Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 70x^{8} + 1645x^{6} - 14700x^{4} + 44100x^{2} - 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.917374\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.917374 | 0.324341 | 0.162170 | − | 0.986763i | \(-0.448151\pi\) | ||||
0.162170 | + | 0.986763i | \(0.448151\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.15843 | −0.894803 | ||||||||
\(5\) | −15.4704 | −1.38372 | −0.691858 | − | 0.722034i | \(-0.743208\pi\) | ||||
−0.691858 | + | 0.722034i | \(0.743208\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 20.5833 | 1.11140 | 0.555698 | − | 0.831384i | \(-0.312451\pi\) | ||||
0.555698 | + | 0.831384i | \(0.312451\pi\) | |||||||
\(8\) | −13.9059 | −0.614562 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −14.1922 | −0.448795 | ||||||||
\(11\) | −65.8420 | −1.80474 | −0.902369 | − | 0.430964i | \(-0.858173\pi\) | ||||
−0.902369 | + | 0.430964i | \(0.858173\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 18.8826 | 0.360471 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 44.5105 | 0.695476 | ||||||||
\(17\) | −44.2956 | −0.631957 | −0.315979 | − | 0.948766i | \(-0.602333\pi\) | ||||
−0.315979 | + | 0.948766i | \(0.602333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −147.053 | −1.77560 | −0.887798 | − | 0.460234i | \(-0.847766\pi\) | ||||
−0.887798 | + | 0.460234i | \(0.847766\pi\) | |||||||
\(20\) | 110.744 | 1.23815 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −60.4017 | −0.585350 | ||||||||
\(23\) | −53.1586 | −0.481928 | −0.240964 | − | 0.970534i | \(-0.577464\pi\) | ||||
−0.240964 | + | 0.970534i | \(0.577464\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 114.334 | 0.914669 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −147.344 | −0.994480 | ||||||||
\(29\) | 38.6257 | 0.247331 | 0.123666 | − | 0.992324i | \(-0.460535\pi\) | ||||
0.123666 | + | 0.992324i | \(0.460535\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −88.3894 | −0.512104 | −0.256052 | − | 0.966663i | \(-0.582422\pi\) | ||||
−0.256052 | + | 0.966663i | \(0.582422\pi\) | |||||||
\(32\) | 152.080 | 0.840133 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −40.6357 | −0.204969 | ||||||||
\(35\) | −318.433 | −1.53786 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −78.9587 | −0.350831 | −0.175415 | − | 0.984495i | \(-0.556127\pi\) | ||||
−0.175415 | + | 0.984495i | \(0.556127\pi\) | |||||||
\(38\) | −134.903 | −0.575898 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 215.131 | 0.850379 | ||||||||
\(41\) | −354.966 | −1.35211 | −0.676054 | − | 0.736852i | \(-0.736311\pi\) | ||||
−0.676054 | + | 0.736852i | \(0.736311\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −407.846 | −1.44642 | −0.723208 | − | 0.690630i | \(-0.757333\pi\) | ||||
−0.723208 | + | 0.690630i | \(0.757333\pi\) | |||||||
\(44\) | 471.325 | 1.61489 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −48.7663 | −0.156309 | ||||||||
\(47\) | −67.9674 | −0.210938 | −0.105469 | − | 0.994423i | \(-0.533634\pi\) | ||||
−0.105469 | + | 0.994423i | \(0.533634\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 80.6738 | 0.235201 | ||||||||
\(50\) | 104.887 | 0.296664 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −226.572 | −0.587209 | −0.293604 | − | 0.955927i | \(-0.594855\pi\) | ||||
−0.293604 | + | 0.955927i | \(0.594855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1018.60 | 2.49724 | ||||||||
\(56\) | −286.231 | −0.683021 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 35.4342 | 0.0802196 | ||||||||
\(59\) | 142.031 | 0.313404 | 0.156702 | − | 0.987646i | \(-0.449914\pi\) | ||||
0.156702 | + | 0.987646i | \(0.449914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 266.831 | 0.560069 | 0.280035 | − | 0.959990i | \(-0.409654\pi\) | ||||
0.280035 | + | 0.959990i | \(0.409654\pi\) | |||||||
\(62\) | −81.0862 | −0.166096 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −216.569 | −0.422987 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 411.187 | 0.749768 | 0.374884 | − | 0.927072i | \(-0.377683\pi\) | ||||
0.374884 | + | 0.927072i | \(0.377683\pi\) | |||||||
\(68\) | 317.087 | 0.565477 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −292.122 | −0.498789 | ||||||||
\(71\) | −91.5052 | −0.152953 | −0.0764765 | − | 0.997071i | \(-0.524367\pi\) | ||||
−0.0764765 | + | 0.997071i | \(0.524367\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −63.1328 | −0.101221 | −0.0506105 | − | 0.998718i | \(-0.516117\pi\) | ||||
−0.0506105 | + | 0.998718i | \(0.516117\pi\) | |||||||
\(74\) | −72.4347 | −0.113789 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1052.67 | 1.58881 | ||||||||
\(77\) | −1355.25 | −2.00578 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −287.115 | −0.408899 | −0.204449 | − | 0.978877i | \(-0.565540\pi\) | ||||
−0.204449 | + | 0.978877i | \(0.565540\pi\) | |||||||
\(80\) | −688.595 | −0.962341 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −325.637 | −0.438543 | ||||||||
\(83\) | −373.812 | −0.494352 | −0.247176 | − | 0.968971i | \(-0.579503\pi\) | ||||
−0.247176 | + | 0.968971i | \(0.579503\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 685.272 | 0.874449 | ||||||||
\(86\) | −374.147 | −0.469132 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 915.595 | 1.10912 | ||||||||
\(89\) | 119.403 | 0.142209 | 0.0711047 | − | 0.997469i | \(-0.477348\pi\) | ||||
0.0711047 | + | 0.997469i | \(0.477348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 380.532 | 0.431231 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −62.3515 | −0.0684157 | ||||||||
\(95\) | 2274.97 | 2.45692 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −554.650 | −0.580579 | −0.290290 | − | 0.956939i | \(-0.593752\pi\) | ||||
−0.290290 | + | 0.956939i | \(0.593752\pi\) | |||||||
\(98\) | 74.0080 | 0.0762851 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −818.449 | −0.818449 | ||||||||
\(101\) | 462.565 | 0.455712 | 0.227856 | − | 0.973695i | \(-0.426828\pi\) | ||||
0.227856 | + | 0.973695i | \(0.426828\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1122.07 | 1.07341 | 0.536704 | − | 0.843771i | \(-0.319669\pi\) | ||||
0.536704 | + | 0.843771i | \(0.319669\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −207.851 | −0.190456 | ||||||||
\(107\) | −602.756 | −0.544585 | −0.272293 | − | 0.962214i | \(-0.587782\pi\) | ||||
−0.272293 | + | 0.962214i | \(0.587782\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1421.89 | −1.24947 | −0.624735 | − | 0.780837i | \(-0.714793\pi\) | ||||
−0.624735 | + | 0.780837i | \(0.714793\pi\) | |||||||
