Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2401,4,Mod(1,2401)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2401, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2401.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2401 = 7^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2401.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: | \(141.663585924\) |
Analytic rank: | \(0\) |
Dimension: | \(39\) |
Twist minimal: | no (minimal twist has level 49) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 2401.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.93571 | −1.39148 | −0.695742 | − | 0.718292i | \(-0.744924\pi\) | ||||
−0.695742 | + | 0.718292i | \(0.744924\pi\) | |||||||
\(3\) | −3.09696 | −0.596009 | −0.298005 | − | 0.954564i | \(-0.596321\pi\) | ||||
−0.298005 | + | 0.954564i | \(0.596321\pi\) | |||||||
\(4\) | 7.48982 | 0.936227 | ||||||||
\(5\) | −18.2977 | −1.63659 | −0.818297 | − | 0.574795i | \(-0.805082\pi\) | ||||
−0.818297 | + | 0.574795i | \(0.805082\pi\) | |||||||
\(6\) | 12.1887 | 0.829337 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.00794 | 0.0887390 | ||||||||
\(9\) | −17.4089 | −0.644773 | ||||||||
\(10\) | 72.0144 | 2.27729 | ||||||||
\(11\) | 11.1264 | 0.304977 | 0.152489 | − | 0.988305i | \(-0.451271\pi\) | ||||
0.152489 | + | 0.988305i | \(0.451271\pi\) | |||||||
\(12\) | −23.1956 | −0.558000 | ||||||||
\(13\) | −32.1274 | −0.685425 | −0.342713 | − | 0.939440i | \(-0.611346\pi\) | ||||
−0.342713 | + | 0.939440i | \(0.611346\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 56.6671 | 0.975425 | ||||||||
\(16\) | −67.8212 | −1.05971 | ||||||||
\(17\) | 68.2593 | 0.973842 | 0.486921 | − | 0.873446i | \(-0.338120\pi\) | ||||
0.486921 | + | 0.873446i | \(0.338120\pi\) | |||||||
\(18\) | 68.5163 | 0.897191 | ||||||||
\(19\) | 113.492 | 1.37036 | 0.685182 | − | 0.728372i | \(-0.259722\pi\) | ||||
0.685182 | + | 0.728372i | \(0.259722\pi\) | |||||||
\(20\) | −137.046 | −1.53222 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −43.7905 | −0.424371 | ||||||||
\(23\) | 151.295 | 1.37161 | 0.685807 | − | 0.727784i | \(-0.259449\pi\) | ||||
0.685807 | + | 0.727784i | \(0.259449\pi\) | |||||||
\(24\) | −6.21849 | −0.0528893 | ||||||||
\(25\) | 209.805 | 1.67844 | ||||||||
\(26\) | 126.444 | 0.953758 | ||||||||
\(27\) | 137.532 | 0.980300 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −183.747 | −1.17658 | −0.588291 | − | 0.808649i | \(-0.700199\pi\) | ||||
−0.588291 | + | 0.808649i | \(0.700199\pi\) | |||||||
\(30\) | −223.025 | −1.35729 | ||||||||
\(31\) | 167.796 | 0.972162 | 0.486081 | − | 0.873914i | \(-0.338426\pi\) | ||||
0.486081 | + | 0.873914i | \(0.338426\pi\) | |||||||
\(32\) | 250.861 | 1.38582 | ||||||||
\(33\) | −34.4581 | −0.181769 | ||||||||
\(34\) | −268.649 | −1.35508 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −130.389 | −0.603654 | ||||||||
\(37\) | 255.519 | 1.13533 | 0.567663 | − | 0.823261i | \(-0.307848\pi\) | ||||
0.567663 | + | 0.823261i | \(0.307848\pi\) | |||||||
\(38\) | −446.673 | −1.90684 | ||||||||
\(39\) | 99.4970 | 0.408520 | ||||||||
\(40\) | −36.7406 | −0.145230 | ||||||||
\(41\) | −238.493 | −0.908447 | −0.454223 | − | 0.890888i | \(-0.650083\pi\) | ||||
−0.454223 | + | 0.890888i | \(0.650083\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −90.2895 | −0.320210 | −0.160105 | − | 0.987100i | \(-0.551183\pi\) | ||||
−0.160105 | + | 0.987100i | \(0.551183\pi\) | |||||||
\(44\) | 83.3350 | 0.285528 | ||||||||
\(45\) | 318.542 | 1.05523 | ||||||||
\(46\) | −595.452 | −1.90858 | ||||||||
\(47\) | 353.761 | 1.09790 | 0.548950 | − | 0.835855i | \(-0.315028\pi\) | ||||
0.548950 | + | 0.835855i | \(0.315028\pi\) | |||||||
\(48\) | 210.039 | 0.631595 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −825.732 | −2.33552 | ||||||||
\(51\) | −211.396 | −0.580419 | ||||||||
\(52\) | −240.628 | −0.641714 | ||||||||
\(53\) | 231.242 | 0.599311 | 0.299656 | − | 0.954047i | \(-0.403128\pi\) | ||||
0.299656 | + | 0.954047i | \(0.403128\pi\) | |||||||
\(54\) | −541.287 | −1.36407 | ||||||||
\(55\) | −203.588 | −0.499124 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −351.481 | −0.816750 | ||||||||
\(58\) | 723.174 | 1.63720 | ||||||||
\(59\) | 238.752 | 0.526827 | 0.263414 | − | 0.964683i | \(-0.415152\pi\) | ||||
0.263414 | + | 0.964683i | \(0.415152\pi\) | |||||||
\(60\) | 424.426 | 0.913220 | ||||||||
\(61\) | 33.1087 | 0.0694940 | 0.0347470 | − | 0.999396i | \(-0.488937\pi\) | ||||
0.0347470 | + | 0.999396i | \(0.488937\pi\) | |||||||
\(62\) | −660.396 | −1.35275 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −444.747 | −0.868646 | ||||||||
\(65\) | 587.856 | 1.12176 | ||||||||
\(66\) | 135.617 | 0.252929 | ||||||||
\(67\) | −505.936 | −0.922537 | −0.461268 | − | 0.887261i | \(-0.652605\pi\) | ||||
−0.461268 | + | 0.887261i | \(0.652605\pi\) | |||||||
\(68\) | 511.249 | 0.911737 | ||||||||
\(69\) | −468.553 | −0.817494 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 683.159 | 1.14192 | 0.570958 | − | 0.820979i | \(-0.306572\pi\) | ||||
0.570958 | + | 0.820979i | \(0.306572\pi\) | |||||||
\(72\) | −34.9559 | −0.0572165 | ||||||||
\(73\) | 587.218 | 0.941489 | 0.470745 | − | 0.882269i | \(-0.343985\pi\) | ||||
0.470745 | + | 0.882269i | \(0.343985\pi\) | |||||||
\(74\) | −1005.65 | −1.57979 | ||||||||
\(75\) | −649.757 | −1.00037 | ||||||||
\(76\) | 850.037 | 1.28297 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −391.592 | −0.568449 | ||||||||
\(79\) | −50.1378 | −0.0714043 | −0.0357022 | − | 0.999362i | \(-0.511367\pi\) | ||||
−0.0357022 | + | 0.999362i | \(0.511367\pi\) | |||||||
\(80\) | 1240.97 | 1.73431 | ||||||||
\(81\) | 44.1082 | 0.0605050 | ||||||||
\(82\) | 938.639 | 1.26409 | ||||||||
\(83\) | 559.144 | 0.739446 | 0.369723 | − | 0.929142i | \(-0.379453\pi\) | ||||
0.369723 | + | 0.929142i | \(0.379453\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1248.99 | −1.59378 | ||||||||
\(86\) | 355.353 | 0.445566 | ||||||||
\(87\) | 569.055 | 0.701254 | ||||||||
\(88\) | 22.3412 | 0.0270634 | ||||||||
\(89\) | −1171.00 | −1.39468 | −0.697338 | − | 0.716743i | \(-0.745632\pi\) | ||||
−0.697338 | + | 0.716743i | \(0.745632\pi\) | |||||||
\(90\) | −1253.69 | −1.46834 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1133.17 | 1.28414 | ||||||||
\(93\) | −519.656 | −0.579418 | ||||||||
\(94\) | −1392.30 | −1.52771 | ||||||||
\(95\) | −2076.65 | −2.24273 | ||||||||
\(96\) | −776.905 | −0.825964 | ||||||||
\(97\) | 5.56045 | 0.00582039 | 0.00291019 | − | 0.999996i | \(-0.499074\pi\) | ||||
0.00291019 | + | 0.999996i | \(0.499074\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −193.699 | −0.196641 | ||||||||
\(100\) | 1571.40 | 1.57140 | ||||||||
\(101\) | 1560.22 | 1.53710 | 0.768552 | − | 0.639787i | \(-0.220977\pi\) | ||||
0.768552 | + | 0.639787i | \(0.220977\pi\) | |||||||
\(102\) | 831.993 | 0.807643 | ||||||||
\(103\) | 958.221 | 0.916663 | 0.458332 | − | 0.888781i | \(-0.348447\pi\) | ||||
0.458332 | + | 0.888781i | \(0.348447\pi\) | |||||||
