Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(1,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.a (trivial) |
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: | yes |
Analytic conductor: | \(45.3134668844\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{11}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 192) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.31662\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 19.8997 | 1.77989 | 0.889944 | − | 0.456070i | \(-0.150743\pi\) | ||||
0.889944 | + | 0.456070i | \(0.150743\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 19.8997 | 1.07449 | 0.537243 | − | 0.843428i | \(-0.319466\pi\) | ||||
0.537243 | + | 0.843428i | \(0.319466\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −48.0000 | −1.31569 | −0.657843 | − | 0.753155i | \(-0.728531\pi\) | ||||
−0.657843 | + | 0.753155i | \(0.728531\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 79.5990 | 1.69821 | 0.849107 | − | 0.528220i | \(-0.177141\pi\) | ||||
0.849107 | + | 0.528220i | \(0.177141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 59.6992 | 1.02762 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −42.0000 | −0.599206 | −0.299603 | − | 0.954064i | \(-0.596854\pi\) | ||||
−0.299603 | + | 0.954064i | \(0.596854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 92.0000 | 1.11086 | 0.555428 | − | 0.831565i | \(-0.312555\pi\) | ||||
0.555428 | + | 0.831565i | \(0.312555\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 59.6992 | 0.620354 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −39.7995 | −0.360816 | −0.180408 | − | 0.983592i | \(-0.557742\pi\) | ||||
−0.180408 | + | 0.983592i | \(0.557742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 271.000 | 2.16800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −19.8997 | −0.127424 | −0.0637119 | − | 0.997968i | \(-0.520294\pi\) | ||||
−0.0637119 | + | 0.997968i | \(0.520294\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −139.298 | −0.807055 | −0.403527 | − | 0.914968i | \(-0.632216\pi\) | ||||
−0.403527 | + | 0.914968i | \(0.632216\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −144.000 | −0.759612 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 396.000 | 1.91246 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 198.997 | 0.884189 | 0.442094 | − | 0.896969i | \(-0.354236\pi\) | ||||
0.442094 | + | 0.896969i | \(0.354236\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 238.797 | 0.980465 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.0228547 | 0.0114273 | − | 0.999935i | \(-0.496362\pi\) | ||||
0.0114273 | + | 0.999935i | \(0.496362\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 92.0000 | 0.326276 | 0.163138 | − | 0.986603i | \(-0.447838\pi\) | ||||
0.163138 | + | 0.986603i | \(0.447838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 179.098 | 0.593296 | ||||||||
\(46\) | 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 | ||||||||
\(51\) | −126.000 | −0.345952 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −497.494 | −1.28936 | −0.644679 | − | 0.764453i | \(-0.723009\pi\) | ||||
−0.644679 | + | 0.764453i | \(0.723009\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −955.188 | −2.34177 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 276.000 | 0.641353 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −516.000 | −1.13860 | −0.569301 | − | 0.822129i | \(-0.692786\pi\) | ||||
−0.569301 | + | 0.822129i | \(0.692786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −358.195 | −0.751840 | −0.375920 | − | 0.926652i | \(-0.622673\pi\) | ||||
−0.375920 | + | 0.926652i | \(0.622673\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 179.098 | 0.358162 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1584.00 | 3.02263 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −524.000 | −0.955474 | −0.477737 | − | 0.878503i | \(-0.658543\pi\) | ||||
−0.477737 | + | 0.878503i | \(0.658543\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −119.398 | −0.208317 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 994.987 | 1.66314 | 0.831572 | − | 0.555416i | \(-0.187441\pi\) | ||||
0.831572 | + | 0.555416i | \(0.187441\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 430.000 | 0.689420 | 0.344710 | − | 0.938709i | \(-0.387977\pi\) | ||||
0.344710 | + | 0.938709i | \(0.387977\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 813.000 | 1.25170 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −955.188 | −1.41369 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1174.09 | −1.67209 | −0.836044 | − | 0.548663i | \(-0.815137\pi\) | ||||
−0.836044 | + | 0.548663i | \(0.815137\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −432.000 | −0.571303 | −0.285652 | − | 0.958334i | \(-0.592210\pi\) | ||||
−0.285652 | + | 0.958334i | \(0.592210\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −835.789 | −1.06652 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −59.6992 | −0.0735682 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −630.000 | −0.750336 | −0.375168 | − | 0.926957i | \(-0.622415\pi\) | ||||
−0.375168 | + | 0.926957i | \(0.622415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1584.00 | 1.82471 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −417.895 | −0.465953 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | −432.000 | −0.438562 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 457.694 | 0.450914 | 0.225457 | − | 0.974253i | \(-0.427613\pi\) | ||||
0.225457 | + | 0.974253i | \(0.427613\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 537.293 | 0.513991 | 0.256996 | − | 0.966413i | \(-0.417267\pi\) | ||||
0.256996 | + | 0.966413i | \(0.417267\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1188.00 | 1.10416 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1380.00 | −1.24682 | −0.623410 | − | 0.781896i | \(-0.714253\pi\) | ||||
−0.623410 | + | 0.781896i | \(0.714253\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1273.58 | 1.11915 | 0.559574 | − | 0.828780i | \(-0.310965\pi\) | ||||
0.559574 | + | 0.828780i | \(0.310965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 596.992 | 0.510487 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2106.00 | 1.75324 | 0.876619 | − | 0.481186i | \(-0.159794\pi\) | ||||
