Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(127,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.g (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: | \(31.3897264543\) |
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: | \( 2^{22} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.8 | ||
Root | \(-0.581861 - 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.127 |
Dual form | 1152.3.g.d.127.7 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 8.11993 | 1.62399 | 0.811993 | − | 0.583667i | \(-0.198383\pi\) | ||||
0.811993 | + | 0.583667i | \(0.198383\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.48331i | 1.35476i | 0.735634 | + | 0.677380i | \(0.236885\pi\) | ||||
−0.735634 | + | 0.677380i | \(0.763115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 10.5830i | − 0.962091i | −0.876696 | − | 0.481046i | \(-0.840257\pi\) | ||||
0.876696 | − | 0.481046i | \(-0.159743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.9666 | −1.61282 | −0.806409 | − | 0.591358i | \(-0.798592\pi\) | ||||
−0.806409 | + | 0.591358i | \(0.798592\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 26.9666i | 1.41930i | 0.704556 | + | 0.709648i | \(0.251146\pi\) | ||||
−0.704556 | + | 0.709648i | \(0.748854\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 43.7934i | 1.90406i | 0.306001 | + | 0.952031i | \(0.401009\pi\) | ||||
−0.306001 | + | 0.952031i | \(0.598991\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 40.9333 | 1.63733 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14.5075 | 0.500258 | 0.250129 | − | 0.968212i | \(-0.419527\pi\) | ||||
0.250129 | + | 0.968212i | \(0.419527\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | 77.0038i | 2.20011i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12.9666 | 0.350449 | 0.175225 | − | 0.984528i | \(-0.443935\pi\) | ||||
0.175225 | + | 0.984528i | \(0.443935\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −50.1810 | −1.22393 | −0.611963 | − | 0.790886i | \(-0.709620\pi\) | ||||
−0.611963 | + | 0.790886i | \(0.709620\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 5.03337i | − 0.117055i | −0.998286 | − | 0.0585276i | \(-0.981359\pi\) | ||||
0.998286 | − | 0.0585276i | \(-0.0186406\pi\) | |||||||
\(44\) | 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 | ||||||||
\(53\) | 27.2826 | 0.514766 | 0.257383 | − | 0.966309i | \(-0.417140\pi\) | ||||
0.257383 | + | 0.966309i | \(0.417140\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 85.9333i | − 1.56242i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 24.0888i | 0.408285i | 0.978941 | + | 0.204143i | \(0.0654406\pi\) | ||||
−0.978941 | + | 0.204143i | \(0.934559\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 28.9666 | 0.474863 | 0.237431 | − | 0.971404i | \(-0.423695\pi\) | ||||
0.237431 | + | 0.971404i | \(0.423695\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −170.248 | −2.61919 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 65.7998i | − 0.982086i | −0.871135 | − | 0.491043i | \(-0.836616\pi\) | ||||
0.871135 | − | 0.491043i | \(-0.163384\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 90.5097i | 1.27478i | 0.770540 | + | 0.637392i | \(0.219987\pi\) | ||||
−0.770540 | + | 0.637392i | \(0.780013\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −127.800 | −1.75068 | −0.875341 | − | 0.483506i | \(-0.839363\pi\) | ||||
−0.875341 | + | 0.483506i | \(0.839363\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 100.362 | 1.30340 | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 101.093i | 1.21798i | 0.793176 | + | 0.608992i | \(0.208426\pi\) | ||||
−0.793176 | + | 0.608992i | \(0.791574\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 40.0000 | 0.470588 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.6979 | −0.176381 | −0.0881906 | − | 0.996104i | \(-0.528108\pi\) | ||||
−0.0881906 | + | 0.996104i | \(0.528108\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 198.833i | − 2.18498i | ||||||||
\(92\) | 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 | ||||||||
\(101\) | 114.869 | 1.13732 | 0.568661 | − | 0.822572i | \(-0.307462\pi\) | ||||
0.568661 | + | 0.822572i | \(0.307462\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 121.483i | − 1.17945i | −0.807604 | − | 0.589725i | \(-0.799236\pi\) | ||||
