Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,4,Mod(1,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.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: | \(12.7444125612\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 13.2337 | 1.18366 | 0.591829 | − | 0.806064i | \(-0.298406\pi\) | ||||
0.591829 | + | 0.806064i | \(0.298406\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.23369 | −0.282593 | −0.141296 | − | 0.989967i | \(-0.545127\pi\) | ||||
−0.141296 | + | 0.989967i | \(0.545127\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.0274101 | −0.0137051 | − | 0.999906i | \(-0.504363\pi\) | ||||
−0.0137051 | + | 0.999906i | \(0.504363\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 84.9348 | 1.81205 | 0.906025 | − | 0.423223i | \(-0.139101\pi\) | ||||
0.906025 | + | 0.423223i | \(0.139101\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −40.9348 | −0.584008 | −0.292004 | − | 0.956417i | \(-0.594322\pi\) | ||||
−0.292004 | + | 0.956417i | \(0.594322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 57.5326 | 0.694678 | 0.347339 | − | 0.937740i | \(-0.387085\pi\) | ||||
0.347339 | + | 0.937740i | \(0.387085\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −114.935 | −1.04198 | −0.520990 | − | 0.853563i | \(-0.674437\pi\) | ||||
−0.520990 | + | 0.853563i | \(0.674437\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 50.1305 | 0.401044 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 202.467 | 1.29646 | 0.648228 | − | 0.761446i | \(-0.275510\pi\) | ||||
0.648228 | + | 0.761446i | \(0.275510\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 274.168 | 1.58846 | 0.794228 | − | 0.607620i | \(-0.207876\pi\) | ||||
0.794228 | + | 0.607620i | \(0.207876\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −69.2610 | −0.334493 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 242.935 | 1.07941 | 0.539706 | − | 0.841854i | \(-0.318535\pi\) | ||||
0.539706 | + | 0.841854i | \(0.318535\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 328.337 | 1.25067 | 0.625337 | − | 0.780355i | \(-0.284962\pi\) | ||||
0.625337 | + | 0.780355i | \(0.284962\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 281.272 | 0.997524 | 0.498762 | − | 0.866739i | \(-0.333788\pi\) | ||||
0.498762 | + | 0.866739i | \(0.333788\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −23.8695 | −0.0740793 | −0.0370396 | − | 0.999314i | \(-0.511793\pi\) | ||||
−0.0370396 | + | 0.999314i | \(0.511793\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −315.609 | −0.920141 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −300.038 | −0.777611 | −0.388805 | − | 0.921320i | \(-0.627112\pi\) | ||||
−0.388805 | + | 0.921320i | \(0.627112\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.2337 | −0.0324442 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −753.609 | −1.66291 | −0.831453 | − | 0.555595i | \(-0.812491\pi\) | ||||
−0.831453 | + | 0.555595i | \(0.812491\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 495.478 | 1.03999 | 0.519996 | − | 0.854169i | \(-0.325934\pi\) | ||||
0.519996 | + | 0.854169i | \(0.325934\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1124.00 | 2.14485 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −409.945 | −0.747504 | −0.373752 | − | 0.927529i | \(-0.621929\pi\) | ||||
−0.373752 | + | 0.927529i | \(0.621929\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1114.80 | −1.86342 | −0.931711 | − | 0.363201i | \(-0.881684\pi\) | ||||
−0.931711 | + | 0.363201i | \(0.881684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −287.000 | −0.460148 | −0.230074 | − | 0.973173i | \(-0.573897\pi\) | ||||
−0.230074 | + | 0.973173i | \(0.573897\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.23369 | 0.00774590 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1231.48 | −1.75382 | −0.876912 | − | 0.480651i | \(-0.840400\pi\) | ||||
−0.876912 | + | 0.480651i | \(0.840400\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 942.478 | 1.24639 | 0.623195 | − | 0.782066i | \(-0.285834\pi\) | ||||
0.623195 | + | 0.782066i | \(0.285834\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −541.718 | −0.691265 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 190.206 | 0.226537 | 0.113269 | − | 0.993564i | \(-0.463868\pi\) | ||||
0.113269 | + | 0.993564i | \(0.463868\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −444.522 | −0.512072 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 761.369 | 0.822261 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −306.870 | −0.321215 | −0.160608 | − | 0.987018i | \(-0.551345\pi\) | ||||
−0.160608 | + | 0.987018i | \(0.551345\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 672.897 | 0.662928 | 0.331464 | − | 0.943468i | \(-0.392457\pi\) | ||||
0.331464 | + | 0.943468i | \(0.392457\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 840.152 | 0.803715 | 0.401857 | − | 0.915702i | \(-0.368365\pi\) | ||||
0.401857 | + | 0.915702i | \(0.368365\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1658.09 | −1.49807 | −0.749034 | − | 0.662532i | \(-0.769482\pi\) | ||||