0.876619 | + | 0.481186i | \(0.159794\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −792.000 | −0.642212 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 716.391 | 0.566072 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −835.789 | −0.643838 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 973.000 | 0.731029 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.0000 | 0.0131952 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2905.36 | 2.07891 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 139.298 | 0.0973285 | 0.0486643 | − | 0.998815i | \(-0.484504\pi\) | ||||
0.0486643 | + | 0.998815i | \(0.484504\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 276.000 | 0.188376 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 540.000 | 0.360153 | 0.180076 | − | 0.983653i | \(-0.442365\pi\) | ||||
0.180076 | + | 0.983653i | \(0.442365\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1830.78 | 1.19360 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 537.293 | 0.342540 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1446.00 | 0.901753 | 0.450876 | − | 0.892586i | \(-0.351112\pi\) | ||||
0.450876 | + | 0.892586i | \(0.351112\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1892.00 | −1.15451 | −0.577257 | − | 0.816563i | \(-0.695877\pi\) | ||||
−0.577257 | + | 0.816563i | \(0.695877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 119.398 | 0.0713132 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3820.75 | −2.23432 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −396.000 | −0.226800 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 159.000 | 0.0892116 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2805.86 | 1.54272 | 0.771360 | − | 0.636399i | \(-0.219577\pi\) | ||||
0.771360 | + | 0.636399i | \(0.219577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −298.496 | −0.160869 | −0.0804347 | − | 0.996760i | \(-0.525631\pi\) | ||||
−0.0804347 | + | 0.996760i | \(0.525631\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −378.000 | −0.199735 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2772.00 | −1.43647 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2348.17 | −1.19366 | −0.596829 | − | 0.802368i | \(-0.703573\pi\) | ||||
−0.596829 | + | 0.802368i | \(0.703573\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1492.48 | −0.744412 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −792.000 | −0.387692 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3188.00 | 1.53192 | 0.765961 | − | 0.642887i | \(-0.222263\pi\) | ||||
0.765961 | + | 0.642887i | \(0.222263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2865.56 | −1.35202 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1989.97 | −0.922089 | −0.461045 | − | 0.887377i | \(-0.652525\pi\) | ||||
−0.461045 | + | 0.887377i | \(0.652525\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4139.00 | 1.88393 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 828.000 | 0.370285 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −378.095 | −0.166162 | −0.0830811 | − | 0.996543i | \(-0.526476\pi\) | ||||
−0.0830811 | + | 0.996543i | \(0.526476\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5392.83 | 2.32948 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1548.00 | −0.657372 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2844.00 | −1.18754 | −0.593772 | − | 0.804633i | \(-0.702362\pi\) | ||||
−0.593772 | + | 0.804633i | \(0.702362\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2228.77 | −0.915267 | −0.457633 | − | 0.889141i | \(-0.651303\pi\) | ||||
−0.457633 | + | 0.889141i | \(0.651303\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1074.59 | −0.434075 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3960.00 | 1.57376 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2016.00 | 0.788366 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 537.293 | 0.206785 | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 4752.00 | 1.74512 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4238.65 | −1.53295 | −0.766475 | − | 0.642274i | \(-0.777991\pi\) | ||||
−0.766475 | + | 0.642274i | \(0.777991\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3243.66 | 1.15546 | 0.577731 | − | 0.816227i | \(-0.303938\pi\) | ||||
0.577731 | + | 0.816227i | \(0.303938\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1572.00 | −0.551643 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −396.000 | −0.136915 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 119.398 | 0.0406788 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −358.195 | −0.120272 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4416.00 | −1.46154 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2356.00 | 0.768691 | 0.384345 | − | 0.923189i | \(-0.374427\pi\) | ||||
0.384345 | + | 0.923189i | \(0.374427\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2984.96 | 0.960217 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1830.78 | 0.580735 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2772.00 | −0.867169 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1290.00 | 0.398037 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3343.16 | −1.01758 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1771.08 | −0.531839 | −0.265920 | − | 0.963995i | \(-0.585676\pi\) | ||||
−0.265920 | + | 0.963995i | \(0.585676\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2439.00 | 0.722667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3864.00 | −1.12979 | −0.564896 | − | 0.825162i | \(-0.691084\pi\) | ||||
−0.564896 | + | 0.825162i | \(0.691084\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 557.193 | 0.160788 | 0.0803938 | − | 0.996763i | \(-0.474382\pi\) | ||||
0.0803938 | + | 0.996763i | \(0.474382\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2865.56 | −0.816192 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2814.00 | −0.791207 | −0.395604 | − | 0.918421i | \(-0.629465\pi\) | ||||
