Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(449,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.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: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(-0.765367i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.449 |
Dual form | 896.2.b.h.449.4 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 2.61313i | − 1.50869i | −0.656479 | − | 0.754344i | \(-0.727955\pi\) | ||||
0.656479 | − | 0.754344i | \(-0.272045\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.61313i | − 1.16863i | −0.811529 | − | 0.584313i | \(-0.801364\pi\) | ||||
0.811529 | − | 0.584313i | \(-0.198636\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.82843 | −1.27614 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.16478i | − 0.652707i | −0.945248 | − | 0.326354i | \(-0.894180\pi\) | ||||
0.945248 | − | 0.326354i | \(-0.105820\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.448342i | 0.124348i | 0.998065 | + | 0.0621738i | \(0.0198033\pi\) | ||||
−0.998065 | + | 0.0621738i | \(0.980197\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.82843 | −1.76309 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.65685 | −1.85706 | −0.928530 | − | 0.371257i | \(-0.878927\pi\) | ||||
−0.928530 | + | 0.371257i | \(0.878927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.77791i | − 1.09613i | −0.836436 | − | 0.548064i | \(-0.815365\pi\) | ||||
0.836436 | − | 0.548064i | \(-0.184635\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 2.61313i | − 0.570231i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.82843 | 1.42383 | 0.711913 | − | 0.702268i | \(-0.247829\pi\) | ||||
0.711913 | + | 0.702268i | \(0.247829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.82843 | −0.365685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.16478i | 0.416613i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.55582i | 1.77447i | 0.461316 | + | 0.887236i | \(0.347377\pi\) | ||||
−0.461316 | + | 0.887236i | \(0.652623\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.65685 | −0.984732 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.61313i | − 0.441699i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.22625i | − 0.859191i | −0.903022 | − | 0.429595i | \(-0.858656\pi\) | ||||
0.903022 | − | 0.429595i | \(-0.141344\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.17157 | 0.187602 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.65685 | −0.571105 | −0.285552 | − | 0.958363i | \(-0.592177\pi\) | ||||
−0.285552 | + | 0.958363i | \(0.592177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.16478i | 0.330127i | 0.986283 | + | 0.165063i | \(0.0527828\pi\) | ||||
−0.986283 | + | 0.165063i | \(0.947217\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.0042i | 1.49133i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.0083i | 2.80173i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4525i | 1.43576i | 0.696166 | + | 0.717881i | \(0.254888\pi\) | ||||
−0.696166 | + | 0.717881i | \(0.745112\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.65685 | −0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.4853 | −1.65372 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.448342i | 0.0583691i | 0.999574 | + | 0.0291845i | \(0.00929105\pi\) | ||||
−0.999574 | + | 0.0291845i | \(0.990709\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 12.1689i | − 1.55807i | −0.626978 | − | 0.779037i | \(-0.715708\pi\) | ||||
0.626978 | − | 0.779037i | \(-0.284292\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.82843 | −0.482336 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.17157 | 0.145316 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 3.06147i | − 0.374018i | −0.982358 | − | 0.187009i | \(-0.940121\pi\) | ||||
0.982358 | − | 0.187009i | \(-0.0598793\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 17.8435i | − 2.14811i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.34315 | 0.278080 | 0.139040 | − | 0.990287i | \(-0.455598\pi\) | ||||
0.139040 | + | 0.990287i | \(0.455598\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6569 | 1.36433 | 0.682166 | − | 0.731198i | \(-0.261038\pi\) | ||||
0.682166 | + | 0.731198i | \(0.261038\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.77791i | 0.551706i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.16478i | − 0.246700i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.34315 | −0.263624 | −0.131812 | − | 0.991275i | \(-0.542080\pi\) | ||||
−0.131812 | + | 0.991275i | \(0.542080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.82843 | −0.647603 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0656i | 1.43414i | 0.697002 | + | 0.717070i | \(0.254517\pi\) | ||||
−0.697002 | + | 0.717070i | \(0.745483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.0083i | 2.17021i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 24.9706 | 2.67713 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.448342i | 0.0469990i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 14.7821i | − 1.53283i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.4853 | −1.28096 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.28772i | 0.832947i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.77791i | 0.475420i | 0.971336 | + | 0.237710i | \(0.0763968\pi\) | ||||
−0.971336 | + | 0.237710i | \(0.923603\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.6569 | 1.34565 | 0.672825 | − | 0.739802i | \(-0.265081\pi\) | ||||
0.672825 | + | 0.739802i | \(0.265081\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.82843 | −0.666386 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 13.5140i | − 1.30644i | −0.757166 | − | 0.653222i | \(-0.773417\pi\) | ||||
0.757166 | − | 0.653222i | \(-0.226583\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 11.3492i | − 1.08705i | −0.839391 | − | 0.543527i | \(-0.817088\pi\) | ||||
0.839391 | − | 0.543527i | \(-0.182912\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.6569 | −1.29625 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.82843 | 0.830509 | 0.415254 | − | 0.909705i | \(-0.363693\pi\) | ||||