\(110\) | 934.440 | 0.809958 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 916.174 | 0.772949 | ||||||||
\(113\) | 396.719 | 0.330267 | 0.165134 | − | 0.986271i | \(-0.447194\pi\) | ||||
0.165134 | + | 0.986271i | \(0.447194\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 822.386 | 0.666851 | ||||||||
\(116\) | −276.499 | −0.221313 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 130.295 | 0.101650 | ||||||||
\(119\) | −911.752 | −0.702354 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3004.17 | 2.25708 | ||||||||
\(122\) | 244.784 | 0.181653 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 632.729 | 0.458232 | ||||||||
\(125\) | 165.013 | 0.118074 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 437.868 | 0.305941 | 0.152970 | − | 0.988231i | \(-0.451116\pi\) | ||||
0.152970 | + | 0.988231i | \(0.451116\pi\) | |||||||
\(128\) | −1415.32 | −0.977324 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1657.44 | −1.10543 | −0.552715 | − | 0.833370i | \(-0.686408\pi\) | ||||
−0.552715 | + | 0.833370i | \(0.686408\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3026.85 | −1.97339 | ||||||||
\(134\) | 377.212 | 0.243180 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 615.973 | 0.388377 | ||||||||
\(137\) | 1967.42 | 1.22692 | 0.613460 | − | 0.789725i | \(-0.289777\pi\) | ||||
0.613460 | + | 0.789725i | \(0.289777\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2825.13 | 1.72392 | 0.861960 | − | 0.506977i | \(-0.169237\pi\) | ||||
0.861960 | + | 0.506977i | \(0.169237\pi\) | |||||||
\(140\) | 2279.48 | 1.37608 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −83.9445 | −0.0496089 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −597.555 | −0.342236 | ||||||||
\(146\) | −57.9164 | −0.0328301 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 565.220 | 0.313924 | ||||||||
\(149\) | 797.658 | 0.438569 | 0.219284 | − | 0.975661i | \(-0.429628\pi\) | ||||
0.219284 | + | 0.975661i | \(0.429628\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 161.987 | 0.0873003 | 0.0436501 | − | 0.999047i | \(-0.486101\pi\) | ||||
0.0436501 | + | 0.999047i | \(0.486101\pi\) | |||||||
\(152\) | 2044.91 | 1.09121 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1243.27 | −0.650555 | ||||||||
\(155\) | 1367.42 | 0.708606 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −342.000 | −0.173851 | −0.0869255 | − | 0.996215i | \(-0.527704\pi\) | ||||
−0.0869255 | + | 0.996215i | \(0.527704\pi\) | |||||||
\(158\) | −263.392 | −0.132622 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2352.74 | −1.16250 | ||||||||
\(161\) | −1094.18 | −0.535613 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 556.597 | 0.267460 | 0.133730 | − | 0.991018i | \(-0.457304\pi\) | ||||
0.133730 | + | 0.991018i | \(0.457304\pi\) | |||||||
\(164\) | 2541.00 | 1.20987 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −342.926 | −0.160339 | ||||||||
\(167\) | 3136.42 | 1.45332 | 0.726658 | − | 0.686999i | \(-0.241072\pi\) | ||||
0.726658 | + | 0.686999i | \(0.241072\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 628.650 | 0.283619 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2919.53 | 1.29426 | ||||||||
\(173\) | −3324.19 | −1.46089 | −0.730444 | − | 0.682972i | \(-0.760687\pi\) | ||||
−0.730444 | + | 0.682972i | \(0.760687\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2353.37 | 1.01656 | ||||||||
\(176\) | −2930.66 | −1.25515 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 109.537 | 0.0461243 | ||||||||
\(179\) | 3313.25 | 1.38349 | 0.691743 | − | 0.722144i | \(-0.256843\pi\) | ||||
0.691743 | + | 0.722144i | \(0.256843\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 76.0118 | 0.0312150 | 0.0156075 | − | 0.999878i | \(-0.495032\pi\) | ||||
0.0156075 | + | 0.999878i | \(0.495032\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 739.221 | 0.296174 | ||||||||
\(185\) | 1221.52 | 0.485450 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2916.51 | 1.14052 | ||||||||
\(188\) | 486.540 | 0.188748 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2087.00 | 0.796879 | ||||||||
\(191\) | 4073.39 | 1.54314 | 0.771572 | − | 0.636142i | \(-0.219471\pi\) | ||||
0.771572 | + | 0.636142i | \(0.219471\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −867.581 | −0.323574 | −0.161787 | − | 0.986826i | \(-0.551726\pi\) | ||||
−0.161787 | + | 0.986826i | \(0.551726\pi\) | |||||||
\(194\) | −508.821 | −0.188305 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −577.497 | −0.210458 | ||||||||
\(197\) | −1887.69 | −0.682703 | −0.341352 | − | 0.939936i | \(-0.610885\pi\) | ||||
−0.341352 | + | 0.939936i | \(0.610885\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2786.22 | 0.992511 | 0.496256 | − | 0.868176i | \(-0.334708\pi\) | ||||
0.496256 | + | 0.868176i | \(0.334708\pi\) | |||||||
\(200\) | −1589.92 | −0.562120 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 424.345 | 0.147806 | ||||||||
\(203\) | 795.045 | 0.274883 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5491.47 | 1.87093 | ||||||||
\(206\) | 1029.36 | 0.348150 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9682.28 | 3.20448 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 708.789 | 0.231256 | 0.115628 | − | 0.993293i | \(-0.463112\pi\) | ||||
0.115628 | + | 0.993293i | \(0.463112\pi\) | |||||||
\(212\) | 1621.90 | 0.525436 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −552.953 | −0.176631 | ||||||||
\(215\) | 6309.54 | 2.00143 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1819.35 | −0.569150 | ||||||||
\(218\) | −1304.40 | −0.405254 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7291.59 | −2.23454 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5396.64 | −1.62056 | −0.810281 | − | 0.586041i | \(-0.800686\pi\) | ||||
−0.810281 | + | 0.586041i | \(0.800686\pi\) | |||||||
\(224\) | 3130.32 | 0.933720 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 363.940 | 0.107119 | ||||||||
\(227\) | 3181.79 | 0.930321 | 0.465160 | − | 0.885226i | \(-0.345997\pi\) | ||||
0.465160 | + | 0.885226i | \(0.345997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2034.00 | −0.586945 | −0.293473 | − | 0.955967i | \(-0.594811\pi\) | ||||
−0.293473 | + | 0.955967i | \(0.594811\pi\) | |||||||
\(230\) | 754.435 | 0.216287 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −537.126 | −0.152000 | ||||||||
\(233\) | 2794.22 | 0.785645 | 0.392823 | − | 0.919614i | \(-0.371499\pi\) | ||||
0.392823 | + | 0.919614i | \(0.371499\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1051.48 | 0.291878 | ||||||||