−0.749034 | + | 0.662532i | \(0.769482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1263.76 | −1.11052 | −0.555258 | − | 0.831678i | \(-0.687381\pi\) | ||||
−0.555258 | + | 0.831678i | \(0.687381\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −474.358 | −0.394901 | −0.197451 | − | 0.980313i | \(-0.563266\pi\) | ||||
−0.197451 | + | 0.980313i | \(0.563266\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1521.01 | −1.23335 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 214.240 | 0.165036 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.00 | −0.999249 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −990.800 | −0.708959 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −560.375 | −0.391537 | −0.195769 | − | 0.980650i | \(-0.562720\pi\) | ||||
−0.195769 | + | 0.980650i | \(0.562720\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −789.304 | −0.526426 | −0.263213 | − | 0.964738i | \(-0.584782\pi\) | ||||
−0.263213 | + | 0.964738i | \(0.584782\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −301.108 | −0.196311 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1330.47 | 0.829704 | 0.414852 | − | 0.909889i | \(-0.363833\pi\) | ||||
0.414852 | + | 0.909889i | \(0.363833\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3139.37 | 1.91567 | 0.957834 | − | 0.287323i | \(-0.0927653\pi\) | ||||
0.957834 | + | 0.287323i | \(0.0927653\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −84.9348 | −0.0496685 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2679.39 | 1.53456 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2666.24 | −1.46595 | −0.732977 | − | 0.680253i | \(-0.761870\pi\) | ||||
−0.732977 | + | 0.680253i | \(0.761870\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 479.407 | 0.258368 | 0.129184 | − | 0.991621i | \(-0.458764\pi\) | ||||
0.129184 | + | 0.991621i | \(0.458764\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3628.26 | 1.88019 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2004.83 | −1.01912 | −0.509562 | − | 0.860434i | \(-0.670193\pi\) | ||||
−0.509562 | + | 0.860434i | \(0.670193\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 601.533 | 0.294456 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −832.043 | −0.399820 | −0.199910 | − | 0.979814i | \(-0.564065\pi\) | ||||
−0.199910 | + | 0.979814i | \(0.564065\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2871.65 | 1.33063 | 0.665314 | − | 0.746563i | \(-0.268297\pi\) | ||||
0.665314 | + | 0.746563i | \(0.268297\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5016.91 | 2.28353 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3579.44 | −1.57306 | −0.786531 | − | 0.617551i | \(-0.788125\pi\) | ||||
−0.786531 | + | 0.617551i | \(0.788125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −262.367 | −0.113332 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2162.09 | 0.902804 | 0.451402 | − | 0.892321i | \(-0.350924\pi\) | ||||
0.451402 | + | 0.892321i | \(0.350924\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1740.26 | 0.714655 | 0.357328 | − | 0.933979i | \(-0.383688\pi\) | ||||
0.357328 | + | 0.933979i | \(0.383688\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3214.92 | 1.27765 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 40.9348 | 0.0160077 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2537.80 | −0.961408 | −0.480704 | − | 0.876883i | \(-0.659619\pi\) | ||||
−0.480704 | + | 0.876883i | \(0.659619\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 190.348 | 0.0709923 | 0.0354962 | − | 0.999370i | \(-0.488699\pi\) | ||||
0.0354962 | + | 0.999370i | \(0.488699\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5314.25 | −1.92195 | −0.960977 | − | 0.276629i | \(-0.910783\pi\) | ||||
−0.960977 | + | 0.276629i | \(0.910783\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3787.15 | 1.34906 | 0.674532 | − | 0.738246i | \(-0.264346\pi\) | ||||
0.674532 | + | 0.738246i | \(0.264346\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1059.65 | −0.366369 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4345.11 | 1.48037 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −57.5326 | −0.0190412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2442.05 | 0.796768 | 0.398384 | − | 0.917219i | \(-0.369571\pi\) | ||||
0.398384 | + | 0.917219i | \(0.369571\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3722.26 | 1.18073 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1434.91 | −0.448886 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3476.78 | −1.05825 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2329.87 | −0.699639 | −0.349820 | − | 0.936817i | \(-0.613757\pi\) | ||||
−0.349820 | + | 0.936817i | \(0.613757\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1326.39 | −0.387822 | −0.193911 | − | 0.981019i | \(-0.562117\pi\) | ||||
−0.193911 | + | 0.981019i | \(0.562117\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1544.13 | −0.445585 | −0.222793 | − | 0.974866i | \(-0.571517\pi\) | ||||
