Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,4,Mod(289,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.289");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.d (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: | \(33.9851001633\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 192) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.4 | ||
Root | \(1.65831 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.289 |
Dual form | 576.4.d.f.289.2 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 19.8997i | 1.77989i | 0.456070 | + | 0.889944i | \(0.349257\pi\) | ||||
−0.456070 | + | 0.889944i | \(0.650743\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 19.8997 | 1.07449 | 0.537243 | − | 0.843428i | \(-0.319466\pi\) | ||||
0.537243 | + | 0.843428i | \(0.319466\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 48.0000i | 1.31569i | 0.753155 | + | 0.657843i | \(0.228531\pi\) | ||||
−0.753155 | + | 0.657843i | \(0.771469\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 79.5990i | 1.69821i | 0.528220 | + | 0.849107i | \(0.322859\pi\) | ||||
−0.528220 | + | 0.849107i | \(0.677141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 42.0000 | 0.599206 | 0.299603 | − | 0.954064i | \(-0.403146\pi\) | ||||
0.299603 | + | 0.954064i | \(0.403146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 92.0000i | − 1.11086i | −0.831565 | − | 0.555428i | \(-0.812555\pi\) | ||||
0.831565 | − | 0.555428i | \(-0.187445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 39.7995 | 0.360816 | 0.180408 | − | 0.983592i | \(-0.442258\pi\) | ||||
0.180408 | + | 0.983592i | \(0.442258\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −271.000 | −2.16800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 19.8997i | 0.127424i | 0.997968 | + | 0.0637119i | \(0.0202939\pi\) | ||||
−0.997968 | + | 0.0637119i | \(0.979706\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 139.298 | 0.807055 | 0.403527 | − | 0.914968i | \(-0.367784\pi\) | ||||
0.403527 | + | 0.914968i | \(0.367784\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 396.000i | 1.91246i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 198.997i | − 0.884189i | −0.896969 | − | 0.442094i | \(-0.854236\pi\) | ||||
0.896969 | − | 0.442094i | \(-0.145764\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.0228547 | 0.0114273 | − | 0.999935i | \(-0.496362\pi\) | ||||
0.0114273 | + | 0.999935i | \(0.496362\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 92.0000i | 0.326276i | 0.986603 | + | 0.163138i | \(0.0521616\pi\) | ||||
−0.986603 | + | 0.163138i | \(0.947838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 39.7995 | 0.123518 | 0.0617591 | − | 0.998091i | \(-0.480329\pi\) | ||||
0.0617591 | + | 0.998091i | \(0.480329\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 53.0000 | 0.154519 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 497.494i | − 1.28936i | −0.764453 | − | 0.644679i | \(-0.776991\pi\) | ||||
0.764453 | − | 0.644679i | \(-0.223009\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −955.188 | −2.34177 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 516.000i | 1.13860i | 0.822129 | + | 0.569301i | \(0.192786\pi\) | ||||
−0.822129 | + | 0.569301i | \(0.807214\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 358.195i | − 0.751840i | −0.926652 | − | 0.375920i | \(-0.877327\pi\) | ||||
0.926652 | − | 0.375920i | \(-0.122673\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1584.00 | −3.02263 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 524.000i | 0.955474i | 0.878503 | + | 0.477737i | \(0.158543\pi\) | ||||
−0.878503 | + | 0.477737i | \(0.841457\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −994.987 | −1.66314 | −0.831572 | − | 0.555416i | \(-0.812559\pi\) | ||||
−0.831572 | + | 0.555416i | \(0.812559\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −430.000 | −0.689420 | −0.344710 | − | 0.938709i | \(-0.612023\pi\) | ||||
−0.344710 | + | 0.938709i | \(0.612023\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 955.188i | 1.41369i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1174.09 | 1.67209 | 0.836044 | − | 0.548663i | \(-0.184863\pi\) | ||||
0.836044 | + | 0.548663i | \(0.184863\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 432.000i | − 0.571303i | −0.958334 | − | 0.285652i | \(-0.907790\pi\) | ||||
0.958334 | − | 0.285652i | \(-0.0922100\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 835.789i | 1.06652i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −630.000 | −0.750336 | −0.375168 | − | 0.926957i | \(-0.622415\pi\) | ||||
−0.375168 | + | 0.926957i | \(0.622415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1584.00i | 1.82471i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1830.78 | 1.97720 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 862.000 | 0.902297 | 0.451149 | − | 0.892449i | \(-0.351014\pi\) | ||||
0.451149 | + | 0.892449i | \(0.351014\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 457.694i | 0.450914i | 0.974253 | + | 0.225457i | \(0.0723875\pi\) | ||||
−0.974253 | + | 0.225457i | \(0.927613\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 537.293 | 0.513991 | 0.256996 | − | 0.966413i | \(-0.417267\pi\) | ||||