\(104\) | −64.5097 | −0.0608240 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −910.100 | −0.833932 | ||||||||
\(107\) | −1596.71 | −1.44262 | −0.721308 | − | 0.692614i | \(-0.756459\pi\) | ||||
−0.721308 | + | 0.692614i | \(0.756459\pi\) | |||||||
\(108\) | 1030.09 | 0.917783 | ||||||||
\(109\) | −1383.90 | −1.21609 | −0.608044 | − | 0.793904i | \(-0.708045\pi\) | ||||
−0.608044 | + | 0.793904i | \(0.708045\pi\) | |||||||
\(110\) | 801.264 | 0.694523 | ||||||||
\(111\) | −791.330 | −0.676664 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2107.11 | 1.75416 | 0.877080 | − | 0.480345i | \(-0.159489\pi\) | ||||
0.877080 | + | 0.480345i | \(0.159489\pi\) | |||||||
\(114\) | 1383.33 | 1.13649 | ||||||||
\(115\) | −2768.34 | −2.24477 | ||||||||
\(116\) | −1376.23 | −1.10155 | ||||||||
\(117\) | 559.301 | 0.441944 | ||||||||
\(118\) | −939.657 | −0.733071 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 113.784 | 0.0865583 | ||||||||
\(121\) | −1207.20 | −0.906989 | ||||||||
\(122\) | −130.306 | −0.0966998 | ||||||||
\(123\) | 738.602 | 0.541443 | ||||||||
\(124\) | 1256.76 | 0.910165 | ||||||||
\(125\) | −1551.74 | −1.11033 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2051.74 | −1.43356 | −0.716781 | − | 0.697299i | \(-0.754385\pi\) | ||||
−0.716781 | + | 0.697299i | \(0.754385\pi\) | |||||||
\(128\) | −256.493 | −0.177117 | ||||||||
\(129\) | 279.622 | 0.190848 | ||||||||
\(130\) | −2313.63 | −1.56092 | ||||||||
\(131\) | 158.468 | 0.105691 | 0.0528453 | − | 0.998603i | \(-0.483171\pi\) | ||||
0.0528453 | + | 0.998603i | \(0.483171\pi\) | |||||||
\(132\) | −258.085 | −0.170177 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1991.22 | 1.28369 | ||||||||
\(135\) | −2516.52 | −1.60435 | ||||||||
\(136\) | 137.060 | 0.0864178 | ||||||||
\(137\) | −70.9378 | −0.0442381 | −0.0221191 | − | 0.999755i | \(-0.507041\pi\) | ||||
−0.0221191 | + | 0.999755i | \(0.507041\pi\) | |||||||
\(138\) | 1844.09 | 1.13753 | ||||||||
\(139\) | 1374.54 | 0.838753 | 0.419377 | − | 0.907812i | \(-0.362249\pi\) | ||||
0.419377 | + | 0.907812i | \(0.362249\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1095.58 | −0.654358 | ||||||||
\(142\) | −2688.72 | −1.58896 | ||||||||
\(143\) | −357.464 | −0.209039 | ||||||||
\(144\) | 1180.69 | 0.683270 | ||||||||
\(145\) | 3362.14 | 1.92559 | ||||||||
\(146\) | −2311.12 | −1.31007 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1913.79 | 1.06292 | ||||||||
\(149\) | 349.364 | 0.192087 | 0.0960436 | − | 0.995377i | \(-0.469381\pi\) | ||||
0.0960436 | + | 0.995377i | \(0.469381\pi\) | |||||||
\(150\) | 2557.26 | 1.39199 | ||||||||
\(151\) | −1660.64 | −0.894975 | −0.447488 | − | 0.894290i | \(-0.647681\pi\) | ||||
−0.447488 | + | 0.894290i | \(0.647681\pi\) | |||||||
\(152\) | 227.885 | 0.121605 | ||||||||
\(153\) | −1188.32 | −0.627907 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3070.28 | −1.59104 | ||||||||
\(156\) | 745.215 | 0.382467 | ||||||||
\(157\) | 3076.18 | 1.56373 | 0.781867 | − | 0.623446i | \(-0.214268\pi\) | ||||
0.781867 | + | 0.623446i | \(0.214268\pi\) | |||||||
\(158\) | 197.328 | 0.0993580 | ||||||||
\(159\) | −716.145 | −0.357195 | ||||||||
\(160\) | −4590.18 | −2.26803 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −173.597 | −0.0841918 | ||||||||
\(163\) | −2772.40 | −1.33222 | −0.666108 | − | 0.745855i | \(-0.732041\pi\) | ||||
−0.666108 | + | 0.745855i | \(0.732041\pi\) | |||||||
\(164\) | −1786.27 | −0.850513 | ||||||||
\(165\) | 630.503 | 0.297483 | ||||||||
\(166\) | −2200.63 | −1.02893 | ||||||||
\(167\) | −593.286 | −0.274909 | −0.137455 | − | 0.990508i | \(-0.543892\pi\) | ||||
−0.137455 | + | 0.990508i | \(0.543892\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1164.83 | −0.530192 | ||||||||
\(170\) | 4915.65 | 2.21772 | ||||||||
\(171\) | −1975.77 | −0.883574 | ||||||||
\(172\) | −676.251 | −0.299789 | ||||||||
\(173\) | −1622.53 | −0.713058 | −0.356529 | − | 0.934284i | \(-0.616040\pi\) | ||||
−0.356529 | + | 0.934284i | \(0.616040\pi\) | |||||||
\(174\) | −2239.64 | −0.975784 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −754.609 | −0.323186 | ||||||||
\(177\) | −739.403 | −0.313994 | ||||||||
\(178\) | 4608.73 | 1.94067 | ||||||||
\(179\) | 2025.46 | 0.845756 | 0.422878 | − | 0.906187i | \(-0.361020\pi\) | ||||
0.422878 | + | 0.906187i | \(0.361020\pi\) | |||||||
\(180\) | 2385.82 | 0.987936 | ||||||||
\(181\) | −2765.94 | −1.13586 | −0.567930 | − | 0.823077i | \(-0.692255\pi\) | ||||
−0.567930 | + | 0.823077i | \(0.692255\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −102.536 | −0.0414191 | ||||||||
\(184\) | 303.790 | 0.121716 | ||||||||
\(185\) | −4675.40 | −1.85807 | ||||||||
\(186\) | 2045.22 | 0.806250 | ||||||||
\(187\) | 759.483 | 0.297000 | ||||||||
\(188\) | 2649.60 | 1.02788 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8173.08 | 3.12072 | ||||||||
\(191\) | 976.430 | 0.369906 | 0.184953 | − | 0.982747i | \(-0.440787\pi\) | ||||
0.184953 | + | 0.982747i | \(0.440787\pi\) | |||||||
\(192\) | 1377.36 | 0.517721 | ||||||||
\(193\) | 4578.51 | 1.70761 | 0.853805 | − | 0.520593i | \(-0.174289\pi\) | ||||
0.853805 | + | 0.520593i | \(0.174289\pi\) | |||||||
\(194\) | −21.8843 | −0.00809898 | ||||||||
\(195\) | −1820.57 | −0.668581 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1085.93 | 0.392737 | 0.196369 | − | 0.980530i | \(-0.437085\pi\) | ||||
0.196369 | + | 0.980530i | \(0.437085\pi\) | |||||||
\(198\) | 762.343 | 0.273623 | ||||||||
\(199\) | −2662.01 | −0.948267 | −0.474133 | − | 0.880453i | \(-0.657239\pi\) | ||||
−0.474133 | + | 0.880453i | \(0.657239\pi\) | |||||||
\(200\) | 421.275 | 0.148943 | ||||||||
\(201\) | 1566.86 | 0.549840 | ||||||||
\(202\) | −6140.57 | −2.13886 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1583.32 | −0.543404 | ||||||||
\(205\) | 4363.87 | 1.48676 | ||||||||
\(206\) | −3771.28 | −1.27552 | ||||||||
\(207\) | −2633.87 | −0.884379 | ||||||||
\(208\) | 2178.92 | 0.726349 | ||||||||
\(209\) | 1262.77 | 0.417930 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3338.26 | 1.08917 | 0.544586 | − | 0.838705i | \(-0.316687\pi\) | ||||
0.544586 | + | 0.838705i | \(0.316687\pi\) | |||||||
\(212\) | 1731.96 | 0.561091 | ||||||||
\(213\) | −2115.71 | −0.680593 | ||||||||
\(214\) | 6284.19 | 2.00738 | ||||||||
\(215\) | 1652.09 | 0.524053 | ||||||||
\(216\) | 276.156 | 0.0869909 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5446.63 | 1.69217 | ||||||||
\(219\) | −1818.59 | −0.561136 | ||||||||
\(220\) | −1524.84 | −0.467293 | ||||||||
\(221\) | −2192.99 | −0.667496 | ||||||||
\(222\) | 3114.45 | 0.941568 | ||||||||
\(223\) | −272.956 | −0.0819663 | −0.0409832 | − | 0.999160i | \(-0.513049\pi\) | ||||
−0.0409832 | + | 0.999160i | \(0.513049\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3652.47 | −1.08221 | ||||||||
\(226\) | −8292.96 | −2.44088 | ||||||||
\(227\) | 3637.99 | 1.06371 | 0.531855 | − | 0.846836i | \(-0.321495\pi\) | ||||
0.531855 | + | 0.846836i | \(0.321495\pi\) | |||||||
\(228\) | −2632.53 | −0.764664 | ||||||||