−0.222793 | + | 0.974866i | \(0.571517\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2266.32 | 0.637216 | 0.318608 | − | 0.947887i | \(-0.396785\pi\) | ||||
0.318608 | + | 0.947887i | \(0.396785\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −315.882 | −0.0876844 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 51.6752 | 0.0139857 | 0.00699286 | − | 0.999976i | \(-0.497774\pi\) | ||||
0.00699286 | + | 0.999976i | \(0.497774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2323.95 | −0.621158 | −0.310579 | − | 0.950548i | \(-0.600523\pi\) | ||||
−0.310579 | + | 0.950548i | \(0.600523\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4176.66 | −1.08913 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4886.52 | 1.25879 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6958.52 | 1.74987 | 0.874936 | − | 0.484239i | \(-0.160903\pi\) | ||||
0.874936 | + | 0.484239i | \(0.160903\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 114.935 | 0.0285608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2974.91 | 0.722062 | 0.361031 | − | 0.932554i | \(-0.382425\pi\) | ||||
0.361031 | + | 0.932554i | \(0.382425\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1271.44 | −0.305034 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 116.847 | 0.0273958 | 0.0136979 | − | 0.999906i | \(-0.495640\pi\) | ||||
0.0136979 | + | 0.999906i | \(0.495640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3970.61 | −0.920425 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3334.81 | 0.755863 | 0.377932 | − | 0.925834i | \(-0.376635\pi\) | ||||
0.377932 | + | 0.925834i | \(0.376635\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3120.23 | −0.699412 | −0.349706 | − | 0.936860i | \(-0.613718\pi\) | ||||
−0.349706 | + | 0.936860i | \(0.613718\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −50.1305 | −0.0109927 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2594.39 | −0.562750 | −0.281375 | − | 0.959598i | \(-0.590791\pi\) | ||||
−0.281375 | + | 0.959598i | \(0.590791\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2283.11 | −0.484693 | −0.242347 | − | 0.970190i | \(-0.577917\pi\) | ||||
−0.242347 | + | 0.970190i | \(0.577917\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1647.60 | 0.346076 | 0.173038 | − | 0.984915i | \(-0.444642\pi\) | ||||
0.173038 | + | 0.984915i | \(0.444642\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1718.41 | −0.353431 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3237.35 | −0.658935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2933.31 | 0.584867 | 0.292434 | − | 0.956286i | \(-0.405535\pi\) | ||||
0.292434 | + | 0.956286i | \(0.405535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9973.02 | −1.96831 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9761.95 | −1.88812 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1472.09 | −0.281893 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6557.00 | 1.23099 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8216.93 | −1.52757 | −0.763787 | − | 0.645468i | \(-0.776662\pi\) | ||||
−0.763787 | + | 0.645468i | \(0.776662\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 337.630 | 0.0615602 | 0.0307801 | − | 0.999526i | \(-0.490201\pi\) | ||||
0.0307801 | + | 0.999526i | \(0.490201\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −772.566 | −0.139514 | −0.0697572 | − | 0.997564i | \(-0.522222\pi\) | ||||
−0.0697572 | + | 0.997564i | \(0.522222\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7773.93 | −1.37737 | −0.688686 | − | 0.725059i | \(-0.741812\pi\) | ||||
−0.688686 | + | 0.725059i | \(0.741812\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −202.467 | −0.0355360 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2355.08 | −0.405698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4257.82 | 0.726712 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 124.926 | 0.0209342 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4261.31 | 0.707622 | 0.353811 | − | 0.935317i | \(-0.384886\pi\) | ||||
0.353811 | + | 0.935317i | \(0.384886\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5425.09 | −0.884789 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4728.91 | −0.764393 | −0.382196 | − | 0.924081i | \(-0.624832\pi\) | ||||
−0.382196 | + | 0.924081i | \(0.624832\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −274.168 | −0.0435397 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3446.95 | 0.542618 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2584.04 | 0.399765 | 0.199883 | − | 0.979820i | \(-0.435944\pi\) | ||||
0.199883 | + | 0.979820i | \(0.435944\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4122.46 | 0.632292 | 0.316146 | − | 0.948711i | \(-0.397611\pi\) | ||||
0.316146 | + | 0.948711i | \(0.397611\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9524.92 | 1.43615 | 0.718074 | − | 0.695967i | \(-0.245024\pi\) | ||||
0.718074 | + | 0.695967i | \(0.245024\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14753.0 | −2.20565 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3048.39 | 0.448156 | 0.224078 | − | 0.974571i | \(-0.428063\pi\) | ||||
