Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(609,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, 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("1216.609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.2702336256.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 56x^{4} + 225x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 609.2 | ||
Root | \(0.656712 + 2.13746i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.609 |
Dual form | 1216.2.c.i.609.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.04547i | − 1.36198i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) | ||||
0.732294 | − | 0.680989i | \(-0.238450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.418627 | 0.158226 | 0.0791130 | − | 0.996866i | \(-0.474791\pi\) | ||||
0.0791130 | + | 0.996866i | \(0.474791\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.27492i | 1.59045i | 0.606316 | + | 0.795224i | \(0.292647\pi\) | ||||
−0.606316 | + | 0.795224i | \(0.707353\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.62685i | 0.728557i | 0.931290 | + | 0.364278i | \(0.118684\pi\) | ||||
−0.931290 | + | 0.364278i | \(0.881316\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.27492 | 0.794284 | 0.397142 | − | 0.917757i | \(-0.370002\pi\) | ||||
0.397142 | + | 0.917757i | \(0.370002\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410 | 0.722315 | 0.361158 | − | 0.932505i | \(-0.382382\pi\) | ||||
0.361158 | + | 0.932505i | \(0.382382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.27492 | −0.854983 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.62685i | 0.487793i | 0.969801 | + | 0.243897i | \(0.0784258\pi\) | ||||
−0.969801 | + | 0.243897i | \(0.921574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.09095 | 1.09397 | 0.546983 | − | 0.837143i | \(-0.315776\pi\) | ||||
0.546983 | + | 0.837143i | \(0.315776\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.27492i | − 0.215500i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 9.55505i | − 1.57084i | −0.618963 | − | 0.785420i | \(-0.712447\pi\) | ||||
0.618963 | − | 0.785420i | \(-0.287553\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.54983 | 0.710565 | 0.355282 | − | 0.934759i | \(-0.384385\pi\) | ||||
0.355282 | + | 0.934759i | \(0.384385\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.72508i | 0.415571i | 0.978174 | + | 0.207786i | \(0.0666256\pi\) | ||||
−0.978174 | + | 0.207786i | \(0.933374\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 9.13642i | − 1.36198i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.418627 | −0.0610630 | −0.0305315 | − | 0.999534i | \(-0.509720\pi\) | ||||
−0.0305315 | + | 0.999534i | \(0.509720\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.82475 | −0.974965 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 10.3923i | − 1.42749i | −0.700404 | − | 0.713746i | \(-0.746997\pi\) | ||||
0.700404 | − | 0.713746i | \(-0.253003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.0646 | 2.16615 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 6.54983i | − 0.852716i | −0.904555 | − | 0.426358i | \(-0.859796\pi\) | ||||
0.904555 | − | 0.426358i | \(-0.140204\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 3.04547i | − 0.389933i | −0.980810 | − | 0.194967i | \(-0.937540\pi\) | ||||
0.980810 | − | 0.194967i | \(-0.0624598\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.25588 | 0.158226 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.00000 | 0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.54983i | − 0.800190i | −0.916474 | − | 0.400095i | \(-0.868977\pi\) | ||||
0.916474 | − | 0.400095i | \(-0.131023\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3446 | −1.34636 | −0.673181 | − | 0.739478i | \(-0.735072\pi\) | ||||
−0.673181 | + | 0.739478i | \(0.735072\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.27492 | −0.383300 | −0.191650 | − | 0.981463i | \(-0.561384\pi\) | ||||
−0.191650 | + | 0.981463i | \(0.561384\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.20822i | 0.251650i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.0192 | 1.46477 | 0.732385 | − | 0.680891i | \(-0.238407\pi\) | ||||
0.732385 | + | 0.680891i | \(0.238407\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.0997i | 1.87693i | 0.345371 | + | 0.938466i | \(0.387753\pi\) | ||||
−0.345371 | + | 0.938466i | \(0.612247\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 9.97368i | − 1.08180i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.09967i | 0.115277i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.04547 | 0.312459 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.5498 | 1.68038 | 0.840191 | − | 0.542291i | \(-0.182443\pi\) | ||||
0.840191 | + | 0.542291i | \(0.182443\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.8248i | 1.59045i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8564i | 1.37876i | 0.724398 | + | 0.689382i | \(0.242118\pi\) | ||||
−0.724398 | + | 0.689382i | \(0.757882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.09095 | 0.600159 | 0.300080 | − | 0.953914i | \(-0.402987\pi\) | ||||
0.300080 | + | 0.953914i | \(0.402987\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.45017i | 0.140193i | 0.997540 | + | 0.0700964i | \(0.0223307\pi\) | ||||
−0.997540 | + | 0.0700964i | \(0.977669\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.46410i | 0.331801i | 0.986143 | + | 0.165900i | \(0.0530530\pi\) | ||||