0.415254 | + | 0.909705i | \(0.363693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 17.8435i | − 1.66392i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1.71644i | − 0.158685i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.65685 | −0.701903 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.31371 | 0.573973 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.55582i | 0.861619i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 8.28772i | − 0.741276i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.48528 | −0.398004 | −0.199002 | − | 0.979999i | \(-0.563770\pi\) | ||||
−0.199002 | + | 0.979999i | \(0.563770\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.65685 | 0.498058 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 18.2919i | − 1.59817i | −0.601219 | − | 0.799085i | \(-0.705318\pi\) | ||||
0.601219 | − | 0.799085i | \(-0.294682\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.77791i | − 0.414297i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.65685 | 0.486864 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 19.5600i | − 1.65906i | −0.558465 | − | 0.829528i | \(-0.688610\pi\) | ||||
0.558465 | − | 0.829528i | \(-0.311390\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.9050i | 1.76052i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.970563 | 0.0811625 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.9706 | 2.07369 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2.61313i | − 0.215527i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.5754i | 1.35791i | 0.734179 | + | 0.678956i | \(0.237567\pi\) | ||||
−0.734179 | + | 0.678956i | \(0.762433\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1421 | −1.47639 | −0.738193 | − | 0.674590i | \(-0.764321\pi\) | ||||
−0.738193 | + | 0.674590i | \(0.764321\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.3137 | 2.36987 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 14.7821i | − 1.18732i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.77791i | 0.381319i | 0.981656 | + | 0.190659i | \(0.0610626\pi\) | ||||
−0.981656 | + | 0.190659i | \(0.938937\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.3137 | 2.16612 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.82843 | 0.538155 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.95815i | 0.310026i | 0.987912 | + | 0.155013i | \(0.0495420\pi\) | ||||
−0.987912 | + | 0.155013i | \(0.950458\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.7821i | 1.15078i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.0000 | 1.23812 | 0.619059 | − | 0.785345i | \(-0.287514\pi\) | ||||
0.619059 | + | 0.785345i | \(0.287514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7990 | 0.984538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.2919i | 1.39882i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 16.1271i | − 1.22612i | −0.790036 | − | 0.613060i | \(-0.789938\pi\) | ||||
0.790036 | − | 0.613060i | \(-0.210062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.82843 | −0.138216 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.17157 | 0.0880608 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 22.1731i | − 1.65730i | −0.559770 | − | 0.828648i | \(-0.689111\pi\) | ||||
0.559770 | − | 0.828648i | \(-0.310889\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.61313i | 0.194232i | 0.995273 | + | 0.0971161i | \(0.0309618\pi\) | ||||
−0.995273 | + | 0.0971161i | \(0.969038\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −31.7990 | −2.35065 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.6569 | −1.00407 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.5754i | 1.21212i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.16478i | 0.157465i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3137 | 1.39749 | 0.698745 | − | 0.715370i | \(-0.253742\pi\) | ||||
0.698745 | + | 0.715370i | \(0.253742\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.7990 | 0.993273 | 0.496637 | − | 0.867959i | \(-0.334568\pi\) | ||||
0.496637 | + | 0.867959i | \(0.334568\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 3.06147i | − 0.219236i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 6.12293i | − 0.436241i | −0.975922 | − | 0.218121i | \(-0.930007\pi\) | ||||
0.975922 | − | 0.218121i | \(-0.0699926\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.97056 | 0.635906 | 0.317953 | − | 0.948106i | \(-0.397005\pi\) | ||||
0.317953 | + | 0.948106i | \(0.397005\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.55582i | 0.670687i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.55582i | 0.667407i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −26.1421 | −1.81700 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.3431 | −0.715450 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 9.18440i | − 0.632280i | −0.948712 | − | 0.316140i | \(-0.897613\pi\) | ||||
0.948712 | − | 0.316140i | \(-0.102387\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 6.12293i | − 0.419537i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.65685 | 0.385794 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.65685 | 0.384012 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 30.4608i | − 2.05835i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 3.43289i | − 0.230921i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.97056 | −0.600713 | −0.300357 | − | 0.953827i | \(-0.597106\pi\) | ||||
−0.300357 | + | 0.953827i | \(0.597106\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.3337i | 0.951363i | 0.879618 | + | 0.475682i | \(0.157799\pi\) | ||||
−0.879618 | + | 0.475682i | \(0.842201\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.67459i | 0.374988i | 0.982266 | + | 0.187494i | \(0.0600365\pi\) | ||||
−0.982266 | + | 0.187494i | \(0.939964\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.65685 | −0.372194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.9050i | 1.36369i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.12293i | 0.397727i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.1421 | −1.17352 | −0.586759 | − | 0.809762i | \(-0.699596\pi\) | ||||
−0.586759 | + | 0.809762i | \(0.699596\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.31371 | 0.0846234 | 0.0423117 | − | 0.999104i | \(-0.486528\pi\) | ||||
0.0423117 | + | 0.999104i | \(0.486528\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.7248i | 1.39364i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2.61313i | − 0.166946i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.14214 | 0.136301 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 34.1421 | 2.16367 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.819760i | 0.0517428i | 0.999665 | + | 0.0258714i | \(0.00823604\pi\) | ||||