0.807604 | − | 0.589725i | \(-0.200764\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 156.931i | 1.46664i | 0.679883 | + | 0.733320i | \(0.262030\pi\) | ||||
−0.679883 | + | 0.733320i | \(0.737970\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 114.766 | 1.05290 | 0.526451 | − | 0.850205i | \(-0.323522\pi\) | ||||
0.526451 | + | 0.850205i | \(0.323522\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 355.600i | 3.09217i | ||||||||
\(116\) | 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 | ||||||||
\(125\) | 129.377 | 1.03502 | ||||||||
\(126\) | 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 | ||||||||
\(131\) | − 169.328i | − 1.29258i | −0.763092 | − | 0.646290i | \(-0.776319\pi\) | ||||
0.763092 | − | 0.646290i | \(-0.223681\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −255.733 | −1.92280 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −235.207 | −1.71684 | −0.858420 | − | 0.512948i | \(-0.828553\pi\) | ||||
−0.858420 | + | 0.512948i | \(0.828553\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 30.2002i | − 0.217268i | −0.994082 | − | 0.108634i | \(-0.965352\pi\) | ||||
0.994082 | − | 0.108634i | \(-0.0346476\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | 170.519 | 1.14442 | 0.572210 | − | 0.820107i | \(-0.306086\pi\) | ||||
0.572210 | + | 0.820107i | \(0.306086\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 87.1496i | 0.577150i | 0.957457 | + | 0.288575i | \(0.0931814\pi\) | ||||
−0.957457 | + | 0.288575i | \(0.906819\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 206.923i | 1.33499i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −98.7664 | −0.629085 | −0.314543 | − | 0.949243i | \(-0.601851\pi\) | ||||
−0.314543 | + | 0.949243i | \(0.601851\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −415.307 | −2.57955 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 67.2336i | 0.412476i | 0.978502 | + | 0.206238i | \(0.0661221\pi\) | ||||
−0.978502 | + | 0.206238i | \(0.933878\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 216.044i | − 1.29368i | −0.762626 | − | 0.646839i | \(-0.776090\pi\) | ||||
0.762626 | − | 0.646839i | \(-0.223910\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 270.600 | 1.60118 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −118.876 | −0.687145 | −0.343573 | − | 0.939126i | \(-0.611637\pi\) | ||||
−0.343573 | + | 0.939126i | \(0.611637\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 388.183i | 2.21819i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.0888i | 0.134574i | 0.997734 | + | 0.0672872i | \(0.0214344\pi\) | ||||
−0.997734 | + | 0.0672872i | \(0.978566\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 131.033 | 0.723941 | 0.361971 | − | 0.932189i | \(-0.382104\pi\) | ||||
0.361971 | + | 0.932189i | \(0.382104\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 105.288 | 0.569125 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 52.1335i | − 0.278789i | ||||||||
\(188\) | 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 | ||||||||
\(197\) | −122.341 | −0.621020 | −0.310510 | − | 0.950570i | \(-0.600500\pi\) | ||||
−0.310510 | + | 0.950570i | \(0.600500\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 363.283i | − 1.82554i | −0.408470 | − | 0.912772i | \(-0.633938\pi\) | ||||
0.408470 | − | 0.912772i | \(-0.366062\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 137.579i | 0.677729i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −407.466 | −1.98764 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 285.388 | 1.36549 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 138.067i | 0.654345i | 0.944965 | + | 0.327172i | \(0.106096\pi\) | ||||
−0.944965 | + | 0.327172i | \(0.893904\pi\) | |||||||
\(212\) | 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 | ||||||||
\(221\) | −103.285 | −0.467352 | ||||||||
\(222\) | 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 | ||||||||
\(227\) | 243.409i | 1.07229i | 0.844127 | + | 0.536143i | \(0.180119\pi\) | ||||
−0.844127 | + | 0.536143i | \(0.819881\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 234.232 | 1.02285 | 0.511425 | − | 0.859328i | \(-0.329118\pi\) | ||||
0.511425 | + | 0.859328i | \(0.329118\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −35.4025 | −0.151942 | −0.0759711 | − | 0.997110i | \(-0.524206\pi\) | ||||