\(229\) | −853.825 | −0.246386 | −0.123193 | − | 0.992383i | \(-0.539313\pi\) | ||||
−0.123193 | + | 0.992383i | \(0.539313\pi\) | |||||||
\(230\) | 10895.4 | 3.12357 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −368.951 | −0.104409 | ||||||||
\(233\) | −6233.09 | −1.75255 | −0.876273 | − | 0.481816i | \(-0.839977\pi\) | ||||
−0.876273 | + | 0.481816i | \(0.839977\pi\) | |||||||
\(234\) | −2201.25 | −0.614958 | ||||||||
\(235\) | −6473.00 | −1.79682 | ||||||||
\(236\) | 1788.21 | 0.493230 | ||||||||
\(237\) | 155.275 | 0.0425577 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4372.77 | 1.18348 | 0.591739 | − | 0.806130i | \(-0.298442\pi\) | ||||
0.591739 | + | 0.806130i | \(0.298442\pi\) | |||||||
\(240\) | −3843.23 | −1.03366 | ||||||||
\(241\) | 374.956 | 0.100220 | 0.0501101 | − | 0.998744i | \(-0.484043\pi\) | ||||
0.0501101 | + | 0.998744i | \(0.484043\pi\) | |||||||
\(242\) | 4751.20 | 1.26206 | ||||||||
\(243\) | −3849.97 | −1.01636 | ||||||||
\(244\) | 247.978 | 0.0650621 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2906.92 | −0.753409 | ||||||||
\(247\) | −3646.21 | −0.939283 | ||||||||
\(248\) | 336.923 | 0.0862687 | ||||||||
\(249\) | −1731.64 | −0.440717 | ||||||||
\(250\) | 6107.18 | 1.54501 | ||||||||
\(251\) | −5177.11 | −1.30190 | −0.650949 | − | 0.759122i | \(-0.725629\pi\) | ||||
−0.650949 | + | 0.759122i | \(0.725629\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1683.37 | 0.418311 | ||||||||
\(254\) | 8075.04 | 1.99478 | ||||||||
\(255\) | 3868.05 | 0.949910 | ||||||||
\(256\) | 4567.46 | 1.11510 | ||||||||
\(257\) | 2579.54 | 0.626099 | 0.313049 | − | 0.949737i | \(-0.398649\pi\) | ||||
0.313049 | + | 0.949737i | \(0.398649\pi\) | |||||||
\(258\) | −1100.51 | −0.265562 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4402.94 | 1.05023 | ||||||||
\(261\) | 3198.82 | 0.758629 | ||||||||
\(262\) | −623.686 | −0.147067 | ||||||||
\(263\) | −3988.24 | −0.935078 | −0.467539 | − | 0.883973i | \(-0.654859\pi\) | ||||
−0.467539 | + | 0.883973i | \(0.654859\pi\) | |||||||
\(264\) | −69.1897 | −0.0161300 | ||||||||
\(265\) | −4231.19 | −0.980829 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3626.54 | 0.831239 | ||||||||
\(268\) | −3789.37 | −0.863704 | ||||||||
\(269\) | 3146.82 | 0.713252 | 0.356626 | − | 0.934247i | \(-0.383927\pi\) | ||||
0.356626 | + | 0.934247i | \(0.383927\pi\) | |||||||
\(270\) | 9904.30 | 2.23243 | ||||||||
\(271\) | 2115.95 | 0.474298 | 0.237149 | − | 0.971473i | \(-0.423787\pi\) | ||||
0.237149 | + | 0.971473i | \(0.423787\pi\) | |||||||
\(272\) | −4629.42 | −1.03199 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 279.190 | 0.0615566 | ||||||||
\(275\) | 2334.39 | 0.511886 | ||||||||
\(276\) | −3509.37 | −0.765360 | ||||||||
\(277\) | −3176.01 | −0.688910 | −0.344455 | − | 0.938803i | \(-0.611936\pi\) | ||||
−0.344455 | + | 0.938803i | \(0.611936\pi\) | |||||||
\(278\) | −5409.78 | −1.16711 | ||||||||
\(279\) | −2921.14 | −0.626824 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1518.75 | 0.322424 | 0.161212 | − | 0.986920i | \(-0.448460\pi\) | ||||
0.161212 | + | 0.986920i | \(0.448460\pi\) | |||||||
\(282\) | 4311.89 | 0.910529 | ||||||||
\(283\) | 1518.90 | 0.319044 | 0.159522 | − | 0.987194i | \(-0.449005\pi\) | ||||
0.159522 | + | 0.987194i | \(0.449005\pi\) | |||||||
\(284\) | 5116.74 | 1.06909 | ||||||||
\(285\) | 6431.28 | 1.33669 | ||||||||
\(286\) | 1406.87 | 0.290875 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4367.21 | −0.893542 | ||||||||
\(289\) | −253.671 | −0.0516326 | ||||||||
\(290\) | −13232.4 | −2.67942 | ||||||||
\(291\) | −17.2205 | −0.00346901 | ||||||||
\(292\) | 4398.16 | 0.881448 | ||||||||
\(293\) | −6408.29 | −1.27774 | −0.638868 | − | 0.769317i | \(-0.720597\pi\) | ||||
−0.638868 | + | 0.769317i | \(0.720597\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4368.60 | −0.862202 | ||||||||
\(296\) | 513.065 | 0.100748 | ||||||||
\(297\) | 1530.25 | 0.298969 | ||||||||
\(298\) | −1374.99 | −0.267286 | ||||||||
\(299\) | −4860.70 | −0.940139 | ||||||||
\(300\) | −4866.56 | −0.936570 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6535.81 | 1.24534 | ||||||||
\(303\) | −4831.93 | −0.916129 | ||||||||
\(304\) | −7697.19 | −1.45218 | ||||||||
\(305\) | −605.812 | −0.113733 | ||||||||
\(306\) | 4676.87 | 0.873722 | ||||||||
\(307\) | −4645.18 | −0.863565 | −0.431783 | − | 0.901978i | \(-0.642115\pi\) | ||||
−0.431783 | + | 0.901978i | \(0.642115\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2967.57 | −0.546340 | ||||||||
\(310\) | 12083.7 | 2.21390 | ||||||||
\(311\) | −829.604 | −0.151262 | −0.0756311 | − | 0.997136i | \(-0.524097\pi\) | ||||
−0.0756311 | + | 0.997136i | \(0.524097\pi\) | |||||||
\(312\) | 199.784 | 0.0362517 | ||||||||
\(313\) | 7156.11 | 1.29229 | 0.646146 | − | 0.763214i | \(-0.276380\pi\) | ||||
0.646146 | + | 0.763214i | \(0.276380\pi\) | |||||||
\(314\) | −12107.0 | −2.17591 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −375.523 | −0.0668507 | ||||||||
\(317\) | 3114.62 | 0.551844 | 0.275922 | − | 0.961180i | \(-0.411017\pi\) | ||||
0.275922 | + | 0.961180i | \(0.411017\pi\) | |||||||
\(318\) | 2818.54 | 0.497031 | ||||||||
\(319\) | −2044.45 | −0.358831 | ||||||||
\(320\) | 8137.84 | 1.42162 | ||||||||
\(321\) | 4944.94 | 0.859813 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7746.91 | 1.33452 | ||||||||
\(324\) | 330.362 | 0.0566465 | ||||||||
\(325\) | −6740.49 | −1.15045 | ||||||||
\(326\) | 10911.4 | 1.85376 | ||||||||
\(327\) | 4285.87 | 0.724799 | ||||||||
\(328\) | −478.878 | −0.0806147 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2481.48 | −0.413942 | ||||||||
\(331\) | −8372.51 | −1.39032 | −0.695158 | − | 0.718857i | \(-0.744666\pi\) | ||||
−0.695158 | + | 0.718857i | \(0.744666\pi\) | |||||||
\(332\) | 4187.88 | 0.692289 | ||||||||
\(333\) | −4448.29 | −0.732027 | ||||||||
\(334\) | 2335.00 | 0.382532 | ||||||||
\(335\) | 9257.46 | 1.50982 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4752.53 | 0.768210 | 0.384105 | − | 0.923290i | \(-0.374510\pi\) | ||||
0.384105 | + | 0.923290i | \(0.374510\pi\) | |||||||
\(338\) | 4584.44 | 0.737753 | ||||||||
\(339\) | −6525.62 | −1.04550 | ||||||||
\(340\) | −9354.68 | −1.49214 | ||||||||
\(341\) | 1866.97 | 0.296487 | ||||||||
\(342\) | 7776.07 | 1.22948 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −181.295 | −0.0284151 | ||||||||
\(345\) | 8573.43 | 1.33791 | ||||||||
\(346\) | 6385.82 | 0.992208 | ||||||||
\(347\) | −5903.14 | −0.913248 | −0.456624 | − | 0.889660i | \(-0.650941\pi\) | ||||
−0.456624 | + | 0.889660i | \(0.650941\pi\) | |||||||
\(348\) | 4262.12 | 0.656533 | ||||||||
\(349\) | 446.879 | 0.0685412 | 0.0342706 | − | 0.999413i | \(-0.489089\pi\) | ||||
0.0342706 | + | 0.999413i | \(0.489089\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4418.55 | −0.671923 | ||||||||
\(352\) | 2791.19 | 0.422645 | ||||||||
\(353\) | 7681.47 | 1.15820 | 0.579098 | − | 0.815258i | \(-0.303405\pi\) | ||||
0.579098 | + | 0.815258i | \(0.303405\pi\) | |||||||
\(354\) | 2910.08 | 0.436917 | ||||||||