−0.999665 | + | 0.0258714i | \(0.991764\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 14.7821i | − 0.929341i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 52.2843 | 3.27417 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.31371 | −0.580973 | −0.290487 | − | 0.956879i | \(-0.593817\pi\) | ||||
−0.290487 | + | 0.956879i | \(0.593817\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 5.22625i | − 0.324743i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 36.5838i | − 2.26448i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.34315 | 0.144485 | 0.0722423 | − | 0.997387i | \(-0.476985\pi\) | ||||
0.0722423 | + | 0.997387i | \(0.476985\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.3137 | 1.67787 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.22625i | 0.319841i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 8.21080i | − 0.500621i | −0.968166 | − | 0.250311i | \(-0.919467\pi\) | ||||
0.968166 | − | 0.250311i | \(-0.0805327\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.34315 | −0.142336 | −0.0711680 | − | 0.997464i | \(-0.522673\pi\) | ||||
−0.0711680 | + | 0.997464i | \(0.522673\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.17157 | 0.0709068 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.95815i | 0.238685i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 14.7821i | − 0.888169i | −0.895985 | − | 0.444084i | \(-0.853529\pi\) | ||||
0.895985 | − | 0.444084i | \(-0.146471\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.6569 | −1.29656 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.8281i | 1.23810i | 0.785351 | + | 0.619051i | \(0.212482\pi\) | ||||
−0.785351 | + | 0.619051i | \(0.787518\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 32.6256i | 1.93257i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.65685 | −0.215857 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26.1313i | 1.53184i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.9008i | 0.636834i | 0.947951 | + | 0.318417i | \(0.103151\pi\) | ||||
−0.947951 | + | 0.318417i | \(0.896849\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.17157 | 0.0682116 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.68629 | 0.271926 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.06147i | 0.177049i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.16478i | 0.124776i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.4853 | 0.717261 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −31.7990 | −1.82080 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.73606i | 0.498593i | 0.968427 | + | 0.249297i | \(0.0801994\pi\) | ||||
−0.968427 | + | 0.249297i | \(0.919801\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 35.6871i | − 2.03017i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.6274 | 0.829445 | 0.414722 | − | 0.909948i | \(-0.363879\pi\) | ||||
0.414722 | + | 0.909948i | \(0.363879\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.34315 | −0.471582 | −0.235791 | − | 0.971804i | \(-0.575768\pi\) | ||||
−0.235791 | + | 0.971804i | \(0.575768\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.0042i | 0.563671i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.65914i | 0.486346i | 0.969983 | + | 0.243173i | \(0.0781882\pi\) | ||||
−0.969983 | + | 0.243173i | \(0.921812\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.6863 | 1.15821 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −35.3137 | −1.97102 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.5838i | 2.03558i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 0.819760i | − 0.0454721i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −29.6569 | −1.64003 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.00000 | −0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 18.7402i | − 1.03006i | −0.857173 | − | 0.515028i | \(-0.827782\pi\) | ||||
0.857173 | − | 0.515028i | \(-0.172218\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.0083i | 1.09645i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1716 | 0.608554 | 0.304277 | − | 0.952584i | \(-0.401585\pi\) | ||||
0.304277 | + | 0.952584i | \(0.401585\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 23.0698i | − 1.25298i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 12.2459i | − 0.663151i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −46.6274 | −2.51034 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 12.6173i | − 0.677332i | −0.940907 | − | 0.338666i | \(-0.890024\pi\) | ||||
0.940907 | − | 0.338666i | \(-0.109976\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.6215i | 1.21090i | 0.795884 | + | 0.605449i | \(0.207007\pi\) | ||||
−0.795884 | + | 0.605449i | \(0.792993\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.970563 | −0.0518048 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6569 | 0.833330 | 0.416665 | − | 0.909060i | \(-0.363199\pi\) | ||||
0.416665 | + | 0.909060i | \(0.363199\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 6.12293i | − 0.324972i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 20.0083i | 1.05895i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.82843 | 0.360391 | 0.180195 | − | 0.983631i | \(-0.442327\pi\) | ||||
0.180195 | + | 0.983631i | \(0.442327\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.82843 | −0.201496 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 16.4985i | − 0.865947i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 30.4608i | − 1.59439i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.9706 | 1.30345 | 0.651726 | − | 0.758454i | \(-0.274045\pi\) | ||||
0.651726 | + | 0.758454i | \(0.274045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.0000 | 0.728811 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.4525i | 0.542667i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.8937i | 1.75495i | 0.479622 | + | 0.877475i | \(0.340774\pi\) | ||||
−0.479622 | + | 0.877475i | \(0.659226\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −21.6569 | −1.11836 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.28427 | −0.220651 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 23.0698i | − 1.18502i | −0.805565 | − | 0.592508i | \(-0.798138\pi\) | ||||
