Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2340,2,Mod(181,2340)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2340, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("2340.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2340.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: | \(18.6849940730\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.9144576.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 12x^{4} + 36x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.1 | ||
Root | \(2.60168i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2340.181 |
Dual form | 2340.2.c.d.181.6 |
$q$-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 \(\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times\).
\(n\) | \(937\) | \(1081\) | \(1171\) | \(2081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.76873i | − | 1.04648i | −0.852184 | − | 0.523242i | \(-0.824723\pi\) | ||
0.852184 | − | 0.523242i | \(-0.175277\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.16706i | 0.653392i | 0.945130 | + | 0.326696i | \(0.105935\pi\) | ||||
−0.945130 | + | 0.326696i | \(0.894065\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.167055 | + | 3.60168i | −0.0463328 | + | 0.998926i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.03630i | 1.15541i | 0.816247 | + | 0.577704i | \(0.196051\pi\) | ||||
−0.816247 | + | 0.577704i | \(0.803949\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.93579 | 1.02918 | 0.514592 | − | 0.857435i | \(-0.327944\pi\) | ||||
0.514592 | + | 0.857435i | \(0.327944\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.43462 | 0.823489 | 0.411744 | − | 0.911299i | \(-0.364920\pi\) | ||||
0.411744 | + | 0.911299i | \(0.364920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.37041i | − | 0.605344i | −0.953095 | − | 0.302672i | \(-0.902121\pi\) | ||
0.953095 | − | 0.302672i | \(-0.0978787\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.76873 | −0.468002 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.97209i | 0.653008i | 0.945196 | + | 0.326504i | \(0.105871\pi\) | ||||
−0.945196 | + | 0.326504i | \(0.894129\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.66589i | 0.260168i | 0.991503 | + | 0.130084i | \(0.0415247\pi\) | ||||
−0.991503 | + | 0.130084i | \(0.958475\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.80504 | 1.49525 | 0.747627 | − | 0.664119i | \(-0.231193\pi\) | ||||
0.747627 | + | 0.664119i | \(0.231193\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.6380i | 1.69757i | 0.528735 | + | 0.848787i | \(0.322667\pi\) | ||||
−0.528735 | + | 0.848787i | \(0.677333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.665890 | −0.0951271 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.7408 | 1.75009 | 0.875044 | − | 0.484044i | \(-0.160833\pi\) | ||||
0.875044 | + | 0.484044i | \(0.160833\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.16706 | 0.292206 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 8.16706i | − | 1.06326i | −0.846977 | − | 0.531630i | \(-0.821580\pi\) | ||
0.846977 | − | 0.531630i | \(-0.178420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.3062 | −1.31957 | −0.659787 | − | 0.751453i | \(-0.729354\pi\) | ||||
−0.659787 | + | 0.751453i | \(0.729354\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.60168 | + | 0.167055i | 0.446733 | + | 0.0207206i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.10284i | − | 0.867751i | −0.900973 | − | 0.433875i | \(-0.857146\pi\) | ||
0.900973 | − | 0.433875i | \(-0.142854\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 16.1112i | − | 1.91205i | −0.293281 | − | 0.956026i | \(-0.594747\pi\) | ||
0.293281 | − | 0.956026i | \(-0.405253\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.9721i | − | 1.86939i | −0.355448 | − | 0.934696i | \(-0.615672\pi\) | ||
0.355448 | − | 0.934696i | \(-0.384328\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | 0.683763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.9442 | 1.34383 | 0.671913 | − | 0.740630i | \(-0.265473\pi\) | ||||
0.671913 | + | 0.740630i | \(0.265473\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.97209i | 0.435994i | 0.975949 | + | 0.217997i | \(0.0699523\pi\) | ||||
−0.975949 | + | 0.217997i | \(0.930048\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.94419i | − | 0.842082i | −0.907042 | − | 0.421041i | \(-0.861665\pi\) | ||
0.907042 | − | 0.421041i | \(-0.138335\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.97209 | + | 0.462531i | 1.04536 | + | 0.0484865i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.03630 | 0.516714 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.462531i | 0.0469629i | 0.999724 | + | 0.0234815i | \(0.00747507\pi\) | ||||
−0.999724 | + | 0.0234815i | \(0.992525\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.7408 | −1.26776 | −0.633880 | − | 0.773432i | \(-0.718539\pi\) | ||||
−0.633880 | + | 0.773432i | \(0.718539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.13915 | −0.407842 | −0.203921 | − | 0.978987i | \(-0.565369\pi\) | ||||