0.256996 | + | 0.966413i | \(0.417267\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1380.00i | 1.24682i | 0.781896 | + | 0.623410i | \(0.214253\pi\) | ||||
−0.781896 | + | 0.623410i | \(0.785747\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1273.58i | 1.11915i | 0.828780 | + | 0.559574i | \(0.189035\pi\) | ||||
−0.828780 | + | 0.559574i | \(0.810965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2106.00 | −1.75324 | −0.876619 | − | 0.481186i | \(-0.840206\pi\) | ||||
−0.876619 | + | 0.481186i | \(0.840206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 792.000i | 0.642212i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 835.789 | 0.643838 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −973.000 | −0.731029 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 2905.36i | − 2.07891i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −139.298 | −0.0973285 | −0.0486643 | − | 0.998815i | \(-0.515496\pi\) | ||||
−0.0486643 | + | 0.998815i | \(0.515496\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 540.000i | 0.360153i | 0.983653 | + | 0.180076i | \(0.0576345\pi\) | ||||
−0.983653 | + | 0.180076i | \(0.942365\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1830.78i | − 1.19360i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1446.00 | 0.901753 | 0.450876 | − | 0.892586i | \(-0.351112\pi\) | ||||
0.450876 | + | 0.892586i | \(0.351112\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1892.00i | − 1.15451i | −0.816563 | − | 0.577257i | \(-0.804123\pi\) | ||||
0.816563 | − | 0.577257i | \(-0.195877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3820.75 | −2.23432 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −396.000 | −0.226800 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2805.86i | 1.54272i | 0.636399 | + | 0.771360i | \(0.280423\pi\) | ||||
−0.636399 | + | 0.771360i | \(0.719577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −298.496 | −0.160869 | −0.0804347 | − | 0.996760i | \(-0.525631\pi\) | ||||
−0.0804347 | + | 0.996760i | \(0.525631\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2772.00i | 1.43647i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2348.17i | − 1.19366i | −0.802368 | − | 0.596829i | \(-0.796427\pi\) | ||||
0.802368 | − | 0.596829i | \(-0.203573\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 792.000 | 0.387692 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 3188.00i | − 1.53192i | −0.642887 | − | 0.765961i | \(-0.722263\pi\) | ||||
0.642887 | − | 0.765961i | \(-0.277737\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1989.97 | 0.922089 | 0.461045 | − | 0.887377i | \(-0.347475\pi\) | ||||
0.461045 | + | 0.887377i | \(0.347475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4139.00 | −1.88393 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 378.095i | 0.166162i | 0.996543 | + | 0.0830811i | \(0.0264760\pi\) | ||||
−0.996543 | + | 0.0830811i | \(0.973524\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5392.83 | −2.32948 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2844.00i | − 1.18754i | −0.804633 | − | 0.593772i | \(-0.797638\pi\) | ||||
0.804633 | − | 0.593772i | \(-0.202362\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2228.77i | 0.915267i | 0.889141 | + | 0.457633i | \(0.151303\pi\) | ||||
−0.889141 | + | 0.457633i | \(0.848697\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3960.00 | 1.57376 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2016.00i | 0.788366i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −875.589 | −0.331704 | −0.165852 | − | 0.986151i | \(-0.553037\pi\) | ||||
−0.165852 | + | 0.986151i | \(0.553037\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2882.00 | 1.07488 | 0.537438 | − | 0.843304i | \(-0.319392\pi\) | ||||
0.537438 | + | 0.843304i | \(0.319392\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4238.65i | − 1.53295i | −0.642274 | − | 0.766475i | \(-0.722009\pi\) | ||||
0.642274 | − | 0.766475i | \(-0.277991\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3243.66 | 1.15546 | 0.577731 | − | 0.816227i | \(-0.303938\pi\) | ||||
0.577731 | + | 0.816227i | \(0.303938\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 396.000i | 0.136915i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 119.398i | 0.0406788i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4416.00 | 1.46154 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2356.00i | − 0.768691i | −0.923189 | − | 0.384345i | \(-0.874427\pi\) | ||||
0.923189 | − | 0.384345i | \(-0.125573\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1830.78 | −0.580735 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2772.00 | 0.867169 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3343.16i | 1.01758i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1771.08 | 0.531839 | 0.265920 | − | 0.963995i | \(-0.414324\pi\) | ||||
0.265920 | + | 0.963995i | \(0.414324\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3864.00i | − 1.12979i | −0.825162 | − | 0.564896i | \(-0.808916\pi\) | ||||
0.825162 | − | 0.564896i | \(-0.191084\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 557.193i | − 0.160788i | −0.996763 | − | 0.0803938i | \(-0.974382\pi\) | ||||