0.805565 | − | 0.592508i | \(-0.201862\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.7206i | 0.600465i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.3137 | −0.986884 | −0.493442 | − | 0.869779i | \(-0.664262\pi\) | ||||
−0.493442 | + | 0.869779i | \(0.664262\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.65685 | −0.288300 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 8.28772i | − 0.421288i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 20.0083i | − 1.01446i | −0.861810 | − | 0.507231i | \(-0.830669\pi\) | ||||
0.861810 | − | 0.507231i | \(-0.169331\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −52.2843 | −2.64413 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −47.7990 | −2.41114 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.12293i | 0.308078i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2919i | 0.918043i | 0.888425 | + | 0.459022i | \(0.151800\pi\) | ||||
−0.888425 | + | 0.459022i | \(0.848200\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.4853 | −0.625046 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.51472 | 0.475142 | 0.237571 | − | 0.971370i | \(-0.423649\pi\) | ||||
0.237571 | + | 0.971370i | \(0.423649\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.53620i | 0.126337i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.2304i | 0.756805i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.3137 | −0.560800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.31371 | 0.262746 | 0.131373 | − | 0.991333i | \(-0.458061\pi\) | ||||
0.131373 | + | 0.991333i | \(0.458061\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 5.22625i | − 0.257792i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.448342i | 0.0220614i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.1421 | 1.67597 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −51.1127 | −2.50300 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 13.0656i | − 0.638298i | −0.947705 | − | 0.319149i | \(-0.896603\pi\) | ||||
0.947705 | − | 0.319149i | \(-0.103397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 2.53620i | − 0.123607i | −0.998088 | − | 0.0618035i | \(-0.980315\pi\) | ||||
0.998088 | − | 0.0618035i | \(-0.0196852\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.6274 | 1.48916 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.0000 | 0.679100 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 12.1689i | − 0.588897i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 2.53620i | − 0.122449i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.82843 | 0.328914 | 0.164457 | − | 0.986384i | \(-0.447413\pi\) | ||||
0.164457 | + | 0.986384i | \(0.447413\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.3431 | −0.593174 | −0.296587 | − | 0.955006i | \(-0.595848\pi\) | ||||
−0.296587 | + | 0.955006i | \(0.595848\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 65.2512i | − 3.12856i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 32.6256i | − 1.56069i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.970563 | 0.0463224 | 0.0231612 | − | 0.999732i | \(-0.492627\pi\) | ||||
0.0231612 | + | 0.999732i | \(0.492627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.82843 | −0.182306 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.18440i | 0.436364i | 0.975908 | + | 0.218182i | \(0.0700127\pi\) | ||||
−0.975908 | + | 0.218182i | \(0.929987\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.22625i | 0.247748i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 43.3137 | 2.04867 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.6274 | −1.16224 | −0.581120 | − | 0.813818i | \(-0.697385\pi\) | ||||
−0.581120 | + | 0.813818i | \(0.697385\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.91630i | 0.372764i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 47.4077i | 2.22741i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.17157 | 0.0549242 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.4853 | −0.490481 | −0.245240 | − | 0.969462i | \(-0.578867\pi\) | ||||
−0.245240 | + | 0.969462i | \(0.578867\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 16.5754i | − 0.773675i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3756i | 0.483239i | 0.970371 | + | 0.241619i | \(0.0776786\pi\) | ||||
−0.970371 | + | 0.241619i | \(0.922321\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −38.6274 | −1.79130 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.34502i | 0.0622403i | 0.999516 | + | 0.0311202i | \(0.00990745\pi\) | ||||
−0.999516 | + | 0.0311202i | \(0.990093\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 3.06147i | − 0.141365i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.4853 | 0.575291 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.68629 | 0.215476 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.73606i | 0.400838i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 40.0166i | − 1.83224i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.65685 | 0.258468 | 0.129234 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129234 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.34315 | 0.106838 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 17.8435i | − 0.811909i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.1313i | 1.18656i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.7990 | −1.44095 | −0.720475 | − | 0.693481i | \(-0.756076\pi\) | ||||
−0.720475 | + | 0.693481i | \(0.756076\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.3431 | 0.467733 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.6256i | 1.47237i | 0.676779 | + | 0.736187i | \(0.263375\pi\) | ||||
−0.676779 | + | 0.736187i | \(0.736625\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 73.1675i | − 3.29530i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21.6569 | 0.973403 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.34315 | 0.105104 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.7206i | 0.524686i | 0.964975 | + | 0.262343i | \(0.0844952\pi\) | ||||
−0.964975 | + | 0.262343i | \(0.915505\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 41.8100i | − 1.86793i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.65685 | 0.252227 | 0.126113 | − | 0.992016i | \(-0.459750\pi\) | ||||