−0.203921 | + | 0.978987i | \(0.565369\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.06421 | −0.682923 | −0.341462 | − | 0.939896i | \(-0.610922\pi\) | ||||
−0.341462 | + | 0.939896i | \(0.610922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.8692i | 1.42422i | 0.702070 | + | 0.712108i | \(0.252259\pi\) | ||||
−0.702070 | + | 0.712108i | \(0.747741\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.13075 | −0.294516 | −0.147258 | − | 0.989098i | \(-0.547045\pi\) | ||||
−0.147258 | + | 0.989098i | \(0.547045\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.93579i | − | 0.460265i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.30387 | 0.573079 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.1391 | 1.43212 | 0.716059 | − | 0.698040i | \(-0.245944\pi\) | ||||
0.716059 | + | 0.698040i | \(0.245944\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.86925 | 0.774910 | 0.387455 | − | 0.921889i | \(-0.373354\pi\) | ||||
0.387455 | + | 0.921889i | \(0.373354\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.9442 | 1.20911 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.66589i | − | 0.142327i | −0.997465 | − | 0.0711633i | \(-0.977329\pi\) | ||
0.997465 | − | 0.0711633i | \(-0.0226711\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.2760 | 1.63497 | 0.817483 | − | 0.575953i | \(-0.195369\pi\) | ||||
0.817483 | + | 0.575953i | \(0.195369\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.80504 | − | 0.362018i | −0.652690 | − | 0.0302734i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.43462i | − | 0.368275i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.9442i | 1.14235i | 0.820828 | + | 0.571176i | \(0.193513\pi\) | ||||
−0.820828 | + | 0.571176i | \(0.806487\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.96370i | − | 0.566698i | −0.959017 | − | 0.283349i | \(-0.908555\pi\) | ||
0.959017 | − | 0.283349i | \(-0.0914454\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.37041 | −0.270718 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3341 | 0.984369 | 0.492185 | − | 0.870491i | \(-0.336199\pi\) | ||||
0.492185 | + | 0.870491i | \(0.336199\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 13.6659i | − | 1.07702i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.5072i | 1.60625i | 0.595810 | + | 0.803125i | \(0.296831\pi\) | ||||
−0.595810 | + | 0.803125i | \(0.703169\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.3039i | 1.49378i | 0.664948 | + | 0.746889i | \(0.268453\pi\) | ||||
−0.664948 | + | 0.746889i | \(0.731547\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9442 | − | 1.20336i | −0.995707 | − | 0.0925660i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.61007 | −0.730640 | −0.365320 | − | 0.930882i | \(-0.619041\pi\) | ||||
−0.365320 | + | 0.930882i | \(0.619041\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.76873i | 0.209297i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.87158 | 0.737836 | 0.368918 | − | 0.929462i | \(-0.379728\pi\) | ||||
0.368918 | + | 0.929462i | \(0.379728\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.97209 | −0.146584 | −0.0732922 | − | 0.997311i | \(-0.523351\pi\) | ||||
−0.0732922 | + | 0.997311i | \(0.523351\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.97209 | 0.292034 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.73850 | 0.415223 | 0.207611 | − | 0.978211i | \(-0.433431\pi\) | ||||
0.207611 | + | 0.978211i | \(0.433431\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.07261i | 0.293153i | 0.989199 | + | 0.146576i | \(0.0468254\pi\) | ||||
−0.989199 | + | 0.146576i | \(0.953175\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.6101i | 1.53965i | 0.638253 | + | 0.769827i | \(0.279658\pi\) | ||||
−0.638253 | + | 0.769827i | \(0.720342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.6101 | −0.823016 | −0.411508 | − | 0.911406i | \(-0.634998\pi\) | ||||
−0.411508 | + | 0.911406i | \(0.634998\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 12.2783i | − | 0.861767i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.66589 | 0.116351 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.9139 | −0.754933 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2783 | 1.12064 | 0.560322 | − | 0.828275i | \(-0.310677\pi\) | ||||
0.560322 | + | 0.828275i | \(0.310677\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 9.80504i | − | 0.668698i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.33178 | −0.633482 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.4370i | 0.765875i | 0.923774 | + | 0.382938i | \(0.125088\pi\) | ||||
−0.923774 | + | 0.382938i | \(0.874912\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.9721i | 1.06011i | 0.847965 | + | 0.530053i | \(0.177828\pi\) | ||||
−0.847965 | + | 0.530053i | \(0.822172\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.12842i | − | 0.140650i | −0.997524 | − | 0.0703250i | \(-0.977596\pi\) | ||
0.997524 | − | 0.0703250i | \(-0.0224036\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.86925 | 0.187971 | 0.0939853 | − | 0.995574i | \(-0.470039\pi\) | ||||