−0.986143 | + | 0.165900i | \(0.946947\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.5498 | 1.18059 | 0.590295 | − | 0.807188i | \(-0.299012\pi\) | ||||
0.590295 | + | 0.807188i | \(0.299012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 10.5498i | − 0.983777i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.88054i | 0.728557i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.37097 | 0.125676 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.8248 | −1.52952 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 2.20822i | − 0.197509i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.4356 | −1.54716 | −0.773579 | − | 0.633699i | \(-0.781536\pi\) | ||||
−0.773579 | + | 0.633699i | \(0.781536\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.27492i | 0.460872i | 0.973088 | + | 0.230436i | \(0.0740152\pi\) | ||||
−0.973088 | + | 0.230436i | \(0.925985\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.418627i | 0.0362995i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.7251 | −1.08718 | −0.543589 | − | 0.839352i | \(-0.682935\pi\) | ||||
−0.543589 | + | 0.839352i | \(0.682935\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.72508i | 0.231139i | 0.993299 | + | 0.115569i | \(0.0368692\pi\) | ||||
−0.993299 | + | 0.115569i | \(0.963131\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.8564 | −1.15873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00000 | 0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.0646i | 1.31607i | 0.752989 | + | 0.658033i | \(0.228611\pi\) | ||||
−0.752989 | + | 0.658033i | \(0.771389\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.837253 | −0.0681347 | −0.0340674 | − | 0.999420i | \(-0.510846\pi\) | ||||
−0.0340674 | + | 0.999420i | \(0.510846\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.82475 | 0.794284 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 18.5498i | − 1.48996i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 12.1819i | − 0.972221i | −0.873897 | − | 0.486111i | \(-0.838415\pi\) | ||||
0.873897 | − | 0.486111i | \(-0.161585\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.45017 | 0.114289 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.1101 | −1.47878 | −0.739392 | − | 0.673275i | \(-0.764887\pi\) | ||||
−0.739392 | + | 0.673275i | \(0.764887\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.09967 | 0.469205 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000i | 0.229416i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.71780i | 0.662802i | 0.943490 | + | 0.331401i | \(0.107521\pi\) | ||||
−0.943490 | + | 0.331401i | \(0.892479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.78959 | −0.135281 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 21.0997i | − 1.57706i | −0.614994 | − | 0.788532i | \(-0.710842\pi\) | ||||
0.614994 | − | 0.788532i | \(-0.289158\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3.46410i | − 0.257485i | −0.991678 | − | 0.128742i | \(-0.958906\pi\) | ||||
0.991678 | − | 0.128742i | \(-0.0410940\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −29.0997 | −2.13945 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.2749i | 1.26327i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.7633 | 0.851161 | 0.425580 | − | 0.904921i | \(-0.360070\pi\) | ||||
0.425580 | + | 0.904921i | \(0.360070\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0997 | 0.798972 | 0.399486 | − | 0.916739i | \(-0.369189\pi\) | ||||
0.399486 | + | 0.916739i | \(0.369189\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 5.25370i | − 0.374310i | −0.982330 | − | 0.187155i | \(-0.940073\pi\) | ||||
0.982330 | − | 0.187155i | \(-0.0599267\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.2750 | −1.01193 | −0.505965 | − | 0.862554i | \(-0.668864\pi\) | ||||
−0.505965 | + | 0.862554i | \(0.668864\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.09967i | 0.0771816i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 13.8564i | − 0.967773i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.3923 | 0.722315 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.27492 | −0.364874 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 26.5498i | − 1.82777i | −0.405978 | − | 0.913883i | \(-0.633069\pi\) | ||||
0.405978 | − | 0.913883i | \(-0.366931\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.29917 | 0.565999 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.54983 | 0.173094 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.60271i | 0.578681i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.4356 | 1.16757 | 0.583787 | − | 0.811907i | \(-0.301570\pi\) | ||||
0.583787 | + | 0.811907i | \(0.301570\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.8248 | −0.854983 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.00000i | 0.265489i | 0.991150 | + | 0.132745i | \(0.0423790\pi\) | ||||
−0.991150 | + | 0.132745i | \(0.957621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.7391i | 1.17224i | 0.810226 | + | 0.586118i | \(0.199344\pi\) | ||||
−0.810226 | + | 0.586118i | \(0.800656\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.3746 | −1.33478 | −0.667392 | − | 0.744707i | \(-0.732589\pi\) | ||||
−0.667392 | + | 0.744707i | \(0.732589\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.27492i | 0.0831664i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.6197 | −1.65720 | −0.828600 | − | 0.559842i | \(-0.810862\pi\) | ||||