−0.395604 | + | 0.918421i | \(0.629465\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 792.000 | 0.219848 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3522.26 | −0.965380 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1054.69 | 0.275026 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7323.11 | 1.88647 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1296.00 | −0.329842 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5136.00 | 1.29156 | 0.645780 | − | 0.763524i | \(-0.276532\pi\) | ||||
0.645780 | + | 0.763524i | \(0.276532\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1910.38 | 0.474721 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2507.37 | −0.615755 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −174.000 | −0.0422328 | −0.0211164 | − | 0.999777i | \(-0.506722\pi\) | ||||
−0.0211164 | + | 0.999777i | \(0.506722\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3960.00 | 0.950048 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −179.098 | −0.0424746 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4775.94 | −1.11976 | −0.559880 | − | 0.828573i | \(-0.689153\pi\) | ||||
−0.559880 | + | 0.828573i | \(0.689153\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9900.00 | −2.29491 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1890.00 | −0.433206 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1134.29 | −0.257095 | −0.128548 | − | 0.991703i | \(-0.541032\pi\) | ||||
−0.128548 | + | 0.991703i | \(0.541032\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −179.098 | −0.0401454 | −0.0200727 | − | 0.999799i | \(-0.506390\pi\) | ||||
−0.0200727 | + | 0.999799i | \(0.506390\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4752.00 | 1.05349 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13008.0 | −2.85241 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6367.92 | −1.38127 | −0.690634 | − | 0.723205i | \(-0.742668\pi\) | ||||
−0.690634 | + | 0.723205i | \(0.742668\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1253.68 | −0.269018 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −558.000 | −0.118461 | −0.0592304 | − | 0.998244i | \(-0.518865\pi\) | ||||
−0.0592304 | + | 0.998244i | \(0.518865\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2068.00 | 0.434381 | 0.217191 | − | 0.976129i | \(-0.430311\pi\) | ||||
0.217191 | + | 0.976129i | \(0.430311\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5492.33 | 1.14154 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 119.398 | 0.0245570 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3149.00 | −0.640953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2586.00 | 0.520942 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3363.06 | −0.670553 | −0.335276 | − | 0.942120i | \(-0.608830\pi\) | ||||
−0.335276 | + | 0.942120i | \(0.608830\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10268.3 | −2.02658 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1296.00 | −0.253204 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3168.00 | −0.612743 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1830.78 | 0.350579 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1373.08 | 0.260335 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7128.00 | −1.33819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6860.00 | −1.27531 | −0.637656 | − | 0.770321i | \(-0.720096\pi\) | ||||
−0.637656 | + | 0.770321i | \(0.720096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1611.88 | 0.296753 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10427.5 | 1.90125 | 0.950623 | − | 0.310348i | \(-0.100446\pi\) | ||||
0.950623 | + | 0.310348i | \(0.100446\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6262.00 | −1.13083 | −0.565414 | − | 0.824807i | \(-0.691284\pi\) | ||||
−0.565414 | + | 0.824807i | \(0.691284\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3564.00 | 0.637488 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 776.090 | 0.137507 | 0.0687533 | − | 0.997634i | \(-0.478098\pi\) | ||||
0.0687533 | + | 0.997634i | \(0.478098\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 955.188 | 0.167650 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4140.00 | −0.719851 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3864.00 | −0.665631 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21571.3 | 3.68173 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3820.75 | 0.646141 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 792.000 | 0.132718 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6460.00 | 1.07273 | 0.536365 | − | 0.843986i | \(-0.319797\pi\) | ||||
0.536365 | + | 0.843986i | \(0.319797\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1790.98 | 0.294730 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 6318.00 | 1.01223 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6686.32 | 1.06183 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5770.93 | −0.908457 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2376.00 | −0.370781 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6888.00 | −1.06561 | −0.532806 | − | 0.846238i | \(-0.678862\pi\) | ||||
−0.532806 | + | 0.846238i | \(0.678862\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −676.591 | −0.103774 | −0.0518870 | − | 0.998653i | \(-0.516524\pi\) | ||||
−0.0518870 | + | 0.998653i | \(0.516524\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2149.17 | 0.326822 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1830.00 | −0.275924 | −0.137962 | − | 0.990438i | \(-0.544055\pi\) | ||||
−0.137962 | + | 0.990438i | \(0.544055\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19800.0 | 2.96021 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2507.37 | −0.371720 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6646.52 | −0.977130 | −0.488565 | − | 0.872527i | \(-0.662479\pi\) | ||||
−0.488565 | + | 0.872527i | \(0.662479\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1605.00 | 0.233999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2919.00 | 0.422060 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8556.89 | 1.22709 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3164.06 | −0.450034 | −0.225017 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225017 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 54.0000 | 0.00761823 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9900.00 | −1.38540 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9750.88 | −1.35357 | −0.676785 | − | 0.736181i | \(-0.736627\pi\) | ||||
