Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(197,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("882.197");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.b (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: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.197 |
Dual form | 882.3.b.h.197.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.41421i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | − 4.00000i | − 0.800000i | −0.916515 | − | 0.400000i | \(-0.869010\pi\) | ||||
0.916515 | − | 0.400000i | \(-0.130990\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.65685 | −0.565685 | ||||||||
\(11\) | 2.82843i | 0.257130i | 0.991701 | + | 0.128565i | \(0.0410371\pi\) | ||||
−0.991701 | + | 0.128565i | \(0.958963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.7279 | 0.979071 | 0.489535 | − | 0.871983i | \(-0.337166\pi\) | ||||
0.489535 | + | 0.871983i | \(0.337166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 4.00000i | − 0.235294i | −0.993055 | − | 0.117647i | \(-0.962465\pi\) | ||||
0.993055 | − | 0.117647i | \(-0.0375352\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22.6274 | 1.19092 | 0.595458 | − | 0.803386i | \(-0.296970\pi\) | ||||
0.595458 | + | 0.803386i | \(0.296970\pi\) | |||||||
\(20\) | 8.00000i | 0.400000i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.181818 | ||||||||
\(23\) | − 36.7696i | − 1.59868i | −0.600882 | − | 0.799338i | \(-0.705184\pi\) | ||||
0.600882 | − | 0.799338i | \(-0.294816\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.00000 | 0.360000 | ||||||||
\(26\) | − 18.0000i | − 0.692308i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 32.5269i | − 1.12162i | −0.827945 | − | 0.560809i | \(-0.810490\pi\) | ||||
0.827945 | − | 0.560809i | \(-0.189510\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −50.9117 | −1.64231 | −0.821156 | − | 0.570703i | \(-0.806671\pi\) | ||||
−0.821156 | + | 0.570703i | \(0.806671\pi\) | |||||||
\(32\) | − 5.65685i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.65685 | −0.166378 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −32.0000 | −0.864865 | −0.432432 | − | 0.901666i | \(-0.642345\pi\) | ||||
−0.432432 | + | 0.901666i | \(0.642345\pi\) | |||||||
\(38\) | − 32.0000i | − 0.842105i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11.3137 | 0.282843 | ||||||||
\(41\) | 38.0000i | 0.926829i | 0.886142 | + | 0.463415i | \(0.153376\pi\) | ||||
−0.886142 | + | 0.463415i | \(0.846624\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20.0000 | 0.465116 | 0.232558 | − | 0.972582i | \(-0.425290\pi\) | ||||
0.232558 | + | 0.972582i | \(0.425290\pi\) | |||||||
\(44\) | − 5.65685i | − 0.128565i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −52.0000 | −1.13043 | ||||||||
\(47\) | 20.0000i | 0.425532i | 0.977103 | + | 0.212766i | \(0.0682472\pi\) | ||||
−0.977103 | + | 0.212766i | \(0.931753\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 12.7279i | − 0.254558i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −25.4558 | −0.489535 | ||||||||
\(53\) | − 94.7523i | − 1.78778i | −0.448287 | − | 0.893890i | \(-0.647966\pi\) | ||||
0.448287 | − | 0.893890i | \(-0.352034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.3137 | 0.205704 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −46.0000 | −0.793103 | ||||||||
\(59\) | − 4.00000i | − 0.0677966i | −0.999425 | − | 0.0338983i | \(-0.989208\pi\) | ||||
0.999425 | − | 0.0338983i | \(-0.0107922\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 83.4386 | 1.36785 | 0.683923 | − | 0.729554i | \(-0.260272\pi\) | ||||
0.683923 | + | 0.729554i | \(0.260272\pi\) | |||||||
\(62\) | 72.0000i | 1.16129i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − 50.9117i | − 0.783257i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −48.0000 | −0.716418 | −0.358209 | − | 0.933641i | \(-0.616612\pi\) | ||||
−0.358209 | + | 0.933641i | \(0.616612\pi\) | |||||||
\(68\) | 8.00000i | 0.117647i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 76.3675i | − 1.07560i | −0.843073 | − | 0.537800i | \(-0.819256\pi\) | ||||
0.843073 | − | 0.537800i | \(-0.180744\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −120.208 | −1.64669 | −0.823344 | − | 0.567543i | \(-0.807894\pi\) | ||||
−0.823344 | + | 0.567543i | \(0.807894\pi\) | |||||||
\(74\) | 45.2548i | 0.611552i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −45.2548 | −0.595458 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −148.000 | −1.87342 | −0.936709 | − | 0.350109i | \(-0.886144\pi\) | ||||
−0.936709 | + | 0.350109i | \(0.886144\pi\) | |||||||
\(80\) | − 16.0000i | − 0.200000i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 53.7401 | 0.655367 | ||||||||
\(83\) | − 80.0000i | − 0.963855i | −0.876211 | − | 0.481928i | \(-0.839937\pi\) | ||||
0.876211 | − | 0.481928i | \(-0.160063\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.0000 | −0.188235 | ||||||||
\(86\) | − 28.2843i | − 0.328887i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.00000 | −0.0909091 | ||||||||
\(89\) | 106.000i | 1.19101i | 0.803351 | + | 0.595506i | \(0.203048\pi\) | ||||
−0.803351 | + | 0.595506i | \(0.796952\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 73.5391i | 0.799338i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 28.2843 | 0.300897 | ||||||||
\(95\) | − 90.5097i | − 0.952733i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 154.149 | 1.58917 | 0.794584 | − | 0.607154i | \(-0.207689\pi\) | ||||
0.794584 | + | 0.607154i | \(0.207689\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.0000 | −0.180000 | ||||||||
\(101\) | − 126.000i | − 1.24752i | −0.781614 | − | 0.623762i | \(-0.785603\pi\) | ||||
0.781614 | − | 0.623762i | \(-0.214397\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −73.5391 | −0.713972 | −0.356986 | − | 0.934110i | \(-0.616196\pi\) | ||||
−0.356986 | + | 0.934110i | \(0.616196\pi\) | |||||||
\(104\) | 36.0000i | 0.346154i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −134.000 | −1.26415 | ||||||||
\(107\) | − 70.7107i | − 0.660847i | −0.943833 | − | 0.330424i | \(-0.892808\pi\) | ||||
0.943833 | − | 0.330424i | \(-0.107192\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −86.0000 | −0.788991 | −0.394495 | − | 0.918898i | \(-0.629081\pi\) | ||||
−0.394495 | + | 0.918898i | \(0.629081\pi\) | |||||||
\(110\) | − 16.0000i | − 0.145455i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 21.2132i | 0.187727i | 0.995585 | + | 0.0938637i | \(0.0299218\pi\) | ||||
