Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(127,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.b (of order \(2\), degree \(1\), not 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: | \(62.7794529086\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(1.28897 - 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.127 |
Dual form | 2304.3.b.r.127.8 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 8.11993i | − 1.62399i | −0.583667 | − | 0.811993i | \(-0.698383\pi\) | ||||
0.583667 | − | 0.811993i | \(-0.301617\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 9.48331i | − 1.35476i | −0.735634 | − | 0.677380i | \(-0.763115\pi\) | ||||
0.735634 | − | 0.677380i | \(-0.236885\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.5830 | −0.962091 | −0.481046 | − | 0.876696i | \(-0.659743\pi\) | ||||
−0.481046 | + | 0.876696i | \(0.659743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 20.9666i | − 1.61282i | −0.591358 | − | 0.806409i | \(-0.701408\pi\) | ||||
0.591358 | − | 0.806409i | \(-0.298592\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.92615 | 0.289774 | 0.144887 | − | 0.989448i | \(-0.453718\pi\) | ||||
0.144887 | + | 0.989448i | \(0.453718\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.9666 | −1.41930 | −0.709648 | − | 0.704556i | \(-0.751146\pi\) | ||||
−0.709648 | + | 0.704556i | \(0.751146\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 43.7934i | − 1.90406i | −0.306001 | − | 0.952031i | \(-0.598991\pi\) | ||||
0.306001 | − | 0.952031i | \(-0.401009\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −40.9333 | −1.63733 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14.5075i | 0.500258i | 0.968212 | + | 0.250129i | \(0.0804731\pi\) | ||||
−0.968212 | + | 0.250129i | \(0.919527\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 25.4833i | 0.822042i | 0.911626 | + | 0.411021i | \(0.134828\pi\) | ||||
−0.911626 | + | 0.411021i | \(0.865172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −77.0038 | −2.20011 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 12.9666i | − 0.350449i | −0.984528 | − | 0.175225i | \(-0.943935\pi\) | ||||
0.984528 | − | 0.175225i | \(-0.0560652\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 50.1810 | 1.22393 | 0.611963 | − | 0.790886i | \(-0.290380\pi\) | ||||
0.611963 | + | 0.790886i | \(0.290380\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.03337 | −0.117055 | −0.0585276 | − | 0.998286i | \(-0.518641\pi\) | ||||
−0.0585276 | + | 0.998286i | \(0.518641\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 40.8706i | − 0.869588i | −0.900530 | − | 0.434794i | \(-0.856821\pi\) | ||||
0.900530 | − | 0.434794i | \(-0.143179\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −40.9333 | −0.835373 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 27.2826i | − 0.514766i | −0.966309 | − | 0.257383i | \(-0.917140\pi\) | ||||
0.966309 | − | 0.257383i | \(-0.0828602\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 85.9333i | 1.56242i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 24.0888 | 0.408285 | 0.204143 | − | 0.978941i | \(-0.434559\pi\) | ||||
0.204143 | + | 0.978941i | \(0.434559\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 28.9666i | 0.474863i | 0.971404 | + | 0.237431i | \(0.0763055\pi\) | ||||
−0.971404 | + | 0.237431i | \(0.923695\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −170.248 | −2.61919 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 65.7998 | 0.982086 | 0.491043 | − | 0.871135i | \(-0.336616\pi\) | ||||
0.491043 | + | 0.871135i | \(0.336616\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 90.5097i | − 1.27478i | −0.770540 | − | 0.637392i | \(-0.780013\pi\) | ||||
0.770540 | − | 0.637392i | \(-0.219987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 127.800 | 1.75068 | 0.875341 | − | 0.483506i | \(-0.160637\pi\) | ||||
0.875341 | + | 0.483506i | \(0.160637\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 100.362i | 1.30340i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 35.5501i | 0.450001i | 0.974359 | + | 0.225000i | \(0.0722383\pi\) | ||||
−0.974359 | + | 0.225000i | \(0.927762\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −101.093 | −1.21798 | −0.608992 | − | 0.793176i | \(-0.708426\pi\) | ||||
−0.608992 | + | 0.793176i | \(0.708426\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 40.0000i | − 0.470588i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.6979 | 0.176381 | 0.0881906 | − | 0.996104i | \(-0.471892\pi\) | ||||
0.0881906 | + | 0.996104i | \(0.471892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −198.833 | −2.18498 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 218.967i | 2.30492i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 73.8665 | 0.761510 | 0.380755 | − | 0.924676i | \(-0.375664\pi\) | ||||
0.380755 | + | 0.924676i | \(0.375664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 114.869i | − 1.13732i | −0.822572 | − | 0.568661i | \(-0.807462\pi\) | ||||
0.822572 | − | 0.568661i | \(-0.192538\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 121.483i | 1.17945i | 0.807604 | + | 0.589725i | \(0.200764\pi\) | ||||