0.126113 | + | 0.992016i | \(0.459750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.4853 | 0.555588 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 33.4454i | − 1.48536i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.50981i | 0.155570i | 0.996970 | + | 0.0777848i | \(0.0247847\pi\) | ||||
−0.996970 | + | 0.0777848i | \(0.975215\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.6569 | 0.515669 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.3431 | 0.456661 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 35.6871i | − 1.57256i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.3183i | 0.761657i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −42.1421 | −1.84983 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.6863 | 0.643418 | 0.321709 | − | 0.946839i | \(-0.395743\pi\) | ||||
0.321709 | + | 0.946839i | \(0.395743\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7.46796i | − 0.326551i | −0.986581 | − | 0.163276i | \(-0.947794\pi\) | ||||
0.986581 | − | 0.163276i | \(-0.0522060\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.77791i | 0.208525i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −43.3137 | −1.88677 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.6274 | 1.02728 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1.71644i | − 0.0744873i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.63952i | − 0.0710155i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.3137 | −1.52674 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −57.9411 | −2.50034 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.16478i | − 0.0932439i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.3575i | 1.34816i | 0.738656 | + | 0.674082i | \(0.235461\pi\) | ||||
−0.738656 | + | 0.674082i | \(0.764539\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.82843 | 0.293036 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −29.6569 | −1.27036 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.9748i | 1.88023i | 0.340862 | + | 0.940113i | \(0.389281\pi\) | ||||
−0.340862 | + | 0.940113i | \(0.610719\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 46.5879i | 1.98832i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 45.6569 | 1.94505 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.34315 | −0.0996407 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 35.6871i | 1.51483i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 14.7821i | − 0.626337i | −0.949698 | − | 0.313168i | \(-0.898610\pi\) | ||||
0.949698 | − | 0.313168i | \(-0.101390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.970563 | −0.0410504 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 43.3137 | 1.82871 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.7666i | 0.748774i | 0.927273 | + | 0.374387i | \(0.122147\pi\) | ||||
−0.927273 | + | 0.374387i | \(0.877853\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 23.0698i | − 0.970553i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.82843 | −0.244771 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.5147 | −0.734255 | −0.367128 | − | 0.930171i | \(-0.619659\pi\) | ||||
−0.367128 | + | 0.930171i | \(0.619659\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.7402i | 0.784254i | 0.919911 | + | 0.392127i | \(0.128261\pi\) | ||||
−0.919911 | + | 0.392127i | \(0.871739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 50.4692i | − 2.10838i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.4853 | −0.520672 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.9706 | −0.956277 | −0.478139 | − | 0.878284i | \(-0.658688\pi\) | ||||
−0.478139 | + | 0.878284i | \(0.658688\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 36.0585i | − 1.49854i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.0656i | 0.542054i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.6274 | 0.937132 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.48528 | −0.185444 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.4454i | 1.38044i | 0.723600 | + | 0.690219i | \(0.242486\pi\) | ||||
−0.723600 | + | 0.690219i | \(0.757514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 27.0279i | − 1.11367i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.0000 | −0.658152 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.3137 | −1.03951 | −0.519755 | − | 0.854316i | \(-0.673977\pi\) | ||||
−0.519755 | + | 0.854316i | \(0.673977\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.0083i | 0.820261i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 23.4412i | − 0.959385i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.00000 | 0.326871 | 0.163436 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163436 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.3137 | 1.68522 | 0.842611 | − | 0.538523i | \(-0.181018\pi\) | ||||
0.842611 | + | 0.538523i | \(0.181018\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.7206i | 0.477300i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 16.4985i | − 0.670760i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.3137 | 1.10863 | 0.554315 | − | 0.832307i | \(-0.312980\pi\) | ||||
0.554315 | + | 0.832307i | \(0.312980\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.9706 | 1.01186 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 3.58673i | − 0.145104i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.1313i | 1.05543i | 0.849421 | + | 0.527716i | \(0.176951\pi\) | ||||
−0.849421 | + | 0.527716i | \(0.823049\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.9706 | 1.00691 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.7990 | −1.68276 | −0.841382 | − | 0.540441i | \(-0.818257\pi\) | ||||
−0.841382 | + | 0.540441i | \(0.818257\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 33.9706i | − 1.36540i | −0.730701 | − | 0.682698i | \(-0.760807\pi\) | ||||
0.730701 | − | 0.682698i | \(-0.239193\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.7821i | 0.593184i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.00000 | −0.0801283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7990 | −1.23196 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.0279i | 1.07939i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 40.0166i | 1.59557i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.6274 | 1.21926 | 0.609629 | − | 0.792687i | \(-0.291318\pi\) | ||||