−0.995585 | + | 0.0938637i | \(0.970078\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −147.078 | −1.27894 | ||||||||
\(116\) | 65.0538i | 0.560809i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.65685 | −0.0479394 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 113.000 | 0.933884 | ||||||||
\(122\) | − 118.000i | − 0.967213i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 101.823 | 0.821156 | ||||||||
\(125\) | − 136.000i | − 1.08800i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.0314961 | 0.0157480 | − | 0.999876i | \(-0.494987\pi\) | ||||
0.0157480 | + | 0.999876i | \(0.494987\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −72.0000 | −0.553846 | ||||||||
\(131\) | 24.0000i | 0.183206i | 0.995796 | + | 0.0916031i | \(0.0291991\pi\) | ||||
−0.995796 | + | 0.0916031i | \(0.970801\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 67.8823i | 0.506584i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.3137 | 0.0831890 | ||||||||
\(137\) | − 72.1249i | − 0.526459i | −0.964733 | − | 0.263230i | \(-0.915212\pi\) | ||||
0.964733 | − | 0.263230i | \(-0.0847877\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 141.421 | 1.01742 | 0.508710 | − | 0.860938i | \(-0.330123\pi\) | ||||
0.508710 | + | 0.860938i | \(0.330123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −108.000 | −0.760563 | ||||||||
\(143\) | 36.0000i | 0.251748i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −130.108 | −0.897294 | ||||||||
\(146\) | 170.000i | 1.16438i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 64.0000 | 0.432432 | ||||||||
\(149\) | − 26.8701i | − 0.180336i | −0.995927 | − | 0.0901680i | \(-0.971260\pi\) | ||||
0.995927 | − | 0.0901680i | \(-0.0287404\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 152.000 | 1.00662 | 0.503311 | − | 0.864105i | \(-0.332115\pi\) | ||||
0.503311 | + | 0.864105i | \(0.332115\pi\) | |||||||
\(152\) | 64.0000i | 0.421053i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 203.647i | 1.31385i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 94.7523 | 0.603518 | 0.301759 | − | 0.953384i | \(-0.402426\pi\) | ||||
0.301759 | + | 0.953384i | \(0.402426\pi\) | |||||||
\(158\) | 209.304i | 1.32471i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −22.6274 | −0.141421 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −152.000 | −0.932515 | −0.466258 | − | 0.884649i | \(-0.654398\pi\) | ||||
−0.466258 | + | 0.884649i | \(0.654398\pi\) | |||||||
\(164\) | − 76.0000i | − 0.463415i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −113.137 | −0.681549 | ||||||||
\(167\) | − 116.000i | − 0.694611i | −0.937752 | − | 0.347305i | \(-0.887097\pi\) | ||||
0.937752 | − | 0.347305i | \(-0.112903\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.0414201 | ||||||||
\(170\) | 22.6274i | 0.133102i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −40.0000 | −0.232558 | ||||||||
\(173\) | 222.000i | 1.28324i | 0.767024 | + | 0.641618i | \(0.221737\pi\) | ||||
−0.767024 | + | 0.641618i | \(0.778263\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.3137i | 0.0642824i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 149.907 | 0.842172 | ||||||||
\(179\) | − 59.3970i | − 0.331827i | −0.986140 | − | 0.165913i | \(-0.946943\pi\) | ||||
0.986140 | − | 0.165913i | \(-0.0530572\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 80.6102 | 0.445360 | 0.222680 | − | 0.974892i | \(-0.428519\pi\) | ||||
0.222680 | + | 0.974892i | \(0.428519\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 104.000 | 0.565217 | ||||||||
\(185\) | 128.000i | 0.691892i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3137 | 0.0605011 | ||||||||
\(188\) | − 40.0000i | − 0.212766i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −128.000 | −0.673684 | ||||||||
\(191\) | 302.642i | 1.58451i | 0.610189 | + | 0.792256i | \(0.291093\pi\) | ||||
−0.610189 | + | 0.792256i | \(0.708907\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 218.000 | 1.12953 | 0.564767 | − | 0.825251i | \(-0.308966\pi\) | ||||
0.564767 | + | 0.825251i | \(0.308966\pi\) | |||||||
\(194\) | − 218.000i | − 1.12371i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 287.085i | − 1.45729i | −0.684894 | − | 0.728643i | \(-0.740151\pi\) | ||||
0.684894 | − | 0.728643i | \(-0.259849\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −67.8823 | −0.341117 | −0.170558 | − | 0.985348i | \(-0.554557\pi\) | ||||
−0.170558 | + | 0.985348i | \(0.554557\pi\) | |||||||
\(200\) | 25.4558i | 0.127279i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −178.191 | −0.882133 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 152.000 | 0.741463 | ||||||||
\(206\) | 104.000i | 0.504854i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 50.9117 | 0.244768 | ||||||||
\(209\) | 64.0000i | 0.306220i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 132.000 | 0.625592 | 0.312796 | − | 0.949820i | \(-0.398734\pi\) | ||||
0.312796 | + | 0.949820i | \(0.398734\pi\) | |||||||
\(212\) | 189.505i | 0.893890i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −100.000 | −0.467290 | ||||||||
\(215\) | − 80.0000i | − 0.372093i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 121.622i | 0.557901i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −22.6274 | −0.102852 | ||||||||
\(221\) | − 50.9117i | − 0.230370i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −169.706 | −0.761012 | −0.380506 | − | 0.924778i | \(-0.624250\pi\) | ||||
−0.380506 | + | 0.924778i | \(0.624250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 30.0000 | 0.132743 | ||||||||
\(227\) | 300.000i | 1.32159i | 0.750568 | + | 0.660793i | \(0.229780\pi\) | ||||
−0.750568 | + | 0.660793i | \(0.770220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −250.316 | −1.09308 | −0.546541 | − | 0.837432i | \(-0.684056\pi\) | ||||
−0.546541 | + | 0.837432i | \(0.684056\pi\) | |||||||
\(230\) | 208.000i | 0.904348i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 92.0000 | 0.396552 | ||||||||
\(233\) | − 29.6985i | − 0.127461i | −0.997967 | − | 0.0637307i | \(-0.979700\pi\) | ||||
0.997967 | − | 0.0637307i | \(-0.0202999\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 80.0000 | 0.340426 | ||||||||
\(236\) | 8.00000i | 0.0338983i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 161.220i | − 0.674562i | −0.941404 | − | 0.337281i | \(-0.890493\pi\) | ||||