0.0939853 | + | 0.995574i | \(0.470039\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.6380 | 0.759178 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3.16939i | − | 0.205011i | −0.994732 | − | 0.102505i | \(-0.967314\pi\) | ||
0.994732 | − | 0.102505i | \(-0.0326859\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.79664i | − | 0.308979i | −0.987994 | − | 0.154489i | \(-0.950627\pi\) | ||
0.987994 | − | 0.154489i | \(-0.0493733\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.665890i | 0.0425421i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.1391 | − | 0.841340i | −1.15417 | − | 0.0535332i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00233 | −0.0632666 | −0.0316333 | − | 0.999500i | \(-0.510071\pi\) | ||||
−0.0316333 | + | 0.999500i | \(0.510071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.6961i | 0.672460i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.4817 | 1.21523 | 0.607616 | − | 0.794231i | \(-0.292126\pi\) | ||||
0.607616 | + | 0.794231i | \(0.292126\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.9977 | 0.683362 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.19496 | 0.258672 | 0.129336 | − | 0.991601i | \(-0.458715\pi\) | ||||
0.129336 | + | 0.991601i | \(0.458715\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 12.7408i | − | 0.782663i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.4793 | −1.85836 | −0.929179 | − | 0.369631i | \(-0.879484\pi\) | ||||
−0.929179 | + | 0.369631i | \(0.879484\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.83528i | 0.293722i | 0.989157 | + | 0.146861i | \(0.0469170\pi\) | ||||
−0.989157 | + | 0.146861i | \(0.953083\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.16706i | − | 0.130678i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.00233 | 0.180393 | 0.0901963 | − | 0.995924i | \(-0.471251\pi\) | ||||
0.0901963 | + | 0.995924i | \(0.471251\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 21.6101i | − | 1.28915i | −0.764542 | − | 0.644574i | \(-0.777035\pi\) | ||
0.764542 | − | 0.644574i | \(-0.222965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.47326 | 0.147020 | 0.0735100 | − | 0.997294i | \(-0.476580\pi\) | ||||
0.0735100 | + | 0.997294i | \(0.476580\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.61241 | 0.272262 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 23.9163i | − | 1.39720i | −0.715511 | − | 0.698602i | \(-0.753806\pi\) | ||
0.715511 | − | 0.698602i | \(-0.246194\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.16706 | −0.475504 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.824549 | + | 17.7771i | −0.0476849 | + | 1.02808i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 27.1475i | − | 1.56476i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.3062i | 0.590131i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.5654i | − | 0.774217i | −0.922034 | − | 0.387108i | \(-0.873474\pi\) | ||
0.922034 | − | 0.387108i | \(-0.126526\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.12842 | 0.120692 | 0.0603458 | − | 0.998178i | \(-0.480780\pi\) | ||||
0.0603458 | + | 0.998178i | \(0.480780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.6077 | −1.27787 | −0.638933 | − | 0.769263i | \(-0.720624\pi\) | ||||
−0.638933 | + | 0.769263i | \(0.720624\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.6357i | − | 0.597358i | −0.954354 | − | 0.298679i | \(-0.903454\pi\) | ||
0.954354 | − | 0.298679i | \(-0.0965459\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.61007i | 0.538061i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.167055 | − | 3.60168i | 0.00926655 | − | 0.199785i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.2225 | 1.77648 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.16472i | 0.0640190i | 0.999488 | + | 0.0320095i | \(0.0101907\pi\) | ||||
−0.999488 | + | 0.0320095i | \(0.989809\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.10284 | −0.388070 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.0000 | −1.08947 | −0.544735 | − | 0.838608i | \(-0.683370\pi\) | ||||
−0.544735 | + | 0.838608i | \(0.683370\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.30387 | 0.395527 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.5375i | − | 0.946934i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.67429 | −0.250929 | −0.125464 | − | 0.992098i | \(-0.540042\pi\) | ||||
−0.125464 | + | 0.992098i | \(0.540042\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.33411i | 0.232000i | 0.993249 | + | 0.116000i | \(0.0370072\pi\) | ||||
−0.993249 | + | 0.116000i | \(0.962993\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.3085i | 1.13414i | 0.823670 | + | 0.567069i | \(0.191923\pi\) | ||||
−0.823670 | + | 0.567069i | \(0.808077\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.1112 | −0.855096 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.7795i | 0.674474i | 0.941420 | + | 0.337237i | \(0.109492\pi\) | ||||