\(236\) | −1016.72 | −0.280435 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −836.417 | −0.227802 | ||||||||
\(239\) | −5493.81 | −1.48688 | −0.743442 | − | 0.668800i | \(-0.766808\pi\) | ||||
−0.743442 | + | 0.668800i | \(0.766808\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4061.27 | −1.08552 | −0.542758 | − | 0.839889i | \(-0.682620\pi\) | ||||
−0.542758 | + | 0.839889i | \(0.682620\pi\) | |||||||
\(242\) | 2755.95 | 0.732062 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1910.09 | −0.501152 | ||||||||
\(245\) | −1248.06 | −0.325451 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1229.14 | 0.314719 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 151.379 | 0.0382961 | ||||||||
\(251\) | 3570.88 | 0.897977 | 0.448988 | − | 0.893538i | \(-0.351784\pi\) | ||||
0.448988 | + | 0.893538i | \(0.351784\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3500.07 | 0.869753 | ||||||||
\(254\) | 401.688 | 0.0992290 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 434.179 | 0.106001 | ||||||||
\(257\) | 7518.26 | 1.82481 | 0.912405 | − | 0.409288i | \(-0.134223\pi\) | ||||
0.912405 | + | 0.409288i | \(0.134223\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1625.23 | −0.389912 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1520.49 | −0.358536 | ||||||||
\(263\) | 4660.18 | 1.09262 | 0.546310 | − | 0.837583i | \(-0.316032\pi\) | ||||
0.546310 | + | 0.837583i | \(0.316032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3505.16 | 0.812530 | ||||||||
\(266\) | −2776.75 | −0.640050 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2943.45 | −0.670895 | ||||||||
\(269\) | −5347.44 | −1.21204 | −0.606021 | − | 0.795449i | \(-0.707235\pi\) | ||||
−0.606021 | + | 0.795449i | \(0.707235\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2973.08 | −0.666427 | −0.333214 | − | 0.942851i | \(-0.608133\pi\) | ||||
−0.333214 | + | 0.942851i | \(0.608133\pi\) | |||||||
\(272\) | −1971.62 | −0.439511 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1804.86 | 0.397940 | ||||||||
\(275\) | −7527.96 | −1.65074 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −764.153 | −0.165753 | −0.0828764 | − | 0.996560i | \(-0.526411\pi\) | ||||
−0.0828764 | + | 0.996560i | \(0.526411\pi\) | |||||||
\(278\) | 2591.70 | 0.559137 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4428.11 | 0.945107 | ||||||||
\(281\) | −7040.34 | −1.49463 | −0.747316 | − | 0.664469i | \(-0.768658\pi\) | ||||
−0.747316 | + | 0.664469i | \(0.768658\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9035.17 | −1.89783 | −0.948913 | − | 0.315537i | \(-0.897815\pi\) | ||||
−0.948913 | + | 0.315537i | \(0.897815\pi\) | |||||||
\(284\) | 655.033 | 0.136863 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7306.39 | −1.50273 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2950.90 | −0.600630 | ||||||||
\(290\) | −548.181 | −0.111001 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 451.931 | 0.0905729 | ||||||||
\(293\) | 1785.23 | 0.355954 | 0.177977 | − | 0.984035i | \(-0.443045\pi\) | ||||
0.177977 | + | 0.984035i | \(0.443045\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2197.27 | −0.433662 | ||||||||
\(296\) | 1098.00 | 0.215607 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 731.751 | 0.142246 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8394.83 | −1.60754 | ||||||||
\(302\) | 148.603 | 0.0283150 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6545.40 | −1.23488 | ||||||||
\(305\) | −4127.99 | −0.774977 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5323.13 | −0.989600 | −0.494800 | − | 0.869007i | \(-0.664759\pi\) | ||||
−0.494800 | + | 0.869007i | \(0.664759\pi\) | |||||||
\(308\) | 9701.45 | 1.79478 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1254.44 | 0.229830 | ||||||||
\(311\) | −6265.64 | −1.14242 | −0.571209 | − | 0.820805i | \(-0.693525\pi\) | ||||
−0.571209 | + | 0.820805i | \(0.693525\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7193.77 | 1.29909 | 0.649547 | − | 0.760322i | \(-0.274959\pi\) | ||||
0.649547 | + | 0.760322i | \(0.274959\pi\) | |||||||
\(314\) | −313.742 | −0.0563869 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2055.29 | 0.365884 | ||||||||
\(317\) | −9576.87 | −1.69682 | −0.848408 | − | 0.529343i | \(-0.822439\pi\) | ||||
−0.848408 | + | 0.529343i | \(0.822439\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2543.19 | −0.446368 | ||||||||
\(320\) | 3350.41 | 0.585293 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1003.77 | −0.173721 | ||||||||
\(323\) | 6513.81 | 1.12210 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 510.608 | 0.0867483 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4936.14 | 0.830953 | ||||||||
\(329\) | −1399.00 | −0.234435 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5773.13 | −0.958670 | −0.479335 | − | 0.877632i | \(-0.659122\pi\) | ||||
−0.479335 | + | 0.877632i | \(0.659122\pi\) | |||||||
\(332\) | 2675.91 | 0.442348 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2877.27 | 0.471370 | ||||||||
\(335\) | −6361.23 | −1.03747 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1238.09 | 0.200127 | 0.100063 | − | 0.994981i | \(-0.468095\pi\) | ||||
0.100063 | + | 0.994981i | \(0.468095\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4905.47 | −0.782460 | ||||||||
\(341\) | 5819.74 | 0.924213 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5399.55 | −0.849995 | ||||||||
\(344\) | 5671.48 | 0.888912 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3049.53 | −0.473826 | ||||||||
\(347\) | −5449.97 | −0.843140 | −0.421570 | − | 0.906796i | \(-0.638521\pi\) | ||||
−0.421570 | + | 0.906796i | \(0.638521\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1374.03 | 0.210746 | 0.105373 | − | 0.994433i | \(-0.466396\pi\) | ||||
0.105373 | + | 0.994433i | \(0.466396\pi\) | |||||||
\(350\) | 2158.92 | 0.329711 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10013.3 | −1.51622 | ||||||||
\(353\) | −5970.44 | −0.900211 | −0.450106 | − | 0.892975i | \(-0.648614\pi\) | ||||
−0.450106 | + | 0.892975i | \(0.648614\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1415.62 | 0.211644 | ||||||||
\(356\) | −854.734 | −0.127249 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3039.49 | 0.448720 | ||||||||
\(359\) | −7813.71 | −1.14872 | −0.574362 | − | 0.818602i | \(-0.694750\pi\) | ||||
−0.574362 | + | 0.818602i | \(0.694750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14765.6 | 2.15274 | ||||||||
