Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
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: | \( 2 \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.31662\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-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 | ||||||||
\(5\) | 2.63325 | 0.235525 | 0.117763 | − | 0.993042i | \(-0.462428\pi\) | ||||
0.117763 | + | 0.993042i | \(0.462428\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 24.4327 | 0.669705 | 0.334852 | − | 0.942271i | \(-0.391314\pi\) | ||||
0.334852 | + | 0.942271i | \(0.391314\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 83.0660 | 1.77218 | 0.886091 | − | 0.463512i | \(-0.153411\pi\) | ||||
0.886091 | + | 0.463512i | \(0.153411\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.89975 | 0.135980 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 110.232 | 1.57266 | 0.786331 | − | 0.617806i | \(-0.211978\pi\) | ||||
0.786331 | + | 0.617806i | \(0.211978\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.7335 | −0.322794 | −0.161397 | − | 0.986890i | \(-0.551600\pi\) | ||||
−0.161397 | + | 0.986890i | \(0.551600\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 50.1003 | 0.454201 | 0.227101 | − | 0.973871i | \(-0.427075\pi\) | ||||
0.227101 | + | 0.973871i | \(0.427075\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −118.066 | −0.944528 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 16.7335 | 0.107149 | 0.0535747 | − | 0.998564i | \(-0.482938\pi\) | ||||
0.0535747 | + | 0.998564i | \(0.482938\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 129.266 | 0.748934 | 0.374467 | − | 0.927240i | \(-0.377826\pi\) | ||||
0.374467 | + | 0.927240i | \(0.377826\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 73.2982 | 0.386654 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 18.4327 | 0.0890201 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −122.264 | −0.543245 | −0.271623 | − | 0.962404i | \(-0.587560\pi\) | ||||
−0.271623 | + | 0.962404i | \(0.587560\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 249.198 | 1.02317 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −417.430 | −1.59004 | −0.795020 | − | 0.606583i | \(-0.792540\pi\) | ||||
−0.795020 | + | 0.606583i | \(0.792540\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −153.330 | −0.543781 | −0.271891 | − | 0.962328i | \(-0.587649\pi\) | ||||
−0.271891 | + | 0.962328i | \(0.587649\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 23.6992 | 0.0785083 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −175.662 | −0.545170 | −0.272585 | − | 0.962132i | \(-0.587879\pi\) | ||||
−0.272585 | + | 0.962132i | \(0.587879\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 330.697 | 0.907977 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 487.594 | 1.26370 | 0.631851 | − | 0.775090i | \(-0.282296\pi\) | ||||
0.631851 | + | 0.775090i | \(0.282296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 64.3375 | 0.157732 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −80.2005 | −0.186365 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −496.327 | −1.09519 | −0.547596 | − | 0.836743i | \(-0.684457\pi\) | ||||
−0.547596 | + | 0.836743i | \(0.684457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −274.464 | −0.576091 | −0.288046 | − | 0.957617i | \(-0.593006\pi\) | ||||
−0.288046 | + | 0.957617i | \(0.593006\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 218.734 | 0.417393 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −396.201 | −0.722442 | −0.361221 | − | 0.932480i | \(-0.617640\pi\) | ||||
−0.361221 | + | 0.932480i | \(0.617640\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 150.301 | 0.262233 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 844.824 | 1.41214 | 0.706071 | − | 0.708141i | \(-0.250466\pi\) | ||||
0.706071 | + | 0.708141i | \(0.250466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 895.931 | 1.43645 | 0.718225 | − | 0.695811i | \(-0.244955\pi\) | ||||
0.718225 | + | 0.695811i | \(0.244955\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −354.198 | −0.545323 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 171.029 | 0.253125 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1310.86 | 1.86688 | 0.933439 | − | 0.358737i | \(-0.116792\pi\) | ||||
0.933439 | + | 0.358737i | \(0.116792\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1365.33 | −1.80560 | −0.902798 | − | 0.430065i | \(-0.858491\pi\) | ||||
−0.902798 | + | 0.430065i | \(0.858491\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 290.269 | 0.370401 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 50.2005 | 0.0618627 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 683.890 | 0.814519 | 0.407259 | − | 0.913313i | \(-0.366485\pi\) | ||||
0.407259 | + | 0.913313i | \(0.366485\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 581.462 | 0.669822 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 387.799 | 0.432397 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −70.3960 | −0.0760261 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1430.73 | 1.49761 | 0.748807 | − | 0.662789i | \(-0.230627\pi\) | ||||
0.748807 | + | 0.662789i | \(0.230627\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 219.895 | 0.223235 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −329.293 | −0.324415 | −0.162207 | − | 0.986757i | \(-0.551861\pi\) | ||||
−0.162207 | + | 0.986757i | \(0.551861\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 40.7385 | 0.0389717 | 0.0194859 | − | 0.999810i | \(-0.493797\pi\) | ||||
0.0194859 | + | 0.999810i | \(0.493797\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 55.2982 | 0.0513958 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1282.42 | 1.15865 | 0.579327 | − | 0.815095i | \(-0.303315\pi\) | ||||
0.579327 | + | 0.815095i | \(0.303315\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −128.132 | −0.112595 | −0.0562973 | − | 0.998414i | \(-0.517929\pi\) | ||||
−0.0562973 | + | 0.998414i | \(0.517929\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −366.792 | −0.313643 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −570.117 | −0.474620 | −0.237310 | − | 0.971434i | \(-0.576266\pi\) | ||||