−0.941420 | + | 0.337237i | \(0.890508\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.36435 | −0.334966 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.9721 | −0.836018 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.1950 | 0.636572 | 0.318286 | − | 0.947995i | \(-0.396893\pi\) | ||||
0.318286 | + | 0.947995i | \(0.396893\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 35.2760i | − | 1.83144i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.2225 | −1.46130 | −0.730652 | − | 0.682750i | \(-0.760784\pi\) | ||||
−0.730652 | + | 0.682750i | \(0.760784\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.740827 | + | 15.9721i | −0.0381545 | + | 0.822605i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.3146i | − | 1.19759i | −0.800902 | − | 0.598795i | \(-0.795646\pi\) | ||
0.800902 | − | 0.598795i | \(-0.204354\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.02791i | 0.410207i | 0.978740 | + | 0.205103i | \(0.0657531\pi\) | ||||
−0.978740 | + | 0.205103i | \(0.934247\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 6.00000i | − | 0.305788i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.7385 | −1.20359 | −0.601795 | − | 0.798651i | \(-0.705547\pi\) | ||||
−0.601795 | + | 0.798651i | \(0.705547\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 11.9442i | − | 0.600977i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.04703i | 0.152926i | 0.997072 | + | 0.0764630i | \(0.0243627\pi\) | ||||
−0.997072 | + | 0.0764630i | \(0.975637\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 31.2201i | − | 1.55906i | −0.626365 | − | 0.779530i | \(-0.715458\pi\) | ||
0.626365 | − | 0.779530i | \(-0.284542\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.1391 | + | 0.563045i | 0.604694 | + | 0.0280473i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.60774 | −0.426670 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.4090i | 1.65197i | 0.563691 | + | 0.825986i | \(0.309381\pi\) | ||||
−0.563691 | + | 0.825986i | \(0.690619\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.6124 | −1.11268 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.97209 | 0.194982 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.7408 | 1.50179 | 0.750894 | − | 0.660423i | \(-0.229623\pi\) | ||||
0.750894 | + | 0.660423i | \(0.229623\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.2806i | 0.939680i | 0.882752 | + | 0.469840i | \(0.155688\pi\) | ||||
−0.882752 | + | 0.469840i | \(0.844312\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.5351i | 1.38091i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.44535i | 0.117788i | 0.998264 | + | 0.0588942i | \(0.0187575\pi\) | ||||
−0.998264 | + | 0.0588942i | \(0.981243\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.8581i | 1.18913i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.6659 | −0.556783 | −0.278391 | − | 0.960468i | \(-0.589801\pi\) | ||||
−0.278391 | + | 0.960468i | \(0.589801\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.8074 | −0.988588 | −0.494294 | − | 0.869295i | \(-0.664573\pi\) | ||||
−0.494294 | + | 0.869295i | \(0.664573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.94419 | −0.376590 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.2783i | 1.42892i | 0.699676 | + | 0.714461i | \(0.253328\pi\) | ||||
−0.699676 | + | 0.714461i | \(0.746672\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.61007 | −0.169992 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.462531 | − | 9.97209i | 0.0216838 | − | 0.467499i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.6124i | 1.05776i | 0.848695 | + | 0.528882i | \(0.177389\pi\) | ||||
−0.848695 | + | 0.528882i | \(0.822611\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 18.9419i | − | 0.882210i | −0.897455 | − | 0.441105i | \(-0.854587\pi\) | ||
0.897455 | − | 0.441105i | \(-0.145413\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11.6380i | − | 0.540863i | −0.962739 | − | 0.270431i | \(-0.912834\pi\) | ||
0.962739 | − | 0.270431i | \(-0.0871663\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.0642 | 1.15983 | 0.579917 | − | 0.814676i | \(-0.303085\pi\) | ||||
0.579917 | + | 0.814676i | \(0.303085\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.6659 | −0.908086 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.2481i | 0.976987i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.03630i | − | 0.231081i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 18.4407i | − | 0.842577i | −0.906927 | − | 0.421288i | \(-0.861578\pi\) | ||
0.906927 | − | 0.421288i | \(-0.138422\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.3062 | − | 0.663559i | −0.652307 | − | 0.0302557i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.462531 | 0.0210025 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.1196i | 1.13828i | 0.822241 | + | 0.569140i | \(0.192724\pi\) | ||||
−0.822241 | + | 0.569140i | \(0.807276\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.73850 | 0.258975 | 0.129487 | − | 0.991581i | \(-0.458667\pi\) | ||||