0.941404 | − | 0.337281i | \(-0.109507\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 377.595 | 1.56678 | 0.783392 | − | 0.621528i | \(-0.213488\pi\) | ||||
0.783392 | + | 0.621528i | \(0.213488\pi\) | |||||||
\(242\) | − 159.806i | − 0.660356i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −166.877 | −0.683923 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 288.000 | 1.16599 | ||||||||
\(248\) | − 144.000i | − 0.580645i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −192.333 | −0.769332 | ||||||||
\(251\) | − 476.000i | − 1.89641i | −0.317653 | − | 0.948207i | \(-0.602895\pi\) | ||||
0.317653 | − | 0.948207i | \(-0.397105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 104.000 | 0.411067 | ||||||||
\(254\) | − 5.65685i | − 0.0222711i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 102.000i | − 0.396887i | −0.980112 | − | 0.198444i | \(-0.936411\pi\) | ||||
0.980112 | − | 0.198444i | \(-0.0635887\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 101.823i | 0.391628i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 33.9411 | 0.129546 | ||||||||
\(263\) | 364.867i | 1.38733i | 0.720299 | + | 0.693664i | \(0.244005\pi\) | ||||
−0.720299 | + | 0.693664i | \(0.755995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −379.009 | −1.43022 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 96.0000 | 0.358209 | ||||||||
\(269\) | 196.000i | 0.728625i | 0.931277 | + | 0.364312i | \(0.118696\pi\) | ||||
−0.931277 | + | 0.364312i | \(0.881304\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 175.362 | 0.647094 | 0.323547 | − | 0.946212i | \(-0.395125\pi\) | ||||
0.323547 | + | 0.946212i | \(0.395125\pi\) | |||||||
\(272\) | − 16.0000i | − 0.0588235i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −102.000 | −0.372263 | ||||||||
\(275\) | 25.4558i | 0.0925667i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 256.000 | 0.924188 | 0.462094 | − | 0.886831i | \(-0.347098\pi\) | ||||
0.462094 | + | 0.886831i | \(0.347098\pi\) | |||||||
\(278\) | − 200.000i | − 0.719424i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 26.8701i | − 0.0956230i | −0.998856 | − | 0.0478115i | \(-0.984775\pi\) | ||||
0.998856 | − | 0.0478115i | \(-0.0152247\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 503.460 | 1.77901 | 0.889505 | − | 0.456925i | \(-0.151049\pi\) | ||||
0.889505 | + | 0.456925i | \(0.151049\pi\) | |||||||
\(284\) | 152.735i | 0.537800i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 50.9117 | 0.178013 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 273.000 | 0.944637 | ||||||||
\(290\) | 184.000i | 0.634483i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 240.416 | 0.823344 | ||||||||
\(293\) | 190.000i | 0.648464i | 0.945978 | + | 0.324232i | \(0.105106\pi\) | ||||
−0.945978 | + | 0.324232i | \(0.894894\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.0000 | −0.0542373 | ||||||||
\(296\) | − 90.5097i | − 0.305776i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −38.0000 | −0.127517 | ||||||||
\(299\) | − 468.000i | − 1.56522i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 214.960i | − 0.711790i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 90.5097 | 0.297729 | ||||||||
\(305\) | − 333.754i | − 1.09428i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 265.872 | 0.866033 | 0.433017 | − | 0.901386i | \(-0.357449\pi\) | ||||
0.433017 | + | 0.901386i | \(0.357449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 288.000 | 0.929032 | ||||||||
\(311\) | 532.000i | 1.71061i | 0.518124 | + | 0.855305i | \(0.326631\pi\) | ||||
−0.518124 | + | 0.855305i | \(0.673369\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 148.492 | 0.474417 | 0.237208 | − | 0.971459i | \(-0.423768\pi\) | ||||
0.237208 | + | 0.971459i | \(0.423768\pi\) | |||||||
\(314\) | − 134.000i | − 0.426752i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 296.000 | 0.936709 | ||||||||
\(317\) | − 230.517i | − 0.727182i | −0.931559 | − | 0.363591i | \(-0.881551\pi\) | ||||
0.931559 | − | 0.363591i | \(-0.118449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 92.0000 | 0.288401 | ||||||||
\(320\) | 32.0000i | 0.100000i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 90.5097i | − 0.280216i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 114.551 | 0.352466 | ||||||||
\(326\) | 214.960i | 0.659388i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −107.480 | −0.327684 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 268.000 | 0.809668 | 0.404834 | − | 0.914390i | \(-0.367329\pi\) | ||||
0.404834 | + | 0.914390i | \(0.367329\pi\) | |||||||
\(332\) | 160.000i | 0.481928i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −164.049 | −0.491164 | ||||||||
\(335\) | 192.000i | 0.573134i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 170.000 | 0.504451 | 0.252226 | − | 0.967668i | \(-0.418838\pi\) | ||||
0.252226 | + | 0.967668i | \(0.418838\pi\) | |||||||
\(338\) | 9.89949i | 0.0292884i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 32.0000 | 0.0941176 | ||||||||
\(341\) | − 144.000i | − 0.422287i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 56.5685i | 0.164443i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 313.955 | 0.907386 | ||||||||
\(347\) | 280.014i | 0.806958i | 0.914989 | + | 0.403479i | \(0.132199\pi\) | ||||
−0.914989 | + | 0.403479i | \(0.867801\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −241.831 | −0.692924 | −0.346462 | − | 0.938064i | \(-0.612617\pi\) | ||||
−0.346462 | + | 0.938064i | \(0.612617\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.0000 | 0.0454545 | ||||||||
\(353\) | − 532.000i | − 1.50708i | −0.657401 | − | 0.753541i | \(-0.728344\pi\) | ||||
0.657401 | − | 0.753541i | \(-0.271656\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −305.470 | −0.860479 | ||||||||
\(356\) | − 212.000i | − 0.595506i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −84.0000 | −0.234637 | ||||||||
\(359\) | 342.240i | 0.953314i | 0.879089 | + | 0.476657i | \(0.158152\pi\) | ||||
−0.879089 | + | 0.476657i | \(0.841848\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 151.000 | 0.418283 | ||||||||
\(362\) | − 114.000i | − 0.314917i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 480.833i | 1.31735i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −684.479 | −1.86507 | −0.932533 | − | 0.361084i | \(-0.882407\pi\) | ||||
−0.932533 | + | 0.361084i | \(0.882407\pi\) | |||||||