−0.237310 | + | 0.971434i | \(0.576266\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 131.926 | 0.106976 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 747.594 | 0.590727 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 771.626 | 0.594410 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −734.041 | −0.551496 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1252.29 | −0.918010 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −640.053 | −0.457985 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −43.1245 | −0.0301313 | −0.0150657 | − | 0.999887i | \(-0.504796\pi\) | ||||
−0.0150657 | + | 0.999887i | \(0.504796\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −459.990 | −0.313952 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −796.802 | −0.531427 | −0.265713 | − | 0.964052i | \(-0.585607\pi\) | ||||
−0.265713 | + | 0.964052i | \(0.585607\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −187.135 | −0.122005 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 71.0977 | 0.0453268 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 706.464 | 0.440564 | 0.220282 | − | 0.975436i | \(-0.429302\pi\) | ||||
0.220282 | + | 0.975436i | \(0.429302\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1965.46 | −1.19934 | −0.599669 | − | 0.800248i | \(-0.704701\pi\) | ||||
−0.599669 | + | 0.800248i | \(0.704701\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −526.987 | −0.314754 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2029.53 | 1.18684 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 44.0635 | 0.0252364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2118.54 | 1.16481 | 0.582407 | − | 0.812897i | \(-0.302111\pi\) | ||||
0.582407 | + | 0.812897i | \(0.302111\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 192.127 | 0.103544 | 0.0517718 | − | 0.998659i | \(-0.483513\pi\) | ||||
0.0517718 | + | 0.998659i | \(0.483513\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 992.090 | 0.524221 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 340.391 | 0.176393 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2991.63 | 1.52075 | 0.760375 | − | 0.649484i | \(-0.225015\pi\) | ||||
0.760375 | + | 0.649484i | \(0.225015\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1462.78 | 0.729598 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 350.702 | 0.171672 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3083.76 | −1.48183 | −0.740916 | − | 0.671598i | \(-0.765608\pi\) | ||||
−0.740916 | + | 0.671598i | \(0.765608\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 193.013 | 0.0910667 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.591457 | −0.000274062 0 | −0.000137031 | − | 1.00000i | \(-0.500044\pi\) | ||||
−0.000137031 | 1.00000i | \(0.500044\pi\) | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4702.96 | 2.14063 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −240.602 | −0.107598 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3212.70 | 1.41189 | 0.705946 | − | 0.708266i | \(-0.250522\pi\) | ||||
0.705946 | + | 0.708266i | \(0.250522\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −826.462 | −0.356998 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1488.98 | −0.632309 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −624.179 | −0.260633 | −0.130317 | − | 0.991472i | \(-0.541599\pi\) | ||||
−0.130317 | + | 0.991472i | \(0.541599\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1658.25 | −0.680978 | −0.340489 | − | 0.940248i | \(-0.610593\pi\) | ||||
−0.340489 | + | 0.940248i | \(0.610593\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −823.393 | −0.332607 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −321.952 | −0.127948 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2693.28 | 1.05322 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3904.22 | −1.47906 | −0.739528 | − | 0.673126i | \(-0.764951\pi\) | ||||
−0.739528 | + | 0.673126i | \(0.764951\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2236.53 | 0.834141 | 0.417070 | − | 0.908874i | \(-0.363057\pi\) | ||||
0.417070 | + | 0.908874i | \(0.363057\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 656.201 | 0.240982 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1276.25 | −0.461568 | −0.230784 | − | 0.973005i | \(-0.574129\pi\) | ||||
−0.230784 | + | 0.973005i | \(0.574129\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4069.15 | −1.44952 | −0.724760 | − | 0.689001i | \(-0.758049\pi\) | ||||
−0.724760 | + | 0.689001i | \(0.758049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1188.60 | −0.417102 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 117.135 | 0.0404987 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1099.20 | −0.374494 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 450.902 | 0.151400 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −653.173 | −0.216177 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2093.57 | 0.683069 | 0.341535 | − | 0.939869i | \(-0.389053\pi\) | ||||
0.341535 | + | 0.939869i | \(0.389053\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2534.47 | 0.815301 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −403.756 | −0.128074 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 904.865 | 0.283070 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2687.79 | 0.829335 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9156.55 | 2.78704 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6481.00 | 1.94619 | 0.973093 | − | 0.230412i | \(-0.0740073\pi\) | ||||
0.973093 | + | 0.230412i | \(0.0740073\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1062.59 | −0.314843 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3001.49 | −0.877603 | −0.438802 | − | 0.898584i | \(-0.644597\pi\) | ||||
−0.438802 | + | 0.898584i | \(0.644597\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3843.71 | −1.10917 | −0.554584 | − | 0.832128i | \(-0.687123\pi\) | ||||
−0.554584 | + | 0.832128i | \(0.687123\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 513.088 | 0.146142 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3378.85 | 0.950024 | 0.475012 | − | 0.879979i | \(-0.342444\pi\) | ||||
0.475012 | + | 0.879979i | \(0.342444\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −462.563 | −0.128401 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3932.58 | 1.07784 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4653.65 | −1.25950 | −0.629748 | − | 0.776800i | \(-0.716842\pi\) | ||||
−0.629748 | + | 0.776800i | \(0.716842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5108.74 | 1.36549 | 0.682745 | − | 0.730657i | \(-0.260786\pi\) | ||||