\(362\) | 69.7313 | 0.0101243 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 976.690 | 0.140061 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1688.39 | 0.240145 | 0.120073 | − | 0.992765i | \(-0.461687\pi\) | ||||
0.120073 | + | 0.992765i | \(0.461687\pi\) | |||||||
\(368\) | −2366.11 | −0.335169 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1120.59 | 0.157451 | ||||||||
\(371\) | −4663.61 | −0.652622 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1870.61 | 0.259670 | 0.129835 | − | 0.991536i | \(-0.458555\pi\) | ||||
0.129835 | + | 0.991536i | \(0.458555\pi\) | |||||||
\(374\) | 2675.53 | 0.369916 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 945.151 | 0.129634 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11667.0 | 1.58125 | 0.790627 | − | 0.612298i | \(-0.209755\pi\) | ||||
0.790627 | + | 0.612298i | \(0.209755\pi\) | |||||||
\(380\) | −16285.2 | −2.19846 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3736.82 | 0.500504 | ||||||||
\(383\) | 6676.60 | 0.890753 | 0.445376 | − | 0.895343i | \(-0.353070\pi\) | ||||
0.445376 | + | 0.895343i | \(0.353070\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20966.3 | 2.77543 | ||||||||
\(386\) | −795.896 | −0.104948 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3970.42 | 0.519504 | ||||||||
\(389\) | −14285.3 | −1.86194 | −0.930969 | − | 0.365099i | \(-0.881035\pi\) | ||||
−0.930969 | + | 0.365099i | \(0.881035\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2354.69 | 0.304558 | ||||||||
\(392\) | −1121.85 | −0.144545 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1731.72 | −0.221428 | ||||||||
\(395\) | 4441.79 | 0.565800 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3569.28 | 0.451227 | 0.225614 | − | 0.974217i | \(-0.427561\pi\) | ||||
0.225614 | + | 0.974217i | \(0.427561\pi\) | |||||||
\(398\) | 2556.00 | 0.321912 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5089.04 | 0.636130 | ||||||||
\(401\) | −499.348 | −0.0621852 | −0.0310926 | − | 0.999517i | \(-0.509899\pi\) | ||||
−0.0310926 | + | 0.999517i | \(0.509899\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3311.23 | −0.407772 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 729.354 | 0.0891557 | ||||||||
\(407\) | 5198.80 | 0.633158 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10457.5 | 1.26428 | 0.632140 | − | 0.774855i | \(-0.282177\pi\) | ||||
0.632140 | + | 0.774855i | \(0.282177\pi\) | |||||||
\(410\) | 5037.73 | 0.606819 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8032.27 | −0.960489 | ||||||||
\(413\) | 2923.47 | 0.348316 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5783.03 | 0.684043 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8882.27 | 1.03934 | ||||||||
\(419\) | 1705.42 | 0.198843 | 0.0994215 | − | 0.995045i | \(-0.468301\pi\) | ||||
0.0994215 | + | 0.995045i | \(0.468301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8765.57 | −1.01475 | −0.507373 | − | 0.861727i | \(-0.669383\pi\) | ||||
−0.507373 | + | 0.861727i | \(0.669383\pi\) | |||||||
\(422\) | 650.225 | 0.0750058 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3150.70 | 0.360876 | ||||||||
\(425\) | −5064.48 | −0.578032 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5492.28 | 0.622459 | ||||||||
\(428\) | 4314.79 | 0.487297 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5788.21 | 0.649145 | ||||||||
\(431\) | 8080.37 | 0.903057 | 0.451529 | − | 0.892257i | \(-0.350879\pi\) | ||||
0.451529 | + | 0.892257i | \(0.350879\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4124.48 | −0.457760 | −0.228880 | − | 0.973455i | \(-0.573506\pi\) | ||||
−0.228880 | + | 0.973455i | \(0.573506\pi\) | |||||||
\(434\) | −1669.02 | −0.184598 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10178.5 | 1.11803 | ||||||||
\(437\) | 7817.14 | 0.855709 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6115.52 | −0.664870 | −0.332435 | − | 0.943126i | \(-0.607870\pi\) | ||||
−0.332435 | + | 0.943126i | \(0.607870\pi\) | |||||||
\(440\) | −14164.6 | −1.53471 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11058.8 | 1.18605 | 0.593025 | − | 0.805184i | \(-0.297933\pi\) | ||||
0.593025 | + | 0.805184i | \(0.297933\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1847.21 | −0.196777 | ||||||||
\(446\) | −4950.73 | −0.525614 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4457.72 | −0.470106 | ||||||||
\(449\) | −242.012 | −0.0254371 | −0.0127185 | − | 0.999919i | \(-0.504049\pi\) | ||||
−0.0127185 | + | 0.999919i | \(0.504049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23371.7 | 2.44020 | ||||||||
\(452\) | −2839.88 | −0.295524 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2918.89 | 0.301741 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11052.2 | 1.13129 | 0.565644 | − | 0.824650i | \(-0.308628\pi\) | ||||
0.565644 | + | 0.824650i | \(0.308628\pi\) | |||||||
\(458\) | −1865.94 | −0.190370 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5886.99 | −0.596700 | ||||||||
\(461\) | 273.763 | 0.0276582 | 0.0138291 | − | 0.999904i | \(-0.495598\pi\) | ||||
0.0138291 | + | 0.999904i | \(0.495598\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11579.2 | −1.16227 | −0.581134 | − | 0.813808i | \(-0.697391\pi\) | ||||
−0.581134 | + | 0.813808i | \(0.697391\pi\) | |||||||
\(464\) | 1719.25 | 0.172013 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2563.34 | 0.254817 | ||||||||
\(467\) | −902.915 | −0.0894688 | −0.0447344 | − | 0.998999i | \(-0.514244\pi\) | ||||
−0.0447344 | + | 0.998999i | \(0.514244\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8463.59 | 0.833289 | ||||||||
\(470\) | 964.604 | 0.0946678 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1975.07 | −0.192606 | ||||||||
\(473\) | 26853.4 | 2.61040 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16813.1 | −1.62408 | ||||||||
\(476\) | 6526.71 | 0.628469 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5039.88 | −0.482257 | ||||||||
\(479\) | −12068.8 | −1.15122 | −0.575611 | − | 0.817723i | \(-0.695236\pi\) | ||||
−0.575611 | + | 0.817723i | \(0.695236\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −3725.70 | −0.352077 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21505.1 | −2.01964 | ||||||||
\(485\) | 8580.66 | 0.803356 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11492.5 | −1.06936 | −0.534678 | − | 0.845056i | \(-0.679567\pi\) | ||||
−0.534678 | + | 0.845056i | \(0.679567\pi\) | |||||||
\(488\) | −3710.54 | −0.344197 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1144.93 | −0.105557 | ||||||||
\(491\) | −15704.2 | −1.44342 | −0.721710 | − | 0.692196i | \(-0.756643\pi\) | ||||