−0.676785 | + | 0.736181i | \(0.736627\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8716.09 | 1.20026 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1584.00 | −0.216393 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8332.00 | −1.12925 | −0.564625 | − | 0.825347i | \(-0.690979\pi\) | ||||
−0.564625 | + | 0.825347i | \(0.690979\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 417.895 | 0.0561926 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 828.000 | 0.108759 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5870.43 | −0.765148 | −0.382574 | − | 0.923925i | \(-0.624962\pi\) | ||||
−0.382574 | + | 0.923925i | \(0.624962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1671.58 | 0.216203 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1620.00 | 0.207934 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23364.0 | −2.97613 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2666.57 | 0.337106 | 0.168553 | − | 0.985693i | \(-0.446091\pi\) | ||||
0.168553 | + | 0.985693i | \(0.446091\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5492.33 | 0.689124 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2634.00 | −0.328019 | −0.164010 | − | 0.986459i | \(-0.552443\pi\) | ||||
−0.164010 | + | 0.986459i | \(0.552443\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11088.0 | −1.37055 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1611.88 | 0.197765 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9551.88 | −1.16331 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −506.000 | −0.0611738 | −0.0305869 | − | 0.999532i | \(-0.509738\pi\) | ||||
−0.0305869 | + | 0.999532i | \(0.509738\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4338.00 | 0.520627 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10268.3 | −1.22341 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8596.69 | −1.01686 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5676.00 | −0.666559 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15480.0 | 1.80489 | 0.902443 | − | 0.430809i | \(-0.141772\pi\) | ||||
0.902443 | + | 0.430809i | \(0.141772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10666.3 | −1.23478 | −0.617390 | − | 0.786658i | \(-0.711810\pi\) | ||||
−0.617390 | + | 0.786658i | \(0.711810\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 358.195 | 0.0411727 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11382.0 | −1.29908 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7128.00 | −0.807841 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11462.3 | −1.28998 | ||||||||
\(430\) | 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 | ||||||||
\(435\) | −1188.00 | −0.130943 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3661.55 | −0.400814 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 776.090 | 0.0843753 | 0.0421877 | − | 0.999110i | \(-0.486567\pi\) | ||||
0.0421877 | + | 0.999110i | \(0.486567\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 477.000 | 0.0515063 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 408.000 | 0.0437577 | 0.0218789 | − | 0.999761i | \(-0.493035\pi\) | ||||
0.0218789 | + | 0.999761i | \(0.493035\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12536.8 | −1.33551 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8417.59 | 0.890690 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11658.0 | −1.22533 | −0.612667 | − | 0.790341i | \(-0.709903\pi\) | ||||
−0.612667 | + | 0.790341i | \(0.709903\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −288.000 | −0.0300696 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −895.489 | −0.0928780 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 31521.2 | 3.24777 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16486.0 | 1.68749 | 0.843745 | − | 0.536745i | \(-0.180346\pi\) | ||||
0.843745 | + | 0.536745i | \(0.180346\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1134.00 | −0.115317 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4119.25 | −0.416166 | −0.208083 | − | 0.978111i | \(-0.566722\pi\) | ||||
−0.208083 | + | 0.978111i | \(0.566722\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13472.1 | −1.35227 | −0.676137 | − | 0.736776i | \(-0.736347\pi\) | ||||
−0.676137 | + | 0.736776i | \(0.736347\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8316.00 | −0.829345 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4440.00 | −0.439954 | −0.219977 | − | 0.975505i | \(-0.570598\pi\) | ||||
−0.219977 | + | 0.975505i | \(0.570598\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10427.5 | −1.02664 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7044.51 | −0.689159 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4416.00 | −0.429277 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24932.0 | 2.40833 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4477.44 | −0.429786 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | −2376.00 | −0.223834 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17153.6 | 1.60599 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1333.28 | −0.124059 | −0.0620296 | − | 0.998074i | \(-0.519757\pi\) | ||||
−0.0620296 | + | 0.998074i | \(0.519757\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9564.00 | 0.884456 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7404.00 | −0.680525 | −0.340263 | − | 0.940330i | \(-0.610516\pi\) | ||||
−0.340263 | + | 0.940330i | \(0.610516\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 835.789 | 0.0763531 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8596.69 | −0.780591 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19800.0 | 1.78702 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5740.00 | 0.514945 | 0.257473 | − | 0.966286i | \(-0.417110\pi\) | ||||
0.257473 | + | 0.966286i | \(0.417110\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5969.92 | −0.532368 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16039.2 | −1.42177 | −0.710887 | − | 0.703306i | \(-0.751706\pi\) | ||||