0.682745 | + | 0.730657i | \(0.260786\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 129.029 | 0.0336464 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2220.64 | −0.572050 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4095.99 | −1.04246 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.20553 | −0.000554628 0 | −0.000277314 | − | 1.00000i | \(-0.500088\pi\) | ||||
−0.000277314 | 1.00000i | \(0.500088\pi\) | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1224.09 | 0.304181 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 870.807 | 0.213851 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1348.65 | 0.327341 | 0.163670 | − | 0.986515i | \(-0.447667\pi\) | ||||
0.163670 | + | 0.986515i | \(0.447667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −855.848 | −0.205327 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 150.602 | 0.0357165 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2645.77 | −0.620324 | −0.310162 | − | 0.950684i | \(-0.600383\pi\) | ||||
−0.310162 | + | 0.950684i | \(0.600383\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1283.96 | 0.297633 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2051.67 | 0.470263 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3378.90 | −0.765856 | −0.382928 | − | 0.923778i | \(-0.625084\pi\) | ||||
−0.382928 | + | 0.923778i | \(0.625084\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2875.38 | −0.644527 | −0.322263 | − | 0.946650i | \(-0.604444\pi\) | ||||
−0.322263 | + | 0.946650i | \(0.604444\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1744.39 | 0.386722 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2884.68 | −0.632555 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3125.88 | 0.678037 | 0.339018 | − | 0.940780i | \(-0.389905\pi\) | ||||
0.339018 | + | 0.940780i | \(0.389905\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1163.40 | 0.249645 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3185.38 | −0.676241 | −0.338121 | − | 0.941103i | \(-0.609791\pi\) | ||||
−0.338121 | + | 0.941103i | \(0.609791\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2516.34 | 0.528554 | 0.264277 | − | 0.964447i | \(-0.414867\pi\) | ||||
0.264277 | + | 0.964447i | \(0.414867\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −211.188 | −0.0438937 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2922.01 | −0.600979 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7238.15 | 1.47326 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4292.19 | 0.864647 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −978.409 | −0.195083 | −0.0975415 | − | 0.995231i | \(-0.531098\pi\) | ||||
−0.0975415 | + | 0.995231i | \(0.531098\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1306.95 | −0.257945 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 659.684 | 0.128885 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4161.63 | 0.804927 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1073.31 | −0.205530 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −987.880 | −0.187301 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −722.734 | −0.135684 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10331.0 | 1.92059 | 0.960297 | − | 0.278981i | \(-0.0899967\pi\) | ||||
0.960297 | + | 0.278981i | \(0.0899967\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 122.216 | 0.0225003 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9222.57 | −1.68156 | −0.840778 | − | 0.541380i | \(-0.817902\pi\) | ||||
−0.840778 | + | 0.541380i | \(0.817902\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5812.84 | −1.04972 | −0.524858 | − | 0.851190i | \(-0.675882\pi\) | ||||
−0.524858 | + | 0.851190i | \(0.675882\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 165.895 | 0.0296734 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5280.27 | 0.935550 | 0.467775 | − | 0.883847i | \(-0.345056\pi\) | ||||
0.467775 | + | 0.883847i | \(0.345056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 408.845 | 0.0717585 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3847.25 | 0.668949 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2946.89 | −0.507646 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9807.27 | −1.67388 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −384.396 | −0.0650066 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1229.64 | −0.206055 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7462.67 | 1.23923 | 0.619615 | − | 0.784906i | \(-0.287289\pi\) | ||||
0.619615 | + | 0.784906i | \(0.287289\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1100.38 | −0.181082 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1043.29 | −0.170153 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6866.68 | 1.10995 | 0.554973 | − | 0.831869i | \(-0.312729\pi\) | ||||
0.554973 | + | 0.831869i | \(0.312729\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1710.35 | −0.274022 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3158.34 | 0.501564 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 395.779 | 0.0617625 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6347.14 | −0.981937 | −0.490969 | − | 0.871177i | \(-0.663357\pi\) | ||||
−0.490969 | + | 0.871177i | \(0.663357\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6712.06 | −1.02948 | −0.514740 | − | 0.857347i | \(-0.672111\pi\) | ||||
−0.514740 | + | 0.857347i | \(0.672111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2242.78 | 0.341057 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4834.01 | 0.728862 | 0.364431 | − | 0.931230i | \(-0.381263\pi\) | ||||
0.364431 | + | 0.931230i | \(0.381263\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2224.63 | 0.332595 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2314.88 | 0.343183 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2504.35 | −0.368174 | −0.184087 | − | 0.982910i | \(-0.558933\pi\) | ||||
−0.184087 | + | 0.982910i | \(0.558933\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6144.32 | −0.895804 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2202.12 | −0.318406 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2359.21 | 0.338320 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10447.9 | 1.48604 | 0.743019 | − | 0.669270i | \(-0.233393\pi\) | ||||