\(355\) | −12500.2 | −1.86885 | ||||||||
\(356\) | −8770.60 | −1.30573 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7971.64 | −1.17686 | ||||||||
\(359\) | 9406.07 | 1.38282 | 0.691411 | − | 0.722461i | \(-0.256989\pi\) | ||||
0.691411 | + | 0.722461i | \(0.256989\pi\) | |||||||
\(360\) | 639.612 | 0.0936402 | ||||||||
\(361\) | 6021.51 | 0.877900 | ||||||||
\(362\) | 10885.9 | 1.58053 | ||||||||
\(363\) | 3738.65 | 0.540574 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10744.7 | −1.54084 | ||||||||
\(366\) | 403.552 | 0.0576340 | ||||||||
\(367\) | −445.233 | −0.0633268 | −0.0316634 | − | 0.999499i | \(-0.510080\pi\) | ||||
−0.0316634 | + | 0.999499i | \(0.510080\pi\) | |||||||
\(368\) | −10261.0 | −1.45351 | ||||||||
\(369\) | 4151.89 | 0.585742 | ||||||||
\(370\) | 18401.0 | 2.58547 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3892.13 | −0.542467 | ||||||||
\(373\) | 9545.30 | 1.32503 | 0.662516 | − | 0.749048i | \(-0.269489\pi\) | ||||
0.662516 | + | 0.749048i | \(0.269489\pi\) | |||||||
\(374\) | −2989.11 | −0.413270 | ||||||||
\(375\) | 4805.66 | 0.661768 | ||||||||
\(376\) | 710.328 | 0.0974266 | ||||||||
\(377\) | 5903.30 | 0.806460 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 321.340 | 0.0435518 | 0.0217759 | − | 0.999763i | \(-0.493068\pi\) | ||||
0.0217759 | + | 0.999763i | \(0.493068\pi\) | |||||||
\(380\) | −15553.7 | −2.09971 | ||||||||
\(381\) | 6354.14 | 0.854416 | ||||||||
\(382\) | −3842.95 | −0.514718 | ||||||||
\(383\) | 4423.96 | 0.590219 | 0.295110 | − | 0.955463i | \(-0.404644\pi\) | ||||
0.295110 | + | 0.955463i | \(0.404644\pi\) | |||||||
\(384\) | 794.348 | 0.105563 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18019.7 | −2.37611 | ||||||||
\(387\) | 1571.84 | 0.206462 | ||||||||
\(388\) | 41.6467 | 0.00544921 | ||||||||
\(389\) | −9517.64 | −1.24052 | −0.620262 | − | 0.784395i | \(-0.712974\pi\) | ||||
−0.620262 | + | 0.784395i | \(0.712974\pi\) | |||||||
\(390\) | 7165.22 | 0.930320 | ||||||||
\(391\) | 10327.3 | 1.33573 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −490.770 | −0.0629925 | ||||||||
\(394\) | −4273.90 | −0.546488 | ||||||||
\(395\) | 917.405 | 0.116860 | ||||||||
\(396\) | −1450.77 | −0.184101 | ||||||||
\(397\) | −1484.81 | −0.187710 | −0.0938548 | − | 0.995586i | \(-0.529919\pi\) | ||||
−0.0938548 | + | 0.995586i | \(0.529919\pi\) | |||||||
\(398\) | 10476.9 | 1.31950 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14229.2 | −1.77865 | ||||||||
\(401\) | 6186.84 | 0.770464 | 0.385232 | − | 0.922820i | \(-0.374121\pi\) | ||||
0.385232 | + | 0.922820i | \(0.374121\pi\) | |||||||
\(402\) | −6166.72 | −0.765094 | ||||||||
\(403\) | −5390.84 | −0.666345 | ||||||||
\(404\) | 11685.8 | 1.43908 | ||||||||
\(405\) | −807.077 | −0.0990222 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2843.02 | 0.346248 | ||||||||
\(408\) | −424.469 | −0.0515058 | ||||||||
\(409\) | 10738.0 | 1.29819 | 0.649093 | − | 0.760709i | \(-0.275149\pi\) | ||||
0.649093 | + | 0.760709i | \(0.275149\pi\) | |||||||
\(410\) | −17174.9 | −2.06880 | ||||||||
\(411\) | 219.691 | 0.0263663 | ||||||||
\(412\) | 7176.90 | 0.858205 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 10366.1 | 1.23060 | ||||||||
\(415\) | −10231.0 | −1.21017 | ||||||||
\(416\) | −8059.51 | −0.949879 | ||||||||
\(417\) | −4256.88 | −0.499905 | ||||||||
\(418\) | −4969.88 | −0.581543 | ||||||||
\(419\) | 4920.15 | 0.573663 | 0.286832 | − | 0.957981i | \(-0.407398\pi\) | ||||
0.286832 | + | 0.957981i | \(0.407398\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11804.0 | −1.36648 | −0.683242 | − | 0.730192i | \(-0.739431\pi\) | ||||
−0.683242 | + | 0.730192i | \(0.739431\pi\) | |||||||
\(422\) | −13138.4 | −1.51557 | ||||||||
\(423\) | −6158.57 | −0.707896 | ||||||||
\(424\) | 464.318 | 0.0531823 | ||||||||
\(425\) | 14321.1 | 1.63454 | ||||||||
\(426\) | 8326.83 | 0.947034 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11959.1 | −1.35062 | ||||||||
\(429\) | 1107.05 | 0.124589 | ||||||||
\(430\) | −6502.14 | −0.729212 | ||||||||
\(431\) | 2901.97 | 0.324323 | 0.162161 | − | 0.986764i | \(-0.448153\pi\) | ||||
0.162161 | + | 0.986764i | \(0.448153\pi\) | |||||||
\(432\) | −9327.60 | −1.03883 | ||||||||
\(433\) | 398.338 | 0.0442099 | 0.0221049 | − | 0.999756i | \(-0.492963\pi\) | ||||
0.0221049 | + | 0.999756i | \(0.492963\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10412.4 | −1.14767 | ||||||||
\(436\) | −10365.2 | −1.13853 | ||||||||
\(437\) | 17170.8 | 1.87961 | ||||||||
\(438\) | 7157.44 | 0.780812 | ||||||||
\(439\) | −4977.64 | −0.541161 | −0.270580 | − | 0.962697i | \(-0.587216\pi\) | ||||
−0.270580 | + | 0.962697i | \(0.587216\pi\) | |||||||
\(440\) | −408.792 | −0.0442918 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8630.98 | 0.928810 | ||||||||
\(443\) | −2201.59 | −0.236119 | −0.118059 | − | 0.993007i | \(-0.537667\pi\) | ||||
−0.118059 | + | 0.993007i | \(0.537667\pi\) | |||||||
\(444\) | −5926.92 | −0.633512 | ||||||||
\(445\) | 21426.6 | 2.28252 | ||||||||
\(446\) | 1074.28 | 0.114055 | ||||||||
\(447\) | −1081.96 | −0.114486 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18314.1 | 1.92494 | 0.962468 | − | 0.271395i | \(-0.0874851\pi\) | ||||
0.962468 | + | 0.271395i | \(0.0874851\pi\) | |||||||
\(450\) | 14375.1 | 1.50588 | ||||||||
\(451\) | −2653.58 | −0.277056 | ||||||||
\(452\) | 15781.8 | 1.64229 | ||||||||
\(453\) | 5142.94 | 0.533414 | ||||||||
\(454\) | −14318.1 | −1.48013 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −705.750 | −0.0724776 | ||||||||
\(457\) | −8747.89 | −0.895425 | −0.447712 | − | 0.894178i | \(-0.647761\pi\) | ||||
−0.447712 | + | 0.894178i | \(0.647761\pi\) | |||||||
\(458\) | 3360.41 | 0.342842 | ||||||||
\(459\) | 9387.85 | 0.954657 | ||||||||
\(460\) | −20734.4 | −2.10162 | ||||||||
\(461\) | 9307.86 | 0.940370 | 0.470185 | − | 0.882568i | \(-0.344187\pi\) | ||||
0.470185 | + | 0.882568i | \(0.344187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14225.1 | −1.42785 | −0.713927 | − | 0.700220i | \(-0.753085\pi\) | ||||
−0.713927 | + | 0.700220i | \(0.753085\pi\) | |||||||
\(464\) | 12461.9 | 1.24683 | ||||||||
\(465\) | 9508.50 | 0.948272 | ||||||||
\(466\) | 24531.6 | 2.43864 | ||||||||
\(467\) | 5884.52 | 0.583090 | 0.291545 | − | 0.956557i | \(-0.405831\pi\) | ||||
0.291545 | + | 0.956557i | \(0.405831\pi\) | |||||||
\(468\) | 4189.06 | 0.413760 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 25475.8 | 2.50024 | ||||||||
\(471\) | −9526.80 | −0.931999 | ||||||||
\(472\) | 479.398 | 0.0467501 | ||||||||
\(473\) | −1004.60 | −0.0976567 | ||||||||
\(474\) | −611.115 | −0.0592183 | ||||||||
\(475\) | 23811.3 | 2.30008 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4025.66 | −0.386420 | ||||||||
\(478\) | −17210.0 | −1.64679 | ||||||||
\(479\) | 12489.8 | 1.19138 | 0.595692 | − | 0.803213i | \(-0.296878\pi\) | ||||
0.595692 | + | 0.803213i | \(0.296878\pi\) | |||||||
\(480\) | 14215.6 | 1.35177 | ||||||||
\(481\) | −8209.15 | −0.778181 | ||||||||