\(368\) | − 147.078i | − 0.399669i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 181.019 | 0.489241 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 382.000 | 1.02413 | 0.512064 | − | 0.858947i | \(-0.328881\pi\) | ||||
0.512064 | + | 0.858947i | \(0.328881\pi\) | |||||||
\(374\) | − 16.0000i | − 0.0427807i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −56.5685 | −0.150448 | ||||||||
\(377\) | − 414.000i | − 1.09814i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −140.000 | −0.369393 | −0.184697 | − | 0.982796i | \(-0.559130\pi\) | ||||
−0.184697 | + | 0.982796i | \(0.559130\pi\) | |||||||
\(380\) | 181.019i | 0.476367i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 428.000 | 1.12042 | ||||||||
\(383\) | − 248.000i | − 0.647520i | −0.946139 | − | 0.323760i | \(-0.895053\pi\) | ||||
0.946139 | − | 0.323760i | \(-0.104947\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 308.299i | − 0.798701i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −308.299 | −0.794584 | ||||||||
\(389\) | 340.825i | 0.876158i | 0.898936 | + | 0.438079i | \(0.144341\pi\) | ||||
−0.898936 | + | 0.438079i | \(0.855659\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −147.078 | −0.376159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −406.000 | −1.03046 | ||||||||
\(395\) | 592.000i | 1.49873i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −244.659 | −0.616269 | −0.308135 | − | 0.951343i | \(-0.599705\pi\) | ||||
−0.308135 | + | 0.951343i | \(0.599705\pi\) | |||||||
\(398\) | 96.0000i | 0.241206i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 36.0000 | 0.0900000 | ||||||||
\(401\) | − 29.6985i | − 0.0740611i | −0.999314 | − | 0.0370305i | \(-0.988210\pi\) | ||||
0.999314 | − | 0.0370305i | \(-0.0117899\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −648.000 | −1.60794 | ||||||||
\(404\) | 252.000i | 0.623762i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 90.5097i | − 0.222382i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 606.698 | 1.48337 | 0.741684 | − | 0.670749i | \(-0.234027\pi\) | ||||
0.741684 | + | 0.670749i | \(0.234027\pi\) | |||||||
\(410\) | − 214.960i | − 0.524294i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 147.078 | 0.356986 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −320.000 | −0.771084 | ||||||||
\(416\) | − 72.0000i | − 0.173077i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 90.5097 | 0.216530 | ||||||||
\(419\) | 692.000i | 1.65155i | 0.563999 | + | 0.825776i | \(0.309262\pi\) | ||||
−0.563999 | + | 0.825776i | \(0.690738\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 384.000 | 0.912114 | 0.456057 | − | 0.889951i | \(-0.349261\pi\) | ||||
0.456057 | + | 0.889951i | \(0.349261\pi\) | |||||||
\(422\) | − 186.676i | − 0.442361i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 268.000 | 0.632075 | ||||||||
\(425\) | − 36.0000i | − 0.0847059i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 141.421i | 0.330424i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −113.137 | −0.263109 | ||||||||
\(431\) | − 110.309i | − 0.255937i | −0.991778 | − | 0.127968i | \(-0.959154\pi\) | ||||
0.991778 | − | 0.127968i | \(-0.0408456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −156.978 | −0.362535 | −0.181268 | − | 0.983434i | \(-0.558020\pi\) | ||||
−0.181268 | + | 0.983434i | \(0.558020\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 172.000 | 0.394495 | ||||||||
\(437\) | − 832.000i | − 1.90389i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 203.647 | 0.463888 | 0.231944 | − | 0.972729i | \(-0.425491\pi\) | ||||
0.231944 | + | 0.972729i | \(0.425491\pi\) | |||||||
\(440\) | 32.0000i | 0.0727273i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −72.0000 | −0.162896 | ||||||||
\(443\) | 811.759i | 1.83241i | 0.400707 | + | 0.916206i | \(0.368764\pi\) | ||||
−0.400707 | + | 0.916206i | \(0.631236\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 424.000 | 0.952809 | ||||||||
\(446\) | 240.000i | 0.538117i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 284.257i | − 0.633089i | −0.948578 | − | 0.316544i | \(-0.897477\pi\) | ||||
0.948578 | − | 0.316544i | \(-0.102523\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −107.480 | −0.238315 | ||||||||
\(452\) | − 42.4264i | − 0.0938637i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 424.264 | 0.934502 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −288.000 | −0.630197 | −0.315098 | − | 0.949059i | \(-0.602038\pi\) | ||||
−0.315098 | + | 0.949059i | \(0.602038\pi\) | |||||||
\(458\) | 354.000i | 0.772926i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 294.156 | 0.639470 | ||||||||
\(461\) | 706.000i | 1.53145i | 0.643166 | + | 0.765727i | \(0.277620\pi\) | ||||
−0.643166 | + | 0.765727i | \(0.722380\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −356.000 | −0.768898 | −0.384449 | − | 0.923146i | \(-0.625609\pi\) | ||||
−0.384449 | + | 0.923146i | \(0.625609\pi\) | |||||||
\(464\) | − 130.108i | − 0.280404i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −42.0000 | −0.0901288 | ||||||||
\(467\) | 884.000i | 1.89293i | 0.322801 | + | 0.946467i | \(0.395375\pi\) | ||||
−0.322801 | + | 0.946467i | \(0.604625\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 113.137i | − 0.240717i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.3137 | 0.0239697 | ||||||||
\(473\) | 56.5685i | 0.119595i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 203.647 | 0.428730 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −228.000 | −0.476987 | ||||||||
\(479\) | − 508.000i | − 1.06054i | −0.847828 | − | 0.530271i | \(-0.822090\pi\) | ||||
0.847828 | − | 0.530271i | \(-0.177910\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −407.294 | −0.846764 | ||||||||
\(482\) | − 534.000i | − 1.10788i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −226.000 | −0.466942 | ||||||||
\(485\) | − 616.597i | − 1.27133i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −624.000 | −1.28131 | −0.640657 | − | 0.767827i | \(-0.721338\pi\) | ||||
−0.640657 | + | 0.767827i | \(0.721338\pi\) | |||||||
\(488\) | 236.000i | 0.483607i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 840.043i | 1.71088i | 0.517901 | + | 0.855441i | \(0.326714\pi\) | ||||
−0.517901 | + | 0.855441i | \(0.673286\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −130.108 | −0.263910 | ||||||||