−0.710887 | + | 0.703306i | \(0.751706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9108.00 | 0.802576 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12417.0 | 1.08769 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16377.5 | 1.42617 | 0.713084 | − | 0.701078i | \(-0.247298\pi\) | ||||
0.713084 | + | 0.701078i | \(0.247298\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8556.89 | 0.740772 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2484.00 | 0.213784 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10692.0 | 0.914846 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1910.38 | −0.162511 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1134.29 | −0.0959337 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22098.0 | −1.85822 | −0.929108 | − | 0.369807i | \(-0.879424\pi\) | ||||
−0.929108 | + | 0.369807i | \(0.879424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16436.0 | 1.37418 | 0.687090 | − | 0.726572i | \(-0.258888\pi\) | ||||
0.687090 | + | 0.726572i | \(0.258888\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16178.5 | 1.34493 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5850.53 | 0.483592 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10583.0 | −0.869812 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4644.00 | −0.379534 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 477.594 | 0.0388122 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27461.7 | −2.21920 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8532.00 | −0.685629 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2544.00 | −0.203298 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11143.9 | 0.885604 | 0.442802 | − | 0.896619i | \(-0.353984\pi\) | ||||
0.442802 | + | 0.896619i | \(0.353984\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6686.32 | −0.528430 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25344.0 | 1.99196 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1316.00 | 0.102867 | 0.0514334 | − | 0.998676i | \(-0.483621\pi\) | ||||
0.0514334 | + | 0.998676i | \(0.483621\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3223.76 | −0.250613 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1830.78 | −0.141549 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23364.0 | −1.79663 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11880.0 | 0.908609 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3402.86 | −0.258858 | −0.129429 | − | 0.991589i | \(-0.541314\pi\) | ||||
−0.129429 | + | 0.991589i | \(0.541314\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7323.11 | 0.554087 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6048.00 | 0.455164 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19560.0 | −1.46422 | −0.732110 | − | 0.681187i | \(-0.761464\pi\) | ||||
−0.732110 | + | 0.681187i | \(0.761464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 41908.9 | 3.12057 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1611.88 | 0.119387 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20838.0 | 1.53528 | 0.767640 | − | 0.640881i | \(-0.221431\pi\) | ||||
0.767640 | + | 0.640881i | \(0.221431\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1100.00 | −0.0806192 | −0.0403096 | − | 0.999187i | \(-0.512834\pi\) | ||||
−0.0403096 | + | 0.999187i | \(0.512834\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2626.77 | −0.191509 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 8646.00 | 0.620579 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8596.69 | −0.613857 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23879.7 | 1.69639 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14256.0 | 1.00754 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7644.00 | −0.537482 | −0.268741 | − | 0.963213i | \(-0.586607\pi\) | ||||
−0.268741 | + | 0.963213i | \(0.586607\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12815.4 | −0.896521 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12715.9 | −0.885049 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26874.0 | 1.86102 | 0.930508 | − | 0.366271i | \(-0.119366\pi\) | ||||
0.930508 | + | 0.366271i | \(0.119366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16632.0 | −1.14596 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9730.98 | 0.667106 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9750.88 | 0.665125 | 0.332563 | − | 0.943081i | \(-0.392087\pi\) | ||||
0.332563 | + | 0.943081i | \(0.392087\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −650.000 | −0.0441166 | −0.0220583 | − | 0.999757i | \(-0.507022\pi\) | ||||
−0.0220583 | + | 0.999757i | \(0.507022\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4716.00 | −0.318491 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19362.5 | 1.30115 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16695.9 | 1.11642 | 0.558209 | − | 0.829701i | \(-0.311489\pi\) | ||||
0.558209 | + | 0.829701i | \(0.311489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1188.00 | −0.0790479 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3168.00 | 0.209760 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7522.11 | −0.495620 | −0.247810 | − | 0.968809i | \(-0.579711\pi\) | ||||
−0.247810 | + | 0.968809i | \(0.579711\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 358.195 | 0.0234859 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2526.00 | −0.164818 | −0.0824092 | − | 0.996599i | \(-0.526261\pi\) | ||||
−0.0824092 | + | 0.996599i | \(0.526261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4372.00 | 0.283886 | 0.141943 | − | 0.989875i | \(-0.454665\pi\) | ||||
0.141943 | + | 0.989875i | \(0.454665\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1074.59 | −0.0694391 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12536.8 | −0.806225 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23941.0 | 1.53222 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13248.0 | −0.843818 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8357.89 | −0.529811 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23979.2 | 1.51283 | 0.756416 | − | 0.654091i | \(-0.226949\pi\) | ||||