−0.807604 | + | 0.589725i | \(0.799236\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 156.931 | 1.46664 | 0.733320 | − | 0.679883i | \(-0.237970\pi\) | ||||
0.733320 | + | 0.679883i | \(0.237970\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 114.766i | 1.05290i | 0.850205 | + | 0.526451i | \(0.176478\pi\) | ||||
−0.850205 | + | 0.526451i | \(0.823522\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 179.180 | 1.58567 | 0.792834 | − | 0.609438i | \(-0.208605\pi\) | ||||
0.792834 | + | 0.609438i | \(0.208605\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −355.600 | −3.09217 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 46.7162i | − 0.392573i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.0743802 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 129.377i | 1.03502i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 96.5834i | 0.760499i | 0.924884 | + | 0.380250i | \(0.124162\pi\) | ||||
−0.924884 | + | 0.380250i | \(0.875838\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 169.328 | 1.29258 | 0.646290 | − | 0.763092i | \(-0.276319\pi\) | ||||
0.646290 | + | 0.763092i | \(0.276319\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 255.733i | 1.92280i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 235.207 | 1.71684 | 0.858420 | − | 0.512948i | \(-0.171447\pi\) | ||||
0.858420 | + | 0.512948i | \(0.171447\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −30.2002 | −0.217268 | −0.108634 | − | 0.994082i | \(-0.534648\pi\) | ||||
−0.108634 | + | 0.994082i | \(0.534648\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 221.890i | 1.55168i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 117.800 | 0.812412 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 170.519i | − 1.14442i | −0.820107 | − | 0.572210i | \(-0.806086\pi\) | ||||
0.820107 | − | 0.572210i | \(-0.193914\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 87.1496i | − 0.577150i | −0.957457 | − | 0.288575i | \(-0.906819\pi\) | ||||
0.957457 | − | 0.288575i | \(-0.0931814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 206.923 | 1.33499 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 98.7664i | − 0.629085i | −0.949243 | − | 0.314543i | \(-0.898149\pi\) | ||||
0.949243 | − | 0.314543i | \(-0.101851\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −415.307 | −2.57955 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −67.2336 | −0.412476 | −0.206238 | − | 0.978502i | \(-0.566122\pi\) | ||||
−0.206238 | + | 0.978502i | \(0.566122\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 216.044i | 1.29368i | 0.762626 | + | 0.646839i | \(0.223910\pi\) | ||||
−0.762626 | + | 0.646839i | \(0.776090\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −270.600 | −1.60118 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 118.876i | − 0.687145i | −0.939126 | − | 0.343573i | \(-0.888363\pi\) | ||||
0.939126 | − | 0.343573i | \(-0.111637\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 388.183i | 2.21819i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.0888 | −0.134574 | −0.0672872 | − | 0.997734i | \(-0.521434\pi\) | ||||
−0.0672872 | + | 0.997734i | \(0.521434\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 131.033i | − 0.723941i | −0.932189 | − | 0.361971i | \(-0.882104\pi\) | ||||
0.932189 | − | 0.361971i | \(-0.117896\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −105.288 | −0.569125 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −52.1335 | −0.278789 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 128.457i | − 0.672552i | −0.941763 | − | 0.336276i | \(-0.890832\pi\) | ||||
0.941763 | − | 0.336276i | \(-0.109168\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −167.666 | −0.868737 | −0.434369 | − | 0.900735i | \(-0.643028\pi\) | ||||
−0.434369 | + | 0.900735i | \(0.643028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 122.341i | 0.621020i | 0.950570 | + | 0.310510i | \(0.100500\pi\) | ||||
−0.950570 | + | 0.310510i | \(0.899500\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 363.283i | 1.82554i | 0.408470 | + | 0.912772i | \(0.366062\pi\) | ||||
−0.408470 | + | 0.912772i | \(0.633938\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 137.579 | 0.677729 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 407.466i | − 1.98764i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 285.388 | 1.36549 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −138.067 | −0.654345 | −0.327172 | − | 0.944965i | \(-0.606096\pi\) | ||||
−0.327172 | + | 0.944965i | \(0.606096\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 40.8706i | 0.190096i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 241.666 | 1.11367 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 103.285i | − 0.467352i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 264.316i | 1.18528i | 0.805469 | + | 0.592638i | \(0.201913\pi\) | ||||
−0.805469 | + | 0.592638i | \(0.798087\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −243.409 | −1.07229 | −0.536143 | − | 0.844127i | \(-0.680119\pi\) | ||||
−0.536143 | + | 0.844127i | \(0.680119\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 234.232i | − 1.02285i | −0.859328 | − | 0.511425i | \(-0.829118\pi\) | ||||
0.859328 | − | 0.511425i | \(-0.170882\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 35.4025 | 0.151942 | 0.0759711 | − | 0.997110i | \(-0.475794\pi\) | ||||