0.996763 | − | 0.0803938i | \(-0.0256178\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2814.00 | −0.791207 | −0.395604 | − | 0.918421i | \(-0.629465\pi\) | ||||
−0.395604 | + | 0.918421i | \(0.629465\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 792.000i | 0.219848i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4616.74 | 1.24951 | 0.624754 | − | 0.780822i | \(-0.285199\pi\) | ||||
0.624754 | + | 0.780822i | \(0.285199\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 362.000 | 0.0967571 | 0.0483786 | − | 0.998829i | \(-0.484595\pi\) | ||||
0.0483786 | + | 0.998829i | \(0.484595\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1054.69i | 0.275026i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7323.11 | 1.88647 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 5136.00i | − 1.29156i | −0.763524 | − | 0.645780i | \(-0.776532\pi\) | ||||
0.763524 | − | 0.645780i | \(-0.223468\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1910.38i | 0.474721i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 174.000 | 0.0422328 | 0.0211164 | − | 0.999777i | \(-0.493278\pi\) | ||||
0.0211164 | + | 0.999777i | \(0.493278\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 3960.00i | − 0.950048i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4775.94 | 1.11976 | 0.559880 | − | 0.828573i | \(-0.310847\pi\) | ||||
0.559880 | + | 0.828573i | \(0.310847\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9900.00 | 2.29491 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1134.29i | 0.257095i | 0.991703 | + | 0.128548i | \(0.0410315\pi\) | ||||
−0.991703 | + | 0.128548i | \(0.958968\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 179.098 | 0.0401454 | 0.0200727 | − | 0.999799i | \(-0.493610\pi\) | ||||
0.0200727 | + | 0.999799i | \(0.493610\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 13008.0i | − 2.85241i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6367.92i | 1.38127i | 0.723205 | + | 0.690634i | \(0.242668\pi\) | ||||
−0.723205 | + | 0.690634i | \(0.757332\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −558.000 | −0.118461 | −0.0592304 | − | 0.998244i | \(-0.518865\pi\) | ||||
−0.0592304 | + | 0.998244i | \(0.518865\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2068.00i | 0.434381i | 0.976129 | + | 0.217191i | \(0.0696893\pi\) | ||||
−0.976129 | + | 0.217191i | \(0.930311\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 119.398 | 0.0245570 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3149.00 | −0.640953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3363.06i | − 0.670553i | −0.942120 | − | 0.335276i | \(-0.891170\pi\) | ||||
0.942120 | − | 0.335276i | \(-0.108830\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10268.3 | −2.02658 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3168.00i | 0.612743i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1830.78i | 0.350579i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7128.00 | 1.33819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6860.00i | 1.27531i | 0.770321 | + | 0.637656i | \(0.220096\pi\) | ||||
−0.770321 | + | 0.637656i | \(0.779904\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10427.5 | −1.90125 | −0.950623 | − | 0.310348i | \(-0.899554\pi\) | ||||
−0.950623 | + | 0.310348i | \(0.899554\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6262.00 | 1.13083 | 0.565414 | − | 0.824807i | \(-0.308716\pi\) | ||||
0.565414 | + | 0.824807i | \(0.308716\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 776.090i | − 0.137507i | −0.997634 | − | 0.0687533i | \(-0.978098\pi\) | ||||
0.997634 | − | 0.0687533i | \(-0.0219021\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −955.188 | −0.167650 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3864.00i | − 0.665631i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 21571.3i | − 3.68173i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 792.000 | 0.132718 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6460.00i | 1.07273i | 0.843986 | + | 0.536365i | \(0.180203\pi\) | ||||
−0.843986 | + | 0.536365i | \(0.819797\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10427.5 | −1.70064 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −74.0000 | −0.0119615 | −0.00598077 | − | 0.999982i | \(-0.501904\pi\) | ||||
−0.00598077 | + | 0.999982i | \(0.501904\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6686.32i | 1.06183i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5770.93 | −0.908457 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6888.00i | 1.06561i | 0.846238 | + | 0.532806i | \(0.178862\pi\) | ||||
−0.846238 | + | 0.532806i | \(0.821138\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 676.591i | − 0.103774i | −0.998653 | − | 0.0518870i | \(-0.983476\pi\) | ||||
0.998653 | − | 0.0518870i | \(-0.0165236\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1830.00 | 0.275924 | 0.137962 | − | 0.990438i | \(-0.455945\pi\) | ||||
0.137962 | + | 0.990438i | \(0.455945\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 19800.0i | − 2.96021i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6646.52 | 0.977130 | 0.488565 | − | 0.872527i | \(-0.337521\pi\) | ||||