−0.828600 | + | 0.559842i | \(0.810862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.5498 | −0.808406 | −0.404203 | − | 0.914669i | \(-0.632451\pi\) | ||||
−0.404203 | + | 0.914669i | \(0.632451\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.7846i | 1.32788i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.62685 | −0.167142 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 10.7251i | − 0.676961i | −0.940973 | − | 0.338481i | \(-0.890087\pi\) | ||||
0.940973 | − | 0.338481i | \(-0.109913\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.2728i | 1.14880i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.45017 | 0.464729 | 0.232364 | − | 0.972629i | \(-0.425354\pi\) | ||||
0.232364 | + | 0.972629i | \(0.425354\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 4.00000i | − 0.248548i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.88054i | 0.487793i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.25588 | 0.0774409 | 0.0387204 | − | 0.999250i | \(-0.487672\pi\) | ||||
0.0387204 | + | 0.999250i | \(0.487672\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −31.6495 | −1.94421 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.13861i | 0.313306i | 0.987654 | + | 0.156653i | \(0.0500705\pi\) | ||||
−0.987654 | + | 0.156653i | \(0.949929\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.8279 | −1.69042 | −0.845212 | − | 0.534431i | \(-0.820526\pi\) | ||||
−0.845212 | + | 0.534431i | \(0.820526\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 22.5498i | − 1.35981i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 16.0646i | − 0.965230i | −0.875833 | − | 0.482615i | \(-0.839687\pi\) | ||||
0.875833 | − | 0.482615i | \(-0.160313\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.2728 | 1.09397 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0997 | 0.662151 | 0.331075 | − | 0.943604i | \(-0.392589\pi\) | ||||
0.331075 | + | 0.943604i | \(0.392589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 26.3746i | − 1.56781i | −0.620883 | − | 0.783903i | \(-0.713226\pi\) | ||||
0.620883 | − | 0.783903i | \(-0.286774\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.90468 | 0.112430 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.27492 | −0.369113 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.3397i | 1.77246i | 0.463244 | + | 0.886231i | \(0.346685\pi\) | ||||
−0.463244 | + | 0.886231i | \(0.653315\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.9474 | −1.16138 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.09967i | 0.526247i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.14079i | 0.0657542i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.27492 | −0.531080 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.45017i | − 0.0827653i | −0.999143 | − | 0.0413827i | \(-0.986824\pi\) | ||||
0.999143 | − | 0.0413827i | \(-0.0131763\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.7824 | −1.40528 | −0.702641 | − | 0.711544i | \(-0.747996\pi\) | ||||
−0.702641 | + | 0.711544i | \(0.747996\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0997 | 0.853484 | 0.426742 | − | 0.904373i | \(-0.359661\pi\) | ||||
0.426742 | + | 0.904373i | \(0.359661\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 3.82475i | − 0.215500i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 8.71780i | − 0.489640i | −0.969569 | − | 0.244820i | \(-0.921271\pi\) | ||||
0.969569 | − | 0.244820i | \(-0.0787289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.8564 | −0.775810 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.27492i | 0.182221i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 11.2296i | − 0.622904i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.175248 | −0.00966175 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.45017i | 0.519428i | 0.965686 | + | 0.259714i | \(0.0836283\pi\) | ||||
−0.965686 | + | 0.259714i | \(0.916372\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 28.6652i | − 1.57084i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.9474 | −1.08984 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.6495 | 1.83301 | 0.916503 | − | 0.400029i | \(-0.131000\pi\) | ||||
0.916503 | + | 0.400029i | \(0.131000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.1293i | 1.73990i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.78741 | −0.312491 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.82475i | 0.420055i | 0.977696 | + | 0.210027i | \(0.0673553\pi\) | ||||
−0.977696 | + | 0.210027i | \(0.932645\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.7156i | 0.680651i | 0.940308 | + | 0.340326i | \(0.110537\pi\) | ||||
−0.940308 | + | 0.340326i | \(0.889463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.0000 | −0.532246 | −0.266123 | − | 0.963939i | \(-0.585743\pi\) | ||||
−0.266123 | + | 0.963939i | \(0.585743\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 34.5498i | 1.83371i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.6005 | −0.665030 | −0.332515 | − | 0.943098i | \(-0.607897\pi\) | ||||
−0.332515 | + | 0.943098i | \(0.607897\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.97368i | 0.522046i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.6460 | 0.816715 | 0.408357 | − | 0.912822i | \(-0.366102\pi\) | ||||