0.0759711 | + | 0.997110i | \(0.475794\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −331.867 | −1.41220 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 32.1022i | 0.134319i | 0.997742 | + | 0.0671594i | \(0.0213936\pi\) | ||||
−0.997742 | + | 0.0671594i | \(0.978606\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −103.800 | −0.430704 | −0.215352 | − | 0.976536i | \(-0.569090\pi\) | ||||
−0.215352 | + | 0.976536i | \(0.569090\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 332.375i | 1.35663i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 565.399i | 2.28907i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −312.753 | −1.24603 | −0.623014 | − | 0.782211i | \(-0.714092\pi\) | ||||
−0.623014 | + | 0.782211i | \(0.714092\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 463.466i | 1.83188i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −33.5636 | −0.130598 | −0.0652988 | − | 0.997866i | \(-0.520800\pi\) | ||||
−0.0652988 | + | 0.997866i | \(0.520800\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −122.967 | −0.474775 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 338.656i | − 1.28767i | −0.765166 | − | 0.643833i | \(-0.777343\pi\) | ||||
0.765166 | − | 0.643833i | \(-0.222657\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −221.533 | −0.835973 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 310.832i | 1.15551i | 0.816211 | + | 0.577754i | \(0.196071\pi\) | ||||
−0.816211 | + | 0.577754i | \(0.803929\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 266.749i | − 0.984314i | −0.870506 | − | 0.492157i | \(-0.836209\pi\) | ||||
0.870506 | − | 0.492157i | \(-0.163791\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 433.197 | 1.57526 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 458.766i | − 1.65620i | −0.560583 | − | 0.828098i | \(-0.689423\pi\) | ||||
0.560583 | − | 0.828098i | \(-0.310577\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −395.602 | −1.40784 | −0.703919 | − | 0.710281i | \(-0.748568\pi\) | ||||
−0.703919 | + | 0.710281i | \(0.748568\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −375.733 | −1.32768 | −0.663839 | − | 0.747875i | \(-0.731074\pi\) | ||||
−0.663839 | + | 0.747875i | \(0.731074\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 475.882i | − 1.65813i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −264.733 | −0.916031 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 9.74572i | − 0.0332619i | −0.999862 | − | 0.0166309i | \(-0.994706\pi\) | ||||
0.999862 | − | 0.0166309i | \(-0.00529403\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 195.600i | − 0.663049i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −918.201 | −3.07090 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 47.7330i | 0.158582i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 235.207 | 0.771170 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 89.5328 | 0.291638 | 0.145819 | − | 0.989311i | \(-0.453418\pi\) | ||||
0.145819 | + | 0.989311i | \(0.453418\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 274.452i | 0.882482i | 0.897389 | + | 0.441241i | \(0.145462\pi\) | ||||
−0.897389 | + | 0.441241i | \(0.854538\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 151.666 | 0.484557 | 0.242278 | − | 0.970207i | \(-0.422105\pi\) | ||||
0.242278 | + | 0.970207i | \(0.422105\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 201.914i | − 0.636954i | −0.947931 | − | 0.318477i | \(-0.896829\pi\) | ||||
0.947931 | − | 0.318477i | \(-0.103171\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 153.533i | − 0.481294i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −132.842 | −0.411275 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 858.232i | 2.64072i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −387.589 | −1.17808 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −195.600 | −0.590935 | −0.295468 | − | 0.955353i | \(-0.595475\pi\) | ||||
−0.295468 | + | 0.955353i | \(0.595475\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 534.290i | − 1.59489i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.9333 | 0.0710186 | 0.0355093 | − | 0.999369i | \(-0.488695\pi\) | ||||
0.0355093 | + | 0.999369i | \(0.488695\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 269.690i | − 0.790880i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 76.4994i | − 0.223030i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −139.796 | −0.402869 | −0.201435 | − | 0.979502i | \(-0.564560\pi\) | ||||
−0.201435 | + | 0.979502i | \(0.564560\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.2336i | 0.0608412i | 0.999537 | + | 0.0304206i | \(0.00968468\pi\) | ||||
−0.999537 | + | 0.0304206i | \(0.990315\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 515.669 | 1.46082 | 0.730409 | − | 0.683010i | \(-0.239329\pi\) | ||||
0.730409 | + | 0.683010i | \(0.239329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −734.932 | −2.07023 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 253.992i | − 0.707499i | −0.935340 | − | 0.353749i | \(-0.884907\pi\) | ||||