0.224078 | + | 0.974571i | \(0.428063\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3549.00 | −0.517422 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3798.07 | −0.544658 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5237.90 | −0.745003 | −0.372501 | − | 0.928032i | \(-0.621500\pi\) | ||||
−0.372501 | + | 0.928032i | \(0.621500\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1570.30 | 0.219747 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2871.50 | 0.398608 | 0.199304 | − | 0.979938i | \(-0.436132\pi\) | ||||
0.199304 | + | 0.979938i | \(0.436132\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17196.5 | 2.34925 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1649.20 | 0.223518 | 0.111759 | − | 0.993735i | \(-0.464351\pi\) | ||||
0.111759 | + | 0.993735i | \(0.464351\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8182.76 | −1.09170 | −0.545848 | − | 0.837884i | \(-0.683792\pi\) | ||||
−0.545848 | + | 0.837884i | \(0.683792\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 69.2610 | 0.00916849 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1380.58 | 0.179944 | 0.0899719 | − | 0.995944i | \(-0.471322\pi\) | ||||
0.0899719 | + | 0.995944i | \(0.471322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4704.83 | 0.608525 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16297.0 | −2.07593 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5772.41 | −0.729746 | −0.364873 | − | 0.931057i | \(-0.618888\pi\) | ||||
−0.364873 | + | 0.931057i | \(0.618888\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9378.85 | 1.16797 | 0.583987 | − | 0.811763i | \(-0.301492\pi\) | ||||
0.583987 | + | 0.811763i | \(0.301492\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23286.4 | 2.87836 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −242.935 | −0.0295868 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7073.09 | 0.855114 | 0.427557 | − | 0.903988i | \(-0.359374\pi\) | ||||
0.427557 | + | 0.903988i | \(0.359374\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3944.15 | 0.469925 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12472.5 | 1.47530 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9435.65 | 1.10015 | 0.550073 | − | 0.835116i | \(-0.314600\pi\) | ||||
0.550073 | + | 0.835116i | \(0.314600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2620.13 | −0.303319 | −0.151659 | − | 0.988433i | \(-0.548462\pi\) | ||||
−0.151659 | + | 0.988433i | \(0.548462\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2052.08 | −0.234213 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2593.18 | −0.293894 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3485.65 | −0.389555 | −0.194777 | − | 0.980847i | \(-0.562398\pi\) | ||||
−0.194777 | + | 0.980847i | \(0.562398\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9818.69 | 1.08974 | 0.544869 | − | 0.838521i | \(-0.316579\pi\) | ||||
0.544869 | + | 0.838521i | \(0.316579\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6612.50 | −0.723841 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1235.00 | −0.134268 | −0.0671338 | − | 0.997744i | \(-0.521385\pi\) | ||||
−0.0671338 | + | 0.997744i | \(0.521385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10744.3 | −1.15232 | −0.576162 | − | 0.817336i | \(-0.695450\pi\) | ||||
−0.576162 | + | 0.817336i | \(0.695450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2517.13 | 0.268143 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16166.3 | −1.69919 | −0.849595 | − | 0.527435i | \(-0.823154\pi\) | ||||
−0.849595 | + | 0.527435i | \(0.823154\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −328.337 | −0.0342811 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5882.67 | −0.606118 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2122.26 | −0.217232 | −0.108616 | − | 0.994084i | \(-0.534642\pi\) | ||||
−0.108616 | + | 0.994084i | \(0.534642\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3473.41 | 0.350917 | 0.175459 | − | 0.984487i | \(-0.443859\pi\) | ||||
0.175459 | + | 0.984487i | \(0.443859\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3575.70 | 0.358913 | 0.179457 | − | 0.983766i | \(-0.442566\pi\) | ||||
0.179457 | + | 0.983766i | \(0.442566\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9406.95 | 0.932124 | 0.466062 | − | 0.884752i | \(-0.345672\pi\) | ||||
0.466062 | + | 0.884752i | \(0.345672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2145.53 | 0.211239 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −281.272 | −0.0273422 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2884.14 | 0.278597 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18524.0 | 1.76698 | 0.883492 | − | 0.468447i | \(-0.155186\pi\) | ||||
0.883492 | + | 0.468447i | \(0.155186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20633.6 | 1.95595 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4061.02 | −0.380209 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −825.955 | −0.0768533 | −0.0384267 | − | 0.999261i | \(-0.512235\pi\) | ||||