0.488565 | + | 0.872527i | \(0.337521\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1605.00 | −0.233999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 8556.89i | − 1.22709i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3164.06 | 0.450034 | 0.225017 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225017 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 9900.00i | − 1.38540i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9750.88i | 1.35357i | 0.736181 | + | 0.676785i | \(0.236627\pi\) | ||||
−0.736181 | + | 0.676785i | \(0.763373\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1584.00 | −0.216393 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 8332.00i | − 1.12925i | −0.825347 | − | 0.564625i | \(-0.809021\pi\) | ||||
0.825347 | − | 0.564625i | \(-0.190979\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6765.91 | 0.902669 | 0.451334 | − | 0.892355i | \(-0.350948\pi\) | ||||
0.451334 | + | 0.892355i | \(0.350948\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19008.0 | −2.51620 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 5870.43i | − 0.765148i | −0.923925 | − | 0.382574i | \(-0.875038\pi\) | ||||
0.923925 | − | 0.382574i | \(-0.124962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1671.58 | 0.216203 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23364.0i | 2.97613i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2666.57i | 0.337106i | 0.985693 | + | 0.168553i | \(0.0539095\pi\) | ||||
−0.985693 | + | 0.168553i | \(0.946091\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2634.00 | 0.328019 | 0.164010 | − | 0.986459i | \(-0.447557\pi\) | ||||
0.164010 | + | 0.986459i | \(0.447557\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11088.0i | 1.37055i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9551.88 | 1.16331 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 506.000 | 0.0611738 | 0.0305869 | − | 0.999532i | \(-0.490262\pi\) | ||||
0.0305869 | + | 0.999532i | \(0.490262\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10268.3i | 1.22341i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8596.69 | 1.01686 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15480.0i | 1.80489i | 0.430809 | + | 0.902443i | \(0.358228\pi\) | ||||
−0.430809 | + | 0.902443i | \(0.641772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10666.3i | 1.23478i | 0.786658 | + | 0.617390i | \(0.211810\pi\) | ||||
−0.786658 | + | 0.617390i | \(0.788190\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11382.0 | −1.29908 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 7128.00i | − 0.807841i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17153.6 | 1.91707 | 0.958537 | − | 0.284968i | \(-0.0919828\pi\) | ||||
0.958537 | + | 0.284968i | \(0.0919828\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2014.00 | 0.223526 | 0.111763 | − | 0.993735i | \(-0.464350\pi\) | ||||
0.111763 | + | 0.993735i | \(0.464350\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3661.55i | − 0.400814i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 776.090 | 0.0843753 | 0.0421877 | − | 0.999110i | \(-0.486567\pi\) | ||||
0.0421877 | + | 0.999110i | \(0.486567\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 408.000i | − 0.0437577i | −0.999761 | − | 0.0218789i | \(-0.993035\pi\) | ||||
0.999761 | − | 0.0218789i | \(-0.00696481\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 12536.8i | − 1.33551i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11658.0 | 1.22533 | 0.612667 | − | 0.790341i | \(-0.290097\pi\) | ||||
0.612667 | + | 0.790341i | \(0.290097\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 288.000i | 0.0300696i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −31521.2 | −3.24777 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16486.0 | −1.68749 | −0.843745 | − | 0.536745i | \(-0.819654\pi\) | ||||
−0.843745 | + | 0.536745i | \(0.819654\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4119.25i | 0.416166i | 0.978111 | + | 0.208083i | \(0.0667224\pi\) | ||||
−0.978111 | + | 0.208083i | \(0.933278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13472.1 | 1.35227 | 0.676137 | − | 0.736776i | \(-0.263653\pi\) | ||||
0.676137 | + | 0.736776i | \(0.263653\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 4440.00i | − 0.439954i | −0.975505 | − | 0.219977i | \(-0.929402\pi\) | ||||
0.975505 | − | 0.219977i | \(-0.0705983\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10427.5i | 1.02664i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4416.00 | −0.429277 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24932.0i | 2.40833i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10626.5 | −1.01364 | −0.506822 | − | 0.862051i | \(-0.669180\pi\) | ||||
−0.506822 | + | 0.862051i | \(0.669180\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15840.0 | 1.50154 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17153.6i | 1.60599i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1333.28 | −0.124059 | −0.0620296 | − | 0.998074i | \(-0.519757\pi\) | ||||
−0.0620296 | + | 0.998074i | \(0.519757\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7404.00i | 0.680525i | 0.940330 | + | 0.340263i | \(0.110516\pi\) | ||||