\(494\) | − 407.294i | − 0.824481i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −203.647 | −0.410578 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −940.000 | −1.88377 | −0.941884 | − | 0.335939i | \(-0.890946\pi\) | ||||
−0.941884 | + | 0.335939i | \(0.890946\pi\) | |||||||
\(500\) | 272.000i | 0.544000i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −673.166 | −1.34097 | ||||||||
\(503\) | − 632.000i | − 1.25646i | −0.778027 | − | 0.628231i | \(-0.783779\pi\) | ||||
0.778027 | − | 0.628231i | \(-0.216221\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −504.000 | −0.998020 | ||||||||
\(506\) | − 147.078i | − 0.290668i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.00000 | −0.0157480 | ||||||||
\(509\) | 220.000i | 0.432220i | 0.976369 | + | 0.216110i | \(0.0693370\pi\) | ||||
−0.976369 | + | 0.216110i | \(0.930663\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 22.6274i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −144.250 | −0.280642 | ||||||||
\(515\) | 294.156i | 0.571178i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −56.5685 | −0.109417 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 144.000 | 0.276923 | ||||||||
\(521\) | − 508.000i | − 0.975048i | −0.873110 | − | 0.487524i | \(-0.837900\pi\) | ||||
0.873110 | − | 0.487524i | \(-0.162100\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 814.587 | 1.55753 | 0.778764 | − | 0.627317i | \(-0.215847\pi\) | ||||
0.778764 | + | 0.627317i | \(0.215847\pi\) | |||||||
\(524\) | − 48.0000i | − 0.0916031i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 516.000 | 0.980989 | ||||||||
\(527\) | 203.647i | 0.386426i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −823.000 | −1.55577 | ||||||||
\(530\) | 536.000i | 1.01132i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 483.661i | 0.907432i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −282.843 | −0.528678 | ||||||||
\(536\) | − 135.765i | − 0.253292i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 277.186 | 0.515215 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −464.000 | −0.857671 | −0.428835 | − | 0.903383i | \(-0.641076\pi\) | ||||
−0.428835 | + | 0.903383i | \(0.641076\pi\) | |||||||
\(542\) | − 248.000i | − 0.457565i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −22.6274 | −0.0415945 | ||||||||
\(545\) | 344.000i | 0.631193i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −80.0000 | −0.146252 | −0.0731261 | − | 0.997323i | \(-0.523298\pi\) | ||||
−0.0731261 | + | 0.997323i | \(0.523298\pi\) | |||||||
\(548\) | 144.250i | 0.263230i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 36.0000 | 0.0654545 | ||||||||
\(551\) | − 736.000i | − 1.33575i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 362.039i | − 0.653499i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −282.843 | −0.508710 | ||||||||
\(557\) | − 912.168i | − 1.63764i | −0.574047 | − | 0.818822i | \(-0.694628\pi\) | ||||
0.574047 | − | 0.818822i | \(-0.305372\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 254.558 | 0.455382 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −38.0000 | −0.0676157 | ||||||||
\(563\) | − 316.000i | − 0.561279i | −0.959813 | − | 0.280639i | \(-0.909453\pi\) | ||||
0.959813 | − | 0.280639i | \(-0.0905465\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 84.8528 | 0.150182 | ||||||||
\(566\) | − 712.000i | − 1.25795i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 216.000 | 0.380282 | ||||||||
\(569\) | − 1112.99i | − 1.95604i | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
0.208514 | − | 0.978019i | \(-0.433137\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −440.000 | −0.770578 | −0.385289 | − | 0.922796i | \(-0.625898\pi\) | ||||
−0.385289 | + | 0.922796i | \(0.625898\pi\) | |||||||
\(572\) | − 72.0000i | − 0.125874i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 330.926i | − 0.575523i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −318.198 | −0.551470 | −0.275735 | − | 0.961234i | \(-0.588921\pi\) | ||||
−0.275735 | + | 0.961234i | \(0.588921\pi\) | |||||||
\(578\) | − 386.080i | − 0.667959i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 260.215 | 0.448647 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 268.000 | 0.459691 | ||||||||
\(584\) | − 340.000i | − 0.582192i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 268.701 | 0.458533 | ||||||||
\(587\) | 300.000i | 0.511073i | 0.966799 | + | 0.255537i | \(0.0822521\pi\) | ||||
−0.966799 | + | 0.255537i | \(0.917748\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1152.00 | −1.95586 | ||||||||
\(590\) | 22.6274i | 0.0383516i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −128.000 | −0.216216 | ||||||||
\(593\) | 1036.00i | 1.74705i | 0.486780 | + | 0.873524i | \(0.338171\pi\) | ||||
−0.486780 | + | 0.873524i | \(0.661829\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 53.7401i | 0.0901680i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −661.852 | −1.10678 | ||||||||
\(599\) | 981.464i | 1.63850i | 0.573433 | + | 0.819252i | \(0.305611\pi\) | ||||
−0.573433 | + | 0.819252i | \(0.694389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −352.139 | −0.585922 | −0.292961 | − | 0.956124i | \(-0.594641\pi\) | ||||
−0.292961 | + | 0.956124i | \(0.594641\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −304.000 | −0.503311 | ||||||||
\(605\) | − 452.000i | − 0.747107i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 865.499 | 1.42586 | 0.712931 | − | 0.701234i | \(-0.247367\pi\) | ||||
0.712931 | + | 0.701234i | \(0.247367\pi\) | |||||||
\(608\) | − 128.000i | − 0.210526i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −472.000 | −0.773770 | ||||||||
\(611\) | 254.558i | 0.416626i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −264.000 | −0.430669 | −0.215334 | − | 0.976540i | \(-0.569084\pi\) | ||||
−0.215334 | + | 0.976540i | \(0.569084\pi\) | |||||||
\(614\) | − 376.000i | − 0.612378i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.5563i | 0.0252129i | 0.999921 | + | 0.0126064i | \(0.00401286\pi\) | ||||
−0.999921 | + | 0.0126064i | \(0.995987\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −401.637 | −0.648848 | −0.324424 | − | 0.945912i | \(-0.605170\pi\) | ||||
−0.324424 | + | 0.945912i | \(0.605170\pi\) | |||||||
\(620\) | − 407.294i | − 0.656925i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 752.362 | 1.20958 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −319.000 | −0.510400 | ||||||||