0.935340 | − | 0.353749i | \(-0.115093\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 366.199 | 1.01440 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1037.73i | − 2.84308i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 384.682i | 1.04818i | 0.851663 | + | 0.524090i | \(0.175595\pi\) | ||||
−0.851663 | + | 0.524090i | \(0.824405\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −258.730 | −0.697384 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 197.501i | − 0.529492i | −0.964318 | − | 0.264746i | \(-0.914712\pi\) | ||||
0.964318 | − | 0.264746i | \(-0.0852881\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 304.173 | 0.806825 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 234.433 | 0.618556 | 0.309278 | − | 0.950972i | \(-0.399913\pi\) | ||||
0.309278 | + | 0.950972i | \(0.399913\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 315.322i | − 0.823296i | −0.911343 | − | 0.411648i | \(-0.864953\pi\) | ||||
0.911343 | − | 0.411648i | \(-0.135047\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 814.932 | 2.11671 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 486.760i | 1.25131i | 0.780099 | + | 0.625656i | \(0.215169\pi\) | ||||
−0.780099 | + | 0.625656i | \(0.784831\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 215.733i | − 0.551747i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 288.664 | 0.730795 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 115.300i | − 0.290429i | −0.989400 | − | 0.145215i | \(-0.953613\pi\) | ||||
0.989400 | − | 0.145215i | \(-0.0463872\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −52.3487 | −0.130545 | −0.0652727 | − | 0.997867i | \(-0.520792\pi\) | ||||
−0.0652727 | + | 0.997867i | \(0.520792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 534.299 | 1.32580 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 137.226i | 0.337164i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −345.333 | −0.844334 | −0.422167 | − | 0.906518i | \(-0.638730\pi\) | ||||
−0.422167 | + | 0.906518i | \(0.638730\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 228.442i | − 0.553128i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 820.865i | 1.97799i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 644.151 | 1.53735 | 0.768676 | − | 0.639638i | \(-0.220916\pi\) | ||||
0.768676 | + | 0.639638i | \(0.220916\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 756.700i | 1.79739i | 0.438578 | + | 0.898693i | \(0.355482\pi\) | ||||
−0.438578 | + | 0.898693i | \(0.644518\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −201.643 | −0.474455 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 274.700 | 0.643325 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 49.6391i | 0.115172i | 0.998341 | + | 0.0575859i | \(0.0183403\pi\) | ||||
−0.998341 | + | 0.0575859i | \(0.981660\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 581.066 | 1.34195 | 0.670976 | − | 0.741479i | \(-0.265875\pi\) | ||||
0.670976 | + | 0.741479i | \(0.265875\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1180.96i | 2.70243i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 274.482i | 0.625244i | 0.949878 | + | 0.312622i | \(0.101207\pi\) | ||||
−0.949878 | + | 0.312622i | \(0.898793\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −466.760 | −1.05364 | −0.526818 | − | 0.849978i | \(-0.676615\pi\) | ||||
−0.526818 | + | 0.849978i | \(0.676615\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 127.466i | − 0.286441i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 479.347 | 1.06759 | 0.533794 | − | 0.845615i | \(-0.320766\pi\) | ||||
0.533794 | + | 0.845615i | \(0.320766\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −531.066 | −1.17753 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1614.51i | 3.54838i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 405.600 | 0.887526 | 0.443763 | − | 0.896144i | \(-0.353643\pi\) | ||||
0.443763 | + | 0.896144i | \(0.353643\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 636.171i | 1.37998i | 0.723819 | + | 0.689990i | \(0.242385\pi\) | ||||
−0.723819 | + | 0.689990i | \(0.757615\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 323.016i | − 0.697659i | −0.937186 | − | 0.348830i | \(-0.886579\pi\) | ||||
0.937186 | − | 0.348830i | \(-0.113421\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −128.104 | −0.274313 | −0.137157 | − | 0.990549i | \(-0.543796\pi\) | ||||
−0.137157 | + | 0.990549i | \(0.543796\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 624.000i | − 1.33049i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 53.2682 | 0.112618 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1103.83 | 2.32386 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 67.1272i | 0.140140i | 0.997542 | + | 0.0700701i | \(0.0223223\pi\) | ||||
−0.997542 | + | 0.0700701i | \(0.977678\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −271.867 | −0.565211 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 599.791i | − 1.23668i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 180.183i | 0.369986i | 0.982740 | + | 0.184993i | \(0.0592262\pi\) | ||||
−0.982740 | + | 0.184993i | \(0.940774\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 423.320 | 0.862159 | 0.431080 | − | 0.902314i | \(-0.358133\pi\) | ||||