0.743019 | + | 0.669270i | \(0.233393\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3756.87 | −0.530013 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3413.16 | 0.477634 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2205.68 | 0.306181 | 0.153091 | − | 0.988212i | \(-0.451077\pi\) | ||||
0.153091 | + | 0.988212i | \(0.451077\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1920.16 | −0.264418 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1389.98 | 0.189888 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3786.31 | −0.513165 | −0.256582 | − | 0.966522i | \(-0.582596\pi\) | ||||
−0.256582 | + | 0.966522i | \(0.582596\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −129.373 | −0.0173963 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1139.11 | −0.151973 | −0.0759865 | − | 0.997109i | \(-0.524211\pi\) | ||||
−0.0759865 | + | 0.997109i | \(0.524211\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 450.363 | 0.0596172 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1379.97 | −0.181260 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6105.58 | 0.795797 | 0.397898 | − | 0.917429i | \(-0.369740\pi\) | ||||
0.397898 | + | 0.917429i | \(0.369740\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5522.66 | 0.714305 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2390.41 | −0.306819 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3451.82 | 0.439696 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3444.26 | −0.435422 | −0.217711 | − | 0.976013i | \(-0.569859\pi\) | ||||
−0.217711 | + | 0.976013i | \(0.569859\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −561.404 | −0.0704394 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4128.09 | −0.514082 | −0.257041 | − | 0.966400i | \(-0.582748\pi\) | ||||
−0.257041 | + | 0.966400i | \(0.582748\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10737.7 | 1.32725 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 213.293 | 0.0261694 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2987.25 | −0.363814 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10637.8 | 1.28607 | 0.643036 | − | 0.765836i | \(-0.277675\pi\) | ||||
0.643036 | + | 0.765836i | \(0.277675\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2119.39 | 0.254360 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3474.29 | −0.413944 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3595.25 | −0.425263 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5896.37 | −0.692438 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5226.38 | 0.609368 | 0.304684 | − | 0.952453i | \(-0.401449\pi\) | ||||
0.304684 | + | 0.952453i | \(0.401449\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8271.22 | −0.957517 | −0.478759 | − | 0.877947i | \(-0.658913\pi\) | ||||
−0.478759 | + | 0.877947i | \(0.658913\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1580.96 | −0.181723 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13014.7 | −1.48542 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1921.25 | −0.217742 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6088.59 | 0.685221 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8341.80 | 0.932275 | 0.466137 | − | 0.884712i | \(-0.345645\pi\) | ||||
0.466137 | + | 0.884712i | \(0.345645\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12866.3 | 1.42798 | 0.713991 | − | 0.700155i | \(-0.246886\pi\) | ||||
0.713991 | + | 0.700155i | \(0.246886\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 132.190 | 0.0145702 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1339.36 | −0.146613 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 479.599 | 0.0521413 | 0.0260706 | − | 0.999660i | \(-0.491701\pi\) | ||||
0.0260706 | + | 0.999660i | \(0.491701\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3894.58 | 0.417691 | 0.208845 | − | 0.977949i | \(-0.433029\pi\) | ||||
0.208845 | + | 0.977949i | \(0.433029\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1800.85 | 0.191840 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6355.61 | 0.672506 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5428.50 | −0.570572 | −0.285286 | − | 0.958442i | \(-0.592089\pi\) | ||||
−0.285286 | + | 0.958442i | \(0.592089\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10199.0 | −1.06486 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 576.381 | 0.0597809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1531.13 | 0.157760 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9577.50 | −0.980343 | −0.490171 | − | 0.871626i | \(-0.663066\pi\) | ||||
−0.490171 | + | 0.871626i | \(0.663066\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2976.27 | 0.302659 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11198.0 | −1.13133 | −0.565664 | − | 0.824636i | \(-0.691380\pi\) | ||||
−0.565664 | + | 0.824636i | \(0.691380\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17391.1 | −1.74564 | −0.872821 | − | 0.488041i | \(-0.837712\pi\) | ||||
−0.872821 | + | 0.488041i | \(0.837712\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1021.17 | 0.101840 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10757.5 | −1.06595 | −0.532973 | − | 0.846132i | \(-0.678925\pi\) | ||||
−0.532973 | + | 0.846132i | \(0.678925\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2773.40 | −0.273057 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8974.88 | 0.878006 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3746.27 | −0.364173 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3156.32 | 0.304888 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4388.35 | 0.421234 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2742.63 | −0.261615 | −0.130808 | − | 0.991408i | \(-0.541757\pi\) | ||||
−0.130808 | + | 0.991408i | \(0.541757\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10156.0 | −0.962729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1052.11 | 0.0991148 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3767.47 | 0.352725 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16970.3 | 1.57905 | 0.789526 | − | 0.613718i | \(-0.210327\pi\) | ||||
0.789526 | + | 0.613718i | \(0.210327\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9251.28 | −0.855536 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18794.0 | −1.72742 | −0.863709 | − | 0.503991i | \(-0.831864\pi\) | ||||