0.129487 | + | 0.991581i | \(0.458667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −44.6077 | −2.00093 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 33.3704i | − | 1.49386i | −0.664900 | − | 0.746932i | \(-0.731526\pi\) | ||
0.664900 | − | 0.746932i | \(-0.268474\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.6789 | 0.565326 | 0.282663 | − | 0.959219i | \(-0.408782\pi\) | ||||
0.282663 | + | 0.959219i | \(0.408782\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.7408i | 0.566959i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 17.6147i | − | 0.780759i | −0.920654 | − | 0.390380i | \(-0.872344\pi\) | ||
0.920654 | − | 0.390380i | \(-0.127656\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44.2225 | −1.95629 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.13915i | 0.182393i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.2201 | −1.10918 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.4346 | 0.720014 | 0.360007 | − | 0.932950i | \(-0.382774\pi\) | ||||
0.360007 | + | 0.932950i | \(0.382774\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.4733 | −0.895233 | −0.447617 | − | 0.894226i | \(-0.647727\pi\) | ||||
−0.447617 | + | 0.894226i | \(0.647727\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.36202 | 0.0592182 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.00000 | − | 0.278295i | −0.259889 | − | 0.0120543i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.06421i | 0.305412i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.44302i | − | 0.0621553i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 41.2928i | − | 1.77531i | −0.460505 | − | 0.887657i | \(-0.652332\pi\) | ||
0.460505 | − | 0.887657i | \(-0.347668\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.8692 | 0.636929 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.4174 | −0.445418 | −0.222709 | − | 0.974885i | \(-0.571490\pi\) | ||||
−0.222709 | + | 0.974885i | \(0.571490\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.3341i | 0.951465i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 33.0703i | − | 1.40629i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.5845i | 0.872193i | 0.899900 | + | 0.436097i | \(0.143639\pi\) | ||||
−0.899900 | + | 0.436097i | \(0.856361\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.63798 | + | 35.3146i | −0.0692793 | + | 1.49365i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.6766 | 0.997850 | 0.498925 | − | 0.866645i | \(-0.333728\pi\) | ||||
0.498925 | + | 0.866645i | \(0.333728\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.13075i | 0.131712i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.43695 | −0.227929 | −0.113965 | − | 0.993485i | \(-0.536355\pi\) | ||||
−0.113965 | + | 0.993485i | \(0.536355\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.2760 | 0.639279 | 0.319640 | − | 0.947539i | \(-0.396438\pi\) | ||||
0.319640 | + | 0.947539i | \(0.396438\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.93579 | −0.205837 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.76640i | − | 0.0735363i | −0.999324 | − | 0.0367682i | \(-0.988294\pi\) | ||
0.999324 | − | 0.0367682i | \(-0.0117063\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.9977 | 0.456260 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.6101i | 1.14349i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.9139i | 0.945760i | 0.881127 | + | 0.472880i | \(0.156786\pi\) | ||||
−0.881127 | + | 0.472880i | \(0.843214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9744 | 0.699419 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6.72404i | − | 0.276123i | −0.990424 | − | 0.138062i | \(-0.955913\pi\) | ||
0.990424 | − | 0.138062i | \(-0.0440872\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.8669 | 0.811740 | 0.405870 | − | 0.913931i | \(-0.366969\pi\) | ||||
0.405870 | + | 0.913931i | \(0.366969\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.2201 | −1.35508 | −0.677539 | − | 0.735487i | \(-0.736954\pi\) | ||||
−0.677539 | + | 0.735487i | \(0.736954\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 6.30387i | − | 0.256289i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.4174 | 0.585186 | 0.292593 | − | 0.956237i | \(-0.405482\pi\) | ||||
0.292593 | + | 0.956237i | \(0.405482\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −41.9163 | − | 1.94419i | −1.69575 | − | 0.0786533i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.3364i | 0.457875i | 0.973441 | + | 0.228937i | \(0.0735251\pi\) | ||||
−0.973441 | + | 0.228937i | \(0.926475\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 34.8907i | − | 1.40465i | −0.711858 | − | 0.702323i | \(-0.752146\pi\) | ||
0.711858 | − | 0.702323i | \(-0.247854\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 32.6464i | − | 1.31217i | −0.754688 | − | 0.656084i | \(-0.772212\pi\) | ||
0.754688 | − | 0.656084i | \(-0.227788\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.9953 | −0.881225 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 47.3146i | − | 1.88356i | −0.336224 | − | 0.941782i | \(-0.609150\pi\) | ||