\(626\) | − 210.000i | − 0.335463i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −189.505 | −0.301759 | ||||||||
\(629\) | 128.000i | 0.203498i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −676.000 | −1.07132 | −0.535658 | − | 0.844435i | \(-0.679936\pi\) | ||||
−0.535658 | + | 0.844435i | \(0.679936\pi\) | |||||||
\(632\) | − 418.607i | − 0.662353i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −326.000 | −0.514196 | ||||||||
\(635\) | − 16.0000i | − 0.0251969i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 130.108i | − 0.203930i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 45.2548 | 0.0707107 | ||||||||
\(641\) | 909.339i | 1.41863i | 0.704894 | + | 0.709313i | \(0.250995\pi\) | ||||
−0.704894 | + | 0.709313i | \(0.749005\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 480.833 | 0.747796 | 0.373898 | − | 0.927470i | \(-0.378021\pi\) | ||||
0.373898 | + | 0.927470i | \(0.378021\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −128.000 | −0.198142 | ||||||||
\(647\) | 588.000i | 0.908810i | 0.890795 | + | 0.454405i | \(0.150148\pi\) | ||||
−0.890795 | + | 0.454405i | \(0.849852\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.3137 | 0.0174325 | ||||||||
\(650\) | − 162.000i | − 0.249231i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 304.000 | 0.466258 | ||||||||
\(653\) | − 453.963i | − 0.695195i | −0.937644 | − | 0.347598i | \(-0.886998\pi\) | ||||
0.937644 | − | 0.347598i | \(-0.113002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 96.0000 | 0.146565 | ||||||||
\(656\) | 152.000i | 0.231707i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 755.190i | 1.14596i | 0.819568 | + | 0.572982i | \(0.194213\pi\) | ||||
−0.819568 | + | 0.572982i | \(0.805787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 241.831 | 0.365856 | 0.182928 | − | 0.983126i | \(-0.441443\pi\) | ||||
0.182928 | + | 0.983126i | \(0.441443\pi\) | |||||||
\(662\) | − 379.009i | − 0.572522i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 226.274 | 0.340774 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1196.00 | −1.79310 | ||||||||
\(668\) | 232.000i | 0.347305i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 271.529 | 0.405267 | ||||||||
\(671\) | 236.000i | 0.351714i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1176.00 | 1.74740 | 0.873700 | − | 0.486465i | \(-0.161714\pi\) | ||||
0.873700 | + | 0.486465i | \(0.161714\pi\) | |||||||
\(674\) | − 240.416i | − 0.356701i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.0000 | 0.0207101 | ||||||||
\(677\) | 222.000i | 0.327917i | 0.986467 | + | 0.163959i | \(0.0524264\pi\) | ||||
−0.986467 | + | 0.163959i | \(0.947574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 45.2548i | − 0.0665512i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −203.647 | −0.298602 | ||||||||
\(683\) | − 517.602i | − 0.757836i | −0.925430 | − | 0.378918i | \(-0.876296\pi\) | ||||
0.925430 | − | 0.378918i | \(-0.123704\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −288.500 | −0.421167 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 80.0000 | 0.116279 | ||||||||
\(689\) | − 1206.00i | − 1.75036i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 644.881 | 0.933258 | 0.466629 | − | 0.884453i | \(-0.345468\pi\) | ||||
0.466629 | + | 0.884453i | \(0.345468\pi\) | |||||||
\(692\) | − 444.000i | − 0.641618i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 396.000 | 0.570605 | ||||||||
\(695\) | − 565.685i | − 0.813936i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 152.000 | 0.218077 | ||||||||
\(698\) | 342.000i | 0.489971i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 657.609i | − 0.938102i | −0.883171 | − | 0.469051i | \(-0.844596\pi\) | ||||
0.883171 | − | 0.469051i | \(-0.155404\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −724.077 | −1.02998 | ||||||||
\(704\) | − 22.6274i | − 0.0321412i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −752.362 | −1.06567 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 106.000 | 0.149506 | 0.0747532 | − | 0.997202i | \(-0.476183\pi\) | ||||
0.0747532 | + | 0.997202i | \(0.476183\pi\) | |||||||
\(710\) | 432.000i | 0.608451i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −299.813 | −0.421086 | ||||||||
\(713\) | 1872.00i | 2.62553i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 144.000 | 0.201399 | ||||||||
\(716\) | 118.794i | 0.165913i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 484.000 | 0.674095 | ||||||||
\(719\) | − 1216.00i | − 1.69124i | −0.533787 | − | 0.845619i | \(-0.679232\pi\) | ||||
0.533787 | − | 0.845619i | \(-0.320768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 213.546i | − 0.295770i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −161.220 | −0.222680 | ||||||||
\(725\) | − 292.742i | − 0.403782i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 73.5391 | 0.101154 | 0.0505771 | − | 0.998720i | \(-0.483894\pi\) | ||||
0.0505771 | + | 0.998720i | \(0.483894\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 680.000 | 0.931507 | ||||||||
\(731\) | − 80.0000i | − 0.109439i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 420.021 | 0.573017 | 0.286508 | − | 0.958078i | \(-0.407505\pi\) | ||||
0.286508 | + | 0.958078i | \(0.407505\pi\) | |||||||
\(734\) | 968.000i | 1.31880i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −208.000 | −0.282609 | ||||||||
\(737\) | − 135.765i | − 0.184212i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −408.000 | −0.552097 | −0.276049 | − | 0.961144i | \(-0.589025\pi\) | ||||
−0.276049 | + | 0.961144i | \(0.589025\pi\) | |||||||
\(740\) | − 256.000i | − 0.345946i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 489.318i | − 0.658571i | −0.944230 | − | 0.329285i | \(-0.893192\pi\) | ||||
0.944230 | − | 0.329285i | \(-0.106808\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −107.480 | −0.144269 | ||||||||
\(746\) | − 540.230i | − 0.724168i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.6274 | −0.0302506 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −136.000 | −0.181092 | −0.0905459 | − | 0.995892i | \(-0.528861\pi\) | ||||
−0.0905459 | + | 0.995892i | \(0.528861\pi\) | |||||||
\(752\) | 80.0000i | 0.106383i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −585.484 | −0.776505 | ||||||||
\(755\) | − 608.000i | − 0.805298i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 758.000 | 1.00132 | 0.500661 | − | 0.865644i | \(-0.333091\pi\) | ||||