−0.863709 | + | 0.503991i | \(0.831864\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1844.57 | 0.168510 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 579.038 | 0.0525774 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5913.77 | 0.533740 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −62.5430 | −0.00561084 | −0.00280542 | − | 0.999996i | \(-0.500893\pi\) | ||||
−0.00280542 | + | 0.999996i | \(0.500893\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.77437 | −0.000158230 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5222.59 | −0.462950 | −0.231475 | − | 0.972841i | \(-0.574355\pi\) | ||||
−0.231475 | + | 0.972841i | \(0.574355\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −867.111 | −0.0764078 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14108.9 | 1.23589 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4387.65 | 0.382081 | 0.191040 | − | 0.981582i | \(-0.438814\pi\) | ||||
0.191040 | + | 0.981582i | \(0.438814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6271.52 | 0.542927 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −721.805 | −0.0621217 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 107.275 | 0.00917881 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4291.92 | −0.365103 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9638.11 | 0.815156 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15313.8 | −1.28773 | −0.643865 | − | 0.765139i | \(-0.722670\pi\) | ||||
−0.643865 | + | 0.765139i | \(0.722670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3114.32 | −0.260381 | −0.130191 | − | 0.991489i | \(-0.541559\pi\) | ||||
−0.130191 | + | 0.991489i | \(0.541559\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2479.39 | −0.206113 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14249.3 | 1.17782 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9656.96 | −0.793701 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4466.95 | −0.365064 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34674.3 | −2.81784 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3376.93 | 0.272892 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1872.54 | −0.150477 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1197.20 | 0.0956721 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5285.36 | 0.420028 | 0.210014 | − | 0.977698i | \(-0.432649\pi\) | ||||
0.210014 | + | 0.977698i | \(0.432649\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4974.76 | −0.393163 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −337.404 | −0.0265189 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1010.34 | −0.0789741 | −0.0394871 | − | 0.999220i | \(-0.512572\pi\) | ||||
−0.0394871 | + | 0.999220i | \(0.512572\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2470.18 | −0.192030 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −447.345 | −0.0345872 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9176.02 | 0.705613 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −965.855 | −0.0738707 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21461.8 | 1.63262 | 0.816308 | − | 0.577616i | \(-0.196017\pi\) | ||||
0.816308 | + | 0.577616i | \(0.196017\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12736.5 | −0.963680 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8079.83 | 0.608076 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17791.0 | −1.33180 | −0.665900 | − | 0.746041i | \(-0.731952\pi\) | ||||
−0.665900 | + | 0.746041i | \(0.731952\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1501.26 | −0.111785 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5817.45 | −0.428612 | −0.214306 | − | 0.976767i | \(-0.568749\pi\) | ||||
−0.214306 | + | 0.976767i | \(0.568749\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13391.6 | −0.981476 | −0.490738 | − | 0.871307i | \(-0.663273\pi\) | ||||
−0.490738 | + | 0.871307i | \(0.663273\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11712.7 | −0.853933 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5915.14 | −0.429006 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8391.88 | −0.605474 | −0.302737 | − | 0.953074i | \(-0.597900\pi\) | ||||
−0.302737 | + | 0.953074i | \(0.597900\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6709.60 | 0.481591 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9557.31 | −0.682451 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11913.3 | 0.846307 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1968.60 | 0.139131 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23828.4 | −1.67547 | −0.837736 | − | 0.546075i | \(-0.816121\pi\) | ||||
−0.837736 | + | 0.546075i | \(0.816121\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3455.75 | −0.241751 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3828.75 | −0.266487 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4159.17 | −0.288021 | −0.144011 | − | 0.989576i | \(-0.546000\pi\) | ||||
−0.144011 | + | 0.989576i | \(0.546000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2031.88 | 0.139998 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12207.5 | −0.836881 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27461.8 | −1.87322 | −0.936610 | − | 0.350374i | \(-0.886055\pi\) | ||||
−0.936610 | + | 0.350374i | \(0.886055\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1290.98 | −0.0876209 | −0.0438104 | − | 0.999040i | \(-0.513950\pi\) | ||||
−0.0438104 | + | 0.999040i | \(0.513950\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3565.80 | −0.240814 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1932.91 | −0.129891 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21953.6 | 1.46799 | 0.733994 | − | 0.679156i | \(-0.237654\pi\) | ||||
0.733994 | + | 0.679156i | \(0.237654\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 351.404 | 0.0233819 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14591.6 | −0.966141 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12068.0 | 0.795141 | 0.397570 | − | 0.917572i | \(-0.369853\pi\) | ||||
0.397570 | + | 0.917572i | \(0.369853\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3297.59 | −0.216214 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10838.3 | 0.707184 | 0.353592 | − | 0.935400i | \(-0.384960\pi\) | ||||
0.353592 | + | 0.935400i | \(0.384960\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7521.36 | −0.488383 | −0.244191 | − | 0.969727i | \(-0.578523\pi\) | ||||