−0.940330 | + | 0.340263i | \(0.889484\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 835.789i | 0.0763531i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19800.0 | −1.78702 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 5740.00i | − 0.514945i | −0.966286 | − | 0.257473i | \(-0.917110\pi\) | ||||
0.966286 | − | 0.257473i | \(-0.0828897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16039.2 | 1.42177 | 0.710887 | − | 0.703306i | \(-0.248294\pi\) | ||||
0.710887 | + | 0.703306i | \(0.248294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9108.00 | −0.802576 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 16377.5i | − 1.42617i | −0.701078 | − | 0.713084i | \(-0.747298\pi\) | ||||
0.701078 | − | 0.713084i | \(-0.252702\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8556.89 | −0.740772 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10692.0i | 0.914846i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1910.38i | 0.162511i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22098.0 | −1.85822 | −0.929108 | − | 0.369807i | \(-0.879424\pi\) | ||||
−0.929108 | + | 0.369807i | \(0.879424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16436.0i | 1.37418i | 0.726572 | + | 0.687090i | \(0.241112\pi\) | ||||
−0.726572 | + | 0.687090i | \(0.758888\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5850.53 | 0.483592 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10583.0 | −0.869812 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 477.594i | 0.0388122i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27461.7 | −2.21920 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2544.00i | 0.203298i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11143.9i | 0.885604i | 0.896619 | + | 0.442802i | \(0.146016\pi\) | ||||
−0.896619 | + | 0.442802i | \(0.853984\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25344.0 | −1.99196 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1316.00i | − 0.102867i | −0.998676 | − | 0.0514334i | \(-0.983621\pi\) | ||||
0.998676 | − | 0.0514334i | \(-0.0163790\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1830.78 | 0.141549 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23364.0 | 1.79663 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3402.86i | 0.258858i | 0.991589 | + | 0.129429i | \(0.0413144\pi\) | ||||
−0.991589 | + | 0.129429i | \(0.958686\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7323.11 | −0.554087 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 19560.0i | − 1.46422i | −0.681187 | − | 0.732110i | \(-0.738536\pi\) | ||||
0.681187 | − | 0.732110i | \(-0.261464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 41908.9i | − 3.12057i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20838.0 | 1.53528 | 0.767640 | − | 0.640881i | \(-0.221431\pi\) | ||||
0.767640 | + | 0.640881i | \(0.221431\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1100.00i | − 0.0806192i | −0.999187 | − | 0.0403096i | \(-0.987166\pi\) | ||||
0.999187 | − | 0.0403096i | \(-0.0128344\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10785.7 | −0.782249 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1730.00 | −0.124819 | −0.0624097 | − | 0.998051i | \(-0.519879\pi\) | ||||
−0.0624097 | + | 0.998051i | \(0.519879\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 8596.69i | − 0.613857i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23879.7 | 1.69639 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7644.00i | 0.537482i | 0.963213 | + | 0.268741i | \(0.0866075\pi\) | ||||
−0.963213 | + | 0.268741i | \(0.913393\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 12815.4i | − 0.896521i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26874.0 | −1.86102 | −0.930508 | − | 0.366271i | \(-0.880634\pi\) | ||||
−0.930508 | + | 0.366271i | \(0.880634\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16632.0i | 1.14596i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9750.88 | −0.665125 | −0.332563 | − | 0.943081i | \(-0.607913\pi\) | ||||
−0.332563 | + | 0.943081i | \(0.607913\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 650.000 | 0.0441166 | 0.0220583 | − | 0.999757i | \(-0.492978\pi\) | ||||
0.0220583 | + | 0.999757i | \(0.492978\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 19362.5i | − 1.30115i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16695.9 | −1.11642 | −0.558209 | − | 0.829701i | \(-0.688511\pi\) | ||||
−0.558209 | + | 0.829701i | \(0.688511\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3168.00i | 0.209760i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7522.11i | 0.495620i | 0.968809 | + | 0.247810i | \(0.0797108\pi\) | ||||
−0.968809 | + | 0.247810i | \(0.920289\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2526.00 | −0.164818 | −0.0824092 | − | 0.996599i | \(-0.526261\pi\) | ||||
−0.0824092 | + | 0.996599i | \(0.526261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4372.00i | 0.283886i | 0.989875 | + | 0.141943i | \(0.0453350\pi\) | ||||