0.609629 | + | 0.792687i | \(0.291318\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.0000 | −0.953914 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.7206i | 0.465118i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.448342i | 0.0177639i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.97056 | −0.354870 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.4558 | 1.08444 | 0.542220 | − | 0.840236i | \(-0.317584\pi\) | ||||
0.542220 | + | 0.840236i | \(0.317584\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.98454i | 0.117699i | 0.998267 | + | 0.0588495i | \(0.0187432\pi\) | ||||
−0.998267 | + | 0.0588495i | \(0.981257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 14.7821i | − 0.582044i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.6569 | 1.16593 | 0.582966 | − | 0.812497i | \(-0.301892\pi\) | ||||
0.582966 | + | 0.812497i | \(0.301892\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.970563 | 0.0380979 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 14.7821i | − 0.579355i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.5445i | 0.882236i | 0.897449 | + | 0.441118i | \(0.145418\pi\) | ||||
−0.897449 | + | 0.441118i | \(0.854582\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −47.7990 | −1.86766 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −44.6274 | −1.74108 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 10.0811i | − 0.392703i | −0.980534 | − | 0.196352i | \(-0.937091\pi\) | ||||
0.980534 | − | 0.196352i | \(-0.0629094\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.448342i | 0.0174385i | 0.999962 | + | 0.00871923i | \(0.00277545\pi\) | ||||
−0.999962 | + | 0.00871923i | \(0.997225\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.97056 | −0.348388 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.4853 | −0.484158 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 65.2512i | 2.52654i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.4412i | 0.906290i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.3431 | −1.01697 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.6274 | 1.10351 | 0.551753 | − | 0.834008i | \(-0.313959\pi\) | ||||
0.551753 | + | 0.834008i | \(0.313959\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 3.95815i | − 0.152349i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.73606i | 0.335754i | 0.985808 | + | 0.167877i | \(0.0536912\pi\) | ||||
−0.985808 | + | 0.167877i | \(0.946309\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0000 | −0.383765 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.4558 | 1.43531 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5.59767i | − 0.214189i | −0.994249 | − | 0.107094i | \(-0.965845\pi\) | ||||
0.994249 | − | 0.107094i | \(-0.0341547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 5.22625i | − 0.199685i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.8284 | 0.565740 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.68629 | −0.178533 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.7640i | 1.36053i | 0.732968 | + | 0.680263i | \(0.238135\pi\) | ||||
−0.732968 | + | 0.680263i | \(0.761865\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.28772i | 0.314824i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −51.1127 | −1.93882 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.0000 | 1.06058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.1313i | 0.988375i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.9133i | 1.54528i | 0.634847 | + | 0.772638i | \(0.281063\pi\) | ||||
−0.634847 | + | 0.772638i | \(0.718937\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.9706 | −0.941783 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 54.6274 | 2.05739 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.77791i | 0.179692i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 17.4721i | − 0.656179i | −0.944647 | − | 0.328090i | \(-0.893595\pi\) | ||||
0.944647 | − | 0.328090i | \(-0.106405\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.97056 | 0.336422 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38.6274 | 1.44661 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.53620i | − 0.0948486i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 47.4077i | 1.77047i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.31371 | 0.123580 | 0.0617902 | − | 0.998089i | \(-0.480319\pi\) | ||||
0.0617902 | + | 0.998089i | \(0.480319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.6569 | 0.508608 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 3.43289i | − 0.127670i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 17.4721i | − 0.648898i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.6863 | 0.767212 | 0.383606 | − | 0.923497i | \(-0.374682\pi\) | ||||
0.383606 | + | 0.923497i | \(0.374682\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 39.2843 | 1.45497 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 16.5754i | − 0.613065i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.7248i | 0.802423i | 0.915986 | + | 0.401211i | \(0.131411\pi\) | ||||
−0.915986 | + | 0.401211i | \(0.868589\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.82843 | −0.251870 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.62742 | −0.244124 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.8632i | 0.914606i | 0.889311 | + | 0.457303i | \(0.151185\pi\) | ||||
−0.889311 | + | 0.457303i | \(0.848815\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 5.59767i | − 0.205636i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.5147 | 1.00942 | 0.504709 | − | 0.863290i | \(-0.331600\pi\) | ||||
0.504709 | + | 0.863290i | \(0.331600\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43.3137 | 1.58689 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 50.0208i | − 1.83017i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 13.5140i | − 0.493790i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.4558 | 1.65871 | 0.829354 | − | 0.558724i | \(-0.188709\pi\) | ||||
0.829354 | + | 0.558724i | \(0.188709\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.14214 | 0.0780638 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47.4077i | 1.72534i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.5445i | 0.819395i | 0.912221 | + | 0.409697i | \(0.134366\pi\) | ||||