−0.244191 | + | 0.969727i | \(0.578523\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1352.71 | 0.0874110 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4787.23 | 0.307859 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13072.8 | 0.836661 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1959.52 | −0.124810 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13477.4 | −0.854341 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11401.1 | 0.719287 | 0.359643 | − | 0.933090i | \(-0.382898\pi\) | ||||
0.359643 | + | 0.933090i | \(0.382898\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6280.72 | 0.394370 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −113.557 | −0.00709668 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4070.23 | 0.253169 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7603.41 | 0.470714 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6995.08 | −0.431028 | −0.215514 | − | 0.976501i | \(-0.569143\pi\) | ||||
−0.215514 | + | 0.976501i | \(0.569143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −964.431 | −0.0591500 | −0.0295750 | − | 0.999563i | \(-0.509415\pi\) | ||||
−0.0295750 | + | 0.999563i | \(0.509415\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1211.27 | −0.0739436 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19435.6 | −1.18098 | −0.590489 | − | 0.807046i | \(-0.701065\pi\) | ||||
−0.590489 | + | 0.807046i | \(0.701065\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12126.6 | −0.733455 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2714.60 | 0.163431 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4134.87 | −0.247795 | −0.123897 | − | 0.992295i | \(-0.539539\pi\) | ||||
−0.123897 | + | 0.992295i | \(0.539539\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2098.18 | −0.125164 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8063.38 | 0.478817 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16958.3 | −1.00243 | −0.501214 | − | 0.865323i | \(-0.667113\pi\) | ||||
−0.501214 | + | 0.865323i | \(0.667113\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25074.5 | −1.47547 | −0.737736 | − | 0.675090i | \(-0.764105\pi\) | ||||
−0.737736 | + | 0.675090i | \(0.764105\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27469.7 | 1.60910 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −492.772 | −0.0287351 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 838.353 | 0.0486674 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19443.0 | 1.12363 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6705.92 | −0.385811 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17078.4 | −0.978195 | −0.489098 | − | 0.872229i | \(-0.662674\pi\) | ||||
−0.489098 | + | 0.872229i | \(0.662674\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3187.78 | −0.181774 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16960.2 | −0.962829 | −0.481414 | − | 0.876493i | \(-0.659877\pi\) | ||||
−0.481414 | + | 0.876493i | \(0.659877\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10015.1 | 0.566045 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9004.47 | −0.506684 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5365.07 | −0.300569 | −0.150285 | − | 0.988643i | \(-0.548019\pi\) | ||||
−0.150285 | + | 0.988643i | \(0.548019\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1860.30 | 0.103764 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11531.1 | −0.640379 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40502.5 | 2.23951 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17463.3 | 0.961411 | 0.480706 | − | 0.876882i | \(-0.340381\pi\) | ||||
0.480706 | + | 0.876882i | \(0.340381\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1539.26 | 0.0843748 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5175.54 | −0.282474 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −46014.3 | −2.50060 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10136.5 | 0.548496 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3312.57 | 0.178479 | 0.0892396 | − | 0.996010i | \(-0.471556\pi\) | ||||
0.0892396 | + | 0.996010i | \(0.471556\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3268.54 | 0.175356 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1387.69 | −0.0741325 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2305.05 | −0.122617 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1722.66 | −0.0912494 | −0.0456247 | − | 0.998959i | \(-0.514528\pi\) | ||||
−0.0456247 | + | 0.998959i | \(0.514528\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11797.7 | 0.622293 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6476.28 | 0.340167 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5344.26 | 0.279530 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13960.9 | −0.727170 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16424.6 | 0.851927 | 0.425964 | − | 0.904740i | \(-0.359935\pi\) | ||||
0.425964 | + | 0.904740i | \(0.359935\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 285.170 | 0.0147299 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15326.2 | 0.788366 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1975.66 | −0.101206 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3615.78 | 0.184459 | 0.0922297 | − | 0.995738i | \(-0.470601\pi\) | ||||
0.0922297 | + | 0.995738i | \(0.470601\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16901.9 | −0.855184 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12093.0 | 0.609368 | 0.304684 | − | 0.952453i | \(-0.401449\pi\) | ||||
0.304684 | + | 0.952453i | \(0.401449\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 387.088 | 0.0194258 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9680.27 | −0.483823 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18840.3 | −0.937824 | −0.468912 | − | 0.883245i | \(-0.655354\pi\) | ||||
−0.468912 | + | 0.883245i | \(0.655354\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6661.93 | −0.330273 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5559.28 | 0.274495 | 0.137248 | − | 0.990537i | \(-0.456174\pi\) | ||||
0.137248 | + | 0.990537i | \(0.456174\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5578.64 | 0.274343 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12288.0 | −0.601865 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8976.92 | 0.437930 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30552.5 | 1.48452 | 0.742260 | − | 0.670112i | \(-0.233754\pi\) | ||||