−0.989875 | + | 0.141943i | \(0.954665\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12536.8 | −0.806225 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23941.0 | 1.53222 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 8357.89i | − 0.529811i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23979.2 | 1.51283 | 0.756416 | − | 0.654091i | \(-0.226949\pi\) | ||||
0.756416 | + | 0.654091i | \(0.226949\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 2772.00i | − 0.173234i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4218.75i | 0.262406i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1374.00 | −0.0846642 | −0.0423321 | − | 0.999104i | \(-0.513479\pi\) | ||||
−0.0423321 | + | 0.999104i | \(0.513479\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 4196.00i | − 0.257347i | −0.991687 | − | 0.128673i | \(-0.958928\pi\) | ||||
0.991687 | − | 0.128673i | \(-0.0410719\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17392.4 | 1.05682 | 0.528412 | − | 0.848988i | \(-0.322788\pi\) | ||||
0.528412 | + | 0.848988i | \(0.322788\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24768.0 | −1.49804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18685.9i | 1.11981i | 0.828558 | + | 0.559904i | \(0.189162\pi\) | ||||
−0.828558 | + | 0.559904i | \(0.810838\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10745.9 | −0.641032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16380.0i | 0.968246i | 0.875000 | + | 0.484123i | \(0.160861\pi\) | ||||
−0.875000 | + | 0.484123i | \(0.839139\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5850.53i | 0.344265i | 0.985074 | + | 0.172132i | \(0.0550657\pi\) | ||||
−0.985074 | + | 0.172132i | \(0.944934\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36432.0 | 2.12447 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 792.000i | 0.0459766i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17193.4 | 0.989185 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13250.0 | −0.758915 | −0.379458 | − | 0.925209i | \(-0.623889\pi\) | ||||
−0.379458 | + | 0.925209i | \(0.623889\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14347.7i | 0.814516i | 0.913313 | + | 0.407258i | \(0.133515\pi\) | ||||
−0.913313 | + | 0.407258i | \(0.866485\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17153.6 | 0.969505 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 28272.0i | − 1.58389i | −0.610591 | − | 0.791946i | \(-0.709068\pi\) | ||||
0.610591 | − | 0.791946i | \(-0.290932\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28775.0i | 1.60502i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39600.0 | 2.18961 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16828.0i | 0.926436i | 0.886244 | + | 0.463218i | \(0.153305\pi\) | ||||
−0.886244 | + | 0.463218i | \(0.846695\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 37650.3 | 2.05490 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 252.000 | 0.0136947 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18088.9i | 0.974618i | 0.873230 | + | 0.487309i | \(0.162021\pi\) | ||||
−0.873230 | + | 0.487309i | \(0.837979\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18307.8 | −0.982206 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9108.00i | 0.484500i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36854.3i | 1.95218i | 0.217373 | + | 0.976089i | \(0.430251\pi\) | ||||
−0.217373 | + | 0.976089i | \(0.569749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5544.00 | 0.291198 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 76032.0i | − 3.97683i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21849.9 | −1.13333 | −0.566665 | − | 0.823948i | \(-0.691767\pi\) | ||||
−0.566665 | + | 0.823948i | \(0.691767\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10692.0 | 0.552276 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 5392.83i | − 0.276255i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35282.3 | 1.79993 | 0.899963 | − | 0.435966i | \(-0.143593\pi\) | ||||
0.899963 | + | 0.435966i | \(0.143593\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3864.00i | 0.195506i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8198.70i | 0.413132i | 0.978433 | + | 0.206566i | \(0.0662288\pi\) | ||||
−0.978433 | + | 0.206566i | \(0.933771\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25152.0 | −1.25710 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 35404.0i | − 1.76232i | −0.472815 | − | 0.881162i | \(-0.656762\pi\) | ||||
0.472815 | − | 0.881162i | \(-0.343238\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9711.08 | −0.479495 | −0.239748 | − | 0.970835i | \(-0.577065\pi\) | ||||
−0.239748 | + | 0.970835i | \(0.577065\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −55836.0 | −2.74587 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27461.7i | 1.33969i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21631.0 | 1.05104 | 0.525518 | − | 0.850783i | \(-0.323872\pi\) | ||||
0.525518 | + | 0.850783i | \(0.323872\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 5940.00i | − 0.286329i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 26984.1i | − 1.29558i | −0.761820 | − | 0.647789i | \(-0.775694\pi\) | ||||
0.761820 | − | 0.647789i | \(-0.224306\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14382.0 | 0.685082 | 0.342541 | − | 0.939503i | \(-0.388713\pi\) | ||||