−0.0384267 | + | 0.999261i | \(0.512235\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8918.35 | −0.819714 | −0.409857 | − | 0.912150i | \(-0.634421\pi\) | ||||
−0.409857 | + | 0.912150i | \(0.634421\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8287.95 | −0.757141 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5834.54 | 0.526589 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18214.4 | 1.63404 | 0.817022 | − | 0.576606i | \(-0.195623\pi\) | ||||
0.817022 | + | 0.576606i | \(0.195623\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2264.42 | −0.200726 | −0.100363 | − | 0.994951i | \(-0.532000\pi\) | ||||
−0.100363 | + | 0.994951i | \(0.532000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8904.91 | 0.784679 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14235.2 | 1.23961 | 0.619806 | − | 0.784755i | \(-0.287211\pi\) | ||||
0.619806 | + | 0.784755i | \(0.287211\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1502.07 | 0.130034 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11118.3 | 0.951323 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.8695 | 0.00203052 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11343.3 | −0.953856 | −0.476928 | − | 0.878942i | \(-0.658250\pi\) | ||||
−0.476928 | + | 0.878942i | \(0.658250\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20464.1 | −1.71096 | −0.855482 | − | 0.517832i | \(-0.826739\pi\) | ||||
−0.855482 | + | 0.517832i | \(0.826739\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11223.0 | −0.927670 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1043.00 | 0.0857234 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27887.2 | 2.26628 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21942.6 | −1.77320 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 315.609 | 0.0252212 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1993.69 | −0.158439 | −0.0792196 | − | 0.996857i | \(-0.525243\pi\) | ||||
−0.0792196 | + | 0.996857i | \(0.525243\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16724.2 | −1.31447 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2724.02 | −0.212926 | −0.106463 | − | 0.994317i | \(-0.533953\pi\) | ||||
−0.106463 | + | 0.994317i | \(0.533953\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11648.5 | 0.900621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6445.17 | 0.495618 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15046.5 | −1.14460 | −0.572299 | − | 0.820045i | \(-0.693948\pi\) | ||||
−0.572299 | + | 0.820045i | \(0.693948\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23889.7 | 1.80756 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19608.6 | 1.46786 | 0.733928 | − | 0.679228i | \(-0.237685\pi\) | ||||
0.733928 | + | 0.679228i | \(0.237685\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6277.51 | −0.467428 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13968.5 | −1.02916 | −0.514580 | − | 0.857443i | \(-0.672052\pi\) | ||||
−0.514580 | + | 0.857443i | \(0.672052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23614.0 | −1.73068 | −0.865339 | − | 0.501188i | \(-0.832897\pi\) | ||||
−0.865339 | + | 0.501188i | \(0.832897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5761.74 | −0.417880 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23002.4 | −1.65962 | −0.829811 | − | 0.558044i | \(-0.811552\pi\) | ||||
−0.829811 | + | 0.558044i | \(0.811552\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4932.64 | −0.352221 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 300.038 | 0.0213144 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8100.44 | 0.569576 | 0.284788 | − | 0.958591i | \(-0.408077\pi\) | ||||
0.284788 | + | 0.958591i | \(0.408077\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15773.6 | 1.10347 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22256.2 | −1.54124 | −0.770618 | − | 0.637298i | \(-0.780052\pi\) | ||||
−0.770618 | + | 0.637298i | \(0.780052\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2835.18 | 0.195346 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8386.30 | 0.572045 | 0.286023 | − | 0.958223i | \(-0.407667\pi\) | ||||
0.286023 | + | 0.958223i | \(0.407667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9814.21 | −0.666107 | −0.333053 | − | 0.942908i | \(-0.608079\pi\) | ||||
−0.333053 | + | 0.942908i | \(0.608079\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17600.8 | −1.18277 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24077.7 | −1.61002 | −0.805011 | − | 0.593260i | \(-0.797841\pi\) | ||||
−0.805011 | + | 0.593260i | \(0.797841\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2027.35 | −0.134235 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18679.6 | −1.23077 | −0.615386 | − | 0.788226i | \(-0.711000\pi\) | ||||
−0.615386 | + | 0.788226i | \(0.711000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1650.88 | 0.107718 | 0.0538589 | − | 0.998549i | \(-0.482848\pi\) | ||||
0.0538589 | + | 0.998549i | \(0.482848\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25032.9 | 1.62545 | 0.812727 | − | 0.582645i | \(-0.197982\pi\) | ||||