0.742260 | + | 0.670112i | \(0.233754\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.61658 | −0.000320215 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 505.918 | 0.0243871 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20415.9 | −0.980223 | −0.490112 | − | 0.871660i | \(-0.663044\pi\) | ||||
−0.490112 | + | 0.871660i | \(0.663044\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3672.26 | 0.175619 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37041.9 | −1.76448 | −0.882238 | − | 0.470804i | \(-0.843964\pi\) | ||||
−0.882238 | + | 0.470804i | \(0.843964\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −896.924 | −0.0425568 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2612.42 | 0.123467 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −41227.9 | −1.94088 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5163.09 | 0.242114 | 0.121057 | − | 0.992646i | \(-0.461372\pi\) | ||||
0.121057 | + | 0.992646i | \(0.461372\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4045.95 | 0.188990 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6634.38 | −0.308696 | −0.154348 | − | 0.988017i | \(-0.549328\pi\) | ||||
−0.154348 | + | 0.988017i | \(0.549328\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15262.0 | −0.707389 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2567.54 | −0.118546 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11159.4 | 0.513255 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20641.4 | 0.945718 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 451.805 | 0.0206209 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7877.70 | 0.358175 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22692.6 | 1.02783 | 0.513915 | − | 0.857841i | \(-0.328195\pi\) | ||||
0.513915 | + | 0.857841i | \(0.328195\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7937.32 | −0.358145 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3990.82 | −0.179390 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22798.7 | −1.02094 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3851.87 | 0.171839 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24145.0 | −1.07310 | −0.536549 | − | 0.843869i | \(-0.680272\pi\) | ||||
−0.536549 | + | 0.843869i | \(0.680272\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19363.7 | −0.857368 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6155.01 | 0.271506 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21890.1 | 0.961997 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 923.485 | 0.0404330 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10136.7 | −0.442167 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41683.5 | −1.81151 | −0.905756 | − | 0.423800i | \(-0.860696\pi\) | ||||
−0.905756 | + | 0.423800i | \(0.860696\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37899.1 | 1.64096 | 0.820480 | − | 0.571675i | \(-0.193706\pi\) | ||||
0.820480 | + | 0.571675i | \(0.193706\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8626.14 | −0.372118 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8120.31 | −0.349009 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4099.05 | 0.175529 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5233.16 | 0.223274 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8724.19 | −0.370860 | −0.185430 | − | 0.982657i | \(-0.559368\pi\) | ||||
−0.185430 | + | 0.982657i | \(0.559368\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12245.0 | −0.518633 | −0.259317 | − | 0.965792i | \(-0.583497\pi\) | ||||
−0.259317 | + | 0.965792i | \(0.583497\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8654.03 | −0.365206 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16038.0 | −0.674360 | −0.337180 | − | 0.941440i | \(-0.609473\pi\) | ||||
−0.337180 | + | 0.941440i | \(0.609473\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15359.7 | −0.643504 | −0.321752 | − | 0.946824i | \(-0.604272\pi\) | ||||
−0.321752 | + | 0.946824i | \(0.604272\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9377.65 | 0.391465 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5401.38 | 0.224666 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.55745 | −6.45484e−5 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3490.20 | 0.144132 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21290.9 | 0.876095 | 0.438047 | − | 0.898952i | \(-0.355670\pi\) | ||||
0.438047 | + | 0.898952i | \(0.355670\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24109.0 | −0.988519 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9556.14 | −0.390428 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12384.1 | 0.504171 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5138.29 | −0.208446 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7549.01 | 0.305161 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6125.46 | −0.246743 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31764.2 | −1.27501 | −0.637506 | − | 0.770446i | \(-0.720034\pi\) | ||||
−0.637506 | + | 0.770446i | \(0.720034\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −633.564 | −0.0253420 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25128.3 | 1.00159 | 0.500797 | − | 0.865565i | \(-0.333040\pi\) | ||||
0.500797 | + | 0.865565i | \(0.333040\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37614.5 | 1.49405 | 0.747026 | − | 0.664795i | \(-0.231481\pi\) | ||||
0.747026 | + | 0.664795i | \(0.231481\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8766.03 | −0.346975 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16990.0 | −0.670158 | −0.335079 | − | 0.942190i | \(-0.608763\pi\) | ||||
−0.335079 | + | 0.942190i | \(0.608763\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8459.85 | 0.332536 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21714.4 | 0.850590 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32027.9 | 1.25026 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32910.8 | −1.28030 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12876.6 | 0.499204 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4480.37 | −0.173102 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39804.7 | 1.53262 | 0.766312 | − | 0.642469i | \(-0.222090\pi\) | ||||
0.766312 | + | 0.642469i | \(0.222090\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2935.23 | −0.112631 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42647.7 | 1.63092 | 0.815458 | − | 0.578816i | \(-0.196485\pi\) | ||||