−0.0759711 | + | 0.997110i | \(0.524206\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 331.867i | − 1.41220i | ||||||||
\(236\) | 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 | ||||||||
\(245\) | −332.375 | −1.35663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 565.399i | − 2.28907i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 312.753i | − 1.24603i | −0.782211 | − | 0.623014i | \(-0.785908\pi\) | ||||
0.782211 | − | 0.623014i | \(-0.214092\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 463.466 | 1.83188 | ||||||||
\(254\) | 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 | ||||||||
\(259\) | 122.967i | 0.474775i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 338.656i | 1.28767i | 0.765166 | + | 0.643833i | \(0.222657\pi\) | ||||
−0.765166 | + | 0.643833i | \(0.777343\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 221.533 | 0.835973 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 310.832 | 1.15551 | 0.577754 | − | 0.816211i | \(-0.303929\pi\) | ||||
0.577754 | + | 0.816211i | \(0.303929\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | − 433.197i | − 1.57526i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 458.766 | 1.65620 | 0.828098 | − | 0.560583i | \(-0.189423\pi\) | ||||
0.828098 | + | 0.560583i | \(0.189423\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 395.602 | 1.40784 | 0.703919 | − | 0.710281i | \(-0.251432\pi\) | ||||
0.703919 | + | 0.710281i | \(0.251432\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 375.733i | − 1.32768i | −0.747875 | − | 0.663839i | \(-0.768926\pi\) | ||||
0.747875 | − | 0.663839i | \(-0.231074\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | 9.74572 | 0.0332619 | 0.0166309 | − | 0.999862i | \(-0.494706\pi\) | ||||
0.0166309 | + | 0.999862i | \(0.494706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 195.600i | 0.663049i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 918.201i | − 3.07090i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 47.7330 | 0.158582 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 235.207 | 0.771170 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 89.5328i | − 0.291638i | −0.989311 | − | 0.145819i | \(-0.953418\pi\) | ||||
0.989311 | − | 0.145819i | \(-0.0465817\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 274.452i | − 0.882482i | −0.897389 | − | 0.441241i | \(-0.854538\pi\) | ||||
0.897389 | − | 0.441241i | \(-0.145462\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −151.666 | −0.484557 | −0.242278 | − | 0.970207i | \(-0.577895\pi\) | ||||
−0.242278 | + | 0.970207i | \(0.577895\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −201.914 | −0.636954 | −0.318477 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318477 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 153.533i | − 0.481294i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 132.842i | 0.411275i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −858.232 | −2.64072 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 387.589 | 1.17808 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 195.600i | − 0.590935i | −0.955353 | − | 0.295468i | \(-0.904525\pi\) | ||||
0.955353 | − | 0.295468i | \(-0.0954754\pi\) | |||||||
\(332\) | 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 | ||||||||
\(341\) | 269.690 | 0.790880 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 76.4994i | 0.223030i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 139.796i | − 0.402869i | −0.979502 | − | 0.201435i | \(-0.935440\pi\) | ||||
0.979502 | − | 0.201435i | \(-0.0645603\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.2336 | 0.0608412 | 0.0304206 | − | 0.999537i | \(-0.490315\pi\) | ||||
0.0304206 | + | 0.999537i | \(0.490315\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 734.932i | 2.07023i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 253.992i | 0.707499i | 0.935340 | + | 0.353749i | \(0.115093\pi\) | ||||
−0.935340 | + | 0.353749i | \(0.884907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −366.199 | −1.01440 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1037.73 | −2.84308 | ||||||||
\(366\) | 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 | ||||||||