0.408357 | + | 0.912822i | \(0.366102\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.6495 | 0.710565 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 4.35050i | − 0.225867i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.952341i | 0.0493104i | 0.999696 | + | 0.0246552i | \(0.00784878\pi\) | ||||
−0.999696 | + | 0.0246552i | \(0.992151\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.90033 | −0.355385 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.6495i | 1.21479i | 0.794399 | + | 0.607397i | \(0.207786\pi\) | ||||
−0.794399 | + | 0.607397i | \(0.792214\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.1293 | −1.64173 | −0.820864 | − | 0.571124i | \(-0.806508\pi\) | ||||
−0.820864 | + | 0.571124i | \(0.806508\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.72508 | 0.342742 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.17525i | 0.415571i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 4.71998i | − 0.239313i | −0.992815 | − | 0.119656i | \(-0.961821\pi\) | ||||
0.992815 | − | 0.119656i | \(-0.0381793\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.3446 | 0.573723 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 39.6495i | − 1.99498i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.6630i | 1.63931i | 0.572859 | + | 0.819654i | \(0.305834\pi\) | ||||
−0.572859 | + | 0.819654i | \(0.694166\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.0997 | 1.75279 | 0.876397 | − | 0.481590i | \(-0.159940\pi\) | ||||
0.876397 | + | 0.481590i | \(0.159940\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.0000i | 0.797017i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 27.4093i | − 1.36198i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 50.4021 | 2.49834 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.0000 | 0.890043 | 0.445021 | − | 0.895520i | \(-0.353196\pi\) | ||||
0.445021 | + | 0.895520i | \(0.353196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.74194i | − 0.134922i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 52.0766 | 2.55634 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000i | 0.586238i | 0.956076 | + | 0.293119i | \(0.0946933\pi\) | ||||
−0.956076 | + | 0.293119i | \(0.905307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 24.2487i | − 1.18181i | −0.806741 | − | 0.590905i | \(-0.798771\pi\) | ||||
0.806741 | − | 0.590905i | \(-0.201229\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.25588 | −0.0610630 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.0000 | −0.679100 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.27492i | − 0.0616976i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.67451 | 0.0806582 | 0.0403291 | − | 0.999186i | \(-0.487159\pi\) | ||||
0.0403291 | + | 0.999186i | \(0.487159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.6495 | −0.848181 | −0.424091 | − | 0.905620i | \(-0.639406\pi\) | ||||
−0.424091 | + | 0.905620i | \(0.639406\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.46410i | 0.165710i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.2920 | −1.49349 | −0.746743 | − | 0.665113i | \(-0.768383\pi\) | ||||
−0.746743 | + | 0.665113i | \(0.768383\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.4743 | −0.974965 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 10.3746i | − 0.492911i | −0.969154 | − | 0.246456i | \(-0.920734\pi\) | ||||
0.969154 | − | 0.246456i | \(-0.0792660\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.4547i | 1.44369i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.5498 | −0.969807 | −0.484903 | − | 0.874568i | \(-0.661145\pi\) | ||||
−0.484903 | + | 0.874568i | \(0.661145\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.0000i | 1.13012i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.34901 | 0.157004 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.2749 | −0.714530 | −0.357265 | − | 0.934003i | \(-0.616291\pi\) | ||||
−0.357265 | + | 0.934003i | \(0.616291\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.7156i | 0.592225i | 0.955153 | + | 0.296113i | \(0.0956904\pi\) | ||||
−0.955153 | + | 0.296113i | \(0.904310\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.93039 | −0.136187 | −0.0680933 | − | 0.997679i | \(-0.521692\pi\) | ||||
−0.0680933 | + | 0.997679i | \(0.521692\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8.17525i | − 0.378305i | −0.981948 | − | 0.189153i | \(-0.939426\pi\) | ||||
0.981948 | − | 0.189153i | \(-0.0605741\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 2.74194i | − 0.126611i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.3746 | −0.660944 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 4.27492i | − 0.196147i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 31.1769i | − 1.42749i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.3205 | −0.791394 | −0.395697 | − | 0.918381i | \(-0.629497\pi\) | ||||
−0.395697 | + | 0.918381i | \(0.629497\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.0997 | 1.14445 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 50.4021i | − 2.28864i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.0575 | 1.76986 | 0.884931 | − | 0.465722i | \(-0.154205\pi\) | ||||
0.884931 | + | 0.465722i | \(0.154205\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000i | 0.541552i | 0.962642 | + | 0.270776i | \(0.0872803\pi\) | ||||