\(482\) | −1475.72 | −0.139455 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9041.72 | −0.849147 | ||||||||
\(485\) | −101.743 | −0.00952562 | ||||||||
\(486\) | 15152.4 | 1.41425 | ||||||||
\(487\) | 8170.07 | 0.760208 | 0.380104 | − | 0.924944i | \(-0.375888\pi\) | ||||
0.380104 | + | 0.924944i | \(0.375888\pi\) | |||||||
\(488\) | 66.4801 | 0.00616683 | ||||||||
\(489\) | 8586.00 | 0.794013 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5894.06 | 0.541741 | 0.270871 | − | 0.962616i | \(-0.412688\pi\) | ||||
0.270871 | + | 0.962616i | \(0.412688\pi\) | |||||||
\(492\) | 5531.99 | 0.506913 | ||||||||
\(493\) | −12542.4 | −1.14581 | ||||||||
\(494\) | 14350.4 | 1.30700 | ||||||||
\(495\) | 3544.24 | 0.321822 | ||||||||
\(496\) | −11380.1 | −1.03021 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6815.25 | 0.613250 | ||||||||
\(499\) | 7089.14 | 0.635979 | 0.317989 | − | 0.948094i | \(-0.396992\pi\) | ||||
0.317989 | + | 0.948094i | \(0.396992\pi\) | |||||||
\(500\) | −11622.2 | −1.03952 | ||||||||
\(501\) | 1837.38 | 0.163849 | ||||||||
\(502\) | 20375.6 | 1.81157 | ||||||||
\(503\) | −2916.01 | −0.258486 | −0.129243 | − | 0.991613i | \(-0.541255\pi\) | ||||
−0.129243 | + | 0.991613i | \(0.541255\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28548.4 | −2.51562 | ||||||||
\(506\) | −6625.26 | −0.582073 | ||||||||
\(507\) | 3607.43 | 0.315999 | ||||||||
\(508\) | −15367.1 | −1.34214 | ||||||||
\(509\) | 11495.4 | 1.00104 | 0.500518 | − | 0.865726i | \(-0.333143\pi\) | ||||
0.500518 | + | 0.865726i | \(0.333143\pi\) | |||||||
\(510\) | −15223.5 | −1.32178 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −15924.2 | −1.37453 | ||||||||
\(513\) | 15608.9 | 1.34337 | ||||||||
\(514\) | −10152.3 | −0.871206 | ||||||||
\(515\) | −17533.2 | −1.50021 | ||||||||
\(516\) | 2094.32 | 0.178677 | ||||||||
\(517\) | 3936.10 | 0.334834 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5024.92 | 0.424989 | ||||||||
\(520\) | 1180.38 | 0.0995442 | ||||||||
\(521\) | 16479.2 | 1.38574 | 0.692868 | − | 0.721064i | \(-0.256347\pi\) | ||||
0.692868 | + | 0.721064i | \(0.256347\pi\) | |||||||
\(522\) | −12589.6 | −1.05562 | ||||||||
\(523\) | 12363.5 | 1.03369 | 0.516844 | − | 0.856080i | \(-0.327107\pi\) | ||||
0.516844 | + | 0.856080i | \(0.327107\pi\) | |||||||
\(524\) | 1186.90 | 0.0989503 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15696.6 | 1.30115 | ||||||||
\(527\) | 11453.6 | 0.946732 | ||||||||
\(528\) | 2336.99 | 0.192622 | ||||||||
\(529\) | 10723.1 | 0.881324 | ||||||||
\(530\) | 16652.7 | 1.36481 | ||||||||
\(531\) | −4156.39 | −0.339684 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7662.15 | 0.622673 | ||||||||
\(534\) | −14273.0 | −1.15666 | ||||||||
\(535\) | 29216.1 | 2.36098 | ||||||||
\(536\) | −1015.89 | −0.0818650 | ||||||||
\(537\) | −6272.77 | −0.504078 | ||||||||
\(538\) | −12385.0 | −0.992479 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −18848.3 | −1.50204 | ||||||||
\(541\) | −5706.02 | −0.453458 | −0.226729 | − | 0.973958i | \(-0.572803\pi\) | ||||
−0.226729 | + | 0.973958i | \(0.572803\pi\) | |||||||
\(542\) | −8327.76 | −0.659978 | ||||||||
\(543\) | 8565.98 | 0.676983 | ||||||||
\(544\) | 17123.6 | 1.34957 | ||||||||
\(545\) | 25322.1 | 1.99024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6452.32 | 0.504354 | 0.252177 | − | 0.967681i | \(-0.418854\pi\) | ||||
0.252177 | + | 0.967681i | \(0.418854\pi\) | |||||||
\(548\) | −531.311 | −0.0414169 | ||||||||
\(549\) | −576.385 | −0.0448078 | ||||||||
\(550\) | −9187.46 | −0.712281 | ||||||||
\(551\) | −20853.8 | −1.61235 | ||||||||
\(552\) | −940.823 | −0.0725437 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12499.9 | 0.958607 | ||||||||
\(555\) | 14479.5 | 1.10743 | ||||||||
\(556\) | 10295.0 | 0.785263 | ||||||||
\(557\) | 8462.90 | 0.643778 | 0.321889 | − | 0.946777i | \(-0.395682\pi\) | ||||
0.321889 | + | 0.946777i | \(0.395682\pi\) | |||||||
\(558\) | 11496.7 | 0.872215 | ||||||||
\(559\) | 2900.76 | 0.219480 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2352.09 | −0.177014 | ||||||||
\(562\) | −5977.36 | −0.448647 | ||||||||
\(563\) | 16622.0 | 1.24429 | 0.622145 | − | 0.782902i | \(-0.286262\pi\) | ||||
0.622145 | + | 0.782902i | \(0.286262\pi\) | |||||||
\(564\) | −8205.70 | −0.612628 | ||||||||
\(565\) | −38555.2 | −2.87085 | ||||||||
\(566\) | −5977.96 | −0.443944 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1371.74 | 0.101333 | ||||||||
\(569\) | −5553.95 | −0.409198 | −0.204599 | − | 0.978846i | \(-0.565589\pi\) | ||||
−0.204599 | + | 0.978846i | \(0.565589\pi\) | |||||||
\(570\) | −25311.7 | −1.85998 | ||||||||
\(571\) | 17365.2 | 1.27270 | 0.636351 | − | 0.771399i | \(-0.280443\pi\) | ||||
0.636351 | + | 0.771399i | \(0.280443\pi\) | |||||||
\(572\) | −2677.34 | −0.195708 | ||||||||
\(573\) | −3023.96 | −0.220467 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31742.4 | 2.30217 | ||||||||
\(576\) | 7742.54 | 0.560080 | ||||||||
\(577\) | 14165.9 | 1.02207 | 0.511035 | − | 0.859560i | \(-0.329262\pi\) | ||||
0.511035 | + | 0.859560i | \(0.329262\pi\) | |||||||
\(578\) | 998.376 | 0.0718460 | ||||||||
\(579\) | −14179.5 | −1.01775 | ||||||||
\(580\) | 25181.8 | 1.80279 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 67.7747 | 0.00482707 | ||||||||
\(583\) | 2572.90 | 0.182776 | ||||||||
\(584\) | 1179.10 | 0.0835469 | ||||||||
\(585\) | −10233.9 | −0.723283 | ||||||||
\(586\) | 25221.2 | 1.77795 | ||||||||
\(587\) | 13013.6 | 0.915043 | 0.457521 | − | 0.889199i | \(-0.348737\pi\) | ||||
0.457521 | + | 0.889199i | \(0.348737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19043.5 | 1.33222 | ||||||||
\(590\) | 17193.5 | 1.19974 | ||||||||
\(591\) | −3363.07 | −0.234075 | ||||||||
\(592\) | −17329.6 | −1.20311 | ||||||||
\(593\) | 1489.95 | 0.103179 | 0.0515894 | − | 0.998668i | \(-0.483571\pi\) | ||||
0.0515894 | + | 0.998668i | \(0.483571\pi\) | |||||||
\(594\) | −6022.60 | −0.416011 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2616.67 | 0.179837 | ||||||||
\(597\) | 8244.13 | 0.565176 | ||||||||
\(598\) | 19130.3 | 1.30819 | ||||||||
\(599\) | −11764.0 | −0.802446 | −0.401223 | − | 0.915980i | \(-0.631415\pi\) | ||||
−0.401223 | + | 0.915980i | \(0.631415\pi\) | |||||||
\(600\) | −1304.67 | −0.0887715 | ||||||||
\(601\) | 11373.3 | 0.771925 | 0.385962 | − | 0.922515i | \(-0.373869\pi\) | ||||
0.385962 | + | 0.922515i | \(0.373869\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8807.78 | 0.594827 | ||||||||
\(604\) | −12437.9 | −0.837900 | ||||||||
\(605\) | 22089.0 | 1.48437 | ||||||||
\(606\) | 19017.1 | 1.27478 | ||||||||
\(607\) | −20896.4 | −1.39730 | −0.698648 | − | 0.715465i | \(-0.746215\pi\) | ||||
−0.698648 | + | 0.715465i | \(0.746215\pi\) | |||||||
\(608\) | 28470.8 | 1.89909 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2384.30 | 0.158258 | ||||||||
\(611\) | −11365.4 | −0.752528 | ||||||||
\(612\) | −8900.27 | −0.587863 | ||||||||
\(613\) | −4220.00 | −0.278049 | −0.139024 | − | 0.990289i | \(-0.544397\pi\) | ||||