−0.912221 | + | 0.409697i | \(0.865634\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −38.6274 | −1.40209 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.9706 | 0.687682 | 0.343841 | − | 0.939028i | \(-0.388272\pi\) | ||||
0.343841 | + | 0.939028i | \(0.388272\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 11.3492i | − 0.410868i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 76.6004i | − 2.76949i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.201010 | −0.00725806 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.2548 | 1.27132 | 0.635661 | − | 0.771968i | \(-0.280728\pi\) | ||||
0.635661 | + | 0.771968i | \(0.280728\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.3379i | 0.876508i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 8.73606i | − 0.314214i | −0.987582 | − | 0.157107i | \(-0.949783\pi\) | ||||
0.987582 | − | 0.157107i | \(-0.0502168\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.3431 | −0.371537 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.6569 | −0.489937 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.4721i | 0.626004i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 5.07241i | − 0.181505i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.6863 | −0.739268 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.4853 | 0.445619 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.46796i | 0.266204i | 0.991102 | + | 0.133102i | \(0.0424938\pi\) | ||||
−0.991102 | + | 0.133102i | \(0.957506\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 6.12293i | − 0.217982i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.82843 | 0.313903 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.45584 | 0.193743 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 71.3742i | − 2.53138i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.4763i | 0.973260i | 0.873608 | + | 0.486630i | \(0.161774\pi\) | ||||
−0.873608 | + | 0.486630i | \(0.838226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 61.2548 | 2.16704 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.65685 | 0.270542 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 25.2346i | − 0.890509i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 17.8435i | − 0.628902i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.4558 | −0.755281 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.1716 | −1.09593 | −0.547967 | − | 0.836500i | \(-0.684598\pi\) | ||||
−0.547967 | + | 0.836500i | \(0.684598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 20.9819i | − 0.736775i | −0.929672 | − | 0.368388i | \(-0.879910\pi\) | ||||
0.929672 | − | 0.368388i | \(-0.120090\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.12293i | 0.214741i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.3431 | 0.362305 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.3431 | 0.361861 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 1.71644i | − 0.0599774i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.65914i | 0.302206i | 0.988518 | + | 0.151103i | \(0.0482825\pi\) | ||||
−0.988518 | + | 0.151103i | \(0.951717\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.9706 | 1.42814 | 0.714072 | − | 0.700072i | \(-0.246849\pi\) | ||||
0.714072 | + | 0.700072i | \(0.246849\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.3431 | 0.360102 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 10.9778i | − 0.381734i | −0.981616 | − | 0.190867i | \(-0.938870\pi\) | ||||
0.981616 | − | 0.190867i | \(-0.0611300\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.19986i | 0.215330i | 0.994187 | + | 0.107665i | \(0.0343374\pi\) | ||||
−0.994187 | + | 0.107665i | \(0.965663\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −38.6274 | −1.33997 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.65685 | −0.265294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 41.8100i | − 1.44690i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.2459i | 0.423279i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.2843 | 1.25267 | 0.626336 | − | 0.779553i | \(-0.284554\pi\) | ||||
0.626336 | + | 0.779553i | \(0.284554\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −62.3137 | −2.14875 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.22625i | 0.180002i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 33.4454i | − 1.15056i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.31371 | 0.216942 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 54.4264 | 1.86791 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 35.6871i | − 1.22334i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 47.3308i | − 1.62057i | −0.586033 | − | 0.810287i | \(-0.699311\pi\) | ||||
0.586033 | − | 0.810287i | \(-0.300689\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 47.7990 | 1.63469 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.627417 | 0.0214322 | 0.0107161 | − | 0.999943i | \(-0.496589\pi\) | ||||
0.0107161 | + | 0.999943i | \(0.496589\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 3.50981i | − 0.119753i | −0.998206 | − | 0.0598766i | \(-0.980929\pi\) | ||||
0.998206 | − | 0.0598766i | \(-0.0190707\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.55582i | 0.325661i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −51.3137 | −1.74674 | −0.873369 | − | 0.487058i | \(-0.838070\pi\) | ||||
−0.873369 | + | 0.487058i | \(0.838070\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42.1421 | −1.43288 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 108.778i | − 3.69428i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.07241i | 0.172070i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.37258 | 0.0465082 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 38.2843 | 1.29573 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 8.28772i | − 0.280176i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.2542i | 1.08915i | 0.838713 | + | 0.544573i | \(0.183308\pi\) | ||||
−0.838713 | + | 0.544573i | \(0.816692\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.4853 | 0.960785 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.9706 | 0.369608 | 0.184804 | − | 0.982775i | \(-0.440835\pi\) | ||||
0.184804 | + | 0.982775i | \(0.440835\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 51.7373i | − 1.74110i | −0.492082 | − | 0.870549i | \(-0.663764\pi\) | ||||