\(371\) | 258.730i | 0.697384i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 197.501 | 0.529492 | 0.264746 | − | 0.964318i | \(-0.414712\pi\) | ||||
0.264746 | + | 0.964318i | \(0.414712\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −304.173 | −0.806825 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 234.433i | 0.618556i | 0.950972 | + | 0.309278i | \(0.100087\pi\) | ||||
−0.950972 | + | 0.309278i | \(0.899913\pi\) | |||||||
\(380\) | 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 | ||||||||
\(389\) | −486.760 | −1.25131 | −0.625656 | − | 0.780099i | \(-0.715169\pi\) | ||||
−0.625656 | + | 0.780099i | \(0.715169\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 215.733i | 0.551747i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 288.664i | 0.730795i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −115.300 | −0.290429 | −0.145215 | − | 0.989400i | \(-0.546387\pi\) | ||||
−0.145215 | + | 0.989400i | \(0.546387\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − 534.299i | − 1.32580i | ||||||||
\(404\) | 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 | \(-0.361270\pi\) | ||||
0.422167 | + | 0.906518i | \(0.361270\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −228.442 | −0.553128 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 820.865i | 1.97799i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 644.151i | − 1.53735i | −0.639638 | − | 0.768676i | \(-0.720916\pi\) | ||||
0.639638 | − | 0.768676i | \(-0.279084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −756.700 | −1.79739 | −0.898693 | − | 0.438578i | \(-0.855482\pi\) | ||||
−0.898693 | + | 0.438578i | \(0.855482\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 201.643 | 0.474455 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 274.700i | 0.643325i | ||||||||
\(428\) | 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 | ||||||||
\(437\) | −1180.96 | −2.70243 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 274.482i | − 0.625244i | −0.949878 | − | 0.312622i | \(-0.898793\pi\) | ||||
0.949878 | − | 0.312622i | \(-0.101207\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 466.760i | − 1.05364i | −0.849978 | − | 0.526818i | \(-0.823385\pi\) | ||||
0.849978 | − | 0.526818i | \(-0.176615\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −127.466 | −0.286441 | ||||||||
\(446\) | 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 | ||||||||
\(451\) | 531.066i | 1.17753i | ||||||||
\(452\) | 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 | \(-0.646357\pi\) | ||||
−0.443763 | + | 0.896144i | \(0.646357\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 636.171 | 1.37998 | 0.689990 | − | 0.723819i | \(-0.257615\pi\) | ||||
0.689990 | + | 0.723819i | \(0.257615\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | 128.104i | 0.274313i | 0.990549 | + | 0.137157i | \(0.0437964\pi\) | ||||
−0.990549 | + | 0.137157i | \(0.956204\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 624.000 | 1.33049 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −53.2682 | −0.112618 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1103.83i | 2.32386i | ||||||||
\(476\) | 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 | ||||||||
\(485\) | 599.791 | 1.23668 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 180.183i | − 0.369986i | −0.982740 | − | 0.184993i | \(-0.940774\pi\) | ||||
0.982740 | − | 0.184993i | \(-0.0592262\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 423.320i | 0.862159i | 0.902314 | + | 0.431080i | \(0.141867\pi\) | ||||
−0.902314 | + | 0.431080i | \(0.858133\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 71.4661 | 0.144962 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −858.332 | −1.72703 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 830.932i | − 1.66519i | −0.553879 | − | 0.832597i | \(-0.686853\pi\) | ||||
0.553879 | − | 0.832597i | \(-0.313147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 359.116i | 0.713948i | 0.934114 | + | 0.356974i | \(0.116192\pi\) | ||||
−0.934114 | + | 0.356974i | \(0.883808\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 932.732 | 1.84699 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 43.3093 | 0.0850870 | 0.0425435 | − | 0.999095i | \(-0.486454\pi\) | ||||