−0.962642 | + | 0.270776i | \(0.912720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.60271i | 0.387447i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 48.1939 | 2.16615 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.74917 | −0.213029 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 26.7251i | − 1.19638i | −0.801355 | − | 0.598190i | \(-0.795887\pi\) | ||||
0.801355 | − | 0.598190i | \(-0.204113\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −41.6843 | −1.85861 | −0.929306 | − | 0.369311i | \(-0.879594\pi\) | ||||
−0.929306 | + | 0.369311i | \(0.879594\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.1993 | 1.87785 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 4.30136i | − 0.190654i | −0.995446 | − | 0.0953271i | \(-0.969610\pi\) | ||||
0.995446 | − | 0.0953271i | \(-0.0303897\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.37097 | −0.0606480 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 18.5498i | − 0.817403i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.20822i | − 0.0971175i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.0997 | −1.18726 | −0.593629 | − | 0.804739i | \(-0.702305\pi\) | ||||
−0.593629 | + | 0.804739i | \(0.702305\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 5.45017i | − 0.238319i | −0.992875 | − | 0.119160i | \(-0.961980\pi\) | ||||
0.992875 | − | 0.119160i | \(-0.0380200\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.9474 | 0.868920 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 19.6495i | − 0.852716i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.9517i | 0.517687i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.41644 | 0.190939 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 36.0000i | − 1.55063i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 29.0838i | − 1.25041i | −0.780461 | − | 0.625205i | \(-0.785015\pi\) | ||||
0.780461 | − | 0.625205i | \(-0.214985\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.5498 | 0.451905 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0000i | 1.36822i | 0.729378 | + | 0.684111i | \(0.239809\pi\) | ||||
−0.729378 | + | 0.684111i | \(0.760191\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 9.13642i | − 0.389933i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.62685 | −0.111907 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.45017 | 0.231765 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 29.9210i | − 1.26779i | −0.773417 | − | 0.633897i | \(-0.781454\pi\) | ||||
0.773417 | − | 0.633897i | \(-0.218546\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.15838 | −0.302767 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 24.0000i | − 1.01148i | −0.862686 | − | 0.505740i | \(-0.831220\pi\) | ||||
0.862686 | − | 0.505740i | \(-0.168780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 38.2202i | − 1.60794i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.76764 | 0.158226 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.4502 | −0.815393 | −0.407697 | − | 0.913117i | \(-0.633668\pi\) | ||||
−0.407697 | + | 0.913117i | \(0.633668\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.0997i | 1.71997i | 0.510321 | + | 0.859984i | \(0.329526\pi\) | ||||
−0.510321 | + | 0.859984i | \(0.670474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.8087 | −0.617567 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.2749 | 0.968947 | 0.484474 | − | 0.874806i | \(-0.339011\pi\) | ||||
0.484474 | + | 0.874806i | \(0.339011\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.15838i | 0.296980i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 54.8185 | 2.27035 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.0000 | 0.992278 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.2749i | 1.53850i | 0.638948 | + | 0.769250i | \(0.279370\pi\) | ||||
−0.638948 | + | 0.769250i | \(0.720630\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.09095i | 0.250973i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.0997 | 0.784329 | 0.392165 | − | 0.919895i | \(-0.371726\pi\) | ||||
0.392165 | + | 0.919895i | \(0.371726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4.17525i | − 0.171168i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.43996 | −0.385706 | −0.192853 | − | 0.981228i | \(-0.561774\pi\) | ||||
−0.192853 | + | 0.981228i | \(0.561774\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.0997 | 0.452765 | 0.226382 | − | 0.974038i | \(-0.427310\pi\) | ||||
0.226382 | + | 0.974038i | \(0.427310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 19.6495i | − 0.800190i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 51.2394i | 2.08318i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.3873 | 1.19279 | 0.596397 | − | 0.802689i | \(-0.296598\pi\) | ||||
0.596397 | + | 0.802689i | \(0.296598\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1.09967i | − 0.0444878i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 29.9210i | − 1.20850i | −0.796795 | − | 0.604250i | \(-0.793473\pi\) | ||||
0.796795 | − | 0.604250i | \(-0.206527\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.7251 | 0.512293 | 0.256146 | − | 0.966638i | \(-0.417547\pi\) | ||||
0.256146 | + | 0.966638i | \(0.417547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 4.00000i | − 0.160774i | −0.996764 | − | 0.0803868i | \(-0.974384\pi\) | ||||