−0.721710 | + | 0.692196i | \(0.756643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1710.95 | −0.156303 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3934.25 | −0.356156 | ||||||||
\(497\) | −1883.48 | −0.169991 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9019.80 | −0.809181 | −0.404591 | − | 0.914498i | \(-0.632586\pi\) | ||||
−0.404591 | + | 0.914498i | \(0.632586\pi\) | |||||||
\(500\) | −1181.23 | −0.105653 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3275.83 | 0.291250 | ||||||||
\(503\) | 6033.84 | 0.534862 | 0.267431 | − | 0.963577i | \(-0.413825\pi\) | ||||
0.267431 | + | 0.963577i | \(0.413825\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7156.06 | −0.630576 | ||||||||
\(506\) | 3210.87 | 0.282096 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3134.44 | −0.273757 | ||||||||
\(509\) | 22451.5 | 1.95510 | 0.977551 | − | 0.210699i | \(-0.0675741\pi\) | ||||
0.977551 | + | 0.210699i | \(0.0675741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1299.48 | −0.112497 | ||||||||
\(512\) | 11720.8 | 1.01170 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6897.06 | 0.591860 | ||||||||
\(515\) | −17358.9 | −1.48529 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4475.11 | 0.380687 | ||||||||
\(518\) | −1490.95 | −0.126464 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15674.7 | −1.31808 | −0.659040 | − | 0.752108i | \(-0.729037\pi\) | ||||
−0.659040 | + | 0.752108i | \(0.729037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13510.8 | 1.12961 | 0.564804 | − | 0.825225i | \(-0.308952\pi\) | ||||
0.564804 | + | 0.825225i | \(0.308952\pi\) | |||||||
\(524\) | 11864.7 | 0.989142 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4275.13 | 0.354381 | ||||||||
\(527\) | 3915.27 | 0.323627 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9341.16 | −0.767746 | ||||||||
\(530\) | 3215.55 | 0.263537 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 21667.4 | 1.76580 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9324.89 | 0.753551 | ||||||||
\(536\) | −5717.94 | −0.460778 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4905.60 | −0.393114 | ||||||||
\(539\) | −5311.73 | −0.424475 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12103.6 | −0.961875 | −0.480937 | − | 0.876755i | \(-0.659704\pi\) | ||||
−0.480937 | + | 0.876755i | \(0.659704\pi\) | |||||||
\(542\) | −2727.43 | −0.216149 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6736.49 | −0.530928 | ||||||||
\(545\) | 21997.2 | 1.72891 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15228.6 | −1.19036 | −0.595181 | − | 0.803592i | \(-0.702920\pi\) | ||||
−0.595181 | + | 0.803592i | \(0.702920\pi\) | |||||||
\(548\) | −14083.6 | −1.09785 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6905.95 | −0.535401 | ||||||||
\(551\) | −5680.03 | −0.439160 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5909.79 | −0.454448 | ||||||||
\(554\) | −701.014 | −0.0537603 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20223.5 | −1.54257 | ||||||||
\(557\) | 23596.9 | 1.79503 | 0.897516 | − | 0.440982i | \(-0.145370\pi\) | ||||
0.897516 | + | 0.440982i | \(0.145370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −14173.6 | −1.06954 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6458.63 | −0.484770 | ||||||||
\(563\) | −7941.62 | −0.594493 | −0.297246 | − | 0.954801i | \(-0.596068\pi\) | ||||
−0.297246 | + | 0.954801i | \(0.596068\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6137.40 | −0.456996 | ||||||||
\(566\) | −8288.63 | −0.615542 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1272.47 | 0.0939991 | ||||||||
\(569\) | −2274.65 | −0.167590 | −0.0837948 | − | 0.996483i | \(-0.526704\pi\) | ||||
−0.0837948 | + | 0.996483i | \(0.526704\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4499.84 | −0.329794 | −0.164897 | − | 0.986311i | \(-0.552729\pi\) | ||||
−0.164897 | + | 0.986311i | \(0.552729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6702.69 | −0.487395 | ||||||||
\(575\) | −6077.82 | −0.440804 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25253.3 | 1.82202 | 0.911011 | − | 0.412381i | \(-0.135303\pi\) | ||||
0.911011 | + | 0.412381i | \(0.135303\pi\) | |||||||
\(578\) | −2707.08 | −0.194809 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4277.55 | 0.306234 | ||||||||
\(581\) | −7694.31 | −0.549421 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14918.0 | 1.05976 | ||||||||
\(584\) | 877.921 | 0.0622066 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1637.73 | 0.115450 | ||||||||
\(587\) | −11285.2 | −0.793508 | −0.396754 | − | 0.917925i | \(-0.629863\pi\) | ||||
−0.396754 | + | 0.917925i | \(0.629863\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12997.9 | 0.909289 | ||||||||
\(590\) | −2015.72 | −0.140654 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3514.49 | −0.243994 | ||||||||
\(593\) | 12824.5 | 0.888090 | 0.444045 | − | 0.896005i | \(-0.353543\pi\) | ||||
0.444045 | + | 0.896005i | \(0.353543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14105.2 | 0.971859 | ||||||||
\(596\) | −5709.98 | −0.392433 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26180.3 | 1.78581 | 0.892905 | − | 0.450245i | \(-0.148664\pi\) | ||||
0.892905 | + | 0.450245i | \(0.148664\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16012.6 | 1.08680 | 0.543399 | − | 0.839474i | \(-0.317137\pi\) | ||||
0.543399 | + | 0.839474i | \(0.317137\pi\) | |||||||
\(602\) | −7701.20 | −0.521391 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1159.57 | −0.0781166 | ||||||||
\(605\) | −46475.8 | −3.12316 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9531.48 | −0.637349 | −0.318674 | − | 0.947864i | \(-0.603238\pi\) | ||||
−0.318674 | + | 0.947864i | \(0.603238\pi\) | |||||||
\(608\) | −22363.9 | −1.49174 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3786.91 | −0.251356 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10187.1 | −0.671211 | −0.335605 | − | 0.942003i | \(-0.608941\pi\) | ||||
−0.335605 | + | 0.942003i | \(0.608941\pi\) | |||||||
\(614\) | −4883.30 | −0.320967 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18846.0 | 1.23267 | ||||||||
\(617\) | 8012.62 | 0.522813 | 0.261407 | − | 0.965229i | \(-0.415814\pi\) | ||||
0.261407 | + | 0.965229i | \(0.415814\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1886.59 | −0.122501 | −0.0612506 | − | 0.998122i | \(-0.519509\pi\) | ||||
−0.0612506 | + | 0.998122i | \(0.519509\pi\) | |||||||
\(620\) | −9788.58 | −0.634063 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5747.94 | −0.370533 | ||||||||