0.0425435 | + | 0.999095i | \(0.486454\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 1211.97i | − 2.37175i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 986.436i | − 1.91541i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −432.534 | −0.836623 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 426.407 | 0.818440 | 0.409220 | − | 0.912436i | \(-0.365801\pi\) | ||||
0.409220 | + | 0.912436i | \(0.365801\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 384.366i | − 0.734925i | −0.930038 | − | 0.367463i | \(-0.880227\pi\) | ||||
0.930038 | − | 0.367463i | \(-0.119773\pi\) | |||||||
\(524\) | 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 | ||||||||
\(533\) | 1052.13 | 1.97397 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1274.26i | 2.38180i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 433.197i | 0.803705i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 403.033 | 0.744979 | 0.372489 | − | 0.928037i | \(-0.378504\pi\) | ||||
0.372489 | + | 0.928037i | \(0.378504\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 931.895 | 1.70990 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1066.43i | − 1.94960i | −0.223075 | − | 0.974801i | \(-0.571609\pi\) | ||||
0.223075 | − | 0.974801i | \(-0.428391\pi\) | |||||||
\(548\) | 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 | ||||||||
\(557\) | −221.406 | −0.397497 | −0.198749 | − | 0.980051i | \(-0.563688\pi\) | ||||
−0.198749 | + | 0.980051i | \(0.563688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 105.533i | 0.188789i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 747.764i | − 1.32818i | −0.747654 | − | 0.664089i | \(-0.768820\pi\) | ||||
0.747654 | − | 0.664089i | \(-0.231180\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1454.93 | 2.57510 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 489.199 | 0.859752 | 0.429876 | − | 0.902888i | \(-0.358557\pi\) | ||||
0.429876 | + | 0.902888i | \(0.358557\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 784.198i | − 1.37338i | −0.726952 | − | 0.686688i | \(-0.759064\pi\) | ||||
0.726952 | − | 0.686688i | \(-0.240936\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | −958.694 | −1.65008 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 288.732i | − 0.495252i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 84.6640i | − 0.144232i | −0.997396 | − | 0.0721159i | \(-0.977025\pi\) | ||||
0.997396 | − | 0.0721159i | \(-0.0229751\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −687.199 | −1.16672 | ||||||||
\(590\) | 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 | ||||||||
\(595\) | 379.333i | 0.637534i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 411.678i | − 0.687275i | −0.939102 | − | 0.343638i | \(-0.888341\pi\) | ||||
0.939102 | − | 0.343638i | \(-0.111659\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −463.666 | −0.771491 | −0.385746 | − | 0.922605i | \(-0.626056\pi\) | ||||
−0.385746 | + | 0.922605i | \(0.626056\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 73.0794 | 0.120792 | ||||||||
\(606\) | 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 | ||||||||
\(611\) | 856.919i | 1.40249i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −459.567 | −0.749702 | −0.374851 | − | 0.927085i | \(-0.622306\pi\) | ||||
−0.374851 | + | 0.927085i | \(0.622306\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 370.052 | 0.599760 | 0.299880 | − | 0.953977i | \(-0.403053\pi\) | ||||
0.299880 | + | 0.953977i | \(0.403053\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 10.7987i | − 0.0174453i | −0.999962 | − | 0.00872267i | \(-0.997223\pi\) | ||||
0.999962 | − | 0.00872267i | \(-0.00277655\pi\) | |||||||
\(620\) | 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 | ||||||||
\(629\) | 63.8756 | 0.101551 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 63.9505i | 0.101348i | 0.998715 | + | 0.0506739i | \(0.0161369\pi\) | ||||
−0.998715 | + | 0.0506739i | \(0.983863\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 784.251i | 1.23504i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 858.232 | 1.34730 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | − 23.3671i | − 0.0363407i | −0.999835 | − | 0.0181704i | \(-0.994216\pi\) | ||||