−0.139024 | + | 0.990289i | \(0.544397\pi\) | |||||||
\(614\) | 18282.1 | 1.20164 | ||||||||
\(615\) | −13514.7 | −0.886122 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −250.008 | −0.0163127 | −0.00815634 | − | 0.999967i | \(-0.502596\pi\) | ||||
−0.00815634 | + | 0.999967i | \(0.502596\pi\) | |||||||
\(618\) | 11679.5 | 0.760223 | ||||||||
\(619\) | −10844.4 | −0.704158 | −0.352079 | − | 0.935970i | \(-0.614525\pi\) | ||||
−0.352079 | + | 0.935970i | \(0.614525\pi\) | |||||||
\(620\) | −22995.8 | −1.48957 | ||||||||
\(621\) | 20807.9 | 1.34459 | ||||||||
\(622\) | 3265.08 | 0.210479 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6748.01 | −0.432911 | ||||||||
\(625\) | 2167.54 | 0.138722 | ||||||||
\(626\) | −28164.4 | −1.79820 | ||||||||
\(627\) | −3910.73 | −0.249090 | ||||||||
\(628\) | 23040.0 | 1.46401 | ||||||||
\(629\) | 17441.5 | 1.10563 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12729.0 | −0.803061 | −0.401531 | − | 0.915846i | \(-0.631522\pi\) | ||||
−0.401531 | + | 0.915846i | \(0.631522\pi\) | |||||||
\(632\) | −100.673 | −0.00633635 | ||||||||
\(633\) | −10338.4 | −0.649157 | ||||||||
\(634\) | −12258.2 | −0.767882 | ||||||||
\(635\) | 37542.0 | 2.34616 | ||||||||
\(636\) | −5363.80 | −0.334416 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8046.35 | 0.499307 | ||||||||
\(639\) | −11893.0 | −0.736277 | ||||||||
\(640\) | 4693.23 | 0.289869 | ||||||||
\(641\) | −9838.08 | −0.606210 | −0.303105 | − | 0.952957i | \(-0.598023\pi\) | ||||
−0.303105 | + | 0.952957i | \(0.598023\pi\) | |||||||
\(642\) | −19461.9 | −1.19642 | ||||||||
\(643\) | −16456.6 | −1.00931 | −0.504655 | − | 0.863321i | \(-0.668380\pi\) | ||||
−0.504655 | + | 0.863321i | \(0.668380\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5116.44 | −0.312341 | ||||||||
\(646\) | −30489.6 | −1.85696 | ||||||||
\(647\) | −8370.82 | −0.508641 | −0.254321 | − | 0.967120i | \(-0.581852\pi\) | ||||
−0.254321 | + | 0.967120i | \(0.581852\pi\) | |||||||
\(648\) | 88.5664 | 0.00536916 | ||||||||
\(649\) | 2656.46 | 0.160670 | ||||||||
\(650\) | 26528.6 | 1.60083 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20764.8 | −1.24726 | ||||||||
\(653\) | 9681.16 | 0.580173 | 0.290087 | − | 0.957000i | \(-0.406316\pi\) | ||||
0.290087 | + | 0.957000i | \(0.406316\pi\) | |||||||
\(654\) | −16868.0 | −1.00855 | ||||||||
\(655\) | −2899.61 | −0.172972 | ||||||||
\(656\) | 16174.9 | 0.962687 | ||||||||
\(657\) | −10222.8 | −0.607047 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3978.93 | 0.235200 | 0.117600 | − | 0.993061i | \(-0.462480\pi\) | ||||
0.117600 | + | 0.993061i | \(0.462480\pi\) | |||||||
\(660\) | 4722.35 | 0.278511 | ||||||||
\(661\) | −23777.7 | −1.39916 | −0.699581 | − | 0.714554i | \(-0.746630\pi\) | ||||
−0.699581 | + | 0.714554i | \(0.746630\pi\) | |||||||
\(662\) | 32951.8 | 1.93460 | ||||||||
\(663\) | 6791.60 | 0.397834 | ||||||||
\(664\) | 1122.72 | 0.0656177 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17507.2 | 1.01860 | ||||||||
\(667\) | −27799.9 | −1.61382 | ||||||||
\(668\) | −4443.61 | −0.257378 | ||||||||
\(669\) | 845.333 | 0.0488527 | ||||||||
\(670\) | −36434.7 | −2.10089 | ||||||||
\(671\) | 368.382 | 0.0211941 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6783.00 | −0.388507 | −0.194254 | − | 0.980951i | \(-0.562228\pi\) | ||||
−0.194254 | + | 0.980951i | \(0.562228\pi\) | |||||||
\(674\) | −18704.6 | −1.06895 | ||||||||
\(675\) | 28855.0 | 1.64538 | ||||||||
\(676\) | −8724.38 | −0.496380 | ||||||||
\(677\) | −19979.7 | −1.13424 | −0.567121 | − | 0.823635i | \(-0.691943\pi\) | ||||
−0.567121 | + | 0.823635i | \(0.691943\pi\) | |||||||
\(678\) | 25682.9 | 1.45479 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2507.88 | −0.141431 | ||||||||
\(681\) | −11266.7 | −0.633981 | ||||||||
\(682\) | −7347.86 | −0.412557 | ||||||||
\(683\) | 7057.33 | 0.395375 | 0.197688 | − | 0.980265i | \(-0.436657\pi\) | ||||
0.197688 | + | 0.980265i | \(0.436657\pi\) | |||||||
\(684\) | −14798.2 | −0.827226 | ||||||||
\(685\) | 1298.00 | 0.0723998 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2644.26 | 0.146848 | ||||||||
\(688\) | 6123.54 | 0.339328 | ||||||||
\(689\) | −7429.19 | −0.410783 | ||||||||
\(690\) | −33742.5 | −1.86168 | ||||||||
\(691\) | 9084.49 | 0.500131 | 0.250065 | − | 0.968229i | \(-0.419548\pi\) | ||||
0.250065 | + | 0.968229i | \(0.419548\pi\) | |||||||
\(692\) | −12152.5 | −0.667584 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23233.0 | 1.27077 | ||||||||
\(695\) | −25150.8 | −1.37270 | ||||||||
\(696\) | 1142.63 | 0.0622286 | ||||||||
\(697\) | −16279.3 | −0.884683 | ||||||||
\(698\) | −1758.79 | −0.0953740 | ||||||||
\(699\) | 19303.6 | 1.04453 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15607.4 | 0.840920 | 0.420460 | − | 0.907311i | \(-0.361869\pi\) | ||||
0.420460 | + | 0.907311i | \(0.361869\pi\) | |||||||
\(702\) | 17390.1 | 0.934969 | ||||||||
\(703\) | 28999.4 | 1.55581 | ||||||||
\(704\) | −4948.45 | −0.264917 | ||||||||
\(705\) | 20046.6 | 1.07092 | ||||||||
\(706\) | −30232.0 | −1.61161 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5537.99 | −0.293970 | ||||||||
\(709\) | −14222.5 | −0.753367 | −0.376684 | − | 0.926342i | \(-0.622936\pi\) | ||||
−0.376684 | + | 0.926342i | \(0.622936\pi\) | |||||||
\(710\) | 49197.3 | 2.60048 | ||||||||
\(711\) | 872.842 | 0.0460396 | ||||||||
\(712\) | −2351.30 | −0.123762 | ||||||||
\(713\) | 25386.6 | 1.33343 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6540.75 | 0.342112 | ||||||||
\(716\) | 15170.3 | 0.791819 | ||||||||
\(717\) | −13542.3 | −0.705363 | ||||||||
\(718\) | −37019.6 | −1.92418 | ||||||||
\(719\) | −2333.58 | −0.121040 | −0.0605200 | − | 0.998167i | \(-0.519276\pi\) | ||||
−0.0605200 | + | 0.998167i | \(0.519276\pi\) | |||||||
\(720\) | −21603.9 | −1.11824 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −23698.9 | −1.22158 | ||||||||
\(723\) | −1161.22 | −0.0597321 | ||||||||
\(724\) | −20716.4 | −1.06342 | ||||||||
\(725\) | −38551.0 | −1.97482 | ||||||||
\(726\) | −14714.2 | −0.752200 | ||||||||
\(727\) | −21602.3 | −1.10204 | −0.551020 | − | 0.834492i | \(-0.685761\pi\) | ||||
−0.551020 | + | 0.834492i | \(0.685761\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10732.3 | 0.545256 | ||||||||
\(730\) | 42288.2 | 2.14405 | ||||||||
\(731\) | −6163.09 | −0.311833 | ||||||||
\(732\) | −767.977 | −0.0387776 | ||||||||
\(733\) | −33179.7 | −1.67192 | −0.835961 | − | 0.548789i | \(-0.815089\pi\) | ||||
−0.835961 | + | 0.548789i | \(0.815089\pi\) | |||||||
\(734\) | 1752.31 | 0.0881183 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 37953.9 | 1.90082 | ||||||||
\(737\) | −5629.27 | −0.281353 | ||||||||
\(738\) | −16340.6 | −0.815050 | ||||||||
\(739\) | −19573.5 | −0.974322 | −0.487161 | − | 0.873312i | \(-0.661968\pi\) | ||||
−0.487161 | + | 0.873312i | \(0.661968\pi\) | |||||||
\(740\) | −35017.9 | −1.73957 | ||||||||
\(741\) | 11292.2 | 0.559821 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27842.0 | 1.37473 | 0.687365 | − | 0.726312i | \(-0.258767\pi\) | ||||