0.336224 | − | 0.941782i | \(-0.390850\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 16.1391i | − | 0.640463i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.111240 | − | 2.39832i | 0.00440750 | − | 0.0950249i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.4817 | −1.71742 | −0.858711 | − | 0.512460i | \(-0.828734\pi\) | ||||
−0.858711 | + | 0.512460i | \(0.828734\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.3062i | 0.800798i | 0.916341 | + | 0.400399i | \(0.131129\pi\) | ||||
−0.916341 | + | 0.400399i | \(0.868871\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.8027 | −1.21098 | −0.605490 | − | 0.795853i | \(-0.707023\pi\) | ||||
−0.605490 | + | 0.795853i | \(0.707023\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.6985 | 0.694725 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.61007 | −0.141273 | −0.0706366 | − | 0.997502i | \(-0.522503\pi\) | ||||
−0.0706366 | + | 0.997502i | \(0.522503\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 8.86925i | − | 0.346550i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.74083 | 0.262585 | 0.131293 | − | 0.991344i | \(-0.458087\pi\) | ||||
0.131293 | + | 0.991344i | \(0.458087\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.6682i | 1.03727i | 0.854995 | + | 0.518637i | \(0.173560\pi\) | ||||
−0.854995 | + | 0.518637i | \(0.826440\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 13.9442i | − | 0.540732i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.8884 | 0.847521 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 22.3341i | − | 0.862199i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.61241 | −0.331984 | −0.165992 | − | 0.986127i | \(-0.553083\pi\) | ||||
−0.165992 | + | 0.986127i | \(0.553083\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.12842 | −0.312401 | −0.156200 | − | 0.987725i | \(-0.549925\pi\) | ||||
−0.156200 | + | 0.987725i | \(0.549925\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.28063 | 0.0491459 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 8.02791i | − | 0.307179i | −0.988135 | − | 0.153590i | \(-0.950917\pi\) | ||
0.988135 | − | 0.153590i | \(-0.0490834\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.66589 | −0.0636504 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.12842 | + | 45.8884i | −0.0810864 | + | 1.74821i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 22.1112i | − | 0.841151i | −0.907257 | − | 0.420576i | \(-0.861828\pi\) | ||
0.907257 | − | 0.420576i | \(-0.138172\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 19.2760i | − | 0.731179i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.47932 | 0.244721 | 0.122360 | − | 0.992486i | \(-0.460954\pi\) | ||||
0.122360 | + | 0.992486i | \(0.460954\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.0047 | −0.754490 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 35.2760i | 1.32669i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2.85246i | − | 0.107126i | −0.998564 | − | 0.0535631i | \(-0.982942\pi\) | ||
0.998564 | − | 0.0535631i | \(-0.0170578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 16.6357i | − | 0.623010i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.362018 | + | 7.80504i | −0.0135387 | + | 0.291892i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.0941 | −1.56984 | −0.784922 | − | 0.619595i | \(-0.787297\pi\) | ||||
−0.784922 | + | 0.619595i | \(0.787297\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.4602i | 0.426800i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.43462 | −0.164698 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.8027 | −1.21659 | −0.608293 | − | 0.793713i | \(-0.708145\pi\) | ||||
−0.608293 | + | 0.793713i | \(0.708145\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 2.38993i | − | 0.0882739i | −0.999025 | − | 0.0441370i | \(-0.985946\pi\) | ||
0.999025 | − | 0.0441370i | \(-0.0140538\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.3923 | 0.566981 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.4988i | 1.52656i | 0.646068 | + | 0.763280i | \(0.276412\pi\) | ||||
−0.646068 | + | 0.763280i | \(0.723588\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.8046i | 1.46029i | 0.683292 | + | 0.730145i | \(0.260548\pi\) | ||||
−0.683292 | + | 0.730145i | \(0.739452\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.9442 | 0.510875 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.5589i | 0.714667i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.6659 | 0.571656 | 0.285828 | − | 0.958281i | \(-0.407731\pi\) | ||||
0.285828 | + | 0.958281i | \(0.407731\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.96370 | −0.253435 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.2736 | 1.17301 | 0.586503 | − | 0.809947i | \(-0.300504\pi\) | ||||
0.586503 | + | 0.809947i | \(0.300504\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 13.2806i | − | 0.481422i | −0.970597 | − | 0.240711i | \(-0.922619\pi\) | ||