0.999835 | − | 0.0181704i | \(-0.00578412\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 686.130i | 1.06048i | 0.847848 | + | 0.530239i | \(0.177898\pi\) | ||||
−0.847848 | + | 0.530239i | \(0.822102\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 254.932 | 0.392808 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 899.686 | 1.37777 | 0.688887 | − | 0.724869i | \(-0.258100\pi\) | ||||
0.688887 | + | 0.724869i | \(0.258100\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1374.93i | − 2.09913i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 217.506i | 0.330054i | 0.986289 | + | 0.165027i | \(0.0527712\pi\) | ||||
−0.986289 | + | 0.165027i | \(0.947229\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 829.234 | 1.25451 | 0.627257 | − | 0.778812i | \(-0.284178\pi\) | ||||
0.627257 | + | 0.778812i | \(0.284178\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2076.53 | −3.12261 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 635.333i | 0.952523i | ||||||||
\(668\) | 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 | ||||||||
\(677\) | 772.690 | 1.14134 | 0.570672 | − | 0.821178i | \(-0.306683\pi\) | ||||
0.570672 | + | 0.821178i | \(0.306683\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 700.499i | 1.03166i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 640.522i | 0.937806i | 0.883250 | + | 0.468903i | \(0.155351\pi\) | ||||
−0.883250 | + | 0.468903i | \(0.844649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1909.86 | −2.78812 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −572.024 | −0.830224 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 973.300i | − 1.40854i | −0.709933 | − | 0.704269i | \(-0.751275\pi\) | ||||
0.709933 | − | 0.704269i | \(-0.248725\pi\) | |||||||
\(692\) | 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 | ||||||||
\(701\) | 759.045 | 1.08280 | 0.541401 | − | 0.840764i | \(-0.317894\pi\) | ||||
0.541401 | + | 0.840764i | \(0.317894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 349.666i | 0.497392i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1089.34i | 1.54080i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −334.034 | −0.471135 | −0.235567 | − | 0.971858i | \(-0.575695\pi\) | ||||
−0.235567 | + | 0.971858i | \(0.575695\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1116.00 | −1.56522 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1801.73i | 2.51990i | ||||||||
\(716\) | 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 | ||||||||
\(725\) | 593.839 | 0.819088 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 877.617i | 1.20718i | 0.797296 | + | 0.603588i | \(0.206263\pi\) | ||||
−0.797296 | + | 0.603588i | \(0.793737\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 24.7951i | − 0.0339195i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1001.70 | 1.36657 | 0.683287 | − | 0.730150i | \(-0.260550\pi\) | ||||
0.683287 | + | 0.730150i | \(0.260550\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −696.359 | −0.944857 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 648.999i | − 0.878212i | −0.898435 | − | 0.439106i | \(-0.855295\pi\) | ||||
0.898435 | − | 0.439106i | \(-0.144705\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 411.678i | 0.554075i | 0.960859 | + | 0.277038i | \(0.0893526\pi\) | ||||
−0.960859 | + | 0.277038i | \(0.910647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1384.60 | 1.85852 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1488.22 | −1.98694 | ||||||||
\(750\) | 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 | ||||||||
\(755\) | 707.649i | 0.937283i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 164.101 | 0.216778 | 0.108389 | − | 0.994109i | \(-0.465431\pi\) | ||||
0.108389 | + | 0.994109i | \(0.465431\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −331.562 | −0.435693 | −0.217846 | − | 0.975983i | \(-0.569903\pi\) | ||||
−0.217846 | + | 0.975983i | \(0.569903\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1088.37i | 1.42643i | ||||||||
\(764\) | 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 | ||||||||
\(773\) | 980.557 | 1.26851 | 0.634254 | − | 0.773125i | \(-0.281307\pi\) | ||||