0.812727 | + | 0.582645i | \(0.197982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −995.481 | −0.0640178 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19378.2 | −1.24021 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9944.47 | −0.630385 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1666.38 | 0.105131 | 0.0525653 | − | 0.998617i | \(-0.483260\pi\) | ||||
0.0525653 | + | 0.998617i | \(0.483260\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7415.83 | −0.463446 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26806.1 | −1.66734 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24026.5 | 1.48049 | 0.740243 | − | 0.672339i | \(-0.234710\pi\) | ||||
0.740243 | + | 0.672339i | \(0.234710\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12772.5 | −0.783356 | −0.391678 | − | 0.920102i | \(-0.628105\pi\) | ||||
−0.391678 | + | 0.920102i | \(0.628105\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19420.6 | 1.18007 | 0.590034 | − | 0.807378i | \(-0.299114\pi\) | ||||
0.590034 | + | 0.807378i | \(0.299114\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 753.609 | 0.0455805 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −811.744 | −0.0486462 | −0.0243231 | − | 0.999704i | \(-0.507743\pi\) | ||||
−0.0243231 | + | 0.999704i | \(0.507743\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10445.4 | −0.623108 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12165.8 | 0.719138 | 0.359569 | − | 0.933119i | \(-0.382924\pi\) | ||||
0.359569 | + | 0.933119i | \(0.382924\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3004.33 | −0.176785 | −0.0883925 | − | 0.996086i | \(-0.528173\pi\) | ||||
−0.0883925 | + | 0.996086i | \(0.528173\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3984.77 | −0.232365 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23270.5 | −1.35088 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −495.478 | −0.0285063 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1272.83 | −0.0729032 | −0.0364516 | − | 0.999335i | \(-0.511605\pi\) | ||||
−0.0364516 | + | 0.999335i | \(0.511605\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11039.9 | 0.626731 | 0.313366 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313366 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1606.06 | 0.0907730 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6103.65 | −0.341947 | −0.170974 | − | 0.985276i | \(-0.554691\pi\) | ||||
−0.170974 | + | 0.985276i | \(0.554691\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17607.0 | 0.982085 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25483.6 | −1.40907 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30759.2 | 1.69340 | 0.846698 | − | 0.532074i | \(-0.178587\pi\) | ||||
0.846698 | + | 0.532074i | \(0.178587\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41545.4 | 2.26749 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13440.4 | −0.730403 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30619.5 | 1.64976 | 0.824880 | − | 0.565308i | \(-0.191243\pi\) | ||||
0.824880 | + | 0.565308i | \(0.191243\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13976.7 | 0.749844 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3521.73 | −0.187339 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28651.0 | 1.51764 | 0.758822 | − | 0.651298i | \(-0.225775\pi\) | ||||
0.758822 | + | 0.651298i | \(0.225775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31511.5 | −1.65514 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1124.00 | −0.0587905 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24899.6 | −1.29151 | −0.645756 | − | 0.763544i | \(-0.723458\pi\) | ||||
−0.645756 | + | 0.763544i | \(0.723458\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4397.09 | −0.227124 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10149.8 | 0.519936 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34318.0 | −1.75074 | −0.875369 | − | 0.483456i | \(-0.839381\pi\) | ||||
−0.875369 | + | 0.483456i | \(0.839381\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11513.8 | −0.582562 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27751.9 | 1.39842 | 0.699209 | − | 0.714917i | \(-0.253536\pi\) | ||||
0.699209 | + | 0.714917i | \(0.253536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 409.945 | 0.0204892 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24701.0 | −1.22955 | −0.614777 | − | 0.788701i | \(-0.710754\pi\) | ||||
−0.614777 | + | 0.788701i | \(0.710754\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23186.8 | 1.14488 | 0.572438 | − | 0.819948i | \(-0.305998\pi\) | ||||
0.572438 | + | 0.819948i | \(0.305998\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35284.2 | −1.73519 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8677.91 | 0.423343 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24909.9 | 1.21035 | 0.605177 | − | 0.796091i | \(-0.293102\pi\) | ||||
0.605177 | + | 0.796091i | \(0.293102\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6344.32 | 0.305819 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2659.35 | 0.127682 | 0.0638412 | − | 0.997960i | \(-0.479665\pi\) | ||||