0.996764 | − | 0.0803868i | \(-0.0256155\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.18627 | −0.167719 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.0997 | −1.12399 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 31.2920i | − 1.24769i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.4378 | 0.534950 | 0.267475 | − | 0.963565i | \(-0.413811\pi\) | ||||
0.267475 | + | 0.963565i | \(0.413811\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 53.0997i | 2.10720i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 17.9276i | − 0.710317i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −34.0339 | −1.34636 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5498 | −0.495689 | −0.247844 | − | 0.968800i | \(-0.579722\pi\) | ||||
−0.247844 | + | 0.968800i | \(0.579722\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.9244i | 1.77165i | 0.464023 | + | 0.885823i | \(0.346405\pi\) | ||||
−0.464023 | + | 0.885823i | \(0.653595\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.6197 | 1.00721 | 0.503607 | − | 0.863933i | \(-0.332006\pi\) | ||||
0.503607 | + | 0.863933i | \(0.332006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.5498 | 1.35620 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 16.0646i | − 0.628657i | −0.949314 | − | 0.314329i | \(-0.898221\pi\) | ||||
0.949314 | − | 0.314329i | \(-0.101779\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.0646 | 0.627697 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.82475 | −0.383300 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.4502i | 0.523944i | 0.965075 | + | 0.261972i | \(0.0843728\pi\) | ||||
−0.965075 | + | 0.261972i | \(0.915627\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 9.55505i | − 0.371648i | −0.982583 | − | 0.185824i | \(-0.940505\pi\) | ||||
0.982583 | − | 0.185824i | \(-0.0594955\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.27492 | 0.0494392 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.09967i | 0.352341i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.0646 | 0.620168 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −47.0997 | −1.81556 | −0.907779 | − | 0.419448i | \(-0.862224\pi\) | ||||
−0.907779 | + | 0.419448i | \(0.862224\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 0.722166i | − 0.0277551i | −0.999904 | − | 0.0138775i | \(-0.995582\pi\) | ||||
0.999904 | − | 0.0138775i | \(-0.00441750\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.92820 | 0.265880 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 22.1993i | − 0.849434i | −0.905326 | − | 0.424717i | \(-0.860374\pi\) | ||||
0.905326 | − | 0.424717i | \(-0.139626\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.7539i | 1.48071i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.2990 | 1.04001 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 23.4743i | − 0.893003i | −0.894783 | − | 0.446501i | \(-0.852670\pi\) | ||||
0.894783 | − | 0.446501i | \(-0.147330\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.62466i | 0.251650i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.29917 | 0.314806 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.9003 | 0.564390 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 21.0148i | − 0.793717i | −0.917880 | − | 0.396859i | \(-0.870100\pi\) | ||||
0.917880 | − | 0.396859i | \(-0.129900\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.55505 | 0.360376 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.80066i | 0.218156i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.2202i | 1.43539i | 0.696358 | + | 0.717695i | \(0.254803\pi\) | ||||
−0.696358 | + | 0.717695i | \(0.745197\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 39.0575 | 1.46477 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.0997 | 0.790189 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.1993i | 1.57817i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 51.6580 | 1.92652 | 0.963259 | − | 0.268575i | \(-0.0865526\pi\) | ||||
0.963259 | + | 0.268575i | \(0.0865526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.54983 | 0.0949608 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 11.2296i | − 0.417055i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.9260 | −0.405224 | −0.202612 | − | 0.979259i | \(-0.564943\pi\) | ||||
−0.202612 | + | 0.979259i | \(0.564943\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.92442i | 0.330082i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 19.1101i | − 0.705848i | −0.935652 | − | 0.352924i | \(-0.885187\pi\) | ||||
0.935652 | − | 0.352924i | \(-0.114813\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.5498 | 1.27266 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 7.82475i | − 0.287838i | −0.989589 | − | 0.143919i | \(-0.954029\pi\) | ||||
0.989589 | − | 0.143919i | \(-0.0459705\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −52.9139 | −1.94122 | −0.970611 | − | 0.240655i | \(-0.922638\pi\) | ||||
−0.970611 | + | 0.240655i | \(0.922638\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.9244 | 1.79245 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 51.2990i | 1.87693i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.607078i | 0.0221822i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.3155 | −1.32517 | −0.662586 | − | 0.748986i | \(-0.730541\pi\) | ||||