0.756416 | + | 0.654091i | \(0.226949\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7068.00 | 0.443804 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2772.00 | 0.173234 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4218.75 | 0.262406 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8954.89 | 0.554382 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1374.00 | 0.0846642 | 0.0423321 | − | 0.999104i | \(-0.486521\pi\) | ||||
0.0423321 | + | 0.999104i | \(0.486521\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4196.00 | 0.257347 | 0.128673 | − | 0.991687i | \(-0.458928\pi\) | ||||
0.128673 | + | 0.991687i | \(0.458928\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5492.33 | 0.335287 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17392.4 | −1.05682 | −0.528412 | − | 0.848988i | \(-0.677212\pi\) | ||||
−0.528412 | + | 0.848988i | \(0.677212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24768.0 | 1.49804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8316.00 | −0.500660 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18685.9 | −1.11981 | −0.559904 | − | 0.828558i | \(-0.689162\pi\) | ||||
−0.559904 | + | 0.828558i | \(0.689162\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10745.9 | 0.641032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3870.00 | 0.229807 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16380.0 | 0.968246 | 0.484123 | − | 0.875000i | \(-0.339139\pi\) | ||||
0.484123 | + | 0.875000i | \(0.339139\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5850.53 | −0.344265 | −0.172132 | − | 0.985074i | \(-0.555066\pi\) | ||||
−0.172132 | + | 0.985074i | \(0.555066\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10029.5 | −0.587500 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36432.0 | 2.12447 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 792.000 | 0.0459766 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5313.23 | −0.307057 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 7317.00 | 0.417232 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14347.7 | 0.814516 | 0.407258 | − | 0.913313i | \(-0.366485\pi\) | ||||
0.407258 | + | 0.913313i | \(0.366485\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17153.6 | 0.969505 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11592.0 | −0.652285 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28272.0 | 1.58389 | 0.791946 | − | 0.610591i | \(-0.209068\pi\) | ||||
0.791946 | + | 0.610591i | \(0.209068\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28775.0 | 1.60502 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1671.58 | 0.0928307 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39600.0 | −2.18961 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16828.0 | −0.926436 | −0.463218 | − | 0.886244i | \(-0.653305\pi\) | ||||
−0.463218 | + | 0.886244i | \(0.653305\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8596.69 | −0.471228 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −37650.3 | −2.05490 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −252.000 | −0.0136947 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8442.00 | −0.456804 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18088.9 | −0.974618 | −0.487309 | − | 0.873230i | \(-0.662021\pi\) | ||||
−0.487309 | + | 0.873230i | \(0.662021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18307.8 | 0.982206 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2376.00 | 0.126930 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9108.00 | 0.484500 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36854.3 | −1.95218 | −0.976089 | − | 0.217373i | \(-0.930251\pi\) | ||||
−0.976089 | + | 0.217373i | \(0.930251\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10566.8 | −0.557362 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5544.00 | 0.291198 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −76032.0 | −3.97683 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13850.2 | 0.721403 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 1086.00 | 0.0558628 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5392.83 | −0.276255 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35282.3 | 1.79993 | 0.899963 | − | 0.435966i | \(-0.143593\pi\) | ||||
0.899963 | + | 0.435966i | \(0.143593\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3864.00 | −0.195506 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8198.70 | 0.413132 | 0.206566 | − | 0.978433i | \(-0.433771\pi\) | ||||
0.206566 | + | 0.978433i | \(0.433771\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3164.06 | 0.158787 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25152.0 | 1.25710 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35404.0 | 1.76232 | 0.881162 | − | 0.472815i | \(-0.156762\pi\) | ||||
0.881162 | + | 0.472815i | \(0.156762\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21969.3 | 1.08915 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9711.08 | 0.479495 | 0.239748 | − | 0.970835i | \(-0.422935\pi\) | ||||
0.239748 | + | 0.970835i | \(0.422935\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55836.0 | 2.74587 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3888.00 | −0.190434 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27461.7 | −1.33969 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21631.0 | −1.05104 | −0.525518 | − | 0.850783i | \(-0.676128\pi\) | ||||
−0.525518 | + | 0.850783i | \(0.676128\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15408.0 | 0.745682 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5940.00 | −0.286329 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26984.1 | 1.29558 | 0.647789 | − | 0.761820i | \(-0.275694\pi\) | ||||
0.647789 | + | 0.761820i | \(0.275694\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5731.13 | 0.274080 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14382.0 | 0.685082 | 0.342541 | − | 0.939503i | \(-0.388713\pi\) | ||||