0.634254 | + | 0.773125i | \(0.281307\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1043.12i | 1.34596i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1353.21i | − 1.73711i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 957.864 | 1.22646 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −801.976 | −1.02163 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 335.832i | 0.426724i | 0.976973 | + | 0.213362i | \(0.0684414\pi\) | ||||
−0.976973 | + | 0.213362i | \(0.931559\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | −283.114 | −0.355224 | −0.177612 | − | 0.984101i | \(-0.556837\pi\) | ||||
−0.177612 | + | 0.984101i | \(0.556837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 201.335i | − 0.251984i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1352.51i | 1.68432i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3372.26 | −4.18915 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 117.308 | 0.145004 | 0.0725019 | − | 0.997368i | \(-0.476902\pi\) | ||||
0.0725019 | + | 0.997368i | \(0.476902\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1235.43i | 1.52334i | 0.647963 | + | 0.761672i | \(0.275621\pi\) | ||||
−0.647963 | + | 0.761672i | \(0.724379\pi\) | |||||||
\(812\) | 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 | ||||||||
\(821\) | −823.364 | −1.00288 | −0.501440 | − | 0.865192i | \(-0.667196\pi\) | ||||
−0.501440 | + | 0.865192i | \(0.667196\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 743.249i | − 0.903097i | −0.892247 | − | 0.451548i | \(-0.850872\pi\) | ||||
0.892247 | − | 0.451548i | \(-0.149128\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 542.352i | 0.655806i | 0.944711 | + | 0.327903i | \(0.106342\pi\) | ||||
−0.944711 | + | 0.327903i | \(0.893658\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −906.564 | −1.09356 | −0.546782 | − | 0.837275i | \(-0.684147\pi\) | ||||
−0.546782 | + | 0.837275i | \(0.684147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −201.643 | −0.242069 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1754.26i | − 2.10092i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1015.97i | 1.21093i | 0.795873 | + | 0.605464i | \(0.207012\pi\) | ||||
−0.795873 | + | 0.605464i | \(0.792988\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −630.533 | −0.749742 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2197.25 | 2.60030 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 85.3498i | 0.100767i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 567.853i | 0.667277i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 102.568 | 0.120244 | 0.0601222 | − | 0.998191i | \(-0.480851\pi\) | ||||
0.0601222 | + | 0.998191i | \(0.480851\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1081.85 | 1.26237 | 0.631183 | − | 0.775634i | \(-0.282570\pi\) | ||||
0.631183 | + | 0.775634i | \(0.282570\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 597.231i | − 0.695264i | −0.937631 | − | 0.347632i | \(-0.886986\pi\) | ||||
0.937631 | − | 0.347632i | \(-0.113014\pi\) | |||||||
\(860\) | 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 | ||||||||
\(869\) | 376.226 | 0.432942 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1379.60i | 1.58393i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1226.92i | 1.40220i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 395.899 | 0.451424 | 0.225712 | − | 0.974194i | \(-0.427529\pi\) | ||||
0.225712 | + | 0.974194i | \(0.427529\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 1548.96i | 1.75421i | 0.480302 | + | 0.877103i | \(0.340527\pi\) | ||||
−0.480302 | + | 0.877103i | \(0.659473\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1544.41i | 1.74116i | 0.492023 | + | 0.870582i | \(0.336257\pi\) | ||||
−0.492023 | + | 0.870582i | \(0.663743\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −915.931 | −1.03029 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1102.14 | 1.23420 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 195.600i | 0.218547i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 369.699i | 0.411233i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 134.398 | 0.149166 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1063.98 | 1.17567 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 472.831i | − 0.521313i | −0.965432 | − | 0.260657i | \(-0.916061\pi\) | ||||
0.965432 | − | 0.260657i | \(-0.0839390\pi\) | |||||||