0.342541 | + | 0.939503i | \(0.388713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25344.0i | 1.20251i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −41073.1 | −1.93359 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32978.0 | 1.54645 | 0.773223 | − | 0.634134i | \(-0.218643\pi\) | ||||
0.773223 | + | 0.634134i | \(0.218643\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 28914.3i | − 1.34538i | −0.739926 | − | 0.672688i | \(-0.765139\pi\) | ||||
0.739926 | − | 0.672688i | \(-0.234861\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37749.8 | −1.74970 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 552.000i | − 0.0253883i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 47759.4i | − 2.18818i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46728.0 | 2.12458 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 24572.0i | − 1.11296i | −0.830862 | − | 0.556479i | \(-0.812152\pi\) | ||||
0.830862 | − | 0.556479i | \(-0.187848\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −41908.9 | −1.88383 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28512.0 | 1.27679 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19720.7i | 0.876463i | 0.898862 | + | 0.438232i | \(0.144395\pi\) | ||||
−0.898862 | + | 0.438232i | \(0.855605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1671.58 | 0.0740128 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 20640.0i | − 0.907061i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15760.6i | 0.690047i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35286.0 | 1.53349 | 0.766743 | − | 0.641955i | \(-0.221876\pi\) | ||||
0.766743 | + | 0.641955i | \(0.221876\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 556.000i | − 0.0240737i | −0.999928 | − | 0.0120369i | \(-0.996168\pi\) | ||||
0.999928 | − | 0.0120369i | \(-0.00383155\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 63440.4 | 2.72665 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8464.00 | 0.362445 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 33769.9i | − 1.43554i | −0.696281 | − | 0.717769i | \(-0.745163\pi\) | ||||
0.696281 | − | 0.717769i | \(-0.254837\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26247.8 | −1.11171 | −0.555856 | − | 0.831278i | \(-0.687610\pi\) | ||||
−0.555856 | + | 0.831278i | \(0.687610\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1116.00i | − 0.0469252i | −0.999725 | − | 0.0234626i | \(-0.992531\pi\) | ||||
0.999725 | − | 0.0234626i | \(-0.00746906\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 23242.9i | − 0.973775i | −0.873465 | − | 0.486888i | \(-0.838132\pi\) | ||||
0.873465 | − | 0.486888i | \(-0.161868\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2226.00 | 0.0925886 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39600.0i | 1.64121i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29650.6 | 1.22009 | 0.610044 | − | 0.792368i | \(-0.291152\pi\) | ||||
0.610044 | + | 0.792368i | \(0.291152\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23993.0 | 0.983763 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 82365.1i | − 3.35319i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19362.5 | −0.785480 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 7920.00i | − 0.319029i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 17074.0i | − 0.685348i | −0.939454 | − | 0.342674i | \(-0.888667\pi\) | ||||
0.939454 | − | 0.342674i | \(-0.111333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1206.00 | 0.0480702 | 0.0240351 | − | 0.999711i | \(-0.492349\pi\) | ||||
0.0240351 | + | 0.999711i | \(0.492349\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 34756.0i | − 1.38051i | −0.723565 | − | 0.690256i | \(-0.757498\pi\) | ||||
0.723565 | − | 0.690256i | \(-0.242502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1034.79 | 0.0408164 | 0.0204082 | − | 0.999792i | \(-0.493503\pi\) | ||||
0.0204082 | + | 0.999792i | \(0.493503\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7524.00 | −0.295750 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 56356.1i | 2.19994i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41709.9 | −1.62260 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 57816.0i | − 2.23376i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19382.4i | 0.746289i | 0.927773 | + | 0.373145i | \(0.121720\pi\) | ||||
−0.927773 | + | 0.373145i | \(0.878280\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5310.00 | 0.203063 | 0.101531 | − | 0.994832i | \(-0.467626\pi\) | ||||
0.101531 | + | 0.994832i | \(0.467626\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23308.0i | 0.888309i | 0.895950 | + | 0.444154i | \(0.146496\pi\) | ||||
−0.895950 | + | 0.444154i | \(0.853504\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21969.3 | −0.831632 | −0.415816 | − | 0.909449i | \(-0.636504\pi\) | ||||
−0.415816 | + | 0.909449i | \(0.636504\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2772.00 | −0.104578 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 3661.55i | − 0.137211i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 56594.9 | 2.11370 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2772.00i | 0.102838i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 20894.7i | − 0.772591i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44352.0 | −1.62907 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27596.0i | 1.01026i | 0.863042 | + | 0.505132i | \(0.168556\pi\) | ||||