0.0638412 | + | 0.997960i | \(0.479665\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25415.3 | −1.21065 | −0.605324 | − | 0.795980i | \(-0.706956\pi\) | ||||
−0.605324 | + | 0.795980i | \(0.706956\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6614.13 | 0.313824 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −64007.6 | −3.01327 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30053.1 | 1.40929 | 0.704645 | − | 0.709560i | \(-0.251106\pi\) | ||||
0.704645 | + | 0.709560i | \(0.251106\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6066.30 | 0.282263 | 0.141132 | − | 0.989991i | \(-0.454926\pi\) | ||||
0.141132 | + | 0.989991i | \(0.454926\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13744.2 | 0.637040 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18890.1 | 0.868816 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1114.80 | 0.0510766 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26531.2 | −1.20629 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5496.18 | −0.248942 | −0.124471 | − | 0.992223i | \(-0.539723\pi\) | ||||
−0.124471 | + | 0.992223i | \(0.539723\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2482.64 | 0.111596 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42083.3 | 1.88452 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27808.0 | 1.23590 | 0.617949 | − | 0.786218i | \(-0.287964\pi\) | ||||
0.617949 | + | 0.786218i | \(0.287964\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 977.092 | 0.0432629 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 287.000 | 0.0126127 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7960.50 | 0.348535 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6720.58 | 0.292068 | 0.146034 | − | 0.989280i | \(-0.453349\pi\) | ||||
0.146034 | + | 0.989280i | \(0.453349\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9923.66 | 0.429675 | 0.214838 | − | 0.976650i | \(-0.431078\pi\) | ||||
0.214838 | + | 0.976650i | \(0.431078\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11011.0 | −0.473249 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16182.3 | 0.692958 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19118.8 | 0.812728 | 0.406364 | − | 0.913711i | \(-0.366797\pi\) | ||||
0.406364 | + | 0.913711i | \(0.366797\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28343.3 | 1.20047 | 0.600234 | − | 0.799825i | \(-0.295074\pi\) | ||||
0.600234 | + | 0.799825i | \(0.295074\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25909.2 | −1.08942 | −0.544711 | − | 0.838624i | \(-0.683361\pi\) | ||||
−0.544711 | + | 0.838624i | \(0.683361\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3137.00 | −0.131426 | −0.0657132 | − | 0.997839i | \(-0.520932\pi\) | ||||
−0.0657132 | + | 0.997839i | \(0.520932\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12919.4 | 0.537370 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 38002.5 | 1.57501 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8110.63 | −0.333743 | −0.166871 | − | 0.985979i | \(-0.553366\pi\) | ||||
−0.166871 | + | 0.985979i | \(0.553366\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16604.0 | 0.680800 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 66392.2 | 2.70291 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6960.80 | 0.282380 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27921.6 | −1.12473 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20317.3 | 0.815536 | 0.407768 | − | 0.913085i | \(-0.366307\pi\) | ||||
0.407768 | + | 0.913085i | \(0.366307\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2938.63 | −0.117132 | −0.0585658 | − | 0.998284i | \(-0.518653\pi\) | ||||
−0.0585658 | + | 0.998284i | \(0.518653\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10710.3 | −0.425412 | −0.212706 | − | 0.977116i | \(-0.568228\pi\) | ||||
−0.212706 | + | 0.977116i | \(0.568228\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12400.3 | 0.489122 | 0.244561 | − | 0.969634i | \(-0.421356\pi\) | ||||
0.244561 | + | 0.969634i | \(0.421356\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −47369.2 | −1.86197 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1231.48 | 0.0480725 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34818.6 | −1.35452 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5185.54 | 0.200346 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30790.2 | −1.18553 | −0.592765 | − | 0.805375i | \(-0.701964\pi\) | ||||
−0.592765 | + | 0.805375i | \(0.701964\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20320.3 | −0.777082 | −0.388541 | − | 0.921431i | \(-0.627021\pi\) | ||||
−0.388541 | + | 0.921431i | \(0.627021\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27680.1 | 1.05494 | 0.527468 | − | 0.849575i | \(-0.323141\pi\) | ||||
0.527468 | + | 0.849575i | \(0.323141\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41124.8 | 1.55675 | 0.778374 | − | 0.627801i | \(-0.216045\pi\) | ||||