0.342541 | + | 0.939503i | \(0.388713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25344.0 | 1.20251 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7522.11 | −0.355506 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | −522.000 | −0.0243831 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28914.3 | −1.34538 | −0.672688 | − | 0.739926i | \(-0.734861\pi\) | ||||
−0.672688 | + | 0.739926i | \(0.734861\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37749.8 | −1.74970 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11880.0 | 0.548510 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 552.000 | 0.0253883 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47759.4 | −2.18818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −537.293 | −0.0245227 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −46728.0 | −2.12458 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24572.0 | 1.11296 | 0.556479 | − | 0.830862i | \(-0.312152\pi\) | ||||
0.556479 | + | 0.830862i | \(0.312152\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14327.8 | −0.646494 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 41908.9 | 1.88383 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28512.0 | −1.27679 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −29700.0 | −1.32497 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19720.7 | −0.876463 | −0.438232 | − | 0.898862i | \(-0.644395\pi\) | ||||
−0.438232 | + | 0.898862i | \(0.644395\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1671.58 | −0.0740128 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5670.00 | −0.250112 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20640.0 | −0.907061 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15760.6 | −0.690047 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3402.86 | −0.148434 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35286.0 | 1.53349 | 0.766743 | − | 0.641955i | \(-0.221876\pi\) | ||||
0.766743 | + | 0.641955i | \(0.221876\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −556.000 | −0.0240737 | −0.0120369 | − | 0.999928i | \(-0.503832\pi\) | ||||
−0.0120369 | + | 0.999928i | \(0.503832\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −537.293 | −0.0231780 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 63440.4 | 2.72665 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8464.00 | 0.362445 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14256.0 | 0.608236 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33769.9 | −1.43554 | −0.717769 | − | 0.696281i | \(-0.754837\pi\) | ||||
−0.717769 | + | 0.696281i | \(0.754837\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26247.8 | −1.11171 | −0.555856 | − | 0.831278i | \(-0.687610\pi\) | ||||
−0.555856 | + | 0.831278i | \(0.687610\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −39024.0 | −1.64684 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1116.00 | 0.0469252 | 0.0234626 | − | 0.999725i | \(-0.492531\pi\) | ||||
0.0234626 | + | 0.999725i | \(0.492531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23242.9 | −0.973775 | −0.486888 | − | 0.873465i | \(-0.661868\pi\) | ||||
−0.486888 | + | 0.873465i | \(0.661868\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19103.8 | −0.797475 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2226.00 | −0.0925886 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −39600.0 | −1.64121 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3761.05 | −0.155318 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29650.6 | −1.22009 | −0.610044 | − | 0.792368i | \(-0.708848\pi\) | ||||
−0.610044 | + | 0.792368i | \(0.708848\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23993.0 | −0.983763 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1674.00 | −0.0683934 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 82365.1 | 3.35319 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19362.5 | 0.785480 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6204.00 | 0.250790 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7920.00 | −0.319029 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17074.0 | 0.685348 | 0.342674 | − | 0.939454i | \(-0.388667\pi\) | ||||
0.342674 | + | 0.939454i | \(0.388667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16477.0 | 0.659066 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1206.00 | 0.0480702 | 0.0240351 | − | 0.999711i | \(-0.492349\pi\) | ||||
0.0240351 | + | 0.999711i | \(0.492349\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34756.0 | −1.38051 | −0.690256 | − | 0.723565i | \(-0.742502\pi\) | ||||
−0.690256 | + | 0.723565i | \(0.742502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 358.195 | 0.0141780 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | −9447.00 | −0.370054 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 56356.1 | 2.19994 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41709.9 | −1.62260 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7758.00 | 0.300766 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 57816.0 | 2.23376 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19382.4 | 0.746289 | 0.373145 | − | 0.927773i | \(-0.378280\pi\) | ||||
0.373145 | + | 0.927773i | \(0.378280\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10089.2 | −0.387144 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5310.00 | −0.203063 | −0.101531 | − | 0.994832i | \(-0.532374\pi\) | ||||
−0.101531 | + | 0.994832i | \(0.532374\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23308.0 | −0.888309 | −0.444154 | − | 0.895950i | \(-0.646496\pi\) | ||||
−0.444154 | + | 0.895950i | \(0.646496\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −30804.8 | −1.17005 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21969.3 | 0.831632 | 0.415816 | − | 0.909449i | \(-0.363496\pi\) | ||||
0.415816 | + | 0.909449i | \(0.363496\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2772.00 | 0.104578 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3888.00 | −0.146187 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3661.55 | 0.137211 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −56594.9 | −2.11370 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9504.00 | −0.353767 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2772.00 | 0.102838 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20894.7 | 0.772591 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5492.33 | 0.202407 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44352.0 | −1.62907 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27596.0 | 1.01026 | 0.505132 | − | 0.863042i | \(-0.331444\pi\) | ||||