0.431080 | + | 0.902314i | \(0.358133\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 71.4661i | 0.144962i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −858.332 | −1.72703 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 830.932 | 1.66519 | 0.832597 | − | 0.553879i | \(-0.186853\pi\) | ||||
0.832597 | + | 0.553879i | \(0.186853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 359.116i | − 0.713948i | −0.934114 | − | 0.356974i | \(-0.883808\pi\) | ||||
0.934114 | − | 0.356974i | \(-0.116192\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −932.732 | −1.84699 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 43.3093i | 0.0850870i | 0.999095 | + | 0.0425435i | \(0.0135461\pi\) | ||||
−0.999095 | + | 0.0425435i | \(0.986454\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 1211.97i | − 2.37175i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 986.436 | 1.91541 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 432.534i | 0.836623i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −426.407 | −0.818440 | −0.409220 | − | 0.912436i | \(-0.634199\pi\) | ||||
−0.409220 | + | 0.912436i | \(0.634199\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −384.366 | −0.734925 | −0.367463 | − | 0.930038i | \(-0.619773\pi\) | ||||
−0.367463 | + | 0.930038i | \(0.619773\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 125.535i | 0.238206i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1388.86 | −2.62545 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1052.13i | − 1.97397i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1274.26i | − 2.38180i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 433.197 | 0.803705 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 403.033i | 0.744979i | 0.928037 | + | 0.372489i | \(0.121496\pi\) | ||||
−0.928037 | + | 0.372489i | \(0.878504\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 931.895 | 1.70990 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1066.43 | 1.94960 | 0.974801 | − | 0.223075i | \(-0.0716094\pi\) | ||||
0.974801 | + | 0.223075i | \(0.0716094\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 391.218i | − 0.710015i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 337.132 | 0.609643 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 221.406i | − 0.397497i | −0.980051 | − | 0.198749i | \(-0.936312\pi\) | ||||
0.980051 | − | 0.198749i | \(-0.0636877\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 105.533i | 0.188789i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 747.764 | 1.32818 | 0.664089 | − | 0.747654i | \(-0.268820\pi\) | ||||
0.664089 | + | 0.747654i | \(0.268820\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1454.93i | − 2.57510i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −489.199 | −0.859752 | −0.429876 | − | 0.902888i | \(-0.641443\pi\) | ||||
−0.429876 | + | 0.902888i | \(0.641443\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −784.198 | −1.37338 | −0.686688 | − | 0.726952i | \(-0.740936\pi\) | ||||
−0.686688 | + | 0.726952i | \(0.740936\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1792.61i | 3.11758i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −239.132 | −0.414441 | −0.207220 | − | 0.978294i | \(-0.566442\pi\) | ||||
−0.207220 | + | 0.978294i | \(0.566442\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 958.694i | 1.65008i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 288.732i | 0.495252i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −84.6640 | −0.144232 | −0.0721159 | − | 0.997396i | \(-0.522975\pi\) | ||||
−0.0721159 | + | 0.997396i | \(0.522975\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 687.199i | − 1.16672i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1135.38 | −1.91463 | −0.957317 | − | 0.289041i | \(-0.906664\pi\) | ||||
−0.957317 | + | 0.289041i | \(0.906664\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −379.333 | −0.637534 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 411.678i | 0.687275i | 0.939102 | + | 0.343638i | \(0.111659\pi\) | ||||
−0.939102 | + | 0.343638i | \(0.888341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 463.666 | 0.771491 | 0.385746 | − | 0.922605i | \(-0.373944\pi\) | ||||
0.385746 | + | 0.922605i | \(0.373944\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 73.0794i | 0.120792i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 803.016i | − 1.32293i | −0.749978 | − | 0.661463i | \(-0.769936\pi\) | ||||
0.749978 | − | 0.661463i | \(-0.230064\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −856.919 | −1.40249 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 459.567i | 0.749702i | 0.927085 | + | 0.374851i | \(0.122306\pi\) | ||||
−0.927085 | + | 0.374851i | \(0.877694\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −370.052 | −0.599760 | −0.299880 | − | 0.953977i | \(-0.596947\pi\) | ||||
−0.299880 | + | 0.953977i | \(0.596947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.7987 | −0.0174453 | −0.00872267 | − | 0.999962i | \(-0.502777\pi\) | ||||
−0.00872267 | + | 0.999962i | \(0.502777\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 148.868i | − 0.238954i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27.2002 | 0.0435204 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 63.8756i | − 0.101551i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 63.9505i | − 0.101348i | −0.998715 | − | 0.0506739i | \(-0.983863\pi\) | ||||