0.778374 | + | 0.627801i | \(0.216045\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2932.83 | 0.110646 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1373.28 | −0.0514613 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28612.4 | 1.06861 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 55510.2 | 2.05936 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12282.0 | 0.454131 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23030.1 | 0.845907 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26971.3 | 0.987397 | 0.493698 | − | 0.869633i | \(-0.335645\pi\) | ||||
0.493698 | + | 0.869633i | \(0.335645\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46282.0 | −1.68319 | −0.841597 | − | 0.540105i | \(-0.818384\pi\) | ||||
−0.841597 | + | 0.540105i | \(0.818384\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −942.478 | −0.0341637 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4130.97 | 0.148764 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36864.3 | 1.32322 | 0.661611 | − | 0.749847i | \(-0.269873\pi\) | ||||
0.661611 | + | 0.749847i | \(0.269873\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −94685.6 | −3.37661 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12178.4 | 0.432891 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34278.6 | −1.21060 | −0.605299 | − | 0.795998i | \(-0.706946\pi\) | ||||
−0.605299 | + | 0.795998i | \(0.706946\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18157.8 | −0.639202 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 541.718 | 0.0189477 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 450.515 | 0.0157072 | 0.00785362 | − | 0.999969i | \(-0.497500\pi\) | ||||
0.00785362 | + | 0.999969i | \(0.497500\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7098.87 | 0.245926 | 0.122963 | − | 0.992411i | \(-0.460760\pi\) | ||||
0.122963 | + | 0.992411i | \(0.460760\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −37737.3 | −1.30318 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9833.35 | −0.337425 | −0.168712 | − | 0.985665i | \(-0.553961\pi\) | ||||
−0.168712 | + | 0.985665i | \(0.553961\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24376.3 | −0.833812 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41260.1 | 1.40246 | 0.701231 | − | 0.712934i | \(-0.252634\pi\) | ||||
0.701231 | + | 0.712934i | \(0.252634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33584.5 | −1.13798 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6963.25 | −0.234468 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45377.3 | 1.52319 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2519.00 | 0.0840305 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22642.8 | −0.752992 | −0.376496 | − | 0.926418i | \(-0.622871\pi\) | ||||
−0.376496 | + | 0.926418i | \(0.622871\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3166.82 | 0.104663 | 0.0523316 | − | 0.998630i | \(-0.483335\pi\) | ||||
0.0523316 | + | 0.998630i | \(0.483335\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16430.5 | −0.541353 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20643.0 | 0.675976 | 0.337988 | − | 0.941150i | \(-0.390254\pi\) | ||||
0.337988 | + | 0.941150i | \(0.390254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −190.206 | −0.00620942 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −59289.5 | −1.92374 | −0.961872 | − | 0.273498i | \(-0.911819\pi\) | ||||
−0.961872 | + | 0.273498i | \(0.911819\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −70327.2 | −2.27493 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32327.9 | −1.03940 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14404.0 | −0.461712 | −0.230856 | − | 0.972988i | \(-0.574153\pi\) | ||||
−0.230856 | + | 0.972988i | \(0.574153\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 50117.9 | 1.59683 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48894.9 | −1.55318 | −0.776588 | − | 0.630009i | \(-0.783051\pi\) | ||||
−0.776588 | + | 0.630009i | \(0.783051\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 216.4.a.e.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 216.4.a.h.1.1 | yes | 2 | ||
4.3 | odd | 2 | 432.4.a.o.1.2 | 2 | |||
8.3 | odd | 2 | 1728.4.a.bs.1.1 | 2 | |||
8.5 | even | 2 | 1728.4.a.bt.1.1 | 2 | |||
9.2 | odd | 6 | 648.4.i.m.433.2 | 4 | |||
9.4 | even | 3 | 648.4.i.s.217.1 | 4 | |||
9.5 | odd | 6 | 648.4.i.m.217.2 | 4 | |||
9.7 | even | 3 | 648.4.i.s.433.1 | 4 | |||
12.11 | even | 2 | 432.4.a.s.1.1 | 2 | |||
24.5 | odd | 2 | 1728.4.a.bh.1.2 | 2 | |||
24.11 | even | 2 | 1728.4.a.bg.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.4.a.e.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
216.4.a.h.1.1 | yes | 2 | 3.2 | odd | 2 | ||
432.4.a.o.1.2 | 2 | 4.3 | odd | 2 | |||
432.4.a.s.1.1 | 2 | 12.11 | even | 2 | |||
648.4.i.m.217.2 | 4 | 9.5 | odd | 6 | |||
648.4.i.m.433.2 | 4 | 9.2 | odd | 6 | |||
648.4.i.s.217.1 | 4 | 9.4 | even | 3 | |||
648.4.i.s.433.1 | 4 | 9.7 | even | 3 | |||
1728.4.a.bg.1.2 | 2 | 24.11 | even | 2 | |||
1728.4.a.bh.1.2 | 2 | 24.5 | odd | 2 | |||
1728.4.a.bs.1.1 | 2 | 8.3 | odd | 2 | |||
1728.4.a.bt.1.1 | 2 | 8.5 | even | 2 |