0.687365 | + | 0.726312i | \(0.258767\pi\) | |||||||
\(744\) | −1043.44 | −0.0514170 | ||||||||
\(745\) | −6392.55 | −0.314369 | ||||||||
\(746\) | −37567.6 | −1.84376 | ||||||||
\(747\) | −9734.06 | −0.476775 | ||||||||
\(748\) | 5688.39 | 0.278059 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −18913.7 | −0.920840 | ||||||||
\(751\) | −29613.8 | −1.43891 | −0.719455 | − | 0.694539i | \(-0.755608\pi\) | ||||
−0.719455 | + | 0.694539i | \(0.755608\pi\) | |||||||
\(752\) | −23992.5 | −1.16345 | ||||||||
\(753\) | 16033.3 | 0.775943 | ||||||||
\(754\) | −23233.7 | −1.12218 | ||||||||
\(755\) | 30385.9 | 1.46471 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7371.98 | 0.353949 | 0.176974 | − | 0.984215i | \(-0.443369\pi\) | ||||
0.176974 | + | 0.984215i | \(0.443369\pi\) | |||||||
\(758\) | −1264.70 | −0.0606016 | ||||||||
\(759\) | −5213.33 | −0.249317 | ||||||||
\(760\) | −4169.77 | −0.199018 | ||||||||
\(761\) | 24101.3 | 1.14806 | 0.574029 | − | 0.818835i | \(-0.305380\pi\) | ||||
0.574029 | + | 0.818835i | \(0.305380\pi\) | |||||||
\(762\) | −25008.1 | −1.18891 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7313.28 | 0.346316 | ||||||||
\(765\) | 21743.4 | 1.02763 | ||||||||
\(766\) | −17411.4 | −0.821281 | ||||||||
\(767\) | −7670.46 | −0.361101 | ||||||||
\(768\) | −14145.2 | −0.664611 | ||||||||
\(769\) | 34245.7 | 1.60589 | 0.802947 | − | 0.596051i | \(-0.203264\pi\) | ||||
0.802947 | + | 0.596051i | \(0.203264\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7988.73 | −0.373161 | ||||||||
\(772\) | 34292.2 | 1.59871 | ||||||||
\(773\) | −21268.3 | −0.989609 | −0.494804 | − | 0.869004i | \(-0.664760\pi\) | ||||
−0.494804 | + | 0.869004i | \(0.664760\pi\) | |||||||
\(774\) | −6186.30 | −0.287289 | ||||||||
\(775\) | 35204.4 | 1.63172 | ||||||||
\(776\) | 11.1650 | 0.000516496 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37458.7 | 1.72617 | ||||||||
\(779\) | −27067.1 | −1.24490 | ||||||||
\(780\) | −13635.7 | −0.625944 | ||||||||
\(781\) | 7601.13 | 0.348259 | ||||||||
\(782\) | −40645.1 | −1.85865 | ||||||||
\(783\) | −25271.1 | −1.15340 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −56287.0 | −2.55920 | ||||||||
\(786\) | 1931.53 | 0.0876531 | ||||||||
\(787\) | 1773.26 | 0.0803173 | 0.0401587 | − | 0.999193i | \(-0.487214\pi\) | ||||
0.0401587 | + | 0.999193i | \(0.487214\pi\) | |||||||
\(788\) | 8133.41 | 0.367691 | ||||||||
\(789\) | 12351.4 | 0.557315 | ||||||||
\(790\) | −3610.64 | −0.162609 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −388.935 | −0.0174497 | ||||||||
\(793\) | −1063.70 | −0.0476329 | ||||||||
\(794\) | 5843.80 | 0.261195 | ||||||||
\(795\) | 13103.8 | 0.584583 | ||||||||
\(796\) | −19938.0 | −0.887793 | ||||||||
\(797\) | 4473.60 | 0.198825 | 0.0994123 | − | 0.995046i | \(-0.468304\pi\) | ||||
0.0994123 | + | 0.995046i | \(0.468304\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24147.4 | 1.06918 | ||||||||
\(800\) | 52631.9 | 2.32602 | ||||||||
\(801\) | 20385.8 | 0.899249 | ||||||||
\(802\) | −24349.6 | −1.07209 | ||||||||
\(803\) | 6533.66 | 0.287133 | ||||||||
\(804\) | 11735.5 | 0.514776 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21216.8 | 0.927208 | ||||||||
\(807\) | −9745.56 | −0.425105 | ||||||||
\(808\) | 3132.82 | 0.136401 | ||||||||
\(809\) | −15255.6 | −0.662989 | −0.331494 | − | 0.943457i | \(-0.607553\pi\) | ||||
−0.331494 | + | 0.943457i | \(0.607553\pi\) | |||||||
\(810\) | 3176.42 | 0.137788 | ||||||||
\(811\) | −4911.79 | −0.212671 | −0.106336 | − | 0.994330i | \(-0.533912\pi\) | ||||
−0.106336 | + | 0.994330i | \(0.533912\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6553.00 | −0.282686 | ||||||||
\(814\) | −11189.3 | −0.481799 | ||||||||
\(815\) | 50728.5 | 2.18030 | ||||||||
\(816\) | 14337.1 | 0.615073 | ||||||||
\(817\) | −10247.2 | −0.438804 | ||||||||
\(818\) | −42261.5 | −1.80640 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 32684.5 | 1.39194 | ||||||||
\(821\) | 22792.2 | 0.968884 | 0.484442 | − | 0.874823i | \(-0.339023\pi\) | ||||
0.484442 | + | 0.874823i | \(0.339023\pi\) | |||||||
\(822\) | −864.640 | −0.0366883 | ||||||||
\(823\) | 17358.6 | 0.735216 | 0.367608 | − | 0.929981i | \(-0.380177\pi\) | ||||
0.367608 | + | 0.929981i | \(0.380177\pi\) | |||||||
\(824\) | 1924.05 | 0.0813438 | ||||||||
\(825\) | −7229.49 | −0.305089 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34567.7 | −1.45349 | −0.726745 | − | 0.686907i | \(-0.758968\pi\) | ||||
−0.726745 | + | 0.686907i | \(0.758968\pi\) | |||||||
\(828\) | −19727.2 | −0.827980 | ||||||||
\(829\) | −568.054 | −0.0237990 | −0.0118995 | − | 0.999929i | \(-0.503788\pi\) | ||||
−0.0118995 | + | 0.999929i | \(0.503788\pi\) | |||||||
\(830\) | 40266.4 | 1.68394 | ||||||||
\(831\) | 9835.96 | 0.410597 | ||||||||
\(832\) | 14288.6 | 0.595392 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16753.8 | 0.695609 | ||||||||
\(835\) | 10855.8 | 0.449915 | ||||||||
\(836\) | 9457.89 | 0.391277 | ||||||||
\(837\) | 23077.3 | 0.953011 | ||||||||
\(838\) | −19364.3 | −0.798243 | ||||||||
\(839\) | 28050.8 | 1.15426 | 0.577129 | − | 0.816653i | \(-0.304173\pi\) | ||||
0.577129 | + | 0.816653i | \(0.304173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9373.83 | 0.384347 | ||||||||
\(842\) | 46457.0 | 1.90144 | ||||||||
\(843\) | −4703.50 | −0.192167 | ||||||||
\(844\) | 25003.0 | 1.01971 | ||||||||
\(845\) | 21313.7 | 0.867709 | ||||||||
\(846\) | 24238.4 | 0.985026 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15683.1 | −0.635094 | ||||||||
\(849\) | −4703.98 | −0.190153 | ||||||||
\(850\) | −56363.9 | −2.27443 | ||||||||
\(851\) | 38658.6 | 1.55723 | ||||||||
\(852\) | −15846.3 | −0.637189 | ||||||||
\(853\) | −8242.71 | −0.330862 | −0.165431 | − | 0.986221i | \(-0.552901\pi\) | ||||
−0.165431 | + | 0.986221i | \(0.552901\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 36152.1 | 1.44605 | ||||||||
\(856\) | −3206.09 | −0.128016 | ||||||||
\(857\) | −21781.0 | −0.868175 | −0.434087 | − | 0.900871i | \(-0.642929\pi\) | ||||
−0.434087 | + | 0.900871i | \(0.642929\pi\) | |||||||
\(858\) | −4357.02 | −0.173364 | ||||||||
\(859\) | −46751.1 | −1.85696 | −0.928480 | − | 0.371383i | \(-0.878884\pi\) | ||||
−0.928480 | + | 0.371383i | \(0.878884\pi\) | |||||||
\(860\) | 12373.8 | 0.490633 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11421.3 | −0.451290 | ||||||||
\(863\) | −20805.6 | −0.820663 | −0.410331 | − | 0.911936i | \(-0.634587\pi\) | ||||
−0.410331 | + | 0.911936i | \(0.634587\pi\) | |||||||
\(864\) | 34501.5 | 1.35852 | ||||||||
\(865\) | 29688.6 | 1.16699 | ||||||||
\(866\) | −1567.74 | −0.0615173 | ||||||||
\(867\) | 785.608 | 0.0307735 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −557.856 | −0.0217767 | ||||||||
\(870\) | 40980.1 | 1.59696 | ||||||||
\(871\) | 16254.4 | 0.632330 | ||||||||
\(872\) | −2778.78 | −0.107914 | ||||||||
\(873\) | −96.8011 | −0.00375283 | ||||||||
\(874\) | −67579.2 | −2.61545 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13620.9 | −0.525351 | ||||||||