0.492082 | − | 0.870549i | \(-0.336236\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 3.06147i | − 0.102910i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.6274 | −0.759754 | −0.379877 | − | 0.925037i | \(-0.624034\pi\) | ||||
−0.379877 | + | 0.925037i | \(0.624034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.48528 | −0.150432 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.6173i | 0.422695i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.2233i | 1.27909i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −57.9411 | −1.93676 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.00000 | 0.267112 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 54.0559i | 1.80286i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 80.0333i | − 2.66630i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.65685 | 0.188248 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.82843 | 0.226985 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.26810i | 0.0421066i | 0.999778 | + | 0.0210533i | \(0.00670197\pi\) | ||||
−0.999778 | + | 0.0210533i | \(0.993298\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 18.2919i | − 0.606703i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.8284 | −1.28644 | −0.643222 | − | 0.765680i | \(-0.722403\pi\) | ||||
−0.643222 | + | 0.765680i | \(0.722403\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.2843 | 0.936073 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 83.0948i | 2.74703i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 18.2919i | − 0.604051i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.34315 | 0.0772932 | 0.0386466 | − | 0.999253i | \(-0.487695\pi\) | ||||
0.0386466 | + | 0.999253i | \(0.487695\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.8284 | 0.752222 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.05053i | 0.0345786i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.55582i | 0.314193i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −52.2843 | −1.71724 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.2843 | 0.337416 | 0.168708 | − | 0.985666i | \(-0.446041\pi\) | ||||
0.168708 | + | 0.985666i | \(0.446041\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 4.77791i | − 0.156590i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 38.2233i | − 1.25137i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 43.3137 | 1.41651 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.2843 | −1.25069 | −0.625346 | − | 0.780347i | \(-0.715042\pi\) | ||||
−0.625346 | + | 0.780347i | \(0.715042\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.8017i | 0.711471i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.7749i | 1.23143i | 0.787970 | + | 0.615714i | \(0.211132\pi\) | ||||
−0.787970 | + | 0.615714i | \(0.788868\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.9706 | −0.813153 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.65685 | 0.184017 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 48.3044i | − 1.56968i | −0.619698 | − | 0.784841i | \(-0.712745\pi\) | ||||
0.619698 | − | 0.784841i | \(-0.287255\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.22625i | 0.169651i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.6274 | 0.733744 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.3137 | 1.20871 | 0.604355 | − | 0.796715i | \(-0.293431\pi\) | ||||
0.604355 | + | 0.796715i | \(0.293431\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 50.4692i | − 1.63314i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 54.0559i | − 1.74738i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.00000 | 0.0645834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 51.7373i | 1.66721i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 36.0585i | − 1.16076i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.8579 | −0.960164 | −0.480082 | − | 0.877224i | \(-0.659393\pi\) | ||||
−0.480082 | + | 0.877224i | \(0.659393\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 95.5980 | 3.07105 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 52.5570i | − 1.68663i | −0.537416 | − | 0.843317i | \(-0.680599\pi\) | ||||
0.537416 | − | 0.843317i | \(-0.319401\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 19.5600i | − 0.627064i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.14214 | −0.0686032 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.0000 | 0.959785 | 0.479893 | − | 0.877327i | \(-0.340676\pi\) | ||||
0.479893 | + | 0.877327i | \(0.340676\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.32957i | 0.138374i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.4495i | 1.38724i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.0294 | 0.734525 | 0.367262 | − | 0.930117i | \(-0.380295\pi\) | ||||
0.367262 | + | 0.930117i | \(0.380295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.0000 | −0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.9050i | 0.665414i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.7821i | 0.470043i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.6569 | −0.942081 | −0.471041 | − | 0.882112i | \(-0.656121\pi\) | ||||
−0.471041 | + | 0.882112i | \(0.656121\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −48.9706 | −1.55403 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 23.4412i | − 0.743136i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 0.0769232i | − 0.00243618i | −0.999999 | − | 0.00121809i | \(-0.999612\pi\) | ||||
0.999999 | − | 0.00121809i | \(-0.000387731\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.3137 | 0.357950 |
(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 | 896.2.b.h.449.1 | yes | 4 | |
4.3 | odd | 2 | 896.2.b.f.449.4 | yes | 4 | ||
8.3 | odd | 2 | 896.2.b.f.449.1 | ✓ | 4 | ||
8.5 | even | 2 | inner | 896.2.b.h.449.4 | yes | 4 | |
16.3 | odd | 4 | 1792.2.a.w.1.1 | 4 | |||
16.5 | even | 4 | 1792.2.a.u.1.1 | 4 | |||
16.11 | odd | 4 | 1792.2.a.w.1.4 | 4 | |||
16.13 | even | 4 | 1792.2.a.u.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.b.f.449.1 | ✓ | 4 | 8.3 | odd | 2 | ||
896.2.b.f.449.4 | yes | 4 | 4.3 | odd | 2 | ||
896.2.b.h.449.1 | yes | 4 | 1.1 | even | 1 | trivial | |
896.2.b.h.449.4 | yes | 4 | 8.5 | even | 2 | inner | |
1792.2.a.u.1.1 | 4 | 16.5 | even | 4 | |||
1792.2.a.u.1.4 | 4 | 16.13 | even | 4 | |||
1792.2.a.w.1.1 | 4 | 16.3 | odd | 4 | |||
1792.2.a.w.1.4 | 4 | 16.11 | odd | 4 |