−0.662586 | + | 0.748986i | \(0.730541\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.54983i | 0.0927980i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.04547i | 0.110690i | 0.998467 | + | 0.0553448i | \(0.0176258\pi\) | ||||
−0.998467 | + | 0.0553448i | \(0.982374\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.27492 | 0.118716 | 0.0593578 | − | 0.998237i | \(-0.481095\pi\) | ||||
0.0593578 | + | 0.998237i | \(0.481095\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.45017i | 0.0524995i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 29.9210i | − 1.08180i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.2054 | 0.621252 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.8248 | −0.498533 | −0.249267 | − | 0.968435i | \(-0.580190\pi\) | ||||
−0.249267 | + | 0.968435i | \(0.580190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.7561i | 1.25009i | 0.780589 | + | 0.625045i | \(0.214919\pi\) | ||||
−0.780589 | + | 0.625045i | \(0.785081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.0383 | −0.935324 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.54983i | 0.163015i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 59.8421i | − 2.14132i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37.0997 | −1.32414 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.1993i | 0.506152i | 0.967446 | + | 0.253076i | \(0.0814422\pi\) | ||||
−0.967446 | + | 0.253076i | \(0.918558\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.25370 | 0.186800 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.00000 | 0.284088 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.2487i | 0.858933i | 0.903083 | + | 0.429467i | \(0.141298\pi\) | ||||
−0.903083 | + | 0.429467i | \(0.858702\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.37097 | −0.0485014 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.0000 | −1.06000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 17.2749i | − 0.609619i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 4.41644i | − 0.155659i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.82475 | −0.204787 | −0.102394 | − | 0.994744i | \(-0.532650\pi\) | ||||
−0.102394 | + | 0.994744i | \(0.532650\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 47.2990i | − 1.66089i | −0.557099 | − | 0.830446i | \(-0.688085\pi\) | ||||
0.557099 | − | 0.830446i | \(-0.311915\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.1819 | 0.426713 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.72508 | −0.0953386 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.29901i | 0.115277i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.5720i | 0.927370i | 0.886000 | + | 0.463685i | \(0.153473\pi\) | ||||
−0.886000 | + | 0.463685i | \(0.846527\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.4334 | −0.747122 | −0.373561 | − | 0.927606i | \(-0.621863\pi\) | ||||
−0.373561 | + | 0.927606i | \(0.621863\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 47.6495i | − 1.65694i | −0.560037 | − | 0.828468i | \(-0.689213\pi\) | ||||
0.560037 | − | 0.828468i | \(-0.310787\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 25.3161i | − 0.879266i | −0.898178 | − | 0.439633i | \(-0.855109\pi\) | ||||
0.898178 | − | 0.439633i | \(-0.144891\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.3505 | −0.774399 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 58.1993i | 2.01407i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.6602 | −1.64541 | −0.822706 | − | 0.568467i | \(-0.807537\pi\) | ||||
−0.822706 | + | 0.568467i | \(0.807537\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.0997 | 0.762058 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 18.5764i | − 0.639047i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.04329 | −0.242010 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 33.0997i | − 1.13464i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.9665i | 1.12875i | 0.825518 | + | 0.564376i | \(0.190883\pi\) | ||||
−0.825518 | + | 0.564376i | \(0.809117\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.13642 | 0.312459 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.1993 | −0.553359 | −0.276679 | − | 0.960962i | \(-0.589234\pi\) | ||||
−0.276679 | + | 0.960962i | \(0.589234\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 55.4743i | − 1.89276i | −0.323060 | − | 0.946379i | \(-0.604711\pi\) | ||||
0.323060 | − | 0.946379i | \(-0.395289\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.7994 | −1.42287 | −0.711434 | − | 0.702753i | \(-0.751954\pi\) | ||||
−0.711434 | + | 0.702753i | \(0.751954\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.5498 | 0.902721 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 68.6750i | 2.32964i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.2054 | 0.582983 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 49.6495 | 1.68038 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 0.924421i | − 0.0312511i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 31.4071i | − 1.06054i | −0.847828 | − | 0.530271i | \(-0.822090\pi\) | ||||
0.847828 | − | 0.530271i | \(-0.177910\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.82475 | 0.0614774 | 0.0307387 | − | 0.999527i | \(-0.490214\pi\) | ||||
0.0307387 | + | 0.999527i | \(0.490214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 13.6254i | − 0.458532i | −0.973364 | − | 0.229266i | \(-0.926367\pi\) | ||||
