\(402\) | 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 | \(-0.431694\pi\) | ||||
0.212946 | + | 0.977064i | \(0.431694\pi\) | |||||||
\(420\) | 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 | \(-0.567334\pi\) | ||||
−0.209961 | + | 0.977710i | \(0.567334\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.7945i | 1.04738i | 0.851910 | + | 0.523688i | \(0.175444\pi\) | ||||
−0.851910 | + | 0.523688i | \(0.824556\pi\) | |||||||
\(434\) | 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 | \(-0.288296\pi\) | ||||
0.617127 | + | 0.786863i | \(0.288296\pi\) | |||||||
\(450\) | 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 | \(0.0325083\pi\) | ||||
−0.994789 | + | 0.101950i | \(0.967492\pi\) | |||||||
\(458\) | − | 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 | \(-0.866681\pi\) | ||||
−0.913564 | + | 0.406696i | \(0.866681\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.0767i | − | 0.607726i | −0.952716 | − | 0.303863i | \(-0.901724\pi\) | ||
0.952716 | − | 0.303863i | \(-0.0982765\pi\) | |||||||
\(464\) | 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 | \(-0.436178\pi\) | ||||
0.199163 | + | 0.979966i | \(0.436178\pi\) | |||||||
\(480\) | 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 | \(-0.798117\pi\) | ||
0.805525 | − | 0.592562i | \(-0.201883\pi\) | |||||||
\(488\) | − | 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 | \(-0.404657\pi\) | ||||
0.295072 | + | 0.955475i | \(0.404657\pi\) | |||||||
\(492\) | 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 | \(-0.593591\pi\) | ||||
−0.289807 | + | 0.957085i | \(0.593591\pi\) | |||||||
\(510\) | 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 | \(-0.624742\pi\) | ||||
−0.381934 | + | 0.924190i | \(0.624742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 34.8712i | − | 1.52481i | −0.647100 | − | 0.762405i | \(-0.724018\pi\) | ||
0.647100 | − | 0.762405i | \(-0.275982\pi\) | |||||||
\(524\) | −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 | \(0.121584\pi\) | ||||
−0.927933 | + | 0.372746i | \(0.878416\pi\) | |||||||
\(548\) | − | 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 | \(-0.619091\pi\) | ||||
−0.365469 | + | 0.930823i | \(0.619091\pi\) | |||||||
\(570\) | 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 | \(0.118222\pi\) | ||||
−0.931818 | + | 0.362927i | \(0.881778\pi\) | |||||||
\(578\) | − | 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 | \(-0.679424\pi\) | ||||
−0.534299 | + | 0.845295i | \(0.679424\pi\) | |||||||
\(600\) | 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 | \(0.0566141\pi\) | ||||
−0.984225 | + | 0.176922i | \(0.943386\pi\) | |||||||
\(608\) | 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 | \(0.0563334\pi\) | ||||
−0.984380 | + | 0.176054i | \(0.943667\pi\) | |||||||
\(614\) | 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 | \(-0.555077\pi\) | ||||
−0.172166 | + | 0.985068i | \(0.555077\pi\) | |||||||
\(642\) | 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 | \(-0.472943\pi\) | ||||
0.0848993 | + | 0.996390i | \(0.472943\pi\) | |||||||
\(660\) | 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 | \(0.0810997\pi\) | ||||
−0.967718 | + | 0.252035i | \(0.918900\pi\) | |||||||
\(674\) | 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 | \(-0.635024\pi\) | ||||
−0.411583 | + | 0.911372i | \(0.635024\pi\) | |||||||
\(702\) | 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 | \(-0.274669\pi\) | ||||
0.650238 | + | 0.759731i | \(0.274669\pi\) | |||||||
\(720\) | 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 | \(-0.740691\pi\) | ||
0.686127 | − | 0.727482i | \(-0.259309\pi\) | |||||||
\(728\) | 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 | \(-0.948528\pi\) | ||
0.986954 | − | 0.161000i | \(-0.0514718\pi\) | |||||||
\(734\) | 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 | \(-0.949358\pi\) | ||
0.987371 | − | 0.158427i | \(-0.0506422\pi\) | |||||||
\(758\) | − | 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 | \(-0.896958\pi\) | ||||
−0.948060 | + | 0.318092i | \(0.896958\pi\) | |||||||
\(762\) | 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 | \(0.100582\pi\) | ||||
−0.950490 | + | 0.310756i | \(0.899418\pi\) | |||||||
\(788\) | 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 | ||||||||
\(795\) |