\(908\) | 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 | ||||||||
\(917\) | 1605.79 | 1.75114 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 152.850i | − 0.166323i | −0.996536 | − | 0.0831613i | \(-0.973498\pi\) | ||||
0.996536 | − | 0.0831613i | \(-0.0265017\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1897.68i | − 2.05599i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 530.766 | 0.573802 | ||||||||
\(926\) | 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 | ||||||||
\(931\) | − 1103.83i | − 1.18564i | ||||||||
\(932\) | 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 | \(-0.251068\pi\) | ||||
0.704731 | + | 0.709475i | \(0.251068\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.41027 | −0.00574949 | −0.00287475 | − | 0.999996i | \(-0.500915\pi\) | ||||
−0.00287475 | + | 0.999996i | \(0.500915\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2197.60i | − 2.33043i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 83.9577i | 0.0886565i | 0.999017 | + | 0.0443283i | \(0.0141147\pi\) | ||||
−0.999017 | + | 0.0443283i | \(0.985885\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2679.53 | 2.82353 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1577.15 | −1.65494 | −0.827468 | − | 0.561513i | \(-0.810220\pi\) | ||||
−0.827468 | + | 0.561513i | \(0.810220\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1043.07i | − 1.09222i | ||||||||
\(956\) | 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 | ||||||||
\(965\) | −1361.44 | −1.41082 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 278.616i | − 0.288124i | −0.989569 | − | 0.144062i | \(-0.953984\pi\) | ||||
0.989569 | − | 0.144062i | \(-0.0460164\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 380.684i | 0.392053i | 0.980599 | + | 0.196027i | \(0.0628039\pi\) | ||||
−0.980599 | + | 0.196027i | \(0.937196\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 286.398 | 0.294346 | ||||||||
\(974\) | 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 | ||||||||
\(979\) | 166.131i | 0.169695i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 928.382i | − 0.944437i | −0.881482 | − | 0.472219i | \(-0.843453\pi\) | ||||
0.881482 | − | 0.472219i | \(-0.156547\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −993.399 | −1.00853 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 220.429 | 0.222880 | ||||||||
\(990\) | 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 | ||||||||
\(995\) | − 2949.83i | − 2.96466i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −595.567 | −0.597359 | −0.298680 | − | 0.954353i | \(-0.596546\pi\) | ||||
−0.298680 | + | 0.954353i | \(0.596546\pi\) | |||||||
\(998\) | 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 | 1152.3.g.d.127.8 | yes | 8 | |
3.2 | odd | 2 | inner | 1152.3.g.d.127.2 | yes | 8 | |
4.3 | odd | 2 | inner | 1152.3.g.d.127.7 | yes | 8 | |
8.3 | odd | 2 | 1152.3.g.e.127.1 | yes | 8 | ||
8.5 | even | 2 | 1152.3.g.e.127.2 | yes | 8 | ||
12.11 | even | 2 | inner | 1152.3.g.d.127.1 | ✓ | 8 | |
16.3 | odd | 4 | 2304.3.b.s.127.2 | 8 | |||
16.5 | even | 4 | 2304.3.b.s.127.7 | 8 | |||
16.11 | odd | 4 | 2304.3.b.r.127.8 | 8 | |||
16.13 | even | 4 | 2304.3.b.r.127.1 | 8 | |||
24.5 | odd | 2 | 1152.3.g.e.127.8 | yes | 8 | ||
24.11 | even | 2 | 1152.3.g.e.127.7 | yes | 8 | ||
48.5 | odd | 4 | 2304.3.b.s.127.1 | 8 | |||
48.11 | even | 4 | 2304.3.b.r.127.2 | 8 | |||
48.29 | odd | 4 | 2304.3.b.r.127.7 | 8 | |||
48.35 | even | 4 | 2304.3.b.s.127.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.g.d.127.1 | ✓ | 8 | 12.11 | even | 2 | inner | |
1152.3.g.d.127.2 | yes | 8 | 3.2 | odd | 2 | inner | |
1152.3.g.d.127.7 | yes | 8 | 4.3 | odd | 2 | inner | |
1152.3.g.d.127.8 | yes | 8 | 1.1 | even | 1 | trivial | |
1152.3.g.e.127.1 | yes | 8 | 8.3 | odd | 2 | ||
1152.3.g.e.127.2 | yes | 8 | 8.5 | even | 2 | ||
1152.3.g.e.127.7 | yes | 8 | 24.11 | even | 2 | ||
1152.3.g.e.127.8 | yes | 8 | 24.5 | odd | 2 | ||
2304.3.b.r.127.1 | 8 | 16.13 | even | 4 | |||
2304.3.b.r.127.2 | 8 | 48.11 | even | 4 | |||
2304.3.b.r.127.7 | 8 | 48.29 | odd | 4 | |||
2304.3.b.r.127.8 | 8 | 16.11 | odd | 4 | |||
2304.3.b.s.127.1 | 8 | 48.5 | odd | 4 | |||
2304.3.b.s.127.2 | 8 | 16.3 | odd | 4 | |||
2304.3.b.s.127.7 | 8 | 16.5 | even | 4 | |||
2304.3.b.s.127.8 | 8 | 48.35 | even | 4 |