\(623\) | 2457.70 | 0.158051 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16844.5 | −1.07805 | ||||||||
\(626\) | 6599.38 | 0.421349 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2448.18 | 0.155562 | ||||||||
\(629\) | 3497.53 | 0.221710 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14956.1 | −0.943569 | −0.471784 | − | 0.881714i | \(-0.656390\pi\) | ||||
−0.471784 | + | 0.881714i | \(0.656390\pi\) | |||||||
\(632\) | 3992.61 | 0.251293 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8785.57 | −0.550346 | ||||||||
\(635\) | −6773.99 | −0.423335 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2333.06 | −0.144775 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 21895.5 | 1.35234 | ||||||||
\(641\) | −23691.7 | −1.45985 | −0.729927 | − | 0.683525i | \(-0.760446\pi\) | ||||
−0.729927 | + | 0.683525i | \(0.760446\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13651.3 | −0.837254 | −0.418627 | − | 0.908158i | \(-0.637489\pi\) | ||||
−0.418627 | + | 0.908158i | \(0.637489\pi\) | |||||||
\(644\) | 7832.62 | 0.479268 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5975.60 | 0.363943 | ||||||||
\(647\) | 18132.3 | 1.10178 | 0.550892 | − | 0.834577i | \(-0.314288\pi\) | ||||
0.550892 | + | 0.834577i | \(0.314288\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9351.59 | −0.565612 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3984.36 | −0.239324 | ||||||||
\(653\) | −6363.47 | −0.381351 | −0.190675 | − | 0.981653i | \(-0.561068\pi\) | ||||
−0.190675 | + | 0.981653i | \(0.561068\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25641.3 | 1.52960 | ||||||||
\(656\) | −15799.7 | −0.940358 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1283.40 | −0.0760369 | ||||||||
\(659\) | 1051.43 | 0.0621518 | 0.0310759 | − | 0.999517i | \(-0.490107\pi\) | ||||
0.0310759 | + | 0.999517i | \(0.490107\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8119.75 | −0.477794 | −0.238897 | − | 0.971045i | \(-0.576786\pi\) | ||||
−0.238897 | + | 0.971045i | \(0.576786\pi\) | |||||||
\(662\) | −5296.12 | −0.310936 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5198.21 | 0.303810 | ||||||||
\(665\) | 46826.5 | 2.73061 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2053.29 | −0.119196 | ||||||||
\(668\) | −22451.9 | −1.30043 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5835.62 | −0.336492 | ||||||||
\(671\) | −17568.7 | −1.01078 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −190.264 | −0.0108977 | −0.00544885 | − | 0.999985i | \(-0.501734\pi\) | ||||
−0.00544885 | + | 0.999985i | \(0.501734\pi\) | |||||||
\(674\) | 1135.79 | 0.0649093 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4861.93 | −0.276010 | −0.138005 | − | 0.990431i | \(-0.544069\pi\) | ||||
−0.138005 | + | 0.990431i | \(0.544069\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11416.5 | −0.645253 | ||||||||
\(680\) | −9529.35 | −0.537403 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5338.88 | 0.299760 | ||||||||
\(683\) | −14539.6 | −0.814556 | −0.407278 | − | 0.913304i | \(-0.633522\pi\) | ||||
−0.407278 | + | 0.913304i | \(0.633522\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30436.8 | −1.69771 | ||||||||
\(686\) | −4953.40 | −0.275688 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18153.4 | −1.00595 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22106.5 | 1.21703 | 0.608517 | − | 0.793541i | \(-0.291765\pi\) | ||||
0.608517 | + | 0.793541i | \(0.291765\pi\) | |||||||
\(692\) | 23796.0 | 1.30721 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4999.66 | −0.273465 | ||||||||
\(695\) | −43706.0 | −2.38541 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15723.4 | 0.854474 | ||||||||
\(698\) | 1260.50 | 0.0683534 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −16846.4 | −0.909620 | ||||||||
\(701\) | −229.971 | −0.0123907 | −0.00619535 | − | 0.999981i | \(-0.501972\pi\) | ||||
−0.00619535 | + | 0.999981i | \(0.501972\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11611.1 | 0.622934 | ||||||||
\(704\) | 14259.4 | 0.763380 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5477.13 | −0.291975 | ||||||||
\(707\) | 9521.12 | 0.506476 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4802.22 | 0.254374 | 0.127187 | − | 0.991879i | \(-0.459405\pi\) | ||||
0.127187 | + | 0.991879i | \(0.459405\pi\) | |||||||
\(710\) | 1298.66 | 0.0686446 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1660.40 | −0.0873965 | ||||||||
\(713\) | 4698.66 | 0.246797 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23717.6 | −1.23795 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7168.09 | −0.372578 | ||||||||
\(719\) | 11016.9 | 0.571435 | 0.285718 | − | 0.958314i | \(-0.407768\pi\) | ||||
0.285718 | + | 0.958314i | \(0.407768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23096.0 | 1.19298 | ||||||||
\(722\) | 13545.6 | 0.698221 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −544.125 | −0.0279313 | ||||||||
\(725\) | 4416.21 | 0.226226 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13498.2 | −0.688612 | −0.344306 | − | 0.938857i | \(-0.611886\pi\) | ||||
−0.344306 | + | 0.938857i | \(0.611886\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 895.990 | 0.0454275 | ||||||||
\(731\) | 18065.8 | 0.914073 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17014.7 | 0.857368 | 0.428684 | − | 0.903455i | \(-0.358977\pi\) | ||||
0.428684 | + | 0.903455i | \(0.358977\pi\) | |||||||
\(734\) | 1548.88 | 0.0778888 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8084.38 | −0.404883 | ||||||||
\(737\) | −27073.4 | −1.35313 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13392.6 | −0.666651 | −0.333326 | − | 0.942812i | \(-0.608171\pi\) | ||||
−0.333326 | + | 0.942812i | \(0.608171\pi\) | |||||||
\(740\) | −8744.19 | −0.434382 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4278.27 | −0.211672 | ||||||||
\(743\) | 11796.5 | 0.582467 | 0.291233 | − | 0.956652i | \(-0.405934\pi\) | ||||
0.291233 | + | 0.956652i | \(0.405934\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12340.1 | −0.606854 | ||||||||
\(746\) | 1716.05 | 0.0842214 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20877.6 | −1.02054 | ||||||||
\(749\) | −12406.7 | −0.605250 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12450.5 | −0.604961 | −0.302480 | − | 0.953156i | \(-0.597815\pi\) | ||||
−0.302480 | + | 0.953156i | \(0.597815\pi\) | |||||||