0.998715 | − | 0.0506739i | \(-0.0161369\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 784.251 | 1.23504 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 858.232i | 1.34730i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 772.748 | 1.20554 | 0.602768 | − | 0.797917i | \(-0.294065\pi\) | ||||
0.602768 | + | 0.797917i | \(0.294065\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.3671 | 0.0363407 | 0.0181704 | − | 0.999835i | \(-0.494216\pi\) | ||||
0.0181704 | + | 0.999835i | \(0.494216\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 686.130i | − 1.06048i | −0.847848 | − | 0.530239i | \(-0.822102\pi\) | ||||
0.847848 | − | 0.530239i | \(-0.177898\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −254.932 | −0.392808 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 899.686i | 1.37777i | 0.724869 | + | 0.688887i | \(0.241900\pi\) | ||||
−0.724869 | + | 0.688887i | \(0.758100\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1374.93i | − 2.09913i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −217.506 | −0.330054 | −0.165027 | − | 0.986289i | \(-0.552771\pi\) | ||||
−0.165027 | + | 0.986289i | \(0.552771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 829.234i | − 1.25451i | −0.778812 | − | 0.627257i | \(-0.784178\pi\) | ||||
0.778812 | − | 0.627257i | \(-0.215822\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2076.53 | 3.12261 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 635.333 | 0.952523 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 306.554i | − 0.456861i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −234.400 | −0.348292 | −0.174146 | − | 0.984720i | \(-0.555716\pi\) | ||||
−0.174146 | + | 0.984720i | \(0.555716\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 772.690i | − 1.14134i | −0.821178 | − | 0.570672i | \(-0.806683\pi\) | ||||
0.821178 | − | 0.570672i | \(-0.193317\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 700.499i | − 1.03166i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 640.522 | 0.937806 | 0.468903 | − | 0.883250i | \(-0.344649\pi\) | ||||
0.468903 | + | 0.883250i | \(0.344649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1909.86i | − 2.78812i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −572.024 | −0.830224 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 973.300 | 1.40854 | 0.704269 | − | 0.709933i | \(-0.251275\pi\) | ||||
0.704269 | + | 0.709933i | \(0.251275\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 245.224i | 0.352840i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 247.199 | 0.354662 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 759.045i | 1.08280i | 0.840764 | + | 0.541401i | \(0.182106\pi\) | ||||
−0.840764 | + | 0.541401i | \(0.817894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 349.666i | 0.497392i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1089.34 | −1.54080 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 334.034i | 0.471135i | 0.971858 | + | 0.235567i | \(0.0756948\pi\) | ||||
−0.971858 | + | 0.235567i | \(0.924305\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1116.00 | 1.56522 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1801.73 | 2.51990 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 318.196i | − 0.442554i | −0.975211 | − | 0.221277i | \(-0.928977\pi\) | ||||
0.975211 | − | 0.221277i | \(-0.0710225\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1152.06 | 1.59787 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 593.839i | − 0.819088i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 877.617i | − 1.20718i | −0.797296 | − | 0.603588i | \(-0.793737\pi\) | ||||
0.797296 | − | 0.603588i | \(-0.206263\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.7951 | −0.0339195 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1001.70i | 1.36657i | 0.730150 | + | 0.683287i | \(0.239450\pi\) | ||||
−0.730150 | + | 0.683287i | \(0.760550\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −696.359 | −0.944857 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 648.999 | 0.878212 | 0.439106 | − | 0.898435i | \(-0.355295\pi\) | ||||
0.439106 | + | 0.898435i | \(0.355295\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 411.678i | − 0.554075i | −0.960859 | − | 0.277038i | \(-0.910647\pi\) | ||||
0.960859 | − | 0.277038i | \(-0.0893526\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1384.60 | −1.85852 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1488.22i | − 1.98694i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 471.882i | 0.628338i | 0.949367 | + | 0.314169i | \(0.101726\pi\) | ||||
−0.949367 | + | 0.314169i | \(0.898274\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −707.649 | −0.937283 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 164.101i | − 0.216778i | −0.994109 | − | 0.108389i | \(-0.965431\pi\) | ||||
0.994109 | − | 0.108389i | \(-0.0345693\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 331.562 | 0.435693 | 0.217846 | − | 0.975983i | \(-0.430097\pi\) | ||||