0.973364 | − | 0.229266i | \(-0.0736325\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.837253 | 0.0281122 | 0.0140561 | − | 0.999901i | \(-0.495526\pi\) | ||||
0.0140561 | + | 0.999901i | \(0.495526\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.29901 | −0.244801 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 47.4743i | 1.59045i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 0.418627i | − 0.0140088i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −64.2585 | −2.14793 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.0000i | 0.533630i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 34.0339i | − 1.13383i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.5498 | −0.350688 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 23.6495i | − 0.785269i | −0.919695 | − | 0.392634i | \(-0.871564\pi\) | ||||
0.919695 | − | 0.392634i | \(-0.128436\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 41.5692i | 1.37876i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.0339 | 1.12759 | 0.563797 | − | 0.825913i | \(-0.309340\pi\) | ||||
0.563797 | + | 0.825913i | \(0.309340\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −90.1993 | −2.98516 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.20822i | 0.0729219i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.115088 | 0.00379639 | 0.00189820 | − | 0.999998i | \(-0.499396\pi\) | ||||
0.00189820 | + | 0.999998i | \(0.499396\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 29.8007i | − 0.980901i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.8471i | 1.34304i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.2728 | 0.600159 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.09967 | −0.232933 | −0.116466 | − | 0.993195i | \(-0.537157\pi\) | ||||
−0.116466 | + | 0.993195i | \(0.537157\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 6.82475i | − 0.223672i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 52.6103 | 1.72054 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.9244 | −0.487560 | −0.243780 | − | 0.969831i | \(-0.578387\pi\) | ||||
−0.243780 | + | 0.969831i | \(0.578387\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 31.1769i | − 1.01634i | −0.861257 | − | 0.508169i | \(-0.830322\pi\) | ||||
0.861257 | − | 0.508169i | \(-0.169678\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.7611 | 0.513252 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 30.1993i | − 0.981347i | −0.871344 | − | 0.490673i | \(-0.836751\pi\) | ||||
0.871344 | − | 0.490673i | \(-0.163249\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 8.60271i | − 0.279256i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.2990 | −1.46738 | −0.733689 | − | 0.679485i | \(-0.762203\pi\) | ||||
−0.733689 | + | 0.679485i | \(0.762203\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 35.8248i | − 1.15926i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.32706 | −0.172020 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.09967 | 0.196764 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.35050i | 0.140193i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 33.8038i | − 1.08818i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.5407 | 1.78607 | 0.893034 | − | 0.449988i | \(-0.148572\pi\) | ||||
0.893034 | + | 0.449988i | \(0.148572\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.0000i | 1.41203i | 0.708198 | + | 0.706014i | \(0.249508\pi\) | ||||
−0.708198 | + | 0.706014i | \(0.750492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.14079i | 0.0365721i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.1993 | −0.902177 | −0.451088 | − | 0.892479i | \(-0.648964\pi\) | ||||
−0.451088 | + | 0.892479i | \(0.648964\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 52.7492i | − 1.68587i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.3923i | 0.331801i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.6893 | −0.723676 | −0.361838 | − | 0.932241i | \(-0.617851\pi\) | ||||
−0.361838 | + | 0.932241i | \(0.617851\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.0000 | −0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.43996i | 0.300173i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.0531 | 1.49469 | 0.747345 | − | 0.664436i | \(-0.231328\pi\) | ||||
0.747345 | + | 0.664436i | \(0.231328\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.4743i | 1.37823i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 42.1029i | − 1.33341i | −0.745320 | − | 0.666707i | \(-0.767703\pi\) | ||||
0.745320 | − | 0.666707i | \(-0.232297\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1216.2.c.i.609.2 | yes | 8 | |
4.3 | odd | 2 | inner | 1216.2.c.i.609.1 | ✓ | 8 | |
8.3 | odd | 2 | inner | 1216.2.c.i.609.7 | yes | 8 | |
8.5 | even | 2 | inner | 1216.2.c.i.609.8 | yes | 8 | |
16.3 | odd | 4 | 4864.2.a.bj.1.1 | 4 | |||
16.5 | even | 4 | 4864.2.a.bj.1.4 | 4 | |||
16.11 | odd | 4 | 4864.2.a.bk.1.4 | 4 | |||
16.13 | even | 4 | 4864.2.a.bk.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.c.i.609.1 | ✓ | 8 | 4.3 | odd | 2 | inner | |
1216.2.c.i.609.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1216.2.c.i.609.7 | yes | 8 | 8.3 | odd | 2 | inner | |
1216.2.c.i.609.8 | yes | 8 | 8.5 | even | 2 | inner | |
4864.2.a.bj.1.1 | 4 | 16.3 | odd | 4 | |||
4864.2.a.bj.1.4 | 4 | 16.5 | even | 4 | |||
4864.2.a.bk.1.1 | 4 | 16.13 | even | 4 | |||
4864.2.a.bk.1.4 | 4 | 16.11 | odd | 4 |