0.500661 | + | 0.865644i | \(0.333091\pi\) | |||||||
\(758\) | 197.990i | 0.261200i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 256.000 | 0.336842 | ||||||||
\(761\) | 58.0000i | 0.0762155i | 0.999274 | + | 0.0381078i | \(0.0121330\pi\) | ||||
−0.999274 | + | 0.0381078i | \(0.987867\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 605.283i | − 0.792256i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −350.725 | −0.457865 | ||||||||
\(767\) | − 50.9117i | − 0.0663777i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 292.742 | 0.380679 | 0.190340 | − | 0.981718i | \(-0.439041\pi\) | ||||
0.190340 | + | 0.981718i | \(0.439041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −436.000 | −0.564767 | ||||||||
\(773\) | − 302.000i | − 0.390686i | −0.980735 | − | 0.195343i | \(-0.937418\pi\) | ||||
0.980735 | − | 0.195343i | \(-0.0625819\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −458.205 | −0.591233 | ||||||||
\(776\) | 436.000i | 0.561856i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 482.000 | 0.619537 | ||||||||
\(779\) | 859.842i | 1.10378i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 216.000 | 0.276569 | ||||||||
\(782\) | 208.000i | 0.265985i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 379.009i | − 0.482814i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −497.803 | −0.632533 | −0.316266 | − | 0.948670i | \(-0.602429\pi\) | ||||
−0.316266 | + | 0.948670i | \(0.602429\pi\) | |||||||
\(788\) | 574.171i | 0.728643i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 837.214 | 1.05977 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1062.00 | 1.33922 | ||||||||
\(794\) | 346.000i | 0.435768i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 135.765 | 0.170558 | ||||||||
\(797\) | − 30.0000i | − 0.0376412i | −0.999823 | − | 0.0188206i | \(-0.994009\pi\) | ||||
0.999823 | − | 0.0188206i | \(-0.00599113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 80.0000 | 0.100125 | ||||||||
\(800\) | − 50.9117i | − 0.0636396i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −42.0000 | −0.0523691 | ||||||||
\(803\) | − 340.000i | − 0.423412i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 916.410i | 1.13699i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 356.382 | 0.441067 | ||||||||
\(809\) | − 982.878i | − 1.21493i | −0.794346 | − | 0.607465i | \(-0.792186\pi\) | ||||
0.794346 | − | 0.607465i | \(-0.207814\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −458.205 | −0.564988 | −0.282494 | − | 0.959269i | \(-0.591162\pi\) | ||||
−0.282494 | + | 0.959269i | \(0.591162\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −128.000 | −0.157248 | ||||||||
\(815\) | 608.000i | 0.746012i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 452.548 | 0.553915 | ||||||||
\(818\) | − 858.000i | − 1.04890i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −304.000 | −0.370732 | ||||||||
\(821\) | 606.698i | 0.738974i | 0.929236 | + | 0.369487i | \(0.120467\pi\) | ||||
−0.929236 | + | 0.369487i | \(0.879533\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −68.0000 | −0.0826245 | −0.0413123 | − | 0.999146i | \(-0.513154\pi\) | ||||
−0.0413123 | + | 0.999146i | \(0.513154\pi\) | |||||||
\(824\) | − 208.000i | − 0.252427i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 195.161i | − 0.235987i | −0.993014 | − | 0.117994i | \(-0.962354\pi\) | ||||
0.993014 | − | 0.117994i | \(-0.0376462\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1245.92 | 1.50292 | 0.751461 | − | 0.659778i | \(-0.229350\pi\) | ||||
0.751461 | + | 0.659778i | \(0.229350\pi\) | |||||||
\(830\) | 452.548i | 0.545239i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −101.823 | −0.122384 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −464.000 | −0.555689 | ||||||||
\(836\) | − 128.000i | − 0.153110i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 978.636 | 1.16782 | ||||||||
\(839\) | 1196.00i | 1.42551i | 0.701415 | + | 0.712753i | \(0.252552\pi\) | ||||
−0.701415 | + | 0.712753i | \(0.747448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −217.000 | −0.258026 | ||||||||
\(842\) | − 543.058i | − 0.644962i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −264.000 | −0.312796 | ||||||||
\(845\) | 28.0000i | 0.0331361i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 379.009i | − 0.446945i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −50.9117 | −0.0598961 | ||||||||
\(851\) | 1176.63i | 1.38264i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1217.64 | −1.42748 | −0.713738 | − | 0.700412i | \(-0.752999\pi\) | ||||
−0.713738 | + | 0.700412i | \(0.752999\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 200.000 | 0.233645 | ||||||||
\(857\) | 634.000i | 0.739790i | 0.929074 | + | 0.369895i | \(0.120606\pi\) | ||||
−0.929074 | + | 0.369895i | \(0.879394\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1600.89 | −1.86367 | −0.931833 | − | 0.362886i | \(-0.881791\pi\) | ||||
−0.931833 | + | 0.362886i | \(0.881791\pi\) | |||||||
\(860\) | 160.000i | 0.186047i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −156.000 | −0.180974 | ||||||||
\(863\) | − 461.034i | − 0.534222i | −0.963666 | − | 0.267111i | \(-0.913931\pi\) | ||||
0.963666 | − | 0.267111i | \(-0.0860690\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 888.000 | 1.02659 | ||||||||
\(866\) | 222.000i | 0.256351i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 418.607i | − 0.481711i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −610.940 | −0.701424 | ||||||||
\(872\) | − 243.245i | − 0.278950i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1176.63 | −1.34625 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1256.00 | 1.43216 | 0.716078 | − | 0.698021i | \(-0.245936\pi\) | ||||
0.716078 | + | 0.698021i | \(0.245936\pi\) | |||||||
\(878\) | − 288.000i | − 0.328018i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 45.2548 | 0.0514259 | ||||||||
\(881\) | − 1092.00i | − 1.23950i | −0.784799 | − | 0.619750i | \(-0.787234\pi\) | ||||
0.784799 | − | 0.619750i | \(-0.212766\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 284.000 | 0.321631 | 0.160815 | − | 0.986985i | \(-0.448588\pi\) | ||||
0.160815 | + | 0.986985i | \(0.448588\pi\) | |||||||
\(884\) | 101.823i | 0.115185i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1148.00 | 1.29571 | ||||||||
\(887\) | − 716.000i | − 0.807215i | −0.914932 | − | 0.403608i | \(-0.867756\pi\) | ||||