0.970597 | − | 0.240711i | \(-0.0773807\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.1690 | 1.49042 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29.4151 | + | 1.36435i | 1.06212 | + | 0.0492638i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.2010i | 0.439980i | 0.975502 | + | 0.219990i | \(0.0706025\pi\) | ||||
−0.975502 | + | 0.219990i | \(0.929397\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.9721i | 1.00609i | 0.864261 | + | 0.503043i | \(0.167786\pi\) | ||||
−0.864261 | + | 0.503043i | \(0.832214\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.37041i | 0.121069i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.38993 | −0.300600 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.9139 | 1.24932 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 12.3341i | − | 0.440223i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 10.2336i | − | 0.364788i | −0.983225 | − | 0.182394i | \(-0.941615\pi\) | ||
0.983225 | − | 0.182394i | \(-0.0583847\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.66822i | 0.308206i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.72170 | − | 37.1196i | 0.0611395 | − | 1.31816i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.3532 | 0.827214 | 0.413607 | − | 0.910456i | \(-0.364269\pi\) | ||||
0.413607 | + | 0.910456i | \(0.364269\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.6124 | 1.22145 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.6659 | −0.481659 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.1364 | −1.30565 | −0.652824 | − | 0.757510i | \(-0.726416\pi\) | ||||
−0.652824 | + | 0.757510i | \(0.726416\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 20.6296i | − | 0.724403i | −0.932100 | − | 0.362201i | \(-0.882025\pi\) | ||
0.932100 | − | 0.362201i | \(-0.117975\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.5072 | 0.718337 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.3811i | 1.72763i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 20.6077i | − | 0.719215i | −0.933104 | − | 0.359608i | \(-0.882911\pi\) | ||
0.933104 | − | 0.359608i | \(-0.117089\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.8050 | 1.38752 | 0.693758 | − | 0.720208i | \(-0.255954\pi\) | ||||
0.693758 | + | 0.720208i | \(0.255954\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 55.8605i | − | 1.94246i | −0.238146 | − | 0.971229i | \(-0.576540\pi\) | ||
0.238146 | − | 0.971229i | \(-0.423460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.5822 | −1.16636 | −0.583178 | − | 0.812344i | \(-0.698191\pi\) | ||||
−0.583178 | + | 0.812344i | \(0.698191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.3039 | 0.668038 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 26.4454i | − | 0.912995i | −0.889725 | − | 0.456497i | \(-0.849104\pi\) | ||
0.889725 | − | 0.456497i | \(-0.150896\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.33411 | −0.321866 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.20336 | + | 12.9442i | −0.0413968 | + | 0.445294i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 17.4537i | − | 0.599718i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.6054i | 0.672065i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 35.7153i | − | 1.22287i | −0.791296 | − | 0.611433i | \(-0.790593\pi\) | ||
0.791296 | − | 0.611433i | \(-0.209407\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.0894 | −0.754559 | −0.377280 | − | 0.926099i | \(-0.623140\pi\) | ||||
−0.377280 | + | 0.926099i | \(0.623140\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.2201 | −1.33817 | −0.669087 | − | 0.743184i | \(-0.733315\pi\) | ||||
−0.669087 | + | 0.743184i | \(0.733315\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.9744i | 0.986301i | 0.869944 | + | 0.493150i | \(0.164155\pi\) | ||||
−0.869944 | + | 0.493150i | \(0.835845\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.61007i | 0.326752i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.8837i | 0.878045i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.5822 | + | 1.18657i | 0.866819 | + | 0.0402053i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.76873 | 0.0936003 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.9251i | 1.04427i | 0.852864 | + | 0.522133i | \(0.174863\pi\) | ||||
−0.852864 | + | 0.522133i | \(0.825137\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.2695 | −1.39041 | −0.695203 | − | 0.718814i | \(-0.744685\pi\) | ||||
−0.695203 | + | 0.718814i | \(0.744685\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.1973 | 0.511430 | 0.255715 | − | 0.966752i | \(-0.417689\pi\) | ||||
0.255715 | + | 0.966752i | \(0.417689\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.4174 | 0.416937 | 0.208468 | − | 0.978029i | \(-0.433152\pi\) | ||||
0.208468 | + | 0.978029i | \(0.433152\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 44.6850i | − | 1.49869i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −58.6124 | −1.96139 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 9.87158i | − | 0.329970i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 14.9465i | − | 0.498494i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.97209i | 0.0655546i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.4709 | −0.380886 | −0.190443 | − | 0.981698i | \(-0.560992\pi\) | ||||