−0.863042 | + | 0.505132i | \(0.831444\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12099.0 | 0.440021 | 0.220011 | − | 0.975497i | \(-0.429391\pi\) | ||||
0.220011 | + | 0.975497i | \(0.429391\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20736.0 | 0.751655 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10745.9i | 0.386979i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14029.3 | 0.503574 | 0.251787 | − | 0.967783i | \(-0.418982\pi\) | ||||
0.251787 | + | 0.967783i | \(0.418982\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 79200.0i | − 2.82438i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 53928.3i | 1.91692i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12438.0 | −0.439265 | −0.219633 | − | 0.975583i | \(-0.570486\pi\) | ||||
−0.219633 | + | 0.975583i | \(0.570486\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 4876.00i | − 0.171648i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −40117.9 | −1.40320 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8278.00 | 0.288613 | 0.144307 | − | 0.989533i | \(-0.453905\pi\) | ||||
0.144307 | + | 0.989533i | \(0.453905\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 5114.24i | − 0.177172i | −0.996069 | − | 0.0885862i | \(-0.971765\pi\) | ||||
0.996069 | − | 0.0885862i | \(-0.0282349\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 238.797 | 0.00824634 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16980.0i | 0.582657i | 0.956623 | + | 0.291328i | \(0.0940972\pi\) | ||||
−0.956623 | + | 0.291328i | \(0.905903\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 34227.6i | − 1.17078i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31998.0 | 1.08764 | 0.543818 | − | 0.839203i | \(-0.316978\pi\) | ||||
0.543818 | + | 0.839203i | \(0.316978\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 17424.0i | − 0.590395i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28775.0 | 0.968920 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10387.0 | −0.348662 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 57351.1i | 1.91316i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8059.40 | −0.268017 | −0.134009 | − | 0.990980i | \(-0.542785\pi\) | ||||
−0.134009 | + | 0.990980i | \(0.542785\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 29664.0i | − 0.980395i | −0.871612 | − | 0.490197i | \(-0.836925\pi\) | ||||
0.871612 | − | 0.490197i | \(-0.163075\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 37650.3i | − 1.24051i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3354.00 | 0.109830 | 0.0549150 | − | 0.998491i | \(-0.482511\pi\) | ||||
0.0549150 | + | 0.998491i | \(0.482511\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 30240.0i | − 0.987206i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29610.8 | −0.960772 | −0.480386 | − | 0.877057i | \(-0.659503\pi\) | ||||
−0.480386 | + | 0.877057i | \(0.659503\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 84348.0 | 2.72848 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3661.55i | 0.117726i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38506.0 | 1.23429 | 0.617146 | − | 0.786848i | \(-0.288289\pi\) | ||||
0.617146 | + | 0.786848i | \(0.288289\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 64548.0i | 2.05659i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54326.3i | 1.72571i | 0.505453 | + | 0.862854i | \(0.331326\pi\) | ||||
−0.505453 | + | 0.862854i | \(0.668674\pi\) | |||||||
\(998\) | 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 | 576.4.d.f.289.4 | 4 | ||
3.2 | odd | 2 | 192.4.d.b.97.1 | ✓ | 4 | ||
4.3 | odd | 2 | inner | 576.4.d.f.289.3 | 4 | ||
8.3 | odd | 2 | inner | 576.4.d.f.289.1 | 4 | ||
8.5 | even | 2 | inner | 576.4.d.f.289.2 | 4 | ||
12.11 | even | 2 | 192.4.d.b.97.3 | yes | 4 | ||
16.3 | odd | 4 | 2304.4.a.y.1.2 | 2 | |||
16.5 | even | 4 | 2304.4.a.y.1.1 | 2 | |||
16.11 | odd | 4 | 2304.4.a.bl.1.1 | 2 | |||
16.13 | even | 4 | 2304.4.a.bl.1.2 | 2 | |||
24.5 | odd | 2 | 192.4.d.b.97.4 | yes | 4 | ||
24.11 | even | 2 | 192.4.d.b.97.2 | yes | 4 | ||
48.5 | odd | 4 | 768.4.a.i.1.2 | 2 | |||
48.11 | even | 4 | 768.4.a.l.1.2 | 2 | |||
48.29 | odd | 4 | 768.4.a.l.1.1 | 2 | |||
48.35 | even | 4 | 768.4.a.i.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
192.4.d.b.97.1 | ✓ | 4 | 3.2 | odd | 2 | ||
192.4.d.b.97.2 | yes | 4 | 24.11 | even | 2 | ||
192.4.d.b.97.3 | yes | 4 | 12.11 | even | 2 | ||
192.4.d.b.97.4 | yes | 4 | 24.5 | odd | 2 | ||
576.4.d.f.289.1 | 4 | 8.3 | odd | 2 | inner | ||
576.4.d.f.289.2 | 4 | 8.5 | even | 2 | inner | ||
576.4.d.f.289.3 | 4 | 4.3 | odd | 2 | inner | ||
576.4.d.f.289.4 | 4 | 1.1 | even | 1 | trivial | ||
768.4.a.i.1.1 | 2 | 48.35 | even | 4 | |||
768.4.a.i.1.2 | 2 | 48.5 | odd | 4 | |||
768.4.a.l.1.1 | 2 | 48.29 | odd | 4 | |||
768.4.a.l.1.2 | 2 | 48.11 | even | 4 | |||
2304.4.a.y.1.1 | 2 | 16.5 | even | 4 | |||
2304.4.a.y.1.2 | 2 | 16.3 | odd | 4 | |||
2304.4.a.bl.1.1 | 2 | 16.11 | odd | 4 | |||
2304.4.a.bl.1.2 | 2 | 16.13 | even | 4 |