0.914932 | − | 0.403608i | \(-0.132244\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 599.627i | − 0.673738i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 339.411 | 0.380506 | ||||||||
\(893\) | 452.548i | 0.506773i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −237.588 | −0.265461 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −402.000 | −0.447661 | ||||||||
\(899\) | 1656.00i | 1.84205i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −379.009 | −0.420654 | ||||||||
\(902\) | 152.000i | 0.168514i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −60.0000 | −0.0663717 | ||||||||
\(905\) | − 322.441i | − 0.356288i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 724.000 | 0.798236 | 0.399118 | − | 0.916900i | \(-0.369316\pi\) | ||||
0.399118 | + | 0.916900i | \(0.369316\pi\) | |||||||
\(908\) | − 600.000i | − 0.660793i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 302.642i | 0.332208i | 0.986108 | + | 0.166104i | \(0.0531188\pi\) | ||||
−0.986108 | + | 0.166104i | \(0.946881\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 226.274 | 0.247836 | ||||||||
\(914\) | 407.294i | 0.445617i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 500.632 | 0.546541 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 376.000 | 0.409140 | 0.204570 | − | 0.978852i | \(-0.434420\pi\) | ||||
0.204570 | + | 0.978852i | \(0.434420\pi\) | |||||||
\(920\) | − 416.000i | − 0.452174i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 998.435 | 1.08290 | ||||||||
\(923\) | − 972.000i | − 1.05309i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −288.000 | −0.311351 | ||||||||
\(926\) | 503.460i | 0.543693i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −184.000 | −0.198276 | ||||||||
\(929\) | − 1210.00i | − 1.30248i | −0.758874 | − | 0.651238i | \(-0.774250\pi\) | ||||
0.758874 | − | 0.651238i | \(-0.225750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 59.3970i | 0.0637307i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1250.16 | 1.33851 | ||||||||
\(935\) | − 45.2548i | − 0.0484009i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 994.192 | 1.06104 | 0.530519 | − | 0.847673i | \(-0.321997\pi\) | ||||
0.530519 | + | 0.847673i | \(0.321997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −160.000 | −0.170213 | ||||||||
\(941\) | 44.0000i | 0.0467588i | 0.999727 | + | 0.0233794i | \(0.00744257\pi\) | ||||
−0.999727 | + | 0.0233794i | \(0.992557\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1397.24 | 1.48170 | ||||||||
\(944\) | − 16.0000i | − 0.0169492i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 80.0000 | 0.0845666 | ||||||||
\(947\) | 1009.75i | 1.06626i | 0.846033 | + | 0.533130i | \(0.178984\pi\) | ||||
−0.846033 | + | 0.533130i | \(0.821016\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1530.00 | −1.61222 | ||||||||
\(950\) | − 288.000i | − 0.303158i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1322.29i | 1.38750i | 0.720215 | + | 0.693751i | \(0.244043\pi\) | ||||
−0.720215 | + | 0.693751i | \(0.755957\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1210.57 | 1.26761 | ||||||||
\(956\) | 322.441i | 0.337281i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −718.420 | −0.749917 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1631.00 | 1.69719 | ||||||||
\(962\) | 576.000i | 0.598753i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −755.190 | −0.783392 | ||||||||
\(965\) | − 872.000i | − 0.903627i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 876.000 | 0.905895 | 0.452947 | − | 0.891537i | \(-0.350373\pi\) | ||||
0.452947 | + | 0.891537i | \(0.350373\pi\) | |||||||
\(968\) | 319.612i | 0.330178i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −872.000 | −0.898969 | ||||||||
\(971\) | 1448.00i | 1.49125i | 0.666368 | + | 0.745623i | \(0.267848\pi\) | ||||
−0.666368 | + | 0.745623i | \(0.732152\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 882.469i | 0.906026i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 333.754 | 0.341961 | ||||||||
\(977\) | − 1489.17i | − 1.52422i | −0.647445 | − | 0.762112i | \(-0.724163\pi\) | ||||
0.647445 | − | 0.762112i | \(-0.275837\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −299.813 | −0.306244 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1188.00 | 1.20978 | ||||||||
\(983\) | − 32.0000i | − 0.0325534i | −0.999868 | − | 0.0162767i | \(-0.994819\pi\) | ||||
0.999868 | − | 0.0162767i | \(-0.00518126\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1148.34 | −1.16583 | ||||||||
\(986\) | 184.000i | 0.186613i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −576.000 | −0.582996 | ||||||||
\(989\) | − 735.391i | − 0.743570i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −280.000 | −0.282543 | −0.141271 | − | 0.989971i | \(-0.545119\pi\) | ||||
−0.141271 | + | 0.989971i | \(0.545119\pi\) | |||||||
\(992\) | 288.000i | 0.290323i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 271.529i | 0.272893i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1093.19 | 1.09648 | 0.548238 | − | 0.836322i | \(-0.315299\pi\) | ||||
0.548238 | + | 0.836322i | \(0.315299\pi\) | |||||||
\(998\) | 1329.36i | 1.33202i | ||||||||
\(999\) | 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 | 882.3.b.h.197.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 882.3.b.h.197.4 | yes | 4 | |
7.2 | even | 3 | 882.3.s.g.557.1 | 8 | |||
7.3 | odd | 6 | 882.3.s.g.863.3 | 8 | |||
7.4 | even | 3 | 882.3.s.g.863.4 | 8 | |||
7.5 | odd | 6 | 882.3.s.g.557.2 | 8 | |||
7.6 | odd | 2 | inner | 882.3.b.h.197.2 | yes | 4 | |
21.2 | odd | 6 | 882.3.s.g.557.4 | 8 | |||
21.5 | even | 6 | 882.3.s.g.557.3 | 8 | |||
21.11 | odd | 6 | 882.3.s.g.863.1 | 8 | |||
21.17 | even | 6 | 882.3.s.g.863.2 | 8 | |||
21.20 | even | 2 | inner | 882.3.b.h.197.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.3.b.h.197.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
882.3.b.h.197.2 | yes | 4 | 7.6 | odd | 2 | inner | |
882.3.b.h.197.3 | yes | 4 | 21.20 | even | 2 | inner | |
882.3.b.h.197.4 | yes | 4 | 3.2 | odd | 2 | inner | |
882.3.s.g.557.1 | 8 | 7.2 | even | 3 | |||
882.3.s.g.557.2 | 8 | 7.5 | odd | 6 | |||
882.3.s.g.557.3 | 8 | 21.5 | even | 6 | |||
882.3.s.g.557.4 | 8 | 21.2 | odd | 6 | |||
882.3.s.g.863.1 | 8 | 21.11 | odd | 6 | |||
882.3.s.g.863.2 | 8 | 21.17 | even | 6 | |||
882.3.s.g.863.3 | 8 | 7.3 | odd | 6 | |||
882.3.s.g.863.4 | 8 | 7.4 | even | 3 |