0.217846 | + | 0.975983i | \(0.430097\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1088.37 | 1.42643 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 505.061i | − 0.658489i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 847.533 | 1.10212 | 0.551062 | − | 0.834465i | \(-0.314223\pi\) | ||||
0.551062 | + | 0.834465i | \(0.314223\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 980.557i | − 1.26851i | −0.773125 | − | 0.634254i | \(-0.781307\pi\) | ||||
0.773125 | − | 0.634254i | \(-0.218693\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1043.12i | − 1.34596i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1353.21 | −1.73711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 957.864i | 1.22646i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −801.976 | −1.02163 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −335.832 | −0.426724 | −0.213362 | − | 0.976973i | \(-0.568441\pi\) | ||||
−0.213362 | + | 0.976973i | \(0.568441\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 1699.22i | − 2.14820i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 607.333 | 0.765867 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 283.114i | − 0.355224i | −0.984101 | − | 0.177612i | \(-0.943163\pi\) | ||||
0.984101 | − | 0.177612i | \(-0.0568372\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 201.335i | − 0.251984i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1352.51 | −1.68432 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3372.26i | 4.18915i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −117.308 | −0.145004 | −0.0725019 | − | 0.997368i | \(-0.523098\pi\) | ||||
−0.0725019 | + | 0.997368i | \(0.523098\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1235.43 | 1.52334 | 0.761672 | − | 0.647963i | \(-0.224379\pi\) | ||||
0.761672 | + | 0.647963i | \(0.224379\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 545.932i | 0.669855i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 135.733 | 0.166136 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 823.364i | 1.00288i | 0.865192 | + | 0.501440i | \(0.167196\pi\) | ||||
−0.865192 | + | 0.501440i | \(0.832804\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 743.249i | 0.903097i | 0.892247 | + | 0.451548i | \(0.149128\pi\) | ||||
−0.892247 | + | 0.451548i | \(0.850872\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 542.352 | 0.655806 | 0.327903 | − | 0.944711i | \(-0.393658\pi\) | ||||
0.327903 | + | 0.944711i | \(0.393658\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 906.564i | − 1.09356i | −0.837275 | − | 0.546782i | \(-0.815853\pi\) | ||||
0.837275 | − | 0.546782i | \(-0.184147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −201.643 | −0.242069 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1754.26 | 2.10092 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1015.97i | − 1.21093i | −0.795873 | − | 0.605464i | \(-0.792988\pi\) | ||||
0.795873 | − | 0.605464i | \(-0.207012\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 630.533 | 0.749742 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2197.25i | 2.60030i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 85.3498i | 0.100767i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −567.853 | −0.667277 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 102.568i | − 0.120244i | −0.998191 | − | 0.0601222i | \(-0.980851\pi\) | ||||
0.998191 | − | 0.0601222i | \(-0.0191490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1081.85 | −1.26237 | −0.631183 | − | 0.775634i | \(-0.717430\pi\) | ||||
−0.631183 | + | 0.775634i | \(0.717430\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −597.231 | −0.695264 | −0.347632 | − | 0.937631i | \(-0.613014\pi\) | ||||
−0.347632 | + | 0.937631i | \(0.613014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 537.261i | 0.622551i | 0.950320 | + | 0.311275i | \(0.100756\pi\) | ||||
−0.950320 | + | 0.311275i | \(0.899244\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −965.266 | −1.11591 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 376.226i | − 0.432942i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1379.60i | − 1.58393i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1226.92 | 1.40220 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 395.899i | 0.451424i | 0.974194 | + | 0.225712i | \(0.0724708\pi\) | ||||
−0.974194 | + | 0.225712i | \(0.927529\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −289.066 | −0.328111 | −0.164056 | − | 0.986451i | \(-0.552458\pi\) | ||||
−0.164056 | + | 0.986451i | \(0.552458\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1548.96 | −1.75421 | −0.877103 | − | 0.480302i | \(-0.840527\pi\) | ||||
−0.877103 | + | 0.480302i | \(0.840527\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1544.41i | − 1.74116i | −0.492023 | − | 0.870582i | \(-0.663743\pi\) | ||||
0.492023 | − | 0.870582i | \(-0.336257\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 915.931 | 1.03029 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1102.14i | 1.23420i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 195.600i | 0.218547i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −369.699 | −0.411233 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 134.398i | − 0.149166i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1063.98 | −1.17567 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −472.831 | −0.521313 | −0.260657 | − | 0.965432i | \(-0.583939\pi\) | ||||