\(752\) | −3025.26 | −0.146702 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2506.01 | −0.120799 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7029.84 | −0.337522 | −0.168761 | − | 0.985657i | \(-0.553977\pi\) | ||||
−0.168761 | + | 0.985657i | \(0.553977\pi\) | |||||||
\(758\) | 10703.0 | 0.512865 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −31635.6 | −1.50993 | ||||||||
\(761\) | 17740.6 | 0.845067 | 0.422533 | − | 0.906347i | \(-0.361141\pi\) | ||||
0.422533 | + | 0.906347i | \(0.361141\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29267.2 | −1.38866 | ||||||||
\(764\) | −29159.1 | −1.38081 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6124.94 | 0.288907 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31976.5 | −1.49948 | −0.749741 | − | 0.661732i | \(-0.769822\pi\) | ||||
−0.749741 | + | 0.661732i | \(0.769822\pi\) | |||||||
\(770\) | 19233.9 | 0.900184 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6210.51 | 0.289535 | ||||||||
\(773\) | −2135.11 | −0.0993463 | −0.0496732 | − | 0.998766i | \(-0.515818\pi\) | ||||
−0.0496732 | + | 0.998766i | \(0.515818\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10105.9 | −0.468405 | ||||||||
\(776\) | 7712.93 | 0.356802 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13105.0 | −0.603902 | ||||||||
\(779\) | 52198.9 | 2.40080 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6024.89 | 0.276040 | ||||||||
\(782\) | 2160.14 | 0.0987804 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3590.83 | 0.163576 | ||||||||
\(785\) | 5290.89 | 0.240560 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11704.4 | 0.530134 | 0.265067 | − | 0.964230i | \(-0.414606\pi\) | ||||
0.265067 | + | 0.964230i | \(0.414606\pi\) | |||||||
\(788\) | 13512.9 | 0.610885 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4074.78 | 0.183512 | ||||||||
\(791\) | 8165.80 | 0.367057 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 3274.37 | 0.146351 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19944.9 | −0.888102 | ||||||||
\(797\) | 149.733 | 0.00665474 | 0.00332737 | − | 0.999994i | \(-0.498941\pi\) | ||||
0.00332737 | + | 0.999994i | \(0.498941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3010.66 | 0.133304 | ||||||||
\(800\) | 17387.9 | 0.768443 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −458.089 | −0.0201692 | ||||||||
\(803\) | 4156.79 | 0.182677 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16927.4 | 0.741135 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6432.40 | −0.280063 | ||||||||
\(809\) | −23520.8 | −1.02219 | −0.511093 | − | 0.859526i | \(-0.670759\pi\) | ||||
−0.511093 | + | 0.859526i | \(0.670759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29604.8 | −1.28183 | −0.640915 | − | 0.767612i | \(-0.721445\pi\) | ||||
−0.640915 | + | 0.767612i | \(0.721445\pi\) | |||||||
\(812\) | −5691.27 | −0.245966 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4769.25 | 0.205359 | ||||||||
\(815\) | −8610.79 | −0.370089 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 59975.0 | 2.56825 | ||||||||
\(818\) | 9593.44 | 0.410057 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −39310.3 | −1.67412 | ||||||||
\(821\) | 43034.7 | 1.82938 | 0.914691 | − | 0.404154i | \(-0.132434\pi\) | ||||
0.914691 | + | 0.404154i | \(0.132434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5584.95 | 0.236548 | 0.118274 | − | 0.992981i | \(-0.462264\pi\) | ||||
0.118274 | + | 0.992981i | \(0.462264\pi\) | |||||||
\(824\) | −15603.5 | −0.659675 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2681.91 | 0.112973 | ||||||||
\(827\) | −4788.13 | −0.201330 | −0.100665 | − | 0.994920i | \(-0.532097\pi\) | ||||
−0.100665 | + | 0.994920i | \(0.532097\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32392.2 | −1.35709 | −0.678546 | − | 0.734558i | \(-0.737390\pi\) | ||||
−0.678546 | + | 0.734558i | \(0.737390\pi\) | |||||||
\(830\) | 5305.20 | 0.221863 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3573.50 | −0.148637 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48521.8 | −2.01098 | ||||||||
\(836\) | −69309.9 | −2.86738 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1564.51 | 0.0644929 | ||||||||
\(839\) | 13598.9 | 0.559577 | 0.279788 | − | 0.960062i | \(-0.409736\pi\) | ||||
0.279788 | + | 0.960062i | \(0.409736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22897.1 | −0.938827 | ||||||||
\(842\) | −8041.31 | −0.329123 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5073.82 | −0.206929 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 61835.9 | 2.50851 | ||||||||
\(848\) | −10084.8 | −0.408390 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4646.02 | −0.187479 | ||||||||
\(851\) | 4197.34 | 0.169075 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41037.0 | −1.64722 | −0.823611 | − | 0.567155i | \(-0.808044\pi\) | ||||
−0.823611 | + | 0.567155i | \(0.808044\pi\) | |||||||
\(854\) | 5038.47 | 0.201889 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8381.89 | 0.334681 | ||||||||
\(857\) | 39959.3 | 1.59275 | 0.796374 | − | 0.604804i | \(-0.206749\pi\) | ||||
0.796374 | + | 0.604804i | \(0.206749\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32570.5 | −1.29371 | −0.646853 | − | 0.762615i | \(-0.723915\pi\) | ||||
−0.646853 | + | 0.762615i | \(0.723915\pi\) | |||||||
\(860\) | −45166.4 | −1.79088 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7412.72 | 0.292898 | ||||||||
\(863\) | −16951.8 | −0.668652 | −0.334326 | − | 0.942457i | \(-0.608509\pi\) | ||||
−0.334326 | + | 0.942457i | \(0.608509\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 51426.6 | 2.02145 | ||||||||
\(866\) | −3783.69 | −0.148470 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13023.7 | 0.509277 | ||||||||
\(869\) | 18904.3 | 0.737955 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 19772.7 | 0.767876 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7171.24 | 0.277541 | ||||||||
\(875\) | 3396.52 | 0.131227 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45939.2 | 1.76882 | 0.884411 | − | 0.466709i | \(-0.154561\pi\) | ||||
0.884411 | + | 0.466709i | \(0.154561\pi\) | |||||||
\(878\) | −5610.22 | −0.215644 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 45338.5 | 1.73677 | ||||||||
\(881\) | −37960.5 | −1.45167 | −0.725836 | − | 0.687868i | \(-0.758547\pi\) | ||||
−0.725836 | + | 0.687868i | \(0.758547\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43172.9 | 1.64539 | 0.822697 | − | 0.568480i | \(-0.192468\pi\) | ||||
0.822697 | + | 0.568480i | \(0.192468\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10145.1 | 0.384684 | ||||||||