−0.190443 | + | 0.981698i | \(0.560992\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.5734 | −1.80810 | −0.904048 | − | 0.427430i | \(-0.859419\pi\) | ||||
−0.904048 | + | 0.427430i | \(0.859419\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.60774 | −0.284875 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 24.5566i | − | 0.810930i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.05815 | 0.298801 | 0.149400 | − | 0.988777i | \(-0.452266\pi\) | ||||
0.149400 | + | 0.988777i | \(0.452266\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 58.0275 | + | 2.69147i | 1.91000 | + | 0.0885907i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 3.97209i | − | 0.130602i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.2225i | 1.64775i | 0.566774 | + | 0.823873i | \(0.308191\pi\) | ||||
−0.566774 | + | 0.823873i | \(0.691809\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 3.35362i | − | 0.109911i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.38759 | 0.176005 | 0.0880025 | − | 0.996120i | \(-0.471952\pi\) | ||||
0.0880025 | + | 0.996120i | \(0.471952\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 58.8302i | − | 1.91781i | −0.283726 | − | 0.958905i | \(-0.591571\pi\) | ||
0.283726 | − | 0.958905i | \(-0.408429\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.22248i | 0.267761i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 12.6403i | − | 0.410755i | −0.978683 | − | 0.205377i | \(-0.934158\pi\) | ||
0.978683 | − | 0.205377i | \(-0.0658422\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.5264 | + | 2.66822i | 1.86738 | + | 0.0866141i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.6077 | 1.05627 | 0.528134 | − | 0.849161i | \(-0.322892\pi\) | ||||
0.528134 | + | 0.849161i | \(0.322892\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 5.73850i | − | 0.185693i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.61241 | −0.148942 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.6403 | 0.633558 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.07261 | 0.131102 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.5845i | 0.661953i | 0.943639 | + | 0.330976i | \(0.107378\pi\) | ||||
−0.943639 | + | 0.330976i | \(0.892622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 60.8349 | 1.95228 | 0.976142 | − | 0.217132i | \(-0.0696703\pi\) | ||||
0.976142 | + | 0.217132i | \(0.0696703\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 53.3700i | − | 1.71096i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 7.30387i | − | 0.233672i | −0.993151 | − | 0.116836i | \(-0.962725\pi\) | ||
0.993151 | − | 0.116836i | \(-0.0372751\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.2155 | 0.550209 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 40.2504i | − | 1.28379i | −0.766793 | − | 0.641894i | \(-0.778149\pi\) | ||
0.766793 | − | 0.641894i | \(-0.221851\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.6101 | 0.688554 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.3956 | 1.53889 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.2271 | −1.59552 | −0.797759 | − | 0.602977i | \(-0.793981\pi\) | ||||
−0.797759 | + | 0.602977i | \(0.793981\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.6101i | 0.368064i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.273633 | 0.00866606 | 0.00433303 | − | 0.999991i | \(-0.498621\pi\) | ||||
0.00433303 | + | 0.999991i | \(0.498621\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2340.2.c.d.181.1 | 6 | ||
3.2 | odd | 2 | 260.2.f.a.181.6 | yes | 6 | ||
12.11 | even | 2 | 1040.2.k.c.961.2 | 6 | |||
13.12 | even | 2 | inner | 2340.2.c.d.181.6 | 6 | ||
15.2 | even | 4 | 1300.2.d.d.649.1 | 6 | |||
15.8 | even | 4 | 1300.2.d.c.649.6 | 6 | |||
15.14 | odd | 2 | 1300.2.f.e.701.2 | 6 | |||
39.5 | even | 4 | 3380.2.a.n.1.3 | 3 | |||
39.8 | even | 4 | 3380.2.a.m.1.3 | 3 | |||
39.38 | odd | 2 | 260.2.f.a.181.5 | ✓ | 6 | ||
156.155 | even | 2 | 1040.2.k.c.961.1 | 6 | |||
195.38 | even | 4 | 1300.2.d.d.649.6 | 6 | |||
195.77 | even | 4 | 1300.2.d.c.649.1 | 6 | |||
195.194 | odd | 2 | 1300.2.f.e.701.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.f.a.181.5 | ✓ | 6 | 39.38 | odd | 2 | ||
260.2.f.a.181.6 | yes | 6 | 3.2 | odd | 2 | ||
1040.2.k.c.961.1 | 6 | 156.155 | even | 2 | |||
1040.2.k.c.961.2 | 6 | 12.11 | even | 2 | |||
1300.2.d.c.649.1 | 6 | 195.77 | even | 4 | |||
1300.2.d.c.649.6 | 6 | 15.8 | even | 4 | |||
1300.2.d.d.649.1 | 6 | 15.2 | even | 4 | |||
1300.2.d.d.649.6 | 6 | 195.38 | even | 4 | |||
1300.2.f.e.701.1 | 6 | 195.194 | odd | 2 | |||
1300.2.f.e.701.2 | 6 | 15.14 | odd | 2 | |||
2340.2.c.d.181.1 | 6 | 1.1 | even | 1 | trivial | ||
2340.2.c.d.181.6 | 6 | 13.12 | even | 2 | inner | ||
3380.2.a.m.1.3 | 3 | 39.8 | even | 4 | |||
3380.2.a.n.1.3 | 3 | 39.5 | even | 4 |