−0.260657 | + | 0.965432i | \(0.583939\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1094.84i | 1.20180i | 0.799326 | + | 0.600898i | \(0.205190\pi\) | ||||
−0.799326 | + | 0.600898i | \(0.794810\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1069.86 | 1.17181 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1605.79i | − 1.75114i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 152.850i | 0.166323i | 0.996536 | + | 0.0831613i | \(0.0265017\pi\) | ||||
−0.996536 | + | 0.0831613i | \(0.973498\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1897.68 | −2.05599 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 530.766i | 0.573802i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 63.7112 | 0.0685804 | 0.0342902 | − | 0.999412i | \(-0.489083\pi\) | ||||
0.0342902 | + | 0.999412i | \(0.489083\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1103.83 | 1.18564 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 423.320i | 0.452749i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1320.67 | −1.40946 | −0.704731 | − | 0.709475i | \(-0.748932\pi\) | ||||
−0.704731 | + | 0.709475i | \(0.748932\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 5.41027i | − 0.00574949i | −0.999996 | − | 0.00287475i | \(-0.999085\pi\) | ||||
0.999996 | − | 0.00287475i | \(-0.000915061\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2197.60i | − 2.33043i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −83.9577 | −0.0886565 | −0.0443283 | − | 0.999017i | \(-0.514115\pi\) | ||||
−0.0443283 | + | 0.999017i | \(0.514115\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 2679.53i | − 2.82353i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1577.15 | 1.65494 | 0.827468 | − | 0.561513i | \(-0.189780\pi\) | ||||
0.827468 | + | 0.561513i | \(0.189780\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1043.07 | −1.09222 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2230.54i | − 2.32590i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 311.601 | 0.324246 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1361.44i | 1.41082i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 278.616i | 0.288124i | 0.989569 | + | 0.144062i | \(0.0460164\pi\) | ||||
−0.989569 | + | 0.144062i | \(0.953984\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 380.684 | 0.392053 | 0.196027 | − | 0.980599i | \(-0.437196\pi\) | ||||
0.196027 | + | 0.980599i | \(0.437196\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 286.398i | 0.294346i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1630.75 | 1.66914 | 0.834571 | − | 0.550901i | \(-0.185716\pi\) | ||||
0.834571 | + | 0.550901i | \(0.185716\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −166.131 | −0.169695 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 928.382i | 0.944437i | 0.881482 | + | 0.472219i | \(0.156547\pi\) | ||||
−0.881482 | + | 0.472219i | \(0.843453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 993.399 | 1.00853 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 220.429i | 0.222880i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1399.98i | − 1.41269i | −0.707865 | − | 0.706347i | \(-0.750342\pi\) | ||||
0.707865 | − | 0.706347i | \(-0.249658\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2949.83 | 2.96466 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 595.567i | 0.597359i | 0.954353 | + | 0.298680i | \(0.0965462\pi\) | ||||
−0.954353 | + | 0.298680i | \(0.903454\pi\) | |||||||
\(998\) | 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 | 2304.3.b.r.127.1 | 8 | ||
3.2 | odd | 2 | inner | 2304.3.b.r.127.7 | 8 | ||
4.3 | odd | 2 | 2304.3.b.s.127.2 | 8 | |||
8.3 | odd | 2 | inner | 2304.3.b.r.127.8 | 8 | ||
8.5 | even | 2 | 2304.3.b.s.127.7 | 8 | |||
12.11 | even | 2 | 2304.3.b.s.127.8 | 8 | |||
16.3 | odd | 4 | 1152.3.g.e.127.1 | yes | 8 | ||
16.5 | even | 4 | 1152.3.g.d.127.8 | yes | 8 | ||
16.11 | odd | 4 | 1152.3.g.d.127.7 | yes | 8 | ||
16.13 | even | 4 | 1152.3.g.e.127.2 | yes | 8 | ||
24.5 | odd | 2 | 2304.3.b.s.127.1 | 8 | |||
24.11 | even | 2 | inner | 2304.3.b.r.127.2 | 8 | ||
48.5 | odd | 4 | 1152.3.g.d.127.2 | yes | 8 | ||
48.11 | even | 4 | 1152.3.g.d.127.1 | ✓ | 8 | ||
48.29 | odd | 4 | 1152.3.g.e.127.8 | yes | 8 | ||
48.35 | even | 4 | 1152.3.g.e.127.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.g.d.127.1 | ✓ | 8 | 48.11 | even | 4 | ||
1152.3.g.d.127.2 | yes | 8 | 48.5 | odd | 4 | ||
1152.3.g.d.127.7 | yes | 8 | 16.11 | odd | 4 | ||
1152.3.g.d.127.8 | yes | 8 | 16.5 | even | 4 | ||
1152.3.g.e.127.1 | yes | 8 | 16.3 | odd | 4 | ||
1152.3.g.e.127.2 | yes | 8 | 16.13 | even | 4 | ||
1152.3.g.e.127.7 | yes | 8 | 48.35 | even | 4 | ||
1152.3.g.e.127.8 | yes | 8 | 48.29 | odd | 4 | ||
2304.3.b.r.127.1 | 8 | 1.1 | even | 1 | trivial | ||
2304.3.b.r.127.2 | 8 | 24.11 | even | 2 | inner | ||
2304.3.b.r.127.7 | 8 | 3.2 | odd | 2 | inner | ||
2304.3.b.r.127.8 | 8 | 8.3 | odd | 2 | inner | ||
2304.3.b.s.127.1 | 8 | 24.5 | odd | 2 | |||
2304.3.b.s.127.2 | 8 | 4.3 | odd | 2 | |||
2304.3.b.s.127.7 | 8 | 8.5 | even | 2 | |||
2304.3.b.s.127.8 | 8 | 12.11 | even | 2 |