\(887\) | −28706.3 | −1.08665 | −0.543327 | − | 0.839521i | \(-0.682836\pi\) | ||||
−0.543327 | + | 0.839521i | \(0.682836\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9012.78 | 0.340021 | ||||||||
\(890\) | −1694.58 | −0.0638229 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 38631.4 | 1.45008 | ||||||||
\(893\) | 9994.83 | 0.374540 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51257.3 | −1.91435 | ||||||||
\(896\) | −29131.9 | −1.08619 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −222.015 | −0.00825027 | ||||||||
\(899\) | −3414.10 | −0.126659 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10036.2 | 0.371091 | ||||||||
\(902\) | 21440.6 | 0.791456 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5516.75 | −0.202969 | ||||||||
\(905\) | −1175.93 | −0.0431927 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22356.1 | −0.818435 | −0.409218 | − | 0.912437i | \(-0.634198\pi\) | ||||
−0.409218 | + | 0.912437i | \(0.634198\pi\) | |||||||
\(908\) | −22776.6 | −0.832454 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6953.80 | −0.252897 | −0.126449 | − | 0.991973i | \(-0.540358\pi\) | ||||
−0.126449 | + | 0.991973i | \(0.540358\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24612.6 | 0.892176 | ||||||||
\(914\) | 10139.0 | 0.366923 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14560.2 | 0.525200 | ||||||||
\(917\) | −34115.7 | −1.22857 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40625.2 | 1.45822 | 0.729108 | − | 0.684399i | \(-0.239935\pi\) | ||||
0.729108 | + | 0.684399i | \(0.239935\pi\) | |||||||
\(920\) | −11436.0 | −0.409821 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 251.143 | 0.00897068 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9027.64 | −0.320894 | ||||||||
\(926\) | −10622.4 | −0.376971 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5874.20 | 0.207791 | ||||||||
\(929\) | 42813.8 | 1.51203 | 0.756014 | − | 0.654555i | \(-0.227144\pi\) | ||||
0.756014 | + | 0.654555i | \(0.227144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11863.3 | −0.417621 | ||||||||
\(932\) | −20002.2 | −0.702998 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −828.311 | −0.0290184 | ||||||||
\(935\) | −45119.7 | −1.57815 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43484.1 | 1.51608 | 0.758038 | − | 0.652210i | \(-0.226158\pi\) | ||||
0.758038 | + | 0.652210i | \(0.226158\pi\) | |||||||
\(938\) | 7764.28 | 0.270269 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7526.97 | −0.261173 | ||||||||
\(941\) | −7108.58 | −0.246263 | −0.123131 | − | 0.992390i | \(-0.539294\pi\) | ||||
−0.123131 | + | 0.992390i | \(0.539294\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18869.5 | 0.651618 | ||||||||
\(944\) | 6321.85 | 0.217965 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24634.6 | 0.846660 | ||||||||
\(947\) | 1938.99 | 0.0665351 | 0.0332676 | − | 0.999446i | \(-0.489409\pi\) | ||||
0.0332676 | + | 0.999446i | \(0.489409\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −15423.9 | −0.526756 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12678.8 | 0.431640 | ||||||||
\(953\) | 47806.7 | 1.62498 | 0.812492 | − | 0.582972i | \(-0.198110\pi\) | ||||
0.812492 | + | 0.582972i | \(0.198110\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63017.1 | −2.13527 | ||||||||
\(956\) | 39327.1 | 1.33047 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11071.6 | −0.373388 | ||||||||
\(959\) | 40496.1 | 1.36359 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21978.3 | −0.737750 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 29072.3 | 0.971323 | ||||||||
\(965\) | 13421.8 | 0.447735 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2832.71 | 0.0942025 | 0.0471013 | − | 0.998890i | \(-0.485002\pi\) | ||||
0.0471013 | + | 0.998890i | \(0.485002\pi\) | |||||||
\(968\) | −41775.8 | −1.38711 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7871.68 | 0.260561 | ||||||||
\(971\) | 41276.3 | 1.36418 | 0.682090 | − | 0.731268i | \(-0.261071\pi\) | ||||
0.682090 | + | 0.731268i | \(0.261071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 58150.7 | 1.91596 | ||||||||
\(974\) | −10542.9 | −0.346835 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11876.8 | 0.389515 | ||||||||
\(977\) | 4278.89 | 0.140117 | 0.0700583 | − | 0.997543i | \(-0.477681\pi\) | ||||
0.0700583 | + | 0.997543i | \(0.477681\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7861.70 | −0.256651 | ||||||||
\(980\) | 8934.12 | 0.291214 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14406.6 | −0.468159 | ||||||||
\(983\) | 22652.9 | 0.735011 | 0.367505 | − | 0.930021i | \(-0.380212\pi\) | ||||
0.367505 | + | 0.930021i | \(0.380212\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29203.4 | 0.944667 | ||||||||
\(986\) | −1569.58 | −0.0506953 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21680.5 | 0.697068 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22060.2 | 0.707131 | 0.353565 | − | 0.935410i | \(-0.384969\pi\) | ||||
0.353565 | + | 0.935410i | \(0.384969\pi\) | |||||||
\(992\) | −13442.3 | −0.430235 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1727.86 | −0.0551351 | ||||||||
\(995\) | −43103.9 | −1.37335 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35635.5 | 1.13198 | 0.565992 | − | 0.824411i | \(-0.308493\pi\) | ||||
0.565992 | + | 0.824411i | \(0.308493\pi\) | |||||||
\(998\) | −8274.52 | −0.262450 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1521.4.a.bk.1.6 | 10 | ||
3.2 | odd | 2 | 507.4.a.r.1.5 | 10 | |||
13.2 | odd | 12 | 117.4.q.e.82.3 | 10 | |||
13.7 | odd | 12 | 117.4.q.e.10.3 | 10 | |||
13.12 | even | 2 | inner | 1521.4.a.bk.1.5 | 10 | ||
39.2 | even | 12 | 39.4.j.c.4.3 | ✓ | 10 | ||
39.5 | even | 4 | 507.4.b.i.337.6 | 10 | |||
39.8 | even | 4 | 507.4.b.i.337.5 | 10 | |||
39.20 | even | 12 | 39.4.j.c.10.3 | yes | 10 | ||
39.38 | odd | 2 | 507.4.a.r.1.6 | 10 | |||
156.59 | odd | 12 | 624.4.bv.h.49.4 | 10 | |||
156.119 | odd | 12 | 624.4.bv.h.433.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.3 | ✓ | 10 | 39.2 | even | 12 | ||
39.4.j.c.10.3 | yes | 10 | 39.20 | even | 12 | ||
117.4.q.e.10.3 | 10 | 13.7 | odd | 12 | |||
117.4.q.e.82.3 | 10 | 13.2 | odd | 12 | |||
507.4.a.r.1.5 | 10 | 3.2 | odd | 2 | |||
507.4.a.r.1.6 | 10 | 39.38 | odd | 2 | |||
507.4.b.i.337.5 | 10 | 39.8 | even | 4 | |||
507.4.b.i.337.6 | 10 | 39.5 | even | 4 | |||
624.4.bv.h.49.4 | 10 | 156.59 | odd | 12 | |||
624.4.bv.h.433.2 | 10 | 156.119 | odd | 12 | |||
1521.4.a.bk.1.5 | 10 | 13.12 | even | 2 | inner | ||
1521.4.a.bk.1.6 | 10 | 1.1 | even | 1 | trivial |