0.815458 | + | 0.578816i | \(0.196485\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42853.2 | −1.63321 | −0.816605 | − | 0.577198i | \(-0.804146\pi\) | ||||
−0.816605 | + | 0.577198i | \(0.804146\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3920.86 | −0.148925 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13409.9 | 0.507622 | 0.253811 | − | 0.967254i | \(-0.418316\pi\) | ||||
0.253811 | + | 0.967254i | \(0.418316\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −301.871 | −0.0113886 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1979.05 | 0.0744116 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4696.07 | 0.175978 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1643.62 | −0.0613856 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12484.9 | 0.464725 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2163.08 | 0.0802478 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53748.6 | 1.98737 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3219.93 | −0.118663 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4366.60 | −0.160387 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10223.5 | −0.374272 | −0.187136 | − | 0.982334i | \(-0.559921\pi\) | ||||
−0.187136 | + | 0.982334i | \(0.559921\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2963.64 | −0.108138 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12069.3 | −0.438938 | −0.219469 | − | 0.975619i | \(-0.570433\pi\) | ||||
−0.219469 | + | 0.975619i | \(0.570433\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33358.8 | −1.20922 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2168.20 | −0.0783372 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5577.61 | −0.200860 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20488.5 | 0.735421 | 0.367711 | − | 0.929940i | \(-0.380142\pi\) | ||||
0.367711 | + | 0.929940i | \(0.380142\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30993.0 | 1.10885 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 70176.1 | 2.50257 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14435.2 | 0.513110 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 366.647 | 0.0129906 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31335.6 | 1.10666 | 0.553330 | − | 0.832962i | \(-0.313357\pi\) | ||||
0.553330 | + | 0.832962i | \(0.313357\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1309.94 | −0.0461134 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27667.7 | −0.970847 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7092.07 | 0.248059 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2075.56 | −0.0723646 | −0.0361823 | − | 0.999345i | \(-0.511520\pi\) | ||||
−0.0361823 | + | 0.999345i | \(0.511520\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17438.5 | −0.606054 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35604.9 | 1.23346 | 0.616730 | − | 0.787174i | \(-0.288457\pi\) | ||||
0.616730 | + | 0.787174i | \(0.288457\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20913.4 | −0.722198 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 497.684 | 0.0171319 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30879.9 | 1.05962 | 0.529810 | − | 0.848116i | \(-0.322263\pi\) | ||||
0.529810 | + | 0.848116i | \(0.322263\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 74421.4 | 2.54565 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15840.8 | 0.540140 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35653.5 | 1.21189 | 0.605944 | − | 0.795507i | \(-0.292795\pi\) | ||||
0.605944 | + | 0.795507i | \(0.292795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10280.8 | −0.348355 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1226.54 | 0.0414298 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4945.25 | 0.166518 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13081.2 | −0.439098 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11541.8 | 0.386218 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5889.35 | 0.196461 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44294.9 | −1.47304 | −0.736520 | − | 0.676416i | \(-0.763532\pi\) | ||||
−0.736520 | + | 0.676416i | \(0.763532\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8840.68 | −0.293089 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37669.1 | −1.24496 | −0.622482 | − | 0.782634i | \(-0.713876\pi\) | ||||
−0.622482 | + | 0.782634i | \(0.713876\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13758.2 | −0.453307 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −29421.8 | −0.966412 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41450.1 | −1.35732 | −0.678662 | − | 0.734451i | \(-0.737440\pi\) | ||||
−0.678662 | + | 0.734451i | \(0.737440\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16709.3 | 0.545487 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1153.19 | −0.0375316 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41027.9 | 1.33122 | 0.665609 | − | 0.746301i | \(-0.268172\pi\) | ||||
0.665609 | + | 0.746301i | \(0.268172\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3360.68 | −0.108711 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3688.91 | −0.118966 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7681.87 | −0.246986 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2049.50 | 0.0656959 | 0.0328479 | − | 0.999460i | \(-0.489542\pi\) | ||||
0.0328479 | + | 0.999460i | \(0.489542\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22388.0 | 0.715470 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10715.1 | −0.341398 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12662.9 | 0.402245 | 0.201122 | − | 0.979566i | \(-0.435541\pi\) | ||||
0.201122 | + | 0.979566i | \(0.435541\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3301.13 | −0.104548 |
(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 | 1344.4.a.bn.1.2 | 2 | ||
4.3 | odd | 2 | 1344.4.a.bf.1.2 | 2 | |||
8.3 | odd | 2 | 672.4.a.l.1.1 | yes | 2 | ||
8.5 | even | 2 | 672.4.a.g.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 2016.4.a.l.1.2 | 2 | |||
24.11 | even | 2 | 2016.4.a.k.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.g.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
672.4.a.l.1.1 | yes | 2 | 8.3 | odd | 2 | ||
1344.4.a.bf.1.2 | 2 | 4.3 | odd | 2 | |||
1344.4.a.bn.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2016.4.a.k.1.2 | 2 | 24.11 | even | 2 | |||
2016.4.a.l.1.2 | 2 | 24.5 | odd | 2 |