0.505132 | + | 0.863042i | \(0.331444\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4119.25 | 0.150305 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | −21384.0 | −0.772605 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10745.9 | 0.386979 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14029.3 | 0.503574 | 0.251787 | − | 0.967783i | \(-0.418982\pi\) | ||||
0.251787 | + | 0.967783i | \(0.418982\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20580.0 | −0.736302 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 79200.0 | 2.82438 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 53928.3 | 1.91692 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4835.64 | 0.171330 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12438.0 | 0.439265 | 0.219633 | − | 0.975583i | \(-0.429514\pi\) | ||||
0.219633 | + | 0.975583i | \(0.429514\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4876.00 | 0.171648 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31282.4 | 1.09768 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 40117.9 | 1.40320 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8278.00 | −0.288613 | −0.144307 | − | 0.989533i | \(-0.546095\pi\) | ||||
−0.144307 | + | 0.989533i | \(0.546095\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18786.0 | −0.652884 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5114.24 | 0.177172 | 0.0885862 | − | 0.996069i | \(-0.471765\pi\) | ||||
0.0885862 | + | 0.996069i | \(0.471765\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −238.797 | −0.00824634 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10692.0 | 0.368054 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16980.0 | 0.582657 | 0.291328 | − | 0.956623i | \(-0.405903\pi\) | ||||
0.291328 | + | 0.956623i | \(0.405903\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34227.6 | 1.17078 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2328.27 | 0.0793894 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31998.0 | 1.08764 | 0.543818 | − | 0.839203i | \(-0.316978\pi\) | ||||
0.543818 | + | 0.839203i | \(0.316978\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17424.0 | −0.590395 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2865.56 | 0.0967926 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28775.0 | 0.968920 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10387.0 | −0.348662 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12420.0 | −0.415606 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 57351.1 | 1.91316 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8059.40 | −0.268017 | −0.134009 | − | 0.990980i | \(-0.542785\pi\) | ||||
−0.134009 | + | 0.990980i | \(0.542785\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11592.0 | −0.384302 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29664.0 | 0.980395 | 0.490197 | − | 0.871612i | \(-0.336925\pi\) | ||||
0.490197 | + | 0.871612i | \(0.336925\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −37650.3 | −1.24051 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 64714.0 | 2.12565 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3354.00 | −0.109830 | −0.0549150 | − | 0.998491i | \(-0.517489\pi\) | ||||
−0.0549150 | + | 0.998491i | \(0.517489\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30240.0 | 0.987206 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11462.3 | 0.373050 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29610.8 | 0.960772 | 0.480386 | − | 0.877057i | \(-0.340497\pi\) | ||||
0.480386 | + | 0.877057i | \(0.340497\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −84348.0 | −2.72848 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2376.00 | 0.0766250 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3661.55 | −0.117726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38506.0 | −1.23429 | −0.617146 | − | 0.786848i | \(-0.711711\pi\) | ||||
−0.617146 | + | 0.786848i | \(0.711711\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19380.0 | 0.619341 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 64548.0 | 2.05659 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54326.3 | −1.72571 | −0.862854 | − | 0.505453i | \(-0.831326\pi\) | ||||
−0.862854 | + | 0.505453i | \(0.831326\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5372.93 | 0.170162 |
(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 | 768.4.a.l.1.2 | 2 | ||
3.2 | odd | 2 | 2304.4.a.bl.1.1 | 2 | |||
4.3 | odd | 2 | 768.4.a.i.1.2 | 2 | |||
8.3 | odd | 2 | inner | 768.4.a.l.1.1 | 2 | ||
8.5 | even | 2 | 768.4.a.i.1.1 | 2 | |||
12.11 | even | 2 | 2304.4.a.y.1.1 | 2 | |||
16.3 | odd | 4 | 192.4.d.b.97.1 | ✓ | 4 | ||
16.5 | even | 4 | 192.4.d.b.97.2 | yes | 4 | ||
16.11 | odd | 4 | 192.4.d.b.97.4 | yes | 4 | ||
16.13 | even | 4 | 192.4.d.b.97.3 | yes | 4 | ||
24.5 | odd | 2 | 2304.4.a.y.1.2 | 2 | |||
24.11 | even | 2 | 2304.4.a.bl.1.2 | 2 | |||
48.5 | odd | 4 | 576.4.d.f.289.1 | 4 | |||
48.11 | even | 4 | 576.4.d.f.289.2 | 4 | |||
48.29 | odd | 4 | 576.4.d.f.289.3 | 4 | |||
48.35 | even | 4 | 576.4.d.f.289.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
192.4.d.b.97.1 | ✓ | 4 | 16.3 | odd | 4 | ||
192.4.d.b.97.2 | yes | 4 | 16.5 | even | 4 | ||
192.4.d.b.97.3 | yes | 4 | 16.13 | even | 4 | ||
192.4.d.b.97.4 | yes | 4 | 16.11 | odd | 4 | ||
576.4.d.f.289.1 | 4 | 48.5 | odd | 4 | |||
576.4.d.f.289.2 | 4 | 48.11 | even | 4 | |||
576.4.d.f.289.3 | 4 | 48.29 | odd | 4 | |||
576.4.d.f.289.4 | 4 | 48.35 | even | 4 | |||
768.4.a.i.1.1 | 2 | 8.5 | even | 2 | |||
768.4.a.i.1.2 | 2 | 4.3 | odd | 2 | |||
768.4.a.l.1.1 | 2 | 8.3 | odd | 2 | inner | ||
768.4.a.l.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2304.4.a.y.1.1 | 2 | 12.11 | even | 2 | |||
2304.4.a.y.1.2 | 2 | 24.5 | odd | 2 | |||
2304.4.a.bl.1.1 | 2 | 3.2 | odd | 2 | |||
2304.4.a.bl.1.2 | 2 | 24.11 | even | 2 |