\(877\) | 3507.96 | 0.135069 | 0.0675345 | − | 0.997717i | \(-0.478487\pi\) | ||||
0.0675345 | + | 0.997717i | \(0.478487\pi\) | |||||||
\(878\) | 19590.5 | 0.753017 | ||||||||
\(879\) | 19846.2 | 0.761542 | ||||||||
\(880\) | 13807.6 | 0.528925 | ||||||||
\(881\) | 29531.8 | 1.12934 | 0.564671 | − | 0.825316i | \(-0.309003\pi\) | ||||
0.564671 | + | 0.825316i | \(0.309003\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41514.5 | −1.58219 | −0.791096 | − | 0.611692i | \(-0.790489\pi\) | ||||
−0.791096 | + | 0.611692i | \(0.790489\pi\) | |||||||
\(884\) | −16425.1 | −0.624928 | ||||||||
\(885\) | 13529.4 | 0.513881 | ||||||||
\(886\) | 8664.81 | 0.328555 | ||||||||
\(887\) | 36859.9 | 1.39530 | 0.697652 | − | 0.716437i | \(-0.254228\pi\) | ||||
0.697652 | + | 0.716437i | \(0.254228\pi\) | |||||||
\(888\) | −1588.94 | −0.0600466 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −84329.1 | −3.17609 | ||||||||
\(891\) | 490.767 | 0.0184527 | ||||||||
\(892\) | −2044.39 | −0.0767391 | ||||||||
\(893\) | 40149.1 | 1.50452 | ||||||||
\(894\) | 4258.30 | 0.159305 | ||||||||
\(895\) | −37061.3 | −1.38416 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15053.4 | 0.560332 | ||||||||
\(898\) | −72079.0 | −2.67852 | ||||||||
\(899\) | −30831.9 | −1.14383 | ||||||||
\(900\) | −27356.3 | −1.01320 | ||||||||
\(901\) | 15784.4 | 0.583634 | ||||||||
\(902\) | 10443.7 | 0.385518 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4230.94 | 0.155662 | ||||||||
\(905\) | 50610.2 | 1.85894 | ||||||||
\(906\) | −20241.1 | −0.742236 | ||||||||
\(907\) | −17428.2 | −0.638031 | −0.319016 | − | 0.947749i | \(-0.603352\pi\) | ||||
−0.319016 | + | 0.947749i | \(0.603352\pi\) | |||||||
\(908\) | 27247.9 | 0.995874 | ||||||||
\(909\) | −27161.6 | −0.991083 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14994.7 | −0.545333 | −0.272666 | − | 0.962109i | \(-0.587906\pi\) | ||||
−0.272666 | + | 0.962109i | \(0.587906\pi\) | |||||||
\(912\) | 23837.8 | 0.865515 | ||||||||
\(913\) | 6221.28 | 0.225514 | ||||||||
\(914\) | 34429.2 | 1.24597 | ||||||||
\(915\) | 1876.17 | 0.0677862 | ||||||||
\(916\) | −6394.99 | −0.230673 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −36947.9 | −1.32839 | ||||||||
\(919\) | 24719.2 | 0.887280 | 0.443640 | − | 0.896205i | \(-0.353687\pi\) | ||||
0.443640 | + | 0.896205i | \(0.353687\pi\) | |||||||
\(920\) | −5558.65 | −0.199199 | ||||||||
\(921\) | 14385.9 | 0.514693 | ||||||||
\(922\) | −36633.1 | −1.30851 | ||||||||
\(923\) | −21948.1 | −0.782698 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 53609.2 | 1.90558 | ||||||||
\(926\) | 55985.9 | 1.98684 | ||||||||
\(927\) | −16681.5 | −0.591040 | ||||||||
\(928\) | −46094.9 | −1.63054 | ||||||||
\(929\) | −41255.1 | −1.45698 | −0.728490 | − | 0.685056i | \(-0.759778\pi\) | ||||
−0.728490 | + | 0.685056i | \(0.759778\pi\) | |||||||
\(930\) | −37422.7 | −1.31950 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −46684.7 | −1.64078 | ||||||||
\(933\) | 2569.25 | 0.0901536 | ||||||||
\(934\) | −23159.8 | −0.811361 | ||||||||
\(935\) | −13896.8 | −0.486068 | ||||||||
\(936\) | 1123.04 | 0.0392177 | ||||||||
\(937\) | −30271.6 | −1.05542 | −0.527711 | − | 0.849424i | \(-0.676950\pi\) | ||||
−0.527711 | + | 0.849424i | \(0.676950\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22162.1 | −0.770218 | ||||||||
\(940\) | −48481.6 | −1.68223 | ||||||||
\(941\) | 49515.6 | 1.71537 | 0.857685 | − | 0.514175i | \(-0.171902\pi\) | ||||
0.857685 | + | 0.514175i | \(0.171902\pi\) | |||||||
\(942\) | 37494.7 | 1.29686 | ||||||||
\(943\) | −36082.7 | −1.24604 | ||||||||
\(944\) | −16192.4 | −0.558282 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3953.82 | 0.135888 | ||||||||
\(947\) | −48772.3 | −1.67359 | −0.836794 | − | 0.547518i | \(-0.815573\pi\) | ||||
−0.836794 | + | 0.547518i | \(0.815573\pi\) | |||||||
\(948\) | 1162.98 | 0.0398436 | ||||||||
\(949\) | −18865.8 | −0.645321 | ||||||||
\(950\) | −93714.3 | −3.20052 | ||||||||
\(951\) | −9645.84 | −0.328904 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43341.2 | −1.47320 | −0.736599 | − | 0.676329i | \(-0.763570\pi\) | ||||
−0.736599 | + | 0.676329i | \(0.763570\pi\) | |||||||
\(954\) | 15843.8 | 0.537697 | ||||||||
\(955\) | −17866.4 | −0.605386 | ||||||||
\(956\) | 32751.3 | 1.10800 | ||||||||
\(957\) | 6331.56 | 0.213867 | ||||||||
\(958\) | −49156.2 | −1.65779 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −25202.5 | −0.847300 | ||||||||
\(961\) | −1635.54 | −0.0549006 | ||||||||
\(962\) | 32308.8 | 1.08283 | ||||||||
\(963\) | 27796.9 | 0.930160 | ||||||||
\(964\) | 2808.35 | 0.0938288 | ||||||||
\(965\) | −83776.2 | −2.79466 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −636.799 | −0.0211769 | −0.0105885 | − | 0.999944i | \(-0.503370\pi\) | ||||
−0.0105885 | + | 0.999944i | \(0.503370\pi\) | |||||||
\(968\) | −2423.98 | −0.0804853 | ||||||||
\(969\) | −23991.8 | −0.795385 | ||||||||
\(970\) | 400.432 | 0.0132547 | ||||||||
\(971\) | −19763.9 | −0.653195 | −0.326598 | − | 0.945163i | \(-0.605902\pi\) | ||||
−0.326598 | + | 0.945163i | \(0.605902\pi\) | |||||||
\(972\) | −28835.6 | −0.951545 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −32155.0 | −1.05782 | ||||||||
\(975\) | 20875.0 | 0.685676 | ||||||||
\(976\) | −2245.47 | −0.0736432 | ||||||||
\(977\) | 40980.6 | 1.34195 | 0.670975 | − | 0.741480i | \(-0.265876\pi\) | ||||
0.670975 | + | 0.741480i | \(0.265876\pi\) | |||||||
\(978\) | −33792.0 | −1.10486 | ||||||||
\(979\) | −13029.1 | −0.425344 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24092.1 | 0.784100 | ||||||||
\(982\) | −23197.3 | −0.753824 | ||||||||
\(983\) | 9296.84 | 0.301651 | 0.150826 | − | 0.988560i | \(-0.451807\pi\) | ||||
0.150826 | + | 0.988560i | \(0.451807\pi\) | |||||||
\(984\) | 1483.06 | 0.0480471 | ||||||||
\(985\) | −19870.0 | −0.642752 | ||||||||
\(986\) | 49363.3 | 1.59437 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27309.5 | −0.879382 | ||||||||
\(989\) | −13660.3 | −0.439204 | ||||||||
\(990\) | −13949.1 | −0.447810 | ||||||||
\(991\) | 6575.47 | 0.210774 | 0.105387 | − | 0.994431i | \(-0.466392\pi\) | ||||
0.105387 | + | 0.994431i | \(0.466392\pi\) | |||||||
\(992\) | 42093.4 | 1.34725 | ||||||||
\(993\) | 25929.3 | 0.828641 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48708.6 | 1.55193 | ||||||||
\(996\) | −12969.7 | −0.412611 | ||||||||
\(997\) | −5380.51 | −0.170915 | −0.0854576 | − | 0.996342i | \(-0.527235\pi\) | ||||
−0.0854576 | + | 0.996342i | \(0.527235\pi\) | |||||||
\(998\) | −27900.8 | −0.884954 | ||||||||
\(999\) | 35142.1 | 1.11296 |
(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 | 2401.4.a.d.1.7 | 39 | ||
7.6 | odd | 2 | 2401.4.a.c.1.7 | 39 | |||
49.22 | even | 7 | 49.4.e.a.43.3 | yes | 78 | ||
49.29 | even | 7 | 49.4.e.a.8.3 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.e.a.8.3 | ✓ | 78 | 49.29 | even | 7 | ||
49.4.e.a.43.3 | yes | 78 | 49.22 | even | 7 | ||
2401.4.a.c.1.7 | 39 | 7.6 | odd | 2 | |||
2401.4.a.d.1.7 | 39 | 1.1 | even | 1 | trivial |